Sulfur Chemistry in the Middle Atmosphere of Venus
Zhang X., Liang, M-C, Belyaev D., and Yung, Y. L.
To be submitted to Icarus 2011
Abstract
1: Introduction
Venus is a natural laboratory of sulfur chemistry, including the surface chemistry
between the minerals and OCS and SO2, gas phase chemistry between the sulfur species
and other species such as oxygen and chlorine species, and the heterogeneous chemistry
on the sulfuric acid aerosol surface, and so on. The sulfur chemistry is also closely related
to many processes. The volcanic process may be the dominant source of SO2 in the lower
atmosphere. The dynamic processes including the large-scale circulation modulating the
latitudinal distribution of species, small-scale turbulence resulting vertical mixing,
convection in the cloud layers transporting species to the higher altitude, and the fast
zonal flow smearing large horizontal longitudinal gradients between the dayside and
nightside. The microphysical processes between the gas and aerosols, especially the
sulfuric acid formation and movements, not only have local effects on the chemistry and
radiation field, but also exchange the sulfur content between the upper and lower
atmosphere. The radiation processes such as aerosol scattering and gas absorption,
redistribute the photons dissociating sulfuric gases in the upper atmosphere. Particularly,
the unknown UV absorbers in the Venus cloud region absorb roughly half of he deposited
solar energy, which significantly influences the chemistry in the cloud region.
Venus has a thick atmosphere (~95 bar at the surface). The CO2 greenhouse effect
maintains very high temperature in the lower atmosphere therefore the sulfur chemistry is
very close the thermochemistry. Above the tropopause (~60 km), the photochemistry
plays a major role. The study of chemistry in Venus atmosphere is mainly driven by the
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observations. Due to the difficulty of penetrating down to the lower atmosphere, we are
still far from unveiling the lower atmosphere chemistry without available evidences. On
the other hand, the relatively enrichment of the observations above the middle cloud top
(~58 km) allows us to test the sulfur chemical models in the low temperature
photochemical regime. Mills et al. (2007) summarizes the important observations on
Venus before Venus Express and gives a nice review of the Venus sulfur chemistry.
Recent measurements by Venus Express and some ground-based observations greatly
improve our knowledge of the sulfur chemistry. Marcq et al. (2005; 2006; 2008) reported
the latitudinal distributions of CO, OCS, SO2 and H2O in the 30-40 km region retrieved
from the Visible and Infrared Thermal Imaging Spectrometer (VIRTIS) instrument
(VIRTIS-H) aboard Venus Express and the NASA Infrared Telescope Facility (IRTF).
The anti-correlation of CO and OCS latitudinal profiles might imply the conversion of
CO and OCS in the lower atmosphere (Yung et al., 2009). The latitudinal and vertical
temperature map above the cloud top (Pätzold et al., 2007) reveals the Venus thermal
structure and also the dynamical structure. The zonal wind field derived from the
latitudinal temperature gradient (Picciani et al., 2008) implies weaker zonal flow with
altitude above the upper cloud top (~70 km). The discovery of the nightside warm layer
(Bertaux et al., 2007) is a strong evidence of the existence of subsolar-anti-solar (SSAS)
circulation in the lower thermosphere (above 90 km). Through the occultation technique,
Solar Occultation at Infrared (SOIR) and the Spectroscopy for Investigation of
Characteristics of the Atmosphere of Venus (SPICAV) onboard Venus Express carry out
substantial measurements of the vertical profiles of the major species above 70 km, such
as H2O, HDO, HCl and HF (Bertaux, et al., 2007), and CO (Vandaele et al., 2008), SO
and SO2 (Belyaev et al., 2008; 2010). These high vertical resolution profiles are mainly
obtained in the polar region. The ground-based measurements also provide the valuable
data. Krasnolposky (2010a; 2010b) uses the NASA/IRTF to get the spatially resolved
distributions of CO2, CO, HDO, HCl, HF, OCS and SO2 at the cloud tops. Sandor et al.
(2010) reported their ground-based observations of SO and SO2 above 90 km, in
consistent with the later published Venus Express data (Balyaev et al., 2010). Those
measurements provide a good chance to study the photochemical and transport processes
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in the Venus middle atmosphere. The HDO/H2O ratio is interpreted as the photolysis
induced isotopic fractionation effect (Liang et al., 2009). Krasnolposky (2010) published
the night chemistry model based on the OH and O2 airglow measurements in the night
side of Venus. Zhang et al. (2010) studied the SO and SO2 inversion layers above 90 km.
They proposed that the evaporation of the sulfuric acid aerosol above the 90 km would
provide the major sulfur source in the lower thermosphere but the photolysis of H2SO4
vapor seems not efficient enough. Their models also predict a largely supersaturated
H2SO4 vapor pressure around 100 km. The latest SO and SO2 profiles retrieved from the
Venus Express measurements show a fair agreement with their model results above 85
km (Belyaev et al., 2010). This mechanism reveals the close connection between the
gaseous sulfur chemistry and aerosols. Previously the sulfuric acid is only considered as
the ultimate sink of sulfur species in the upper atmosphere. If it could also be a source,
the thermodynamics and microphysical properties of H2SO4 need to be examined
carefully. The purpose of this study to discuss the sulfur chemistry in the middle
atmosphere and its relation with the aerosols based on our current knowledge of
observational evidences and laboratory measurements.
Previous models?
Above the middle cloud top (~58 km), the aerosols are found to have a bi-modal
distribution in the upper cloud layer (58-70 km) and upper haze layer (70-90 km). In this
study we combine the upper haze profiles from Wilquet et al. (2010) above 72 km and
upper cloud particle profiles from Knollenberg and Hunten (1980) from 58-65 km. Due
to the lack of data for the intermediate altitudes (65-72km) at present, interpolation is
applied. Fig. 1 shows the bi-modal aerosol profiles (left panel).
From the aerosol abundances, we can roughly estimate the sulfur content. The mode 1
aerosols are roughly 0.2 μm in radius constantly for all altitudes. For the mode 2 aerosols,
we use 0.7 μm above 72 km (Wilquet et al. 2010) for the haze particle and 1.1 μm below
for the cloud particle (Knollenberg and Hunten, 1980). The right panel of Fig. 1 shows
the equivalent sulfur mixing ratio (ESMR) by volume computed from the H2SO4 aerosol
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(solid line) abundances by assuming the H2SO4 aerosol density is 2 g cm-3 and weight
percent are 85% and 75% below and above 72 km, respectively. The ESMR in the H2SO4
droplet is close to 1 ppm at all altitudes, which is enough for the enhancement of sulfur
oxides above 80 km. In addition, if the polysulfur (Sx) is the unknown UV absorber,
previous study (e.g., Carlson, et al. 2010) estimated that the elemental sulfur is about 1%
of H2SO4 content. By assuming that the radius of elemental sulfur is about half of the
H2SO4 aerosol radius and the density is also 2 g cm-3, we found the ESMR in elemental
sulfurs in excess of 1 ppb level at most altitude (Fig. 1, right panel, dashed line), which is
also enough to produce the sulfur species if the Sx aerosol is a steady source (see section
4). Since both the H2SO4 and Sx could provide the source of sulfur oxides above 90 km,
we will discuss both possibilities in this study.
According to the turning point of SO2 profile around 80 km, we separate the Venus
middle atmosphere into two regions: the lower region (below 80 km) and the upper
region (above 80 km). In this paper, we will first introduce the photochemical model in
section 2, and discuss the chemistry in the lower region and compare the model results
with the observations in section 3. The upper region chemistry is presented in section 4,
where we provide a detailed discussion on the two possible sulfur sources above 90 km,
H2SO4 and Sx, respectively, the roles they play in the sulfur chemistry, their implications
and how to distinguish the two sources by the future observations. Thee last section
provides a summary of the paper and conclusions.
2: Model Description
Our photochemical-diffusive transport model is based on the 1-D Caltech/JPL kinetics
code for Venus (Allen et al., 1981; Yung and DeMore, 1982; Mills, 1998) with updated
reaction rate coefficients. The model solves the coupled continuity equations with
chemical kinetics and diffusion processes, as function of time and altitude from 58 to 112
km. The atmosphere is assumed to be in hydrostatic equilibrium because the self-rotation
is extremely slow. We use 32 altitude grids with the increment of 0.4 km from 58 to 60
km and 2 km from 60 to 112 km. The diurnally averaged radiation field from 100-800 nm
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is calculated using a modified radiative transfer scheme including the gas absorption,
Rayleigh scattering and Mie-particle aerosol scattering with wavelength-dependent
optical properties (see Appendix I). The unknown UV absorber is approximated by
changing the single scattering albedo of the mode 1 aerosol beyond 310 nm, as suggested
by Crisp et al. (1985). The calculations are set at polar-latitude (70N) because most of the
SO, SO2 and aerosol profiles are observed in the polar region. The model uses the
combination of the low solar activity solar spectra for the time period of the Spacelab 3
ATMOS experiment with an overlay of Lyman alpha as measured by the Solar
Mesospheric Explorer (SME).
In this study we select 43 species for the reference model (model A), including O, O(1D),
O2, O2(1D), O3, H, H2, OH, HO2, H2O, H2O2, N2, Cl, Cl2, ClO, HCl, HOCl, ClCO,
COCl2, ClC(O)OO, CO, CO2 , S, S2 , S3, S4, S5, S7, S8, SO, (SO)2, SO2, SO3, S2O, HSO3,
H2SO4, OCS, OSCl, ClSO2, ClS, ClS2, Cl2S, and Cl2S2. The last four chlorosulfanes
(SmCln) are included because they open an important pathway to form S2 and polysulfur
Sx(x=2→8) in the upper cloud region (Mills et al., 2007), although their chemistry is not yet
known very well. The chlorosulfanes chemistry is not important for the sulfur cycles
above ~80 km because the SmCln abundances are less. Nitrogen species, especially NO
and NO2 also play an important role in converting SO to SO2 and O to O2 in the 70-80 km
region (Krasnopolsky 2006). In order to simulate the full nitrogen chemistry, 8 nitrogen
species: N, NO, NO2, NO3, N2O, HNO, HNO2, and HNO3 are included. The nitrogen
chemistry is not important above 80 km either. In the region from 58-80 km, we will
compare three models: model A (the reference model), model B (same as model A but
without SmCln) and model C (same as model A but with Nitrogen chemistry). In section 4
for the sulfur chemistry above 80 km, we will use the model A although the results would
not change if we use models B and C instead.
In Zhang et al. (2010), the chemistry is simplified because (SO)2, S2O and HSO3 are only
considered as the sinks of the sulfur species. This may not be accurate enough for the
lower region chemistry below 80 km where there seems to be difficult in matching the
SO2 observations below 80 km. Instead, a full chemical reaction set with 35
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photodissociation reactions and about 260 neutral reactions are used in model A, as listed
in Table A1 and A2, respectively. We take the ClCO thermal equilibrium constant from
the 1-sigma model in Mills et al. (2007) so that we could constrain the total O2 column
abundances below 2×1018 cm-2 to match the observations. In addition, we introduce the
heterogeneous nucleation processes of elemental sulfurs (S, S2 and polysulfur) because
these sulfur species are readily to stick onto the sulfuric acid droplet and may provide the
required albedo of the unknown UV absorber (Carlson et al. 2010). But we neglect all the
heterogeneous reactions within the condensed elemental sulfurs on the droplet surface.
The calculation of the heterogeneous condensation rates is described in Appendix II. The
accommodation coefficient  is varying from 0.01 to 1 for the sensitivity study.
The temperature profiles are shown in Fig. 2 (left panel). The daytime temperature profile
below 100 km (solid line) is obtained from the VeRa observations of Venus Express
around the polar region (71 N, figure 1 of Pätzold et al., 2007). Above 100 km the
temperature is from Seiff (1983). The nighttime temperature profile (dashed line) used
here is measured by Venus Express in orbit 104 at latitude 4° S and local time 23:20 h
(black curve in the figure 1 of Bertaux et al., 2007). The nighttime temperature profile is
only used to calculate the H2SO4 saturated vapor pressure in section 4.
In the 1-D model, species are assumed to be mainly diffused vertically by the turbulent
eddies. The molecular diffusion becomes important above the homopause region (~130135 km). The eddy diffusivity would increase with altitude in the Venus mesosphere
because it is stably stratified (Yung and DeMore, 1982). Since the zonal wind is observed
decreasing with altitude above the cloud top due to the temperature gradient from pole to
the equator (Picciani et al., 2008), we assume that the mixing of the transient internal
gravity waves is more important than the vertical transport due to the zonal circulation
above 80 km, as proposed by Prinn (1975). In this situation the eddy diffusion coefficient
will be inversely proportional to the square of the number density (Lindzen, 1971). Von
Zahn et al. (1980) derived the eddy profile as function of number density ~1.4×1013 [M]0.5
cm2 s-1 within a factor of 2 around the homopause region from the mass spectrometer
measurements on board Pioneer Venus. In our model we use the formula Kz = 2.8×1013
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[M]-0.5 cm2 s-1 above 80 km. In the region below 80 km, Woo and Ishmaru (1981)
estimated the diffusivity  4.0×104 cm2 s-1 at ~60 km from the radio signal scintillations.
Therefore the eddy diffusivity profile from 58-60 km is estimated by linearly
interpolation and extrapolation based on the two points at 80 and 60 km. The eddy
diffusion profile (eddy profile Ⅰ) is shown in Fig. 2 (right panel, solid line). In the upper
region above 90 km, the vertical advection due to the SSAS circulation might be
dominant. The SPICAV measurements shows that the SO2 mixing ratio from ~87-100 km
is almost constant with altitude, which implies a very efficient transport process.
Therefore we increase the eddy diffusivity in section 4 (eddy profile Ⅱ, dashed line).
The SO2 and OCS mixing ratios at the 58 km are adjusted to match the SO2 observations
in 70-80 km (Belyaev et al., 2010) and OCS observations around 65 km (Krasnopolsky,
2010). The upper and lower boundary conditions for the important species are listed in
Table 1. We set the HCl as 4 ppm at 58 km, which is about factor of 2 larger than the
Venus Express observations (Bertaux et al., 2007). However, other observations also
reported 4 ppm HCl (Connes et al., 1967; Dalton et al., 2000; Krasnopolsky, 2010). Since
ClC(O)OO is the key species to convert CO and O2 to CO2 (Mills, et al., 2007), 0.4 ppm
HCl is needed in our model to constrain the total column abundances of O2.
Section 3: Chemistry in the 58-80 km region
3. 1 Reference Model
First we consider a reference model (model A) where we fixed the vertical profiles of N2,
H2O, and H2SO4, which is appropriate if the phase change processes (evaporation,
condensation and nucleation) are much faster than the gas-phase chemical reactions. The
N2 profile is given by a constant mixing ratio of 3.5%. The H2O profile (see Fig. 4) is
prescribed on the basis of the Venus Express observations (Bertaux, et al., 2007) above
70 km and the mixing ratio profile is assumed to be constant below. The H2SO4 vapor
pressure is calculated by assuming H2SO4 weight percent of 85% below 70 km, 75%
from 70 to 90 km and 100% (i.e., pure sulfuric acid) above 90 km (see section 4 for
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details). Model A uses the eddy diffusivity profile Ⅰand the daytime H2SO4 abundances
(see Fig. 14). The accommodation coefficient of the sulfur nucleation is set to unity (the
upper limit). Model A requires 4.5 ppm SO2 and 1.5 ppm OCS at the lower boundary to
match the observations. Figures 3-8 show the volume mixing ratios of oxygen species,
hydrogen species (including HOx), chlorine species, sulfur oxides, chlorine-sulfur
species, and elemental sulfurs, respectively. The observations of SO, SO2 and OCS are
also plotted in Fig. 6. It is clearly that model A results agree with the SO2 profile below
80 km but significantly deviate from the SO and SO2 measurements in the upper regions.
The photolysis of the parent species CO2, OCS, SO2, H2O and HCl, which are transported
by eddy diffusion from 58 km, provides the sources of the other species. Although the
sulfur chemistry is closely coupled with the oxygen and chlorine chemistry in the upper
cloud layer, the sulfur species have little effect on the abundances of the oxygen species
(including HOx) and chlorine species above the cloud top, but not vice versa. In other
words, the model without sulfur chemistry would produce roughly the same amount of
oxygen and chlorine species as the model with sulfur species does above the cloud top
where the sulfur species are less abundant and no longer largely consume the chlorine
and oxygen species. The free oxygen and chlorine bearing radicals, such as O, OH, Cl
and ClO, etc., are the key catalysts in recycling sulfur species in their inner cycle. On the
other hand, however, the sulfur species do not act actively as the catalysts in the Venus
chemistry. Therefore, to some extent the sulfur cycle in the mesosphere can be separated
from the other cycles above the cloud top. Fig. 9 illustrates the important pathways of the
sulfur cycle. For simplicity, the chlorosulfane chemistry is connected with elemental
sulfur chemistry but not shown explicitly here (see Mills et al. (2007) for detailed
discussion). The polysulfur chemistry within the allotropes is not illustrated in Fig. 9
either (see Yung et al. (2008) for detailed discussion). A fast inner cycle, including the
phtodissociation and oxidization processes, exists among the sulfur species. H2SO4 and Sx
in model A act as the ultimate sinks rather than the sources of the sulfur species. The total
production rate of H2SO4 from 58-112 km is 1.2×1012 cm-3s-1 with peaks 2.8×106 cm-3s-1
at around 62-64 km, while the total loss rate of gaseous elemental sulfurs to aerosol
through heterogeneous nucleation processes is 6.4×1012 cm-3s-1, equivalent to sulfur atom
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loss rate ~1.4×1013 cm-3s-1. Therefore, the major sink of sulfur species in model A is the
nucleation of the polysulfur aerosol. The polysulfur sink decreases with altitude mainly
because both the aerosol and elemental sulfurs are less abundant at higher altitude.
Below ~65 km, SO2 is roughly in equilibrium with ClSO2. SO2 reacts with the chlorine
radical: Cl + SO2 + CO2 → ClSO2 + CO2, and ClSO2 reacts with O, S, S2, SO, ClSO2, etc.
(Reactions R292-R299 in table A1) to return back SO2 and produce chlorine species
including chlorosulfanes. Above ~65 km, the photolysis of SO2 becomes the dominant
sink, with a minor branch of oxidization to SO3. The three-body reaction O + SO
produces more SO2, and ClO and ClC(O)OO reacting with SO also play important roles
in SO2 production. Fig. 10 shows the main production and loss pathways of SO2 in model
A. Fig. 11 shows the sensitivity study with various SO2 lower boundary conditions from
3.5-5.5 ppm.
The OCS mixing ratio in the cloud layer is puzzling. OCS originates from the lower
atmosphere. Marcq et al. (2005; 2006) reported that the OCS mixing ratio is ~0.55  0.15
ppm at ~36 km and decreasing with altitude with the gradient of -0.28 ppm/km based on
the ground-based telescope IRTF observation. The VIRTIS measurement (Marcq et al.,
2008) found the OCS mixing ratio ranging between 2.5  1 and 4  1 ppmv at 33 km,
agreeing with the previous value ~4.4 ppm from Pollack et al. (1993). Therefore, the
OCS would only be in the 0.1 ppm level or less in the lower cloud layer (~47 km).
However, the sensitivity study of model A (Fig. xxx) shows that 0.5-3 ppm OCS at the
upper cloud deck (~58 km) is required to produce the OCS mixing ratio at 65 km in the
observation range 0.3-9 ppb reported by Krasnopolsky (2010). Krasnopolsky (2008)
reported even larger values, ~14 ppb around 65 km and ~2 ppb around 70 km. Venus
Express results suggest that the upper limit of OCS as 1.6 ± 2 ppb in 70-90 km. The
model A is only able to produce 0.01 ppb level OCS around 70 km. Besides, the scale
height of OCS in the model A is ~1 km at 65 km, which is only the lower limit of the
observations (1-4 km from Krasnopolsky, 2010). It seems the eddy transport in the upper
cloud region might not be efficient to transport the OCS upward. And the SO2 scale
height around 68 km in the Venus Express measurements might also imply the same
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situation but more observations are needed. Although the eddy diffusivity at ~60 km has
been estimated  4.0×104 cm2 s-1 (Woo and Ishmaru, 1981), it could have large variations
in the cloud layer, resulting in the large variation of the detected OCS values and maybe
the decadal variation of SO2 at the cloud top (Belyaev et al., 2008). The unexpected large
amount of OCS will change the polysulfur production pathway. In model A, the primary
source of atomic sulfur below ~62 km is from the photolysis of OCS instead of SO and
ClS. And the reaction rate of S + OCS is as large as ClS2 photolysis below 60 km.
Therefore if there is a abundant OCS layer near the lower boundary, it may greatly
enhance the production of Sx in the 58-60 km region.
3.2 Supersaturation of elemental sulfurs
Even under the fastest heterogeneous nucleation processes (unity accommodation
coefficient), the model A results show that the S2, S3, and S4 are highly supersatured in
the Venus atmosphere (see Fig. 8) based on the monoclinic sulfur vapor pressures over
the solid phase from Lyons (2008). The column abundances of gaseous S2, S3, and S4
above 58 km are 8.1×1013 cm-2, 4.6×1013 cm-2, and 3.7×1012 cm-2, respectively. In fact S5
is also supersaturated with saturation ratio ~10 at 58 km but decreases quickly below the
saturated abundance above 60 km. The saturation ratio of S4 is about 107 at the lower
boundary and becomes unsaturated above 76 km. S3 is oversaturated by a factor of 103107 from 58-100km. S2 is extremely supersaturated at all altitudes. The saturation ratio is
107 at the bottom and 105 at the top, with the peak in 1015 at 90 km, where the aerosol
heterogeneous nucleation of S2 is negligible compared with the production processes
from atomic sulfur through the three body reaction 2S + M, and the major loss processes
of S2 are the oxidization to SO and photolysis to atomic sulfur. As illustrated in Fig. 9,
the main production processes of Sx can be summarized as S + Sx-1 → Sx and S2 + Sx-2 →
Sx, but the reactions ClS + S2 and S2O + S2O are also important for S3 production in the
bottom and top atmosphere, respectively. The loss mechanisms of Sx include the
heterogeneous nucleation, conversion to other allotropes, and oxidization through Sx + O
→ Sx-1 + SO, which we think may provide the sources of the upper atmosphere sulfur
oxides and will be discussed in section 4. Fig. A3 shows the diurnal-averaged photolysis
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timescales of S2, S3 and S4 in comparison with the nucleation timescale and eddy
transport timescale. The S2 loss process is dominated by the condensation from 58 km to
about 72 km where the photolysis is as fast as the condensation loss, but the conversion
from S2 to S4 is also important around 60 km. The photolysis timescales of S3 and S4 are
in the order of 1s, much smaller than the nucleation timescale (~10 s at 60 km and ~100 s
at 70 km). Therefore, for S3 and S4, photolysis by the visible light is the major loss
pathway and the heterogeneous nucleation processes are negligible. Since the S3 and S4
aerosols are one of the leading candidates of the unknown UV absorbers although they
are unstable (Carlson, et al., 2010), the condensed S3 and S4 are probably produced from
the heterogeneous Sx chemistry over the H2SO4 droplet surfaces (Lyons, 2008). A proper
treatment of the microphysical processes coupled with atmosphere dynamical processes
within the cloud layer is needed to elucidate the Sx chemistry.
3.3 Sensitivity to the accommodation coefficient
Due to the uncertainty of accommodation coefficient, we slow down the heterogeneous
nucleation processes by reducing . As  decreases, the formation of Sx aerosols is
slower so there are more sulfur species in the gas phase. Therefore, the model requires
less SO2 at the lower boundary and smaller eddy diffusivity between 74-80 km to
reproduce the SO2 observations. In table 2 we summarized the 3 cases with 1 (model A),
0.1 and 0.01 , respectively. All the three cases show that most of sulfur species are
eventually going into the polysuflur aerosols. As the polysulfur sinks are reduced, the
H2SO4 production rate is also decreased because of the lower SO2 abundances around 6264 km where the production peak is. The total column abundance of O2 and the column
production rate of O above 80 km have almost no difference when  changes. The
production rates of condensed Sx aerosol are almost the same because: (1) The other sinks
of elemental sulfur include the photolysis of S3 and S4, and the oxidization which is
controlled by the abundances O2 below 65 km. But there are only small differences of the
O2 concentrations among these models (all are 1-sigma ClCO stability model (Mills et al.,
2007); (2) The net production of S2 is from OCS in the 58-60 km region and the
chlorosulfane reactions (Mills et al., 2007) above 60 km. However, the chlorosulfanes do
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not vary too much when changing the heterogeneous nucleation rate. The OCS profile
does not change much either because it is mainly determined by the eddy transport from
below and photodissociation processes. Therefore, more future modeling work and
observations of the OCS in the upper cloud layer will help to identify the Sx aerosol
nucleation process.
3.4 Comparison between different chemical schemes
Since the chlorosulfane chemistry still has some uncertainties (Mills et al., 2007), we also
test the model without chlorosulfanes (ClS, ClS2, Cl2S, and Cl2S2) (model B) and their
chemistry for comparison. Another model with Nitrogen species and Nitrogen chemistry
(from Yung and DeMore, 1982 and Mills, 1998) (model C) is also discussed. Fig. 12
shows the mixing ratio profiles of Nitrogen species from model C. The NO mixing ratio
is 5.5 ppb below 60 km is 5.5 ppm, in good agreement of observations (Krasnopolsky,
2005). However, we are not trying to discuss the nitrogen chemistry and chlorosulfane
chemistry in details here (see Yung and DeMore, 1982 and Mills et al., 2007). Table 3
summarizes the results of model A, B and C. The total column abundances of O2 and O
total production rates above 80 km are roughly the same for all three chemistry schemes.
The model without chlorosulfane chemistry (model B) would have slower loss of sulfur
oxides in the cloud layer than model A, so it requires less sulfur flux from the lower
boundary to match the SO2 observations. The side effect is that the total sulfuric acid
production rate would decrease from 1.2×1012 cm-2 s-1 (model A) to 5.9×1011 cm-2 s-1 in
(model B). Since model C with Nitrogen species would convert more SO to SO2 around
70-80 km (~15% of the SO2 production rate at those altitudes), the SO2 lower boundary is
smaller than model A and hence the H2SO4 production rate is less (~9×1011 cm-2s-1) than
model A results. For reference, the Krasnopolsky and Pollack [1994] requires the H2SO4
production rate of 2.2×1012 cm-2 s-1. Some previous models range from 9×1011-1×1013
cm-2s-1 (Yung and DeMore, 1982; Krasnopolsky and Pollack, 1994). The SO2 production
and loss mechanisms are roughly the same for the 3 models except the region below 65
km where ClSO2 in model B does not reacts with elemental sulfur to produce SO2 and
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chlorosulfanes. And the SO2 production rate in model C is larger than that of model A
and B due to the NO2 oxidization in 70-80 km region. The SO2 production rates for the
three models are shown in table 3.
4: Chemistry above 80 km
Large enhancement of SO2 and SO above 80 km is not expected from the models in
section 2, especially SO2, because it is thought to be one of the parent species that is
transported from the lower atmosphere. This phenomenon should not be confused with
another similar phenomenon just revealed by Venus Express as well. That is, there exist
local minima around 88 km consistently for the observed profiles of CO, H2O and HCl.
These local minima are hard to be explained by the chemistry but probably caused by
atmospheric dynamics, such as a divergence zone (Liang et al., 2009). The SO2 minimum
is different because: (1) although we cannot conclude the exact altitude of the SO2
minimum between 80-85 km (since we don’t have data in that region), it should be lower
than that of other species because the existing SO2 data in 85-90 km do not show any
minimum; (2) The CO, H2O and HCl profiles were assumed to be roughly constant below
90 km from all the previous models because they don’t have very large production or loss
mechanisms. But SO2 profile was predicted to be decreasing with altitude due to the
photodissociation and oxidization processes. The imposed local minimum on a
decreasing profile (SO2) should be higher than that on a constant profile (other species).
However, this is contradicted with the observations. Therefore, the SO2 and SO
enhancement should be treated differently.
Since the photochemical models in section 3 could reproduce the data below 80 km, it’s
reasonable to hypothesize that the cause of the inversion layers is located in the upper
regions. Eddy diffusion process is only able to transport the species from high mixing
ratio regions to low mixing ratio regions so it cannot generate an inversion layer. A
sudden large injection of SO2 from either volcano or the instability in the cloud region
(VMC measurements, Markiewicz et al., 2007) may provide the sulfur source at the ~70
km, where the long-term natural variability of SO2 has yet not been solved. However, it’s
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hard to contribute to the SO2 inversion layer above 80 km because: (1) Volcano eruption
may only be able to reach 70 km but not higher based on a recent Venus convective
plume model (Glaze et al. 2010); (2) Even if the sudden injection reaches ~100 km high,
it’s also difficult to maintain the steady SO2 profile (Belyaev et al. 2010, this issue) for an
extended period in the Venus Express era because SO2 lifetime is short (~a few earth
days).
Based on model A, we set the initial condition to 1 ppm SO2 above 90 km as a test. Fig.
11 shows that the mixing ratio of SO2 drops off very rapidly with time and the system
returns back to the steady state solution (the model A results) in ~100 earth days.
Therefore, unless the transport is continuous, it is not likely to be the solution. A
continuous upwelling of SO2 from the lower region to the upper region (advection) may
exist although the dynamics maintaining the inversion profiles is not clear right now.
Provided the net chemical loss timescale ~7 earth days and the total column of SO2 above
80 km ~1×1015 cm-2, we estimate the ‘continuously upward’ SO2 flux from the lower
boundary (80-85 km) of the inversion layer is ~1×109 cm-2s-1. Another way to estimate
the upward flux is to calculate the downward diffused flux:
  K[M ]
df
dz
(1)
where  is the vertical flux, K eddy diffusivity, [M] number density, f mixing ratio, and
z altitude. Assuming the K~105 cm2s-1, df ~ 10-7, [M]~1017 cm-3, dz~106 cm (80-90 km),
we obtain  ~ 109 cm-2s-1. The same magnitude of upward flux is required to balance it.
The upward fluxes of CO, H2O and HCl could also be estimated in the same way.
Note that if treating the SO2 and SO enhancement differently from the other minima, one
should also explain why there is no minimum around 88 km for SO2 profile if it is the
atmospheric dynamics that causes the local minima. Our interpretation is that there is an
unknown chemical source above and a chemical loss below. The combination of the two
effects will mimic the local minimum due to the dynamics. The chemical source is also
the cause of the inversion layer. We further propose that the strong chemical source
above 90 km could be the aerosols (H2SO4, Sx), which might also be continuously
14
transported into the upper regions to supply the sulfur. In this case it is possible that the
upper atmospheric system could be shifted to another chemical steady state and sustained
the steady SO and SO2 inversion layers. Compared with the dynamics mechanism which
transports SO2 directly from lower region, this mechanism is more acceptable because:
(1) the inversion profiles can be explained by the shape of the equilibrium vapor pressure
profile above 90 km (see discussion later); (2) it only needs the upward transport of
aerosols around the 90 km region, where the subsolar-anti-solar circulation is stronger
and has been verified by the nighttime temperature inversion layer. Zhang et al. (2010)
has suggested the H2SO4 aerosol could be the sulfur source. We will further discuss this
possibility in detail in section 4.1. In section 4.2, we will discuss another possible sulfur
source, polysulfur aerosol, although the existence of which in the upper regions remains
uncertain.
4.1 H2SO4 aerosol as the sulfur source (model D)
4.1.1 H2SO4 vapor abundance
If sulfuric acid is in thermodynamic equilibrium with the surrounding atmosphere, the
saturation vapor pressure (SVP) over H2SO4 aerosol should mainly depend on the
temperature and aerosol composition. However, non-thermodynamic equilibrium in the
real atmosphere is common because the chemical and dynamic processes, such as the
chemical production, nucleation and transport, are often involved and play important
roles. The nucleation efficiency, which depends on many microphysical properties of the
system like the temperature, diffusivity, aerosol size, surface tension, and interaction
between molecules and aerosols, will greatly affect the H2SO4 vapor pressure over the
liquid droplets. The very low nucleation rate could cause large supersaturation of the
H2SO4 vapor. For example, the saturation ratio of H2SO4 in the lower stratospheric sulfate
layer (Junge layer) on Earth has been observed as large as 102-103 (Arnold, 2006). A
similar situation may exist in the Venus upper haze layer on the dayside when the H2SO4
vapor on the night side is transported to the dayside, because the SVP of H2SO4 in the
night side is several orders of magnitude larger than that in the dayside (Zhang et al.
15
(2010)) due to the large temperature difference above 90 km. Zhang et al. (2010)
proposed that this might be the key mechanism to explain the SO2 inversion layer
because the nighttime H2SO4 abundance could be enough to produce the observed SO2
under photochemical processes if the H2SO4 photolysis cross section is 100 time larger
than the current data from Vaida et al. (2003).
In the nucleation processes, we assume that the sulfate aerosol will quickly establish
equilibrium with respect to water because there are more collisions of aerosol particles
with H2O molecules than with H2SO4 molecules. Therefore, we could derive the H2SO4
aerosol composition (weight percent) from the water activity (or equilibrium relative
humidity) defined as the partial pressure of water vapor divided by the SVP over pure
water under the same temperature. The water activity is shown in Fig. 13 (left panel) for
day and night temperature profile, respectively. We used the H2O SVP as function of
temperature from Tabazadeh et al. (1997), which is valid between 185-260K.
P 0H 2 O  exp(18.4524 
3.5052  10 3 3.3092  10 5 1.2725  10 7


)
T
T2
T3
(2)
where P 0H 2 O is the SVP of H2O in mbar and T is temperature. We extrapolated the formula
to the entire temperature range (156-274 K) of Venus mesosphere so there would be
some uncertainties above 84 km for the dayside temperature and in the 84-90 km for the
nighttime temperature.
The H2SO4 weight percent is therefore roughly estimated by comparing the observed H2O
mixing ratio profile with the theoretical profiles under different H2SO4 compositions, as
shown in Fig. 13 (the middle and right panels). For the 50-80 wt% H2SO4, we used the
table from Tabazadeh (1997), calculated based on the Clegg and Brimblecombe (1995).
For the more concentrated acids, our calculation is based on Gmitro and Vermeulen
(1964) although it may not be very accurate for the low temperature (Mills, 1998). There
are also some uncertainties to apply the Tabazadeh (1997) formula in Venus case because
the Clegg and Brimblecombe (1995) is only valid if the water activity larger than 0.01.
Venus’ atmosphere is very dry (Fig. 13) so actually only the results in the region from
16
85-100 km in the dayside and 85-90 km in the nightside seem robust. However, as we
showed in the last paragraph, the H2O SVP may have some uncertainties in those regions.
Therefore, the H2SO4 weight percent derived here is only a rough estimate based on the
current knowledge.
The H2SO4 weight percent falls with altitude, associated with the increase of relative
humidity due to the temperature decrease. The values are about 90%-84% in 58-70 km
and 84%-60% in 70-90 km, which are roughly consistent with the H2SO4 compositions
obtained from aerosol refractive indexes based on the photometry measurements (85%
and 75%, respectively). But in the region above 90 km, the large contrast of dayside and
nightside temperatures results in large difference of the local H2SO4 weight percent. For
example, H2SO4 at 100 km is ~75% in the dayside but can be larger than 96% in the
nightside. Actually the temperature profile above 90 km has been found to be a function
of longitude (Bertaux, et al., 2007). Therefore, if the transport is efficient, the H2SO4
aerosols could have a broad range distribution of various concentrations above 90 km but
the H2SO4 vapor abundances might be mainly determined by the warmest nightside
temperature since the vapor abundances is extremely sensitive to the temperature.
The H2SO4 SVP is another uncertainty and maybe the major one. In the supplementary
material of Zhang et al. (2010), three H2SO4 SVP formulas as function of temperature
and H2SO4 concentration have been discussed in details. These formulas could differ by
several orders of magnitude but none of them has been verified in the temperature range
of upper atmosphere of Venus. Instead of using the H2SO4 weight percent profile derived
in Fig. 13, we simply assumed 85% H2SO4 below 70 km and 75% from 70-90 km and
used the vapor pressure formulas from Ayers et al. (1980) corrected by Kulmala and
Laaksonen (1990):
ln P 0H 2 SO4  16.259+
  0
8.3143T
 10156  [
1
0.38
T
T

(1  ln( 0 )  0 )]
T Tc  T0
T
T
(3)
where Tc = 905 K, T0 = 360.15 K, pH 2 SO4 is SVP of H2SO4 in atm, T is the temperature, 
and 0 are the chemical potentials of H2SO4 solutions of certain composition and pure
17
acid, respectively. The values of -0 for the 85% and 75% H2SO4 are 1555 cal-1 mole
and 3681 cal-1 mole based on Giauque et al. (1960), respectively.
In fact the H2SO4 abundances in the lower region (below 80 km) is not important because
the H2SO4 photolysis is negligible for the lower region chemistry. But in the upper region
the H2SO4 might behave like a sulfur source rather than a sink, and large abundance of
H2SO4 is required in the upper region in order to reproduce the SO2 inversion layer
(Zhang et al., 2010). So we adopted the formula by Stull (1947) just for reference, simply
because it gives the largest SVP in the Venus temperature range:
PH2 SO4  103954.90/T 9.4570
(4)
where pH 2 SO4 is the SVP of H2SO4 in mmHg and T is temperature. The H2SO4 SVP
profiles in Fig. 14 (left panel) show large difference between the dayside and nightside
temperature situations. Since H2SO4 is very hygroscopic, the right panel shows the
abundance of monohydrate (H2SO4H2O), estimated based on the extrapolation of the
equilibrium constants from the Vaida et al. (2003) for the earth atmosphere (223-271 K in
the literature). The abundances of H2SO4H2O above 90 km are less than 5% and much
less (<10-5) of that of pure H2SO4 for the dayside and nightside, respectively, although the
equilibrium constants have not been verified in the Venus temperature region (~160-240
K).
4.1.2 H2SO4 photolysis cross section
H2SO4 was thought to be photodissociated by the UV photons only. Burkholder et al.
(2000) and Hintze et al. (2003) estimated the upper limits for the UV cross section of
H2SO4 based on the failure to detect any absorption beyond 140 nm. The upper limits are
assumed to be 1×10-21 cm2 molecule-1 in 330-195 nm, 1×10-19 cm2 molecule-1 in 195-160
nm, and 1×10-18 cm2 molecule-1 in 160-140 nm. Lane et al. (2008) revisited UV cross
sections by calculating the electronic transitions based on the theoretical twin hierarchial
approach and they found that the cross section in the Lyman- region (~121.6 nm) is about
~6×10-17 cm2 molecule-1, much larger than the previously assumed value. And it also
18
seems that the cross section in 195-330 nm is much smaller than the upper limits from
Buikholder et al. (2000).
Vaida et al. (2003) proposed that in the visible region the excitation of the OH-stretching
overtone transitions with   4 (~38.6 kcal mole-1, or ~742 nm) is also enough to
photolyze H2SO4 because the energy required for H2SO4 + hυ → SO3 + H2O is only 32-40
kcal mole-1. This mechanism has been verified by the laboratory experiments in 49 and
59 bands from the cavity ring-down spectroscopy by Feierabend et al. (2006). Vaida et al.
(2003) also proposed that, in the IR and visible regions the OH-stretching overtone
transitions with   3 (~26.3 kcal/mole, or ~1.09 m) are able to generate the
photodissociation of H2SO4H2O as well (required energy ~25 kcal mole-1) and the total
photolysis rate is about ~100 times larger than that of pure H2SO4, although recent
simulation by Miller et al. (2007) suggested that the H2SO4H2O is more likely to
thermally decompose to H2SO4 and H2O before photodissociation.
In the previous models A, B and C, we take the cross sections from Lane et al. (2008) for
the UV region and Mills et al. (2005) and Feierabend et al. (2006) data for the visible
region. The solid line in Fig. 15 shows the cross section binned in our model spectral grid.
As shown in Table A1, the H2SO4 photolysis rate in model A is generally ~10-7 s-1 in the
upper atmosphere. It is ~10-6 s-1 near the upper boundary (112 km) due to the photolysis by
the lyman- line but only in a very thin layer (<1 km) because the layman alpha intensity
decreases very quickly by the CO2 absorption. The major contribution of the photolysis
rate is the solar pumping of the vibrational overtones by the 740 nm red light (49 band,
Vaida et al., 2003). The collisional deactivation rate mainly depends on the atmospheric
pressure. In Miller et al. (2007) the quantum yield is nearly unity above 60 km where the
pressure is 0.2 mbar in the Earth atmosphere. In Venus, this pressure level (0.2 mbar) is at
~90 km which is the lower boundary of the region we are interested here. Therefore the
quantum yield is assumed to be unity above 90 km.
However, Zhang et al. (2010) shows that the photolysis rate ~10-7 s-1 is not enough to
produce the observed SO2, otherwise a very large supersaturation of H2SO4 (~100) under
19
nighttime temperature is needed. Although this supersaturation is possible (as seen in
Earth), empirically they also found the required cross section is about ~100 times larger
than that of pure H2SO4 if keeping the H2SO4 vapor abundances roughly the same as the
nighttime saturated abundances. This extreme situation may suggest the existence of
large amount of H2SO4H2O and maybe other hydrates (like H2SO42H2O), although it
seems no very likely not only because the equilibrium abundance of the monohydrate is
small (see fig. 14) but also because the sulfuric acid hydrates might be readily to
condense into the crystal phase even under the nighttime temperature (McGouldrick et
al., 2010). Alternatively, the required large cross section actually could be achieved by
assuming the UV cross section as the upper limit of 1×10-21 cm2 molecule-1 between 195
and 330 nm, as shown in dashed line in Fig. 14. We will consider this possibility in the
model D. Note that this change of H2SO4 photolysis may not affect much for the earth
stratosphere below 35 km because of the absorption of O3 Hartley band dominates the
actinic flux in that region. However, this is very important for Venus mesosphere above
the cloud top since the SO2 absorption is not as strong as O3. The H2SO4 photolysis rate
in this case is ~8.3×10-6 s-1 at 90 km, roughly the same as that of ~8.2×10-6 s-1 if we use
the H2SO4H2O photolysis cross section instead (model B in Zhang et al., 2010).
4.1.3 Model D results
Our model D is same as model A except using the nighttime H2SO4 profile and the
H2SO4 photolysis cross sections with high UV cross section in 195-330 nm. Since the
large sulfuric acid vapor abundance only exists above 90 km, the 80-90 km SO2 inversion
layer has to be a result of diffusion process. The original eddy mixing profile is decreased
by a factor of 4 in 80-86 km in order to reproduce the data. The saturation ratio of H2SO4
is 0.5 (sub-saturated H2SO4 under nighttime temperature), corresponding to ~0.25 ppm at
100km.
The SO and SO2 enhancements above 80 km are successfully reproduced in Model D
(Fig. 16, red line) although not perfectly agreeing with each other. We attribute the
reason to be the constant H2SO4 saturation ratio above 90 km. The SO2 measurements
20
imply that the H2SO4 abundance in model D might be underestimated above 100 km. Fig.
17 compares the selected sulfur species mixing ratio profiles between models A and D.
When the H2SO4 source is included, all sulfur species abundances are increased,
especially SO3 because it is the direct photolysis product of H2SO4. The major production
and loss pathways for SO, SO2 and SO3 in model D are plotted in Fig. 18.
In the upper region the SOx chemistry is relatively simple compared with the lower
region because the catalysts like chlorine species are in the trace amount. The chemistry
is mainly driven by the photolysis reactions and backward recombination with O and O2.
The fast recycling between the sulfur species can be seen from the largest production and
loss rates in Fig. 18. At 98 km where the peaks of the reaction rates are, the SO3
photolysis rate (~2×103 cm-3 s-1) and SO3 + H2O rate (~3×103 cm-3 s-1) are roughly
comparable which means about 40% of the sulfur in H2SO4 goes into SOx and produce
this inversion layers of SO2 and SO. The model D predict the existence of a SO3 inversion
layer as well, with the peak value of ~30 ppb at 100 km. More discussion will be in
section 4.3.
4.2 Sx aerosol as the sulfur source (model E)
The Sx aerosol might be another possible sulfur source in the upper region because Sx
could react with atomic oxygen to produce SO. But this possibility is more ambiguous
because: (1) The Sx aerosol has not been indentified although it is one of possible UV
absorbers in the cloud region (Carlson et al. 2010); (2) As shown in the section 3 for the
lower region chemistry, the production of Sx is mainly constraint below 65 km in the
upper cloud region. So the Sx in the haze layer might be not enough to supply the sulfur
source; (3) The Sx chemistry has large uncertainty due to the lack of laboratory
experiments. The reaction coefficients of Sx + O in our model are estimated by Moses et
al. (2002) based on the S2 + O.
The day and nighttime Sx saturated mixing ratio profiles based on Lyons (2008) are
shown in Fig. 19. The S8 mixing ratio under nighttime temperature could achieve 1 ppb at
21
~98 km. Based on this fact, we assume S8 as the sulfur source in our model E. We fixed
the S8 profile based on model A results but changed the mixing ratio based on the
nighttime SVP scaled by a constant saturation ratio above 90 km. The eddy diffusivity is
same as models A and D. The H2SO4 mixing ratio profile is assumed to be the dayside
saturated profile (same as model A) so that it has a negligible effect on the sulfur source.
The required saturation ratio of S8 is only 0.0004 in order to produce SO and SO2
inversion layer. That means we only need the 0.1 ppt level Sx vapor in the upper region.
However, it has to be a constant source supplied by the aerosol evaporation because the
total ESMR required for SO and SO2 enhancements is at least 0.1 ppm level.
The blue lines in Fig. 16 show that model E could also reproduce the inversion layers
above 80 km. The SO and SO2 profiles (in fact for other sulfur spices as well) from
model D and E are really similar because of the fast inner sulfur cycle. However, there is
large difference in SO3 profiles because the SO3 in model E is mainly converted from SO2
but not from the photolysis of H2SO4 as in model D. The SO3 at 100 km predicted by
model E is ~0.1 ppb, which is two orders of magnitude less than that in model D.
Therefore, future measurement of SO3 could distinguish the two mechanisms.
The major production and loss pathways for SO, SO2 and SO3 in model E are plotted in
Fig. 20. Note that not only S8 + O produces SO but other Sx produced by S8 would also
react with O to produce SO, so in fact a S8 gas molecule could produce about eight SO
molecule eventually. The major differences between models D and E are the SO and SO3
production mechanisms.
4.3 Discussion
4.3.1 Summary of Chemistry
The results of models D and E are summarized in Table 3.
For model D, the simplified SOx chemistry from Fig. 9 can be illustrated as:

à ààEvaporation
àà àà àà ààÜ
à ààhà
àà SO3 á
à ààhàà
Ü
à ààhàà
Ü
à ààhààÜ
à àà àà àà ààÜ
Aerosol á
à H 2 SO4 á
àÜ
à SO2 á
à SO á
à Sá
à Sx
Condensation
H O
O
O
O
O(weak )
2
2
22
Similar to model D, the chemistry in model E:
H2O
O
à ààEvaporation
ààààààààÜ
à ààààOà
à ààOàà
Ü
à ààOàà
Ü
à àààà
ààààÜ
Aerosol á
à Sx á
àààSOààÜ
à SO á
à SO2 á
à SO3 á
à H 2 SO4
2Ü
Condensation
h
h
h (weak )
S ààà
á àhàà
In fact the OCS, S2O and (SO)2 are also in equilibrium with the species above but not
shown here (see Fig. 9). Therefore, the fast inner cycle allows us to derive the ratios of
the sulfur species above 90 km analytically by equating the production and loss rates for
each species:
[OCS] k176 [ClCO]  k178 [CO]

[S]
k300 [S]  J 33
(5)
[S]
J 28

[SO] k159 [O2 ]
(6)
[SO]
J 30

[SO2 ] k236 [O][M ]
(7)
[SO2 ] J 31  k170 [H 2O]

[SO3 ]
k254 [O][M ]
(8)
In model E:
But in model D, SO3 is relatively independent of other SOx:
[SO3 ] 
J 315 [H 2 SO4 ]
J 31  k170 [H 2O]
(9)
Again, SO3 is the key species to distinguish the two pathways because other sulfur
species are closely connected to SO2 no matter what causes this inversion layers.
The S2O and (SO)2 chemistry is less clear so needs more careful simulations in the future.
In models D and E, the steady-state results are:
[S2O]
k246 [O]

[(SO)2 ] J 327  k262 [O]
(10)
[(SO)2 ]
k245 [SO]

[SO]
k246 [O]  k250 [M ]
(11)
The atomic oxygen (O) column production rate above 80 km is ~5.9×1012 cm-2s-1 in
model A but enhanced by ~10% in models D and E (Table 3). Correspondingly, we
found the total column abundance of O2 is slight less in models D and E compared with
the model A result. The reason is that the significantly increased atomic sulfur in the
23
upper region will consume more molecular oxygen and produce SO and O. The O flux
required to reproduce the mean O2 emission 0.52 MR in the nightside is ~2.9×1012 cm-2s-1
(Krasnopolsky, 2010). It suggests that about 45% of the O atoms produced in the dayside
are transported to the nightside and recombine to O2. Therefore, the transport process is at
least as fast as the chemical loss processes. The loss timescale of O is ~10 5-106 s above
80 km. The transport timescale is estimated as ~105 s, based on the SSAS downward
velocity around 100 km in the night side ~0.01 m s-1 derived by Liang et al. (2009) from
the adiabatic heating rate and the scale height of 4 km in the upper atmosphere.
4.3.2 Reactions discussion
Both of the SO and SO2 profiles are derived from the observations above 90 km. It
provides us a chance to test the three body reaction SO + O + M → SO2 + M in the low
temperature region, where there is no laboratory measurements so far. The reaction
coefficient k0~3×10-30 at 100 km (168 K) is inferred from observations. The value
adopted in our models is from Singleton and Cvetanovic (1988) at 298 K, k0 = 4.2×10-31
cm6 s-1and k∞ = 5.3×10-11 cm3 s-1, and corrected by a factor of 8.2 for the third-body CO2.
This reaction coefficient produces the [SO2]/[SO] ~2, which lies in the Venus Express
observations range (Beyleav, et al., 2010). That implies this reaction may have no or very
weak temperature dependence. Grillo et al. (1979) and Lu et al. (2003) measured the
temperature dependence in the high temperature region (~300-3000 K) and provided the
dependence as T-1.84 and T-2.17, respectively. However, this temperature dependence is too
steep for the low temperature region.
One puzzle from the observed [SO2]/[SO] ratio is that it seems the ratio increases with
temperature at 100 km, although this different is within the noise level which may be due
to less measurements in the high temperature situations (their T2 and T3 regions) and the
difficulty to separate the SO and SO2 signals in the spectrum. However, if this
observational temperature dependence is real, it should result from the transport rather
than the chemistry because the recombination rate should decrease with temperature,
although maybe weakly.
24
4.3.3 Sensitivity study
The major uncertainties of model D arise from the H2SO4 vapor abundances and the
photolysis rate of H2SO4. From the expressions (6) and (7) we would expect a linear
relationship between [SO2] and the product of J315 and [H2SO4]. We build a series of
models by varying the values of J315 and [H2SO4] in model D. The SO2 mixing ratios at
90 km and 100 km as function of J315[H2SO4] (the product of J315 and [H2SO4]) at 100 km
are shown in Fig. 21. The arrows indicate model D, where J315 and [H2SO4] at 100 km are
6.4×10-6 s-1 and 2.5×108 cm-3, respectively, so the J315[H2SO4] is ~1.6×103 cm-3 s-1. Fig.
21 implies that it is necessary to maintain this value to explain the inversion layers in the
H2SO4 source case.
The similar sensitivity study is also applied to models E and is shown in Fig. 22.
Although the relationship between the S8 and SO2 abundances is not derived explicitly,
we also expect this linear trend because all the major sulfur species in model E above 90
km are linearly dependent with each other and the total ESMR is from the oxidization of
Sx. The arrows indicate model E, where k228 (reaction coefficient of S8 + O) and [S8] at
100 km are 7.4×10-12 cm3 s-1 and 1.6×102 cm-3 respectively, so k228[S8] (the product of
k228 and [S8]) is ~1.2×10-9 s-1. Assuming all the eight sulfur atoms in S8 eventually goes
into SO, the sulfur flux is about ~1×1013 cm-3 s-1 given the O abundance ~1×1011 cm-3 at
100 km. This value is in the same order of magnitude of the sulfur flux (J315[H2SO4]) in
model D (note that 60% of the sulfur returns back to H2SO4 in model D). Therefore, both
models show that this magnitude of sulfur flux is necessary to explain the inversion
layers.
4.3.4 Sulfur Budget
The recycling of aerosols from the region below 90 km is essential to maintain the steady
inversion because the sulfur will diffused downward due to the inversed mixing ratio
gradient. The production rates of H2SO4 and Sx aerosol for models A, D and E are shown
25
in Fig. 23. The H2SO4 production rate has a second peak at 100 km where the SO3 peak is
in the model D. But even after we have greatly increased the S8 vapor abundances in
model E, the Sx aerosol production does not change significantly. That is because the
nucleation process is really slow in the upper region due to less aerosol nuclei there.
In model D, the net column loss rate of H2SO4 vapor above 90 km is ~8.9×108 cm-2 s-1,
roughly 40% of the column photolysis rate of H2SO4 in that region. Only ~2% sulfur is
converted into polysulfur aerosol. So the total downward diffused sulfur flux is ~8.8×108
to keep a steady-state inversed mixing ratio profile above 80 km. For reference, the
8.9×109 cm-2 s-1 H2SO4 loss rate above 90 km is roughly equal the H2SO4 column
production rate above 78 km through the hydration of SO3. However, it is difficult to
transport the H2SO4 vapor below 90 km to compensate the loss in the upper region
because it will be quickly condensed into the aerosols. Instead, the aerosols might be
transported upward in the dayside by the SSAS circulation. Assuming all the aerosols
above 90 km are the mode 1 aerosols with the mean radius ~0.2 m and the density is 2 g
cm-3, the aerosol column loss rate is ~2 cm-2 s-1 if the aerosols are pure H2SO4. The
column abundance of mode 1 aerosol above 90 km from Wilquet et al. (2010) is
~5.0×106 cm-2. Therefore the aerosol lifetime is about a month in model D. The loss rate
imply that the upward aerosol flux is also ~2 cm-2 s-1 across 90 km to supply the aerosol
budget. Provided that the concentration of mode 1 aerosol at 90 km is ~10 cm-3, the
estimated flux is equivalent to an effective upward transport velocity ~0.2 cm s-1. If the
SSAS circulation dominates the upper region, this velocity is readily to be achieved.
Liang et al. (2007) estimated the downward velocity at ~100 km in the night side to be
~0.01 m s-1, which suggests the SSAS might be very efficient to recycle the aerosols in
the upper regions.
In model E, the total equivalent sulfur column loss rate of the Sx vapor above 90 km is
~8.8×108 cm-2 s-1, which is roughly the same as the net sulfur flux from H2SO4 photolysis
in the model D, but the production rate of Sx aerosol is only roughly ~1.7×107 cm-2 s-1.
The H2SO4 aerosol production rate in model E is ~4.4×107 cm-2 s-1. Therefore, most of the
sulfur (~94%) from Sx aerosol is diffused downward. For reference, the equivalent sulfur
26
column production rate of the Sx aerosol above 78 km is roughly ~1.0×109 cm-2 s-1. If
those aerosols can be transported upward in the dayside, it would be enough to
compensate the loss in the region above 90 km. Assuming that all the polysulfur aerosol
above 90 km has a mean radius of ~0.1 m (half of the H2SO4 aerosol) and the density is
2 g cm-3, the aerosol column loss rate is ~5 cm-2 s-1. If the polysulfur aerosol abundance is
about 1% of that of H2SO4 aerosol, Sx aerosol above 90 km will be cleared out in ~3-4
hours. The estimated upward flux cross the 90 km is equivalent to an effective upward
transport velocity ~50 cm s-1, which is roughly in the same magnitude of the downward
velocity at 100 km in the nightside from Bertaux, et al. (2007) but larger than the
estimation by Liang et al. (2009).
4.3.5 Timescale
The dynamics in the 1-D photochemical-diffusive transport model is only a simple
parameterization for the complicated transition zone between 90-100 km. The aerosol
microphysics is also simplified because we just assumed the instantaneous condensations
of H2O and H2SO4 and ignored the aerosol growth and loss processes. Future 2-D models
including SSAS, zonal wind transport, microphysical processes and photochemical
processes for both the dayside and nightside might be sufficient to represent all the
dynamical and chemical processes in the upper regions. We discuss some typical
timescales here.
(1) Transport: The timescale for the SSAS transport SSAS is ~105 s (section 3) from
Liang, et al. (2009) above 100 km. Zonal transport timescale due to RZ flow RZ is ~105
s, assuming the thermal wind velocity ~50 m s-1 by Piccialli et al. (2008) based on the
cyclostrophic approximation. Eddy diffusion timescale eddy is also ~105 s (Fig. A3).
(2) Aerosol condensation: We assume the condensation is dominated by the
heterogeneous nucleation with timescale (Fig. A3) cond~104-105 s if the accommodation
coefficient =1 (Fig. A3). cond is inversely proportional to  in the free molecular regime
for the upper region. Therefore, the lower value of  might be more appropriate for the
27
H2SO4 condensation in model D since the mechanism assumes that the nighttime H2SO4
vapor could be transported to the dayside and involved in the photolysis process. The
homogeneous nucleation may be important in the dayside since both of the H2SO4 and Sx
are highly supersaturated. For example, the saturation ratios at 100 km are about 106 and
104 for H2SO4 in model D and S8 in model E, respectively. In model D, this dayside
condensation processes will compete with the photodissociation of H2SO4. However, the
homogeneous nucleation rate markedly depends on the SVP, which is a steep function of
temperature but not well determined in the lower temperature range. If the dayside
condensation process were fast, a zonal gradient of the H2SO4 vapor abundance from the
nightside to the dayside would be expected.
(3) Chemistry: H2SO4 photolysis timescale photo depends on the cross section. For model
A, photo is ~107 s. For model D, photo is ~105 s. Sx + O timescale sx+o depends on the
reaction coefficient and the atomic oxygen abundance, Sx+O is ~1-10 s in model E. The
reaction between polysulfur and atomic oxygen is so quickly that it has to happen in the
nightside. That’s why the 0.1 ppt level Sx could provide a large sulfur flux as efficiently
as the photolysis of 0.1 ppm level H2SO4 does. However, as shown in section 4.3.4,
whether the circulation could support the Sx aerosol upward transport across 90 km needs
more future modeling work.
5: Summary and conclusion remarks
One of the specialties of Venus compared with other planets is its slow rotation, which
directly results in a large dayside and nightside difference. Not only the difference of the
temperature which determines the thermochemistry and the solar flux which drives the
photochemistry, but also that of the atmospheric circulation derived from both the
temperature gradient and solar flux, lead to a great contrast of the dynamical and
chemical behavior between the day and night hemispheres. In this study, we separate the
Venus atmosphere from 58-112 km into two regions, the lower mesosphere below 80 km
and the upper mesosphere coupled with the lower thermosphere above 80 km. A strong
zonal wind transport dominates the lower region therefore a diurnal-averaged 1-D
28
photochemical-diffusive transport model is a good approximation. In lower thermosphere
above 90 km, SSAS circulation plays a significant role in transporting chemical species
including the haze particles, so the diffusion could only roughly represent the other
dynamical processes including the upward transport in the dayside, downward transport
in the nightside, and the zonal advection. The upper mesosphere region between 80-90
km can be considered as a transition zone and affected by the both the upper and lower
regimes.
We focus on the sulfur chemistry in this study motivated by the very recent
measurements from Venus Express, especially the SO2 profile from 70-110 km and the
SO profile above 80 km, and some ground-based observations (SO and SO2 from Sandor
et al., 2010; OCS from Krasnopolsky, 2010). First we discussed the chemistry between
58-80 km. The three primary chemical cycles: oxygen cycle, chlorine cycle and sulfur
cycle are closely coupled with each other in the cloud layer. We tested three different
chemical schemes in the models A, B and C, respectively. All the cases could reproduce
the observed SO2 profile below 80 km although with different SO2 boundary mixing
ratios. The NO and NO2 also contribute to the conversion of SO to SO2 in 70-80 km
region. We include the heterogeneous nucleation of elemental sulfur and found that the
S2, S3, S4 and S5 near the lower boundary are highly supersaturated, even under the fastest
nucleation situation. Chlorosulfanes chemistry might play very important roles in
producing the polysulfurs in the cloud layer. However, in order to reproduce the recent
ground-based observations, the required OCS mixing ratio at the lower boundary (~6
ppm) is found to be significantly larger than the previous estimations. This enhanced
OCS layer near 60 km would greatly increase the polysulfur production rate through the
photolysis to atomic sulfur. But it is also possible to lower down the required OCS
abundance at the lower boundary if we speed up the eddy diffusion transport in the cloud
layer.
In the second part of this paper, we proposed two possible solutions to explain the
inversion layers of SO2 and SO above 80 km. The essence of our idea to solve this
problem is to ‘reverse’ the sulfur cycle in the lower region. In 58-80 km, the SO2 and
29
OCS are the parent species transported from the lower atmosphere as the sulfur source,
while the H2SO4 and possible polysulfur aerosols are considered to be the ultimate sulfur
sink and their production rates are shown in Fig. 23. However, in the upper region the
aerosols might become the sulfur source rather than a sink to provide enough amount of
sulfur for the inversion layers but it requires large aerosol evaporation. We correlated this
possible evaporation with the fact of the warmer layer above 90 km in the night side
observed by Venus Express (Bertaux et al., 2007). Therefore the SO and SO2 inversion
layers above 90 km are the natural results of the temperature inversion induced by the
adiabatic heating of the SSAS flow. While the inversion layers the region between 80-90
km are due to the downward diffusion from the lower thermosphere.
If H2SO4 aerosol is the source, the cross section of H2SO4 photolysis and the SVP is
needed to be determined accurately. However, the laboratory work has yet to be done in
the future. From the modeling results, the possible solutions are:
(1) Use the cross sections in model A, from Lane et al. (2008) for the UV region and
Mills et al. (2005) and Feierabend et al. (2006) data for the visible region, but the
H2SO4 saturation ratio is about ~100 under nighttime temperature. That means the
large suppersaturation does not only exist in the dayside but also in the nightside.
The photolysis rate at 90 km is ~8.8×10-8 s-1.
(2) Use the UV cross sections from Lane et al. (2008) but H2SO4H2O cross sections
in the visible region from Vaida et al. (2003). This case requires that the hydrate
abundance is roughly the same order of magnitude of the pure H2SO4 saturated
vapor abundance. The photolysis rate at 90 km is ~8.2×10-6 s-1.
(3) Use the cross sections same as (1) but also use 1×10-21 cm2 molecule-1 in the UV
region of 195-330 nm, as shown in dashed line in Fig. 14. The required H2SO4
saturation ratio is ~0.5 under nighttime temperature. The photolysis rate at 90 km
is ~8.3×10-6 s-1.
30
The major difference between (3) and the other two possibilities is that, in (3) the
photolysis rate is mainly contributed by the UV flux, while in (1) and (2) the dominant
sources are the visible and IR photons.
In the model D we discussed the possibility (3), and the model E considers the Sx aerosol
as the source instead. The models D and E show some similar behaviors, which represent
the general features of the upper region chemistry despite of the different sulfur sources.
Since there are uncertainties of the model parameters, we did the sensitivity studies for
both models. Both of the sensitivity studies show that there is a clear trend of SO2 mixing
ratio with the input sulfur flux: in terms of the H2SO4 photolysis production rate in model
D and the S8 oxidization rate in model E, respectively. Because of the existence of the
fast inner cycle, we consider all the sulfur oxides in the upper region as a box, and the
required sulfur flux inputs in the box above 90 km is nearly 109 cm-2 s-1, consistent in
both models D and E. All the sulfur oxides output from models D and E, except SO3, are
very similar. This is because that the gas phase sulfur chemistry in the upper region is
relatively simpler than that in the lower region because it is driven by the photolysis
reactions and backward recombination with O and O2. However, the complexity comes
from the coupling of the gaseous chemistry with the aerosol microphysics and the SSAS
and zonal transport, both of which are poorly determined at this time. Future observations
and more complete modeling work are needed to fully reveal the behavior of the whole
system.
Here, we present several basic differences between model D and E for the future
considerations.
First, the two mechanisms probably happen in different regions. By roughly estimating
the chemical timescales and dynamical timescales (section 4.3.5), we found that the Sx +
O reaction in model E is much faster than the transport. As the Sx aerosols are evaporated
in the nightside, the Sx vapor will be oxidized in less than 10 seconds, therefore the SOx
is actually first produced around the anti-solar region and then transported to the dayside
by the zonal wind and photodissociated. On the other hand, H2SO4 photolysis has to
31
happen in the dayside in the model D. So the SOx should be first produced in the dayside
and then transported to the nightside. One big issue of the model D is the H2SO4
condensation rate in the dayside since it’s highly supersaturated. If the homogenous
nucleation were very fast, the photolysis would be violated. Therefore, the nightside
H2SO4 abundances would be also supersaturated in order to supply enough H2SO4 for the
dayside.
Secondly, the two mechanisms might require different aerosol flux from below. Since the
aerosols cannot be fully recycled above 90 km due to diffusion loss of sulfur, an upward
aerosol flux is needed. The estimated flux is ~2 cm-2 s-1 and ~5 cm-2 s-1, corresponding to
an effective upward transport velocity ~0.2 cm s-1 and ~50 cm s-1 for model D and model
E, respectively. However, the estimation of Sx transport velocity here is based on the
assumption of the Sx/H2SO4 ratio ~1%, which remains to be confirmed by future
measurements.
Thirdly, in terms of the possible observational evidences, the model D requires the H2SO4
number density ~108 cm-3 around 100 km in the dayside, which might be observed in the
future. But the estimated abundance of S8 in the nightside is only ~102 cm-3 around 100
km, which is hardly to be observed. SO3 might provide another possibility to distinguish
the two mechanisms because SO3 is mainly controlled by the H2SO4 photolysis in model
D but by the SO2 oxidization in model E. The abundance of SO3 at 100 km is ~3.0×107
cm-3 and ~1.7×105 cm-3 for models D and E, respectively. Future observations might be
able to detect this difference.
Future work may concern:
(1) The observations of SO3 and H2SO4 in the lower thermosphere and better
constraints of SO2 and OCS abundances in the upper cloud region.
(2) The measurements of photodissociation cross section of H2SO4 in the UV region,
especially in the lower energy range (~195-330 nm).
32
(3) The laboratory measurements of H2SO4 SVP in the lower temperature region
(~150-240 K).
(4) The determination of polysuflur reaction coefficients.
(5) The physical explanation of the lower eddy diffusivity in the haze layer than that
in the cloud layer.
(6) The cause of the local minima for HCl, H2O, HDO and CO in the region between
85-90 km. This may require 3-D maps of the wind and temperature fields.
(7) The explanations of the longtime variation of SO2 at the cloud top ~70 km and the
possible variation of the OCS abundance in the upper cloud region.
(8) The microphysics properties of Sx and H2SO4 aerosols, their formation and loss
processes, transport, vertical profiles and the cause of the multi-modal
distributions.
(9) Coupled mesosphere-thermosphere (~58-135 km) chemistry including the neutral
species and ions to reveal the role of SSAS transport in both dayside and
nightside of Venus.
Appendix A1
Radiative Transfer
The diurnal-averaged radiation calculation here is modified based on Mills (1998). The
direct attenuated flux and Rayleigh scattering calculations remain the same (see details in
the Appendix H, and I of Mills, 1998). In this study we adopt 550 log-linear optical depth
grid, 112 wavelengths from 960-8000 Å, 14 zenith angles for the incoming photons, 8
Gaussian angles for the diffused photons, and 16 azimuthal angles. The wavelengthindependent middle cloud albedo at the lower boundary is assumed to be 0.6. The
depolarization factor of CO2 Rayleigh scattering is set as 0.443.
The absorption of unknown UV absorber and scattering processes of haze and cloud
particles are crucial for the radiation field, especially in the upper cloud layer. We follow
the procedure described in Crisp (1985). First, we calculated the optical depths from the
33
bi-modal aerosol profiles in Fig. 1 and scaled to match the optical depth values in their
table 2 (equatorial cloud model) in Crisp (1985). Aerosol optical properties are calculated
using Mie-code based on the parameters of equator hazes in the Table 1 of Crisp (1985).
For mode 1, the refractive index is 1.45, radius 0.490.22 m. For mode 2, the refractive
index is 1.44, radius 1.180.07 m. Fig. A1 shows the scattering efficiencies (upper
panel) and asymmetry factors (middle panel) of the two aerosol modes. Since the
asymmetry factors are not varying significantly, we choose 0.74 as the mean value for all
the wavelengths. UV absorber is introduced by decreasing the single scattering albedo of
the mode 1 aerosol between 3100-7800 Å. We take the empirical absorption efficiency
values from the Table 4 of Crisp (1985). Fig. A1 (lower panel) shows the single
scattering albedo of the mode 1 aerosol mixed with the UV absorber. Because the single
scattering albedo is not constant (from 0.85 to 1) with wavelength, we use the
wavelength-dependent values in the calculation. The spectral actinic fluxes (in units of
photons cm-2 s-1 Å-1) for 58, 62, 70, 90 and 112 km are plotted as function of wavelength
in Fig. A2. Due to the absorption of CO2, SO2 and SO, the UV flux decreases quickly
when penetrating downward. Rayleigh scattering and aerosol scattering result in the
larger actinic flux in the cloud and haze layers than that at the top of the atmosphere. In
the wavelength range large than 2000 Å, the actinic flux peaks around ~65 km. The UV
actinic flux at the lower boundary (~58 km) between 2000-3000 Å is roughly anticorrelated with the SO2 cross sections and the gap of the cross section profile near 2400
Å may open a window for the UV flux to penetrate down to the lower atmosphere of
Venus for further photolysis.
Appendix II
Heterogeneous Nucleation Rate Constant of Elemental Sulfurs
We used the same aerosol profiles shown in Fig. 1 to estimate the heterogeneous
nucleation rate of elemental sulfurs onto H2SO4 droplets. The nucleation rate constant in
the continuum regime (where the particle size is much larger than the vapor mean free
34
path ) is expressed as (Seinfeld and Pandis, 2006): J c  4 Rp Ds , where Rp is the H2SO4
aerosol radius and Ds the molecular diffusivity of elemental sulfur vapor.
However, in the Venus cloud layer, the Knudsen Number Kn = /Rp of Sx vapor is not
far from 1, so the nucleation process lies in the transition regime where the mean free
path  of the diffusing vapor molecule (e.g., Sx vapor) is comparable to the pre-existing
aerosol size. Therefore, we adopt the Dahneke approach (Dehneke, 1983), which matches
the fluxes of continuum regime ( Kn = 1 ) and free molecular regime ( Kn ? 1 ) by
introducing a function f (Kn) :
f (Kn) 
(1  Kn)
1  2Kn(1  Kn) / 
where  is the molecular accommodation coefficient, which is the probability of sticking
when the vapor molecule encounters a particle. Here the mean free path  in Kn is
defined as 2Ds/v, where v is the mean thermal velocity of the vapor molecule.
Finally we obtain the nucleation rate constant:
J  f (Kn)J c 
4 Rp Ds (1  Kn)
1  2Kn(1  Kn) / 
The molecular diffusivity Ds of sulfur vapor can be estimated using hard sphere
approximation: Ds=b/N, where N is the total CO2 gas density in the environment and b is
the binary collision parameter:
 2 kT (ms  mg ) 
3
b

4 (ds  dg )2 
ms mg

1/2
where ds and dg are the diameters of sulfur vapor and CO2 gas molecule, respectively
(assume ds=dg=3 Å), k Boltzmann constant, T temperature, ms and mg the mass of sulfur
vapor and CO2 gas molecule, respectively. Fig A3 shows the total nucleation timescale
(from two modes of aerosols) of S2 (roughly the same as other allotropes), together with
the eddy transport timescale of model A and photolysis timescales of S2, S3 and S4. See
the discussion in section 3.
35