Sulfur Chemistry in the Middle Atmosphere of Venus
Zhang X., Liang, M-C, Belyaev D., and Yung, Y. L.
$$$ Need to include frank mills because we take some of his chlorine chemistry? $$$
To be submitted to Icarus 2011
Abstract
1. Introduction (not complete yet)
1. Big picture review…
2. Measurement summary (gases), especially SO and SO2 from Belyaev et al. (2010)
3. Summary of Zhang et al. (2010).
4. Aerosol profile
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). In fig 1/ used ***
symbols where the information is from interpolation/ state that in the caption/ do not need
in text
1
From the aerosol abundances, we can roughly estimate the sulfur content. The mode 1
aerosols are roughly 0.2 micron $$$ replace all micron by m $$$ in radius that is
constant for all altitudes. For the mode 2 aerosols, we use 0.7 micron above 72 km
(Wilquet et al. 2010) for the haze particle and 1.1 micron below for the cloud particle
(Knollenberg and Hunten, 1980). The right panel of Fig. 1 shows the equivalent sulfur
mixing ratio (ESMR) by volume $$$ use equivalent sulfur mixing ratio instead of sulfur
content $$$ computed from the H2SO4 aerosol (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 sulfur content in elemental sulfur in excess of 10 ppb at most
altitudes (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 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, 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. The last section provides a
summary of the paper and conclusions.
2: Model Description
2
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 a function of time and altitude from 58 to
112 km. 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 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 mid-latitude (45N) and we use 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 $$$
change all Nitrogen to nitrogen $$$ 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
3
for the sulfur chemistry above 80 km, we will use 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 below 80 km, where there seems to be difficult in matching the SO2
observations. Instead, a full chemical reaction set with 35 photodissociation reactions and
about 260 neutral reactions are used in model A, as listed in Tables 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
dayside temperature profile and original eddy diffusion coefficient profile from Yung and
DeMore (1982) are shown in Fig. 2 (solid line). The nighttime temperature profile
(dashed line in Fig. 2) is measured by Venus Express in orbit 104 at latitude 4° S and
local time 23:20 h (black curve in the Fig. 1 of Bertaux et al.11). This temperature profile
is only used to calculate the H2SO4 saturated vapor pressure in section 3. The SO2 mixing
ratio at the 58 km and the eddy diffusivity profile can be adjusted to match the SO2
observations in 70-80 km (Belyaev et al., 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 (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. $$$ mention earlier work by cones et al. 1967 $$$
4
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 3.4%. 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
details). Model A uses the daytime H2SO4 abundances (see Fig. 14). The accommodation
coefficient of the sulfur nucleation is set to unity (the upper limit). Around the turning
point of the observed SO2 mixing ratio profile (~80 km), we reduce the eddy diffusivity
by a factor of 4 in 74-80 km to reproduce the data. In fact the eddy diffusivity also needs
to be decreased by a factor of 4 in 80-86 km $$$ need some dynamical reason $$$ in
order to match the SO2 profile above 80 km when we add the sulfur sources in the upper
region in section 4. The new eddy diffusion coefficient profile is plotted as a dashed line
in Fig. 1. Model A requires 5 ppm SO2 the lower boundary to match the SO2
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 clear 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 cycle is closely coupled with the oxygen and chlorine cycles 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
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words, the model without sulfur cycle 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. The reason is that, the oxygen and chlorine
bearing radicals, such as O, OH, Cl and ClO, are the key catalysts in recycling sulfur
species in their inner cycle, but the sulfur species do not act as catalysts in the Venus
chemistry. Therefore, to some extent, the sulfur chemistry 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 not shown
explicitly here locates $$$ ??? not clear $$$ in the upper left part with elemental sulfurs
(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. If we ignore the aerosol evaporation (Zhang et al., 2010)
above 80 km at this moment, H2SO4 and Sx 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 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 altitudes.
Below ~65 km, SO2 is roughly in equilibrium with ClSO2. SO2 reacts with chlorine the
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.
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The OCS mixing ratio in the cloud layer is puzzling. OCS originates from the lower
atmosphere. At 33 km, the maximum mixing ratio of OCS is ~6 ppm at equator observed
by the Venus Express and ground-based telescope IRTF observation (see Yung et al.,
2009). But 6 ppm OCS at the lower boundary (~58 km) is only able to produce ~1 ppb
and 0.02 ppb OCS at 65 km and 70 km, respectively. Although 1 ppb OCS lies in the
observation range 0.3-9 ppb reported by Krasnopolsky (2010), it is difficult for model A
to achieve the 10 ppb level OCS at 65 km. 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. 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 model A between 58-70 km
may not be efficient to transport the OCS upward. The eddy mixing in the cloud layer
could have large variations, resulting in the large variation of the detected OCS values.
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 sulfur
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 1e7 $$$ change
notation 107 $$$ at the lower boundary and becomes unsaturated above 76 km. S3 is
oversaturated by a factor of 103-107 from 58-100km. S2 is extremely supersaturated at all
altitudes. The saturation ratio is 107 at the bottom and 1e5 $$$ at the top, with the peak in
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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 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
8
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 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
9
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 and 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 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 between 85-90 km for all of the observed profiles of CO, H2O, HDO, HCl
and HF. These local minima are hard to be explained by the chemistry but probably
caused by atmospheric dynamics, such as a divergence zone where the zonal wind is also
expected to have a minimum. The SO2 minimum is different because: (1) The SO2
minimum occurs around 80 km, about 5 km lower than that of other species; (2) From
the observations, SO2 mixing ratio decreases by 2 order of magnitude from 58 km to 80
km, while the other minima are only factor of 2-4 less than the maximum values in the
lower region; (3) The CO, H2O, HDO, HCl and HF 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
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altitude due to the photodissociation and oxidization processes. Therefore, the SO2 and
SO enhancement should be treated differently.
Since the photochemical models in section 3 can reproduce the data below 80 km, it is
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. It is not
likely that the minimum corresponds to a large divergence region resulting from
atmospheric dynamics because the other species do not $$$ show the same phenomenon
at ~80 km. Thus, we conclude there is an unknown source of sulfur above 80 km.
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
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 as 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 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 at the lower boundary of the inversion layer
(80 km) is ~1×109 cm-2s-1
11
In the view of chemistry, if the aerosols (H2SO4, Sx) can also be continuously transported
into the upper regions to supply the sulfur, it is possible that the upper atmosphere could
be shifted to another chemical steady state and produces the sustained 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
night-time temperature inversion layer. Zhang et al. (2010) 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 in 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.
12
(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(18.452406985 
3505.1578807 330918.55082 12725068.262


)
T
T2
T3
(1)
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
85-100 km in the dayside and 85-90 km in the nightside seem robust. However, as we
13
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
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 pH 2 SO4  16.259 
  0
8.3143T
 10156  [
1
1
T
T

(1.  ln( 0 )  0 )]
T Tc  T0
T
T
(2)
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
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.
14
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
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
seems that the cross section in 195-330 nm is much smaller than the upper limits from
Buikholder et al. (2000).
15
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
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
16
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. This change 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.
Therefore, we summarized the possible solutions so far:
(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 (see model D below). The
photolysis rate at 90 km is ~8.3×10-6 s-1.
17
In each case, both the cross sections and SVP of H2SO4 and H2SO4H2O need to be
verified in future laboratory measurements.
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 (the possible
solution (3) above). 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
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
18
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
~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 sulfur content 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
19
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:
h
Evaporation
h
h
h
à àà àà àà àà ààÜ
à àà ààÜ
àà SO3 á
à àà àà
Ü
à àà àà
Ü
à àà ààÜ
à àà àà àà ààÜ
Aerosol á
à H 2 SO4 á
à SO2 á
à SO á
à Sá
à Sx
Condensation
H O
O
O
O
O(weak )
2
2
Similar to model D, the chemistry in model E:
Evaporation
O
O
O
H O
à ààààààààààÜ
à ààààOààààààÜ
à àààà
Ü
à àààà
Ü
à àààà2ààààÜ
Aerosol á
à Sx á
à SO á
à SO2 á
à SO3 á
à H 2 SO4
2Ü
Condensation
h
h
h (weak )
ààà
S á à àà SO
h
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: $$$ move to center of page $$$
[OCS] k176 [ClCO]  k178 [CO]

[S]
k300 [S]  J 33
(3)
$$$ equation number must be in middle of
line
[S]
J 28

[SO] k159 [O2 ]
(4)
20
[SO]
J 30

[SO2 ] k236 [O][M ]
(5)
In model E:
[SO2 ] J 31  k170 [H 2O]

[SO3 ]
k254 [O][M ]
(6)
But in model D, SO3 is relatively independent of other SOx:
[SO3 ] 
J 315 [H 2 SO4 ]
J 31  k170 [H 2O]
(7)
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]
(8)
[(SO)2 ]
k245 [SO]

[SO]
k246 [O]  k250 [M ]
(9)
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
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 ~105-106 s above
80 km. The transport timescale is estimated as ~104 s, based on the subsolar-anti-solar
circulation (SSAS) downward velocity in the night side ~0.43 m s-1 derived by Bertaux et
al. (2007) from the adiabatic heating rate and the scale height of 4 km in the upper
atmosphere.
21
4.3.2 Reactions
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.
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
22
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 sulfur content 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
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
23
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 could be
transported upward. 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 subsolar-anti-solar circulation dominates the upper
region, this velocity is readily to be achieved. Bertaux et al. (2007) estimated the
downward velocity at ~100 km in the night side to be ~0.43 m s-1, which suggests the
SSAS might be very efficient to recycle the aerosols in the upper regions.
In model E, the total column loss rate of Sx vapor converted to sulfur atom content 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
aerosol column production rate converted to sulfur atom content above 78 km is roughly
~1.0×109 cm-2 s-1. If those aerosols can be transported upward, it would be enough to
compensate the loss in the region above 90 km. Assuming 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 (1% is the ratio estimated by Carlson et al., 2010 in
the cloud region but may be less in the haze region), the polysulfur 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
24
same magnitude of the downward velocity at 100 km in the nightside from Bertaux, et al.
(2007).
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 don’t include the H2O and H2SO4
condensation and the aerosol grow 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. But some typical timescales can be estimated
here.
(1) Transport: The timescale for the SSAS transport SSAS is ~104 s (section 3) from
Bertaux, et al. (2007) 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 ~105 s (Fig. A3).
(2) Aerosol condensation: The coagulation timescale coag is very slow, estimated as
2/KN, where the Brownian motion coagulation kernel K ~10-9 cm3 s-1 (Esposito et al.,
1983) and the aerosol number density N~1-10 above 90 km, so coag is ~108-109 s.
Therefore, the condensation is dominated by the heterogeneous nucleation timescale (Fig.
A3) cond~104-105 s if the accommodation coefficient =1. cond is inversely proportional
to  in the free molecular regime for the upper region.
(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. This
conversion is much faster than any other processes in that region. That’s why the 0.1 ppt
25
level Sx could provide a large sulfur flux as efficiently as the photolysis of 0.1 ppm level
H2SO4 does.
Summarized as:
Sx+O < SSAS < cond (=1) < RZ ~ eddy ~ photo (model D) < cond (=0.1) < cond (=0.01)
< photo (model A) < coag
Therefore, the =0.1 might be more appropriate for the 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. But the upper limit (=1) could be used
in model E since the reaction between polysulfur and atomic oxygen is so efficient that it
has to happen in the nightside. 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
5.1 Summary of the chemistry
Difference between the lower and upper region chemistry (upper chemistry is much
simpler but aerosol chemistry is the big uncertainty)
Lower:
1. Sx supersaturation
2. Eddy x0.25
3. OCS problem
Upper:
UV v.s. visible in H2SO4 photolysis
H2SO4 from nightside to dayside and photolysis in the dayside
Sx happens at nightside
26
Rxn and possible observations.
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
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
27
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
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) / 
28
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

2 
4 (ds  dg ) 
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.
29