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
Section 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).
From the aerosol abundances, we can roughly estimate the sulfur content. The mode 1
aerosols are roughly 0.2 micron in radius constantly 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 sulfur content mixing ratio converted 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 sulfur content 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 sulfurs in the ppb level at all 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 the two candidates in this study.
According to the turning point of SO2 profile around 80 km, we separate the Venus upper
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 in section 4, where we provide
the 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. Then we come to the summary of
the chemical mechanisms and conclusion remarks.
Section 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. 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 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 need to
be 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 using 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 proper for the lower region
chemistry therefore they could not match the SO2 observations below 80 km. Instead, a
full chemical reaction set with 35 photodissociation reactions and about 260 neutral
reactions are used in model A and 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 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.
Section 3: Chemistry between 58-80 km
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 has a constant mixing ratio of 3.4%. The H2O profile (see Fig. 4) is prescribed
based on 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 based on H2SO4 weight percent as 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 as 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 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 in 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 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 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
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 free oxygen and
chlorine radicals, such as O, OH, Cl, ClO, etc., are the key catalysts in recycling sulfur
species in their inner cycle, but the sulfur species do not act as the 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 not shown
explicitly here locates 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 ignoring 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 sinks decreases with
altitude mainly because both the aerosol and elemental sulfurs are more abundant at
lower altitude.
Below ~65 km, SO2 is roughly in equilibrium with ClSO2. SO2 reacts with 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.
The OCS mixing ratio in the cloud layer is puzzling. OCS is believed to be transported
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 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 1e7 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 1e5 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
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
don’t 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 chemistry 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. And some previous models range from 9×10111×1013 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.
Section 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 mixed 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 other observed profiles of CO, H2O, HDO,
HCl and HF. These local minima are hard to be explained by the chemistry but probably
caused by the 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
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 have reproduced 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. It is not
likely that the minimum corresponds to a large divergence region resulted from
atmospheric dynamics because the other species don’t 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 to test the
system stability. Fig. 11 shows that the mixing ratio of SO2 drops off very fast 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 at the lower
boundary of the inversion layer (80 km) is ~1×109 cm-2s-1
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 atmospheric
system could be shifted to another chemical equilibrium state and produces 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) 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). The
similar situation may exist in the Venus upper haze layer in the dayside when the H2SO4
vapor in 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.
(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
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 drops 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 kinds of 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.
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).
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
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 agree 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
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
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 Chemistry Summary
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
H2O
O
O
O2
O(weak )
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
(3)
[S]
J 28

[SO] k159 [O2 ]
(4)
[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.
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.
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 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
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 SSAS 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 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 (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
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 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. 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: 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. 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.
(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
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)
Therefore, the =0.1 or lower 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. If the dayside
condensation is very large due to the homogeneous nucleation, a zonal gradient of the
H2SO4 vapor abundance from the nightside to the dayside might be expected. The upper
limit of the accommodation coefficient (=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.
Section 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
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
boundary abundance if we speed up the eddy diffusion transport in the cloud layer. The
eddy diffusivity is reduced by a factor of 4 between the 76-80 km to reproduce the slope
of SO2 profile in that region, but we don’t have a good explanation for it because the
eddy diffusivity is an empirical parameterization of all the dynamical processes. It could
be a result of the complex dynamics pattern of the transition zone. The eddy diffusivity
also needs to be decreased by 4 in the region 80-86 km in models D and E.
In the second part, 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 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.
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.
Finally, 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
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.
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
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) / 
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.