# Effective parameterization of absorption by gaseous species and unknown UV
absorber in 125-400 nm region of Venus atmosphere

Boris Fomin
Central Aerological Observatory, Moscow
<EMAIL_ADDRESS>
& Mikhail Razumovskiy
Moscow Institute of Physics and Technology
Instituskii per. 9, 141701, Moscow, Russia
<EMAIL_ADDRESS>
corresponding author

###### Abstract

We present an effective parameterization of molecular absorption of shortwave
solar radiation in Venus atmosphere. It is addressed to general circulation
modeling to accelerate radiative transfer calculations in the spectral
interval 125 – 400 nm (25000 – 80000 cm-1 ). In F-UV and M-UV regions strong
absorption of CO2 ans SO2 enables to parameterize gaseous absorption with only
three effective cross-sections. In N-UV region absorption of SO2 and the
unknown UV absorber are parameterized with six effective cross-sections for
each species. For treatment of Rayleigh scattering and optical properties of
Venus clouds eight effective spectral points are recommended.
Parameterizations were validated by the original reference line-by-line Monte-
Carlo radiative transfer model. The outcome of the validation shows the
discrepancy in fluxes less than 3%. Thus, it takes only eight-fold solution of
radiative transfer equations to correctly describe solar fluxes and heating
rates in the whole ultraviolet region.

_Keywords_ Venus $\cdot$ radiative transfer $\cdot$ atmospheres $\cdot$
molecular absorption $\cdot$ parameterization $\cdot$ unknown UV absorber

##  1 Introduction

General circulation models (GCMs) require high accuracy solutions of radiative
transfer equation at every grid step (spatial and temporal) in order to
reproduce peculiar mesoscale structures that are notably presented in Venus
atmosphere. However, it is unfeasible to include detailed line-by-line
calculations to GCMs, subsequently some ways of parameterization should be
involved.

By this time there is a sufficient lack of self-consistent parameterizations
that whether are not too simplistic (e.g. double-gray radiative transfer or
Newtonian approximation) or not too much constrained to various atmospheric
parameters, specific GCM or way of solving radiative transfer equation. Thus,
our motivation is to offer the fresh way to accelerate radiative calculations
suitable to climate modeling. The earlier approach is based on look-up-tables
of heating and cooling rates generated by Haus et al. (2017) and utilized in
IPSL GCM by Garate-Lopez and Lebonnois (2018). However, we adhere to the
different concept of speeding up the radiation block of GCM.

In our approach we follow original k-distribution technique described in
(Fomin and de Paula Correa, 2005) instead of familiar correlated-k method. We
construct effective cross-sections for absorption by gaseous constituents and
unknown UV absorber regardless of its chemical composition. Mentioned
parameterizations depend only on initial absorption cross-sections. In
addition, we also suggest spectral points for calculation of Rayleigh
scattering and clouds optical features (extinction coefficient and scattering
indicatrix). Thus, we propose a universal tool to accelerate radiative
transfer calculations. One needs to solve radiative transfer equation just
eight times using our effective cross-sections to accurately reproduce fluxes
and heating rates in UV region, while other blocks in atmospheric modeling
scheme can be unchanged. We validate the efficiency of our parameterizations
through line-by-line procedures with reference Monte-Carlo model. Construction
of parameterizations of molecular absorption in other spectral regions will be
the subject of future works.

The paper is organized as follows. In section 2 we explain the modeling part
of the work: the technique for constructing the parameterizations and
description of the reference Monte-Carlo model used in validation procedures.
Section 3 refers to the dataset with parameterizations and the result of
validation procedures. We provide some conclusive remarks in section 4.

##  2 Methodology

###  2.1 Construction of parameterizations

The way we construct the parameterizations essentially corresponds to the one
used in (Fomin and de Paula Correa, 2005; Fomin and Kolokutin, 2017) for
shortwave region of Earth’s atmosphere with some revision. In the case of
Venus atmosphere in UV spectral region this method is simplified due to
ignorance of absorption cross-sections temperature dependence (Haus et al.,
2015). The idea of creating parameterizations is the following. Let us
consider two modeling atmospheres: “simple” atmosphere with no scattering and
no reflection from surface (A) and full-consistent Venus atmosphere (used in
reference line-by-line calculations) (B). And suppose that one needs to find
(“retrieve”) absorption cross-section of fixed gaseous species from given
radiative fluxes obtained in the atmospheres A and B. For fixed wavelength
$\lambda^{*}$ “retrieval” procedures for both atmospheres obviously will give
the same value: $\sigma(\lambda^{*})$, where $\sigma(\lambda)$ is the initial
absorption cross-section. However, radiation calculations for atmosphere A are
much faster and simpler than for atmosphere B, because they are based on the
trivial Beer-Lambert law. We can follow the same procedure in simple
atmosphere A but for the given spectral interval $\Delta\lambda$ and instead
of monochromatic cross-sections “retrieve” effective cross-sections:
$\sigma_{\text{eff}}(\Delta\lambda)$. Effective cross-sections represent
profile of initial absorption cross-sections averaged with solar spectrum in
the interval $\Delta\lambda$. We define effective cross-section in the i-th
atmospheric layer through the following formula:

$\sigma_{\text{eff},\,i}=\frac{\text{ln}(F_{i+1}^{\,\downarrow}/F_{i}^{\,\downarrow})}{\Delta\zeta_{i}},$

where $F_{i}^{\,\downarrow}$ and $F_{i+1}^{\,\downarrow}$ are the downward
fluxes at the bottom and at the top of the $i$-th discrete height layer.
$\Delta\zeta_{i}=\zeta_{i+1}-\zeta_{i}$ is the number of absorber molecules
along the direct solar radiation in $i$-th layer. As the absorber amount along
the radiation path strongly correlates with the zenith angle, it is more
useful to introduce dependence of the effective cross-sections from the value
$\zeta$, instead of height $h$. Thus defined values $\sigma_{\text{eff},\,i}$
can be used in one-time solution of radiative transfer equation to find
radiative fluxes and heating rates in the given spectral interval
$\Delta\lambda$.

More wider the interval $\Delta\lambda$ – more bigger the difference between
radiative fluxes and heating rates calculated for simple atmosphere A and
“real” atmosphere B. Nevertheless, we found out that spectral intervals where
effective cross-sections obtained in simple atmosphere A yield good accuracy,
appear to be very large. Thus, we divide 125-400 nm region into eight
k-intervals, where effective cross-sections yield good accuracy in fluxes and
heating rates. For providing stable justification of our approach, we validate
our parameterizations with reference Monte Carlo model. During the validation
procedures for each k-interval we compare radiative fluxes and heating rates
calculated in two ways: as a result of one-time solution of radiative transfer
equation using effective cross-section for this k-interval and as a result of
line-by-line calculations in this k-interval with reference Monte Carlo model.

After thorough manual inspection of the whole UV spectral interval, we divided
it into 8 k-intervals to calculate effective cross-sections for each of them.
In each k-interval we selected wavelength points for calculation of Rayleigh
scattering in order to obtain best fits with reference simulations. For
convenience, optical features of the Venus clouds (extinction coefficient and
scattering indicatrix) could be taken at the same point since they don’t
significantly depend on wavelength in UV region. We also specify the incident
solar flux at the top of the atmosphere (TOA) for each k-interval as this
value relates to the way of choosing solar spectrum data. All detailed
information about the k-intervals is summarized in Table 1.

Table 1: Detailed information about k-intervals for accelerating radiative
calculations in UV region

k-interval |  Spectral region, $\bf 10^{4}\text{cm}^{-1}$ |  Superior absorbers |  ${\bf\nu_{R}}$, $\bf\text{cm}^{-1}$ |  Incident solar flux, W/m2
---|---|---|---|---
F-UV |  5 - 8 |  CO2 |  66000 |  0.20
M-UV |  3.(3) – 5 |  SO2, CO2 |  36000 |  27.74
N-UVa |  3.1 – 3.(3) |  SO2, UVA |  32000 |  28.19
N-UVb |  3.0 – 3.1 |  SO2, UVA |  30000 |  19.91
N-UVc |  2.9 – 3.0 |  UVA, SO2 |  30000 |  20.20
N-UVd |  2.7 – 2.9 |  UVA, SO2 |  28000 |  52.40
N-UVe |  2.55 - 2.7 |  UVA, SO2 |  26250 |  17.64
N-UVf |  2.5 - 2.55 |  UVA, SO2 |  25250 |  47.27

  * •

$\nu_{R}$ – is the recommended wavenumber for calculation of Rayleigh
scattering and clouds optical features during one-time radiative transfer
simulation

  * •

UVA relates to the unknown ultraviolet absorber

  * •

The left border of M-UV region was chosen for convenience (300 nm)

  * •

More dominant absorber goes first. Other active absorbers can be neglected
while considering the whole UV-region (more in Section 3.2).

###  2.2 Monte-Carlo reference model

Our reference Monte-Carlo model was previously successfully exploited for
Earth’ conditions in UV region by Sukhodolov et al. (2016). It is a high-
resolution (0.25 cm-1) plane-parallel short-wave version of FLBLM model
(Forster et al., 2011; Fomin and Falaleeva, 2012). For the present studies it
was adopted to the Venus conditions according to the baseline work by Haus et
al. (2015), in which authors performed line-by-line calculations along with
sensitivity analysis to various spectroscopic and atmospheric parameters from
125 nm to 1000 $\mu$m. Hereafter we list the key parameters of the atmospheric
model.

####  2.2.1 UV absorption cross-sections

Photoabsorption spectra of gaseous components in the atmosphere are relatively
smooth in comparison with visible and IR-spectra. This fact is largely
determined by the nature of absorption of UV rays: it drives the course of the
chemical reaction of photodissociation. Thus, to incorporate UV spectroscopy
into simulations, there is no need to trace the contours of individual lines.
Relevant sources on absorption cross-sections of atmospheric gaseous
constituents are summarized in Table 2. Note that in some experiments
extinction coefficients or absorption coefficients were measured, which are
not so convenient in our studies. We refer to MPI-Mainz spectral atlas
(Keller-Rudek et al., 2013) to gain datasets in unique format: absorption
cross-section in cm2/molecule from wavelength in nm. Figure 1 shows absorption
cross-sections as functions from wavelength for all gaseous constituents which
are considered to be active in UV-region. The strongest absorption for all
gaseous components is manifested in the far ultraviolet in 125-200 nm, where
the intensity of solar radiation is insignificant. In present paper cross-
sections of carbon dioxide are represented as a combination of data from
Shemansky (1972), Parkinson et al. (2003), Yoshino et al. (1996) in different
spectral intervals. As Haus et al. (2015) we also neglected the temperature
dependence of the cross-sections for all gases. Nonetheless, Marcq et al.
(2019) consider temperature dependent absorption cross-sections for CO2 and
SO2. We address this possible issue in Section 3.2.

Figure 1: Absorption cross-sections of gaseous constituents in Venus atmosphere in UV region Table 2: Sources of wavelength-dependent absorption cross-sections Species | Spectral region | Source paper | Temperature
---|---|---|---
CO2 | 125 – 163 nm | (Yoshino et al., 1996) | 295K
CO2 | 163 – 200 nm | (Parkinson et al., 2003) | 295K
CO2 | 200 – 300 nm | (Shemansky, 1972) | 298K
SO2 | 125 – 400 nm | (Manatt and Lane, 1993) | 293K
SO | 125 – 330 nm | (Phillips, 1981; Belyaev et al., 2012) | 293K
O3 | 125 – 186 nm | (Mason et al., 1996) | 298K
O3 | 186 – 400 nm | (Sander et al., 2011) | 293-298K
H2O | 125 – 198 nm | (Sander et al., 2011) | 298K
HCl | 140 – 220 nm | (Inn, 1975) | 298K
OCS | 185 – 300 nm | (Molina et al., 1981) | 295K

####  2.2.2 Unknown UV absorber

The unknown UV absorber (UVA) is considered to be an additional source of
radiation absorption in the spectral range 320-400 nm (Pollack et al., 1980).
We include the UVA to our atmospheric model according to one of the latest
parameterizations by Haus et al. (2015) (we use in simulations both high-
altitude and low-altitude models, fig. 18) in contrast to Crisp (1986); Marcq
et al. (2019) who effectively considered it by depressing single scattering
albedo of cloud mode 1. Haus et al. (2015) extracted (“retrieved”) the
absorption cross-sections and concentration in such a way that the simulation
results were in adequate agreement with the experimental Bond albedo data by
Moroz (1981). This approach allows to treat unknown UV absorber as another
species with its own concentration profile and absorption cross-section
without specifying a concrete molecular formula. Though nominal high-altitude
model given by Haus et al. (2015) features only 10 particles per cm3 in 58-72
km region, huge absorption cross-sections conduce effective optical depths of
UV absorber comparable to corresponding ones of SO2. The active debate about
the chemical composition of UVA is still going and the cycle of sulfur species
in the upper clouds layer is not yet fully understood. Because the frontier
OSSO parameterization by Frandsen et al. (2016) didn’t yield realistic
radiance factors in radiation scheme in (Marcq et al., 2019), we decided to
keep “retrieved” cross-section by Haus et al. (2015) regardless of chemical
composition.

####  2.2.3 Other parameters

According to Haus et al. (2015); Marcq et al. (2019), CO2, SO2, SO, H2O, OCS,
HCl and O3 are the only active gases in UV-region which may possibly affect
the outcome of radiation simulations. CO2 abundance is assumed to be uniform
in height and equals to 0.965. Due to the strong variability of SO2
concentrations we incorporate two vertical profiles in radiative transfer
simulations. The first one is taken from Haus et al. (2015) fig. 5, that
corresponds to 150 ppmv below the clouds, 15% larger than recommended by
Bezard et al. (1993). The second profiles features abundance of SO2 below the
clouds in according with Vandaele et al. (2017), fig 1. Meanwhile,
concentrations above the clouds in this profile is taken from theoretical
models of Zhang et al. (2012). SO:SO2 ratio is set to be constant and equal to
10% (Marcq et al., 2019, 2020). The volume mixing ratio of water vapor is
assumed to be 32.5 ppmv below 50 km (Marcq et al., 2009; Arney et al., 2014)
and 3 ppmv above 70 km (Cottini et al., 2012; Fedorova et al., 2016). Recently
discovered ozone is accounted in radiative transfer simulations via profile
from theoretical model by Krasnopolsky (2013), which features typical
abundance of 10 ppbv at 90 km. OCS concentrations are significant only below
clouds, while HCl volume mixing ratio is set to be 0.5 ppmv for all heights.
However, during validation we show that most radiation redistribution occurs
only up above the clouds layer, so the influence of H2O, OCS and HCl is
negligibly small.

Strength of the Rayleigh scattering is proportional to fourth power of
wavenumber. Thus, it is assumed to be a crucial ingredient in radiation
simulations in UV region. We take Rayleigh scattering into consideration in
the way similar that Haus et al. (2015) do. They made slight correction to
formula of Hansen and Travis (1974) for pure CO2 atmosphere, changing the
surface pressure. We use the same value of $p_{0}=92.1$ bar in agreement with
VIRA model. Despite Rayleigh scattering optical depth surges while going to
the depth of the atmosphere, it will be shown that in UV region taking this
scattering into account is minor compared to gaseous absorption. For example
in F-UV region it can be completely neglected as it manifests itself in
heights where nearly all the radiation is already absorbed.

Solar spectrum in the UV region may vary slightly depending on solar activity.
We utilized the COSI spectrum from Shapiro et al. (2010, 2011), which was
recommended in (Sukhodolov et al., 2016). As shown by numerical experiments,
usage of a various spectra does not significantly affect the resulting
parameterizations of gaseous absorption. It is only required to change
accordingly the solar fluxes in each k-interval falling on the upper boundary
of the atmosphere.

We used fixed VIRA (Zasova et al., 2006) thermal profile for equatorial region
on the night side from 0 to 150 km in our modeling purposes. With this
approximation we abide by Marcq et al. (2019) due to above mentioned
assumption of temperature independence of absorption cross-sections. So, the
present parameterization could not be affected by applying different
temperature profiles. However the heating rates depend on pressure, we expect
that they predominantly are influenced by absorption features and incident
solar flux.

Our simulating scheme uses recent cloud model that consists of four modes of
75% H2SO4 spherical aerosols (Pollack et al., 1993; Zasova et al., 2007; Haus
et al., 2013). To find microphysical parameters we apply Mie theory code
(Fomin and Mazin, 1998). All four modes are log-normally distributed with
parameters of modal radii of 0.3, 1.0, 1.4, 3.65 $\mu$m and unitless
dispersions of 1.56, 1.29, 1.23, 1.28, respectively (Pollack et al., 1993;
Haus et al., 2013). Refractive indices data were taken from Palmer and
Williams (1975). Scattering properties do not significantly alter with
wavelength in UV region. Thus, any other clouds parameters may be easily
inserted in atmospheric model, as our gaseous absorption parameterization is
obtained regardless of clouds features.

##  3 Result and validation with the reference model

Original data of this study (mainly including resulting effective cross-
sections) are available at Mendeley Data
(https://dx.doi.org/10.17632/97rskzggbj.1)

###  3.1 Effective cross-sections

Figure 2: CO2 (left) and SO2 (right) effective cross-sections in F-UV and M-UV
k-intervals respectively

In this section we present some information about the resulting
parameterizations. In all tables $\sigma$ is an effective cross-section (in
cm2 per one molecule) and $\zeta$ is the absorber amount along the direct
solar radiation from TOA to the given point (in molecules per cm2). Tables are
given for eight k-intervals defined in Table 1. Fig.2 shows effective cross-
sections for CO2 and SO2 in F-UV and M-UV k-intervals respectively. Obtained
effective cross-sections are literally the result of averaging the initial
absorption cross-sections over the solar spectrum reached the current
atmospheric level. At the upper levels, solar radiation is still weakly
transformed and the averaging is actually carried out over the initial solar
spectrum. While penetrating in the atmosphere, the solar spectrum changes so
that the radiation remains only in those spectral regions where the absorption
is weak. This explains the decrease in effective cross-sections with
increasing absorber amount.

###  3.2 Validation

Validation of the presented parameterizations was performed by comparison of
downward and upward solar fluxes and heating rates obtained through fast and
reference simulations. Figs. 3 and 4 show upward and downward fluxes for
different atmospheric profiles for 0° zenith angle. Fig. 3 displays results of
calculations with two different SO2 profiles (see 2.2.3), keeping UVA profile
fixed (high-altitude model by Haus et al. (2015)). On fig. 4 we present
results of calculations with high-altitude and low altitude models by Haus et
al. (2015), keeping fixed SO2 profile from the latter study. For verification
the sustainability of our approach we also checked the parameterizations for
two solar zenith angles: 0° and 75° (see fig. 5). Featured heights lie in
range below 100 km. Validation displays good fits, resulting with relative
discrepancies of less than 3% for fluxes and less than 1% for heating rates.
During this procedure we also could analyze the contribution of each absorber.
Atmospheric O3 and SO play minor role in UV interval, less than 1 K/day
contribution to the heating rate. However, we added cross-sections of this
species to the dataset. Thus, we state that only CO2, SO2 and unknown UV
absorber are relevant in terms of examination the integrated UV fluxes and
heating rates.

Figure 3: Downward and upward fluxes obtained from Monte-Carlo line-by-line
simulations and from fast simulations with employing k-distribution (KD)
technique with effective cross-sections. Profiles of SO2 are taken from Haus
et al. (2015) (left) and from Zhang et al. (2012); Vandaele et al. (2017)
(right). Spectral interval 125 – 400 nm.

Figure 4: Downward and upward fluxes obtained from Monte-Carlo line-by-line
simulations and from fast simulations with employing k-distribution (KD)
technique with effective cross-sections. Profiles of unknown ultraviolet
absorber are: high-altitude model (left) and low-altitude model (right) by
Haus et al. (2015). Spectral interval 300 – 400 nm. Figure 5: Solar heating
rates for zenith angles $\theta=0\,\degree$ and $\theta=75\,\degree$ for Venus
middle atmosphere. SO2 and UVA profiles are taken from Haus et al. (2015).
Spectral interval 125 – 400 nm. Dashed lines for the fast (KD) calculations
are almost invisible due to good fit.

We investigated temperature dependence of absorption cross-sections of CO2 in
F-UV region taking data of Parkinson for 195 and 295 K (Yoshino et al., 1996;
Parkinson et al., 2003) and linearly extrapolating it between those
temperatures. Resulting heating rates discrepancies appeared to be less than
1%. We expect that for climate modeling purposes the temperature dependence
could be ignored as the relevant atmosphere is from 50 – 100 km where cross-
sections doesn’t change dramatically. However, we do not dismiss the interest
that future research should be conducted on this issue.

##  4 Conclusion

In this work we present parameterizations of absorption by gaseous species and
unknown UV absorber in 25000 - 80000 cm-1 spectral interval. Such
parameterizations are determined only by wavelength-dependent absorption
cross-sections. Thus, it easily can be inserted in any radiative transfer
scheme of any GCM. The result was validated with the help of original high-
resolution line-by-line Monte-Carlo radiative transfer model. We expect that
such parameterizations can facilitate Venus climate modeling studies. Future
works will be dedicated to creating effective parameterizations of molecular
and clouds absorption in visible and infrared spectral interval.

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