Carbon dioxide opacity of the Venus׳ atmosphere

Planetary and Space Science ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Planetary Pioneers Series

Carbon dioxide opacity of the Venus' atmosphere Marcel Snels a,n, Stefania Stefani b, Davide Grassi b, Giuseppe Piccioni b, Alberto Adriani b a b

Istituto di Scienze dell'Atmosfera e del Clima (ISAC) - Consiglio Nazionale delle Ricerche (CNR), Rome, Italy Istituto di Astrofisica e Planetologia Spaziali (IAPS) - Istituto Nazionale di AstroFisica (INAF), Rome, Italy

art ic l e i nf o

a b s t r a c t

Article history: Received 22 March 2014 Received in revised form 29 July 2014 Accepted 2 August 2014

Venus' atmosphere consists of about 95% of carbon dioxide, which accounts for most of the absorption of the radiation emitted by its hot surface. The large densities and high temperatures of Venus' atmosphere make the absorption much more complex than for low density atmospheres such as Earth or Mars. Available experimental data are at present insufficient and theoretical models inadequate to describe complex absorption line shapes and collision-induced phenomena. Here we present a survey of all absorption and scattering processes which influence the transparency of Venus' atmosphere for what concerns carbon dioxide. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Carbon dioxide Absorption Collision induced Continuum Opacity

Contents 1. 2.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Absorption by carbon dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Linear absorption by carbon dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Collision-induced absorption by carbon dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Rayleigh scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Venus has often been considered a twin planet of the Earth, although many differences exist. Venus' atmosphere consists mainly of carbon dioxide, which causes a strong greenhouse effect, by capturing most of the radiation emitted by the planet. The temperature at the surface is about 730 K, and the pressure is about 90 atm. An important part of what we know at present about Venus is due to observation of radiation both from the Earth and from spacecraft. Carbon dioxide, being the major absorber, conditions the observation of minor gases, clouds and the surface, which are mainly observed in spectral windows being partially transparent to carbon dioxide absorption. The opacity of Venus' atmosphere is mainly due to the absorption by its main constituent, carbon dioxide, and to a lesser extent n

Corresponding author. E-mail address: [email protected] (M. Snels).

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to absorption by water vapor and other trace species (CO, SO2 HF, HCl, HBr, HI, and others) and by the cloud opacity. A proper understanding of the carbon dioxide opacity is necessary in order to model radiative transfer through the atmosphere of Venus. The cloud opacity depends on wavelength and plays an important role at wavelengths greater than 2.5 μm (Pollack et al., 1993), while the near infrared region is relatively transparent. While carbon dioxide absorbs most of the radiation emitted by the surface for midinfrared wavelengths, some spectral transparency windows occur at near infrared wavelengths (1.10, 1.18, 1.27, 1.31, 1.74 and 2.3 μm). The opacity of these windows can be divided into gaseous opacity, due to the absorption and scattering of gases, and cloud opacity. The gaseous opacity can be further divided into absorption by dipole allowed absorption bands and collision-induced or continuum opacity. The continuum opacity is caused by transitions which occur due to the interaction of the absorbing molecule with another molecule, and is thus proportional to the square of the density. In this definition not only collision-induced absorption

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bands contribute to the continuum absorption, but also the dimer absorption and far wings of allowed bands do so. The pioneering work of Pollack et al. (1993) describes the analysis of ground based Venus' nightside thermal emission in terms of carbon dioxide continuum opacity. The near-infrared windows of the nightside of Venus have also been exploited to determine the water content of the deep atmosphere. A detailed study of high resolution spectra recorded in the spectral transparency windows at 1.1, 1.18, 1.27, 1.31, 1.74 and 2.3 μm by using the Fourier Transform Spectrometer at the 3.6 m Canada–France– Hawaii telescope revealed H2O mixing ratios of about 30 ppm in the 30–40 km altitude range. The analysis was based on a line-byline radiative transfer model including permitted CO2 bands, and an additional opacity assumed to be proportional to the square of the CO2 density (de Bergh et al., 1995). With the advent of spectral information from satellite-borne (Galileo, NIMS, Pioneer, Venera, Venus Express) instruments, a wealth of data has become available for analysis. Recently Bailey (2009) reported a review of water vapor mixing ratios in the Venus deep atmosphere, determined from nightside spectra in the 1.18, 1.27, 1.74 and 2.3 μm transparency windows recorded by different instruments. Very recently, Bézard and de Bergh (2007) and Bézard et al. (2009, 2011) analyzed the 1.10 and 1.18 nightside windows observed by SPICAV and VIRTIS in order to determine the water vapor mixing ratio. They determined a water vapor mixing ratio of 30 ppm continuum between 5 and 25 km while assuming a carbon dioxide binary absorption coefficient of 7(2)
10  10 cm  1 amagat  2 for both transparency windows. Laboratory experiments at room temperature in the 1.18 μm window have been reported by Snels et al. (2014). They performed cavity ring down measurements on pure carbon dioxide and on mixtures of carbon dioxide with small water vapor mixing ratios (40 ppm) and determined a binary absorption coefficient of 5.47 (28)
10  10 cm  1 amagat  2 at 1180.7 nm. Dipole allowed absorption of carbon dioxide is well understood for what concerns the central part of the bands, including line mixing effects, but lineshapes at high pressure are difficult to model and are often treated in a semi-empirical way. Collisioninduced bands have been observed in Venus' atmosphere and in laboratory, but a theoretical model to describe intensities, line shapes and temperature behavior is not yet available. As a result the so-called continuum absorption, including far wings and collision-induced absorption, becoming important at high densities, although in principle theory has been developed to deal with all collision-induced processes (Hartmann et al., 2008), is still difficult to simulate due to the lack of feasible calculations, except for the far infrared region. More experimental measurements are required in order to test model calculations and to fit empirical models. Here we will present a survey of the current state of spectroscopic knowledge concerning carbon dioxide absorption in dense and hot atmospheres, both from a theoretical and an experimental point of view. A concise introduction will be given for what concerns the effect of collisions on molecular spectra and the various theoretical efforts to deal with these, but for a more general background we refer to an excellent review by Hartmann et al. (2008), while the collision-induced absorption in gases has been extensively discussed in Frommhold (1993) and van Kranendonk (1957, 1958, 1974).

2. Absorption by carbon dioxide 2.1. Linear absorption by carbon dioxide The absorption spectrum of carbon dioxide is well documented and is based on a wealth of spectroscopic data obtained with a

variety of experimental techniques. Theoretical studies have been performed with the goal to model and predict line positions and intensities. An effective Hamiltonian has been developed, for a global fit of about 13,000 experimental line positions initially for the major isotopomer of carbon dioxide, 12C16O2 (Tashkun et al., 1998) but subsequently extended to other, also asymmetric isotopomers (Tashkun et al., 2000, 2001). The global treatment of vibrational–rotational states of a molecule allows us to calculate rovibrational levels which have not yet been explored by experiment and thus predict rovibrational transitions, which have not yet been measured. The effective Hamiltonian coupled with the effective dipole moment approach can be used to calculate line intensities with a good precision, up to within a few percent of the measured values (Perevalov et al., 1995; Tashkun et al., 1999). During the last few decades effective Hamiltonians have been developed to perform global fits of experimental lines for symmetric (13C16O2, Tashkun et al., 2000) and non-symmetric carbon dioxide isotopomers (16O13C18O, Ding et al., 2003; 16O12C17O and 16 12 18 O C O, Tashkun et al., 2001). The availability of line positions and intensities is a necessary, but not sufficient ingredient for the simulation of absorption spectra in planetary atmospheres. Collisions between absorbing molecules with other molecules (which can be absorbers or not) are important for line shapes, line mixing, collision-induced absorption and dimer formation. Pioneering work has been done by Anderson (1949), Tsao and Curnutte (1962), Welsh et al. (1949), Welsh (1972), van Kranendonk (1952, 1957, 1958, 1974), van Kranendonk and Kiss (1959), Robert and Bonamy (1979) and many others to develop a theory which can account for line broadening, Dicke narrowing and collision-induced absorption. Generally several assumptions are made such as limiting the problem to binary collisions involving non-reactive molecules in local thermal equilibrium conditions. Moreover most theories have been developed in the impact approximation, which means that the duration of the collision is short with respect to the time between successive strong collisions and small with respect to 1=ð2π∣ν ν0 ∣Þ, which implies that only wavelengths are considered relatively close to the center wavelength ν0. Another approximation is that the velocities during the collisions are constant and that the collision parameters possess no velocity dependence. This allows us to treat the Doppler broadening and the pressure broadening independently and to obtain a Voigt line shape, which is a convolution of a Gaussian and a Lorentzian line shape. For low respectively high pressure the Voigt line shape becomes approximately a Gaussian respectively Lorentzian line shape. When one takes into account velocity changes due to the collisions and a velocity dependence of the broadening parameters, more complex line shapes have to be used, which present small, but significant deviations from the Voigt line shape, such as the Galatry line shape (soft collision) and the Nelkin–Ghatak and Rautian line shape (hard collision). An intercomparison of measured pressure broadening and pressure shifting parameters of carbon dioxide has been reported recently by Gamache et al. (2014). The authors discuss the effect of the line shape models used on the half widths obtained. The rotational and the vibrational dependence of the half widths have also been discussed by these authors. In conclusion they state that the temperature dependence of the broadening parameters is not well documented and that a great experimental effort is required to produce these data. A very thorough review on the collisional effects on molecular spectra has been given by Boulet (2004) and Hartmann et al. (2008). Up to so far isolated lines have been considered, but when broadened lines start to overlap one has to take line mixing into account. Line mixing occurs, due to transfer of vibrational and/or rotational energy within the absorber during the collision, thus transferring line intensity within the spectral manifold involved.

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A frequency independent impact relaxation matrix W can be defined (Hartmann et al., 2008), depending on the initial and final states of the perturbed molecule and on the impact parameter and the relative velocity between absorber and collision partner. The diagonal elements of the W matrix contain line broadening and lineshift parameters of the Lorentz lineshape, while the offdiagonal elements describe the collision transfers between initial and final states of the absorber. Line mixing can be described as follows: suppose that we consider two optical transitions between initial states i1 and i2 and final states f1 and f2, giving rise to two absorption lines at frequencies νi1;f 1 and νi2;f 2 . A molecule in the initial state i1 can be transferred to state i2 by collision, absorb a photon with wavelength νi2;f 2 and end up in the final state f2, and be again transferred by collision to state f1. In this way absorption intensity has been transferred from wavelength νi1;f 1 to νi2;f 2 by collision. In order for this transfer to happen, the collisional transfer of internal energy has to be efficient, which is for instance true for rotational energy transfer, but much less for vibrational energy transfer and even less for transfer between different nuclear spin states. It also needs sufficient energy to be available, which depends on the line width. This implies that line mixing becomes more important for increasing densities. The population of the internal energy levels is governed by the Maxwell Boltzmann distribution, and is not disturbed by collisions; this means that the exchange terms due to collisions are subject to a detailed energy balance relation. It implies that exchange terms which correspond with an energy transfer from a weakly populated level to a more populated level are larger than vice versa and results in a transfer of intensity from weak lines to strong lines (i.e. transitions starting from weakly respectively strongly populated levels), that is from spectral regions with weak absorption (wings) to regions with strong absorption. It has been shown that the influence of line mixing among carbon dioxide lines on the retrieval of atmospheric remote sensing data cannot be neglected and has an impact on the retrieved pressure, temperature fields and on the retrieval of minor atmospheric species (trace gases) (Niro et al., 2005a, 2005b; Hartmann et al., 2009). Initially radiative transfer models included a code to account for line mixing in Q-branches only (see e.g. Rodrigues et al., 1997), but subsequently models have been developed to include broader spectral regions and band wings (Niro et al., 2004, 2005a). Hartmann and co-workers have developed an approach (Jucks et al., 1999; Niro et al., 2004) based on the energy corrected sudden (ECS) scaling law which accounts for all line-mixing effects within any vibrational band. In a series of publications they have compared model calculations with laboratory measurements (Niro et al., 2004; Tran et al., 2011) and atmospheric transmission spectra (Hartmann et al., 2009). The line mixing programs presented in Niro et al. (2004, 2005a,b,c) have been updated recently and tested on laboratory spectra (Lamouroux et al., 2010) and retrievals of atmospheric CO2 (Hartmann et al., 2009) in the 1.5–2.3 μm region. The theoretical approach based on impact and Energy Corrected Sudden approximation produces excellent results for band centers and near wing regions (Tran et al., 2011), but fails for far wing regions, due to the breakdown of the impact approximation. In optically thick atmospheres, absorption is observed far from the line center; this so-called far wing absorption is not tractable within the impact approximation, since the collision time is not anymore negligible with respect to 1=ð2π∣ν  ν0 ∣Þ. Far wings become important for high densities, such as those occurring in the Venus' atmosphere and are important because they account for a consistent part of the absorption in the atmospheric transparency windows. In order to extend the method described above to the far wings of an absorption line, the impact approximation has to be relaxed. Both the finite duration of a collision and the initial statistical

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correlation contribute to the frequency dependence of the relaxation matrix W. Furthermore the line mixing, which transfers line intensities from the wings to the band center, has to be considered when calculating the intensities of the far wings. Fano (1963) and Ben-Reuven (1966, 1971) proposed a formal theoretical approach, but a practical application of these and other approaches (see Breene, 1981 for a summary) remained out of reach. Often semiempirical methods have been described in the literature, employing experimentally determined parameters for fitting observed far wing intensities to empirical model equations. A popular method uses the χ factor, which corrects the Lorentz line shapes for the wings. The χ parameter depends both on the distance from the band center and on the temperature, and corrects the band shape rather than the line shapes of single transitions. The temperature dependence of the χ factor is then fitted to experimental data in all spectral intervals from the band center up to the far wings. Tonkov et al. (1996) performed an analysis of laboratory measurements at room temperature and at a density of 20 amagat in the 2.3 μm transparency window (3900–4700 cm  1), including allowed bands, by using the HITRAN-92 and HITEMP databases, far wings and collision-induced bands. They deduced a χ factor for this spectral region which provided a good agreement up to 600 cm  1 from the band center. The authors identified a series of collision-induced bands, based on residual spectral features after subtraction of allowed bands and far wings, and taking into account the pressure dependence. Perrin and Hartmann (1989) studied the 4.3 μm band of carbon dioxide at high pressures at temperatures ranging from 193 to 773 K and fitted the temperature dependence of the χ factor to analytical expressions. The effect of line mixing in the far wings is in this approach included in the χ factors and may lead to a super Lorentzian line shape in spectral regions with increased intensity due to line mixing. The temperature dependence obtained in this empirical way, including line mixing effects, non-identified collision-induced bands and insufficient or incorrect simulation of permitted bands (and hotbands), produces temperature dependent χ factors which vary noticeably between different vibrational bands (Tran et al., 2011; Tonkov et al., 1996). Another method (see e.g. Brodbeck et al., 1991 for the carbon dioxide continuum and the CKD model, Clough et al., 1989, for the water vapor continuum) defines empirical binary continuum absorption coefficients, which depend on the wavenumber and describe the experimental absorption at different densities and temperatures. A method based on more physical principles follows the quasistatic formalism proposed by Rosenkranz (1985) and has been further elaborated by Ma and Tipping (1990, 1992), and Ma et al. (1999). Ma et al. (1999) use the quasi-static approximation, which is valid for far wings, but fails close to the line center and calculated the absorption coefficients of the high frequency wing of the ν3 band up to 200 cm  1 from the band center for a range of temperatures and compared their calculations with experimental results. They conclude that their model gives a good agreement with experiment for a wide range of temperatures (218–751 K) and provides a proper description of the variation of the far wings with temperature. The model is inadequate close to the line center and depends strongly on the intermolecular potential used. A completely different theoretical approach to the calculation of carbon dioxide spectra has been proposed by Hartmann et al. (2010, 2011a), Hartmann and Boulet (2011b) , and Lamouroux et al. (2013) and uses the classical molecular dynamics simulation (CMDS) method taking into account the permanent and collision-induced terms simultaneously. The CMDS reproduces the strong sub-Lorentzian behavior in the ν3 band wing excellently (Hartmann et al., 2010; Hartmann and Boulet, 2011b) and demonstrates that in the ν3 band the cross-term due to interference

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between the permanent and the induced tensors gives a significant contribution to the intensity of the wings of the ν3 band of carbon dioxide and also reproduces the experimental spectra in the far infrared region (Hartmann et al., 2011a). The non-Markovian Energy Corrected Sudden (ECS) approximation, which has been successfully used for the anisotropic Raman scattering spectrum of N2, proved to be inadequate for the far-wing Raman spectrum of carbondioxide (Benec'h et al., 2002), because the assumption that the perturbers can be treated as a point-like molecule is apparently not valid for carbon dioxide. Also Filippov et al. (2013) used the ECS model with a nonMarkovian (i.e. frequency dependent) relaxation matrix and compared their simulation with experimental carbon dioxide spectra recorded at room temperature at densities between 20 and 92 amagat. However, they had to introduce empirical correction factors to get reasonable agreement with experimental spectra, and although they use a non-Markovian ECS model, which in principle should be applicable to the far wings, they limit their calculations to band centers and near wings (at most 100 cm  1 from the band center). These theoretical efforts have been accompanied by extensive experimental work, involving both traditional spectroscopic methods, not only by using FTIR spectrometers (see e.g. Miller et al., 2004; Miller and Brown, 2004; Lyulin et al., 2012; Ding et al., 2003), but also by applying very sensitive laser based techniques. Pioneering work in the Campargue group has to be mentioned for what concerns cavity ring down spectroscopy (CRD) (Ding et al., 2004; Karlovets et al. 2013, 2014a,b,c; Kassi et al., 2009; Perevalov et al. 2006, 2008a,b,c; Song et al., 2010) and intracavity laser absorption spectroscopy (ICLAS) (Weirauch and Campargue, 2001; Ding et al., 2002, 2005; Garnache et al., 2005) on weak carbon dioxide bands in the near infrared. Geng et al. (2001) measured absolute intensities and pressure broadening coefficients in the 2 μm band by ICLAS technique. Line shapes have been studied by many groups, mostly by using diode laser spectrometers, producing self- and foreign-broadening coefficients for the stronger carbon dioxide bands (see e.g. Barbu et al., 2006). 2.2. Collision-induced absorption by carbon dioxide Collision-induced absorption occurs when collisions induce a dipole moment in molecules giving rise to translational, rotational or rovibrational bands, which become evident at higher densities. Pioneering work has been done by Crawford et al. (1949), Welsh et al. (1949) and van Kranendonk (1952, 1957, 1958, 1974). A review of experimental and theoretical achievements in this field has been given by Frommhold (1993). A review of the theoretical basis of CIA and selected examples of calculations can be found in Hartmann et al. (2008). In most cases the calculations of CIA spectra are based on the isotropic approximation. This approach is valid for systems as H2– H2, N2–N2, H2–rare gas, where the anisotropy is weak, but for a strongly anisotropic system such as CO2–CO2, the correct method is to solve the Schrödinger equations for two interacting molecules. For CO2–CO2 such exact quantum mechanical calculations are not feasible, and in alternative classical molecular dynamics calculations can be performed, as has been shown by Gruszka and Borysow (1997, 1998) for the far infrared spectrum of carbon dioxide. They proposed a theoretical model, based on an anisotropic intermolecular potential, and simulated the rototranslational spectrum from 0–250 cm  1 at conditions of the Venus' atmosphere (200–800 K). Experimental measurements of the rotational–translational CIA band had been reported by Ho et al. (1971) , in the spectral range between 7 and 250 cm  1, at temperatures from 233 to 333 K. Values of the far-infrared CIA coefficient α vary between 0 and 10  4 cm  1 amagat  2, which

amounts to an integrated CIA absorption coefficient of about 5
10  3 cm  2 amagat  2. At present similar calculations for vibrational CIA bands of carbon dioxide are still in a very early stage. Another topic concerns the simultaneous presence of bound– bound (dimer), bound–free, free–bound and free–free (collisional) transitions in collision-induced processes, and their theoretical treatment. In principle they all should be treated by using the same theoretical framework as has been stated by Hartmann et al. (2008), since also free–bound and bound–free transitions contribute to the spectra. A different approach is suggested by Vigasin and co-workers, who subtract the broad features due to CIA absorption (free–free transitions) from the total spectrum and treat the remaining sharp features as dimer absorption. This approach is justified by the fact that dimer spectra are expected to be narrower than free–free transitions, which have an extremely short life time, but ignores coupling between free and bound states. In an early paper (Vigasin et al., 1993) they state that CIA absorption in compressed carbon dioxide is mainly due to bound and quasi-bound dimer absorption. In more recent papers (Baranov et al., 2002; Vigasin et al., 2002) a separation is made between the “true” dimer (the tightly bound dimer), which gives rise to sharp spectral features and metastable short-lived dimeric states and free collisional pair states, which produce a broad featureless spectrum. They estimate a “true” dimer contribution between 12 and 21% for the Fermi dyad (2ν2, ν1) and Fermi triad 2(ν1,2ν2) of the carbon dioxide spectrum (1250–1420 cm  1 and 2500–2850 cm  1 respectively). The contribution of the “true” dimer absorption to the CIA spectra depends on temperature and varies from 12% at 296 K to 21% at 206 K and is expected to increase for very low temperatures (Baranov et al., 2002; Vigasin et al., 2002). The Fermi dyad and triad are the only CIA bands which show narrow spectral features, due to dimer absorption. Other CIA bands have been observed at higher wavenumbers, but exhibit only broad structures. Probably the transition dipole moments of the bound–bound transitions are decreasing faster than those of the corresponding free–free transitions. Experimental observations of CIA in carbon dioxide date back to 1949, when Welsh et al. (1949) observed two intense collisioninduced absorption (CIA) bands near 1285 and 1388 cm  1 in high pressure carbon dioxide. Mannik and Stryland (1972) measured the pressure induced absorption of the ν1 band at temperatures of 190, 300 and 470 K, over a density range from 0.5 to 300 amagat. These bands at 1285 cm  1 and 1388 cm  1 are the strongest CIA bands of carbon dioxide and have been reported by many authors (Welsh et al., 1949; Burch and Gryvnak, 1971; Manzanares et al., 1984; Baranov and Vigasin, 1999; Vigasin, 2000; Vigasin et al., 2002; Baranov et al., 2003) and can be assigned to the dipole forbidden 2ν1 and ν1 bands. As already mentioned before, Vigasin et al. (1993), Baranov and Vigasin (1999), Vigasin (2000), and Baranov et al. (2003) assigned some well resolved spectral features in these bands to absorption by dimers, while the underlying smooth bands were supposed to be due to metastable complexes and free molecular pairs. For practical applications, in the absence of obvious dimer structures, the shape of a CIA band can be modeled empirically, as has been proposed by Tonkov et al. (1996) for the near infrared bands between 3900 and 4500 cm  1. Several spectroscopic investigations of high pressure carbon dioxide have been reported for other spectral regions. Integrated band intensities were calculated from spectra recorded at different pressures. While the integrated band intensities of allowed absorption bands vary linearly with density, collision-induced bands increase with the second power of density. The CIA integrated absorption

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Fig. 1. The integrated band intensity of the two strongest CIA bands of carbon dioxide is reported as a function of the square of the density for temperatures of 294, 373 and 473 K and pressures of 10, 20, 30 and 40 bar. The straight lines are a linear fit of the data with respect to the squared density.

coefficients are thus expressed in cm  2 amagat  2 or as cm4/mole2 (1 cm4/mole2 E2
10  9 cm  2 amagat  2). The strongest vibrational CIA bands, the (2ν2,ν1) Fermi doublet, between 1200 and 1500 cm  1 have an integrated CIA absorption coefficient of 5.38
10  3 cm  2 amagat  2 (Manzanares et al., 1984), with a negligible variation between 273 and 323 K. Thomas and Linevsky (1989) report CIA absorption bands between 2570 and 2870 cm  1 and between 2870 and 3120 cm  1, the 2ν1 and the ν2 þ ν3 bands with integrated CIA absorption coefficients of 2.4
10  5 and 3.2
10  4 cm  2 amagat  2 respectively, which were found to be constant within the experimental error between 295 and 367 K. Still weaker CIA bands have been discovered by Tonkov et al. (1996), between 3900 and 4700 cm  1, with integrated CIA absorption coefficients between 2
10  7 and 1.4
10  6 cm  2 amagat  2, and measured at temperatures between 290 and 301 K. A temperature dependence of the Fermi doublet has been observed by Vigasin et al. (2002) who report an integrated CIA absorption coefficient which varies from 8.65 to 5.03
10  3 cm  2 amagat  2 between 206 and 295 K respectively. It can be observed that the integrated absorption coefficients of CIA bands decrease rapidly with increasing wavenumber, similar to what can be observed for the integrated band intensities of allowed bands, due to the larger number of vibrational quanta involved in the transitions. The temperature dependence of the rotational–translational CIA bands of carbon dioxide has been well documented and understood (Ho et al., 1971; Gruszka and Borysow, 1997), while for the vibrational CIA bands more experiments are required and theory has to be developed. Recently we have investigated the temperature dependence of the strongest CIA bands experimentally at temperatures of 294, 373 and 473 K, and pressures up to 40 bar (Stefani et al., 2013) (see Fig. 1). Fig. 1 shows that the integrated band intensities of the two CIA bands depend very little on temperature (between 294 K and 473 K), in agreement with Thomas and Linevsky (1989), who observed a negligible temperature dependence of the 2870– 3120 cm  1 band at temperatures between 295 and 367 K. Vigasin et al. (2002) report that the integrated band intensity of

the Fermi doublet (1200–1500 cm  1) increases for lower temperatures (206–295 K), but confirms that the temperature dependence for higher temperatures (300–400 K) is very small. Part of the increased integrated absorption intensity might be due to the increasing dimer fraction at low temperatures, while another part might be due to a stronger absorption by the free pair states and quasi-bound states, as has been observed for N2 and O2 (Manzanares et al., 1984). From a practical point of view, concerning the opacity of Venus' atmosphere, one should bear in mind that at 55 km above the surface the temperature is about 300 K and the pressure 0.5 bar (von Zahn and Moroz, 1985; Moroz and Zasova, 1997). This implies that a temperature dependence of the integrated band intensities of the CIA bands below 300 K produces a very small effect on the opacity of the atmosphere, while below 55 km, where the atmosphere is dense and the contribution of the CIA bands is appreciable, the temperature dependence between 300 and 700 K is expected to be small and can be in good approximation neglected. It should be mentioned that although far wing absorption and collision-induced absorption are both proportional to the square of the density, some fundamental differences exist. The CIA bands are predictable, when the vibrational energy levels are known. This allows us to exclude the presence of CIA bands in spectral regions where no forbidden transitions are present. The temperature dependence of CIA bands can be in principle inferred from intermolecular potential calculations, but is small at high densities and temperatures encountered in the lower part of Venus' atmosphere. The far wing absorptions on the other hand are almost ubiquitous, and the contributions of different allowed absorption bands are not easily separable. This implies that, even with a reasonable model for far wings (up to 200–300 cm  1 from the band center) it will be difficult to predict continuum opacity for the full spectral range. For the far wing calculations the quasistatic approach pursued by Ma and Tipping (1990, 1992) and Ma et al. (1999), and the classical molecular dynamics simulation (CMDS) proposed by Hartmann et al. (2010, 2011a), Hartmann and Boulet (2011b) and Lamouroux et al. (2013) might provide a powerful tool to deal with these collision-induced processes.

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3. Rayleigh scattering The Rayleigh scattering by carbon dioxide contributes to the opacity of the atmosphere, although its effect is rather small, and varies roughly with the inverse of the fourth power of the wavelength (1/λ4). The Rayleigh scattering cross-section can be obtained from the index of refraction by using the formula !2 24π 3 nðλÞ2 1 σR ¼ 4 2 F k ðλÞ ð1Þ λ N nðλÞ2 þ2 where λ is the wavelength in cm, N is the density in molecules per cm3, nðλÞ is the wavelength dependent refractive index and Fk is the King correction factor for the depolarization. Direct measurements of the Rayleigh scattering cross-section can be obtained by cavity ring down measurements. Ityaksov et al. (2008) measured the Rayleigh scattering cross-section for several gases in the UV and in the visible spectral range (Sneep and Ubachs, 2005; Naus and Ubachs, 2000) by CRD techniques, while Snels et al. (2013) demonstrated that the Rayleigh scattering cross-section can also be measured by using the CRD technique in the near infrared at 1.18 μm. The contribution of the Rayleigh scattering by carbon dioxide to the opacity varies from 3.32
10  7 cm  1 amagat  1 at 532 nm (Sneep and Ubachs, 2005) to 1.02(14)
10  8 cm  1 amagat  1 at 1.18 μm (Snels et al., 2013). Teboul et al. (1995) observed the Rayleigh scattering in the far infrared region and reported collision-induced scattering in the 150–450 cm  1 region.

4. Databases Absorption line positions and intensities of carbon dioxide can be found in the HIgh-resolution TRANsmission molecular absorption (HITRAN) database (Rothman et al., 2009, 2013), which is updated regularly with new experimental data and model calculations. The most recent version is of 2012 (Rothman et al., 2013). More than 140,000 measured line positions and 44,000 measured line intensities belonging to 12 isotopomers of carbon dioxide were included in the data set covering the spectral range from 3.68 to 12784 cm  1. Calculated lines with a line intensity greater than 10  30 cm  1/(molecule cm  2) were also included. A new section dedicated to collision-induced absorption (Richard et al., 2012) has been added recently, but does not include carbon dioxide. A high temperature version of HITRAN (HITEMP, Rothman et al., 2010) provides line lists of many molecules of interest in planetary atmospheres and astrophysics and for what concerns carbon dioxide is based on CDSD-1000 (see below). An alternative database dedicated exclusively to carbon dioxide, the carbon dioxide Spectroscopic Databank (CDSD), has been made available by the Laboratory of Theoretical Spectroscopy in Tomsk, and was first published as CDSD-296 (Tashkun et al., 2006) and later updated (Perevalov et al., 2008a) with a reference temperature of 296 K, an intensity cutoff of 10  28 cm  1 and a spectral range from 405 to 12,784 cm  1. Other versions were produced for applications of planetary atmospheres and combustion processes, including absorption lines at high temperatures: the CDSD-1000 version (Tashkun et al., 2003; Tashkun and Perevalov, 2008) and more recently the CDSD-4000 version (Tashkun and Perevalov, 2011). The GEISA (Gestion et Etude des Informations Spectroscopiques Atmospheriques; Management and Study of Atmospheric Spectroscopic Information) database is a computeraccessible system comprising three independent sub-databases devoted to line parameters, infrared and ultraviolet/visible absorption cross-sections, microphysical and optical properties of atmospheric aerosols. In this edition, 50 molecules are involved in the

Table 1 Carbon dioxide databases. Database

HITRAN2008

Wavelength range (cm  1)

Intensity cut-off (cm  1/(molecule cm  2))

3.68–12,784 4
10  30  30

Number of Ref isotopomers

10

HITRAN2012

3.68–12,784 10

HITEMP

260–9600

10  27

7

CDSD-296

405–12,784 10  28

4

CDSD-296

 28

7

7–12,784 10

12

CDSD-1000

260–8310

10  27

4

CDSD-1000

260–8310

10  27

7

CDSD-4000

226–8310

10  27

4

6–12,784 10  30

9

GEISA

TOTH EXACT

4300–4700 750–8500

4
10  30

9

Rothman et al. (2009) Rothman et al. (2013) Rothman et al. (2010) Tashkun et al. (2006) Perevalov et al. (2008a) Tashkun et al. (2003) Tashkun and Perevalov (2008) Tashkun and Perevalov (2011) JacquinetHusson et al. (2011) Toth et al. (2008) Stefani et al. (2013)

line parameters sub-database, including 111 isotopologues, for a total of 3,807,997 entries, in the spectral range from 10  6 to 35,877.031 cm  1 (Jacquinet-Husson et al., 2011). A database with experimental data in the 4300–7000 cm  1 range has been reported by Toth et al. (2008) and provides more extensive data in this range than HITRAN2008 (Rothman et al., 2009), and has been included in the recent HITRAN compilation (HITRAN2012 Rothman et al., 2013). Recently the experimental absorption coefficients of carbon dioxide recorded from 750 to 8500 cm  1 for temperatures and pressures corresponding to the Venus' atmosphere from 22 to 50 km , according to the VIRA profile (von Zahn and Moroz, 1985; Moroz and Zasova, 1997) has been made available on the web-site exact.iaps.inaf.it (Stefani et al., 2013). The content of all recent databases has been listed in Table 1, in terms of the wavelength range covered, the intensity cut-off of absorption lines and the number of carbon dioxide isotopomers involved. Note that the EXACT database is different from the others, since it contains spectra and no line parameters.

5. Conclusions Valuable information can be obtained from near infrared spectra recorded in the night side transparency windows, for what concerns the composition of Venus' atmosphere, the radiative properties of the clouds, the winds near the lower cloud level and the surface emission (Pollack et al., 1993; Taylor et al., 1997; Bézard and de Bergh, 2007), but depends strongly on the quality of carbon dioxide opacity calculations. Experimental data is available for what concerns the allowed absorption bands of the most abundant carbon dioxide isotopomers and theory has been developed to simulate central band regions and near band center wings, taking into account line mixing. Collision-induced opacity, including far wings, is still requiring experimental efforts and theoretical modeling. Cavity ring down experiments have shown to be able to measure very weak features, from weak permitted bands of many isotopomers to Rayleigh scattering, and continuum absorption in

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transparency windows. Since most experimental measurements have been performed at room temperature, or in limited temperature intervals, an effort should be made to extend these measurements to temperatures which are close to those encountered in the Venus' atmosphere. From a theoretical point of view the temperature dependence of far wings and of all contributions to the continuum opacity needs a further understanding.

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Please cite this article as: Snels, M., et al., Carbon dioxide opacity of the Venus' atmosphere. Planetary and Space Science (2014), http: //dx.doi.org/10.1016/j.pss.2014.08.002i