Does spectroscopic evidence require two scattering layers in the Venus atmosphere?

The phase variation of lines in the 7820 and 7883 Å CO₂ bands has been interpreted by Hunt using an inhomogeneous, anisotropic scattering model of the Venus atmosphere. He concluded that the Venus atmosphere contains two scattering layers. We show that the observed phase variation may be due to the strong backward lobe in the Venus cloud phase function and that two cloud layers are not necessarily required.     

An efficient approach for the implementation of the SNB based correlated-k method and its evaluation

The current implementation of the SNB based correlated-k method consumes a significant portion of the total cpu time on the on-line inversion of the cumulative distribution function. An approach was developed to pre-calculate the absorption coefficients of real gases from the inversion procedure. This approach results in significant improvement in the efficiency of the SNB based correlated-k method with slight loss in accuracy. This approach was evaluated against other implementation approaches of the SNB based correlated-k method in several non-isothermal and/or inhomogeneous problems.     

Narrow-band and full-spectrum k-distributions for radiative heat transfer—correlated-k vs. scaling approximation

The correlated-k and scaled-k distribution methods for radiative heat transfer in molecular gases are developed based on precise mathematical principles, for both narrow band and full spectrum models. Their differences and commonalities are high-lighted and discussed. Applications to narrow spectral bands of nonhomogeneous gases show both methods to be about equally accurate. For full-spectrum calculations, on the other hand, the scaled-k distribution consistently outperforms the correlated-k model.     

Extension of the weak-line approximation and application to correlated-k methods

Global climate models require accurate and rapid computation of the radiative transfer through the atmosphere. Correlated-k methods are often used. One of the approximations used in correlated-k models is the weak-line approximation. We introduce an approximation T_γ which reduces to the weak-line limit when optical depths are small, and captures the deviation from the weak-line limit as the extinction deviates from the weak-line limit. This approximation is constructed to match the first two moments of the gamma distribution to the k-distribution of the transmission. We compare the errors of the weak-line approximation with T_γ in the context of a water vapor spectrum. The extension T_γ is more accurate and converges more rapidly than the weak-line approximation.     

Line parameters for the 01111-00001 band of COO from SOIR measurements of the Venus atmosphere

CO₂ is the major constituent of the atmosphere of Venus. Absorption lines due to its ¹²C¹⁶O¹⁸O isotopologue have been observed for the first time in Venus spectra in the 2930-3015 cm⁻¹ spectral region, where the HITRAN database does not contain any line from this isotopologue. The measurements were performed by the SOIR instrument, which is part of the SPICAV/SOIR instrument on board the Venus Express mission of ESA. SOIR measured the atmospheric transmission of the upper atmosphere of Venus (z>70 km) by performing a solar occultation experiment using the atmosphere as a gigantic absorption cell. The identification of this newly observed band was first made recently from Mars atmosphere observations by US colleagues. We have made independent theoretical calculations of the positions of the lines of this new 01111-00001 absorption band, which coincide perfectly with the positions of the observed lines. Assuming an oxygen isotopic ratio similar to the one measured previously in the lower atmosphere of Venus, the line strengths of each observed line are deduced and listed.     

The NEMESIS planetary atmosphere radiative transfer and retrieval tool

With the exception of in situ atmospheric probes, the most useful way to study the atmospheres of other planets is to observe their electromagnetic spectra through remote observations, either from ground-based telescopes or from spacecraft. Atmospheric properties most consistent with these observed spectra are then derived with retrieval models. All retrieval models attempt to extract the maximum amount of atmospheric information from finite sets of data, but while the problem to be solved is fundamentally the same for any planetary atmosphere, until now all such models have been assembled ad hoc to address data from individual missions.In this paper, we describe a new general-purpose retrieval model, Non-linear Optimal Estimator for MultivariatE Spectral analySIS (NEMESIS), which was originally developed to interpret observations of Saturn and Titan from the composite infrared spectrometer on board the NASA Cassini spacecraft. NEMESIS has been constructed to be generally applicable to any planetary atmosphere and can be applied from the visible/near-infrared right out to microwave wavelengths, modelling both reflected sunlight and thermal emission in either scattering or non-scattering conditions. NEMESIS has now been successfully applied to the analysis of data from many planetary missions and also ground-based observations.     

Infrared radiative transfer modelling in a 3D scattering cloudy atmosphere: Application to limb sounding measurements of cirrus

The Monte Carlo cloud scattering forward model (McClouds_FM) has been developed to simulate limb radiative transfer in the presence of cirrus clouds, for the purposes of simulating cloud contaminated measurements made by an infrared limb sounding instrument, e.g. the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS). A reverse method three-dimensional Monte Carlo transfer model is combined with a line-by-line model for radiative transfer through the non-cloudy atmosphere to explicitly account for the effects of multiple scattering by the clouds. The ice cloud microphysics are characterised by a size distribution of randomly oriented ice crystals, with the single scattering properties of the distribution determined by accurate calculations accounting for non-spherical habit.A comparison of McClouds_FM simulations and real MIPAS spectra of cirrus shows good agreement. Of particular interest are several noticeable spectral features (i.e. H₂O absorption lines) in the data that are replicated in the simulations: these can only be explained by upwelling tropospheric radiation scattered into the line-of-sight by the cloud ice particles.     

Inverse multiple scattering problems—II. Limited information content of partially fitted planetary curves with application to the Venusian visual phase curve

The random grid search method and the minimization search method recently developed by Fymat (1972) for solving inverse multiple-scattering problems of planetary atmospheres are employed for a study of the extent and nature of true information yielded by theoretical partial fits of observed planetary curves. The study is conducted with the Venusian visual phase curve as a background example. It is shown that such fits cannot be used toinfer the model scattering parameters of the planet's atmosphere. They cannot provide any indication of the shape of the scattering diagram, even in the region of the fit. It is also shown that the measured Bond albedo can provide neither a criterion for sorting out different possible scattering model candidates nor a means for accurately determining the single scattering albedo. A high value of the latter albedo for Venus' atmosphere at visible wavelengths(ω̃_o ≈ 0·99) is also found, and Euler's scattering model is definitely discarded for this planet.     

Retrieval of ozone profile from ground-based measurements with polarization: A synthetic study

We perform a retrieval based on optimal estimation theory to retrieve the vertical distribution of ozone from simulated spectra in the Huggins bands. The model atmosphere includes scattering by aerosol as well as Rayleigh scattering. The virtual instrument is ground-based and zenith-viewing. Using this algorithm, we show that it is possible to retrieve the ozone profile provided that the spectral resolution is at least 0.2 nm and the signal to noise ratio greater than 500. Our synthetic retrievals suggest that if we are able to measure the Stokes parameters Q, U and V with accuracy comparable to that of the intensity, the information contained in the measurements, and therefore the inversion, will improve. Furthermore, we find that the measurement of the full Stokes vector from the ground-based instrument will especially enhance the retrieval of tropospheric ozone. Utilizing concepts from information theory, our arguments are confirmed by increases in the degrees of freedom and the Shannon information content in the simulated measurements.     

The method of lines solution of discrete ordinates method for non-grey media

A radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) for radiative heat transfer in non-grey absorbing-emitting media was developed by incorporation of a gas spectral radiative property model, namely wide band correlated-k (WBCK) model, which is compatible with MOL solution of DOM. Predictive accuracy of the code was evaluated by applying it to 1-D parallel plate and 2-D axisymmetric cylindrical enclosure problems containing absorbing-emitting medium and benchmarking its predictions against line-by-line solutions available in the literature. Comparisons reveal that MOL solution of DOM with WBCK model produces accurate results for radiative heat fluxes and source terms and can be used with confidence in conjunction with computational fluid dynamics codes based on the same approach.     

Investigation of the thermal structure of the upper atmosphere of Venus by 10 μm heterodyne spectroscopy

The Venusian atmosphere has been investigated using a 10 μm heterodyne spectrometer (spectral resolution λ/Δλ = 3 × 10⁶) during upper conjunction and during elongation in 1983. In both cases a variety of spectra from the subsolar region were taken with high spatial resolution showing fully-resolved lines of the 10μm laser transition of CO₂. From these measurements kinetic and rotational temperatures are derived (T∼200K.). These spectroscopically-derived temperatures represent the atmospheric temperature for extended areas (1000–6000 km dia) at an altitude of 100–120 km. They are in agreement with on-the-spot temperature measurements indirectly obtained by space probes during descent. Multiple-line structures have been observed in the 10 μm spectra, which indicate a wave-like perturbation of the vertical temperature profile above a cloud layer at ∼ 20 mb atmospheric pressure.     

The importance of thermal radiation transfer in laminar diffusion flames at normal and microgravity

The importance of radiation heat loss in laminar and turbulent diffusion flames at normal gravity has been relatively well recognized in recent years. There is currently lack of quantitative understanding on the importance of radiation heat loss in relatively small scale laminar diffusion flames at microgravity. The effects of radiation heat transfer and radiation absorption on the structure and soot formation characteristics of a coflow laminar ethylene/air diffusion flame at normal- and microgravity were numerically investigated. Numerical calculations were conducted using GRI-Mech 3.0 combustion chemistry without the NO_x mechanism and complex thermal and transport properties, an acetylene based soot formation model, and a statistical narrow-band correlated-k non-grey gas radiation model. Radiation heat transfer and radiation absorption in the microgravity flame were found to be much more important than their counterparts at normal gravity. It is important to calculate thermal radiation transfer accurately in diffusion flame modelling under microgravity conditions.     

A new k-interval selection technique for fast atmospheric radiance calculation in remote sensing applications

A new technique is proposed to generate the k-interval parameters, including the number of k-intervals, the equivalent absorption coefficients, and the quadrature weights when using the correlated k-distribution method for the computation of spectrally integrated three-dimensional (3D) atmospheric radiance. The main difference between the proposed technique and the traditional exponential sum fitting technique is that only quadrature weights are involved in the optimization process. To avoid the ill-conditioned problem in the proposed technique, the absorption coefficients with high value are dealt with by the delta log(k) (Δlog(k)) technique instead of involving them in the fitting procedure. The performance of the proposed technique is illustrated by radiance calculation results of cloudless and cloudy atmosphere for three different band settings. Results show that there are less relative errors with the proposed optimization technique than with the Δlog(k) technique under the same number of k-intervals. However, as the absorption becomes stronger, the performance of the proposed technique gradually decreases to the Δlog(k) technique. The relative root-mean-square error (RMSE) of radiance for 3D cloudy atmosphere can be controlled in less than 2% when the number of k-intervals is less than 10 particularly for weak absorption band, the RMSEs are less than 1% with only 6 terms.     

Interpretation of NO2 absorption in twilight sky spectra

A multiple scattering model has been developed to calculate nitrogen dioxide (NO₂) absorption in the light from the zenith sky during twilight. Model studies show that this absorption is not very sensitive to the atmospheric temperature profile or to tropospheric NO₂.The model was used to interpret some ground-based measurements of NO₂ sky absorption. Values for the total stratospheric column amount vary from 2 to 12×10¹⁵moleccm^-2, and the mean altitude of the stratospheric concentration profile is around 35 km. These observations are in broad agreement with those of other workers.     

On the effect of the width of the scattering indicatrix on the dispersion of photon density waves in a strongly scattering medium

The dispersion of photon density waves in strongly scattering media with different widths of the scattering indicatrix is studied by the spherical harmonics method using approximations of various orders (up to the P ₇ approximation inclusive). It is shown that, beginning from the P ₃ approximation, the reduction in the velocity of photon density waves that is characteristic of the P ₁ approximation is eliminated and, independently of the width of the scattering indicatrix in the region of modulation frequencies exceeding 10¹⁰ Hz, the velocity of photon density waves asymptotically approaches the speed of light. Our study of the damping of photon density waves has shown that the formula obtained previously for the calculation of the damping coefficient (Imk(μ _s ^′ , ω)) as a function of the transport scattering coefficient and the velocity is valid at Imk ≤ μ_s (μ_s is the light scattering coefficient). The maximum growth in the damping coefficient of photon density waves with a further increase in the frequency is limited by the value of the light scattering coefficient Imk _max ≈ μ_s.     

Optical constants of sulphuric acid in the far infrared

The i.r. absorption spectrum of a 75% sulphuric acid solution is obtained experimentally in the 20–50μm wavelength region. The complex refractive index (n = n_r ? in_i) is determined from these measurements by integration of the Kramers-Kronig dispersion relation. The application of this data to radiative transfer processes in the atmosphere of Venus is briefly discussed.     

The spectral-line moment-based (SLMB) modeling of the wide band and global blackbody-weighted transmission function and cumulative distribution function of the absorption coefficient in uniform gaseous media

The spectral-line moment-based (SLMB) modeling is proposed for the calculation of radiative properties of gases on any spectral width. The associated mathematical formulation is obtained by applying several concepts of the k-distribution methods such as the reordering of the wavenumber scale by monotonic variations of the absorption coefficient, together with the application of the k-moment method's principles. This approach gives both a general formula for the BTF and a simple and readily applicable approximation for the blackbody-weighted cumulated k-distribution function of the absorption coefficient. The model is applied for the computation of wide band BTFs and cumulative k-distributions for uniform columns of CO₂ and H₂O in the temperature range (300-2400 K) at atmospheric pressure. Model parameters are deduced from line-by-line (LBL) spectra calculated using the HITEMP database. Comparisons with LBL reference data as well as with contemporary modeling approaches (SLW, FSK, SNB) are performed and discussed.     

A new approach to solve correlated k-distribution function

The resorting profile of absorption coefficient is fitted with Voigt function by employing the similarity between it and a single mixed broadened Voigt line type. In this way, simple mathematical fitting formulae are obtained to solve k-distribution (k-D) function at any pressure and temperature. Thus, a new correlated k-D method is proposed on the basis of it. Finally, taking mid-latitude summer atmosphere as an example, longwave cooling rates are calculated for three major gases by the new method, and then compared with the corresponding results by line-by-line integration.     

Self-consistent calculation of the optical potential and ground-state properties of nuclear matter

On the basis of the Green-function formalism, we performed a self-consistent calculation of the self-energy ∑(k, ω) of a particle interacting with the infinite nuclear medium. The function ∑(k, ω) was mapped out in the energy-momentum plane, and the single-particle energy ω(k), momentum distribution ?(k) and the “on-shell” part of the self-energy, ∑(k, ω(k)), were defined, from which all physical properties followed. In particular we investigated the ground-state properties of nuclear matter in two Λ-approximations of the T-matrix. In one, the intermediate two-particle propagator, Λ₀₀, represented free-particle propagation; in the other, called Λ₁₁, intermediate states included both interacting particles and holes. Pauli principle effects were included in both approximations. The second approximation was expected to be conserving because it included a large part of the rearrangement effects which, we found, contributed ～6 MeV per particle to the average energy and ～28 MeV to the singleparticle energy at zero momentum. The Hugenholtz-van Hove theorem was nearly satisfied, with only 1 MeV separating the chemical potential from the average energy. We also studied, in the Λ₀₀-approximation, the optical potential for the scattering of a particle by a large nucleus; it was directly related to the “on-shell” part of the self-energy. It was found that, below 100 MeV, the real part varied as (?90 + 0.584E) [MeV], and the imaginary part as (2.4 + 0.009 E) [MeV].     

Comparison of single and multiple scattering approaches for the simulation of limb-emission observations in the mid-IR

The validity of single scattering radiative transfer calculations for simulation of limb-emission measurements of clouds in the mid-infrared spectral region was investigated by comparison with a multiple scattering model. For in limb direction optically thin clouds, like polar stratospheric clouds, errors of the single scattering scheme range below 3%. For optically thick clouds deviations are below 3% in case of low single scattering albedo (ω₀=0.24) increasing up to 10-30% for ω₀=0.84. Clouds which are optically thick in limb, but thin in nadir direction, can cause limb radiances which are by a factor of 1.7 higher than the blackbody radiance at cloud altitude.