Radiative absorption in an infinitely long hollow cylinder with Fresnel surfaces

Radiation absorption in an infinitely long hollow cylinder with Fresnel surfaces is studied using the ray tracing method. It is found that the inner boundary can be modeled as a total reflective surface for the infinitely long hollow cylinder. Radiative absorption of hollow cylinders with Fresnel surfaces is compared to diffusive surfaces predicted by the finite volume method. Effects of refractive index, optical thickness and hole size on radiative absorption are studied. Abrupt changes in radiative absorption near τ_r/τ_Ro=1/n are observed for hollow cylinders with Fresnel surfaces. It is because the Fresnel relation predicts a critical angle at . This trend is not observed in diffusive surfaces. Refractive index and optical thickness are two competing factors that govern the radiative absorption. Higher refractive index drives higher absorption close to the inner surface, while higher optical thickness yields higher absorption near the outer surface. The results of this study can also serve as benchmark solutions for modeling radiative heat transfer in hollow cylinders with Fresnel surfaces. It is also found that the directional or hemispherical emittance can be calculated without solving the radiative transfer equation in the media when the temperature variation in the media is small.     

Fast radiative transfer modeling for infrared imaging radiometry

Fast radiative transfer codes have been developed for simulating the outgoing radiance (and corresponding brightness temperature) to be measured by the Infrared Imaging Radiometer (IIR) of the space Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission. Two simple codes (FASRAD and FASAA), for which scattering is neglected, as well as an accurate code (FASDOM), accounting for scattering and absorption with the Discrete Ordinate Method (DOM), are presented. Their accuracy has been estimated with a reference code including a line-by-line model and the DOM. Simulations have shown that the accuracy is generally better than 0.3 K on the brightness temperature for clear or cloudy atmospheres. This accuracy agrees with the expected one of future IIR measurements. In addition, the impact of scattering on the brightness temperature has been evaluated for semi-transparent liquid clouds in the IIR spectral range. Especially, simulations have shown that cloud microphysics retrieval might be possible with the Brightness Temperature Difference (BTD) between two IIR bands, using the couple of wavelengths (8.7-) or (10.6-). However, scattering strongly influences the radiation for shorter wavelengths. The error on the BTD with (8.7-) can reach 4 K when scattering is neglected, leading to large uncertainties in the retrieval of droplet effective radius.     

The physical parameterization of the top-of-atmosphere reflection function for a cloudy atmosphere—underlying surface system: the oxygen A-band case study

The paper is devoted to the physical parameterization of the top-of-atmosphere reflection function. The accuracy of the parameterization is checked against exact radiative transfer calculations in a cloudy atmosphere for various cloud-top-heights, cloud optical and geometrical thicknesses, solar illumination and surface reflection conditions. It was found that the error of approximation is smaller than 5% for most cases studied at the wavelength interval , which corresponds to the oxygen A-band. This band is routinely used in cloud-top-height retrievals. The model proposed can be used for cloud-top-height and cloud geometrical thickness retrievals. This allows to avoid a standard look-up-table retrieval scheme, involving complex numerical procedures.     

Determination of optical properties of slices of turbid media by diffuse CW laser light scattering profilometry

In this work we present a method for determining the optical parameters of turbid media, namely its absorption coefficient (μ_a) and its reduced scattering coefficient . It is based on the measurement of CW transmittance profiles and analysis of the experimental data by a theoretical model based on the diffusion approximation (DA) of the radiative transfer equation (RTE). The method developed has been investigated with solid polymer probes but it could be applied for liquid materials as well. Experimental results are presented and compared to those of other authors together with a discussion about the accuracy of measurements. In addition, measurements using integrating spheres as well as Monte Carlo simulations are also presented to validate these results.     

A half-moment model for radiative transfer in a 3D gray medium and its reduction to a moment model for hot, opaque sources

We present in this paper a new 3D half-moment model for radiative transfer in a gray medium, called the model, which uses maximum entropy closure. This model is a generalization to 3D of the 1D version recently proposed in (J. Comp. Phys. 180 (2002) 584). The direction space Ω is divided into two pieces, Ω⁺ and Ω^-, in a dynamical way by the plane perpendicular to the total radiative flux, and the half moments are defined from these subspaces. The model closure and the integrations of the radiative transfer equation performed on the moving Ω^± spaces are detailed. 1D planar results, which have motivated the extension of the model of (J. Comp. Phys. 180 (2002) 584) to multi-dimensions, are shown. These results are very good. The model is thereafter derived for 3D spherically symmetric geometry, where the correctness of the non-trivial border terms can be checked. Two 3D spherically symmetric problems are numerically solved in order to show the accuracy of the closure and the role of the border terms. Once again, compared to the solution obtained with a ray tracing solver, results are very good. From the 3D half-moment model, a new moment model, called , is derived for the particular case of a 3D hot and opaque source radiating into a cold medium, for applications such as simulations of stellar atmospheres and fires. Two-dimensional numerical results are presented and compared to those obtained solving the RTE and with other moment models. They demonstrate the very good accuracy of the model, its good convergence properties, and better prediction compared to all other existing moment models in its domain of applicability.     

A full spectrum k-distribution based non-gray radiative property model for unburnt char

By using the concept of weighted sum of four gray particles and spectrum k-distribution (WSGP-SK), a non-gray radiative property model for unburnt char particles is developed. Based on the carbon burnout kinetic model for structure during oxidation, and the linear mixed approximation theory for complex index of refraction, spectral radiative properties of unburnt char particles are first calculated as function of the burnout ratio by Mie theory. Referring to the full spectrum k-distribution model, k-distribution is applied to reorder absorption and scattering efficiencies of particles. Then, weighting factors and efficiency factors of the non-gray radiative property model are directly obtained from Gaussian integral points of k-distribution. The model is validated against the benchmark solutions of line-by-line (LBL) model. Maximum relative errors of this model are 3% and 15% for radiative heat fluxes and source terms in non-isothermal inhomogeneous particulate media, respectively. The assumption of linearly varying radiative properties with burnout ratio (Lockwood et al. 1986) will result in a predicted deviation of 53% for radiative source terms. Results also show that this non-gray model is remarkably better than the Planck mean method. Moreover, a satisfactory comparison with LBL solutions is achieved in the gas and particle mixture by combining the non-gray WSGG-SK model (Guo et al. 2015). As a radiation sub-model, this non-gray radiative property model can significantly improve prediction accuracy of radiative heat transfer in oxy-fuel combustion.     

The relationship between absorption coefficient and temperature and their effect on the atmospheric cooling rate

Several approaches are considered to determine the temperature effect on the absorption coefficient within a correlated k-distribution method. Taking in the 610- region for example, the absorption coefficients and atmospheric cooling rates calculated using these approaches are compared with line-by-line integration. It is emphasized in this paper by numerical calculation that the effect of pressure on absorption coefficient is related to temperature and vise versa; the larger the pressure, the larger the effect of temperature on absorption coefficient. Results show that the temperature effect must be considered in radiative calculations although its effect on the absorption coefficient is much smaller than that of pressure.     

The role of cloud-scale resolution on radiative properties of oceanic cumulus clouds

Both individual and combined effects of the horizontal and vertical variability of cumulus clouds on solar radiative transfer are investigated using a two-dimensional (x- and z-directions) cloud radar dataset. This high-resolution dataset of typical fair-weather marine cumulus is derived from ground-based cloud radar observations. The domain-averaged (along x-direction) radiative properties are computed by a Monte Carlo method. It is shown that (i) different cloud-scale resolutions can be used for accurate calculations of the mean absorption, upward and downward fluxes; (ii) the resolution effects can depend strongly on the solar zenith angle; and (iii) a few cloud statistics can be successfully applied for calculating the averaged radiative properties.     

Parametrization of the effect of surface reflection on spectral infrared radiance measurements. Application to IASI

The recent launch of the Advanced Infrared Sounder (AIRS) on board EOS-Aqua and the scheduled launch of the Infrared Atmospheric Sounder Interferometer (IASI) on board the Meteorological Operational Satellite (METOP) in 2005 open interesting perspectives for remote sensing applications. Owing to their enhanced spectral resolution and sensitivity, this new generation of high-resolution infrared vertical sounders is first aimed at improving the vertical resolution of temperature and water vapor profile retrievals needed by the weather forecasting community. Another important possible use of these instruments, in the context of the study of global warming, is to permit the retrieval of the concentrations of greenhouse gases like , etc. In order to reach these two main objectives, improvement in the modeling of the radiative transfer is therefore necessary. One of the points which still needs some improvements is the contribution of the downward radiation reflected by the surface back to the satellite which is often improperly accounted for in radiative transfer calculation to save computer time. In this article, we show how it is possible to simplify the problem through the computation of a spectrally dependent “effective” emissivity for which a simple parametrization is proposed, while preserving the accuracy of the results.     

Solution of the equation of radiative transfer for interlocked doublets by double interval spherical harmonic method

The double-ordinate spherical harmonic method presented by Wilson and Sen (Publ. Astron. Soc. Jpn. 15 (1963) 351) has been used to solve the equation of radiative transfer in the Milne-Eddington model for interlocked doublets. Solutions have been obtained in the first and second approximation in a particular case η₁=1; .     

Test of far-infrared atmospheric spectroscopy using wide-band balloon-borne measurements of the upwelling radiance

The spectroscopy of the constituents of the Earth's atmosphere that are active in the far infrared spectral region, among which the water vapour is the main one, has been validated through the analysis of wide-band nadir-looking spectra acquired with the Radiation Explorer in the Far Infrared—Prototype for Applications and Development (REFIR-PAD) Fourier transform spectroradiometer. The spectra, covering from 100 to with a unapodized resolution, were acquired during a balloon flight performed in a tropical region in 2005. Atmospheric variables, namely water vapour and temperature vertical profiles, were retrieved from the REFIR-PAD data, and the residuals of the fitting are here critically analysed for the search of systematic effects that can be ascribed to spectroscopic errors. In the spectral interval between 150 and nosignificant inconsistency is detected between the residuals and the measurement uncertainty, proving the good quality of the radiative transfer model and of the HITRAN 2004 spectroscopic database. Significant difference are instead observed when the HITRAN 2000 database is used.     

Non-gray chemical composition based radiative property model of fly ash particles

Particle radiation has a spectral dependence and is closely related to the chemical composition of the material. Iron oxide, one of the main components of fly ash, observably affects the complex index of refraction of the particles. In this study, following the theory of the spectrum k-distribution based weighted sum of gray particles model (Guo et al. [4,13]), a non-gray fly ash radiative property model involving the chemical composition was developed. First, four typical fly ash particles with different iron oxide contents were selected, and the corresponding particle radiative parameters were obtained using the Mie theory. Then, the absorption efficiency and weighting factors of the non-gray model were directly obtained from the Gaussian integral points of the k-distribution. The scattering efficiency of the particles was obtained from the Planck mean. The accuracy of the newly developed model was evaluated in a one-dimensional plane-parallel slab system through comparison with the line-by-line (LBL) model and two commonly used gray radiative property models. The results show that the new non-gray model agrees well with the LBL solution and becomes more accurate as the iron oxide content increases. When the iron oxide content of the fly ash increased from 5.47% to 30.50%, the maximum relative error of the radiative heat flux and the radiative source term decreased from 12.50% to 5.68% and from 20.97% to 12.62%, respectively. The new model can improve the prediction accuracy of radiative heat transfer in pulverized coal-fired furnaces.     

Investigation of the water-vapor continuum in the THz region using a multipass cell

Laboratory absorption measurements of the water-vapor continuum in the far infrared region from 12 to (0.4 - 1.83 THz) were obtained using a multipass absorption cell, a Fourier transform spectrometer and a liquid-He-cooled bolometer detector. Measurements were made at a temperature, with water vapor and nitrogen pressures up to 2.2 and , respectively. The effects of the choice of lineshape function and far-wing cut-off factors on the reported continuum absorption are analyzed by modeling the resonant water-vapor spectrum using van Vleck-Weisskopf and Lorentzian lineshapes. Comparisons with available microwave data and model calculations are also presented.     

A simplified model to predict the effects of aggregation on the absorption properties of soot particles

An exact electrostatics formulation for sphere clusters is used to predict the Rayleigh-limit radiative absorption properties of soot aggregates. In the near to mid IR wavelengths, it is shown that aggregation can result in absorption cross sections that are significantly larger than that predicted by an independent-sphere (Rayleigh–Gans) model. The relative increase in absorption increases with the number of spheres in the aggregate, and reaches an asymptote for aggregates containing 100–200 spheres. A simplified correlation is developed to predict the aggregate absorption cross section as a function of number of spheres and refractive index. Implications of the effects of aggregation on absorption and emission of thermal radiation by soot in flame and atmospheric environments are discussed.     

Theoretical calculation of the isoelectronic line ratio of Li-like Ti and Cr under different mixture ratios

With the consideration of coronal conditions, a simplified model and the steady-state rate-equation are used to calculate the isoelectronic line ratio for transition in Li-like Ti and Cr from the electron temperature 400 to . The relation between the isoelectronic line ratio and the electron temperature are provided under different mixture ratios of Ti and Cr. Then, the mixture ratio from 2:1 to 3:1 between Ti and Cr are obtained that are suitable for the electron temperature diagnostic by using isoelectronic line ratio of Li-like Ti and Cr. The relative abundance of two close ionization stages, which is from bare nucleus to Be-like ionization stage, are given and show that the He-, Li- and Be-like are the principal ionization stages from 400 to for Ti and from 500 to for Cr. The Li-like charge state will reach the maximum distribution approximately from 400 to for Ti and from 547 to for Cr. The paper also shows that the dielectronic recombination and spontaneous radiative recombination rates only have small effects on the isoelectronic line ratio in the electron temperature 400-.