Numerical explanation for accurate radiative cooling rates resulting from the correlated k-distribution hypothesis

Numerical simulations are conducted to demonstrate that (a) correlation between spectral absorption at two levels decreases with increasing level distance; and (b) the contribution to the flux gained by one layer from another decreases rapidly with the layer separation. The combination of the two facts explains why the existence of poor correlation between distant layers produces insignificant radiative cooling rate error. Therefore, the overall accuracy of cooling rate calculations under the correlated k-distribution hypothesis is high.     

The effects of the choice of the k-interval number on radiative calculations

The selection of the number of k-interval is a foundation to correlated k-distribution method and the problem of how to do it still remains unsettled. It is pointed out by numerical computation in this work that choosing the number of k-interval is a major factor affecting accuracy and speed in radiative calculation. To increase the number of k-interval is an efficient method to improve the accuracy. However, it is found by this study that there exists a saturation of the accuracy to an increase of the number. The optimal rules on the number of k-interval choosing are proposed in the paper. Then, five versions on atmospheric absorption by gases appropriate for GCMs are given according to them.     

The sensitivity of radiative transfer calculations to the changes in the HITRAN database from 1982 to 2004

Over the last quarter century, improvements in the determination of the spectroscopic characteristics of the infrared-active trace species have enhanced our ability to retrieve quantitative distributions of temperatures, clouds, and abundances for various trace species within the Earth's atmosphere. These improvements have also allowed for refinements in the estimates of climatic effects attributed to changes in the Earth's atmospheric composition. Modeling efforts, however, have frequently experienced significant delays in assimilating improved spectroscopic information. Such is the case for highly parameterized models, where considerable effort is typically required to incorporate any revisions. Thus, a line-by-line radiative transfer model has been used to investigate the magnitude of the effects resulting from modifications to the spectroscopic information. Calculations from this line-by-line model have demonstrated that recent modifications to the HITRAN (High Resolution Transmission) line parameters, the continuum formulation, and the CO₂ line-mixing formulation can significantly affect the interpretation of the high spectral resolution radiance and brightness temperature retrievals. For certain moderate-resolution satellite remote sensing channels, modifications to these spectroscopic parameters and formulations have shown the capacity to induce changes in the calculated radiances equivalent to brightness temperature differences of 1-2 K. Model calculations have further shown that modifications of the spectroscopic characteristics tend to have a modest effect on the determination of spectrally integrated radiances, fluxes, and radiative forcing estimates, with the largest differences being of order 1 W m⁻² for the total thermal infrared fluxes, and of order 2-3% of the calculated radiative forcing at the tropopause attributed to the combined doubling of CO₂, N₂O, and CH₄. The results from this investigation are intended to function as a guide to differentiate between cases where older parameterizations provide acceptable results, within specified accuracy bounds, and cases where upgrades to the latest spectroscopic database are necessary.     

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.     

The k-moment method for the narrow band modeling of radiative properties of nonuniform gaseous media

Moments of the absorption coefficient distribution function are used for the derivation of statistical narrow band (SNB) model parameters of nonuniform optical paths in gases. The approach yields approximations for the path-averaged first- and second-order k-moments from which equivalent SNB parameters are determined in the frame of the Malkmus model. The approach is assessed through comparisons with LBL data. The nonuniform approximation is shown to enable the computation of transmissivities and radiation intensities with accuracy similar to or higher than those achieved by the Curtis-Godson one.     

A correlated-k model of radiative transfer in the near-infrared windows of Venus

We present a correlated-k-based model for generating synthetic spectra in the near-infrared window regions, from 1.0 to 2.5 μm, emitted from the deep atmosphere of Venus on the nightside. This approach is applicable for use with any near-infrared instrument, ground-based and space-borne, for analysis of the thermal emissions in this spectral range. We also approach this work with the view of using the model, in conjunction with a retrieval algorithm, to retrieve minor species from the Venus Express/VIRTIS instrument. An existing radiative-transfer model was adapted for Venusian conditions to deal with the prevailing high pressures and temperatures and other conditions. A comprehensive four-modal cloud structure model based on Pollack et al. [Near-infrared light from venus’ nightside: a spectroscopic analysis. Icarus 1993;103:1-42], using refractive indices for a 75% H₂SO₄25% H₂O mixture from Palmer and Williams [Optical constants of sulfuric acid; application to the clouds of Venus? Appl Opt 1975;14(1):208-19], was also implemented. We then utilized a Mie scattering algorithm to account for the multiple scattering effect between cloud and haze layers that occur in the Venusian atmosphere. The correlated-k model is shown to produce good agreement with ground-based spectra of Venus in the near infrared, and to match the output from a line-by-line radiative-transfer model to better than 10%.     

A fast infrared radiative transfer model based on the adding-doubling method for hyperspectral remote-sensing applications

A fast infrared radiative transfer (RT) model is developed on the basis of the adding-doubling principle, hereafter referred to as FIRTM-AD, to facilitate the forward RT simulations involved in hyperspectral remote-sensing applications under cloudy-sky conditions. A pre-computed look-up table (LUT) of the bidirectional reflection and transmission functions and emissivities of ice clouds in conjunction with efficient interpolation schemes is used in FIRTM-AD to alleviate the computational burden of the doubling process. FIRTM-AD is applicable to a variety of cloud conditions, including vertically inhomogeneous or multilayered clouds. In particular, this RT model is suitable for the computation of high-spectral-resolution radiance and brightness temperature (BT) spectra at both the top-of-atmosphere and surface, and thus is useful for satellite and ground-based hyperspectral sensors. In terms of computer CPU time, FIRTM-AD is approximately 100-250 times faster than the well-known discrete-ordinate (DISORT) RT model for the same conditions. The errors of FIRTM-AD, specified as root-mean-square (RMS) BT differences with respect to their DISORT counterparts, are generally smaller than 0.1 K.     

A study of the radiative forcing and global warming potentials of hydrofluorocarbons

We developed a new radiation parameterization of hydrofluorocarbons (HFCs), using the correlated k-distribution method and the high-resolution transmission molecular absorption (HITRAN) 2004 database. We examined the instantaneous and stratospheric adjusted radiative efficiencies of HFCs for clear-sky and all-sky conditions. We also calculated the radiative forcing of HFCs from preindustrial times to the present and for future scenarios given by the Intergovernmental Panel on Climate Change Special Report on Emission Scenarios (SRES, in short). Global warming potential and global temperature potential were then examined and compared on the basis of the calculated radiative efficiencies. Finally, we discuss surface temperature changes due to various HFC emissions.     

A multi-spectral reordering technique for the full spectrum SLMB modeling of radiative heat transfer in nonuniform gaseous mixtures

A Multi-Spectral Reordering (MSR) scheme is introduced to improve the performances of the Spectral-Line Moment-Based (SLMB) modeling for the handling of full spectrum radiative heat transfer calculations in nonuniform media. Using this simultaneous reordering of the spectrum for several thermophysical conditions together with employing approximate formulations to evaluate path-averaged transmission functions for nonisothermal and nonhomogenous gaseous paths, a novel full spectrum gas radiation modeling method in nonuniform gaseous mixtures is constituted. The method is presented in details as well as the building of associated databases for CO₂ and H₂O at atmospheric pressure and for the temperature range of 300-2700 K. The new model is validated against line-by-line reference computations for a series of existing benchmarks and for a flame configuration. The MSR-SLMB modeling is shown to perform accurately and better than the standard SLMB one, while involving reasonable additional computational costs.     

A database for the SLMB modeling of the full spectrum radiative properties of CO2

Development and application of a database for the Spectral-Line Moment-Based (SLMB) modeling of the full spectrum radiative properties of mixtures of carbon dioxide and nitrogen is presented. The critical issue of the definition of a reference thermophysical condition is addressed together with the suggestion of a coherent and precise methodology to derive parameters of the model for any other configuration. The database is built accordingly from the CDSD-1000 high temperature spectroscopic databank for gas and blackbody-weighting temperatures in the range [300; 2700 K]. Accuracy of both the modeling and the database is assessed through comparisons with LBL results in terms of full spectrum k-distributions and emission functions. Results obtained from the application of FSK correlations and the Leckner's formula are also provided for extended analyses.     

Evaluation of solution methods for radiative heat transfer in gaseous oxy-fuel combustion environments

The exact solution to radiative heat transfer in combusting flows is not possible analytically due to the complex nature of the integro-differential radiative transfer equation (RTE). Many different approximate solution methods for the solution of the RTE in multi-dimensional problems are available. In this paper, two of the principal methods, the spherical harmonics (P₁) and the discrete ordinates method (DOM) are used to calculate radiation. The radiative properties of the gases are calculated using a non-gray gas full spectrum k-distribution method and a gray method. Analysis of the effects of numerical quadrature in the DOM and its effect on computation time is performed. Results of different radiative property methods are compared with benchmark statistical narrow band (SNB) data for both cases that simulate air combustion and oxy-fuel combustion. For both cases, results of the non-gray full spectrum k-distribution method are in good agreement with the SNB data. In the case of oxy-fuel simulations with high partial pressures of carbon dioxide, use of gray method for the radiative properties may cause errors and should be avoided.     

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.     

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.     

Understanding nitrogen-induced effects on the performance of ultra low-k dielectric systems through ab initio simulations

Large scale ab initio molecular dynamics simulations were performed to investigate how Cu/ultra low-k systems are improved when N is incorporated into the pore-sealing layers. It was found that the high affinity of N to Ta and H gives rise to new phases that prevent H atoms from penetrating the Ta diffusion barrier layer. Consequently, the Ta layer forms organized structures with good barrier performance and electrical conductivity. Furthermore, a continuous ductile film is formed to seal the highly porous polymer dielectrics. Interfacial adhesion between the pore-sealing layer and the dielectrics is also enhanced by inter-diffusion.     

Optical properties and thermal stability of LaYbO3 ternary oxide for high-k dielectric application

A new ternary rare oxide dielectric LaYbO₃ film had been prepared on silicon wafers and quartz substrates by reactive sputtering method using a La-Yb metal target. A range of analysis techniques was performed to determine the optical band gap, thermal stability, and electrical property of the deposited samples. It was found the band gap of LaYbO₃ film was about 5.8 eV. And the crystallization temperature for rapid thermal annealing (20 s) was between 900 and 950 °C. X-ray photoelectron spectroscopy results indicate the formation of the SiO₂ and silicate in the interface between silicon wafer and LaYbO₃ film. The dielectric constant is about 23 from the calculation of capacitance-voltage curve, which is comparable higher than previously reported La₂O₃ or Yb₂O₃ film.     

Comparison of the standard weighted-sum-of-gray-gases with the absorption-line blackbody distribution function for the computation of radiative heat transfer in H2O/CO2 mixtures

This paper presents the computation of radiation heat transfer in a cylindrical enclosure in which the dimensions, the chemical species concentrations and the temperature fields make a realistic representation of an actual combustion chamber. Two gas models are applied and compared: the absorption-line blackbody distribution function (ALBDF), and the standard weighted-sum-of-gray-gases (WSGG) based on coefficients and correlations that are widely used in engineering. While the standard WSGG is restricted to the assumption of homogeneous gas mixture, the ALBDF can be applied to both homogeneous and non-homogeneous media. For the two gas models, the radiative exchanges are computed with the aid of the Monte Carlo method. The results show considerable discrepancies between the WSGG and the ALBDF models for the homogeneous medium. In addition, the importance of considering the non-homogeneity of the medium for an accurate computation of the radiative heat transfer is shown.     

An individual-based model for evolutionary effects of selective fishing applied to Pseudoplatystoma corruscans

This paper proposes an individual-based model that takes into account the evolutionary effects of selective fishing on exploited populations. The model is an adaptation of the Penna model based on the biology of exploited species and characteristics of fishing. Given the importance of the Pintado Pseudoplatystoma corruscans, a native species of great economic value in the Brazilian fishery, the model was applied to study the effects of selective fishing on the growth characteristics of this species.     

Approximate analytical representation of Wigner distribution function for Gaussian beams passing through ABCD optical systems with hard aperture

Based on the treatment that a rectangular function can be expanded as an approximate sum of complex Gaussian functions with finite numbers, the analytical expression of the Wigner distribution function for a Gaussian beam passing through a paraxial ABCD optical system with hard-edged aperture is obtained. By numerical simulation, it is shown that the effect of the aperture on the Wigner distribution function is prominent. By comparing the analytical results with the numerical integral results, it is shown that this method of expanding hard-edged aperture into Gaussian functions with finite numbers is proper and ascendant. This method could be extended to study the Wigner distribution functions of other light beams passing through a paraxial ABCD optical system with hard-edged aperture.     

The nonlinear refraction and absorption dependence on the thermal effect for 4 ns pulse duration in binuclear Zn(II) phthalocyanine solution

The influence of thermal effect on the third-order nonlinear optical properties of binuclear Zn(II) phthalocyanine in chloroform solution was studied. The nonlinear refraction and absorption of the sample was measured by using Z-scan technique with 4 ns laser pulses at 532 nm wavelength. The opposite signs of the effective nonlinear refraction index were observed by changing the focal length of focusing lens from 10 cm to 20 cm in the experimental setup. Changing the focusing lens increased the beam waist radius from 7 μm to 20 μm. The nonlinear absorption coefficient was reduced about 200 times based on changing the fluence or beam waist radius. The drastic changes in the third-order nonlinear optical parameters were attributed to thermal effect. To investigate the role of thermal effects even further the effective nonlinear refraction and absorption coefficients were studied by using different repetition rates, input powers and concentrations.     

Quantum-chemical ab initio study of the crystal-field and charge transfer energies of nanocrystalline Y2O3: Eu

The 4f energy levels and crystal-field parameters for several clusters representing the local coordination surroundings of Eu³⁺ in the bulk and nanocrystalline cubic Y₂O₃: Eu³⁺ crystals are obtained by using a method based on the combination of the DV-X_α calculation and the effective Hamiltonian method initialized by M.F. Reid et al. (J. Phys.: Condens. Matter, 2011, 23: 045501). The results are in reasonable agreement with the measured energy levels and the crystal-field parameters obtained from the least-square fitting. The charge transfer energies are also obtained for all the clusters from the DV-X_α calculation. The results indicate that, compared with the bulk Y₂O₃: Eu³⁺ crystal, the charge transfer band in the excitation spectra is red-shifted in the nanocrystal.