A radiative transfer model for an idealized and non-scattering atmosphere and its application for ground-based remote sensing

Inversion of tropospheric profiles from ground-based microwave measurements requires a simple and accurate model for calculating the brightness temperatures as received by the radiometer. In the first part, an analytic solution of the radiative transfer equation is derived for an exponentially decaying absorption coefficient and a linear temperature gradient. Based on the obtained analytic expressions, a discretized radiative transfer scheme is developed in the second part. The new scheme incorporates the generic behavior of the atmosphere with the effect that brightness temperatures can be modeled more accurately and with fewer grid points compared to commonly used radiative transfer schemes. The brightness temperature modeling accuracy was improved by a factor of six. The results suggest that the model could be employed for the retrieval of temperature and humidity profiles.     

Multilayer modeling of radiative transfer by SLW and CW methods in non-isothermal gaseous medium

Non-isothermal gaseous medium is modeled using the multilayer approach, breaking the one-dimensional system into a series of isothermal layers. Spectral integration of the radiative transfer equation (RTE) is performed for the spectral line weighted-sum-of-gray-gases and cumulative wavenumber approaches to modeling the spectral nature of the gas radiation. An exact analytical solution of RTE is obtained for the layers with both black and gray walls. Predictions show high accuracy, even with surprisingly few layers.     

Comparison of the radiative transfer equations for constant and spatially varying refraction

The radiative transfer equation for scattering media with constant refraction index (RTE) and the radiative transfer equation for scattering media with spatially varying refraction index (RTEvri) are compared by using the principle of conservation of energy. It is shown that the RTEvri, not only accounts for the spatial variations of refraction index, but also contains a term that accounts for the divergence of the rays. The latter term is missing in the RTE. A corrected RTE is proposed.     

Parallel Jacobian-free Newton Krylov solution of the discrete ordinates method with flux limiters for 3D radiative transfer

The present study introduces a parallel Jacobian-free Newton Krylov (JFNK) general minimal residual (GMRES) solution for the discretized radiative transfer equation (RTE) in 3D, absorbing, emitting and scattering media. For the angular and spatial discretization of the RTE, the discrete ordinates method (DOM) and the finite volume method (FVM) including flux limiters are employed, respectively. Instead of forming and storing a large Jacobian matrix, JFNK methods allow for large memory savings as the required Jacobian-vector products are rather approximated by semiexact and numerical formulations, for which convergence and computational times are presented. Parallelization of the GMRES solution is introduced in a combined memory-shared/memory-distributed formulation that takes advantage of the fact that only large vector arrays remain in the JFNK process. Results are presented for 3D test cases including a simple homogeneous, isotropic medium and a more complex non-homogeneous, non-isothermal, absorbing–emitting and anisotropic scattering medium with collimated intensities. Additionally, convergence and stability of Gram–Schmidt and Householder orthogonalizations for the Arnoldi process in the parallel GMRES algorithms are discussed and analyzed. Overall, the introduction of JFNK methods results in a parallel, yet scalable to the tested 2048 processors, and memory affordable solution to 3D radiative transfer problems without compromising the accuracy and convergence of a Newton-like solution.     

Refractive index imaging from radiative transfer equation-based reconstruction algorithm: Fundamentals

We present the first reconstruction algorithm for refractive index imaging, which is based on the radiative transfer equation (RTE). An objective function is iteratively minimized to find a solution to the problem of inversion of the refractive index field. The function describes the discrepancies of the emerging light measurements on the surface of the sample to be probed with predicted data from the corresponding numerical model. The unknown refractive index field is updated within each reconstruction iteration according to a search direction on the index distribution given by the adjoint model to the RTE. In this paper, emphasis is placed on the theoretical aspects. Preliminary tests are demonstrated on generic phantoms.     

任意入射辐射条件下介质特性对瞬态辐射传递的影响

用基于Monte Carlo法的DRESOR法在平行平板系统内具有吸收、无发射介质中研究不同波形入射、壁面反射、介质散射率、光学厚度、各向异性散射等条件对瞬态辐射传递的影响.任意连续波形入射辐射是目前大多数数值方法很难处理的瞬态辐射问题,而DRESOR法通过在系统内计算一单位入射辐射能对介质的DRESOR数分布,就能计算任意连续波形入射辐射条件下高方向分辨率的瞬态辐射强度结果.DRESOR法和Monte Carlo法计算的结果进行了比较验证,两者吻合较好,证明了DRESOR法处理瞬态入射辐射问题的正确性和有效性.     

Light Reflection and Transmission by layers with oriented spheroidal particles

On the basis of the numerical solution of the radiative transfer equation (RTE), the influence of non-sphericity of oriented spheroidal particles on radiation intensity formation in a layer with a multiple scattering regime is considered. For solving the RTE with characteristics depending on the propagation direction of the radiation beam, an algorithm is developed based on the method of layer doubling. Calculations are presented of angle correlations for intensities of radiation in a layer with Fresnel reflection on the boundaries, and reflection and transmission coefficients.     

DRESOR法对平行入射辐射问题的研究

本采用一种基于蒙特卡洛法(Monte Carlo Method,MCM)求解辐射传递方程(Radiative Transfer Equation, RTE)的快捷、有效的方法-DRESOR法(Distributions of Ratios of Energy Scattered Or Reflected)在一维充满吸收、各向同性散射介质平行平板中,外部有平行入射条件下,求解计算空间点的辐射强度沿空间方向角的分布,而不需要辐射平衡和在空间位置坐标和方向角度坐标上同时离散辐射传递方程进行迭代求解。     

Discrete ordinates solution of coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation

The coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation is solved. The collimated and diffuse components problems are treated separately. The solution for diffuse radiation is obtained by using a composite discrete ordinates method and includes the development of adaptive directional quadratures to overcome the difficulties usually encountered at the interfaces. The complete radiation numerical model is validated against the predictions obtained by using the Monte Carlo method.     

Application of the singularity-subtraction technique to isotropic scattering in a planar layer

A numerical procedure for solving a singular Fredholm integral equation, which describes radiative transfer in an absorbing and isotropically scattering layer exposed to collimated radiation, is studied. The integral equation is solved by subtracting out the singularity and then approximating the integral term by a Gaussian quadrature. Bidirectional and hemispherical properties are found from the source function. Any arbitrary directional distribution of incident radiation can be handled by superimposing the collimated radiation case. In particular, the case of isotropic incident radiation is presented. The method gives accurate results, even for the extreme conditions of large optical thickness and large angle of incidence.     

Coupled radiative and conductive heat transfer in a non-grey absorbing and emitting semitransparent media under collimated radiation

This paper deals with heat transfer in non-grey semitransparent two-dimensional sample. Considering an homogeneous purely absorbing medium, we calculated the temperature field and heat fluxes of a material irradiated under a specific direction. Coupled radiative and conductive heat transfer were considered. The radiative heat transfer equation (RTE) was solved using a S₈ quadrature and a discrete ordinate method. Reflection and absorption coefficients of the medium were calculated with the silica optical properties. The conduction inside the medium was linked to the RTE through the energy conservation. Validation of the model and two original cases are also presented.     

Radiative and conductive heat transfer in a nongrey semitransparent medium. Application to fire protection curtains

This paper deals with heat transfer in nongrey media which scatter, absorb and emit radiation. Considering a two dimensional geometry, radiative and conductive phenomena through the medium have been taken into account. The radiative part of the problem was solved using the discrete ordinate method with classical S_n quadratures. The absorption and scattering coefficients involved in the radiative transfer equation (RTE) were obtained from the Mie theory. Conduction inside the medium was linked to the RTE through the energy conservation. Validation of the model has been achieved with several simulation of water spray curtains used as fire protection walls.     

Multiple scattering by particles embedded in an absorbing medium. 2. Radiative transfer equation

This paper continues a systematic theoretical analysis of electromagnetic scattering by a group of arbitrarily sized, shaped, and oriented particles embedded in an absorbing, homogeneous, isotropic, and unbounded medium. The previously developed microphysical approach is used to derive the generalized form of the radiative transfer equation (RTE) applicable to a large group of sparsely, randomly, and uniformly distributed particles. The derivation of the RTE directly from the macroscopic Maxwell equations yields unambiguous and definitive analytical expressions for the participating quantities and thereby fully resolves the lasting controversy caused by the conflicting outcomes of several phenomenological approaches.     

用于光谱基准定标传递技术的传递辐射计研究综述

传递辐射计是实现卫星遥感仪器在轨光谱辐射定标传递的核心设备,也是地面实验室高精度光谱定标系统的关键。介绍了不同机构研制的覆盖350～700, 700～2 500 nm谱段的多个传递辐射计的结构组成、工作原理及辐射定标基准传递方式,及其异同点的比对,再通过它们在不同谱段的定标过程中所应用的关键技术的分析,说明每种技术的优缺点和所能达到的精度,及其应用条件。文中通过对国际上标准计量机构采用的光谱辐亮度基准定标传递过程的介绍,突出了传递辐射计系统的重要作用,再结合其对光谱仪等遥感器定标光源的定标监测应用,说明了传递辐射计在航天辐射定标领域的不可或缺性。最后,通过国内设计的新型传递辐射计的介绍,对传递辐射计未来研究的发展方向和关键问题进行了展望,并对传递辐射计搭配低温辐射计组成的未来实现可溯源国际单位制在轨基准定标传递系统所存在的研究难点予以预测分析。     

A quasi-analytic solution of the radiative transfer equation for three-dimensional atmospheres

In this study, we present a new solution of the three-dimensional (3-D) radiation transfer equation (RTE). The solution employs a discretization technique to separate the independent variables involved in the 3-D RTE, and the doubling-adding method to solve the RTE explicitly and quasi-analytically. The remarkable feature of the present solution is the application of scaling-function expansion to those terms that are dependent on horizontal coordinates. Scaling-function expansion is suitable for representing irregular horizontal inhomogeneities with small-scale variations. By applying scaling-function expansion, the 3-D RTE can be formulated in the form of a vector-matrix differential equation; matrices involved in the equation are generally sparse and dominantly diagonal matrices, and this considerably reduces the labor involved in matrix calculations. We tested the performance of the present solution via radiative transfer calculations of solar radiation in horizontally inhomogeneous two-dimensional cloud models. The calculated results indicate that even if the resolution of the scaling-function expansion is too coarse in regions around small-scale variations, the influence does not spread problematically to other regions far from the variations; this illustrates the advantage of the scaling-function expansion. The present solution can be used to investigate quantitatively and to estimate the effects of cloud spatial inhomogeneity on the corresponding radiation field.     

Analysis of directional radiative behavior and heating efficiency for a gas-fired radiant burner

For the purpose of energy conservation and uniform heating of object surface, a gas-fired porous radiant burner with a bundle of reflecting tubes is developed. A physical model is developed to simulate the directional radiative behavior of this heating device, in which the Monte Carlo method based on the concept of radiation distribution factor is used to compute the directional radiative behavior. The effects of relating parameters on the directional behavior of radiative heating and the heating efficiency are analyzed. With the increase of the length-to-radius ratio of tube, the radiation heating efficiency decreases, but the radiation energy incident on the object surface is more collimated. The radiation heating efficiency increases with the specular reflectivity. With the increase in length of tube segment with specular reflective surface, the radiation heating efficiency increases, but the extent of concentration and collimation of radiative energy decreases. For real design of the heating device, some trade-offs are needed to balance the radiation heating efficiency and the uniformity of radiative heating of object surface.     

On the combined heat transfer in the multilayer non-gray porous fibrous insulation

A detailed numerical modeling is performed to investigate coupled heat transfer of natural convection, radiation and conduction in high-temperature multilayer thermal insulation (MTI), which consists of high-porous, non-gray semitransparent fibrous materials and reflective foils. Radiation within fibers, radiation between fibers and the reflective foils, conduction within fibers and convection from the fibers to the surrounding fluid are considered. Macroscopic (porous media) modeling is used to determine velocity, pressure and temperatures fields for fibrous insulation with a random packing geometry under natural convection, whereas the radiative transfer equation (RTE) is used to solve the radiative heat flux for non-gray materials. Key features of the macroscopic model include two-dimensional effects, non-gray radiative exchange, and the relaxation of the local thermodynamic non-equilibrium (LTNE). This model was validated by comparison with experimental data and it was used to investigate natural convection of coupled heat transfer in multilayer insulation, numerical results showed that natural convection is more likely to occur when the heated/cooled rate is low, while natural convection can be ignored in simulating steady-state coupled heat transfer in MTI.     

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.     

RADIATIVE AND TOTAL HEAT FEEDBACK FROM FLAMES TO SURFACE IN VERTICAL WALL FIRES

Measurements of radiative and total heat transfer from turbulent flames to a wall are presented for combustion of propane, methane, and natural gas. Flames were generated by a linear burner placed at the bottom of an instrumented, cooled copper wall. The radiative heat feedback from the flames to the wall was determined from measurements using a narrow-angle radiometer and by employing mean-beam-length analysis. The radiative fraction of the total heat feedback was found to be almost independent of the burner power output when plotted against scaled height (vertical distance normalized with flame length). Among the three fuels tested, radiative fraction in flame-to-wall heat transfer was the maximum, for propane and minimum for methane, which can be explained based on sooting characteristics of flames. The total radiative energy transfer as a fraction of the burner output power is also presented for the three fuels.     

Modifications of discrete ordinate method for computations with high scattering anisotropy: Comparative analysis

A numerical accuracy analysis of the radiative transfer equation (RTE) solution based on separation of the diffuse light field into anisotropic and smooth parts is presented. The analysis uses three different algorithms based on the discrete ordinate method (DOM). Two methods, DOMAS and DOM2+, that do not use the truncation of the phase function, are compared against the TMS-method. DOMAS and DOM2+ use the Small-Angle Modification of RTE and the single scattering term, respectively, as anisotropic parts. The TMS method uses the Delta-M method for truncation of the phase function along with the single scattering correction. For reference, a standard discrete ordinate method, DOM, is also included in analysis. The obtained results for cases with high scattering anisotropy show that at low number of streams (16, 32) only DOMAS provides an accurate solution in the aureole area. Outside aureole, the convergence and accuracy of DOMAS, and TMS is found to be approximately similar: DOMAS was found more accurate in cases with coarse aerosol and liquid water cloud models, except low optical depth, while the TMS showed better results in case of ice cloud.