An efficient diffusion approximation for 3D radiative transfer parameterization: application to cloudy atmospheres

The three-dimensional (3D) diffusion radiative transfer equation, which utilizes a four-term spherical harmonics expansion for the scattering phase function and intensity, has been efficiently solved by using the full multigrid numerical method. This approach can simulate the transfer of solar and thermal infrared radiation in inhomogeneous cloudy conditions with different boundary conditions and sharp boundary discontinuity. The correlated k-distribution method is used in this model for incorporation of the gaseous absorption in multiple-scattering atmospheres for the calculation of broadband fluxes and heating rates in the solar and infrared spectra. Comparison of the results computed from this approach with those computed from plane-parallel and 3D Monte Carlo models shows excellent agreement. This 3D radiative transfer approach is well suited for radiation parameterization involving 3D and inhomogeneous clouds in climate models.     

Discrete vs. continuum-scale simulation of radiative transfer in semitransparent two-phase media

The mathematical formulation of the continuum approach to radiative transfer modeling in two-phase semi-transparent media is numerically validated by comparing radiative fluxes computed by (i) direct, discrete-scale and (ii) continuum-scale approaches. The analysis is based on geometrical optics. The discrete-scale approach uses the Monte Carlo ray-tracing applied directly to real 3D geometry measured by computed tomography. The continuum-scale approach is based on a set of continuum-scale radiative transfer equations and associated radiative properties, and employs the Monte Carlo ray-tracing for computations of radiative fluxes and for computations of the radiative properties. The model two-phase media are reticulate porous ceramics and a particle packed bed, each composed of semitransparent solid and fluid phases. The results obtained by the two approaches are in good agreement within the limits of statistical uncertainty. The continuum-scale approach leads to a reduction in computational time by approximately one order of magnitude, and is therefore suited to treat radiative transfer problems in two-phase media in a wide range of engineering applications.     

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.     

A diffusion-based approximate model for radiation heat transfer in a solar thermochemical reactor

An approximate numerical method for fast calculations of the radiation heat transfer in a solar thermochemical reactor cavity is formulated based on the separate treatment of the solar and thermal radiative exchange by the diffusion approach. The usual P₁ approximation is generalized by applying an equivalent radiation diffusion coefficient for the optically thin central part of the cavity. The resulting boundary-value problems are solved using the finite element algorithm. The accuracy of the model is assessed by comparing the results to those obtained by a pathlength-based Monte Carlo simulation. The applicability of the proposed model is demonstrated by performing calculations for an example problem, which incorporates a range of parameters typical for a solar chemical reactor and the spectral radiative properties of polydisperse zinc oxide particles.     

热辐射输运问题的隐式蒙特卡罗方法求解

热辐射与物质相互作用及辐射光子在物质中的传输是惯性约束聚变研究中的重要课题. 介绍了基于隐式蒙特卡罗方法的辐射输运方程,在该方程的积分-微分形式基础上,推导了利于蒙特卡罗方法模拟的等价的积分输运方程;基于积分方程设计数值模拟流程,编写三维蒙特卡罗数值模拟程序;针对热辐射输运典型问题及benchmark问题开展了数值实验,计算结果验证了方法的适应性及程序的正确性. 关键词： 热辐射 惯性约束聚变 输运方程 隐式蒙特卡罗     

Forward Monte Carlo computations of fully polarized microwave radiation in non-isotropic media

A completely forward Monte Carlo radiative transfer code has been developed with biasing techniques to efficiently solve the polarized radiative transfer equation for the full Stokes vector. The code has been adapted to accommodate plane parallel/3-D vertically/horizontally inhomogeneous scattering atmospheres in Cartesian geometries. Particular attention has been paid in stochastically treating the propagation, the emission and the scattering through anisotropic media particularly suited for clouds containing perfectly or partially oriented particles. Our modelling is very appealing because all its biasing techniques do not introduce unphysical Stokes vector. Numerical results and comparisons with benchmark tests are presented for verification.     

Cloud 3D effects on broadband heating rate profiles: I. Model simulation

Solar broadband heating directly drives the atmospheric and ocean circulations, and is largely determined by cloud spatial 3-diminesional (3D) structures. To study the cloud 3D effects on radiation, a 3D broadband Monte-Carlo radiative transfer model, along with an Independent Pixel/Column Approximation (IPA) method, is used to simulate radiation and heating rate of three typical cloud fields generated by cloud resolving models (CRM). A quantitative and statistical estimation of cloud 3D effects has been developed to investigate the impact of cloud 3D structures on both heating rate strength, STD_Bias, and vertical distribution, CorrCoef. The cloud 3D structures affect some clouds more in heating rate strength and others more in vertical distribution. It is crucial to use the combination of CorrCoef and STD_Bias for better quantitative evaluation of the 3D effects. Furthermore, there is no simple way to define a critical resolution (or average radius), within which the IPA heating rate profiles closely represent the true 3D heating rate profiles. The critical radius (or resolution) strongly depends on solar incident angle as well as cloud vertical distribution. Also, the critical radii for clear-sky columns are larger than for cloudy columns, although the corresponding STD_Bias for clear-sky columns are smaller than for cloudy columns. Analysis based on two different statistical average methods illustrates that the cloud 3D effects due to the dimensionality difference between the 3D clouds (circle average) and 2D clouds (line average) significantly impact on the heating rate profiles.     

Microwave radiative transfer intercomparison study for 3-D dichroic media

Three different numerical methods capable of solving the radiative transfer of microwave radiation within 3-D dichroic media are compared. A case study, represented by an intense rain shaft populated by perfectly oriented oblate raindrops, is analysed in detail, including a discussion of the behaviour of all four Stokes components.Results demonstrate an acceptable agreement between all Monte Carlo methods. The method based on a discrete ordinates scheme agrees only qualitatively with the Monte Carlo outputs. Because of its lower computational cost the backward Monte Carlo technique based on importance sampling represents the most efficient way to face passive microwave radiative transfer problems related to optically thick 3-D structured clouds including non-spherical preferentially oriented hydrometeors.     

Boundary conditions for differential approximations

Low order spherical harmonic (P-N) approximations are applied to a radiative transfer Marshak wave problem. A modified Milne boundary condition is developed for the P-2 approximation, similar to one suggested earlier for the P-1 approximation. Comparison with exact Monte Carlo results suggests that this modified P-2 method may be an accurate and generally applicable differential approximation to the equation of transfer. The Monte Carlo results presented should be useful for testing other approximate formulations of radiative transfer and validating time dependent numerical solution methods for the equation of transfer.     

Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud

A polarized atmospheric radiative transfer model for the computation of radiative transfer inside three-dimensional inhomogeneous mediums is described. This code is based on Monte Carlo methods and takes into account the polarization state of the light. Specificities introduced by such consideration are presented. After validation of the model by comparisons with adding-doubling computations, examples of reflectances simulated from a synthetic inhomogeneous cirrus cloud are analyzed and compared with reflectances obtained with the classical assumption of a plane parallel homogeneous cloud (1D approximation). As polarized reflectance is known to saturate for optical thickness of about 3, one could think that they should be less sensitive to 3D effects than total reflectances. However, at high spatial resolution (80 m), values of polarized reflectances much higher than the ones predicted by the 1D theory can be reached. The study of the reflectances of a step cloud shows that these large values are the results of illumination and shadowing effects similar to those often observed on total reflectances. In addition, we show that for larger spatial resolution (10 km), the so-called plane-parallel bias leads to a non-negligible overestimation of the polarized reflectances of about 7–8%.     

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.     

基于能量密度分布的辐射源粒子空间抽样方法研究

利用隐式蒙特卡罗方法模拟热辐射光子在物质中的输运过程时,物质辐射源粒子是需要细致处理的物理量.传统的物质辐射源粒子抽样方法是体平均抽样方法,对于大多数问题,这样处理不会带来大的偏差.但是对于一些辐射吸收截面大、单一网格内温差显著的问题,体平均抽样方法的计算结果偏差较大.分析了产生偏差原因,提出一种基于辐射能量密度分布的辐射源粒子空间位置抽样方法,并推导了相应的抽样公式以解决此类问题.数值实验表明,新方法计算结果明显优于原方法且与解析结果基本一致.     

An alternative Monte Carlo approach to the thermal radiative transfer problem

The usual Monte Carlo approach to the thermal radiative transfer problem is to view Monte Carlo as a solution technique for the nonlinear thermal radiative transfer equations. The equations contain time derivatives which are approximated by introducing small time steps. An alternative approach avoids time steps by using Monte Carlo to directly sample the time at which the next event occurs. That is, the time is advanced on a natural event-by-event basis rather than by introducing an artificial time step.     

Application of the modified differential approximation for radiative transfer to arbitrary geometry

The first-order spherical harmonics method (or P₁ approximation) has found prolific usage for approximate solution of the radiative transfer equation (RTE) in participating media. However, the accuracy of the P₁ approximation deteriorates as the optical thickness of the medium is decreased. The modified differential approximation (MDA) was originally proposed to remove the shortcomings of the P₁ approximation in optically thin situations. This article presents algorithms to apply the MDA to arbitrary geometry—in particular, geometry with obstructions, and inhomogeneous media. The wall-emitted component of the intensity was computed using a combined view-factor and ray-tracing approach. The Helmholtz equation, arising out of the medium-emitted component, was solved using an unstructured finite-volume procedure. The general procedure was validated for both two-dimensional (2D) and three-dimensional (3D) geometries against benchmark Monte Carlo results. The accuracy of MDA was found to be superior to the P₁ approximation for all optical thicknesses. Its accuracy, when compared with the discrete ordinates method (both S₆ and S₈), was found to be clearly superior in optically thin situations, but problem dependent in optically intermediate and thick situations. For 3D geometries, calculation and storage of the view-factor matrix was found to be a major shortcoming of the MDA. In addition, for inhomogeneous media, calculation of optical distances requires a ray-tracing procedure, which was found to be a bottleneck from a computational efficiency standpoint. Several strategies to reduce both memory and computational time are discussed and demonstrated.     

A Monte Carlo implementation to solve radiation heat transfer in non-uniform media with spectrally dependent properties

This paper presents the application of the Monte Carlo method to solve the radiative heat exchange in non-homogeneous, non-isothermal gases with spectrally dependent properties. Among others models, the absorption-line blackbody (ALB) distribution function, originally defined and derived for the spectral line-based weighted-sum-of-gray-gases (SLW) model, allows an immediate, simple implementation of the Monte Carlo method to account the spectral dependence of the radiative properties. This work shows how the Monte Carlo method can be combined to the ALB distribution function, and provides results for heat transfer in a mixture of water vapor, carbon dioxide and nitrogen that have satisfactory agreement with the SLW method and with line-by-line integration. Finally, the solution technique is employed to solve two examples aiming at demonstrating the effect of the absorbing species concentration on the thermal radiative exchanges. The method is of great interest for the computation of radiative transfer in combustion systems where the chemical species concentration and the temperature are not uniform.     

降雨融化层后向散射的蒙特卡罗仿真

云层上端冰雪粒子的融化形成了降雨融化层，随着粒子的下落融化过程开始，因此融化层的微观特性在垂直方向上是连续变化的.建立了降雨融化层的仿真模型，应用更为切合实际的三层球形粒子代替了融化层中的粒子.根据降雨过程中雨滴的尺寸分布推导了融化层中融化粒子的尺寸分布.根据Mie理论，计算了降雨率小于12.5 mm/h时，降雨融化层对5，10，35，94 GHz电磁波的雷达反射率和特征衰减因子的垂直廓线.计算结果表明，当电磁波频率高于20 GHz时，将无法观测到“雷达亮带”，这与实验结果相符.根据辐射传输理论，应用蒙特卡罗方法计算了垂直方向微观特性连续变化的降雨融化层对不同频率电磁波的反射率，比较了两种不同尺寸分布(Gamma分布和Marshall-Palmer分布)融化层反射率的差别，这为利用高频电磁波对降雨融化层进行遥感提供了理论和数值依据. 关键词： 降雨融化层 蒙特卡罗方法 后向散射 电磁波     

AO3D: A Monte Carlo code for modeling of environmental light propagation

A Monte Carlo radiative transfer program (Atmosphere-Ocean 3-Dimensional, AO3D) for modeling the coupled atmosphere-ocean environment has been developed. The code allows for the specification of optical properties for the atmosphere, land and ocean. Light rays are tracked as they pass between the atmosphere and the ocean, reflect off the ocean surface, the ocean floor, and off land, or are absorbed. In this version the polarization of light rays is not considered. The optical properties of each horizontally homogeneous layer within the atmosphere and ocean can be set on a layer-by-layer basis with a choice of phase functions, absorption and scattering coefficients, and index of refraction. A wind-dependent Cox and Munk ocean surface realization (with whitecaps) is implemented to model refraction and reflection from surface waves. Either spherical- or flat-Earth models can be used, and all refraction and reflection are accounted for. The AO3D model has been tested by parts, and as a whole by comparison with single- and total-scattering calculations from other radiative transfer codes. Comparisons with Monte Carlo calculations by Adams and Kattawar (agreement in TOA radiance within the published precision ∼2%), MODTRAN4 (agreement in spherical-shell atmosphere (SSA) sky radiance within about 2%) and Coupled DIScrete Ordinate Radiative Transfer (COART) (agreement in plane-parallel (PP) sky radiance within 2%) are shown. Sun photometer measurements (including large air mass values) at the Mauna Loa Observatory are compared to AO3D simulations (for a spherical Earth) and suggest that a thin aerosol layer was present above the observatory at the time of the measurements.     

星载多波段红外光学系统的杂散辐射分析

引入反向蒙特卡罗法与双向蒙特卡罗法对红外光学系统的杂散辐射进行分析,基于光谱辐射传递因子导出了焦平面辐射能流计算式.以某星载多波段红外光学系统为例,在检验计算可靠性的基础上,模拟了各波段辐射能从地球背景和光机内壁面到焦平面的传播过程,分析了壁面吸收率与温度的影响.结果表明,采用双向蒙特卡罗法可有效地模拟辐射能从地球向星载光学系统焦平面的传播过程,采用反向蒙特卡罗法可容易地分析光机内部热辐射的影响;光机内壁面吸收率对视场外杂散辐射的传播有很大影响,温度高于250 K的光机内壁面热辐射成为主要的杂散光源.     

高斯光束在双层云中传输的蒙特卡罗模拟

基于辐射传输理论, 利用蒙特卡罗方法模拟了无限窄(冲击函数)准直光束入射到典型水云以及冰水双层云时的后向散射特性, 进而将得到的冲击响应与高斯光束卷积, 得到高斯光束在云层中传输的多次散射特性. 文中给出了两种波束入射时水云以及冰水双层云的反射函数随径向r和天顶角α的变化关系, 并给出了光强在云层内部的二维分布图. 计算结果表明, 高斯光束入射时, 云层反射函数的特点与无限窄准直光束入射时有较大区别. 因此在利用激光雷达进行云层探测时需要考虑激光的散斑, 文中的方法可以为此提供理论依据.