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.     

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.     

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.     

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.     

Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere-ocean system

A vector radiative transfer model has been developed for a coupled atmosphere-ocean system. The radiative transfer scheme is based on the discrete ordinate and matrix operator methods. The reflection/transmission matrices and source vectors are obtained for each atmospheric or oceanic layer through the discrete ordinate solution. The vertically inhomogeneous system is constructed using the matrix operator method, which combines the radiative interaction between the layers. This radiative transfer scheme is flexible for a vertically inhomogeneous system including the oceanic layers as well as the ocean surface. Compared with the benchmark results, the computational error attributable to the radiative transfer scheme has been less than 0.1% in the case of eight discrete ordinate directions. Furthermore, increasing the number of discrete ordinate directions has produced computations with higher accuracy. Based on our radiative transfer scheme, simulations of sun glint radiation have been presented for wavelengths of 670 nm and 1.6 μm. Results of simulations have shown reasonable characteristics of the sun glint radiation such as the strongly peaked, but slightly smoothed radiation by the rough ocean surface and depolarization through multiple scattering by the aerosol-loaded atmosphere. The radiative transfer scheme of this paper has been implemented to the numerical model named Pstar as one of the OpenCLASTR/STAR radiative transfer code systems, which are widely applied to many radiative transfer problems, including the polarization effect.     

Anisotropic scattering in inhomogeneous media—1. A new representation formula for the solution of the auxiliary integral equation for the source function

A new representation formula for the solution of the auxiliary integral equation for the source function in inhomogeneous, anisotropically scattering media is presented. It involves two new functions Φ and ψ of two variables instead of the original five variables. This generalizes earlier results of Kagiwada et al. (1969) and Sobolev (1972) applicable to homogeneous atmospheres. The corresponding Bellman-Krein formula for the resolvent kernel is also derived. The present representation for the solution of Fredholm integral equations of second kind with unsymmetric kernels provides a new approach to radiative transfer in anisotropic inhomogeneous media.     

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 fast linearized pseudo-spherical two orders of scattering model to account for polarization in vertically inhomogeneous scattering-absorbing media

We calculate the reflection matrix for the first two orders of scattering in a vertically inhomogeneous, scattering-absorbing medium. We take full account of polarization and perform a complete linearization (analytic differentiation) of the reflection matrix with respect to both the inherent optical properties of the medium and the surface reflection condition. Further, we compute a scalar-vector correction to the total intensity due to the effect of polarization; this correction is also fully linearized. The solar beam attenuation has been computed for a pseudo-spherical atmosphere.Results from the two orders of scattering (2OS) model have been tested against scalar intensities for an inhomogeneous atmosphere, and against Stokes vector results for a homogeneous atmosphere. We have also performed backscatter simulations of reflected sunlight in the O₂A band for a variety of geometries, and compared our results with those from a full vector multiple scattering code. Our results are exact in the center of strong lines and most inaccurate in the continuum, where polarization is least significant. The s- and p-polarized radiances are always computed very accurately. The effect of gas absorption optical depth, solar zenith angle, viewing geometry, surface albedo and wind speed (in the case of ocean glint) on the intensity, polarization and corresponding weighting functions have been investigated. It is shown that the 2OS model provides fast and reliably accurate polarization corrections to the scalar-model radiance and weighting function fields. The model can be implemented in operational retrieval algorithms as an adjunct radiative transfer code to deal with polarization effects.     

A Monte Carlo method for 3D thermal infrared radiative transfer

A 3D Monte Carlo model for specific application to the broadband thermal radiative transfer has been developed in which the emissivities for gases and cloud particles are parameterized by using a single cubic element as the building block in 3D space. For spectral integration in the thermal infrared, the correlated k-distribution method has been used for the sorting of gaseous absorption lines in multiple-scattering atmospheres involving 3D clouds. To check the Monte-Carlo simulation, we compare a variety of 1D broadband atmospheric fluxes and heating rates to those computed from the conventional plane-parallel (PP) model and demonstrate excellent agreement between the two. Comparisons of the Monte Carlo results for broadband thermal cooling rates in 3D clouds to those computed from the delta-diffusion approximation for 3D radiative transfer and the independent pixel-by-pixel approximation are subsequently carried out to understand the relative merits of these approaches.     

Uncertainty evaluation of the spectral UV irradiance evaluated by using the UVSPEC radiative transfer model

The radiative transfer models allow calculating the spectral UV irradiance from some set of measured input quantities linked with the surface reflectivity, the solar zenith angle, the ozone column and the characteristics of clouds and aerosols. The spectral irradiance yielded by a model is influenced by errors in the measurement of the input quantities. In this paper, the influences of these errors are characterized and compared with other systematic effects through an uncertainty analysis. We evaluated the uncertainty of the spectral UV irradiance rendered by the UVSPEC model, under cloudless sky conditions. In order to express the uncertainty of the output quantities (the global, direct and diffuse irradiances) in terms of the standard uncertainties of the input quantities, we used a Monte Carlo-based uncertainty propagation technique. We found that the uncertainty of the irradiance in the UV-B part of the spectrum was strongly influenced by the uncertainty attributed to the ozone column datum. Moreover, the uncertainities associated with the aerosol parameters accounted for most of the UV-A global irradiance uncertainty; the latter increased from about 4% under low aerosol conditions, up to about 14% in case of polluted air. We conclude that the UV irradiance evaluation through radiative transfer models requires paying special attention to the assessment of the aerosols properties.     

污染云团红外辐射传输模型与红外光谱的计算机仿真

针对建立的三层结构污染云团红外辐射传输模型,采用实测场地背景和各种干扰物辐射光谱作为基本的辐射数据,对不同浓度的污染云团红外辐射光谱进行仿真.结果表明:利用实测场地背景辐射光谱和该模型仿真污染云团DMMP红外光谱,光谱在810 cm-1,920 cm-1和1 040 cm-1波段上有明显的特征峰.当模型考虑干扰物和背景辐射的变化影响时,污染云团在810 cm-1,920 cm-1和1 040 cm-1波段上的光谱特征明显减弱.仿真光谱与场地实测光谱有比较好的符合,两者的RMS误差约为1.0.     

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.     

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.     

Combining the independent pixel and point-spread function approaches to simulate the actinic radiation field in moderately inhomogeneous 3D cloudy media

A fast method is presented for gaining 3D actinic flux density fields, F_act, in clouds employing the Independent Pixel Approximation (IPA) with a parameterized horizontal photon transport to imitate radiative smoothing effects. For 3D clouds the IPA is an efficient method to simulate radiative transfer, but it suffers from the neglect of horizontal photon fluxes leading to significant errors (up to locally 30% in the present study). Consequently, the resulting actinic flux density fields exhibit an unrealistically rough and rugged structure. In this study, the radiative smoothing is approximated by applying a physically based smoothing algorithm to the calculated IPA actinic flux field.     

Scattering and emission from inhomogeneous vegetation canopy and alien target beneath by using three-dimensional vector radiative transfer (3D-VRT) equation

To solve the 3D-VRT equation for the model of spatially inhomogeneous scatter media, the finite enclosure of the scatter media is geometrically divided, in both vertical z and transversal (x,y) directions, to form very thin multi-boxes. The zeroth order emission, first-order Mueller matrix of each thin box and an iterative approach of high-order radiative transfer are applied to derive high-order scattering and emission of whole inhomogeneous scatter media. Numerical results of polarized brightness temperature at microwave frequency and under different radiometer resolutions from inhomogeneous scatter model such as vegetation canopy and alien target beneath canopy are simulated and discussed.     

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.     

The opacity coefficient method—nongray determination of inhomogeneous atmospheric extinction

The computation of radiation transmittance in nongray, inhomogeneous atmospheric models is frequently complicated by complex bands of line spectra which range in value over many orders of magnitudes and depend strongly on either or both of pressure and temperature. We present here a new opacity sampling technique which is shown to determine correctly the wavelength-averaged extinction due to path-dependent realizations of banded line spectra. The technique is easy to implement computationally and is applicable to a wide variety of atmospheric problems in which frequent iteration of the radiative transfer model is required. We consider two such instances: modeling of solar flux attenuation for use in a time-dependent planetary ionosphere model and retrieval from nadir measurements of backscattered solar irradiance. The power of the new method lies in its straightforward analytical treatment of both atmospheric inhomogeneity and spectral complexity. It is thus relevant for both retrieval and radiative transfer modeling purposes.     

Radiative transfer through an arbitrarily thick,scattering atmosphere

A method is presented for solving the equation of radiative transfer in a vertically inhomogeneous planetary atmosphere. The method, based on the spherical harmonics expansion, can be used to compute models with an arbitrarily large optical thickness and any scattering phase function. It is extremely efficient, requiring the equivalent of only two matrix multiplications per layer. This efficiency combined with its stability makes the method useful for computing realistic models of planetary atmospheres. To illustrate the range of validity of this method, we compute the plane albedo from model atmospheres containing clouds with optical thicknesses ranging from 0 to 10⁶.     

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.     

Scattering in thick multifractal clouds, Part II: Multiple scattering

In Part I of this paper, we developed asymptotic approximations for single photon scattering in thick, highly heterogeneous, “Log-Lévy” multifractal clouds. In Part II, theoretical multiple scattering predictions are numerically tested using Monte Carlo techniques, which show that, due to long range correlations, the photon paths are “subdiffusive” with the corresponding fractal dimensions tending to increase slowly with mean optical thickness. We develop reasonably accurate statistical relations between N scatter statistics in thick clouds and single scatter statistics in thin clouds. This is explored further using discrete angle radiative transfer (DART) approach in which the radiances decouple into non-interacting families with only four (for 2-D clouds) radiance directions each. Sparse matrix techniques allow for rapid and extremely accurate solutions for the transfer; the accuracy is only limited by the spatial discretization.By “renormalizing” the cloud density, we relate the mean transmission statistics to those of an equivalent homogeneous cloud. This simple idea is remarkably effective because two complicating effects act in contrary directions: the “holes” which lead to increased single scatter transmission and the tendency for multiply scattered photons to become “trapped” in optically dense regions, thus decreasing the overall transmission.