Linearization of radiative transfer with respect to surface properties

The linearization of radiative transfer with respect to surface properties in the UV and visible part of the solar spectrum is presented. The proposed method is a rigorous extension of the radiative perturbation theory with respect to surface properties. Given the forward and adjoint intensity field, analytical expressions are provided for the linearization of any observable related to the radiation field with respect to surface properties characterized by Minnaert's and Lambertian bidirectional reflection distribution function. For the considered surface reflection characteristics, we also discuss an extension of the reduction approach of Chandrasekhar as an alternative linearization method. The suitability of both approaches for the combined retrieval of trace gas and surface properties from the backscattered sunlight in the UV and visible part of the spectrum is discussed. The authors come to the conclusion that the perturbation theory, for this purpose, represents the superior method because of its general applicability to any parameter characterizing the optical properties of the atmosphere and the underlying surface.     

VLIDORT: A linearized pseudo-spherical vector discrete ordinate radiative transfer code for forward model and retrieval studies in multilayer multiple scattering media

We describe a new vector discrete ordinate radiative transfer model with a full linearization facility. The VLIDORT model is designed to generate simultaneous output of Stokes vector light fields and their derivatives with respect to any atmospheric or surface property. We develop new implementations for the linearization of the vector radiative transfer solutions, and go on to show that the complete vector discrete ordinate solution is analytically differentiable for a stratified multilayer multiply scattering atmospheric medium. VLIDORT will generate all output at arbitrary viewing geometry and optical depth. The model has the ability to deal with attenuation of solar and line-of-sight paths in a curved atmosphere, and includes an exact treatment of the single scatter computation. VLIDORT also contains a linearized treatment for non-Lambertian surfaces. A number of performance enhancements have been implemented, including a facility for multiple solar zenith angle output. The model has been benchmarked against established results in the literature.     

Linearization of the interaction principle: Analytic Jacobians in the “Radiant” model

In this paper we present a new linearization of the Radiant radiative transfer model. Radiant uses discrete ordinates for solving the radiative transfer equation in a multiply-scattering anisotropic medium with solar and thermal sources, but employs the adding method (interaction principle) for the stacking of reflection and transmission matrices in a multilayer atmosphere. For the linearization, we show that the entire radiation field is analytically differentiable with respect to any surface or atmospheric parameter for which we require Jacobians (derivatives of the radiance field). Derivatives of the discrete ordinate solutions are based on existing methods developed for the LIDORT radiative transfer models. Linearization of the interaction principle is completely new and constitutes the major theme of the paper. We discuss the application of the Radiant model and its linearization in the Level 2 algorithm for the retrieval of columns of carbon dioxide as the main target of the Orbiting Carbon Observatory (OCO) mission.     

低太阳高度角条件下的天空偏振模式模拟及大气折射影响研究

为模拟低太阳高度角条件下的天空偏振模式,自主开发了考虑大气球形几何及大气折射效应的辐射传输模式VSPART,并将其运用于漫射光偏振特性仿真.在模式中,基于射线追踪法实现了光线传播轨迹的追踪和入射光偏振态及透过率的计算,基于矩阵算法实现了辐射传输方程的求解.将VSPART模拟结果与基准值、SPDISORT模拟值进行了比较,验证了模型的准确性.在瑞利散射大气和含气溶胶大气条件下,模拟并分析了漫射光偏振度及偏振方向的分布特征,讨论了大气球形几何及折射效应对天空偏振度的影响.结果表明,低太阳高度角条件下,随着波长增加,瑞利散射大气对应的偏振度整体随之增强,中性点向大天顶角方向移动;气溶胶的存在并不改变天空偏振度分布特征,但对偏振方向影响显著,随着光学厚度的增加,天空偏振度值迅速降低;中性点的偏移可能与低阶散射过程紧密相关;大气球形几何和折射效应的主要影响区域为地平线区域、两中性点附近及天顶区域;瑞利散射大气条件下,随着波长增加,大气球形几何及折射效应的影响逐步减弱,特别在中性点附近及天顶区域,其影响逐步消失;随着气溶胶光学厚度的增加,其影响随之增强.     

Adjoint problem of radiative transfer for a pseudo-spherical atmosphere and general viewing geometries

We formulate the adjoint radiative transfer for a pseudo-spherical atmosphere and various retrieval scenarios. The single scattering radiance is computed in a spherical atmosphere by using the source integration technique, while for the multiple scattering radiance we formulate an one-dimensional adjoint radiative transfer equation in a plane-parallel atmosphere. The adjoint solution of the radiative transfer equation is obtained by employing the discrete ordinate method with matrix exponential. We provide an abbreviated derivation of our formalism as well as a discussion of the numerical implementation of the theory.     

Radiative heat transfer between two concentric spheres separated by a two-phase mixture of non-gray gas and particles using the modified discrete-ordinates method

The radiative heat transfer between two concentric spheres separated by a two-phase mixture of non-gray gas and a cloud of particles is investigated by using the combined finite-volume and discrete-ordinates method, named modified discrete-ordinates method (MDOM), which integrates the radiative transfer equation (RTE) over a control volume and a control angle simultaneously like in the finite-volume method (FVM) and treats the angular derivative terms due to spherical geometry as the conventional discrete-ordinates method (DOM). The radiative properties involving non-gray gas and particle behavior are modeled by using the extended weighted sum of gray gases model (WSGGM) with particles. Mathematical formulation and final discretization equations for the RTE are introduced by considering the behavior of a two-phase mixture of non-gray gas and particles in a spherically symmetric concentric enclosure. The present approach is validated by comparing with the results of previous works including gray and non-gray radiative heat transfer. Finally, a detailed investigation of the radiative heat transfer with non-gray gases and/or a two-phase mixture is conducted to examine the dependence of the radiative heat transfer upon temperature ratio between inner and outer spherical enclosure, particle concentration, and particle temperature.     

The spatial polarization distribution over the dome of the sky for abnormal irradiance of the atmosphere

The paper deals with the polarized radiative transfer within a slab irradiated by a collimated infinitely wide beam of arbitrary polarized light. The efficiency of the proposed analytical solution lies in the assumption that the complete vectorial radiative transfer solution is the superposition of the most anisotropic and smooth parts, computed separately. The vectorial small-angle modification of the spherical harmonics method is used to evaluate the anisotropic part, and the vectorial discrete ordinates method is used to obtain the smooth one. The azimuthal expansion is used in order to describe the light field spatial distribution for the case of abnormal irradiance and to obtain some known neutral points in the sky especially useful for polarized remote sensing of the atmosphere.     

辐射传输中的一个伪极限问题及其数学物理原理

当太阳入射角度和观测角都趋向于水平时,由平面平行大气辐射传输方程计算得到的大气顶的反射辐射值不唯一,其值依赖于太阳和观测角的趋近于水平方向的路径曲线,即从数学角度称为出现极限的不唯一或极限不连续.事实上这违背了辐射场物理原理,这种不连续是由于常规算法中忽略了大气辐射传输中一个隐含的物理原理而导出的.在极限条件下必须引入满足Snell光学定律的界面边界条件,否则会导致错误的结论. 关键词： 辐射传输 局地热力学平衡 大气光学 Snell定律     

Photon conservation in scattering by large ice crystals with the SASKTRAN radiative transfer model

The scattering of visible light by ice crystals and dust in radiative transfer models is challenging in part due to the large amount of scattering in the forward direction. We introduce a technique that ensures numerical conservation of photons in any radiative transfer model and that quantifies the integration error associated with highly asymmetric phase functions. When applied to a successive-orders of scatter model, the technique illustrates the high accuracy obtained in numerical integration of molecular and aerosol scattering. As well, a phase function truncation and renormalization technique is applied to scattering by ice crystals with very large size parameters, between 100 and 1000, and the scaled radiative transfer equation is solved with the spherical successive-orders model, SASKTRAN. Since computations shown this work are performed in a fully spherical model atmosphere, the computed radiances are not subject to the discontinuity at the horizon that is inherent in models using a plane–parallel assumption. The methods introduced in this work are of particular interest in modeling limb radiances in the presence of thin cirrus clouds.     

Comparison between radiative transfer theory and the simplified spherical harmonics approximation for a semi-infinite geometry

In this study, the third-order simplified spherical harmonics equations (SP3), an approximation of the radiative transfer equation, are solved for a semi-infinite geometry considering the exact simplified spherical harmonics boundary conditions. The obtained Green's function is compared to radiative transfer calculations and the diffusion theory. In general, it is shown that the SP3 equations provide better results than the diffusion approximation in media with high absorption coefficient values but no improvement is found for small distances to the source.     

Adjoint sensitivity analysis of radiative transfer equation: 2. Applications to retrievals of temperature in scattering atmospheres in thermal IR

An approach to formulation of inversion algorithms for thermal sounding in the case of scattering atmosphere based on the adjoint equation of radiative transfer (Ustinov, JQSRT 68 (2001) 195, referred to as Paper 1 in the main text) is applied to temperature retrievals in the scattering atmosphere for the nadir viewing geometry. Analytical expressions for the weighting functions involving the integration of the source function are derived. Temperature weighting functions for a simple model of the atmosphere with scattering are evaluated and convergence to the case of pure atmospheric absorption is demonstrated. The numerical experiments on temperature retrievals are carried out to demonstrate the validity of the expressions obtained.     

Attenuation of solar radiation by a water mist from the ultraviolet to the infrared range

A model is developed for the hemispherical transmittance of direct and scattered solar radiation from a cloudless atmosphere by a mist layer of water droplets in order to investigate the potential of water misting systems to serve as a protection from solar irradiation with particular emphasis on harmful UV radiation. The proposed model is based on published spectral experimental data for solar irradiation, Mie theory for interaction of the radiation with single spherical droplets, and radiative transfer theory. Known limiting solutions are employed to simplify the Mie calculations. The modified two-flux approximation is used to account for both direct and diffuse irradiation in lieu of a numerical solution for the full radiative transfer equation in anisotropically scattering media. The role of the governing parameters of a disperse water curtain of water droplets, water content, and droplet size for sample conditions is studied in some detail, particularly in the near-ultraviolet part of the spectrum where radiation can result in human tissue damage.     

Recent developments in the line-by-line modeling of outgoing longwave radiation

High frequency resolution radiative transfer model calculations with the Atmospheric Radiative Transfer Simulator (ARTS) were used to simulate the clear-sky outgoing longwave radiative flux (OLR) at the top of the atmosphere. Compared to earlier calculations by Clough and coworkers the model used a spherical atmosphere instead of a plane parallel atmosphere, updated spectroscopic parameters from HITRAN, and updated continuum parameterizations from Mlawer and coworkers. These modifications lead to a reduction in simulated OLR by approximately 4.1%, the largest part, approximately 2.5%, being due to the absence of the plane parallel approximation. As a simple application of the new model, the sensitivity of OLR to changes in humidity, carbon dioxide concentration, and temperature were investigated for different cloud-free atmospheric scenarios. It was found that for the tropical scenario a 20% change in humidity has a larger impact than a doubling of the carbon dioxide concentration. The sensitive altitude region for temperature and humidity changes is the entire free troposphere, including the upper troposphere where humidity data quality is poor.     

SASKTRAN: A spherical geometry radiative transfer code for efficient estimation of limb scattered sunlight

The inversion of satellite-based observations of limb scattered sunlight for the retrieval of constituent species requires an efficient and accurate modelling of the measurement. We present the development of the SASKTRAN radiative transfer model for the prediction of limb scatter measurements at optical wavelengths by method of successive orders along rays traced in a spherical atmosphere. The component of the signal due to the first two scattering events of the solar beam is accounted for directly along rays traced in the three-dimensional geometry. Simplifying assumptions in successive scattering orders provide computational optimizations without severely compromising the accuracy of the solution. SASKTRAN is designed for the analysis of measurements from the OSIRIS instrument and the implementation of the algorithm is efficient such that the code is suitable for the inversion of OSIRIS profiles on desktop computers. SASKTRAN total limb radiance profiles generally compare better with Monte-Carlo reference models over a large range of solar conditions than the approximate spherical and plane-parallel models typically used for inversions.     

Passive remote sensing of planetary atmospheres and retrievals of atmospheric macro- and microphysical parameters

In two recent papers, referred to as Paper 1 and Paper 2 in the main text, we have pursued an idea that atmospheric weighting functions for any geophysical parameters essentially consist of two kinds of entities: weighting functions for the atmospheric radiative parameters, which directly enter the radiative transfer equation, and partial derivatives of the atmospheric radiative parameters with respect to atmospheric geophysical parameters. Corresponding analysis was performed for non-scattering and scattering planetary atmospheres for nadir-viewing geometry and thermal spectral region. In the present paper we conduct a study of the second group of above entities, the partial derivatives of atmospheric radiative parameters with respect to atmospheric geophysical parameters. Along the way, we analyze the role of radiative parameters of individual atmospheric constituents, which serve as intermediaries between the total radiative parameters of the atmosphere and its geophysical parameters. The obtained expressions, combined with radiative weighting functions, are used in the end-to-end expressions for the weighting functions obtained for various specific geophysical parameters.     

Numerical solution of the radiative transfer equation in spherically symmetric dust shells

An efficient numerical method is presented for solving problems of radiative transfer in dust shells with spherical symmetry. The method can be applied to a wide variety of radiative transfer problems in planetary atmospheres, circumstellar dust envelopes and extended stellar atmospheres. The computational procedure and practical considerations for implementing the method are described in detail. As an illustration, the method is used to determine the grain temperature distribution and far i.r. emission from interstellar dust clouds associated with compact HII regions. Generalizations to problems involving cylindrical geometry and multi-temperature dust shells are discussed in the appendices.     

Solution of the equation of transfer for coherent anisotropic scattering by double interval spherical harmonic method

The double interval spherical harmonic method introduced effectively by Wilson and Sen has already been used by Ghosh and Karanjai to solve the equation of radiative transfer in coherent isotropic scattering atmosphere, originally developed by Woolley and Stibbs. The same method has been successfully used in this paper to solve the equation of transfer for coherent anisotropic scattering.     

Simultaneous retrieval of aerosols and ocean properties: A classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model

In this paper and the sequel, we investigate the application of classic inverse methods based on iterative least-squares cost-function minimization to the simultaneous retrieval of aerosol and ocean properties from visible and near infrared spectral radiance measurements such as those from the SeaWiFS and MODIS instruments. Radiance measurements at the satellite are simulated directly using an accurate coupled atmosphere-ocean-discrete-ordinate radiative transfer (CAO-DISORT) code as the main component of the forward model. For this kind of cost-function inverse problem, we require the forward model to generate weighting functions (radiance partial derivatives) with respect to the aerosol and marine properties to be retrieved, and to other model parameters which are sources of error in the retrievals.In this paper, we report on the linearization of the CAO-DISORT model. This linearization provides a complete analytic differentiation of the coupled-media radiative transfer theory, and it allows the model to generate analytic weighting functions for any atmospheric or marine parameter. For high solar zenith angles, we give an implementation of the pseudo-spherical (P-S) approach to solar beam attenuation in the atmosphere in the linearized model. We summarize a number of performance enhancements such as the use of an exact single-scattering calculation to improve accuracy. We derive inherent optical property inputs for the linearized CAO-DISORT code for a simple 2-parameter bio-optical model for the marine environment coupled to a 2-parameter bimodal atmospheric aerosol medium.     

Radiative transfer solutions for coupled atmosphere ocean systems using the matrix operator technique

Accurate radiative transfer models are the key tools for the understanding of radiative transfer processes in the atmosphere and ocean, and for the development of remote sensing algorithms. The widely used scalar approximation of radiative transfer can lead to errors in calculated top of atmosphere radiances. We show results with errors in the order of±8% for atmosphere ocean systems with case one waters. Variations in sea water salinity and temperature can lead to variations in the signal of similar magnitude. Therefore, we enhanced our scalar radiative transfer model MOMO, which is in use at Freie Universität Berlin, to treat these effects as accurately as possible. We describe our one-dimensional vector radiative transfer model for an atmosphere ocean system with a rough interface. We describe the matrix operator scheme and the bio-optical model for case one waters. We discuss some effects of neglecting polarization in radiative transfer calculations and effects of salinity changes for top of atmosphere radiances. Results are shown for the channels of the satellite instruments MERIS and OLCI from 412.5 nm to 900 nm.