Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Scalar case

We present a discrete-ordinate algorithm using the matrix-exponential solution for pseudo-spherical radiative transfer. Following the finite-element technique we introduce the concept of layer equation and formulate the discrete radiative transfer problem in terms of the level values of the radiance. The layer quantities are expressed by means of matrix exponentials, which are computed by using the matrix eigenvalue method and the Padé approximation. These solution methods lead to a compact and versatile formulation of the radiative transfer. Simulated nadir and limb radiances for an aerosol-loaded atmosphere and a cloudy atmosphere are presented along with a discussion of the model intercomparisons and timings.     

大气折射对可见光波段辐射传输特性的影响

折射是影响辐射传输的重要因素. 为分析大气折射对辐射传输的影响, 基于Monte Carlo方法, 给出了考虑大气折射的矢量辐射传输模型, 实现了均匀气层和耦合面处光子随机运动过程的模拟, 实现了直射光及漫射光Stokes矢量、偏振度和辐射通量等参数的计算. 在考虑和不考虑大气折射两种条件下, 验证了模型的准确性; 在纯瑞利散射条件下, 讨论了大气折射对不同方向漫射光Stokes矢量的影响; 在不同太阳天顶角、大气廓线、气溶胶及含云大气条件下, 分析了大气折射对辐射传输过程的影响. 结果表明: 大气折射对漫射光Stokes矢量的影响主要体现在天顶角70°–110°区间, 且随着太阳入射角增大, 其影响更为显著; 不同大气廓线情形下, 大气折射对Stokes矢量的影响不一致, 其原因是不同大气廓线对应的折射率廓线存在差异. 含云及含气溶胶大气条件下, 大气折射对辐射传输的影响变弱, 沙尘型及海盐型气溶胶条件下, 折射对辐射传输的影响强于可溶型气溶胶情形; 不同形状气溶胶条件下, 大气折射对辐射传输的影响也存在显著差异; 不同云高条件下, 大气折射对漫射光Stokes矢量的影响无显著差异, 但随着云光学厚度增大, 大气折射的影响减弱.     

Integration of Chandrasekhar's integral equation

We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA “explicitly” in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness.     

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.     

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.     

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.     

空间遥感仪器探测器工作温度对信噪比的影响分析

临边观测是一种新的空间大气遥感探测方式,但大气散射光谱辐射随临边高度的增加而迅速减弱。所以信噪比是临边遥感仪器的关键性能指标。在深入分析典型仪器信号光谱辐射传输特性和噪声来源的基础上建立了随探测器制冷温度变化的信噪比模型,并在一台临边遥感光谱仪原理样机上模拟试验验证了空间环境下临边高度70km处的信噪比,理论分析和实验结果一致表明:探测器制冷到一定温度时,仪器的信噪比达到了一个极限值。在综合考虑功耗、散热等问题的基础上获得了探测器的最优工作温度。     

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.     

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.     

On the accuracy of double scattering approximation for atmospheric polarization computations

Interpretation of multi-angle spectro-polarimetric data in remote sensing of atmospheric aerosols requires fast and accurate methods of solving the vector radiative transfer equation (VRTE). The single and double scattering approximations could provide an analytical framework for the inversion algorithms and are relatively fast; however accuracy assessments of these approximations for the aerosol atmospheres in the atmospheric window channels have been missing. This paper provides such analysis for a vertically homogeneous aerosol atmosphere with weak and strong asymmetry of scattering. In both cases, the double scattering approximation gives a high accuracy result (relative error ～0.2%) only for the low optical path ～10^?2. As the error rapidly grows with optical thickness, a full VRTE solution is required for the practical remote sensing analysis. It is shown that the scattering anisotropy is not important at low optical thicknesses neither for reflected nor for transmitted polarization components of radiation.     

Influence of the vertical profile of Saharan dust on the visible direct radiative forcing

The vertical profile of Saharan dust in the atmosphere is generally characterized by a large aerosol concentration in the mid troposphere, differently from the climatological distribution of other types of particles, that show a peak at the surface and a rapid decrease with height. Saharan dust is also characterized by particles of relatively large size of irregular shape, and variable values of the single scattering albedo (the ratio between radiation scattering and extinction). The dust's peculiar vertical distribution is expected to produce an effect on the calculation of the direct aerosol radiative forcing at the surface and at the top of the atmosphere. This effect is investigated by comparing estimates of aerosol direct visible radiative forcing at the surface and at the top of the atmosphere for dust vertical profiles measured in the Mediterranean, and for the climatological profile. The radiative forcing is estimated by means of an accurate radiative transfer model, and for the ocean surface. The sensitivity of the results on the solar zenith angle, aerosol optical depth, and aerosol absorption is also investigated. The aerosol radiative forcing at the surface shows a very small dependency on the aerosol vertical profile. At the top of the atmosphere, the radiative forcing is weakly dependent on the vertical profile (up to 10% variation on the daily average forcing) for low absorbing particles; conversely, it shows a strong dependency (the daily radiative forcing may vary up to 100%) for absorbing particles. The top of the atmosphere visible radiative forcing efficiency produced by dust having single scattering albedo <0.7 is higher by 4 W m⁻² when the observed vertical profile instead of the standard profile is used in the calculations (i.e. it produces a lower cooling). For values of the single scattering albedo around 0.67, the sign of the forcing depends on the vertical profile. The influence of the vertical distribution on the radiative forcing is largest at small values of the solar zenith angle, and at short wavelengths.     

气溶胶对大气CO_2短波红外遥感探测影响的模拟分析

气溶胶引起的光学路径长度改变是影响高分辨率近红外光谱反演大气CO_2浓度的重要误差源.本文利用高精度大气辐射传输模式模拟中国碳卫星观测,结合CALIPSO(Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations)卫星的气溶胶廓线产品研究了不同特性的气溶胶对卫星观测光谱的影响.模拟结果显示:气溶胶散射引起的光学路径长度改变与气溶胶类型、模态以及垂直分布密切相关;城市型和海洋型气溶胶对观测光谱影响很大;多层分布的积聚模态大陆型和海洋型气溶胶在光学厚度小于0.3时,会引起5%以内的负辐射变化,随光学厚度不断增加会引起正的辐射变化;主要以粗粒子模态存在的气溶胶在不同的垂直分布情况下均会引起辐射的负变化,从而造成CO_2浓度的高估;另外,随气溶胶分布高度变高,负的辐射变化程度会逐渐减小.     

Improving the description of sunglint for accurate prediction of remotely sensed radiances

The bidirectional reflection distribution function (BRDF) of the ocean is a critical boundary condition for radiative transfer calculations in the coupled atmosphere-ocean system. Existing models express the extent of the glint-contaminated region and its contribution to the radiance essentially as a function of the wind speed. An accurate treatment of the glint contribution and its propagation in the atmosphere would improve current correction schemes and hence rescue a significant portion of data presently discarded as “glint contaminated”. In current satellite imagery, a correction to the sensor-measured radiances is limited to the region at the edge of the glint, where the contribution is below a certain threshold. This correction assumes the sunglint radiance to be directly transmitted through the atmosphere. To quantify the error introduced by this approximation we employ a radiative transfer code that allows for a user-specified BRDF at the atmosphere-ocean interface and rigorously accounts for multiple scattering. We show that the errors incurred by ignoring multiple scattering are very significant and typically lie in the range 10-90%. Multiple reflections and shadowing at the surface can also be accounted for, and we illustrate the importance of such processes at grazing geometries.     

Radiative transfer in finite participating atmospheric aerosol media

The properties of radiation transfer through a plane-parallel atmospheric aerosol medium has been studied. It has been done by employing Mie theory to calculate the radiation transfer scattering parameters of the medium in the form of extinction, scattering, and absorption efficiencies. Then, the equation of radiative transfer through a plane-parallel atmosphere of aerosol has been solved for partial heat fluxes using two different analytical techniques, namely, the Variational Pomraning -Eddington approximation and Galerkin technique. Average efficiencies over log-normal and modified gamma size distributions are calculated. Therefore, the radiative properties of Carbon, Anthracite, Bituminous, Lignite, and Fly ash have been calculated. The obtained numerical results show very good agreement with each other in addition to the previous published work.     

Transmission of radiation through an aerosol medium

The properties of radiation through an aerosol medium have been achieved. This has been done by employing Mie scattering theory to calculate the radiation transfer scattering parameters in the form of extinction, absorption and scattering efficiencies. The equation of radiative transfer for the heat flux through a plane parallel atmosphere of aerosol has been solved. The aerosol size distributions are found in practical systems. Average efficiencies over size distribution for spherical particles of complex refractive index are calculated. Therefore, the radiative properties of stratospheric aerosols have been done. The obtained results found to be in a good agreement with the previous work.     

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.     

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.     

海洋气溶胶多光谱偏振特性研究

为提高海洋气溶胶的反演精度,定量研究了气溶胶在可见近红外波段的多光谱偏振辐射特性。首先建立了合理的海洋气溶胶及海面模型,基于逐次散射法准确模拟了光在气溶胶中及大气—海洋交界面处的矢量辐射传输过程,接着从光谱角度定量分析了典型波段处的反射率和偏振反射率,在此基础上提出了海洋气溶胶偏振辐射的光谱分布模型,并用卫星数据对模型进行验证,最后研究了气溶胶光学厚度、观测角度、海水叶绿素a浓度和海面风速对气溶胶多光谱偏振辐射的影响。研究表明,在可见近红外波段不考虑大气吸收和耀斑效应时,气溶胶偏振辐射的光谱变化符合幂函数模型;在不同波段处,海洋气溶胶的偏振辐射受海水叶绿素a浓度和海面风速的影响不同;海洋气溶胶的多光谱偏振辐射信息有效体现了气溶胶的自身特性,且与反射率相比,偏振反射率随各因素的变化存在更明显的谱段差异性。因此,可以运用气溶胶的多光谱偏振信息反演海洋气溶胶参数,多光谱探测的加入对提高气溶胶反演精度具有重要意义。     

The Role of Aerosols in Light Scattering in the Atmosphere

This paper addresses the important role of how aerosols play in light scattering in the earth’s atmosphere and how their characteristics can be retrieved. It is shown here, by referring to typical aerosol types, that more than a half of the atmospheric light is scattered by aerosols, and the aerosol optical properties can be estimated in terms of the scattering behavior. It is also confirmed that aerosol retrieval can be accurately determined by combining polarization and radiance data.Presented at the 7th International Workshop on Multiple Scattering Lidar/Light Experiments (MUSCLE7), July 21–23 1994, Chiba, Japan.