Scattering in thick multifractal clouds, Part I: Overview and single scattering

Over the last twenty years, many studies have been made of radiative transfer in scaling cloud fields, the vast majority of which have been limited to numerical studies in clouds with relatively small optical thickness. An exception to this was the development of a formalism for treating single scattering in optically thick but conservative multifractal clouds without significant holes. In part I of this paper we show how these results can be extended to general “universal” multifractal clouds dominated by low density “Lévy holes”. In part II, we demonstrate how the analytic single scattering results can be generalized to multiple scattering including the case of very thick clouds as well as to realistic nonconservative clouds.     

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.     

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.     

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.     

Representation of the photon pathlength distribution in a cloudy atmosphere using finite elements

A new method to derive the photon pathlength probability density function with respect to the photon geometrical path (PDF-GP) is proposed in this paper. This method is based on a finite elements fit of the true PDF-GP using a step function with equidistant intervals. The new method is evaluated based on reference PDF-GPs derived via Monte-Carlo radiative transfer simulations for different single and multilayer clouds with and without surface albedo. The finite elements method was found to perform better than classical Laplace inversion techniques. For the case of two-layer clouds with a thin cirrus cloud (optical thickness 0.5) above a low-level cloud, it is shown that the finite elements method is able to separate the contribution of both cloud layers to the total radiance and, in principle, allows to simultaneously infer cloud top heights of both cloud layers given that enough independent radiance observations at different gas absorption optical depths are taken.     

High-speed observation of cavitation bubble clouds near a tissue boundary in high-intensity focused ultrasound fields

Cavitation bubble clouds generated near a tissue boundary by high-intensity focused ultrasound (HIFU) were studied using high-speed photography. In all, 171 image series were captured during the initial 100 ms of continuous HIFU exposure, which showed that cavitation bubble clouds at the tissue boundary organized into two structures - “cone-shape bubble cloud structure” recorded in 146 image series and “crown-shape bubble cloud structure” recorded in 18 image series. The remaining 7 image series showed the interchanging of these two structures. It was found that when cavitation bubbles first appeared at the tissue boundary, they developed to cone-shape bubble cloud. The cone-shape bubble cloud structure was characterized by a nearly fixed tip in front of the tissue boundary. When the cavitation bubbles initially appeared away from the tissue boundary they evolved into a crown-shape bubble cloud. Deformation of tissue boundary was shown in all the recorded image series.     

On the retrieval of ice cloud particle shapes from POLDER measurements

Shapes of ice crystals can significantly affect the radiative transfer in ice clouds. The angular distribution of the polarized reflectance over ice clouds strongly depends on ice crystal shapes. Although the angular-distribution features of the total or polarized reflectance over ice clouds imply a possibility of retrieving ice cloud particle shapes by use of remote sensing data, the accuracy of the retrieval must be evaluated. In this study, a technique that applies single ice crystal habit and multidirectional polarized radiance to retrieve ice cloud particle shapes is assessed. Our sensitivity studies show that the retrieved particle shapes from this algorithm can be considered good approximations to those in actual clouds in calculation of the phase matrix elements. However, this algorithm can only work well under the following conditions: (1) the retrievable must be overcast and thick ice cloud pixels, (2) the particles in the cloud must be randomly oriented, (3) the particle shapes and size distributions used in the lookup tables must be representative, and (4) the multi-angle polarized measurements must be accurate and sufficient to identify ice cloud pixels of randomly oriented particles. In practice, these conditions will exclude most of the measured cloud pixels. Additionally, because the polarized measurements are only sensitive to the upper cloud part not deeper than an optical thickness of 4, the retrieved particle shapes with the polarized radiance may only approximate those in the upper parts of the clouds. In other words, for thicker clouds with vertical inhomogeneity in particle shapes, these retrieved particle shapes cannot represent those of whole clouds. More robust algorithm is needed in accurate retrieval of ice cloud particle shapes.     

Validation of the community radiative transfer model

To validate the Community Radiative Transfer Model (CRTM) developed by the U.S. Joint Center for Satellite Data Assimilation (JCSDA), the discrete ordinate radiative transfer (DISORT) model and the line-by-line radiative transfer model (LBLRTM) are combined in order to provide a reference benchmark. Compared with the benchmark, the CRTM appears quite accurate for both clear sky and ice cloud radiance simulations with RMS errors below 0.2 K, except for clouds with small ice particles. In a computer CPU run time comparison, the CRTM is faster than DISORT by approximately two orders of magnitude. Using the operational MODIS cloud products and the European Center for Medium-range Weather Forecasting (ECMWF) atmospheric profiles as an input, the CRTM is employed to simulate the Atmospheric Infrared Sounder (AIRS) radiances. The CRTM simulations are shown to be in reasonably close agreement with the AIRS measurements (the discrepancies are within 2 K in terms of brightness temperature difference). Furthermore, the impact of uncertainties in the input cloud properties and atmospheric profiles on the CRTM simulations has been assessed. The CRTM-based brightness temperatures (BTs) at the top of the atmosphere (TOA), for both thin (τ<5) and thick (τ>30) clouds, are highly sensitive to uncertainties in atmospheric temperature and cloud top pressure. However, for an optically thick cloud, the CRTM-based BTs are not sensitive to the uncertainties of cloud optical thickness, effective particle size, and atmospheric humidity profiles. On the contrary, the uncertainties of the CRTM-based TOA BTs resulting from effective particle size and optical thickness are not negligible in an optically thin cloud.     

激光在准球形边界卷云中传输的衰减和透过特性

高空卷云主要由各种不同形状的冰晶粒子组成,是地空链路上激光信号传输的重要影响因素。依据高空卷云中冰晶粒子的分布特征和散射特性,采用C版本的离散纵标法（CDISORT）,充分考虑地球球形曲率及云层冰晶粒子多次散射影响因素,研究准球形边界云层的激光透过率和衰减特性,并比较了太阳天顶角不同时平面平行模式和准球面模式下卷云大气激光透过率的差异,数值计算了三种激光波长（0.65,1.06和3.8 μm）在卷云中传输时的衰减和透过特性。计算结果表明：较小太阳天顶角（小于80°）入射时,两种模式下卷云大气激光透过率相对误差很小,其中0.65 μm激光波长入射时两种模式下的相对误差仅为1.72%,较大太阳天顶角（大于80°）入射时,两种模式下卷云大气激光透过率相对误差明显增大,0.65 μm激光波长入射时两种模式下的相对误差最大达到69%;卷云粒子单次散射时,激光在云层的衰减与卷云粒子有效半径、传输距离、光学厚度及激光波长等因素有关,随光学厚度的增加,云层的激光透过率减少,1.06 μm激光波长入射时透过率最大,3.8 μm激光波长入射时透过率最小;0.65和1.06 μm激光波长入射时,随云层粒子有效半径的增加激光透过率逐渐增加,而3.8 μm波长激光,随云层粒子有效半径的增加激光透过率逐渐减少,随相对方位角的增加,云层的激光透过率减少,且不同卷云传输模型对激光透过率也存在不同的影响。该研究工作将为开展地空链路星载、机载激光通信、激光雷达探测等工程系统中的激光信号云层传输特性的应用提供理论支持,同时也可进一步拓展为地空链路激光遥感、制导和预警等应用提供预先理论研究基础。     

Lidar Multiple Scattering in Water Droplet Clouds: Toward an Improved Treatment

Although it has long been recognized that the effects of photon multiple scattering generally need to be accounted for in the analysis of lidar cloud returns, this is a difficult problem and current approaches are still rudimentary. The multiple scattering process is controlled by the size of the lidar beamwidth and the distance to the cloud, which jointly determine the lidar footprint, but cloud microphysical content (i.e., particle size, concentration, and shape) exerts a strong influence on the range distribution and depolarization of the returned energy. Since clouds are inherently inhomogeneous with height, it is our premise that vertically homogeneous cloud simulations based on idealized particle size distributions lead to misleading results. We offer a more realistic approach based on the contents of growing water droplet clouds predicted by a sophisticated adiabatic cloud model, which are offered for use as new standard vertically-inhomogeneous cloud models. Lidar returned signal and depolarization profiles derived from our analytical double-scattering method are given for inter-comparison purposes.Presented at the 7th International Workshop on Multiple Scattering Lidar/Light Experiments (MUSCLE7), July 21–23 1994, Chiba, Japan.     

Radiative transfer with internal reflection via the converged discrete ordinates method

In response to the challenge of establishing highly accurate solutions to the plane layer radiative transfer equation with the simplest of methods, the converged discrete ordinates method is presented. With this algorithm of only finite difference, quadrature and acceleration, we show how to obtain highly accurate intensities for radiative transfer in a finite layer with internal surface reflection. The method features angular smoothing and angular interpolation through “faux” quadrature. In addition, a manufactured solution demonstrates the high accuracy of the method for forward peaked scattering. We consider scattering in a heterogeneous medium as a final demonstration.     

Photon and axion splitting in an inhomogeneous magnetic field

The axion–photon system in an external magnetic field, when the direction of propagation of axions and photons is orthogonal to the direction of the external magnetic field, displays a continuous axion–photon duality symmetry in the limit the axion mass is neglected. The conservation law that follow in this effective (2+1)$(2+1)$-dimensional theory from this symmetry is obtained. The magnetic field interaction is seen to be equivalent to first order to the interaction of a complex charged field with an external electric potential, where this fictitious “electric potential” is proportional to the external magnetic field. This allows one to solve for the scattering amplitudes using already known scalar QED results. From the scalar QED analog the axion and the photon are symmetric and antisymmetric combinations of particle and antiparticle. If one considers therefore scattering experiments in which the two spatial dimensions of the effective theory are involved nontrivially, one observes that both particle and antiparticle components of photons and axions are preferentially scattered in different directions, thus producing the splitting or decomposition of the photon and axion into their particle and antiparticle components in an inhomogeneous magnetic field. This observable in principle effect is of first order in the axion–photon coupling, unlike the “light shining through a wall phenomena”, which is second order.     

Quantitative optical techniques for dense sprays investigation: A survey

The experimental study of dense sprays by optical techniques poses many challenges and no methods have proven to be completely reliable when accurate quantitative data are required, for example to validate breakup models and CFD simulations. The present survey is aimed to a critical analysis of optical techniques capable to provide quantitative and reliable data in dense sprays and to point out the conditions necessary to safely obtain such measurements. A single parameter, the optical depth, is proposed to quantify the concept of dense spray and to indicate when multiple scattering becomes predominant and could make the experimental results questionable. Many available optical techniques are divided into two categories: the “classical” ones, like PDA, LDV, PIV, etc., that work well in dilute sprays but show many limitations in dense sprays, and the “emerging” ones more suitable for dense sprays. Among the last ones, those considered more promising are discussed in detail. A number of significant applications are also presented and discussed to better clarify the nature of such complex problem and the feasibility of the new proposed approaches.     

Vibration transmission between coupled plates using finite element methods and statistical energy analysis. Part 2: The effect of window apertures in masonry flanking walls

Part 1 of this paper demonstrated the validity of predictions of vibration transmission across junctions of masonry walls using Finite Element Methods (FEM). Part 2 uses numerical experiments with FEM to calculate the vibration transmission between masonry walls with window apertures at different positions in the flanking wall(s). Results from the numerical experiments are used to assess a simple “rule-of-thumb” estimate for calculating the change in the coupling parameters due to the introduction of an aperture into a flanking wall. Conclusions are drawn concerning use of the “rule-of-thumb” estimate for the coupling loss factor in Statistical Energy Analysis and the vibration reduction index in European standard EN 12354.     

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.     

Single transverse spin asymmetry of prompt photon production

We study the single transverse spin asymmetry of prompt photon production in high energy proton–proton scattering. We include the contributions from both the direct and fragmentation photons. While the asymmetry for direct photon production receives only the Sivers type of contribution, the asymmetry for fragmentation photons receives both the Sivers and Collins types of contributions. We make a model calculation for quark-to-photon Collins function, which is then used to estimate the Collins asymmetry for fragmentation photons. We find that the Collins asymmetry for fragmentation photons is very small, thus the single transverse spin asymmetry of prompt photon production is mainly coming from the Sivers asymmetry in direct and fragmentation photons. We make predictions for the prompt photon spin asymmetry at RHIC energy, and emphasize the importance of such a measurement. The asymmetry of prompt photon production can provide a good measurement for the important twist-three quark–gluon correlation function, which is urgently needed in order to resolve the “sign mismatch” puzzle.     

Modification of radiation pressure due to cooperative scattering of light

Cooperative spontaneous emission of a single photon from a cloud of N atoms modifies substantially the radiation pressure exerted by a far-detuned laser beam exciting the atoms. On one hand, the force induced by photon absorption depends on the collective decay rate of the excited atomic state. On the other hand, directional spontaneous emission counteracts the recoil induced by the absorption. We derive an analytical expression for the radiation pressure in steady-state. For a smooth extended atomic distribution we show that the radiation pressure depends on the atom number via cooperative scattering and that, for certain atom numbers, it can be suppressed or enhanced. Cooperative scattering of light by extended atomic clouds can become important in the presence of quasi-resonant light and could be addressed in many cold atoms experiments.     

A method for estimating optical properties of dusty cloud

Based on the scattering properties of nonspherical dust aerosol, a new method is developed for retrieving dust aerosol optical depths of dusty clouds. The dusty clouds are defined as the hybrid system of dust plume and cloud. The new method is based on transmittance measurements from surface-based instruments multi-filter rotating shadowband radiometer （MFRSR） and cloud parameters from lidar measurements. It uses the difference of absorption between dust aerosols and water droplets for distinguishing and estimating the optical properties of dusts and clouds, respectively. This new retrieval method is not sensitive to the retrieval error of cloud properties and the maximum absolute deviations of dust aerosol and total optical depths for thin dusty cloud retrieval algorithm are only 0.056 and 0.1, respectively, for given possible uncertainties. The retrieval error for thick dusty cloud mainly depends on lidar-based total dusty cloud properties.     

相态对冰水混合云微观特性反演的影响研究

当云层的温度在－40℃~0℃之间时, 云层中会存在冰和水两种相态的云滴, 其散射特性与纯水云以及纯冰云特性有较大差异, 因此遥感反演混合相云层的微观和宏观物理特性具有重要的意义。本文采用冰水双层球模型模拟了冰水混合云中的云滴, 利用Mie理论计算了纯水、纯冰和冰水颗粒的单次散射特性, 分析了单次散射相函数, 不对称因子, 单次散射反照率等随着有效半径、相态、内外半径比等的变化特性。利用离散纵标法(DISORT)计算了水云和冰云对0.75 μm、2.16 μm和3.3 μm的双向反射函数, 讨论了利用纯水滴和纯冰滴反演冰水混合云滴的误差。分析结果表明, 利用0.75 μm和2.16 μm的太阳光反演冰水混合云的光学厚度和有效半径时, 光学厚度误差较大, 有效半径误差较小; 结合0.75 μm和3.3 μm的太阳光反演冰水混合云的光学厚度和有效半径时, 光学厚度误差较小, 有效半径误差较大, 其会高估其有效半径; 另外结合0.75 μm和3.3 μm这两个波长的反射函数反演冰水云的冰水混合比更为有效。