A 3D implementation of ray tracing combined with diffraction on facets: Verification and a potential application

A 3D implementation of a new model of light scattering applicable to dielectric faceted objects is introduced. The model combines standard geometric optics with diffraction on individual facets. It can be applied to any faceted geometry. The model adds no significant computational overheads to classical geometric optics yet provides much improved results. Initial results for long hexagonal columns are compared to SVM and appear favourable. 2D scattering patterns are calculated for a hexagonal column in a fixed orientation and compared to those created by ice analogue crystals in the laboratory with close agreement. The comparison includes the observation of a guided wave propagating along the length of the column. The new model is then applied to a selection of geometries to illustrate how it could be used to aid particle characterization, particularly in the case of cirrus ice.     

A simple new radiative transfer model for simulating the effect of cirrus clouds in the microwave spectral region

The upwelling atmospheric radiation in the millimeter wave spectral range is influenced by the presence of cirrus clouds. A plane parallel radiative transfer model which can take into account the effect of multiple scattering by ice particles in the cirrus has been developed and is used to simulate the brightness temperatures as they would be measured by a satellite instrument. The model uses an iterative procedure to solve the radiative transfer equation. The formulation of the model is such that it can easily be adapted to treat the full specific intensity vector instead of just the scalar total intensity. A convergence test for the model is explained and two cirrus cloud scenarios are simulated. The results illustrate the linearity of microwave radiative transfer for not too strong cirrus clouds in this frequency region.     

三波长激光雷达拟合卷云的粒子形状

卷云在全球出现的概率可达30%,其散射特性在气候模式、光辐射传输和遥感领域都具有非常重要的意义。卷云的散射特性主要由冰晶粒子形状、尺度谱、折射率等因素所决定。利用355, 532和1 064 nm三个波长激光雷达数据反演卷云的后向散射系数颜色比,利用模拟计算获得不同形状冰晶粒子的卷云在上述三个波长上的后向散射系数颜色比,通过拟合得出被测卷云的冰晶粒子形状。拟合结果表明,合肥上空卷云中冰晶粒子大部分可能呈聚合物状。     

卷云短波红外辐射特性

 采用离散纵标法耦合大气分子吸收,模拟计算了卷云大气的反射特性。研究了在短波波段卷云辐射性质随波长、卷云光学厚度、卷云有效尺度、云高和卷云中冰晶粒子形状等的变化关系,分析了卷云对大气红外背景辐射的影响。结果表明：在2.7 μm的水汽强吸收带上,卷云的出现明显增强了该波段的大气背景辐射,反射率随光学厚度和云高增大而增大。     

On the reflection and polarisation properties of ice cloud

A number of cirrus ice crystal scattering models are tested using measurements of total reflectance and polarised reflectance obtained from the space-based polarisation and directionality of Earth's reflectances (POLDER) instrument. In this paper, 1 day of global POLDER data is utilised taken from the 25 June 2003 to test the assumed ice crystal models. The POLDER instrument is able to test the validity of various ice crystal models since it can measure the total reflectance and polarised reflectance at up to 14 different viewing directions almost simultaneously between the scattering angles of about 60–180°. It is found that ice crystal models that are randomised (in this case the randomisation element is through distortion) from some pristine ice crystal geometry best fit simultaneous measurements of total and polarised reflectance. The optimal distortion parameter that best describes the POLDER measurements is found to be 0.40, which has been applied to a randomly oriented six-branched bullet-rosette and randomly oriented chain-like aggregate. Moreover, distorted ice crystals that have undergone significant distortions beyond 0.40 may fit the total reflectance measurements but not the polarisation measurements. Therefore, total reflectance measurements by themselves do not provide sufficient information to constrain assumed complex/distorted ice crystal models.     

Influence of particle orientation on retrieving cirrus cloud properties by use of total and polarized reflectances from satellite measurements

The influence of ice crystal orientation was investigated on retrieving cirrus optical thickness (τ) and aspect ratio of ice crystals (Q) from satellite measurements using the total and polarized reflectances at a wavelength of . We considered columnar and plate like hexagonal ice crystals whose long axes are randomly oriented in the horizontal plane (2D model) with some amplitude of oscillation expressed by a Gaussian distribution function with the standard deviation of σ.The retrieved τ and Q values significantly depend on the assumption of σ, in particular for the plate type. Furthermore, the relationship between σ and the retrieved values depends on the solar, satellite, and target geometries. In our case study, for one target area, τ value retrieved using the 2D model with σ=5° was approximately twice larger than that using the 2D model with σ=20°, while the retrieved Q value was not significantly influenced by σ. For another target area, the τ(Q) retrieved using the 2D model with σ=5° was about 1.5 (1.8) times larger than that retrieved using the 2D model with σ=20°.     

Temperature dependence of ice optical constants: Implications for simulating the single-scattering properties of cold ice clouds

For a spectrum from ultraviolet to microwave and a temperature range from 160 to 270 K, the optical constants of water ice are compiled on the basis of the Kramers-Kronig relation in conjunction with existing datasets reported in literature. Significant temperature dependence is observed in both the mid-infrared and longer wavelengths. A sensitivity study at wavelengths in the infrared split window region indicates that the temperature dependence of the single-scattering properties of ice crystals is not negligible. Thus, it is necessary to take into account the temperature dependence of ice optical constants when simulating the radiative properties of cirrus clouds for various applications to remote sensing under cirrus cloud conditions.     

Scattering matrices for horizontally oriented ice crystals

Scattering matrices for horizontally oriented ice crystals are calculated with a code based on the geometric optics. The main physical regularities inherent to the scattering matrices are discussed. Degree of polarization of the scattered light is shown to be a qualitative criterion of number of photon trajectories that contribute effectively to the scattered light. The inverse scattering problem of retrieving aspect ratios of the horizontally oriented hexagonal ice plates from polarization of the scattered light in the bistatic sounding scheme has been proposed and discussed.     

Radiative properties of cirrus clouds in the infrared (8–13 μm) spectral region

Atmospheric radiation in the infrared (IR) 8–13 μm spectral region contains a wealth of information that is very useful for the retrieval of ice cloud properties from aircraft or space-borne measurements. To provide the scattering and absorption properties of nonspherical ice crystals that are fundamental to the IR retrieval implementation, we use the finite-difference time-domain (FDTD) method to solve for the extinction efficiency, single-scattering albedo, and the asymmetry parameter of the phase function for ice crystals smaller than 40 μm. For particles larger than this size, the improved geometric optics method (IGOM) can be employed to calculate the asymmetry parameter with an acceptable accuracy, provided that we properly account for the inhomogeneity of the refracted wave due to strong absorption inside the ice particle. A combination of the results computed from the two methods provides the asymmetry parameter for the entire practical range of particle sizes between 1 and 10,000 μm over the wavelengths ranging from 8 to 13 μm. For the extinction and absorption efficiency calculations, several methods including the IGOM, Mie solution for equivalent spheres (MSFES), and the anomalous diffraction theory (ADT) can lead to a substantial discontinuity in comparison with the FDTD solutions for particle sizes on the order of 40 μm. To overcome this difficulty, we have developed a novel approach called the stretched scattering potential method (SSPM). For the IR 8–13 μm spectral region, we show that SSPM is a more accurate approximation than ADT, MSFES, and IGOM. The SSPM solution can be further refined numerically. Through a combination of the FDTD and SSPM, the extinction and absorption efficiencies are computed for hexagonal ice crystals with sizes ranging from 1 to 10,000 μm at 12 wavelengths between 8 and 13 μm.

Calculations of the cirrus bulk scattering and absorption properties are performed for 30 size distributions obtained from various field campaigns for midlatitude and tropical cirrus cloud systems. Ice crystals are assumed to be hexagonal columns randomly oriented in space. The bulk scattering properties are parameterized through the use of second-order polynomial functions for the extinction efficiency and the single-scattering albedo and a power-law expression for the asymmetry parameter. We note that the volume-normalized extinction coefficient can be separated into two parts: one is inversely proportional to effective size and is independent of wavelength, and the other is the wavelength-dependent effective extinction efficiency. Unlike conventional parameterization efforts, the present parameterization scheme is more accurate because only the latter part of the volume-normalized extinction coefficient is approximated in terms of an analytical expression. After averaging over size distribution, the single-scattering albedo is shown to decrease with an increase in effective size for wavelengths shorter than 10.0 μm whereas the opposite behavior is observed for longer wavelengths. The variation of the asymmetry parameter as a function of effective size is substantial when the effective size is smaller than 50 μm. For effective sizes larger than 100 μm, the asymmetry parameter approaches its asymptotic value. The results derived in this study can be useful to remote sensing studies of ice clouds involving IR window bands.