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An ice crystal single-scattering property database is developed in the microwave spectral region (1 to 874 GHz) to provide the scattering, absorption, and polarization properties of 12 ice crystal habits (10-plate aggregate, 5-plate aggregate, 8-column aggregate, solid hexagonal column, hollow hexagonal column, hexagonal plate, solid bullet rosette, hollow bullet rosette, droxtal, oblate spheroid, prolate spheroid, and sphere) with particle maximum dimensions from 2 µm to 10 mm. For each habit, four temperatures (160, 200, 230, and 270 K) are selected to account for temperature dependence of the ice refractive index. The microphysical and scattering properties include projected area, volume, extinction efficiency, single-scattering albedo, asymmetry factor, and six independent nonzero phase matrix elements (i.e. P 11 , P 12 , P 22 , P 33 , P 43 and P 44 ). The scattering properties are computed by the Invariant Imbedding T-Matrix (II-TM) method and the Improved Geometric Optics Method (IGOM). The computation results show that the temperature dependence of the ice single-scattering properties in the microwave region is significant, particularly at high frequencies. Potential active and passive remote sensing applications of the database are illustrated through radar reflectivity and radiative transfer calculations. For cloud radar applications, ignoring temperature dependence has little effect on ice water content measurements. For passive microwave remote sensing, ignoring temperature dependence may lead to brightness temperature biases up to 5 K in the case of a large ice water path. [ABSTRACT FROM AUTHOR]

To derive the bulk radiative properties of ice clouds, aircraft contrails and snow grains, which are fundamental to atmospheric radiative transfer calculations in downstream applications, it is necessary to accurately simulate the scattering of light by individual ice particles. An ice particle optical property database reported in 2013 (hereafter, TAMUice2013) is updated (hereafter, TAMUice2016) to incorporate recent advances in computation of the optical properties of nonspherical particles. Specifically, we employ the invariant imbedding T-matrix (II-TM) method to compute the optical properties of particles with small to moderate size parameters. Both versions use the Improved Geometric Optics Method (IGOM) to compute the optical properties of large ice crystals, but TAMUice2016 improves the treatment of inhomogeneous waves inside the scattering particles in the case where ice is absorptive such as at infrared wavelengths. To bridge the gap between the extinction efficiencies computed from the II-TM and the IGOM, TAMUice2016 includes spectrally dependent higher order terms of the edge effect in addition to the first order counterpart considered in TAMUice2013. Furthermore, the differences between TAMUice2013 and TAMUice2016 are quantified with respect to the computation of the bulk optical properties of ice clouds. [ABSTRACT FROM AUTHOR]

Constructing an appropriate particle morphology model is essential for realistic simulation of optical properties of atmospheric particles. This paper presents a model for generating surface roughness based on a combination of methods from discrete differential geometry combined with a stochastic partial differential equation for surface evolution introduced by Edwards and Wilkinson. Scattering of light by roughened particles is simulated using the Invariant Imbedding T-Matrix (II-TM) method. The effects of surface roughness on the single-scattering properties, namely, the phase matrix, asymmetry factor, and extinction efficiency, are investigated for a single wavelength in the visible range and for a range of size parameters up to x =50. Three different smooth shapes are considered: spherical, spheroidal, and hexagonal, the latter two in just the “compact particle” case of unit aspect ratio. It is shown that roughness has negligible effects on the optical scattering properties for size parameters less than 20. For size parameters ranging from 20 to 50, the phase matrix elements are more sensitive to the surface roughness than are two important integral optical properties, the extinction efficiency and asymmetry factor. As has been seen in studies using other forms of roughening, the phase function is progressively smoothed as roughness increases. The effect on extinction efficiency is to increase it, and on asymmetry factor is to decrease it. Each of these effects is relatively modest in the size range considered, but the trend of results suggests that greater effects will be seen for size parameters larger than ones considered here. [ABSTRACT FROM AUTHOR]

Abstract: The invariant imbedding T-matrix method (II-TM) is employed to compute the optical properties of randomly oriented ice crystals of various shapes including hexagonal columns, hollow columns, droxtals, bullet rosettes and aggregates. The II-TM is shown to be numerically stable and capable of obtaining the single-scattering properties of hexagonal ice crystals with size parameters up to 150. The 22° and 46° halo peaks in the phase function of compact hexagonal ice crystals begin to emerge at a size parameter of approximately 80 and tend to become insensitive to particle size as the corresponding size parameter approaches 150. Furthermore, the II-TM solutions are shown to be in agreement with their counterparts based on the discrete dipole approximation (DDA) method and the pseudo-spectral time-domain (PSTD) method. In addition, the accuracy of the improved geometric-optics method (IGOM) is examined for randomly oriented hexagonal ice crystal cases over a wide size-parameter range from the resonant to geometric-optics regimes. The II-TM is also used to study the effects of particle surface roughness and internal inclusions on the single-scattering properties of ice particles. [Copyright &y& Elsevier]

Abstract: The conventional Lorenz–Mie theory is generalized for a case when the light source is partially spatially coherent. The influence of the degree of coherence of the incident field on the generalized Mueller matrix and the spectral degree of coherence of the scattered light is analytically studied by using the vector field instead of the scalar field to extend previous results on the angular intensity distribution. The results are compared with the Mueller matrix obtained from the Discrete Dipole Approximation (DDA) method, which is an average over an ensemble of stochastic incident beams. Special attention is paid to the Mueller matrix elements in the backward direction, and the results show some Mueller matrix elements, such as P22, depend monotonically on the coherence length of the incident beam. Therefore, detecting back scattering Mueller matrix elements may be a promising method to measure the degree of coherence. The new formalism is applied to cases of large spherical droplets in water clouds and hexagonal ice crystals in cirrus clouds. The corona and glory phenomena due to spheres and halos associated with hexagonal ice crystals are found to disappear if the incident light tends to be highly incoherent. [Copyright &y& Elsevier]

Abstract: A new physical-geometric optics hybrid (PGOH) method is developed to compute the scattering and absorption properties of ice particles. This method is suitable for studying the optical properties of ice particles with arbitrary orientations, complex refractive indices (i.e., particles with significant absorption), and size parameters (proportional to the ratio of particle size to incident wavelength) larger than ∼20, and includes consideration of the edge effects necessary for accurate determination of the extinction and absorption efficiencies. Light beams with polygon-shaped cross sections propagate within a particle and are traced by using a beam-splitting technique. The electric field associated with a beam is calculated using a beam-tracing process in which the amplitude and phase variations over the wavefront of the localized wave associated with the beam are considered analytically. The geometric-optics near field for each ray is obtained, and the single-scattering properties of particles are calculated from electromagnetic integral equations. The present method does not assume additional physical simplifications and approximations, except for geometric optics principles, and may be regarded as a “benchmark” within the framework of the geometric optics approach. The computational time is on the order of seconds for a single-orientation simulation and is essentially independent of the size parameter. The single-scattering properties of oriented hexagonal ice particles (ice plates and hexagons) are presented. The numerical results are compared with those computed from the discrete-dipole-approximation (DDA) method. [Copyright &y& Elsevier]

Abstract: The scattering of light by dielectric particles much larger than the wavelength of incident light is attributed to diffraction, external reflection and outgoing refracted waves. This paper focuses on diffraction and external reflection by faceted particles, which can be calculated semi-analytically based on physical optics. Three approximate methods; the surface-integral method (SIM), the volume-integral method (VIM), and the diffraction plus reflection pattern from ray optics (DPR) are compared. Four elements of the amplitude scattering matrix in the SIM and the VIM are presented in an explicit form. Of interest is that diffraction and external reflection are separable in the SIM, whereas they are combined in the VIM. A feature of zero forward reflection is noticed in the SIM. The applicability of the DPR method is restricted to particles with random orientations. In the manner of van de Hulst, we develop a new technique to compute the reflection pattern of randomly oriented convex particles using spheres with the same refractive index, resulting in an improvement in the precision of the reflection calculation in near-forward and near-backward directions. The accuracy of the aforementioned three methods is investigated by comparing their results with those from the discrete-dipole-approximation (DDA) method for hexagonal particles at the refractive index of 1.3+i1.0. For particles with fixed orientations, it is found that the SIM and the VIM are comparable in accuracy and applicable when the size parameter is on the order of 20. The ray-spreading effect on the phase function is evident from the results of various size parameters. For randomly oriented particles, the DPR is more efficient than the SIM and the VIM. [ABSTRACT FROM AUTHOR]

Inclusions of air bubbles or soot particles have significant effects on the single-scattering properties of ice crystals, effects that in turn have significant impacts on the radiation budget of an atmosphere containing the crystals. This study investigates some of the single-scattering effects in the case of hexagonal ice crystals, including effects on the backscattering depolarization ratio, a quantity of practical importance in the interpretation of lidar observations. One distinguishing feature of the study is an investigation of scattering properties at a visible wavelength for a crystal with size parameter ( x ) above 100, a size regime where one expects some agreement between exact methods and geometrical optics methods. This expectation is generally borne out in a test comparison of how the sensitivity of scattering properties to the distribution of a given volume fraction of included air is represented using (i) an approximate Monte Carlo Ray Tracing (MCRT) method and (ii) a numerically exact pseudo-spectral time-domain (PSTD) method. Another distinguishing feature of the study is a close examination, using the numerically exact Invariant-Imbedding T-Matrix (II-TM) method, of how some optical properties of importance to satellite remote sensing vary as the volume fraction of inclusions and size of crystal are varied. Although such an investigation of properties in the x >100 regime faces serious computational burdens that force a large number of idealizations and simplifications in the study, the results nevertheless provide an intriguing glimpse of what is evidently a quite complex sensitivity of optical scattering properties to inclusions of air or soot as volume fraction and size parameter are varied. [ABSTRACT FROM AUTHOR]

Abstract: This note reports on the effects of the polarization state of an incident quasi-monochromatic parallel beam of radiation and the orientation of a hexagonal ice particle with respect to the incident direction on the extinction process. When the incident beam is aligned with the six-fold rotational symmetry axis, the extinction is independent of the polarization state of the incident light. For other orientations, the extinction cross-section for linearly polarized light can be either larger or smaller than its counterpart for an unpolarized incident beam. Therefore, the attenuation of a quasi-monochromatic radiation beam by an ice cloud depends on the polarization state of the beam if ice crystals within the cloud are not randomly oriented. Furthermore, a case study of the extinction of light by a quartz particle is also presented to illustrate the dependence of the extinction cross-section on the polarization state of the incident light. [Copyright &y& Elsevier]