Single-scattering Properties Of Ice Crystals Research Articles

Theoretical Calculations of Directional Scattering Intensities of Small Nonspherical Ice Crystals: Implications for Forward Scattering Probes

In situ aircraft measurements of the sizes and concentrations of liquid cloud droplets and ice crystals with maximum dimensions (Dmax) less than ~50 μm have been measured mainly using forward scattering probes over the past half century. The operating principle of forward scattering probes is that the measured intensity of light scattered by a cloud particle at specific forward scattering angles can be related to the size of that particle assuming the shape and thermodynamic phase of the target are known. Current forward-scattering probes assume spherical liquid cloud droplets and use the Lorenz–Mie theory to convert the scattered light to particle size. Uncertainties in sizing ice crystals using forward scattering probes are unavoidable since the single-scattering properties of ice crystals differ from those of spherical liquid cloud droplets and because their shapes can vary. In this study, directional scattering intensities of four different aspect ratios (ARs = 0.25, 0.50, 1.00, and 2.00) of hexagonal ice crystals with random orientations and of spherical liquid cloud droplets were calculated using the discrete dipole approximation (i.e., ADDA) and Lorenz–Mie code, respectively, to quantify the errors in sizing small ice crystals and cloud droplets using current forward scattering probes and to determine the ranges of optimal scattering angles that would be used in future forward scattering probes. The calculations showed that current forward scattering probes have average 5.0% and 17.4% errors in sizing liquid cloud droplets in the forward (4–12°) and backward (168–176°) direction, respectively. For measurements of hexagonal ice crystals, average sizing errors were 42.1% (23.9%) in the forward (backward) direction and depended on the ARs of hexagonal ice crystals, which are larger than those for liquid cloud droplets. A newly developed size conversion table based on the calculated single-scattering properties of hexagonal ice crystals using the ADDA reduced the sizing errors for the hexagonal ice crystals down to 14.2% (21.9%) in the forward (backward) direction. This study is a purely theoretical examination of the operating principle of forward scattering probes and there are several limitations, such as assumed hexagonal ice crystals with smooth surfaces and random orientations.

Q-space analysis of light scattering by ice crystals

Q-space analysis is applied to extensive simulations of the single-scattering properties of ice crystals with various habits/shapes over a range of sizes. The analysis uncovers features common to all the shapes: a forward scattering regime with intensity quantitatively related to the Rayleigh scattering by the particle and the internal coupling parameter, followed by a Guinier regime dependent upon the particle size, a complex power law regime with incipient two dimensional diffraction effects, and, in some cases, an enhanced backscattering regime. The effects of significant absorption on the scattering profile are also studied. The overall features found for the ice crystals are similar to features in scattering from same sized spheres.

Light scattering by hexagonal ice crystals with distributed inclusions

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.

An efficient algorithm for simulation of stochastic scattering cross-sections

We present an efficient algorithm for uncertainty quantification of scattering cross-sections of stochastic configurations comprising multiple two dimensional sound-soft particles whose locations and orientations are random. Our algorithm has two components. Firstly, we use a high order generalised polynomial chaos approximation of the stochastic cross-sections in the random variables that requires realisation of the exterior sound propagation model for high order quadrature sampling parameters. For each such realisation, we use an efficient spectrally accurate algorithm for deterministic scattering simulations based on solving a boundary integral equation reformulation of the acoustic model. We present numerical results for a stochastic configuration of particles with rough surfaces. Our numerical result demonstrate the high order accuracy of both components of the algorithm for simulation of moments of the scattering cross-section of the configuration. References M. Abramowitz and I. Stegun. Handbook of Mathematical Functions. Dover Publications, New York, 1970. A. Baren. From the single-scattering properties of ice crystals to climate prediction: A way forward. Atmospheric Research, 112:45--69, 2012. doi:10.1016/j.atmosres.2012.04.010. D. Colton and R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. Springer, 1998. M. Ganesh and I. G. Graham. A high-order algorithm for obstacle scattering in three dimensions. J. Comput. Phys., 198:211--242, 2004. doi:10.1016/j.jcp.2004.01.007. M. Ganesh and S. C. Hawkins. A high-order algorithm for multiple electromagnetic scattering in three dimensions. Numer. Algorithms, 50:469--510, 2009. doi:10.1007/s11075-008-9238-z. M. Ganesh and S. C. Hawkins. A stochastic pseudospectral and T-matrix algorithm for acoustic scattering by a class of multiple particle configurations. J. Quant. Spectrosc. Radiat. Transfer, 2013 (in press). doi:10.1016/j.jqsrt.2013.01.011. O. P. Le Maitre and O. M. Kino. Spectral Methods for Uncertainty Quantification. Springer, 2010. H. C. van de Hulst. Light Scattering by Small Particles. Dover, 1957.

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.

Uncertainties Associated With the Surface Texture of Ice Particles in Satellite-Based Retrieval of Cirrus Clouds—Part I: Single-Scattering Properties of Ice Crystals With Surface Roughness

Surface roughness of ice crystals is a morphological parameter important to the scattering characteristics of these particles. The intent of this paper, reported in two parts (hereafter, Parts I and II), is to investigate the accuracy associated with some simplifications in calculating the single-scattering properties of roughened ice crystals and to quantify the effect of surface roughness on the retrieval of the optical and microphysical properties of ice clouds from satellite observations. In Part I, two ray-tracing schemes, a rigorous algorithm and an approximate algorithm with a simplified treatment of surface roughness, are employed to calculate the single-scattering properties of randomly oriented hexagonal ice crystals with size parameters in the geometric optics regime. With the rigorous approach, it requires substantial computational effort to accurately account for the multiple external reflections between various roughness facets and the reentries of outgoing rays into the particles in the ray-tracing computation. With the simplified ray-tracing scheme, the ray-tracing calculation for roughened particles is similar to that for smooth particles except that, in the former case, the normal of the particle surface is statistically perturbed for each reflection-refraction event. The simplified ray-tracing scheme can account for most the effects of surface roughness on particle single-scattering properties without incurring substantial demand on computational resources and, thus, provides an efficient way to compute the single-scattering properties of roughened particles. The effect of ice-crystal surface roughness on the retrieval of the optical thicknesses and effective particle sizes of cirrus clouds is reported in Part II.

Parameterization of the Radiative Properties of Cirrus Clouds

Abstract A new approach for parameterization of the broadband solar and infrared radiative properties of ice clouds has been developed. This parameterization scheme integrates in a coherent manner the δ-four-stream approximation for radiative transfer, the correlated k-distribution method for nongray gaseous absorption, and the scattering and absorption properties of hexagonal ice crystals. A mean effective size is used, representing an area-weighted mean crystal width, to account for the ice crystal size distribution with respect to radiative calculation. Based on physical principles, the basic single-scattering properties of ice crystals, including the extinction coefficient divided by ice water content single-scattering albedo, and expansion coefficients of the phase function, can be parameterized using third-degree polynomials in terms of the mean effective size. In the development of this parameterization the results computed from a light scattering program that includes a Geometric ray-tracing progr...