Experimental and theoretical analyses on the microwave backscattering ability and differential radar reflectivity of non-spherical hydrometeors

This paper experimentally and theoretically examines the scattering properties of simulated non-spherical hydrometeors including water oblates, ice oblates and ice sphere-cone-oblates, in terms of the backscattering cross-section and the differential reflectivity. The experimental measurements of the backscattering cross-sections of non-spherical hydrometeor samples were performed in the Electromagnetic Scattering Laboratory of China National Space Industrial Corporation. Meanwhile, the backscattering cross-sections have been computed with the transition (T) matrix method. The theoretical results are compared with the experimental data, showing that the calculations are consistent with the observations in general. Experimental and theoretical analyses indicate that the backscattering cross-section of non-spherical particles increases as the particle size parameter increases, and fluctuates when the sizes are larger under the effect of resonance scattering. Differential reflectivity Z_DR of water oblates in natural rainfall is always greater than 0 dB whereas Z_DR of hailstones may be negative. There is a good linear relationship between differential reflectivity and aspect ratio of a particle. These derivations agree with the literature and can be used to identify the presence of hail particles and distinguish between plate-type and columnar-type hydrometeors. In this study, the measuring experiment and the T-matrix method calculations for the scattering of simulated raindrop and ice particles are also briefly described.     

Effect of instrumental particle sizing resolution on the modelling of aerosol radiative parameters

A more realistic estimation of the scattering and hemispheric backscattering coefficients, σ_sp and σ_bsp, and their respective optical cross section, C_sca and C_bk, of aerosol particles is presented on the basis of the exact resolution of the width of the size bins of the particle counter instruments when size distribution measurements are used, and, with the exact optical detector instruments ability. The scattering and hemispheric backscattering cross sections, C_sca and C_bk, of the particles are averaged over the full size bins of the particle counter instrument, while these quantities are usually estimated only on the value of the mean geometric diameter of each size bin. Six instruments, the APS, ASASP-X, DMPS, FSSP-100, ELPI, and SMPS frequently used in particle size distribution measurements are reviewed, for spherical sea-salt particles at a wavelength λ=0.55 μm. The comparison using the conventional geometric mean diameter versus the use of the full size bin leads to large amount of errors for the optical cross section with non-negligible effects on their respective optical coefficients. The maximal accuracy expected for these optical quantities depend on the particle diameter as well as on the channel width of the instruments, and are also function of the angular detector probe used to measure them.     

The impact of ice particle roughness on the scattering phase matrix

The goal of this study is to explore the influence of ice particle habit (or shape) and surface roughness on the scattering phase matrix. As an example, reported here are the results for two wavelengths: 0.67 and 1.61 μm. For this effort, a database of single-scattering properties has been computed for a set of habits including hexagonal plates, hollow and solid columns, hollow and solid 3D bullet rosettes, droxtals, aggregates of solid columns, and aggregates of plates. The database provides properties for each of the habits at 101 wavelengths between 0.45 and 2.24 μm for smooth, moderately roughened, and severely roughened particles. At each wavelength, the scattering properties are provided at 233 discrete particle diameters ranging from 2 to 10,000 μm. A single particle size distribution from a very cold ice cloud sampled during the CRYSTAL-FACE field campaign (T_cld=–76 °C) is used to illustrate the influence of habit and roughness on the phase matrix. In all, four different habit mixtures are evaluated. The nonzero elements of the phase matrix are shown to be quite sensitive to the assumed habit, particularly in the case of ?P₁₂/P₁₁ that is associated with the degree of linear polarization of scattered radiation. Surface roughness is shown to smooth out maxima in the scattering phase function and in the other elements of the phase matrix, consistent with other studies. To compare with the theoretical simulations of the phase matrix for smooth and roughened particles, a full year of cloud-aerosol lidar with orthogonal polarization (CALIOP) data from 2008 is analyzed to provide global statistics on the values of P₁₁ and P₂₂/P₁₁ in the backscattering direction. In a comparison of two of the habit mixtures (one used for MODIS Collection 5 and another that incorporates new habits including hollow bullet rosettes and aggregates of plates) with the CALIOP data, the values for P₁₁ are higher regardless of the degree of particle surface roughness, and the values for P₂₂/P₁₁ are lower than those for CALIOP. Further investigation is warranted to better understand this discrepancy.     

Light scattering properties of sea-salt aerosol particles inferred from modeling studies and ground-based measurements

Direct climate radiative forcing depends on the aerosol optical depth τ, the single scattering albedo ?, and the up-scatter fraction β; these quantities are functions of the refractive index of the particles, their size relative to the incident wavelength, and their shape. Sea-salt aerosols crystallize into cubic shapes or in agglomerates of cubic particles under low relative humidity conditions. The present study investigates the effects of the shape of dried sea-salt particles on the detection of light scattering from the particles. Ground-based measurements of scattering and backscattering coefficients have been performed with an integrating nephelometer instrument for a wavelength . The measurements are compared to two models: the Mie theory assuming a spherical shape for the particles and the Discrete Dipole Approximation (DDA) model for the hypothesis of cubic shape of the sea-salt aerosols. The comparison is made accurately by taking into account the actual range of the scattering angles measured by the nephelometer in both models that is from 7° to 170° for the scattering coefficient and from 90° to 170° for the backscattering coefficient. Modeled scattering and backscattering coefficients increase for nonspherical particles compared to spherical shape of particles with diameter larger than about 1 μm. However, the comparison of the modeling results with the measurements gives best agreement for particles diameter less than about 1 μm. The size distribution of the particles is measured with two instruments with different size bins: an electrical low-pressure impactor (ELPI) and an aerodynamic particle sizer (APS). It is found that the size of the bins of the instruments to determine the number concentration of the particles in accordance with their diameter is critical in the comparison of measurements with modeling.     

Radar polarimetry of Saturn's rings: Modeling ring particles as fractal aggregates built of small ice monomers

We analyze ground-based radar polarimetric observations of Saturn's rings at a wavelength of 12.6 cm by employing the model of a vertically and horizontally plane-parallel homogeneous slab composed of clumpy particles in the form of fractal aggregates of small ice monomers. Our model takes full account of the effects of polarization, multiple scattering, and coherent backscattering. Using efficient superposition T-matrix and vector radiative transfer codes, we perform computations of the backscattering circular polarization ratio for fractal aggregates generated with a cluster–cluster aggregation model and having the following characteristics: monomer refractive index m=1.78+i0.003; monomer packing density p=0.2; fractal dimensions D_f=2.5 and 3; and overall fractal radii R in the range 4?R?10 cm. In order to obtain physically realistic values of single-scattering properties of the aggregates we perform averaging over an ensemble of clusters generated for the same values of fractal parameters but having different geometrical configurations of the monomers. We conclude that in the framework of the above morphological model of Saturn's rings and the specific cluster–cluster aggregation procedure, it may be problematic to obtain a satisfactory and realistic agreement between theoretical computations and the observed values of the radar circular polarization ratio.     

Flame propagation of nano/micron-sized aluminum particles and ice (ALICE) mixtures

Flame propagation of aluminum–ice (ALICE) mixtures is studied theoretically and experimentally. Both a mono distribution of nano aluminum particles and a bimodal distribution of nano- and micron-sized aluminum particles are considered over a pressure range of 1–10 MPa. A multi-zone theoretical framework is established to predict the burning rate and temperature distribution by solving the energy equation in each zone and matching the temperature and heat flux at the interfacial boundaries. The burning rates are measured experimentally by burning aluminum–ice strands in a constant-volume vessel. For stoichiometric ALICE mixtures with 80 nm particles, the burning rate shows a pressure dependence of r_b = aPⁿ, with an exponent of 0.33. If a portion of 80 nm particles is replaced with 5 and 20 μm particles, the burning rate is not significantly affected for a loading density up to 15–25% and decreases significantly beyond this value. The flame thickness of a bimodal-particle mixture is greater than its counterpart of a mono-dispersed particle mixture. The theoretical and experimental results support the hypothesis that the combustion of aluminum–ice mixtures is controlled by diffusion processes across the oxide layers of particles.     

The scattering matrix of transparent particles of random shape in the geometrical optics approximation

A numerical model that allows one to calculate elements of the scattering matrix for transparent particles of random shape in the geometrical optics approximation is presented. It is shown that a deviation from sphericity, which, in particular, is modeled by a reduction of the number of triangular facets approximating a sphere, essentially affects the magnitude, position, and width of peaks of the photometric and polarimetric indicatrices. Thus, when 1500 facets were used for the approximation, the amplitude of the polarimetric peak associated with the first rainbow, which is located close to the scattering angle 160°, decreases by a factor of two. Calculations showed that, in the region of backscattering, for particles of an arbitrary shape, the linear polarization ?F ₁₂/F ₁₁ has no negative branch, which is well observed for spherical particles. In going from spherical to nonspherical particles, the backscattering peak also disappears. The indicatrices for particles of irregular shape that were calculated for small distances from the center of a particle noticeably differ from the indicatrices at infinity. Thus, when simulating multiple scattering in dense powderlike media, the use of particle scattering indicatrices that were calculated for infinite distances is incorrect even in the geometrical optics approximation.     

Polarization of light backscattered by small particles

We study scattering of light by wavelength-scale spherical, cubic, and spheroidal particles as well as clusters of spherical particles for equal-volume-sphere size parameters 4≤x≤10 and refractive indices 1.1≤m≤2.0. Such particles exhibit three specific features in the regime of backscattering: first, the intensity shows a backscattering peak; second, the degree of linear polarization for unpolarized incident light is negative; and, third, the depolarization ratio is double-lobed. We find that the overall characteristics of the scattering-matrix elements can be explained by an internal field composed of waves propagating in opposite directions near the particle perimeter and forming standing waves, as well as a wave propagating forward with the wavelength of the internal medium. When moving from the central axis of the particle toward its perimeter, the internal field changes from a forward-propagating wave with a wavelength dictated by the particle refractive index toward a standing wave with an apparent wavelength of the surrounding medium. The mapping of the internal field to the scattered far field is like an interference dial where rotation of the dial by a quarter of a wavelength on the particle perimeter results in a change from a destructive to constructive interference feature in the angular patterns (or vice versa). The dial is a manifestation of a well-known rule of thumb: the number of maxima or minima in the scattering-matrix elements is given by the size parameter. We explain the backscattering peak as deriving from the backward-propagating internal wave near the particle perimeter. Negative polarization follows from the spatial asymmetry of the internal fields: inside the particle, the fields are amplified near the central plane perpendicular to the polarization state of incident light, resulting in more pronounced interference effects for the perpendicular polarization than for the parallel polarization. The double-lobe feature in the depolarization results from the same internal-field structure with leading cross-polarized fields located slightly different from the copolarized fields. We discuss practical implications of these findings for the retrieval of particle sizes, shapes, and refractive indices from observations and laboratory experiments.     

Interpretation of photo-polarimetric observations of comet 17P/Holmes

We present multispectral photo-polarimetric observations of comet 17P/Holmes taken at three different dates. These observations show the evolution of the negative polarization branch (NPB) as a function of time and wavelength. We perform discrete-dipole approximation (DDA) simulations on agglomerated debris particles of various sizes and refractive indices. Our simulations show that the observations are consistent with the cloud being composed of agglomerated debris particles having refractive indices of approximately m=1.5-1.6+0.1i. Our results are also consistent with the particles obeying a power-law size distribution r^-a and having a lower particle-radius cut-off of approximately 0.6 μm, where the index a∼3.5 for the early observations and shrinks to a∼1.5 for the later observations. This is consistent with the smaller, more accelerated particles in the distribution being propelled out of the field of view.     

On the relation between inclusive and exclusive p⊥ distributions

Inclusive and exclusive scattering is studied within an impact parameter framework. It is shown that the inclusive p_⊥ distribution at a fixed value of c.m. longitudinal momentum, p_6;, is governed only by the impact parameter structure of the observed particle. Next we introduce to each of the produced particles a radius, which is assumed to be independent of all the other particles, including those in the initial state. This enables us, at a fixed value of p₆, to relate the elastic πN, KN and NN data, at lab momenta of less than 20 GeV, to the pion, kaon, proton and antiproton inclusive p_⊥ distributions at ISR energies.     

DDA simulations of light scattering by small irregular particles with various structure

We present DDA investigations of light scattering by irregular particles whose size is comparable with wavelength. We consider four types of randomly irregular particles: strongly damaged spheres, rough-surface spheres, pocked spheres, and agglomerated debris particles. Each type of particle is generated with a well defined algorithm producing an ensemble of stochastically different particles that have a common origin. The different types of irregular particles produce different angular dependencies of intensity and linear polarization degree. Transformation of phase curves of intensity and polarization with changing size parameter for irregular particles tends to be more monotonic, unlike spheres. We find that the magnitude of the negative polarization branch (NPB) tends to shrink as particle absorption increases; whereas, the maximal value and position of the positive polarization branch tends to increase. The most frequently observed shape of the negative polarization at small phase angles is asymmetric with a shift of the minimum position towards the angle of polarization sign inversion. All types of considered irregular particles reveal such asymmetry at x<10. Symmetric negative polarization branches occur seldom. The necessary conditions for their appearance are a relatively large size parameter x?10 to 12 and low absorption.     

Particle size Effects on Optical Transport through strongly scattering media

Measurements of transmission and enhanced backscattering from powder beds of α-AI ₂O₃ consisting of particles with different average sizes are reported. The values of the mean free path and the absorption length, as inferred from these measurements, are compared and good agreement between the two measurement is found when the internal reflections are properly taken into account. A particle size measurement method is suggested on the basis of the linear dependence found experimentally between the transport mean free path and the mean particle size.     

Analysis of arsenic range distributions in silicon

MeV⁴He ion backscattering and differential sheet resistivity measurements were made on As implants into silicon at room temperature. Analysis of backscattering measurements yields the projected rangeR _p and projected standard deviation ΔR _p . Over the energy range of 50 to 250 keV, the values ofR _p are found to agree well with LSS theoretical predictions; however, values of ΔR _p are systematically higher than theoretical calculations. Backscattering and differential sheet resistivity measurements on samples annealed at 950°C are in general agreement and indicate diffusional broadening of the profile.     

Novel neon-hydrate of cubic ice structure

The stability of ice I cubic (ice I_c) whose voids are occupied by neon particles is investigated using a hybrid type of isobaric grand-canonical Monte Carlo simulation. We show that the resulting neon hydrate is stable under high pressure and temperature where ice I_c alone is unstable, suggesting the existence of a novel neon hydrate of ice I_c. We also show through chemical potential calculation that the neon hydrate of the ice I_c structure is more favorable than the neon hydrate of the ice II structure, whose existence was proven from experiment under high pressure condition.     

Performance of discrete dipole approximation for prediction of amplitude and phase of electromagnetic scattering by particles

Electromagnetic scattering provides useful signatures for nonintrusive particle characterization. Scattered wave which carries characteristic information about particles is identified completely by its intensity, polarization state and phase. Recent developments in measurement techniques have enabled measurement of phase of the scattered wave which is a source of additional information about particles. In the present study, accuracy of discrete dipole approximation (DDA) in predicting amplitude and phase of scattered wave is investigated via publicly available DDSCAT code by Draine and Flatau, which is a well-established tool for DDA and has found wide range of applications in the literature due to its flexibility. DDSCAT routine is modified to enable accurate computation of phase of complex amplitude scattering matrix (ASM) elements as well as their magnitude. DDA method was implemented by using lattice dispersion relation for dipole polarizabilities, generalized prime factor algorithm for fast-Fourier transformation and pre-conditioned bi-conjugate gradient method with stabilization for the solution of the complex linear system of equations. Accuracy of ASM elements predicted by DDA is assessed on single sphere problems with various size parameters and refractive indices by validation against Mie theory solutions. Excellent agreement between predictions and exact solutions proves the reliability of the modified DDSCAT code for prediction of amplitude and phase of scattered electromagnetic wave. Applicability conditions and requirements of the present DDA application to ensure accurate prediction of complete set of scattering parameters are mapped for single spheres, on an extensive domain of size parameters and refractive indices. A correlation is presented to estimate the magnitude and phase errors associated with given size parameter, refractive index and cubic lattice subdivision. Assessment of computational time requirements for different optical constants shows that implementation of DDA with the present specifications is unfeasible for size parameters larger than 4 when Re(m)>2 and Im(m)<0.1 at the same time, due to slow convergence rate.     

Highlights of the beam energy scan from STAR

The first part of the beam energy scan (BES) program at RHIC was successfully completed in the years 2010 and 2011. First STAR results from particle yield measurements are in good agreement with previously published data from SPS and AGS experiments whereas other results like azimuthal HBT and K/?? event-by-event fluctuations differ at some energies. In addition, new observations like the centrality dependence of chemical freeze-out parameters (T _ch and ?? _B ) or the smoothly increasing difference with decreasing energy in the elliptic flow v ₂ between particles and corresponding anti-particles, are discussed.     

Renormalization of the electroweak ϱ-parameter from supersymmetric particles

We compute the renormalization of the neutral-to-charged current Fermi constant ratio, arising from the new particles required in supersymmetric scheme?.We find that ? is insensitive to the scale of the supersymmetry mass-splitting. For a t-quark mass m_t greater than this scale, the scalar-t and scalar-b contribution increases proportionally to m_t² and it is essentially equal, in sign and magnitude, to the t-, b-quark contribution.Contributions from the gaugino-higgsino-Higgs boson sector are generally of the order of a few parts in 10^?3.For a class of models under consideration these results can be traced back to an approximate SU(2) symmetry which is also useful in the classification of the new particle spectrum.     

Impact of trailing wake drag on the statistical properties and dynamics of finite-sized particle in turbulence

We study by means of an Eulerian-Lagrangian model the statistical properties of velocity and acceleration of a neutrally-buoyant finite-sized particle in a turbulent flow statistically homogeneous and isotropic. The particle equation of motion, besides added mass and steady Stokes drag, keeps into account the unsteady Stokes drag force-known as Basset-Boussinesq history force-and the non-Stokesian drag based on Schiller-Naumann parametrization, together with the finite-size Faxén corrections. We focus on the case of flow at low Taylor-Reynolds number, Re_λ?31, for which fully resolved numerical data which can be taken as a reference are available [Homann H., Bec J. Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow. J Fluid Mech 651 (2010) 81-91]. Remarkably, we show that while drag forces have always minor effects on the acceleration statistics, their role is important on the velocity behavior. We propose also that the scaling relations for the particle velocity variance as a function of its size, which have been first detected in fully resolved simulations, does not originate from inertial-scale properties of the background turbulent flow but it is likely to arise from the non-Stokesian component of the drag produced by the wake behind the particle. Furthermore, by means of comparison with fully resolved simulations, we show that the Faxén correction to the added mass has a dominant role in the particle acceleration statistics even for particles whose size attains the integral scale.     

Constraints on PSC particle microphysics derived from lidar observations

Based on extensive T-matrix computations of light scattering by polydispersions of randomly oriented, rotationally symmetric nonspherical particles, we analyze existing lidar observations of polar stratospheric clouds (PSCs) and derive several constraints on PSC particle microphysical properties. We show that sharp-edged nonspherical particles (finite circular cylinders) exhibit less variability of lidar backscattering characteristics with particle size and aspect ratio than particles with smooth surfaces (spheroids). For PSC particles significantly smaller than the wavelength, the backscatter color index and the depolarization color index β are essentially shape independent. Observations for type Ia PSCs can be reproduced by spheroids with aspect ratios larger than 1.2, oblate cylinders with diameter-to-length ratios greater than 1.6, and prolate cylinders with length-to-diameter ratios greater than 1.4. The effective equal-volume-sphere radius for type Ia PSCs is about 0.8 μm or larger. Type Ib PSCs are likely to be composed of spheres or nearly spherical particles with effective radii smaller than 0.8 μm. Observations for type II PSCs are consistent with large ice crystals (effective radius greater than 1 μm) modeled as cylinders or prolate spheroids.