Timo Nousiainen

Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm

We present measured scattering matrices as functions of the scattering angle in the range 5°–173° and at wavelengths of 441.6 nm and 632.8 nm for seven distinct irregularly shaped mineral aerosol samples with properties representative of mineral aerosols present in the Earths atmosphere. The aerosol samples, i.e., feldspar, red clay, quartz, loess, Pinatubo and Lokon volcanic ash, and Sahara sand, represent a wide variety of particle size (typical diameters between 0.1 and 100 μm) and composition (mainly silicates). We investigate the effects of differences in size and complex refractive index on the light-scattering properties of these irregular particles. In particular, we find that the measured scattering matrix elements when plotted as functions of the scattering angle are confined to rather limited domains. This similarity in scattering behavior justifies the construction of an average aerosol scattering matrix as a function of scattering angle to facilitate, for example, the use of our results for the interpretation of remote sensing data. We show that results of ray-optics calculations, using Gaussian random shapes, are able to describe the experimental data well when taking into account the high irregularity in shape of the aerosols, even when these aerosols are rather small. Using the results of ray-optics calculations, we interpret the differences found between the measured aerosol scattering matrices in terms of differences in complex refractive index and particle size relative to the wavelength. The importance of our results for studies of astronomical objects, such as planets, comets, asteroids, and circumstellar dust shells is discussed.

Light scattering by Gaussian random particles: Ray optics approximation

We model the shapes of irregular small particles using multivariate lognormal statistics (Gaussian random shape), and compute absorption and scattering cross sections, asymmetry parameters, and scattering phase matrices in the ray optics approximation. The random shape is fully described by the autocovariance function, which can be conveniently modeled by two statistical parameters: the standard deviation of radius and the correlation length of angular variations. We present an efficient spherical harmonics method for generating sample Gaussian random particles, and outline a ray tracing algorithm that can be adapted to almost arbitrary, mathematically star-like particles. We study the scattering and absorption properties of Gaussian random particles much larger than the wavelength by systematically varying their statistical parameters and complex refractive indices. The results help us understand, in part, light scattering by solar system dust particles, and thereby constrain the physical properties of, for example, asteroid regoliths and cometary comae.

Scattering matrix of large Saharan dust particles: Experiments and computations

We present measurements of the complete scattering matrix as a function of the scattering angle of a sample of Sahara sand particles collected from a dune in Libya. The measurements were performed at a wavelength of 632.8 nm in the scattering angle range from 4° to 174°. To facilitate the use of the experimental data for multiple-scattering calculations with polarization included, we present a synthetic scattering matrix based on the measurements and defined in the full angle range from 0° to 180°. The Libyan sample consists of large particles distributed over a narrow size distribution which makes it an interesting test case for the Ray Optics Approximation (ROA) that provides accurate results for particles with curvature radii much larger than the wavelength. Numerical simulations using the ROA are compared with the experimental data. Moreover, the traditional ROA was modified with ad hoc simple schemes of Lambertian surface elements and internal screens to study the effects of small-scale surface roughness and internal structures, respectively. Model particle shapes used in the simulations are based on a shape analysis of our sample. The traditional ray optics approximation does not reproduce the experimental data although a significant improvement is obtained if unrealistically spiky particle shapes are used. When the Lambertian schemes are applied the agreement with the experimental data improves. Still, to get a good agreement with the experimental data we need unrealistic spiky particles together with the inclusion of external Lambertian reflections. This seems to indicate that a more refined treatment is needed to reproduce the scattering effects of the small-scale surface roughness of the Libyan sand particles.

Light Scattering by Quasi-Spherical Ice Crystals

Abstract The shapes and single-scattering properties of small, irregular, quasi-spherical ice crystals, with equivalent radii between approximately 8 and 90 μm and size parameters from about 90 to 1000, are studied using two-dimensional images measured by a cloud particle imager in midlatitude cirrus during the 2000 Cloud Intensive Operation Period conducted over the Atmospheric Radiation Measurement programs Southern Great Plains site. A statistical shape analysis of the ice crystal images is carried out to obtain size-dependent relative standard deviations of radius and correlation functions of logradius, which together define the shape statistics of the sample ice crystals. The former describes the overall variation in the lengths of radius vectors defining the particle surface from a given origin, whereas the latter describes correlations of lengths of radius vectors as functions of angular distance between them. The logradius is essentially the natural logarithm of radius. There is no strong depende...

Radar Backscattering from Snowflakes: Comparison of Fractal, Aggregate, and Soft Spheroid Models

AbstractThe sensitivity of radar backscattering cross sections on different snowflake shapes is studied at C, Ku, Ka, and W bands. Snowflakes are simulated using two complex shape models, namely, fractal and aggregate, and a soft spheroid model. The models are tuned to emulate physical properties of real snowflakes, that is, the mass–size relation and aspect ratio. It is found that for particle sizes up to 5 mm and for frequencies from 5 to 35 GHz, there is a good agreement in the backscattering cross section for all models. For larger snowflakes at the Ka band, it is found that the spheroid model underestimates the backscattering cross sections by a factor of 10, and at W band by a factor of 50–100. Furthermore, there is a noticeable difference between spheroid and complex shape models in the linear depolarization ratios for all frequencies and particle sizes.

Comparison of measured single-scattering matrix of feldspar particles with T-matrix simulations using spheroids

Abstract Simulated and measured scattering matrices of feldspar are compared at wavelength 633 nm to evaluate the accuracy of using spheroids to model single-scattering properties of natural irregular mineral particles (feldspar). The results of the comparison show that the model of spheroids, whose scattering properties are calculated using a T-matrix method, is usable and far superior to spheres in describing scattering by feldspar particles not much larger than the wavelength. Simulations with prolate ellipsoids are better in agreement with measurements than those with oblates, and an average over a wide range of axis ratios is better than any single value. The refractive index affects the angle dependence of scattering rather weakly, as long as its real and imaginary parts are varied in reasonable ranges. These findings imply that an inversion of a refractive index or shape information would be quite difficult. On the other hand, they indicate that the T-matrix method is easier to apply to different problems, as less information about the target particles is required.

Validity criteria of the discrete dipole approximation.

There are two widely accepted restrictions on the application of the discrete dipole approximation (DDA) in the study of light scattering by particles comparable to the wavelength: (1) when considering dielectric particles, the size of the cells must satisfy the condition kd|m|<0.5, where k is the wavenumber, d is the size of the cells, and m is the complex refractive index of the constituent material and (2) when considering conductive particles, the size of the cells must be small enough to reproduce sufficiently the evolution of the electromagnetic field in the skin layer. We examine both restrictions when the DDA is applied to irregularly shaped particles and show that its restrictions are not as strong as is widely accepted. For instance, when studying irregularly shaped particles averaged over orientations, even at kd|m|=1, the DDA provides highly accurate numerical results. Moreover, we show that the impact of using large constituent cells is similar to that produced by surface roughness; therefore, the replacement of the target particle by an array of large constituent cells has the same effect, qualitatively, as incorporating additional small-scale surface roughness on the particle. Such a modification of the target particle can be desirable in many practical applications of DDA when irregularly shaped particles are considered. When applying DDA to conductive, nonspherical particles, the insufficient description of the electromagnetic field in the skin layer does not lead to a violation of the Maxwell equations, although it has a visible but nonmajor influence on the light-scattering properties of the target.

Optical properties of light absorbing carbon aggregates mixed with sulfate: assessment of different model geometries for climate forcing calculations

Light scattering by light absorbing carbon (LAC) aggregates encapsulated into sulfate shells is computed by use of the discrete dipole method. Computations are performed for a UV, visible, and IR wavelength, different particle sizes, and volume fractions. Reference computations are compared to three classes of simplified model particles that have been proposed for climate modeling purposes. Neither model matches the reference results sufficiently well. Remarkably, more realistic core-shell geometries fall behind homogeneous mixture models. An extended model based on a core-shell-shell geometry is proposed and tested. Good agreement is found for total optical cross sections and the asymmetry parameter.

Models for integrated and differential scattering optical properties of encapsulated light absorbing carbon aggregates

Optical properties of light absorbing carbon (LAC) aggregates encapsulated in a shell of sulfate are computed for realistic model geometries based on field measurements. Computations are performed for wavelengths from the UV-C to the mid-IR. Both climate- and remote sensing-relevant optical properties are considered. The results are compared to commonly used simplified model geometries, none of which gives a realistic representation of the distribution of the LAC mass within the host material and, as a consequence, fail to predict the optical properties accurately. A new core-gray shell model is introduced, which accurately reproduces the size- and wavelength dependence of the integrated and differential optical properties.

Light scattering by Gaussian particles: a solution with finite-difference time-domain technique

The understanding of single-scattering properties of complex ice crystals has significance in atmospheric radiative transfer and remote-sensing applications. In this work, light scattering by irregularly shaped Gaussian ice crystals is studied with the finite-difference time-domain (FDTD) technique. For given sample particle shapes and size parameters in the resonance region, the scattering phase matrices and asymmetry factors are calculated. It is found that the deformation of the particle surface can significantly smooth the scattering phase functions and slightly reduce the asymmetry factors. The polarization properties of irregular ice crystals are also significantly different from those of spherical cloud particles. These FDTD results could provide a reference for approximate light-scattering models developed for irregular particle shapes and can have potential applications in developing a much simpler practical light scattering model for ice clouds angular-distribution models and for remote sensing of ice clouds and aerosols using polarized light.