Lidar inelastic multiple-scattering parameters of cirrus particle ensembles determined with geometrical-optics crystal phase functions.

Multiple-scattering correction factors for cirrus particle extinction coefficients measured with Raman and high spectral resolution lidars are calculated with a radiative-transfer model. Cirrus particle-ensemble phase functions are computed from single-crystal phase functions derived in a geometrical-optics approximation. Seven crystal types are considered. In cirrus clouds with height-independent particle extinction coefficients the general pattern of the multiple-scattering parameters has a steep onset at cloud base with values of 0.5-0.7 followed by a gradual and monotonic decrease to 0.1-0.2 at cloud top. The larger the scattering particles are, the more gradual is the rate of decrease. Multiple-scattering parameters of complex crystals and of imperfect hexagonal columns and plates can be well approximated by those of projected-area equivalent ice spheres, whereas perfect hexagonal crystals show values as much as 70% higher than those of spheres. The dependencies of the multiple-scattering parameters on cirrus particle spectrum, base height, and geometric depth and on the lidar parameters laser wavelength and receiver field of view, are discussed, and a set of multiple-scattering parameter profiles for the correction of extinction measurements in homogeneous cirrus is provided.

How big should hexagonal ice crystals be to produce halos?

It has been hypothesized that the frequent lack of halos in observations of cirrus and contrails and laboratory measurements is caused by small ice crystal sizes that put the particles outside the geometrical optics domain of size parameters. We test this hypothesis by exploiting a strong similarity of ray tracing phase functions for finite hexagonal and circular ice cylinders and using T-matrix computations of electromagnetic scattering by circular cylinders with size parameters up to 180 in the visible. We conclude that well-defined halos should be observable for ice crystal size parameters of the order of 100 and larger and discuss remote-sensing implications of this result.

Improved T-matrix computations for large, nonabsorbing and weakly absorbing nonspherical particles and comparison with geometrical-optics approximation.

We show that the use of a matrix inversion scheme based on a special lower triangular-upper triangular factorization rather than on the standard Gaussian elimination significantly improves the numerical stability of T-matrix computations for nonabsorbing and weakly absorbing nonspherical particles. As a result, the maximum convergent size parameter for particles with small or zero absorption can increase by a factor of several and can exceed 100. We describe an improved scheme for evaluating Clebsch-Gordon coefficients with large quantum numbers, which allowed us to extend the analytical orientational averaging method developed by Mishchenko [J. Opt. Soc. Am. A 8, 871 (1991)] to larger size parameters. Comparisons of T-matrix and geometrical optics computations for large, randomly oriented spheroids and finite circular cylinders show that the applicability range of the ray-tracing approximation depends on the imaginary part of the refractive index and is different for different elements of the scattering matrix.

Integral light-scattering and absorption characteristics of large, nonspherical particles.

We obtain and analyze simple analytical formulas for asymmetry parameters and absorption cross sections of large, nonspherical particles. The formulas are based on the asymptotic properties of these characteristics at strong and weak absorption of radiation inside particles. The absorption cross section depends on parameter phi, which determines the value of the light-absorption cross section for weakly absorbing particles. It is larger for nonspherical scatterers. The asymmetry parameter depends on two parameters. The first is the asymmetry parameter g(0) of a nonspherical, transparent particle with the same shape as an absorbing one. The second parameter, beta, determines the strength of the influence of light absorption on the value of the asymmetry parameter. Parameter beta is larger for nonspherical particles. One can find these three parameters (phi, g(0), and beta) using a ray-tracing code (RTC) for nonabsorbing and weakly absorbing particles. The RTC can then be used to check the accuracy of the equations at any absorption for hexagonal cylinders and spheroids. It is found that the error of computing the absorption cross section and 1 - g (g is the asymmetry parameter) is less than 20% at the refractive index of particles n = 1.333. Values for asymmetry parameters of large, nonabsorbing, spheroidal particles with different aspect ratios are tabulated for the first time to our knowledge. They do not depend on the size of particles and can serve as an independent check of the accuracy of T-matrix codes for large parameters.

Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles.

We ascertain the usefulness of simple ice particle geometries for modeling the intensity distribution of light scattering by atmospheric ice particles. To this end, similarities and differences in light scattering by axis-equivalent, regular and distorted hexagonal cylindric, ellipsoidal, and circular cylindric ice particles are reported. All the results pertain to particles with sizes much larger than a wavelength and are based on a geometrical optics approximation. At a nonabsorbing wavelength of 0.55 µm, ellipsoids (circular cylinders) have a much (slightly) larger asymmetry parameter g than regular hexagonal cylinders. However, our computations show that only random distortion of the crystal shape leads to a closer agreement with g values as small as 0.7 as derived from some remote-sensing data analysis. This may suggest that scattering by regular particle shapes is not necessarily representative of real atmospheric ice crystals at nonabsorbing wavelengths. On the other hand, if real ice particles happen to be hexagonal, they may be approximated by circular cylinders at absorbing wavelengths.

Scattering of light by polydisperse, randomly oriented, finite circular cylinders.

We use the T-matrix method, as described by Mishchenko [Appl. Opt. 32, 4652 (1993)], to compute rigorously light scattering by finite circular cylinders in random orientation. First we discuss numerical aspects of T -matrix computations specific for finite cylinders and present results of benchmark computations for a simple cylinder model. Then we report results of extensive computations for polydisperse, randomly oriented cylinders with a refractive index of 1.53 + 0.008i, diameter-to-length ratios of 1/2, 1/1.4, 1, 1.4, and 2, and effective size parameters ranging from 0 to 25. These computations parallel our recent study of light scattering by polydisperse, randomly oriented spheroids and are used to compare scattering properties of the two classes of simple convex particles. Despite the significant difference in shape between the two particle types (entirely smooth surface for spheroids and sharp rectangular edges for cylinders), the comparison shows rather small differences in the integral photometric characteristics (total optical cross sections, single-scattering albedo, and asymmetry parameter of the phase function) and the phase function. The general patterns of the other elements of the scattering matrix for cylinders and aspect-ratio-equivalent spheroids are also qualitatively similar, although noticeable quantitative differences can be found in some particular cases. In general, cylinders demonstrate much less shape dependence of the elements of the scattering matrix than do spheroids. Our computations show that, like spheroids and bispheres, cylinders with surface-equivalent radii smaller than a wavelength can strongly depolarize backscattered light, thus suggesting that backscattering depolarization for nonspherical particles cannot be universally explained by using only geometric-optics considerations.

Scattering of light by large nonspherical particles: ray-tracing approximation versus T-matrix method.

We report, for the f irst time to our knowledge, comparisons of light-scattering computations for large, randomly oriented, moderately absorbing spheroids based on the geometric-optics approximation and the exact T-matrix method. We show that in most cases the geometric-optics approximation is (much) more accurate for spheroids than for surface-equivalent spheres and can be used in phase function computations (but not in polarization computations) for nonspherical particles with size parameters as small as 60. Differences in the single-scattering albedo between geometric-optics and T-matrix results are surprisingly small, even for small size parameters.

Scattering of light by polyhedral ice crystals.

The single-scattering phase functions of polyhedral-shaped ice particles are calculated by means of geometric optics and the diffraction theory. Particle orientation is assumed to be random in space. Particle shapes are taken both from ice-crystal classifications and from in situ measurements. The effects of particle concavity on the scattering signature are discussed in detail. A common feature is the pronounced forward-scattering peak, as well as different halo peaks that are due to a minimum deviation at corresponding ice prisms. An unusual halo phenomena, which results from a minimum deviation in a double-prism configuration, is found and verified. The comparison of different particle types shows that backscattering is a sensitive indicator for the identification of types of ice-crystal. Aggregate particles, like bullet rosettes, basically show the scattering characteristics of their individual components.

[Diagnosis of neurologic and motor development in pre-school age children with minimal cerebral dysfunction]. / Zur entwicklungsneurologischen und motoskopischen Diagnostik bei leicht hirngeschädigten Kindern im "Vorschulalter".

An investigation on neurologic development of pre-school children does not yet clearly differentiate between children with minimal neuromotor disturbances and healthy ones. This is due to the lack of knowledge on brain function in normal children. Diagnostic problems on Minimal Brain Dysfunction are demonstrated by neurologic and motor examinations of 4 to 6 years old children.

[Developmental neurological examinations in preparatory school children (author's transl)]. / Entwicklungsneurologische Untersuchungen im Vorschulalter

302 primarily healthy preparatory school children aged from 4-6 years were examined neurologically, using a slightly modified Touwen-Prechtl examination scheme. It was possible to make statistically confirmed statements on the individual tests of neurological function for a German kindergarten population. To develop a short (screening) test representative of the entire nervous system would be very difficult indeed. We hope, however, by means of rational data reduction, to be able to find a compromise between the complexity of the nervous system and the necessities of practice.