Andreas Macke

Single Scattering Properties of Atmospheric Ice Crystals

Abstract Simulations of scattering and polarization properties for randomly oriented polyhedral ice crystals are presented based on the geometric optics and the far-field diffraction approximation. Particle shapes range from various hexagonal symmetric particles to highly complex shaped deterministic and random fractals. All calculations are performed at a wavelength of 0.55 µm. Hexagonal symmetric particles show several narrow scattering peaks besides the well known 22° and 46° halos. Column-like ice crystals provide neutral points (NP) at larger scattering angles than plate-like ice crystals. The ranges of NPs for column-like and plate-like crystals are separated at a scattering angle of about 156°, which may allow a polarimetric distinction between these two crystal types. The effects of particle size are studied by applying observationally derived aspect-ratio parameterizations to the individual particle types. Differences in the asymmetry parameter versus size relations for column-like particle types...

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.

Modeling Cirrus Clouds. Part II: Treatment of Radiative Properties

Abstract A new radiation scheme, suitable for two-stream radiation transfer models, was developed for cirrus clouds. Analytical expressions were derived for the extinction and absorption coefficients and the asymmetry parameter. These are functions of the ice particle size distribution parameters, ice particle shapes, and wavelength. The ice particle shapes considered were hexagonal plates and columns, bullet rosettes, and planar polycrystals. These appear to be the principal crystal types found in cirrus clouds. The formulation of radiative properties accounts for the size distribution projected area and the distance radiation travels through ice particles. For absorption, refraction and internal reflection of radiation were parameterized. By assuming an idealized cirrus cloud, the dependence of the single scatter albedo, reflectance, and emissivity on wavelength, ice particle shape, and size distribution was demonstrated. Reflectance and emissivity exhibited a strong dependence on ice particle shape, wi...

Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape

We examine the sensitivity of cirrus cloud albedo and bidirectional reflection function to particle shape using the phase functions of liquid water spheres, regular hexagonal ice crystals, and random-fractal ice particles calculated at a nonabsorbing visible wavelength of 0.63 μm. Accurate multiple-scattering calculations for plane-parallel clouds show that hexagonal ice crystal clouds have systematically larger planetary and global albedos than liquid water clouds of the same optical thickness. There is accumulating evidence that the idealized phase function of regular hexagonal crystals, which causes pronounced halos, is not necessarily the best representation of the range of reflectance characteristics of the majority of ice clouds. A more typical representation of the scattering phase function for ice clouds that are composed of a complex set of crystal shapes and sizes may be obtained using a model of randomly shaped irregular particles. Even larger cloud albedos are obtained for the random-fractal particle model because of its smaller asymmetry parameter. Our computations also show that a larger planetary albedo does not always imply a larger reflectance and that the relative brightness of ice versus liquid water clouds is highly scattering-geometry dependent. Use of the wrong particle shape model (crystal instead of water droplet and vice versa) in retrieving cloud optical thickness from bidirectional reflectance measurements can result in an underestimation or overestimation of the true optical thickness by a factor that can exceed 3. At some scattering geometries, use of the wrong model can give an unrealistically large optical thickness or no solution at all. Overall, bidirectional reflectance differences between random-fractal and regular hexagonal particle shapes are significantly smaller than those between either ice crystal and liquid water spheres, except at the back scattering direction.

Effect of crystal size spectrum and crystal shape on stratiform cirrus radiative forcing

Sensitivities of cirrus cloud radiative forcing as well as solar albedo and infrared emittances to ice crystal size spectrum and ice crystal shape were examined using a coupled cloud-radiation model. The single- and bi-modal crystal size distribution were considered and simulated based on field measurements. Optical parameters of ice crystals shaped as hexagonal columns and random polycrystals (being frequently found in cirrus clouds) were calculated with a ray-tracing method. Both solar and infrared cirrus radiative forcing are influenced by the pattern of crystal size spectra. The net radiative forcing is lower for bi-modal than for single-modal spectra. The solar radiative forcing of cirrus cloud is reduced by nonspherical ice crystals, due to larger albedo effects of nonspherical crystals compared to those of equivalent spherical crystals. Moreover, this reduction in solar radiative forcing by random polycrystals is even larger than that by hexagonal column crystals. The cloud radiative forcing, solar albedo and infrared emittance are changed significantly as the mean crystal size approaches the smaller size end. Furthermore, net cloud radiative forcing is positive in most cirrus cases. Exceptions are cirrus clouds with a large number (>107 m−3) of small (mean maximum dimension <30 μm) ice crystals and cirrus clouds with bi-modal crystal size distribution and large particle size for the second maximum peak.

The influence of inclusions on light scattering by large ice particles

The scattering of visible light by ice crystals containing scattering and absorbing inclusions is calculated by a combination of ray-tracing and Monte Carlo techniques. Results are shown for a randomly oriented hexagonal ice column containing ammonium sulfate particles, soot particles, and air bubbles. It is shown that a noticeable change in the ice crystal scattering properties compared to a pure crystal requires about 103 to 104 internal scatterers of a size comparable to the wavelength. While the nonabsorbing ammonium and air bubble inclusions generally decrease the asymmetry parameter g, soot provides a strong increase in g caused by the additional absorption. An independent superposition of the scattering properties of ice crystal and inclusions does not give satisfactory results because of the strong influence of internal scatterers on the characteristic ray paths inside the crystal. Multiple-scattering calculations show that the strongest changes in the radiative fluxes are associated with the soot contaminated ice crystals.

Asymmetry parameters of the phase function for isolated and densely packed spherical particles with multiple internal inclusions in the geometric optics limit

Since large, homogeneous dielectric particles have positive asymmetry parameters even when they are densely packed, it has been hypothesized that negative asymmetry parameters retrieved with Hapkes phenomenological model of bidirectional reflectance result from a complicated internal structure of planetary regolith particles. This paper tests that hypothesis by theoretically computing asymmetry parameters for isolated and densely packed composite spherical particles with size typical of regolith grains. It is assumed that the wavelength of the scattered light is much smaller than the particle size, and that particles are filled with large numbers of small inclusions. The computations show that it is essentially impossible to make asymmetry parameters of planetary regolith particles even slightly negative by filling the particles with large numbers of internal inclusions in the form of voids and/or grains with a refractive index substantially different from that of the host medium. Asymmetry parameters are positive even for densely packed composite particles with no internal absorption and extreme values of the internal scattering coefficient. Furthermore, they are sharply increased by even modest absorption inside composite particles, by reducing the refractive index contrast between the inclusions and the host particles, and/or by decreasing the packing density. Thus, the negative asymmetry parameters retrieved with Hapkes model need another explanation rather than assuming that they are real and are the result of a complicated internal structure of regolith particles. Besides the opposition-effect term, Hapkes model is nothing more than an approximate solution of the radiative transfer equation which inherently violates the energy conservation law. Therefore, the negative asymmetry parameters are likely to be numerical artefacts resulting from the approximations made in the model.

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 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.

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.