Identification of Odd-Radius Halo Arcs and of 44 degrees /46 degrees Parhelia by Their Inner-Edge Polarization

Birefringence of ice causes the inner edges of refraction halos to be polarized. The direction of this polarization relates directly to the projection of the crystal main axis onto the sky. This implies that the inner-edge polarization can serve as an observational diagnostic for determining the actual nature of a halo arc if two competing explanations exist. The direction and the visibility of the inner-edge polarization of arcs and circular halos arising from usual ice crystals and from ice crystals with pyramidal ends are calculated. It is found that the observation of inner-edge polarization can be decisive for the identification of a spot that might be either a 44 degrees parhelion or a 46 degrees parhelion, of an arc that might be either a 22 degrees sunvex Parry arc or a 20 degrees Parroid arc arising from plate-oriented pyramidal crystals, and of an arc that might be either a 22 degrees suncave Parry arc or a 23 degrees Parroid arc from plate-oriented pyramidal crystals. (With a Parroid arc, a halo is that which arises from an ice wedge made up of two faces of a crystal that rotates about a vertically oriented spin axis, and the edge of the wedge is perpendicular to this spin axis.) Polarization properties of other rare arcs are discussed. Practical hints are given for observing visually the inner-edge polarization of halos.     

Effects of ice-crystal structure on halo formation: cirrus cloud experimental and ray-tracing modeling studies

During the 1986 Project FIRE (First International Satellite Cloud Climatology Project Regional Experiment) field campaign, four 22° halo-producing cirrus clouds were studied jointly from a groundbased polarization lidar and an instrumented aircraft. The lidar data show the vertical cloud structure and the relative position of the aircraft, which collected a total of 84 slides by impaction, preserving the ice crystals for later microscopic examination. Although many particles were too fragile to survive impaction intact, a large fraction of the identifiable crystals were columns and radial bullet rosettes, with both displaying internal cavitations, and radial plate-column combinations. Particles that were solid or displayed only a slight amount of internal structure were relatively rare, which shows that the usual model postulated by halo theorists, i.e., the randomly oriented, solid hexagonal crystal, is inappropriate for typical cirrus clouds. With the aid of new ray-tracing simulations for hexagonal hollow ended column and bullet-rosette models, we evaluate the effects of more realistic ice-crystal structures on halo formation and lidar depolarization and consider why the common halo is not more common in cirrus clouds.     

Cirrus cloud iridescence: a rare case study

On the evening of 25 November 1998, a cirrus cloud revealing the pastel colors of the iridescence phenomenon was photographed and studied by a polarization lidar system at the University of Utah Facility for Atmospheric Remote Sensing (FARS). The diffraction of sunlight falling on relatively minute cloud particles, which display spatial gradients in size, is the cause of iridescence. According to the 14-year study of midlatitude cirrus clouds at FARS, cirrus rarely produce even poor iridescent patches, making this particularly long-lived and vivid occurrence unique. In this unusually high (13.2-14.4-km) and cold (-69.7 degrees to -75.5 degrees) tropopause-topped cirrus cloud, iridescence was noted from approximately 6.0 degrees to approximately 13.5 degrees from the Sun. On the basis of simple diffraction theory, this indicates the presence of particles of 2.5-5.5-microm effective diameter. The linear depolarization ratios of delta = 0.5 measured by the lidar verify that the cloud particles were nonspherical ice crystals. The demonstration that ice clouds can generate iridescence has led to the conclusion that iridescence is rarely seen in midlatitude cirrus clouds because populations of such small particles do not exist for long in the presence of the relatively high water-vapor supersaturations needed for ice-particle nucleation.     

Influence of crystal tilt on solar irradiance of cirrus clouds

The single and multiple scattering and absorption properties of hexagonal ice columns with different degrees of particle orientation are modeled in the solar spectral range by means of a ray-tracing single-scattering code and a Monte Carlo radiative-transfer code. The scattering properties are most sensitive to particle orientation for the solar zenith angles of 50 degrees (asymmetry parameter) and 90 degrees (single-scattering albedo). Provided that the ice columns are horizontally oriented, the usual assumption of random orientation leads to an overestimation (underestimation) of the reflected (transmitted) solar broadband radiation at high Sun elevation and to an underestimation (overestimation) at medium solar zenith angles. The orientation effect is more (less) pronounced in scattering and transmission (absorption) for smaller ice crystals.     

Origin of Kern's arc

With the aid of computer-simulated halo patterns, we show that Kern's arc, as seen on the latitude of the circumzenithal arc and on the other side of the zenith, is produced by double-plate ice crystals with a vertical principal axis. Light rays that contribute to Kern's arc are demonstrated by geometric ray tracing. We also discuss the condition under which an arc that is opposite a circumhorizontal arc can appear.     

Light-scattering properties of plate and column ice crystals generated in a laboratory cold chamber

Angular scattering properties of ice crystal particles generated in a laboratory cloud chamber are measured with a lightweight polar nephelometer with a diode laser beam. This cloud chamber produces distinct plate and hollow column ice crystal types for light-scattering experiments and provides a controlled test bed for comparison with results computed from theory. Ice clouds composed predominantly of plates and hollow columns generated noticeable 22 degrees and 46 degrees halo patterns, which are predicted from geometric ray-tracing calculations. With the measured ice crystal shape and size distribution, the angular scattering patterns computed from geometrical optics with a significant contribution by rough surfaces closely match those observed from the nephelometer.     

Use of equivalent spheres to model the relation between radar reflectivity and optical extinction of ice cloud particles

The effect of ice crystal size and shape on the relation between radar reflectivity and optical extinction is examined. Discrete-dipole approximation calculations of 95-GHz radar reflectivity and ray-tracing calculations are applied to ice crystals of various habits and sizes. Ray tracing was used primarily to calculate optical extinction and to provide approximate information on the lidar backscatter cross section. The results of the combined calculations are compared with Mie calculations applied to collections of different types of equivalent spheres. Various equivalent sphere formulations are considered, including equivalent radar-lidar spheres; equivalent maximum dimension spheres; equivalent area spheres, and equivalent volume and equivalent effective radius spheres. Marked differences are found with respect to the accuracy of different formulations, and certain types of equivalent spheres can be used for useful prediction of both the radar reflectivity at 95 GHz and the optical extinction (but not lidar backscatter cross section) over a wide range of particle sizes. The implications of these results on combined lidar-radar ice cloud remote sensing are discussed.     

Twilight polarization and optical depth of stratospheric aerosols over Beijing after the Pinatubo volcanic eruption

After the volcanic eruption of Mt. Pinatubo the degree of polarization of skylight during twilight over Beijing was monitored with a polarimeter aimed at the local zenith. We analyze the effect of changes in the scattering coefficient of atmospheric aerosols for the case of multiple scattering on skylight polarization at the zenith and then discuss the evolution of skylight polarization over Beijing during the posteruption period. As a reference and for comparison we also discuss the evolution of the aerosol optical depth retrieved from the combination of skylight polarization and backscattering ratio measured by the polarimeter and a lidar for the period beginning with the eruption of Mt. Pinatubo through the end of 1993. The contributions of atmospheric aerosols at different altitudes to the ground-observed twilight polarization depend on the solar zenith angle. For larger solar zenith angles, the skylight polarization is mostly sensitive to aerosol variations in the upper layer that range from 15 to 30 km. The twilight polarization at the zenith from June 1991 to mid-1994 shows different features for three periods: (1) From October 1991 to February 1992, volcanic dust traveled to mid-latitudes, and the degree of polarization decreased substantially. (2) From February 1992 to November 1993, volcanic dust was dispersed the minimum degree of polarization at the solar zenith angle of 93.5 degrees disappeared and the maximum increased. In addition, polarization for solar zenith angles less than 90 degrees also increased. (3) From November 1993 to May 1994, most of the volcanic dust had fallen off, the atmosphere was restored to the background state, and the skylight polarization approached the preeruption condition.     

Ice analog halos

Crystals of sodium fluorosilicate are used to produce easy to set up visual displays of atmospheric halos, including the 22 degrees halo, the Parry arc, and upper tangent arcs. Scattering phase functions for single ice-analog rosettes, including a rough one, and a column aggregate, measured in randomized orientation, are also given. The phase functions show prominent halo features, with the exception of the rough crystal.     

Multiple scattering from clear atmosphere obscured by transparent crystal clouds in satellite-borne lidar sensing

The contribution of multiple scattering to a spaceborne lidar return from clear molecular atmosphere obscured by transparent upper-level crystal clouds is assessed by the use of the variance-reduction Monte Carlo technique. High anisotropy of scattering in the forward direction by polydispersions of ice crystals is the basis of a significant effect of multiple scattering for small values of the lidar receiver field of view. Because of scattering by large nonspherical crystal particles, the lidar signal backscattered from the molecular atmosphere under the cloud increases significantly compared with the single-scattering return. The ratio of the multiple-to-single-scattering contributions from the clear atmosphere hidden by the clouds is greater than from the crystal clouds themselves, and it is proportional to the values of cloud optical thickness.     

Lidar ratio and depolarization ratio for cirrus clouds

We report on studies of the lidar and the depolarization ratios for cirrus clouds. The optical depth and effective lidar ratio are derived from the transmission of clouds, which is determined by comparing the backscattering signals at the cloud base and cloud top. The lidar signals were fitted to a background atmospheric density profile outside the cloud region to warrant the linear response of the return signals with the scattering media. An average lidar ratio, 29 +/- 12 sr, has been found for all clouds measured in 1999 and 2000. The height and temperature dependences ofthe lidar ratio, the optical depth, and the depolarization ratio were investigated and compared with results of LITE and PROBE. Cirrus clouds detected near the tropopause are usually optically thin and mostly subvisual. Clouds with the largest optical depths were found near 12 km with a temperature of approximately -55 degrees C. The multiple-scattering effect is considered for clouds with high optical depths, and this effect lowers the lidar ratios compared with a single-scattering condition. Lidar ratios are in the 20-40 range for clouds at heights of 12.5-15 km and are smaller than approximately 30 in height above 15 km. Clouds are usually optically thin for temperatures below approximately -65 degrees C, and in this region the optical depth tends to decrease with height. The depolarization ratio is found to increase with a height at 11-15 km and smaller than 0.3 above 16 km. The variation in the depolarization ratio with the lidar ratio was also reported. The lidar and depolarization ratios were discussed in terms of the types of hexagonal ice crystals.     

Ice clouds and Asian dust studied with lidar measurements of particle extinction-to-backscatter ratio, particle depolarization, and water-vapor mixing ratio over Tsukuba

The tropospheric particle extinction-to-backscatter ratio, the depolarization ratio, and the water-vapor mixing ratio were measured by use of a Raman lidar and a polarization lidar during the Asian dust seasons in 2001 and 2002 in Tsukuba, Japan. The apparent (not corrected for multiple-scattering effects) extinction-to-backscatter ratios (Sp) showed a dependence on the relative humidity with respect to ice (RHice) obtained from the lidar-derived water-vapor mixing ratio and radiosonde-derived temperature; they were mostly higher than 30 sr in dry air (RHice < 50%), whereas they were mostly lower than 30 sr in ice-supersaturated air (RHice > or = 100%), where the apparent extinction coefficients were larger than 0.036 km(-1). Both regions showed mean particle depolarization ratios of 20%-22%. Comparisons with theoretical calculations and the previous experiments suggest that the observed dependence of Sp on RHice is attributed to the difference in the predominant particles: nonspherical aerosols (mainly the Asian dust) in dry air and cloud particles in ice-supersaturated air.     

Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals

A new geometric-optics model has been developed for the calculation of the single-scattering and polarization properties for arbitrarily oriented hexagonal ice crystals. The model uses the ray-tracing technique to solve the near field on the ice crystal surface, which is then transformed to the far field on the basis of the electromagnetic equivalence theorem. From comparisons with the results computed by the finite-difference time domain method, we show that the novel geometric-optics method can be applied to the computation of the extinction cross section and single-scattering albedo for ice crystals with size parameters along the minimum dimension as small as ~6. Overall agreement has also been obtained for the phase function when size parameters along the minimum dimension are larger than ~20. We demonstrate that the present model converges to the conventional ray-tracing method for large size parameters and produces single-scattering results close to those computed by the finite-difference time domain method for size parameters along the minimum dimension smaller than ~20. The present geometric-optics method can therefore bridge the gap between the conventional ray-tracing and the exact numerical methods that are applicable to large and small size parameters, respectively.     

Classification of particle effective shape ratios in cirrus clouds based on the lidar depolarization ratio

A shape classification technique for cirrus clouds that could be applied to future spaceborne lidars is presented. A ray-tracing code has been developed to simulate backscattered and depolarized lidar signals from cirrus clouds made of hexagonal-based crystals with various compositions and optical depth, taking into account multiple scattering. This code was used first to study the sensitivity of the linear depolarization rate to cloud optical and microphysical properties, then to classify particle shapes in cirrus clouds based on depolarization ratio measurements. As an example this technique has been applied to lidar measurements from 15 mid-latitude cirrus cloud cases taken in Palaiseau, France. Results show a majority of near-unity shape ratios as well as a strong correlation between shape ratios and temperature: The lowest temperatures lead to high shape ratios. The application of this technique to space-borne measurements would allow a large-scale classification of shape ratios in cirrus clouds, leading to better knowledge of the vertical variability of shapes, their dependence on temperature, and the formation processes of clouds.     

Laboratory measurements of spectral reflection from ice clouds of various habits

Spectral light from 550 to 650 nm reflected from the surface of an ice cloud produced in a temperature-controlled column is measured at seven different angles between 16.7 degrees and 29.9 degrees . Cloud optical depth (tau) is determined from the extinction of a 670 nm laser and is corrected for forward scattering using a Monte Carlo ray-tracing algorithm. Reflection measurements are compared to expectations from a plane-parallel radiative transfer model with input parameters based on the measured tau and a phase function for the observed ice crystal types. The plane-parallel radiative transfer model can be used to interpret the measured reflection for tau less than about 0.4 for this particular experiment, ideal for providing a validation data set to assist with the development of satellite bidirectional remote sensing.     

Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase

The Mueller matrix (M) corresponding to the phase matrix in the backscattering region (scattering angles ranging from 175 degrees to 180 degrees) is investigated for light scattering at a 0.532-microm wavelength by hexagonal ice crystals, ice spheres, and water droplets. For hexagonal ice crystals we assume three aspect ratios (plates, compact columns, and columns). It is shown that the contour patterns of the backscattering Mueller matrix elements other than M11, M44, M14, and M41 depend on particle geometry; M22 and M33 are particularly sensitive to the aspect ratio of ice crystals. The Mueller matrix for spherical ice particles is different from those for nonspherical ice particles. In addition to discriminating between spherical and nonspherical particles, the Mueller matrix may offer some insight as to cloud thermodynamic phase. The contour patterns for large ice spheres with an effective size of 100 microm are substantially different from those associated with small water droplets with an effective size of 4 microm.     

Can cirrus clouds produce glories?

A vague glory display was photographed over central Utah from an airplane beginning its descent through a cirrus cloud layer with an estimated cloud top temperature of -45 and -55 degrees C. Photographic analysis reveals a single reddish-brown ring of 2.5-3.0 degrees radius around the antisolar point, although a second ring appeared visually to have been present over the brief observation period. Mie and approximate nonspherical theory scattering simulations predict a population of particles with modal diameters between 9 and 15 mum. Although it is concluded that multiple-ringed glories can be accounted for only through the backscattering of light from particles that are strictly spherical in shape, the poor glory colorization in this case could imply the presence of slightly aspherical ice particles. The location of this display over mountainous terrain suggests that it was generated by an orographic wave cloud, which we speculate produced numerous frozen cloud droplets that only gradually took on crystalline characteristics during growth.     

Icy wave-cloud lunar corona and cirrus iridescence

Dual-polarization lidar data and radiosonde data are used to determine that iridescence in cirrus and a lunar corona in a thin wave cloud were caused by tiny ice crystals, not droplets of liquid water. The size of the corona diffraction rings recorded in photographs is used to estimate the mean diameter of the diffracting particles to be 14.6 μm, much smaller than conventional ice crystals. The iridescent cloud was located at the tropopause [~11-13.6 km above mean sea level (ASL)] with temperature near -70 °C, while the more optically pure corona was located at approximately 9.5 km ASL with temperature nearing -60 °C. Lidar cross-polarization ratios of 0.5 and 0.4 confirm that ice formed both the iridescence and the corona, respectively.     

Scattering matrices for large ice crystal particles

The problem of light scattering by ice crystal particles whose sizes are essentially larger than the incident wavelength is divided into two parts. First, the scattered field is represented as a set of plane-parallel outgoing beams in the near zone of the particle. Then, in the far zone the scattered field is represented as a result of both diffraction and interference of these beams within the framework of physical optics. A proper ray-tracing algorithm for calculation of the amplitude (Jones) scattering matrix is developed and applied. For large particles, a number of reduced Mueller matrices are introduced and discussed, since the pure Mueller matrix obtained from the Jones matrix becomes a rather cumbersome and quickly oscillating value. Backscattering by hexagonal ice crystals, including polarization properties, is considered in detail.     

Reflection halo twins: subsun and supersun

From an aircraft, a short distinct vertical structure is sometimes seen above the setting sun. Such a feature can be understood as a halo, which is the counterpart of the well-known subsun. Whereas the latter arises from reflections off basal faces of plate-oriented ice crystals illuminated from above, what we call the supersun emerges when these crystals are illuminated from below. The supersun occurs when the sun is below the true horizon and is only visible from elevated positions. The curvature of the Earth causes the ensemble of reflecting crystal faces to act as a hollow mirror and the supersun appears as a vertical band of uniform width, extending from the sun upwards to its supersolar point. We discuss the geometrical properties of the phenomenon and simulate its shape and radiance distribution with an extended version of an atmospheric ray-tracing program.