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A new approach is described for calculating the mass (m) and terminal velocity (V t) of ice particles from airborne and balloon-borne imaging probe data as well as its applications for remote sensing and modeling studies. Unlike past studies that derived these parameters from the maximum (projected) dimension (D) and habit alone, the ''two-parameter approach'' uses D and the particle's projected cross-sectional area (A). Expressions were developed that relate the area ratio (A r ; the projected area of an ice particle normalized by the area of a circle with diameter D) to its effective density (e) and to V t. Habit-dependent, power-law relationships between e and A r were developed using analytic representations of the geometry of various types of planar and spatial ice crystals. Relationships were also derived from new or reanalyzed data for single ice particles and aggregates observed in clouds and at the ground. The mass relationships were evaluated by comparing calculations to direct measurements of ice water content (IWC). The calculations were from Particle Measuring Systems (PMS) 2D-C and 2D-P probes of particle size distributions in ice cloud layers on 3 days during an Atmospheric Radiation Measurement (ARM) field campaign in Oklahoma; the direct measurements were from counterflow virtual impactor (CVI) observations in ice cloud layers during the field campaign. Agreement was generally to within 20%, whereas using previous massdimension relationship approaches usually produced larger differences. Comparison of ground-based measurements of radar reflectivity with calculations from collocated balloon-borne ice crystal measurements also showed that the new method accurately captured the vertical reflectivity structure. Improvements in the accuracy of the estimates from the earlier mass-dimension relationships were achieved by converting them to the new form. A new, more accurate mass-dimension relationship for spatial, cirrus-type crystals was deduced from the comparison. The relationship between V t and A r was derived from a combination of theory and observations. A new expression accounting for the drag coefficients of large aggregates was developed from observational data. Explicit relationships for calculating V t as a function of D for aggregates with a variety of component crystals were developed.

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Abstract.During the Central Equatorial Pacific Experiment, ice crystal sizes and shapes were measured in an outflow anvil. A habit (i.e., column, bullet rosette, Koch fractal polycrystal, sphere) was assigned to each particle using a self-organized neural network based on simulations of how the maximum particle dimension and area ratio varied for random orientations of these crystals. Average ice crystal size and shape distributions were calculated for 25 km long segments at six altitudes using measurements from a two-dimensional cloud probe for crystals larger than 90 /zm and a parameterization for smaller crystals based on measurements from the Video Ice Particle Sampler (VIPS). Mean-scattering properties were determined by weighting the size and shape dependent single-scattering properties computed with ray-tracing algorithms according to scattering cross-section. Reflectances at 0.664, 0.875, 1.621, and 2.142 /zm were then calculated using a Monte Carlo radiative transfer routine. Although these reflectances agree reasonably with those measured by the MODIS airborne simulator (MAS) above the anvil, uncertainties in cloud base and system evolution prevent a determination of whether ray-tracing or anomalous diffraction theory better predict reflectance. The calculated reflectances are as sensitive to the numbers and shapes of crystals smaller than 90 /zm as to those of larger crystals. The calculated reflectances were insensitive to the classification scheme (i.e., neural network, discriminator analysis, and previously used classification scheme) for assigning particle shape to observed crystals. However, the reflectances significantly depended on assumed particle shape.

Bullet rosette particles are common in ice clouds, and the bullets may often be hollow. Here the singlescattering properties of randomly oriented hollow bullet rosette ice particles are investigated. A bullet, which is an individual branch of a rosette, is defined as a hexagonal column attached to a hexagonal pyramidal tip. For this study, a hollow structure is included at the end of the columnar part of each bullet branch and the shape of the hollow structure is defined as a hexagonal pyramid. A hollow bullet rosette may have between 2 and 12 branches. An improved geometric optics method is used to solve for the scattering of light in the particle. The primary optical effect of incorporating a hollow end in each of the bullets is to decrease the magnitude of backscattering. In terms of the angular distribution of scattered energy, the hollow bullets increase the scattering phase function values within the forward scattering angle region from 1°to 20°but decrease the phase function values at side-and backscattering angles of 60°-180°. As a result, the presence of hollow bullets tends to increase the asymmetry factor. In addition to the scattering phase function, the other elements of the phase matrix are also discussed. The backscattering depolarization ratios for hollow and solid bullet rosettes are found to be very different. This may have an implication for active remote sensing of ice clouds, such as from polarimetric lidar measurements. In a comparison of solid and hollow bullet rosettes, the effect of the differences on the retrieval of both the ice cloud effective particle size and optical thickness is also discussed. It is found that the presence of hollow bullet rosettes acts to decrease the inferred effective particle size and to increase the optical thickness in comparison with the use of solid bullet rosettes.

Cirrus clouds in the midlatitude and Arctic regions are often composed of bullet rosette–shaped ice crystals. Bullet rosette–shaped ice crystals are composed of a number of bullets radiating from a central point. The bullets that make up the rosette will grow to be hollow in some conditions. To understand better the radiative impact of cirrus clouds, the authors have used a ray-tracing code to calculate the scattering properties of solid and hollow bullet rosettes at visible wavelengths. Results show that hollow bullet rosettes exhibit a broader forward-scattering peak than do solid bullet rosettes. This difference results in an asymmetry parameter that is as much as 0.08 lower for hollow bullet rosettes than for solid rosettes. The effective asymmetry parameter of spheres with the same particle volume and total surface area of the bullet rosettes has also been calculated. Asymmetry parameter estimates for equivalent spheres were similar to those calculated using the ray tracing. Asymmetry parameter calculations were used in combination with direct aircraft measurements from the Atmospheric Radiation Measurement Program intensive operational period in March of 2000. Asymmetry parameter estimates were used with particle size distributions for three cirrus cloud flights for which the observed large particles were predominantly bullet rosettes. Calculated asymmetry parameter values (0.80–0.84) agreed poorly with published cirrus parameterizations (0.75–0.84) when applied to the same aircraft data. Differences lead to 4.5–9 W m−2 differences in reflected and transmitted visible light energy for a cloud of 0.5 optical depth.