[1] A cloud of nonspherical ice particles may be represented in radiation models by a collection of spheres, in which the model cloud contains the same total volume of ice and the same total surface area as the real cloud but not the same number of particles. The spheres then have the same volume-to-area (V/A) ratio as the nonspherical particle. In previous work this approach was shown to work well to represent randomly oriented infinitely long circular cylinders for computation of hemispherical reflectance, transmittance, and absorptance. In this paper the results have been extended to hexagonal columns and plates using a geometric optics technique for large particles and finitedifference-time-domain theory (FDTD) for small particles. The extinction efficiency and single-scattering coalbedo for these prisms are closely approximated by the values for equal-V/A spheres across the ultraviolet, visible, and infrared from 0.2 to 25 mm wavelength. Errors in the asymmetry factor can be significant where ice absorptance is weak, at visible wavelengths for example. These errors are greatest for prisms with aspect ratios close to 1. Errors in hemispheric reflectance, absorptance, and transmittance are calculated for horizontally homogeneous clouds with ice water paths from 0.4 to 200,000 g m À2 and crystal thicknesses of 1 to 400 mm, to cover the range of crystal sizes and optical depths from polar stratospheric clouds (PSCs) through cirrus clouds to surface snow. The errors are less than 0.05 over most of these ranges at all wavelengths but can be larger at visible wavelengths because of the ideal shapes of the prisms. The method was not tested for, and is not expected to be accurate for, angle-dependent radiances.

Abstract. We present the first clearly resolved observations of surfaces of growing and ablating hexagonal ice crystals using variable-pressure scanning electron microscopy. The ice surface develops trans-prismatic strands, separated from one another by distances of 5-10 µm. The strands are present at a wide range of supersaturations, but are most pronounced at temperatures near the frost point. Pyramidal facets consistent with Miller-Bravais indices of 1011, and possibly also 2021, are associated with ice growth under these conditions. A molecular-dynamics model of a free-standing ice I h nanocolumn containing 8400 water molecules does not develop trans-prismatic strands, suggesting these features originate at larger spatial or temporal scales. The possible relevance of these surface features to cirrus ice is discussed.

Molecular dynamics simulations of ice I h in a slab geometry with a free basal (0001) surface are carried out at 250 K in order to study the structure and dynamics of the ice/vapor interface, focusing on processes associated with sublimation and deposition. Surface melting, which results in the formation of a quasi-liquid layer, causes about 8% of the molecules originally constituting the surface bilayer to leave their crystal lattice positions and form an outer, highly mobile sublayer. Molecules in this sublayer typically form two H bonds, predominantly in a dangling-O orientation, with preference for a dangling-H orientation also evident. The remaining 92% of the quasi-liquid layer molecules belong to the deeper, more crystalline sublayer, typically forming three H bonds in an orientational distribution that closely resembles bulk crystalline ice. Transitions between the quasi-liquid layer and the first underlying crystalline bilayer were also observed on the molecular dynamics simulation time scale, albeit with substantially longer characteristic times. Regarding deposition, a very high (>99%) probability of water vapor molecules sticking to the ice surface was found. A total of 70% of incident molecules adsorb to the outer sublayer, whereas 30% are accommodated directly to the inner sublayer of the quasi-liquid layer, with an orientational relaxation time of ∼2 ps and a thermal relaxation time of ∼10 ps for molecules adsorbing to the outermost sublayer. Regarding the mechanism of sublimation, we found that prior to sublimation, departing molecules are predominantly located in the outermost sublayer and show a distinct preference for a dangling-O orientation.

We present an Arrhenius analysis of self-diffusion on the prismatic surface of ice calculated from molecular dynamics simulations. The six-site water model of Nada and van der Eerden was used in combination with a structure-based criterion for determining the number of liquid-like molecules in the quasi-liquid layer. Simulated temperatures range from 230 K-287 K, the latter being just below the melting temperature of the model, 289 K. Calculated surface diffusion coefficients agree with available experimental data to within quoted precision. Our results indicate a positive Arrhenius curvature, implying a change in the mechanism of self-diffusion from low to high temperature, with a concomitant increase in energy of activation from 29.1 kJ mol(-1) at low temperature to 53.8 kJ mol(-1) close to the melting point. In addition, we find that the surface self-diffusion is anisotropic at lower temperatures, transitioning to isotropic in the temperature range of 240-250 K. We also present a framework for self-diffusion in the quasi-liquid layer on ice that aims to explain these observations.