Roughness metrics of prismatic facets of ice

摘要

We define a surface normal roughness metric for mesoscopically rough ice facets and present methods for inferring its value from variable pressure scanning electron micrographs. The methods rely on the anisotropic morphology of roughening in the prismatic plane, in which nearly all the variation in surface height occurs in the direction of the main symmetry axis of hexagonal-habit ice prisms. Because of this symmetry, roughening appears at boundaries between prismatic facets in a way that readily permits quantitative analysis. Prismatic surfaces of four ice crystals grown between -45 and -30°C are found to have mean surface normal roughness values of 0.04-0.1, a range that corresponds to Cox-Munk roughness scale parameters 0.3-0.5. The distribution of tilt angles also suggests a Weibull shape parameter smaller than unity, a result that compares favorably with field observations. Shortwave scattering calculations of hexagonal polyhedra with surface morphologies derived from these observations indicate substantial retention of the well-known 22° halo, despite a large (4-6%) reduction in the asymmetry parameter compared to smooth-surface counterparts. We argue that this signature is a generic outcome of the symmetry of the roughening, which in turn originates in the anisotropic surface self-diffusivity of these facets.