The Theoretical Basis for the Parameterization of Ice Crystal Habits: Growth by Vapor Deposition

Abstract

A theoretical analysis of surface kinetic and gas-phase diffusional effects permits the growth rates and habits of ice crystals to be specified in a self-consistent way. The analysis makes use of the fact that the difference between the condensation coefficients of the prism and basal faces determines the primary crystal habits, whereas the spatial variations of the vapor density contribute to the secondary habits. The parameterization scheme that results from the theoretical analysis yields a power law relationship between the a and c axial lengths that matches earlier empirical formulas derived from observational data for the temperature range of ?30° to 0°C. Through application of this adaptive parameterization in a microphysical model that categorizes ice particles according to both their masses and shapes, it is shown that deviations from the power law relationship may develop if the crystals experience significant variations in the air temperature and in their inherent growth habits. A mass-dimension relationship is also derived through the theoretical analysis that can be used as a less detailed parameterization scheme for the growth of ice crystals by vapor deposition.