The Capacitance of Pristine Ice Crystals and Aggregate Snowflakes

Abstract

A new method of accurately calculating the capacitance of realistic ice particles is described: such values are key to accurate estimates of deposition and evaporation (sublimation) rates in numerical weather models. The trajectories of diffusing water molecules are directly sampled, using random ?walkers.? By counting how many of these trajectories intersect the surface of the ice particle (which may be any shape) and how many escape outside a spherical boundary far from the particle, the capacitances of a number of model ice particle habits have been estimated, including hexagonal columns and plates, ?scalene? columns and plates, bullets, bullet rosettes, dendrites, and realistic aggregate snowflakes. For ice particles with sharp edges and corners this method is an efficient and straightforward way of solving Laplace?s equation for the capacitance. Provided that a large enough number of random walkers are used to sample the particle geometry (?104) the authors expect the calculated capacitances to be accurate to within ?1%. The capacitance for the modeled aggregate snowflakes (C/Dmax = 0.25, normalized by the maximum dimension Dmax) is shown to be in close agreement with recent aircraft measurements of snowflake sublimation rates. This result shows that the capacitance of a sphere (C/Dmax = 0.5), which is commonly used in numerical models, overestimates the evaporation rate of snowflakes by a factor of 2. The effect of vapor ?screening? by crystals growing in the vicinity of one another has also been investigated. The results clearly show that neighboring crystals growing on a filament in cloud chamber experiments can strongly constrict the vapor supply to one another, and the resulting growth rate measurements may severely underestimate the rate for a single crystal in isolation (by a factor of 3 in this model setup).