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 rates in NWP 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 capacitance 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 the authors expect the calculated capacitances to be accurate to within ~1%. The capacitance for our modelled aggregate snowflakes (C/Dmax=0.25, normalised 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 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 neighbouring crystals growing on a filament in cloud chamber experiments can strongly constrict the vapor supply to each other, and the resulting growth rate measurements may severely underestimate the rate for a single crystal in isolation (by a factor of 3 in our model setup).