The capacitance of pristine ice crystals and aggregate snowflakes

TL;DR

This paper introduces a novel random walk-based method to accurately calculate the capacitance of various ice particle shapes, improving estimates of sublimation rates in weather models and highlighting the impact of neighboring crystals on vapor supply.

Contribution

The authors develop a straightforward, efficient approach to compute ice particle capacitance using random walkers, applicable to complex shapes like aggregate snowflakes, with validation against measurements.

Findings

Capacitance estimates closely match aircraft measurements of snowflake sublimation.

Using sphere approximation overestimates evaporation rates by a factor of 2.

Neighboring crystals can significantly restrict vapor supply, affecting growth rate measurements.

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).