The capacitance of realistic ice particles
The `electrostatic analogy' has been around for 60-odd years, but to apply it we need to know the capacitance C for ice crystals and snowflakes. For columns and plates it seems likely that prolate and oblate spheroids are not too bad an approximation, and analytic formulas exist for these shapes. Progress on calculating C for more complex shapes has been slow however: the metal model experiments of the 60s were not very accurate because of the wire connecting the model to the capacitance meter; the challenge of solving Laplace's equation numerically in three dimensions has made theoretical progress difficult. We have shown that a good way to solve this problem is to use random walks to sample the trajectories of the diffusing water molecules, and simply count how many of these walkers hit the ice particle. This allows the capacitance for an arbitrary particle to be estimated rather accurately (the only real error is a sampling one, which can be reduced by simply sampling more trajectories). We have applied the method to a variety of realistic ice particle habits including hexagonal columns and plates, bullet-rosettes, stellars, dendrites, and aggregates (see our paper for details).
In collaboration with Andy Heymsfield, I recently validated the capacitance-based growth rates against crystals grown in laboratory supercooled clouds between -2 and -22C: we found that they were in very good agreement, and also tested out various ventilation parameterisations for needles and dendrites. We also used the lab data to look at how realistic GCM parameterisations are at capturing the growth of ice at the expense of liquid water. See our paper in JAS for more details.