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 (ϳ10 4 ) the authors expect the calculated capacitances to be accurate to within ϳ1%. The capacitance for the modeled aggregate snowflakes (C/D max ϭ 0.25, normalized by the maximum dimension D max ) 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/D max ϭ 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).Here we show that the capacitance of a hexagonal column with width 2a and length L (see Fig. 3) must be

Doppler lidar measurements of oriented planar ice crystals falling from supercooled and glaciated layer clouds

“…The latter case is also evidence that the whole crystal surface is close to ice saturation (Nelson, 1998), and that the crystal evaporation rates are governed by the standard electrostatic approximation (Mason, 1971;Westbrook et al, 2008).…”

“…If the subsaturation is very slight, evaporation occurs slowly in discrete layers, allowing the crystal to maintain its faceted structure (Hallett et al, 2001). If the crystal falls into drier air, however, multiple steps form at the edges (Mason, 1971) and the evaporation rate becomes limited by the diffusion of the molecules through the air, leading to strong vapour gradients at the edges and corners (Nelson, 1998;Westbrook et al, 2008), producing smooth, rounded crystals (Nelson, 1998). Rounding also appears to be more favourable at warmer temperatures (Hallett et al, 2001).…”

The fall speeds of sub‐100 µm ice crystals

“…However capacitance is not readily measured from in situ probes (unlike A and D). For the crystal shapes considered here, the capacitance may be calculated directly from D using the results in Westbrook et al (2008). However there is evidence that many crystals in cirrus clouds may be complex polycrystals of irregular shape Hallett, 2002, 2004).…”

“…Kajikawa (1973) and Michaeli (1977) also made measurements of the fall speed of branched and dendritic crystals, and their experimental results are shown in Figure 2. Based on photographs in Kajikawa's paper the capacitance of a 'representative' branched crystal has been calculated for aspect ratios L/2a between 0.05 and 0.35 using the method outlined in Westbrook et al (2008). The outline of the model crystal is shown inset in Figure 2.…”

“…New estimates of the 'capacitance' for realistic ice crystal shapes (Westbrook et al, 2008) allows the application of two theoretical results from the physics literature (Roscoe, 1949;1244 C. D. WESTBROOK Hubbard and Douglas, 1993) to calculate crystal fall speeds; these estimates are then compared to experimental data, and to the fall-speed parametrizations of Mitchell (1996), Mitchell and Heymsfield (2005) and Khvorstyanov andCurry (2002, 2005); the latter four studies are collectively referred to as MHKC from now on. Upper and lower bounds are also constructed where possible using analytical results for spheres and spheroids, providing further insight.…”