Release a planar snow crystal at the top of a supercooled cloud. It collects droplets that freeze on contact: first the rime fills the crystal's open structure, then the pellet grows into graupel and falls faster. Between -3 and -8 °C the rime also throws off ice splinters.
The current particle is released again for each liquid water content and falls through the whole cloud. The table shows what reaches cloud base.
Size of the large droplet class is swept (the small class stays as set). Droplets that are too small are not collected at all; splinters need large droplets above 24 µm and small ones below 13 µm together.
The science
Fall speed. The particle (mass m, volume V, equivalent diameter D) falls at the speed where drag equals weight: (m − ρaV) g = ½ ρa Cd Cs (π/4) D² v², with the sphere drag law Cd(Re) = 24/Re (1 + 0.15 Re0.687) + 0.42/(1 + 42500 Re−1.16), Re = ρa v D/μ (Sutherland viscosity, ISA pressure, a 6.5 K/km lapse rate). The shape factor Cs runs from 2.0 for an open crystal to 1.35 for lumpy graupel (illustrative). The relaxation time to terminal speed is well below a second, so the quasi-steady speed is used.
Accretion. Rime mass grows as dm/dt = (π/4) D² v · LWC · [(1−φ) Es + φ El], where LWC is the cloud liquid water content, φ the fraction of it in the large droplet class and E the collection efficiency. E follows the Stokes number K = ρw d² v / (9 μ D): E = ((K−K₀)/(K−K₀+½))² for K above a cut-off K₀ = 0.125, zero below it. This is a simple impaction fit with the shape of the Langmuir-Blodgett curves, not a measured table; it correctly gives no collection for small droplets and E → 1 for large droplets on big particles.
Infilling, then growth. A crystal occupies an envelope volume Venv (sphere of diameter D₀, bulk density ρenv, typically 5-20 kg/m³ for dendrites). Rime of density ρr first fills the open space: V = max(Venv, mice/ρice + mrime/ρr). Size stays at D₀ while the mass climbs, so the fall speed rises quickly; once the envelope is full the particle is graupel and its diameter grows as dD/dz ≈ E LWC / (2 ρr) per metre fallen, independent of fall speed.
Hallett-Mossop splintering. Between -3 and -8 °C, rime accretion of large droplets (> 24 µm) in the presence of small ones (< 13 µm) ejects about 350 ice splinters per milligram of rime, peaking at -5 °C. Here the splinter count is 350 per mg × w(T) × (rime from the large class) with a triangular weight w(T) (0 at -3 and -8 °C, 1 at -5 °C). Real counts are laboratory values with a large scatter, and the process needs small droplets to be present, as modelled by a yes/no condition.
Simplifications. Bulk accretion with a monodisperse small and a monodisperse large droplet class; no aerodynamic flutter or tumbling; the particle never melts and no wet growth or hail is modelled (see the hailstone sims for that); rime density is a constant you choose (in reality it depends on droplet size, impact speed and surface temperature); no horizontal wind, so the particle falls straight; latent heating of the particle is ignored; the 6.5 K/km lapse rate is used throughout the cloud. Typical values (ρenv, ρr, K₀, Cs) are illustrative. Models built with Blender, scene by Three.js.