A rising parcel cools, aerosol particles turn into cloud droplets, and then either collisions make rain or ice crystals eat the liquid. Change the aerosol, the updraft and the ice nuclei and see which path the cloud takes.
Sliders marked * restart the parcel (they change the starting state); the others act at once.
Each button runs several complete parcels headless (50 min of model time, 400 super-droplets per run, so noisier than the live 1200) and tabulates the result. Base settings come from the sliders.
The science
Parcel. An air parcel rises at w without mixing with its surroundings. It cools dry-adiabatically, dT/dz = −g/cp, pressure follows the hydrostatic law, and condensation heats it by Lv dql/cp. Saturation ratio S = qv/qvs(T,p) with qvs = ε es/(p − es) (Bolton formula for es).
Activation (Köhler, κ form). A solution droplet of wet radius r around a dry particle rd is in equilibrium at Seq = [(r³ − rd³)/(r³ − rd³(1 − κ))] · exp(A/r), A = 2σ/(ρw Rv T). The maximum of this curve is the critical supersaturation, Sc ≈ √(4A³/(27 κ rd³)); once S exceeds it the droplet grows without bound. Bigger or more soluble particles activate first, so the peak supersaturation of the parcel decides how many become droplets.
Diffusional growth. r dr/dt = (S − Seq)/(Fk + Fd), Fk = (L/(RvT) − 1) L ρw/(K T) (heat conduction), Fd = ρw Rv T/(D es) (vapour diffusion). The radius obeys r² ≈ r₀² + 2GSt, so growth slows as the droplet gets bigger: condensation alone narrows the spectrum and stalls near 10 to 20 µm. Each step is solved implicitly (Newton with bisection fallback), the time step adapts to the relaxation time of S.
Collision-coalescence. Drops of radius R and r merge at rate K = π(R + r)² E |vR − vr|. E is the Long (1974) gravitational collection efficiency (small for drops below about 20 µm, 1 above 50 µm), terminal velocities come from a Schiller-Naumann drag balance (Atlas-Ulbrich above 0.7 mm radius). This is the step that bridges the size gap between 20 µm cloud droplets and 100 µm drizzle. Merging uses the super-droplet method (Shima et al. 2009): each computational particle carries a multiplicity ξ; random pairs collide with probability P = K ξmax Δt/ΔV · N(N−1)/2 / ⌊N/2⌋. Liquid particles that fall faster than they are lifted leave the cloud layer at the rate vt/H (reported as precipitation in mm).
Ice and the Bergeron process. Ice nuclei activate following the Cooper (1986) fit N = 0.005 exp(0.304 ΔT) L⁻¹ (ΔT below 0 °C, scaled by your factor). Because es,w > es,i, air that is just saturated over liquid is supersaturated over ice (about 10 % at −15 °C), so crystals grow by deposition dm/dt = 4πC (Si − 1)/(Fk,i + Fd,i) while droplets evaporate to keep Sw near 0. Crystals above about 75 µm radius rime (collect supercooled droplets), freezing releases Lf, and heavily rimed particles are drawn as graupel. Below −38 °C all droplets freeze.
Simplifications, stated honestly. Adiabatic parcel (no entrainment, no mixing, constant updraft until the chosen depth, then still air). No turbulence enhancement of collisions. Drops above 3 mm radius do not merge further (breakup not resolved). Ice: one capacitance factor (0.7) for all habits, an illustrative bulk-density closure, no aggregation, no secondary ice production (Hallett-Mossop), constant riming efficiencies of illustrative size; habit follows nucleation temperature only. No kinetic (accommodation) correction to diffusion. Surface tension and fall-out height are fixed. Aerosol is a single lognormal mode plus an optional giant sea-salt mode, with typical κ values (ammonium sulfate about 0.6, sea salt about 1.2, organic-rich 0.1 to 0.3). The 3D scene shows a schematic cloud tower whose height follows the parcel height; sphere sizes in the glass sample are log-scaled for visibility. Treat absolute times as typical, not forecasts.
Typical values to check against textbooks: typical cloud droplet number 50 (maritime) to 1000+ (polluted) cm⁻³; adiabatic LWC about 1.5 to 2.5 g m⁻³ per km; drizzle onset in clean marine cumulus within 15 to 30 min; Cooper ice nuclei about 0.1 per litre at −10 °C and 10 per litre at −25 °C.