How Clouds Form: Lapse Rates, Nucleation and the LCL

Cooling air until it can't hold its water

Warm, moist air near the ground is buoyant and rises. As it climbs, the surrounding pressure drops, so the parcel expands and, with essentially no heat exchanged with its surroundings, cools adiabatically. Dry air cools at the dry adiabatic lapse rate of about 9.8°C per kilometre; once condensation begins and releases latent heat back into the parcel, the cooling slows to the moist adiabatic lapse rate of roughly 5-6°C per kilometre. The parcel's actual water content, though, does not change on the way up — only its capacity to hold that water as invisible vapour does.

Warm air can hold more water vapour than cold air; the maximum it can hold at a given temperature is the saturation vapour pressure. The height at which the rising, cooling parcel's temperature drops to its dew point — where actual vapour content equals the saturation value — is the Lifted Condensation Level (LCL), and that height is exactly where a cloud's flat base forms. Below the LCL the sky is clear even though the air is full of invisible vapour; above it, the excess vapour has nowhere to go but into liquid droplets.

Nucleation needs a surface to condense on

Pure water vapour resists condensing on itself — forming a new droplet from scratch (homogeneous nucleation) requires enormous supersaturation, several hundred percent, because a tiny droplet has so much surface tension relative to its volume that it evaporates faster than it grows. The atmosphere never gets anywhere near that. Instead, condensation happens on cloud condensation nuclei (CCN) — dust, sea salt, and other tiny aerosol particles a few tenths of a micron across — which let droplets nucleate at barely 100-101% relative humidity. Köhler theory formalises this: it combines the surface-tension penalty (Kelvin effect, which resists growth on tiny curved droplets) with the vapour-pressure-lowering effect of dissolved solute (Raoult effect, which helps growth) to predict the critical supersaturation each aerosol size needs to activate into a cloud droplet.

dT/dz ≈ -9.8 °C/km        dry adiabatic lapse rate (unsaturated air)
dT/dz ≈ -5 to -6 °C/km    moist adiabatic lapse rate (after condensation begins)
LCL height ≈ 125 × (T - Td) metres     quick estimate from surface T and dew point Td
supersaturation needed:
  homogeneous nucleation   ~300-400%   (essentially never happens in the atmosphere)
  heterogeneous on CCN     ~0.1-1%     (what actually happens, constantly)

From flat cumulus to towering cumulonimbus

Whether a cloud stays a shallow, cotton-ball cumulus or grows explosively into a cumulonimbus depends on the stability of the atmosphere above the LCL: how the environment's actual temperature profile compares to the rate the rising parcel is cooling at. If the environment is colder than the parcel at every height — an unstable atmosphere — the parcel keeps accelerating upward, drawing in more moist air, releasing more latent heat, and the cloud can punch through the tropopause as a full cumulonimbus with hail and lightning. If the environment warms back up relative to the parcel a short distance above the LCL — a stable layer, or an inversion — vertical growth is capped and the moisture instead spreads sideways into a flat layer: stratus. The energy available to a rising, unstable parcel is quantified as CAPE (Convective Available Potential Energy); forecasters use it directly to predict whether a day will produce fair-weather cumulus or severe thunderstorms.

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