A parcel of air lifted from the surface cools at the dry adiabatic lapse rate Γd = 9.8 °C/km until it reaches the lifting condensation level (LCL) — the altitude where its falling temperature meets its falling dew point (dew point drops roughly 1.8 °C/km as the parcel expands), computed here from surface temperature and relative humidity via the Magnus/Bolton dew-point formula. Above the LCL the parcel is saturated and cools at the slower saturated adiabatic lapse rate Γs, recomputed at every level from the actual latent-heat release:
Γs = g·(1 + Lv·rs /(Rd·T)) / (cp + Lv²·rs·ε /(Rd·T²))
rs = 0.622·es(T) / (p − es(T)) (saturation mixing ratio)
es(T) = 611.2·exp(17.67·T /(T+243.5)) (Bolton, Pa)
p(z) = 101325·exp(−z / 8000) (barometric)
Below the LCL the parcel is often still cooler than the environment (negative buoyancy = CIN, convective inhibition); once the parcel curve crosses back above the environment curve it reaches the level of free convection (LFC) and rises freely until it cools below the environment again at the equilibrium level (EL) — that crossing is the real cloud-top height, capped at the tropopause ceiling where the anvil spreads out.
- CAPE — ∫g·(Tparcel−Tenv)/Tenv dz between LFC and EL, the positive-buoyancy area on the temperature–altitude plot; this is the actual instability energy meteorologists read off a skew-T diagram.
- CIN — the same integral, sign-flipped, between the surface and the LFC: energy that must be overcome (a trigger, e.g. a front or daytime heating) before free convection begins.
- Max updraft — wmax = √(2·CAPE), the textbook parcel-theory ceiling on vertical velocity (ignores entrainment, water loading and drag, so real storms top out well below it).