MY SIMULATOR

LCL -cloud top -CAPE -w_max -FPS 0

Sounding: parcel vs air

● air● parcel■ CAPE■ CIN

Drag to orbit · wheel / pinch to zoom · orange arrows = rising warm air, white = cloud (starts at the condensation level)

Rising Air Parcel Lab: Lifting Condensation Level, Lapse Rates, CAPE and Cumulus Growth

Warm a patch of ground and let a parcel of moist air rise. It cools as it expands, condenses at the lifting condensation level and then keeps climbing only if it stays warmer than the surrounding air. Change the weather and watch the cloud base, the top and the updraft speed move.

Educational parcel model. One undiluted parcel in a hydrostatic atmosphere: no mixing with the surroundings, no water loading, no wind shear. Real cloud tops and updrafts are lower than parcel theory says (updrafts about half). Not a forecast.

Weather

Air and ground

Live readout

Temperature profile

Updraft speed with height

Experiment: condensation level against dew point

Sweeps the surface dew point from 0 C to just below the air temperature and compares the numerical parcel lifting with the textbook rule 125 m per degree of dew-point depression and with the Bolton closed form.

Independent numerical checks

Also run in Node: node src/check.js (same checks plus seven weather scenarios and a moisture monotonicity test).

Controls

Drag / one finger: orbit; wheel / pinch: zoom; Valley / Cloud / Ground views; Replay growth restarts the rising cloud.
Surface temperature and dew point set the moisture of the parcel; the lapse rate is how fast the surrounding air cools with height; the parcel excess stands for daytime ground heating; the inversion is a warm lid.
Playback speed is simulated seconds per real second.

The science

Dry ascent. An unsaturated parcel keeps its potential temperature, so T = T₀ (p/p₀)^R/c_p, about 9.8 K/km, while its mixing ratio r is fixed. Pressure follows the hydrostatic equation dp/dz = −p g/(R T_env).

Lifting condensation level. The parcel saturates when r = r_s(T,p) = 0.622 e_s/(p − e_s) with e_s = 6.112 exp(17.67 T/(T + 243.5)) hPa (Bolton 1980). Rule of thumb: LCL ≈ 125 m × (T − T_d).

Moist ascent. Condensation releases latent heat, so the lapse rate shrinks to Γ_m = g (1 + L r_s/(R T)) / (c_p + L² r_s ε/(R T²)) (3–6 K/km in the lower troposphere). The equivalent potential temperature of Bolton (1980, eq. 43) stays constant: this is one of the page checks.

Buoyancy, CAPE, CIN. B = g (T_parcel − T_env)/T_env. The level of free convection (LFC) is where B first becomes positive above the LCL, the equilibrium level (EL) where it turns negative again. CAPE = ∫_LFC^EL B dz, CIN is the negative area below the LFC. The undiluted upper bound for the updraft is w_max = √(2 CAPE); the cloud top rises at about half of √(2 ∫B dz) as a rough allowance for mixing [model factor].

Shallow cumulus rule [model]. If there is no LFC but the parcel is less than 3 K colder than the air within 3 km above the LCL and the LCL is below 3 km, the picture shows a shallow cloud about 300–600 m deep (fair-weather cumulus pushed up by turbulence); otherwise the sky stays clear. Rain is drawn when the cloud is deeper than 4 km.

Simplifications. Reversible moist adiabat (no fallout), virtual temperature and liquid water loading neglected, constant parcel moisture, environment profile piecewise linear with an optional inversion and an isothermal stratosphere above 11 km.