MY SIMULATOR

Cold Front Lab

Density current, frontal lift and squall-line rain.

INTERACTIVE 3D

Time 0:00Front 0 m/sFPS 0

STATION TEMP22.0°C

PRESSURE1003 hPa

RAIN RATE0 mm/h

TIME☀🌧

Cold Front Lab: Density Current, Frontal Lift & Squall-Line Rain

A cold air mass is a heavy layer that slides under warm moist air. Watch the wedge advance, the warm air being lifted, the cloud and rain it makes, and what a station on the ground reads as the front passes.

Time speed

Preset

Air masses

Live numbers

Station record (T, p, rain) through the passage

Missions

Independent numerical checks

Also run outside the browser: node src/check.js (dam-break vs exact Stoker profile, mass conservation, Margules in two forms, LCL, Magnus table, drag-limited front speed).

Educational model, not a forecast. The cold pool is a one-dimensional reduced-gravity shallow-water layer; cloud, rain and the station record are derived from it with simple parcel physics. Constants marked [assumption] are illustrative. Clouds and the terrain are schematic and vertically scaled for readability.

Controls

Drag / one finger: orbit; wheel / pinch: zoom; Hero, Section and Map buttons (or keys H, S, T) jump the camera.
The TIME slider scrubs the whole passage (the run is precomputed, so it is exact in both directions); Start front plays it forward.
Sliders change the air masses: the model re-runs at once. Blue = cold side, orange = warm side.
Keys: Space play/pause, R reset.

The science

Cold air is a gravity current. With reduced gravity g′ = g ΔT / T̄ a cold layer of depth h obeys the shallow-water equations ∂h/∂t + ∂(hu)/∂x = 0, ∂(hu)/∂t + ∂(hu² + ½ g′h²)/∂x = −C_d u|u|. A frictionless dam break has the exact (Stoker) solution with front speed 2√(g′h₀); real heads are slower (Benjamin: Fr√(g′H), Fr about 1), so a drag term is used and the front speed is measured, not assumed.

Lift. The warm air above cannot cross the interface, so w = ∂h/∂t + u ∂h/∂x at the surface of the wedge. Where w > 0 the warm air rises.

Slope. Margules: tanα = f (T_wu_c − T_cu_w) / (g (T_w − T_c)), with f = 2Ω sinφ and along-front winds u. Real cold fronts are steeper at the nose than this large-scale average.

Cloud. The surface parcel rises dry-adiabatically (9.8 K/km) to the lifting condensation level LCL ≈ 125 (T − T_d) m, then along a moist adiabat. If it becomes buoyant within reach of the lifting (LFC) it keeps rising to the equilibrium level (deep convection, CAPE > 0); otherwise a shallower layer cloud forms. Rain rate R = ε ρ w (q_base − q_top) with precipitation efficiency ε = 0.5 [assumption] and Magnus e_s = 6.112 exp(17.62T/(243.12+T)).

Station. Temperature steps down when the cold pool is deeper than about 300 m; pressure rises by ρ g′ h behind the front (hydrostatic weight of the dense layer) and dips ahead of it (modelled trough [assumption]); wind veers from SW to NW.

Not modelled: Coriolis inside the shallow-water layer, turbulence and mixing at the head, ice, topographic blocking, 3D structure along the front.