Teaching model. A surface-based parcel lifted through an idealised sounding (mixed layer, cap, constant lapse rate to a 12 km tropopause) with an idealised wind profile. All numbers are computed from the sliders; the 3D cloud is a visual interpretation of them, not a cloud-resolving simulation. It is not a forecast tool and not for safety decisions: follow your national weather service for real warnings.
Parcel theory. The parcel rises dry-adiabatically (Γd = g/cp = 9.77 K/km) until its mixing ratio saturates at the lifting condensation level, then along a pseudo-adiabat with the moist lapse rate Γm = g (1 + Lv rs/(RdT)) / (cp + Lv2 rs ε / (RdT2)). Saturation vapour pressure follows Bolton (1980); pressure comes from hydrostatic integration of the virtual temperature.
CAPE = ∫LFCEL g (Tv,parcel − Tv,env) / Tv,env dz CIN = −∫sfcLFC (same, where negative) dz
Simplifications: no entrainment, no hydrometeor loading (this overestimates CAPE by perhaps 10-20 %), no ice phase, a surface (not mixed-layer) parcel. The dominant buoyant layer sets the LFC and the highest level where buoyancy returns to zero sets the EL.
LCL. The 125 m per kelvin rule, LCL ≈ 125 (T − Td) (Espy; see Lawrence 2005), is compared with the parcel-lift computation in Experiment 2.
Updraft speed. Converting CAPE to kinetic energy gives an upper bound:
wmax ≤ sqrt(2 CAPE)
Observed maxima are usually about half to 60 % of it (Weisman and Klemp 1982; Markowski and Richardson 2010), so the page also shows 0.5 × the parcel value.
Shear, BRN, helicity. The 0-6 km bulk shear is |V(6 km) − V(0)|; values of about 20 m/s (roughly 40 knots) or more favour supercells, 10-18 m/s multicells, below 10 m/s single or pulse cells (public rules of thumb: Rasmussen and Blanchard 1998; Thompson et al. 2003). The bulk Richardson number compares buoyancy with shear (Weisman and Klemp 1982, 1984):
BRN = CAPE / (½ U2), U = | Vmean,0-6 km − Vmean,0-0.5 km |
Supercells are favoured for BRN of about 10-45; much lower means the shear tears the storm apart, much higher that buoyancy dominates and outflow-driven multicells win. Storm-relative helicity measures the streamwise vorticity ingested by the updraft:
SRH = −∫0h k · [ (V − C) × ∂V/∂z ] dz = ∫ [ (v − cy) ∂u/∂z − (u − cx) ∂v/∂z ] dz
It equals twice the hodograph area swept relative to the storm motion C (Davies-Jones 1984), here integrated numerically from the profile over 0-1 and 0-3 km. C is the right-mover estimate of Bunkers et al. (2000): the 0-6 km mean wind plus 7.5 m/s perpendicular and to the right of the 0-6 km shear vector. SRH of 150 m2/s2 or more through 3 km is typical of supercell environments. The classifier box combines these thresholds heuristically: it is a rule of thumb, not a probability.
Structure. The rotating updraft (mesocyclone) feeds the anvil that the upper-level storm-relative wind blows downstream. Precipitation falls into the forward-flank downdraft (FFD) downstream; the rear-flank downdraft (RFD) brings dry mid-level air down on the rear side and rain wraps round the updraft as the hook echo. A wall cloud is a lowered, rotating cloud base next to the rain-free base; mammatus are pouches under the anvil; the overshooting top is the updraft punching above the equilibrium level. The 3D scene models these as a ray-marched density field (updraft, anvil, rain) plus Blender cloud shells; sizes scale with CAPE, shear and SRH but are illustrative.
Hail. The terminal speed of a solid ice sphere (density 900 kg/m3, drag coefficient about 0.6; cf. Heymsfield and Wright 2014):
vt = sqrt( 4 ρice g D / (3 CD ρair) ) ⇒ Dmax = 3 CD ρair w2 / (4 ρice g)
This is a ceiling: real stones also need supercooled liquid water, time in the growth zone, and are not spheres, so the page shows both the half-updraft estimate and the parcel upper bound.
Not covered. Cold pools and storm splitting dynamics, microphysics, dynamic pressure forcing, tornadogenesis, lightning. The synthetic radar view is a schematic. Terrain, farm buildings and clouds are original models built in Blender 5.2; rendering uses Three.js r160 and WebGL.