Arena time
12:00
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Clock Dome: Twelve Weather Zones

A glass dome split into 12 hour wedges. A rotating hour hand triggers a real weather phenomenon in each wedge, with the physics numbers live.

Arena clock

One lap is 6 minutes at 1x (30 s per hour). Click a wedge in the 3D view, or a button below, to trigger that hour.

The twelve hours

Event

Environment

Sunset and night shift the base temperature by -3 and -7 degrees C and raise humidity, which matters for fog.

View and quality

High is the default on every device. Low renders at 1x pixel ratio with fewer particles and smaller shadow maps.

Independent checks

Each check recomputes a result with a separate numerical method (time stepping, integration, closed form) and compares it with the formula the simulation uses.

The science

Scale: one scene unit is 250 m, so the island is about 5 km across and the observer (a weather station) stands at the hub of the clock. All twelve wedges are teaching models with one governing idea each; they run in compressed time and are drawn with exaggerated heights.

1 Thunderstorm: charge separation and the 3 s per km rule

Ice and graupel collisions separate charge until the field in the cloud reaches the initiation value (about 300 kV/m here, far below the 3 MV/m of dry air in a lab because of precipitation particles). A strike then relaxes the field. Light arrives at once; sound travels at c = 331.3 sqrt(1 + T/273.15) m/s.

delay = d / c c(20 C) = 343.4 m/s -> 2.9 s per km

2 Fog: dew point, supersaturation, visibility

Dew point from the Magnus formula. When the air cools below it, the excess vapour condenses: LWC = rho_sat(Td) - rho_sat(T). Kunkel's fit gives the extinction, and Koschmieder's law the visual range.

es = 6.112 exp(17.62 T / (243.12 + T)) hPa beta = 144.7 LWC^0.88 per km V = 3.912 / beta

3 Heavy rain: drops and drains

Marshall-Palmer drop sizes (median diameter D0 = 0.9 R^0.21 mm) and a Gunn-Kinzer style fall speed v = 9.65 - 10.3 exp(-0.6 D). When the rain rate exceeds the drainage capacity (20 mm/h here) the excess accumulates as a puddle.

4 Hail: terminal velocity and kinetic energy

v_t = sqrt(4 rho_ice g D / (3 rho_air Cd)) Cd = 0.6 E = (1/2) (rho_ice pi D^3 / 6) v_t^2

A 2.5 cm stone falls near 20 m/s and carries about 1.5 J. Real stones are not smooth spheres, so Cd varies from 0.5 to 1.0.

5 Heat wave: heat index

With the dew point fixed, heating lowers relative humidity. The NWS Rothfusz regression turns temperature and humidity into an apparent temperature (valid roughly above 27 C).

6 Wildfire smoke: Byram intensity and a box model

I = H w R (H = 18 000 kJ/kg) L_flame = 0.0775 I^0.46 R = R0 (1 + (U/5)^1.4) illustrative wind factor, not a fitted fuel model PM2.5 = E / (U h W) h = 800 m mixing depth, W = 500 m width

PM2.5 bands follow the US EPA 2024 index breakpoints. The spread law and emission factor (12 g/kg) are simplified.

7 Flash flood: rational method and Manning

Q = C i A C = 0.8, A = 2.2 km2 Q = (1/n) A R^(2/3) sqrt(S) b = 8 m, n = 0.035, S = 0.01

Depth is solved from Q by bisection. The bridge deck is overtopped above 1.5 m. Real catchments add routing delay and infiltration.

8 Tornado: the Rankine vortex

v(r) = Vmax r / Rc (r < Rc, solid-body core) v(r) = Vmax Rc / r (r > Rc, free vortex) dP_centre = rho Vmax^2 (cyclostrophic balance)

EF ratings use 3-second gust speeds in miles per hour. The funnel is drawn about twice as wide as its scale for visibility. Debris orbits with the true angular speed v(r)/r.

9 Snow squall: visibility from flake extinction

Snowfall rate S (liquid equivalent) fixes the flake count N = S / (volume x density ratio x fall speed) for 3 mm flakes of density 100 kg/m3. Then beta = N x 2 x (pi D^2 / 4) and V = 3.912 / beta, giving a few hundred metres at 5 mm/h. Wind chill is the Canadian/US formula.

10 Gale: wind power goes as v cubed

P = (1/2) rho A Cp v^3 capped at 3.5 MW (rated, 12 m/s), cut-out at 25 m/s omega = lambda v / R lambda = 7 q = (1/2) rho v^2

11 Drought: a water balance

Hargreaves evapotranspiration ET0 = 0.0023 Ra (T + 17.8) sqrt(dT) with Ra = 16 mm/day equivalent and dT = 12 C drains a 150 mm soil store; evaporation slows once the store falls below half. Six model days pass per second.

12 Cold front: Margules slope

tan(alpha) = f Tm dV / (g dT) f = 1.03e-4 1/s, dV = 20 m/s

The dense cold air wedges under warm air on a slope of order 1:100 to 1:200. Pressure rises and the wind veers as the front passes.

What is simplified

Heights, sizes and time are compressed; the dome is one island, so winds and clouds are confined to wedges. The numbers are textbook models for teaching, not a forecast. Independent educational model; no characters, no trade dress, no affiliation with any film, game or organisation.

Made with 🟠 Blender · Three.js