An explosive eruption sends ash up to a height set by its power. Wind layers then stretch the cloud, particles fall at speeds that depend on size, and a satellite tries to see what is left.
Educational model, not a forecast. Aviation and roof-load thresholds are illustrative and must never be used for real decisions.
Top-down map, 200 km wide, north up. Colours: 0.01 mm (pale) to 1 m (purple) of settled ash; the white dot is the vent, the dashed line the airliner route.
Grey = 11 µm brightness temperature (brighter = colder = thicker cloud). Red pixels have BTD = BT11 − BT12 below −0.5 K, i.e. are flagged as ash. Very thick cores may not be flagged: they look like an opaque cold cloud (BTD near 0).
Runs a 3-hour eruption headless for four wind-turn values and measures how wide the suspended fine-ash cloud has spread.
The science
Column height. The empirical Mastin-type fit is H [km] = 2.00 V^0.241 with V the dense-rock-equivalent volume flux in m³/s; the mass flux is Mdot = ρDRE V, ρDRE = 2500 kg/m³. The button switches to a theory-style scaling H ∝ Mdot^(1/4) matched at V = 10⁴ m³/s. Most ash (70 %) is released near the neutral-buoyancy level, taken as 0.8 H, and 30 % along the column.
Settling. Small particles follow Stokes: vs = (ρp − ρa) g d² / (18 μ) with ρa = 1.225 exp(−z/8.4 km), μ = 1.8×10⁻⁵ Pa s. For particle Reynolds number above 1 the drag law Cd = 24/Re (1 + 0.15 Re^0.687) (Schiller-Naumann) is balanced against weight. Four size classes are drawn: 1 µm (v ≈ 7×10⁻⁵ m/s), 10 µm (≈ 0.007 m/s: days to fall out of the stratosphere), 100 µm (≈ 0.5 m/s) and 1 mm pumice (≈ 5 m/s). Each drawn particle carries a mass weight, so a small mass share of fine ash is still visible.
Transport. Each particle moves with the layered wind, dx/dt = u(z) + u′ + (0, −vs), advanced by a midpoint (RK2) step, with Ornstein-Uhlenbeck turbulence (σ = 1.5 m/s, TL = 600 s). The four layers (0-3, 3-8, 8-12, above 12 km) have their own speed; the direction turns by the chosen angle per layer. That wind shear stretches and fans the cloud. Rain below 5 km removes particles with rate λ = 1.2×10⁻⁴ P^0.8 s⁻¹ (illustrative wet scavenging).
Deposit and loads. Settled mass per cell gives a thickness h = m / (ρbulk A), ρbulk = 1000 kg/m³, and a static roof load q = ρbulk g h. The 1 kPa marker is educational only.
Satellite. Column mass m (g/m²) of the fine classes sets the transmission τλ = exp(−kλ m) and the brightness temperature BTλ = τλ BTbg,λ + (1 − τλ) Tcloud (Tcloud = 235 K, BTbg = 290 / 288.5 K). With k11 = 0.18 and k12 = 0.12 m²/g (illustrative, silicate-like) the brightness-temperature difference BTD = BT11 − BT12 turns negative for ash; pixels below −0.5 K are flagged. The image refreshes every 15 simulated minutes and has 0.1 K-scale noise.
Aviation indicator. Concentration of particles below 10 µm within 5 km and ±1 km of the 10.7 km route: under 2 mg/m³ low, 2-4 medium, above 4 high. These are only teaching thresholds, not operational limits.
Simplifications. Fixed layered wind (no weather model), ISA-like exponential atmosphere, no pyroclastic flows, no aggregation, no electrical effects, no orographic wind, no gas phase; the column is drawn as a wind-bent puff stack rather than solved; the terrain is procedural. Constants are typical values; verify before quoting. Assets built with Blender; scene by Three.js. This is not affiliated with any observatory or agency.