The science Close
What the dashboard computes
Four sliders drive one chain of simplified, textbook models. Everything shown on the labels, charts and maps is computed from them. Numbers are of the right order of magnitude, not a forecast of a real volcano.
Vent exit speed. Gas exsolving from the melt expands from the chamber pressure P to atmospheric pressure. The isothermal expansion work per kg of mixture is n Rg T ln(P/pa ) and a fraction η becomes jet kinetic energy: w = √(2 η n Rg T ln(P/pa )), n = gas mass fraction, Rg = 461.5 J/kg/K (water vapour). η = 0.313/(1+√(μ/104 )): thicker magma loses more energy in the conduit (illustrative, calibrated).Mass flux. ṁ = Cd ρmix A w with the mixture density of gas and melt at the vent and A = πD²/4. Cd = 0.306 is a calibration constant (the real flow fills only part of the vent) chosen so the default settings give a 12.4 km cloud.Split of the mass. A share goes to effusive lava 1/(1+(n/2%)²); of the rest, a logistic criterion in gas content, viscosity and vent width decides how much collapses into pyroclastic flows and how much stays buoyant . This criterion is qualitative (after Wilson, Sparks & Wilson 1978); it is not a fluid simulation.Column height. Mastin et al. (2009): Htop = 2.00 V0.241 (km, V = dense-rock-equivalent volume flux in m³/s). The umbrella level (neutral buoyancy) is about 0.7 Htop (Sparks et al. 1997); the dashboard labels the 0.7 Htop level as the eruption column and the top as the ash cloud.Lava fountain. Height of a vesicular 8 cm bomb launched at w with quadratic drag: H = ln(1 + k w²/g)/(2k), k = 3 ρa CD / (4 ρp d).Lava flow (cellular automaton)
Lava is a thickness h and temperature T on a 78 m grid over the real height field. Each step moves lava to lower neighbours with the mean speed of a Bingham sheet on a slope θ: v = ρ g h² sinθ /(3μ) · (1 − 1.5ξ + 0.5ξ³), ξ = τy /(ρ g h sinθ); if ξ ≥ 1 the lava stops. Viscosity rises about one decade per 120 K of cooling. Cooling: dT/dt = −[εσ(T&sup4;−Ta &sup4;) + hc (T−Ta )]/(ρ c h). Heat moves with the lava (mass-weighted mixing). Simplified: no tubes, no crust insulation, lava viscosity equals magma viscosity at the vent temperature.
Pyroclastic flow, ash cloud, seismicity
Pyroclastic flow. Puffs slide as Coulomb blocks over the height field: a = −g∇h/(1+|∇h|²) − μg/√(1+|∇h|²) · v̂ − c|v|v, released with v = 0.85 √(2 g Hc ) from the collapse height Hc = 0.25 Hnb . They follow valleys, slow down and stop; run-out comes from the energy balance, not from a fixed length.
Ash cloud. Particles rise on h(t) = H(1 − (1 − t/τ)²) (jet decelerating from w), then spread as an umbrella r ∝ t0.62 , drift with a height-dependent wind (1.5 + 0.7 z m/s) and settle slowly. The side-view chart is a histogram of particle altitude against time.
Seismic panel. Tremor amplitude follows the discharge; discrete explosive events draw their magnitude from the Gutenberg-Richter law N(>M) = 10−b(M−Mmin ) (b = 1). The scheduled paroxysm at about 15 min has M = ⅔(log10 E − 4.8) with E = ½ m w² for 200 s of column discharge. The magnitude scale of the tremor trace is illustrative.
Time. 1.0x = 10 simulated seconds per real second, so the 20 minute scenario takes about 2 minutes.
Independent numerical checks (run in your browser) running…
Experiment: does the height follow Mastin's V0.241 law?
Sweeps the vent diameter from 40 to 400 m with the other sliders fixed, recomputes the column and fits the log-log slope of Htop against the buoyant volume flux. Prediction: 0.241.
Run experiment
Not a forecast. Typical literature values quoted on labels (e.g. 700–1000 °C pyroclastic flows, 100–300 m/s) are order-of-magnitude. Assets: terrain textures, trees, bombs and the volcano pictures were modelled and baked in Blender; the 3D runs on Three.js r160.
