Town AQI -PM2.5 at town 0 µg/m³Plume rise to 0 mOver the lid 0 %--FPS 0

Drag to orbit, wheel or pinch to zoom. Dots = smoke (brown-grey) drawn from the plume equations; the ground is coloured by air-quality category (yellow, orange, red, purple, maroon); the pale blue sheet is the mixing-height lid; the coloured column over the town is its AQI. The town, trees and fire are stylised and enlarged; distances and heights are to scale.

Wildfire Smoke Plume: Briggs Rise, Mixing-Height Lid and PM2.5 at a Valley Town

How much smoke reaches the town depends on how hot the fire is, how stable the air is and how low the inversion lid sits. Change them, or run a whole day, and read the air quality index.

The fire

The weather

Place and time

Live readouts

Ground-level PM2.5 along the plume axis

Where the plume is: height against distance

PM2.5 at the town through a 24-hour day

Experiment: does turbulence or the lid matter more?

First table: the six Pasquill classes with everything else as now. Second table: six lid heights. Prediction: stable air (E, F) and a low lid both raise the smoke at the town, but a strong plume escapes a low lid.

Independent numerical checks

Controls

Drag or one finger: orbit; wheel or pinch: zoom. The three view buttons jump to the whole valley, the town or the fire.
Manual weather uses the sliders directly. With the day-night cycle on, the slider values for wind and lid height are the afternoon values and the clock supplies stability class, lid and wind hour by hour; the hour slider sets the clock.
Wind direction turns the plume about the fire so the town sits off the axis.

The science

Fire power. Byram's fireline intensity is I = H w R (kW per metre of fire front) for heat content H = 18 000 kJ/kg of dry fuel (typical), fuel burned per area w and spread rate R. Fire power is I times the length of the front. Half of it is taken as convective heat that drives the plume (illustrative fraction).

Buoyancy and rise. The Briggs buoyancy flux is F = g Q_c / (π ρ c_p T). In neutral or unstable air the final rise is 21.4 F^3/4/u for F < 55 and 38.7 F^3/5/u otherwise (Briggs); in stable air 2.6 (F/(u s))^1/3 with s = (g/T) dθ/dz. On the way up the rise follows 1.6 F^1/3 x^2/3/u. Fire plumes are far larger and more turbulent than the stack plumes these formulas were fitted to, so rises are rough.

Dispersion. Smoke spreads as a Gaussian plume with Briggs rural widths σ_y(x), σ_z(x) for each Pasquill class. The long fire line is a virtual source of width L/4.3, and the buoyant plume adds a rise-related spread of Δh/3.5. A mixing-height lid H reflects the plume like a mirror (an image sum), so far downwind the smoke is spread evenly through the layer. The ground concentration at z = 0 is C = Q/(π u σ_y σ_z) e^{−y²/2σ_y²} Σ_n e^{−(h+2nH)²/2σ_z²}.

Two kinds of smoke. The flaming part (here 85 % by default) is buoyant. The smouldering part rises little and is released near the ground. A flaming plume whose final height exceeds about 1.1 H counts as overshooting the lid (a smooth ramp between 0.9 H and 1.1 H, illustrative) and is not reflected.

Emissions and air quality. PM2.5 emission = emission factor x fuel burned per second (12 g/kg, a typical value for forest fuel). The air quality index uses the US EPA PM2.5 breakpoints (the 2024 table: 9.0, 35.4, 55.4, 125.4, 225.4 µg/m³); check the current EPA table before real use. A background of 5 µg/m³ is added.

Honest simplifications: steady state, straight-line wind over flat ground, no terrain channelling, chemistry, smoke ageing, fire growth, spotting or pyrocumulus; the stability class, mixing height and wind are held constant unless the day-night cycle is on (the hourly mapping is an illustrative schedule). The smoke dots are a visualisation of the formulas, not a fluid simulation. Town, trees and the fire are stylised and enlarged. This is an educational model and must not be used for real smoke forecasting or evacuation decisions. Models built with Blender and Three.js.

Educational model; no affiliation.