A continuous elevated release into a steady horizontal wind spreads as a Gaussian plume. On the wind-axis vertical plane (crosswind offset y = 0), downwind distance is x, height is z, source height is H:
C(x,0,z) = Q / (2π u σy σz) ·
[exp(-(z-H)²/2σz²) + exp(-(z+H)²/2σz²)]
This 2D view renders exactly that vertical slice as a heat field — the top panel — instead of a top-down map. The two bracketed exponentials are the real plume (centred on height H) and its mirror image below ground, added by the method of images so that no mass can pass through z = 0. You can watch both lobes directly: as the plume drifts downwind and σz(x) grows, the mirror lobe rises up through the ground line and merges with the real one, which is exactly the moment the ground starts to see hazardous concentration. The bottom panel plots the resulting ground-level (z = 0) concentration C(x,0,0) against downwind distance, with the IDLH threshold drawn as a horizontal line — the same curve emergency planners read to size an evacuation zone.
The plume widens through the dispersion coefficients σy(x) and σz(x), whose growth rate depends on the Pasquill–Gifford stability class — from A (strong daytime turbulence, spreads and dilutes fast) to F (calm stable night air, stays narrow and concentrated far downwind). This simulator uses the standard Briggs rural power-law fits for σy(x) and σz(x) per class — identical formulas to the 3D version of this simulator.
- Release rate Q — how much toxic mass leaves the source per second; concentration scales linearly with it.
- Stack height H — releases above ground level dilute more before the mirror lobe reaches the ground; the peak ground concentration moves further downwind as H increases.
- Wind speed u — concentration is inversely proportional to u: a light breeze traps the release near the source, a strong wind stretches and dilutes it.
- Stability class — sets how fast σy and σz grow with distance; class F can carry a hazardous concentration many times further downwind than class A for the same release.
Small markers drift through the cross-section as a real ensemble draw from this same distribution — each keeps a fixed standard-normal height offset and is displaced by σz(x)·z-score as it advects downwind, reflecting off the ground exactly like the mirror-image term predicts.