A simplified Gaussian-plume dispersion model: emission rate, wind speed, stack height and atmospheric stability class drive a downwind ground-level concentration curve.
C(x) ≈ Q / (u·σy·σz·2π) × exp(−h²/(2σz²)) estimates ground-level concentration downwind of a source. Q is the emission rate, u is wind speed, h is the source (stack) height, and σy, σz are the plume's horizontal and vertical spread — both growing with downwind distance x. A ground-reflection term (doubling the concentration) accounts for pollutants bouncing back off the ground rather than diffusing into it.
For an elevated source (h > 0), concentration at ground level is actually low very close to the stack, because the plume hasn't spread down to the ground yet (σz is still small, making the exponential term tiny). As the plume travels downwind, σz grows and the plume touches the ground, so concentration rises — then falls again as the ever-widening σy·σz spreads the same total mass over a larger area. The result is a peak some distance downwind, not directly beneath the stack.
Atmospheric stability controls how fast σy and σz grow with distance. Class A (very unstable, typically strong sun and light wind) disperses pollutants quickly, spreading and diluting the plume fast. Class F (stable, typically calm clear nights) disperses very slowly, so pollutants stay concentrated much further downwind — the classic "temperature inversion" scenario behind many severe smog episodes.
This simulation is a simplified Gaussian plume dispersion model, the classic textbook approach to estimating how a pollutant released from a point source (a chimney, stack, or vent) spreads downwind. Concentration at ground level depends on the emission rate Q, the wind speed u (which dilutes the plume by carrying it away faster), the source height h, and the atmospheric stability class, which controls how quickly the plume mixes vertically and horizontally as it travels. The units on the concentration axis are normalized for teaching purposes, not real µg/m³ readings.
A blue curve traces estimated ground-level concentration against downwind distance, typically rising from a low value near the stack to a peak (marked with a pulsing yellow dot) before decaying as the plume disperses. A dashed red line marks an illustrative guideline reference level, loosely modelled on the WHO's PM2.5 annual guideline of 5 µg/m³ (though in normalized, not real, units).
Increase Emission rate to scale the whole curve up, increase Wind speed to dilute and lower it, and raise Stack height to push the ground-level peak further downwind. Switch Stability class from A (very unstable, fast dispersion) to F (stable, poor dispersion) to see how a calm, stable night traps pollution much closer to the source at higher concentrations than a windy, unstable afternoon.
Temperature inversions — when a layer of warm air traps cooler air (and pollution) near the ground — correspond to the most "stable" class (F) in this model, and are responsible for many of history's worst smog episodes, because they suppress the vertical mixing that would otherwise disperse pollutants upward and away.
For an elevated stack, the plume takes some distance to spread down to ground level. Very close to the source, the vertical spread σz is still small, so little of the pollutant has reached the ground yet. As the plume travels further, σz grows, more of it reaches ground level, and concentration rises — until the plume has spread so wide that the same amount of pollutant is diluted over a much larger area, and concentration falls again.
Atmospheric stability describes how readily air mixes vertically. Unstable conditions (strong sun, light wind, rising warm air) mix and disperse pollutants quickly; stable conditions (calm, clear nights with a temperature inversion) suppress vertical mixing, letting pollutants accumulate close to the ground at much higher concentrations for the same emission rate.
No. This is explicitly a simplified, illustrative teaching model — the concentration axis uses normalized relative units, not measured micrograms per cubic metre. Real air-quality modelling requires detailed emission inventories, meteorological data and validated dispersion software such as AERMOD.