Gaussian Plume Model Calculator
Estimate ground-level concentration downwind of a release, or solve for the emission rate or wind speed that produces a target concentration. Includes Briggs dispersion coefficients, distance and crosswind charts, and reference tables.
Ground reflection
The ground reflects the plume, which is why the ground-level formula has π rather than 2π in the denominator.
Wind dilutes
C is inversely proportional to u: doubling the wind speed halves the concentration.
Stability matters
Stable air (E, F) spreads the plume less, so concentrations are higher but peak farther from the source's reach of mixing.
Model limits
Assumes steady wind, flat terrain, a non-reactive gas and distances of about 100 m to 10 km. Not valid in near-calm winds.
Typical release scenarios
Illustrative ground-level releases with centerline concentrations (y = 0, H = 0) computed by this model with rural Briggs coefficients. The emission rates are example values, not measured data for any specific site. Click Load to open one.
| Scenario | Q (g/s) | u (m/s) | Class | x (m) | σy / σz (m) | C (µg/m³) |
|---|
Pasquill stability classes
Daytime classes depend on wind speed and incoming solar radiation, night classes on cloud cover (typical Pasquill scheme).
| Surface wind (m/s) | Day: strong sun | Moderate | Slight | Night: cloud ≥ 4/8 | Night: cloud ≤ 3/8 |
|---|---|---|---|---|---|
| < 2 | A | A–B | B | F | F |
| 2–3 | A–B | B | C | E | F |
| 3–5 | B | B–C | C | D | E |
| 5–6 | C | C–D | D | D | D |
| > 6 | C | D | D | D | D |
Dispersion coefficients σy / σz (m)
Briggs formulas for the terrain selected above (rural). Read across a row to see how stability changes plume spread.
| x (m) | A | B | C | D | E | F |
|---|
Formulas
Q = C · u · π·σy·σz / (exp(−y²/2σy²)·exp(−H²/2σz²))
u = Q · exp(…) / (π·σy·σz·C)
Rural class D: σy = 0.08x(1+0.0001x)^−½, σz = 0.06x(1+0.0015x)^−½
1 g/m³ = 10⁶ µg/m³
With H = 0 this reduces to the formula at the top of the page. Results are screening estimates, not a substitute for regulatory dispersion models such as AERMOD.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| C | Concentration | g/m³ |
| Q | Emission rate | g/s |
| u | Wind speed | m/s |
| σ_y,σ_z | Dispersion coefficients | m |
What it means
The Gaussian plume model is the most widely used method for predicting the downwind concentration of pollutants emitted from a continuous point source (e.g., a smokestack) under steady‑state conditions. The formula gives the ground‑level concentration (z=0) at a downwind distance x and crosswind distance y. It depends on the emission rate Q, wind speed u, and the dispersion parameters σ_y and σ_z, which vary with atmospheric stability and distance. The equation assumes a Gaussian distribution of the plume in the horizontal and vertical directions. This model is used for regulatory compliance, environmental impact assessments, and stack design. Example: For a stack emitting 100 g/s of SO₂ at a wind speed of 5 m/s, with σ_y=20 m and σ_z=10 m at a given x, the concentration at the plume centreline (y=0) is C = 100/(π × 5 × 20 × 10) = 100/(3141.6) ≈ 0.032 g/m³. This allows engineers to determine if ground‑level concentrations meet air quality standards.
Worked example
Gaussian Plume Concentration – Two Examples
Real‑World| Parameter | Value |
|---|---|
| Q | 100 g/s |
| u | 2 m/s |
| σ_y | 20 m |
| σ_z | 10 m |
| y | 0 m |
| Parameter | Value |
|---|---|
| Q | 100 g/s |
| u | 2 m/s |
| σ_y | 20 m |
| σ_z | 10 m |
| y | 10 m |
Common mistakes
- Unit of C: Concentration (e.g., µg/m³, mg/m³) – ensure Q has matching units (e.g., µg/s, mg/s).
- Dispersion coefficients σ_y and σ_z: Depend on atmospheric stability class and downwind distance – use appropriate Pasquill‑Gifford curves or calculations.
- Wind speed u: The average wind speed at release height – in m/s.
- Ground‑level concentration: The formula given is for z=0 (ground level) – for elevated releases, additional terms (reflection) are needed.
- Assumptions: Steady‑state, continuous point source, constant wind speed, flat terrain, no deposition.
Applications
The Gaussian plume concentration equation estimates the ground‑level concentration of a pollutant released from a point source, such as a smokestack, under steady‑state atmospheric conditions. It accounts for emission rate (Q), wind speed (u), and atmospheric dispersion parameters (σ_y, σ_z) that depend on atmospheric stability. This model is widely used in air quality management to predict the impact of industrial emissions, to set permit limits, and to assess compliance with ambient air quality standards. Environmental engineers use it to design stacks of adequate height, to evaluate the effectiveness of emission controls, and to conduct risk assessments for accidental releases. While simplified, the Gaussian plume remains a foundational tool in regulatory air pollution modelling.
- Air quality impact assessment for industrial facilities
- Design of stack height and emission controls
- Evaluation of compliance with National Ambient Air Quality Standards (NAAQS)
- Risk assessment for hazardous air pollutants (HAPs)
- Emergency response planning for accidental releases
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