Gaussian Air Pollutant Dispersion Plume & Concentration Calculator

Environmental Fluid Dynamics & Atmospheric Science: The Gaussian Plume Model

The Gaussian plume model, adopted globally by the US EPA and WHO, models the 3-dimensional steady-state dispersion of continuous industrial point-source emissions:

• The Three Dispersion Assumptions:

• Pollutant mass is conserved with 100% reflection at the ground surface (no chemical deposition).

• Advective transport dominates downwind (wind speed u is constant with height).

• Lateral (y) and vertical (z) concentration profiles follow a bell-shaped Gaussian normal distribution with standard deviations σ_y and σ_z.

• Pasquill-Gifford Atmospheric Stability Classes (A through F):

• Class A (Extremely Unstable): Strong solar radiation and light wind cause rapid turbulent mixing and looping plumes.

• Class D (Neutral): Overcast skies or windy days typical of temperate climates.

• Class F (Moderately Stable): Nocturnal radiation inversions trap pollutants in narrow fanning plumes that travel tens of kilometers without dispersing.

• Effective Stack Height): High flue gas exit velocity and thermal buoyancy lift the plume far above the physical stack rim, exponentially reducing ground-level impacts.

How to Use This Calculator

Enter your Pollutant Mass Emission Rate (Q in grams/second) (e.g. 50 (50 g/s SO2, NOx, or PM2.5)), Physical Chimney / Stack Height (h_s in meters) (e.g. 60.0), Thermal Buoyancy Plume Rise (Δh in meters) (e.g. 20.0 (Effective height H = hs + Δh)), Downwind Receptor Distance (x in kilometers) (e.g. 1.5 (1.5 km = 1,500 meters)), Crosswind Offset Distance (y in meters) (e.g. 0 (0 = Plume Centerline)), Mean Wind Speed at Release Height (u in m/s) (e.g. 4.5), and Atmospheric Pasquill-Gifford Stability Class — choose from Class A — Extremely Unstable (Strong sunny day, light wind), Class B — Moderately Unstable (Sunny daytime, moderate wind), Class C — Slightly Unstable (Daytime overcast / moderate sun). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

EPA Gaussian Dispersion Plume \& Pasquill-Gifford equations:

Effective Release Height: H = h_stack + Δ h_plume rise (meters)

Ground-Level Concentration ( z = 0 ):

C(x, y, 0) = (Q) / (π u σ_y σ_z) (-(y^2) / (2σ_y^2)) (-(H^2) / (2σ_z^2)) × 10^6 (μg/m^3)

Pasquill-Gifford Dispersion Coefficients: σ_y = a y · x^b_y, σ_z = a z · x^b_z (x in km)

Worked Example

For example, evaluating a power plant chimney emitting \ from a 60.0 m stack with 20.0 m plume rise) under Pasquill Class C stability in a \ at a receptor 1.5 km downwind along the centerline): The dispersion coefficients are \^0.894 = 149.3 m, and \^0.911 = 88.0 m. The resulting ground-level ambient concentration is \ × 10^6 = 177.38 μg/m^

3.

Understanding Your Result

Evaluate your result in the context of your specific use case and relevant industry standards or reference values. A single calculated result is a starting point — test two to three scenarios to understand how sensitive the outcome is to your key input assumptions. For high-stakes decisions, verify your result against a secondary source or subject-matter expert before acting.