Atmospheric Dispersion Calculator
Calculate pollutant concentration using Gaussian plume model, effective stack height, wind speed at elevation, and plume rise for environmental air quality analysis.
What is Atmospheric Dispersion?
Atmospheric dispersion models predict how pollutants spread downwind from a source like a smokestack. The Gaussian plume model calculates the concentration of a contaminant at any point in space by combining the emission rate, wind speed, and the horizontal and vertical spread of the plume (sigma y and sigma z).
The effective stack height combines the physical chimney height with the extra rise the hot plume gains from buoyancy and momentum. Plume rise formulas differ by atmospheric stability: superadiabatic (unstable), neutral, and subadiabatic (inversion) conditions each have distinct coefficients.
How to Use the Atmospheric Dispersion Calculator
Select a calculation mode from the dropdown. Each mode has its own set of inputs:
- Gaussian Plume: Estimate downwind pollutant concentration using emission rate, wind speed, and dispersion coefficients. Four plume types are available: Point in Space, Ground Level, Plume Centerline, and Ground Source.
- Effective Stack Height: Calculate H = hp + Dh where hp is the physical stack height and Dh is the plume rise.
- Wind Speed at Elevation: Use the power-law wind profile u = u0 × (h / h0)n to extrapolate wind speed to any height.
- Plume Rise: Estimate buoyant plume rise for superadiabatic, neutral, or subadiabatic stability conditions using stack exit velocity, diameter, wind speed, and heat emission rate.
Example: Effective Stack Height Calculation
A power plant has a 60 m physical stack and the plume rise is estimated at 25 m. The effective stack height is H = 60 + 25 = 85 m. This is the elevation used as the release point in the Gaussian dispersion model, not the 60 m physical chimney height.
Key Concepts
The Gaussian plume model assumes pollutant concentrations follow a bell-curve distribution in both horizontal and vertical directions as the plume travels downwind. Effective stack height determines the initial release elevation. Atmospheric stability (classified from A through F by Pasquill) controls how quickly the plume disperses: unstable conditions spread pollutants rapidly, while stable inversions trap them near the surface.
Sigma y and sigma z (the dispersion coefficients) depend on downwind distance x and the Pasquill stability class. For a quick estimate, typical values at 500-1000 m downwind in neutral conditions are sigma y = 20-40 m and sigma z = 10-20 m.
For related atmospheric and fluid calculations, explore the Dry Adiabatic Lapse Rate Calculator to understand how temperature changes with altitude, or the Dew Point Calculator for humidity-related atmospheric conditions. The Specific Gas Constant Calculator is also useful for computing the gas constant of different air mixtures in dispersion modeling.
Frequently Asked Questions
What is effective stack height in air pollution modeling?
Effective stack height H is the physical chimney height plus the plume rise produced by buoyancy and exit momentum. It is the elevation Gaussian models use as the release point. A 60 m stack with 25 m of plume rise behaves like an 85 m release, dramatically reducing predicted ground-level concentrations.
How does atmospheric stability change dispersion behavior?
Unstable (superadiabatic) air mixes pollutants vertically and dilutes them quickly. Stable (subadiabatic or inversion) layers suppress vertical motion and can trap a plume near the surface, producing fumigation events. The stability parameter n in the wind-profile law and the Pasquill class (A-F) capture this effect.
How does the Gaussian plume model estimate concentrations?
It assumes the pollutant cloud spreads as a bivariate normal distribution around the plume centerline as it moves downwind. Concentration at any (x, y, z) point depends on emission rate Q, wind speed u, lateral and vertical spread sigma y and sigma z, and the effective release height H. A ground-reflection term accounts for pollutants that bounce off the surface.
Why is the power-law wind profile used in dispersion modeling?
Weather stations measure wind at about 10 m, but the dispersion equation needs wind at stack-top height. The power law u = u0 x (h/h0)^n extrapolates upward, with the exponent n encoding stability (roughly 0.10 for unstable, 0.15 neutral, 0.30+ for stable).
What are the main limitations of the Gaussian plume approach?
It assumes steady-state, uniform wind, level terrain, no chemical reactions, and continuous emissions. It fails for calm winds (u below 1 m/s), complex terrain, short-duration releases, and reactive pollutants. For those cases, regulators use models like AERMOD, CALPUFF, or computational fluid dynamics.
What units does the Gaussian model use for emission rate?
Q is the mass emission rate in grams per second (g/s). When wind speed is in m/s and sigma y, sigma z, H are in meters, the resulting concentration C comes out in g/m3. The calculator converts to micrograms per cubic meter (ug/m3) for comparison with most air quality standards.
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