Gaussian Plume Model
The Gaussian plume model estimates pollutant concentration at any downwind point by assuming the plume spreads in a normal distribution both horizontally and vertically. It requires emission rate, wind speed, dispersion coefficients, and effective stack height.
C(x,y,z) from Q, u, σy, σz, H
Effective Stack Height
Effective stack height combines the physical chimney height with the extra rise the hot plume gains from buoyancy and momentum.
H = hp + Δh
Wind Speed at Elevation
The power law wind profile extrapolates a wind speed measured at one height to any other elevation. Widely used in air quality modeling and wind energy assessments.
u = u₀(h/h₀)ⁿ
How It Works
Atmospheric dispersion models predict how pollutants spread downwind from a source like a smokestack. The Gaussian plume model, developed by Pasquill, 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 (σy and σz). 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. The power-law wind profile adjusts a measured wind speed at one elevation to any other height.
Example Problem
A power plant has a 60 m physical stack and the plume rise is estimated at 25 m. What is the effective stack height?
- H = 60 + 25 = 85 m
- For superadiabatic plume rise with Vs = 15 m/s, d = 3 m, u = 6 m/s, Qh = 5000 kJ/s: Δh = 3.47(15)(3)/6 + 5.15√5000/6 ≈ 26.03 + 60.71 = 86.7 m
When to Use Each Variable
- Gaussian Plume: Point in Space — when you need the pollutant concentration at a specific (x, y, z) location downwind of a stack, e.g., assessing exposure at a nearby school.
- Gaussian Plume: Ground Level — when you need concentration at ground level (z = 0) at a lateral offset y, e.g., predicting worst-case exposure along a property boundary.
- Gaussian Plume: Plume Centerline — when you need the maximum concentration directly downwind at plume height, e.g., determining the peak concentration footprint.
- Gaussian Plume: Ground Source — when the emission comes from ground level with no stack, e.g., modeling fugitive dust from a construction site.
- Solve for Effective Stack Height — when you know the physical chimney height and plume rise, e.g., combining stack measurements with meteorological data for a permit application.
- Solve for Wind Speed at Elevation — when you need to extrapolate a surface wind measurement to stack-top height, e.g., adjusting weather station data for dispersion modeling.
- Solve for Plume Rise — when you know the stack exit conditions and need to estimate how high the plume rises above the stack, e.g., calculating effective release height for an EIS.
Key Concepts
The Gaussian plume model assumes pollutant concentrations follow a bell-curve distribution in both the horizontal and vertical directions as the plume travels downwind. Effective stack height — the sum of physical stack height and buoyancy-driven plume rise — 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.
Applications
- Air quality permitting: demonstrating compliance with National Ambient Air Quality Standards (NAAQS) for new industrial sources
- Environmental impact assessment: predicting downwind pollutant concentrations from power plants, refineries, and incinerators
- Emergency response: estimating chemical plume extent after an accidental release at a chemical plant
- Urban planning: siting schools, hospitals, and residential developments at safe distances from major emission sources
- Wind energy: using the power-law wind profile to estimate wind resources at turbine hub height from ground-level weather data
Common Mistakes
- Using ground-level wind speed directly in the Gaussian equation instead of adjusting it to stack height with the power-law profile — this overestimates concentrations because the actual wind speed at release height is usually higher
- Confusing physical stack height with effective stack height — ignoring plume rise can overpredict ground-level concentrations by a large margin, especially for hot buoyant plumes
- Applying the wrong stability class — using neutral stability when conditions are actually stable can underpredict peak concentrations by a factor of 5 to 10
- Forgetting that the Gaussian model assumes steady-state, uniform wind — it is not valid for calm winds, complex terrain, or rapidly shifting meteorological conditions
Frequently Asked Questions
What is effective stack height in air pollution?
Effective stack height is the sum of the physical chimney height and the plume rise caused by buoyancy and exit velocity. It determines the initial release elevation in Gaussian dispersion models and directly affects predicted ground-level concentrations.
How does atmospheric stability affect dispersion?
Unstable atmospheres promote vertical mixing and dilute pollutants faster, while stable conditions suppress mixing and can trap emissions near the surface. The stability parameter n in the wind profile equation captures this effect, with higher values indicating more stable conditions.
What is the Gaussian plume model?
The Gaussian plume model, developed by Pasquill, estimates the concentration of a pollutant at any downwind point by assuming the plume spreads in a normal (Gaussian) distribution both horizontally and vertically. It requires the emission rate, wind speed, dispersion coefficients, and effective stack height as inputs.
What is the difference between superadiabatic and subadiabatic plume rise?
Superadiabatic conditions (unstable atmosphere) produce the highest plume rise because strong convection enhances vertical mixing. Subadiabatic conditions (stable/inversion) suppress vertical motion, resulting in lower plume rise. Neutral conditions fall in between. Each regime uses different empirical coefficients in the plume rise formula.
What is the power law wind profile used for?
The power law wind profile extrapolates a wind speed measured at one height (typically 10 m at a weather station) to any other elevation. It is widely used in air quality modeling, wind energy assessments, and structural engineering.
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