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Air Quality Modelling: Gaussian Plume Model

Source of Pollution can be point (vent) , area (pond) or volume (conveyor)

Mathematical relationship between emissions and air quality that incorporates the transport, dispersion and transformation of compounds emitted into the air.

Input data required for Air Quality Modeling

  • Source characteristics
  • Meteorological conditions
  • Site and surrounding conditions

Types of Air Quality Modelling

Types of Air Quality Modelling

Gaussian Plume Model

Gaussian Plume Model
H - Effective Stack Height
  • Steady-state conditions - rate of emission from the point source is constant.
  • Homogeneous flow - wind speed is constant both in time and with height (wind direction shear is not considered) .
  • Pollutant is conservative and no gravity fallout.
  • Perfect reflection of the plume at the underlying surface, i.e.. no ground absorption.
  • The turbulent diffusion in the x-direction is neglected relative to advection in the transport direction, which implies that the model should be applied for average wind speeds of more than .
  • The coordinate system is directed with its x-axis into the direction of the flow, and the v (lateral) and w (vertical) components of the time averaged wind vector are set to zero.
  • The terrain underlying the plume is flat
  • All variables are ensemble averaged, which implies long-term averaging with stationary conditions.

In the lateral, or y, direction the profile shape is given by

Whilst in the vertical, or z, direction it is given by

Gaussian Spreading in 2 D Binormal

The concentration at any point is given by

Plume Centre Line
Upper Edge of Plume


steady-state concentration at a point

emissions rate,

Horizontal and vertical spread parameters, m (these are functions of distance, and atmospheric stability)

Average wind speed at stack height,

Horizontal distance from ground level,

Vertical distance from ground level, m

Effective stack height where physical stack height and

When at ground level – impact on crops

It should be noted that the maximum concentration occurs when

If only concentrations at ground level on the centre-line of the plume (along the x-axis direction) are required, &

Rate of emission from the source (Q)

Prevailing wind speed (U)

Direction (x)

Height of the centre-line of the plume above ground (H)


Cannot be applied for pollutants with chemical transformations

Finding 3 Unknowns

Where and are the turbulent wind speed fluctuations (turbulence intensities)

Where “ln” is the natural log, is the release height and is the aerodynamic roughness representing different topographic ground conditions

Environmental Lapse Rate

Plume Rise

This is the path or trajectory of the plume centre-line after it leaves the source. Its course depends upon atmospheric conditions and the amount of buoyancy and vertical momentum in the initial plume at the source.

  • Buoyancy forces causes the plume rise to vary with
  • Momentum forces cause the plume rise to vary with

Acceleration due to gravity

Stack exit velocity

Exit gas diameter

Stack gas exit temperature

Ambient air temperature

Buoyancy Flux

Momentum Flux

When we consider only momentum (unstable & neutral conditions)

Where Diameter of the source, e. g chimney exit diameter

Initial vertical velocity of the plume

For Calm Conditions

For wind speeds

Calm Conditions

The plume rise for a jet is computed as follows:

Crosswind Condition

Buoyant plumes

For Unstable and Neutral conditions

Downwind distance to the point of final rise

For Stable conditions

✍ Mayank