# Gaussian Model

Topics: Pollution, Air pollution, Dimension Pages: 3 (743 words) Published: August 23, 2013
Session 9: Gaussian Plume Model

Gaussian Plume Model
The Gaussian plume model is a (relatively) simple mathematical model that is typically applied to point source emitters, such as coal-burning electricity-producing plants. Occassionally, this model will be applied to non-point source emitters, such as exhaust from automobiles in an urban area. One of the key assumptions of this model is that over short periods of time (such as a few hours) steady state conditions exists with regard to air pollutant emissions and meteorological changes. Air pollution is represented by an idealized plume coming from the top of a stack of some height and diameter. One of the primary calculations is the effective stack height. As the gases are heated in the plant (from the burning of coal or other materials), the hot plume will be thrust upward some distance above the top of the stack -- the effective stack height. We need to be able to calculate this vertical displacement, which depends on the stack gas exit velocity and temperature, and the temperature of the surrounding air. Once the plume has reached its effective stack height, dispersion will begin in three dimensions. Dispersion in the downwind direction is a function of the mean wind speed blowing across the plume. Dispersion in the cross-wind direction and in the vertical direction will be governed by the Gaussian plume equations of lateral dispersion. Lateral dispersion depends on a value known as the atmospheric condition, which is a measure of the relative stability of the surrounding air. The model assumes that dispersion in these two dimensions will take the form of a normal Gaussian curve, with the maximum concentration in the center of the plume. The "standard" algorithm used in plume studies is the Gaussian plume model, develped in 1932 by O.G. Sutton. The algorithm is as follows:

where: 1. C(x,y,z) is the concentration of the emission (in micrograms per cubic meter) at any point x meters downwind of the...