## The Gaussian Model

The goal of air quality dispersion modeling is to estimate a pollutant's concentration at a point downwind of one or more emission sources. Since the early 1970s, the U.S. EPA has developed several computer models based on the Gaussian (or normal) distribution function curve. The models were developed from the research of Turner (1964; 1970); Pasquill (1974; 1967), Gifford (1968; 1975), and others. The Gaussian-based model is effective for representing the plume diffusion for a range of atmospheric conditions. The technique applies the standard deviations of the Gaussian distribution in two directions to represent the characteristics of the plume downwind of its origin. The plume's shape, and hence the standard deviations, varies according to different meteorological conditions. The following equation gives the ordinate value of the Gaussian distribution:

which is depicted as a bell-shaped curve as shown in Figure 5.8.1.

The coordinate system used in models dealing with the Gaussian equation defines the x axis as downwind of the source, the y axis as horizontal (lateral) to the x axis, and the z axis as the vertical direction. The Gaussian lateral distribution can be restated as follows:

Shown in Figure 5.8.2.

A second, similar Gaussian distribution describes the distribution of the plume in the vertical, or z, direction. The distribution of the plume around the centerline in both the y and z directions can be represented when the two single distributions in each of the two coordinate directions are multiplied to give a double Gaussian distribution. Projecting this distribution downwind through x gives the volume of space that contains the plume as shown in Figure 5.8.3.

Shifting the centerline upward a distance H corrects the equation for emissions at the effective stack height (stack height plus plume rise above stack) as follows:

where:

^(x,y,z; H) = the downwind concentration at a point x,y,z, fg/m3

Q = the emission rate of pollutants, g/s

^(x,y,z; H) = the downwind concentration at a point x,y,z, fg/m3

Q = the emission rate of pollutants, g/s

FIG. 5.8.1 The Gaussian distribution (or normal) curve. (Reprinted from D.B. Turner, 1970, Workbook of atmospheric dispersion estimates (Revised), Office of Air Programs Pub. No. AP-26, Research Triangle Park, N.C.: U.S. EPA.)

Plume Centerline

Plume Centerline

FIG. 5.8.2 Properties of the Gaussian distribution. Adapted, with permission, from H.A. Panofsky and J. A. Dutton, 1984. Atmospheric Turbulence: Models and Methods for Engineering Applications, John Wiley & Sons, New York.

FIG. 5.8.2 Properties of the Gaussian distribution. Adapted, with permission, from H.A. Panofsky and J. A. Dutton, 1984. Atmospheric Turbulence: Models and Methods for Engineering Applications, John Wiley & Sons, New York.

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