## Cbs

FIG. 5.8.3 Coordinate system showing Gaussian distribution in the horizontal and vertical. (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.)

FIG. 5.8.3 Coordinate system showing Gaussian distribution in the horizontal and vertical. (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.)

= the plume standard deviations, m = the mean vertical wind speed across the plume height, m/s = the lateral distance, m = the vertical distance, m = the effective stack height, m

As the plume propagates downwind, at some point the lowest edge of the plume strikes the ground. At that point, the portion of the plume impacting the ground is reflected upward since no absorption or deposition is assumed to occur on the ground (conservation of matter). This reflec tion causes the concentration of the plume to be greater in that area downwind and near the ground from the impact site. Functionally this effect can be mimicked, within the model with a virtual point source created identical to the original, emitting from a mirror image below the stack base as shown in Figure 5.8.4. Adding another term to the equation can account for this reflection of the pollutants as follows:

{exp[(-1/2)(z - H/oJ2] + exp[(-1/2)(z + H/oJ2]} 5.8(4)

When the plume reaches equilibrium (total mixing) in the layer, several more iterations of the last two terms can be added to the equation to represent the reflection of the plume at the mixing layer and the ground. Generally, no more than four additional terms are needed to approximate total mixing in the layer.

For the concentrations at ground level, z can be set equal to zero, and Equation 5.8(4) reduces as follows:

In addition, the plume centerline gives the maximum values. Therefore, setting y equal to zero gives the following equation:

which can estimate the concentration of pollutants for a distance x.

Finally, if the emission source is located at ground level with no effective plume rise, the equation can be reduced to its minimum as follows:

A number of assumptions are typically used for Gaussian modeling. First, the analysis assumes a steady-state system (i.e., a source continuously emits at a constant strength; the wind speed, direction, and diffusion characteristics of the plume remain steady; and no chemical transformations take place in the plume). Second, diffusion in the x direction is ignored although transport in this direction is accounted for by wind speed. Third, the plume is reflected up at the ground rather than being deposited, according to the rules of conservation of matter (i.e., none of the pollutant is removed from the plume as it moves downwind). Fourth, the model applies to an ideal aerosol or an inert gas. Particles greater than 20 /m in diameter tend to settle out of the atmosphere at an appreciable rate. More sophisticated EPA models consider this deposition, as well as the decay or scavenging of gases. Finally, the calculations are only valid for wind speeds greater than or equal to 1 m per sec.

Application of the Gaussian models is limited to no more than 50 km due to extrapolation of the dispersion coefficients. Other factors that influence the Gaussian dis

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