The Gaussian Plume Model

The Gaussian plume model is a fundamental and widely used model of atmospheric dispersion. Mathematically, the Gaussian plume model is the integration over time of the Gaussian puff model (Barrat, 2001). It is both a puff and a plume model. You can use it to compute steady-state concentrations from a continuous release or to compute the total quantity of substance that passes some geographic point after a puff release. A number of researchers have used the Gaussian plume model to model releases of B. anthracis spores, (Wein et al., 2003, Meselson et al., 1994, Buckeridge et al., 2004) including Meselson (1994) in his famous study of Sverdlovsk discussed above.

The Gaussian plume model makes several simplifying assumptions: (1) the source of the substance is a point,

(2) weather conditions do not vary over time or location,

(3) the released material behaves as a gas (that has the same density as air), (4) the material does not settle out of the air or otherwise decay (such as might occur due to chemical reactions with air or sunlight), and (5) the terrain is flat. Of the five assumptions, the ones least likely to hold in a bioterrorism scenario are (1), (2), and (5), but these assumptions did not affect the conclusions of Meselson and colleagues. Assumptions (3) and (4) are reasonable. The size of particles that most effectively enter the lung to cause infection is 1 to 5 microns, a particle size that behaves like a gas with respect to atmospheric dispersion (Office of Technology Assessment, 1993). For B. anthracis spores, ultraviolet light has an insignificant effect on the infectivity of spores as they travel through the atmosphere (World Health Organization, 1970).

Hanna et al. (1982) cite several reasons for the popularity of the Gaussian plume model, including:

1. It produces results that agree with experimental data as well as any model.

2. It is fairly easy to perform mathematical operations on this equation.

3. It is appealing conceptually.

4. It is consistent with the random nature of turbulence.

The Gaussian plume model is given by the following equation, which computes the atmospheric concentration C at a given point (x, y, z) downwind from the release point:

where

C = concentration of the substance at location x, y, z in |ig/m3 Q = rate that the substance is released into atmosphere (in |g/ second)

x = number of meters downwind from release point at which C is measured y = number of meters cross wind from release point at which C is measured z = number of meters above ground at which C is measured u = wind speed in meters/second h = height above ground in meters at which the substance was released oy(x) = standard deviation of the distribution of the substance in the crosswind (y) direction, as a function of x az(x) = standard deviation of the distribution of the substance in the vertical (z) direction, as a function of x

The parameters oy(x) and az(x) are the standard deviations of the distribution of C in the y and z directions. They are functions of the downwind distance x and atmospheric turbulence (dispersion is greater in more turbulent air). Stability classes are commonly used as a measurement of turbulence because they can be derived from inexpensive and easy meteorological measurements. There are a number of stability classification schemes, but most atmospheric dispersion models use Pasquill's scheme in conjunction with Brigg's formulas (Gifford, 1976) for calculating oy(x) and az(x) for each stability class (Table 19.1).

The Gaussian plume model produces a pattern of concentrations that is longer than it is wide, with the highest concentrations occurring at locations where y = 0. Although the Gaussian plume equation is the integration over time of the Gaussian puff equation, and therefore can be used to estimate total inhaled dose, different dispersion parameters ay(x) and az(x) are necessary for puff versus plume scenarios and

table 19.1 Briggs Formulas for Computing ay(x) and ffz(x), 10 m< x <10 km

Pasquill Stability Class

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