Gaussian plume formula

Problems arise to get informations about the diffusion coeffients Ky and Kz. If equation (3.4) is interpreted as Gaussian distribution, a lot of available dispersion data can be taken into consideration because they are expressed in terms of standard deviations of the concentration distribution. Though there is no theoretical justification the Gaussian plume formula is converted to the K-theory expression by the transformation /11/... 

However, we must keep in mind the limitations of this approach, especially the transfer of consistent sets of dispersion parameters to the propagation of air pollution in the vicinity of a source. The Gaussian plume formula should be used only for those downwind distances for which the empirical diffusion coefficients have been determined by standard diffusion experiments. Because we are interested in emissions near ground level and immissions nearby the source, we use those diffusion parameters which are based on the classification of Klug /12/ and Turner /13/. The parameters are expressible as power functions,... 

Dispersion Models Based on Inert Pollutants. Atmospheric spreading of inert gaseous contaminant that is not absorbed at the ground has been described by the various Gaussian plume formulas. Many of the equations for concentration estimates originated with the work of Sutton (3). Subsequent applications of the formulas for point and line sources state the Gaussian plume as an assumption, but it has been rigorously shown to be an approximate solution to the transport equation with a constant diffusion coefficient and with certain boundary conditions (4). These restrictive conditions occur only for certain special situations in the atmosphere thus, these approximate solutions must be applied carefully. 

Analysis and tabulations of data to be used in Gaussian plume formulas are also available. The report for the St. Louis Dispersion Study (13) gives further insight into tracer-spreading over urban areas in contradistinction to open areas where many measurements have been made. Detailed working charts and numerous examples in Turners workbook (14) aid practical estimation of atmospheric dispersions under the conditions outlined above. 

Here the Gaussian plume formula for uniform flow conditions above the ground... 

Assuming a 5 km h wind and conditions of neutral stability, with no elevated inversion layer present, determine the average ground-level CO concentration as a function of downwind distance, using the appropriate Gaussian plume formula. 

The Gaussian plume model estimates the average pheromone flux by multiplying the measured odor concentration by mean wind speed, using the following formula (Elkinton etal, 1984). Everything is the same as in the Sutton model, except that ay and az, respectively, replace the terms Cy and Cz of the Sutton model. Dispersion coefficients are determined for each experiment separately. 

Up to this point in this chapter we have developed the common theories of turbulent diffusion in a purely formal manner. We have done this so that the relationship of the approximate models for turbulent diffusion, such as the K theory and the Gaussian formulas, to the basic underlying theory is clearly evident. When such relationships are clear, the limitations inherent in each model can be appreciated. We have in a few cases applied the models obtained to the prediction of the mean concentration resulting from an instantaneous or continuous source in idealized stationary, homogeneous turbulence. In Section 18.7.1 we explore further the physical processes responsible for the dispersion of a puff or plume of material. Section 18.7.2 can be omitted on a first reading of this chapter that section goes more deeply into the statistical properties of atmospheric dispersion, such as the variances a (r), which are needed in the actual use of the Gaussian dispersion formulas. 

We have seen that under certain idealized conditions the mean concentration of a species emitted from a point source has a Gaussian distribution. This fact, although strictly true only in the case of stationary, homogeneous turbulence, serves as the basis for a large class of atmospheric diffusion formulas in common use. The collection of Gaussian-based formulas is sufficiently important in practical application that we devote a portion of this chapter to them. The focus of these formulas is the expression for the mean concentration of a species emitted from a continuous, elevated point source, the so-called Gaussian plume equation. 

Dispersion coefficients and a, for diffiision of Gaussian plumes are available as graphs (Figure 2.27). Predictive formulas for these are available in Hanna ct al. (1982), Lees (1980), andTNO (1979) and are given in Table 2.12. Use of such formulas allow for easy application of spreadsheets. 

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