Page 340 - Fundamentals of Air Pollution 3E

296 19. Transport and Dispersion of Air Pollutants

methods vary from direct measurement of wind fluctuations by sensitive
wind measurement systems; to classification based on the appearance of
the chart record of the wind direction trace; to classification of atmospheric
stability indirectly by wind speed and estimates of insolation (incoming
solar radiation) or outgoing longwave radiation. Details of these methods
are given in the next section.

III. ESTIMATING CONCENTRATIONS FROM POINT SOURCES

The principal framework of empirical equations which form a basis for
estimating concentrations from point sources is commonly referred to as
the Gaussian plume model. Employing a three-dimensional axis system of
downwind, crosswind, and vertical with the origin at the ground, it as-
sumes that concentrations from a continuously emitting plume are propor-
tional to the emission rate, that these concentrations are diluted by the
wind at the point of emission at a rate inversely proportional to the wind
speed, and that the time- averaged (about 1 h) pollutant concentrations
crosswind and vertically near the source are well described by Gaussian
or normal (bell-shaped) distributions. The standard deviations of plume
concentration in these two directions are empirically related to the levels
of turbulence in the atmosphere and increase with distance from the source.
In its simplest form, the Gaussian model assumes that the pollutant does
not undergo chemical reactions or other removal processes in traveling
away from the source and that pollutant material reaching the ground or
the top of the mixing height as the plume grows is eddy-reflected back
toward the plume centerline.

A. The Gaussian Equations

All three of the Gaussian equations (19-2 through 19-4) are based on a
coordinate scheme with the origin at the ground, x downwind from the
source, y crosswind, and z vertical. The normal vertical distribution near
the source is modified at greater downwind distances by eddy reflection
at the ground and, when the mixing height is low, by eddy reflection at
the mixing height. Eddy reflection refers to the movement away ("reflection')
of circular eddies of air from the earth's surface, since they cannot penetrate
that surface. Cross sections in the horizontal and vertical at two downwind
distances through a plume from a 20-m-high source with an additional
20 m of plume rise (to result in a 40-m effective height) are shown in Fig.
19-5. The following symbols are used:

X, concentration, g rn~ 3
1
Q, emission rate, g s ~