Industrial air pollution source
Atmospheric dispersion modeling is the
mathematical simulation of how
air pollutants disperse in the ambient
atmosphere. It is performed with
computer programs that solve the mathematical equations and
algorithms which simulate the pollutant
dispersion. The
dispersion models are
used to estimate or to predict the downwind
concentration of air pollutants emitted from
sources such as industrial plants and vehicular traffic. Such
models are important to governmental agencies tasked with
protecting and managing the ambient
air
quality.
The models are typically employed to
determine whether existing or proposed new industrial facilities
are or will be in compliance with the National Ambient Air
Quality Standards (NAAQS) in the United States and other nations. The models also serve to
assist in the design of effective control strategies to reduce
emissions of harmful air
pollutants.
The dispersion models require the input of data which
includes:
 Meteorological conditions such as
wind speed and direction, the amount of atmospheric turbulence (as characterized by what is called
the
"stability class"), the ambient air temperature and the height
to the bottom of any inversion
aloft that may be present.
 Emissions parameters such as source location and height, source
vent stack diameter and exit velocity, exit
temperature and mass flow rate.
 Terrain elevations at the source location and at the receptor
location.
 The location, height and width of any obstructions (such as
buildings or other structures) in the path of the emitted gaseous
plume.
Many of the modern, advanced dispersion modeling programs include a
preprocessor module for the input of meteorological and other
data, and many also include a postprocessor module for graphing
the output data and/or plotting the area impacted by the air
pollutants on maps.
The atmospheric dispersion models are also known as atmospheric
diffusion models, air dispersion models, air quality models, and
air pollution dispersion models.
Atmospheric layers
Discussion of the layers in the
Earth's atmosphere is needed to
understand where airborne pollutants disperse in the atmosphere.
The layer closest to the Earth's surface is known as the
troposphere. It extends from
sealevel to a height of about 18 km and contains about 80
percent of the mass of the overall atmosphere. The
stratosphere is the next layer
and extends from 18 km to about 50 km. The third layer is
the
mesosphere which
extends from 50 km to about 80 km. There are other layers
above 80 km, but they are insignificant with respect to
atmospheric dispersion modeling.
The lowest part of the troposphere is called the
atmospheric boundary layer
or the
planetary boundary
layer and extends from the Earth's surface to about 1.5 to
2.0 km in height. The air temperature of the atmospheric
boundary layer decreases with increasing altitude until it reaches
what is called the
inversion
layer (where the temperature increases with increasing
altitude) that caps the atmospheric boundary layer. The upper part
of the troposphere (i.e., above the inversion layer) is called the
free troposphere and it extends up to the 18 km
height of the troposphere.
The ABL is of the most important with respect to the emission,
transport and dispersion of airborne pollutants. The part of the
ABL between the Earth's surface and the bottom of the inversion
layer is known as the mixing layer. Almost all of the airborne
pollutants emitted into the ambient atmosphere are transported and
dispersed within the mixing layer. Some of the emissions penetrate
the inversion layer and enter the free troposphere above the
ABL.
In summary, the layers of the Earth's atmosphere from the surface
of the ground upwards are: the ABL made up of the mixing layer
capped by the inversion layer; the free troposphere; the
stratosphere; the mesosphere and others. Many atmospheric
dispersion models are referred to as
boundary layer models
because they mainly model air pollutant dispersion within the ABL.
To avoid confusion, it should be noted that models referred to as
mesoscale models have dispersion modelling capabilities
that extend horizontally up to a few hundred kilometres. It does
not mean that they model dispersion in the mesosphere.
Gaussian air pollutant dispersion equation
The technical literature on air pollution dispersion is quite
extensive and dates back to the 1930s and earlier. One of the early
air pollutant plume dispersion equations was derived by Bosanquet
and Pearson. Their equation did not assume
Gaussian distribution nor did it include
the effect of ground reflection of the pollutant plume.
Sir Graham Sutton derived an air pollutant plume dispersion
equation in 1947 which did include the assumption of Gaussian
distribution for the vertical and crosswind dispersion of the plume
and also included the effect of ground reflection of the
plume.
Under the stimulus provided by the advent of stringent
environmental control regulations, there was
an immense growth in the use of air pollutant plume dispersion
calculations between the late 1960s and today. A great many
computer programs for calculating the dispersion of air pollutant
emissions were developed during that period of time and they were
called "air dispersion models". The basis for most of those models
was the
Complete Equation For Gaussian Dispersion Modeling
Of Continuous,
Buoyant Air Pollution Plumes shown below:
C =
\frac{\;Q}{u}\cdot\frac{\;f}{\sigma_y\sqrt{2\pi}}\;\cdot\frac{\;g_1
+ g_2 + g_3}{\sigma_z\sqrt{2\pi}}
where: 

f 
= crosswind dispersion parameter 

= \exp\;[\,y^2/\,(2\;\sigma_y^2\;)\;] 
g 
= vertical dispersion parameter = \,g_1 + g_2 +
g_3 
g_1 
= vertical dispersion with no reflections 

= \; \exp\;[\,(z 
H)^2/\,(2\;\sigma_z^2\;)\;] 
g_2 
= vertical dispersion for reflection from the
ground 

= \;\exp\;[\,(z +
H)^2/\,(2\;\sigma_z^2\;)\;] 
g_3 
= vertical dispersion for reflection from an
inversion aloft 

= \sum_{m=1}^\infty\;\big\{\exp\;[\,(z  H 
2mL)^2/\,(2\;\sigma_z^2\;)\;] 

+\,
\exp\;[\,(z + H + 2mL)^2/\,(2\;\sigma_z^2\;)\;] 

+\,
\exp\;[\,(z + H  2mL)^2/\,(2\;\sigma_z^2\;)\;] 

+\,
\exp\;[\,(z  H + 2mL)^2/\,(2\;\sigma_z^2\;)\;] 
C 
= concentration of emissions, in g/m³, at any
receptor located: 

x meters
downwind from the emission source
point 

y meters
crosswind from the emission plume centerline 

z meters above
ground level 
Q_{} 
= source pollutant emission rate, in g/s 
u 
= horizontal wind velocity along the plume
centerline, m/s 
H 
= height of emission plume centerline above ground
level, in m 
\sigma_z 
= vertical standard
deviation of the emission distribution, in m 
\sigma_y 
= horizontal standard deviation of the emission
distribution, in m 
L_{} 
= height from ground level to bottom of the
inversion aloft, in m 
\exp 
= the exponential
function 
The above equation not only includes upward reflection from the
ground, it also includes downward reflection from the bottom of any
inversion lid present in the atmosphere.
The sum of the four exponential terms in g_3 converges to a final
value quite rapidly. For most cases, the summation of the series
with
m = 1,
m = 2 and
m = 3 will provide
an adequate solution.
It should be noted that \sigma_z and \sigma_y are functions of the
atmospheric stability class (i.e., a measure of the turbulence in
the ambient atmosphere) and of the downwind distance to the
receptor. The two most important variables affecting the degree of
pollutant emission dispersion obtained are the height of the
emission source point and the degree of atmospheric turbulence. The
more turbulence, the better the degree of dispersion.
The resulting calculations for air pollutant concentrations are
often expressed as an
air pollutant
concentration
contour map in order to
show the spatial variation in contaminant levels over a wide area
under study. In this way the contour lines can overlay sensitive
receptor locations and reveal the spatial relationship of air
pollutants to areas of interest.
The Briggs plume rise equations
The Gaussian air pollutant dispersion equation (discussed above)
requires the input of
H which is the pollutant plume's
centerline height above ground level—and His the sum of
H_{s} (the actual physical height of the pollutant
plume's emission source point) plus Δ
H (the plume rise due
the plume's buoyancy).
Visualization of a buoyant Gaussian
air pollutant dispersion plume
To determine Δ
H, many if not most of the air dispersion
models developed between the late 1960s and the early 2000s used
what are known as "the Briggs equations." G.A. Briggs first
published his plume rise observations and comparisons in 1965. In
1968, at a symposium sponsored by CONCAWE (a Dutch organization),
he compared many of the plume rise models then available in the
literature. In that same year, Briggs also wrote the section of the
publication edited by Slade dealing with the comparative analyses
of plume rise models. That was followed in 1969 by his classical
critical review of the entire plume rise literature, in which he
proposed a set of plume rise equations which have become widely
known as "the Briggs equations". Subsequently, Briggs modified his
1969 plume rise equations in 1971 and in 1972.
Briggs divided air pollution plumes into these four general
categories:
 Cold jet plumes in calm ambient air conditions
 Cold jet plumes in windy ambient air conditions
 Hot, buoyant plumes in calm ambient air conditions
 Hot, buoyant plumes in windy ambient air conditions
Briggs considered the trajectory of cold jet plumes to be dominated
by their initial velocity momentum, and the trajectory of hot,
buoyant plumes to be dominated by their buoyant momentum to the
extent that their initial velocity momentum was relatively
unimportant. Although Briggs proposed plume rise equations for each
of the above plume categories,
it is important to
emphasize that "the Briggs equations" which become widely used are
those that he proposed for bentover, hot buoyant
plumes.
In general, Briggs's equations for bentover, hot buoyant plumes
are based on observations and data involving plumes from typical
combustion sources such as the
flue gas
stacks from steamgenerating boilers burning
fossil fuels in large power plants. Therefore
the stack exit velocities were probably in the range of 20 to
100 ft/s (6 to 30 m/s) with exit temperatures ranging from 250
to 500 °F (120 to 260 °C).
A logic diagram for using the Briggs equations to obtain the plume
rise trajectory of bentover buoyant plumes is presented
below:
 { border="0" cellpadding="2"
The above parameters used in the Briggs' equations are discussed in
Beychok's book.
See also
Atmospheric dispersion models
Organizations
Others
References
 Bosanquet, C.H. and Pearson, J.L., "The spread of smoke and
gases from chimneys", Trans. Faraday Soc., 32:1249, 1936
 Sutton, O.G., "The problem of diffusion in the lower
atmosphere", QJRMS, 73:257, 1947 and "The theoretical distribution
of airborne pollution from factory chimneys", QJRMS, 73:426,
1947
 Briggs, G.A., "A plume rise model compared with observations",
JAPCA, 15:433438, 1965
 Briggs, G.A., "CONCAWE meeting: discussion of the comparative
consequences of different plume rise formulas", Atmos. Envir.,
2:228232, 1968
 Slade, D.H. (editor), "Meteorology and atomic energy 1968", Air
Resources Laboratory, U.S. Dept. of Commerce, 1968
 Briggs, G.A., "Plume Rise", USAEC Critical Review Series,
1969
 Briggs, G.A., "Some recent analyses of plume rise observation",
Proc. Second Internat'l. Clean Air Congress, Academic Press, New
York, 1971
 Briggs, G.A., "Discussion: chimney plumes in neutral and stable
surroundings", Atmos. Envir., 6:507510, 1972
Further reading
Books
 Introductory
 Advanced
Proceedings
External links
 * EPA's Preferred/Recommended Models
 * EPA's Alternative Models
 * EPA's Photochemical Models
 * EPA's Preliminary Screening Models

where: 


Δh 
= plume rise, in m 

F^{ } 
= buoyancy factor, in
m^{4}s^{−3} 

x 
= downwind distance from plume source, in m 

x_{f} 
= downwind distance from plume source to point of
maximum plume rise, in m 

u 
= windspeed at actual stack height, in m/s 

s^{ } 
= stability parameter, in s^{−2} 