Encyclopedia of Environmental Science and Engineering, Volume I and II

URBAN AIR POLLUTION MODELING 1167

I Ii

i

 QQIi

∑( )

1

4

S Si

i

 QQSi

∑( )

1

4

 Total


abcTIS ik

i

p

1

4

∑

where

 : concentration (g/m^3 )

Q: source strength (g/sec)

T: subscript to denote transportation sources

I: subscript to denote industrial and commercial

sources

S: subscript to denote space-heating sources

p: subscript to denote point sources

i: refers to the annular sectors

The above equations with some modification are taken

from Clarke’s report (1967). Values of the constants a, b, and

c can be determined from information concerning the diur-

nal variation of transportation, industrial and commercial,

and space-heating sources. The coefficient k i represents a

calibration factor applied to the point sources.

The Linear Regression-Type Model

A second example of the receptor-oriented model is one

developed by Roberts and Croke (Roberts et al., 1970)^ using

regression techniques. Here,


   

CCQCQ kQii

i

n

01122

1

∑

In applying this equation, it is necessary first to stratify

the data by wind direction, wind speed, and time of day.

C 0 represents the background level of the pollutant; Q 1

represents one type of source, such as commercial and

industrial emissions; and Q 2 may represent contributions

due to large individual point sources. It is assumed that

there are n point sources. The coefficients C 1 and C 2 and k i

represent the 1/ s (^) y s z term as well as the contribution of the
exponential factor of the Gaussian-type diffusion equation
(see Equation 1).
Multiple discriminant analysis techniques for indi-
vidual monitoring stations may be used to determine
the probability that pollutant concentrations fall within
a given range or that they exceed a given critical value.
Meteorological variables, such as temperature, wind
speed, and stability, are used as the independent variable
in the discriminant function.
The Martin Model
A diffusion model specifically suited to the estimation
of long-term average values of air quality was developed
by Martin (1971). The basic equation of the model is the
Gaussian diffusion equation for a continuous point source. It
is modified to allow for a multiplicity of point sources and a
variety of meteorological conditions.
The model is receptor-oriented. The equations for the
ground-level concentration within a given 22 1/2 sector
at the receptor for a given set of meteorological conditions
(i.e., wind speed and atmospheric stability) and a specified
source are listed in his work. The assumption is made that
all wind directions within a 22 1/2 sector corresponding to
a 16-point compass occur with equal probability.
In order to estimate long-term air quality, the single-
point-source equations cited above are evaluated to deter-
mine the contribution from a given source at the receptor for
each possible combination of wind speed and atmospheric
stability. Then, using Martin’s notation, the long-term aver-
age is given by

FD LSnnLS
SLN
∑∑∑ (,,)(,)xr ,
where D n indicates the wind-direction sector in which transport
from a particular source ( n ) to the receptor occurs; r n is the
distance from a particular source to the receptor; F ( D n , L, S )
denotes the relative frequency of winds blowing into the given
wind-direction sector ( D n ) for a given wind-speed class ( S ) and
atmospheric stability class ( L ); and N is the total number of
sources. The joint frequency distribution F ( D n , L, S ) is deter-
mined by the use of hourly meteorological data.
A system of modified average mixing heights based on
tabulated climatological values is developed for the model.
In addition, adjustments are made in the values of some
mixing heights to take into account the urban influence.
Martin has also incorporated the exponential time decay of
pollutant concentrations, since he compared his calculations
with measured sulfur-dioxide concentrations for St. Louis,
Missouri.
The Tabulation Prediction Scheme
This method, developed at the Argonne National Laboratory,
consists of developing an ordered set of combinations of rel-
evant meteorological variables and presenting the percentile
distribution of SO 2 concentrations for each element in the
set. In this table, the independent variables are wind direc-
tion, hour of day, wind speed, temperature, and stability. The
10, 50, 75, 90, 98, and 99 percentile values are presented
as well as the minimum and the maximum values. Also
presented are the interquartile range and the 75 to 95 per-
centile ranges to provide measures of dispersion and skew-
ness, respectively. Since the meteorological variables are
ordered, it is possible to look up any combination of meteo-
rological variables just as one would look up a name in a
telephone book or a word in a dictionary. This method, of
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