1168 URBAN AIR POLLUTION MODELING
course, can be applied only as long as the source distribu-
tion and terrain have not changed appreciably. For contin-
ued use of this method, one must be cognizant of changes
in the sources as well as changes in the terrain due to new
construction.
In preparing the tabulation, the data are first stratified
by season and also by the presence or absence of precipita-
tion. Further, appropriate group intervals must be selected
for the meteorological variables to assure that within each
grouping the pollution values are not sensitive to changes
in that variable. For example, of the spatial distribution of
the sources, one finds that the pollution concentration at a
station varies markedly with changes in wind direction. If
one plots percentile isopleths for concentration versus wind
direction, one may choose sectors in which the SO 2 concen-
trations are relatively insensitive to direction change. With
the exception of wind direction and hour of day, the meteo-
rological variables of the table vary monotonically with SO 2
concentration. The tabulation prediction method has advan-
tages over other receptor-oriented technique in that (1) it is
easier to use, (2) it provides predictions of pollution con-
centrations more rapidly, (3) it provides the entire percentile
distribution of pollutant concentration to allow a forecaster
to fine-tune his prediction based on synoptic conditions, and
(4) it takes into account nonlinearities in the relationships
of the meteorological variables and SO 2 concentrations. In
a sense, one may consider the tabulation as representing a
nonlinear regression hypersurface passing through the data
that represents points plotted in n -dimensional space. The
analytic form of the hypersurface need not be determined in
the use of this method.
The disadvantages of this method are that (1) at least
2 years of meteorological data are necessary, (2) changes in
the emission sources degrade the method, and (3) the model
could not predict the effect of adding, removing, or modify-
ing important pollution sources; however, it can be designed
to do so.
Where a network of stations is available such as exists in
New York City, Los Angeles, or Chicago, then the receptor-
oriented technique may be applied to each of the stations
to obtain isopleths or concentration similar to that obtained
in the source-oriented model. It would be ideal to have a
source-oriented model that could be applied to any city,
given the source inventory. Unfortunately, the nature of the
terrain, general inaccuracies in source-strength information,
and the influence of factors such as synoptic effect or the
peculiar geometries of the buildings produce substantial
errors. Similarly, a receptor-oriented model, such as the
Clarke model or one based on regression techniques, must
be tailored to the location. Every urban area must therefore
be calibrated, whether one desires to apply a source-oriented
model or a tabulation prediction scheme. The tabulation pre-
diction scheme, however, does not require detailed informa-
tion on the distribution and strength of emission sources.
Perhaps the optimum system would be one that would
make use of the advantages of both the source-oriented
model, with its prediction capability concerning the effects
of changes in the sources, and the tabulation predictionscheme, which could provide the probability distributions
of pollutant concentrations. It appears possible to develop
a hybrid system by developing means for appropriately
modifying the percentile entries when sources are modified,
added, or removed. The techniques for constructing such a
system would, of course, have general applicability.The Fixed-Volume Trajectory ModelIn the trajectory model, the path of a parcel of air is predicted
as it is acted upon by the wind. The parcel is usually con-
sidered as a fixed-volume chemical reactor with pollutant
inputs only from sources along its path; in addition, various
mathematical constraints placed on mass transport into and
out of the cell make the problem tractable. Examples of this
technique are discussed by Worley (1971). In this model,
derived pollution concentrations are known only along the
path of the parcel considered. Consequently, its use is limited
to the “strategy planning” problem. Also, initial concentra-
tions at the origin of the trajectory and meteorological vari-
ables along it must be well known, since input errors along
the path are not averageable but, in fact, are propagated.The Basic ApproachAttempts have been made to solve the entire system of three-
dimensional time-dependent continuity equations. The ever-
increasing capability of computer systems to handle such
complex problems easily has generally renewed interest in this
approach. One very ambitious treatment is that of Lamb and
Neiburger (1971),^ who have applied their model to carbon-
monoxide concentrations in the Los Angeles basin. However,
chemical reactions, although allowed for in their general for-
mulation, are not considered because of the relative inertness
of CO. Nevertheless, the validity of the diffusion and emission
subroutines is still tested by this procedure.
The model of Friedlander^ and Seinfeld (1969) also
considers the general equation of diffusion and chemical
reaction. These authors extend the Lagrangian similarity
hypothesis to reacting species and develop, as a result, a
set of ordinary differential equations describing a variable-
volume chemical reactor. By limiting their chemical system
to a single irreversible bimolecular reaction of the form
A B C, they obtain analytical solutions for the ground-
level concentration of the product as a function of the mean
position of the pollution cloud above ground level. These
solutions are also functions of the appropriate meteorologi-
cal variables, namely solar radiation, temperature, wind con-
ditions, and atmospheric stability.ADAPTATION OF THE BASIC EQUATION TO
URBAN AIR POLLUTION MODELSThe basic equation, (1), is the continuous point-source equa-
tion with the source located at the ground. It is obvious that the
sources of an urban complex are for the most part located above
the ground. The basic equation must, therefore, be modifiedC021_001_r03.indd 1168C021_001_r03.indd 1168 11/18/2005 1:31:35 PM11/18/2005 1:31:35 PM