URBAN AIR POLLUTION MODELING 1171
wind and stability conditions. In the St. Louis model, Turner^
developed a computer program using the available winds to
provide pollutant trajectories. Distances obtained from the tra-
jectories are then used in the Pasquill diagrams or equations to
determine the values of σ y( x y 0 x ) and σ z ( x z 0 x ).Time-Dependent Emissions (The Roberts Model)The integrated puff transport algorithm of Roberts et al.
(1970), a source-oriented model, uses a three-dimensional
Gaussian puff kernel as a basis. It is designed to simulate the
time-dependent or transient emissions from a single source.
Concentrations are calculated by assuming that dispersion
occurs from Gaussian diffusion of a puff whose centroid
moves with the mean wind. Time-varying source emissions
as well as variable wind speeds and directions are approxi-
mated by a time series of piecewise continuous emission and
meteorological parameters. In addition, chemical reactions
are modeled by the inclusion of a removal process described
by an exponential decay with time.
The usual approximation for inversion lids of constant
height, namely uniform mixing arising from the superpo-
sition of an infinite number of multiple source reflections,
is made. Additionally, treatments for lids that are steadily
rising or steadily falling and the fumigation phenomenon are
incorporated.
The output consists of calculated concentrations for a
given source for each hour of a 24-hour period. The concen-
trations can be obtained for a given receptor or for a uniform
horizontal or vertical grid up to 1000 points.
The preceding model also forms the basis for two other
models, one whose specific aim is the design of optimal
control strategies, and a second that repetitively applies the
single-source algorithm to each point and area source in the
model region.METEOROLOGICAL MEASUREMENTSWind speed and direction data measured by weather bureaus are
used by most investigators, even though some have a number
of stations and towers of their own. Pollutants are measured
for periods of 1 hour, 2 hours, 12 hours, or 24 hours. 12- and
24-hour samples of pollutants such as SO 2 leave much to be
desired, since many features of their variations with time are
obscured. Furthermore, one often has difficulty in determining
a representative wind direction or even a representative wind
speed for such a long period.
The total amount of data available varies considerably in
the reviewed studies. Frenkiel’s study (1956)^ was based on
data for 1 month only. A comparatively large amount of data
was gathered by Davidson (1967),^ but even these in truth
represent a small sample. One of the most extensive studies
is the one carried out by the Argonne National Laboratory
and the city of Chicago in which 15-minute readings of SO 2
for 8 stations and wind speed and direction for at least 13
stations are available for a 3-year period.In the application of the mathematical equations, one is
required to make numerous arbitrary decisions: for example,
one must choose the way to handle the vertical variation of
wind with height when a high stack, about 500 ft, is used as
a point source; or how to test changes in wind direction or
stability when a change occurs halfway through the 1-hour
or 2-hour measuring period. In the case of an elevated point
source, Turner^ in his St. Louis model treated the plume as one
originating from the point source up to the time of a change in
wind direction and as a combination of an instantaneous line
puff and a continuous point source thereafter. The occurrence
of precipitation presents serious problems, since adequate
diffusion measurements under these conditions are lacking.
Furthermore, the chemical and physical effects of precipita-
tion on pollutants are only poorly understood. In carrying
forward a pollutant from a source, one must decide on how
long to apply the calculations. For example, if a 2-mph wind is
present over the measuring grid and a source is 10 miles away,
one must take account of the transport for a total of 5 hours.
Determining a representative wind speed and wind direc-
tion over an urban complex with its variety of buildings and
other obstructions to the flow is frequently difficult, since
the horizontal wind field is quite heterogeneous. This is so
for light winds, especially during daytime when convective
processes are taking place. With light-wind conditions, the
wind direction may differ by 180 within a distance of 1 mile.
Numerous land stations are necessary to depict the true wind
field. With high winds, those on the order of 20 mph, the
wind direction is quite uniform over a large area, so that
fewer stations are necessary.^METHODS FOR EVALUATING URBAN AIR
POLLUTION MODELSTo determine the effectiveness of a mathematical model,
validation tests must be applied. These usually include a
comparison of observed and calculated values. Validation
tests are necessary not only for updating the model because
of changes in the source configuration or modification in
terrain characteristics due to new construction, but also for
comparing the effectiveness of the model with any other that
may be suggested. Of course, the primary objective is to see
how good the model really is, both for incident control as
well as for long-range planning.Scatter Plots and Correlation MeasuresOf the validation techniques appearing in the literature, the
most common involves the preparation of a scatter diagram
relating observed and calculated values ( Y obs vs. Y calc ).^ The
degree of scatter about the Y obs Y calc line provides a mea-
sure of the effectiveness of the model. At times, one finds
that a majority of the points lies either above the line or
below the line, indicating systematic errors.
It is useful to determine whether the model is equally
effective at all concentration levels. To test this, the calcu-
lated scale may be divided into uniform bandwidths and theC021_001_r03.indd 1171C021_001_r03.indd 1171 11/18/2005 1:31:36 PM11/18/2005 1:31:36 PM