EPA-R4-73-030d
July 1973 ENVIRONMENTAL MONITORING SERIES
>£&:•
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EPA-R4-73-030d
URBAN AIR SHED PHOTOCHEMICAL
SIMULATION MODEL STUDY
VOLUME 1 - DEVELOPMENT AND EVALUATION
Appendix C - Microscale Model
of Local Vehicular Source Contributions
to Measured Pollutant Concentrations
by
Mei-Kao Lui and P.M. Roth
Systems Applications, Inc.
9418 Wilshire Boulevard
Beverly Hills, California 90212
Contract No. 68-02-0339
Program Element No. 1A1009
EPA Project Officer: Herbert Viebrock
Meteorology Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
July 1973
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This report has been reviewed by the Environmental Protection Agency and
approved for publication. Approval does not signify that the contents
necessarily reflect the views and policies of the Agency, nor does
mention of trade names or commercial products constitute endorsement
or recommendation for use.
11
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CONTENTS
Page
I. INTRODUCTION 1
II. SURVEY OF PREVIOUS STUDIES 5
III. THE MICROSCALE MODEL 9
A. Identifying the Flow Regime 9
B. The Governing Equations and Their Solution 14
IV. RESULTS 26
V. RECOMMENDATIONS FOR FUTURE WORK 51
References 54
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I. INTRODUCTION
One of the important considerations in the development of an urban
airshed model is the selection of an appropriate spatial scale. The
choice of scale is influenced by a number of factors, including:
The degree of detail with which emissions patterns are known.
The density of the meteorological data collection network,
and thus the spatial resolution of the measured windfield.
The increases in computing time and storage requirements
that are associated with increasing fineness of spatial
resolution.
The relationship between spatial and temporal scales.
As a result, scale selection frequently represents an attempt to effect
a compromise between degree of detail incorporated and magnitude of
computing requirements.*
While the selection of a particular grid size is required for
solution of the governing equations of the model, the consequences of
having to make such a choice are often unsatisfactory. There are three
principal sources of difficulty.
The impossibility of describing turbulent transfer processes
using one scale of resolution when these processes occur over
a broad range of scales, from the very coarse (movement of
large air masses) to the very fine (the smallest of eddies).
Large eddies derive their energy from the main stream of flow
and are relatively unstable. They tend to break down into
eddies of smaller size, which in turn fragment in still smaller
eddies. This cascading process continues until the scale char-
acterized by molecular viscosity is reached. The theoretical
treatment of this continuous spectrum of energy (or eddy sizes)
is extremely complex. The adoption of K-theory has permitted
the development of semi-empirical models of turbulent processes,
but has not dealt with the problem of the spectrum of scales.
The inability to account for the effects of sub-grid scale
variations in source emissions (and thus contaminant concentrations),
such as occur in the vicinity of major roadways, strong point sources,
and large airports. These variations are properly characterized on a
In the application of our model to the Los Angeles Basin, we have
adopted a square grid network of 625 2x2 mile grid squares.
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scale that is small (or fine) compared with the scale
adopted for use in urban airshed modeling. Such variations
will not be taken into account, for example, on the 2x2
mile grid used in the SAI model.
The inability to account for the effects of sub-grid scale
variations in surface features, such as buildings and elevated
freeway structures. Such structures alter local wind patterns
and turbulence levels, which contribute to the establishment
of local concentration levels. Similarly, the presence of
high-rise buildings along the street borders, the so-called
"street canyon", can reduce considerably the influence of
"main stream" convective transport processes on the dilution
of street level emissions. These effects occur on a scale
that is small compared with that typically adopted in urban
modeling and are thus "lost in the shuffle".
These deficiencies are of particular concern when one wishes to validate
an airshed model by comparing its predictions with point measurements of
contaminant concentrations.
Consider the validation of an urban airshed model, where carbon
monoxide is the pollutant of concern.* The model is based on the assump-
tion that emissions are uniformly distributed in space and time (over
an hourly interval) over each 2x2 mile cell and that meteorological
conditions are also invariant over this scale. The direct result of these
assumptions is that the predicted pollutant concentrations are uniform
within each grid square (or cell). The observed values of CO, however,
typically are representative only of the CO concentrations in the immedi-
ate vicinity of the monitoring station. Of the nine monitoring stations
operated by the Los Angeles County APCD, seven are located within 100
feet of a roadway having a daily traffic count in excess of 15,000 vehicles.
Ott (1971) has shown that CO concentrations measured at a monitoring
station situated along a busy city street are approximately twice the
background level (400 feet or more away from the street) and slightly
more than half that measured at the sidewalk located between the street
and the station. While we may expect that a properly formulated urban
scale model will predict background levels with reasonable accuracy on
a 2 x 2 mile scale, there is no justification for comparing these predic-
tions with local point observations. Some basis for comparison is required,
We assume for the purposes of this discussion that CO is unreactive.
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however, if the validity of the model is to be established. Either back-
ground observations may be made, or a model may be developed that is
capable of predicting concentrations at a nearby point that are due to
local emissions. Since a measurement program is beyond the scope of
this contract, and since we are limited to validation for six days in
1969, only the second of the two possibilities was open to us.
As we have noted, the main source of CO emissions in the vicinity
of Los Angeles County air pollution monitoring stations is the automobile.
Thus, to establish a basis for validation, we foresaw the need for a
sub-grid, or microscale, model capable of predicting the elevation in
concentration at the monitoring station, above background levels, that
is contributed by local automotive emissions. The sum of this predicted
concentration and the background concentration predicted using the urban
scale model can then be compared with observed concentrations for the
purpose of validation. We undertook the development and validation of
a simple diffusion model for CO to investigate the feasibility of modeling
at two spatial scales. We obtained limited results for four LA County
stations, which we report herein. However, much remains to be done,
both for CO and for the more complex situation in which chemical reactions
take place, as in the case of NO and hydrocarbons.
While the main purpose of developing a microscale model was to
provide a realistic basis for validating an urban scale model, the
microscale model (or "micromodel") may well be useful in other contexts.
The coarse resolution of the urban scale model does not suggest its use
in the prediction of dosage in areas of substantial local variation
in concentrations, such as along the sidewalk, in street canyons, and
in areas of public access at airports. The "micromodel" may be of con-
siderable value in estimating dosages in such situations, when used in
concert with the urban scale model. The micromodel may also be of value
in establishing a basis for formulating air quality standards. As con-
centrations can vary substantially in the vicinity of strong sources,
perhaps air quality standards should be based on obtaining measurements
at locations of greatest exposure—along sidewalks, within :the automobile,
inside the school yard. To properly establish such standards, based on
historical measurements, one must rely on a model capable of describing
local variations.
In this report, we review previous efforts in measuring and pre-
dicting local variations in concentrations due to nearby sources
(Section II ). We then present the microscale model developed in this
study (Section III). We give a general description of the model, dis-
cuss details of its formulation for application in the vicinity of low
structures (one to two story buildings) and present graphs displaying
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the relationship between the magnitude of concentration elevation
and the distance of the sampling probe from the street, the speed
and direction of the local wind, and the magnitude of the local
turbulent eddy diffusivity. We then present the results of apply-
ing the model in the prediction of hourly carbon monoxide concen-
trations at the Lennox, West Los Angeles, Whittier and Long Beach
monitoring stations for the six validation days (Section IV).
Finally, we make recommendations as to future needs in the continued
development of microscale models (Section V).
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II. SURVEY OF PREVIOUS STUDIES
Because emissions from automobiles constitute a major contribu-
tion to the total atmospheric pollutant load in urban areas, a number
of studies have been undertaken in recent years that have been con-
cerned with the dispersion of air contaminants in the vicinity of city
streets. We summarize some of the important findings of these inves-
tigations in this section.
Carbon monoxide concentrations at "curbside" locations were
measured by McCormick and Xintaras (1962) in Nashville, Tennessee and
Cincinnati, Ohio. They found that the temporal variation in carbon
monoxide concentration at both sites were correlated with hourly traffic
counts made at the street along which the concentrations were measured,
thus confirming the conclusions of an earlier study by Brief (1960) .
Furthermore, they noted that meteorological conditions, such as wind
speed, wind direction, turbulence level and atmospheric stability,
also played an important role in determining the level of carbon
monoxide concentrations .
An extensive investigation was later carried out in Germany by
Georgii and his co-workers (1967, 1969). Carbon monoxide concentrations,
traffic density, and pertinent meteorological variables were measured
at three sites located near three major streets in downtown Frankfurt/
Main. (Traffic counts on the streets ranged between 1200 and 1800 cars
per hour during peak hours.) Their findings are briefly summarized as
follows :
A. Good correlation was established between the diurnal carbon
monoxide concentration and the temporal variation in traffic den-
sity. Specifically, they found that the mean CO concentration c
increases exponentially with the traffic density n , as given by
c = Ae (1)
Different values of a and A were used to describe the concen-
tration along the windward and leeward sides of the street. That
Georgii selected a functional relationship of exponential form is
attributable to the fact that as traffic density increases, the average
speed will decrease, which in turn, will result in an increase in
emission rates.
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B. One of two distinct local flow regimes will be established
within a street canyon. Which regime persists is dependent upon
whether the rooftop wind speed exceeds, is less than, or is greater
than 2 meters per second (or 4.5 mph), as shown schematically in
Figure 1.
C. The decrease in the mean CO concentration with rooftop wind
speed, U, can be approximated by the following equation:
c = Ku"P (2a)
where K and p are both empirically determined constants.
D. Carbon monoxide concentration within a street canyon varies
exponentially with height z, as given by
c = Be~bZ (2b)
However, different value of b and B are required for the wind-
ward and leeward sides.
The results of Georgii, et al. are generally confirmed by Schnelle,
et al. (1969) and Johnson, et al. (1972). In particular, Johnson, et al.
have proposed the following composite equation to describe the concentrations
in a street canyon:
-3/4
. 0.1 K N S ' ,, .
Cw - °b + W(U + 0.5) (3S)
0.1 K N S~3/4
C. = C. + r 0 -i/? (3b)
1 ^ (U + 0.5)[(x2 + z2)172 + 2]
where c windward side concentration
w
c leeward side concentration
c background concentration
b
K dimensionless constant (=7)
N traffic density (vehicles/hr)
S average vehicle speed (miles/hr)
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Windcvaid
FIGURE 1. Air Circulation Within Streets at Different Wind Speeds
(Georgii, 1969)
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U rooftop wind speed (m/sec)
w width of the street (m)
x horizontal distance to the receptor point (m)
z vertical distance to the receptor point (m)
Although the numerical coefficients were obtained from an extensive
measurement program carried out in San Jose, these formulae also
correlated well with Georgii's data. Unfortunately, due to the limited
number of parameters included, as pointed by Johnson et al. (1971),
they failed to apply when the CAMP data were used. Nevertheless this
work still represents the most comprehensive study on the effect of
street canyon undertaken thus far.
The studies cited above, in general, have involved attempts to
establish empirical or correlational relationships between concentra-
tion and meteorological and spatial variables. We have not attempted
to review pertinent numerical modeling efforts, as we consider these
to be too complex for this particular application. Readers interested
in this area are referred to papers presented at the Air Pollutiop &
Diffusion Symposium, Las Cruces, New Mexico (1971) by R.S. Hotchkiss,
by D. Djurifi et. al. and by P.C. Chang et. al. In the next section, we
describe a simple but somewhat more fundamentally based modeling approach
to predicting local pollutant concentrations and their variations.
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III. THE MICROSCALE MODEL
No single model will suffice for describing transport and dispersion
phenomena in the vicinity of a street, largely because distinctly dif-
ferent flow patterns can occur above the roadway surface. In the first
part of this section we identify two flow patterns that are often observed
and suggest a criterion for distinguishing between them. In the second
part, we present a model for one of the two flow regimes, give the
solution of the governing equations, and illustrate their application in
a typical situation.
A. Identifying the Flow Regime
For the purpose of describing the dispersion of atmospheric
contaminants in an urban environment, we first distinguish between
the two circulation patterns that generally exist in the vicinity of
a city block, as illustrated in Figure 2.
1. Free Flow Regime
Air at street level is directly ventilated by the pre-
vailing wind at the rooftop. This case may be characterized
by the fact that the directions of the street-level wind and
the rooftop wind are the same.
2. Street Canyon
Air at street level does not have direct access to the
prevailing wind. Instead, a vortex of direction opposite to
that of the rooftop wind will be generated.
For modeling purposes we must be able to determine which of these regimes
obtains for a particular set of meteorological conditions.
In order to develop a criterion to aid in identification of the
appropriate regime, we consider the following very simple situation — •
a constant wind leaving the edge of a building as shown in Figure 3.
Writing the two-dimensional, steady-state continuity and momentum
equations for this situation, we have
2
3u , 3u „ 3 u
U ax" + W 3l " KM
where K is the turbulent diffusivity of momentum.
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n
M
o
/
F/
&»/ K&jcfjfne,
C r
FIGURE 2. Typical Flow Patterns
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FIGURE 3. Flow Pattern at the Leeward Edge of a Building
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The boundary conditions are:
!U o < z < <»
at x = 0
0 -«> < z < 0
u = U for x > 0 as z -»• «
u = 0 for x > 0 as z -*• -°°
The solution to this boundary layer problem, given by Lock (1951) ,
is shown in Figure 4. If we define a depth of penetration of the
rooftop wind, 6 , by choosing a corresponding u such that,
1 - - 99%
then from Figure 4, we obtain
_ .rv^~
(5)
We can now employ equation (5) as a criterion in identifying the
appropriate wind regime. If 6 , the estimated depth of penetration
of the rooftop wind, exceeds the average height of the upwind buildings,
W , then street level air has access to the main stream and Case 1
applies. However, if 6 < w , Case 2 applies. Consider as an example
two streets described by Georgii, et al. (1967):
Street height (in meters) width(in meters)
Karlstrasse 35.0 22.5
Stiftstrasse 25.7 17.5
Let us interpret x in equation (5) as street width. If we assume a
street width of 20 meters (the average width of the two streets), a
diffusivity K^ of lo4 cm2/second, and a mean wind of 2 meters/second,
then
x 2 x 10 ,, . ' .
cm = 31.4 meters
200
Thus, 6 > W for Stiftstrasse and Case 1 applies, whereas 6 < W for
Karlstrasse and Case 2 applies.
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u
7
6
5
3
^
t
3
-5
-7
FIGURE 4. Calculated Velocity Profile Downwind of the Rooftop
of a Building (lock, 1951)
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B. The Governing Equations and Their Solution
All nine Los Angeles County monitoring stations are located along
a city street. In some instances the adjacent street is lightly traveled,
as at Azusa and Reseda. More frequently, however, it is heavily traveled.
With the exception of the downtown station, however, all are situated
within, adjacent to, and in the vicinity of structures that are no more than
one or two stories high. In such situations 6 > W for all meteorological
conditions except that of extremely light winds (less than 1/4 meter/second).
We have thus restricted our efforts in this very limited study to the de-
velopment of a model for Case 1, the free flow regime. In order to compute
the contributions of local emitters to concentrations measured at the down-
town station, it would necessary to develop a model describing the Case 2
flow regime; we have not attempted to do this in the present study.
We have made a number of assumptions in formulating a local
scale transport and dispersion model for Case 1 flows. Most
notable among them are the assumptions of
steady state
transport restricted to two dimensions
averaged, instead of instantaneous, concentrations and
velocities
K- theory
. a line source
constant horizontal wind speed and direction
constant vertical diffusivity, invariant with height
at a given time
vertical dif fusivity • equal to horizontal diffusivity
A detailed derivation of the governing equations, together with an
evaluation of these assumptions and their effect on predictions, is
given by Seinfeld, et al. (1972) .
Under the stated assumptions we can write the continuity
equation as
„
where
Q at z = 0 , x = 0
0 at z = 0 , x jf 0
0 as z -»• « for all x
0 as x •*• * for all z
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In contrast to the treatment of the velocity distributions, as pre-
scribed by equation (4) . We have in this instance retained the
diffusion term in the flow direction, primarily because of the steep
concentration gradients that are frequently observed in the vicinity
of strong line sources.
The solution is given by Carslaw and Jaeger (1959); as
.2—
-f z)
n
/2Kc]
(7)
where K is the modified Bessel function of the second kind
of order zero. The ground concentration (z = 0) is given by
z=0 2irK
(8}
where
and
ux
2K
The function *(5) is plotted in Figure 5.
In applying equation (8), we take x to be a coordinate
oriented parallel to the direction of the wind. Thus, distances
are measured from the intake port of the monitoring station along
the coordinate axis (which passes through the location of the
intake port) to the intersection of the axis with the centerline
of the street. Also, x is measured along a streamline that
passes over the street near the surface, in the free flow regime.
Thus,
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n
/.a
FIGURE 5. Plot of *(?) [Equation (8)]
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As we have noted the solution of equation (6) is based on the
assumption of a constant vertical diffusivity, invariant with
height. Because we are examining a region adjacent to the surface
of very shallow depth, and in which mixing is vigorous due to the
flow, this assumption is probably fairly good. However, during
the period over which the change in surface temperature with time
is large—the morning hours following sunrise—the changes in
diffusivity with time are also substantial. To account for these
changes, we have assumed that K changes with time in a manner
shown in Figure 6. The functional relationship, as well as the
magnitude of K (note that the plot is semilogarithmic), is based
on the research results of Staley (1956). While we are aware that
the values of KC are subject to considerable uncertainty, the
relationship shown also corresponds with the findings of other in-
vestigations, for example, Jehn and Gerhardt (1950).
To illustrate the use of equation (8), consider the case of
a 1 meter/second (or 2.25 mph) wind blowing from east to west,
perpendicular to the San Diego Freeway. This highway has a traffic
volume of about 26,000 vehicles/hour at 6 A.M. Assuming that
carbon monoxide is emitted at a rate of 25.6 grams/mile (at 60 mph),
the line source strength, in ppm-ft2/minute, is
vehicles x oc 6 grams ppm-ft /minutes
. x Z3.o ., . . , x .uoy ., .,
hour mile vehicle 'grams/hour mile
The distance from the freeway to the intake port at the Lennox
monitoring station is approximately 150 meters (or about 500 feet) .
If we assume that K = 5 x 103 cm2 /second (= 323 ft2/minute) , then
=2.9 ppm .
If the wind were from the northeast, bringing contaminants emitted
along Imperial Highway and the San Diego Freeway to the station, then
the concentration increase is estimated by superposition of the
individual contributions of the two sources. Thus, if
U = 1 meter/second
3 2
K = 5 x 10 cm /second
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10—
9—.
8
7
6
5
4
3
2..-
I...
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and
Q(vehicles/hour)
x(meters)
Imperial Highway San Diego Freeway
4000
25 esc 45
26,000
150 esc 45*
then
c S c + c
SD Freeway Imperial
= 2.1 ppm + 2.4 ppm
= 4.5 ppm
An emissions rate of 68.6 grams/mile of carbon monoxide is assumed
for the calculation of the Imperial Highway contribution.
One cause of concern to us was the assumption of emissions
being concentrated along the centerline of the street, in effect
treating the street as a source of infinitesimal width. In
reality typical distances of interest from centerline to sampling
port are of the order of 10 to 40 meters. Street widths are of
the magnitude of these transport distances, varying from 8 to 30 meters.
In order to assess the effect of the line source assumption on predicted
concentrations, we compared the solution of equation (6) with the
solution of the continuity equations for emissions from a street
of finite width. The major change in the governing equation in
the latter case, when compared with equation (6), is in the boundary
conditions,
-K
3c
at z = 0 for -£ < x < I
at z = 0 for Ixl > £
The remaining boundary conditions are unchanged.
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The solution of the governing equation for the finite
width case is given by
/* 2K
L x.*,c
2K
'Z=o - •*& I ° e^-™ ^ I"! > £ <9>
2K
c
This equation has been integrated numerically by using Simpson's
rule. To assess the effect of the finite street width, we com-
pared the solutions of equation (6) for the two street emissions
configurations for the case in which
Q = 1000 vehicles/hour
K = 1 meter /second
C
U = 1 meter/second
The results, plotted as CO concentration vs. distance from street
centerline, are shown in Figure 7. At a distance of 15 meters,
the minimum at any of the Los Angeles monitoring stations that we
considered, the discrepancy in predicted concentrations is .025 ppm
at an average level of .72 ppm, or about 3.5%. This discrepancy
decreases as the distance from centerline increases, becoming zero
at distances in excess of 50 meters. Based on this comparison, we
felt that the assumption of emissions emanating from a source of
infinitesinal width is justified.
The solution of equation (6) is straightforward, but it does
require the availability of a table of Bessel functions. To elim-
inate this need, and for that matter the need to evaluate equation
(6) at all, we have computed solutions of the equation for a range
of variables that commonly arise in applying the model in Los
Angeles. These solutions, given in Figures 8 to 11, apply for
0.5 < u (meters/second) < 4.0
2
0.125 < K (meters /second) < 2.0
c
10 < x (meters) < 1000
Note that the ordinate of these plots is given as 1000(c/fo), where
N is the number of vehicles passing per hour along a surface street.
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FIGURE 7. Comparison Between Solution of the Continuity Equation for
Finite and Zero Street Widths .
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B ^ SEMI LOGARITHMIC 46 4972
l Z CYCLtS X 7O DIVISIONS --OF I-. L -. c.
go o o
n. 7 Tf.i-
u JLi:l
. , i i ! I I
1 - i n H r
-------
SEMI LOGARITHMIC 46 4972
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a J j^ SEMIUOGARITHMIC 46 -3972
VrJ=* 2 CYCLES > 7n DIVISION*'- •> -L.:' , .: : •
i. a C^^FR CO.
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SEMI-LOGARITHMIC 46 4972
2 CYCLES X 70 DIVISION" • •-., . . L -
KKUFKEL a ESSER CO.
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IV. RESULTS
As we have discussed earlier, the main purpose of this limited
modeling effort was to investigate the feasibility of developing a
simple model capable of describing local or sub-grid scale emissions
and transport processes and thus their contributions to measured air
quality levels. Since the scope of the effort is quite restricted, there
are necessarily a number of considerations of practical importance that
we have not addressed. In particular, we have limited application to
roadway sources
inert pollutants, in this case carbon monoxide
the free flow regime
.. a selected group of monitoring sites
times of day when corrections are likely to be
significant. The primary period of interest
is between 5 A.M. and 10 A.M., when heavy
traffic and light winds are common.
Fifteen monitoring stations were operative during the six "valida-
tion days" in 1969—11, 29, and 30 September, 29 and 30 October, and
4 November. Ten were operated by the LA APCD, three by the Orange County
APCD, and two by Scott Research Laboratories. Of these the Orange County
stations and the Pasadena station were not considered for this feasibility
study because they were inoperative on several of ,the validation days.
The mobile Scott stations were not considered, because their locations
with respect to neighboring streets were unknown. Of the remaining nine
stations, two (at Reseda and Azusa) are located on streets havinq little
or no traffic, one (downtown Los Angeles) is situated along a street canyon,
one (Burbank) is located in a region of complex and rapidly varying wind
patterns, and one (Pomona) is located one mile outside of the modeling
region. The remaining four stations—Lennox, West Los Angeles, Whittier,
and Long Beach—were selected for application of the model. The locations
of these stations are illustrated diagrammatically in Figures 12 to 15.
Hourly averaged carbon monoxide concentrations attributable to local
roadway sources were estimated for the period 5 A.M. to 10 A.M. (local
time) for each of the six validation days using the diffusivity vs. time
curve of Figure 6 and the plots given in Figures 8 to 11. The estimated
increases in CO concentration above background are given in Figures 16
to 33.* These increases are also shown in the plots in the main report
* No results are plotted for cases in which increases are negligible.
These are:
Date Station
September 11, 1969 West Los:Angeles
September 11, 1969 Whittier
September 30, 1969 West Los Angeles
October 29, 1969 West Los Angeles
October 30, 1969 Long Beach
.November 4, 1969 West Los Angeles
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which display CO validation results for the full airshed model. Traffic
counts used in these calculations were taken from average traffic statis-
tics made available by the traffic department of the municipality in which
the station is located. Wind speed and direction were measured continuously
at each monitoring station, with the exception of Lennox; however, the re-
corder sheets were unavailable. Thus, average hourly wind statistics were
used.* We are unable at present to estimate the errors that these two
averaging processes introduce.
In all respects but one the calculations were based on the measured
values of variables and the plots displaying the solutions of equation (6).
The exception involves the use of wind statistics at low wind speeds. In
perhaps four or five instances of low winds we predicted little or no local
contribution to measured concentrations when, in fact, such contributions
were clearly being made. We attributed this anomaly to the fact that under
the prevailing calm conditions, anemometers either drift or are not dis-
placed by the light force exerted on the vanes. In any case, the instan-
taneous and average hourly wind statistics are very likely poorly correlated.
Thus, in instances in which high local contributions were evident but not
predicted on the basis of average hourly statistics, we assumed a wind
direction that maximized the local contribution to measured concentrations. *
The monitoring sites, validation days, and times for which this extraordinary
calculation was made are the following:
STATION
DAY
West LA 9/29/69
Long Beach 9/11/69
Long Beach 9/30/69
Whittier 9/30/69
TIME
5-9 A.M.
5-6 A.M.
5-8 A.M.
6 A.M.
WIND SPEED
1 mph
1 mph
1 mph
1 mph
.HOURLY
AVERAGE
WIND DIRECTION
w -»• sw
NW -*• WNW
NE •»• SE
W
ASSUMED
WIND
DIRECTION
E
NE
W
NE
*In essence, the wind-direction dependence in the present model has been
abandoned in the low-wind cases. This is in line with a comment made by'
Dr. Ralph Sklarew of EPA who suggested that a simple correlation of the
following type be established for each station,
"observed
model
AC
local
where
AC
local
with Q and U having temporal dependence and a characterizing the station,
Note that, in this relationship, predicted concentrations are independent
of wind direction.
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More acceptable procedures for dealing with calm conditions depend
upon having access to the continuously recorded wind data.
In evaluating the results, comparisons can only be made between
measured concentrations and the sum of predicted concentrations calcu-
lated using both the microscale model and the full airshed model. For
this reason, evaluation of results is presented in the main text. It
should suffice here to say that the results appear to be quite promising,
given the restricted nature of the data. However, a full and fair evalua-
tion must await the acquisition of a more complete data base, more suited
to the temporal and spatial resolution of the microscale model. In
addition, the model must be applied in a wider variety of situations.
Finally, it must be extended so as to be applicable in situations in-
volving street canyon vortex flows and reacting pollutants (notably
nitrogen oxides and oxidants).
C-28
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-------
V. RECOMMENDATIONS FOR FUTURE WORK
We believe that a microscale or sub-grid scale model is an
essential ingredient in an urban or regional scale model, as it is
not possible to adequately describe all pertinent physical phenom-
ena at the coarser scale, or for that matter, with a model res-
tricted to only one scale. We further believe that the feasibility
of developing and applying a microscale model has been demonstrated
in this study. But, because of the limited scope of this effort, the
model developed constitutes only a beginning. A major second phase
study is needed, the primary goal of which is the development and
validation of a sub-grid scale model that is capable of predicting
concentration "elevations" due to local transport, diffusion and
reaction phenomena. We briefly mentioned in the last section the
major objectives that such an effort should satisfy. In this section,
we discuss them in more detail.
As noted, we have attempted to formulate a model only for the
relatively simple case of the free flow regime. We have considered
the most pertinent parameters in our formulation—the strength of the
source, the wind, the dispersion coefficient and the distance be-
tween the source and the receptor. For more complicated cases where
recirculating flows are set up, i.e., for cases where 6 < W , additional
model development is needed, particularly for application in the
commercial areas of large cities. Two alternative modeling approaches
are envisioned—the correlation model and the physical model. The
first alternative, as indicated in the previous sections, has already
been developed by Georgii, et al. (1967), Georgii (1969), Schnelle, et al.
(1969) and Johnson, et al. (1971). Improvements may be made by including
parameters that have been omitted from these relationships thus far,
such as the diffusion coefficient, the distance from the roadway, and
geometric factors that characterize the street configuration. The
second approach, on the other hand, involves solving a simplified form
of the governing equations of continuity and momentum, probably the
species continuity equation with a parameterized velocity field. How-
ever, successful development of this type of model will require the
thorough study of recirculatory flows and careful formulation of the
simplified equations.
An undertaking of equal importance is the expansion of modeling
approaches, both for Case 1 and 2 flows, so that they are applicable
for reactive pollutants. Both nitric oxide and hydrocarbons are
emitted from automobiles in substantial quantities? thus, the concen-
trations of these species in the immediate vicinity of the roadway is
high. At locations at which concentrations are elevated, atmospheric
reactions can proceed quite rapidly. It is therefore important to con-
sider reactions, as well as transport and dispersion, in phenomenological
modeling.
C-40
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We can envision writing equations of continuity for NO, NO ,
and 03 , including reaction terms in each, to account for the fastest
reactions
NO + hv NO + 0
0+0 + M+O+M
NO + 03 '-»• N02 + 0
These equations, being coupled through the reaction terms, theoretically
would have to be numerically integrated to obtain solutions. However,
because these reactions proceed rapidly, steady-state concentrations
may be established on a time scale that is short compared with the scale
of transport. If the validity of this supposition can be demonstrated,
we could decouple the transport and reaction portions of the equations
and solve them separately, thus considerably easing the calculational
burden. However, there are many aspects to a complex physical situation
such as this, and each must be carefully evaluated before a particular
modeling approach can be adopted.
To properly validate a local model, it is most important to have
available a data base collected for the specific purpose of filling
this role. In order to distinguish between local and background
contributions to air quality at a particular location, pollutant con-
centrations should be measured on a temporary basis upwind of the mon-
itoring or test site. In addition, we would wish to have available con-
tinuous recordings of wind speed and direction and pollutant concentration.
The data could then be averaged over varying periods of time—say from
one minute to one hour—and the model tested in order to establish both
appropriate averaging periods and the effects of selecting averaging
periods that are too long. Finally, turbulence measurements would be
most helpful in obtaining improved estimates of K and its variation in
time during the morning hours following sunrise.
A final requirement, perhaps one that ought to be satisfied first,
is that of a fuller evaluation of the present model using data that are
readily available. For it may be some time until a more suitable data
base becomes available for this use. The model might be applied at those
C-41
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monitoring sites that have not been considered for application thus
far (with the exception, of course, of the downtown station). When
sites are near busy intersections, in the vicinity of a freeway and
major arterials (and on/off ramps), or near a service station, the
effects of all possible sources should be evaluated. Since we are
concerned heavily with the early hours of the day in assessing local
effects, attention should be given to the treatment of vehicle emissions
rates in terms of degree of congestion, frequency with which vehicles
are stopped at red lights near the intake port of the station (and
thus, in the idle mode), estimated fraction of vehicles that are cold
and hot running, and other sources of variation in emissions.
C-42
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REFERENCES
Brief, R.S., et al., "Lead, Carbon Monoxide, and Traffic," JAPCA,
_10, 5, pp. 384-388 (1960).
Carslaw, H.S. and J.C. Jaeger, Conduction of Heat in Solids,
Second Edition, Oxford University Press (1959).
Georgii, H.W., E. Busch, and E. Weber, "Investigation of the
Temporal and Spatial Distribution of the Emission Concentration
of Carbon Monoxide in Frankfurt/Main," Report No. 11 of the
Institute for Meteorology and Geophysics, University of
Frankfurt/Main (1967).
Georgii, H.W., "The Effects of Air Pollution on Urban Climates,"
Bull, of the World Health Org., 40, 4, pp. 624-635 (1969).
Jehn, K.H. and J.R. Gerhardt, "A Preliminary Study of the Eddy
Transfer of Heat near the Earth's Surface," Electronics
Engineering Research Laboratory Report, No. 37, Univ. of Texas (1950)
Johnson, W.B., F.L. Ludwig, W.F. Dabberdt, R.J. Allen, "An Urban
Diffusion Simulation Model for Carbon Monoxide," Proceedings
Summer Computer Simulation Conf. San Diego, (1972).
Lock, R.C., "The Velocity Distribution in the Laminar Boundary
Layer Between Parallel Streams," Quart. J. Mech. Appl. Math.
±, p. 42 (1951).
McCormick, R.A. and C. Xintaras, "Variation of Carbon Monoxide
Concentrations as Related to Sampling Interval, Traffic and
Meteorological Factors," J. Appl. Meterol., ±, 2, pp. 237-243
(1962).
Ott, W., "An Urban Survey Technique for Measuring the Spatial
Variation of Carbon Monoxide Concentrations in Cities," -
Ph.D. Thesis, Stanford University (1971).
C-43
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REFERENCES (Continued)
Schnelle, K.B., F.G. Ziegler and P.A. Krenkel, "A Study of the
Vertical Distribution of Carbon Monoxide and Temperature
Above an Urban Intersection/1 APCA Paper No. 69-152, 1969.
Seinfeld, J.H., P.M. Roth and S.D. Reynolds, "Simulation of Urban
Air Pollution," Advances in Chemistry, in press (1972).
Staley, D.O., "The Diurnal Temperature Wave for Bounded Eddy
Conductivity," J. of Meteorology, _13, pp. 13-20 (1956).
C-44
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