xvEPA
United States
Environmental Protection
Agency
Environmental Sciences Research EPA-600/4-78-044
Laboratory August 1978
Research Triangle Park NC 27711
Research and Development
A Pilot Study on
Dispersion Near
Roadways
₯:
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
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The nine series are:
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This report has been assigned to the ENVIRONMENTAL MONITORING series.
This series describes research conducted to develop new or improved methods
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This document is available to the public through the National Technical Informa-
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EPA-600/4-78-044
August 1978
A PILOT STUDY ON DISPERSION NEAR ROADWAYS
by
William B. Petersen
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
-------
DISCLAIMER
This report has been reviewed by the Environmental Sciences Research
Laboratory, U.S. Environmental Protection Agency, and approved for
publication. Approval does not signify that the contents necessarily
reflect the views and policies of the U.S. Environmental Protection
Agency, nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
AUTHOR'S AFFILIATION
The author, William B. Petersen, is on assignment with the U.S.
Environmental Protection Agency from the National Oceanic and Atmospheric
Administration, U.S. Department of Commerce.
n
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ABSTRACT
High frequency wind fluctuation data from the General Motors Sulfate
Dispersion Experiment were used to estimate the dispersion near roadways.
The standard deviations of the wind direction and the elevation angle
were computed for six averaging times for three half-hour periods when
the winds were nearly parallel to the test track. The EPA HIWAY model
was modified to use these fluctuation statistics directly to estimate
dispersion. Results from analysis show that model performance was improved
for parallel wind conditions when the fluctuation statistics of the wind
were used to estimate dispersion. The results also show that model estimates
are most sensitive to the vertical dispersion parameter. Indeed, concentra-
tions seem to be insensitive to the horizontal dispersion parameter.
-------
CONTENTS
Abstract iii
Figures and Tables vi
Acknowledgments vii
1. Introduction 1
2. Data Base 3
3. Analysis of the Data 5
4. Summary 17
References 18
Appendix
A. Determination of the stability class
from the Richardson Number 19
-------
Number
1
2
3
4
5
A-l
FIGURES
Orientation of test track and perpendicular
distances of the meteorological towers from
the center of the test track
a and DZ computed from a and a respectively
Page
4
9
SFK concentrations (ppb) 11
14
16
Measured SFC versus estimated SFC
b o
Measured SFg versus estimated SFg
-1
Turner stability class as a function of L and z
21
TABLES
Number Page
1 a and a for Different Averaging Times 8
2 Wind Direction and Wind Speed During the Three
Half-Hour Periods
3 Stability Class for Each Half-Hour Period 12
4 Regression Analysis 15
5 Comparison of Model Estimates 17
A-l Stability Class as a Function of L" 21
VI
-------
ACKNOWLEDGEMENTS
The author wishes to express his appreciation to Bruce Turner and
John Irwin for their helpful discussions and review; to John Ashley and
Tim Christiansen for their computer programming assistance; and to Caryl
Whaley and Joan Emory for their aid.
VII
-------
1, INTRODUCTION
This paper discusses the results of a pilot study on data ob-
tained from the General Motors Sulfate Dispersion Experiment (Cadle et
al, 1976). The purpose of this study is to investigate and develop
methods for estimating dispersion near roadways. A major objective of
this study is to investigate the performance of the EPA HIWAY model
(Zimmerman and Thompson, 1975) using dispersion estimates from the
fluctuation statistics of the wind.
The HIWAY model does not use the infinite line source approximation
to estimate concentrations downwind of a line source. Concentration
estimates are made by numerical integration of the Gaussian plume point
source equation. Thus, concentration estimates are functions of the
horizontal and vertical dispersion parameters (a and o ). Pasquill
(1976) stated that the horizontal dispersion parameters (Pasquill-
Gifford (PG) dispersion curves) are most appropriate to a 3-minute
sampling time. One would expect that for longer sampling times, say
1 hour, a would increase and thus increase dispersion.
«/
For the case where the wind is near perpendicular to the roadway,
the infinite line source equation is a good approximation. The effects
of crosswind dispersion are not important since the crosswind dispersion
from one segment of the line is compensated by dispersion in the oppo-
site direction from adjacent segments. However, when the winds are near
parallel to the roadway, it is no longer appropriate to assume that the
dispersion from one point is compensated by that of adjacent points. In
the past it has been observed that HIWAY overestimates concentrations
when the winds are near parallel to the road. If the overestimation of
HIWAY is due to a conservative estimate of 0 , it should be most noticeable
during parallel wind conditions.
-------
The General Motors (GM) Sulfate Dispersion Experiment provides an
excellent data base for investigating dispersion near roadways. Not only
was this a controlled roadway study, but also three components of the wind
were measured and recorded every second at 20 locations across the
test track. This high frequency wind data is the most valuable in estima-
ting dispersion. The data used in this pilot study represent three half-
hour periods during which the winds were nearly parallel with the the road.
While the analysis of the data from the three periods gives valuable
insight into the dispersion during parallel wind conditions, the major
function of this paper is to set forth the techniques that will be
used to analyze the whole data set. The entire data set consists of
about 60 half-hour periods. A brief description of the GM data follows
in the next section.
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2, DATA BASE
The data used in this analysis is a small part of a data set col-
lected at Mil ford Proving Ground by General Motors during the sulfate
dispersion experiment. The experiment was performed during October
1975. The data used in this paper consists of three half-hour periods
on October 24. A fleet of 352 catalyst-equipped automobiles were driven
around a 10 km narrow oval track. At the sampling locations, about
halfway down the track, the cross section simulated a 4-lane road with a
median. Eight vehicles were equipped to release sulfur hexafluoride
(SFfi) as a tracer. The SFfi was sampled at 20 locations in the vicinity
of the test track (see Figure 1). SFg samplers were located on towers
1 through 6 at heights of 0.5, 3.5, and 9.5 m. Samplers were also located
on stands 7 and 8 at 0.5 m. Gill u-v-w anemometers were on towers 1 through
6 at heights of 1.5, 4.5, and 10.5 m. On stands 7 and 8 the anemometers were
at 1.5 m. The meteorological data consisted of 1-second values of the u-v-w
components of the wind from the 20 anemometers. The sampling time for SFg
was 30 min. For a more detailed discussion of the experiment and the data
set, see Cadle et al. (1976), and EPA (1976).
-------
TOWER 1(
42.7m
TOWER 2QT
LANE1
LANE 2
14.6m
TOWER 3O-
16.5m
25.4m 11.8m
LANE 3
LANE 4
TOWER'
TOWER5(
TOWER 6(j-
27.7m
I
42.7m
62.7m
STAND 7
112.7m
NORTH
STAND 8
Figure 1. Orientation of test track and perpendicular distances of the meteorological
towers from the center of the test track.
-------
3, ANALYSIS OF THE DATA
The data chosen for this pilot study were three half-hour periods
on October 24. These periods were chosen because the winds were within
5° of parallel to the test track. The fluctuation statistics a. (standard
y
deviation of the horizontal wind direction) and a. (standard deviation
of the vertical wind direction) were calculated from the wind data
collected by the anemometer on Tower 1 at the 4.5 m level (see Figure
1).
The standard deviation of the wind direction was calculated from
the u and v components of the Gill anemometer. The mean wind direction
i is given by,
6 -
n
E
where 9. = arctan ()
To avoid the discontinuity at 360°, each 9.. was assumed to be a unit
vector with components u and v. e is now defined as,
~n * ~1
E u.
e = arctan
Defining e in this way eliminates the discontinuity problem and avoids
the effect of the wind speed on the mean wind direction, a is now
9
given as,
-nV2
n
E
1=1
i)
-------
It is apparent that the maximum deviation between 9. and e is 180°.
Therefore, if the absolute value (ABS) of the difference (e. - e)
was greater than 180°, the deviation is equal to 360-ABS(e.-e).
The standard deviation of the vertical wind direction was computed
from the three components of the wind field. The horizontal wind speed
Vu is defined as,
n
VH - (u2 + v2)1/2
'H
The mean elevation angle $ is given as,
= arctan
n A
z VH
1=1 Hi
where w is the vertical component of the wind.
unit vector. aA is given as,
~~ 1/2
s (<(>, -
w and Vn are components of a
n
The relationship between the horizontal dispersion parameter, a ,
and aQ was suggested by Hay and Pasquill (1957, 1959).
a (x) = a x,
J T,S
(1)
where; x = BUS
3 = ratio of the Lagrangian to the Eulerian time scales,
u = mean wind speed,
s = averaging time,
T = sampling time.
-------
The relationship between a and a, is not as well understood as that for
Z cf>
the horizontal dispersion. In this analysis the following relationship
was used to estimate a :
a_(x) = V x. (2)
f- T j D
For each half-hour period an and a, were calculated for different
o
that the dispersion during these three half-hour periods is that typical
of B-C stability.
The EPA HIWAY model was modified for this analysis to make concen-
tration estimates from the dispersion parameters determined from a. and
h
a,. Both a and a are assumed to have the form of ax , where a and b
y z
are constants determined from the data. For example, a. is determined
o
for six averaging times. 0 and x are then calculated using Equation (1)
J
for each of the six averaging times, a is then known for six downwind
distances. The constants a and b are calculated for each interval in
the following way:
-------
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C£
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tf\ ^^ IO
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OX CMDGDD X
-------
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JC
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uj
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t/5
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rO
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'oJ
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r
TD
-o
to
00
S_
03
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o
(U
Q. «
oo oo
0) O)
-e- 3
D cr
oo
(O
00
ro
CDT3
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-t->
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en
c o
rO S-
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r- at a>
u- a. s-
SJS13U1 'A
-------
a. and b. are used to determine a when the downwind distance is between
J J J
the intervals x. and x/.+1% . There are five intervals for which a and b
are determined. For downwind distances less than that given by the 5-
second averaging times, a-| and b-j are used to determine a . For x greater
than that given by the 90-second averaging time, ag and
are used as the
appropriate constants. Similarly, constants (c and d) are determined for
az(x).
The initial dispersion parameters a and a used in the modified
HIWAY model were not changed. The appropriate victual distances nec-
essary to account for the initial dispersion are:
i
1
Where:
0 = 3 m,
yo
= 1.5m.
Finally, the equations used to estimate 0 and a are
°y (XJ} =
(x
b,
x)
(x.) = c. (x_ + x)
d.
where x. = x + x or xz + x in the j
.th
interval.
The modified HIWAY model was used to estimate SFC concentrations at
D
the 20 sampler locations (See Figure 1). In Figure 3 are scatter plots
of measured SFC concentrations versus model estimates for the three
b
half-hour periods. Figure 3 also contains a composite of all the data for
the three periods. The dashed lines on the plots are least squares fits
to the data with the regression information in the upper left-hand
corner of the plot. Table 2 shows that the mean wind speed and direction
were steady during this time.
10
-------
PERIOD ONE
<
DC
o
u
IB
B =-0.650
M= 0.904
9
R= 0.881
N=20
&"
]
o/
/
/**
£
/ c
/
0
PERIOD TWO
0)234
ESTIMATED SFg CONCENTRATION
z
o
<
CC
LL.
CO
a
CO
<
B =-0.732
M= 1.027 i
R= 0.948
N=20
"/^
/
/a
<
D / u
/
3
O
D
5
/
/'
<'
12345
ESTIMATED SFe CONCENTRATION
PERIOD THREE
a
LU
OC
3
C/l
LU
B =-0.309
M= 0.967
R= 0.897
N- 20
o'/i
n
9-X
/
a
/
c
a
/^
/
;
^/
/
ALL PERIODS
12345
ESTIMATED SFe CONCENTRATION
<
oc
o
o
to
CO
<
B =-0.404
M= 0.875
R= 0.892
0 2 4 6 8 10
ESTIMATED SFe CONCENTRATION
Figure 3. SPQ concentrations (ppb). B, M, R, N in the plots are the intercept
slope, correlation coefficient, and number of data points respectively.
11
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TABLE 2. WIND DIRECTION AND WIND SPEED DURING
THE THREE HALF-HOUR PERIODS
Half-hour periods
1
2
3
Wind direction
182
183
175
Wind speed )m
2.5
2.2
2.9
sec"1)
The improvement in the performance of HIWAY can be shown by analyzing
concentration estimates using three different approaches to estimating
atmospheric dispersion. The approach described in Turner (1964) uses cloud
cover, ceiling height, and wind speed to determine the stability class. The
stability class for each half-hour period was determined using the wind
speed at the experimental site and the observations of cloud cover and ceil-
ing height at 3-hour intervals for Flint, Michigan (about 44 km north of
the site). The Richardson Number measured at the site was used subjectively
to determine how fast the atmospheric stability was changing. The stabili-
ty was never allowed to change more than one class from one half-hour period
to the next. Another approach used to determine the stability class was
that suggested by Golder (1972). Solder showed an empirical relationship
between the Richardson Number, roughness height and the stability class.
Appendix A contains a more complete description of how Golder1s technique
was applied to this data set. The stability class for each half-hour period
was determined by the two techniques mentioned above is shown in Table 3.
TABLE 3. STABILITY CLASS FOR EACH HALF-HOUR PERIOD
Stability class
determined from
Turner (1964)
Golder (1972)
First
E
F
Half-hour period
Second Third
D D
F F
12
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Figure 4 is a scatter plot of measured SFg concentration versus
model estimates using HIWAY with the three different techniques to estimate
dispersion. For the data plotted as squares and stars, the stability class
was determined from the Richardson Number and the Turner (1964) approach,
respectively. In both cases a and a came from the PG curves once the
stability class was determined. In the third data set, plotted as diamonds,
the dispersion was estimated from a. and a, using Equations (1) and (2).
o y
Table 4 shows a summary of the regression analysis of the three sets of data.
The slope of the regression line was significantly improved using on-site
estimates of dispersion. However, the correlation coefficient was not
improved.
Using two different sets of dispersion parameters in HIWAY, then analy-
sing the results from model estimates, is analogous to using two different
models. When two models are compared with the same measured concentrations,
one has to be very careful about statistical statements concerning the
regression results. For the case in which both models are compared with the
same measured concentrations, the deviations from the regression lines could
be correlated. Thus for the same measured concentrations, it is not appro-
priate to use a T-test, formed using a pooled variance in the standard way,
to test the difference between the regression slopes from the two models.
A suggested way to overcome this is to split the data into two sets (private
communication from R. J. Hader, N. C. State University, 1977). The two
data sets should have the same characteristics. One approach to insure that
the range of concentration is the same for both data sets is to rank the
measured concentrations and assign every other value to a different data set.
One set would then be used for comparison by one model and the other set with
the other model. A T-test could then be used to test for the significant
difference between the two slopes. This approach was not used for this pilot
study because of the limited size of the data set. However, this approach
will be pursued with further analysis of the GM data.
Four data points (squares) were not plotted on Figure 4. Although
the concentration estimates fell outside the boundaries of the plot, they
were used in the regression analysis.
13
-------
10
CJ
Z
o
o
CO
4 6
ESTIMATED SFe CONCENTRATION, ppb
10
Figure 4. For the data plotted as squares the stability class for each half-hour
period was determined from the Richardson Number. For the data plotted
as stars the stability class was determined from the Turner (1964) classifica-
tion scheme. For the data plotted as diamonds the dispersion parameters ay
and az were determined directly from OQ and o0.
14
-------
TABLE 4. REGRESSION ANALYSIS
Type of dispersion
Slope
Correlation
Intercept coefficient
Dispersion
parameters from
Equations 1 and 2
PG curves
stability class
from Turner (1964)
PG curves
stability class
from Richardson No.
0.875
0.536
0.268
-0.404
-0.087
0.065
0.892
0.923
0.890
As suggested in the introduction, concentrations in the vicinity of a
line source should be most sensitive to crosswind dispersion when the winds
are parallel to the line source. In order to investigate this, concentra-
tion estimates, using a modified HIWAY model, were made using
-------
4 6
ESTIMATED SF6 CONCENTRATION, ppb
10
Figure 5. For the data plotted as squares oy was determined from OQ and az
from the PG curves. For the data plotted as stars ay and az were determined
from the PG curves. For data plotted as diamonds ay and az were determined
from OQ and a0 respectively.
16
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TABLE 5. COMPARISON OF MODEL ESTIMATES
Measured Model Ratio of
concentration (ppb) estimate (ppb) model/measured
Stability class
from Richardson No. 5 18.41 3.68
Stability class
from Turner (1964)
Dispersion parameters
from Equations (1)&(2)
5
5
9.49
6.18
1.90
1.24
4, SlfMARY
The major objectives of this pilot study were to develop the
methodology to estimate the dispersion parameters from the fluctuation
statistics of the wind using a small sample of the GM data, and to
modify the HIWAY model to incorporate these dispersion parameters into
the model computations. To that end the pilot study has been a success.
The following conclusions can be made as a result of the analysis
of the data used in this pilot study: (1) during conditions when the winds
are nearly parallel to the test track, concentrations are less sensitive
to crosswind dispersion then expected; (2) dispersion parameters determined
from the fluctuation statistics of the wind have a shape similar to the
PG curves for downwind distances up to 500 m; (3) the fluctuation statistics
of the wind indicate that the atmosphere near the ground was more dispersive
than the stability class indicated; and (4) the performance of the model
was significantly improved using the dispersion parameters determined from
wind fluctuations.
17
-------
REFERENCES
Cadle, S. H., D. P. Chock, J. M. Heuss, and P. R. Monson, 1976:
Results of the General Motors Sulfate Dispersion Experiment. GMR-
2107. General Motors Corporation, Warren, Mich. 178 p.
Golder, D., 1972: Relations Among Stability Parameters in the
Surface Layer. Boundary-Layer Meteorology 3, 47-58.
Hay, J. S., and F. Pasquill, 1957: Diffusion from a fixed source at
a height of a few hundred feet in the atmosphere. J. Fluid Mech.,
2^ 299-310.
Hay, J. S., and F. Pasquill, 1959: Diffusion from a continuous source
in relation to the spectrum and scale of turbulence, pp 345-365
in Atmospheric Diffusion and Air Pollution, edited by F. N. Frenkiel
and P. A. Sheppard, Advances in Geophysics, 6, New York, Academic
Press, 471 pp.
Pasquill, F., 1976: Atmospheric Dispersion Parameters in Gaussian
Plume Modeling, Part II. Environmental Monitoring Series. EPA-
600/4-76-030b. US EPA, Research Triangle Park, NC 44 p.
Selected EPA Research Papers, 1976: The General Motors/Environmental
Protection Agency Sulfate Dispersion Experiment. EPA-600/3-76-035.
US EPA, Research Triangle Park, NC 146 p.
Turner, D. B., 1964: A Diffusion Model for an Urban Area. J. Appl.
Meteor. 3, 83-91 .
Zimmerman, J. R., and R. S. Thompson, 1973: User's Guide for HIWAY,
A Highway Air Pollution Model. EPA-650/4-74-008. US EPA, Research
Triangle Park, NC 59 p.
18
-------
APPENDIX A,
DETERMINATION OF THE STABILITY CLASS
FROM THE RICHARDSON NUMBER
19
-------
The Richardson Number (Ri) was calculated for each half-hour period in
the following way:
Ri =
where g = gravitational acceleration,
T = absolute temperature,
z = height,
u = wind speed.
Wind speeds and temperatures used in the calculation of Ri were measured
at 1.5 and 10.5 m. The appropriate height for z is given by the geo-
metric mean of 1.5 and 10.5, equal to (1.5 x 10.5)"1. For unstable
atmospheric conditions, Paridolfo and Businger hypothesised that Ri is
related to the Monin Obukhov length (L), (Paulson, 1970).
,-1 _ Ri
L =F~ (A-l)
For stable air, an empirical relationship was found by McVehil (1964).
,-1 = Ri
L ~ z (1-0R1) (A-2)
Colder (1972) showed an empirical relationship between L and the Turner
stability types. Consistent with Golder, e was assigned a value of 7 in
Equation (A-2). e is the reciprocal of the critical Ri (Binkowski, 1975).
The figure below shows the Turner stability types as a function of L~
and roughness height z . The roughness height typical of the terrain
around the test track is 3 cm. Figure A-l below is very similar to
Figure 5 in the Golder paper.
20
-------
(cm)
_.12 -.10 -.08 -
.04
.06 .08
Figure A-1. Turner stability class as a function of L~ and z .
If a horizontal line is drawn across the figure at z = 3 cm, the
stability classes are determined by the ranges of L~ bounded by the
dotted lines. For Ri greater than zero Equation (A-2) is used to
calculate L~ . For the Ri less than zero, Equation (A-1) is used to
determine L . The following values were used to define each stability
class.
TABLE A-1. STABILITY CLASS AS A FUNCTION OF L"1
Range of
L
L
L
L
L
L
-1 <
-1
-1 <
-1
-1
-1
L"
-0.
-0.
-0.
0.
0.
0.
1
095
055
018
005
013
013
and
and
and
and
> -0.
> -0.
> -0.
> 0.
095
055
018
005
Stability Class
A
B
C
D
E
F
21
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REFERENCES
Binkowski, F. S., 1975: On The Empirical Relationship Between The
Richardson Number and The Monin-Obukhov Stability Parameter.
Atmos. Environ. 6, 453-454.
Colder, D., 1972: Relations Among Stability Parameters in the
Surface Layer. Boundary-Layer Meteorology 3^ 47-58.
McVehil, G. A., 1964: Wind and Temperature Profiles Near the Ground
in Stable Stratification. Quart. J. Roy. Meteor. Soc. 90. 136-146.
Paulson, C. A., 1970: The Mathematical Representation of Wind Speed
and Temperature Profiles in the Unstable Atmospheric Surface Layer.
J. Appl. Meteor. 9. 857-861.
22
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1 REPORT NO
EPA-600/4-78-044
3 RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
A PILOT STUDY ON DISPERSION NEAR ROADWAYS
5. REPORT DATE
Auaust 1978
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
William B. Petersen
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
10 PROGRAM ELEMENT NO.
1AA603 AB26 (FY-78)
(same as block 12)
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory - RTP, NC
Office of Research and Development
U. S. Environmental Protection Agency
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
In-House
14. SPONSORING AGENCY CODE
EPA/600/09
15. SUPPLEMENTARY NOTES
16. ABSTRACT
High frequency wind fluctuation data were used to estimate the dispersion
near roadways. The standard deviations of the wind direction and the elevation
angle were computed for six averaging times. The EPA HIWAY model was modified
to use these fluctuation statistics directly to estimate dispersion. The data
from the General Motors Sulfate Dispersion Experiment were used in this study.
In particular, the data used in this pilot study were three half-hour periods when
the winds were nearly parallel with the test track. Results from analysis show
that model performance was improved for parallel wind conditions when the fluctuation
statistics of the wind were used to estimate dispersion. The results also show
that model estimates are most sensitive to the vertical dispersion parameter. Indeed,
concentrations seem to be insensitive to the horizontal dispersion parameter.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
*Air pollution
*Wind (meteorology)
*Atmospheric diffusion
*Roads
*Mathematical models
13B
04B
04A
13B
12A
13. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThisReport)
UNCLASSIFIED
21. ^O. OF PAGFS
31
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
23
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