ST. LOUIS DISPERSION STUDY
OLUME II-
ANALYSIS
DEPARTM
Consumer
LTH,
d Environmental Health Service
ALTH, EDUCATION, AND WELFARE
Public Health Service
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ST. LOUIS DISPERSION STUDY
VOLUME II -
ANALYSIS
James L. McElroy and Francis Pooler, Jr.
Bureau of Engineering and Physical Sciences
Division of Meteorology
U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE
Public Health Service
Consumer Protection and Environmental Health Service
National Air Pollution Control Administration
Arlington, Virginia
December 1968
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The authors are meteorologists assigned to the National Air Pollution
Control Administration by the Air Resources Laboratory, Environ-
mental Science Services Administration.
The AP series of reports is issued by the National Air Pollution Con-
trol Administration to report the results of scientific and engineering
studies, and information of general interest in the field of air pollution.
Information reported in this series includes coverage of NAPCA intra-
mural activities and of cooperative studies conducted in conjunction
with state and local agencies, research institutes, and industrial
organizations. Copies of AP reports may be obtained upon request,
as supplies permit, from the Office of Technical Information and Pub-
lications, National Air Pollution Control Administration, U.S. Depart-
ment of Health, Education, and Welfare, 801 North Randolph Street,
Arlington, Virginia 22203.
National Air Pollution Control Administration Publication No. AP-53
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CONTENTS
ABSTRACT iv
INTRODUCTION 1
DESCRIPTION OF TRACER DATA . . . . 3
Total Dosage at Surface. . . . . .... 3
Sequential Dosage at Surface . ... . . ... 3
Total Dosage in the Vertical . ... 4
DISPERSION PARAMETERS . . 5
Normalized Axial Concentration . . ... 5
Cross-Wind Parameters . . ... ... ... .5
Vertical Parameters . 6
Tabulation of Results . . .... ... . 9
Loss of Tracer Material . 9
Effective Transport Wind Speed .... 10
METEOROLOGICAL INDICES OF TURBULENCE 15
Pasquill-Turner Stability Classes .15
Modified "Brookhaven" Gustiness Classes . . .... 15
Horizontal Wind Direction Fluctuations and Conditions of
Vertical Stability 16
Tabulation of Results ... ..... 17
RELATION OF DISPERSION PARAMETERS TO METEORO-
LOGICAL INDICES OF TURBULENCE . . 19
COMPARISONS WITH OTHER EXPERIMENTAL PROGRAMS . . 21
INITIAL DIMENSIONS OF TRACER CLOUD 23
CONCLUSIONS AND RECOMMENDATIONS . . ... 45
ACKNOWLEDGMENTS 47
REFERENCES . .... .... . . 49
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ABSTRACT
The primary analyses performed on data collected during low-
level tracer experiments conducted over metropolitan St. Louis, Mis-
souri, are described. Values of dispersion parameters derived from
the tracer data are related to readily derived or measured meteoro-
logical indices of turbulence. The results are graphically presented
in terms of best-fit curves as functions of downwind distance and
travel time. Comparisons are made with the results of previous dif-
fusion experiments conducted over relatively uncomplicated terrain
in open country. It is concluded that for low-level point sources the
urban area affects cross-wind dispersion primarily by enhancing the
initial size (i.e. , close to the source) of the plume. As the plume
becomes much larger than the size of eddies created by the local ob-
structions, the dispersion approaches that associated with flow over
open country. In the vertical, significantly enhanced dispersion as
well as an enlarged initial spread of the tracer cloud seem to occur;
this enhancement in the rate of dispersion over that in open country
appears somewhat greater for stable than for unstable meteorological
conditions. Values of dispersion parameters from limited tracer ex-
periments in other urban areas are similar to those reported here for
St. Louis under the same gross meteorological conditions.
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ST. LOUIS DISPERSION STUDY
VOLUME II-
ANALYSIS
INTRODUCTION
The St. Louis Dispersion Study consisted of a series of experi-
ments in which fluorescent zinc cadmium sulfide particles were releas-
ed and traced across the relatively flat urban area of metropolitan St.
Louis. The measurement program began in the spring of 1963 and
ended in the spring of 1965. Over this 2-year period 26 daytime and
16 evening experiments were conducted in seven series. Dissemina-
tion of fluorescent particles from either of the two pre-selected sites
near ground level was usually 1 hour long. For each experiment,
measurements of total dosage at the surface were obtained on three
nearly circular arcs at distances between 1/2 and 10 miles from the
dissemination site. The use of particular arcs varied, usually depend-
ing on appropriate forecasts of •wind direction and speed. In addition,
time-sequential measurements of dosage at the surface were made on
each arc at a few locations near the anticipated mean centerline of the
tracer cloud. During nine experiments, total dosage was measured at
several heights along the tether of a balloon flown at a single site. The
site was usually a park or vacant lot between the inner and outer sam-
pling arcs and as near as possible to the anticipated mean centerline.
Also, a mesometeorological network composed of three stations on the
periphery of the urban area and an instrumented television tower
(KMOX) in the downtown area provided continuous records of •wind,
temperature, and relative humidity. The TV tower was instrumented
at three levels to provide information on the vertical gradients of wind
and temperature. Single-theodolite (pibal) observations of winds aloft
and measurements of winds near the surface "were made at the tracer
dissemination site; free or tethered radiosonde ascents were made from
the roof of a building in the downtown area; and transponder-equipped
tetroons were released near the dissemination site. The tetroons •were
tracked by radar located at Lambert Field, northwest of the metropoli-
tan area.
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Volume I of this report (APTD-68-12) presents a detailed descrip-
tion of the experimental equipment and procedures employed in the
study, and provides in tabular form the dispersion and related meteoro-
logical data collected during the tracer experiments. Because Volume
I is mainly data tables, it is not being given general distribution.
Volume II describes the primary analyses performed on the dis-
persion and related meteorological data collected during the tracer
experiments. The main objectives of the analyses were to obtain at
least gross estimates of (1) the values of dispersion parameters over
urban areas and (2) the relation of these parameters to meteorological
indices of turbulence. A secondary objective was to compare the re-
sults of the St. Louis Dispersion Study with those of past experimental
programs, especially those conducted over relatively "open" country.
ST. LOUIS DISPERSION STUDY II
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DESCRIPTION OF TRACER DATA
TOTAL DOSAGE AT SURFACE
For our purposes, measurements of total dosage were converted
to equivalent concentration, X (particles/m ), by the equation
(v) (e) (Dt)
where:
n = total number of particles (dosage)
v = flow rate of sampler
e = collection efficiency of sampler
Df- = time duration of tracer dissemination
For each sampling arc of an experiment, values of X •were plotted as a
function of azimuth direction (degrees) from the tracer dissemination
site. A continuous, smoothed curve was drawn through the plotted
values. Whenever necessary, curves were extrapolated to zero con-
centration. In such extrapolations, the continuity and similarity of
distributions between sampling arcs were maintained, and, whenever
feasible, curves or portions of curves were made to resemble a Gaus-
sian shape.
Multi-peaked or otherwise complex cross-wind distributions of
tracer material occasionally occurred, particularly in data from the
close-in sampling arcs. Channeling of the airflow due to the spatial
distribution of obstructions or locally induced circulations may be
largely responsible for this physical appearance of the distributions.
Effects of sampler exposure were considered to be insignificant, since
the placement of samplers at the nominally designated locations was
somewhat random over the Z-year period of the experimental program.
SEQUENTIAL DOSAGE AT SURFACE
Measurements of sequential dosage at the surface were trans-
formed into concentration Xs by the formula
here:
n number of particles (dosage)
v flow rate of sampler
-------
e collection efficiency of sampler
Dj time duration of sequential sampler interval
For each designated location, a plot was made of Xs as a function of
time. The physical appearances of the resulting histograms differed
somewhat for daytime and evening experiments.
For daytime experiments, the histograms showed that the number
of major concentration peaks decreased with downwind distance from
the tracer dissemination site. At inner sampling arcs, concentration
was usually continuous with time, though varying widely. At interme-
diate arcs, the sequential concentration often went to zero, suggesting
the occurrence of "puffs" of tracer material. At greater downwind
distances, the concentration patterns usually became more uniform in
appearance. From these patterns, it is inferred that the horizontally
meandering cloud is carried selectively aloft by convective motions.
When most of the cloud has been affected by these motions, convective
overturning results in a relatively uniform vertical distribution of
tracer material.
For evening experiments, the histogram patterns generally were
more uniform, although many suggested the existence of weak convec-
tive activity. Temperature gradient data from the TV tower, analyzed
by the authors and by Schiermeier (1967), also suggest the occurrence
of such activity, especially in the lowest 250 feet above the ground.
The vertical extent of convective activity probably depends strongly on
details of the vertical temperature structure since air flowing into
urban areas from the surrounding countryside must always be in a
transitional state.
TOTAL DOSAGE IN THE VERTICAL
During nine of the experiments, total dosage was measured at
several heights, to a maximum of roughly 1000 feet above ground,
along the tether of a balloon flown at a single location. Passage of a
squall line during one of these experiments and of a front during an-
other experiment prevented these measurements from being used to
develop generalizations. Of the remaining seven experiments (four
daytime and three evening), the measurements of one daytime and one
evening experiment showed an anomalous increase of dosage -with
height above the surface. A possible explanation of the anomalies is
that on both occasions considerable vertical shear of wind direction
occurred in the lower atmosphere. The sampling sites "were far from
the mean centerlines of the tracer clouds, but with respect to the dis-
semination site were in the azimuth direction of this shear. The
remaining measurements were too limited to allow direct computations
of parameter values or to provide definitive information concerning
concentration distributions.
ST. LOUIS DISPERSION STUDY II
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DISPERSION PARAMETERS
For the purposes of this report, 32 of the 42 experiments yielded
usable dispersion data; 22 of these were conducted in the daytime and
10 in the evening. Many of the excluded experiments yielded usable
data for which analysis could not be made in the conventional manner
used here. A separate publication is planned to report analyses of
these data.
NORMALIZED AXIAL CONCENTRATION
From the plots of equivalent concentration at the surface, X,
(particles /meter^) versus azimuth (degrees), 0, from the tracer dis-
semination site for each sampling arc of an experiment, peak or axial
values, Xp, -were determined. These values -were converted to nor-
malized peak concentrations, (X/Q)_ (seconds/meter3), through divi-
sion by the tracer emission rate, Q (particles/second).
CROSS-WIND PARAMETERS
From each plot of X versus 0, values of X were read at equally
spaced azimuth intervals, beginning at an edge of the tracer cloud.
The intervals were equivalent to the tracer measurement resolution.
Measures of the statistical cross-wind standard deviation, fy (meters),
and the cross-•wind integrated concentration, CIC (particles /meter ),
•were then computed from these values.
The equation for the root-mean-square standard deviation,
N 2f. (I ) ( If I }L I
' * »T? ^—^~ A (1)
"y
where:
A frequency class interval
Ij deviation of class midpoint i from the assumed mean
in terms of class intervals
f^ - frequency of the distribution for class interval i
N total !, i. e. , Xf
When a plot of X versus 9 is considered to be a frequency histogram of
X in terms of S, the values of X at the equal azimuth increments may
be taken as the mean values of increments for which they are the mid-
points. Thus, Xi f^ and 2X^ N. The proper A is not A (azi-
muth degrees) but rather A (arc length) written
-------
3—J-and X: is the equivalent
concentration at a. given sampling site along the arc located a distance
Xi from the dissemination site.
With these definitions equation (1) maybe rewritten as
1/2|
' ' SX.x .
' (3)
180
/
*/-»
Surface cross-wind integrated concentration, CICg, defined as
x(y)dy was approximated by SX • A . When A from equation (2) is
y y
substituted into the latter, the appropriate formulation becomes
SX.x .
(4)
VERTICAL PARAMETERS
Estimates of vertical dispersion parameters were based on the
surface tracer measurements and hence represent only "effective" val-
ues. As previously noted, the measurements of tracer material in the
vertical were too limited for direct computation of vertical parameter
values. The rationale for describing dispersion in the vertical differed
for daytime and evening experiments.
Daytime Experiments
For each arc of a daytime experiment, a derived estimate of the
vertical standard deviation, az (meters), was computed from the appro-
priate mass continuity equation, assuming no loss of tracer in transit,
uncorrelated horizontal and vertical tracer distributions, and a Gaus-
sian distribution of material in the vertical. This equation may be
written as
Q
u x(y) X(z) dy dz
(5)
where:
Q quantity of tracer material disseminated per unit time
u effective transport wind speed
Since "u is assumed to be independent of y and z and / x(y)dy is CICg,
Q
u CIC
X(z) dz
ST. LOUIS DISPERSION STUDY II
-------
With X(z) = 1/2 exp (-z2/2
-------
Q = (CICa) (uh) (h) (9)
or h = Q/CIC u,
s h
where u^ is the effective mean transport wind through depth, h, at a
particular arc. The appropriate u^ for h at each arc was defined by
the relation
I
I
X(z)u dz
_ 'o z
u =-
h
X(z) dz
/o
where X(z) in this case is a. constant, C.
Integration of this equation with the substitutions u azn and
X(z) C yields
When this value for ui^ is substituted into equation (8), the relation
becomes
_ 1
h =f^^ 7^-r T' (12)
1 n + 1
d
Now it is necessary to determine horizontally and vertically
averaged travel speeds, uj^, based on the horizontal variation of verti-
cally averaged speeds, u^. Since h from equation (8) has been defined
as a function of t,
\ (t) dt
dt
*1
where tj and t2 are travel times from the dissemination site to particu-
lar arcs. From equations (11) and (8),
t,
•,n
dt /n+1 n + lv
(14)
t
2 dt (n+1) (h2
where, again, the subscripts indicate particular arcs.
ST. LOUIS DISPERSION STUDY II
-------
For particular arcs
xz xi
— - (15)
'2 *1
where x is the mean distance from dissemination site to an arc and t
is the corresponding travel time based on the appropriate value of u^.
Combining equations (14) and (15),
(x x ) (h h )(n + I)2
1 Z I - (16)
For each evening experiment, the coefficients a and n "were first
determined from mean wind profiles measured at the downtown TV
tower or by pilot balloon ascents, after which the h for the appropriate
sampling arcs "was computed from equation (12). A value for u^ cor-
responding to each h was calculated from equation (11), and travel
times between arcs were determined from equation (16).
TABULATION OF RESULTS
Symbols used in the foregoing calculations are listed in Table 1,
and dispersion data resulting from the calculations are summarized
in Table 2. In addition, in Table 2 values of an "equivalent" Gaus-
sian
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In addition, tracer material collected by samplers may not be
measured because of loss of fluorescence, particularly when exposed
to high humidity and ultraviolet radiation. A recent study (Grinnel,
1965) has demonstrated that the loss in fluorescence of the type of
tracer material utilized in St. Louis is no more than 5 percent.
EFFECTIVE TRANSPORT WIND SPEED
As previously discussed, for daytime experiments a single effec-
tive transport wind seemed to exist and was represented best by the
mean tetroon trajectory, when the tetroon was found in the airflow
dispersing the tracer cloud. It was assumed that during the more
stable conditions of the evening experiments the vertical profiles of
wind and tracer distribution were interrelated, resulting in a transport
wind increasing with vertical spreading of the tracer cloud, and thus
with travel time.
Instrumental measures of "wind speed over tracer dissemination
periods were qualitatively evaluated in terms of mean transport wind
speeds. Values computed from average pilot balloon observations were
of limited use, since deviations from the average (at a particular level)
usually were a. significant fraction of that average. Wind speed meas-
urements at the tracer dissemination sites provided insufficient data
to permit meaningful comparisons with other wind data. Wind speeds
measured at about 60 feet above ground at the peripheral sites and at
the 127-foot level of the downtown tower were consistently lower than
both the daytime and evening effective transport wind speeds. Meas-
urements at the 255-foot level of the tower, during the limited number
of experiments for which this wind equipment was operating, usually
were of the appropriate magnitude for both daytime and evening effec-
tive transport winds. Although measurements at the 459-foot level of
the tower usually provided better estimates of daytime transport wind
speeds than did measurements at the 255-foot level, they generally
overestimated evening transport wind speeds.
Table 1. LIST OF SYMBOLS DESCRIBING DISPERSION DATA
x Downwind distance from dissemination site
t Travel time from dissemination site
cry Cross-wind standard deviation of tracer material
o-z Effective vertical standard deviation of tracer
material
h Height of uniformly mixed layer
(X/Q)p Relative axial concentration
u Effective transport wind speed
u Wind speed at height z
z Height
a, n Empirical constants
10 ST. LOUIS DISPERSION STUDY It
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H
GO
>O
Table 2. SUMMARY OF DISPERSION DATA
!
Exper iment
No.
2
3.
4
5
6
7
8
3
Diurnal
period
Day
Day
Day
Day
Day
Day
Day
Day
Arc
No.
1
2
3
1
2
3
1
2
3
4
5
6
4
5
6
4
5
6
4
5
6
1
2
3
x, m
732
3152
6445
761
3156
6770
882
3323
7590
1937
4267
8065
2022
4286
7938
1994
4258
7999
1994
4171
7988
715
3296
6607
t, sec
105
453
926
81
337
722
102
385
879
575
1266
2393
479
1016
1882
361
772
1450
274
572
1096
112
516
1034
v m
87
268
498
152
399
717
189
451
692
596
1094
1908
379
557
806
340
599
702
282
444
855
145
420
732
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Table 2 (continued). SUMMARY OF DISPERSION DATA
O
TJ
PI
a
V3
5
z
Experiment
No.
11
12
14
16
18
19
20
2,b
Diurnal
period
Day
Evening
Day
Evening
Evening
Day
Day
Day
Arc
No.
4
5
6
4
5
6
4
5
6
1
2
3
1
2
3
1
2
3
1
2
3
4
6
7
x, m
1998
4197
7964
2032
4294
8058
2030
4157
7932
710
3241
6404
914
3377
7200
712
3198
6440
823
3284
7421
1994
7984
16935
t, sec
313
658
1249
628
1115
1747
155
317
605
181
529
856
369
975
1645
132
594
1196
300
1197
2704
465
1862
3949
ffy> m
301
615
681
126
212
302
262
528
729
123
4go
497
102
298
343
159
657
972
182
519
1055
319
2779
6430
"z> m
323
814
1511
98
86
224
123
459
637
64
277
470
24
65
173
14g
999
3180
480
17930
3445a
931
544
725
h, m
123
107
280
80
346
589
30
81
217
(x/0jp x 10"8,
sec/m^
48.6
10.2
4.48
542.0
40.3
72.6
70.5
13.4
6.85
614.0
39.8
23.7
3530.0
342.0
78.5
314.0
10.4
2.70
146.0
1.82
3.65a
24.2
11.6
4.59
u,
m/sec
6.4
4.9
4.5
7.3
13-1
5-3
8.7
10.4
4.8
4.7
6.6
5.4
2.7
4.3
0.68Z0'49
n 7li
1.58Z0'34
n 7ii
1.38Z0'34
Values considered to be significantly affected by a limited mixing layer in the vertical.
Values of dispersion parameters not used in the establishment of generalizations; meandering wind or
changing mean wind resulted in inflated values of
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Table 2 (continued). SUMMARY OF DISPERSION DATA
Experiment
No.
22
23
2k
25
28
30b
31
32b
Diurnal
period
Day
Day
Day
Day
Day
Evening
Day
Evening
Arc
No.
1
2
3
1
2
3
1
2
3
1
2
3
4
5
7
it
5
6
1
2/6
7
1
2
3
x, m
945
3378
7370
825
3274
7601
949
3384
7*04
698
3245
6384
2019
4238
15960
1923
4274
8291
940
3371
13375
643
3236
6440
t, sec
206
738
1610
151
601
1395
90
320
703
299
1388
2732
427
897
3379
144
516
2048
245
853
1461
ffy, m
162
450
1022
121
374
722
160
326
570
151
814
1252
350
476
1470
381
615
780
138
270
910
176
659
1169
az, m
104
1771
1222a
99
984
4112
44
343
2418
516
1204a
1106a
2148
3466
124la
17k
192
56
2535
1982
82
196
290
h, m
217
240
102
245
363
(X/Oj x 10"8,
sec/nr
472.0
9.45
6.63a
486.0
19.4
1.81
428.0
24.1
2.28
212.0
14. 3a
8.79a
10.7
4.93
4.10a
137.0
76.2
8.89
604.0
7.22
2.83
591.0
46.9
31.5
u,
m/sec
4.6
5.4
10.6
2.3
4.7
6.5
3.6
5.0
5.7
n
u = az
A ?£.
0.91Z0'36
Values considered to be significantly affected by a limited mixing layer in the vertical.
Values of dispersion parameters not used in the establishment of generalizations; meandering wind or
changing mean wind resulted in inflated values of a .
-------
Table 2 (continued). SUMMARY OF DISPERSION DATA
r
o
PS
Experiment
No.
33
35
36^
37
40
41
k2
43
Diurnal
period
Evening
Day
Day
Evening
Day
Evening
Evening
Evening
Arc
No.
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
4
5
6
1
2
3
x, m
959
3398
7047
734
3245
6395
620
3236
6833
753
3162
6514
733
3207
6445
627
3223
7459
1989
4205
7501
757
3186
6607
t , sec
348
732
1234
88
391
770
87
452
955
224
644
1077
772
316
635
380
1262
2566
220
372
538
94
298
546
"y. m
68
113
298
58
181
322
152
744
1194
54
205
289
120
474
645
207
370
588
202
413
665
101
372
699
"z> m
65
144
109
250
662
597a
85
430,
66la
68
171
345
147
872
1211
66
102
98
97
154
204
63
304
420
h, m
81
180
136
85
213
431
82
127
122
121
193
255
91
380
526
(x/0jp x 10"8,
sec/nK
1710.0
244.0
140.0
271 .0
31.6
19. oa
374.0
16.2
6.56a
2070.0
145.0
41.5
233.0
7.87
5.14
1330.0
253.0
166.0
146.0
37.2
16.1
515.0
20.2
7-27
u,
m/sec
4.6
7-9
6.5
8.3
7.2
4.7
6.6
8.7
10.1
2.6
3-3
3-2
12.8
17.4
19-9
11.3
13-5
14.0
n
u = az
n 68
0.40Z°'6b
1.16Z0'39
r\ c£
0.35Z0'56
n £ i
1.18Z0'51
rt 19
5.87Z0'12
Values considered to be significantly affected by a limited mixing layer in the vertical.
Values of dispersion parameters not used in the establishment of generalizations; meandering wind or
changing mean wind resulted in inflated values of ".
-------
METEOROLOGICAL INDICES OF TURBULENCE
The calculated values of dispersion parameters were related to
several readily measured or derived meteorological indices of turbu-
lence. These indices included stability classes, gustiness classes
based on patterns of wind direction fluctuations, and a classification
based jointly on measures of wind direction fluctuations and conditions
of vertical stability. Values of the indices were determined for semi-
rural or peripheral locations as well as for urban locations. This ap-
proach allows at least qualitative inferences concerning the applicability
of the various indices and of station locales in describing dispersion
over urban areas.
PASQUILL-TURNER STABILITY CLASSES
In the scheme devised by Pasquill (1961) and later slightly modi-
fied by Turner (1964), the diffusive ability of the lower atmosphere is
represented by stability classes determined jointly from estimates of
net radiation and wind speed . Determinations of these stability classes
over periods of tracer dissemination were made for three "wind meas-
urement locations in the St. Louis area: the lower level (127 feet above
ground) on the TV tower, the peripheral site west of downtown, and the
Weather Bureau Airport Station at Lambert Field in comparatively rural
surroundings. The net radiation estimates were based on solar altitude,
obtained from the Smithsonian Meteorological Tables (1963), and cloud
cover and ceiling height, taken from records of hourly observations at
the airport.
The use of Pa squill-Turner stability classes for peripheral and
urban locations may, of course, be questioned, since the scheme was
devised primarily for application over relatively open country. Also,
information on cloud cover at the airport may not always be appropri-
ate for the other locations.
MODIFIED "BROOKHAVEN" GUSTINESS CLASSES
In the gustiness classification scheme due to Singer and Smith
(1953) at Brookhaven National Laboratory, the diffusive ability of the
lower atmosphere is described by the range and rapidity of horizontal
wind direction fluctuations; a less detailed scheme had been designed
previously by Giblett et al. (1932) for use at Cardington. The range
furnishes an estimate of the turbulent velocity component in the cross-
wind direction and hence of cross-wind dispersion. The rapidity of
the fluctuations also indicates the general degree of vertical stability
and thus of dispersion in the vertical.
The basic Brookhaven gustiness classes were used in St. Louis,
15
-------
but different class limits on the ranges of wind direction fluctuations
were adopted. Although the St. Louis wind sensors were the same type
as those used at Brookhaven, they were located near larger roughness
elements and usually nearer the ground. In addition to the urban (lower
level on TV tower) and peripheral sites discussed earlier, wind data
for the upper level (459 feet above the ground) of the TV tower were
utilized also. With these additional data, comparisons can be made
between wind direction fluctuations at 127 feet, slightly above nearby
building tops, and those at 459 feet, well above the buildings. For each
site, range limits for the specific classes were derived from appropri-
ate analog traces obtained from a climatological analysis of the (analog)
records and were, without exception, greater than those found by Singer
and Smith (1953) at the Brookhaven site.
HORIZONTAL WIND DIRECTION FLUCTUATIONS
AND CONDITIONS OF VERTICAL STABILITY
This joint meteorological index employs the standard deviation of
horizontal wind direction fluctuations, "g , and a direct estimate of
vertical stability expressed as a gradient Richardson number. Indices
based partially or totally on these elements have been applied .by such
investigators as Cramer (1959), Fuquay et al. (1964), and Slade (1965)
to organize dispersion data from other experimental programs.
Estimates of ag over the tracer dissemination periods were made
from frequency histograms of azimuth angle derived from records of
the analog wind traces. Since the chart speed of wind recorders was a
slow 3 inches per hour, portions of the analog traces were occasionally
"painted" (i.e., the more commonly occurring azimuth directions).
Frequencies for the "painted" azimuth angles were extrapolated from
those of the "non-painted" angles under the assumption that the fre-
quency distributions of azimuth angle were Gaussian or resulted from
sums of Gaussian distributions.
Comparisons of these values of "g with the extreme, third highest,
and fifth highest ranges of wind direction fluctuations over the tracer
dissemination periods showed statistically linear relationships for each
range for each meteorological site. Linear correlation coefficients
varied from 0. 8 to slightly over 0. 9, the higher correlations generally
occurring for the peripheral and upper-level urban locations. Some-
what better correlations were attained with the third highest range than
with the extreme or fifth highest ranges. Average values of the ratio
of range to ag for the extreme, third highest, and fifth highest range
were, respectively, about 7. 5, 6. 0, and 5. 5. The value of 7. 5 for the
extreme range is slightly different from the 6. 0 found by Markee (1963)
and Slade (1965) for other locations and exposures.
Estimates of stability were based on wind and temperature meas-
urements at the downtown TV tower or temperature measurements from
the downtown radiosonde ascents. Lapse rates, stability ratios, and
various forms of the gradient Richardson number for several layers in
the lower atmosphere were considered. Thorough evaluation of these
16 ST. LOUIS DISPERSION STUDY II
-------
parameters was difficult because of incomplete data. A limited ap-
praisal, however, indicated that the most meaningful parameter was
the "bulk" Richardson number Rig. Fortunately, adequate data were
available to compute this value for most experiments. The Rig was
based on temperature and wind measurements at the 1Z7- and 459-foot
levels of the TV tower. Temperature information from the radiosonde
ascents was substituted when the corresponding tower data were miss-
ing. Following Lettau (1957), the Rig may be defined:
[AT/AZ
+ rd]
z2
2
V
RiB
where:
g acceleration of gravity
AT - temperature difference between top and bottom of the
layer
AZ = height difference between top and bottom of the layer
T = mean absolute temperature through the layer
F(j = dry adiabatic temperature lapse rate
Z = height of upper anemometer
v = mean speed for anemometer at height Z
Originally, a measure of a transport wind speed, u, •was also in-
corporated into the joint index; its utilization as an additional parameter
or in the form ay u generally increased data scatter. It should be noted,
however, that the tracer experiments were not usually conducted under
very strong or very light "wind speed conditions, resulting in a reduc-
tion in the overall and perhaps within-class range of u. Dispersion in
the cross-wind and in the vertical were better ordered by an and Rig
jointly than by either alone. Axial concentrations also were better re-
presented by this joint classification than by ag or Rig alone.
TABULATION OF RESULTS
For each of the experiments, values of the meteorological indices
at the locations specified in the preceding sections are presented in
Table 3. Values of Rig denoted with superscripts were those that were
inconsistent with all other coincident measures of stability, e.g. , Pas-
quill-Turner classes or gustiness classes. Without exception, these
inconsistencies were for cases in which the radiosonde temperature
data were substituted for missing TV tower data.
Meteorological Indices of Turbulence 17
-------
Table 3. SUMMARY OF METEOROLOGICAL INDICES
Exper i ment
No.
2
3
4
5
6
7
8
9
] 1
12
14
16
18
19
20
21
22
23
24
25
28
30
31
32
33
35
36
37
AO
Al
1)2
43
R1B
-0.05
-0.03
-0.25
-0.13
0.03a
-0.07
-0.08
-0.04
0
0. 14
Qa
O.OSa
-0.51
-0.10
0.01
-0.02
-0.40
-0. 11
-0.03
-0.03
-0.01
-0.02
0.01
-0.05
0. 12
0
-0.01
-------
RELATION OF DISPERSION PARAMETERS
TO METEOROLOGICAL INDICES OF TURBULENCE
Values of a
-------
1. The ordering of data was poorest for the close-in sampling
arcs at which multi-peaked or otherwise complex distributions in the
cross-wind occurred in greater proportion than at more distant arcs.
As previously noted, channeling of the airflow due to various locally
induced circulations may be largely responsible for the appearance of
such distributions.
2. The scatter of data points about best-fit lines was much
greater in
-------
COMPARISONS WITH OTHER EXPERIMENTAL
PROGRAMS
The results (i.e. , the derived dispersion relationships) of the
St. Louis tracer experiments can be compared with those of past "open
country" programs for which the dispersion parameters are described
by comparable meteorological indices. Specifically, the St. Louis
results based on values of
-------
open country is greatest near the source and is greater for stable than
for unstable meteorological conditions, as expected (Figures 16a and
16b). Overall relations similar to those in Figure 16 are generally
noted in Figures 15 and 17 despite the differences in terrain, sensor
exposures, and response characteristics of equipment used in the
various studies. Some of the apparent differences in Figure 17 can
also be accounted for by the fact that Pasquill-Turner class A's and
F's, which constitute a sizable fraction of the Brookhaven B2 and D
class members, respectively, "were seldom represented in the data
collected in the St. Louis experimental series.
Values of dispersion parameters obtained in fluorescent particle
tracer experiments in Johnstown, Pennsylvania (Smith, 1967), and
Fort Wayne, Indiana (Csanady et al. , 1967), are also presented in
Figure 16. The values are similar to those obtained in St. Louis
under the same overall meteorological conditions. In Johnstown, dis-
seminations were from a low-level point source in the urban area; in
Fort Wayne they were from a 90-meter-high, cross-wind line source
located 1 mile upwind of the urban area. Values of az for this elevated
line source that were reported for the 1-mile downwind distance (i.e. ,
at the upwind edge of the urban area) are not shown here; a direct com-
parison of the other values, particularly for shorter distances, with
those of low-level sources can be questioned since the effects of local
obstructions may not have become significant until the tracer plume
reached near ground level.
For the St. Louis experiments a ratio of peak to mean concentra-
tions (P/M) was computed for each case in which the appropriate se-
quential sampler "was on or quite near the mean centerline of a tracer
cloud. The ratios were formed from the peak and arithmetic average
(mean) values of concentration of the time-concentration histograms;
intervals of beginning and ending "dribble" were excluded. Plots of
P/M as a function of downwind distance and travel time showed little
variability, even when data were separated according to stability.
Gifford (I960) presents similar results for ground-level emission
sources.
A plot of P/M as a function of the ratio of averaging time, ta, to
sampling time, tg, is shown in Figure 18. Averaging time is the time
interval required for passage of the tracer cloud, excluding beginning
and ending dribble. Sampling time is the finite time increment,
usually 1 or 2 minutes, over which the peak concentration was meas-
ured. In this figure, P/M values show a very slight tendency to in-
crease with increasing ta/ts. The values of P/M vary from about Z to
6. Gifford (1960) shows similar values for ground-level sources;
Singer et al. (1963) found that values decreased in proportion to in-
creasing density of vegetation near receptors.
22 ST. LOUIS DISPERSION STUDY I[
-------
INITIAL DIMENSIONS OF TRACER CLOUD
The effects of a building upon a. plume generated in its vicinity
have been studied extensively in wind tunnel experiments (e.g. , Halit-
sky, 1963). More recently, a full-scale investigation was conducted
in the atmosphere (Dickson et al. , 1967). Essentially, these studies
show that the primary effect is an enhancement close to the source of
the size of the plume, hereafter referred to as the initial size of the
plume.
Pasquill-Gifford (Gifford, 1961) "C" stability curves (e.g., see
Figure 16) for a and
-------
103
CO 5
0}
E
, degrees R i
' -a- • 30 +
—•—24 -29
— 'tf — 18 - 22
......-15 -20
...0---- 8 -13
^ - 0.01
<-0.01
± o'.oi
>0.01
10
I I I I I I
I I Mill
I I I I I 111
102
103
5
x, meters
104
105
Figure 1. Cross-wind standard deviation of tracer material as a function
of downwind distance in terms of standard deviation of wind
direction fluctuations (ffg) and bulk Richardson number (Rig).
ST. LOUIS DISPERSION STUDY II
-------
10'
10*
1 Cl-
/ / .'
*/* X » p-'
* + .* o
' .A/
of,°
jf*
RESTRICTIVE
Q. degrees Rig L|p _
.•_ 24 +
-A.-18 -22
«...15 -20
•o— 8-13
+ 0.01
> 0.01
102
103
10"
105
x, meters
Figure 2. Effective vertical standard deviation of tracer material as a
function of downwind distance in terms of standard deviation
of wind direction fluctuations (ae) and bulk Richardson
number (Rig).
Initial Dimensions of Tracer Cloud
Z5
-------
10"
10
,-5
ID'1
xlO
10-
10"
10-
10-
g9. degrees RiB RESTRICTIVE
-•— 24 + <-0.01 Q
-*• —18-22 < - 0.01 A
-*- • • 1 5 - 20 t 0.01 ®
.0"" 8-13 >0.01
10-
10-'
x, meters
~nq
Figure 3. Relative axial concentration as a function of downwind distance
in terms of standard deviation of wind direction fluctuations (ag)
and bulk Richardson number (Rig).
26
ST. LOUIS DISPERSION STUDY II
-------
10"
5 —
10-
10'
10"
10"
10-f
ae. degrees Rig RESTRICTIVE
LID
24 +
18 -22
-15-20
. 8 -13
<-0.01
<-0.01
tO.01
>0.01
102
103
104
x, meters
105
Figure 4. Normalized relative axial concentration as a function of down -
wind distance in terms of standard deviation of wind direction
fluctuations (°s) and bulk Richardson number (Rig).
Initial Dimensions of Tracer Cloud
27
-------
10"
103
102
101
a , degrees Rig —
-_•— 24 + <-0.01
_ -*, _ 18 - 22 < - 0.01
....... 15 -20 +0.01
....o--- 8 -13 >0.01
10'
102 5 103
TRAVEL TIME, seconds
10"
Figure 5. Cross -wind standard deviation of tracer material as a function
of travel time in terms of standard deviation of wind direction
fluctuations (erg) and bulk Richardson number (Rig).
28
ST. LOUIS DISPERSION STUDY II
-------
104
103
0.01
102 5 103
TRAVEL TIME, seconds
104
Figure 6. Effective vertical standard deviation of tracer material as a
function of travel time in terms of standard deviation of wind
direction fluctuations (oe) and bulk Richardson number (Rig).
Initial Dimensions of Tracer Cloud
29
-------
10-6
10-7
J I
o. degrees Ri_ RESTRICTIVE
a o I I n
i_24+ <-0.01 a
- — 18-22 <-0.01 A
15 - 20 t 0.01
—• 8 -13 >0.01
10'
102 5 103
TRAVEL TIME, seconds
Figure 7. Relative axial concentration as a function of travel time in
terms of standard deviation of wind direction fluctuations (06
and bulk Richardson number (Rig).
30
ST. LOUIS DISPERSION STUDY II
-------
10"
10"
io-!
10-'
10-
10-
O
o *.
101
102 5 103
TRAVEL TIME, seconds
104
Figure 8. Normalized relative axial concentration as a function of travel
time in terms of standard deviation of wind direction fluctuations
(cig) and bulk Richardson number (Rig).
Initial Dimensions of Tracer Cloud
31
-------
104
103
102
E-F
PASQUILL-
TURNER CLASS
T A
• B
A C
• D
o E-F
103
5
x, meters
10"
105
Figure 9. Cross -wind standard deviation of tracer material as a function
of downwind distance in terms of Pasquill - Turner stability
classes.
32
ST. LOUIS DISPERSION STUDY II
-------
104
5 —
103
10'
PASQU ILL-
TURNER RESTRICTIVE-
CLASS LID
* A
• B
A C
• D
O E - F
V
D
©
102
103
10"
10s
x, meters
Figure 10. Effective vertical standard deviation of tracer material as a
function of downwind distance in terms of Pasquill - Turner
stability classes.
Initial Dimensions of Tracer Cloud
33
-------
10'
10-7 _
5 —
10"
C
D
E -F
PASQUILL-
TURNER RESTRICTIVE
CLASS LID
©
®
102
5 103
10"
5 105
Figure 11. Relative axial concentration as a function of downwind dis-
tance in terms of Pasquill - Turner stability classes.
34
ST. LOUIS DISPERSION STUDY II
-------
5 —
103
102
10!
MODIFIED GUSTIIMESS CLASS
D1
102
5 103 5 104 5 105
x, meters
Figure 12. Cross-wind standard deviation of tracer material as a
function of downwind distance in terms of modified Brook-
haven gustiness classes.
Initial Dimensions of Tracer Cloud
35
-------
103
102
10
102
103 5 10"
A, meters
105
Figure 13. Effective vertical standard deviation of tracer material as
a function of downwind distance in terms of modified Brook-
haven gustiness classes.
36
ST. LOUIS DISPERSION STUDY II
-------
ID'6
— MODIFIED GUSTINESS
CLASS
102
103
5 10"
Figure 14. Relative axial concentration as a function of downwind distance
in terms of modified Brookhaven gustiness classes.
Initial Dimensions of Tracer Cloud
37
-------
f
O
G
O
I
104
5
103
102
5
GREEN GLOW SERIES 30
ST. LOUIS afl (Ri )
I I I I II
I II
5 103
105
x, meters
Figure 15. Comparison of results of St. Louis tracer experi-
mented with those of Green Glow - Series 30 ex-
periments (Fuquay et al. 1964).
io-6,
5
io-7
5
10'
-GREEN GLOW Vo \-
SERIES 30(J(Ri) \
102
103
I I 11
5 ' 104
x, meters
105
-------
JOHNSTOWN, PA.. E - F =
5 104
5 10s
x, meters
103
5
102
•PASQUILL - GIFFORD =
- — -ST. LOUIS
• JOHNSTOWN. PA. (E - F)
A. FORT WAYNE, INDIANA (E - F)
• FORT WAYNE, INDIANA (D)
M
102
103 5
x, meters
104
5 105
Figure 16 (a and b). Comparison of the results of the St. Louis and other urban tracer
experiments with those summarized by Pasquill and Gifford (1961).
Initial Dimensions of Tracer Cloud
39
-------
Note:
The grouping of the St. Louis, Johnstown, and Fort Wayne data in Fig-
ure 16 was by Pasquill-Turner stability classes (Turner, 1964), which
are really only more objective expressions of the Pasquill stability
classes (Pasquill, 1961) in terms of readily available meteorological
variables. The solid curves are based upon data ordered by the Pas-
quill stability classes; those in Figures I6a and 16b were originally
presented by Gifford (1961), and those in Figure 16c by Hilsmeier and
Gifford (1962).
E
b"
x\a
Figure 16 (c). Comparison of the results of the St. Louis tracer experiments with those
summarized by Pasquill and Gifford (1961).
40
ST. LOUIS DISPERSION STUDY II
-------
•BROOK HAVEN
GUST INESS CLASSES
ST. LOUIS "MODIFIED
GUST INESS CLASSES
102
104
103
w
8 5
-------
10
A A
O
O
PASQUILL -TURNER CLASS
C
D
E-F
10
20
50
100
Figure 18. Ratio of peak to mean concentration as a function of ratio
of averaging time to sampling time.
42
ST. LOUIS DISPERSION STUDY II
-------
q
i'
o
5"
REVISED
PASQUILL - GIFFORD —
av (initial), meters H
60
40
20
LL
5 103 5 104
x, meters
5 105
104
5
103
5
CO
0>
OJ
N 102
10'
5
10°
TTTT1
nrq
REVISED
PASQUILL - GIFFORD —
oz (initial), meters —
___ 60
_. 40
20
102
5 103 5 104
x, meters
5 105
Figure 19. Comparison of Pasquill - Gifford "C" stability curves (Gifford, 1961), revised to allow for specified initial plume
dimensions, with best - fit lines for St. Louis tracer data.
-------
CONCLUSIONS AND RECOMMENDATIONS
Results of the St. Louis Dispersion Study reported here support
the following conclusions regarding dispersion of airborne material
emitted from low-level point sources in urban areas:
1. Dispersion can be readily described by commonly utilized
meteorological indices of turbulence. The more detailed indices for
urban locations appeared to be most representative.
2. In terms of the meteorological indices of turbulence, cross-
wind dispersion is better described as a function of downwind distance
than of travel time, whereas vertical dispersion is described about as
well by travel time as by downwind distance. It should be noted, how-
ever, that Pooler (1966) found, for an overall classification of experi-
ments simply as daytime or evening, that cross-wind dispersion was
expressed about as well in terms of travel time as of downwind dis-
tance, whereas vertical dispersion was expressed better in terms of
travel time.
3. The urban area affects cross-wind dispersion primarily by
enhancing the size of the initial plume. When the plume becomes much
larger than the size of eddies created by the local obstructions, the
extent of the dispersion approaches that associated with flow over open
country. In the vertical, significantly enhanced dispersion as well as
a large initial spread of the plume result; the enhancement in the rate
of dispersion over that in open country is somewhat greater for stable
than for unstable meteorological conditions and, presumably, is due
largely to enhanced convective activity over the urban environs.
4. Restrictive mixing layers (e.g. , inversion aloft) can signifi-
cantly alter the values of affected vertical dispersion parameters and
concentrations of airborne material near the surface.
Dispersion from low-level sources in urban areas for downwind
distances of less than about 1/2 mile is conjectural. Here, the effects
of local roughness elements should be most pronounced. Specifically,
initial cloud dimensions as affected by factors such as building width
and height and building density should be ascertained, and the effects
of complexes rather than single structures should be catalogued.
The effects of urban areas on dispersion of plumes from elevated
sources, particularly at the shorter downwind distances, may differ
markedly from those suggested for lower-level sources, and hence may
require independent investigation. As mentioned earlier, the effects
45
-------
of local obstructions may not become significant until a plume nearly
reaches the ground. At this point the plume may also be so large that
the locally created eddies are not significantly effective in dispersing
it. In addition, as the effective source height increases, different
stability regimes about which little is known are encountered.
The analyses reported herein concerning data collected during
the St. Louis Dispersion Study are not considered to be exhaustive. It
is hoped that the body of data can serve a useful purpose for the appli-
cation of more advanced analytical techniques, which are certain to be
developed by meteorological science in the future.
46 ST. LOUIS DISPERSION STUDY II
-------
ACKNOWLEDGMENTS
Sincere appreciation is due the personnel of the Meteorology
Program, National Air Pollution Control Administration for their
support, suggestions, and encouragement during the conduct of this
research. The authors also wish to thank F. A. Gifford, W. C.
Culkowski, and F. B. Smith (Visiting Scientist, British Meteoro-
logical Office) of the Environmental Science Services Administration's
Air Resources Atmospheric Turbulence and Diffusion Laboratory, Oak
Ridge, Tennessee, for many helpful comments.
47
-------
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50 ST. LOUIS DISPERSION STUDY II
-------
Vaughan, L. M. , and R. W. McMullen, 1968: The physical analysis
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References 5!
ftU. S. GOVERNMENT PRINTING OFFICE : 1969 O - 334-656
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