-------
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169
-------
UVW PROPS AT 80 m
FREQUENCY <»)
29.9-
.«-! - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1
8 39
UVW PROPS ATlOm
a.s-
8.0-
7.S-
7.e-
G.S-
G.O-
5.5-
s.e-
3.5-
3.9-
2.5-
2.9-
1.5
1.9-
.5
—I 1 T-
1 - 1
299 aaa
869 sae 399
DIRECTION (dug)
Figure 78. Calculated wind direction distribution functions for Experiment
206, Hour 8 (0700-0800 MST).
170
-------
directions at the 80 m level are limited to about a 10° range. The 10°
range remains indicative of the transport at plume elevation.
In summary, the hour is quite similar to hour 6. The plume was
released at virtually the dividing streamline height, and the transport
direction was very steady.
SFfi Concentrations
The distribution of hourly averaged SFg concentrations over the
surface of the hill is shown in Figure 79. Highest concentrations are found
along the south side of the southeast draw and along the eastern face of the
north peak. These concentrations lie between the 25 m and 50 m height
contours. Other high concentrations are spread over the north peak and the
saddle area.
This pattern is consistent with the observations and the photographs
discussed above. The north peak area was frequently hit, but the plume was
at times mixed down to the ground near the base of the draw, thereby
producing the highest concentration measured during the hour. The broad
distribution of higher concentrations on both the windward and leeward sides
of the north peak indicates that plume material was mixed to the surface as
it met the hill and was then advected directly over and around the hill top.
The distribution of 10-minute average SF5 concentrations is presented
in Figure 80. No information is available for the area near the impingement
zone, but the data indicate that much of the material that came toward the
north peak passed around toward the north side.
4.8.2 Model Performance
This hour is very similar to the previous hour discussed in
Section 4.7.2, The plume was released very close to the calculated dividing
streamline height, and so the Wrap model ought to work quite well.
All meteorological data were prepared for release height as in
Section 4.1.2. The resulting values are summarized in Table 11.
The 1-hour average wind directions measured 25 m below and 45 m above
the release height are 356° and 131°. However, the photographs suggest that
the plume trajectory followed winds in the range of 127° to 170°.
Therefore, 127° is used in the modeling along with the 80 m PDF.
Both Impingement and Wrap were run with the revised meteorological
data, and the results are listed in Table 11, and plotted on a map of CCB in
Figure 81.
The models do well in matching the observed concentration pattern. The
highest observed concentrations occurred around the height of release; the
maximum, 1,512 ppt, is measured at 25 m. The Wrap estimate at this height
is 1,994 ppt, but Wrap estimates a maximum concentration of 2,345 ppt at a
171
-------
Figure 79. Observed SF^ concentrations (ppt) for Experiment 206,
Hour 8 (0700-0800 MST). Source: r = 595.9 m, 9 = 123.6°,
net height = 29.5 m, Q = .062 g/s.
172
-------
TIME PERIOD 0708-871*
TIRE PERIOD 8718-0758
Figure 80.
Observed 10-minute average SFg concentrations for
Experiment 206, Hour 8 (0700-0800 MST).
173 '
-------
TlflE PERIOD 87aO-873t
Figure 80. Continued.
174
-------
TIKE PERIOD 878«a
Figure 80. Continued.
175 .
-------
TABLE 11. IMPINGEMENT AND WRAP MODEL CALCULATIONS - EXPERIMENT 206,
CASH HOUR 8
f'eteorolepical Data
wind directionCdeq) = 127.
wind soeed(m/s) = r?.0
critical dividinq
streamline heiphtCm) = 37.0
Iz = .097
ly = .180
NCl/s) = .OHO
Source Data
direction(deg) = 12/1.
distance(m) = 595.9
release heiqht(m)= 35.0
SF6 emission
rateCg/s) = .062
Receptor Coordinates Observed
X(nO Y(m) 2(m) SF6 (ppt)
208.35
142.00
257.78
72.15
404.91
159.04
85.15
51.04
20.07
15.97
10.61
25.15
2.15
-15.01
-19.85
-9.85
-84.85
248.96
204.16
144.85
77.87
95.80
59.13
199.06
256. HI
204.15
IPS. 15
1"3.53
312.38
359.96
111.85
-40.85
•141.42
109.07
.00
.00
33.94
19.88
111.59
122.04
64.88
387.66
152.45
121.29
80.56
190.88
18.88
-113.99
-149.12
-76.12
-65.12
-66.71
-54.70
-38.12
-290.63
-231.27
-154.04
-259.43
-148.27
-117.12
-61 .12
-49.18
-41.13
207.8?
65.88
28.88
141.42
263.31
31.25
50.00
30.00
80.00
10.00
46.91
80.00
11.78
R1.06
90.94
91.97
65.00
80.00
98.96
90.00
-------
Figure 81. SFg concentrations (ppt) estimated for Experiment 206, Hour 8
by the Impingement (top) and Wrap (bottom) models.
177
-------
height of 30 m (where the observed concentration was 973 ppt). In general,
the predictions from Wrap are no more than 100% greater than the observed
concentrations. On the other hand, the Impingement model underestimates the
observations. The largest estimate is about 636 ppt, or roughly one-half
the maximum observed. The difference between model estimates is directly
related to the treatment of the wind direction probability distribution. In
this case, the Gaussian distribution characterized by iy underestimated
the probability, and the assumed PDF overestimated it.
The
4.9 Experiment 209, Hour 1 (1700-1800 MST)
4.9.1 Summary Description
Thermofogger oil-fog and SFg tracer gas were released from the
northwest side of the hill at 986.1 m, 315.9° for the entire hour.
release height was 40 m. Because the SFg was started at 1654 and
terminated at 1759, the tracer plume was probably well established
throughout the sampling hour.
Local terrain elevations near the release point are estimated to be
-7.0 m relative to the zero of the hill coordinate system, so the net
release height corresponded to the 33.0 m height level on the hill. The
SFs release rate is computed to be 0.156 g/s with an estimated uncertainty
of +5*9%. No Freon was released.
Plume Observations
During the course of this experiment, several people recorded their
observations about the appearance and the trajectory of the oil- fog plume.
Those comments applicable to the first hour are presented below.
Time: 1650 The jet fogger is up at 40 meters at site A2B. The plume
looks quite unstable. There is a great deal of vertical development at
the moment, and it appears to be headed right toward the hill. Looking
from the back side of the hill, the plume looks like it goes to 2 hill
heights at the moment.
Time: 1700 (?) Plume is starting out on a line toward the FAA tower
and then curves to the north side. I see some plume material mixing
down to the hillside at about the 20m elevation.
Time: 1715 Plume is fluctuating across the peaks. From the top, a
little odor is noted, but most of the plume is going overhead.
Time: 1721 The plume is still continuing to go up the shoulder in the
vicinity of tower F, and from the side view it looks like it is not
touching the hill until it gets very near the top in the vicinity of
tower B. In the lee, the plume descends quite a bit and looks like it
almost reaches the ground again about a hill width away to the
southeast.
178
-------
Time; 1724 The plume is traveling right over B2 as it travels to the
southeast.
Time: 1725 I am sitting at 481, and the plume is passing right over
this point.
Time; 1733 From southwest: plume goes towards draw, lifts up and
over, and then comes back down on the lee side at a lower level than
the approach height. The majority of the plume is going up the draw.
Time; 1740 Plume heading directly towards the blockhouse on the south
end and then it bends around to the south (then back towards the east
in the lee of the hill).
Time: 1745 Plume is midway between the blockhouse and tower E. It may
be following this road along the south side.
Time: 1754 Plume has stabilized considerably over the last 5 minutes.
It has a much smaller diameter as it approaches the hill and the loops
are not nearly as great—they are almost gone near the release point.
Time; 1756 View from ERT Base: plume has a puffy appearance and is
broken up somewhat.
These comments indicate that the plume went up and over the hill for
much of the hour, apparently favoring the saddle area over the first half
hour, and the south peak at times during the second half hour. The
trajectory brought the plume up and over the hill, rather than directly into
the hill, and little smoke odor was reported. A strong depression was
reported in the lee of the hill, however. These features of the plume
trajectory are consistent with weakly stratified flow (i.e., a hill Froude
number of order 1).
Photographs of the plume document the described plume features on the
upwind side of the hill. Four photos reproduced in Figure 82 show the plume
trajectory at two times during the hour. One view is from behind the
release crane at camera position B-l (see Figure 46), and the other view is
from a point off to the side of the plume trajectory, at camera position
0-3. Each individual photo is an automatic exposure, so it provides nearly
instantaneous views of the plume rather than 5- or 10-minute averages.
The photos show that the plume trajectory was fairly steady over the
hour and that the vertical dispersion was very large. During the first
5-minute period, the plume traveled toward the north peak. Over the next
15 minutes, however, it appears to have ridden steadily over the saddle
between the two peaks. The lift in the plume as shown in the view from the
side is quite significant, although the plume spread in the vertical appears
great enough to have brought the visible plume material quite near the
surface.
!
The plume tended to wander from the saddle toward the south peak over
the next 15 minutes (periods 5-7) with little change in either plume spread
179
-------
180
-------
or plume lift. But during the remaining 20 minutes in the hour, the plume
traveled preferentially over or around the south side of the hill. Some
plume depression in the lee of the hill can be seen in period 10 (see
Figure 82) as the plume hooked over the south peak. The scale of the
vertical plume spread can be seen to decrease from period 9 to period 12.
Lidar data for this hour are quite extensive and permit quantification
of the plume behavior noted above. The plume was sampled by the lidar along
eight planes. Three of the planes were upwind of the hill, three were
substantially over the hill, and two were in the lee. Plume centroid
positions along these planes are plotted in Figure 83.
Centroid positions indicate that the plume trajectory was initially
oriented toward the north side of the hill in period 2, but quickly shifted
to the center of the hill through period 6. Later in the hour, the
trajectory is seen to shift more toward the south peak. Estimates of the
wind direction at source height, derived from the lidar data upwind of the
hill, vary from 317° early in the hour to 323° in period 6, and then to as
much as 330° later in the hour. Because the source is located at 316°, all
but the earliest trajectories favor the south peak.
Meteorological Information
Wind and temperature data measured at tower A during this hour were
used to characterize the flow in terms of Hc. The average of the 5-minute
values over the hour is 5 m, and the average Frjj above 5 m is 3.1.
Because Hc was so low compared to the 40 m height of release, Hc should
have had little impact on the SFg concentrations. FrL for the layer
above Hc is 0.78, indicating that the stratification may have produced
some streamline depression in the lee.
Figure 84 contains a time series plot of the calculated 5-minute Hc
and Frjj values for this experiment. Hc rises from a low of zero to
about 9 m halfway through the hour and remains there for the rest of the
hour. Frji is very large at the start of the hour but falls to 2.5 halfway
through the hour. As the hour ends, Frjj is as low as 2.3. Because Hc
and Frn changed during the hour, the plume trajectory may not conform to
that expected from average values of the Froude number. For example, Frj,
late in the hour is about 0.58, and more significant streamline depression
in the lee would be expected in conjunction with this value. The observer
log contains a reference to a pronounced depression in the lee at 1721, but
it is unclear if such a depression might have occurred earlier or
intensified later.
Hourly averaged wind speeds at 10 m and 40 m on tower A are 3.3 and
4.3 m/s, respectively. The 10 m winds were from 304°, and those at 40 m
were from 311°. Wind shear (both speed and direction) was therefore small
between the plume elevation and 10 m. Figure 85 shows the trend in wind
speeds over the hour. Winds at all three levels from 10 m to 80 m were
within 2 m/s of one another and were virtually constant over the hour.
Therefore, the hourly average wind values are representative of the entire
hour.
181
-------
IJ I
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182
-------
Hc(m)
•• f i
17. e is.o 19.6 aa.o ai.
aa.e 23.
.8 25.8
TIM (Hour)
'i *
i •
i7.e is.e 19.e ao.e 21.0 aa.e as.e a<.e as.e
Tin (Hour)
Figure 84. Calculated dividing streamline heights (He) and bulk hill Froude
numbers above Hc (F^H) for Experiment 209.
183
-------
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-------
Variations in wind directions measured at 10 m and 40 m are' shown in
Figure 86 as frequency distributions. The 10 m wind directions were a
little more variable than those at plume elevation primarily because of a
shift toward 300° not seen at 40 m. However, the flow structure during this
hour was not as complex as many other hours under study.
In summary, this hour may be characterized as nearly neutral with
steady winds and little wind directional shear. The major complicating
factor is the strengthening of the near-surface temperature gradient with
time. On balance, the meteorology indicates that the plume should have
traveled freely over the hill, much like plumes in a weakly stratified
tow-tank experiment (Frg ^ 1).
Concentrations
The distribution of hourly averaged SFg concentrations over the
surface of the hill is shown in Figure 87. All concentrations are
remarkably low, especially in view of the increased SFg emission rate
begun in Experiment 209. Concentrations were measured on the windward side
of the hill all the way up to the 60 m contour. Low concentrations were
measured at lower elevations on either side of the hill and over the crest
of the hill. The highest concentration is found near the base of the
southeast draw in the lee of the hill.
This pattern is consistent with observations that the plume rose quite
high over the hill and then descended in the lee. It is surprising,
however, that the vertical mixing evident in the photos produced such small
SFg concentrations at the surface.
The 10-minute average SFg concentration distributions are presented
in Figure 88. They also show the lack of even moderate SFg concentrations
on the windward site of the hill. Unfortunately, no 10-minute samplers were
placed in the lee toward the base of the hill to document the time evolution
of the higher concentrations during this hour.
4.9.2 Model Performance
This hour was modeled with the Lift model because all evidence
indicates that the flow was nearly neutral (unstratified) and very steady.
Meteorology for the release was prepared as in Section 4.1.2, except that no
height interpolations were needed because the plume was released at 40 m, an
instrumented level on Tower A. The data are summarized in Table 12.
The 1-hour average wind direction at the release height is 311°.
However, the lidar and photographic data strongly suggest that the mean wind
direction should be about 319°. Both the 10 m and 30 m levels on tower B
recorded mean winds of 324°. Therefore, a mean direction of 319° is used in
the modeling along with the PDF computed with the 40 m wind direction.
185
-------
UVW PROPS AT 40m
9.0-
s.s-
S.9-
7.5-
7.0-
6.S-
e.o-
5.S-
s.o-
4.5-
4.0-
3.5-
3.t-
2.5-
B.»-
1.5-
i.e-
.5
.o-l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 "•"
o EO 40 eo go too lao 140 teo tea aee aae 240 aeo aao 3»e SBO 340 seo
UVW PROPS AT 10m
6.5
6.9
S.S
s.e
3.5-
3,e-
s.s-
2.0-
l.S-
1.0-
,5-
Figure 86.
.oH 1 1 i 1 1 1 1 1 1 1 ' 1 1 ' ' ' '
o ao 40 GO 30 100 lao 140 160 iao aoo aao 240 aee aoo 300 320 340 360
DIRECTION (
Calculated wind direction distribution functions for Experiment
209, Hour 1 (1700-1800 MST).
186
-------
"•* r = 500 m
N
:7
Figure 87. Observed SF6 concentrations (ppt) for Experiment 209,
Hour 1 (1700-1800 MST). Source: r = 986.1 m, 6 = 315 9°
net height = 33 m, Q = .156 g/s. ' '
187
-------
TIHE PERIOD 174»-«7ie
TIME PERIOD 1718-172»
Figure 88. Observed 10-minute average SFg concentrations (ppt) for
Experiment 209, Hour 1 (1700-1800 MST).
188
-------
TIBE PERIOD 1738-1748
Figure 88. Continued.
189
-------
TIME PERIOD 1758-1680
Figure 88. Continued.
190
-------
TABLE 12. NEUTRAL AND LIFT MODEL CALCULATIONS - EXPERIMENT 209, CASE HOUR 1
feteorolopical Data
wind directionCdeq) = 319.
wind speedCm/s) = 4.3
critical dividing
streamline height(m) = 5.0
Iz = .053.
Iy = .093
NCl/s) = .018
Source Data
airection(des) = 316.
distance(m) = 986.1
release heiaht(m)= 40.0
SF6 emission
rate(g/s) = .156
Receptor Coordinates Observed
X(m) YCm) Z(m) SF6 (ppt)
360.22
142.00
257.78
72.15
404.91
159.04
85.15
58.64
51.04
35.92
32.61
20.07
15.97
2.15
-53.69
-45.46
-15.01
-23.49
-19.85
-4.85
-84. B5
396.68
315.76
248.96
'204.16
144.85
238.00
355.15
313.62
108.15
37.15
312.38
243.41
'441.92
359.96
297.11
269.62
246.20
•111.65
•141.42
229.81
-91.99
-65.85
'109.07
-32.85
-40.46
-25.71
.00
.00
33.94
19.88
111,59
122.04
64.88
445.44
387.66
272.83
247.73
152.45
121.29
18.88
-407.79
-345.28
-1 13.99
-178.46
-149.12
-37.12
-65.12
-106.29
-84.61
-66.71
-54.70
-38.12
.00
-205.04
-181.07
-61.12
-21.12
-41.13
65.22
255.14
207.82
171.54
155.66
142.14
65.88
141.42
229.81
119.88
85.88
263.31
122.88
307.35
195.51
13.26
50.00
30.00
80.00
10.00
46.91
80.00 -
3.38
11.78
31.92
41.74
81.06
90.94
80.00 '
3.82
13.70
98.96
80.00
90.00
60.00
90.00
3.44
13.24
32.90
52.26
80.00
50.00
5.69
15.29
50.00
70.00
14.00
50.00
-.90
8.94
28.07
38.07
47.96
80.00
50.00
30.00
64.94
80.00
30.00
80.00
30.00
65.00
8.70
4.90
17.80
4.90
.10
8.82
.00
.00
.00
10.30
14.50
.98
5.00
6.50
.00
4.90
32.00
20.98
17.50
26.00
11.70
.00
12.50
.00
4.90
33.60
.00
102.70
22.70
16.30
14.50
6.90
.00
.00
.00
.00
.10
.00
11.70
2.20
.20
14.60
5.20
.00
8.50
.10
.10
Neutral
Predicted
SF6 (ppt)
4.95
169.28
14.03
313.61
.11
26.63
253.86
.00
.00
1.43
6.02
235.54
302.00
407.88
24.33
56.02
444.90
424.95
439.41
443.58
504.21
.05
3.97
49.00
308.73
542.60
316.79
82.95
105.67
301.06
365.44
20.97
489.42
25.60
183.48
459.36
590.72
714.79
550.56
572.33
655.20
467.78
459.41
65.22
356.81
2.66
184.04
Lift
Predicted
SF6 (pot)
.00
173.68
.00
272.8R
.00
.00
60.16
.00
.00
.00
.00
8.12
63.69
313.65
43.36
81.07
244.56
225.61
228.99
361.41
246.26
.00
.00
37.45
121.05
233.87
125.33
140.43
217.98
289.44
. 302.71
.00
239.47
7.80
199.26
255.58
279.47
278.81
353.48
333.54
340.19
339.87
332.41
.00
299.27
.00
.00
191
-------
Neutral was rerun with the revised meteorological data. Instead of
estimating a peak value that is 883% of the observed peak concentration, it
produced a value 695% of the observed peak. Obviously, the model is
'bringing too much plume material to the surface, especially when the high
modeled concentrations occur on the windward face of the hill where observed
concentrations are nearly zero. Figure 89 shows the distribution of
calculated concentrations plotted on a map of CCB, and the results are also
summarized in Table 12.
Results from Lift computations are also displayed in Figure 89 and in
Table 12. These concentrations are not quite as large as those from
Neutral, but the peak modeled concentration is still 350% of the peak
observed concentration. Both models produce az values of 20 m to 30 m,
and these are large enough to account for the substantial SFg impact on
the hill according to the models.
The observations, however, tell a very different story. When terrain
factors are computed from the observed concentration field and the output of
the Lift model, To values are consistently near 2.0, which implies that
the CTZ values are too large by approximately a factor of 2. Possible
causes for the discrepancy between modeled and observed concentrations are
being investigated.
4.10 Experiment 209, Hour 7 (2300-0000 MST)
4.10.1 Summary Description
SFg tracer gas was released from the east-southeast side of the hill
at 999.2 m, 100.9° for the entire hour. The release height was 40 m.
Because the SFg was not interrupted from the previous hour and continued
through the end of the hour, the sampling data should represent the full
hour. Oil-fog at 40 m was provided by the jet fogger from 2300 until 2329,
so the visual plume was only operational for half the hour. A secondary
oil-fog plume from the thermofogger was released at 30 m from a point on the
northwest side of the hill (^1155 m, 331°) between 2300 and 2340.
Local terrain elevations near the tracer release point are estimated to
be -4.7 m relative to the zero of the hill coordinate system; the net
release height corresponded to the 35.3 m height level on the hill. The
SFg release rate is computed to be 0.160 g/s with an estimated uncertainty
of _+1.5%. No Freon was released.
Plume Observations
During the experiment several people recorded their observations about
the appearance and trajectory of the oil-fog plume. Comments applicable to
this hour are presented below. Note that the comments actually begin during
the preceding hour. These are included because the plume material released
during the previous hour had an important impact during this hour.
192
-------
Figure 89. SF6 concentrations (ppt) estimated for Experiment 209, Hour"'l
by the Neutral (top) and Lift (bottom) models.
193
-------
Time: 2235(?) Plume is heading a little more toward the hill, but it
is hard to tell because the winds are so light that the fog is just
pooling near the source.
Time; 2252 NAWC2 is at a point one-quarter mile south of the 150 m
tower, and he is releasing a second thermofogger from 30 meters, and it
is going to the west.
Time: 2255 The plume is still pooling a lot around the release area.
A lot of fingers are extending in different directions. I still
haven't seen a finger coming past road F. In fact, none of them have
made it halfway to road F.
Time: 2304 There are several interesting things going on. One is that
the release from El is just smearing back and forth, very very wide—a
principal blob looks like it is headed toward the northeast knoll, and
at this time is just beginning to get close to road Fi It may even be
over me now. In fact, yes, it is. The auxiliary release which is a
quarter mile south of tower A (the release from the auxiliary crane) is
traveling to the west under easterly flow and is relatively coherent,
not showing the extreme meandering that we are seeing here. Winds at
second release holding steady to the west. Tethersonde reports winds
of about 2 m/s to the west.
Time; 2306 From road F, plume is about 1 hill width wide, and appears
to be drifting toward north butte.
Time; 2309 From ERT base, the fog pool looks like it extends
everywhere between the trailer and the hill. Second plume still
heading out to the west with some meander.
Time: 2315 Smoke odor is reported at the sampler trailer. The fog is
slowly traveling up the draw. Plume cloud looks like it is covering
everything.
Time; 2320(?) Winds are shifting more to the north now at the second
release. Fog from jet-fogger is cut down. No shift is seen at the
tracer crane.
Time; 2327 I have had the rotating beacon going for about three
minutes at about road F where radial 27 crosses road F.
Time: 2328 Butte is surrounded by smoke in all directions.
Time; 2329
continuing.
of the hill.
Smoke has stopped. The jet fogger is out of oil. SFg is
NAWC2 reports seeing plume smeared all over on all sides
194
-------
Time; 2330 I can smell the oil fog faintly on top of the hill. There
is oil fog everywhere, particularly smeared now to the north, but it
has also been visible on both sides of the hill according to other
reports. It looks to me like it is at least two hill widths to the
north, flying in very flat sheets although there is some definite
vertical depth to it of maybe 10 to 15 meters. I feel like it would be
terribly complicated in the analysis to cope with any kind of height
change or break in the plume because it is smearing so widely so we are
leaving the tracer up at 40 meters, and we are going to try to bring
the thermofogger over and put it up near it at 30 meters.
These comments indicate that the concentrations measured on the hill
from 2300 to 0000 may have been produced in part by plume material that had
been spread out very widely in the horizontal to the south of the hill and
then slowly advected toward the hill; for this hour, words like "blob" and
"cloud" better describe the tracer material than does the word "plume."
A secondary plume released to the north of the hill was observed to
travel toward the west during the same time period. It did not stagnate
near the release, nor did it take on the appearance of a blob or cloud.
Because the behavior of these two plumes is so different, it is unlikely
that the meteorological data measured at tower A (also to the north of the
hill) is representative of the meteorology at the primary release crane.
Photographs of the primary plume show its extraordinary behavior during
the first half hour. Figure 90 contains two representative photos of the
plume; the first was taken from the top of the north peak at camera position
0-15 (see Figure 46), and the second was taken from a position slightly
behind the release at camera position 0-19. Each individual photo is a
5-minute time exposure.
The wide sheet of oil fog can be seen approaching the hill from the
southeast during periods 2-5. This sheet apparently drifted past the hill
by the sixth period, and the primary plume bent around to the north of the
hill. The secondary plume cannot be seen in these photographs. No lidar
data for this hour have yet been reduced.
Meteorological Information
Wind and temperature data measured at tower A during this hour were
used to characterize the flow in terms of Hc. The average of the 5-minute
values over the hour is 58 m, and the average Frji above Hc is 1.2. The
Frj, value corresponding to this bulk hill Froude number is 0.20. These
values indicate that the flow during this hour was dominated by buoyancy
effects. Streamlines above Hc should have exhibited lee wave behavior.
Because the release height was 40 m, the plume was well below HC and might
be expected to have flowed around rather than over the hill.
Figure 84 contains a time series plot of the calculated 5-minute Hc
and Frji values for this experiment. Hc rose from 75 m to 80 m during
the first 15 minutes of the hour but then dropped rapidly during the next 10
195
-------
Figure 90. Two views of the plume trajectory between 2320 and 2325 MST taken
from the top of the north peak (position 15) and taken from
behind the release (position 19) during Experiment 209, Hour 7.
196
-------
minutes to about 40 m. It held at 40 m for the next 5 minutes and then
jumped to more than 55 m in the next 5 minutes. Hc remained between 50 m
and 55 m for the remaining 25 minutes of the hour. Frjj began the hour
near 2.0 but dropped rapidly to less than 1.0 by half-past the hour and held
near 1*0 for the remainder of the hour.
These large changes in Hc during the hour are interesting but may not
be directly relevant to the tracer plume behavior. The observation logs
indicate that a second oil-fog plume just north of the hill (approximately
halfway to tower A) experienced a flow field that was totally different from
that at the primary release site. At best, therefore, all we can learn from
tower A is that the dramatic changes in the wind field were accompanied by
similarly dramatic changes in the density structure.
The hourly averaged wind speed at 40 m on tower A was 2.5 m/s. During
the previous hour, however, the average speed was only 0.6 m/s. Because the
wind shift probably occurred at tower A before it occurred at the release
site, the winds at the release early in the hour may have been close to
0.6 m/s. The mean wind direction at 40 m on tower A was 105°; once again,
though, the wind direction during the previous hour was 045°, and this may
be more indicative of average wind directions over the first part of the
hour at the release point.
Figure 91 shows the trend in tower A wind speeds between 10 m and 80 m
during the hour. Speeds at all levels are less than 3 m/s, and those at
40 m are slightly greater than those at either 10 m or 80 m.. Variations in
wind directions measured at 10 m and 40 m are displayed in Figure 92 as
frequency distributions. It is not surprising that neither distribution
satisfactorily summarizes the wind direction behavior seen at the primary
release site. The 40 m distribution might be applicable to the release site
once the wind shift had taken place.
In summary, winds appeared to be extremely light and variable at the
release location during the hour, but the data from tower A indicate a
steadier flow. HC and Frn values during the hour indicate very stable
flow conditions. Because tower A data is undoubtedly not representative of
the flow at the release site early in the hour and because so much plume
material from the previous hour could have been advected back over the hill,
the measured concentration pattern may not be very useful for model
development.
SFg Concentrations
The distribution of hourly averaged SFg concentrations over the
surface of the hill is shown in Figure 93. The highest concentration
measured is on the north face of the north peak near the 30 m height
contour, the second highest is near the 75 m contour on the same hill face,
and the third highest is located on the saddle point above the northwest
draw. Most of the other nonzero concentrations were measured on the
northwest side of the hill at contour elevations greater than 20 m. This is
197
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UVW PROPS AT 40 m
9.9-
8.5-
8.8-
7.5-
7.8-
6.5-
6.9-
5.5-1
5.9-1
4.5-
4.8-
3.5-
—I 1 1 ,
28 49 69 89 188 128 148 169 188 898 288 248 268 888 389 328 348 369
DIRECTION
UVW PROPS AT 1O m
7.5-
7.e-
6.5-
6.0-
5.5-
5.8-
4.5"
t.e-
3.5 -
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2.5-
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1.5 -
1.0 -
.5-
—I 1 1 1 1 1 1 ! 1 1 " M™1 1 I ' ' "^ '
9 28 48 69 88 189 129 148 168 189 889 288 248 268 288 388 328 348 369
Figure 92. Calculated wind direction distribution functions for Experiment
209, Hour 7 C2300-0000 MST).
199
-------
8.'
Figure 93. Observed SF^ concentrations (ppt) for Experiment 209,
Hour 7 (2300-0000 MST). Source: r = 999.2 m, 6 = 100.9°,
net height = 35.3 m, Q = .160 g/s.
.200
-------
surprising because the source was located to the southeast of the hill and
most concentrations above 20 m on this side of the hill are zero. Perhaps
the SFg measured in the lee of the hill circled round to the south of the
hill and then shifted back across the southwest and west side of the hill
amidst the changing wind directions.
This possibility is certainly suggested by the 10-minute average SFg
concentration distributions presented in Figure 94. All concentrations on
the hill were recorded during the half hour between 2310 and 2340, and a
large concentration is seen on the south side of the hill in two out of the
three 10-minute periods.
4.10.2 Model Performance
This hour is very difficult to model properly. Observed concentrations
may have resulted from plume material released during the previous hour.
Also, the meteorological data from tower A is not representative of
conditions at the release point. Nonetheless, model calculations have been
done to see what kind of correspondence between modeled and observed
concentrations might be obtained. The Wrap and Impingement models were run
because the release was substantially below Hc.
All meteorological data were prepared as in Section 4.1.2, except that
no interpolation to source height was needed because the plume was released
from 40 m, an instrumented height on Tower A. The resulting values are
summarized in Table 13. Because of the large uncertainty in the winds at
release height, the average 40 m wind direction (105°) was used in the
modeling directly. Note, however, that tower B winds were from 160° and
188° at 10 m and 30 m, respectively. ,
Botii Impingement and Wrap were run with the revised meteorological
data; the results are listed in Table 13, and plotted on a map of CCB in
Figure 95.
Although the release height of 40 m was well below Hc (58 m), some of
the highest observed concentrations (ranging from 120 ppt to 185 ppt)
occurred near the top of the hill at 80 m. This pattern cannot be
reproduced by the models. The highest observed concentration of 196 ppt
does, however, occur close to the release height. This value should be
compared with the highest Wrap estimate of 174 ppt at 42 m. The estimates
from Impingement are generally much higher than the observations, probably a
result of the overestimation of the probability of the wind direction along
the stagnation streamline. In any case, the apparent agreement in peak
modeled (Wrap) and observed concentrations is probably accidental.
201
-------
Tine PERIOD 2309-aste
TIHE PERIOD 231«-232e
Figure 94. Observed 10-minute average SFg concentrations (ppt) for
Experiment 209, Hour 7 (2300-0000 MST).
202
-------
TIHE PERIOD 2328-2338
TIME PERIOD 233«-234«
Figure 94. Continued.
203
-------
TIME PERIOD 23H9-S3SO
TIRE PERIOD 235»-«88»
Figure 94. Continued.
204
-------
TABLE 13. IMPINGEMENT AND WRAP MODEL CALCULATIONS - EXPERIMENT 209,
CASE HOUR 7
ie\eorological Data
wind dipection(deg) = 105.
wind sp^ecCm/s) = 2.5
critical tividing
streailine heightdtO = 58.0
Iz = .046
Iy = .121
N(l/s) = .094
Source Data
airection(deg) = 101.
distance(m) =' 999.2
release heiciht Cm)= 40.0
SF6 emission
rateCa/s) = .160
Keceptor Coordinates Observed
X(mj Y(m) Z(m) SF6 Cppt)
360.2?
142.00
257.76
404.91
195.15
72.^9
66. >0
58. ,4
40.17
35.92
32.61
-53.6V
-45. 4o
-15.01
-19.8a
-84. Pa
396.6'
•315.76
•248.96
•204.16
•238.00
95.80
59.13
43.00
355.15
256.81
204.15
108.15
37.15
312.38
243.41
441.92
359.96
297.11
269.62
111.85
-40.85
141 .42
229. SI
-91.99
-65.85
109.07
-80.75
-32.85
-40.46
-25.71
.00
.00
33.94
111.59
149.74
126.43
505.92
445.44
305.14
272.83
247.73
-407.79
-345.28
-113.99
-149.12
-65.12
-106.29
-84.61
-66.71
-54.70
.00
-231.27
-154.04
-74.48
-205.04
-148.27
-117.12
-61.12
-21.12
-41.13
65.22
255.14
207.82
171.54
155.66
65.88
26.88
141.42
229.81
119.88
85.88
263.31
194.94
122.88
307.35
195.51
13.26
50.00
30.00
10.00
27.41
77.02
-6.52
3.38
22.10
31.92
41.74
3.82
13.70
98.96
90.00
90.00
3.44
13.24
32.90
52.26
50.00
52.96
80.00
80.00
5.69
25.29
30.00
50.00
70.00
14.00
50.00
-.90
8.94
28.07
38.07
80.00
80.00
50.00
30.00
64.94
80.00
30.00
50.00
80.00
30.00
65.00
.00
28.80
.00
.00
8.50
185.40
.00
.00
6.80
.00
.00
.00
4.90
.00
62.20
21.50
.00
31.50
62.30
38.20
28.00
61.60
146.40
62.20
71.60
.00
.00
.00
44.20
4.90
18.70
.00
.00
34.70
48.80
69.30
120.30
79.00
.00
.00
170.70
85.90
79.70
107.10
196.10
35.10
Impingement
Predicted
SF6 Cppt)
39.66
891.52
859.60
13.61
570.31
3.20
.21
5.05
2t>3.02
706.01
898.09
5.22
60.54
.00
.05
.15
9.69
69.49
574.67
41P.57
466.29
531.87
.92
.74
2.84
462.20
857.36
85K.89
12.27
33.73
455.70
3.59
32.52
420.55
647.11
4.49
4.27
505.60
505.60
91.31
3.52
549.10
549.10
2.63
581.55
64.57
Wrap
Predicted
SF6 (pet)
1.21
139.86
136.03
.44
83.57
.07
.00
.14
31.90
124.57
173.73
.1'4
4.14
.00
.00
.00
.39
5.79
104.90
67.89
80.65
77.47
.01
.01
.05
57.31
135.76
135.94
.36
1.39
78.9«
.10
2.07
69.10
124.73
.14
.13
86.76
86.76
8.17
.09
93.40
93.40
.06
98.25
6.90
205
-------
Figure 95. SFg concentrations (ppt) estimated for Experiment 209, Hour 7
by the Impingement (top) and Wrap (bottom) models.
206
-------
4.11 Experiment 210, Hour 3 (0200-0300 MST)
4.11.1 Summary Description
Thermofogger oil-fog, SF6, and Freon were released from the southeast
side of the hill at 1084.3 m, 113.7° for the entire hour. The oil-fog and
SFg were released at a height of 57 m, and the Freon was released at
30 m. Because all releases were continuous from the preceding hour, all
tracer sampling data should be representative of the full hour.
Local terrain elevations near the release point are estimated to be
-7.2 m relative to the zero of the hill coordinate system, so the net
release height of the SFg and oil-fog correspond to the 49.8 m height
level on the hill, and that for the Freon release corresponds to the 22.8 m
height level. The SFg release rate is computed to be 0.169 g/s with an
estimated uncertainty of j+6.3%. The Freon release rate is 0.926 g/s +2.0%.
No Freon concentration patterns have been modeled for this hour.
Plume Observations
Many observations about the plume appearance and trajectory were
recorded during this experiment. Comments relevant to this hour are
presented below.
Time; 0155 The plume looks like it is going around the south side at
about the level of tower D.
Time: 0200 From south peak: Seeing some material come right up..,.
Time: 0202 Smoke odor is reported at tower D; I can see the plume
coming into the vicinity of tower D, I believe it is on the south side
of D and then rising quite a bit. The plume centerline is going
directly towards the tower on the south peak. Presently the
nephelometer crane seems to be right in the center of the plume.
Time: 0204 The plume now looks like it is going up the draw, not
really touching the bottom of the draw, but going around the north side
of the south peak.
Time; 0206 Plume is heading toward FAA tower, then it takes a sharp
turn (^20°) and goes up the draw.
Time; 0208 The plume was going up the draw and then it swept right
past me. I'm on the north butte, and it is barely going around the
north side and up and over. I'm looking straight down the axis, and it
comes right over the north edge of the flat area by the FAA tower,. It
is climbing quite a bit and going over at about 3 meters above the
ground.
207
-------
Time: 0210 I'm standing on the northeast point of the north flat
area. The plume is going up and over me and I do not smell it, yet it
is close enough that I feel like I can touch it. ERT 1, on the south
butte, estimates that the centerline is maybe 9-10 m above the butte,
with vertical dimensions of about 6 m. It is very coherent.
Time: 0213 Centerline has dropped maybe 5 m as the plume swings a
little off to the north side—it is about even with the top of the
hill. Plume is coherent and very visible; it is still almost touching
the north side. After looking at another sweep, it's gone off the
north side and has sunk down to the hill height.
Time: 0214 The plume is coming a little bit back over the top of the
butte, about right over the very north extreme of the FAA flat area and
now it is going up and over again. I cannot smell it, yet I feel like
I can reach up and touch it. It is passing through the first white
section of the FAA tower, which I would estimate, puts it at about 8
meters.
Time; 0216 The plume is passing right through the FAA tower, coming
down as low as the top of the building at times.
Time: 0219 The plume now has moved just north of the FAA tower, and it
is passing I would guess, about 5 to 8, maybe 10 meters above the
ground. Now it is just streaming by here, yet, we cannot smell it.
Time: 0222 We're smelling the smoke now on top of the north butte.
Time: 0225 The plume is much more dispersed now horizontally and
vertically. It's now approaching the north butte and going around the
north side of the north butte. The top of the plume seems to be about
even with the top of the hill right now, so the plume centerline is
about 80 meters. There is quite a bit of plume meander evident between
the hill and the source. The plume is very close to the top of the
north peak, just barely off the north side, at time 0226.
Time; 0228 Ten meter winds at the ERT base are 130°, and are beginning
to trend more toward the southeast.
Time; 0231 We have just had about a 10° change in wind direction at
the. source. Wind direction is now more to the southeast. It looks
like about 130°, so we are missing the hill on the north side, and the
plume is no longer rising as it approaches the hill. The plume is also
more constricted now. There is a lot less horizontal and vertical
mixing noticeable.
Time; 0233 The plume, as it is traveling over the northeast knoll, is
not hitting the hill and is considerably more compact. As usual, we
are seeing that as it gets off that stagnation streamline its character
goes back to a more normal coherent compact plume.
208
-------
Time: 0234 The plume centerline is slightly north of the north hill.
You can see dramatic change in the centerline in about the point where
it approaches the hill and the centerline turns to the right. It
appears about 5° to 10° at that point.
Time; 0239 The plume is sweeping to the south now. Plume centerline
is almost directly towards the draw. The plume still has a significant
kink in it as it approaches the hill. It looks like the angle
difference between the plume from the release point and the plume as it
bends around the hill is at least 30°. The plume appears to be turning
as it approaches the FAA tower. ,
Time: 0240 The plume is coming directly over on the north peak, but we
cannot smell it. ERT 3 feels like if he were standing on top of my car
that he could smell it. Looking at the source, it looks like the plume
was swept back and is now aimed at the south shoulder.
Time: 0241 The plume is coming right at the draw and then dramatically
rising and going through the draw at about the level of the two peaks.
• As I am looking across, the plume is obscuring the lower half of the
100-foot tower from me. It is going over the saddle and really diving
on the back side. Occasionally a puff comes maybe 2, 3, maybe 4 meters
below the level of the peaks (eye level looking across the two buttes).
Time; 0243 It is still going through the draw at about the height of
the two peaks and just diving in the back. It looks like it may be
going just barely south of tower F and really at the level of tower F.
It really dives down, and we don't smell it on top of the hill. It
looks to me like the height of the nephelometer intake on the northeast
corner of the FAA fence is about 3 meters.
Time: 0250- The wind has picked up, and you can smell the plume now on
the north butte. It looks quite a bit wider..
Time: 0254 I can faintly smell the plume on the north butte. It
appears to be coming right at the FAA tower and going up and over.
These observations are quite extensive, providing a description of the
plume during each 5-minute period. In summary, the plume initially streamed
toward tower D or the southeast side of the hill during the first 5-minute
period. It then shifted across the hill to the north side and remained
either along the north shoulder of the hill, or over the north peak during
periods 2-6. The plume shifted more to the north away from the hill in sthe
seventh period, and remained there into period 8. Late in the eighth
period, the plume again swept back toward the center of the hill and rose
over the saddle between the peaks during period 9«. In the last 15 minutes,
the plume again flowed over the north peak.
209
-------
Smoke odor was noted at several times during the hour, yet was
noticeably absent at other times. Smoke odor was noted early when the plume
was streaming near tower D, and it was also noted on top of the hill late in
the hour after the wind speed increased. No smoke odor was noted at times
in between because the plume was deflected directly over the north peak.
Two representative photographs of the oil-fog plume are presented in
Figure 96. The first was taken from the top of the north peak at camera
position 0-15 (see Figure 46), and the second was taken to the side of the
plume at position 0-10. Each photo is a 5-minute time exposure.
The photos show the plume was near the southeast side of the hill
during period 1, and over the north peak during periods 2-5. It then
streamed around the north side of the hill during period 6, and shifted away
from the hill to the north during period 7. The plume swept back toward the
hill during period 8, and remained over the saddle or the south side of the
north peak for the remainder of the hour. This is in substantial agreement
with the recorded observer notes. The marked increase in plume dispersion
in periods 10-12 noted by observers can also be seen in the photo record.
This photographic series clearly shows that the plume is able to rise
over the hill at times, conforming to the hill shape but not mixing down to
the surface. This behavior is a typical case in which the plume is Compact
enough, and the Froude number high enough, that the plume surmounts the hill
with little impact.
Lidar data taken during this hour are extensive. The lidar sampled the
plume along seven planes: three upwind of the hill, three over the hill,
and one in the lee of the hill. Plume centroid positions derived from the
lidar data are plotted in Figure 97. This figure shows that the plume
preferentially traveled toward the north peak, either passing to the south,
north, or directly over the top. The only periods in which the plume took a
substantially different course are periods 1, 6, and 7. The plume passed to
the north of the hill during periods 6 and 7, and it was directed more
towards the southeast shoulder of the hill during the first period, as noted
in the previous discussions.
Of additional interest is the plume centroid height in the lee of the
hill. The lidar shows the centroid between 7 m and 33 m above the zero of
the coordinate system in the lee, although it began at roughly 50 m in the
sampling plane closest to the release point. Therefore, a marked streamline
depression existed in the lee of the hill.
Initial wind directions at source height were calculated from centroid
positions in the sampling planes closest to the release point. These vary
from 106° in period 1, to 117° in period 6. Directions between these
extremes vary from 108° to 114°. Because the source was located along the
113.7° ray, these wind directions should have taken the plume just left of
the hill center. However, many of the centroid positions over the hill lie
nearer the north peak. This shift may be due to uneven sampling in time at
locations near the source, so wind directions were probably more southerly
(say 118°-119°), taking the plume more toward the north peak.
210
-------
\
iOCAT.ON Q-/0
EXP6B1MENT2JO
Figure 96. Two views of the plume trajectory between 0215 and 0220 MST
taken from the top of the north peak (position 15) and taken
off to the side of the release (position 10) during Experiment
210, Hour 3.
211
-------
Its
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Meteorological Information
Wind and temperature data measured at tower A during this hour were
used to characterize the flow in terms of Hc. However, because of a
partial failure of the 40 m wind set, 40 m wind speeds were inferred for
each 5-minute period before calculating Hc. The method followed in
calculating speeds at 40 m was outlined in Section 4.4.1.
The average Hc over this hour is 26 m, and Frjj above this height is
2.1. Because the SFg plume was released at 57 m, its trajectory should
have been similar to that for weakly stratified flows. Fr^ above 26 m is
0.55, so a significant streamline depression in the lee of the hill is
expected. Lidar data in the lee of the hill indicate a substantial
depression.
Figure 98 contains a time series plot of the calculated 5-minute Hc
and FTJI values for this experiment. Hc dropped from 25 m to 20 m during
the first half hour, only to rise rapidly to 30 m until late in the hour,
when it again dropped to 20 m. Frjj rose from just under 2.0 to over 3.5.
These changes in Hc probably had only a minor effect on surface SFg
concentrations; however, the changes in Frg imply that the greatest
streamline depression in the lee would have occurred early in the hour.
Hourly averaged wind speeds measured at 80 m and estimated at 40 m on
tower A are 7.6 and 6.3 m/s, respectively. The 80 m wind direction, which
is assumed to be applicable at source height, is 122°. Figure 99 shows the
trend in wind speeds between 10 m and 80 m over the hour. The 10 m and 80 m
winds are nearly constant, but the winds inferred at 40 m drop significantly
in the eighth through eleventh 5-minute periods. This event coincides with
a plume shift toward the center of the hill from a trajectory around the
north side. If the wind at release height also dropped, then the hourly
averaged concentrations over the saddle and the north peak may have been
slightly greater than those calculated with the hourly average wind speed.
Variations in wind directions measured at 10 m and 80 m are shown in
Figure 100 as frequency distributions. The 80 m distribution is much
narrower than the 10 m distribution and is therefore indicative of the 57 m
plume trajectories seen in the photographs. Because the plume was high
above Hc (and high above the 10 m level, for that matter), the broad wind
distribution at 10 m probably had little effect on measured SFg
concentrations.
In summary, the plume was released well above Hc. Froude numbers
were low enough to suggest the presence of lee waves, which were noted by
the lidar.
213
-------
Hc(m)
FrH
»•_ ,4
7.« 8.8
!»•• (Hour)
* /~%^XA/V. A* M ?.,\
• A *' * '. ^i A J
Z '-f v' • V A *
vu*
a.e 3.0
-4.0 s.e e.« ?.e
Tin* (Hour)
Figure 98. Calculated dividing streamline heights (Hc) and bulk hill Froude
numbers above Hc (FrH) for Experiment 210.
214
-------
-. E
'-. o
•. 00
» «
§ 3
H
to
o
o
to
o
I
o
o
CN
o
to
f-t
o
•p
G
CO
CT>
-------
UVW PROPS AT 80m
8.S-
8.0-
7.5-
7.0
6.5-
s.o-
s.s-
s.o-
4.5-
4.0-
3.5-
3.0-
2.5-
2.0-
t.s-
i.e-
.s-
too iso MO 160 igo ago 220 340 eeo ego 300 320 340 3so
DIRECTION (dig)
UVW PROPS AT 10m
9.0-
a.s-
8.0-
7.5-
7.0-
,,H
5
4.0-j
3.5-
3.0-
2.5-
2.0-
l.S-
1.0-
.5
Figure 100.
0 20 40 60 89 100 120 140 160 180 200 220 240 360 280 300 320 340 360
DIRECTION (d«g>
Calculated wind direction distribution functions for Experiment
210, Hour 3 (0200-0300 MST).
216
-------
Concentrations
The distribution of hourly averaged SFg concentrations over the
surface of the hill is shown in Figure 101. All of'the large concentrations
measured lie at the base of the northwest draw in the lee of the hill. The
largest is located at the downwind edge of the sampling network. Other
sizeable concentrations are seen near the 80 m - 85 m height contour around
both peaks and across the saddle. Concentrations below 30 m on the upwind
side of the hill are very small.
This pattern is consistent with the observations and the photographs
discussed above. The concentrations in the lee may be very large because
the plume was depressed in the lee, and the moderate concentrations over the
top of the hill may have arisen during those periods late in the hour when
the plume appeared to undergo increased .dispersion.
The distribution of 10-minute average SFg concentration presented in
Figure 102 provides more information on the evolution of the pattern. The
concentrations near the top of the north and south peaks arose in the first
half hour, when the plume first traveled near the southeast side of the hill
and'then rested over the north peak. The sizable concentrations in .the
saddle area built up primarily during the last 10 minutes of the hour. This
was the period of time when observers noted an increase in the dispersion of
the plume.
4.11.2 Model Performance
This hour was modeled with the Lift model because all evidence
indicates that streamlines at plume height traveled over the hill.
Meteorology used in the modeling was prepared as in Section 4.1.2 and is
summarized in Table 14.
The 1-hour wind directions measured 47 m below and 23 m above the
release height are 113° and 122°, respectively. Directions at 10 m and 30 m
on tower B are 119° and 124°, respectively. But the direction inferred from
the lidar and photographic data indicate a wind direction of 118°-119°.
Therefore, the model wind direction is set to 118°. The 80 m PDF is also
used in the modeling.
Neutral was rerun with the new meteorological data. Instead of
estimating a peak value 31% of the peak observed concentration, it produced
a peak 8% of the peak observed. Figure 103 shows the distribution of
calculated concentrations plotted on a map of CCB, and the results are also
summarized in Table 14.
Results of the Lift computations are also displayed in Figure 103 and
in Table 14. Once again, the computations produce extremely low
concentrations: the peak modeled is only 4% of the peak observed.
217
-------
? r"= 500 m~
207.'
?
N
Figure 101. Observed SFg concentrations (ppt) for Experiment 210,
Hour 3 (0200-0300 MST). Source: r = 1084.3 m, 6 = 113.7°,
net height = 49.8 m, Q = .169 g/s.
218
-------
TINE PERIOD 3210-025D
Figure 102. Observed 10-minute average SFg concentrations (ppt) for
Experiment 210, Hour 3 (0200-0300 MST).
219
-------
TINE PERIOD 42a«-»23»
TIME PERIOD 823»-«2<«
Figure 102. Continued.
220
-------
TH1E PERIOD 02<0-e250
Tint PERIOD easo-oaae
Figure 102. Continued.
221
-------
TABLE 14. NEUTRAL AND LIFT MODEL CALCULATIONS - EXPERIMENT 210, CASE HOUR 3
Meteoroloqieel Data
wind direction(dep) = 118.
wind speedCm/s) = 6.3
critical dividing
streamline height(m) = 26.0
Iz = .018
ly = .105
NCl/s) = .044
Source Data
direction(deg) =
oistance(m) = 1064.3
release heipht(m)= 57.0
SF6 emission
rate(g/s) = .169
Receptor Coordinates
X(m) Y(m)
Observed
SF6 (ppt)
208.35
257.78
404.91
195.15
159.04
72.99
66.60
51.04
35.92
32.61
29.59 .
15.97
2.15
-66.52
-45.46
-15.01
-19.85
-9.85
-4.85
-84.85
'396.68
315.76
248.96
-60.85
31.69
441.46
355.15
313.62
142.15
108.15
82.15
37.15
157.38
243.41 •
441.92
359.96
297.11
269.62
246.20
•111.85
-40.85
•141.42
•229.81
109.07
-40.46
.00
33.94
111.59
149.74
122.04
126.43
505.92
387.66
272.83
247.73
224.79
121.29
18.88
-505.24
-345.28
-113.99
-149.12
-76.12
-37.12
-65.12
-106.29
-84.61
-66.71
-16.12
-258.06
-254.87
-205.04
-181.07
-81.12
-61.12
-46.12
-21.12
20.72
65.22
255.14
207.82
171.54
155.66
142.14
65.88
2S.88
141.42
229.81
263.31
307.35
31.25
30.00
10.00
27.41
46.91
77.02
-6.52
11.78
31.92
41.74
51.51
90.94
80.00
-3.54
13.70
98.96
90.00
90.00
80.00
90.00
3.44
13.24
32.90
80.00
50.00
-2.45
5.69
15.29
40.00
50.00
60.00
70.00
83. 35
50.00
-.90
8.94
28.07
38.07
47.96
80.00
80.00
50.00
30.00
30.00
30.00
20.80
.00
5.20
.20
20.86
61.20
.00
5.20
15.50
.00
26.98
125.00
71.70
.00
21 .90
36.20
82.30
58.60
76.10
68. 60
112.70
117.40
80.40
84.90
37.90
18.30
.00
.00
47.30
5.20
50.44
36.60
111.00
5.70
297.00
243.90
212.30
195.80
152.30
61.50
13.80
191.60
.10
83.00
17.10
Neutral
Predi cted
SF6 (ppt)
.06
.02
.00
.02
2.06
21.16
.00
.00
.16
1.26
6.84
24.15
JB.68
.00
.00
8.44
5.55
10.70
13.62
11.70
.00
.00
.14
15.62
.05
.00
.00
.00
.35
3.35
12.43
14.90
19.30
8.88
.01
.04
.70
2.92
10.62
23.80
19.94
12.75
.94
.50
.23
Lift
Predicted
SF6 (ppt)
.44
.16
.01
.26
.44
2.12
.14
.43
.55
1.07
1.14
2.19
1.65
.00
.00
.38
.19
.56
1.12
.65
.00
.49 i
.98
1.56
.00
.00
.01
.02
.39
.54
.68
.96
2.51
3.60
11.28
7.79
6.43
5.87
5.40
2.68
1.83
4.89
6.43
5.26
1.19
222 .
-------
Figure 103. SFg concentrations (ppt) estimated for Experiment 210, Hour 3
by the Neutral (top) and Lift (bottom) models.
223
-------
In both cases, the modeled concentrations are low everywhere across the
hill. The observed concentrations are greater over much of the hill but
become particularly greater at the base of the hill on the leeward side.
Computed To values for these observed concentrations are about 0.6 in the
southeast draw, 0.58 to 0.63 in the saddle area, 0.58 on the north peak,
0.50 on the south peak, and 0.48 to 0.50 near the base of the hill on the
lee side.
These values suggest that the az should be larger in order to '
reproduce the observed concentrations. As noted in the discussions above,
the dispersion was seen to increase substantially late in the hour. This is
already shown in the lidar data. The measured az in a plane near the
upwind base of the hill varied between 3.5 and 6.0 m for most of the hour.
But during the last 10 minutes, 0Z increased to 11.0 m at 0252 and to
nearly 15 m at 0256. Therefore, the key to modeling this hour successfully
may be a careful treatment of the last 10 to 20 minutes.
4.12 Experiment 210, Hour 7 (0600-0700 MST)
4.12.1 Summary Description
Thermofogger oil-fog, SFg, and Freon were released from the southeast
side of the hill at 1086.2 m, 122.2° for the entire hour. The oil-fog and
SF6 were released at a height of 58 m, and the Freon was released at
30 m. All releases were continuous from the preceding hour, so all tracer
sampling data should be representative of the full hour.
Local terrain elevations near the release point are estimated to be
-8.2 m relative to the zero of the hill coordinate system, so the net
release height of the SFg and the oil-fog corresponds to the 49.8 height
level on the hill, and that for the Freon release corresponds to the 21.8 m
height level. The SF6 release rate is computed to be 0.178 g/s with an
estimated uncertainty of ^7.4%. The Freon release rate is 0.986 g/s +3.3%.
No Freon concentration patterns have been modeled for this hour.
Plume Observations
Few observer comments and observations about the plume appearance and
trajectory x*ere recorded during this hour. The relevant ones are presented
below.
Time; 0557 I am a third of a mile west of road A doing a north-south
transect with my nose, and I can faintly smell the plume. I would
estimate that it is about half of a hill width wide—that's very
approximate.
Time: 0559 Looking back at the release, it is coming over the butte
just south of tower B and then turning slightly north and then getting
considerably wider as it comes out into the flats again.
224
-------
Time: 0619 It's difficult to see, but it looks to me like the flow in
the lee is no longer as attached as it was earlier, and it is not
coming down as low. The dawn is just breaking so we will be able to
see it better in about 15 minutes. The array I am asking them to
analyze for Freon is again very extensive because we expect the lower
level release to be meandering really all over the place. This
analysis should be very interesting because the upper plume was very,
very steady.
Time; 0702 The thermofogger is down being refueled and will go back up
shortly. I have asked them to co-locate the Freon and SFg at the
same level as the thermofogger, and we will be able to test how the
system is working. The ERT crew is releasing flares all over the south
shoulder of the hill, and most of them are going up the hill—the ones
on the south face are going up the hill, the ones on the draw side of
the shoulder are going across the hill, and the ones down low are going
around the hill.
Although the notes are sketchy, they indicate that the plume was fairly
steady during the first half hour, and that a strong depression in the lee
of the hill at the start of the hour weakened over the same time period.
More information on plume behavior upwind of the hill is contained in the
photographs. Each photo is a 5-minute time exposure, except for one which
covers a 10-minute period.
The available photos only cover S^minute periods 1-7, but show that the
oil-fog plume was fairly steady at least during the first half hour. It ;
remained near the south peak, starting off the hour along the south shoulder
of the peak, and ending over the saddle in period 7. As the plume sails
over the south peak in periods 1-5, clear air can be seen beneath the bottom
edge of the visible plume. SFg concentrations should therefore be small •
in this area. It is much harder to see if the oil-fog cleared the saddle by
a similar amount, but it appears that the plume did rise high enough over
the saddle to produce only small concentrations there too.
Two representative photos of the plume are reproduced in Figure 104.
The first was taken from the top of the south peak at camera location 0-8
(see Figure 46), and the second was taken from behind the plume at ,
location 0-19. :
No photos are available to show what happened to the plume later in the
hour, and no lidar data are yef available to provide this information.
Meteorological Information
Wind and temperature data from tower A were used to characterize the
flow during the hour in terms of Hc. However, because of a partial
failure of the 40 m wind set, 40 m wind speeds were estimated for each
5-minute period before calculating Hc. The method followed in calculating
the 40 m speeds was outlined in Section 4.4.1.
225
-------
iflllfl
Figure 104. Two views of the plume trajectory between 0615 and 0620 (top),
and between 0610 and 0620 MST (bottom) taken from the top of
the south peak (position 8) and taken from behind the release
(position 19) during Experiment 210, Hour 7.
226
-------
The average Hc during this hour is 14 m, and the average FrH is
2.6. Because the SFg plume was released at 58 m, its trajectory should
have been similar to that for weakly stratified flows. Fr^ above the Hc
is 0.63, so some streamline depression in the lee of the hill may be
expected.
Figure 98 contains a time series plot of the calculated 5-minute Hc
and Frji values for this experiment. The Hc pattern exhibits a spike
over the first half hour with a peak value of over 35 m. During the rest of
the hour HC is about 10 m. A much smaller spike is seen in the Frjj
trace. Its peak is centered on the fourth 5-minute period; this coincides
with the observation that the depression of the plume in the lee of the hill
was not as strong as it had been earlier. The peak Frjj value corresponds
to a FrL of 0.80. A weakening of the depression in the lee is consistent
with a change toward greater Frj^ values.
Hourly averaged wind speeds measured at 80 m and estimated for 40 m on
tower A are 9.0 and 7.3 m/s, respectively. The 80 m wind direction, which
is assumed to be applicable to the source height, was 130°. Figure 105
shows the trend in wind speeds between 10 m and 80 m over the hour. A
dramatic decrease in the 40 m speeds occurred during the fourth 5-minute
period, and may be responsible for the changes in the flow parameters (Hc,
Frjj, Fri) discussed above.
Variations in wind directions measured at 10 and 80 m are shown in
Figure 106 as frequency distributions. Each distribution has a mean of
130°, but the 10 m distribution is considerably broader. The 80 m
distribution, undoubtedly more appropriate for the SF6 release height,
illustrates the steadiness observed in the plume trajectory over the hour.
In summary, the SF6 plume was released well above HC. Although
wind directions were very steady at release height, wind speed changes
produced a short period of flow alteration. The hourly SFg concentrations
should be representative of a high release into a weakly stratified flow
(FrH > 1).
SFft Concentrations
The distribution of hourly averaged SFg concentrations over the
surface of the hill is shown in Figure 107. The highest concentration is
found near the 80 m contour on the lee side of the south peak. Other high
concentrations are found toward the base of the hill in the lee. Only zero
concentrations are measured on the windward slope of the hill below 65 m.
In fact, all but one sampler measured zero concentration in the southeast
draw up toward the saddle. This pattern is consistent with weakly
stratified flow over the hill.
The distribution of 10-minute SFg concentrations is presented in
Figure 108. These plots also show the lack of any significant impact on the
windward side of the hill. They illustrate the steadiness of the plume late
in the hour when both photographic and lidar data are missing.
227
-------
1 e E
: O • O
: co
E
: O
a
..« a
.-6
3<0
_r_1 J_
00 U)
A «
s i
c
^ i
in 5
in
PI
in
o>
o>
O
O
O
I
O
O
f-l
O
O
CM
(D
0)
w
bO
.s
TJ
-------
UVW PROPS AT 80m
29 48 68
149 169 180 288 228 248 268 288 399 328 349 3G8
DIRECTION (dog)
UVW PROPS AT 10m
199 128 149 168 188 289 228 249 268 2B9 398 329 348 369
DIRECTION Idoj)
Figure 106. Calculated wind direction distribution functions for Experiment
210, Hour 7 (0600-0700 MST).
229
-------
Figure 107. Observed SFg concentrations (ppt) for Experiment 210,
Hour 7 (0600-0700 MST). Source: r = 1086.2 m, 6 = 122.2°,
net height = 49.8 m, Q = .178 g/s.
230
-------
TIME PERIOD «Eee-esi*
TIME PERIOD SEK-OESO
Figure 108. Observed 10-minute average SFg concentrations (ppt) for
Experiment 210, Hour 7 (0600-0700 MST).
231
-------
TIKE PERIOD «E2>-«63«
TIDE PERIOD «63«-»6«
Figure 108. Continued.
232 -
-------
Tine PERIOD e6se-«?ee
Figure 108. Continued.
233
-------
4.12.2 Model Performance
This hour has been modeled with the Lift model because all evidence
indicates that streamlines at plume height traveled freely over the hill.
Meteorology used in the modeling was prepared as in Section 4.1.2, and the
data is summarized in Table 15. The 1-hour average wind directions measured
48 m below and 22 m above the release height are both 130°, although the
peak of the PDF for each of these heights is considerably different. Wind
directions measured at 10 m and 30 m on tower B are 118° and 123°,
respectively, and directions inferred from the photographs during the first
half hour lie between 117° and 120°. Therefore, considerable weight is
given the data from 10 m on tower B, and the model wind direction is set to
118°. The 80 m PDF is deemed more appropriate than that from 10 m.
Neutral was rerun with the new meteorological data, and instead of
estimating a peak value that is 92% of the observed peak value, it produced
a value 112% of the peak observed. The peak observed value occurs in the
lee of the south peak, and the modeled maximum occurs near the top of the
windward face of the south peak. Figure 109 shows the distribution of
calculated concentrations plotted on a map of CCB, and the results are also
summarized in Table 15.
Results from Lift computations are also displayed in Figure 109 and in
Table 15. The maximum occurs near the top of the hill and is 89% of the
highest observed value. The model overestimates most of the observed
concentrations, particularly on the windward side of the hill, over the
south peak, and on the saddle. Concentrations in the lee are overestimated
to a lesser degree. The degree of overestimation on the south peak produces
a terrain factor (T0) of 1.5 to 1.7, and that near the base of the hill in
the lee produces To values between 1.0 and 1.4.
4.13 Experiment 211, Hour 1 (0000-0100 MST)
4.13.1 Summary Description
Thermofogger oil-fog, SF^ , and Freon were released from the
east-southeast side of the hill at 1001.2 m, 101.4°. The SF6 release
began at 2350 and continued throughout the hour from a height of 30 m. The
oil fogger started a half hour earlier at the same height, but stopped at
0055. The Freon release did not begin until 0045, released from a height of
20 m. The Freon samples are certainly not representative of a 1-hour
average.
Local terrain elevations near the release point are estimated to be
-4.7 m relative to the zero of the hill coordinate system, so the net
release height of the SFg and the oil-fog corresponds to the 25.3 m height
level on the hill, and that for Freon corresponds to the 15.3 m height
level. The SFg release rate is computed to be 0.179 g/s with an estimated
uncertainty of +5.1%. The Freon rate cannot be computed from the field log,
but is estimated to be about 1.0 g/s. No Freon concentration patterns have
been modeled for this hour.
/
234
-------
TABLE 15. NEUTRAL AND LIFT MODEL CALCULATIONS - EXPERIMENT 210, CASE HOUR 7
Neteorological Data
wind direction(deg) = 118.
wind speed(m/s) = 7.3
critical dividing
streamline heiqht(m) = 14.0
Iz = .057
ly = .108
NU/s) = .035
Source Data
direction(deg) = 122.
distance(m) = 1086.2
release heipht(m)= 58.0
SF6 emission
rate(s/s) = .178
Receptor Coordinates Observed
X(m) Y(m) Z(m) SF6 (ppt)
360.22
208.35
142.00
257.78
195.15
72.99
66.60
58.64
40.17
32.61
20.07
10.61
2.15
-66.52
-53.69
-45.46
-32.79
-19.85
-9.85
-4.85
'125.24
-84.65
396.68
315.76
248.96
-60.85
21.74
137.89
441 .46
108.15
82.15
37.15
312.38
157.38
359.96
297.11
269.62
246.20
111.85
-40.85
141.42
229.81
-80.75
.00
.00
.00
33.94
149.74
126.43
505.92
445.44
305.14
247.73
152.45
80.56
18.88
-505.24
-407.79
-345.28
-249.09
-149.12
-76.12
-37.12
-96.10
-65.12
-106.29
-84.61
-66.71
-16.12
-137.29
-137.89
-254.87
-61.12
-46.12
-21.12
-41.13
20.72
207.82
171.54
155.66
142.14
65.88
28.88
141.42
229.81
194.94
13.26
31.25
50.00
30.00
27.41
77.02
-6.52
3.38
22.10
41.74
81.06
91.97
80.00
-3.54
3.82
13.70
48.82
90.00
90.00
80.00
78.81 •
90.00
3.44
13.24
32.90
80.00
90.00
50.00
-2.45
50.00
60.00
70.00
14.00
83.35
8.94
28.07
38.07
47.96
60.00
80.00
50.00
30.00
50.00
.00
.00
.00
.00
.00
.00
.00
60.40
.00
68.40
.07
6.90
.20
.00
.00
.00
.00
31.80
16.40
.20
211.68
68.80
.00
.00
24.80
14.20
21.70
.00
11.50
.00
.04
.00
.20
26.30
109.00
70.90
59.30
50.50
.20
.20
.20
.10
.20
Neutral
Predicted
SF6 (ppt)
1.47
34.42
64.07
9.10
2.fc6
58.11
.02
.09
2.12
7.68
67.70
119.57
158.26
.02
1.10
7.50
75.49
229.15
214.38
197.31
197.53
204.65
34.85
61.80
107.56
190.52
238.27
23B.30
51.90
173.71
186.00
178.39
11.38
176.69
73.89
97.12
110.48
124.06
162.1ft
99.90
61.87
48.04
Lift
Predicted
SF6 (ppt)
.00
.00
13.64
.00
.00
.00
.00
.00
.00
.00
.00
33.54
113.75
.00
.00
.00
.00
173.60
182.86
164.50
166.94
127.23
.00
102.17
158.22
161.20
147.93
187.70
87.20
117.62
153.09
151.20
.00
171.08
123.64
128.2ft
130.34
132.10
141.95
146.63
102.66
39.75
5.72
235
-------
Figure 109. SF6 concentrations (ppt) estimated for Experiment 210, Hour 7
by the Neutral (top) and Lift (bottom) models.
236
-------
Plume Observations
The record of observer comments about the plume appearance and
trajectory during this hour is presented below.
Time: 2350 SF£ release started from E-l at 30 m. Plume now appears
to be heading over the east knoll.
Time: 2355 The fogger is up and I believe the tracer has started. The
plume seems to be running south of the hill at this time. There is a
great deal of mixing and vertical loops in the plume.
Time: 0000 I see a good deal of vertical mixing in plume.
Time: 0004 At the present time the plume is heading to the north of
the butte, and it looks very stable. Approximately 5 minutes ago, the
winds were light and variable. The plume did a complete 360 in its
trajectory.
Time: 0005 Plume looks more stable now.
Time: 0006 The plume, after smearing and even doing 360 is headed
around the north side of the hill and the first 1/3 of travel, on the
plume, looks much more stable than the 2/3 that has gone out.
Time: 0011 The plume seems to be settled in and going around the north
side right over the northeast knoll, and it is looking very stable at
this time. The spotlight is going on the extension of the mobile crane
road.
Time: 0015 Plume is back over the east knoll. The plume seems to have
bend in it, and to my perspective it looks like it goes out
horizontally and then begins to turn around the hill fairly early,
considerably before it reaches road F. ERT 1 is describing the plume
as a "pencil beam" at the moment. It is very compact. ERT 1 is also
describing it as having a very dense central core.
Time: 0020 The plume is getting closer to the north side. ERT 1 is
referring to it as a piece of yarn.
Time: 0022 The plume centerline is continuing to move towards the
south and the plume centerline now appears to be directly towards the
FAA tower. The horizontal dispersion has increased significantly as it
is moving in that direction.
Time: 0025 The plume centerline now would take the plume significantly
south of the hill and the horizontal dispersion still seems to be quite
significant. The plume is south of the butte now.
237
-------
Time: 0028 (?) The plume has definitely shifted toward the hill and is
now looking considerably wider, and wispy, and with a lot of horizontal
spreading. Looking north-northeast, it looks like the plume has been
coming very close to the hill at that point.
Time: 0030 The plume has swung so it is headed more toward tower D. I
can see some plume going in the vicinity of the draw and possibly up
the draw. The plume is looking quite a bit wider and more difuse, a
very radical change from what it was 10 or 12 minutes ago.
Time; 0035 Plume is headed toward the draw.
Time; 0038 The plume has moved back to the north side and is going
around the north and the plume near the source is going back to that
very stable coherent pencil beam look.
Time; 0040 The plume is going entirely north of the hill. It is very
collimated and narrow and stable looking.
Time; 0051 The plume is going to the south, and the thermofogger is
being brought down this time to check on some problems. The gas keeps
on going now, since we've got those ropes holding up the tubes.
Time; 01Q7 The thermofogger is back up. The low level was going to
tiie south, and the higher level flow looks like its going to the SW,
and it should miss the butte. The wind is kind of rocking the car, I'm
sitting here near tower B.
These comments indicate that the oil-fog plume trajectory varied over
the hour from one side of the hill to the other. After initial wandering,
the plume took on a stable appearance as it traveled around the hill on the
north side, and it remained on the north side for most of the first half
hour. By the fifth 5-minute period, however, it moved in close to the north
peak and then shifted to the south side of the hill. As it crossed the
hill, the horizontal spread increased significantly.
During period 7 the plume moved back between the two peaks, but within
the next 5-minute period, it had swung over to the north side once again.
It stayed to the north side until the last 10-15 minutes in the hour, when
it again switched to the south. This sequence is documented in the
photographs.
Only one view of the plume was suitable for analysis during this hour.
It was taken from the top of the north peak at camera location 0-15 (see
Figure 46). The camera was aimed toward magnetic bearings 105°, 90°, and
100° over the course of the hour. Each photo is a 5—minute exposure.
Some lidar data are also available for this hour. The lidar sampled
the plume along five planes: two upwind of the hill and three over the
hill. Plume centroid positions in these planes are presented in
Figure 110. Most of the plume segment sampled followed trajectories toward
238
-------
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239
-------
the north side of the hill. These occurred during periods 1-5, 8, and 9.
Periods 6 and 7 show the most tendency for plume travel toward the southern
part of the hill, and this is consistent with the photographs.
Inferred wind direction estimates for the release height have been
calculated based on the centroid positions closest to the source. They
range from 73° to 118°. Because the source was located along the 101° ray,
this range indicates that the wind trajectory carried the plume material
well to the north and south of the hill at times.
Meteorological Information
Wind and temperature data measured at tower A during the hour have been
used to characterize the flow in terms of Hc. However, because of a
partial failure of the 40 m wind set, 40 m winds were estimated for each
5-minute period before Hc was calculated. The method followed in
calculating speeds at 40 m was outlined in Section 4.4.1.
The average Hc over the hour is 45 m, and Frjj above this height is
2.9. Because the SFg plume was released at 30 m, it was well below the
computed dividing streamline of the flow. Figure 111 contains a time series
plot of the calculated 5-minute values of Hc and Fry. Hc shows a weak
tendency to increase during the hour, but the trend is small compared to the
scatter about it. HC tends to vary by 5 m about its mean value. Frjj
for the flow above Hc follows a stronger trend toward increasing values,
but this is of little consequence because the tracer was released below
Hc. Small variations in Hc illustrated in the plot are likely to have
had only a small effect on surface concentrations, so the mean value should
adequately characterize the hour.
Hourly averaged wind speeds measured at 10 m and estimated at 40 m on
tower A are 2.2 and 1.8 m/s, respectively. The decrease from 10 m to 40 m
may not be significant, however, because of the uncertainty inherent in
estimating the 40 m wind speeds. The direction at 10 m was 353° and that at
80 m (which was used to estimate the 40 m winds) was 128°. With this kind
of wind shear and light 2 m/s wind speeds, an estimation of the wind
directions characteristic of the release height is subject to considerable
error.
Figure 112 shows the trend in wind speeds between 10 and 80 m. The
estimated 40 m wind speeds tend to follow the 80 m speeds, while the trend
in the 10 m speeds remains distinctly different throughout the hour. It
therefore seems likely that the low-level flow exerts only a small influence
on the flow at 40 m, but it is not clear if the same can be said for its
influence on the flow at 30 m.
Variations in wind directions measured at 10 m and 80 m are shown in
Figure 113 as frequency distributions. Because the 80 m distribution spans
20° rather than 100°, it is considered more representative of the flow at
release height. Two peaks can be seen in the distribution; this
corroborates the photographic record, which shows the plume lying primarily
on one side of the hill or the other.
240
-------
Hc(m)
f+.
'*•: " *
.8 1.0
1
4.0
s.e e.e
—I—
7.6
Tin (Hour)
'NA'AW^X
—I '—I 1
5.8 6.8 7.8 8.8
TIM (Hour)
Figure 111. Calculated dividing streamline heights (Hc) and bulk hill Froude
numbers above Hc (Frpj) for Experiment 211.
241
-------
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242
-------
UVW PROPS AT 80 m
s.e-
'8.5-
s.e-
7.5-
7.8-
6.5-
6.8-
5.5-
s.e-
4.5-
4.8-
3.5-
3.8-
2.5-
a.e-
1.5 -
i.e-
.5-
6e se iaa ise no tee IBO see s:« 949
UVW PROPS AT 10m
see 328 3
-------
In summary, during this hour the plume was released into the flow
substantially below Hc. Wind speeds were less than or nearly equal to
2 m/s, and variable; and are therefore difficult to characterize at the
release height. The 80 m wind direction distribution, however, appears to
be similar to what can be observed in the photographs.
Concentrations
The distribution of hourly averaged SFg concentrations over the
surface of the hill is shown in Figure 114. Highest concentrations are
measured across the lower portion of the southeast draw from the 0 m contour
to the 30—35 m contour. Moderately high concentrations cover the rest of
the hill.
This pattern suggests that, with a relative release height of 25 m, the
plume impinged on the hill surface near the draw consistently during the
hour, and mixed enough in the vertical to produce a concentration maximum
below the height of the plume centerline. However, the record of
observations and the photographs indicate otherwise. The SF^ pattern does
not match what would be expected from the appearance and trajectory of the
oil-fog plume over the hour.
The distribution of 10-minute average SFg concentrations presented in
Figure 115, however, indicates that tracer material reached the hill several
times during the hour even though this was not apparent from the
photographs. Substantial concentrations are measured near the 60 m height
contour in the southeast draw in four of the six 10-minute periods.
4.13.2 Model Performance
This hour has been modeled with the Wrap model because the plume was
released significantly below the calculated dividing streamline height.
Meteorological data were prepared for the release height as in
Section 4.1.2, and the resulting values are listed in Table 16. Wind
directions measured at tower A and tower B .are not very helpful in selecting
an appropriate wind direction for use in the modeling. The 10 m directions
average to 353° and the 80 m directions average to 128° on tower A, whereas
the directions at 10 m and 30 m on tower B average to 117° and 124°,
respectively. The lidar data indicate • that the mean direction should lie
between 73° and 118°, and the photographs show the plume frequently on both
sides of the hill. Therefore, the mean wind direction has been set equal to
the direction from the source to the north peak (or 107°) because the plume
appears to spend more time on the north side of the hill than on the south
side. The 80 m PDF is also used because the 10 m PDF seems to be
inappropriate.
Concentration estimates from both Impingement and Wrap are listed in
Table 16 and plotted on a map of CCB in Figure 116. Although the observed
SFg concentration distribution pattern was thought odd when compared with
the photographs of the plume, the Wrap estimates are, in general,
244
-------
Figure 114. Observed SFf, concentrations (ppt) for Experiment 211,
Hour 1 ,(0000-0100 MST). Source:' r = 1001.2 m, 6 = 101.4°,
net height = 25.3 m, Q = .179 g/s.
245
-------
TIHC PERIOD 888
TIRE PERIOD 9«10-082»
Figure 115. Observed 10-minute average SF6 concentrations (ppt) for
Experiment 211, Hour 1 (0000-0100 MST).
246
-------
TIKE PERIOD 9820-0930
Figure 115. Continued.
247
-------
TIKE PERIOD ee<»-»ose
TIKE PERIOD «05«-91«a
Figure 115. Continued.
248
-------
TABLE 16. IMPINGEMENT AND WRAP MODEL CLACULATIONS - EXPERIMENT 211,
CASE HOUR 1
N'eteorol oqical Data
wind direction(deq) = 107.
wind speed(m/s) = t.9
critical dividinp
streamline height(m) = 45.0
Iz = .084
ly = .326
NCl/s) = .058
Source Data
direction(deg) = 101.
distance(m) = 1001.2
release heiqht(m)= 30.0
SF6 emission
rate(q/s) = .179
Receptor Coordinates Observed
X(m) Y(m) Zfm) SF6 (ppt)
360.22
208.35
257.78
404.91
72.99
S8.64
40.17
35.92
20.07
25.15
-53.69
-38.04
-32.79
-15.01
-19.85
125.24
-84.85
396.68
248.96
204.16
-60.85
31.69
95.80
199.06
137.89
441.46
355.15
313.62
256.81
82.15
37.15
183.53
312. 3«
•243.41
•4^1 .05
•297.1 1
•269.62
•246.20
•153.85
•111.85
•141 .42
•229.81
-80.75
.00
.00
33.94
111.59
126.43
445.44
305.14
272.83
152.45
190.88
-407.79
-288.98
-249.09
-113.99
-149.12
-96.10
-65.12
-106.29
-66.71
-54.70
-16.12
-258.06
• -231.27
-259.43
-137.89
-254.87
-205.04
-181 .07
-148.27
-46.12
-21.12
-49.18
-41.13
65.22
255.14
171.54
155.66
142.14
89. 88
65.68
141.42
229.81
194.94
13.26
31.25
30.00
10.00
77.02
3.38
22.10
31.92
81.06
65.00
3.82
32.94
48.82
98.96
90.00
78.81
90.00
3.44
32.90
52.26
80.00
50.00
52.96
30.00
50.00
-2.45
5.69
15.29
25.29
60.00
70.00
30.00
14.00
50.00
-.90
28.07
38.07
47.96
70.00
80.00
50.00
30.00
50.00
229.50
241.20
119.90
194.70
141.60
20.10
116.90
162.40
91.66
134.60
82.10
61.50
64.85
78.80
78.40
65.05
82.50
25.90
53.90
57.20
97.80
78.60
88.10
158.80
202.50
320.20
296.30
260.60
243.60
182.87
170.20
247.60
240.50
17.80
33.60
80.90
90.00
88.20
66.12
120.00
129.10
.00
125.00
Impingement
Predicted
SF6 (ppt)
343.70
502.79
472.17
268.00
34.39
144.95
262.45
276.98
25.35
90.21
152.15
288.98
208.29
3.21
9.61
33.58
12.67
119.64
200.77
139.82
31.57
213.42
200.61
395.47
258.43
119.19
218.21
356.51
459.80
145.77
58.12
540.76
373.98
137.79
97.46
19/1.15
185.69
154.12
61.10
31.80
154.37
209.23
169.06
Wrap
Predicted
SF6 (pot)
471.25
807.87
758.40
350.15
22.74
179.14
408.76
440.54
15.68
92.68
188.04
459.05
291.09
.88
4.03
25.73
6.69
155.64
317.75
192.95
24.80
290.42
255.36
633.19
340.23
108.24
254.46
509.30
729.74
143.49
39.15
870.89
516.29
196.77
1 19.00
307.57
289.26
223.77
62.51
25.42
218.27
332.06
236.88
249
-------
Figure 116. SF6 concentrations (ppt) estimated for Experiment 211, Hour 1
by the Impingement (top) and Wrap (bottom) models.
250
-------
supportive. Thte highest observed concentration, found at the base of the
hill, is not simulated, but those across the face of the hill near release
height are. At this height, the greatest observed SFg concentration is
248 ppt, and the greatest concentration estimate is 871 ppt. The largest
modeled concentration from Impingement in the same area is 541 ppt. Both
models overestimate the observed concentrations in this area; this might
arise from overestimating the probability that the wind transported the
plume along the stagnation streamline. In Impingement, the distribution is
Gaussian and the 5.5° shift of the distribution still places the stagnation
streamline near the peak of the distribution. In Wrap, the probability is
taken from the PDF obtained from 80 m winds. This PDF could very well
overestimate the steadiness of the wind direction at release height.
A second reason for the model overestimates may be related to the
vertical dispersion near the hill. Neither model simulates the high
concentration at the base of the hill. A 0Z large enough to do so would
undoubtedly reduce the concentration estimates further up on the slope.
Because a substantial wind shear existed between the release height and the
surface, some enhanced dispersion near the hill might well be supposed.
4.14 Experiment 211, Hour 5 (0400-0500 MST)
4.14.1 Summary Description
Thermofogger oil-fog, SFg, and Freon were released from the southeast
side of the hill at 1155.1 m, 120.1°. The SF6 release at 20 m and the
Freon release at 58 m were continuous from the previous hour, so all tracer
gas sampler data should be representative of the full sampling hour. The
oil-fog was released at three heights over the course of the hour: 58 m
(0400-0436), 45 m (0436-0444), and 20 m (0444-0500).
Local terrain elevations near the release point are estimated to be
-9.9 m relative to the zero of the hill coordinate system, so the net
release height of the SF6 corresponds to the 11.1 m height level on the
hill, and that for Freon corresponds to the 48.1 m height level. The SFg
release rate is computed to be 0.175 g/s with an estimated error of ^+3.9%.
The Freon release rate is 0.941 g/s j*3.6%. No Freon concentration patterns
have been modeled.
Plume Observations
An extensive record of observer comments about the appearance and the
trajectory of the oil-fog plume during this hour is presented below.
Time: 0358 The plume centerline is at a point slightly to the north of
the FAA tower.
Time: 0400 The plume is continuing to progress slightly northward.
It's at a point now about half way down the hill. (It's approaching
the nephelometer crane.) The plume is passing 20 m north of FAA tower,
above tower C, but below the FAA tower (pretty close to release height).
251
-------
Time: 0404 Plume is shifting more to the south—aimed.more towards the
FAA tower. Plume is going around the north shoulder of the hill with
only a slight rise.
Time: 0406 Plume does rise quite a bit. It is even with the flat top
of the north butte. The plume is passing just north (like I can reach
out and touch it) of the north butte. This plume is passing overhead
now, but I can't smell it. It's about as wide as the parking area here.
Time; 0407 The plume is passing up and over the north butte, just over
the north edge. The plume is passing overhead, clearing by one tower
section. It looks like about 1 tower section thick.
Time; 0408 The plume is passing directly overhead, and I am located
right by the northeast corner of the parking lot on top of the north
butte. I do not smell it, and it is going through the lowest white
section on the FAA tower. It is clearing the top of the hill by about
8 m.
Time; 0411 The plume is now moving towards the south, approaching the
draw.The plume centerline is now between the draw and the FAA tower.
Time: 0414 The plume trajectory is continuing to move south, now
directed towards the tower on the south peak. It is rising quite high
over the draw C\> 20 feet)
Time: 0416 The plume is shifting back toward the FAA tower.
is just below lower red light (?).
Plume top
Time; 0417 The plume trajectory was towards the south peak for a short
period and then started drifting back to the north and is now at a
point slightly north of the FAA tower. The nephelometer crane just
passed through the plume.
Time: 0418 The plume meandered almost to the middle of the draw, then
came back across the north butte and now it is entirely north of the
butte and has gone below the level of the top of the butte. When the
plume was going directly over the north butte, I couldn't smell it. It
was very close to the ground, about 8 meters. As soon as it swings
back off to the north it subsides to nearly its release altitude, and
it does that subsiding back to that altitude very, very close to the
hill.
Time; 0423 The plume centerline now is half way between the FAA tower
and the northeast knoll.
Time; 0424 The plume is going around the north side, and it is
significantly below the elevation of the north butte.
252
-------
Time: 0,432 Plume is north of the north butte. For a time, 15 or 20
minutes ago, the plume was passing up through the draw with a
trajectory which took it probably 10 meters above the level of the two
peaks here or 30 meters above the height of the draw. It's quite
spectacular going up and over.
Time; 0438 At 45 m with the oil fog.
Time: 0439 The lower plume is absolutely creaming the hill, it's
approaching it, it's quite wide and going up and through the draw.
It's nearly extending from the FAA tower to the other side of the draw
and I can smell it quite a bit.
Time: 0442 The plume is leaving the crane and spreading in a uniform
"V" and when it hits the hill it's 1/3 of a hill width wide and it's
going up and through the draw and I can smell it from time to time on
the north butte. It's very dramatic, just filling up the whole draw.
Time: 0443 Release of smoke has been lowered to 20 m. The plume at 45
meters was creaming the hill .right up through the draw. Now that the
plume is at 20 meters, its aimed right at tower D. The whole mast
set-up has probably been getting very much creamed all night.
Time: 0448 (?) Plume is approaching the hill, spreading out quite a
bit. Most of it appears to be going around to the south.
Time: 0450 The lower plume spreads quite a bit, looks very stable and
is almost dying in the draw and now that I walk in the draw it is
definitely going up and through the draw.
Time: 0452 It looks to me like the nephelometers in the draw are
really getting creamed right now, the smell of smoke is very thick on
the south side of the parking area on the north butte. As I look down
the northeast side it looks like part of the plume is also going around.
Time: 0453 Plume is approaching hill in a wide "V"; part of it is
going around to the N. A lot of it is going up the draw, and I can
smell it strongly at the FAA parking lot.
Time: 0455 The plume centerline continues to drift south and is now at
a point about half way down the south slope or down about at the base
of the hill.
Time; 0456 Plume is all over the place., It is approaching the hill in
a wide "V". . .
Time: 0457 Now the plume appears to be heading towards the south
shoulder and it's no longer got that very wide wedge.
253
-------
Time; 0459 Plume is going south of south butte. It is a "pencil"
plume as it goes over the cinder pit—no longer a "V". As the plume
traversed the south flank, it tilted, and followed the contours, so
that the horizontal axis paralleled the hill slope.
These observations indicate that the plume spent the first 20 minutes
of the hour near the north peak, ranging from the saddle between the peaks
to a point along the north side of the hill. Observers consistently
reported no smoke odor as the plume passed overhead. The plume spent the
next 10 minutes well north of the hill.
After the plume was lowered from 58 m (adjacent to the Freon release)
to 45 m at the end of the eighth 5-minute period, the oil-fog traveled
directly toward the hill and filled the draw and saddle between the two
peaks as it went over the hill. Observers definitely reported smoke odor on
the hill at this time.
The plume was lowered once again in the ninth period, and remained
adjacent to the SFg release at 20 m for the rest of the hour. At this
height, the oil-fog plume was directed toward the center of the south peak
below the level of tower D. It was quite steady, and there was considerable
spreading in the horizontal as plume material spread up the draw and over
the saddle and the southern section of the north peak. A very strong smoke
odor was reported on the hill during this episode. This lasted for a^period
of about 10 minutes before the plume swung to the south side of the hill for
the last 5 minutes of the hour.
This sequence of events shows up very well in the photographs. Four
photos showing the plume trajectory during two of the 5-minute periods is
presented in Figure 117. One view is from behind the release crane at
position 0-19 (see Figure 46); another is from the top of the south peak at
location 0-8, and another view is from a point off to the side of the plume
from location 0-11.
Besides illustrating die plume trajectories discussed above, these
photos show the remarkable changes in plume spread as the plume travels
toward the hill. For the high release, the spread is not especially
striking, but the complete lift overhead is spectacular. As the plume is
lowered to 20 m though, the spread is very remarkable, as is the lack of
vertical lift. No lidar data for this hour are yet available.
Meteorological Information
Wind and temperature data measured at tower A during this hour were
used to characterize the flow in terms of Hc. However, because of a
partial failure of the 40 m wind set, 40 m winds were estimated for each
5-minute time period before Hc was calculated. The method followed in
calculating speeds at 40 m is outlined in Section 4.4.1.
The average Hc over the hour is 26 m, and Frn above Hc is 2.5.
The SF6 was released at 20 m, marginally below the mean critical dividing
streamline. Figure 111 contains a time series plot of the calculated
254 /
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5-minute Hc and Fry values for the experiment. Frjj is very steady,
exhibiting a variation of no more than 0.2. Hc , however, drops from 30 to
20 m over the first 40 minutes and then holds steady at 20 m for the rest of
the hour. Therefore, the assumption that the SFg plume remained below
Hc in the mean over the hour is not necessarily true, given the
uncertainty in estimating Hc. The period of the time during which the
smoke plume was placed alongside the SFg release corresponded to the
period during which Hc was equal to the release height.
Hourly average wind speeds measured at 10 m and estimated at 40 m are
1.3 and 2.4 m/s, respectively. The 10 m mean wind direction was 094° and
that at 80 m was 122°. Therefore, both wind direction and wind speed shears
above 10 m were moderate. Figure 118 shows the trend in wind speeds between
10 and 80 m during the hour. The 10 m speeds become very low at times and
rise as high as 2 m/s. Speeds at 40 m are quite steady, varying between 4
and 5 m/s. Winds at all levels tend to pick up toward the end of the hour,
thereby producing the drop in Hc.
Variations in wind directions measured at 10 m and 80 m are shown in
Figure 119 as frequency distributions. The 80 m distribution may be more
representative of that at release height because it is directed more toward
the hill; however, we cannot verify this from smoke plume observations. The
pattern of SFg concentrations over the hill surface may confirm the choice
of the 80 m distribution.
In summary, the plume was released close to the dividing streamline of
the flow and might have spent much of the hour below it. Winds were 2 m/s
or less and variable at the 10 m level but were presumably less variable and
somewhat greater near the release height.
Concentrations
The distribution of hourly averaged SFg conceiitrations over the
surface of the hill is shown in Figure 120. Highest concentrations are
measured between 15 m and 30 in in the southeast draw. Other concentrations
across the hill surface are seen to be quite large and generally tend to
favor the northern side of the hill. Those along the north side tend to fall
into a band between the 25 m and 50 m contours. A fairly large value is
also measured on the saddle toward the top of the northwest draw. Because
the relative release height is 11 m, this pattern tends to confirm oil-fog
plume observations made during the 15 minutes that the fog was released
adjacent to the SFg source. The SFg was apparently transported straight
toward the hill center or possibly the north peak for much of the hour, and
little plume lift occurred.
The distribution of 10-minute average SF£ concentrations is presented
in Figure 121. Fortunately, the location of the largest 10-minute
concentrations lies close to the location of the largest 1-hour average
concentration. Therefore, the evolution of the largest 1-hour concentration
may be seen in the 10-minute data. Large 10-minute concentrations occur in
this area in only three of the six 10-minute periods. The first is between
0410 and 0420, and the other two are between 0440 and 0500 — the period
256
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257
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UVW PROPS AT 80 m
9.0
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ICO 180 200 220 240 260 280 300 320 340 360
DIRECTION (dig)
UVW PROPS AT 10m
FREOUEI-CV <»>
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.0 !•• I 1 I 1—: 1 1 r^ 1
0 20 40 60 80 100 120 140 160
—1 1 1 1 1 1 1 1
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DIRECTION (d>g>
Figure 119. Calculated wind direction distribution functions for Experiment
211, Hour 5 (0400-0500 MST).
258
-------
"?• r = 500m
316.'
680
Figure 120. Observed SF^ concentrations (ppt) for Experiment 211,
Hour 5 (0400-0500 MST). Source: r = 1155.1 m, 9 = 120.1°,
net height = 11.1 m, Q = .175 g/s.
259
-------
TlflE PERIOD 0-4ee-«<19
TIRE PERIOD
Figure 121. Observed 10-minute average SFg concentrations (ppt) for
Experiment 211, Hour 5 (0400-0500 MST).
260
-------
TIKE PERIOD 84ae-6«e
Tint PERIOD 0438-0440
Figure 121. Continued.
261
-------
TIDE PERIOD »4S»-K»»
Figure 121. Continued.
262
-------
documented by the oil-fog plume in the photographs. This information
implies that a peak in the PDF at release height should virtually line up
with the flow toward the center of the hill.
'4.14.2 Model Peformance
This hour has been modeled with the Wrap model because the plume was
released slightly below the calculated dividing streamline height. However,
because the plume was so near Hc, significant vertical smearing of plume
concentrations on the hill was observed. This feature is not accounted for
in the model.
In running the models, meteorological data were prepared as in Section
4.1.2, and the resulting values are listed in Table 17.
The 1-hour average wind directions 10 m below and 60 m above the
release height are 094° and 122°, respectively. Directions at 10 m and 30 m
on tower B are 120° and 126°, respectively. Unfortunately, all we know
about the plume transport from photographs is obtained during the last
15 minutes of the hour, when the plume spent most of the time heading
directly toward the hill center with a brief period of flow along the south
edge of the hill. Because the photo documentation for the release height is
incomplete, the model wind direction is chosen to be 120°, the direction
from source to hill center. The 80 m PDF is also used in the modeling..
Concentration estimates from both Impingement and Wrap are listed in
Table 17 and plotted on a map of CCB in Figure 122. Both models tend to
underestimate peak observed SFg concentrations, but Wrap does better in
estimating concentrations along the sides of the hill, and in the lee (if
some compensation is made for differences between the heights of observed
concentrations, and the heights of modeled concentrations).
Peak observed concentrations occur at higher elevations on the hill
than do the peak modeled concentrations. The peak observed value is
3,885 ppt, and the peak modeled values are 565 ppt and 1,146 ppt for
Impingement and Wrap, respectively.
Larger concentrations can be produced with Wrap if the mean wind
direction is shifted slightly. The discussions above focused on the shape
of the 80 m PDF. The 10-minute SFft data indicated that a peak of the PDF
should be directed toward the hill center. The choice of 120° for the mean
wind direction does not direct a peak of the PDF along the stagnation
streamline. If the mean wind direction were changed from 120° to 118°, the
probability that the wind blew along the stagnation streamline would
increase from .0452 to .0635. This change would produce a peak
concentration of 1,610 ppt or 56% of the peak observed.
263
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TABLE 17. IMPINGEMENT AND WRAP MODEL CALCULATIONS - EXPERIMENT 211,
CASE HOUR 5
Meteorological Data
wind direction(deq) = 120.
wind speed(m/s) = 2,1
critical dividing
streamline height(m) = 26.0
Iz = .068
ly = .277
NCl/s) = .092
Source Data
direction(defl) = 120.
distance(m) = 1155.1
release heiqht(m)= 20.0
SF6 emission
rate(g/s) = .175
Receptor Coordinates Observed
X(m) YCraJ 2(m) SF6 (ppt)
360.22
142.00
257.78
195.15
159.04
72.99
66.60
29.59
10.61
25.15
-53.69
-45.46
-38.04
-15.01
-4.85
•396.68
•315.76
•248.96
•144.85
-60.85
31.69
95.80
163.68
137.89
441.46
313.62
183.53
312.38
•243.41
•441.92
•359.96
•297.11
•111.85
•141.42
•229.81
•109.07
-80.75
.00
.00
33.94
149.74
122.04
126.43
SOS. 92
224.79
80.56
190.88
-407.79
-345.28
-288.98
-113.99
-37.12
-106.29
-84.61
-66.71
-38.12
-16.12
-258.06
-231.27
-175.52
-137.89
-254.87
-181.07
-49.18
-41.13
65.22
255.14
207.82
171.54
65.88
141.42
229.81
263.31
194.94
13.26
50.00
30.00
27.41
46.91
77.02
-6.52
51.51
91.97
65.00
3.82
13.70
32.94
98.96
80.00
3.44
13.24
32.90
80.00
80.00
50.00
52.96
50.00
50.00
-2.45
15.29
30.00
14.00
50.00
-.90
8.94
28.07
80.00
50.00
30.00
30.00
50.00
923.50
1742.00
1461.30
1337.30
1280.22
977.30
.00
767.08
.00
855.30
680.80
380.40
300.20
141.40
264.10
132.60
169.00
64.00
115.20
348.20
508.30
581.80
860.80
900.10
679.60
2238.50
2884.70
1863.40
36.30
315.80
295.90
389.30
1344.10
945.00
.00
486.30
341.30
Impingement
Predicted
SF6 (ppt)
417.45
71.70
354.52
316.63
100.46
1.90
96.81
64.04
.16
14.67
222.27
325.41
261.38
.01
.72
163.25
220.64
188.18
2.04
2.04
73.82
bO.15
69.49
69.08
173.00
565.26
415.60
451.27
69.01
114.66
164.20
175.28
3.10
68.99
179.30
198.17
70.95
Wrap
Predicted
SP6 (ppt)
831.39
72.47
677.58
b2fl.96
129.56
.59
137.19
77.91
.02
10.36
386.29
652.78
482.84
.00
.14
293.25
442.59
356.09
.74
.74
81.26
45.32
66.07
65.02
219.79
1146.27
787.57
904.90
95.65
196.01
319.60
349.33
1.43
95.65
351.69
387.64
95.35
264
-------
Figure 122. SF^ concentrations (ppt) estimated for Experiment 211, Hour 5
by the Impingement (top) and Wrap (bottom) models.
265
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4.15 Summary
Case study analyses of 14 hours of data collected at CCB have produced
a wealth of information to guide the development of improved regulatory
dispersion models for applicaton in rough terrain. From the assembled
meteorological data, tracer concentrations, photographs, and lidar imagery,
we have been able to construct detailed descriptions of plume paths over and
around the hill under various meteorological conditions. Many of these
descriptions are found to be consistent with expectations about plume
behavior built upon theory and laboratory investigations. For example, the
critical dividing streamline height (as calculated by the integral method)
appears to be a good indicator of the basic modeling approach to be
adopted—that is, whether the plume should be modeled with a Wrap or a Lift
type of model.
Most of the experimental evidence supports these key findings about
plume trajectory regimes:
• When the plume was released above HC, it tended to travel over
the hill. The plume path appeared to be consistent with
streamlines in weakly stratified flow, as described both in theory
and laboratory experiments.
• When it was released well below HC, it tended to swing widely
across the hill, preferring to travel around the hill, not over
the hill.
• When it was released very near HC, it tended to travel directly
towards the hill, with only slight-to-moderate vertical
displacement.
Table 18 helps to summarize the observationally-established
relationships that appear to connect plume path behavior to the
meteorological parameters. It lists for each hour the release height
(zr), the dividing streamline height (Hc), the difference between the
two expressed as a function of the release height ((zr - Hc)/zr), as
well as the location of the maximum observed concentrations. In addition,
for those hours in which the release was above HC, the table includes
hourly average Froude numbers (Frjj, Fr^), inferred terrain factors
(TO), and observer notes on whether the streamlines appeared to be
depressed in the lee of the hill. Terrain factors, as inferred from
observed concentrations and the modeled plume dispersion and trajectory, can
be useful in explaining changes in the relative magnitudes of the plume
centerline height, plume distortion, and plume dilution—but only if
interpreted properly. For example, because we assume that only the ratio of
centerline height to az should be adjusted in the terrain factor
computations to make the model reproduce observed concentrations, the model
must be using the "right" values of mean wind direction and horizontal
spread. In addition, because we have assumed that the modeled centerline
concentrations are "correct" in deriving the terrain factor, To can no
longer properly account for changes in plume dilution; this places the
burden on the model to use "correct" values of az. When these
conditions are violated, inferred To values can be misleading.
266
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For hours of release heights less than or equal to HC , maximum
concentrations were measured both above and below the level of the release
height. One of these hours (209-7) is very difficult to interpret because
the winds smeared SFg in all directions before the start of the hour;
therefore, little definitive information can be extracted about plume
behavior. However, data from the other hours for which zr _<_ Hc
indicates that the plume definitely "rode" up the hill slope at times,
especially when zr was nearly equal to the HC- The data also indicate
that when large directional shear was present, a complex flow interaction
below the plume elevation could occur near the base of the hill. This
interaction (for which we have qualitative evidence but as yet no good
quantitative model) appears to have mixed the plume to the ground, producing
maximum concentrations below the release height.
For release heights greater than Hc, maximum concentrations were
measured either near the top of the hill or on the back side, provided that
the mean wind was directed towards the hill center. The deciding factor
that appears to govern whether the peak concentration lies near the top or
in the lee is the ratio (zr - Hc)/crz, not Fr]> The observational
evidence suggests that whenever Frj, was between 0.5 and 0.7, a streamline
depression effect appeared in the lee; but the inferred To values over the
top of the hill and in the lee suggest that leeside concentrations were
increased only moderately over what they might have been in the absence of a
leeside streamline depression. This increase may cause a shift in peak
concentrations from the top to the back of the hill. In cases where az
was small relative to the plume height, the concentrations across the top of
the hill are likely to have been smaller than those near the base of the
hill in the lee, regardless of the size of
Terrain factors inferred on the windward side of the hill suggest that
subtracting the full value of HC from the plume height may be too severe a
correction in cases where HC was a substantial fraction of the release
height. Instead, the model should somehow account for the vertical
deflection of Hc itself in order to better explain the observed
concentrations on the windward face.
The geometry of CCB may also play a major role in determining the size
of concentrations measured high on the windward side and in the saddle,
because the shape of the hill tends to funnel the flow. At times,
concentrations on the saddle were substantially lower than those measured on
one peak or the other or those estimated by the models for plumes well above
Hc. We conjecture that this may indicate a flow channeling effect: flow
up the draw may have been funneled underneath the plume, tending to lift the
plume somewhat, reducing tracer concentrations on the surface of the
saddle. For cases in which the plume was below HC , the same kind of
channeling effect may have forced plume material over the saddle rather than
to one side of the hill or the other. This would tend to promote large
tracer concentrations high on the hill. (This supposed channeling effect is
not taken into account by the Wrap model, which therefore always estimates
small concentrations at elevations well above zr. )
268
-------
Many primary components of the Lift and Wrap models appear to be
appropriate at CCB and need little modification. A comparison of model
estimates with observed concentrations shows that major differences between
modeled and observed concentrations can usually be explained by
uncertainties in the meteorology prevailing at the release point, especially
because of the observed spatial gradients and temporal changes in key
meteorological variables. Therefore, improving the models to take fuller
advantage of observational meteorological information turned out to be a
mixed blessing; because the models rely more heavily on the details of the
meteorology, they are not always better at estimating the observed
concentration field.
The relative performance of the Lift, Wrap, Neutral, and Impingement
models is summarized below for each of the case hours analyzed:
Experiment
Case Hour
202(4)
202(5)
204(1)
205(4)
205(5)
206(4)
206(6)
206(8)
Neutral appears to be better than Lift because the PDF used
in Lift seems to be too narrow. Neither version places the
peak concentration correctly below the release height.
Neutral does well, but the peak observed concentration again
lies closer to the bottom of the windward slope. Lift would
perform better if the PDF were a little broader and if a
terrain factor between 0.7 and 0.8 were used.
The peak concentration well to the side of the hill (nearly
level terrain) cannot be reproduced by either model. Wrap is
much better than Impingement in estimating other large
concentrations because the PDF is highly non-Gaussian.
Lift does better than Neutral. The PDF appears appropriate.
(Model estimates would improve if the terrain factor over the
hill top were about 0.8.)
Questionable SFg pattern precludes model evaluation.
Neutral does better than Lift. The PDF is too narrow, and
subtracting Hc brings the plume too near the surface on the
windward face of the hill.
Wrap overestimates by a factor of 2; Impingement
underestimates by the same factor. (Wrap with a larger
az and slightly broader PDF would work well.)
Same as 206(6).
conditions).
(Both hours have very similar meteorological
269
-------
209(1)
209(7)
210(3)
210(7)
211(1)
211(5)
Neutral and Lift both overestimate observed concentrations.
Either the model az is too large or the emission rate is
grossly in error (not likely). PDF and Gaussian distribution
appear equally suited.
Hour is impossible to model with tower A data.
Neutral and Lift estimates are uniformly low. An increase in
az late in the hour shoul<
PDF is probably adequate.
az late in the hour should be included in the estimates.
Lift estimates of the concentration distribution is better
than that from Neutral, so the PDF is appropriate.
Concentration estimates are too large on the windward face.
Wrap overestimates concentrations more than Impingement.
Either the PDF is too narrow or az is not large enough.
Wrap does better than Impingement because the PDF is a better
representation of the wind distribution. Peak estimate is
half the peak observed concentration. (A smaller az with
some plume lift would improve the model estimates.)
These observations indicate that the correct estimate of crz is
absolutely crucial to model performance. In most cases when the release is
above HC, estimating az only to within a factor of 1.5 to 2 introduces
enough error in modeled concentrations to cause extreme over- or
underestimates. In fact, because most reasonable estimates of To lie
between 0.5 and 1.0, inferred values of To that fall repeatedly between
1.4 and 2.0 could indicate that the "appropriate" az may be as much as
twice as large in these cases.
In all but the lightest wind speed cases, it is not as important to be
able to specify the horizontal distribution correctly. The use of a
Gaussian distribution with interpolated values of iy seems to provide an
adequate description of the variability in the plume trajectory. Indeed, in
some cases the Gaussian distribution offers a better description than does
the PDF measured from the nearest "representative" level above or below the
release height. But when wind speeds are light and variable, the
distribution of wind directions can be highly non—Gaussian, and it is of the
utmost importance, in such cases, to have available a truly representative
PDF.
A quantitative measure of the performance of the Lift and Neutral
models is presented in Table 19. The statistics describe the ability of the
models to reproduce observed concentrations on a point-by-point basis for
modeled and observed concentrations paired in space and time.
270
-------
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271
-------
A linear correlation method is used in which the observed
concentration Co is expressed as a linear function of the model
concentration Cp plus a random variable e
CP
+ B + e
(57)
Ideally, A s 1 and B = 0. If A < 1, the model tends to overestimate
concentrations; if A > 1, the model tends to underestimate
concentrations. However, if A < 1 and B is large, the correlation
between modeled and observed concentrations is likely to be small.
Table 19 contains the values of A and B as well as the
correlation coefficient (R.2), the absolute gross error (AGE), and
the root mean square error (RMSE).
AGE
Co -
(58)
RMSE
(Co - V
.2 */2 ,_
Only concentration samples taken at receptors above
statistics.
are included in the
The correlation coefficient for Lift is better than for Neutral in
case-hours 202(5), 205(4), 209(1), 210(3) and 210(7), but worse for
case-hours 202(4) and 206(4). (No judgment is made in the case of 205(5)
because the SF5 pattern is questionable.) When the linear regression
coefficients A and B are compared in the table for both models, Lift
exhibits less of an improvement. All measures of model performance would be
expected to improve, however, if input data uncertainty could be reduced.
Similar statistics for the Wrap and Impingement models are not
presented because the model is not designed to give the complete
concentration field — only concentrations near the stagnation streamline.
The comparisons we presented between the two models only address the ability
of each model to estimate the highest observed concentration on the hill.
Table 20 summarizes peak modeled and observed concentrations for each of the
fourteen case study hours. Note that these peak concentrations are not
paired in space, so the table in no way reflects the ability of a model to
estimate the spatial distribution of concentrations correctly. In all of
the hours modeled by the Wrap and Impingement models except one, the Wrap
estimate of the peak concentration lies closer to the peak observed
concentrations than does the Impingement estimate. Furthermore, the Wrap
model overestimates the peak concentration on the hill in all but one of the
hours (excluding 209, hour 7). Therefore Wrap (with the PDF formulation)
offers a clear improvement over Impingement.
272
-------
TABLE 20
SUMMARY OF PEAK MODELED AND OBSERVED
1-HOUR AVERAGE SF, CONCENTRATIONS
o
Experiment
Hour
Observed
202
202
204
205
205
206
206
206
209
209
210
210
211
211
4
5
1
4
5
4
6
8
1
7
3
7 •
1
5 ; ,
820
530
249 2
288
(444)
956
1921
2439
66
(123)
176
119
179
1648
647
235
-
207
(345)
1146
-
-
232
-
7
105
-
-
584
498
-
372
(184)
636
-
-
420
-
14
135
-
—
Peak Concentrations (ppt)-*-
Lift Neutral Wrap Impingement
195
262
3771
3782
(199)
487
655
871
1026
(562)
302
323
Concentrations are scaled by 0.1 (g/s)/Q(g/s) to account for differences in
SF, emission rates.
I
The largest concentration measured on the hill was 129 ppt.
273 ',
-------
SECTION 5
QUALITY ASSURANCE AND REFINEMENT OF CCB DATA
Since the first milestone report, the quality of the data taken from
the experiments has been substantially improved. ERT recently received the
original records (strip charts and integrator outputs) of the tracer gas
analysis performed at the North American Weather Consultants (NAWC) field
office in Boise. NAWC also provided a quality assurance report on the CCB
tracer data that indicated that some problems remained with the precision of
the curves used to fit the gas chromatograph (GC) calibration data and with
the interpolation in time between successive calibrations. These problems
have been addressed by new approaches to the calibration of the GC outputs.
ERT has also received the meteorological instrument calibrations
performed during installation and take-down of the tower data. These
provide further documentation of the consistency of instrument response
during the course of the experiments when compared with the data from the
two field audits.
An important experiment with the UVW propellers was performed in the
Colorado State University wind tunnel by staff of ERT's Western Measurements
Division (WMD) in April 1982. This experiment checked the response of a
completely assembled Climatronics triaxial wind component system. The
departures from cosine response were substantially greater than those
suggested by the curves in the manufacturer's literature. The data from
this experiment were combined with the field experiment data from sites
where cup and vane systems were co-located with propeller systems. This
produced correction factors for the propellor data and, in turn, corrections
for the effects of tower wakes. In addition, the locations of the tracer
sources and the rates of tracer emissions were refined.
Because of these refinements to the experimental data, the precision
and accuracy of the data base have been substantially improved. With these
improvements, model development and evaluation can be based on a sounder
foundation.
5.1 Refinement of Tracer Gas Data
NAWC's quality assurance report on the tracer gas samples taken at CCB
pointed out two principal problems with the way the gas GCs were
calibrated. First, the function used to represent the calibration data
often did not fit the responses well at the lower concentrations; second,
the interpolation of calibrations in time to determine an approximate
calibration specific to each sample analysis was technically unjustified and
.274
-------
conceptually somewhat contrary to the quality assurance plan for the
experiment. There is no reason to believe that a GC's calibration should
drift linearly in time, and the calibration span checks run every four hours
on each chromatograph were designed to keep the precision within 5%
tolerance.
To correct these problems, all tracer gas concentrations had to be
recalculated; this is described below.
5.1.1 Calibration Equations
GC responses to tracer gas samples were converted to concentrations of
the tracer by applying calibration equations. These equations were
determined by least-square fits of calibration functions to GC responses
obtained during calibrations with standard gases.
All of the GCs exhibited responses that can be closely approximated by
a power law for concentrations below about 1,500 ppt of SF6. The AID GC
followed the power-law response for both SFg and CF3Br (Freon) over the
entire range of concentrations used for calibrations, but the other GCs
deviated from the power law above about 1,500 ppt. The following
calibration function was used previously in an attempt to treat both the
power-law and nonpower-law concentration ranges
R = A C [1 - exp(-B/C)]
(59)
where R is GC response, C is the tracer gas concentration, and A and B are
.constants independent of concentration. Least—square fits were used to
estimate A and B for each calibration.
An example of the fit of Equation 59 to a calibration is shown in
Figure 123. The fitted function agrees well with the calibration results for
concentrations higher than about 2,000 ppt of SFg, but for lower
concentrations the function deviates significantly from the measured
responses and gives inaccurate concentration measurements. The manner in
which the function deviates from the lower concentrations (higher or lower
than the data) varies among GCs and calibrations.
New calibration curves were used to reduce these inaccuracies. They
combine two functions: a power function for lower concentrations (below
about 1,500 ppt) and an exponential function for higher levels
C = A RB,
R <
exp[B(R-R0)/R0],
(60)
(The two functions are equal in value and slope at response Ro.) For each
calibration, A and B were found first by linear least-square fit to the
logarithm of concentration versus the logarithm of GC response for
calibration values for concentrations below 1,500 ppt. Ro was then
275
-------
s
F
6
C
0
N
C
E
N
T
R
A
T
I
0
N
P
P
T
LEAST-SQUARES
105-3,
1CT-
10"-
10'
10-
i n i
i—i i 1111
7
i—i i 11 n
T 1—I I I I II
10'
10'
GAS CHROMATOGRAPH RESPONSE
Figure 123. Least-squares fit of old calibration function to calibration
of gas chromatograph No. 7, S3, with SF6 at 0615 MST on
November 11, 1980. Note the consistent over-prediction of
concentrations by the least-squares fit below 1,000 ppt.
276
-------
determined by a nonlinear least-square fit to the rest of the data, that is,
by finding the value of Ro that minimizes
N
J {C. - AR®exp[B(R - R )/R ]}
£_n 1 O 1OO
(61)
where the subscript i denotes the ith calibration point above 1,500 ppt.
RO was constrained to fall between the last calibration point below
1,500 ppt and the last point in the calibration.
The calibration data showed that the GC response to the lowest SF*
calibration concentration (which was either 10 or 12 ppt) was extremely
variable. In many cases, for concentrations above the lowest value a GC's
responses agreed within 5% in consecutive calibrations, whereas the'response
to the lowest concentration might differ by as much as 50%. As discussed in
Section 5.1.3, the lower quantifiable limit for SFe analysis was about
10 ppt. For these reasons, the lowest calibration concentration was
excluded from the least-square fits of the calibration functions. (Note
that the power-law concentration curve must go through the point (0,0).)
An example of the fit of the new function to calibrtion dta is shown in
Figure 124. The agreement is good below about 2,000 ppt. Although
percentage differences between the fitted functions and the data were
usually larger above 2,000 ppt than below it, all data agreed with the
function within about 15%.
As mentioned above, the AID GC response followed a power law throughout
the entire calibration range, and only a power-law function was used to fit
it. This GC was operated in several ranges selected through an electronic
attenuator. Separate functins were not fit to the calibrtion data for each
range; instead, the data were combined by multiplying the instrument
response by the attenuation factor. In all cases, the responses at
different attenuation factors agreed within a few percent when scaled to a
common attenuation. The AID GC also exhibited vriable responses to the
lowest SF6 calibration concentration, which was therefore excluded from
the least-square fits of the power law to the calibrations.
An example power-law fit to SFg calibrtion data for the AID
instrument is shown in Figure 125. The figure shows that agreement with the
data is good. The GC responses at two attentuations are plotted for all
calibration gases but those with the highest and lowest concentrations. The
near coincidence of the points demonstrates the validity of scaling the
different ranges to a common attenuation. The plot also shows the deviation
of the lowest concentration from the power law.
The AID GC was the only instrument used to measure Freon 13B1. A power
law was used to fit the Freon 13B1 calibrations, and data from different
ranges were scaled to a common attenuation. As with SF6, the instrument
responded variably to the lowest calibration concentration, 200 ppt; this
concentration was excluded from the fits. Figure 126 shows an example of a
fit to the Freon 13B1 calibration data.
277
-------
s
F
6
C
0
N
C
E
N
T
R
A
T
I
0
N
P
P
T
LEAST-SQUARES
105 ^
10*-
10' —
10-
10'
10-
10'
GAS CHROMATOGRAPH RESPONSE
Figure 124. Least-squares fit of new calibration function to calibration
of gas chromatograph No. 7, S^, with SF^ at 0615 MST on
November 11, 1980. The new function fits concentrations below
1,000 ppt better than the old function shown in Figure 123.
278
-------
LEAST-SQUARES
10'
S
F
6
C
0
N
C
E
N
T
R
A
T
I
0
N
P
P
T
icr
10'
10
10
i—i
i 111
10'
GAS CHROMATOGRAPH RESPONSE
Figure 125..
Least-squares fit of power-law function to calibration
of the AID gas chromatograph with SF6. at 0600 MST on
November 11, 1980.
279
-------
LEAST-SQUARES
F
R
E
0
N
1
3
B
1
C
0
N
C
E
N
T
R
A
T
I
0
N
P
P
T
icr
10'
10V
10'
10
r i i i i
10'
10V
10'
GAS CHROMATOGRAPH RESPONSE
Figure 126. Least-squares fit of power-law function to calibration of the
AID gas chromatograph with Freon 13B1 at 0615 MST on
November 11, 1980.
280
1
-------
5.1.2 Tracer Data Refinement
Tracer gas concentrations were recalculated from instrument responses
by means of the new calibration functions. Previously, linear time
interpolation of the calibration parameters (A and B in Equation 59) had
been used to attempt to account for drifts in GC response between
calibrations. However, data were not available to verify that changes in
response were linear with time, and time interpolation was not used in
reconstructing the data base. Instead, the most recent calibration was used
to calculate concentrations. The response of each GC to a single
calibration concentration was checked every four hours, and the instrument
was recalibrated if the response differed by more than 5% from that obtained
during the most recent calibration. Therefore, according to experimental
design, drift between calibrations should not have introduced an error of
more than 5% in the data. Because the Baseline GCs could not be kept within
this limit, their use was abandoned after a few experiments.
Before concentrations could be recalculated for experiments 201 through
203, it was necessary to enter GC response and analysis time-of-day
information into the data base. These data were not entered originally,
because concentrations had been calculated manually for these experiments
and entered directly into the computer. Some problems in the original data
base were discovered and corrected during this data entry process:
• Erroneous recount results in experiment 201: Results of the first
analysis of re-analyzed samples were entered instead of the
results of the second analysis. These errors were identified by
reviewing the recount log sheets, on which the results of recount
analyses were recorded.
• Incorrect identification of GCs for some analyses in
experiment 203: Corrections for these errors were discovered by
comparing GC analysis log sheets, from which the data were entered
originally, with GC strip charts and integrator printouts.
• Erroneous elimination of samples with collection times after
midnight: These errors were identified by reviewing the field
sampler log sheets, and the samples were restored to the data base.
The improvements in the SFg data can best be evaluated by examining
•recount data, which were obtained by repeating the analyses of some of the
tracer gas samples. In almost all cases, the repeated analysis was not
performed on the same GC as the first analysis, with the exception of
samples that were analyzed for Freon, which could only be reanalyzed on the
AID instrument. Therefore, deviations of the fitted calibration equations
from the true GC response contributed to deviations between the two
analyses. Table 21 shows average absolute percent deviations between the
first and second analyses within various concentration ranges for the
original and refined data bases. The numbers in the table were calculated
only from recount data for samples that were not voided because of sample
collection problems. The absolute percent deviations were calculated by
281
-------
TABLE 21
AVERAGE ABSOLUTE PERCENT DIFFERENCES
OF RECOUNT DATA BY CONCENTRATION RANGES
Concentration
(ppt)
SF&
Old
Data Base
10-50
50-200
200-500
500-1000
1000
Overall
19.5
8.2
5.9
5.9
4.7
11.0
Number of
Samples
119
112
76
35
19
361
Refined
Data Base
16.0
5.5
5.7
3.8
7.8
9.0
Number of
Samples
132
121
92
33
17
394
Freon 13B1
200-500 10.0
500-1000 8.1
1000-6000 3.1
6000-12000 1.0
12000 2.0
Overall 5.8
10
9
16
3
1
39
14.6
8.2
3.6
1.3
1.4
5.3
6
9
14
14
1
44
282
-------
c - c
1 2
x 100
(62)
where c\ and C2 are the first and second analyses of the sample. As
seen in the table, the deviations were reduced substantially for SFg
concentrations below 1,000 ppt. The average deviation tended to increase
above that concentration, probably because the old calibration function
(Equation 59) tended to fit the data better at high concentrations.
However, the cumulative frequency distribution of measured SFg
concentrations in Table 22 shows that more than 98% of the SF6
measurements were below 1,000 ppt, and that 96% of the measurements above
10 ppt were below 1,000 ppt. Hence, the new calibration functions have
resulted in significant improvement in the quality of a large majority of
the SFg data.
5.1.3 Precision and Lower Quantifiable Limit
The recount data provide information to estimate the precision of the
tracer analyses as a function of concentration and to estimate the lower
quantifiable limit of the measurements. Precision is a measure of the
agreement among individual measurements of the same quantity. Because of
the inherent variability in any measurement process, replicate measurements
of the same quantity by the same method yield different results. The
precision can be defined as the standard deviation of an infinite number of
replicate measurements. It cannot be determined exactly, but it can be
estimated.
Several pairs of analyses of the same sample can be used to estimate
the standard deviation of the measurement (EPA 1976)
0.886
N
N
R
(63)
where N is the number of pairs of analyses and R£ is the absolute
difference between the two values in the itn pair. The recount analyses
were not replicate pairs of measurements of a single sample, but Equation 63
can be applied to estimate the precision within concentration ranges. This
application assumes the precision is constant within the ranges used.
Table 23 lists the precision of the SFg analyses for various
concentration ranges and gives the average absolute differences of the
recount data and the estimated standard deviation as a percentage of the
midpoint concentration in the concentration ranges. Between 10 and 30 ppt,
the precision improves rapidly and a decreases from 35% to 11% of the
concentration. Between 50 and 1,000 ppt, a is about 4% of the
concentration; above 1,000 ppt, it averages about 6.5% of the concentration.
283
-------
TABLE 22
CUMULATIVE FREQUENCY DISTRIBUTION
Concentration
OF SF, CONCENTRATIONS
D
Number of Samples
Below Concentration
Percent of Samples
Below Concentration
5
10
20
50
70
100
200
300
500
750
1,000
2,000
5,000
9,821
6,228
6,952
7,677
8,691
9,092
9,526
10,389
10,923
11,469
11,777
11,936
12,082
12,130
12,133
51.3
57.3
63.3
71.6
74.9
78.5
85.6
90.0
94.5
97.1
98.4
99.6
99.98
100.0
284
-------
TABLE 23
PRECISION OF SF, ANALYSIS
o
Concentration
Range
(ppt)
5-10
10-20
20-30
30-40
40-50
50-75
75-100
100-150
150-250
250-400
400-600
600-1000
1000
Number of
Samples
23
49
42
24
17
33
29
37
47
45
30
25
17
Average Absolute
Difference
of Recount Data
(ppt)
3.0
3.1
3.1
3.8
5.6
3.0
5.6
6.8
7.3
21.4
21.4
30.8
189.7
Standard Deviation
of Analysis
(Percent of Midpoint
Concentration)
35
18
11
10
10
4
6
5
3
6
4
4
5*
*Highest concentration of first recount analysis was 6,420 ppt.
Midpoint concentration of 3,710 ppt was used.
285
-------
The lower quantifiable limit (LQL) is the lowest concentration that can
be measured with a specified precision. Usually, it is defined as the
concentration at which the precision is one-third of the value. For SFg,
this concentration is about 10 ppt; for Freon 13B1, it is about 220 ppt.
5.2 Refinement of Meteorological Data
5.2.1 Reasons for Refinement
As stated in the first milestone report, there were consistent
differences in the wind speeds and directions derived from the cup-and-vane
(Climatronics F460) and UVW propeller systems mounted at the same height on
the same tower. This is because the propellor systems do not respond fully
to the wind component along their axes. This deviation from cosine response
has been documented in the past (Horst 1973, Wyngaard 1981, Pond et al.
1979, Gill 1975), but a preliminary examination of CCB data showed that the
discrepancies in the wind speeds derived from the two systems were far
greater than were expected on the basis of deviations from cosine response
shown in the published reports. Accordingly, it was important to test the
responses of a complete three-axis propellor set in a wind tunnel.
Tests on propellor sets could not be run at Colorado State University's
tunnel in Fort Collins until early April 1982. In the two test days
available, one complete set of UVW transmitters was tested for response at
angles of attack incremented every 10° from 0° to 350° and additionally at
45°, 135°, 225°, and 315°. A second set was run to check consistency at a
few angles.
Another characteristic of the wind data measured at CCB was an apparent
effect caused by tower wakes. This appeared to disrupt the propellor data
from the 150 m profile tower when the winds blew from directions between 90°
and 125°. Because many experiments were run when the wind was blowing from
these directions and because the wind profiles from these instruments must
be used for estimating directions and speeds at source height, it was
necessary to correct for these wakes.
Lastly, the information from the audits and calibration records of the
sensors was evaluated to determine whether errors in orientation and
calibration were sufficiently persistent or reproducible to justify
correcting the instrument outputs. Errors in temperature sensors were
evaluated as well as those in wind sensors.
5.2.2 Calibration Histories and Audits
Information on the accuracy of the calibrations of the meteorological
instruments at CCB is contained in calibration records and the reports of
two external performance audits. Each instrument was calibrated when it was
installed in late September or early October 1980. The calibration was
checked when the instruments were removed in the third week of November.
286
-------
TRC Environmental Consultants, under subcontract to ERT, audited the
performance of all the instruments during the first four days of November,
and Mr. Thomas J. Lockhart of Meteorology Research, Inc. (MRI), under EPA'
contract, audited the performance of an easily accessible subset of the
instruments a few days later. . .
TRC audited the systems using standard calibration techniques,
including spinning wind-speed sensors at known rpm with synchronous motors,
checking the orientation of wind vanes and triaxial propeller systems to
true north, and immersing temperature probes in water baths whose
temperatures were determined by precision thermometers certified by the
National Bureau of Standards (NBS). The instruments' measurement values
were determined by converting the voltage put out by the translator cards to
engineering units. TRC's results are therefore directly comparable to the
calibrations done by ERT's field personnel.
Mr. Lockhart's audit differed in two ways. First, he used the
technique he has devised for auditing the performance of temperature probes
by inserting them in "thermal masses." Second, instead of reporting the
voltage outputs of the instruments' translator cards, he held the
instruments in the audit condition for at least one full 5-minute averaging
period of the data acquisition system and reported the output,in engineering
units produced by the data collection computer. Consequently, his audit
checked not only instrument performance but the performance of other
elements of the data system as well, principally the analogue-to-digital
converters in the microprocessors in the instrument shelters. (These
converters had been separately checked by,the TRC audit, however, and were
found to be accurate within a few tenths of a percent.) .
The results of the audits and calibrations of the instruments will be
presented and discussed in greater detail in the forthcoming quality
assurance report for the experiments, now in preparation.
5.2.3 Wind Tunnel Studies
Several wind tunnel studies have been performed on the CCB wind sets by
ERT's Western Measurements Division (WMD) in Colorado State University's
wind tunnel in Fort Collins. Both cup and propellor anemometers have been
studied.
In October 1981 the linearity and calibration of six of the F460 cup
anemometers used at,CCB were checked. The frequency output of the cup
sensors was converted to indicated wind speed by means of Climatronics'
calibration curve for F460s with plastic cups
V,
rraph .= Hz/9.5 + 0.5, or Vm/s = Hz/21.25 + 0.224
(64)
The range of wind speeds tested was 6 to 60 mph (2.7 to 27 m/s). The tunnel
speeds were measured by ERT's cup anemometer with stainless steel cups that
had been calibrated in the NBS wind tunnel in Gaithersburg, .Maryland. A
linear least-square regression was performed on the data from this NBS
287
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calibration for tunnel speeds of 1.7, 5.3, 15.1, 25.2, and 35.2 mph and was
used to convert the frequency output of this transmitter to actual tunnel
speed for comparison with the cups under test. This regression line is
V,
'mph
Hz/10.10 + 0.529, or Vm/s = Hz/22.59 + 0.236
(65)
(The divisor of the frequency in this formula is larger than that shown
above for the plastic cups because the stainless steel cups turn faster at a
given speed.)
In the range 6 to 40 mph (2.7 to 18 m/s), which is relevant to the CCB
data, all the speeds indicated by the CCB cup systems lay within 5% of the
speeds measured by the NBS anemometer, over 85% lay within 3%, and over 50%
within 2%.
The same sort of study was done with five individual Climatronics UVW
wind component transmitters at 0° angle of attack. The manufacturer's
calibration line of Vmp]1 = Hz/4.566 was used to convert the propellor
transmitters' frequency output to speed. These anemometers were even more
accurate than the F460 cups. The largest difference between the speeds
indicated by any propellor transmitter and by the NBS anemometer was only
2.2% for speeds less than 37 mph (16.5 m/s); the other points all lay within
2%.
The most significant experiment done at the CSU tunnel was the
determination of the fraction of cosine response given by the U and V
components of an assembled triaxial UVW propellor component system. WMD
staff from the Fort Collins office did this study during the first week in
April 1982. In the experiments with the cup and propellor anemometers
described above, both the instrument being tested and the NBS cups were in
the tunnel at the same time, situated side by side and at equal distances
from the wall respectively closer to each. The speed measurements given by
each were therefore taken simultaneously, so questions of variation of the
flow are largely irrelevant. The triaxial propellor anemometer, however, is
sufficiently large that both it and the NBS cups could not be placed
simultaneously in the same tunnel section without one or the other getting
too close to a tunnel wall.
As luck would have it, there were hurricane force winds in Fort Collins
on the first day of the experiment, and there was some doubt about the
stability of the tunnel controls in such conditions. However, before the
test of the UVW set at each tunnel setting, the speed was measured by the
NBS cups over a sequence of several periods, each at least 30 seconds long,
to demonstrate that the speed was indeed reasonably steady. The first test
was run at a very light wind speed. The mean value of the frequency output
from the NBS cups during eight 30-second periods was 13.28 Hz with a
standard deviation of only 0.331 Hz. The calibration line for the NBS cups
at 13.28 Hz yields a speed of 0.82 m/s, but the error in the calibration at
such low frequencies is large because of the zero intercept of 0.236 m/s.
The original data from the calibration of this wind set when it was
certified by NBS show that the instrument's output frequency was 14.1 Hz at
approximately 1.7 mph or 0.76 m/s. Linear extrapolation of the NBS data
288
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from the calibration points at 48.0 Hz and 14.1 Hz down to 13.28 Hz gives an
approximate speed of 0.72 m/s.
With the tunnel controls held constant, the output frequencies of the U
and V sensors were measured at angles of attack varying from 0° to 350° in
106 increments as well as at 45°, 135°, 225°, and 315°, where vector
resultant speed is expected to be a minimum fraction of actual flow speed.
The frequency outputs of the U and V arms were converted to meters per
second by the Climatronics formula Vm/s = 0.447 (Hz/4.566) = Hz/10.214.
At the end of the light wind test, the tunnel speed was again measured for
30 seconds by the NBS cups, which now gave a reduced frequency of 9.17 Hz.
Extrapolating down from the NBS calibration data gives 1.2 mph (0.53 m/s) as
the tunnel speed at that time. This is probably a high estimate, however,
because of the diminishing responsiveness of the cups at light speeds. The
data from this first test are apparently not reliable because of the drop in
tunnel speed.
The second tunnel setting gave a frequency output from the NBS cups of
105.9 Hz with no variation in four consecutive 30-second periods; a similar
check for 43 seconds after this test yielded a frequency of 105.7 Hz. Data
from this higher speed test are probably quite reliable therefore. The
calibration line for the NBS sensor gives a speed of 4.92 m/s for a
frequency of 105.9 Hz.
The third test of the UVW sensor response was run at a still higher
wind speed. Six peripds varying in length from 30 to 60 seconds gave a mean
frequency output from the NBS cups of 222.16 Hz with a standard deviation of
0.75 Hz. A 30-second check at the end of this test yielded a frequency of
222.12 Hz; again the data seem reliable. The calibration line of the NBS
cups gives 10.07 m/s for 222.16 Hz.
During this experiment, the W propellor never turned, nor did the U and
V propellors when the flow was normal to them, just as one would expect.
The results of these experiments are shown in Figures 127 and 128
A), in which the plotted values are the observed fractions of cosine
response from the U and V arms of the anemometer; i.e.
(set
p "
u u sin 0'
v
u cos 0
o
(66)
where uo is the tunnel speed indicated by the NBS-calibrated cups, and 6
is the wind direction as it would be with the instruments mounted in the
field; that is, u>0 for winds with westerly components and v>0 for winds
with southerly components. In order to display the symmetry of the
responses of the U and V components, the data are plotted together for the
two components in Figure 129. Here the wind direction for the V response
0V has been set to 0V = 90° - 0. This makes a wind from 90° blow
with an attack angle of 0° (directly onto the outward-facing side of the
propellor), and a wind from 270° blow from the junction block of the three
component arms down the shaft of the arm to the back side of the propellor.
289
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291
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292
-------
The data from the experiment with the tunnel speed less than 1.0 m/s have
been omitted.
Several characteristics of this plot are noteworthy. First, the
responses at 5 m/s and 10 m/s are nearly identical except where the angle of
attack on the propellor approaches 90°. Second, the UVW system seems to
behave quite symmetrically as a whole, but the responses of the individual
arms are not symmetrical about attack angles along the axes of the
transmitters. For example, the responses at 60° are different from those at
120°, and the responses at 250° are different from those at 290°. This
asymmetry is attributable to the wake of one component sensor acting on the
other at 290° and not at 250°, but it is unclear why this should be the case
near 90°, where it would seem that no part of one arm could affect the
other. However, the asymmetry is small in this region. A third obvious
characteristic of the data is the large impact of the sensor components
themselves when they are upwind. This was noted by Gill (1975) during tests
of his early designs, and he modified his later instruments so that the U
and V arms extended from the vertical shaft at different heights, and the
bulky cube at the "origin" of the three arms was eliminated. The
Glimatronics system retains the cube and has no vertical offset of the arms.
Another remarkable feature of the experimental data is the increased
response of the transmitters when the wind is +60° from the axis of the
propellor, that is, at winds from 30° and 150°. This feature is clearly
defined in the data from both arms and at both tunnel speeds, but no
explanation for it is obvious.
A second set of UVW components was assembled and tested at a few angles
of attack to check the reproducibility of the results from the first set.
The people performing the experiment noted that the hardware joining one arm
to the central block caused the angle between the U and V arms to differ by
a few degrees from a right angle. The data from this windset are therefore
somewhat suspect, but they have been plotted as points on Figures 127
and 128 (Set B) nonetheless and appear only slightly displaced from the
results of the more complete experiment with the first set of UVW
transmitters.
Wind data from the CCB experiments were analyzed for comparison to the
results of the wind tunnel experiments. Cup—and—vane and UVW anemometers
were located at the same tower levels at nine sites in the network, but the
winds at the 2 m level of tower A were not analyzed because the speeds there
were so light that the instruments were operating at or near their response
thresholds a large part of the time. Plots of the differences between
cup—and-vane wind directions and propellor wind directions at the 2 m level
show large scatter and no consistent pattern; the differences in wind speeds
measured by the two systems show similar scatter. The data from the
co-located instruments at 10 m on the four towers on the flanks of the butte
(towers C through F) were not analyzed because the large vertical component
of the wind at these sites would confound the analysis. Up to fairly large
angles of attack, cup anemometers respond positively to vertical motions,
either up or down, but at larger angles to the flow they respond negatively,
until they actually turn backwards at very large angles. Only the data from
293 ;
-------
the 10 m and 150 m levels of tower A and the 10 m and 30 m levels of tower B
were judged suitable for this analysis.
After correction for orientation of the vanes and UVW sets to true
north, all the valid 5-minute wind data taken at each of these four sites
during the tracer experiments were classified according to vane direction
into 36 groups, each 10° wide (0°-10°, 10°-20, etc.). Within each direction
class, the data were further classified according to whether the 5-minute
vector-resultant wind speed from the propellers was less than 1.5 m/s,
between 1.5 and 5.0 m/s, or greater than 5.0 m/s. The cup-and-vane data
were assumed to be accurate measures of the mean speed and direction of the
flow. Except for very light wind periods, this assumption seems reasonable
because the generally low turbulence intensities during the experiments mean
that overspeeding of the cups was minor.
The fraction of cosine response, Fu and Fv, from each horizontal
arm of the propellor system were calculated in a manner identical to that
used for the wind tunnel data. The number of points in each wind direction
group and the sample mean and standard deviation of the fractional responses
in each group were then calculated and listed. Data groups whose standard
deviations exceeded 10% of their means were excluded from further
consideration. This latter criterion excluded all the data with
propellor-derived speeds less than 1.5 m/s. The remaining data in the two
speed groups above 1.5 m/s were combined, and the sample means (and standard
deviations) of the fractional responses were again calculated to give an
overall average fractional response for each U and V arm for each 10°
direction class and at each of the four sites.
The average Fu's and Fv's were in turn averaged across the four
tower sites, with any site average excluded if the standard deviation of the
responses at that site exceeded 10% of the mean, but only if there were data
with less variation at some other site. In general, the data show a
satisfactory lack of scatter for wind directions that had a high frequency
of occurrence, were not taken from very high angles of attack, and did not
cause tower wakes on the sensors. These directions are naturally those
which occurred most frequently during the experiments, that is, northwest
and southeast.
The Fu and Fv results from the wind tunnel experiments at 5 m/s and
10 m/s were averaged at each angle of attack. For application to the (JCB
data, a running two—angle averaging was then done. (Data from three angles
of attack were averaged for the 40°-50°, 130°-140°, 220°-230°, and 310°-320°
sectors because of the data also taken at the central angle of the
sectors.) This averaging was done not only because the ambient data had
been averaged in 10° sectors, but also because the sharp peaks and valleys
of the propellor responses in the wind tunnel would have been smoothed out
somewhat by turbulence and meander in the atmosphere.
Finally, the average wind tunnel and ambient Fu's and Fv's were
themselves averaged to give the values to be used in the correction of the
CCB data. Table 24 lists the average ambient values, the average wind
tunnel values, and the values used in the data correction. For wind
294
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TABLE 24
AVERAGE FRACTIONS OF COSINE RESPONSE SHOWN BY U AND V
PROPELLOR ANEMOMETERS: CCB FIELD DATA, CSU WIND TUNNEL DATA,
AND VALUE APPLIED AS CORRECTION FACTOR TO FIELD DATA
Direction
Average Fu
Average Fv
Sector
0-10
10-20
20-30
30-^0
40-50
50-60
60-70
70-80
' 80-90
90-100
100-110
110-120
120-130
130-140
140-150
150-160
160-170
170-180
180-190
190-200
200-210
210-220
220-230
230-240
240-250
250-260
260-270
270-280
280-290
290-300
300-310
310-320
320-330
330-340
340-350
350-360
CCB Data
(.927)
(.751)
__
(.811)
(.846)
(.916)
.979
.959
1.004
.980
.972
.932
.862
.781
.746
.680
(.600)
(-.109)
(.398)
(1.037)
(.833)
(.800)
(1.010)
(.712)
.912
.866
.877
.845
.875
.814
.767
.748
.769
.767
.621
(.484)
Wind Tunnel
(.736)
.743
.781
.802
.833
.904
.950
.974
.980
.975
.965
.937
.882
.811
.785 .
.747
.650
(.601)
(.827)
.884
.843
.823
.855
.907
.936
.939
.885
.880
.828
.831
.796
.731
.754
.776
.776
(.780)
Applied
.736
.743
.781
.807
.840
.910
.965
.966
.992
.978
.968
.935
.872
.796
.766
.714
.625
.677
.827
.935
.843
.823
.855
.907
.924
.903
.881
.863
.852
.823
.782
.740
.762
.771
.699
.632
CCB Data
.949
.927
.909
.843
(.814)
.707
.626
(.694)
(1.410)
(.686)
.917
.870
.826
.798
.844
.823
.806
.796
.839
.831
(.700)
(.908)
(.800)
(.739)
(.802)
.875
.866
(.765)
.760
.820
.815
.866
.937
.941
.960
.970
Wind Tunnel
.975
.969
.947
.897
.825
.794
.758
.672
(.631)
(.860)
.850
.824
.799
.773
.799
.831
.841
.822
.858
.926
.921
.885
, .825
.792
.801
.823
(.836)
(.640)
.672
.748
.786
.820
.896
.943
.967
(.975)
Applied
.962
.948
.928
.870
.820
.758
.709
.683
.694
.821
.884
.847
.813
.786 '
.822
.827
.824
.809
.849
.879
.921
.897
.813
.766
.801
.849
.792
.703
.716
.784
.801
.843
.917
.942
.964
.972
Note: Numbers in parentheses are questionable because of small sample or
high variability.
295
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directions in which the CCB data showed substantial scatter, the ambient
average is enclosed by parentheses, and heavier weight has been given the
wind tunnel result unless it is very close to the ambient value. For those
cases with very few and inconsistent data from CCB, the wind tunnel value
has been used.
5.2.4 Procedures for Refining Meteorological Data
The first milestone report describes the results of the performance
audits of the meteorological instruments by TRC and MRI and points out some
inconsistencies in the differences between instrument responses and audit
values. These audit data have been reexamined together with data from the
calibrations done by WMD at the time of installation and at take-down to try
to find consistent response errors. Where such are found, corrections have
been made to the data. All the audit and calibration information will be
presented in the forthcoming quality assurance report so that other users of
the data base may make any appropriate modifications.
The refinements made to the meteorological data in response to the
audit and calibration data and the wind tunnel studies are described below.
Cup and Vane Wind Data
The performance audit done by TRC checked the response of the F460 cup
anemometers by spinning the sensor shafts at 360 rpm with a synchronous
motor. This corresponds to a wind speed of 8.69 m/s according to
Climatronics1 specified calibration line u(mph) = Hz/9.5 + 0.5, or
u(m/s) = Hz/21.25 + 0.224.
The responses of the F460s on towers A and B, the 150 m tower north of
the butte, and the 30 m tower on top of the south peak of the butte, showed
a very consistent error of 0.15 or 0.16 m/s (except at the 30 m level of
tower B, where the error was 0.26 m/s)(see first milestone report). The
F460s on towers C through F, the 10 m masts on the flanks of the butte, also
showed a consistent error between -0.16 and -0.13 m/s at the audit speed of
8.69 m/s. The calibration records of the translator cards on these
instruments show the reason for both the precision and sign of these errors:
on towers A and B the translator cards were calibrated to 0.045 (0.45 m/s)
vdc at 0 shaft rpm or 0.0 Hz, whereas on towers C through F, they were
zeroed to 0.000 vdc. The span calibration of the translators of all F460s
was done with an oscillator giving 524.8 Hz, which corresponds to 25 m/s or
2.5 vdc, half the scale of these 0-5 v, 0-50 m/s instruments. In fact, the
instruments should have been zeroed at the voltage corresponding to 0.50 mph
(0.224 m/s) or 0.022 vdc.
The output from the F460s (in meters per second) has been
"recalibrated" to give the proper 25 m/s response at 524.8 Hz and the proper
0.224 m/s response at 0 Hz. This recalibration was done with the correction
corrected speed (m/s)
1.008 x (uncorrected speed)
towers A and B
296 ?
- 0.214(m/s) for
-------
corrected speed (m/s) = 0.991 x (uncorrected speed) + 0.224 (m/s)
for towers C through F •
TRC also audited the orientation of the F460 vanes to true north and
the linearity of the potentiometers (and translators). The mean value of
the total error for each vane, including mean nonlinearity, was used to
correct its output.
Temperature Data
..The audit and calibration data for the temperature and temperature
difference systems were examined for consistency. The general variability
of the .errors, even between the two audits done only a few days apart, is so
large that no corrections have been made to the temperature data. The
differences between audit or calibration values and .output measurements are,
in any case, quite small for most of the temperature sensors. All but
two indicated errors (both from MRI's audit) are less than 0.2°C in '
magnitude.
UVW Wind Component Data
The audit and calibration data from the UVW propeller sensors are
fairly consistent for some sensors and not for others. The errors are
generally less than 0.1 m/s, and because these sensors' deviations from
cosine response result in errors far larger than 0.1 m/s, no changes to the
sensor outputs have yet been made to correct any apparent calibration
errors. Effort,has been directed instead to the problem of noncosine
response. . •• . .
, The wind tunnel experiments with these sensors and the derivation of
the average fractions of cosine response by the U and V.arms in the tunnel
and at CCB have been described above. To correct the wind component data,
each measured component value was simply multiplied by the inverse of the
average fraction of cosine response appropriate to the wind direction (see
Table 24).
The wind direction was initially estimated by correcting the wind
direction WD resulting from the measured U and V components by means of the
function
= WD + 4 sin (4WD)
(67.)
This sinusoidal correction is an approximation to the observed difference
between actual wind direction in the wind tunnel and the wind direction
resulting from the U and V sensor responses. According to the tunnel data,
it corrects the direction to within 2.0° in all wind directions.
This corrected wind direction was then used to find the appropriate
values of Fu and Fy from Table 24. The values for a specific wind.
direction were derived by linear interpolation in this table, with the
tabulated values for wind sectors 0°-10°, 10°-200, etc., ascribed to wind
directions 5°, 15°, etc. The measured values of U and V were corrected by
297
-------
dividing by Fu and Fv, respectively. Corrected wind direction and speed
were in turn calculated by changing the corrected U and V values to polar
coordinates.
Corrections for Tower Wakes
Plots of the differences between 5—minute vector—resultant wind speeds
derived from cup-and-vane data (SP) and from propellor data (WS) versus
5-minute vector—resultant vane direction (DR) showed a pattern of deficit in
WS in certain wind directions that corresponds to periods when the propellor
sensors were in the lee of the tower. Figure 130 is the plot of this wind
speed difference at the 150 m level of tower A, where the pattern is best
defined because of the steady winds at that height. (The data plotted have
not been corrected for propellor response.) There is a region between 90°
and 125° and centered near 110° in which the propellor speed is low,
apparently only about 40% of the cup speed in the core of the region. To
the left (north) of this region is a less well-defined deficit in cup speed
relative to propellor speed. Figure 131 is a sketch, approximately to
scale, of the 150 m level of tower A; the 10 m level was the same. Because
no cup—and—vane sets were mounted at the 40 m and 80 m levels, the UVW
component sensors were not offset to the north on a crossarm, and the wake
of the tower should be most pronounced at wind directions slightly south of
90°.
Studies of tower wakes in wind tunnels (Gill et al. 1967, Cermak and
Horn 1968) and in the atmosphere (izumi and Barad 1970, Moses and
Daubek 1961) have indicated substantial speed deficits in the lee of
towers. The amount of the deficit depends on the tower structure, the
distance of the sensors from the tower, and the orientation of the sensors
with respect to the "legs" or sides of the tower. The width of the tower
wake stays approximately constant at 1.5 tower diameters for distances up to
6 diameters downwind. For distances from the tower at which the sensors
were mounted at CCB (3 to 4 diameters, a diameter being the length of a
tower leg), the speed deficit at the center of the wake is expected to be
20% to 30%. The factor of 2 speed deficit in the core of the wake is
therefore somewhat surprising, but the boom carriages of the instrument
elevator presented solid obstacles about 0.5 m square. This may account for
the increased speed deficit shown in the data.
Speed deficits in the tower wakes were corrected by the function
2C
CT s 1 + C w 6o ~ 6 for 9 i
C-p = 1 for 0 elsewhere.
Here C is the speed deficit assumed in the center of the wake (at wind
direction 00), W is the "width" of the wake in degrees, and 0 is
the wind direction derived from propellor sensors after correction for
noncosine response. Wake locations and widths were estimated from the
geometry of the towers and sensors. For the 10 m and 150 m levels of
tower A, GX for the propellor speeds was calculated with C = 0.7,
298
-------
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299
-------
True North
S 1/4 in. = 1ft
Figure 131. Sketch of geometry of tower, booms, and wind instruments at 150 m
level, Tower A.
300
-------
W = 31°, and 6O = 107.5. For the 40 m and 80 m levels of tower A, the
wake on the propellers was assumed to be centered at 92° with a wake 35°
wide. Wake correction for the cups on tower A was calculated with C = 0.7,
W = 30°, and 0O = 70°, and for the cups at 10 m and 30 m on tower B with
G = 0.26, W = 20°, and 6O = 263°. The wake on the propellors at 10 m
and 30 m on tower B was corrected with C = 0.3, W = 30°, and 0O = 227.5°.
There are few data from the appropriate wind directions on tower B with
which to evaluate the corrections for wake effects, and the corrections used
more closely follow the suggestions of Gill et al. (1967).
Wind tunnel studies indicate that there is a speed increment at the
edge of a tower wake amounting to about 10%. No attempt has been made to
correct the CCB data for this increment; it has been assumed that changes of
wind direction caused by turbulence during each 5-minute averaging period
would tend to put the wind sensors alternately in the increment and deficit
regions, which would diminish this effect.
Figure 132 is a plot of the same data after correction that were
plotted in uncorrected form in Figure 130. The general improvement in
correspondence between cup-and-vane measurements and propellor measurements
is obvious. The correction for tower wakes has not been completely
successful in eliminating the peakiness in the plots near 90° and 120°. How
much of these apparent errors is attributable to overspeeding of one sensor
at the edge of a wake and how much to underspeeding at the other is hard to
assess. The strange peak centered at 330° also remains. This feature
appears, though less distinctly, in the data from 10 m and 30 m on tower B.
It is tentatively attributed to the effect of the UVW propellor system on
the cup anemometer. If this premise is true, the UVW wind speed is probably
a more accurate measurement when the wind is near 330° on these towers since
the propellors are upwind of the cups.
Corrections to Turbulence Intensities
The UVW anemometers were used at CCB primarily to determine the
intensities of turbulence ix, iy, and iz. Corrections have been
derived by Horst (1973) for measurements of those variables made with
R.M. Young instruments. Because of the now partially documented disparity
in response between the Young and Climatronics versions of the propellor
systems, and because Horst's corrections were developed from data taken in
only two periods of approximately one-half hour each (neither of which was
stable), the applicability of these corrections to the CCB data is doubtful.
The 5-minute values of intensity of turbulence have therefore not been
altered. We have elected to leave them alone rather than correct them
inappropriately. To some extent the departure from cosine response of the
propellor sensors is self-correcting in the calculation of the intensities
because both the numerator and denominator of the intensity are "scaled" by
the fraction of cosine response achieved by the instruments. However, in
the CCB measurements, the ratio of crosswind intensity iy to alongwind
intensity ix becomes notably smaller as the wind direction approaches the
axis of one propellor transmitter, which is expected given the response
characteristics. This means that the horizontal turbulence intensities
301
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recorded in the data base are not simply wrong by some scaling factor, but
that their errors are functions of wind direction. The vertical turbulence
intensity measurements are almost assuredly underestimates, particularly
near the ground and where the mean vertical components are low. This
underestimate results not only from the poor cosine response of the
propellers to mean flow at high angles of attack but also from the response
distance of approximately 1 meter, which limits the response of the
propeller to high-frequency oscillations in the vertical.
5.2.5 Results of Data Refinements and Conclusions
The improvement in correspondences between wind speeds derived from
propeller systems and wind speeds from cup anemometers has been shown from
one sample site, the 150 m level of tower A, in Figures 130 and 132.
Figures 133 and 134 show the correspondence between wind directions derived
from the two systems at the same site after application of the corrections
described above. A large part of the improvement results from simply
correcting the data for misorientation of the sensors to true north; the
correction for the UVW data at 150 m was +7° and for the vane data, -2°.
The changes resulting from the corrections for propellor response have
removed most of the cyclic quality of the disparities in direction
measurements also. Nevertheless, the sample plots show that there remain
anomalies in the comparative data, one of which is probably an effect of
wakes on wind direction. This effect is complicated by the fact that the U
and V propellers are not normally in the same part of the wake at the same
time. Users of the data should be advised to give precedence to data taken
from outside wakes whenever possible.
In general, clear improvements have been made in the precision and
accuracy of both the tracer and meteorological data from, the CCB
experiments. Recalibration of the tracer data has resulted in increased
precision and reliability of the concentrations. Wind tunnel studies have
explained a large portion of the discrepancies between propellor and
cup-and-vane data, but some anomalies remain. Corrections for orientation
of wind sets has improved the accuracy of wind direction data.
Other improvements in data quality may be possible, but no firm basis
for making them is apparent. The calibration and audit data for a few of
the meteorological instruments show some consistency, but whether this
results from chance or a truly persistent error in response remains a
question because so much of this data shows such large variations.
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SECTION 6
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS
FOR FURTHER STUDY
This document has described in detail the further progress to date in
correcting and refining the CCB data bases, analyzing the case study
experimental hours selected for intensive study, and in improving the
preliminary Neutral and Impingement models and evaluating their
performance. In this section we present an overview of conclusions reached
so far. Much of the technical analysis that underlies these findings is of
very recent completion, and further review, evaluation, and augmentation of
these conclusions will undoubtedly be required.
6.1 Principal Accomplishments and Key Findings
6.1.1 Data Base Refinements
The first milestone report described some of the major uncertainties
and likely sources of error in the data obtained at CCB. During the study
phase just completed, considerable effort was expended to revise the tracer
concentrations and meteorological data. This sub-section summarizes these
activities.
Tracer Concentration Data
The mathematical functions used to fit gas chromatograph calibrations
were revised in order to reduce errors in tracer gas concentrations. All
concentrations were recalculated by means of the new calibration functions.
The SFg and Freon 13B1 recount results were analyzed to estimate the
precision and lower quantifiable limits of the tracer gas analysis.
The new calibration functions fit the calibration data within 15% for
all concentrations. For concentrations below 1500 ppt the calibration fit
is within 5%. The precision (expressed as the standard deviation) of the
SFg analyses varies with concentration. In the range 10-20 ppt, the mean
precision is about 18% of the concentration; in the range 20-50 ppt the mean
precision is about 10%; above 50 ppt the mean precision is about 5%.
The lower quantifiable limit (defined as the concentration at which the
standard deviation of the analysis is 33% of the concentration) is about
10 ppt for SFg. The precision of the Freon 13B1 analysis is about 74 ppt,
independent of concentration. Therefore, the lower quantifiable limit for
Freon 13B1 analysis is about 220 ppt.
306
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Meteorological Data
In addition to problems of data loss or simple instrument malfunctions,
major difficulties which required corrective measures are associated with
basic inadequacies of the propellor anemometer (UVW) wind systems. In
retrospect it is clear that their response characteristics differed
significantly from those of the cup and vane systems at CCB. In particular
the UVW wind speed components were underestimated—sometimes slightly,
sometimes to a large degree—depending upon wind direction. So far as we
have been able to determine, the patterns of UVW system underestimation were
caused by some combinations of:
0 non-cosine response characteristics of the propellers used;
• wake effects of one propellor on another;
• wake effects of a propellor shaft or junction box on an adjacent
propellor; and
• wake effects (shadowing) caused by the supporting tower.
The tower wake also affected winds measured by the cup and vane systems for
some wind directions.
Corrections have been devised from comparisons of the UVW data with the
cup and vane data and from a recent wind tunnel test of the entire UVW wind
set. These corrections improve the correspondence between winds measured by
the cups and props at the same heights. The agreement is also improved by
correcting for errors made in orienting the wind sets to true north. The
improvements are best, characteristically, for wind directions that do not
leave a wind set in the tower's wake.
Although the 5-minute turbulence intensity data obtained by the UVW
wind sets undoubtedly contain similar deficiencies as those noted above, we
do not know of an appropriate method for "correcting" iy and iz for the
errors in propellor response characteristics. In particular, the vertical
turbulence measurements, so critical to describing crz in the model, are
almost assuredly underestimates of the actual turbulence experienced.
Rather than running the risk of "correcting" them inappropriately, we have
elected to leave them as they are. However, in modeling and data analysis
applications requiring 1-hour iz data we have adjusted the data base iz
values in two ways. Firstly, a new 1-hour aw is computed from the
5-minute iz and wind speed values, and this aw is then scaled by the
1-hour scalar average horizontal wind speed. Secondly, adjustments for prop
response suggested by Horst (1973) were applied.
The temperature data have not been adjusted on the basis of the QA
audit dta. The maximum error detected in the QA audits of the, temperature
systems was 0.4°C, but it was not duplicated in the two audits done only a
few days apart. In fact, the general inconsistency between the errors in
temperature systems found in the two audits suggestes that the magnitude of
the errors approaches the resolution of the audit procedures.
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Overall, the revised tracer and meteorological data bases provide a
much better foundation for model development and evaluation, and we are
confident that the many lessons learned at CCB will directly benefit the
quality of data obtained in the next field program.
6.1.2 Investigations of Plume Growth
Some exploratory work has been done to compare the photographic
evidence for vertical plume spread with contemporaneous tower data. The
vertical growth of the visible plume as determined from the plume
photographs agrees reasonably well with tower observations of vertical
turbulence intensity for time averages of 30 minutes or more, but the
agreement for time averages of five minutes is poor. In some light wind
cases, the sinusoidal-like variations in vertical dispersion seen in the
photos are out of phase by 20 to 30 minutes with the variations identified
in the tower data.
In a parallel effort, the lidar measurements of short term average
0V and az have been plotted as functions of downwind distance x.
These show very little variation with x, but when plume meander is accounted
for in the hourly averages, 0y is seen to be proportional to x and the
proportionality factor is equal to the lateral turbulence intensity. Light
wind, stable conditions appear to be necessary but not sufficient for large
values of iy. Under the same conditions vertical turbulence intensity can
be high, due perhaps to transfer of gravity wave energy into the vertical
component.
A number of time series analyses were made to examine the spectral
characteristics of the wind components. These analyses show turbulent
energy maximums at periods of one or two hours, suggesting that this energy
may translate into gradual meandering of the plume across CCB during the
course of an hour.
One-hour average crz values (computed from Equation 47 with 1-hour
iz values adjusted for prop response characteristics and interpolated to
release height) have been compared with effective 1-hour average az
values obtained from lidar data. The comparisons indicate that, in general,
Equation 47 estimates crz to within a factor of 2 when the parameter p is
set equal to 1.5.
6.1.3 Investigations of Flow Patterns
The integral method of calculating Hc appears to be a successful
estimator of dividing streamline heights (and therefore of plume flow
regions) at CCB. Plumes released below HC tended to wander from side to
side without flowing directly over the hill; plumes released close to Hc
travelled directly into the hill, rising along the surface as they flowed
either around one side of the hill or over the saddle; plumes released well
above Hc travelled freely over the top of the hill, usually with very
small impact.
308
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The isentrope analysis suggests that flow above Hc behaves much like
a weakly stratified flow (FrjjXL). The streamline heights over the south
peak of CCB were plotted against their inferred heights well upwind.
Although the scatter is large, the points do show a tendency to cluster in a
near-neutral zone, as predicted from physical modeling studies and theory.
The analysis explicitly accounts for a dead layer below Hc, and the
results suggest that a modeling method which subtracts out the dead layer of
height HC and then treats the flow above HC as neutral flow may be
consistent with flows over CCB.
Theory predicts that in weakly stratified flow over a hill, lee wave
effects begin to influence the pattern of flow over the hill when Frj, is
less than about unity. Observer comments, photos, and lidar data at CCB all
suggest that streamline depressions occurred in the lee of CCB for values of
FrL <0.7. SFg measurements show'that tracer concentrations on the lee
side were often larger than those on the windward side of the hill.
However, the role of streamline depression and plume distortion in producing
the larger concentrations has not been established.
As expected, the relative locations of peak tracer concentrations on
CCB depended to a great extent on the ratio of release height to HC. When
plumes were released above Hc, the larger concentrations were generally
found either over the top of the hill or on the lee side. The position of
these larger concentrations appears to be dictated more by the size of
0Z rather than by FrL. When plumes were released below HCs the
larger concentrations were found primarily on the windward side of the hill,
but not necessarily near the release height. Although some degree of
streamline lift was visually evident, vertical mixing at times was
sufficient to produce peak concentrations at receptors below the release
height.
Effects of directional wind shear can be of central importance for low
release heights at CCB. Some evidence of increased plume dispersion close
to the base of the hill may be associated with such a shear zone. In these
cases the highest concentrations were found below the release heights.
6.1.4 Model Modifications and Testing
Several modifications have been made to the Impingement and Neutral
models since their evaluation in the first milestone report. The purposes
of these changes is to increase their applicability to more general terrain
shapes, and to increase their ability to respond to changes in important
meteorological parameters. The new versions of these models have been named
Wrap and Lift, respectively.
The formulation for oz has been altered in both models.
Now a.
(Equation 47) grows like awt for travel times small compared to 1/N,
where N is the Brunt—Vaisala frequency. This change has very little effect
on the size of az for most values of N encountered at CCB. However,
when N becomes small (weak density stratification), the new expression for
a z no longer tends to overestimate the size of the plume.
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The Gaussian probability density function for the wind direction was
replaced by the probability density function (PDF) constructed from the
5-minute averaged wind directions. With this change, both models are able
to simulate concentration patterns better when the wind distribution is
decidedly non-Gaussian.
The Wrap model allows estimates of concentrations in a band around the
hill for elevations near the height of release. Formerly, the model only
provided a concentration estimate for the stagnation point.
The Lift model allows for broad differences in hill shape. The shape
of the hill in the crosswind direction is characterized by an overall radius
of curvature which determines the amount of horizontal distortion produced
in the plume as the plume travels over the hill. A large radius
characterizes a very broad terrain feature, and produces relatively little
horizontal plume distortion. The curvature is also used to interpolate
between empirically suggested limits for the terrain correction factor
(Tc): 0.5 for R/H ^ 1, 1.0 for R/H »1.
In addition,the Lift model accounts for stratification effects by
treating the layer below Hc as a "dead" layer. This supposes that the
dynamics of the flow above HC are similar to weakly stratified (near
neutral) flow. However, because none of the flow below HC is allowed over
the hill, the plume above Hc passes closer to the hill surface as Hc is
increased.
An evaluation of both the new and old versions of the models has been
completed for 14 of the 45 hours modeled in the first milestone report. The
results are presented in Section 4, and summarized in detail in
Section 4.15. These are the general qualitative results:
• Use of the actual wind direction PDF rather than a Gaussian
distribution is critical when the winds are light and variable -
especially for Wrap model calculations. This modification is the
major reason for the improved results of the Wrap model. However,
use of a PDF when winds are fairly steady could degrade model
performance if wind data at the release height are unavailable.
In this case a Gaussian distribution may be a fair approximation
to a peaked PDF. Use of a Gaussian distribution with iy values
interpolated to release height is often better than use of the
nearest "representative" PDF measured at some other height on the
tower.
• Lift overestimates concentrations on the windward side of the hill
at times. To alleviate this problem, further modifications may be
needed to account for a "dynamic" HC surface (one that may rise
part way up the hill), or to account for (as yet conjectured)
convergence effects caused by the topography at CCB.
• A good estimate of az (x) in the absence of the hill is
crucial to evaluating the structure of the models. Both Neutral
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and Lift overestimate concentrations by a wide margin at times,
apparently because
-------
The modifications we have made to the models encourage their
applicability to sites other than CCB, and make them more useful for
estimating concentrations over several hours. The Lift model incorporates a
measure of the crosswind aspect ratio of the terrain feature. The Wrap
model estimates concentrations at more than one point across the hill
surface. For both models, estimates can be averaged over a 24-hour period,
for example.
The Wrap model estimates (and, in fact, the observed concentrations)
are very sensitive to the actual shape of the horizontal wind direction
distribution when the winds are very light and variable. When the plume is
released above Hc, concentrations over the top of the hill are extremely
sensitive to the size of az. Therefore, the meteorological data should
be measured on-site, at levels representative of plume height. This is
strongly underscored by the CCB field results; often the meteorological data
available within 20-30 m of the release height were inadequate to describe
wind characteristics at release height at the same moment in time. This is
especially true under conditions of light winds and very stable flow.
A number of uncertainties must be better bounded to make further
progress in the development of these complex terrain models. Because of
uncertain CTZ values for a number of the case hours studied, an adequate
evaluation of the terrain factor formulation in Lift could not be
completed. We need to decide, with better assurance than we now have,
whether or not the simple way we interpolated Tc is appropriate (for CCB
at least); and we also must learn whether the scheme is appropriate for
other differently-shaped hills. We expect, for example, that the strength
of the thermal stratification above and below Hc may influence Tc but
any such effects in the case studies at CCB were probably masked by az
uncertainties.
Although HC differentiated well between "neutral" and "stable" layers
at CCB, we must see if the HC parameter works as well in distinguishing
flow regimes for two-dimensional ridges. Most of the modeling concepts we
have adopted should be evaluated at a ridge site. These include: terrain
correction factors, plume distortion, and dynamics of flow around (or along)
the terrain. At CCB, plume material below Hc could pass over the
saddle—but we cannot answer the question: How high might the plume have
risen if there were no draw or saddle at CCB?
We have also made some untested conjectures about convergence or
channeling effects in the draws at CCB. These should be evaluated, because
they could have broad applicability to a wide range of terrain shapes.
Some recommended approaches for addressing these problem? are presented
in the next section.
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6.3 Recommendations for Further Study
More information is needed to better evaluate the individual algorithms
describing flow and dispersion around CCB, and also to extend the
formulation to other sites. This information can be acquired through
additional analyses of the CCB data base, new and old fluid modeling
investigations, and new or recently acquired field measurements.
Flow, Turbulence, Waves, and Eddies
Although 1-hour iz data measured away from the hill at Tower A
compare favorably with 1-hour iz values inferred from averages of
photographic and lidar scanning of the oil-fog plume, the correspondence
among 5-minute data was not as good. This was attributed in part to spatial
and temporal variability in the turbulence field. Because there appeared to
be some organization to this variability, the role of gravity waves and
eddies was postulated. More analysis of the data is needed to better define
the source of this variability, and to understand the mechanisms of
turbulence production in the flow at CCB.
Because the flow structure over the hill changes over periods of one
hour, and because the turbulence also changes, any relationship between the
flow field and the turbulence field could be important in modeling the
1-hour average concentration field correctly. Analyses of profiles of
winds, turbulence, and temperatures measured away from the hill at Tower A
and over the hill at Tower B will be undertaken to identify the
characteristics of the spatial and temporal variability in the turbulence
field (particularly iz), to relate these characteristics to the local
dynamic stability of the flow reflected in the wind and temperature
profiles, and to assess the importance of flow variability and turbulence
intermittancy in modeling 1-hour average concentrations.
The expression for 0Z currently in the models includes a trend with
distance that is in general agreement with 1-hour averages of lidar
measurements upwind of CCB. Because the interpretation of concentrations
over the top and back sides of the hill depends critically on knowing what
the "flat terrain" value of az would have been at corresponding
distances, the assumed distance dependence of az should be validated at
larger distances from the source. In addition, because the az equation
was adjusted to the lidar data through the parameter p, an independent check
on the value of this parameter is needed. ,
Information required to perform these analyses may indeed be available
in the CCB lidar data base, but at present we simply do not know whether or
not sufficient lidar sampling data were obtained from plumes passing well to
the side of the hill, because to date only a portion of the CCB lidar data
has been reduced. Supplementary information may also be available from the
experiments conducted at the BAO tower by WPL; again, we do not know at
present. This is one of the key modeling purposes, we feel, to be- addressed
313 3
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in a comprehensive lidar plume sampling program. Plans should be made to
sample plumes released during this fall's field experiment at the Hogback
with this in mind.
Analysis of Tc
The terrain correction factor Tc is controlled by turbulence levels
over the hill in concert with plume deformation. Therefore, we do not
expect Tc to be a simple function of overall terrain shape only. Neither
do we anticipate that all complex terrain modeling can be formulated wholly
in terms of Tc and level terrain Gaussian plume models. However, we do
feel that Tc, as inferred from observed concentrations and estimated
(level terrain) concentrations, can be useful in assessing the importance of
deformation and turbulence as a function of hill shape, meteorology, and
location (i.e., crest, lee, or windward face).
With progress in reliably estimating plume growth (see az
discussion above) in stably stratified flows over flat terrain, especially
over downwind distances of 1-2 km at CCB, inferred Tc patterns may be more
instructive. However, a better method for calculating Tc patterns is
needed to remove differences between the modeled plume trajectory and the
average of observed plume trajectories (as reflected in the distribution of
tracer gas concentrations). One method to be evaluated is a wind direction
optimization scheme which would compute a plume trajectory that would be
consistent with the observed concentration field. Once useful Tc patterns
are developed, they will guide the investigation of plume deformation and
turbulence mechanisms. This study will rely on analyses of wind and
temperature data from the five meteorological towers on CCB to discern flow
field characteristics, and it will also rely on an analysis of turbulence
daL- measured at these towers as well as those measured in the flow away
from the hill (tower A) to discern changes in turbulence over the hill.
Additional information can be extracted from fluid modeling studies
already completed for a range of simplified terrain shapes and meteorology.
Further analyses of these studies should help in interpreting the more
complicated patterns of Tc values inferred from observed concentrations at
CCB; and they should also provide an additional source of data for
developing and testing models for estimating the effects of flow deformation
and turbulence on plumes in complex terrain. The data to be obtained at the
Hogback will similarly help to illuminate the structure of Tc for flows in
ridge geometries
Generalization of HC
HC has been found to be a very useful measure to differentiate flow
behavior at CCB. Because the simple energy balance argument implicit in
Hc is at least as applicable to ideal two-dimensional flows as it is to a
three-dimensional hill, HC should be, we expect, equally useful in
describing flows near long ridges. Because flows over ridges at low Froude
numbers are very difficult to simulate correctly in tow tanks because of
nonstationarity (see Appendix), the field program at the Hogback offers the
314
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best present opportunity to acquire physical data to evaluate the usefulness
of Hc in describing flows toward a ridge feature.
Dynamics of the HC Surface
flows above and below HC have been modeled as though the two regions
were completely independent. This is a convenient simplification, but it
fails to reproduce important features of the observed flow field and tracer
concentration pattern. Because the theory describing the dynamics of the
flow near Hc is inherently non-linear, simple adjustments are better
parameterized and validated through field experiment and fluid modeling. By
putting more emphasis on describing the structure of the flow near the Hc
surface, we hope to make progress in coupling the Lift and Wrap model
concepts together in one model for complex terrain applications.
Much has already been learned from fluid modeling studies of stratified
flow over simple hill shapes. This information should be included in the
model' formulations. Also, more information may be obtained from additional
analyses of the CCB temperature data (e.g., performing the isentropic
analysis with the data from the 10-m towers on CCB).
Flow Channeling Effects
Small scale variations in the inferred terrain correction factors may
arise because of local terrain effects. The analysis of concentration
patterns at CCB suggest the possibility of flow channeling, which is
important because it would tend to encourage plume material to flow up and
over the saddle between the two peaks in very stable conditions (when the
plume might otherwise be expected to travel around the sides) and also
because it would tend to lift a plume in neutral flow farther from the
surface of the saddle.
Perhaps the best method for studying this type of topographical effect
is fluid modeling: a simple experiment could be designed to compare
streamline heights over the center of a model of CCB with streamline heights
over a modified model of CCB with the peaks removed. (Other small
irregularities would be smoothed out of both models). The intent of such an
experiment is to search for a suitable parameterization of channeling
effects, which could be applied in the model for terrain features with gaps.
315 5
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Hanna S.R., 1981. Lagrangian and Eulerian Time-Scale Relations in the
Daytime Boundary Layer. J. Appl. Meteorol, 20; 243-249.
Holzworth, G.C. 1980. The EPA Program for Dispersion Model Development for
Sources in Complex Terrain. ISecond Joint Conference on Applications of
Air Pollution Meteorology, New Orleans, LA. Am. Meteorol. Soc.,
Boston, MA. I
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Horst, T.W., 1973. Corrections for Response Errors in a Three-Component
Propeller Anemometer. J. Appl. Meteorol., 12: 716-725..
Hovind, E.L., M.W. Edelstein, and V.C. Sutherland 1979. Workshop on '
Atmospheric Dispersion Models in Complex Terrain. EPA-600/9-79-041.
U.S. Environmental Protection Agency, Research Triangle Park, NC.
Hunt, J.C.R., 1982. Diffusion in the Stable Boundary Layer. In
Atmospheric Turbulence and Air Pollution Modelling, D. Reidel
Publishing Company, Dordrecht, Holland.
Hunt, J.C.R., and R.J. Mulhearn 1973.:Turbulent Dispersion from Sources
.Near Two-Dimensional Obstacles. J. Fluid Mech., 61: 245-274.
Hunt, J'.C.R. and J.S. Puttock, and W.H. Snyder 1979. Turbulent Diffusion
from a Point Source in Stratified and Neutral Flows Around A
Three-Dimensional Hill (Part I - Diffusion Equation Analysis). Atmos.
Environ., JL3_: 1227-1239. '
Hunt, J.C.R., and K.J. Richards, 1982. Stratified Shear Flow Over Low
Hills. To be published. ,
Hunt, J.C.R. and W.H. Snyder 1978. Flow Structure and Turbulent Diffusion
Around A Three-Dimensional Hill. (Part II - Surface Concentrations Due
to Upstream Sources - unpublished manuscript).
Hunt, J.C.R. and W.H. Snyder 1980. Experiments on Stably and Neutrally
Stratified Flow Over A Model Three-Dimensional. Hill. J. Fluid Mech.,
96_: 671-704.
Irwin, J.S., 1979. Estimating Plume Dispersion-A Recommended Generalized
Scheme. In preprints of Fourth Symposium on Turbulence, Diffusion, and
Air Pollution, Reno, NV, Jan 15-18, 1979, pp62-79, Am. Meteorol. Soc.,
Boston, MA.
Izumi, Y. , Barad, M.L. 1970. Wind Speeds as Measured by Cup and Sonic
Anemometers and Influenced by Tower Structure. J. Appl. Meteorol., 9^:
851-6.
Jackson, P.S. and \T.C.R. Hunt, 1975. Turbulent Wind Flow Over A Low'Hill.
Quart. J.R. Met. Soc., 101; 929-955.
Lavery, T.F., A. Bass, D.G. Strimaitis, A. Venkatram, B.R. Greene, P.J.
Drivas and B.A. Egan, 1982. EPA Complex Terrain Model Development
Program: First Milestone Report - 1981. EPA-600/3-82-036,
U.S. Environmental Protection Agency, Research Triangle Park, NC, 304p.
Moses, H. and H.G. Danbek, 1961. Errors in Wind Measurements Associated with
Tower-Mounted Anemometers. Bulletin of AMS, 42; 190-194.
Panofsky, H.A., 1982. Personal Communication.
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Pasquill, F., 1976. Atmospheric Dispersion Parameters in Gaussian Plume
Modeling: Part II, Possible Requirements for Change in the Turner
Workbook Values. Report EPA-600/4-760306, U.S. Environmental Protection
Agency.
Pond, S., W.G. Large, M. Miyake, and R.W. Burling, 1979. A Gill Twin
Propeller—Vane Anemometer for Flux Measurements During Moderate and
Strong Winds. Boundary Layer Meteorology, 16; 351-364.
Rayment, R., 1970. Introduction to the Fast Fourier Transform (FFT) in the
Production of Spectra, Met. Mag., 99: 261-269.
Rowe, R.D., S.F. Benjamin, K.P. Chung, J.J. Havlena, and C.Z. Lee, 1982.
Field Studies of Stable Air Flow Over and Around A Ridge. Atmos. Env.
16_: 643-653.
Scorer, R.S., 1949. Theory of Waves in the Lee of Mountains. Quart. J.R.
Met. Soc., 75_: 41-55.
Sheppard, P.A., 1956. Airflow Over Mountains, Quart. J. R. Meteor. Soc., 82;
528-529.
Smith, R.B. 1980. Linear Theory of Stratified Hydrostatic Flow Past an
Isolated Mountain. Tellus, 32; 348-364.
Snyder, W.H., R.E. Britter and J.C.R. Hunt, 1980. A Fluid Modeling Study of
the Flow Structure and Plume Impingement on a Three-Dimensional Hill in
Stably Stratified Flow. Proc. Fifth Int. Conf. on Wind Engr. (J.E.
Cermak, ed.), !_: 319-329, Pergamon Press, NY, NY.
U.S. E.P.A., 1976. Quality Assurance Handbook for Air Pollution Measurement
Systems. Vol. I Principles. Research Triangle Park, N.C. EPA
600/9-76-005.
Van Ulden, A.P. 1978. Simple Estimates for Vertical Diffusion from Sources
Near the Ground. Atmos. Environ., 12; 2125-2129.
Wyngaard, J.C. 1981. Cup, Propeller, Vane, and Sonic Anemometers in
Turbulence Research. Annual Review of Fluid Mechanics, 13; 399-423.
318
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APPENDIX A
THE STRUCTURE OF STRONGLY STRATIFIED FLOW OVER HILLS
DIVIDING STREAMLINE CONCEPT
319
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THE STRUCTURE OF STRONGLY STRATIFIED FLOW OVER HILLS
Dividing-Streamline Concept
William H. Snyder1
Roger S. Thompson
Robert E. Eskridgel
Robert E. Lawson, Jr.l
Meteorology & Assessment Division
Environmental Sciences Research Laboratory
Environmental Protection Agency
Research Triangle Park, NC 27711
Ian P. Castro
Department of Mechanical Engineering
University of Surrey
Guildford, Surrey, England GU2 5XH
J.T. Lee
Los Alamos National Laboratory
Los Alamos, NM 87545
Julian C.R. Hunt2
Department of Applied Mathematics and Theoretical Physics
University of Cambridge
Cambridge, England CBS 9EW
Yasushi Ogawa
National Institute for Environmental Studies
P.O. Yatabe, Ibaraki 305, Japan
August 1982
1) On assignment from the National Oceanic and Atmospheric
Administration, U.S. Department of Commerce.
2) Also, Department of Engineering.
320
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PREFACE
This report pulls together the results of a whole series of experiments
done by numerous investigators and for a variety of different purposes. The
overall objective, of course, was to gain fundamental understanding of flow
and diffusion under stably stratified conditions in complex terrain, but the
individual projects were designed with very specific purposes in mind.
Nevertheless, one aspect of each of the projects was to examine the concept
of a dividing-streamline height, as it has very important consequences in
the assessment of pollutant concentrations in complex terrain. This paper
was written for submission to a journal for possible publication; its
inclusion as an appendix to the CTMD second milestone report is felt to be
justified on the basis of providing additional support and guidance to
(1) mathematical modelers attempting to expand their models to include a
wide variety of terrain shapes and approach flows and (2) planners of the
second Small Hill Impaction Study which is to take place at The Hogback
Ridge in northwestern New Mexico, a very long, 100 m high ridge of fairly
steep slope that is cut periodically by narrow river valleys. Because of
the urgency in getting information to the planners and modelers as soon as
possible, the paper is included here in essentially draft stage.
321
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ABSTRACT
Several laboratory experiments are described that test the
applicability of an integral formula for the dividing-streamline height in
strongly stable flow over hills. The dividing-streamline concept is based
upon simple energy arguments; fluid parcels originating far upstream of a
hill at elevations HR above the dividing-streamline height Hs will have
sufficient kinetic energy to rise over the top, whereas those below Hs
must pass around the sides. The concept is found to be valid when
interpreted as a necessary but not sufficient condition for wide ranges of
hill shapes, density profile shapes, and wind angles, and in strong shear
flows as well. Further, studies on strongly stratified flow over
two-dimensional hills show that steady-state conditions are not established
in a finite-length towing tank; these measurements also suggest that a very
long tank would be required for steady-state conditions to be established
upstream of long ridges with small gaps and cast doubt upon the validity of
previous laboratory studies.
322
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SECTION 1
INTRODUCTION
Hunt and Snyder (1980) conducted towing-tank experiments to test
Drazin's (1961) theory for low-Froude-number flow over three-dimensional
obstacles. They verified that for a bell-shaped hill, a linearly stratified
environment and an effectively uniform approach-flow velocity profile,
Drazin's theory was applicable in the range F<0.4, where F is the Froude
number (F=U/Nh, U being the towing speed, N the Brunt-Vaisala frequency and
h the hill height). They showed evidence for a dividing streamline (on the
center plane determined by the flow and the axis of the axisymmetric hill)
of height Hs such that streamlines below Hs would impinge on the hill
surface and follow the surface around the sides, whereas streamlines above
Hs would go over the top. Moreover, they suggested the simple formula
H = h(l-F)
(1)
as the criterion for determining whether a plume embedded in the flow
approaching the hill would impact on the surface or surmount the top, for
Snyder et al. (1980) presented further laboratory evidence in support
of the simple formula; they showed that it was applicable to other shapes of
axisymmetric hills, including a cone and a hemisphere. Furthermore, they
presented another simple formula (and experimental data to support it) for
determining whether an elevated (step) inversion would surmount a hill.
This second formula is
1/2 1/2
I = (2(h/hQ-D)
(2)
where g is the acceleration due to gravity, h0 is the height of the
interface, Ap is the density difference across the interface^ and p]_
is the density of the fluid between the interface and the surface.
A more general formula for determining this dividing-streamline height
was, in fact, suggested by Sheppard (1956), based upon simple energy
arguments. He asked the question: in a strongly stratified flow
approaching a hill, does a particular fluid parcel at some height upstream
323
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possess sufficient kinetic energy to overcome the potential energy required to
lift the parcel through the (potential) density gradient from its upstream
elevation to the top of the hill? His formula may be written as
(H )
s
g
(3)
where the left side may be interpreted as the kinetic energy of the fluid
parcel far upstream at elevation Hs, and the right side as the potential
energy gained by the parcel in being lifted from the dividing streamline
Hs to the hill top h through the density gradient dp/dz. This integral
formula is, of course, applicable to a fluid with any shape of stable
density profile and, presumably, with any shape of approach-flow velocity
profile. In practice, it must be solved in iterative fashion, since the
unknown Hs is the lower limit of integration. It is not difficult to show
that the formula reduces to the simpler formulas (1) and (2) using the
boundary conditions applicable to those special cases.
The concept of a dividing-streamline height, of course, has very
important consequences in the assessment of pollutant concentrations from
sources located in or near complex terrain. For example, because of the
essentially horizontal flow field below Hs, plume diffusion from a point
source can be modeled by considering horizontal flow and horizontal
diffusion alone, i.e., the three-dimensional problem is reduced to a
two-dimensional one of diffusion from a line source about a circular
cylinder (Hunt et al. 1979). This treatment suggests, and experiments by
Snyder et al. (1980) support, that maximum surface concentrations under such
conditions may approach or even exceed those that would have existed at the
center of the plume in the absence of the hill. These concentrations are,
of course, very much larger than would be obtained from a plume diffusing
normally onto a surface.
Questions that naturally arise concern the applicability of the simple
integral formula and these laboratory results to the atmosphere. For
example, is the formula still applicable as the hill is elongated into a
ridge? What if the ridge is not perpendicular to the approach wind? Is the
hill slope important? What is the effect of shear in the approach flow, as
most certainly occurs in the atmosphere? And, of course, the density
structure of the approach flow is seldom linear; more typical is a strong
surface-based inversion with a weaker gradient approaching neutral above.
A few other studies have shed light on some of these problems. Baines
(1979), for example, conducted towing tank studies of low-Froude-number
flows around a barrier with a gap. His results suggest
Hs/h = 1-2F
(4)
324
-------
for barriers with very small gaps, tending toward Hs/h = 1-F for those
with wider gaps. Weil et al. (1981) conducted similar towing-tank studies,
extending the work of Baines, and found quite similar results. However,
some doubts are expressed (see later discussion) concerning (1) the
experimental techniques, (2) the establishment of "steady-state" conditions,
and (3) the interpretation of results in view of the fairly substantial
scatter in the data.
Data from a field study by Rowe et al. (1982) of stable air flow over a
"long" ridge show much better agreement with the data for axisymmetric hills
(Equation 1) than for ridges with gaps (Equation 4).
A major field study was designed (Holzworth 1980) and the first phase
was conducted (Spangler and Taylor 1982; Lavery et al. 1982 a&b) based
partly upon the results of the laboratory studies described above. This
field study also tended to confirm Equation 3; indeed, Hs was computed in
real-time from incoming meteorological data and used to determine
operational strategy during the field experiment.
In conjunction with that field study, several more laboratory
experiments were conducted to test the general validity of the integral
formula (Equation 3) and to assess its limits of applicability. These
laboratory experiments included:
1) Towing tank studies on a model of the field-study hill called
Cinder Cone Butte in southwestern Idaho. It is an isolated, 100 m
high, roughly axisymmetric hill in the flat, broad Snake River
Basin. Density profiles were set up in the tank to simulate (in
somewhat idealized fashion) those expected during the field-study
period, i.e., strong surface-based inversions over a fraction of
the hill height with weaker (but stable) gradients above to
several hill heights, and towing speeds were established to
simulate field conditions. Dividing-streamline heights were
calculated according to Equation 3 and neutrally buoyant,
different-colored dyes were released upstream slightly above, at
and slightly below the calculated Hs. Visual and photographic
observations were made to establish an observed
dividing-streamline height, which was then compared with the
predicted dividing-streamline height.
2) Towing tank studies on truncated, steep-sided ridges of various
crosswind aspect ratios. These included examination of upstream
"blockage" regions, surface flow patterns and lee-wave structure
and will be reported separately (Castro and Snyder 1982); only
those aspects dealing specifically with the dividing-streamline
concept will >be reported here.
3) Stratified wind tunnel studies on shear flow over vertical fences
of various crosswind aspect ratios and over a model of Cinder Cone
Butte.
4) Towing tank studies on a truncated sinusoidal ridge with a maximum
slope of 40° positioned perpendicular and at other angles to the
approach wind direction.
325
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5) Towing tank studies on an "infinite" triangular ridge and a long
sinusoidal ridge to test the validity of the "steady-state"
assumption of flow upwind of an obstacle under strongly stratified
conditions.
The results of these laboratory experiments are reported herein.
Section 2 provides a rigorous derivation of Sheppard's integral formula and
presents a discussion of blockage effects and upstream influence.
Experimental apparatus, techniques and models are described in Section 3.
Results are presented in Section 4 and conclusions in Section 5.
326
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SECTION 2
REVIEW OF THEORY AND EXPERIMENTS
2.1 Overview
Several theoretical and experimental studies have been performed to
analyze the influence of two-dimensional objects on stratified flow. Much of
the work has been concerned with describing the formation and structure of
lee waves. Some effort, however, has been directed towards determining
conditions under which the upstream flow may be "blocked" by the obstacle. A
description of the path of the dividing streamline for two-dimensional hills
would prove useful in determining the fate of pollutants released upwind of
such hills.
Laboratory studies have been performed by towing freely-mounted or
surface-mounted, two-dimensional objects in layered or continuously
stratified tanks. Many questions remain as to how the results of these
experiments performed in a tank of finite depth and length apply to the
atmosphere. The dimensions of the tank determine possible wave motions of
the fluid.
One feature of stratified experiments conducted in finite towing tanks
that has not been adequately addressed is how the upstream conditions change
during a tow. A fixed end on the tank provides a uniform approach velocity
profile at a distance upstream of the obstacle that varies as the experiment
progresses. If fluid is blocked by the obstacle, the density gradient will
be modified by the blocked fluid as the blockage influence is observed
farther and farther upstream. The assumption usually made, that the approach
flow density gradient remains, throughout the tow, equivalent to the density
gradient at the onset of the tow, could lead to a misinterpretation of the
ob s erva t ions.
In applying the theory of the dividing-streamline height to
three-dimensional axisymmetric hills, the portion of the flow with
insufficient energy to surmount the hill top was able to pass around the
sides. However, the fluid blocked by a two-dimensional hill is trapped
upstream. If the aspect ratio (width of hill perpendicular to flow divided
by hill height) is taken as the experimental variable, the value at which the
centerline flow deviates from the patterns established for axisymmetric cases
can be determined. A complication that arises in towing tank experiments is
that the amount of the test section cross-sectional area that is blocked must
remain below some limiting value. As will be discussed later, the ratio of
the area occupied by the model to the area that would be occupied if the
model were extended to the width of the tank is important in stratified flow.
327
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Long (1953, 1954, 1955) performed both theoretical'and experimental
analyses of two-layer and continuously stratified flow over "easy" shapes in
a finite tank. Long made the hypothesis of an undisturbed approach flow at a
sufficient distance upstream of the obstacle. He was interested in the
upstream propagation of gravity waves rather than blockage effects, and thus,
did not perform experiments at low Froude numbers. The reality of Long's
hypothesis has been the subject of much controversy and has been discussed by
Long (1972), Mclntyre (1972) and more recently by Baines (1977). Application
of Long's hypothesis to a tank experiment implies that for a portion of the
experiment, presumably near the middle of the tow, a "steady-state" exists.
Wei et al. (1975) towed a 1-inch circular cylinder, a 2-inch circular
cylinder, and a 1-inch flat plate through a linearly stratified fluid.
Upstream columnar disturbance modes were observed for Froude numbers based on
the half depth of the tank from 0.084 to 0.24. The disturbances appeared as
unattenuated horizontal jets. Froude numbers based on the radius of the
cylinders (or half-width of the plate) ranged from 0.78 to 4.72. The larger
cylinder towed at a Froude number of 0.78 was the only case with a Froude
number less than 1.0. In this case, the fluid to at least 27 radii upstream
approached the cylinder at a speed of about 0.7 times the towing speed. A
layer of blocked fluid was not apparent. A tow at a Froude number of 1.10
exhibited a fluid layer upstream of the cylinder with a speed toward the
cylinder of 0.9 times the towing speed. This layer extended upstream a
distance of at least 27 times the radius of the cylinder.
Baines (1979) studied stratified flow past a surface-mounted,
two-dimensional barrier and barriers with gaps at the ends with gap widths
G = 1/16, 1/8 and 3/8 (G is defined as the fraction of area removed from the
model that spans the width of the tank). The cross-section of the hill was a
"Witch of Agnesi" shape with a maximum slope of 39.4°. Neutrally buoyant
beads were placed in the fluid to observe the flow over the two-dimensional
model. The flow over models with gaps was observed by releasing dye at
various heights upstream. The density of the dye was adjusted to be
neutrally buoyant at approximately one-half of the barrier height. Thus,
when the release was below this height, the dye was buoyant. The magnitude
of the errors introduced by this buoyancy was not addressed.
Baines made his observation "after steady-state was reached (estimated
by direct observation) and before the reflected upstream motions arrived".
The criterion for the existence of blocked fluid upstream of a
two-dimensional barrier was found to be F < 0.5 (±0.05) based on the
barrier height. The depth of blocked fluid was found to be approximately 0.5
and essentially independent of Froude number. For the barriers with gaps of
G - 1/16 and 1/8, he concluded that the blockage criterion for the
two-dimensional case applied. Further, the height of the dividing streamline
was found to be given by h(l-2F). However, for the barrier with G = 3/8, the
dividing-streamline height (as deduced from Baines1 Figure 7) was more nearly
h(l-0.7F).
328
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Overall, observations of Weil et al. (1981) tended to support those of
Baines (1979), but regarding the depth of blocked fluid upwind of a
two-dimensional ridge, Weil et al. found zb/h = 1-2F, as opposed to the
nearly constant depth of zb/h = 0.5 for 0
-------
The hydrostatic balance of the atmosphere can be expressed as
dP
dz
(6)
where the subscript e is used to denote a local environmental value.
the assumption that P = Pe and combine Equations 5 and 6 to get
Recall
+ gz)
g dz
(7)
Application of the equation of state for dry air yields
2 T_T
C-) g dz
(8)
where T is the absolute temperature. Assuming the existence of a streamline
originating at a height Hs that approaches a stagnation point on the
hilltop (z=h), Equation 8 can be integrated between these limits to obtain
the integral formula
2 ,h
q (HJ - 2g , R
T-T
(9)
Since the parcel moves adiabatically, T = Te (Hs) +Ycl(z-Hs), where
Yd is the dry adiabatic lapse rate. Thus,
q (Hs) =-
e s
T (z)
e
-dz
(10)
This expression can be written in terms of potential temperature 6 through
the application of Poisson's equation
0.286
e
(11)
Integrating by parts, and noting that 8e (Hs)/0e(z) =: 1,
2 fh
CH°)=2S ' \ -p
rh ,
h-z
l*«*^
(22S) dz
dz
(12)
Equation (10), however, is a simpler computational form.
330
-------
To obtain a corresponding formula for flow in a water tank, Equation 7
can be written as
= g(
p-p
dz*
(13)
where z* is directed downward (models are inverted and towed along the
surface of the water tank). Again, assuming the existence of a dividing
streamline, Equation 13 can be integrated to obtain
2
q (H *) = 2g
s P
h
J Po (z*)dz* - g(h-H *)
H * e
(14)
Adding and subtracting hpe(h) and integrating by parts gives
e s
a-*)
(15)
In general, these formulas must be solved iteratively to obtain the height
of the dividing streamline.
As was pointed out earlier, this formula may be reduced to Hs/h = 1-F
under conditions of uniform velocity and linear density gradient. This
assumes that all kinetic energy is converted into potential energy. A more
general formula allowing for only a portion of the kinetic energy to be
converted is Hs/h = 1 - aF, with OKI. In neutral flows, the
pressure field set up by the body will allow kinetic energy along a
streamline to increase (e.g., speed-up over a hill). Hence, a is not
necessarily less than 1 for all F, but the pressure effects are expected to
be small for F<1. The data of Baines (1979) and Weil et al. (1981),
however, suggest that a is greater than 1.0, indeed, as large as 2.0 for
long ridges with narrow gaps. As discussed in the next section and as shown
by the experiments described in Section 4, the validity of their
experiments, or at least the applicability of their results to the
atmosphere, is questioned.
2.3 The Squashing Phenomenon
Drazin's (1961) theory of flow over hills suggests that in the limit of
extreme stability (F •> 0), vertical motions are inhibited, i.e., the flow
is constrained to move in horizontal planes. Let us now imagine a
stratified towing tank of finite length L in which we tow a two-dimensional
obstacle of finite height h at very low speed (i.e., approaching F = 0).
Let us further imagine that the fluid is incompressible and that the tow is
begun at one end of the tank. The fluid initially in the layer between the
331
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top and bottom of the obstacle must conserve its volume (Lh) because of the
incompressibility assumption. Hence, as the distance between the obstacle
and the opposite end wall of the tank decreases (even infinitesimally), the
height of the layer increases (also infinitesimally). What happens in
practice, of course, is that this fluid spills over the top and/or bottom of
the obstacle, filling the void behind it. If the obstacle moves a
distance x down the tank, a volume hx is displaced and fills the void in the
lee. Because of the inhibition of vertical motions, the fluid filling the
void must come from thin layers just below the top and just above the bottom
of the obstacle. Because there are no dynamics involved (U -> 0), these
layers must extend from the obstacle to the opposite end of the tank, and
their thicknesses are xh/2(L-x) each.
The fluid remaining in the space ahead of the obstacle has its density
gradient modified by the multiplicative factor 1-x/L. This phenomenon will
be referred to as the "squashing" phenomenon in analogy with water spilling
over the top of a bucket when the sides are "squashed". These finite
changes in height of fluid parcels upstream of the obstacle are prohibited
by Drazin's theory, which allows only infinitesimal changes of elevation as
the velocity approaches zero.
Of course, in a real towing tank, the obstacle must be towed at some
finite speed, so that dynamics must become important. However, Drazin's
theory has been largely confirmed experimentally and extended (ultimately to
F - 1) by Riley et al. (1976), Brighton (1978) and Hunt and Snyder (1980),
and the experiments to be described in Section 4 certainly confirm the
existence of essentially horizontal flow around three-dimensional obstacles
(including very long ridges) below some height Hs (indeed, the formula
Hs/h = 1-F was derived by Hunt and Snyder (1980) on the basis of Drazin's
theory, not as a special case from Sheppard's integral formula). Hence, we
might expect Drazin's theory (and Sheppard's formula) to apply to alj^
obstacle shapes, including two-dimensional ones.
The results of Baines (1979) and Weil et al. (1981) for two-dimensional
ridges and ridges with small gaps were surprising because they suggested
that fluid parcels could surmount the hills even though they had
insufficient kinetic energy far upwind to do so. It is here suggested that
their results are due largely to the squashing phenomenon, i.e., the gaps in
their ridges were insufficiently large to allow a "relief value" to avoid
the squashing.
This squashing phenomenon seems to have no counterpart in the
atmosphere. If true blocking occurred upwind of an "infinite" ridge in the
atmosphere, it seems that the flow would be blocked to infinity upwind
(i.e., there is no "end-wall" forcing the flow toward the ridge). In more
practical terms, "blocking" upstream of a very long ridge would imply
"upstream influence" to very large distances, possibly through an upstream
propagating front, which would imply non-steady-state behavior. From
another viewpoint, there are no infinite ridges, so that fluid parcels can
always be diverted around the obstacles without changing their elevation.
332 -
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2.4 Upstream Influence and Blocking of Flow over Hills
The energy argument given in Section 2.2 assumes steady-state
conditions upwind of the obstacle. The very low Froude number arguments of
Section 2.3 show that the density profile is continuously modified as, an
obstacle is towed along the tank, due to the squashing phenomenon. At small
but finite Froude number (say, 0.1 < F < 1), it is well known that the
steady-state assumption is incorrect upwind of two-dimensional obstacles.
"Columnar disturbance modes", which are gravity waves of wave number zero,
can propagate upstream. They are not generated near the obstacle, but in
the tails or terminal zones of the lee waves (Mclntyre, 1972).
The dispersion equation for waves in a tank of finite depth d is (see
Turner 1979; Wei et al. 1975) ., .
w (k +
2 2
4n ir
2 2
•) - N k - = 0
(16)
where k=2rr/X is the horizontal wave number, n is the mode in the
vertical, and w is the circular frequency. Columnar disturbance modes, k=0,
have frequency w=0, but group velocity
If
(17)
Since energy is transported at the group velocity, when Cg(n) > U,
energy will be transmitted upstream of the obstacle. Upstream disturbances
are thus generated whenever
-
Nd
mr
(18)
When 1/2TT < F < 1/TT, only one mode can propagate upstream; when
l/3ir < F < 1/2TT, modes 1 and 2 can propagate upstream, etc.
However, as Baines (1979) has pointed out, if the obstacle height h is such
that h>d/2n, the nth mode will be inhibited because the obstacle height
will exceed 1/4 of its verical wavelength and extend into the region of
"reversed" flow for that particular wavelength.
It is clear that the upstream, long waves arrive first, yielding a
broad velocity profile. Short waves, which travel more slowly, arrive later
and result in a region that moves with the velocity of the Cylinder. These
waves eventually reflect from the upstream end-wall of the tank, then
propagate back downstream to influence the flow in the vicinity of the
obstacle. Baines (1979) believed that valid observations could be made of
333
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the flow over and around the obstacle in isolation (in the absence of end
effects) by making the observations after steady state was reached
(estimated by direct observation) and before the reflected upstream motions
arrived. Evidently, he believed that a local steady state was achieved in
that at some not-too-distant point upstream of the obstacle, steady-state
velocity and density profiles were established before the reflected motions
returned to modify them. His results, however, were not specified based
upon the local steady-state conditions, but rather upon the towing speed and
initial density gradient.
The goal of the experiments to be described in Section 4.5 was to test
whether a local steady-state condition is in fact achieved at some
not—too-distant point upstream. For example, does there exist a portion of
the tow wherein the density profile is in steady state, i.e., where it does
not change shape with distance? Another way of asking the question is: At
some point upwind of the obstacle (say ten hill heights), is there a
significant period of time during the tow (in which to make observations)
wherein all upstream propagating modes have passed the point (and so that a
steady-state has been reached) and, at the same time, no upstream modes have
been reflected from the end-wall of the tank and returned to influence the
flow at the point?
2.5 Effects of Shear and Hill Slope on Flow Structure
In the first order solution of Drazin (1961), the flow is assumed to be
inviscid and two-dimensional in horizontal planes with no vertical
coupling. Brighton (1978) has shown how to extend this solution to higher
order, and has shown how to calculate small vertical deflections of
streamlines arising from the vertical pressure gradients requried by the
two-dimensionality of the flow. For an obstacle with circular contours of
radius Ro (and in the absence of rotation), Brighton has shown that the
streamline deflection ,
dU R R
6 = !_[„ °_£_ (2COS26- —
N2 ° dz r2 r2
2U
„ dR R
V_° (COS26. ^
(19)
where U0 is the approach flow velocity (U0 = U0(z)), and (r,0) are
cylindrical coordinates. The first term represents the displacement due to
shear in the approach flow and the second, that due to the slope of the
hill. Assuming dUo/dz > 0 and dRo/dz < 0, it is easily seen that
the shear leads to a drop in the streamline upstream of the hill and a rise
as the fluid passes round the sides. The slope of the hill has just the
opposite effect, a rise upstream and a drop as the fluid passes round the
sides. Note that at the stagnation point, the deflection2due to the slope
is zero, whereas that due to the shear is negative (-U0/N ) (dUo/dz).
It should be pointed out that Equation 19 is valid only when
-------
Let us calculate some typical values to obtain a feel for the
contributions due to the two effects. Let Uo = 4 m/s at z=50m, N=0.1/s
(very strong stratification), Ro =500 m, h=100 m, and dRo/dz=2 (26.5°
slope). The contribution of the shear term at the stagnation point is 32 m,
a value that violates Equation 20, but is certainly indicative of the strong
effect the shear can have. The maximum deflection due to the slope term
occurs at 0=90°, and is -26 m, again violating Equation 20 and again
indicating strong effects. Considering the variability of instantaneous
wind and temperature profiles occurring in a typical nighttime stable
atmosphere, it is not difficult to imagine an extreme variability in plume
behavior as a plume encounters a hill!
For a general body where dRo/dz=0 (as for flow about vertical fences
or flat plates),
dU
& = -
[U
N
o dz
o(1_U_JML>]
(21)
U
where U and V are the horizontal mean velocity components. It is useful to
note that at the stagnation points, where vertical deflections of
streamlines may be expected to be largest, this expression reduces to
U dU
f o o
0 = 2-
N
dz
(22)
which is independent of the plate width. Hence, the centerplane flow
structure of strongly stratified flows about vertical plates (indeed, any
vertical-walled object) may be expected to be independent of aspect ratio.
335
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SECTION 3
APPARATUS
3.1 Towing Tank Experiments
Most of the experiments to be described were conducted in the large
stratified towing tank of the EPA Fluid Modeling Facility. The tank is
1.2 m deep, 2.4 m wide and 24 m long. The sides and bottom are lined with
acrylic plastic for viewing purposes. The model hills were mounted flush on
a 2.4 m square baseplate which was inverted and suspended from a carriage
such that the surface of the baseplate was submerged approximately 4 mm
below the water surface. The carriage permitted towing speeds from 3 to
50 cm/a. For additional details, see Thompson and Snyder (1976) or Hunt et
al. (1978).
Salt water was used to obtain stable density profiles and for the
present work with linear profiles, the Brunt-Vaisala frequencies were
nominally 1.33 rad/s. Towing of the models slowly eroded the linearity of
the density profiles at the top; this non-linear layer was skimmed-off daily
and the water height (108 cm) was restored by filling from the bottom with
saturated salt water (for additional details, see Castro and Snyder 1982).
The linearity and slope were we11-maintained, but there was an increasingly
deep region of saturated salt water at the bottom. In all cases, the depth
of the linear layer exceeded 80 cm (>8 hill heights), so that this
changing bottom boundary condition is not believed to have significantly
affected the results.
Twelve tows were made with the Cinder Cone Butte (CCB) model under
different density profiles, towing speeds, and dye-release heights as shown
in Table A-l. The density profiles consisted of strong near-surface
gradients (N ^ 2.5 rad/s) and weaker gradients above (N ^ 0.86 rad/s)
(in actuality the weaker gradients were below the stronger gradients, as the
models were towed upside down, but for purposes of clarity, the experiments
will be described as if the model were right-side-up). The depth of the
surface layer was initially set at 18 cm (1.25 h); this depth was
successively reduced (by skimming) on subsequent tows to 13, 8, and 5 (0.9,
0.56, and 0.35 h) to simulate different depths of typical nighttime stable
atmospheric flows. These density profiles are shown in Figure A-l, where it
may be observed that the initially sharp break-point between the two layers
was eroded slightly, but for practical purposes, the profiles are
well—described as two linear-gradient layers. The changes in the
Brunt—Vaisala frequencies were due primarily to changes in the reference
densities as opposed to changes in the slopes of the curves.
336
-------
TABLE A-l
SCHEDULE OF TOWS FOR CCB MODEL
TOW
No.
0
1
2
3
4
5
6
7
8
9
10
11
Breakpoint
Ht., cm
18
13
8
rad/s
2.6
2.4
2.2
2.3
rad/s
0.86
0.86
0.86
0.89
Release
Ht., cm
10
8
8
5
2
2
8
5
2
7
4
2
Speed
cm/s
5.0
10.
10.
18.
25.4
25.4
5.7
12,
21,
.5
.5
,3
.5
.5
5.8
11.3
17.4
Notes
height of hill, h = 14.4 cm
height of saddle point = 11.9 cm
337
-------
110
100 --
90 -•
80 --
70 --
UJ 60 •-
50 --
t- to -•
Ou
LU
Q
30 --
20 -•
10 -•
, - 1 - , - 1
A"
f-HILL HEIGHT
SADDLE POINT HEIGHT
A
A
A
A
A
A
A
TOW NUMBERS 0-4-^
A
A
A
A
A
1.05
,1-1
SPECIFIC GRAVITY
1.15
A
A
1.2
Figure A-l. Density Profiles for CCB model tows.
338
-------
Water samples were drawn each day from up to 100 elevations using a
rake and vacuum system. The density of each sample was determined by
measuring the displaced weight of a plumb bob suspended in the sample from
an electronic balance. The standard deviation in repetitive measurements of
specific gravity of a typical sample has been determined to be 0.0002.
These density profiles were fed into a PDF 11/40 minicomputer system
where the numerical integration of Equation 3 was performed to calculate the
towing speed required to obtain a desired Hs value. Dye mixtures were
emitted horizontally at each of three elevations at a distance of 160 cm up-
stream of the hill center. Each dye solution was neutrally buoyant at its
release elevation. Red dye was emitted at Hs and blue dye 1 cm above and
below Hs through 1.6 mm diameter tubing. According to the dividing
streamline concept, the upper streamer should pass freely over the hill and
the lower one should pass round the sides; the middle one, because of its
finite thickness, should split, with the upper portion passing over and the
lower portion passing round the sides. Visual and photographic observations
were thus made during each tow to ascertain the validity of Equation 3. In
practice, the accuracy of this determination was assessed to be
approximately +0.5 cm or +0.03 h.
The CCB model was constructed of acrylic plastic by vacuum molding onto
a wooden form. It was a 1:690 scale model made from enlarged U.S.
Geological Survey maps. A contour map (Figure A-2) shows it to be double-
peaked with a height of approximately 100 m (model height 14.4 cm), a
saddlepoint height of 83 m (model height 11.9 cm), and base diameter of 1 km
(model dia. 1.6 m). The maximum slope was approximately 26°. The wind
direction simulated during this series of tows was 110°, nearly perpendicular
to a line connecting the two peaks; hence, the flow tended to be channelled
through the draw between the two peaks. The appropriate hill height was
thus the saddle point height of 11.9 cm; this height was used in calculating
the dividing-streamline height from Equation 3 and the experimental
criterion was whether or not the dye streamers succeeded in passing through
the draw.
The ridge models were triangular in cross—section with height (9 cm)
equal to base length (63° slope). They were made of acrylic plastic. Four
models were used such that the spanwise width between the vertical end faces
was 1, 2, 4 or 8 h. They were mounted 10 h downstream from the leading edge
of the baseplate such that the ridge axes were normal to the tow direction.
A fairly substantial tripwire (5x5 mm) was mounted 5 cm from the leading
edge of the baseplate. Further details on these models may be obtained from
Castro and Snyder (1982). Dye releases were made on the ridge centerlines
about 8 h upstream at Hsjt^ 1 cm, as described for the CCB model above.
Full—depth linear density profiles were maintained by skimming; density
profiles were measured prior to each tow and the towing speed required to
obtain the desired Hs was calculated from the density profiles as
described above. Filming by motion picture camera was used in addition to
the normal visual and photographic observations.
339
-------
30 cm MODEL SCALE
200 - FIELD SCALE
CINDER CONE
IDRHG
FLUID
MODELING
SECTION
Figure A-2. Contour map of Cinder Cone Butte.
340
-------
The sinusoidal hill is sketched in Figure A-3. The cross-sectional
shape is described by
z = j (1 + cos (2 IT x/W)),
where h=10 cm and W=37 cm, giving a maximum slope of 40°. This was a
truncated ridge with the length of the straight section being 163 cm. The
end caps were of the same vertical cross-section and semi-circular in
horizontal planes. The skirt of the hill was molded in integral fashion
into a flat circular plate that fitted flush into the carriage baseplate.
Thus, the wind direction 0 could easily be changed. When oriented
perpendicular to the tow direction, the cross-sectional area of this hill
was 75% of the area of an "infinite" ridge of the same height stretching
across the width of the channel, i.e., the gap width as defined by Baines
(1979) was G = 0.25.
Tows of this model were made with linear density profiles, Froude
numbers of 0.3, 0.5, and. 0.7 and wind angles of 90°, 60°, 30°. In this
series of tests, neutrally buoyant red dye was released at the upstream edge
of the baseplate (x = -1.2 m) on the centerline at an elevation of Hs +
1 cm and blue dye at Hs-l cm. Additionally, some dye releases were made
during the 0 = 30° case, all releases being at the same elevation but
separated in the lateral direction. The purpose was to examine possible
changes in Hs with source offset from the centerline, as will be discussed
later.
In the "infinite" ridge studies designed to test the "steady-state"
assumptions, the same triangular ridge was used as discussed above except
that it's length was extended fully across the width of the tank and sponge
rubber pads were inserted to seal the small gaps getween the ridge ends and
the tank sidewalls. In this case, the ridge was towed at Froude numbers of
0.25 and 0.5 (based on the near-linear ambient density profiles), and
samples of fluid were drawn during the tow through vertical sampling rakes
positioned at 0.1 m (1 h) and 1.0 m (11 h) upwind of the ridge. The rakes
sampled the fluid at 21 levels each with spacing between individual tubes of
1 cm. The two rakes were laterally offset by 12 cm on opposite sides of the
centerline to avoid influences of the upstream rake on the downstream one.
The total length of the tow was 20 m (222 h). The intention was to take
rapid samples at four points of each tow, i.e., during the first and last
meter and at the one-third and two-thirds points of each tow. Because of
logistics problems in switching banks of tubes, the length of the sampling
intervals varied from 1.0 to 2.5 m and the centerpoints of the sampling
varied slightly from the precise one-third-points, but the basic objective
was accomplished, i.e., to determine whether a local steady state was
realized by comparing the density profiles measured at different periods
during the tow.
341
-------
h = 10 cm
a) cross-sectional view
b) plan view of hill on baseplate
Figure A-3. Details of the sinusoidal hill model,
342
-------
3.2 Wind Tunnel Experiments
One series of expermients was conducted in the stratified wind tunnel
of the National Institute for Environmental Studies of the Japan Environment
Agency (Ogawa et al. 1981). This vertical, closed-return wind tunnel has a
test section 3 m wide, 2 m high and 24 m long. The speed in the test
section may be controlled from 0.1 to 10 m/s and the ambient air temperature
may be maintained at any value between 12 and 87°C. A temperature-profile
cart (TPC) at the entrance to the test section allows the creation of
vertical temperature gradients; the TPC is essentially a series of heaters
dividing the 2 m height of the test section into 20 horizontal sections,
each section (10 cm height) independently increasing the temperature of the
incoming air by a controlled amount (maximum of 30°C). The temperature of
each 3x3 m floor panel may be independently controlled between 7 and 112°C
with a uniformity of +Q.2°C. Previous experience had shown that at high
ambient air temperatues, secondary flows (downward along the test-section
walls) were created; interior sidewalls made of 1m high aluminum plates
were placed 30 cm from the tunnel walls to minimize these secondary flows
(Ogawa et al. 1981).
The tunnel was designed for rather more weakly stable flows (i.e., wind
speeds greater than 'V 1 m/s) and difficulties were encountered in
attempting to obtain the very low bulk Froude numbers (0.2
-------
15 cm
\~—7.5 cm —I
Figure A-4. Model fences.
344
-------
For these flow visualization studies, a flattened, 10 mm diameter
horizontal tube was fastened to a vertical standpipe of 6 trnn diameter to
emit smoke at the desired elevation. Mixtures of nitrogen and helium were
fed into a smoke generator (electrical heating element wrapped around glass
wool soaked in paraffin oil), then to the "stack". The fraction of helium
to be used was determined by trial and error in the absence of the fence,
i.e., the fence was removed from the tunnel, the gas mixture was adjusted to
obtain a neutrally buoyant plume, then the fence was installed and
photographic observations were made while maintaining the nitrogen and
helium flow rates.
For temperature profile measurements, a Tokyo-Denpa quartz thermometer
was used. For velocity profiles, a sonic anenometer (Kaijo Denki Co., Ltd.,
model DA-390) with an x-sensor head oriented to measure horizontal
components of velocity (U and V) was used. This anemometer was specially
constructed for wind tunnel measurements, with a separation distance between
heads of 10 cm. Separate tests showed the velocity indications to be
independent of air temperature over the range of 15 to 50°C. A minicomputer
was used to sample the outputs from the anemometer and to calculate means
and standard deviations of the signals. One-hundred-second averages were
found to be adequate from the velocity measurements.
Photographic equipment included a TOPCON 4x5 graphics camera equipped
with a polaroid back, an Olympus OM-1 camera equipped with a databack (for
unique marking of each photograph), and a Sony Betamax video-tape recorder.
345
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SECTION 4
PRESENTATION AND DISCUSSION OF RESULTS
4.1 Towing Tank Studies with CCB Model
The schedule of tows of the CCB Model was shown in Table A-l and the
density profiles were shown in Figure A-l. For each tow, a particular
source height (center tube) was chosen and Equation 3 was integrated
numerically using the measured density profile to predict the towing speed
required such that the center streamer would rise just to the elevation of
the saddle point, i.e., the minimum height of the draw between the two
peaks. If the formula were correct, then, the lower streamer would be
observed to go around the sides of the hill, the upper streamer over the
top, and the center one, because of its finite thickness, would split, with
the upper portions going over and the lower portions round the sides.
Visual observations and periodic photographs were taken during the full
length (20 m) of each tow.
Figure A-5 shows the results of the integrations of Equation 3 for each
density profile as well as the experimentally observed results of the twelve
tows. The agreement between the predictions and observations is regarded as
excellent. The error bars indicate the best judgement of variability during
the observation. For example, tow number 0 showed little or no deviation of
the splitting of the center steramer, so that the error was judged as zero.
Tow number 3, on the other hand, showed occasional wisps of the lower
streamer rising over the top and of the upper streamer going around the
hill. Figure A-6 shows top and side views of impinging streamers during a
typical tow.
This set of experiments in conjunction with the results of Hunt and
Snyder (1980) and Snyder et al. (1980) for full-depth, linear density
profiles as well as elevated inversions has demonstrated the validity of the
general integral formula for predicting the dividing-streamline height as a
function of wind speed for a wide range of shapes of stable density
profiles. The remainder of the towing tank studies to be described used
only full-depth, linear density profiles.
4.2 Towing Tank Studies with Truncated Triangular Ridges
Figure A-7 shows the observations made during twelve tows of the
triangular ridges with aspect ratios of 1 (L=h) and 8 (L=8 h). It is
apparent that the dividing-streamline height followed the "1-F" rule for
346
-------
12
10 --
8 •-
2 --
Figure A-5. Predictions and observations of dividing-streamline heights
(open symbols: predictions; closed symbols: observations).
347
-------
\S-I05 1
Figure A-6. Top and side views of streamers impinging on the Cinder
Cone Butte model.
348
-------
0 - ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' '
0 .1 .2 .3 .I .5 .6 .7 .8 .9 1
Figure A-7. Dividing-streamline height from the triangular ridge study.
349
-------
F£0.25, and deviated strongly for F>0.25, but there were no observable
differences due to the difference in aspect ratio. The deviation from the
"1-F" rule is due to the formation of an upwind vortex that produces a
downward flow on the front face of the ridge. It is apparently due to the
combination of the steep upwind slope of the ridge and the shear in the
approach flow - as was mentioned earlier, the boundary layer was tripped by
a fairly substantial tripwire and, of course, grew in depth over nearly 1 m
of baseplate upwind of the ridges. The structure of this vortex may be seen
in Figure A-8; its diameter (and, hence, vertical extent) increased as the
Froude number increased, reaching a maximum of about 0.6 h at F=1.0.
Notice that the data in Figure A-7 are on the opposite side of the
"1-F" line from the "1-2F" line suggested by Baines (1979), even for the
ridge with aspect ratio 8. But, of course, the
Baines) was very large (0.7).
"gap" ratio (as defined by
The conclusion from this set of experiments is that Hs is independent
of the width of the hill and that it deviates from the "1-F" rule because of
the combination of the steep upwind slope and the shear in the approach
flow. Unfortunately, it was not possible to further investigate the nature
of the boundary layer in this case, but work in the stratified wind tunnel,
to be described in the next section, tends to support these conclusions.
4.3 Stratified Wind-Tunnel Study of Shear Flow over Fences
Figure A—9 shows the mean velocity profiles measured with the sonic
anemometer. Nine profiles are plotted, eight under "maximum" stratification
and one under neutral conditions. The temperature boundary conditions were
maintained constant and the stratification was varied by changing the fan
speed. Reverse curvature in the pofiles may be observed at fan speds below
220 revolutions per minute (rpm), and reverse flow in the lowest 4 cm was
observed at 200 rpm. A slight overshoot of the velocity is observed near
the top of the boundary layer under neutral conditions; this overshoot seems
to be enhanced by the addition of stratification. The depth of the boundary
layer was about 15 cm in the neutral case and gradually increased to 40 to
50 cm as the stratification increased.
Figure A-10 shows the corresponding temperature profiles. Temperatures
near the floor systematically decreased and temperature gradients increased
slightly as the fan speed was reduced.
Crosswind mean velocities are shown in Figure A-ll. A positive V
implies that a plume could veer to the right (looking downstream) as it was
transported down the tunnel. In neutral flow, the largest crosswind
velocity was 0.9 cm/s, which is to be compared with the streamwise velocity
of 85 cm/s at the same elevation, implying an angle of 0.6°. This is indeed
a very small angle and it is probably not within the capability of the sonic
anemometer to measure such a small deviation. The largest crosswind
velocity was -6.6 cm/s at 220 rpm; this is to be compared with the stream-
wise velocity of 40 cm/s, implying an angle of 10°, not-at-all
insignificant. Indeed, smoke from a vertical rake was frequently observed
350
-------
(a)
(b)
Figure A-8. Multilevel dye release upwind of a triangular ridge with an
aspect ratio of 2: (a) F=0.8; (b) F=1.0.
351
-------
1.05 1.2
Figure A-9. Mean velocity profiles in the stratified wind tunnel.
352
-------
50
lid --
30 --
g
N
20 --
10 -•
Figure A-10. Temperature profiles in the stratified wind tunnel.
353
-------
50
30 --
o
*%
N
20 -•
10 -• <>'
-0.07 -O.OB -0.05 -0.01 -0.03 -0.02 -0.01
V, m/s
.01 .02 .03
Figure A-ll. Crosswind mean velocity profiles in the stratified wind tunnel,
354
-------
to veer away from the tunnel centerline and to follow the directions
indicated in the figure. This crosswind component is not believed to have
had a significant influence on the structure of the flow over the fence.
Lbngitudinal and lateral turbulence intensity profiles are shown in
Figures A-12 and A-13, respectively. The most notable characteristic of the
stratified profiles is the elevated maxima, unlike the neutral case where
the maximum was much nearer ground level. Most noticeable are the very
large intensities at 241 rpm, where the peak value is located at an
elevation of 12 cm and the value is 2.5 times the maximum neutral value.
This corresponds with visual observations of smoke, where Kelvin-Helmholz
rolls were observed. These measurements are indicative of relatively large
scales of turbulence only, since, because of the large path-length, the
sonic anemometer could not resolve scales smaller than about 10 cm. Visual
observations, in fact, suggested there was little energy at scales smaller
than that.
Repeat measurements of longitudinal and .lateral mean velocity profiles
are shown in Figures A-14 and A-15, respectively. The repeatability is
regarded as excellent; the data seem to imply that the crosswind velocity
component can be repeated to within +0.5 cm/si The data also indicate the
very good repeatability of the flow in the tunnel, as the profiles at
205 rpm were taken 5 days apart. Similar repeat measurements of temperature
and turbulence intensities (not shown) also showed excellent correspondence.
From these velocity and temperature profiles, the dividing-streamline
height was calculated using Equation 3. The results are graphed in
Figure A-16; the data appear to fall on a straight'line from 10.5 cm at
200 rpm to 0 at 241 rpm. These data were used to characterize the-
stratification and the results will be described in terms of release height
relative to this dividing-streamline height.
A large number of photographs of smoke plumes flowing over and around
the various fences were obtained. It is not possible to reproduce all of
them here, but a representative set is presented in Figures A-17 through
A-19. At 205 rpm, (Figure A-17), the dividing-streamline height calculated
from Equation 3 (Figure A-16) was apprpximately 9 cm or 0.6 h. It is
obvious from the photographs, however, that the plume from the 9 cm stack
did not split over the fence top, as would be expected from the
dividing-streamline concept. Instead, it went totally around the sides of
the fence, for all aspect ratios. Indeed, only a tiny fraction of the 12 cm
plume (0.8 h) surmounted the fence, and only about half the 15^cm plume
(1 h) passed over the top. Moreover, this behavior was essentially
independent of aspect ratio. Such behavior appears to be due to an upwind
vortex, with downward flow along the front face of the fence; it is very
similar to that observed on the front faces of buildings in shear flows (at
least in wind-tunnel studies1.). One difference, however, is quite evident:
there is a bottom limit to this vortex; it does not extend to the tunnel
floor as would be expected in a neutral shear flow. Instead, the streamline
originating far upstream at fence-top elevation appears to be limited in how
far down it can travel, presumably by the amount of kinetic energy it
possessed initially, i.e., its kinetic energy is used-up in moving
355
-------
N
u'/U, %
Figure A-12. Longitudinal turbulence intensity profiles.
356
-------
50
140 -•
o
1 .8 1.2 1.6
14.14
Figure A-13. Lateral turbulence intensity profiles.
357
-------
50 H—i—i—i—i—I—i—i—i—i—I—i—i—i—i—I—i—i—i—i
.1 .2 .3 .4 .5.6 .7 .8
10 -•
Figure A-14. Repeated measurements of longitudinal mean velocity profiles.
358
-------
i±0 --
3D --
20 --
10 --
0
-0.075
.025
Figure A-15. Repeated measurements of lateral mean velocity profiles.
359
-------
15 -\ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Q
200
210
220 230
FAN SPEED, rpm
2140
250
Figure A-16. Dividing-streamline height for the 15 cm hill as function
of fan speed.
360
-------
Hp=0.8h
L=4h
H =0.8h
L=h
H =0.6h
R.
L=4h
H =0.6h
L=h
Figure A-17. Views of smoke streamers over a vertical fence; Hs=0.6h.
361
-------
H_ = 0.8h
H = 0.6h
x\.
HR = 0.4h
Figure A-18. Views of smoke streamers over a vertical fence; Ils=0.36h, L=2h.
362
-------
L = 8h
L = 2h
L = 0.5h
Figure A-19. Views of smoke streamers over a vertical fence; neutral flow,
HR=0.6h.
363
-------
vertically through the density gradient (increasing its potential energy).
Indeed, the bulk Froude number based on the (far upstream) fence-top
velocity was 0.67. From another viewpoint, the velocity gradient is nearly
constant over the full depth of the fence and the temperature gradient
decreases with height, so that the Richardson number also decreases with
height, i.e., an "outer" layer behaves more like neutral flow and an "inner"
layer exhibits strongly stable, horizontally constrained flow
characteristics.
At 220 rpm (Figure A-18), the calculated dividing-streamline height
(from Figure A-16) was approximately 5.5 cm (0.36 h). The plume behavior
was somewhat similar to the previous case, but here the 15 cm plume
completely surmounted all fences and the upwind vortex appeared to reach the
tunnel floor. Evidently, the streamlines impinging just below the top of
the fence possessed sufficient kinetic energy to overcome the potential
energy difference between the top and base of the fence. Indeed, the bulk
Froude number based on the (far upstream) fence-top velocity was 1.1.
In neutral flow (Figure A—19), the plume behavior appeared to be much
more dependent upon the fence aspect ratio. For long fences, the plume
appeared to surmount the fence (even for the 3 cm plume), whereas for the
short fences, most of the plume appeared to go around rather than over the
fences (even the 12 cm plume).
To summarize, it is evident that even a relatively small amount of
stratification drastically alters the flow structure over fences. And the
shear seems to have an overwhelming influence! Tentative conclusions are
(1) for strongly stratified flows, the basic flow structure is independent
of aspect ratio, (2) the shear creates an upwind vortex so that upwind
plumes are downwashed on the front face of fences and (3) under strong
stratification, the downward penetration of elevated streamlines is limited;
the extent of this downward penetration appears to be predicatable as a
balance between kinetic and potential energies (hence, characterized by the
Froude number), using arguments similar to those from the
dividing-streamline theory.
Later flow visualization studies with the CCB model under these same
stratified flow conditions showed no evidence of upwind vortex formation,
but systematic studies to locate Hs were not conducted. However,
concentration measurements (to be described in another paper) on the hill
surface from an upwind source of 48 mm elevation first showed evidence of
flow through the draw between the two peaks at a fan speed of 220 rpm, where
the calculated dividing-streamline height (based on the saddle-point height)
was 45 mm. These results suggest that, because of the relatively low upwind
slope of the CCB model, the formation of an upwind vortex was not possible.
They also suggest that Equation 3 may be a good indicator of dividing
streamline heights, even in strong shear flows, for the vast majority of
real hills (i.e., maximum slopes less than 26°).
The strong effect of the shear in the fence studies is not surprising
in light of the discussion in Section 2.5. The slope term dR^/dz, which
normally tends to counteract the shear term, was zero. In the CCB model,
364
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the minimum value of dRo/dz was 2.0, so that the slope term evidently
roughly balanced the shear term, thus inhibiting the upwind vortex
formation. Also, as indicated in Section 2.5, it is not surprising that the
centerline flow structure was independent of hill aspect ratio; however,
because of the very large streamline deflections, it is not appropriate to
make estimates using Equation 19.
4.4 Towing Tank Studies with the. Sinusoidal Ridge
A total of 19 tows were made of the truncated sinusoidal ridge at
Froude numbers of 0.3, 0.5, 0.7 and 1.0, and wind directions of 90°, 60°,
and 30°. To conserve space, data from the 90° and 60° cases are not shown,
but these data were completely consistent with all previous data for
axisymmetric hills and supported the "1-F" rule (within the resolution of
the method, +0.1 h). Data from the 30° case are shown in Figure A-20, where
the release heights of the dye streamers are plotted versus Froude number;
open symbols indicate that the streamers passed freely over the ridge,
closed symbols show they were diverted around the ridge, and the half-filled
symbol indicates the streamer split, with half going over the top and half
going round the end. These data suggest something like Hs/h = 1-0.7F, as
the streamers were diverted around the hill even though they had sufficient
kinetic energy to pass over the top. It should be pointed out that this
does not violate Sheppard's (1956) concept; just because a fluid parcel far
upwind has sufficient kinetic energy to surmount the hill does not
necessarily mean it will do so. In this 30° case, the flow, in some sense,
followed the path of least resistance in travelling round the end of the
ridge.
These streamers were released on the centerline of the, towing tank and,
hence, were not on (or even near) a stagnation streamline. A few tows were
made with F=0.5 releasing dye from three tubes positioned at the same
elevation but at different lateral positions. These releases showed the
stagnation streamline to be located very near the most-upwind end of the
ridge, as was also found experimentally and theoretically by Weil et al.
(1981). Further tows showed that streamers released above (at z/h=0.6) the
stagnation streamline travelled over the ridge (Hs/h=0.5) and that
streamers released 1 h on either side of the center streamer travelled
around opposite ends of the ridge, even though their elevation was above
Hs. When the center streamer was released at z/h=0.4. (below Hs), it
travelled round the sides, periodically switching from one side to the
other. These data are consistent with Sheppard's (1956) criterion
interpreted as a necessary but not sufficient condition on the kinetic
energy of a fluid parcel far upstream.
These experiments also suggest that the lateral offset of the source
from the stagnation streamline can be a very important parameter affecting
the location and value of the maximum surface concentration, especially when
the elevation of the source is below Hs. The data of Figure A—20,
however, suggest that lateral offset can be extremely important even when
the source is above Hs. Other tows with truncated ridges (both sinusoidal
and triangular ones) oriented perpendicular to the tow direction suggested
365
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Figure A-20. Dividing-streamline height for a truncated sinusoidal ridge at
30° to tow direction.
366
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that lateral offset was not a significant parameter when the source was
located above Hs unless it was also located very near the ends of the
ridges. Hence, the question of whether a plume will impact on a ridge is
expected to be a function of both the source height relative to the
dividing-streamline height and lateral offset; lateral offset, however,
greatly increases in significance as the angle between the ridge axis and
the wind direction is reduced.
4.5 Strongly stratified towing tank experiments with two-dimensional
triangular ridges
Two tows were made of the two-dimensional triangular ridge at Froude
numbers (based on the tow speed and the undisturbed density profiles) of 0.3
and 0.5. Figure A-21 shows the sampling positions and intervals. One
sampling rake was positioned at the leading edge of the baseplate (11 hill
heights upstream) and the other 10 cm (1.1 hill heights) upstream. A
typical set of density profiles is compared with the initial density profile
in Figure A-22. It is clear that the initial near-linear density profile
was continuously modified during the tow at a position 11 hill heights
upstream and that upstream conditions did not reach a steady state. The
profiles tended toward neutral at elevations below half the hill height.
These results tend to support the squashing model described in Section 2.3.
The profiles taken at 1.1 h upstream and those at F=0.3 showed similar
tendencies, but with the tendency-toward-neutral behavior occurring over
larger depths, i.e., to approximately 0.8 h.
The density profiles measured at 11 h upstream were used to calculate
Hs according to Sheppard's integral formula assuming a uniform approach
wind profile. The results are shown in Figure A-23. Because the density
gradients below hill top were reduced, the dividing-streamline heights were
also reduced as the tow progressed. This behavior was also substantiated by
observing dye streamers released simultaneously at various elevations during
the tow.
It should be pointed out that in Baines (1979) experiments on ridges
with gaps, the dye-release rake was hinged in such a way that dye was
released at 8 different elevations. However, the rake was pivoted from one
elevation to the next during the length of the tow, so that observations of
dye behavior at each level took place for, at most, 1 m. It is not
difficult to imagine that, because of the systematic change of release
elevation with tow distance in conjunction with the decrease in Hs with
tow distance, the results were interpreted incorrectly to arrive at Hs/h =
1-2F.
Some additional experiments with the truncated sinusoidal ridge (G =
0.25, W/h = 16) show that, even though the Hs/h = 1-F formula is
well-verified, a very long time period (or a long length of tow) is required
for steady-state conditions to be established at 10 hill heights upwind.
367
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i"^ a
r^
x '
i
2.13 m 2.1
D
<
4
m 2
25 m
i
r-
<
V
m
Figure A-21. Sketch showing sampling intervals and locations for the
two-dimensional ridge tow at F=0.5.
368
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1. S -r—i i " I i' •+—r-T-"i—i-H—r—r—r—i—I—i—r
1.4 -
IM
1 -
.6
.14
1.005 1.01
.J_uH_i_x__u^H__i_
1.015 1.02
SPECIFIC GRAVITY
1.025 1.03 1.035
Figure A-22. Density profiles measured upstream of the two-dimensional
triangular ridge.
369
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_c
u
re
1 •! i i i i 1 i i i i I i i i i I i i i i I i i i i 1 i i i i I i i i i I i t i i I i i i i
Q I ' '—I—I—j—I—I—1—I—|—I—I—1—I—|—I—I—I—I—{—I—I—I—I—|
0 .1 .2 .3 .14 .5 .6 .7 .8 .9 1
x/L
Figure A-23. Dividing streamline height as function of towing distance for
the two-dimensional triangular ridge.
370
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SECTION 5
CONCLUSIONS
(1) From previous work as well as current studies with the CCB model,
it is concluded that the integral formula of Sheppard (1956) is valid for
predicting the height of the dividing streamline for a wide range of shapes
of stable density profiles and a wide range of roughly axisymmetric hill
shapes.
(2) From the studies with the truncated triangular and sinusoidal
ridges perpendicular to the wind, it is concluded that the aspect ratio,
per se, does not have a significant influence on the dividing-streamline
height Hs. Deviations from the Hs/h = 1-F rule are attributed to the
combination of shear in the approach flow and the steep slope of the
triangular ridges, which resulted in the formation of an upwind vortex with
downward flow on the front face of the ridges. The "1-F" rule was validated
for the sinusoidal ridge with a length-to-height ratio greater than 16:1; in
this case, the shear in the approach flow was much less pronounced and the
upwind slope was substantially smaller. Note that the above deviations from
the "1-F" rule do not invalidate Sheppard's concept; the rule should be
interpreted as a necessary but not sufficient condition, i.e., a fluid
parcel may possess sufficient kinetic energy to surmount a hill, but it does
not necessarily do so.
(3) In the stratified wind tunnel studies, a range of operating modes
was found that yielded reasonably strong shear layers with depths more than
twice the hill heights in conjunction with strong stable temperature
gradients. These provided dividing-streamline heights as large as 0.75 h.
In the vertical fence studies with a stratified approach flow, the shear was
found to have an overwhelming influence. Conclusions are: (a) as in the
triangular ridge studies, the aspect ratio was relatively unimportant; the
basic flow structure was independent of aspect ratio, (b) the shear (in
conjunction with the steep slope) created an upwind vortex such that plumes
were downwashed on the front faces and (c) under strong enough
stratification, there was a limit to the downward penetration of elevated
streamlines; the extent of this penetration is apparently predictable as a
balance between kinetic and potential energies. With these same shear flows
approaching the much lower sloped CCB model, however, there was no evidence
of upwind vortex formation. Limited concentration measurements on the CCB
model suggested that Sheppard's integral formula correctly predicted the
height of the dividing streamline.
371
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(4) From the sinusoidal ridge studies with wind angles at other-than-
90°, it is concluded that the effect of deviations in wind direction (from
90°) are relatively insignificant until the wind direction is something like
45° to the ridge axis. At 30°, significant departures from the Hs/h = 1-F
rule were observed; the fluid had sufficient kinetic energy to surmount the
ridge but, presumably, found a path of lower resistance in travelling round
the end of the ridge. When the streamers were moved closer to the upstream
stagnation streamlines (upwind of the upwind edge of the ridge), they
behaved according to the Hs/h = 1-F rule.
These experiments suggest that the lateral offset of the source from
the (probably contorted) plane of stagnation streamlines is an important
parameter to consider in determining the location and value of surface
concentrations, especially when the wind is at a small angle to the ridge
axis (say, <45°).
(5) The two-dimensional triangular ridge studies showed that steady-
state conditions are not established in strongly stratified flows (say,
F<1). The squashing phenomenon and upstream columnar disturbances
continuously changed the shapes of the "approach flow" velocity and density
profiles. Thus, these experiments have no analog in the real atmosphere.
Further, since long ridges cut by periodic small gaps require very long tow
distances in order for steady state to be established, it is concluded that
previous laboratory studies are not valid; specifically the Hs/h = 1-2F
formula proposed for flow about ridges with small gaps is not expected to be
valid in the real atmosphere. Finally, a suggestion is made that the gap
ratio must exced 25% in order for steady-state conditions to be established
in the usual size and shape of towing tank. More work is required to firmly
establish the relationships between model size and shape, stability, and
tank size and shape in order to determine limits of applicability of fluid
modeling and ranges of tranferability to the atmosphere.
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