MIXING HEIGHT DETERMINATIONS BY MEANS
OF AN INSTRUMENTED AIRCRAFT
ENGINEERING AND INDUSTRIAL EXPERIMENT STATION
College of Engineering
University of Florida
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MIXING HEIGHT DETERMINATIONS BY MEANS
OF AN INSTRUMENTED AIRCRAFT
R. 0. MC CALDIN
R. S. SHOLTES
UNIVERSITY OF FLORIDA
GAINESVILLE, FLORIDA
This work was carried out under the sponsorship of the
Department of Health, Education, and Welfare, U.S. Public
Health Service, National Air Pollution Control Administration,
Research Contract No. CPA 22-69-76
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MIXING HEIGHT DETERMINATIONS BY MEANS OF
AN INSTRUMENTED AIRCRAFT
INTRODUCTION
In a general sense ambient air pollutant concentrations are a
function of the rate of pollutant emission, wind speed and direction,
and the altitude to which pollutants can mix. Air pollution models based
at least in part on relationships such as these are being used by control
agencies to develop optimum control strategies, and by the National Air
Pollution Control Administration to delineate boundaries for most of the
air quality control regions. Information pertaining to mixing heights
and wind speeds are integrated with other meteorological information in
order for ESSA to furnish its forecasts of air pollution potential for
the contigious United States.
2 3
The mixing layer concept has been employed by Holzworth, ' who
used straight forward techniques for estimating mixing heights based on
regular radiosonde observations of the vertical temperature structure and
subsequent surface temperature. The afternoon or daily maximum mixing
height was estimated by constructing a dry adiabat from the maximum surface
temperature to its intersection with the most recently observed temperature
Guidelines for the Development of Air Quality Standards and Implementation
Plans, U.S. Department of Health, Education, and Welfare, National Air
Pollution Control Administration, May, 1969.
2
Holzworth, G. C., "Mixing Depths, Wind Speeds, and Air Pollution Potential
for Selected Locations in the U.S." Journal of Applied Meteorology, Vol. 6,
No. 6, December, 1967, pp. 1039-1044.
3
Holsworth, G. C., "Large-Scale Weather Influences on Community Air Pollution
Potential in the U.S.," Journal of the Air Pollution Control Association,
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profile. He points out that this technique is based mainly on thermally
produced turbulence, caused by the redistribution in the vertical of
heat input at the ground. Since the maximum surface temperature may occur
at about 1200-1600 hours local time, and since the most recent radiosonde
vertical temperature measurement may have been taken 6-9 hours prior to
this time, another important assumption is that the vertical temperature
profile for the upper altitudes has remained reasonably constant over
this period.
OBJECTIVE
This project was performed in order to evaluate mixing height
estimates made by the technique employed by Holzworth and others, here
designated as the Holzworth method.
METHODS
Evaluations were performed by making vertical soundings with an
instrumented aircraft and recording signals that would furnish independent
measures of the mixing height. Signals included a vertical temperature
profile, an accelerometer trace which indicated atmospheric turbulence, and
a record of particle concentrations. The mixing height was then determined
on the basis of each of these parameters as illustrated in Figure 1.
Sketch 1 in this figure illustrates the Holzworth method for
predicting the mixing height.
Sketch 2 illustrates the temperature profile that can be found by
the instrumented aircraft during an afternoon sounding. If the temperature
structure of the air mass remains constant between the time of the radio-
sonde and the aircraft sounding, then the two profiles should be similar.
The altitude identified as the mixing height in sketch 2 is the first point
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SKETCH #1
HOLZWORTH
METHOD
RADIOSONDE
(1200 GMT)
SKETCH #2
AIRCRAFT
TEMP.
SOUNDING
SKETCH #3
SKETCH #4
(SURF. TEMP.)'
TEMPERATURE
TEMPERATURE
TURBULENCE
PARTICLE
CONCENTRATION
FIGURE 1
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Sketch 3 illustrates the form in which the measures of turbulence
are recorded. Signal variations represent the lateral acceleration experi-
enced by the aircraft, and the amplitude of the trace is considered to be
a measure of turbulence. In the mixing layer this was sufficient to cause
lateral aircraft accelerations on the order of 0.1 g. Above the mixing
layer the engine vibration produced an acceleration trace of about 0.02 g.
Thus, there was found to be on the order of a five-fold difference in
accelerometer amplitude below and above the mixing height. In most cases,
there was found to be a rather well defined delineation between the two
zones. Mixing height, as determined by this method, was the height at
which the amplitude of accelerometer trace decreased to 50 percent of
the mean amplitude in the mixing zone.
The size of eddy cells which produce turbulence can be implied
based on the periodicity of the accelerometer trace, recorder chart
speed, and aircraft speed. This and further analysis of the accelerometer
4
readings is the subject of a thesis by Franz.
Sketch 4 illustrates the concentration of suspended participates
detected below and above the mixing height. Particles greater than 0.3 urn
are detected by a forward light scatter dust counter and their concentra-
tion is recorded on a strip chart. The decrease in particle concentration
occurs rapidly at the mixing height if the parent air mass is clean. If
the parent air mass is already laden with particles, then the decrease in
particle count at the top of the mixing zone is less pronounced. The
4
Franz, J. J., "Aircraft Accelerometer Studies for Mixing Height
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mixing height, as determined by this method, was the altitude at which
the particle count dropped to 5 percent of full scale (50,000 particles
per cubic foot or about 2 particles per cubic centimeter).
Soundings of the atmosphere were made on 33 days during the period
of 8 December 1969 through 9 March 1970. On some days, repetitive
soundings were made in order to follow the temporal development of the
mixing height. Thus, 145 separate soundings were made. For each of
these aircraft soundings, Mr. Holzworth, working entirely independently,
estimated the mixing height using the technique described earlier. He
modified it to some extent by interpolating the temperature profile
between several radiosonde locations when flights were made at inter-
mediate locations, and when flights were between radiosonde observation
times by allowing for significant temporal changes in radiosonde temperature
profiles that were due to factors other than the input of heat at the
ground, e.g., cold air advection, subsidence of an inversion, etc. Air-
craft measurements were made when flying a steady climb to about 2000
meters depending on the terrain and mixing height, but in any event,
about 300 meters above the mixing zone. Flight speeds were generally
90 mph (IAS). One crew member flew the aircraft and one operated instru-
ments and made appropriate notation.
EQUIPMENT
A Cessna 172 (Skyhawk) aircraft was used for this activity. The
only aircraft modification involved the installation of a larger than
normal alternator to provide the needed power for the instrument package.
McCaldin, R. 0., and Johnson, L. W., "The Use of Aircraft in Air Pollution
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The instrument package with its several components was approved by
the FAA for restricted category operation. Basically, these restrictions
limited operation to daylight hours and no more than a two person crew.
As installed, the instruments were capable of measuring six para-
meters, although only four were used in this study. As previously
indicated, the variables recorded were altitude, lateral acceleration,
temperature, and aerosol concentration. Humidity and sulfur dioxide
measures were available but not used.
All equipment was designed to operate on 100 volt 60 cycle current.
Power was made available through two inverters operating from the aircraft
12 volt DC system. Altitude was determined by using a potentiometric
absolute pressure transducer acting in a voltage divider network. Excita-
tion was provided by a regulated power supply. The output from the trans-
ducer was fed directly to the null-balance potentiometric recorder. An
adjustable zero was provided on this channel of the recorder to accomodate
barometric pressure changes, and adjustments were made at the beginning
of each flight.
Temperature was measured with a linear thermistor situated in one
or the other of two parallel DC bridge curcuits, providing overlapping
temperature ranges. These circuits proved reliable, but did suffer from
component temperature sensitivity. The error due to this problem became
more acute at very low ambient temperatures. Response time of this
element was on the order of five seconds or less.
Turbulence was sensed by a potentiometric type yaw accelerometer
rigidly fixed to the airframe. The total range of this instrument is
+ 0.33 g. Its excitation was through a regulated DC power supply and the
output fed directly to the null-balance potentiometric recorder.
Aerosol concentrations were sensed with a Bausch and Lomb. 40-1
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measurements of mixing height, aerosols 0.3pm and larger were counted.
The instrument has other size range selections at the discretion of the
user. The output of this device is normally logarithmic. A log-linear
attachment available from the manufacturer provided a linear conditioned
signal directly compatible with the null-balance recorder. Response
time of this instrument as installed in the aircraft has been measured
just under two seconds.
As indicated, all variables are routed to a null-balance potentio-
metric recorder. This unit has four channels, thereby allowing all vari-
ables to be simultaneously recorded on a single chart. Chart speed for
this work was standardized at one inch per minute.
FINDINGS
1. Comparison of ESSA and Aircraft Temperature Profiles
The first step was to see how closely the aircraft temperature
soundings compared with those measured by the ESSA radiosonde. Table 1
shows the date, location, and times for which nearly comparable measure-
ments were taken. The differences between the radiosonde temperature and
that recorded from the aircraft at the surface and at 1000 meters are
shown. The temperatures, as measured by the aircraft, averaged almost
2 C lower than those measured by radiosonde. It should be noted that
the morning flight soundings had to be made approximately one to three
hours later than the radiosonde observations, due to an FAA flight
restriction which limited the aircraft operation to daylight hours.
More important than the absolute difference in values is the ability of
both techniques to disclose similar vertical temperature profiles. This
is because the mixing height based on aircraft temperatures is defined
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TABLE 1
COMPARISON OF RADIOSONDE AND AIRCRAFT
VERTICAL TEMPERATURE PROFILES
Location
Tampa, Fla.
Waycross, Ga.
Way cross, Ga.
Tampa, Fla.
Waycross, Ga.
Grand Junction
Colo.
Date
18 Dec 69
7 Jan 70
8 Jan 70
22 Jan 70
13 Feb 70
7 Mar 70
Hour
Radiosonde Aircraft
0618 0706
1800 1750
1810
0615 0725
0740
0638 0715
0755
1817 1527
1642
0417 0715
TEMP DIFFERENCE
Radiosonde-Aircraft ( C)
Surface 1000m
1.0 -1.0
1.2 2.1
2.6 2.5
5.5 5.0
5.0
2.7 1.1
2.2 1.7
-1.0 1.0
-1.3 0.5
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thermal, and is not dependent on the absolute temperature itself. The
similarity of radiosonde and aircraft temperature profiles is shown
in Figure 2. From these data it was concluded that aircraft temperature
profiles were a true reflection of those obtained by radiosonde.
2. Comparison of Estimated and Measured Mixing Heights
A correlation matrix was developed for the mixing heights as
determined by the Holzworth method, and as compared with that determined
from vertical temperature structure found by the aircraft; that determined
from aircraft turbulence; and that determined by particle concentration.
Figures 3, 4, 5, and 6 show the correlation diagrams when these
various techniques are compared, and Table 3 contains the correlation
statistics for these comparisons.
The sample size in these comparisons varied from 108 to 121 out
of a total of 145 soundings. Differences are due to a combination of
factors including instrument malfunctions resulting in missing data and
several late afternoon flights for which the technique employed by Holzworth
is not applicable, e.g., after the afternoon surface temperature has
begun to cool.
These data suggest that the mean mixing height estimated by the
Holzworth method is not significantly different from that measured by
aircraft turbulence. The Holzworth method and the aircraft turbulence
technique both give a mean mixing height seven to nine percent greater
than that found by the aircraft temperature profile. The smaller mixing
height based on aircraft temperature profiles is probably due to the
significance of the isothermal point identified as the mixing height.
From examination of a number of the original strip charts it appears
that due to momentum parcels of air may continue to rise for several
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2500 —i
2000 —
1500 —
TAMPA, FLA.
18 DEC. 1969
- 1000 —
500
8 9 10 11 12 13
RADIOSONDE, 0618 HRS.
AIRCRAFT, 0706 HRS.
WAYCROSS, GA.
13 FEB. 1970
RADIOSONDE, 1817 HRS
4 5
I I I I I I I I I I I l 1
4 5 6 7 89 10 111213 1415 1617
TEMPERATURE ( C)
FIGURE 2
COMPARISON OF RADIOSONDE AND AIRCRAFT
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2500 —i
2000 -
1500 —
TAMPA, FLA.
18 DEC. 1969
1000 —
RADIOSONDE, 0618 MRS.
500 —
AIRCRAFT, 0706 MRS.
SURFACE
WAYCROSS, GA.
13 FEB. 1970
RADIOSONDE, 1817 MRS.
AIRCRAFT, 1642 MRS.
AIRCRAFT, 1527 MRS.
\\ SURFACE = 43 m
567
910111213 4 5 6 7
TEMPERATURE (°C)
FIGURE 2
COMPARISON OF RADIOSONDE AND AIRCRAFT
VERTICAL TEMPERATURE PROFILES
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TABLE 3
CORRELATION OF VARIOUS MEASURES OF THE
MIXING HEIGHT
Comparison
Holzworth estimated height vs.
aircraft temperature height
Holzworth estimated height vs.
aircraft turbulence height
Holzworth estimated height vs.
aircraft particle concentration
height
Aircraft turbulence height vs.
aircraft temperature height
Sample
Size
113
117
121
108
Correlation
Coefficient
0.87
0.87
0.25
0.93
Slope of Line
of Best Fit
0.91
0.97
1.08
0.93
Significance of Difference
in Slope of Line of Best Fit
and Slope of Line of Unity at
95 Percent Confidence Level
Yes
No
No
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reach equilibrium with their environment. The amount of additional
rise appears to depend upon the stability of the environment air.
As these parcels rise beyond their equilibrium point they continue to cool
adiabatically. Subsequent mixing with the environment air produces a
stable layer such as an inversion. Although Holzworth's estimates do not
allow for this effect, it is compensated to some extent by his neglect
of shallow superadiabatic layers next to the ground.
The mixing height predicted by the Holzworth technique is also
not significantly different from that determined by the height to which
aerosols have mixed. It should be pointed out, however, that the
correlation coefficient for this comparison is only 0.25. This wide
scatter of data points can be best explained by considering the history
of the air mass in question. If mixing occurs in a clean air mass, then
aerosols will be distributed to the top of the mixing layer. In the
evening the mixing activity diminishes, but the aerosols remain aloft.
Although the particles are influenced by gravity, their settling rate is
slow. For example, a one y^ diameter particle of unit density would
settle about three meters over a 24-hour period. Thus, on the second
day small aerosols would remain mixed in the air mass nearly to the
height of the mixing layer of the prior day. If mixing heights were
determined the second or any subsequent day in the air mass, the particle
distribution would be an indicator only of the greatest height the mixing
layer had achieved, and not necessarily the height of the mixing layer
at the time of measurement.
DISCUSSION
Since these aircraft techniques of temperature, turbulence, and
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several portions of the original strip chart data are presented and
discussed for illustrative purposes.
Figure 7 shows measurements made during a climb over Waco,
Texas. The chart reads from right to left, and the aircraft altitude
can be read from the solid line starting at the lower right hand corner
of the figure. Aerosol concentrations are also recorded on the bottom
portion of the figure. This shows a gradually decreasing concentration
of aerosols until the mixing height is reached. At that time there was
a very rapid decrease in aerosol concentration. Appropriate scale units
are shown on the left margin. The turbulence scale shows amplitude only,
and the zero reference was arbitrarily placed on the chart.
On the top portion of the figure the steady line represents the
temperature associated with altitude. It decreased rather steadily with
altitude until 2400 feet was reached. Above this altitude a marked in-
version occurred as shown by the 2 C increase in temperature. Aircraft
turbulence is shown by the fluctuating trace at the top of the figure. The
amplitude of fluctuation decreased as the aircraft climbed above the
mixing layer. The smaller acceleration traces above the mixing layer
represents aircraft vibration and response to movement of aircraft flight
controls.
Using the criteria for measurement which were described earlier,
mixing heights at Waco were as follows:
Method Altitude (ft) M.S.L.
Holzworth Estimate 3000
Aircraft Temperature 2400
Turbulence 2300
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-18-
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- 9
Al
10
-9
-8
-7
-6
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• t
•3
•2
•1
-TEMPERATURE
CHART SPEED IN MIN.
FIGURE 7
MIXING HEIGHT DETERMINATIONS
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Figure 8 illustrates the influence that aerosol concentrations below
the mixing layer have on visibility. This is a composite photograph taken
near Waco about a minute after the aircraft climbed above the mixing layer.
One view faces the sun, and the other is with the sun behind the camera.
The effects of visibility reduction on flying safety can be illustrated
by referring to a fatal mxd-air collision between a North Central airlines
Convair 580 and a Cessna 150 near Milwaukee on August 4, 1968. The National
Transportation Safety Board report said in part the probable cause of the
collision was "... the inability of the Convatr flight crew to detect the
Cessna visually in sufficient time to take evasive action, despite having
been provided with three radar traffic advisories concerning the latter
aircraft." There were no clouds obstructing visibility, but flight
visibility was reduced to about three to five miles due to smoke, haze,
and sun glare. In addition there were insect smears on the Convair
windshield - a fatal combination.
Figure 9 illustrates an anomoly between measurements. The mixing
height by Holzworth's method was estimated to be 2250 feet. Based on the
first isothermal point the mixing height was measured at 1700 feet; based
on turbulence at 1900 feet. However, based on aerosols it was measured
at 4500 feet, and this suggests that aerosols had been moved aloft at a
prior time, and thus were independent of mixing during the day in question.
Figure 10 illustrates developments in the mixing height during
the course of a day as well as some of the unexpected findings. At 0810
there was a strong inversion and good agreement between various mixing
height measurements. By 1115 the inversion was not so pronounced. There
was good agreement between the temperature and turbulence height measure-
ments. However, there was additional turbulence further aloft, and
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I
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BACK TO SUN
FIGURE 8
MIXING LAYER
WACO, TEXAS 4 MARCH 1970 1400 HOURS
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- 6
- 5
. 4
- 3
• 2
• 1
- 0
CHART SPEED IN WIN.
ALTITUDE
FIGURE 9
MIXING HEIGHT DETERMINATION - SHOWING DISPARITY BETWEEN MEASUREMENTS
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30-
25-
°_20-
15-
10-
CHART SPEED IN WIN.
.10
-g
or
-8
-7
-6
-5
•4
-3
.2
- 1
- 0
i- 10
- 9
- 7
- 5
• 4
3
2
1
L 0
FIGURE ID
MIXING HEIGHT DETERMINATION SHOWING DEVELOPMENT DURING DAY
GAINESVILLE, FLORIDA 19 FEB. 1970
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temperature profile suggested a double inversion. In accordance with
the selection criteria, the first isothermal above the ground was chosen
as the mixing height. On the basis of comparison with turbulence and
aerosol data it appears quite likely that the second and larger inversion
actually established the mixing height.
Figures 11, 12, and 13 all pertain to measurements made over
Gainesville, Florida on 16 December 1969. The series of figures are
presented to show how the mixing height developed during the day and to
illustrate the temperature and turbulence patterns.
Figure 11 shows the vertical temperature structure at approximately
two-hour intervals during the day. Notice the cooling that occurs with
time at the top of the mixing layer, e.g., in the 250-650 meter layer
from 0805 to 1010, as discussed on pages 9 and 16.
Figure 12 shows the mixing heights as determined by each technique.
The vertical scale is compressed in order to permit visual comparison with
the temperature profiles in Figure 11.
Figure 13 shows the accelerometer trace for each sounding. The
height of the mixing layer is noted for each trace, but the vertical
scale between traces is not identical. This is because their length
is a function of aircraft climb rate which varied somewhat between the
several flights. Perhaps the most interesting feature of these traces is
the accelerometer amplitude pattern. Amplitude is greatest around mid-
day and suggests that the most vigorous turbulence occurred at that time.
The mixing height increased until about 1605 hours, but by that time
the accelerometer amplitude had diminished rather uniformly through its
height. Then by 1730 it had collapsed in its entirety. The relationship
between heat input, temperature lapse rates, and amplitude of turbulence
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2500 -.
2000 —
1500 —
- 1000 —
500 _
TIME OF SOUNDING
0805
1010
1210 x *
1415 - -
1605
1730
SURFACE - 52 m
T
\
16
I ' I ' I
8 10 12 14
TEMPERATURE (°C)
FIGURE 11
VERTICAL TEMP. STRUCTURE
GAINESVILLE, FLORIDA 16 DEC. 1969
I
20
T
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1500
1000 —
500 —
AIRCRAFT TURB.
AIRCRAFT TEMP.
HOLZWORTH
SUNSET: 1732
(SURFACE: 52 m, M.S.L. )
0600
0800
TIME (HOURS)
FIGURE 12
DEVELOPMENT IN MIXING HEIGHT DURING COURSE OF DAY -
AS DETERMINED BY SEVERAL METHODS.
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a: u
*s. —
Z I—
U 0=
TURBULENCE AMPLITUDE 0.05 g.
HOUR 0805
1010
1210
FIGURE 13
1415
1805
1730
DEVELOPMENT OF MIXING HEIGHT AND AMPLITUDE OF TURBULENCE -
AS DETERMINED BY AIRCRAFT ACCELEROMETER.
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Figure 14 shows the mixing height measurement made in New Orleans
on 9 March 1970. It also shows the influence of Lake Ponchartrain on
turbulence and the contribution of background aerosol concentrations
to New Orleans pollution levels.
Lake Ponchartrain is immediately north of New Orleans, and when
these observations were made, winds were from the north across the lake
and into the city. The flight was started at Lake Front Airport on the
edge of Lake Ponchartrain, and the initial climb was made to the north
over the lake. Then a turn was made to the south and the flight continued
over the shoreline and over an industrial area of town.
The accelerometer trace shows turbulence on the take off roll
over the hot concrete runway. Lack of turbulence can be noted during
the climbing turn over the lake. Then turbulence was picked up again
shortly after passing southward over the shoreline.
During the flight over the lake, the aerosol concentration was
5 3
approximately 3 x 10 particles > 0.3ym Per cubic foot (10 per cm ).
Then shortly after returning over the land mass, the aerosol concentration
gradually increased to a rather uniforn level of 8 to 9 x 10 particles
3
per cubic foot (30 per cm ) until the top of the mixing layer was reached.
These data suggest that about one-third of the total number of
particles in New Orleans originated upwind of that city. This is only
true on a count basis, since emission of relatively larger particles
from sources in New Orleans could markedly affect a weight determination.
These small particles can affect visibility, and Figure 15 shows
the contrast in visibility above and below the mixing layer. This photo
was taken just as the aircraft passed through the top of the mixing layer,
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30 -HO
25 --5
o
o
— 20
15 -
10-
5 -I
r-10
-7
-6
-5
-4
-3
-2
-1
•0
A|
in
- 10
- 9
- 8
- 7
- B
- 5
- 4
- 3
- 2
- 1
- 0
CHART SPEED IN MIN.
FIGURE 14
INFLUENCE OF LAKE PONTCHARTRAIN ON TURBULENCE AND AEROSOL ABUNDANCE.
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FIGURE 15
MIXING LAYER
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SUMMARY AND CONCLUSIONS
A series of measurements were made to evaluate the Holzworth
method used by ESSA for calculating mixing heights. One hundred
forty-five atmospheric soundings were made in an instrumented aircraft
to determine the vertical temperature structure, atmospheric turbulence
as indicated by an accelerometer, and height to which pollutants were
mixed as determined by aerosol concentrations.
Mixing height measures based on each of these techniques were
then compared with estimated mixing heights based on Holzworth's method.
It was found that there was no statistical difference between the Holzworth
estimates and aircraft turbulence measures of the mixing height. Mixing
heights based on aircraft temperature profiles were found to be 7 to 9
percent smaller than the Holzworth and aircraft turbulence techniques.
This is thought to be due to the criteria used to select mixing heights
from the aircraft temperature profiles.
There was no statistical difference between mixing heights based
on Holzworth1s technique and aerosol distribution. However, only a poor
correlation (r = 0.25) was found, probably due to detection of aerosols
which had been moved aloft on previous days.
Marked differences in visibility below and above the mixing layer
were photographed, and particle concentrations in each atmospheric regime
were recorded. In New Orleans for example, there were about fifty times
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