EPA-600/4-75-006
October 1975
Environmental Monitoring Series
DISPERSION FROM TALL STACK!
m.
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EPA-600/4-75-006
DISPERSION FROM TALL STACKS
by
Dr. Werner Klug
Technische Hochschule Darmstadt
Federal Republic of Germany
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, D, C. 20460
October 1975
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EPA REVIEW NOTICE
This report has been reviewed by the U.S. Environmental Protection
Agency and approved for publication. Approval does not signify that
the contents necessarily reflect the views and policies of the Environ-
mental Protection Agency, nor does mention of trade names or commer-
cial products constitute endorsement or recommendation for use.
RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environ-
mental Protection Agency, have been grouped into series. These broad
categories were established to facilitate further development and applica-
tion of environmental technology. Elimination of traditional grouping was
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in related fields. These series are:
1. ENVIRONMENTAL HEALTH EFFECTS RESEARCH
2. ENVIRONMENTAL PROTECTION TECHNOLOGY
3. ECOLOGICAL RESEARCH
4. ENVIRONMENTAL MONITORING
5. SOCIOECONOMIC ENVIRONMENTAL STUDIES
6. SCIENTIFIC AND TECHNICAL ASSESSMENT REPORTS
9. MISCELLANEOUS
This report has been assigned to the ENVIRONMENTAL MONITORING
scries. This series describes research conducted to develop new or
improved methods and instrumentation for the identification and quantifica-
tion of environmental pollutants at the lowest conceivably significant
concentrations. It also includes studies to determine the ambient concentra-
tions of pollutants in the environment and/or the variance of pollutants
as a function of time or meteorological factors.
This document is available to the public for sale through the National
Technical Information Service, Springfield, Virginia 22161.
Publication No. EPA-600/4-75-006
11
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Preface
The present study was initiated during the period August-September
1973, while Dr. Werner Klug (Professor of Meteorology, Technical University
Darmstadt, Federal Republic of Germany) was a visiting scientist at the
Meteorology Laboratory, National Environmental Research Center, Research
Triangle Park, N. C. Dr. Klug had been invited to discuss air quality
modeling activities in the U.S.A. and the F.R.G. in preparation for the
5th Meeting of the NATO Committee on the Challenges to Modern Society,
Expert Panel on Air Pollution Modeling (held at the Danish AEC, Roskilde,
Denmark in June 1974). Among many other activities during his visit,
and largely on his own initiative, Dr. Klug commenced the present study
following a visit to the TVA at Muscle Shoals, Alabama. A preliminary
report on this work was presented at the NATO/CCMS meeting mentioned
above. A more complete analysis is now available and, in view of the
great current interest in the topic of dispersion from tall stacks, it
is now published as a special report so as to make the results more widely
available. It should in no way be regarded as a final analysis of the
problem, but only as contributing to the informational base that is now
rapidly growing as a result of several closely related similar studies
that are near completion. It is hoped that it will make an important
contribution to a more definitive evaluation of the current state-of-the-
art as regards modeling the dispersion of gaseous pollution from tall
stacks.
Kenneth L. Calder
Chief Scientist, Meteorology & Assessment Division
u. 3. Environmental Protection Agency
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Dispersion from Tall Stacks
W. King
Technische Hochschule Darmstadt, FRG
I. Introduction
Concentration fields downwind of large, single emission sources are now-
adays very often calculated in connection with air pollution control measures.
The values for the dispersion parameters that occur in the dispersion equation
(in case of the Gaussian-plume model, the a^ and a values as a function of
•J
downwind distance) are usually those derived from previous diffusion experi-
ments, where source heights were generally much lower than the effective
heights for present-day large emission sources. Furthermore, in order to
calculate a concentration field for a given meteorological situation, a
scheme has to be used which relates easily accessible meteorological
parameters (such as a low-level wind speed, incoming radiation, cloud cover,
vertical temperature differences) to these o-values. Such schemes have been
devised in the past by several investigators, and the most well-known seems
to be the Pasquill classification [1]. Pasquill, however, pointed out that
his scheme, together with his set of a-values, should only be used for
ground or low-level sources and not for effective source heights of the order
of several hundred meters, such as are common in the base of large power
stations. Nevertheless these values are often used because so few others are
available, and in the hope that the errors might cancel out in a statistical
rnntpyt ThnS calculations of concentr?f'on values averaged over a ye?"",
or concentration frequency distributions for the year might be close to
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reality. Another source of error is the calculation of effective source
height, and here again reasonable results would only be expected on the
average.
Looked at from another point of view, many previous investigators have
devised different urban air pollution models where, in most cases, the large
single sources were modelled in the above manner. Attempts have also been
made to validate these models, which usually contain a mixture of large and
small point sources as well as area sources (which may be either real or used
for simulating numerous very small sources, e.g., as for domestic heating).
Such validation attemps would give better insight into the problems connected
with urban air pollution modelling if the verification for the classical
problem of the large single-elevated source had been established in advance.
This is especially true for many of the larger cities where large single
sources, such as power plants or chemical factories, can make major
contributions to the concentration field. Such contributions can be
important over a wide range of distances, depending on the meteorological
situation.
For these reasons it seemed worthwhile to try to validate (or at least
to show the limits of) the model of the single-elevated point source (steady
state short-term Gaussian-plume) when applied to a large source. However,
as we see below, the data actually used in the present paper refer to a
plant consisting of three stacks, i.e., of three elevated point sources.
T!":S ~.eans that, we !-,avc to deal in most cases with the 3-pei-pc^it,1cr. cf thr^v.
plumes. It is obvious that certain conditions must be fulfilled by a data
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set for it to be suitable for such a validation procedure. First of all, the
data relating to the output of the source must be wen-documented and on an
hourly basis. Then the meteorological data for each hour should include wind
direction, wind speed, and some information on atmospheric turbulence and/or
vertical stability, in order to permit use of the Pasquill scheme or one
similar to it. Hourly concentration measurements downwind of the source must
also be available and there should be no background pollution. These are the
minimum requirements for an acceptable data set.
II. Model Validation Procedure
After some discussion with colleagues from the EPA, and examining the
availability of possible data sets, the data most suitable for the purpose
appeared to be those from the TVA electric power generating plants, and
especially those from the Paradise Steam Plant. This is located on the west
bank of the Green River in Muhlenberg County, near the village of Paradise in
Western Kentucky, USA.. The plant has three units, of which units 1 and 2
have a capacity of 704 MW and unit 3 of 1150 MW. The stack heights are
183m, 183m, and 244m, respectively.
The facts which make this data set suitable are as follows. For the
whole of 1971 the following data are available for this particular plant:
1. The daily S02 output data for each unit calculated from the daily
coal consumption and a weekly average sulfur content of the coal.
Since the coal used comes only from adjacent coal fields, the sulfur
content is relatively constant.
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2. The hourly total MW data for the three units together. This hourly
value is used, as below, to estimate an hourly S02 output for each
unit.
3. Hourly meteorological data.- These consist of wind speed and wind
"direction at two different heights (-13.4m and roughly 1-lOm above
the ground), vertical temperature differences between three
different heights, surface temperature, surface pressure, amount of
rainfall, total and solar radiation.
4. Hourly SCL concentration data for 6 sampling stations. Most of
these stations are located downwind in the prevailing wind
direction, and range in distance from approximately 3 to 17 km.
5. Empirical relationships for the dependence of stack gas exit
velocity on MW load. The exit temperature of the gases does not
vary significantly with load and was therefore assumed to be
constant.
Furthermore, there seems to be no background concentration (S02 or
other substances to which the conductivity method of concentration measurement
might be sensitive) in the area and the surroundings of the site are
relatively level compared with the effective heights of the plumes.
The procedures for calculating the surface concentrations-[the concen-
trations due to the three individual units are calculated and then summed]
at a receptor point are the following:
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1. Determine the source output data for each unit.
a. The hourly SCL output is determined for each unit by multi-
plying the daily SCL output by the ratio of total hourly MW
load to the daily average total MW load.
Result: Hourly SCL source strength in g sec" .
b. The hourly exit velocity for each unit is determined by
multiplying the total hourly MW load by a regression factor
(supplied by TVA), multiplied by the ratio of the daily unit
source strength to the sum of the three unit source strengths.
Result: Exit velocity in m sec" .
c. Use- the constant exit temperature of each unit (413.2° for
units 1 and 2, and 402.2°K for unit 3).
Result: Exit temperature in °K.
d. Compute the effective source height for each unit by using
Briggs formulation [2] using the unstable, neutral or stable
equations depending upon the stability. The stability is
determined from the measured temperature differences between
1m and 110m above ground. The wind speed used is measured
at 110m.
Result: Effective source height in m.
2. Calculate the hourly concentrations using the hourly meteorological
data:
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If the wind direction at 110m averaged over one hour is
outside a sector, which is defined by the bearing from
true North of the receptor station with respect to the source,
increased by (180° ±45°), then the concentration at this
-30 -3
receptor point is set equal to 10 g m . (i.e., is
negligible.
If the wind direction is within this sector, the concentration
is calculated by using the standard bivariate Gaussian dis-
tribution for the concentration where -
(1) The wind direction at 110m and the bearing and distance
of the receptor are used to calculate the x and y
coordinates of the receptor.
(2) The temperature difference between 110m and 1.5m and
the wind speed at 13m are used for determining the
stability class by the following scheme:
> 4
A
B
4.0-3.0
B
C
3.0 -0.5
C
C
0.5- -1.5
D
C
E
D
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This scheme for stability classes was set up after a number
of test calculations, by relating the C-class to near
adiabatic stratification, and the extreme values of observed
differences to classes A and E, respectively.
(3) The standard deviations in the vertical and horizontal
direction a and a are used according to the above
J
scheme and
(a) Pasquill's original a-dependencies on distance
and stability classes [See Workbook of Atmospheric
Dispersion Estimates, by D. B. Turner, U.S.
Environmental Protection Agency, 1970].
(b) Pasquill's new power law dependencies for a
obtained from F.B. Smith's K-theory computations,
and given in the latest edition of his book
(Pasquill 1974). The a values were same as for (a).
(4) The wind speed at 110m.
c. After the total hourly concentration due to the three
stacks is computed for this measured wind direction, this
wind direction is then arbitrarily changed by amounts
+10°, +20°, +30° and the total concentrations are computed
again. This is done in order to study the influence of
changing wind direction with height.
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8
d. The concentration which is closest to observed concentration
i s noted.
e. These 8 concentrations (7 computed ones and 1 observed)
are stored on tape.
f. For all 8 data sets the frequency distributions are
calculated and compared. Since the "measured wind
direction" set gave the best agreement with observation
these comparisons are not discussed any further.
g. The annual mean value, the standard error of estimate
and the correlation coefficient between the logarithm
of concentrations are calculated. [The correlation
coefficient, is a measure for the linear (stochastic)
relationship between two normally distributed variables.
Since the distribution of concentrations (not counting
negligible values) is approximately log-normal the
correlation of the log-values appeared appropriate.]
Excluding those periods when either the meteorological
or sampling equipment was not operating, roughly 300,000
concentrations were calculated and compared with some
43,000 observed values, although many of these were
zero.
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III. Results
The screening of the observed concentration data showed that Station 6
(at a distance 12.7 km) showed no concentration values in the range 10~ to
-4 -3 -5 -3
10 g m , which is the decade just above the detection limit of 10 g m .
The data from this station were therefore not used-.
1. Mean Values
The mean values for the whole one-year period were as follows [the
calculated values refer to the measured wind direction at 110m.]
Station
(Number)
I
III
IV
V
II
Distance
(km)
2.9
4.6
6.8
8.4
16.9
Observed
00"5g m"3)
1.0
0.7
1.0
0.9
2.1
Calculated
(10"5g m"3)
0.8
1.3
1.5
1.4
1.1
Ratio
Calc./Obs.
0.82
1.83
1.50
1.55
0.52
These results show an overcalculation at 3 stations and an under-
calculation at 2. A number of different stability - diffusion
category schemes were tried with the hope of improving the results,
However, use of these different schemes only changed the level of
over - or underealculation and did not improve the agreement.
[The class limits of the vertical temperature gradients were
changed so that the number of cases per diffusion category was
changed, which in turn changed the concentration statistics.]
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10
Furthermore, the calculated values show a smooth variation with
distance, with a maximum at about 7 km. On the other hand, the
observed concentrations show an unexplainable irregular behavior
with the highest concentration mean value at 17 km. The results
obtained with the second a -set mentioned above differed insignifi-
cantly from the first, and a separate discussion is therefore omitted.
2. Frequency Distributions
The frequency distribution of concentrations is plotted as
cumulative frequencies on probability paper as a function of the
negative logarithm of the concentration. (See Fig 1-5). The out-
standing feature of all the distributions is the fact that there is
a large fraction of the concentrations (in some cases more than 90%)
-5 -3
that are below the threshold or detection limit of 10 g m . This
would be expected since the wind is only blowing a small fraction of
the total period from the source site to a particular recepltor loca-
tion. The other interesting conclusion that may be drawn from the
figures is that, for all six stations, the highest hourly concentrations
occur more frequently for the computed concentration distribution than
for the observed one, whereas lower concentrations closer to the thres-
hold occur more frequently for the observed than the computed dis-
tribution. This gives rise to suspicion that the instruments measuring
the S02 concentrations may record values of some concentrations
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11
-5 -3
that are below the threshold of 10 g S(L m , as though they were
above this limit. If this turns out to be the case, the conclusions
drawn from this study are, of course, invalid or partly valid.
3. Standard Error of Estimate and Correlation Coefficient. Whereas
the quantities above did not consider observed and computed concen-
trations as synchronous data pairs, i.e., irrespective of when they
occurred, the standard error of estimate and the correlation
coefficient involve consideration of simultaneous values. The
following results were obtained:
Station
I
III
IV
V
II
Changes of Wind
Standard Error
of Estimate
10~5qnf3
8.4
8.7
9.4
9.2
8.5
Direction
Correlation
Coefficient
0.14
0.16
0.16
0.12
0.15
As was mentioned before, concentrations were also computed after
changing the hourly measured wind directions arbitrarily by amounts
of +_ 10°, +_ 20°, i 30°. If, for each hour the concentration value
is picked which gives best agreement with the observation, then the
standard error of estimate reduces considerably, and the correlation
coefficient is increased.
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Station Standard Error Correlation
I
III
IV
V
II
of Estimate
10~5g m~3
3.6
3.0
3.3
2.8
5.9
Coefficient
0.35
0.43
0.44
0.43
0.47
These results indicate the sensitivity of the computed concentrations
to the wind direction (which is equivalent to the orientation of the
coordinate system). It was anticipated that the (arbitrary)
variation of wind direction might reveal a systematic deviation,
in the sense that during daytime there might be better agreement
if the wind direction was turned, say, 10 degrees to the right,
as compared with perhaps 20 - 30 degrees to the right during the
night. Although a systematic deviation of +20° (to the right),
when applied to all the hourly wind direction values at 100 m. height,
was found to give the best agreement for a subset of the observations,
the improvement was insignificant for the whole data set.
IV. Conclusions
The conclusions which can be drawn from this study are the following:
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13
1. The observed and computed mean values of S0» concentrations over a
period of roughly one year, agree within a factor of 2.
2. The highest hourly concentrations occur more frequently for the
computed concentration distribution than for the observed one,
whereas lower concentrations that are closer to the threshold occur
more frequently for the observed than the computed concentration
distribution.
3. The standard error of the estimate between observed and calculated
hourly concentration values is several times the annual mean value,
and the correlation coefficient is low although significantly
different from zero.
4. The standard error of the estimate between observed and calculated
hourly concentration values can be reduced considerably and the
correlation coefficient increased, if the measured hourly wind
direction is changed arbitrarily by an appropriate amount for
each hour.
5. There is some suggestion that the S0? instruments used in this
study may record concentration values that are below the threshold
value as being above it. This is suggested by the findings under
(2) above. Another reason for suspecting instrumental deficiencies
is the irregular behavior of the concentration mean values as a
function of distance.
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V. Acknowledgements
Part of the study was undertaken while the author was a visiting scientist
with the Meteorology Division, NERC, EPA, at Research Triangle Park, N. C.
The stimulating and helpful discussions with Messrs. K. L. Calder and D. B.
Turner, and the programming assistance of-Messrs. A. Busse and B. Dietzer
are gratefully acknowledged.
This study would not have been possible without the help of TVA in
providing and interpreting the raw data; special thanks are due to Dr. L.
Montgomery of TVA.
VI. References
[T] Pasquill, F., 1361. The Estimation of the Dispersion of Windborne
Material, Meteorolog. Mag., 90, p. 33-49.
[2] Briggs, G., 1972. Chimney Plumes in Neutral and Stable Surroundings,
Atmosp. Environment, 6, p. 507-510.
[3] Pasquill, F., 1974. Atmospheric Diffusion. John Wiley & Sons, New York.
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15
90
80
70
60
50
AO-
30-
20
10'
os-
STATION I
3.0
3.2 3A
I.A /le
3.8
4.A
A.6
4.8 5.0
-log C
Figure 1. Cumulative frequency distribution of the negative logarithm of con-
centration (plotted on probability paper) for Station I.
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16
90
80-
70
60-j
50
40-
30-
20
ID-
S'
4.
3
2-
1-
0.5
STATION El
3.0 ' 3,2 3.4 3,6 3,8 4.0 4,2 4.4 4,6 4,8
-log C
5.0
Figure 2. Cumulative frequency distribution of the negative logarithm of con-
centration (plotted on probability paper) for Station III.
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90!
80
70
60^
50
40^
30
20
10
5
4-I
3
2
0.5
STATION B?
3.0 3.2 34 3.6 3.8 4.0 4.2
-log C
44
46
4.8 5,0
Figure 3. Cumulative frequency distribution of the negative logarithm of con-
centration (plotted on probability paper) for Station IV.
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90
80
70
60
50
40
30
20
5-
4-
3-
2
1-
0,5
STATION
COMR
3.0
32
3.4. 3,6
3,8
46
48
50
- log C
Figure 4. Cumulative frequency distribution of the negative logarithm of con-
centration (plotted on probability paper) for Station V.
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T9
90;
80-
70
60
50
40
30
20-
10
5
4
3
2-
1
0.5
STATION E
3.0 3.2 3.4 3.6
3.8
4.0 4,2
-log C
44 4.6 4.8 5.0
Figure 5. Cumulative frequency distribution of the negative logarithm of con-
centration (plotted on probability paper) for Station II.
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/4-75-006
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
DISPERSION FROM TALL STACKS
E.PQRT, DATE,n-.P
October 1975
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Dr. Werner King
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Technische Hochschule Darmstadt
61 Darmstadt, Hochschulstr. 1,
Federal Republic of Germany
10. PROGRAM ELEMENT NO.
1AA009
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA-ORD
15.
UPPL£MENTARYJNOTES ,. /• ,-J , ,. ,. ,- „, „ i-, . ..,-,.
uppTements Proceedings of 5th Meeting of Expert Panel on Air Pollution Modeling,
NATO/CCMS Air Pollution Publication No. 35, August 1974.
16. ABSTRACT
This report analyzes data relating to the atmospheric dispersion of S02 from the
TVA Paradise Steam Plant in Western Kentucky, U.S.A. Extensive hourly air quality
measurements for 1971 are compared with predicted values, obtained by using the
well-known steady-state short-term Gaussian plume model for dispersion from an
elevated point-source release. The comparison is in' terms of-annual average
concentration values and the frequency distributions of the hourly values at five
monitoring stations in the vicinity of the electric-power generating plant.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Air Pollution
*Sulfur Dioxide
*Atmospheric Diffusion
*Chimneys
Plumes
E,l ectric, Power PI ants
Gaussion plume model
13B
07B
04A
13M
21B
10B
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report}
UNCLASSIFIED
21. NO. OF PAGES
25
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
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