EPA-450/3-77-003a
September 1976
IMPROVEMENTS
TO THE SINGLE
SOURCE MODEL
VOLUME I -
TIME CONCENTRATION
RELATIONSHIPS
FINAL REPORT
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
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EPA-450/3-77-003a
IMPROVEMENTS TO THE SINGLE
SOURCE MODEL
VOLUME I -
TIME CONCENTRATION RELATIONSHIPS
FINAL REPORT
by
Michael T. Mills and Roger W. Stern
CCA Corporation
CCA/Technology Division
Bedford, Massachusetts
Contract No. 68-02-1376
Task Order No. 23
EPA Project Officer: Russell F. Lee
Prepared for
ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
September 1976
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This Final Report was furnished to the Environmental Protection Agency by
GCA Corporation, GCA/Technology Division, Bedford, Massachusetts 01730, in ful-
fillment of Contract No. 68-02-1376, Task Order No. 23. The opinions, findings,
and conclusions expressed are those of the authors and not necessarily those of
the Environmental Protection Agency or of the cooperating agencies. Mention of
company or product names is not to be considered as an endorsement by the
Environmental Protection Agency.
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CONTENTS
Page
List of Figures iv
List of Tables vii
Acknowledgments viii
Sections
I Introduction 1
II Site and Data Base Descriptions 4
III Analysis of Concentration Ratio Distributions 19
IV Comparison with Previous Studies 41
V Conclusion 45
VI References 47
iii
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LIST OF FIGURES
No. Page
1 Map of Eastern Massachusetts and Rhode Island Showing 5
the Location of the Canal Plant. Meteorological Obser-
vations Were Used From Quonset Point Naval Air Station
and Nantucket Island
2 Sketch of the Canal Plant Area Showing the Locations of the 8
Four Automatic SO- Stations by the Symbol 0
3 Map of Ohio and Surrounding States Showing the Locations 10
of the J. M. Stuart Plant, Philo Plant, and Muskingum
River Plant
4 Sketch of the J. M. Stuart Plant Area Showing the Locations 12
of the Seven Automatic S0_ Monitoring Stations
5 Sketch of the Muskingum Plant Area Showing the Locations 14
of the Four Automatic S0_ Monitoring Stations
6 Sketch of the Philo Plant Area Showing the Locations of 16
Six Automatic S0_ Monitoring Stations
7 Muskingum River Plant Cumulative Frequency Distribution for 23
1-Hour S02 Concentrations at All Sampling Stations. Number
of Measured Concentrations = 30,622; Number of Calculated
Concentrations = 61,320
8 Canal Plant Cumulative Frequency Distribution of Ratios of 24
Peak to Mean Concentrations for All Cases
9 Canal Plant Cumulative Frequency Distribution of Ratios of 25
Peak to Mean Concentrations for Cases Where the Peak Con-
centrations are Greater Than 18 n.g/m3; 18 jig/m^ is the 95th
Percentile of the 1-Hour Concentrations
10 Canal Plant Cumulative Frequency Distribution of Ratios of 26
Peak to Mean Concentrations for Cases Where the Peak Con-
centrations are Greater Than 35 (ig/m3; 35 |_ig/m3 is the Per-
centile of the 1-Hour Concentrations
iv
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LIST OF FIGURES (continued)
No. Page
11 Canal Plant Cumulative Frequency Distribution of Ratios of 27
Peak to Mean Concentrations for Cases Where the Peak Con-
centrations are Greater Than 55 ug/m^; 55 (j.g/m^ is the 99th
Percentile of the 1-Hour Concentrations
12 J. M. Stuart Plant Cumulative Frequency Distribution of 28
Ratios of Peak to Mean Concentrations for All Cases
13 J. M. Stuart Plant Cumulative Frequency Distribution of 29
Ratios of Peak to Mean Concentrations for Cases Where the
Peak Concentrations are Greater Than 59 pg/m^; 59 ug/m^ is
the 95th percentile of the 1-Hour Concentrations
14 J. M. Stuart Plant Cumulative Frequency Distribution of 30
Ratios of Peak to Mean Concentrations for Cases Where the
Peak Concentrations are Greater Than 140 ug/m^; 140 ug/m^
is the 98th Percentile of the 1-Hour Concentrations
15 J. M. Stuart Plant Cumulative Frequency Distribution of 31
Ratios of Peak to Mean Concentrations for Cases Where the
Peak Concentrations are Greater Than 220 ug/m^; 220 ng/m3
is the 99th Percentile of the 1-Hour Concentrations
16 Muskingum Plant Cumulative Frequency Distribution of Ratios 32
of Peak to Mean Concentrations for All Cases
17 Muskingum Plant Cumulative Frequency Distribution of Ratios 33
of Peak to Mean Concentrations for Cases Where the Peak Con-
centrations are Greater Than 72 ng/m^; 72 ng/m^ is the 95th
Percentile of the 1-Hour Concentrations
18 Muskingum Plant Cumulative Frequency Distribution of Ratios 34
of Peak to Mean Concentrations for Cases Where the Peak
Concentrations are Greater Than 176 ug/m-*; 176 ug/m^ is the
98th Percentile of the 1-Hour Concentrations
19 Muskingum Plant Cumulative Frequency Distribution of Ratios 35
of Peak to Mean Concentrations for Cases Where the Peak Con-
centrations are Greater Than 250 ug/m^; 250 ag/m^ is the
99th Percentile of the 1-Hour Concentrations
20 Philo Plant Cumulative Frequency Distribution of Ratios 36
. of Peak to Mean Concentrations for All Cases
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LIST OF FIGURES (continued)
No. Page
21 Philo Plant Cumulative Frequency Distribution of Ratios 37
of Peak to Mean Concentrations for Cases Where the Peak
Concentrations are Greater Than 53 ug/m^; 53 jig/m^ is the
95th Percentile of the 1-Hour Concentration's
22 Philo Plant Cumulative Frequency Distribution of Ratios 38
of Peak to Mean Concentrations for Cases Where the Peak
Concentrations are Greater Than 123 ug/m^; 123 ug/m^ is
the 98th Percentile of the 1-Hour Concentrations
23 Philo Plant Cumulative Frequency Distribution of Ratios 39
of Peak to Mean Concentrations for Cases Where the Peak
Concentrations are Greater Than 183 ug/in^; 183 ug/m^ is
the 99th Percentile of the 1-Hour Concentrations
vi
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LIST OF TABLES
No. Page
1 Plant Characteristics 6
2 Monthly Percent Sulfur Content of Fuel 6
3 Sulfur Dioxide Monitor Stations 9
4 Statistics for Peak to Mean Ratio Distributions 40
5 Comparison of Peak to Mean Concentration Ratios for 43
Different Source Receptor Distances
vii
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ACKNOWLEDGMENTS
The key data used in carrying out this study were made available to GCA/
Technology Division by the .New England Gas and Electric System, Dayton
Power and Light Company, the Ohio Power Company and the American Electric
Power System. Project direction and guidance were given by Mr. Russell
Lee of the Source-Receptor Analysis Branch, Monitoring and Data Analysis
Division, EPA, Durham, North Carolina.
viii
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SECTION I
INTRODUCTION
Reliable estimates of maximum 3-hour and 24-hour S0_ concentrations due
to power plant emissions are required for a variety of environmental
assessment activities associated with air quality maintenance planning,
fuel switching, plant siting and tall stack policy evaluations. Either
of two methods are generally employed for the prediction of maximum S00
concentrations for these two averaging times. The first technique re-
quires the prediction, by means of a diffusion model, of hourly S0_ con-
centrations for an array of model receptor locations at a variety of
distances and headings from the source. Running 3-hour means and daily
24-hour means are then obtained by averaging the predicted 1-hour con-
centrations. The resultant 3-hour and 24-hour concentrations are then
sorted to find the highest and second highest values. This procedure is
rather costly in terms of computer time since concentration predictions
must be made for every hour of the year. The second method involves the
calculation of a "worst hour" concentration based upon a critical wind-
speed and plume height. This concentration is then used to estimate a
"worst 3-hour" and a "worst 24-hour" concentration through the application
of an appropriate peak to mean concentration ratio.
In the choice of a peak to mean ratio, one must obviously account for
the wide range of possible ratios which could be selected. With a large
number of site years of data one could construct distributions of ratios
of highest 1-hour to highest 3-hour and 24-hour concentrations for the
year and select some percentile of this distribution as the peak to mean
ratio to be used. The choice of a given percentile would be dictated by
the desired degree of conservatism in the 3-hour or 24-hour estimate,
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with peak to mean ratios of 1 being the extreme example. In the absence
of a large number of site years of data, peak to mean ratio distributions
may be constructed by use of all hourly measurements. In two earlier
EPA reports ' GCA analyzed frequency distributions of peak 1-hour to
average 3-hour and peak 1-hour to average 24-hour S00 concentration
ratios based upon hourly concentration measurements at four separate
power plant sites. In all cases the peak to mean ratios were calculated
in terms of concentrations that have been corrected for background con-
centration which was determined on an hourly basis from an average of
measurements at upwind receptor locations. One drawback to this proce-
dure is that the ratio distribution is heavily influenced by those
"peak" concentrations near the background level which occur when the
receptor is not influenced by the point source plume. The purpose of
the present study was therefore to examine the effect upon ratio dis-
tribution statistics if only peak concentrations above a certain cutoff
value were analyzed, and thereby ensure that ratios used for the esti-
mation of maximum 3-hour and 24-hour concentrations from maximum 1-hour
values will be derived from ratio frequency distributions associated
with the highest percentile of 1-hour concentrations. The following
percentile limits for the peak concentration were tested: 95, 98 and
99. The actual concentrations associated with these percentile limits
were determined for each plant site through an examination of the
cumulative frequency distribution of background subtracted concentra-
tions for all receptor sites taken as a whole. Statistics of peak to
mean ratio distributions included in the analysis were the arithmetic
mean, arithmetic standard deviation, geometric mean, geometric standard
deviation, median and correlation between peak concentration and asso-
ciated peak to mean ratio.
In the next section of this report we shall describe the plant site
characteristics and the meteorological and air quality data bases used
in the study. This will be followed by a discussion of the ratio dis-
tributions and their associated statistics, including an analysis of
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the variation of these parameters for different plant sites and peak
concentration cutoffs. We shall then conclude with a discussion re-
garding the general applicability of these results to other point
sources.
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SECTION II
SITE AND DATA BASE DESCRIPTIONS
In this section we shall describe the site characteristics, SO^ monitor-
ing program and meteorological data base for each of the four power plants
included in the study. Each topic will be covered on a plant-by-plant
basis.
CANAL PLANT
Site Description
The Canal Plant is located on the south side of the Cape Cod Canal about
1.6 kilometers from the entrance on Cape Cod Bay (Figure 1). The
surrounding terrain is gently rolling with elevations generally below
60 meters above mean sea level. The highest elevations in the area are
about 90 meters above sea level in the western end of the Cape. Most of
the area is covered with scrub pine forests and low vegetation.
Data for the study were collected in 1971. During that year, the plant
consisted of a single oil-fired unit with a generating capacity of
560 megawatts. The top of the stack was about 91 meters above grade
and 5.6 meters in diameter. The main power plant structure to the north
of the stack totally enclosed the turbine generator and boiler. The
roofs of the turbine and boiler rooms were about 30 meters and 59 meters
above grade respectively. Stack and boiler data are given in Table 1.
The 1971 monthly percent sulfur content of the fuel used at the Canal
Plant is given in Table 2.
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10 20
MASSACHUSETTS
Figure 1. Map of eastern Massachusetts and Rhode Island showing the location
of the Canal Plant. Meteorological observations were used from
Quonset Point Naval Air Station and Nantucket Island
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Table 1. PLANT CHARACTERISTICS
Characteristic
Stack height, m
Diameter, m
Velocity, m/sec
Temperature , °K
Number of boilers
per stack
Maximum generating
capacity per
stack, MW
Average per stack, MW
Plant total, MW
Plant average, MW
Plant
Canal
Stack
1
91
5.6
19.8
469
1
560
-
560
-
Stuart
Stacks,
all four
244
6.0
22.2
373
1 each
610
439
2440
1318
Muskingum
Stack
1
251
7.6
28.5
430
4
876
748
Stack
2
251
6.7
24.8
425
1
591
487
_ - J
1467
1235
Philo
Stack
4
81
5.2
4.5
458
2
166
114
- *
Stack
5
81
3.9
7.7
458
2
166
128
^s~
457
Stack
6
84
2.6
29
433
1
125
84
^
326
Table 2. MONTHLY PERCENT SULFUR
CONTENT OF FUEL
Month
January
February
March
April
May
June
July
August
September
October
November
December
Canal
2.0
1.9
2.1
1.9
2.1
2.1
2.1
2.0
1.9
0.9
1.0
0.9
Stuart
1.8
1.6
1.8
1.7
1.8
1.6
1.5
1.5
1.5
1.5
1.8
2.1
Muskingum
4.9
4.8
4.8
4.5
4.7
5.0
4.7
4.7
4.3
4.6
4.5
4.4
Phllo
3.9
4.8
4.7
4.4
3.3
3.2
2.6
3.2
3.2
2.4
2.6
3.7
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Overview of Monitoring Program
SO- concentrations are measured at four locations on a continuous basis
with Ultragas S02 Analyzers manufactured in Germany by H. Wosthoff. These
instruments measure sulfur dioxide by the increase in conductivity of an
acidified hydrogen peroxide solution and have a full scale reading of
0;4 ppm. The instruments do not conform to the reference method for
4
sulfur dioxide or to any of the specified equivalent methods. They have,
however, been extensively studied and one comparison noted a correlation
coefficient of 0.99 with the West-Gaeke method. The instruments used
provide a continuous real-time chart trace and a tape printout giving
date, time, and average concentration over consecutive 30 minutes. The
sensitivity of the instrument in combination with the chart recorder is
approximately 0.005 ppm. The locations of the S0« monitors with respect
to the Canal Plant are given in Figure 2 and Table 3.
Meteorological Data
Bendix-Friez Aerovanes are used to provide local windspeed and direction
data. Through July 1971, the principal source of wind data was the
Aerovane mounted on a 12.2 meter mast located on the 58.8 meter boiler-
room roof. Since July 1971, wind data are obtained from a second Aerovane
installed on a 44 meter tower near the top of Telegraph Hill approximately
5 kilometers south-southeast of the Canal Plant.
STUART PLANT
Site Description
The J. M. Stuart Plant is located in southwestern Ohio on the Ohio River,
about 9 kilometers southwest of Manchester, Ohio, and 4 kilometers east
of Maysville, Ohio (Figure 3). It is located near the center of
this river valley. The ridges on either side of the valley are about
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oo
RTE3 Q
SAGAMORE
BEACH
CAPE COD BAY
N
^AGAMOREBRI OGE
0.5 I
km
CH
Figure 2. Sketch of the Canal Plant area showing the locations of the four automatic
SO- stations by the symbol © j
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Table 3. SULFUR DIOXIDE MONITOR STATIONS
Plant
Canal
Stuart
Muskingum
Philo
Station
No.
1
2
3
4
1
2
3
4
5
6
7
1
2
3
4
1
2
3
4
5
6
Name
Boone
Brudysville
Bentonville
Manchester
Maysville
Rectorville
Somo
Top of stacks
Beverly
Hackney
Rich Valley
Caldwell
Top of stacks
Philo
Fox Run
Irish Ridge
Duncan Falls
Salt Creek
Indian Run
Top of stacks
Dis tance ,
km
4.7
2.3
1.4
2.0
2.4
6.6
13.4
8.7
3.8
8.4
5.0
5.3
4.3
8.3
19.6
1.7
4.8
5.0
1.3
6.0
4.2
Heading,
degrees
119
138
224
312
35
15
28
49
279
156
220
140
40
35
35
174
166
235
343
25
334
Elevation above
stack base, m
10
4
40
20
115
85
121
-7
-4
115
115
244
64
82
101
128
251
3
2
99
12
26
63
81
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CDAYTON
PITTSBURQ
O
'COLUMBUS QZANESVILLE
-PHILO PLANT
MUSKINGUM
PLANT
>MANCH
^C/
J.M.STUART PLANT
KENTUCKY
Stale Capital
WEST VIRGINIA
Figure 3. Map of Ohio and surrounding states showing the locations
of the J. M. Stuart Plant, Philo Plant, and Muskingum
River Plant
10
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115 meters above the valley floor and 700 meters from the power plant.
The 244 meter stacks rise 130 meters above the surrounding countryside.
The data were collected during the 1-year period from January 1, 1973
to December 31, 1973. The plant consists of four identical coal-fired
boilers with a capacity of 610 megawatts each-. However, one boiler was
under repair during the entire year so that the total generating capacity
was only 1830 megawatts. The yearly average generating load was 1318 mega-
watts, or 72 percent of available capacity. Stack and boiler data are
given in Table 1. Monthly percent sulfur values for 1973 are given in
Table 2.
Overview of Monitoring Program
The monitoring network consists of seven sulfur dioxide monitoring sta-
tions (Figure 4 and Table 3). The monitor at Station 2 was moved
to Station 4 on March 10, 1973, and the monitor at Station 7 was dis-
continued on June 17, 1973. Therefore no data is available at Station 2
for 9 months, Station 4 for 3 months, and Station 7 for 6 months. The
instruments were all Leeds & Northrup Company, Catalog No. 7860-SW,
Aeroscan Air Quality Monitors, purchased in 1968. The sample was obtained
by passing ambient air taken from 5 feet above ground level, through an
absorption column along with an absorption solution. The sample analysis
method was by electrolytic conductivity. Data were taken continuously and
listed every hour. Electrical calibration tests were performed weekly
for zero and half scale operation. Overall calibration tests were made
every 6 months at 0.2 ppm using the permeation tube method whose accuracy
is traceable to the U.S. Bureau of Standards. There were some additional
hours of missing data due to (1) loss of electrical power; (2) periods of
calibration and maintenance; and (3) system failures caused by presence
of foreign material in the sample flow, pump failure, loss of ink supply,
failure of the conductivity cell, etc.
11
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Figure 4. Sketch of the J. M. Stuart Plant area showing the
locations of the seven automatic S0_ monitoring
stations
12
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The manufacturer's performance accuracy specifications are as follows.
In a typical ambient atmosphere which includes the normal interfering
gases, this instrument has:
Zero drift = 2 percent of full scale per week
Sensitivity drift < 1 percent of full scale per week
Reproducibility < 1 percent of full scale
Sensitivity " = 0.01 ppm
Recorder error < 0.5 percent of full scale
Range = approximately 0-1 ppm
Meteorological Data
The meteorological instrumentation at the J. M. Stuart Plant consists of
a Bendix-Friez windspeed and direction device mounted 40 meters above
the ground on the coal stacking tower.
MUSKINGUM PLANT
Site Description
The Muskingum Plant is located in southeastern Ohio on the Muskingum River
about 6 kilometers northwest of the town of Beverly. Figure 5 indicates
the location of the plant, the S0? monitoring sites, and the surrounding
towns. The plant is in the river valley about 500 meters from the valley
walls which rise about 75 meters above the valley floor. The two 251 meter
stacks are 640 meters apart and extend about 185 meters above the surround-
ing terrain. During 1973 the plant consisted of five coal-fired units
with a total capacity of 1467 megawatts (Table 1). Percent sulfur
content of the fuel for 1973 is given in Table 2.
13
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RICH VALLEY
CENTERVILLE
RT 76
MUSKINGUM PLANT
STACK I
'STACK 2
KILOMETERS
012345
Figure 5. Sketch of the Muskingum Plant area showing the locations
of the four automatic S09 monitoring stations
14
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Overview of the Muskingum Monitoring Program
Four sulfur dioxide monitoring stations make up the monitoring network
(Figure 5 and Table 3). Data were available from all stations for
January 1 to November 21, 1973. During the entire'year of 1973,
Station 1 missed 57 days and the other three stations missed approx-
imately 41 days in total. The monitors were the same type used at
the Stuart Plant, with the same calibration procedure, except that
they were automatically zeroed once a day.
Meteorological Data
There were two wind monitoring stations at the Muskingum Plant consisting
of Bendix-Friez Aeronave windspeed and direction devices. One station
was located 33 meters above ground at Beverly, and the other at the
Hackney S0? monitoring station, where the wind monitors were located
22 meters above ground. The data from Hackney was used in this study,
as it was higher and common to more stations, but Beverly data was used
when the Hackney system was not recording.
PHILO PLANT
Site Description
The Philo Plant is a 457 megawatt facility located in eastern Ohio on the
Muskingum River in the town of Philo, about 11 kilometers to the south-
east of Zanesville, Ohio (Figures 3 and 6). The plant is roughly
500 meters from the valley walls to the east and west, although the val-
ley widens to the north. The three stacks are approximately 82 meters
high and rise about 10 meters above the surrounding terrain. During 1974,
the period of this study, the plant consisted of five coal-fired boilers
feeding into three stacks (Table 1). Percent sulfur content of the
fuel by month for 1974 is given in Table 2.
15
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Figure 6. Sketch of the Philo Plant area showing the locations
of the six automatic S0_ monitoring stations
16
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Overview of the Philo Monitoring Program
The monitoring system in 1974 was made up of six Malloy continuous SO-
samplers, located as shown in Figure 3 and Table 3. Data were recorded
for all of 1974 except the following:
Station Outages
Station 1 First 91 days of year
Station 4 First 91 days of year
Station 6 Second 91 days of year April to July
The monitoring system maintenance and data acquisition were performed by
Environmental Research and Technology in Lexington, Massachusetts.
The instruments were calibrated every 6 months in Lexington and zeroed
every night by computer. These monitors were made by Malloy and have
the following specifications:
Malloy S0? Sensor Specifications
Range 0-1 ppm
Sensitivity 0.005 ppm
Noise ±0.5 percent FS
Response lag < 15 seconds
Rise time to 90 percent < 30 seconds
Fall time to 90 percent < 30 seconds
Precision ±1 percent FS
Accuracy ±1 percent FS
Zero drift ±0.01 ppm/day
±0.02 ppm/3 days
Span drift ±0.01 ppm/day
±0.02 ppm/3 days
Linearity ±1 percent FS
17
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Meteorological Data
There were three meteorological stations at Philo:
1. Irish Ridge Upper - elevation 140 meters above plant base;
(50 meters above ground). This station monitored wind-
speed and direction, and temperature difference from the
lower station.
2. Irish Ridge Lower - elevation 104 meters above plant base,
(11 meters above ground). This monitor measured wind speed
and direction, and temperature.
3. Duncan Falls - elevation 14 meters above plant base, (6
meters above ground). Only wind speed and direction were
recorded here.
The instrumentation system components included:
Climet WD-012-10 Vane and WS-011-1 Anemometer
Climet 015-2 and 3 Thermister
Bendix T20-510072-6 3 blade Impeller
The system was maintained by Environmental Research and Technology, Inc.
The first 100 days of meteorological data were not recorded for 1974.
The primary station for wind direction measurements was Irish Ridge
Upper. If this station was not operating, wind direction data was taken
from Irish Ridge Lower or Duncan Falls.
18
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SECTION III
ANALYSIS OF CONCENTRATION RATIO DISTRIBUTIONS
To ensure that the ratio distributions reflect only the influence of the
power plant in question, hourly S02 measurements were corrected for back-
ground contributions from other sources. The background was assumed to be
the average of those concentrations from stations outside of a 90° sector
centered about the wind flow vector, as measured by the plant wind vane.
This average background concentration was subtracted from the concentration
measurements for all stations for that hour. Any negative concentration
values resulting from the background subtraction were set equal to zero.
In the case of missing data or calms, the last recorded wind direction was
assumed to persist until a station reported a concentration over 0.1 ppm,
in which case the wind was assumed to blow towards that station until a
wind direction was recorded or another station reported a concentration
over 0.1 ppm.
These corrected concentrations were then analyzed to obtain peak 1-hour to
average 3-hour and peak 1-hour to average 24-hour concentration ratios.
For the calculation of the 1- to 3-hour ratios, 3-hour intervals were al-
lowed to overlap, giving a new ratio for each hour. In the case of the 1-
to 24-hour ratios, however, only one ratio was evaluated for each calendar
day. If one of the hourly concentrations to be used in a 3-hour or 24-hour
average was missing, then that ratio was omitted from the analysis.
Cases where the 3-hour or 24-hour average concentrations were zero were
also omitted from the analysis. Both 1- to 3-hour and 1- to 24-hour
ratios were sorted into 200 bins to generate a frequency.distribution.
19
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The main purpose of this study was to examine the effect upon the peak
to mean ratio distributions of restricting the peak 1-hour concentration
to be above a certain threshold. Separate frequency distributions of
peak to mean ratios were developed for 1-hour SC>2 concentrations (corrected
for background) above the following 1-hour concentration percenti'le values:
0, 95, 98, and 99. Frequency distributions of measured minus background
2 3
concentrations were previously calculated ' for the Canal, Stuart,
Muskingum and Philo plants. An example of one such distribution is
presented in Figure 7.
In Figures 8 through 23 we present log-probability plots of peak 1-hour
to average 3-hour and peak 1-hour to average 24-hour concentration ratio
cumulative frequency distributions for each plant and each peak 1-hour
concentration cutoff. The statistical parameters associated with these
distributions are given in Table 4.
A cursory examination of these frequency distributions reveals two rather
obvious features. By definition the frequency distributions for the 1-
to 3-hour and 1- to 24-hour concentration ratios are bounded by 1 and 3
and 1 and 24, respectively. Also, the distributions for both the 1- to
3-hour and 1- to 24-hour ratios are described rather well by a log-normal
function especially for high peak concentration cutoffs. The following
observations are based upon a more detailed analysis of the distribution
plots and tabulated statistics:
For the Stuart and Muskingum plants there appear to be a
significant number of 1- to 3-hour peak to mean ratios
exactly equal to 1. This feature persists even as the
threshold for the peak concentration is increased. In
the case of the Canal and Philo plants no peak to mean
ratios equal to 1 were observed once the peak concentra-
tion threshold was increased to the 98th percentile value.
This property of the ratio distributions may be traced to
the fact that 50% concentrations (ppm) were reported to 3
decimal places for the Canal and Philo plants, but only to
2 decimal places for the Stuart and Muskingum plants.
Therefore, variations in concentrations at the ppb level were
not as likely to be observed at Stuart and Muskingum.
20
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Another feature of the cumulative frequency distributions
is the reduction in the number of higher ratios as the
peak concentration limit is increased. This is true both
for the peak 1-hour to average 3-hour and peak 1-hour to average
24-hour ratios. The primary reason for this reduction is
that as the lower limit for the peak concentrations is in-
creased, the peak to mean ratios under analysis would apply
to those time periods for which the plume is actually in-
fluencing a given receptor location. There is less likli-
hood that a high 1-hour concentration will occur in a 3-
hour sequence with two very low concentrations. The latter.
situation was a rather common occurrence when there was
no lower limit to the peak concentration. For example, con-
sider the following situation: SC>2 concentrations of 0.01,
0.01 and 0.03 ppm are reported during a 3-hour period at a
particular receptor location and the corresponding calcula-
ted background concentrations based upon measurements at
upwind receptor locations are 0.01, 0.02, and 0.01 ppm,
respectively. According to the background subtraction
scheme we have employed the corrected concentration would
be 0.0, 0.0 and 0.02 ppm which yields a peak 1-hour to
average 3-hour concentration ratio of 3.
For the Stuart and Muskingum Plants the geometric means of
the peak 1-hour to average 3-hour concentration ratios
decrease when higher lower bounds for the peak concentra-
tions were established. For the Philo and Canal Plants a
corresponding increase was observed. The decrease in peak
1-hour to average 3-hour concentration ratios for increasing
peak concentration limit at Stuart and Muskingum is due in
part to the 0.01 ppm threshold for hourly S02 measurements
at these to sites.
If one restricts the analysis to the highest peak (99 per-
centile) 1-hour concentrations the geometric means of peak
1-hour to average 3-hour concentration ratios are distinctly
higher for the Philo and Canal Plants than for the Stuart
and Muskingum facilities. The corresponding trend toward
lower peak 1-hour to average 24-hour concentration ratios
with distance is much weaker.
As the 1-hour peak concentration is increased both
ratio distributions become smoother although fewer ratios
have been included in the analysis. In the cumulative
distribution for the zero percentile peak concentration
cutoff this is especially evident for a 1- to 3-hour ratio
of 1.5. This peak in the frequency distribution is due to
the large number of combinations of three discrete consecutive
21
-------
1-hour concentrations which can cause a ratio of 1.5. If the
three concentrations are x^, X£, Xn, and x-, is the concentra-
tion for the peak hour then if X2 + Xg = x^ the ratio will be
1.5. Examples of this would be (0.01, 0.01, 0), (0.01, 0,
0.01), (0, 0.01, 0.01), (0.02, 0.02, 0), etc.
It should be pointed out that the statistical relationships for the peak
1-hour to average 3-hour concentration ratios presented in Table 4 are
not strictly valid since a peak 1-hour concentration and the associated
overlapping 3-hour average concentration are not independent. The
relatively high correlation between consecutive 1- to 3-hour peak to
mean ratios is roughly equivalent to including a given ratio in the
analysis three times. This is especially true for those cases where
we have required that only those peak concentrations above a certain
threshold be included in the analysis. This problem could be circum-
vented by tabulating the ratio between the highest 1-hour concentration
for a day and the highest 3-hour average concentration for that day,
with the requirement that the highest 1-hour value occur during the
3-hour period chosen for the highest 3-hour average. The major difficulty
with this procedure, however, is that it is not consistent with the
definition of the 3-hour mean as a sliding average. Nevertheless, it
would be a valuable exercise since it would determine whether the dis-
tribution statistics such as the geometric mean and geometric standard
deviation are strongly influenced by the interdependence between
successive ratios.
22
-------
O
co-
co-
in-
ru-
O
CO
cc
cc
co-
r-.
(a-
uv
PERCENTAGE OF CONCENTRATIONS
GREATER THAN INDICATED VALUE
99 98 99 9O 80 7O 60 SO 40 30 20
I O.S O.2 0.1 O.OI
1 1
MU5KJNGUM RIVER PLMT
CUMULflTIVE FREQUENCY
DISTRIBUTION FOR 1 HOUR
S02 COMCENTRflTlOMS flT flLL STATIONS
AMEHSURED MINUS BflCKGROUND
j.CfiLCULRTED
0.01 0.05 O.I O2 O.» 1 I
J 10 20 10 40 SO 60 TO 80 »0
PERCENTAGE OF CONCENTRATIONS
LESS THAN INDICATED VALUE
9S
9« 99
99.8 99.9
Figure 7. Muskingum River plant cumulative frequency distribution for 1-hour S02 concentrations at all
sampling stations. Number of measured concentrations = 30,622; number of calculated concen-
trations = 61,320
-------
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
993 99.8
9998 99 90 80 TO 60 504030 20 10
2 i as 0.2 0.1 0.01
to-
in-
10
-I(I 1I
H 1 1 1 1I
-+-HI
CflNfil PLflNT
CUMULflTIVE FflEQUtNCY DISTRIBUTION
FOR RHTIOS WITH CONO 0 UG/M3
PLOTTED LOG-rJOflMflLLT
2,1-3 HOUR RRTI05
HOUR ROTI03
-ry
-W
20 30 40 60 60 70 80 90 95 98 99
en
no
CO
in
CC
CC
-eg
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
Figure 8. Canal Plant cumulative frequency distribution of ratios of peak to mean
concentrations for all cases
-------
993 99.8
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
99 98 99 90 80 TO 60 60 40 30 20 10 6 21 0.5 0.2 OJ
0.01
H I-H (-
H 1 hI-
-t-
-t-
H 1I 1+-
ta-
in-
tn-
CflWBL PLflWT
CUMOLHTIVt FREQUENCE DISTRIBUTION
FO RT«.OS WITH CQNC> lo UG/M3
PLOTTED LOG-NOOHHLLY
ol-3 HOUR RRTIOS
HOUR HHTI03
en
CD
.r-
to
-tM
20 30 40 SO 60 70 80 90 95
ox>i aos
9939
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
Figure 9. Canal Plant cumulative frequency distribution of ratios of peak to mean
concentrations for cases where the peak concentrations are greater than
18 ug/m3; 18 ug/m3 is the 95th percentile of the 1-hour concentrations
-------
993 99.8
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
99 98 95 90 80 70 60 60 40 30 20 10 0 21 0.6 0.2 OJ 0.01
oo-
f).
ro
-ti-
-i(*+
CUHULflTlVE FREQUENCY DISTniBUTIOM
FOfl RflTlOS HITH COMC> 35 UG/M3
fLOTTEO LOG-MORMflLLY
ol-3 HOUR flflTlOS
Ai-2U noun
-1 1
-It-
-05
20 30 40 50 60 70 80 90 95
-on
-co
-to
-in
ooi aos O.E 0.5 i
9939
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
Figure 10. Canal Plant cumulative frequency distribution of ratios of peak to mean
concentrations for cases where the peak concentrations are greater than
35 |ig/mj; 35 ng/m^ is the 98th percentile of the 1-hour concentrations
-------
993 99.8
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
99 98 95 90 80 TO 60 50 40 30 20 10 8 21 0.6 0.2 OJ 0.01
o>-
03-
to-
in-
-t t
I t »-
H 1 1-
-i 1-
-+I
ClmULflTlVE FflEQUEfJCY OISTniSOTION
Fon nnTios UITH cono ss UG/M3
TLOTTEO LOG-HOflrtflLLY
ol-3 HOUn OflTlOS
o
0.01 aos 0.2 0.6
20 30 40 60 60 70 80 90 95 98 99 9a8
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
9939
Figure 11.
Canal Plant cumulative frequency distribution of ratios of peak to mean
concentrations for cases where the peak concentrations are greater than
55 ug/m ; 55 ug/m3 is the 99th percentile of the 1-hour concentrations
-------
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
993 99.8 99 98 95 90 80 TO 60 60 40 30 20 10 8 21 0.6 0.2 OJ 0.01
r--
iO-
m
to
oo
4 I I hI
-t-
1 1 1 1
tI 1+-
J. M. 5TUHRT PLRNT
CUMULRTIVE FREQUEWCY CISTfllBUTICN
FOR RflTIOS WITH CQNO 0 UG/M3
PLOTTED LOG-NORMHLir
Ql-2 HOUR RHTI03
HOUR RflTIOS
0.08 0.2 OJ) I 2 6 10 20 30 40 60 60 70 80 90 95 98 99
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
99.8
-01
-w
-r-
-t£>
-in
-3"
-en
9939
Figure 12. J. M. Stuart Plant cumulative frequency distribution of ratios of peak
to mean concentrations for all cases
-------
993 99.8
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
9998 99 90 80 TO 60 50 40 30 20 10 6 21 0.8 0.2 OJ 0.01
I 1-
H 1 1 1 1 H
I I
-I 1I 1»-
QD-
J. M. 5TUHRT PLflMT
CUMULATIVE FREQUENCY DISTRIBUTION
FOR RflTIOS WITH CONG >59
PLOTTED LOG-NORMflLLY
QI-3 HOUR RflTIOS
A1-2U HOUR RflTIOS
-to
-in
O
aos
0.6 i 2
10 20 30 40 50 60 70 80 90 99 98 99
99.8
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
Figure 13. J. M. Stuart Plant cumulative frequency distribution of ratios of peak
to mean concentrations for cases where the peak concentrations are
greater than 59 (ig/m^; 59 ng/nr* is the 95th percentile of the 1-hour
concentrations
-------
993 99.8
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
99 98 95 90 80 70 60 SO 40 30 20 10 6 21 0.6 0.2 OJ
0.01
I- I tIh-
H h
-t-
HIIII
-t-
-II-H th
in-
sf-
cn-
J. M. STURflT PLflNT
CUMULBTIVE FREQUENCY DISTRIBUTION
FOR RflTIOS WITH C3NO1U3 UG/M3
PLOTTED LOG-KiaRMRLLT
Ql-3 HOUR RRTIOS
2U HOUR RflTIO?
-co
-r~-
-CO
-in
88 99 9&8
9939
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
Figure 14. J. M. Stuart Plant cumulative frequency distribution of ratios of peak to
mean concentrations for cases where the peak concentrations are greater than
140 ng/m ; 140 (j.g/m3 is the 98th percentile of the 1-hour concentrations
-------
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
993 998 99 98 95 90 60 TO 60 50 40 30 20
-H(I 1I 1 1 1 1 1 1 1 1 1 H-
00-
10 (5 2 I 0.6 0.2 OJ 0.01
I I III 1I
J. M. STUflflT PlflfJT
CUMULflTIVE FREQUENCY OI5TRI8UTION
FOR RflTIOS WITH CONC > 220 pG/M3
PLOTTED LOG-NORMflLLY
ol-3 HOUR RflTIOS
HOUR RflTIOS
-co
~r-
-tO
-in
0.01 aos
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
Figure 15. J. M. Stuart Plant cumulative frequency distribution of ratios of peak to
mean concentrations for cases where the peak concentrations are greater than
220 ng/m3; 220 |ig/m3 is the 99th percentile of the 1-hour concentrations
-------
993 99.8
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
99 98 95 90 60 70 60 50 40 30 20 10 6 21 0.6 0.2 OJ 0.01
Oi-
co-
r--
tO-
in-
af-
tn-
H I
1 I
-+-
-+-
-t 1 1-
H 1t-
MU3KIWGUM PLflNT
CUHULflTIVE FREQUENCY DISTRIBUTION
FOB flflTIOS WITH CONC> 0 UG/M3
PLOTTED LOG-NORMflLLY
ol-3 HOUR RflTIOS
2U HOUR RflTIOS
-en
-oo
-to
-in
-en
-co
-co
-in
cn
QC
OjQI aOS 0^ 0.6 I 2 6 10 20 30 40 50 60 70 80 90 95 98 99 9a8
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
Figure 16. Muskingum Plant cumulative frequency distribution of ratios of peak to mean
concentrations for all cases
-------
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
993 998
99 98 99 90 60 TO 60 60 40 30 20 10
2 I 0.0 0.2 OJ 0.01
O5-
00-
P--
<£>
in-
=f-
OJ
OJ
H 1 1 1 1
H 1I
MUSKINGUM PLflNT
CUMULflTIVE FREQUENCY DISTRIBUTION
FOR RflTIOS WITH CONd > 72 UG/M3
PLOTTED LOG-MORMBLLTT
Ql-3 HOUR RflTIOS
Al-2>i HOUR RflTIOS
oo
r-
-in
OjOl 0.06 QJt OS I 2
10 20 30 40 SO 60 70 60 90 95 98 99 9ae
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
9939
Figure 17. Muskingum Plant cumulative frequency distribution of ratios of peak to
mean concentrations for cases where the peak concentrations are greater
than 72 ug/m^; 72 ug/m^ is the 95th percentile of the 1-hour concentrations
-------
Co
999 99.8
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
99 98 95 90 80 TO 60 50 40 30 20 10 6 21 0.6 0.2 0.1 0.01
co-
\n
=
H 1 1 1 1 h-
H 1I
MUSKINGUM PLfWT
CUMULflTlVE FREQUENCY DISTRIBUTION
FOR RRTIOS WITH CONC>176 UG/M3
PLOTTED LOG-NORflflLLY
ol-3 HOUR RflTIOS
A1-2U HOUR RflTI03
QjOl 0.05 OJl 0.6 I 2 5 10 20 30 40 60 60 70 80 90 95 98 99 9&8
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
01
CO
to
in
Figure 18. Muskingum Plant cumulative frequency distribution of ratios of peak to mean
concentrations for cases where the peak concentrations are greater than
176.yg/m3; 176 yg/nr is the 98th percentile of the 1-hour concentrations
-------
993 99.8
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
99 96 95 90 60 70 60 60 40 30 20 10 6 21 0.5 0.2 OJ 0.01
cr>
co
r-
tn-
HI
HI+-
H 1
1 »-
H-t-
HUSKINGUM PLflNT
CUMULflTIVE FREQUENCY DISTflI8UT!ON
FOfl RfiTIOS WITH CONC >250UG/M3
PLOTTED LOG-MOmifiLir
(j,l-3 HOUR RflTIOS
A.1-2H HOUR RfYTIOS
O
-co
-r-
-to
-in
0.05 0^ 0.0
10 20 30 40 60 60 70 80 90 95 98 89 99.8
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
Figure 19. Muskingum Plant cumulative frequency distribution of ratios of peak to mean
concentrations for cases where the peak concentrations are greater than
250 jag/nr; 250 ^g/m^ is the 99th percentile of the 1-hour concentrations
-------
993 99.8
t I I
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
99 98 95 90 60 70 60 50 40 30 20 10 6 21 0.5 0.2 OJ
0.01
It-
-IIIII
-f"
1I »f-
O-
00-
(0-
m-
PHILO PLflNT
CUMULflTIVE FREQUENCY DISTRIBUTION
FOR RRTIOS WITH CONO 0 UG/M3
PLOTTED LOG-NORMflLLY
ol-3 HOUR RflTIOS
A1-2U HQUfl RflTIOS
-CO
-r~
-to
-irt
Oil 0.05 0.2 0.6 I 2
10 20 30 40 60 60 70 80 90 95 98 99 9a8
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
Figure 20. Philo Plant cumulative frequency distribution of ratios of peak to mean
concentrations for all cases
-------
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
993 99.8 99 98 95 90 80 TO 60 SO 40 30 20 10 0
-tt1 1I 1 1H 1 1 1 1 1I 1 1 1
00-
r
U)-
in-
ru-
tn-
2 I 0.0 0.2 OJ 0.01
HII II
PHILO PLfiMT
CUMULRTIVE FREQUENCY DISTHI8UTION
FOR RflTIOS WITH CONC >53 |JG/M3
PLOTTED LOG-NORMflLLY
ol-3 HOUR flflTIOS
A1-3U HOUR RflTI03
-co
r-
-in
-en
-00
-to
i i
-Hiiii^
O
-------
995 99.8
-III-
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
99 98 99 90 60 70 60 50 40 30 20 10 6 21 0.9 0.2 OJ 0.01
I
to
tr>
sf-
U)
00
H 1 1 1 1
-I 1I ! I
PHILO PLflNT
CUMULflTIVE FflEOUENCY DISTRIBUTION
FOR RHTI05 WITH CONC>1£3 UC/M3
PLOTTED LOG-NORMflLLY
ol-3 HOUR RflTIOS
A1-2U HOUR RfKIOS
I I Ii1(
<II 1-
-tO
-in
aos 0.2 as i 2 s 10 20 30 40 so so ro eo 90 99 93 99
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
Figure 22. Philo Plant cumulative frequency distribution of ratios of peak to mean
concentrations for cases where the peak concentrations are greater than
123 ng/m3; 123 ug/m3 is the 98th percentile of the 1-hour concentrations
-------
PERCENTAGE OF CONCENTRATION RATIOS
LESS THAN INDICATED VALUE
993 99.8
99 98 99 90 80 70 60 50 40 30 20 10
2 I 0.6 0.2 OJ 0.01
co-
r--
to-
in-
PHILO PLfWT
CUMULATIVE FREQUENCY DISTRIBUTION
FOR RflTIOS WITH CONG >I83UG/M3
PLOTTED LOG-NOflMflLLY
oJ-3 HOUR PflTIOS
Al-24 HOUR RflTJOS
20 30 40 60 60 70 60 90 90
CB
-co
r-
.(3
-in
-en
PERCENTAGE OF CONCENTRATION RATIOS
GREATER THAN INDICATED VALUE
Figure 23. Philo Plant cumulative frequency distribution of ratios of peak to mean
concentrations for cases where the peak concentrations are greater than
183 ng/m , 183 u.g/m3 is the 99th percentile of the 1-hour concentrations
-------
Table 4. STATISTICS FOR PEAK TO MEAN RATIO DISTRIBUTIONS
Plane
Canal
Stuart
Musklngum
Philo
Ratio
1-3 hr
1-24 hr
1-3 hr
1-24 hr
1-3 hr
1-24 hr
1-3 hr
1-24 hr
Lower
percentile
cutoff
for peak
concentration,
%
0
95
98
99
0
95
98
99
0
95
98
99
0
95
98
99
0
95
98
99
0
95
98
99
0
95
98
99
0
95
98
99
Peak
concentration
cutoff,
ug/m3
0
18
35
55
0
18
35
55
0
59
140
220
0
59
140
220
0
72
176
250
0
72
176
250
0
53
123
183
0
53
123
183
Arithmetic
mean
1.868
1.829
1.978
1.977
7.827
7.466
8.634
8.972
1.852
1.761
1.-778
1.722
7.709
7.456
8.127
8.381
1.991
1.882
1.857
1.859
9.232
7.396
7.723
7.957
2.004
1.986
1.964
1.976
8.767
8.332
8.290
8.459
Arithmetic
standard
deviation
0.7175
0.5814
0.5694
0.5595
6.1361
5.033
4.791
4.546
0.7742
0.6138
0.5965
0.5937
5.945
4.353
4.165
4.051
0.7600
0.5671
0.5287
0.5398
6.785
4.027
3.541
3.517
0.7217
0.5862
0.5600
0.5648
5.775
4.337
4.005
3.652
Geometric
mean
1.739
1.743
1.897
1.899
5.892
6.090
7.441
7.915
1.699
1.662
1.685
1.627
5.917
6.268
7.114
7.406
1.847
1.802
1.786
1.785
7.190
6.505
7.053
7.304
1.873
1.901
1.886
1.896
7.158
7.337
7.410
7.725
Geometric
standard
deviation
1.453
1.361
1.337
1.330
2.135
1.892
1.740
1.663
1.512
1.402
1.387
1.396
2.078
1.855
1.722
1.704
1.480
1.342
1.322
1.329
2.032
1.653
1.521
1.506
1.448
1.348
1.332
1.335
1.902
1.661
1.616
1.541
50th
percentile
1.54
1.67
1.89
1.89
5.60
5.90
7.40
8.25
1.50
1.61
1.63
1.58
6.00
6.75
7.35
7.70
1.75
1.76
1.75
1.73
6.75
6.35
6.70
6.90
1.80
1.88
1.88
1.89
6.98
7.30
7.52
7.79
Peak-ratio
correlation
-0.02517
0.12310
-0.00727
-0.00951
0.02344
0.16367
0.06409
0.02142
-0.05517
0.00353
-0.04397
0.02782
0. 00146
0.13190
0.03804
0.00010
-0.07783
-0.03262
-0.03310
-0.06170
-0.15123
0.06867
0.01758
-0.06609
-0.03525
-0.01296
0.01974
0.00985
-0.04030
0.04850
0.10430
0.12208
95% confidence
Interval of correlation.
-0.0113
0.1593
0.0473
0.0578
0.0819
0.2599
0.2000
0.1844
-0.0453
0.3609
0.0079
0.0966
0.0538
0.2191
0. 1606
0.1654
-0.0619
0.0044
0.0250
0.0127
-0.0929
0.1628
0. 1463
0.0909
-0.0214
0.0211
0.0714
0.0786
0.0175
0.1431
0.2322
0.2817
-0.0390
0.0866
-0.0618
-0.0767
-0.0352
0.0643
-0.0743
-0.1427
-0.0715
-0.0290
-0.0956
-0.0412
-0.0509
0.0426
-0.0857
-0.1652
-0.0937
-0.0696
-0.0910
-0.1354
-0.2085
-0.0267
-0.1118
-0.2200
-0.0490
-0.0470
-0.0320
-0.0589
-0.0978
-0.0469
-0.0272
-0.0441
Number
of
values
20,072
2,818
1,293
850
1,119
381
203
144
22,278
3,623
1,427
809
1,402
477
253
141
15,059
2,797
1,140
696
1,100
424
231
158
20,142
3,315
1,437
813
1,152
424
224
141
Significant
to 95%
Yes
Yes
No
No
No
Yes
No
No
Yes
No
No
No
No
Yes
No
No
Yea
No
No
No
Yea
No
No
No
Yes
No
No
No
No
No
No
No
-p-
o
-------
SECTION IV
COMPARISON WITH PREVIOUS STUDIES
A useful mechanism for the analysis of peak to mean concentration ratios
is the fluctuating plume dispersion model first suggested by Gifford.
In this model the plume is composed of a number of contiguous disk
elements perpendicular to the mean plume axis. The center of any one of
these disks will be laterally displaced from the mean plume axis by a
distance D given by
n
where y. = the distance of particle i from the mean plume axis.
The mean square distance, Y , of each of the particles within the disk
element from the center of the disk element itself is
2 1?1(yi-D>
Y2 = iii-; (2)
The ensamble average of x , the plume spreading parameter, may be written
as follows:
Y2 = y2 - D2 (3)
41
-------
where
2
y =
n
n n
" 2
n
~2~
The plume meandering parameter D reduces to the following expression:
2 n y . n(n - 1) ,.*
D = J- + N 2 ' y y (4)
n n J
which for a large number of particles becomes
y±y. (5)
Equation 3 may therefore be written in terms of two particle statistics
to give
y - y±y. (6)
As the diffusion time, or equivalently, the distance from the source
increases, it can be shown by means of statistical theories of turbulent
diffusion that the plume spreading parameter Y^ becomes independent of
y.y. and may be better described in terms of one particle statistics or
42
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K theory. Based upon this analysis we may infer that y.y. and therefore
2 1 x
D will approach a constant value at large distances from the source.
This result implies a smaller average peak to mean ratio for increasing
receptor distances from the source. This trend toward lower peak to
mean ratios at greater distances from the source is not inconsistent with
the results of the present study as shown in Table 5. Further analysis
using individual receptor locations would be required to show whether
these results are statistically significant.
Table 5. COMPARISON OF PEAK TO MEAN CONCENTRA-
TION RATIOS FOR DIFFERENT SOURCE
RECEPTOR DISTANCES
Plant
Canal
Stuart
Muskingum
Philo
Mean source,
receptor
distance, km
2.6
6.9
9.4
3.8
Geometric mean of distributions,
peak to mean ratio
for 99th percentile
peak concentration
1- to 3-hour
1.90
1.63
1.78
1.90
1- to 24-hour
7.91
7.41
7.30
7.72
Most studies of concentration ratio distributions have involved peak
values averaged over periods of only a few minutes. One such evaluation
of S0_ concentration ratio distributions was carried out by the Tennessee
Valley Authority (TVA) in the vicinity of the Paradise Power Plant with
data taken over a 2-1/2 year period from January 1968 through June 1970.
During this time period, 14 S02 monitors located in the 22-1/2 degree
prevailing downwind sector were operated on a continuous basis. All but
one of the stations were located within a distance of from 3 to 10 km
from the plant. From the concentration data peak-to-1-hour average and
peak-to-24-hour average concentration ratios were obtained for each
measuring instrument. The highest 5-minute average concentration that
occurred during a particular hour was considered to be the peak concen-
tration for that hour. To avoid interference from background contributions,
43
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those hours with average concentrations less than 0.10 ppm were excluded
from the analysis. The resulting ratio distributions were analyzed
according to stability type and receptor distance from the source. Sta-
bility assignments (unstable, neutral, stable) were made according to
the potential temperature gradient which was obtained from hourly tem-
perature measurements at 13 m and 110 m meteorological tower levels.
Although the procedure for background subtraction and determination of
peak concentrations was different from those used in our study, their
results correlate quite well with our findings. In particular, they
found a general decrease in concentration ratios (both 1- to 3-hour and
1- to 24-hour) for increasing distance from the source.
44
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SECTION V
CONCLUSION
Through a reexamination of our previous analyses of time-concentration
relationships we have made our results more applicable to the estimation
of maximum 3-hour and 24-hour concentrations based upon predictions of
maximum 1-hour concentrations. By restricting our analysis of peak to
mean ratio distributions to those cases in which the peak concentration
was above a certain threshold level, we ensured that the resultant dis-
tribution statistics would be determined primarily by the combination
of point source emission characteristics, meteorology and topography
rather than spatial variations in the background concentration.
When this restriction was applied, both the 1- to 3-hour and 1- to 24-hour
ratio distributions were found to follow more closely the log-normal dis-
tribution shape with an associated decrease in the standard geometric
deviation as the peak 1-hour concentration threshold was increased. This
reduction in the standard geometric deviation was especially significant
for the 1- to 24-hour concentration ratios where it averaged 25 percent.
The magnitude of the standard geometric deviation is of considerable
importance with regard to any future application of these ratios on an
operational basis for the prediction of 3-hour and 24-hour concentrations.
Estimates of yearly maximum 1-hour concentrations based upon EPA point
source models are generally within 50 percent of measured values but
estimates of 3-hour and 24-hour maximum concentrations obtained from an
analysis of 1-hour predictions based upon an entire hourly year of
meteorological data may differ by more than a factor of 2 from measured
2 3
values. ' If, on the other hand, the 3-hour and 24-hour maximum
45
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concentrations are estimated through application of the geometric mean
of the peak to mean ratio distribution, the accuracy of these predictions
should be comparable to that of the 1-hour predictions except for the
uncertainty associated with the width of the ratio distribution as
parameterized by the standard geometric deviation. A determination of
the relative merits of these two methods for estimation of maximum 3-hour
and 24-hour concentrations must await the results of future model valida-
tion studies. Nevertheless, the ratio method obviously has an operational
advantage in that it does not require the use of an entire year of mete-
orological data.
Finally, we should point out that in addition to the intrinsic spread
of each ratio distribution, the geometric means will vary from one site
to the next depending upon climatology, point source characteristics and
receptor location. Based upon the results of the present study, it would
appear that the 1- to 3-hour ratio distributions are more sensitive to
variations in these parameters than the 1- to 24-hour distributions. A
sufficient range of climatological regimes has not been encountered in
this study to permit us to estimate the effect of these variables upon
the ratio distributions. It should also be noted that the emission rates
for the point sources in this study did not vary to an appreciable de-
gree over the concentration averaging times used in the construction of
the ratio distributions. For sources with significant emissions varia-
tions the peak to mean statistics should be modified to reflect the
time dependence of the source function.
46
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SECTION VI
REFERENCES
1. Turner, D. B. Workbook of Atmospheric Dispersion Estimates. U.S.
Environmental Protection Agency, Office of Air Programs. Publication
Number AP-26.
2. Mills, M. T. and R. W. Stern. Model Validation and Time-Concentration
Analysis of Three Power Plants. Prepared by GCA/Technology Division,
Bedford, Massachusetts for the U.S. Environmental Protection Agency.
Publication Number EPA-450/3-76-002. December- 1975.
3. Mills, M. T. and F. A. Record. Comprehensive Analysis of Time Con-
centration Relationships and the Validation of a Single Source Dis-
persion Model. Prepared by GCA/Technology Division, Bedford,
Massachusetts for the U.S. Environmental Protection Agency, Research
Triangle Park, N.C. Publication Number EPA-450/3-75-083. March 1975.
4. Federal Register. Vol. 36, No. 158. August 14, 1971.
5. Preining, 0., et al. Staab-Reinhalt Luft. Vol. 29, No. 11.
November 1969.
6. Gifford, F. Peak to Average Concentration Ratios According to a
Fluctuating Plume Dispersion Model. Int J Air Pollu. Pergamon
Press, Vol. 3, No. 4. 253-260, 1960.
7. Montgomery, T. L., S. B. Carpenter, and H. E. Lindley. The Relation-
ship Between Peak and Mean S02 Concentrations. (Presented at the
Conference on Air Pollution Meteorology of the American Meteorological
Society in Cooperation With the Air Pollution Control Association.
Raleigh, North Carolina. April 5-9, 1971.)
47
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
2.
3. RECIPIENT'S ACCESSION-NO.
PB-264 686
4. TITLE AND SUBTITLE
5. REPORT DATE
Improvements to Single-Source Model. Volume I.
Time-Concentration Relationships
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Michael T. Mills, and Roger W. Stern
8. PERFORMING ORGANIZATION REPORT NO.
EPA/450/3-77/003a
9. PERFORMING ORGANIZATION NAME AND ADDRESS
10. PROGRAM ELEMENT NO.
GCA Corporation
Bedford, Massachusetts
GCA Technology Division
11. CONTRACT/GRANT NO.
EPA-68-02-1376
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Protection Agency
Research Triangle Park, North Carolina
Office of Air Quality Planning and Standards
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
Reliable estimates of maximum 3-hour and 24-hour SCu concentrations due to power plant
emissions are required for a variety of environmental assessment activities associated
with air quality maintenance planning, fuel switching, plant siting and tall stack
policy evaluations. Either of two methods are generally employed for the prediction
of maximum SCL concentrations for these two averaging times. The purpose of the
present study was to examine the effect upon ratio distribution statistics if only
peak concentrations above a certain cutoff value were analyzed. This report describes
the plant site characteristics and the meteorological and air quality data bases used
in the study. This will be followed by a discussion of the ratio distributions and
their associated statistics, including an analysis of the variation of these
parameters for different plant sites and peak concentration cutoffs. The report
concludes with a discussion regarding the general applicability of these results to
other point sources.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Electric power plants
Sulfur dioxide
Air pollution
Ambient air quality
Averaging times
Mathematical models
Air pollution sampling
Air pollution modeling
Air quality maintenance
Point sources
18. DISTRIBUTION STATEMENT
19. SECURITY CLASS (ThisReport)
Unclassified
21. NO. OF PAGES
57
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
PC A04/MF A01
EPA Form 2220-1 (9-73)
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