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

-------
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	1—I
                                                     H	1	1	1	1—I
                                                                              -+-H—I
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	h—I-
                                                  -t-
                                                         -t-
                                                            H	1—I	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
                                         -t—i-
                                                         -i—(—*—+•
CUHULflTlVE FREQUENCY DISTniBUTIOM
FOfl RflTlOS  HITH COMC> 35 UG/M3
fLOTTEO LOG-MORMflLLY
 ol-3 HOUR flflTlOS
 Ai-2U noun
                                                                            -1	1
                                                                                   -I—t-
                                                                                           -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	h—I
                                                 -t-
                                                           1	1	1	1
                                                                                   t—I	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	1—I	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	t—I—h-
                                H	h
                                       -t-
                                         H—I—I—I—I
                                                           -t-
                                                               -I—I-H	t—h
              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	1—I	1	1	1	1	1	1	1	1	1	H-
             00-
10  (5  2  I 0.6 0.2 OJ  0.01

I   I   I—I—I	1—I	
                   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	1—t-
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	1—I
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	1—I
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-
                H—I
                       H—I—+-
                                     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
                          I—t-
                                      -I—I—I—I—I
                                                    -f"
                                                                 1—I	»—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

               -t—t—1	1—I	1	1—H	1	1	1	1	1—I	1	1	1—
00-
r—
U)-
in-
           ru-
           tn-
 2 I  0.0 0.2 OJ   0.01

H—II  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
                                   -H—i—i—i—i—^
                                                                             O
                                                                             
-------
                           995 99.8
                             -I—I—I-
         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	1—I  •! 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 I—i—1—(
                                                         <—I—I	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

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                               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

-------
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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