f\
United States
Environmental Protection
Agency
Office of Air Quality
Planning and Standards
Research Triangle Park NC 2771
EPA-450/3-7S-039
August 1978
Air
Case Study Analysis
of Supplementary
Control System
Reliability
-------
United States
Environmental Protection
Agency
Office of Air Quality
Planning and Standards
Research Triangle Par* NC 27711
EPA-450/3-78-039
August 1978
Air
Case Study Analysis
of Supplementary
Control System
Reliability
-------
EPA-450/3-78-039
Case Study Analysis of Supplementary
Control System Reliability
by
Environmental Research and Technology, Inc.
3 Militia Drive
Lexington, Massachusetts 02173
Contract No. 68-02-2090
EPA Project Officer: Larry Budney
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air, Noise, and Radiation
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
August 1978
-------
This report is issued by the Environmental Protection Agency to report
technical data of interest to a limited number of readers. Copies are
available free of charge to Federal employees, current contractors and
grantees, and nonprofit organizations - in limited quantities - from the
Library Services Office (MD-35) , U.S. Environmental Protection Agency,
Research Triangle Park, North Carolina 27711; or, for a fee, from the
National Technical Information Service, 5285 Port Royal Road, Springfield,
Virginia 22161.
This report was furnished to the Environmental Protection Agency by
Environmental Research and Technology, Inc., 3 Militia Drive, Lexington,
Massachusetts 02173, in fulfillment of Contract No. 68-02-2090. The contents
of this report are reproduced herein as received from Environmental Research
and Technology, Inc. The opinions, findings, and conclusions expressed are
those of the author and not necessarily those of the Environmental Protection
Agency. Mention of company or product names is not to be considered as an
endorsement by the Environmental Protection Agency.
Publication No. EPA-450/3-78-039
11
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TABLE OF CONTENTS
Page
1. INTRODUCTION 1-1
1.1 Overview and Objectives 1-1
1.2 SCS Reliability Analysis 1-2
1.3 Kincaid SCS Program 1-4
1.4 Detailed Discussion of the Kincaid SCS 1-6
2. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 2-1
3. RELIABILITY ANALYSIS METHODS 3-1
3.1 Discussion of Error Ratios 3-1
3.2 Establishment of Cases for Analysis 3-8
3.3 Data Collection and Processing 3-12
4. RESULTS OF RELIABILITY ANALYSIS 4-1
4.1 Total System Error R_ 4-1
4.1.1 Case 1 4-4
4.1.2 Case 2 4-6
4/1.3 Case 3 4-6
4.1.4 Case 4 4-8
4.1.5 Cases 5 through 7 4-8
4.1.6 Summary of Cases 4-9
4.2 Analyzing Error Ratio of SCS Components 4-9
4.3 Background Concentrations 4-15
4.4 Three- and Twenty-Four-Hour Average Concentrations 4-17
4.5 Prediction of Meteorological Parameters 4-18
5. RESULTS OF PROBABILITY ANALYSIS 5-1
5.1 Data Preparation and Processing 5-1
5.2 PROBL Results 5-7
REFERENCES
APPENDIX A DESCRIPTION OF THE AIR QUALITY FORECAST AND CONTROL
DECISION MODELS
APPENDIX B USER'S MANUAL FOR PROBL
1.1 Description of Program Method
1.2 Program Description
1.3 Program Listing
1.4 Program Flow Chart
APPENDIX C SAMPLE CASES OF PROBL
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LIST OF TABLES
page
1-1 Kincaid Monitoring Network Information 1-9
1-2 Summary of the Days of Operation of the Kincaid Units
During the 123-Day Test Period I"11
1-3 Kincaid Raw Real-Time Data Capture for October 1976
Through January 1977 1'12
3-1 Example of Error Ratio Method 3'7
3-2 SCS Reliability Analysis Cases 3-9
3-3 Background Concentrations, ppm S02 Lookup Table for
Kincaid 3-l5
4-1 Summary of Results for R^ 4-5
4-2 Summary of Results for R, Comparison of Thresholds 4-8
4-3 Summary of Results of R , R , R Threshold of 0.05 ppm 4-11
W CJ 111
4-4 Details of Case 4 4-13
4-5 Comparison of Meteorological Data Observed at Kincaid
and at Springfield 4-15
4-6 Comparison of Background Concentrations Lookup Table
Vs. Upwind Monitor 4-17
4-7 Summary of Results for R™ as a Function of Averaging
Time Case 4 4-19
5-1 Frequency Distributions of Q 5-2
5-2 Frequency Distribution of M(t) Case 1, One-Unit
Example 5-4
5-3 Frequency Distribution of M(t) Case 1, Two-Unit
Example 5-5
5-4 Frequency Distributions of R_ Case 1 5-6
5-5 Distribution of PROBL Results Case 1, One-Unit
Example 5_8
3-6 Distribution of PROBL Results Case 1, Two-Unit
Example 5.9
5-7 Summary of PROBL Results 5-10
VI
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LIST OF FIGURES
Page
1-1 Field Monitoring Network for the Kincaid Area 1-8
1-2 AQFOR-CONDEC Model Grid 1-10
1-3 Model SCL Threshold Curve and Corresponding Threshold
Values 1-15
4-1 Histogram of R versus Percentage Frequency for
Case 2 4-2
4-2 Relationship of 1-Hour Average Values of R to Number
of Hours from Time of Forecast 4-21
VII
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1. INTRODUCTION
1.1 Overview and Objectives
This report was prepared by Environmental Research § Technology,
Inc. (ERT) under Environmental Protection Agency (EPA) Contract 68-02-2090.
It follows an earlier research program performed by ERT (EPA Contract
68-02-1342) in which analytical tools were developed specifically for
evaluating the effectiveness of Supplementary Control Systems (SCS) in
meeting ambient air quality standards (EPA 1976a).
The present study applies those analytical tools to a case study of
an operational SCS. A user manual (Appendix B) is also provided. The
SCS at the Commonwealth Edison Kincaid Station at Kincaid, Illinois, was
chosen.* It was operational as of July 1976. However, neither of the
two 600-Mw generation units at Kincaid was operational until October
1976. The 123-day period October 1, 1976, through January 31, 1977, was
used in this analysis. A 120-day test period is the minimum required to
assess the reliability analysis techniques (EPA 1976b).
A primary objective of this study is to discuss the analytical
techniques themselves and their applicability to the problem of esti-
mating SCS reliability. By reviewing in detail a case study demonstra-
tion of the analysis, a more complete understanding of the usefulness
and appropriateness of these techniques has been obtained.
All the objectives of this study are summarized below.
• Select an SCS for use in the case study analysis and obtain
permission for the use of the data from this SCS.
• Define the air quality forecasting system to be used in the
operation of the case study SCS.
• During 120 days of SCS operations, collect all pertinent data
required for reliability analysis.
• Test the reliability of the SCS through application of error
ratios as defined in the previous work.
*Although EPA has approved SCS for certain S02 sources, SCS is not
approved as a control strategy for the Kincaid Station. It is
referred to here only for case study purposes.
1-1
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• Apply the ERT computer program PROBL to the evaluation of the
120-day test period.
• Document the model PROBL and provide a user manual.
• Evaluate the analytical techniques and their usefulness.
It is important to clarify the intended meaning of the word "relia-
bility". The ultimate reliability of an SCS program is measured in
terms of whether or not the applicable standards have been violated.
The applicable standards for the Kincaid SCS are the National Ambient
Air Quality Standards (NAAQS) for sulfur dioxide (S02), which specify
3- and 24-hour average concentrations that can be exceeded no more than
once per year. Because no excesses of the NAAQS were observed during the
123-day test period, the reliability of the Kincaid SCS has to be
evaluated in other terms.
A second definition of "reliability" for an SCS is the consistent
ability to predict ground-level concentrations accurately. This defini-
tion is a more stringent reliability requirement and represents the
primary focus of this case study -
1.2 SCS Reliability Analysis
ERT developed procedures for evaluating.the uncertainty of meteoro-
logical forecasting, emissions forecasting and air quality modeling
associated with the operation of an SCS. The procedures require that
the following four concentration values be recorded for each forecasting
time:
• the concentration predicted by a model using predicted meteoro-
logical parameters and predicted emissions (this concentration
value is the basis of the real-time SCS control action);
• the concentration predicted by a model using observed meteoro-
logical parameters and predicted emissions;
• the concentration predicted by a model using observed meteoro-
logical parameters and observed emissions and
• the maximum concentration recorded by the monitoring network.
1-2
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The procedure combines the above recorded data and model results
to attempt to isolate the errors due to meteorological forecasting
uncertainty from the errors due to model uncertainty.
The observed maximum concentration C is represented by C = Q • M,
where Q is the emission rate and M is a function of the dispersion-
related meteorology.
The predicted maximum concentration is assumed to be C = Q • M • RT,
where IL, is a ratio describing the total error between predicted and
observed concentrations, that is:
IL, contains contributions from many sources of error and uncertainty.
These sources of uncertainty arise from each component of the SCS -
meteorological forecasting, emissions forecasting and air quality
modeling.
Consider the following formulation of R^
!*„ = R • R • R
T w q m
where R , R and R are the error ratios for meteorological forecasting
(w = weather) , emissions predictions (q = emissions) and air quality
modeling (m = model), respectively.
While the multiplication of the three error ratios above does not
define all the potential errors within an SCS, it does relate to all
errors made in evaluating the predicted concentration (C ) versus the
measured concentrations (C ) in the field. The uncertainty involved in
the actual measurement of concentrations surrounding the source is omitted
from this particular consideration. Aside from the obvious instrumenta-
tion errors in measuring concentrations, there is the additional difficulty
of not having measurements of concentrations at each desirable point.
The theoretically appropriate system would have measured the maximum
concentration at any receptor point in the area of the source. Because
the monitors measure only a fraction of the occurrences of significant
ground- level concentrations, the analysis techniques must be interpreted
in light of that difficulty.
-------
This study has defined seven specific sets of data hours, called
cases, in which comparisons of predicted versus measured concentrations
are made. The specification of these cases is detailed in Section 3.2.
The results obtained in each of the seven cases will lead to a more
complete understanding of the operational SCS than would a single error
ratio analysis for all hours.
Another analysis technique used does not deal with the errors
involved in forecasting methods but rather with the ability of the SCS
to ensure that NAAQS are not exceeded. In general, this can be analyzed
by developing a probability distribution of concentrations. The
probability distribution of the observed maximum concentration around an
uncontrolled source may be defined as the combined probability of the
emissions Q and the meteorology M as defined in the equation for C
above. If it is assumed that Q and M are independent, the analysis is
fairly straightforward. Note, however, that for nonbase-loaded plants,
Q and M may not be independent. Peak loads tend to occur with very cold
winter storms and hot summer afternoons, while nighttime stable atmospheres
are associated with generally light loads.
With an operational SCS the probability of expected ground-level
concentrations is the combined probabilities of Q, M, and IL,, the SCS
total error ratio. The air quality impact of a given meteorological
situation is dependent on the emissions, which are linked to the meteoro-
logy through the application of controls. There is a probable inter-
dependence of emissions and meteorology, but the present analysis will
assume their independence. Combining probabilities has been automated
in a computer program called PROBL. PROBL calculates the probability of
exceeding the ambient air quality standard for various control strategies,
thereby providing a major test of the reliability of an SCS as a function
of control strategy.
1.3 Kincaid SCS Program
The SCS of the Commonwealth Edison Kincaid station was selected as
a test example and permission to use the data was obtained. Because ERT
was responsible for providing the meteorological and air quality forecasting,
1-4
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air quality monitoring, and air quality and emission control decision
modeling, using the Kincaid program was a cost-effective way of completing
the case study of reliability. The SCS program at Kincaid became
operational on July 19, 1976 and produced 123 days (months of October,
November, December and January) of operational SCS data by January 31,
1977.
The Kincaid Generating Station is located approximately 25 km
southeast of Springfield, Illinois, and consists of two adjacent 600-Mw
coal-fired generating units. ERT is under contract to the operator of
Kincaid, Commonwealth Edison Company, to provide nearly all of the SCS
program operations. Important features of the program are:
• a 10-station network of monitors for SO- (the pollutant being
controlled);
• the communications network to collect real-time concentration
and meteorological information for the SCS;
• the meteorological forecasting and support to provide predic-
tions of meteorological conditions;
• air quality modeling to predict the expected concentrations,
not only at the 10 monitor locations, but also at 246 other
model receptor locations spaced around the generating station;
• a control system for evaluating the threshold concentrations
at which emission cutbacks should be initiated and the delivery
system for cutback recommendations and
• data retrieval, storage and validation systems to ensure the
accuracy of the monitored data collected and its retention for
future analysis.
The use of Kincaid, where ERT operates the SCS, has greatly
facilitated the collection and processing of data. Greater difficulties
would have been experienced if another SCS with a different operator had
been used in the analysis.
There is, however, one significant drawback to the use of the
Kincaid SCS system in this case study. Over the four-month period,
October through January, only two control actions were initiated and
1-5
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no violations of the standards were recorded. Because of this very low
number of control actions, the case study method will not effectively
test the response of a control system to predicted excursions above the
standards, nor will it provide information on the establishment of the
threshold for initiating control actions. Although recommendations will
be made on the basis of the analysis of the four-month data record, the
system has not been "put to the test" often enough to evaluate its
response. In spite of this drawback, the case study will provide much
information on the reliability analysis technique and its applicability
to operational situations.
1.4 Detailed Discussion of the Kincaid SCS
ERT is operating the SCS for Commonwealth Edison Company for the
purpose of maintaining NAAQS for SO- in the area of the Kincaid Generating
Station in central Illinois. The Kincaid Station consists of two 600-Mw-
rated generating units that exhaust through two side-by-side 500-ft
stacks. The approximate separation distance between the two stacks is
100 feet. The close proximity of the two stacks has led to the reason-
able assumption in model evaluations that the stacks are, for diffusion
purposes, a single point source. In addition, it is assumed as a matter
of conservative modeling practice that plume rise is not enhanced by the
interaction of the two plumes.
The Kincaid Station is a mine-mouth coal-fired plant that burns
approximately 4.2% sulfur coal. When burned, this fuel produces emissions
on the order of 5840 g/sec for each unit when operated at capacity.
Model calculations at capacity indicate that over a three-year period,
ground-level concentrations could approach the 24-hour average standard
of 365 ug/m (0.14 ppm) of S02 on 22 days (ERT 1976). The maximum
ground-level concentrations were normally expected in the 6 to 8 km
distance from the source but could occur as far as 17 kilometers out.
No occurrences of 3-hour average or annual average concentrations above the
respective standards were expected based on preliminary modeling results.
A real-time air monitoring (AIRMAP ) network in the vicinity of the
Kincaid Generating Station measures SO,,, meteorological and power plant
parameters. The location of the 10 monitoring stations [the required
1-6
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number - (EPA 1976)J and the Kincaid Generating Station are shown in
Figure 1-1. The grid of 256 receptor points used in the Kincaid AQFOR-
CONDEC Model is displayed in Figure 1-2. Table 1-1 presents information
on the monitoring stations in the network.
S0_ concentrations are monitored by Meloy flame photometric analyzers
at all 10 monitoring stations. Commonwealth Edison operates a 76 meter
(250-foot) tower, which is maintained by Murray and Trettel, Inc. and
contains instrumentation for wind speed and wind direction at the 10 meter
(33-foot) and 61 meter (200-foot) levels of the tower. The temperature
difference (AT) between the 10 meter and 61 meter level is also measured.
Low-level atmospheric stability is determined from the AT between these
two levels. Dew point and insolation are measured at the 2 meter level
of the tower. The data obtained from the SCL sensors and these tower
sensors are transmitted in real-time to the SCS control center in Concord,
Massachusetts. Strip charts serve as a backup for the real-time data
acquisition system.
Table 1-2 presents the operating experience of each of the Kincaid
generating units during the 123-day test period. Both units operated
simultaneously for 19 days, mostly in January, which represents 16% of
the test period.
Table 1-3 presents raw real-time data capture statistics by site
for all SCS parameters over the 123-day test period. Raw real-time data
capture is defined as the percentage of data received in real-time via
computer, without review by data analysts or meteorologists for validity
or historical data processing.
A monostatic acoustic sounder manufactured by Aerovironment is
operated by ERT to obtain real-time information on the height of tempera-
ture discontinuities in the vertical (inversions) that may exist. A
remote readout of the instrument output is displayed in real-time at the
SCS control center for use by the SCS forecasters.
The air quality dispersion model that is used in the real-time SCS
program is called the Kincaid AQFOR-CONDEC model (details in Appendix A).
This model calculates the expected ground-level concentrations around
the Kincaid Station (AQFOR portion) and selects a plant operating schedule
from a specified set of emission control actions (CONDEC portion).
1-7
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f
N
NEW CITY 1
El. 179m
9 CASCADE
El. 180m
5
PAWNEE
El. 184m
• EOINBURG
El. 182m
JEISYVILLE
El. 186m
ZENOBIA
El. 184m
CLEAR CREEK
El. 188m
Scale in Kilometers
C3 Kincaid Power Plant
O Monitoring Stations
Figure 1-1 Field Monitoring Network for
the Kincaid Area
1-3
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I |3| 13^'« B^^»
**' "rao c> AuoiUfc«s5iki ol\ ^^
;/.y ^ offTNG/flviU^i vAlJ^T', (
Figure 1-2 AQFOR-CONDEC Model Grid
1-9
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TABLb 1-1
KINCAID MONITORING NETWORK INFORMATION
Stilt lull
Slaluin N.I IMC Niinilier
Stution Llevation
(ra (ft) above msla)
Unit J
336 (1.IOJ)
Sensors
New City I
Cascade 1
lidiiiliiii't; 3
Sangclins 4
Pawnee b
Pawnee Tower
Jm (Ii-lt) Level
Him (33-tt) Level
6lm (JOO-ft) Level
Clark b
,_ Ki nc a id 7
| , .luJ^yville 8
Clear Creek 9
Zenoliia A
Puwcr Plant
Unit 1 Is
179
180
182
183
184
184
184
185
ISd
188
184
183
336
(587)
(590)
(598)
(599)
(604)
(603)
(603)
(t.06)
(610)
(618)
(605)
so2
so2
so2
SO,
S02
ws,
ws ,
so2
S02
SO,
so2
so.
.
insolation
wd, T
wd, AT, 0-
D
(dUJ) Acoustic sounder
(1.IU2)C
Sta
ck gas analyzi
load signal
Stack gas analyzer,
load signal
Distance kilometers (mi)
from k'incaid Plant
Downwind Sector (°)
from Kincaid Plant
Downwind
Direction (°)
12.2 (7.6)
10.9 (6.8)
9.7 (6.0)
3.4 (2.1)
8.0 (5.0)
133" - 193°
154° - 214°
196° - 256°
154° - 214°
063° - 123°
163'
184'
226'
184
093
1.9 (1.2)
5.0 (3.1)
9.3 (5.8)
9.7 (6.0)
8.7 (5.4)
330°
277°
255°
315°
005°
- 030°
- 377"
- 31S°
- 005°
- 01,5°
360
307
285
345'
035
ca 1 eve 1
The downwind direction is defined by tlu; direction from the plant to Iho iiioaitoriug station. Hie dounwind sector is suhtcnded by an arc of J30°
i_eMle ix-d on i lie duwnw i nd d i rect ion .
~ St ,icK lie i i;hl i n t L
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TABLE 1-2
SUMMARY OF THE DAYS OF OPERATION OF THE KINCAID UNITS
DURING THE 123-DAY TEST PERIOD
Unit 1 Unit 2
October 1976 0 21
November 1976 0 20
December 1976 4 28
January 1977 28_ 20_
Total Days 32 89
Percentage of
Period 26% 72%
1-11
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TABLE 1-3
KINCAID RAW REAL-TIME DATA CAPTURE FOR
OCTOBER 1976 THROUGH JANUARY 1977
Site
Bl New City
B2 Cascade
B3 Edinburg
B4 Sangchris
B5 Pawnee
B6 Clark
B7 Kincaid
B8 Jeisyville
B9 Clear Creek
BA Zenobia
BL Pawnee Tower
BU Pawnee Tower
BL Pawnee Tower
BU Pawnee Tower
BL Pawnee Tower
BL Pawnee Tower
BU Pawnee Tower
BL Pawnee Tower
(Lower)
(Upper)
(Lower)
(Upper)
(Lower)
(Lower)
(Upper)
(Lower)
scs
Parameter
so2
so2
S02
so2
so2
so2
so2
so2
so2
so2
ws
ws
WD
WD
Temp.
Td
AT
Insolation
Data
Capture (%)
93.46
99.36
97.53
98.68
98.54
96.24
97.29
98.71
98.78
98.85
99.06
99.06
99.06
99.06
99.06
99.02
99.06
99.06
1-12
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The Air Quality Forecast (AQFOR) model is a state-of-the-art
multiple-source Gaussian diffusion model that has the following charact-
eristics:
• It uses the Briggs plume rise equations but accounts for stack
tip dovmwash where important.
• It accounts for background concentrations from a background
concentration look-up table.
• It accounts for capping of the plume by an elevated inversion
but considers punch through if the final plume rise is more
than 50 meters above the elevated inversion height.
• The concentration is averaged over a sector width at the
receptor in accordance with procedures detailed in Appendix A.
A sector width of 22-1/2° has been used throughout the present
analysis.
The Control Decision (CONDEC) model provides the basis for control
actions, which are defined as any alterations of scheduled plant opera-
tions due to SCS recommendations. CONDEC can be initiated when scheduled
plant operations and forecast meteorological conditions combine to
produce predicted SCL concentrations that approach the NAAQS somewhere
in the receptor field. Control actions can also be initiated whenever
the observed SCL concentrations at monitor locations reach certain
threshold values and the predicted meteorological conditions indicate a
potential violation of the NAAQS. Predicted concentrations and guidance
for control actions are obtained from the AQFOR-CONDEC computer model
for the Kincaid SCS program, which computes maximum hourly SCL concentra-
tions for 24 1-hour periods and compares the predicted concentrations
against the model threshold values. The model first analyzes the long-
term averages (that is, the 24-hour average), then continues to analyze
to the shortest term average (that is, the 1-hour average) and compares
each value against the corresponding model threshold value. Whenever a
receptor average exceeds the specified threshold, CONDEC examines each
forecast period contributing to that average and determines the
operating conditions that will meet all model threshold constraints.
1-13
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Figure 1-3 is a graph of the threshold curve. The 5-hour and
24-hour SCL standards are shown on this graph to illustrate the "safety
factor" between the threshold and the standards. The 3-hour and 24-hour
threshold values on the curve are approximately 80% of the corresponding
S07 standards. If SO- concentrations computed by the model for any
receptor point exceed these model threshold values, control action is
recommended in the computer output. The SCS forecasters analyze this
output and then transmit to Kincaid twice daily a final recommendation
for plant operations. Other features of both the AQFOR and CONDEC
models are detailed in Appendix A.
The models used in this study had not yet been upgraded from their
original design to include the experience gained in actual operations.
It would naturally be expected that improvements could substantially
increase the operational accuracy of the entire SCS.
1-14
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.500
.400
E
3: .300
NAAQ 3-hour Standard
Model SO2 Threshold Curve
and Corresponding
Threshold SO2 Values
.200
.100
Time
Period
(hours)
Threshold
Values
(ppm)
1-3
4-6
7-9
10-12
13-15
16-18
19-21
22-24
0.385
0.319
0.252
0.200
0.172
0.144
0.130
0.119
NAA Q 24-hour Standard
10
12
14
16
18
20
22
24
TIME (Hours)
Figure 1-3 Model S02 Threshold Curve and
Corresponding Threshold Values
ai
o
u>
1-15
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2. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
The reliability analysis technique developed in "Technique for
Supplementary Control System Reliability Analysis and Upgrading" (EPA
1976a) has been tested in a case study using the Kincaid Generating
Station SCS as an example. The reliability of the SCS has been tested
in two ways: (1) the hour-by-hour ability of the SCS to predict the
then-measured ground-level concentration has been evaluated by an error
ratio technique and (2) the ability of the SCS to avoid exceeding NAAQS
has been evaluated by a statistical combination of frequency distribu-
tions (accomplished by the computer program PROBL).
The error ratio analysis involved comparisons of real-time, maximum
predicted ground-level concentrations to maximum measured concentrations
occurring over the 123-day test period. Because the entire set of
1-hour average concentrations contains many hours with very small
values, a. threshold was established for use of the hour. In addition,
subsets of the data were selected to overcome the lack of observed data
at each model receptor point (256 points). The error ratio analysis is
quite sensitive to the selection rules used to define these data subsets.
Specifically, the statistics are systematically biased by the data
selection criteria and by the value of the threshold concentrations. A
further analysis of the source of errors in the SCS divides the total
error into component parts; errors in forecasting the observed meteoro-
logy, errors in projecting the power plant emissions, and errors in
modeling ground-level concentrations.
The conclusions of the error analysis follow:
• The error ratio has a value range between zero and infinity.
It is therefore very sensitive to low values of either the
predicted or observed concentrations. One data subset was
defined by eliminating all hours where the observed concentra-
tion was less than 0.05 ppm (-135 yg/m ). Since predicted
concentrations in the range of 0 to 6.05 ppm still remained in
the data set, a systematic bias towards low prediction results
occurs. A bias toward underprediction occurs because of this
2-1
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lack of symmetry in the observed to predicted data base. The
result is also a large variation in P^,. Two specific difficult^-es
of the Kincaid SCS were found to account for much of the
underprediction: 1) measured ground-level concentrations
caused by other nearby SO- sources and 2) hours when the
mixing depth was forecast to be lower than actually occurred,
and the SCS predicted no contribution from Kincaid.
When the same threshold is used for both the predicted and
observed values the error analysis indicates that the SCS
tends to overpredict and the scatter is greatly reduced. The
symmetry between observed and predicted data sets is restored.
When the predicted values are also restricted to monitored
locations (instead of the entire field of receptors) the
results do not change appreciably. One interpretation of this
result is that data from the monitoring system around Kincaid
is representative of the values resulting from the analysis of
the entire receptor field.
For the limited number of hours in which the predicted and the
observed concentrations at a specific monitor were both above
the threshold, the mean error ratio shows only a slight under-
prediction in the mean. This subset may be a good test of a
model but represents a narrow test of the SCS. This is because
the actual location of the predicted maximum is not the basis
for a control action.
If the subset is determined only by predicted concentrations
above the threshold while measured concentrations can be any
value, an exaggerated overprediction occurs, again because of
the lack of symmetry in the data set.
When the threshold is raised, the mean R_ and its standard
deviation both decrease.
2-;
-------
The analysis was expanded to 3-hour and 24-hour average
concentrations to determine if a larger safety margin existed
with respect to the standards than is apparent from the 1-hour
averaging time analysis. The 3-hour average results did not
show any improvement. For the 24-hour averaging time, the
mean safety margin was much higher, showing a tendency to
overpredict the 24-hour average concentration.
Separating the total system error R^, into its components was
useful in suggesting that the "observed" meteorology did not
result in model predictions as accurate as those using the
predicted meteorology. This somewhat surprising finding
suggests that short term predictions based on synoptic scale
meteorological forecasts may have a higher reliability than
meteorological inputs derived from on site measurements by
instruments at heights that are low in relation to plume
heights.
The error ratio analysis techniques provide a method for
generating gross statistics concerning the SCS model reli-
ability. Two cautionary notes are appropriate for future
applications of this technique.
1) The breakdown of the total system error into component
error ratios provides insight. The analysis for Kincaid
showed that very reasonable total system error ratios
resulted from the balancing of overprediction and under-
prediction factors of the error ratio components.
2) Because the error ratios are severely affected by
extremely low values of measured or predicted values,
care must be taken to ensure that the results are
applicable to the highest air quality concentrations
which by their very nature focus on the occurrences of
worst-case meteorological conditions. For this reason
thresholds should be used in the development of any
meaningful statistics for SCS reliability. Separate
consideration should also be given to evaluating SCS
reliability from a worst-case analysis point of view.
2-3
-------
The analysis for Kincaid using the error ratio method has revealed
some important characteristics about that method.
The analysis of each hour of a test period and the consequent
averaging of all the results is less useful than the analysis of only
those hours with significant measurements. To retain symmetry in the
data base, thresholds need to be applied also to the predicted values.
It is difficult to establish a criterion by which to judge an SCS's
performance. An ideal R_ of 1 with a small geometric standard deviation
(the minimum is 1) appears to be difficult to attain. If a sector-
averaged model is used, as is appropriate to protect against exceeding
the standards, it was shown that large means and standard deviations
could be expected.
The second portion of the reliability analysis is the application
of the PROBL program to the frequency distributions of emissions,
meteorology and SCS total error ratio R_, to evaluate the expected
percentage of the time when the standards.might be exceeded despite the
SCS efforts. This analysis, based on the data subset with the worst SCS
predictive result, projects that the concentrations due to emissions
from the Kincaid Station are expected to exceed the 3-hour standard less
than once per period. The test period was 123 days and the percentages
may not be valid for any other time period, but they are indicative of
the general situation. Because R™ values are higher for 24 hours, the
expectation of exceeding the 24-hour standard (although untested in this
study) would be even lower.
The following conclusion can be drawn. The reliability analysis
technique, error ratios plus PROBL, developed previously and tested in
this study provides a method of analyzing the large quantity of SCS data
to assess the overall reliability of an SCS. The data base for develop-
ing the inputs to PROBL did not include enough observed concentrations
near the NAAQS to define clearly the frequency distributions used at the
high concentration end. Nevertheless, the result of the PROBL analysis
indicates expected violations less than once per year, indicating that
the Kincaid SCS is reliable. This result occurs despite the use of the
original model that had not yet been upgraded based on operational
experience.
2-4
-------
It has become clear, however; that the analysis techniques do not
provide a logical method for the upgrading of SCS forecasting techniques.
It is believed that what is true at Kincaid is true elsewhere; in other
words, that observed meteorology is the greatest weakness in verifying
model results. It is also clear that investigating the individual hours
(such as Case 4), when the forecast system most radically underpredicted
the observed concentrations, is far more likely to result in model and
forecast methodology improvements than the use of the techniques described
and used here. This suggests only limited continued use of these techniques
and more effort to be placed on modeling and forecasting the worst-case
situations.
2-5
-------
3. RELIABILITY ANALYSIS METHODS
3.1 Discussion of Error Ratios
A complete SCS has four general components in which uncertainties
can exist. These components are (1) air quality monitoring, (2) meteoro-
logical forecasting, (3) emissions forecasting and (4) air quality
modeling. The first of these, air quality monitoring, differs signifi-
cantly from the other three components in that inaccuracies in monitor-
ing, if they go undetected, cannot be quantified. Inaccuracies in
measured concentrations can be divided into two categories: instrumen-
ation errors that result in inaccurate measurements of ground-level
concentration, and failure to monitor the maximum ground-level concen-
tration because of inappropriate or insufficient deployment of monitors.
In either event, the actual maximum ground-level concentration will not
be accurately measured.
The first of the possible monitoring errors, instrumentation
inaccuracies, has received a great deal of attention. Significant
portions of the formal structure of an operating monitoring system,
especially a real-time system for an SCS program, are devoted to monitor-
ing accuracy. A complete field testing and calibration system provides
measurement accuracies traceable to the National Bureau of Standards.
In addition, it is common to invest significant time and energy in
editing and validating the monitored data once received. Such a quality
assurance program is the only means to assess the reliability of the
measured concentrations. Any system will, of course, have missing data.
The more data the system captures, the less likely that maximum ground-
level concentrations will be missed.
The second reliability factor in measured concentrations, the
number and placement of monitoring stations, has been addressed in
detail in ERT's previous report on reliability analysis (ERT 1974). Using
an air quality model and an example source emission, it was shown that
in order to observe more than 90% of all SCL concentration values
greater than 0.25 ppm, it would be necessary to have 25 monitoring
stations located around the source. If the threshold concentration were
reduced to 0.1 ppm, the 25 monitors would observe only 72% of the
maximum concentrations. It should be noted that adding the 25th station
3-1
-------
increased the percentage of observed maxima by only 0.3% for the 0.25
threshold. Because of the expense of a monitoring station, it is clear
that all reasonable sets of monitoring stations will miss a relatively
high percentage of significant peak values. Hence, if violations are
expected to occur and monitoring alone is used to guide the decisions
to control emissions, a significant number of undetected violations will
occur. For this reason, and also because many sources require advanced
warning of the need for emission reduction, for an SCS program to be
reliable it must forecast expected severe meteorological conditions
and/or predict expected ground- level concentrations.
The other three components of an SCS program in which uncertainty
can exist, meteorological forecasting, emissions forecasting and air
quality modeling, are interrelated and are portions of the mechanism for
predicting ground- level concentrations. The error in an SCS system at
any given time can be characterized by the ratio between the maximum
predicted concentration and the maximum observed concentration. In
equation form, that is:
where
R_, is the total error ratio of the SCS system,
C is the maximum predicted concentration and
C is the maximum observed concentration.
The definition of C can be expanded to show its dependence on 0 ,
the expected emissions from the source and, in a more complex way, upon
M a variable that includes the meteorological parameters which affect
plume dispersion. The equation for R_ therefore becomes:
V
C
o
3-2
-------
Hence, if the complete air quality forecast C (0 , M ) were correct,
it would equal C , and the ratio R would equal 1. Although it is not
possible to deduce errors in C using the above equation, errors in C
can be deduced by comparison to a "validated" C .
Three possible sources of uncertainty are mentioned above. They
can be included specifically in RT through the following equation:
R_ = R • R • R
T w q m
where
R is the error ratio for meteorological (weather) forecasting,
R is the error ratio for emissions prediction and
q
R is the error ratio for air quality modeling.
By separating the total SCS error R into three components that
can be addressed individually, the relative magnitude of each component
can be assessed. As experience with an SCS program is gained, isolation
of the factors responsible for total system error R provides a reason-
able mechanism for determining areas for improvement.
Since R,^ is defined as a ratio of concentrations, it is desirable
to have each of its component ratios also defined in terms of concen-
trations. The only effective way to produce concentrations for compari-
sons in the ratios is through an air quality dispersion model. Of
course, it is desirable to use the same model for development of each
ratio leading to the total system error. Because the model, therefore,
becomes an important part of the analysis technique, R , the air quality
modeling error, shall be defined first.
The error in the model is defined by the ratio of the concentrations
calculated with the model using observed meteorology and observed emissions
to the measured ground-level concentrations. This ratio can be represented
by the equation:
C (Q , M J
p o o
m ~ C
o
3-3
-------
in which C (Q , M J is the maximum predicted concentration with
observed emissions and observed meteorology. The model used for
evaluating ground-level concentrations must be used consistently in this
and the subsequent ratios.
The error due to the effect of incorrectly forecasting emissions,
R , is the ratio between the ground-level concentration impacts calcu-
H
lated with predicted emissions and observed emissions. The equation is
R
in which C (0 , M ) is the maximum predicted concentration with fore-
cast emissions and observed meteorology and C (Q , M ) is the maximum
predicted concentration with observed emissions and observed meteorology.
Note that the ratio compares model evaluations of the ground-level
concentration, keeping the meteorology constant. The ratio of the
concentrations may or may not be simply the ratio of the emissions; for
example, when a different sulfur content fuel is used for the same
operating load at the plant (a fuel-switching SCS program), R would be
equal to the ratio of emissions only (0 /Q )• However, in a load-
switching SCS program such as that at Kincaid, or when the load of the
power plant varies, the change in load affects not only the pollutant
emissions, but also the plume rise. A decrease in load reduces the
plume rise and brings the plume closer to ground-level, a change in the
opposite direction as the reduction in total SO- emissions. R ,
therefore, must be defined as the ratio of concentrations that includes
the effect of this change of plume rise.
The third and final error ratio is that ratio associated with
meteorological forecasting, RW. By a similar technique to that used for
R , the ratio for meteorological forecasting error is the concentrations
predicted by the model with forecasted meteorology divided by the
concentration predicted with observed meteorology, or
C (0 , M )
R - ^_i E_
w
5-4
-------
in which C (Q , M ) is the concentration predicted by the model using
predicted emissions and predicted meteorology, and C (Q , M ) is the
concentration predicted by the model using predicted emissions and
observed meteorology. This formula, therefore, represents the ratio of
predicted air quality concentrations using predicted versus observed
meteorology: holding the emissions constant at the predicted value.
This ratio defines the meteorological forecasting error in a very specific
way, which is related not to the forecasters' ability to define the
overall synoptic or dispersion situation, but to the forecasters' ability
to specify model input parameters that yield accurate concentrations
predictions.
It is appropriate here to discuss the meteorological input parameters.
Most models require at least three basic meteorological inputs: wind
speed, wind direction and stability class. The first two are usually
derived at stack top height from available measurements at other heights.
The third is normally derived empirically from some other measure of
atmospheric stability. The temperature difference (AT) between two
heights on a meteorological tower is often used to define atmospheric
stability class. A fourth parameter that is often used is commonly
termed the mixing depth. Mixing depth is the total vertical depth of
the atmosphere through which it is assumed that the plume may be mixed.
Normally, the plume can disperse upward without bound, but often meteoro-
logical conditions trap the plume below some specific height. Hourly
mixing depth is approximated from National Weather Service radiosonde
data, which is gathered twice a day, by interpolating to hourly values
by using hourly surface temperature measurements. The forecaster,
therefore, needs to assess each one of those four meteorological parameters
accurately in order to strive for a value of R of 1.
It is now possible to give a more complete formula for the total
system error ratio:
C
p
C
p
cv
cv
M
p
Mo
)
) "
Cp(Q{
c ro
pvxc
, M )
:>' 0'
3' M0}
c (
„ p
Qo5 Mo:
C
0
! C
P
C
o
M J
The separation of R into its component parts has not altered the
fact that it is a ratio of the concentrations predicted with predicted
emissions and predicted meteorology to measured concentrations. If each
3-5
-------
individual component were forecast precisely, then each of the component
R's would equal 1, and the total R would equal 1. The two intermediate
nodel predicted concentrations cancel, which means that errors in
observed emissions and observed meteorology do not show up in the final
error ratio R_. However, errors in observed emissions or meteorology
can be very important to the component R values. "Errors" in observed
meteorology and observed emissions arise from inaccuracy and inappropriate-
ness of measurements. For instance, if wind speed and wind direction at
the top of a tower are unrepresentative of the plume path, an "error" in
observed meteorology is the result. Errors may balance each other,
however. If, for instance, R were 1, an error in observed meteorology
that in the model resulted in a lower than measured concentration would
create a low R , but might be offset by a high R so as to produce an
R_31. Another point worth noting is that the above formula could
equally well have used predicted ground-level concentrations with
observed emissions and predicted meteorology, C (Q , M ). Since changes
in load affect the plume rise, observed meteorology rather than predicted
meteorology was chosen for the plume rise calculation. R is therefore
evaluated with observed meteorology.
An example may help to illustrate the approach. Table 3-1 gives an
example of the error ratio method. Note that each of the component R
values represents a slight overprediction and the total is therefore
well over the measured value, C .
The method described above defines a quantitive way to calculate
the total system error in an SCS program and the three major components
of that error. This systematic approach provides a framework for analyzing
the errors and therefore the reliability of an SCS program.
Because the total system error does not measure the ability of the
SCS program to maintain the ambient air quality standards, a method for
that analysis is given in Section 5.
3-6
-------
TABLE 3-1
EXAMPLE OF ERROR RATIO METHOD
Predicted
Observed
Meteorology
Wind Direction (°)
Wind Speed (mpsj
Mixing Depth (m)
Stability Class
Emissions
Unit 1
Unit 2
Concentrations (ppm of S0«)
VV V
VV V
VV Mo)
150
5
800
4
0
530
148
6
500
4
0
500
0.084
0.080
0.076
0.060
RT = Rw X Rq
R
T=
R
m
VVV VVV
C (0 ,M ) C (Q ,M )
p T> o p^o' oj
0.084 0.080 0.076
T ~ 0.080 0.076 0.060
o
0.084
0.060
= 1.40
R = 1. 05
w
R = 1. 05
q
R = 1.27
m
3-7
-------
3.2 Establishment of Cases for Analysis
As indicated in the previous section, it is unreasonable to maintain
a monitoring system large enough to measure all maximum concentrations.
While it is customary to analyze worst-case meteorology and the historical
records at a specific site in order to locate the limited number of
monitors for maximum coverage, this process still cannot cover all high
concentration situations. As a result, an SCS program which employs an
air quality model should make predictions for locations where no measure-
ment is available. Because the number of points at which concentrations
are predicted is larger than the number of points at which concentrations
are observed in the limited monitoring network, a value of R greater
than 1 on average should be expected.
In evaluating an entire 120 day test period of SCS program opera-
tion, it is evident that a large number of the individual hours may not
be of much interest or import. For instance, for most nighttime hours,
the plume remains well aloft and will not affect any of the monitoring
stations in the flat terrain surrounding Kincaid. While the model will
calculate relatively small concentrations at ground level, any differences
could make substantial changes to the value of IL, . For this reason, it
is appropriate in the analysis to use a threshold concentration value to
limit the number of hours studied to those that are most important.
Establishing a threshold for either the observed or predicted values
produces, however, another systematic bias in the 1^ values. Consider,
for example, the data subset that is characterized by lower-than-threshold
observations but includes the full range of predicted values. If this
data subset is eliminated from the full data set, a systematic bias
toward underprediction (E^ < 1) will result because the mean values of
the observed data become higher when the values below the threshold are
removed, while the mean value of the predicted set is not necessarily
affected.
A number of cases have been constructed that attempt to define the
biases caused by the lack of complete monitoring coverage and the use of
threshold concentrations. These seven cases are presented in Table 3-2.
-------
TABLE 3-2
SCS RELIABILITY ANALYSIS CASES
Case
1.
2.
3.
4.
Maximum Concentration
Measured at a Monitor
Any Monitor > Threshold
Any Monitor > Threshold
Any Monitor > Threshold
Any Monitor > Threshold
Maximum Concentration
Predicted in Real-Time
Any Receptor
Any Receptor > Threshold
Any Monitor > Threshold
Same Monitor > Threshold
5.
6.
7.
Maximum Concentration
Predicted in Real-Time
Any Receptor > Threshold
Any Monitor > Threshold
Any Monitor > Threshold
Maximum Concentration
Measured at a Monitor
Any Monitor
Any Monitor
Same Monitor
3-9
-------
The cases are defined as a set of hours with similar relationships of
maximum concentration measured at monitors, C , to the maximum concentra-
tion predicted in real-time, C (Q , M ). It is useful to describe these
cases individually and to indicate the expected bias.
The first four cases were culled from the 123-day test period by
searching for each hour during which a concentration measured at any
monitor exceeded the threshold. When the values at more than one
monitor exceed the threshold, the monitor with the highest concentration
is selected.
« In Case 1, the maximum measured concentration above the thresh-
old is compared to the maximum predicted concentration at any
receptor location surrounding the source, without regard to
threshold. The receptors are defined as all those locations
for which the air quality model makes an evaluation. This
case is a severe test because a concentration above the
threshold must be predicted'for each hour that such a concentra-
tion was measured. The exact location of the predicted
concentration is not important, however. For R^, to equal one,
the prediction must simply be equal to the monitored concentra-
tion.
• Case 2 requires the additional condition that the maximum
predicted concentration must be above the threshold value.
This case still does not require that the model accurately
predict the location of the maximum concentration, only its
magnitude. This case should be a less severe test of the
system because it eliminates all those cases where very
little ground-level concentration was predicted. Case 2 is a
subset of Case 1.
• In Case 3, the predicted maximum concentrations considered are
only those at monitored locations. The threshold value is
retained, but the concentration may be predicted at any monitored
location, i.e., not necessarily the location where the maximum
concentration was measured. Case 3 is a subset of Case 2.
« Case 4 adds an additional constraint: the maximum predicted
concentration at a monitor occurs at the same monitor that
3-10
-------
experienced the maximum measured concentration. This case
represents a severe test of predictive accuracy as it requires
that the correct location of the measured concentration be
predicted. It is not clear that this is required in an SCS
since a control action is initiated no matter what receptor is
predicted to have a high concentration. The use of a threshold,
however, on both concentrations limits the number of hours
considered to those with some reasonable predicted value.
Case 4 is a subset of Case 3 and represents the smallest data
set of Cases 1 through 4.
• Cases 5 through 7 depend primarily on the maximum predicted
concentration. Case 5 is developed by searching the entire
test period for all those hours in which the predicted maximum
concentration exceeded the threshold at any location in the
model receptor grid. The maximum predicted concentrations are
then compared to the maximum observed concentrations in the
monitoring system. This is specifically the case which would
tend to produce high values of the ratio, RT, because the
predicted maximum concentration may be nowhere near a monitored
location or because no elevated concentrations may in fact
have occurred during the hou^ whether observed or not.
• Case 6 requires that the maximum predicted concentration be at
a monitor site. Although each hour in Case 6 is one of the
hours in Case 5, the maximum predicted concentration will
generally differ since it must be at a monitor instead of at a
receptor. Just as in Case 3, Case 6 would apply to a SCS that
considers monitored sites only.
• Case 7 applies the constraint that the maximum measured con-
centration must be at the same location as the maximum predicted
concentration. This case, like Case 4, is a test of the
ability of the prediction system to forecast the correct
location as well as the correct magnitude of a concentration.
The two groups of cases tend to show completely different aspects
of the SCS reliability. Cases 5 through 7 will, in general, be biased
towards overprediction, first because monitors are not located at all
3-11
-------
the receptors, and second because maximum measured concentrations have
not been restricted by a threshold. Cases 1 through 4, however, are
biased towards underprediction of the forecast system because of the
emphasis on maximum monitored concentrations. By looking at the results
of these two groups of cases simultaneously, a better understanding of
the SCS as a whole can be obtained.
3.3 Data Collection and Processing
The evaluation of error ratios requires the collection and processing
of a large quantity of data. The necessary values are the measured S0_
concentrations, C , at each of the 10 monitoring sites and the following
calculated ground-level concentrations:
V
as they were described in Section 3.1. For the model calculations, the
following input parameters are needed:
• plant emissions
• wind speed
• wind direction
• atmospheric mixing depth
• differential temperature (as a measure of stability)
Both the observed values of these parameters and the predicted
values at the time of the forecast are needed. In the operational
system at Kincaid, a forecast is made twice a day, at 0700 and 1600 hours
Central Standard Time. Each of the input parameters is forecast and the
AQFOR model is run on the computer. The results of these model runs are
logged as well as stored on magnetic tape. This log enabled the study
team for this project to select the maximum predicted concentration over
5-12
-------
the whole field or at any specific monitor. The hour-by-hour values of
predicted concentration for the most recent forecast in relation to each
hour are used. This log therefore provides C (Q , M ). Since the
remainder of the analysis does not require M , there is no need to
handle two sets of meteorological variables.
The other two model calculations require observed meteorological
data and one requires observed emission data. These observations are
available in real-time to the forecasters on duty and are, in fact, used
as historical data in the AQFOR model calculations (the concentrations
from previous hours are used to assess the probability of exceeding the
24-hour standard during the hours for which the forecast is being
made). Although this observed data is placed in computer storage during
the real-time retrieval, it is not considered valid until the strip
chart data and calibration/maintenance reports have been received from
the field. A two-step process follows. The first step, editing,
eliminates from the data base all obvious errors in the values stored in
the computer. It also eliminates values that are indicated as problems
by calibration/maintenance. The second independent process, validation,
samples the strip chart data for agreement with the numbers in computer
storage. This process takes 30 to 45 days, after which the observed
parameters become available for use.
A computer system could model concentrations for each hour of the
test period (in this case 2952 hours). In this study, establishing a
lower threshold of 0.05 ppm reduced the quantity of hours considered to
two sets: the set for Cases 1 through 4, consisting of 321 hours, and
the set for Case 5 through 7, consisting of 905 hours. A total of
177 hours was common to both sets so that a total of 1049 distinct
hours, or 35.7% of the total hours in the 123-day test period, was
considered.
Although the techniques for analyzing the error ratios could have
been computerized, it appeared that the most cost-effective approach for
this data set would be the use of a manual tabular mode of calculation.
This procedure has been carefully reviewed and cross-checked to ensure
the quality of the results.
3-13
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One significant problem encountered in the processing of the
concentration data was the treatment of "background" SO from other
sources. AQFOR is set up to add a background concentration depending
on wind direction, wind speed and stability class to the predicted
concentrations from the Kincaid plume. A background lookup table,
Table 3-3, was developed for Kincaid during July and August of 1976 when
the plant was not operating but the monitoring system was. This lookup
table is, of course, specific to those two summer months and may be of
less value for the winter months of the 123-day test period. An alternative
method of background assessment could be provided by averaging the
concentration values at monitors determined to be upwind, that is, not
within a 90° sector of the observed wind direction. It was decided,
however, that the predicted concentrations that the forecaster receives
from AQFOR are based on the lookup table and therefore so is C (0 , M ).
P t> P
The other model calculations for C therefore ought to use the same
background for consistency.
3-14
-------
TABLE 3-3
BACKGROUND CONCENTRATIONS, ppm S02
LOOKUP TABLE FOR KINCAID
(BASED ON JULY-AUGUST 1976 DATA)
Wind
Direction
N
NNE
NE
ENE
E
ESE
SE
CM
I SSE
On s
ssw
sw
wsw
w
WNW
NW
NNW
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0.
0.
0.
0,
0.
0.
0.
0.
0.
0.
0.
0
0.
0
0
0,
1
.030
.006
.007
.007
.008
.004
.008
,009
.013
.012
.010
.020
.003
.012
.009
.009
0,
0.
0
0
0,
0.
0
0
0
0
0
0
0
0
0
0
2
.010
.013
.011
.007
.008
.004
.007
.003
.010
.016
.012
.003
.003
.012
.011
.009
Unstable
3 4
0.
0.
0
0
0.
0
0
0
0
0
0
0
0
0
0
0
.009
.004
.005
.007
.008
.004
.008
.019
.015
.010
.009
.002
.003
.012
.004
.007
0,
0,
0
0
0.
0,
0
0,
0,
0
0
0
0
0
0
0
.012
.004
.007
.007
.008
.004
.008
.009
.011
.013
.011
.002
.003
.012
.009
.009
5
0.012
0.006
0.007
0.007
0.008
0.004
0.008
0.009
0.013
0.013
0.010
0.003
0.003
0.012
0.009
0.009
6
0.012
0.006
0.007
0.007
0.008
0.004
0.008
0.009
0.013
0.013
0.010
0.003
0.003
0.012
0.009
0.009
0.
0.
0.
0.
0.
0.
1
.004
,009
.008
,007
015
,006
0.009
0.
0.
0.
0.
0,
0,
0.
0.
0,
.023
021
,020
,002
,004
.010
.008
.020
.005
2
0.006
0.008
0.004
0.008
0.009
0.008
0.014
0.012
0.013
0.016
0.013
0.003
0.003
0.008
0.014
0.014
Neutral
3 4
0.006
0.003
0.004
0.008
0.010
0.010
0.013
0.003
0.008
0.023
0.011
0.004
0.003
0.008
0.007
0.006
0.006
0.002
0.005
0.008
0.010
0.007
0.013
0.011
0.027
0.020
0.004
0.004
0.005
0.008
0.014
0.009
5
0.006
0.005
0.005
0.008
0.010
0.007
0.013
0.011
0.015
0.020
0.010
0.004
0.005
0.008
0.014
0.009
6
0.006
0.005
0.005
0.008
0.010
0.007
0.013
0.011
0.015
0.020
0.010
0.004
0.005
0.008
0.014
0.009
1
0.004
0.003
0.004
0.004
0.004
0.005
0.006
0.006
0.006
0.005
0.004
0.002
0.004
0.002
0.003
0.005
2
0.007
0.003
0.003
0.005
0.005
0.006
0.004
0.004
0.006
0.009
0.004
0.002
0.003
0.006
0.002
0.004
Stable
3
0.010
0
0
0
0.
0,
0.
0.
0.
0.
0.
0,
0,
0
0.
0
.002
.003
.005
.004
.005
.005
.003
.008
.011
.009
.002
.003
.003
.013
.008
0.
0,
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
4
.006
.003
.004
,005
006
005
005
004
006
,008
004
.002
.003
,003
,004
.005
5
0.006
0.003
0.004
0.005
0.004
0.005
0.005
0.004
0.006
0.008
0.004
0.002
0.003
0.003
0.004
0.005
6
0.006
0.003
0.004
0.005
0.004
0.005
0.005
0.004
0.006
0.008
0.004
0.002
0.003
0.003
0.004
0.005
Columns labeled 1-6 represent different wind speed classes.
Class
1
2
3
4
5
6
Wind Speed Range (mph)
0-4
5-8
9-12
13-16
17-20
21-greater
-------
4. RESULTS OF RELIABILITY ANALYSIS
4.1 Total System Error R
Table 4-1 presents a summary of the R analysis results. The
geometric mean and standard deviation have been used to characterize the
distribution of R values. The R values are bounded by 0 and infinity
(if a zero observed value occurs) with an ideal mean value of 1.
Because of these bounds, geometric statistics appear more appropriate
than arithmetic statistics (see Figure 4-1).
The geometric mean has been calculated by:
RT = (R:) (R2) . . . . (Rn)
where n is the number of hours in the case.
The geometric standard deviation has been determined by:
1/2
S = exp
(Z In R.)2"1
n-1
where R. is the value of R for the ith hour. Note that in contrast to
the arithmetic standard deviation, for which zero denotes no variations
from the mean value, the minimum value of S (corresponding to no varia-
tions from the mean value of R_) is unity. Therefore, the ideal value
of S is 1.0.
If distributions of RT are log normal, 68.3% of the values are
contained between the values RT/S and (R )(S). Using Case 1 as an
example, where the arithmetic mean and standard deviation are 0.86 and
0.90, respectively, 68.3% of the values lie between R = 0.09 and R =
1.80.
Before reviewing the specific results of the case analyses, it is
of interest to obtain a better feeling for the expected values of the
mean value, R , and variations about this mean as evaluated with S.
4-1
-------
TAB Hi 4-1
SUMMARY OF RESULTS FOR R
I
IV)
Case
1
2
3
4
5
6
7
Number of
Hours
321
177
66
22
905
288
58
Geometric
Mean R^ (JL)
1 1
0.40
1.22
1.21
0.86
4.37
3.56
2.33
Geometric
Standard
Deviation (S)
4.49
1.77
1.79
1.72
2.72
2.65
2.76
Complete
Range of
R Values
0.02 -
0.26 -
0.31 -
0.38 -
0.14 -
0.38 -
0.38 -
6.69
6.69
6.56
3.50
44.00
29.67
22.33
RT/S
0.09
0.69
0.68
0.50
1.61
1.34
0.84
(R,.,) (S)
1.80
2.16
2.17
1.48
11.89
9.43
6.43
See Table 3-2 for definition of cases. The threshold used is 0.05 ppm.
-------
c £
ss*
= in
«
0)
gcc
W H—
„ o
20
15
10
0
Value of R j, the total error ratio
Figure 4-1 Histogram of RT versus Percentage Frequency for Case 2
(177 hours of data)
4-3
-------
Consider the uncertainty associated with not knowing one meteorological
variable wind direction exactly. We have estimated the 1-hour averages
as if concentrations were uniformly distributed over a 22-1/2° wind
direction sector. This is, in effect, a concentration value that
better represents the average of a large number of measurements. Now
suppose that, for any given hour, the actual concentration distribution
was Gaussian and centered about a specific wind direction, within the
22-1/2 sector. Depending on the actual wind direction, a monitor
located on the centerline of the sector would be expected to measure
concentrations that could be above or below the sector-averaged values.
However, by our definitions, the arithmetic average would equal the
sector-averaged value. What values of R_ and 5 could be expected from
the effect of this uncertainty in wind direction alone?
The ratio of the predicted (sector averaged) to observed (Gaussian)
for any single event of this idealized situation would be given by:
^51 Y2/2a 2
a x 2.037TO e y ' y
z
where
x = distance to receptor from source
ay'(3z ~ diffusion coefficients at distance x for a specific
atmospheric stability category
y = crosswind distance from plume centerline
= exp
V / 2 ^
/'max. /2.037ra y /2a " , ,
L_ / ^n I H e / 1 dy
y /
max o
where
y = distance from plume centerline to edge of 22.5
max
sector, i.e., x tan 11.25°
4-4
-------
The integration in the above formula yields:
y 2/6a 2
RT = T e max y
Where 2.03™
T»
Similarly, the geometric standard deviation can be derived as
S = exp
Now we can make an evaluation, but the distance x and the stability
category must be specified. With the ASME unstable category at 2,000
meters from the source, RT = 1.21 and S = 1.47. The plume fits well in
the sector for those conditions (value at y only 0.349 of the sector
_ v 'max J
average) and the RT and S values are small. At ASME neutral category
and 6,400 meters from the source, the plume is quite narrow with respect
to the sector (value at y is 0.000366 of the sector average) and
max
R = 6.22, while S = 15.18. This exercise demonstrates that even in
idealized situations the use of R and S as measures of system error
and/or reliability can be misleading. Moderately large values of S can
be associated with a system which is in fact very reliable. Also note
that the allocation of continuous variables such as wind speed and
atmospheric stability into discrete categories in many modeling approaches
results in errors that affect R and S (primarily) by producing an irre-
ducible limit to the expected accuracy of predictions. No attempt is
made in this study to quantify this lower accuracy limit for the Kincaid
system.
The results in Table 4-1 cover the entire 123-day test period. The
results were evaluated one month at a time, but a review showed no
significant month-to-month variations except those caused in some months
by very small sample sizes. Month-by-month summaries are therefore not
presented.
4-5
-------
A discussion of the results for R on a case-by-case basis follows.
It is helpful to refer to the definitions of the seven cases found in
Table 3-2. The threshold value selected is 0.05 ppra.
4.1.1 Case 1
Case 1 contains 321 hours in which the maximum monitored concentra-
tion was greater than 0.05 ppm. As can be seen from the geometric mean
of 0.40, the values are in general underpredicted and the ratios have a
fairly large geometric standard deviation. Underprediction is expected
from the bias of the sample in Case 1, caused by the inclusion of
predicted values below the threshold. There are bound to be many times
when the SCS would not forecast ground-level concentrations above back-
ground at any receptor, while the monitors could measure a concentration
above the threshold. Such a situation might occur when stable atmos-
pheric conditions are predicted, which then lead to very small concen-
tration predictions since the plume is modeled to remain elevated. If
the stable conditions actually occur, then the monitored ground-level
concentrations may be due to other nearby low-level sources of S0_. The
SCS would be using only the average background concentrations from the
lookup table and thus would underestimate the measured concentration
while not underestimating the impact of the Kincaid plume. This situ-
ation has undoubtedly occurred.
Another source of the low ratios is the set of events for which the
measured concentrations are just above the threshold, while the predicted
concentrations are small or equivalent to background. In order to
quantify how sensitive the results are to the threshold value, the hours
for Case 1 were reviewed for thresholds of 0.10 ppm and 0.14 ppm. The
comparative results are presented in Table 4-2. These results demonstrate
the sensitivity of the results to threshold. The higher the threshold,
the lower the geometric mean and therefore the greater the underprediction,
In the extreme case of the 0.14 threshold, the entire first standard
deviation is below an R of 1. Note, however, that this is a small
sample size representing only the highest 28 hours of measured concen-
trations .
4-6
-------
TABLE 4-2
SUMMARY OF RESULTS FOR R,
COMPARISON OF THRESHOLDS
Threshold
ppm
0.05
0.10
0.14
0.05
0.10
Number
of Hours
321
76
28
177
21
Geometric
Mean (RT)
0.40
0.28
0.25
1.22
1.09
Geometric
Standard
Deviation (S)
CASE 1
4.49
3.67
3.03
CASE 2
1.77
1.34
Complete
Range of
RT Values
0.02 - 6.69
0.02 - 2.22
0.02 - 1.09
0.26 - 6.69
0.59 - 2.22
RT/S
0.09
0.08
0.08
0.69
0.81
(RT) (S)
1.80
1.03
0.76
2.16
1.47
-------
Another reason for the underpredictions evident in Case 1 is the
use in this study of a sector-averaged model in the prediction of
1-hour averaged concentrations for comparison to measured data. A
sector-averaged model is used in AQFOR because the SCS is oriented
toward protecting against exceeding the 3-hour and 24-hour standards.
To realistically assess the average for multiple hours, average expected
1-hour values rather than peak 1-hour values are used in the calculations,
4.1.2 Case 2
The Case 2 hours are a subset of the Case 1 hours with the addi-
tional restriction that a concentration must have been predicted above
the threshold of 0.05 ppm at some receptor. Both predicted and observed
values are above the threshold, and the bias identified in Case 1 is
eliminated. The sample size, however, was reduced from 321 to 177 hours.
Case 2 does show considerably better statistics. On the whole,
when the SCS is predicting a significant concentration, that prediction
is within a factor of two a high percentage of the time. The mean value
of R_ is greater than 1.0.
If the threshold in Case 2 is raised from 0.05 ppm to 0.10 ppm, the
result is a very good geometric mean ratio and standard deviation as
shown in Table 4-2. There are many hours for which neither the model
nor the monitors produced any significant ground-level concentration.
When these hours are eliminated from consideration, the model produces a
more accurate description of the expected concentration.
4.1.3 Case 3
Case 3 adds the additional restriction that the receptor for which
the SCS made a prediction must be a monitor site. This case shows very
little statistical difference from Case 2 even through 111 hours have
been dropped. This fact implies that the monitoring field provides a
good sample of the entire receptor field since the results for the data
subset for monitored locations are nearly the same as the results for
the subset for all receptors.
4-?
-------
4.1.4 Case 4
In Case 4, both the measured and predicted values above the thres-
hold must be at the same monitoring site location. Only 22 hours fit
the criteria of the case, which shows that only rarely did the SCS
predict the exact location where a concentration was subsequently
measured. The percentage is, in fact, 6.9% of all hours with measured
concentrations greater than 0.05 ppm. This fact appears to demonstrate
that the SCS must make predictions for a large number of receptor points
and provide for control actions on the basis of expected contravention
of standards at any one of those points. An SCS should act on predicted
concentrations regardless of the location estimated for the maximum
impact.
Case 4 represents a test of the ability of the SCS to predict at a
specified point the expected concentrations quantitatively. Since
concentrations above the threshold are both measured and predicted at
the same location, the comparison illustrates one measure of the validity
of the SCS prediction. Case 2 is the other best test because in fact in
an SCS one does not generally care where the highest values are predicted
if the value is accurate. Case 4, however, has been used as an example
in some of the subsequent analyses in this section.
The statistics for Case 4 are quite reasonable despite the limited
sample size. The geometric mean of 0.86 shows a tendency for slight
underprediction (recall the underprediction is, in fact, expected since
sector-averaged predicted values are being compared to 1-hour averaged
observations), but most of the values are within a reasonable range of
the perfect score of 1. The lowest value for R is only 0.38.
4.1.5 Cases 5 through 7
Cases 5 through 7 are based on data selection rules in which the
predicted values are above a threshold and thus have a strong bias
toward overprediction. Significant concentrations (in excess of 0.05 ppm)
were predicted for 905 hours or 30.7% of the hours in the 123-day test
period. There were only 321 hours (10.9%) when significant concentra-
tions were measured. These figures are reasonable since significant
concentrations are often predicted at locations with no monitor. It
4-9
-------
appears, however- that there are also many circumstances in which the
SCS overpredicts the concentrations that are measured.at ground level.
The statistics of Cases 5 through 7 support that judgment since even
Case 7, which involves comparisons at the same monitor, shows a geometric
mean greater than 2. Note that there is no threshold restriction on the
measured value for any of these cases. Note also that applying a
threshold restriction to the Case 7 data set would result in a case
equivalent to Case 4.
4.1.6 Summary of Cases
The analysis of Cases 1 through 7 demonstrates the sensitivity of
the predictive statistics to concentrations below the threshold. Bias
towards overprediction occurs when the threshold is applied to predicted
concentrations and not measured, while a bias toward underprediction
occurs when the threshold is applied to observed and not predicted
concentrations. When thresholds are applied to both observed and
predicted values (Cases 2, 3 and 4), there is a slight overprediction,
and the standard deviations are much smaller.
4.2 Analyzing Error Ratios of SCS Components
To understand more fully the complex processes that are summarized
in Table 4-1, consider the results for the three components R , R and
w q
R . Table 4-3 presents the geometric means and standard deviations for
the components. Multiplying the mean values of each of the components
in a case gives, within round-off errors, the R value for that case.
Several general statements about the results in Table 4-3 can be
made. The prediction of the emissions is very good and the impact of
errors in emission projections on the total error is relatively insig-
nificant. This effect is caused by two factors: (1) in a base-loaded
plant, the load is normally not expected to vary greatly from hour to
hour, and prediction of load should be and is fairly accurate (especi-
ally when one of the units isn't operating, which reduces generation
resources, a situation that existed during much of the test period) and
(2} differences in emission strength are somewhat offset by plume rise.
The second effect arises because the method compares the effect of
4-10
-------
TABLE 4-3
SUMMARY OF RESULTS OF R , R , R
w q m
THRESHOLD OF 0.05 ppm
lase
1
2
3
4
5
6
7
Number
of Hours
321
177
66
22
905
288
58
R
w
1.19
1.90
5.69
3.92
3.29
7.03
5.63
R
w
S
4.51
4.79
4.50
3.69
5.56
4.09
4.01
R
q
1.00
1.04
1.01
1.02
1.00
0.99
1.01
R
q
I
S
1.32
1.38
1.06
1.08
1.47
1.27
1.15
R
m
0.34
0.61
0.20
0.21
1.34
0.50
0.41
R
m
S
4.83
4.66
4.74
3.57
5.34
4.31
3.83
(R )(R )
w' v qj
0.40
1.21
1.15
0.84
4.41
3.48
2.33
-------
predicted and observed emissions on ground-level concentrations. If
load is higher at Kincaid, emissions are higher- but so is plume rise,
which reduces ground-level concentrations. This observation does not
imply that estimates of Q are always correct. In any specific hour, the
error in emissions prediction may significantly affect the accuracy of
the concentration prediction.
The statistics for model error, R , indicate that the model is
m
largely at fault in failure to achieve a reasonable R_. The results
indicate that, except for Case 5, the model on the average underpredicts
the measured concentrations. The standard deviations are uniformly
large, indicating a wide variation in results. Thus, even when the
observed meteorology is used, the concentrations predicted by the model
apparently are not conservative.
The geometric mean of R is lower than that of R , which implies
that some component of the SCS counteracts the modeling tendencies to
underpredict. A quick review of the R shows that these values are
generally higher than 1 and do provide the offset required to raise the
overall R_ values above those provided by the model, which implies that
the forecasted meteorology, when converted to ground-level concentra-
tions, is much more conservative on the average than the observed
meteorology. These effects on R and R suggest that the observed
w m
meteorology may be the parameter that causes the high value of R and
the low value of R . To check this hypothesis, the study examined the
individual values in Case 4. This case was chosen because it compares
observed and predicted values at the same monitor location.
Table 4-4 summarizes the results of the detailed analysis of
Case 4. Beside each small value of R is given a major reason for the
underprediction of the observed concentration, C , by the model with
observed meteorology. Hour 3 is an example of the difficulty often
experienced with mixing depth. The meteorological forecast called for
significant concentration at the monitor, and the mixing depth was
forecast to be well above a height that would have any significant
effect. In the observed meteorology, two radiosonde soundings at
Peoria, Illinois, are interpolated to determine the mixing depth. This
observed mixing depth for Hour 3, 450 meters, was so low that the model
assumed that the plume entered and remained in the elevated stable
4-12
-------
TABLE 4-4
DETAILS OF CASE 4
MeteoroloB
Sample
Hours
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Co
0.162
0.136
0.055
0.158
0.079
0.060
0.053
0.067
0.062
0.072
0.062
0.054
0.087
0.12S
0.127
0.179
0.077
0.129
0.126
0.068
0.074
0.052
KT
0.59
0.63
1.09
0.44
0.72
1.33
1.74
0.84
0.87
0.76
0.89
1.63
0.82
0.57
0.52
0.38
0.86
0.52
O.S3
2.01
3.53
0.98
R
w
1.09
0.99
7.5
0.77
19.0
1.05
30.7
2.95
2.84
2.89
3.67
6.29
23.7
23.7
0.86
5.23
0.83
3.35
3.19
0.60
23.5
17.0
Load
Unit 1
R^ Reason OBS PRED
0.52
0.63
0.15
0.41
0.04
1.27
0.06
0.28
0.31
0.26
0.24
0.26
0.03
0.02
0.57
0.07
1.01
0.16
0.17
3.40
0.15
0.06
4 0
4 0
1 0
4 0
2 0
0
2,4 0
2 250
2,4 270
2 291
2 361
2 169
2 0
2 0
1,4 0
1 0
0
2,3 557
3 567
2 557
2 553
2,4 0
0
0
0
0
0
0
0
300
300
400
400
100
0
0
0
0
0
550
550
535
530
0
(Mw)
Unit 2
OBS PRED
530
529
532
368
185
529
534
0
0
0
0
539
532
522
510
484
476
539
507
529
550
529
550
550
550
550
250
530
535
0
0
0
0
550
550
550
550
485
485
550
550
535
530
550
Wind
Direction
(degrees)
OBS PRED
338
346
176
219
281
180
273
163
164
164
174
316
272
267
221
176
183
204
181
151
148
262
340
340
175
230
290
180
290
180
185
185
190
300%
290
290
230
190
190
190
190
170
155
340
Wind
Speed
(mph)
OBS PRED
11
11
9
18
13
21
12
11
12
11
12
22
7
7
21
20
29
2
3
14
15
7
13
14
12
12
8
17
12
8
9
9
9
18
16
16
15
20
22
7
7
14
12
8
Mixing
Depth (m)
OBS PRED
3,000
3,000
450
500
3,000
500
3,000
500
500
600
700
3,000
3,000
3,000
500
200
300
3,000
3,000
400
600
3,000
500
500
3,000
3,000
900
800
500
600
3,000
3,000
3,000
3,000
3,000
3,000
3,000
3,000
3,000
3,000
3,000
3,000
400
700
Stability
OBS PRED
3
3
4
1
1
4
1
2
1
2
3
4
2
2
1
3
1
4
4
4
4
5
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
Reasons Code
1. Observed mixing' depth assumes plume is trapped in elevated layer.
2. Observed wind direction puts plume in different sector.
3. Observed wind speed caused plume rise to be too high.
4. Observed stability class caused alteration of the position of the maximum.
4-13
-------
layer. Consequently, the model with the "observed" meteorology did not
predict any plume impact, only the background lookup concentration.
Hence, the forecast was "right" and the "observed" meteorology was
wrong.
A more frequent difficulty in this example is that the observed
meteorological wind direction places the plume outside the sector of the
target monitor (the model predicts a sector-averaged value for the
22-1/2° sector centered about the observed wind direction). This
suggests that the predicted wind direction, which is forecast from
synoptic considerations, was more accurate for estimating plume tra-
jectories than the observed wind direction at a height of 60 meters on
the meteorological tower. The plume, which exits from the stacks at
152 meters and rises many meters more may be influenced more by the
synoptic weather pattern than the wind direction at 60 meters. There-
fore, the concentration predicted with the forecast wind direction
derived from synoptic analysis may often be more realistic.
Another reason for differences between the predictions with observed
and predicted meteorology is caused by inappropriate observed stability
class. Differential temperature measurements at the meteorological
tower were discovered to overestimate the instability of the atmosphere.
Therefore, the concentration profile given by the model with observed
meteorology had maxima that occurred too close to the power plant and
underprediction occurred at the monitor. The forecasters had suspected
this situation for quite some time and were adjusting for it, as is
evidenced by the column of predicted stability classes.
In order to test the potential errors in the differential tempera-
ture measurements, another source of stability class estimates was
needed. The Springfield, Illinois, Airport is some 31 kilometers north-
west of the Kincaid Station, and hourly observations were used to develop
Turner stability classifications for the hours of Case 4. These classi-
fications along with the other meteorological parameters at Springfield
and Kincaid are presented in Table 4-5.
The Springfield-derived stability classifications support the
iudgment of the forecasters and imply that the "observed" stability
class at Kincaid is for the most part incorrect. The observations of
wind speed and wind direction that were made at Springfield generally
4-14
-------
TABLE 4-5
COMPARISON OF METEOROLOGICAL DATA OBSERVED AT KINCAID AND AT SPRINGFIELD*
CASE 4
Springfield
Wind Direction" Wind Speed (mph) Cloud Stability
Kincaid Springfield Kincaid Springfield Cover Ceiling Kincaid Springfield
Obs. Pred. Obs. (tenths) (100's ft) r"~ ' n—' nu- '
Hour
1
:
5
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Obs.
353
546
176
219
281
180
273
163
164
164
174
316
272
267
221
176
183
204
181
151
148
262
Pred.
340
340
175
230
290
180
290
180
185
185
190
300
290
290
230
190
190
190
190
170
155
340
Obs.
340
10
120
230
270
170
270
170
270
160
180
330
280
250
240
170
170
150
150
150
150
220
11
11
9
18
13
21
12
11
12
11
12
22
7
7
21
20
29
2
3
14
15
7
13
14
12
12
8
17
12
8
9
9
9
18
16
16
15
20
22
7
14
12
8
Obs.
15
16
4
23
16
18
15
12
12
10
12
18
9
12
' 22
21
24
3
5
16
17
9
Obs.1 Pred.
Obs.'
.2
.7
1.0
.7
.1
.1
.1
0
1.0
1.0
1.0
i.o
1.0
1.0
250
250
7
200
30
100
250
250
250
250
250
250
130
250
250
35
35
6
12
Generated from differential temperature measurements.
Turner classification scheme.
•Observations made on the hour.
4-15
-------
agree with the observations at Kincaid. Observations of wind character-
istics at plume height would appear to be needed to verify the forecast
values.
Using more accurate stability class determinations for the observed
meteorology would better balance the R and R .
*•' m w
The information in Table 4-4 supports the hypothesis, which was
derived solely from the error ratio analysis, that the observed meteoro-
logy was a source of difficulty. In fact, it appears that the predicted
ground-level concentrations using forecast meteorology more accurately
describe the observed concentrations than does the "observed" meteorology.
4.3 Background Concentrations
It is interesting to compare the background concentrations developed
with monitored concentrations for July and August and used in the AQFOR
model during the test period with those that were observed in the moni-
toring system around Kincaid. Since monitors are well placed around the
source, it is always possible to select a monitor to represent the
upwind concentrations. A quick resume of the situation is contained in
Table 4-6, which presents a comparison for the Case 4 hours. Until
December 24, there seems to be little real problem with the use of the
lookup table background concentration. Errors in estimating background
were only once greater than 10% of the observed maximum concentration.
Data for December 24 and all of January indicate a much more difficult
problem. Background SO- concentrations appear to be significantly
higher, and in all of the examples the increase over the lookup table
background is more than 10% of the observed maximum concentration. It
seems logical that these higher background concentrations were associ-
ated with the severe cold experienced during the winter of 76-77 and
with the increased fuel use.
Any background concentration different from the lookup value does,
of course, affect the error ratio calculated for the SCS. The last
column of Table 4-6 shows the FL, adjusted by the inclusion of the
measured background concentrations instead of the lookup table values.
Individual values of R_ have changed, and the geometric mean, FL,, has
risen slightly. The geometric standard deviation has not changed. The
4-16
-------
TABLE 4-6
COMPARISON OF BACKGROUND CONCENTRATIONS
LOOKUP TABLE VS. UPWIND MONITOR
Background Concentration (ppm)
our
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Date
10/6
10/6
10/23
11/17
11/29
12/9
12/16
12/18
12/18
12/18
12/18
12/20
12/21
12/21
22/11
12/24
12/24
1/3
1/3
1/13
1/13
1/14
Predicted
Lookup Table
0.007
0.007
0.008
0.011
0.003
0.015
0.003
0.019
0.019
0.019
0.015
0.014
0.003
0.003
0.010
0.013
0.013
0.020
0.021
0.011
0.011
0.003
Observed
0.006
0.009
0.001
0.001
0.001
0.009
0.001
0.029
0.023
0.020
0.014
0.001
0.003
0.002
0.008
0.032
0.021
0.035
0.034
0.029
0.041
0.010
Monitor
8
5
10
8
10
10
10
10
10
10
10
4
10
10
1
7
5
3
8
8
8
3
Maximum
Monitored
0.162
0.136
0.055
0.158
0.079
0.060
0.053
0.067
0.062
0.072
0.062
0.054
0.087
0.125
0.127
0.179
0.077
0.129
0.126
0.068
0.074
0.052
Adjusted
RT
0.58
0.65
1.04
0.37
0.70
1.23
1.77
0.99
0.94
0.78
0.87
1.39
0.82
O.S6
0.50
0.49
0.96
0.64
O.b3
2.28
3.91
1.12
RT 0.89
S 1.72
4-17
-------
effect of using actually measured background would only slightly improve
system accuracy from this point of view. Real-time background data
cannot be used for the forecast period, but would be of greater value
than a lookup table. One possible improvement might be a seasonally-
varying background lookup table.
The analysis of background concentrations revealed that some of the
hours in Case 1 were for times when Kincaid was not operating. There
were 18 hours when measured concentrations were above the 0.05 ppm
threshold (range from 0.052-0.107 ppm) and were, therefore, included in
the sample. The SCS only predicts the background lookup concentration.
The geometric mean of those 18 hours was 0.07, and if they are removed
from Case 1, the geometric mean, R_, is 0.45 and the geometric standard
deviation, S, is 4.07 (compare to 0.40 and 4.49, respectively).
Clearly there were other sources contributing to monitored concen-
trations during those hours. For other hours, those sources also
contribute. Several hours were found when winds from the northwest
coincided with measured concentrations northwest of Kincaid that the SCS
would not have forecast with the background lookup table based on
summer data.
4.4 Three- and Twenty-Four-Hour Average Concentrations
All of the previous comparisons have used 1-hour averages. All
input data as well as measured concentrations were averaged over one
hour, and the model results interpreted to represent 1-hour values even
though the model uses sector-averaged values that would normally only be
applied for longer averaging times. The standards for SO- are, however,
written as 3-hour averages (secondary standard) and 24-hour averages
(primary standard). The data acquisition, storage and model processing
required to do all the cases for the longer averaging times would be a
significantly larger task than that for the 1-hour values. For this
reason, a limited sample again was chosen to test the effect of longer
averaging times. Case 4, again because of its observed versus predicted
comparison at a single monitor, was selected. The results for 1-, 3-
and 24-hour averaging times are presented in Table 4-7. Note that the
number of samples decreases because the 3-hour and the 24-hour periods
4-18
-------
TABLE 4-7
SUMMARY OF RESULTS FOR R? AS A
FUNCTION OF AVERAGING TIME
CASE 4
Geometric _
Averaging Number of Geometric Standard R_T _
Time in Hours Samples Mean RT Deviation(S) S (RT)(S)
1 22 0.86 1.72 0.50 1.48
3 15 0.87 1.89 0.46 1.64
24 14 1.23 1.95 0.63 2.40
4-19
-------
may contain more than one of the one-hour samples. The 3-hour comparisons
are for the highest average 3-hour measured concentration while the
24-hour concentration were evaluated on a midnight to midnight basis.
Two results are discernible: (1) the SCS does not predict 3-hour
average concentrations any more reliably or accurately than 1-hour
concentrations; and (2) the SCS does not predict 24-hour average concen-
trations any more accurately, but predicts 24-hour average concentrations
somewhat more conservatively than 1-hour concentrations.
4.5 Prediction of Meteorological Parameters
The forecaster's primary function is to determine the values of
meteorological forecast parameters entered into the AQFOR model. As was
already indicated for the specific case of the stability class, the
forecaster has some leeway in evaluating whether to use in the predic-
tion a stability class projected from the meteorological tower data or
substitute a stability class based on the synoptic forecast. This
decision making is all part of the experience that the individual
forecaster develops with time. There is also an element of conservative
thinking that forecasters eventually incorporate, whether it is conscious
or not.
Figure 4-2 shows the relationship of 1-hour average values of R_ to
the number of hours from the time of forecast. It shows that as the
time from the forecast increases the R rises, that is, the prediction
becomes more and more conservative. This result is open to a great many
interpretations. Over the period of the forecast, there is a tendency
to expect the occurrence of the persistence of meteorological variables.
When the meteorology is more variable than expected, the R is therefore
higher. A second possible explanation would arise from the contention
that the primary air quality concern at Kincaid, especially with only
one unit running, is excursions above the 24-hour average standard.
Periods of persistent meteorology are feared and perhaps predicted more
often than they actually occur -
More specific and more accurate meteorological data appear to be
needed to provide better inputs for the calculation of measured concen-
trations. A climatology that supplements the information derived from
4-20
-------
0>
£
2
in
"to
+-i
o
h-
oc
0
Time From Forecast (Hours)
Figure 4-2 Relationship of 1-Hour Average Values of RT to Number of
Hours from Time of Forecast
4-21
-------
the synoptic weather situation with specific model input parameters
would be useful in this regard. These parameters will then provide more
accurate and reliable forecasts. Similarly, improvements made in the
model must be made in the context of changes in the forecasting proced-
ures. Improvements, especially with regard to mixing depth, could have
a significantly beneficial effect on SCS performance.
4-22
-------
5. RESULTS OF PROBABILITY ANALYSIS
5.1 Data Preparation and Processing
From the available data developed in the first portion of this
study, it was necessary to derive a data input set for the model PROBL,
which is described in detail in Appendix B. First the data set for
which the PROBL analysis would be performed was defined. Without having
the entire 24-hour times 123-day data set available, any frequency
distributions that are analyzed will be skewed one way or another. It
was decided that the Case 1 data are skewed toward low values of R~ and,
therefore, represent the largest expected adverse error in the SCS. The
selection of Case 1 will overestimate the possibility of exceeding the
standards because it is skewed but will provide a meaningful example of
the application of the reliability analysis system.
PROBL requires as input the frequency distributions of the vari-
ables Q(t), M(t) and R_. The program needs each of these distributions
as step functions with a set of defined classes and the probability of a
value occurring in each class.
The classes for the values of Q(t) differ from the others in that
they are percentages of the rated capacity of the source. In the case
of Kincaid, there are two identical units of the same size. These units
are not in simultaneous operation for most of the data set. (See
Table 1-2). This fact allows for two different ways of analyzing the
data: (1) assume 1,200 Mw is full load for the plant and take the
percentage of time in each class relative to 1,200 Mw and (2) use only
those hours with one unit operational and make the percentages of time
in each class relative to 600 Mw. Table 5-1 shows the distributions of
source emissions, Q(t), for each of the separate operating units at
Kincaid and then for Options (2) and (1) above.
It is clear from this limited data set that when ground-level
concentrations are high, the units that are operational are running just
below full load. This is consistent with the fact that Kincaid is a
base load plant. The last column, which shows all the hours relative to
1,200 Mw, is bimodal with a reasonable fraction of probability in the
1,020 to 1,140 Mw range and an even higher probability that one unit is
operating in the 480 to 600 Mw range.
5-1
-------
TABLE 5-1
FREQUENCY DISTRIBUTIONS OF Q
Percentage of Case 1 Hours in Each Class
ass
1
2
3
4
S
6
7
8
9
10
11
12
13
14
IS
16
17
18
19
20
Percentage of
Mw Capacity
0-5
5-10
10-15
15-20
20-25
25-30
30-35
35-40
40-45
45-50
50-55
55-60
60-65
65-70
70-75
75-80
80-85
85-90
90-95
95-100
Unit 1
600 Mw
14.1
0.3
0.3
0.0
0.3
0.0
0.3
0.9
2.5
0.0
0.6
3.4
2.8
3.7
1.5
2.8
11.0
39.0
15.0
1.5
Unit 2
600 Mw
63.8
0.3
0.6
0.6
0.0
0.3
0.0
1.2
1.5
1.2
0.0
1.5
1.9
0.0
0.0
0.6
2.2
2.5
19.3
2.5
1 Unit
600 Mw
7.8
0.0
0.0
0.0
0.0
0.0
0.4
0.9
3.0
0.9
0.0
3.5
2.6
3.0
1.7
3.9
8.2
43.2
18.2
2.2
2 Units
1,200 Mw
5.6
0.0
0.0
0.9
2.8
2.5
3.7
4.1
38.7
16.5
1.3
2.5
0.6
0.9
0.6
0.9
2.8
5.0
10.3
0.3
-------
The next frequency distribution to be considered is that distribu-
tion for the meteorology; M(t). There are several ways to estimate the
meteorological distribution frequency. The units of M(t) are concentration
divided by emission rate. The two measures of concentration available
to us are the observed and the predicted. Although a complete analysis
of the distribution would include all maximum measured or predicted
concentrations, the use of Case 1 for Q(t) requires the simultaneous use
of only Case 1 hours. The measured concentration data set is more
representative of actual meteorology and has been used.
One other effect needs to be accounted for in the preparation of
the meteorology distribution. If a model were being used to develop the
meteorology distribution, the source emissions could be set to some
constant value. In the Kincaid example case, however, the emissions are
different for each hour. The M(t) distribution based on the one unit
Q(t) distribution has a relatively constant Mw load emission (as shown
in Table 5-1), and it could be assumed that Q equals a constant. Other-
wise, C could be divided by the emissions, Q , for each hour to derive
an emission-weighted distribution. Values of Q have been normalized to
600 Mw or 1,200 Mw as appropriate. Where Q is equal to zero, that hour
has been dropped from the distribution. These distributions are shown
in Table 5-2 for the two-unit example and Table 5-3 for the one-unit
example. The selection of Case 1 means there are no measured concen-
trations less than 0.05 ppm.
The distribution for C as shown in both M(t) tables is artifici-
ally bounded by the threshold value of 0.05 ppm. The distributions do
vary downward when divided by Q but the shifts are not remarkable,
as is to be expected for a base load plant.
The frequency distribution of R is straightforward, as it is
derived from the analysis results in Section 4.2. Values of the R
distribution by class are presented in Table 5-4. The heavy predom-
inance of the lowest classes is expected from the results in Table 4-1.
The final parameter to be set for the running of PROBL is the
threshold value at which a control action will be taken based upon a
predicted concentration. Because this study is evaluating 1-hour
average values, the selection of the 1- to 3-hour threshold actually
used at Kincaid of 0.385 ppm is appropriate.
5-3
-------
TABLE 5-2
FREQUENCY DISTRIBUTION OF M(t)
CASE 1, TWO-UNIT EXAMPLE
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
Class
(ppm)
000-0.
030-0.
060-0.
090-0.
120-0.
150-0.
180-0.
210-0.
240-0.
270-0.
300-0.
330-0.
360-0.
390-0.
420-0.
450-0.
480-0.
510-0.
540-0.
570-0.
Co
029
059
089
119
149
179
209
239
2.69
299
329
359
389
419
449
479
509
539
569
599
% of
0
21
44
15
7
5
1
1
1
0
0
0
0
0
0
0
0
0
0
0
Hours
.0
.2
.6
.6
.8
.2
. 3
.3
. 3
.0
.4
.0
.4
.0
.4
.0
.0
.0
.0
.4
Class
,ppm-sec^
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
gpm
000-0.
025-0.
050-0.
075-0.
100-0.
125-0.
150-0.
175-0.
200-0.
225-0.
250-0.
275-0.
300-0.
325-0.
350-0.
375-0.
400-0.
425-0.
450-0.
475-0.
500-0.
525-0.
550-0.
575-0.
600-0.
625-0.
650-0.
675-0.
700-0.
725-0.
)
024
049
074
099
124
149
174
199
224
249
274
299
324
349
374
399
424
449
474
499
524
549
574
599
624
649
674
699
724
749
% of Hours
1.
0.
27.
25.
10.
12.
5.
7.
1.
1.
1.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
9
5
2
3
-!
7
1
0
9
9
9
9
5
0
5
0
0
5
0
0
0
0
0
5
0
0
0
5
5
0
5-4
-------
TABLE 5-3
FREQUENCY DISTRIBUTION OF M(t)
CASE 1, TWO-UNIT EXAMPLE
c
0
Class
(ppm)
0.000-0.029
0.030-0.059
0.060-0.089
0.090-0.119
0.120-0.149
0.150-0.179
0.180^0.209
0.210-0.239
0.240-0.269
0.270-0.299
0.300-0.329
0.330-0.359
0.360-0.389
0.390-0.419
0.420-0.449
0.450-0.479
0.480-0.509
0.510-0.539
0.540-0.569
0.570-0.599
% of Hours
0.0
24.0
46.5
12.8
8.4
4.4
0.9
0.9
0.9
0.0
0.3
0.0
0.3
0.0
0.3
0.0
0.0
0.0
0.0
0.3
Co^o
Class
..ppm- sec,.
crm
gm
0.00-0.04
0.05-0.09
0.10-0.14
0.15-0.19
0.20-0.24
0.25-0.29
0.30-0.34
0.35-0.39
0.40-0.44
0.45-0.49
0.50-0.54
0.55-0.59
0.60-0.64
0.65-0.69
0.70-0.74
0.75-0.79
0.80-0.84
0.85-0.89
0.90-0.94
0.95-0.99
1.00-1.04
1.05-1.09
1.10-1.14
1.15-1.19
1.20-1.24
1.25-1.29
1.30-1.34
1.35-1.39
1.40-1.44
1.45-1.49
% of Hours
0.0
19.1
26.8
21.5
10.3
8.3
3.6
4.0
1.3
1.3
1.3
0.7
0.3
0.3
0.3
0.0
0.0
0.3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.3
0.3
0,0
5-5
-------
TABLE 5-4
FREQUENCY DISTRIBUTIONS OF R
CASE 1
Class 1 Unit Example 2 Unit Example
R_ % Prob. % Prob.
0.00-0.34 43.7 38.6
0.35-0.69 17.8 13.7
0.70-1.04 16.0 14.0
1.05-1.39 11.3 9.4
1.40-1.74 5.6 7.2
1.75-2.09 5.9 6.9
2.10-2.44 0.0 4.0
2.45-2.79 0.0 2.2
2.80-3.14 0.9 2.5
3.15-3.49 0.0 0.3
3.50-3.84 0.4 0.6
3.85-4.19 0.0 0.3
4.20-4.54 0.0 0.0
4.55-4.89 0.0 0.0
4.90-5.24 0.0 0.0
5.25-5.59 0.0 0.0
5.60-5.94 0.0 0.0
5.95-6.29 0.0 0.0
6.50-6.64 0.0 0.0
6.65-6.99 0.4 0.3
5-6
-------
5.2 PROBL Results
The results of PROBL calculations are provided in Table 5-5 for the
one-unit example case and in Table 5-6 for the two-unit example case.
A summary of the results in terms of percent of the time over the stan-
dard is shown in Table 5-7 along with the expected hours per 123-day
period that they represent, that is percent of time over the standard
multiplied by the 321 hours in Case 1. The results show that using the
frequency distribution of observed concentration over actual emissions
C /Q gives a higher expectation of exceeding the standard than using
just the observed concentrations C . Division by Q does, as indicated
above, stretch the frequency distribution upward and results in more
hours of expected concentrations greater than the standard. The implied
result, that the one-unit example results in a greater number of hours
than the two-unit example, is anomalous. It occurs because the highest
measured ground-level concentrations (on October 2, 1976) occurred with
only one unit operating. In the two-unit example, those concentrations
have a much lower probability of occurrence.
In general, these results point to the low frequency of expected
excess of standards at the Kincaid Station. The example use of PROBL is
for the worst-case distribution of highest observed concentrations and
lowest average error ratio. In other words, Case 1 is the most severe
test that could have been applied. When using C /Q , the expected
frequency of exceeding the 3-hour standard of 0.5 ppm rises to three
separate hours in the 123-day test period. That means that the SCS
would on the average allow three 1-hour periods to exceed 0.5 ppm during
any 123 days of operation. Those three hours would probably need to be
consecutive to actually exceed the standard.
These results are biased by the discontinuous nature of the observed
concentration distribution, especially near the 3-hour standard. More
measurements in the range above 0.30 ppm for instance, would have better
established the distribution and given more confidence that the PROBL
results are representative of the tail of that distribution. This is a
difficulty of applying the analysis to Kincaid where few measurements
near the standard occur. Secondly, it is an argument for the hour-by-
hour type of analysis that evaluates performance only for the worst-case
situations, a specific requirement of standards to be exceeded no more
than once per year.
5-7
-------
TABLE 5-5
DISTRIBUTION OF PROBL RESULTS
CASE 1, ONE-UNIT EXAMPLE
C C /Q
o o ^
Class* Class*
(ppm) % Prob. (ppm) % Prob,
0.000-0.029 10.768 0.000-0.024 9.962
0.030-0.059 26.614 0.025-0.049 7.290
0.060-0.089 36.692 0.050-0.074 27.136
0.090-0.119 15.444 0.075-0.099 24.687
0.120-0.149 4.747 0.100-0.124 10.344
0.150-0.179 1.990 0.125-0.149 6.295
0.180-0.209 1.291 0.150-0.174 6.314
0.210-0.239 0.987 0.175-0.199 1.903
0.240-0.269 0.115 0.200-0.224 1.542
0.270-0.299 0.296 0.225-0.249 1.365
0.300-0.329 0.223 0.250-0.274 0.906
0.330-0.359 0.135 0.275-0.299 0.206
0.360-0.389 0.194 0.300-0.524 0.253
0.590-0.419 0.094 0.325-0.349 0.137
0.420-0.449 0.007 0.350-0.374 0.065
0.450-0.479 0.016 0.375-0.399 0.251
0.480-0.509 0.033 0.400-0.424 0.108
0.510-0.539 0.175 0.425-0.449 0.046
0.540-0.569 0.082 0.450-0.474 0.034
0.570-0.599 0.000 0.475-0.499 0.064
0.500-0.524 0.227
0.525-0.549 0.110
0.550-0.574 0.060
0.575-0.599 0.052
0.600-0.624 0.437
0.625-0.649 0.091
0.650-0.674 0.091
0.675-0.699 0.011
0.700-0.724 0.011
0.725-0.749 0.000
'Maximum ground-level concentration
-------
TABLE 5-6
DISTRIBUTION OF PROBL RESULTS
CASE 1, TWO-UNIT EXAMPLE
c
o
Class*
(ppra)
0.00-0.029
0.03-0.059
0.06-0.089
0.09-0.119
0.12-0.149
0.15-0.179
0.18-0.209
0.21-0.239
0.24-0.269
0.27-0.299
0.03-0.329
0.33-0.359
0.36-0.389
0.39-0.419
0.42-0.449
0.45-0.479
0.48-0.509
0.51-0.539
0.54-0.569
0.57-0.599
% Prob.
30.683
46.925
14.637
4.182
1.711
0.769
0.462
0.196
0.140
0.104
0.030
0.050
0.017
0.035
0.002
0.003
0.008
0.015
0.032
0.000
Class*
(ppm)
0.00-0.04
0.05-0.09
0.10-0.14
0.15-0.19
0.20-0.24
0.25-0.29
0.30-0.34
0.35-0.39
0.40-0.44
0.45-0.49
0.50-0.54
0.55-0.59
0.60-0.64
0.65-0.69
0.70-0.74
0.75-0.79
0.80-0.84
0.85-0.89
0.90-0.94
0.95-0.99
1.00-1.04
1.05-1.09
1.10-1.14
1.15-1.19
1.20-1.24
1.25-1.29
1.30-1.34
1.35-1.59
1.40-1.44
1.45-1.49
C /Q
0 X0
% Prob
24.910
40.938
16.245
8.630
4.088
1.799
1.460
0.481
0.334
0.251
0.173
0.186
0.165
0.134
0.017
0.023
0.038
0.004
0.003
0.004
0.002
0.003
0.011
0.008
0.030
0.031
0.032
0.001
0.000
0.000
''Maximum ground-level concentration
5-9
-------
TABLE 5-7
SUMMARY OF PROBL RESULTS
One-Unit Example
% of Time
Greater Hours Greater
M(t) Basis than 0.5 ppm in 123 Days
Two-Unit Example
% of Time
Greater Hours Greater
than 0.5 ppm in 123 Days
C /Q
o x
0.257
1.091
0.82
3.55
0.055
0.073
0.18
0.24
5-10
-------
LIST OF REFERENCES
EPA 1976a. Technique for Supplementary Control System Reliability
Analysis and Upgrading. QAQPS No. 1.2-057. EPA-450/2-76-015.
U.S. Environmental Protection Agency.
EPA 1976b. Guidelines for Evaluating Supplementary Control Systems.
OAQPS No. 1.2-056. EPA-450/2-76-005. U.S. Environmental
Protection Agency.
ERT 1976. Determination of the Significant Inpact Area of the Kincaid
Power Station. ERT Document P-1902. Environmental Research §
Technology, Inc. Prepared for Commonwealth Edison.
-------
APPENDIX A
DESCRIPTION OF THE AIR QUALITY FORECAST AND
CONTROL DECISION MODELS
-------
APPENDIX A
DESCRIPTION OF THE AIR QUALITY FORECAST AND
CONTROL DECISION MODELS
A. 1 Overview
The Supplementary Control System (SCS) uses a computation model to
predict the air quality at a field of points (receptors) in the vicinity
of the plant and to select a plant operating schedule from a specified
set of emission control actions. The Air Quality Forecast model (AQFOR)
used to generate predictions of S0» is a state-of-the-art diffusion
modeling program capable of handling multiple point source emissions.
The input to AQFOR consists of the elements shown in Figure A-l. Cal-
culations of past, as well as future, S0? values at receptor points, and
actual past SO- observations at sensor locations are input to the
Control Decision (CONDEC) model, which examines all running S0_ averages
to determine the plant operating conditions required to maintain three-
hour and 24-hour SO standards. The computations and information flow
that yields the plant operating recommendations is also shown in Figure
A-l.
The next section discusses the mathematics and physical assumptions used
in AQFOR and the following sections describe the input and functioning
for the AQFOR and CONDEC models.
A.2 AQFOR - Physical-Mathematical Description
A. 2.1 Assumptions
The Air Quality Forecast (AQFOR) model combines calculation routines
from various ERT models to provide a system best suited to the specific
application and with the flexibility required for real-time operation in
an emission limitation program. The component models generally include
a multiple-source Gaussian diffusion model, a terrain model, and the ERT
downwash model. Because the Kincaid plant is situated in nearly level
terrain, and because the stacks are sufficiently high to prevent"aero-
dynamic downwash effect by buildings or other structures in the area,
terrain and downwash effects arc not necessary in the model for this
plant.
A-l
-------
I \TIJT
ACTUAL PAST
EMISSIONS
ACTUAL PAST
METEOROLOGY
PAST S09 OBSERVATIONS
AT SENSOR SITES
PAST S07 CONCENTRATIONS
AT RECEPTORS AND
SENSOR LOCATIONS
METEOROLOGICAL
PREDICTIONS
EMISSION'S
PROJECTIONS
AQFOR [
S02 VERIFICATION AT
SENSOR LOCATIONS
(MODEL ERROR)
FUTURE SO? CONCENTRATIONS
AT RECEPTORS
AND SENSORS
CONTROL DECISION
MODEL
(PLANT STRATEGIES
FOR CONTROL)
RECOMMEND PLANT
OPERATING CONDITIONS
TO MAINTAIN SOo
3-HOUR f, 24-HOUR STANDARDS
Figure A-l Input, Calculations, and Information Flow for SCS Plant
Operating Recommendations
-------
The specific model of the Kincaid plant is a steady-state Gaussian plume
model capable of incorporating multiple sources.
The model assumes that, meteorological condition? nrc uniform over the
region and steady conditions apply for time periods of one-hour duration.
This assumption is appropriate for Kincaid for the following reasons:
1) In relatively flat terrain, systematic large-scale spatial vari-
ations in wind speed, direction, and atmospheric stability condi-
tions are generally not expected. Variations which do occur are
highly unpredictable, and when averaged over periods of time of an
hour or more will tend to cancel.
2) The downwind region of maximum ground level impact for the Kincaid
plant is expected to be well within twenty kilometers for nearly
all meteorological conditions and substantially shorter distances
for high wind speed conditions. Thus, travel times for stack
emissions to reach the region of maximum impact will be generally
less than one hour. More likely, travel' times for periods of SCS
curtailment activities will be of the order of 10 to 15 minutes.
Under these circumstances, since hourly-averaged wind data repre-
sents a reasonable lower limit on the time resolution of meteoro-
logical input data, no improvement of accuracy can be obtained by
using other than a steady-state plume model. Time-dependent models
are appropriate only when the travel time to the region of interest
is larger than meaningful time or spatial scales associated with
changes in meteorological conditions, for example, in situations
involving complex terrain.
The use of a steady-state Gaussian model results in substantial savings
of computation time and computer memory requirements. These savings
permit the use of more sophisticated data reduction and analysis and
data presentation procedures.
The models are described in more detail in the following sections.
A-3
-------
A. 2. 2 Plume Model
Calculations performed in the model involve multiple applications of
the Gaussian plume equation, which represents the concentration pattern
downwind from a point source. The general form of the equation for the
coordinate system presented in Figure A-2 is:
CD
where
X = S0_ concentration
(Xjy.z) = the respective upwind, crosswind and vertical
components of a Cartesian coordinate system, such that
the receptor point is located at or vertically above the
origin (expressed in units of length) and the source at
the point (x,y,H) .
H = the effective height of emission and, therefore, the
centerline height of the plume (length)
q = the source strength (mass/time)
a ,a = dispersion coefficients that are measures of cross-
wind and vertical plume spread. These two parameters are
functions of downwind distance and atmospheric stability
(length)
u = average wind speed (length/time)
The source base is at z = 0 in the coordinate system, and the plume
centerline reaches the equilibrium height H at some distance downwind
from the source. The most important assumptions upon which the equation
is based arc the following:
1) The wind speed and direction in the vicinity of the point
source arc constant throughout the period of interest. The
wind speed, however, is specified as an increasing function of
height.
-------
(x,-y,o)
Plume Axis
(Downwind)
^Receptor
x (Upwind)
Figure A-2 Coordinate System Showing Gaussian Distributions
in the Horizontal and Vertical
A-5
-------
2) When the effluent enters the atmosphere, the plume rises until it
reaches an equilibrium altitude; the plume ccntcrlinc height
remains constant at all downwind distances.
3) At any downwind distance, the maximum concentration occurs at the
plume centerline. The distribution of concentration values off the
centerline is given by the product of two Gaussian, or bell-shaped,
curves.
4) The concentration profiles described by the Gaussian form are not
instantaneous plume profiles. Instead they represent concentra-
tions averaged over one hour.
5) None of the effluent is lost from the plume. Therefore, when the
plume intersects the ground surface, it is assumed that all material
is reflected back above the ground.
6) The effluent rate is constant, and the meteorological parameters
determining plume geometry are constant.
The actual computation of concentrations from heat and SO- emission
rates has two steps:
1) Computations of the effective release heaght (or plume rise)
H from the heat rate P and the meteorology.
2) Computation of the ground-level concentrations given H and
the SO- emission rate Q.
Tiie plume rise is calculated using Briggs' transitional plume rise
equations (Plumcrise by Gary Briggs, AEC Critical Reviews, 1971):
H = SlfT H- AH
where SI IT = stack height (meters)
and where All is calculated according to the following equations:
A-6
-------
1.6 F1/3 (min(x, 3.5x))2/3/u
AH = for stabilities 1, 2, 3, and -I
. , cl/3 2/3,
1.6 F x /u
for stability 5 when u > 1.37 m/s
AH = and x < 2.4 u/S1/2
2.9 CF/(S.u))1/3
AH = for stability 5 when u >_ 1.37 m/s .
1/2 '
and x >_ 2.4 u/S '
5.0 F1/4/ S2/8
AH = for stability 5 when u < 1.37 m/s
where
4 3
F = buoyancy flux of stack emissions (m /s )
= 8.8432.10"6 • P,
P = Heat rate (Watts), .
x = down wind distance (m)
x = down wind distance at which atmospheric turbulence dominates
entrainment in plume rise (m)
= min (14.F5/8, 34.49.F2/5)
u = stack top wind speed (m/s)
ppc
= u (SHT/ZWIND)
u = reference wind speed (m/s)
ZWIND = height at which reference wind speed measured (m),
EPS = stability dependent wind profile parameter,
S = square of the Brunt-VaisJIlS frequency,
= VPTG.g/TA
VPTG = vertical potential temperature gradient ( K/m)
g = acceleration due to gravity (m/s )
=9.8 m/s2
TA = ambient temperature ( K).
A-7
-------
Once plume rise H is calculated, the ground-level concentrations are
calculated in the following way:
XTOT X + XBACK
where
X = computed concentration at the receptor due to the stack
and the meteorology,
and
•
Xm/-f = contribution of background sources (as a function of
BALK
only the meteorology and not the receptor location).
If the plume rise H is greater than DMX + 50.0 meters, where DMX is the
mixing lid, then the plume is considered to have punched through the
region where effective mixing takes place so x = 0.
If the plume rise H is less than DMX + 50.0 it is set to DMX if it exceeds
DMX. Then x is computed as the sums of two terms
X = Q. [(l-f).G H. f.D]/u
where
f = fraction of the plume that is entrained by the building wake,
G = Gaussian dispersion of effluent outside wake,
and D = non-Gaussian dispersion of effluent inside building wake.
The fraction f is set to 0 if building downwash is not to be considered
by the plant. Otherwise the fraction f is computed in terms of an
interaction parameter I,
c _
= exp (4.max (0, 1-1))
wnere
I = SI1T + 300. I.B/(1.7.HBE)
HBE = effective building height (for the given wind direction
and stack) (m)
-------
LB = buoyancy length (m)
= F/(1.15*u)3
(with F = buoyancy flux, u = stacktop wind speed as above).
The Gaussian dispersion term G is calculated by the formula
G = hdf . vdf
where
hdf = a horizontal dispersion j
vdf = a vertical dispersion.
The vertical dispersion is the multiple reflected Gaussian of Turner's
Workbook (pg. 36):
vdf .
AT
/2ir
. . ,
J = 1
J
where a is a stability-dependent dispersion coefficient
a = AZ • X
Z
R7
CZ,
and where D and H' are the mixing lid and plume heights adjusted for
terrain by the formulas
D
H1
A
T.
TUT
DMX-A
II - A
(1-T.) min (H,THT)
a stability-dependent terrain correction parameter
terrain height (relative to stack base) in meters.
The horizontal dispersion term averages the standard Gaussian over a
sector to account for wind variability:
x*S
rfx*S
erf
if |y| < x*S/.
hdf =
2.x*S
1-erf
x*S
2/2~
if x*S/
0 otherwise
A-9
-------
where
y = crosswind distance (m)
a = a stability-dependent horizontal dispersions coefficient
^ 3Y
= AY.x + CY,
and S = sector width (radians)
The sector width is allowed to vary by forecast period to account for
increasing uncertainty of forecast wind direction.
/
The non-Gaussian dispersion term D is taken to be 0 at receptors that
are not on the downwind side of the source. For receptors downwind,
D is computed by
D = hdf.vdf
where the horizontal dispersion is a 22-1/2 sector average
hdf = - - -
S .39S.X + WIDTH
(where WIDTH is an initial mixing width in meters)
and the vertical dispersion vdf is given by
vdf = ( 1-exp [-.0015 (X/!!BE)3(U/1S.)4]) /IIW
where HW = max (o"z> (!IDI2J + 125.x)1/J)
_ TR7
and a. = 1.25.CAZ.X + CCZ •
A. 2. 3 Receptor Grid
The receptor points at which the AQPOR model predicts concentrations are
carefully chosen to provide a non-biased input for the control decision
model. For the Kincaid plant, a radial receptor grid forming concentric
circles about the plant accomplishes this purpose- Additional receptor
points are placed to coincide with the monitoring sites.
A-10
-------
If a rectangular grid is chosen, receptors will not lie at equal
distances from the power plant for all wind directions. Thus for the
same meteorological and plant conditions, but different wind directions,
a critical concentration may be predicted in one wind sector but not
another. This would bias control actions for certain wind sectors.
With the radial receptor grid, seven receptors along each of 16
radials, plus the monitoring receptors, yields a total of 122 receptor
points. The specific radius of each concentric receptor circle is deter-
mined by the significant impact area of the plant. The distances and
number of receptor circles necessary for proper coverage can be readily
modified as experience in operating the Kincaid SCS system accumulates.
A. 3 AQFOR and CONDEC Functional Program Description
The SCS computer program involves three phases, and there is one module
for each phase:
1) EMFOR (for EMissions FORecast) which, based on observed and projected
loads, computes plant SCL emissions, for each specified plant
operating schedule specified by the emissions control strategy.
2) AQFOR (for Mr Quality FORecast) which, based on observed and
predicted meteorological conditions and on estimated emission;.,
computes SO- concentrations at each of the receptor points on a
radial grid centered at the plant for each specified operating
schedule, and
3) CONDEC (for CONtrol DECision) which examines the SO concentration
sequence, for each receptor and operating schedule, and selects a
plant operating schedule, if possible which maintains various S02
average concentrations including, in particular, the 24-hour and
three-hour averages, below specified thresholds, at each of the
receptors.
A-11
-------
The purpose of the SCS program is to project for 24-hours in the future,
the forecast period, and to select an operating schedule which maintains
air quality. The Control Decision procedure requires an historical
operating schedule for that period of the immediate past which is equal
in length to the forecast period. This hindcast period, together with
the forecast period, forms the basic time sequence examined by the three
phases: EMFOR, AQFOR, and CONDEC .
A. 3.1 The Emissions Forecast
A. 3. 1.1 Components of the Emissions Forecast
EMFOR has, itself, three phases:
1) The translation of projected loads and plant operating schedules
into a set of candidate operating schedules for the forecast period
by means of a control strategy. This strategy describes alternative
operational modes which include possible departures from the pro-
jected (and desired) operations schedule;
2) the calculation of S0_ emissions for each alternative operating
mode for the forecast period; and
3) the calculation of SO- emissions for the hindcas"; period based on
the actual operating schedule for that period, and updated by
observed emissions when these are available.
All three of these phases use detailed data on the plant configuration,
together with current information on capacities and fuels.
The air quality calculations require, for each stack, the emission rates
P = stack gas sensible heat (watts)
and Q = stack SO- emission rate (gm/sec) .
These numbers arc computed from the unit loads based on the inputs.
Unit Specific:
Cl = heat rate constant 1, Watts/ (load unit)
^>
C2 = heat rate constant 2, Watts/ (load unit)""
A-I:
-------
Tl = exit temperature constant 1, Kelvin
T2 = exit temperature constant 2, Kelvin/(load unit)
EFF = unit efficiency, percent
AF = flue gas to fuel ratio.
Fuel Specific:
SPC = fuel sulfur content, percent
HHV = higher value of fuel, jouls/gm
A = fuel-specific AF adjustment
Plant Specific:
TA = ambient temperature, Kelvin.
With these inputs, the program computes for each unit
1. The heat rate, HR, in Watts/(load unit)
MR = Cl - C2 * LOAD
2. The heat input rate, HIR, in Watts
HIR = HR * LOAD/(EFF * 0.01)
3. The exit temperature, TS, in Kelvin
TS = Tl -i- T2 * LOAD
4. The flue gas rate, FGR, in g/sec
FGR = HIR * AF * (1 + A)/HHV.
5. The S0_ emission rate, S0_, in g/sec
S02 = 2. *HIR *(SPC * .01)/HHV.
Summing overall units feeding a stack, the program then computes the
totals for each stack
1. The total heat input rate, SHIR, in Watts
SHIR = SUM(Unit HIR)
2. The total flue gas rate, SFGR,
SFGR = SUM(Unit FGR),
3. The weighted average exit temperature- STS, in Kelvin
STS = SUM(Unit TS * FCR)/SFGR
4. The total 50^ nnj??ionS) Q( in c/scc
Q = SUM (Unit SO.,) . A"13
-------
From these data, the stack gas sensible heat P, in Watts, is computed as
P = 1.00417 * SFGR * (STS-TA).
If Stack Gas Analyser data are available then P and Q are calculated as
P = 9.8339E-3 *TFGR * (T-2S8.89)
and Q = 1.2672E-8 * SO, SHIR/CO,
^ *. /
where
TFGR = flue gas rate, in SCF/sec,
= 0.605956 * SHIR/CO2
T = stack temperature reading (°K)
SO 2 = stack SO- reading (ppm)
and C02 = stack C02 reading (percent).
A. 3.1.2 The Control Strategy and Its Translation Into Alternative
Operating Schedules
The preliminary control strategies developed for the Kincaid SCS program
can be found in Appendix B and consist of a succession of steps, -in
order of increasing severity, that may be taken to rearrange loads and
alter the emissions pattern. Each step is a sequence of possible
changes selected from the permissible operations, e.g.:
TRANSFER a specified load FROM unit to "GRID",
TRANSFER ALL of the load on a specified unit TO "GRID", and
SET a specified unit to operate at a specified load.
Where it makes sense in the above operations, a fictitious unit named
GRID may be specified to represent, the transfer of load to or from an
external source.
The control strategies arc designed to be realistic variations from the
projected schedule and are intended to reduce the adverse impact of
plant emissions on air quality.
-------
To translate a control strategy into a set of alternative operating
schedules, EMFOR requires as input, for each time interval of the
forecast period:
the maximum capacity of each unit,
the projected load on each unit,
the minimum capacity of each unit, and
the intended fuel for each unit.
i
The projected loads and fuels become the initial operating schedule for
the forecast period. The remaining operating schedules are generated by
going through the steps of the control strategy, in the order given, and
modifying the existing schedule to generate the new schedule. Thus step
1 of the control strategy transforms schedule 1 (the projected schedule)
into schedule 2, step 2 transforms schedule 2 into schedule 3; and so on
until the steps are exhausted.
The new schedules obey the following rules:
a) no unit may operate above its maximum capacity, and
b) no unit may operate below its minimum capacity,
unless ALL of its load is transferred. In this last case the load on
the unit is set to zero.
A.3.1.3 EMFOR: Generation of SCL Emissions from Operating Schedules
Calculation of S0? emissions for the hindcast period and the forecast
period differ in only two respects: there is only one schedule for the
hindcast period, the actual schedule; and past emissions is updated
using observed emissions when the data is available.
For each schedule and each time interval, F.MFOR has already determined
the load and fuel of each unit. From the load, unit efficiency and
turbine efficiency, EMFOR calculates that heat needed to support that
load. Again using the unit efficiency, EMFOR calculates the heat
A-15
-------
coming out of the associated stack. Using the needed heat and the heat
content of the fuel being used, the amount of fuel consumed is computed.
From the fuel consumption, and the sulfur content of the fuel, the rate
of SO,, emission from the stack is calculated.
The heat output and SCL emission rate are summed for each stack and
transmitted, to AQFOR for the air quality forecast.
A. 5.2 The Air Quality Forecast (AQFOR)
Corresponding to the two time periods, hindcast and forecast, there are
two phases to A'QFOR:
1) the historical phase, which uses actual observed meteorological
conditions to generate past SO-, concentrations at the specified
receptor locations. These estimates are updated using observed S07
concentrations for those receptors corresponding to monitoring
sites.
2) the forecast phase, which uses a predicted meteorological condition
to specify predicted SO- concentrations at receptor locations.
The calculation of SQ concentrations at the receptor sites is the same
for both periods. For each time interval and each schedule, the source
description calculated by EMFOR is used by AQFOR to estimate the S02
concentrations.
Based on the weather condition (wind speed, wind direction, stability,
and mixing depth) and the source description (heat output, exit velocity,
location, height, diameter) AQFOR uses the Gaussian dispersion model
(Section A.2) to calculate the contribution at each receptor due to the
S00 emissions from the stacks. To these calculated concentrations,
AQFOR adds the background concentrations due to other SO emission
sources in the area.
The concentrations for each receptor arc then transferred to CQNDEC for
the control decision phase.
A-lo
-------
A. 3.3 Control Decision Model (CONDEC)
A. 3.3.1 Control Action Criteria
The interaction of observed conditions, predicted conditions and air
quality standards produces recommended actions designed to result in
compliance with these standards. The model operates in real-time,
making use of two distinct dynamic forms of information.
1) predicted air quality based on observed and forecast meteorology
and plant operating conditions, and observed past and current air
quality.
2) predicted air quality based on currently observed trends in air
quality.
If either form of information indicates an actual, impending or potential
SCL level above those given by a threshold values for different time
periods (Figure A-3) of any applicable standard, the control decision
model recommends an adjustment to the operations schedule.
The criteria for specifying control actions are the following:
1) The action must be effective in keeping SO., concentrations below
threshold values, i.e., the control decision model recommends
measures which will reduce ambient SCL concentrations below thres-
hold levels, thus emissions are reduced as required, including
complete shutdown, if necessary.
2) The order in which control measures are applied must be consistent
with plant operations requirements, safety, and economic consider-
ations. In the latter case, for cutback alternatives, the one
chosen must be the one producing the minimum cost penally to the
plant.
3) The parameters which define the model - i.e., the control strategy -
must be easily modified to accommodate changes in plant operating
requirements.
A-17
-------
60
3hr.
Std.1
'.50
40
O
O
CM
O
.30
24 he
Std.
20
.! 4
10
J /^/r Standard
fir. Standard
12
15
18
21
24
Time (hrs.)
Threshold Values
-------
4) The control measures, while providing a margin of safety, must not
be so conservative as to unnecessarily cut back or shutdown opera-
tions.
5) The application of control measures as a function of time must
occur in a smooth, stable manner, avoiding short-term changes which
are impractical from an engineering point of view.
The Control Decision Model (CONDEC) has been developed with these criteria
in mind. A brief discussion of the theory and algorithms of th& control
decision model is given in the following section.
A.3.3.2 Model Theory
A.3.3.2.1 Algorithm Description
CONDEC makes use of a three-dimensional computation space referred to as
the C-K-T [concentration vs. cutback vs. time) space. AQFOR computes
for each receptor the array of concentrations C (K,T) for time periods T
= 1, 24 and operating modes K = 1, N, where K= 1 consists of the most
desirable total plant configuration, and the ordering K = 2, ..., N
corresponds to successive schedule modifications. These concentrations
shall for this discussion be regarded as instantaneous, that is one hour
is the smallest time increment permitted in the system.
The concentrations may be represented in a three dimensional space,
which we shall call the C-K-T diagram, as shown in Figure A-4. If a
surface is passed through the points in this space, one obtains the
representation of Figure A-5, which shows isopleths of concentration
above the .value referred to as the instantaneous or (one-hour) cutback
concentration. (In the diagram, this value is the three-hour standard
0.5 ppm. A value less than 0.5 ppm can be selected to provide a safety
factor.) The shaded area is thus inaccessible, since it is above some
unacceptable threshold value for this receptor.
A-19
-------
307124
I
ro
o
Most
Desired
Mode ~
o>
X)
0
en
c
"5
i_
cu
Q.
O
2
3
6
7
8
9
10
) <>
To Each Point
There is Assigned
A Concentration C
I 23456
T
8 9 10
(Time)
Figure A-4
C-K-T Diagram for one Receptor Represented as an Array of Discrete Points. Shown
are possible order d operating modes (9 stages of cutbackl and 10 time periods.
-------
Most Desired
Operating Level
tn
C7>
a
_v£
o
a
.a
0
4
8
10
(Time)
Figure A-5 C-K-T Diagram for one Receptor Represented as a Surface. The shaded area
represents all operating modes yielding 3-hour concentrations in excess of 0.5 ppm.
-------
For each receptor, there is a similar C-K-T diagram which may contain
within it an inaccessible region. If all such diagrams are superim-
posed, as shown in Figure A-6, the result becomes the inaccessible
region for the entire plant. This diagram defines the set of operating
modes which is inaccessible for at least one receptor - with respect to
1-hour average concentrations. Any projected plan of operation for the
plant may be represented as a line along the surface of the C-K-T dia-
gram. The plan is therefore viable with respect to the instantaneous
(1-hour averaged) concentrations if and only if this line path does not
enter the plant inaccessible region.
Extension to averages of concentration performed over multiples of the
fundamental 1-hcur period requires the added consideration of the
history of actual concentrations. The running average of period P,
beginning at time T is given for a single receptor by:
A(P,T0) - I
r° TT°
/ Co(T')dTf + / C(K',T')dlr
T ° 0
T < 0
o —
••v* /
A(P,TJ = i J C(K',T')dl' , TQ > 0 (6)
To
where C (T) is the one-hour averaged concentration observed for this
receptor at time T (T _<_ 0) and the integral for T > 0 is a line integral
performed along the projected plant operation path. For each averaging
period P, there is a control decision threshold value A (P) as shown
max
for example in Figure A-3. The requirement for viability of any pro-
jected plan with respect to the averaging period P is thus
for all values of T on the range -P to 24-P. Using Equation (6), this
Q
requirement becomes
A-22
-------
6O7I2O
Most
Desired.
Operating
Level
K)
1/4
Figure A-6
Composite K-T Diagram for a 3-Receptor System. The overall plant inaccessible
region is that which includes any inaccessible region for a single receptor (heavy line)
-------
-P+T
l- f C
P J
(C(K',T')tllf < A (P) -
^ ' max
C (T')dT', T < 0
o ' o —
»r
C(K',T')dl' < A (P)
^ ' ' max
, TQ > 0 (8)
The path integrals defining the projected plan of operation must satisfy
the dual requirements of compensating for past occurrences, while pro-
tecting against future occurrences.
Define C (P,T ) as that constant concentration which, if maintained
1 C J L \J
everywhere along the path would just equal the effective control threshold
as given by Equation (8). Thus
P • A (P) -
max
/
J
T
C (T')dT'.
o
• T
o
CTcst(P'V =
, TQ > 0 (9)
Then, Equation (8) becomes
P+T
* L
max(0,T )
C(K',T') -
dl1 < 0
(10)
Thus, if the values of C._ arc kno\«m, the necessary-and sufficient
condition for viability of a projected plan with respect to ;i j;iven
receptor is that C must be less than C_ , averaged over the path. One
sufficient condition is that C(K',T') < C for all points on the
projected path. This would be unnecessarily restrictive however, since
it would limit operations to those modes for which concentrations are
always less than the control decision threshold for the longest averag-
ing period (e.g., the 2^-hour standard of 0.14 ppm from Figure A-5) .
A-2 4
-------
It is important to note, however, that even it' the above condition is
not applicable everywhere on a projected path it must be true on the
average over the path. Figure A-7 represents a simple example for the
case in which concentrations are constant with T. Application of the
one-hour criterion defines the accessible region for this receptor to
paths below A-A" in Figure A-7. Economic considerations thus make the
path A-A" the best first choice for a projected path, subject to
maintenance of long-term average criteria.
In the example shown, the quantity C~ is assumed to be 0.4 ppm for
the averaging period P. The conditions of liquation (10) make it impos-
sible for the first choice level 0.5 ppm to be maintained for the entire
period; hence a revised path A-A'-B'-B" is indicated. Note that the
path shown in Figure A-7 is one of an infinite set of choices which may
satisfy the condition of Equation (10), subject only to the requirement
that the area between the path and CL . before the cutback A'-B' must
Test
equal that after the cut. From the foregoing discussion it is clear
that, if the concentration at any point along a projected plant-operations
path exceeds the value of C_ for any averaging period P and initial
time T , a cutback will have to be made to satisfy Equation (10).
ILe algorithm for computation thus consists of the following:
1) Compute the C(K,T) array for each receptor (AQFOR);
2) Identify the inaccessible area for each receptor as that for which
the instantaneous (one-hour averaged) concentrations exceed the
one-hour threshold.
3) Identify the overall plant inaccessible area as the area which is
inaccessible for one or more receptors.
4) Define the initial first choice projected path as that which
produces minimum cutback and remains in the plant accessible area.
5) Compute the quantities CT (P,TQ) using Equation (9).
6) For each receptor in sequence, and beginning with the earliest
value of T and moving forward, apply the test of Equation (.10) for
each period P under consideration, modifying the path as required
to meet the criterion.
A-25
-------
t
to
cTest
Figure A-7 Application of Averaging Criterion for Averaging Period P
for a Single Receptor
-------
7) The path which results from the above steps will meet ;ill the
criteria for averaging periods from 1 hour on up to the longest
period considered.
A.3.3.2.2 Cutback Thresholds
The algorithm described above is driven by the control point threshold
curve, which determines for any averaging period, the maximum predicted
average concentration which will be allowed at any receptor before
applying the next cutback step in the given switchmode strategy. Figure
A-8 schematically shows three possible cutback threshold curves, labelled
A, B, and C, which are designed to protect the 3-hour (0.5 ppm) and 24-
hour (0.14 ppm) S0_ standards. The actual curve used in the Kincaid
program is given in Figure A-3. However a discussion of the general
concept and objectives of threshold curves in general is useful for
understanding the SCS more fully.
Each of the three curves of Figure A-8 contain a safety factor in that
they all lie below the standards themselves. The difference in the
curves lies in their degree of conservatism: Curve A is the most
conservative since it cuts back at the lowest value for any averaging
period, while curve C is the least conservative.
The trade-off between economic and air quality considerations is thus
determined by the curve chosen: Curve A will be safer in SCS operation,
but will result in higher plant cost due to more frequent cutback.
Conversely, curve C will provide the least plant cost, but will provide
a higher probability of exceeding standards.
A.3.3.2.3 Optimization of Control Action
An important consideration, as expressed in the fourth criterion of
Section A.3.3.1 is the application of control measures during the time
in which they will be most effective in reducing long term averaged
concentrations, and not at other times. This requires that in antici-
pating the need for control, the cutback of plant emissions at some time
A-;
-------
G
o.
Q.
C
O
O
O)
O
c
o
o
CO
O
CO
O.D ~~~ ;t>L^ ' " •" " —~~ —-— --
3-hr Standard
0.14
Averaging Period, Hour
Figure A-8 Three Possible Control-Point Threshold Curves which Protect Both 3- and 24-Hour
Standards, Ranging from Most Conservative (A) to Least Conservative (C)
-------
in the future should he curried out such that (11 \oi\y. term aver.ir.es are
protected at all receptors; and (2) the minimum total cutback is obtained.
The first of these goals could be accomplished simply by reducing
emissions - either immediately or at a time scheduled in the future - to
a constant level such that all applicable long term averages would be
protected for all receptors, and retaining this level for the remainder
of the forecast period. This approach, although computationally simple,
would result in periods of unnecessary load reduction and economic
penalty.
The alternate approach, as implemented in the CONDEC model, provides for
the maximum total generation by staging the cutback in successive steps,
at all times keeping the operation path in the C-K-T space as close as
possible to the forbidden or "plant inaccessible" region in that space.
A simple example of the difference in the two approaches is shown in
Figure A-9, in which an episode beginning at future time T is indicated
by the shaded inaccessible region. In the simple approach, emissions
are cutback at time T to a constant level for the remainder of the
o
forecast period as indicated by path a'-a". In the optimum approach,
each step in the cutback strategy is instituted for the time period
necessary to avoid crossing into the forbidden region, as indicated by
path b-b". The area between the two paths represents the total plant
generation lost in using the former approach.
A.3.3.3 The Final Plant Operating Recommendations
The primary final result is the actual operating schedule for the fore-
cast period. Other information is available to support and expand on
this schedule. This includes the actual record of each cut made by
CONDIIC, the concentrations forecast by AQFOR, as well as the various
average concentrations examined by CONDEC in its decision process.
A-29
-------
007H3
Most
Desired
Operating
Level
Ol
o
Q.
-------
APPENDIX B
USER'S MANUAL FOR PROBL:
THE RELIABILITY OF SCS METHODS PROGRAM
-------
APPENDIX B
USER'S MANUAL FOR PROBL: THE RELIABILITY OF SCS METHODS PROGRAM
This appendix is a user's manual for the computer program PROBL,
which was developed during the previous EPA Contract 68-02-1342 (1976).
It is a relatively simple program, but to be used effectively it requires
the preparation of considerable input data.
1.1 Description of Program Method
A frequency distribution is a representation of the fraction of the
time a variable quantity assumes each of the possible values in its
range. The frequency distribution of ground-level concentrations
downwind of a source can be used in this program to provide information
about the characteristics of the source emissions.
This subsection describes a model that analyzes the effectiveness of
SCS operations in a probabalistic sense on the basis of the frequency
distribution of contaminent concentrations. Figure 1-1A illustrates two
typical concentration distributions. The first represents the frequency
distribution of concentrations at a single receptor; the wind is often
blowing in a direction other than from source to receptor, and hence
concentrations are most frequently near zero. The second is representa-
tive of a distribution of the highest concentrations at any one of a
network of receptors around a source. In the latter case, maximum
concentrations near zero are less likely.
The value C has been designated on the abscissa of the maximum
concentration graph to indicate the value of some air quality standard.
The sum of the frequencies of occurrence of all concentration categories
greater than C is the fraction of the time the air quality standard is
expected to be exceeded. The value f on the ordinate of each graph has
been designated to indicate the permissible frequency of concentration
values exceeding C . To satisfy an air quality standard, the sum of the
frequencies for values of concentration to the right of C must be less
than f . Thus, from a compliance viewpoint, a more useful distribution
is the cumulative frequency distribution associated with each of the
frequency distributions discussed above. In this case, the sum of the
B-l
-------
frequencies of all values greater than the abscissa value is plotted as
the ordinate. Figure 1-1B illustrates the cumulative frequency distri-
butions associated with the distributions of Figure 1-1A. The sum over
the frequency distribution of occurrence for concentrations greater than
C can now be read directly from the ordinate of the graph.
Since a continuous range of concentration values is possible,
the step function presentation of the cumulative frequency distribution
can be replaced by a smooth function as illustrated in Figure 1-1C.
The goal of any control procedure directed toward compliance with an air
quality standard is to reduce the locus of F at the abscissa value GS
below the dashed line representing F . When it is obvious which frequen-
cy distribution of the three presented in Figure 1-1 is being discussed,
the term "distribution" will be used for convenience.
The cumulative frequency distribution can be used to illustrate the
effects of any control procedure. Figure 1-2A represents a hypothetical
distribution of maximum ground-level concentrations. Since the locus of
F is above the dashed line at C = C , the source is in violation of
standards. Assume the graph of F represents the uncontrolled conditions.
Direct application of a constant emission control, which reduces plant
impact uniformly by 50% (say, changing from 2% to 1% sulfur fuel or
installing 50% efficient removal devices that operate continuously and
do not affect plume rise). would move every value of F from the abscissa
value C to the abscissa value C/2 to yield the graph illustrated in
Figure 1-2B. The graph of F has been reduced, as required, below F to
satisfy the air quality requirements. More generally and for the
representation of any effective continuous emission control strategy, you
could have moved every value of F from C to 3-C where 3 is any value
less than BQ such that F(CS/SO) <_ FS> The resulting value of F*(C) =
F(C/8).
An alternative to a rigid emission control system such as discussed
above is an SCS capable of changing the tail of the graph of F to reduce
F* to values below F for C <_ C . Figure 1-2C represents some emission
reduction 3(C), which reduces emissions by exactly the amount required
to achieve the standard all the time. In practice, no system will be so
reliable. It is more likely that some fraction of the attempts to
eliminate concentrations greater than C will be unsuccessful.
-------
24 6 8 10 12 14 16
(A-2)
Maximum Concentration
2 4 6 8 10 12 14 16
(A) Discrete Frequency Distributions
CB-1)
Single Receptor
(B-2)
Maximum Concentration
24 6 8 10 12 14 16
C
2 46 8 10 12 14 16
Cs
(C-l)
\
\
(B) Discrete Cumulative Frequency Distributions
(C-2)
Single Receptor
\
Maximum Concentration
24 6 8 10 12 14 16
C
2 4 6 8 10 12 14 16
(C) Continuous Cumulative Distributions
Figure 1-1 Representative Frequency Distributions for Ambient Concentrations
from a Point Source. (Graphs A-l, B-l and C-l apply to a single
receptor; Graphs A-2, B-2 and C-2 apply to the maximum concentra-
tions from a network of receptors.)
B-3
-------
aiso
A.
\
Maximum Concentration
Uncontrolled F
8.
2 4 6 8 10 12 14 16
c c'
C.
X
X
1
1
1
\
\
X
I
SL
/-Co
\
\
ippJementary Contra/
ntrol
Uncoi
\
ledF
itroll
"^
^^
*-c
£
9d F
^^
7antr
*
Hl«d
2 4 6 8 10 12 14 16
c c*
2 4 6 8 10 12 14 16
0. *
s
—
\
\
N
, /
X
\
—
Sut
r- Co
Ui
\
V
:
op/en
lentat
ntrolled F
Tcontrollat.
\
\;
•^
^
ry Control
,1"
Controlled
24 6 8 10 12 14 16
Figure 1-2 Representative Cumulative Frequency Distributions for Maximum
Concentrations under Conditions of a) no emission controls,
b) absolutely reliable constant emission controls, c) absolutely
reliable supplementary emission controls, d) realistic
supplementary emission controls.
B-4
-------
Figure 1-2D represents a realistic frequency distribution resulting
from the actual operation of an SCS. The curve of F* is not different
from the curve of F at the low concentration end of the graph, in contrast
to the constant emission reduction case of Figure 1-2B where concentra-
tions must be well below standards before controls are reduced. The
tail of the F* curve of Figure 1-2D is below the dashed line for values
of C > C as required. The values of C > C would be the result of
s s
uncertainty (errors) in the operation of the SCS, but their frequency is
so low that a reliable SCS is still maintained.
The ERT PROBL software package generates the frequency distribution
of maximum ground-level concentrations due to the source under study
with or without emission controls for analysis of the reliability of SCS
methods. In particular,- the program can generate the frequency distri-
bution for a wide variety of possible SCS schemes.
The main assumptions of the analysis scheme are:
• a single source of SO- is responsible for observed concen-
tration levels;
• without an SCS, emissions are independent of meteorological
conditions;
• with an SCS, emissions are controlled according to rules that
depend on predicted meteorological conditions and
• error in prediction (RT) is independent of meteorological
conditions.
Consider the following definitions relevant to understanding the
model:
c(x,t) is the concentration at time t and location x
C(t) max c(x,t); maximum concentration over all x locations at time t
x_ is the downwind location of C(t)
C is the air quality standard or SCS threshold
Q(t) is the emission rate without SCS
B-5
-------
M(t) is the meteorological function relating the maximum concentration
C(t) to source emission rate Q(t); it includes the effects of
stack height, wind conditions, mixing depths or any other
pertinent meteorological inputs
!U is the error ratio of concentration prediction defined as
follows:
With or without an operating SCS, the observed maximum concen-
tration C is related to the actual emission rate Q through
the meteorological function M as follows:
C = Q • M 'at time t
With an operating SCS, the corresponding maximum predicted
concentration is related to the actual emission rate Q and the
meteorological function M (defined above) through the Error
Ratio R as follows:
Cp = Q • M • R at time t
From the above, the error ratio can be defined as
*T = cp/co
The observed maximum concentration under SCS control is given by C = Q • M,
where Q is the SCS controlled emission rate determined from the fore-
cast concentration C .
P
The value of Q depends on the SCS control strategy being used.
Two examples of possible control strategies are:
1) Fuel Switching
Q if Cp <_ Y
SQ if C >
P
(Strategy 1)
3-6
-------
where 3 is a constant (less than one) that depends on the
nature of the fuels. A switch from 2% sulfur fuel to 0.5%
sulfur fuel means S = 0.25. The threshold parameter Y is a
function of the air quality levels attempted to be maintained.
2) Process Curtailment
r
Q if Cp < Y
(Strategy 2)
• Q if C > Y
In general, the threshold Y is set below standards to provide
a margin of safety.
The functions Q, M and R require more careful description. Q(t)
can be a well-defined quantity if emission monitors are used. Alternately
emission rate is related simply to the production rate, or to the load
of the plant under study. If the plant emissions are not monitored,
some engineering estimates of the frequency distribution of Q can often
be made from production or process control information.
The function M(t) can be determined in various ways. For an
operation with an extended historical air quality monitoring record,
M(t) could be estimated from the ratios of measured maximum concen-
trations C (t) and known emission rates Q(t). Where a shorter monitoring
record exists with an extended meteorological data bank, M could be the
+ -- + a m
n n
output of a statistical model; for example, M = a..m.. + a-nu
where m.. , nu, m are meteorological parameters, such as stability or
air mass characteristics, and a.. , a,, a are regression coefficients
determined from the available air quality data. If the distributions of
the m.s are known, the statistical data of the shorter monitoring
period can be combined with the longer period meteorological distribu-
tions, as is frequently the case since meteorological data have been
collected at many locations by the National Weather Service for periods
as long as a century. Finally, where little site monitoring data exist,
outputs from Gaussian diffusion or other air pollution models can be
used in conjunction with the meteorological data to construct M.
B-7
-------
An alternative method is available for circumstances when measured
concentration data are not available. The function M can be approxi-
mated with a predicted ground-level concentration divided by the emission
rate. As is the case with the other concentration distribution, it must
be divided by Q to obtain M. The predicted maximum ground-level concen-
tration can be obtained from any reliable model appropriate to the site.
The subroutine METCLASS requires the predicted M value as a function of
user-specified wind speed, wind direction and stability classes. The
subroutine, METDS then requires a frequency of occurrence of each class
set up in METCLASS. Any available joint frequency distribution can be
used for this purpose once a model evaluation for each class is obtained.
Use of the predicted concentrations to develop M eliminates the need for
measured concentrations to be entered in the CLASS and DENSITY subroutines,
The function R— may be determined from historical real-time moni-
toring and forecasting data. Since the function R_ will depend on the
unique forecasting difficulties for each SCS scheme, initial estimates
of R_ must be evaluated during the design and initial testing of the
SCS. The upgrading of an SCS as time proceeds will involve periodic
reevaluations of this function.
Given the functions Q(t), M(t) and R™ over an appropriate averaging
time period, frequency of occurrence distributions can be readily
derived for the various magnitudes of the observed or determined values
of Q, M and R_,. Thus, the time history data are transformed into a
frequency of occurrence distribution. For purposes of future estima-
tions, the frequency of occurrence distributions become expected proba-
bility density functions.
When the frequency distributions are determined, for Q, M and R_,
as defined above, the analysis scheme will be capable of generating the
following basic information:
1) the number of violations to be expected without and with any
SCS scheme;
2) the percentage of production lost if the SCS scheme is a load
reduction program;
B-8
-------
3) the percentage use of high-and low-sulfur fuel in a fuel
switching SCS program and
4) the dependence of the number of violations, production lost
and/or percentage use of high-and low-sulfur fuel on the
implementation threshold (y), model calibration, meteoro-
logical forecasting skill and/or the difference in sulfur
content of the two switching fuels.
The exact mathematical reasoning leading to the previous conclusions
can be shown. P is defined as the probability density function for the
A
variable X. Then, the probability of the variable X having a value
between a and b is
b
a
PX(C)
Assume that there exist probability density functions for M and Q, and
you wish to generate a frequency distribution for C when no SCS is
operating. If A is any concentration value, e is a variable and Q and M
are independent of each other and random variables; then
PC(C = A) = PQ (Q = e) • PM (M = A/e) +
PQ (Q = 2e) • PM (M = A/2e) + —
+ P (Q = ne) • PM (M = A/ne) + —
or, in the limit as Ae approaches 0
P (C = A) = P (Q = C) - PM (M =
•'o
or
Pc (A) = J PQ(?) - PM (A/C)
B-9
-------
Expressing the operator above by *,
p = P * P
FC iM HQ
This equation states that the probability density function for
maximum ground-level concentrations can be derived from the convolution
of the probability density functions for M and Q. Therefore, the
frequency distribution of ground-level concentrations for an uncontrolled
plant can be deduced from determinations of M and Q.
Once Pr is known, the graphs corresponding to Figure 1-1B can be
Li
displayed, and the probability of violating standards is directly known.
Next, consider case when the SCS is operating. In this case,
C = Q • M, where subscript c denotes the functional value when the SCS
is operating. Q is no longer independent of meteorology since the
operation of the SCS depends on meteorological forecasting.
P will, therefore, also be generally dependent on P and will vary
for different control strategies. For computer solutions to the convolu-
tion integration, the dependence of these quantities on each other can
be readily simulated.
Assuming that the error ratio R_ is independent of M and of Q and
given PR, PM and PQ, it is possible to use the control strategy rules
for determining Q to numerically evaluate Pr under the SCS control.
C L*C
In this case C = M • Q • R. The value of Q is determined in each
p c
case from the predicted value of concentration C and from the strategy
(for example, Strategy 1 or 2). From the resulting distribution of Q ,
the value of P is obtained from the equation
P = P * P
Cc Qc M
Note the parallel nature of this equation and the equation for P .
Vj
Thus, the existing frequency distribution of ground-level concen-
trations for a plant can be determined from archived measurements of Q
and M and from records of air quality forecasting accuracy during
operational use of the SCS to determine R.
P- is determined by assuming the values of Q and M are quantified
so they can assume only a finite number of values. Therefore, P and
? represent probabilities rather than probability densities. The
B-IO
-------
integral is then replaced by a numerical scheme, which is solved on a
digital computer. Similarly, for the generation of PC , the function R
is assumed to be quantified and the probabilities of the quantified
values of PC are determined numerically. The numerical scheme employed
by the ERT computer program to generate the above described frequency
distributions can be modified to allow interdependence of Q and M. This
property of the program is particularly valuable for operations where
changes in effluent SCL emission rates may be associated with large
changes in plume rise.
A single hypothetical example of the convolution technique used in
PROBL may help to demonstrate the program's function. The values pre-
sented here are conjectural and only serve as a sample problem. If Q,
the emission rate, is held constant at 1,300 grams per second, sample
ranges of values of the error ratio R and the meteorological function M
(in 10 sec/m ) are given below:
Rj. M (106 sec/m3)
2.0 2.0
1.5 1.0
1.5 1.0
1.5 0.5
1.0 0.5
1.0 0.2
0.5 0.2
0.5 0.1
0.5 0.1
0.2 0.1
These are the values for 10 samples. Values of M > 1 (concentra-
tion greater than 1,300 Mg/m , e.g., the standard) when multiplied by
the small values of R_ would result in combinations exceeding the standard.
The last four R_ values fall into that category. That presupposes that
for all times when M is 2.0 and R_ is greater than 0.5, the SCS calls a
control action.
To ascertain the percentage of time that control actions would be
called and the severity of the reductions, PROBL is used to obtain the
B-ll
-------
convoluted probability summarized in Table 1-1. The values of predicted
concentration in Table 1-1 are produced when the sets of R_ and M are
multiplied together, and the distribution of values is indicated by the
number of events. When the value of predicted concentration is equal
to 1.0, the standard is maintained and no control requirement is neces-
sary. Thus, for values of predicted concentrations less than 1.0, the
ratio Q/Q represents an increase in emissions that could be allowable
to attain the standard. However, when predicted concentrations are
greater than 1.0, the ratio Q/Q shows the reduction in emissions
needed to reach standards (e.g., predicted concentration = 3.0 or
factor of 3 greater than standard, then emissions must be reduced by
1/3 or 0.33). Thus, for these cases, reduction in production is
required, and the frequency is calculated by multiplying the number of
events for those cases with Q/Q . This table indicates that a total of
14% of the time (number of events for four highest predicted concentra-
tions) some reduction from rated capacity would be required. When
combined with the implied reductions from rated capacity, the actual
percentage of rated capacity that the plant would produce is 93.25%
(86% for cases equal to or less than standard plus 7.25% for the cases
that require a reduction from rated capacity.
If the model or methods were altered so that the R_ values are
doubled, the result would be only one possible combination that would
exceed the standard but there would be a generation penalty in that the
percentage capacity *iould fall to 83.125%.
The original study (EPA 1976a) provides a set of example cases of
the use of PROBL that may help the reader understand the sensitivity
analysis with S> and y that can be performed. These examples are pre-
sented in Appendix C.
1.2 Program Description
The program PROBL is arranged as shown in Figure 1 3. The main
program simply calls subroutines directed by the cards submitted by the
user and interpreted by the subroutine INPUT. There is some initial
data required by the subroutine INPUT, which is entered through a name-
list INPUT. Those required data are the number of increments you will
use to specify the probability of occurrence of emissions (Q), meteoro-
logy 'M) and SC5 error ratio (R). These increments are called classes
3-12
-------
TABLE 1-1
SAMPLE DEMONSTRATION OF PROBL CALCULATIONS
Predicted
entration
4.0
3.0
2.0
1.5
1.0
0.75
0.50
0.40
0.30
0.25
0.20
0.15
0.10
0.05
0.04
0.02
Number of
Events
1
3
4
6
9
6
10
3
6
6
9
9
14
9
-2
3
/Qo Implied to
meet C < 1300
0.25
0.33
0.50
0.67
1.00
1.33
2.00
2.50
3.33
4.0
5.0
6.67
10.0
20.0
25.0
50.0
Percenta
Capaci
0.25
1.00
2.00
4.00
9.00
6.00
10.00
3.00
6.00
6.00
9.00
9.00
14.00
9.00
2.00
3.00
100 93.25%
Q = 1300 grams/second
B-13
-------
804487 or
804437
FREQUENCIES
CONCENTRATION AND
EMISSION PROBABILITIES
DO
I
• C£*i:
-------
in the program and a equivalent number of classes can be entered for
each of the three variables. In addition, you must specify:
1) the threshold value (GAMMA), in ppm or ug/m , above which the
SCS calls for either a switch in fuels or reduction in load;
2) a fuel switching ratio (BETA) that gives the ratio of per-
centage sulfur content in the fuel for a fuel switching SCS
and
3) the last increment (HINORM) for the M distribution to be used.
The INPUT namelist is then followed by cards that specify the sub-
routines to be used. Two subroutines are essential to the program
because they process the remainder of the data required for the evalua-
tion. The subroutines are CLASS and DENSITY. In subroutine CLASS, the
increments are specified for each of the three variables: (1) error
ratios, referred to as EPS, (2) the meteorological probability function,
referred to as CONG since most often it is given as a distribution of
ground-level concentrations and (3) the emissions Q. The subroutine
DENSITY then requires the specification of the probability, percentage
occurance expected, for each of the increments entered in CLASS. , You,
therefore, need to provide the probabilities of each of these functions
and the program merely convolutes them into an expected frequency
distribution of maximum ground-level concentrations, in ppm or ug/m .
If the meteorological function cannot be defined by observed data,
predicted results or concentrations that are associated with the joint
occurrence of wind direction, wind speed and stability can be used. This
function can be directed through the subroutines METCLASS and METDS.
The data input deck must be preceeded by a card PARAMETER, which
initiates the program and the last card must be an ENDJOB, which terminates
the program.
The other subroutines can be called as needed and produce the
following outputs.
• RNQSCS - The subroutine this key word calls generates a table
of the frequency distributions of emissions and concentrations
when no SCS is used. Therefore the emissions are independent
of meteorological conditions.
B-15
-------
• RPROD - The subroutine this key word calls generates a table
of frequency distributions of emissions and concentrations
when the load of the plant is reduced for all predicted
concentrations above the threshold (GAMMA).
• RSWITCH - The subroutine this key word calls generates a table
of frequency distributions of emissions and concentrations
when the fuel type is switched by the ratio on BETA for all
predicted concentrations above the threshold (GAMMA).
There are six ERT standard subroutines called in the program that
perform primarily input and output functions. They are HEADR, INPUT,
TXLOC, ERRX, TABLE and INE. Descriptions of the Job Control Language
(JCL) and each keyword that initializes subroutines in the program are
presented in the following section.
1.2.1 Control Language and Data Deck Setup
Control Language Requirements
The following IBM JCL is required to link-edit and execute the
PROBL program on an IBM System/360 Operating System:
// Jobname (Job identification, accounting information),
// MSGLEVEL=1, CLASS=B, TIME=1
// R EXEC FORTHLG, REGION.GO=150K, TIME.GO=1
// LKED.PROB DD DSN=XXXX.PROBL, DISP=SHR
// LKED.ERT DD DISP=SHR, DSN=YYYY.(Library file)
// LXED.SYSLIN DD*
INCLUDE PROB (MAIN, BLOCK, COMP, INPARM, METD, METCLA)
INCLUDE PROB (CLASS, DENS IT, RSWITC, RPROD, TABLR, RNOSCS)
INCLUDE ERT (HEADR, INE, ERRX, INPUT, TABLE, TXLOC)
ENTRY MAIN
// GO.FT09F001 DD DSNAME=YYYY.LOGOATA, DISP=SHR
// GO.F06F001 DD SYSOUT=A
// GO.FT05F001 DD*
B-16
-------
(card input deck)
/*
where:
Job name = user specified job name
(Job identification, accounting information) = job accounting
information, system dependent
XXXX = volume serial name containing program
YYYY = data set number for identification
(Library file) = File containing subroutines such as HEADR, INE, etc.
(card input deck) = cards containing parameter file and probability
distributions for R™, meteorological and emission functions
This example assumed that the PROBL program has been compiled on
the system.
Data Deck Setup
The data card deck required for input to the program must be set up
as follows:
• parameters and input,
• class descriptions for Q, M and R,
• density functions or, more accurately, probabilities for Q,
M, R and
• initialization- cards for determining concentration and emissions
probabilities produced without SCS, with load reduction, and
fuel switching strategy.
The input to PROBL is directed through the use of keywords, which
initiate program functions. There are currently nine keywords in PROBL.
They are PARAMETERS, CLASS, DENSITY, RNOSCS, RPROD, RSWITCH, METCLASS,
METDS and ENDJOB. Each is discussed separately.
B-17
-------
PARAMETERS
The keyword PARAMETERS is used to set program options. The input
to this keyword is in the following format:
CARD 1 - consists only of the word PARAMETERS punched in columns 1-10.
CARD 2 - consists only of the words 5INPUT punched in columns 2-7.
CARD 3-N - must contain the variables in columns 2-80. These
variables, described in Table 1-2, must be specified by the user
since there are no default values. Each is defined by means of an
equal sign, such as NC=20, for 20 meteorological function classes.
LAST CARD - contains only SEND punched in columns 2-5.
CLASS
The keyword CLASS is used to define the lower class limits for
ranges of values for three probability sets: Q, R (described as EPS),
and concentrations (CONG). The format and meaning of the variables used
in this keyword is presented in Table 1-3 with a general description
described as follows:
CARD 1 - contains the word CLASS punched in columns 1-5.
CARD 2 - contains the letter Q in column 1. This introduces the
cards for the class intervals used for the emissions (first set
of data).
CARDS 3-N - contain the lower class limits for different values of
Q, with, at the most, six values per card. Each value is allowed
ten columns starting in column 11.
CARD N+l - contains the data delimiter, 88888, punched in columns 1-5.
FOLLOWING CARDS - repeat the same format as cards 2 through N+l, only
the information for Q is replaced with values for EPS for the second
set of data and concentrations for the third set. As seen from
Table 1-3, EPS and CONC have replaced the letter Q on CARD 2 when
describing the limits for R and concentrations, respectively.
3-18
-------
TABLE 1-2
LIST OF PARAMETER VARIABLES
Name
NC
NE
NQ
GAMMA
BETA
Type
Integer
Integer
Integer
Real
Real
HINORM
Real
Meaning
Number of the meteorological function
classes (must be less than 500)
Number of error classes (must be less
than 500)
Number of emission classes (must be
less than 500)
Switch threshold (in ppm or ug/m )
Ratio of the percent sulfur content
of the low sulfur content fuel to
the percent sulfur of the high sulfur
content fuel (i.e., the fuels used in
fuel switching 0 <_ 1)
The increment of the last meteorological
function category (in ppm or ug/m )
(Note: Parameters are punched in
columns 2-80 and define values by an
equal sign, "=")
B-19
-------
TABLE 1-3
DESCRIPTION OF CLASS CARDS
Class
Limit
Sets
Card
Groups
Name
Data Cards
Number
of Cards
1
NQ/6
Columns
(Format)
Column 1 (Al)
(A4,6X,6G10.5)
Columns 11-20
21-30
Meaning
Emission classes
Q = Actual Mw Capacity
^ * Total Mw Capacity
First lower class limit
Second lower class limit
38888
EPS
DATA
61-70
1 Columns 1-5 (AS)
1 Columns 1-3 (A3)
NE/6 (A4,6X,6G10.5)
Columns 11-20
21-30
Sixth lower class limit
Data delimiter
Error ratio classes
EPS R_CP
Co
where: C predicted concentration
C - observed concentration
o
First lower limit
Second lower limit
88888
CONG
DATA
61-70
1 Columns 1-5 (AS)
1 Columns 1-4 (A4)
NC/6 (A4,6X,6G10.5)
Columns 11-20
21-30
Sixth lower limit
Data delimiter
Meteorological function classes
Observed Concentrations Co
or values of Co/Q
First lower limit
Second lower limit
9
10
S8888
99999
61-70
Columns 1-3 (AS)
Columns 1-5 (AS)
Sixth lower limit
Data delimiter
Subroutine delimiter
8-20
-------
LAST CARD - contains the subroutine delimiter 99999 in columns 1-5.
DENSITY
The keyword DENSITY calls for the subroutine which describes the
probabilities for each class defined in the CLASS keyword for three
sets of data; Q, EPS, and meteorology (MET). The format and meaning of
the variables used in this keyword are presented in Table 1-4 with a
general description as follows:
CARD 1 - contains the word DENSITY punched in columns 1-6.
CARD 2 - contains the letter Q in column 1. This introduces the
frequencies for the emissions punched on the following cards.
CARDS 3-N - contain the frequencies of emissions appropriate for
the class intervals described in the keyword CLASS. At most,
there are six values allowed per card with each value specified in
increments of ten columns starting in column 11.
CARD N+l - contains the data delimiter, 88888, punched in columns 1-5.
FOLLOWING CARDS - repeat the format as cards 2 through N+l, only
the information for Q is replaced with values for EPS, the second
set of data, and Meteorology, the third set. As seen from Table 1-4,
EPS and MET have replaced the letter Q on CARD 2 when describing
the frequencies for EPS and meteorology, respectively.
LAST CARD - contains the subroutine delimiter, 99999, in columns 1-5.
METCLASS
This keyword requires the entry of data for each meteorological
class to be used if predicted M functions are to be substituted for
measured M functions. The M function can be assigned values from the
results of model predictions derived for 480 weather conditions (6 wind
speed classes by 16 wind direction classes by 5 stability classes).
These meteorological conditions which correspond to a particular M
function class are grouped together to define that class. The M function
class limits are those described in the CLASS subroutine for CONC.
B-21
-------
TABLE 1-4
DESCRIPTION OF DENSITY CARDS
Probability
Sets
Card
Groups
Number of
Cards
1
NQ/6
Name
Q
Data
Columns
(Format)
Column 1 (Al)
(10x,6G10.5)
Columns 11-20
Columns 21-30
Meaning
Emission probabilities
*hr Q for c-ach class
total hours
value for first class
value for second class
Columns 61-70
1 88888 Columns 1-5 (AS)
1 EPS Columns 1-3 (A3)
NE/6 Data (10x,6G10.S)
Columns 11-20
Columns 21-30
value for sixth class
data delimiter
error ratio probabilities
»hr EPS for each class
total hours
value for first class
value for second class
Columns 61-70
1 88888 Columns 1-5 (AS)
1 MET Columns 1-3 (A3)
NC/6 Data (10x,6G10.S)
Columns 11-20
Columns 21-30
value for sixth class
data delimiter
meteorological function
probabilities
» CONC for each class
total hours
value for first class
value for second class
9
10
Columns 61-70
88888 Columns 1-S (AS)
99999 Columns 1-S (AS)
value for sixth class
data delimiter
package delimiter
8-2;
-------
The format and meaning of the variables used in this keyword are
presented in Table 1-5 with a general description as follows:
CARD 1 - contains the word METCLASS in columns 1-8.
CARD 2 - contains the word CLAS in columns 1-4 and the sequence
of the meteorological function class in columns 11-20. (For
example, the first class is 1, second is 2, etc.)
CARDS 3-N - contain the appropriate meteorological categories for
the first M function. There are six groups of meteorological
categories allowed per card with 10 columns for each category
starting in column 11. The general format is as follows:
Columns Parameters
First meteorological category:
11-12 Wind Speed class (1-6)
14-16 Wind direction class (1-16)
18-19 Stability (1-5)
Second meteorological category:
21-22 Wind speed class
24-26 Wind direction class
28-29 Stability
Four additional categories can be inserted, if necessary, following
the same format.
CARD N+l - contains the data delimiter, 88888, in columns 1-5.
Each additional M function class follows the same format from CARD 2
through N+l until the entire M function has been defined.
LAST CARD - has the subroutine delimiter, 99999, in columns 1-5.
B-23
-------
TABLE 1-5
DESCRIPTION OF METCLASS CARDS
Cards
(iroups
Name
Number of
Cards
Columns (Format)
Meaning
CO
I
r-o
MLTCLASS
CLAS
Sequence of meteorological
function classes, starting
with 1
Data Cards
M/6
88888
(Card groups
categories.
Colums 1-8 (A8)
Columns 1-4 (A4)
Columns 11-20 (110)
[A4,6X,6(I2,1X,I3,I2,1X)]
Columns 11-12
Columns 14-16
Columns 18-19
Columns 1-5 (A5)
Meteorological function classes
The meteorological function
class defines the meteorolo-
gical categories (following
cards) which are represented by
the class. The first class is
numbered 1, with each succes-
sive class numbered 2 through
last class limit
Applicable meteorological cate-
gories for first M function
Wind speed class (1-6)
Wind direction class (1-16)
Stability (1-5)
Six groups of meteorological
categories may be specified
for each card.
M represents the number of
cards for which there are
meteorological categories for
first M function
Data delimiter
2-4 are repeated for the successive M function classes and the respective meteorological
The total number of M function classes are those described in the subroutine class.]
N+l
Columns 1-5 (AS)
Subroutine delimiter
-------
METDS
The keyword METDS calls the subroutine that describes the frequency
of the meteorological situations specified by the classes and values in
METCLASS. The format and meaning of the variables are shown in
Table 1-6 with the following general description.
CARD 1 - contains the word METDS in columns 1-5
CARDS 2-N - contain the word METD in columns 1-4 followed by the
meteorological category and frequency. The categories are defined
as wind direction, 1-16, and stability, 1-5, while the order of the
frequencies defines the six wind speed classes. The general format
is:
Columns Parameter
1-4 METD (This is included only on the
first card.)
6-7 Wind direction class (1-16)
8-10 Stability class (1-5)
11-20 First wind speed class frequency
associated with the wind direction and
stability classes
21-30 Second wind speed class frequency
61-70 Sixth wind speed class frequency
This format is repeated for each category. Since there are
16 wind direction classes and 5 stability classes (with six wind
speed classes included for any combination of the two), there are
potentially 80 cards needed as input for this subroutine.
LAST CARD - includes the subroutine delimiter, 99999, punched
in columns 1-5.
B-25
-------
TABLE 1-6
DESCRIPTION OF MKTDS CARDS
Curd
Croups
I
i
Name
MUTDS
Delta Cards
MliTD
Number
of Cards
1
N
_
Column
(Format)
Columns 1-5 (AS)
(A4,1X,I2,I3,6G10.5)
Columns 1-4
DO
I
IV)
ON
Meteorological
Categories
Frequencies
6-7
8-10
11-20
21-30
Meaning
Meteorological frequency subroutine
Meteorological categories and frequencies:
Introduces data cards
Wind direction class (1-16)
Stability class (1-5)
First wind speed class frequency
Second wind speed class frequency
61-70
Sixth wind speed class frequency
This second card group is repeated until
all meteorological categories have been
defined by the associated frequencies.
99999
Columns 1-5 (A5)
Subroutine delimiter
-------
RNOSCS, RPROD, RSWITCH
These keywords initiate the subroutines described earlier. Each
keyword requires only one card with the keyword punched in columns 1-7.
The output produces a listing, by classes, of the probabilities of con-
centrations and emissions for the subroutine specified.
ENDJOB
This keyword causes the program to end. There is only one card
with the word ENDJOB punched in columns 1-6.
1.2.2 Diagnostic Messages
Fatal error messages are printed when an error is detected that
causes the program to stop execution. This is normally due to an error
with some input data. The following is a list of the possible fatal
error messages for the subroutines and the corrective action that should
be taken.
Subroutine
INPARM
DENSITY
CLASS
METCLASS
INPUT
Error
Number
800
100
100
250
10
80
Problem
Not all inputs are present
in the parameters package
More density values were
input than were specified
in CLASS
More class values were
input than were specified
in parameters
Data card is incorrectly
punched with keyword
Keyword not included
Error in input packages
Corrective
Action
Check for missing
value; NC, NQ, NE,
BETA, GAMMA, HINORM
Correct the number
of frequencies input
Check the values for
NC, NQ, NE
Change card that
has keyword in wrong
location
Check for keyword CLAS
Correct for missing
input packages
B-27
-------
1.2.3 PROBL Example
Figure 1-4 shows an example of complete input of PROBL including
the JCL, parameters package, and frequencies for Q, MET, and EPS that
were used in Section 5.0 for the one unit case. In this case, neither
METCLASS nor METDS is used since the M function has been defined using
observed concentrations. In the parameters package, there are 20 classes
of emissions (NQ=20), concentrations (NC=20), and error ratios (NE=20).
Also, the threshold value is equal to 0.38S (GAMMA=0.385) with a fuel
switching ratio of 1.0 (BETA=1.0). A value of 1.0 for BETA means that
there will be no reduction in percent sulfur in the fuel although
concentrations may be above the threshold. The last increment of the
M function is set to 0.03 (HINORM=0.03). The class limits (CLASS) for
Q, MET, and CONG follow the parameters with the respective frequencies
described in DENSITY. The subroutines RNOSCS, RPROD, and RSWITCH are
requested with the output presented in Figures 1-5, 1-6, and 1-7, respec-
tively. The results are concentration and emission probabilities
associated with a class limit for the respective output parameters. The
class limits are those described in the CLASS package.
B-28
-------
* F.XFC
' nn
nn
//IKF_(KSYSITM nn *
FMTPVMATM
EPS
nn
nn
nn *
. wr»«?n.
a.o
OM
RAflSA
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OS
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us
n?
DENSITY
EPS
.17A
,1 M
SBAAA
MET
AAAAA
a
.013
.nna
.1 A?
.ona
r»7s
.05?
*
Figure 1-4 Example of PROBL Input
B-29
-------
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Figure 1-5 RNOSCS Output Results
B-30
-------
I CLASS i CMC. i EITSS. T
I * I PPO**. I PwHR. T
I 1.00 10.107*73 tO.077920 T
T 2. no I0.2MMO TO.000015 T
Io.3fe5fl
-------
« *» «
^ ^ «
I
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CLASS
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1 .00
2.00
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5.00
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7.00
8.00
Q.oo
10.00
11.00
12.no
13.oo
14.00
IS. 00
16.00
17.00
1 A.OO
19.00
20.00
T CHNJC.
T PPHR
T0.107fi73
TO.P661 53
T0.3^f>91P
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TO. 0011SO
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T
T
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T
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Figure 1-7 RSWITCH Output Results
-------
1.3 Listing of Program PROBL
MAIN PROGRAM
Subroutines (Called in Main Program):
HEADR
INPUT
METDS
MET CLASS
DENSITY
CLASS
RNOSCS
RSWITCH
RPROD
Auxiliary Subroutines (Called in the Above Subroutines)
PAGE
ERRX
INE
INPARM
COMP
TXLOC
TABLE
B-33
-------
03/360 FOHTKAN *
DATE 77.111/04.S3.30
DO
000?
ISN. 0005
13" oonu
19*
19K OOOb
I A " 0 () 0 I
OP OH
ooov
I8N 0010
IS» 0011
Ib«. 0012
ISr 001 1
IS" 001U
IS- 001^
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IS- 10J7
IS-. 001 M
I3^ 1019
IS" 00«>1
IS'-
la^ 01^1
IS * o 0 2 u
is-, ooas
M nprinwS . UAht« 1* IN, OPT«00, L IN£CNT«60, 8 [ZE'OOOOK ,
Snu»CE,EBCOIC,uOLIST.^nntCK,LOAO,MAP,NOEniT, IO,NO*HEF
PrtflRAHlLITv ANALYSIS (IF 3CS Mt'THOOA
I)«TA ICOO(/«H/. VEUS/I . I
PUdHAifl JLTTY TECHMimiES OFVtLOPtO BY R.J. HORN AND PKOF. SCHufPPE
4Y H| HOHM
1 /71
KEV9(71/lHFTD'. 'METC", • OEMS' . 'CL*S' , 'HMOS' ,«»Swll,'ftpHCl'/
TITLt(tJ)
CALL HFAn>*(rcnnF.,vfW3, LEVEL)
Wt»!>
CAUPS
10 CALL (MPUTfKFVS, 7, 1C, IFniJ«,TlTLt,K,»800)
fin rn rion,2no, ^on,«oo,Sf>0, 601. 7001, K
ion CALL ntrosnc,
'•n TI) 10
?no CALL iFTCLASSdC,
r,n in n
on C«LL '»?» S»Tv f 1C.
GO fn in
G" Tn
CALL ilMTSCSdC,
fi 0 TO 1 O
600 CHI. «
MI rn
Too CALL HPiimjflr,
lid T'l tO
f MO
-------
SUBROUTINE HFAORf1C.VER.LEV)
C IBM IbO/flS E. RFTFENSTEIN FORTRAN IV
C ENVIRONMENTAL RESEARCH AND TECHNOLOGY. IMC., WALTHAM, MASS.
C
C VERSION R LEVEL 711103
c ROES RUN ACCOUNTING AND GENERATES PAGE HEADING
c ******************************************************************
REAL*fl TITLF(6)
RFAL OAr(3),OTAflf101)
INTEGER TronE.NLOG,I RUN,NTAB,LTAB(100),Kl/IOOO/,
X Kfc/1000000/
COMMON /HEAD/ TITLE,TCODF,VEWS.LEVEL.DAT,IR|)N,NPAGF,NLOG
EQUIVALENCE fNTAR,nTAB(l)),(LTAB(l),nTAB(2))
CALL OATE(HAT)
ICOOF=IC
VFRSrVFR
LEVFL=LEV
NTAB=0
LINE=60
IFdCOOF.LE.O.OW.irODE.GE.lOOO.OP.NLOG.LF.O) GO TO
BEAO(MOK) DTAB
00 10 I=1,NTAH
03 IF(N1.NE.ICOOE) GO TO 10
1 M^sMOO (*i 1, K6)
tn \l?sKi3/K3
IF(N2.NE.IVFRS) GO fO 10
GO TO ?0
10 CONTINUE
I.GE.100) GO TO
IsNITAR
M3=l
ML on
MLOG) OTAP
ENOFTLE flLT.G
?? wRITF.(b,?0??) TITLE.VE»S,LtVFL,IMUN,NT»H
?02? FOHMATC BFGIM ',hA8,' VF. «S I ON • , ft, .2, ' LFVFL ',16.' RUN ',
x • TAHLF COUNTS','
RFTU«N
FORMATC LHGOATA
r,n in ??
ENO
!P»TNT
-------
LEVEL 2|.» ( JllN lit )
09/360 FORTRAN
DATE 7l.nl/09t35.tO
CD
I
OJ
ON
ISN 0002
ISN ooo)
ISN OOOU
ISN 0005
IS- 0006
ISN 0007
ISN 0008
ISM 0009
ISM 00|0
ISN 0011
ISN 0012
ISN 0013
OOta
001S
0016
0018
ISN 0019
ISN 00?0
ISN 002^
ISN 002J
ISN oo2a
ISN 0025
oo?6
COMPILE" OPTIONS • NAME" MAlN,OPTiOO,LINECNT*60,8UE»OOOOK.
SOURCE. EBCO 1C .NDl !9T.NODECK,LOAD,MAP,NOEOIT, ID.NOXNEF
SUBROUTINE METOSUX, IFORM)
INTEGER** iCLAss(6,t6,A)
COMMON /HETD/ ICLA3S
REALM NINES/ • 9»99 '/, BLANK/ • »/,KEVH
H6AL*a NAHE/IHCTO'/
COMHON/nENS/ •»LC(5001,PLO(500),PLMET(500) ,PLEP3(900)
REAL*4 VALllE(6)
I OGICAL
DO SO t«J,500
50 PLMET(I)«0.
10 CONTINUE
MEAOfS.TOOOl KCyH,I3TAB,IOIR,VAL'lE
7000 FORMAT (A«.1X,I2,H,6GI0.5)
IF ( KEVU .ED. NINES) GO TO 1000
275 HI, 6
1C • !ClASS(I,IDIR,iaTAB)
IF ( 1C .60. 0) GO TO 275
PlMETUn • PL"ET(IC) * VALUE(I)
CONTINUE
GO rn 10
JOOO METURN
00
275
-------
LEVEL 21.8 ( JUM 74 )
OS/360 FORTRAN H
DATE TT.111/09,34.11
OPTIONS . NAME* HAIN,OPT«00,LINECNT«60»SIZE«OOOOK,
SOURCE,EBCDIC,NOLIST,NDOECK,LOAO,MAP,NOEOIT,10»»JOXREF
0002 SUBROUTINE METCLASSflC.IFOR'l)
ISN 0003 INTEGERS ICLA3S(6,16,8),IOATA(3,6)
ISN OOOU CHMMnw/MtTD/ ICLAS9
ISN 0005 REALM NIHES/«9999l/,EIGHT3/»a888i/,CLA8/»CLAS»/,KEYW
I8N 0006 REAL*a NAME/'MeTCLASS'/
ISN 0007 LOGICAL IOSM
IS* 0008 I09U • .TRUE.
ISM 0004 00 5 «•!,•>
I8K. 0010 on s jn.ib
ISN 0011 on 9 I»l,6
ISN OOia S ICLA3S(I,J.K) • 0
ISN 0013 10 HEAD(S,7000) KEyW.ICL
I3M OOltt 7000 FORMAT(A«,h)(,I10)
ISN 001% IF(KEvw .EQ.EIGHTS) GO TO 10
0017 IFtKEVw ,EQ.NINES) GO TO 1000
0019 IF ( KEVW ,NE. CLAS) CALL ERRX(10,NAME)
ISN 0021 WRITE (6,mio) ICL
ISN 002? 7010 FORMATf'0',T?1,IM6T CLASS ',I10,5X,'CONTAINS MFT CnNOITIONS I '/)
ISN 0083 100 4EAO(3.70nS) KEy^,IOATA
ISN ooaa 7005 Fn«MAT(Aa,6X.6(T2,lX.I3,lX,I2,U))
ISN 0025 IF ( Kfvw ,EO. EIGHTS 1 GO TO 10
ISN 0027 IF ( KEVW ,FO. NINE3) RETURN
I3C 0029 00 200 I«l,b
ISN 0030 III* IDATAd.I)
ISN 0031 IFdll .EO. 0) GO TH 200
ISM 0033 IOIR« IOATA(2,I)
ISN 0034 ISTABiIOATA(3,I)
ISN 0035 ICLASS(IU,IDIR,ISTAB) .ICL
ISM 0036 200 CONTINUE
ISN 0037 WRITE (6,7015) IOATA
0038 7015 FORHAT(T11,6(I2. I X, 13, 1 X , 12, 6X) )
0039 GO TO 100
ISM 0040 1000 RETURN
0041 END
-------
LEVEL 21.8 ( JIIM TO )
03/360 FORTRAN H
DATE 77. 111/09.Jtt,51
DO
I
00
ISM 0002
ISM 0003
ISN 000«
ISN ooos
ISN 0006
ISN 0007
IBM 0008
18^ 0009
IS*J 3010
I9M 0011
I3N 001?
ISw 0011
ISN 001<1
ISN 0015
ooib
0018
0020
00?1
0031
ISM
0027
I9N 00^0
ISN OOJ1
ISM 0032
ISN OOJJ
ISN 001^
IS" oojb
ISN nnir
ISN OOJ8
ISN oooo
ISN noai
ISN oo«£
ISN 0041
ISN ooua
OPTIONS - NAME' H AIN, OPT»00,L INECNT«60, SIZE«OOOOK ,
SOURCE, EBCDIC , NOLI ST. NOOECK , LOAD. HAP, NOEDIT , ID, HIOXREF
SUBROUTINE DENSlTYde, IPORH)
COMMON/DENS/ PLCOOO) ,PLQ(500) ,PLMET(500) ,*Lf PSCSOQ)
LOGICAL PRINT, I08W
COMMON/PA**/ NN(3) , GAMMA, BETA, HINQHM, PRINT, iosu
PL(500,J)
I/
«E»L*8
HE*L*« FIGMTS/«8««B'/,MlNES/'999'»1/, BLANK/I
DEAL'A Ktvw
HEAL*8 KEV4(3)/iO*,|MfTif 'EPS*/
lDSW».TBUt.
10
7000 FO>1H»T f Att.bK . Attl
iF(K£yi« .fa. EIGHTS) an TO in
I^fKEvw .EO. MIMES) GO TO 1000
CALL T*LOcr FORMAT (lox.bGjo.'j)
701S FOBMAT(Tl I . 6 f G 1 0 . a , 1 0 X ) )
joon
-------
LEVEL 21.8 ( JUN 74 )
03/360 FORTRAN H
DATE 77.111/09.35.18
o-i
to
COMPILER OPTIONS . NAME* MAIN,OPT«00,LINECNT«60,31ZEiOOOOK,
SOURCE,EBCDIC,NOL1ST,NOOECK,LOAD,MAP,NOEDIT,ID,NOXREF
ISN 0002 SUBROUTINE RNOSCS(1C,IFQRM)
ISN 0003 LOGICAL IQ3W.PRJNT
ISN 0004 COMMON/PARM/NC,NE,NQ,GAMMA,BETA,HINORM,PRINT,I03U
I'N 0005 REAL*« LIHITCC300),LIMIT£(500),LIMITO(300},CENTRC(SOO),
1 CENTRE(500),CENTRQ<500)
I8N OOOb COMMON /XCLA8S/ L1«ITC,LlMlTE,LIMITQ,CENTRC,CENTRE,CENTRO
ISN 0007 REAL*4 TA«3(500,3)
ISN 0008
ISM 0009
ISN 0010
ISN 0011
ISN 0012
ISN 0013
ISN Q014
I8N 0015
ISN OOlfc
ISN 0017
ISN 001A
ISN 0020
ISN 00?1
ISN 0022
ISN 0023
ISM 0024
ISM 0025
ISN 0027
ISM 0029
I8K. 0030
ISN 0031
ISN 0032
0033
0034
IS*. 0035
ISN Q03t>
ISN 0037
ISN OOJH
ISN 0039
50
400
500
1000
2000
3000
4000
Od 1000 I-t.NQ
00 1000 J«1,NM
CONC«CENTRO(I)*CENTRC(J)
00 400 K*2,NC
IF ( CONC .LT. LIMITC(K)1
CONTINUE
COMMON/FOHMS/FO.FH
COMMON/HENS/ PLC(500),PtO(500),PLMET(500),PLEP3(500)
NM«NC
00 50 I«t,500
TO
K»K«1
PLC(K) • PLC(K) » PLO(I)*PLHET(J)
CONTINUE
IF ( NQ ,GT. NC)
IF ( NO .LE. NC)
00 2000 I«l. N7
TA8S(I,2)>0.
TAQS(I,3)*0.
TABS(I,n*I
00 1000 !•! ,NO
TARS(I,3)*PLO(D
00 4000 I>1(KC
Ttaa(l,2) • PLC(i)
CALL T»BLE(TAB8,500,3,NZ,3,FH,2,FD,5)
RETURN
END
NZ'NQ
NZ»KC
-------
SIIHKOIITINE PAGE
c *«•••»«»•«*••*•*••••««•••»•••**«*«•«*•*«•«*«*««*•***••»***••**»**•
C PRINTS PAGF HEADER A^O KEFPS TRACK OF LI*E COUNT
C VERSION a.O IEVEL 7S090S
C it*****
INTEGER ICOOE,
WfcAL*M TITLF<6)
REAL OATF(S),VEMS
COMMON /HEAO/ TITLE , ICODF , VERS.l F VFL , lUTE , IKUN, NPAGE , W OG
INTEGER
L INt=a
GO TO JP
C ------------------------- .
ENTWY |.INFS(M,*)
K = 0
I INfsl ThF*N
1F(I-IMF.I 1. LrT.AMO.LrT.GI.fi) UFTIIHN
L INf =ht«
W WHTTE(h,?0?0) ICOOF, IHllN. TITIE, WERS,l EVFl ,PATE,NP»r,F
^ snjn FOBMATC i • , n. ib.ax.fcAA. • VEPSIOH '.Ffc.?,' ( • , it>, • ) • , MX,
O X 3A4,10X. 'PAGF'.M/IX. |?7( '*'))
IFfK.EO.n)
c
ENTRY LSFT^p)
LCTrh
RETURN
C
ENTRY
c
FNO
IEOF
BATCH TFRMJNATEIt: 10/0(1/77 1i:S8:]4
-------
03
I
//ERRX EXEC FORTGC,PAKM.FORT=»LOAD'
//FORT.SYSLIN 00 DSNrERT1610.P9990000.ERTLIBCERRX),OISP=OLO,SPACE=
X/FORT.SVSIN OD *
SUBROUTINE ERHX(N.NAME)
C ******************************************************************
C IBM 360 fc.REIFENSTEIN FORTRAN IV
c TERMINATES EXECUTION DUE TO NUMBERED ERROR(N) IN NAMED ROUTINE
C VERSION 2 LEVEL 711115
c ******************************************************************
INTEGER N
REAL'S NAME
rtRITE(6,6000) N.NAME
6000 FORMATCOEXECUTION TEHM1NATED DUE TO ERROR NO. •,!«,' IN ',A8)
STOP
C ENTRY EH«C ISSUES A NON FATAL ERROR MESSAGE AND RETURNS TO
C A USER SELECTED STATEMENT NUMBER.
6100
****!
ENTRY ERRK(N,NAME.,*)
WRITE(6,6100) N.NAME
FORMATCOERROR NUMBER ',14,
RETURN 1
t*****************
1 IN «,A8/)
END
JPRINT ERTLTABLE
100
C
C
200
SUBROUTINE TXLOC(TT.NT,X,IX,*)
>******************
IMPACT VERSION 1.0 LEVEL
REAL*B TT(1),X
IX = 0
DO 100 Net,NT
IF (X.EQ.TT(N)) 60 TO 200
CONTINUE
RETURN 1
k*************************«
IX=N
RETURN
END
IPRINT ERTLERRX
-------
CD
I
-Pi
KJ
//ERRX EXEC FORTMC,PAKM.FORla'LOAO'
//FOHT.SYSL1N 00 OSN=ERT4blO.P9990000.ERTLIB(INE),01SP=OLO,SPACE=
//FOHT.SYSIN 00 •
SUBROUTINE INEUC,PRINT)
c •»••*«••«**«««•*••«•*•«•«••»•««••«•«««•«•*••*••«*•*•«••««••*««••**
C READS AND PHINT8 COMMENTS CARDS
c MARTIK VERSION 2.3 LEVEL 711115
c ••*»•*A***********************************************************
REAL*e NAME/'INE1/
LOGICAL PHINT
INTEGER IFORM,IF(3)/» • , • 0', M • /,COM(13),BLANK/• '/
10 READ(IC,50IU) IFOWM,COM,JF
5010 FORMAT (MX, A1 ,5X, 12A4, A2, A2)
IF(.NOT.PHINT) GO TO 50
DO 20 1=1,3
IF(IFORM.EO.IFU)) GO TO (30,30,40),!
20 CONTINUE
CALL ERRX(20,NAHE)
30 CALL LINES(I,*32>
32 MKlTE(b,6032) IF(I).COM
b032 FORMAT(A1,T21, t<>Ail,A2)
GO TO SO
40 CALL PAGE
1=2
GO TO 30
SO IFUF.NE. BLANK) GO 10 10
RETURN
END
JEOF
BATCH TERMINATED: 10/03/77 i«i2a:so
t£VEL ?».« f JUKI 7U )
OS/lbO
DATE 77.111/09.35.03
ISM
ISM
OPTIONS - «JAM£. MA IM, QPT»00, U IN£CNT«60, 8IZe»OOOOK ,
Si)li«CE,EBCniC,NOLlST,NODCCK,LOAO,HAP,igpEPlT, ID.NOXREF
SU8»0'iTI>gE
-------
LEVEL 21.6 f JllN 74 ) OS/3bO FORTRAN H DATE 77.111/09,34.25
COMPILER OPTIONS • NAME* M*IN,OPT»00,LINECNT«60,SIZe»OOonK,
SOURCE,EBCDICiNQL1ST,NODECK,LOAD,HAP,NOEOIT,
ISN 0002 SUBROUTINE INPARM(IC,TITLE,JF)
ISN 0003
W ISN 0004 LOGICAL PRW,
4^ ISN 0005 COMMON /PARH/ NC,NE,NO,GAMMA,BETA,HINORM,PR INT,IOSW
<" ISN 0006 NAHELIST/INPIIT/ NC,NE,NO,GAMMA,BETA,HlNORM,PRINT,IOSW
ISN 0007 BETQLOiBETA
ISN 0008 REAO(5.'lNPUT,ENOMOO)
ISN 0009 IH BETA ,NE. BETOLD) IOSW».T«UE.
0011 WRITEtfc,INPUT)
0012 RETURN
0013 BOO CALL ERUX (B00»NiME)
ISN 0014 STOP
ISN 0015
-------
LEVEL
i .S I
I s * o n o t
ISN o o n j
ISN ooou
ISN
ISN
ISN 0007
ISN 00OH
ISN 0004
ISN 0010
ISN 0012
Jh'i 71 ) OS/JbO FOUTRAM H
OPTIONS . NAME* HAIN,aPT«OO.LINECNT«60,SI7E»OOOnK,
CLASSdC,
DATE 77.JJI/09.JJ.aj
ISN 001u
ISN
ISN
ISN 00)7
ISN 0018
ISN 0020
I S •J 01i£
IS^ 0125
IHN
ISM 0026
ISN 0027
ISN 002M
ISN 00?9
ISN OOJP
ISN 003 I
ISN OOJ1
ISN ooss
ISN 00.17
ISN POJ8
IS' OOJ
FO'ltVALF.NCF (CEMTER(l.t).CENTKC(l))
LMGTCAL
CnM«n-J /PANH/ NN(5) ,GAMMA, BET»,HINOHM, 1PHINT, ins J
HEAL* 8 KE»S(I )/«NORM< /.NAMES (Jj/'CONC1, «EP8», IQ' /,N»HE/ I CLASS* /
Mt*L»fl € IRHTS/l«888'/,tJINE3/>9<>9'>'/(HL»SK/< •' /
RfclLM
10
IF (Keyw .E'>. EIGHTS) r.n TO i«
If (KEVU ,fn. MfNES) Gn TO 1000
CALL TKLOC
fin TO 200
100 CALL
INPUT CL«SS H"1T3
200
TOIO FORMAT CO CLASS LIMITS OF ',A«)
TOOS
IF (KEV4 .El. EIGHTS) GO TO )60
IF (KCVu .E). NINES) Go TQ JhO
IF (KEru ,NE. 8t»r.N) r, »tL EHRX (?bO,
-RITF (6.7115) n»T»
DO ISO I»I. f>
I IMIT(WT«, II )»D»T»(M
K,QX«NI)V<»I
IF(-JQ« ,6T. N'l ) Gn TO IbO
CONTIMIE
tin TO 2\fi
CALCULATE CENTFM VA
00 ITS I»|,NIJ
F0« EACH CLASS
II)
( I .E'J. MQ) HILIM.HMIT(NQ,U) »
d.Nt.NR) HILIM. LIrtlT(I»l,II)
J75
IF (KEv.J .Et. NJNES) GO TO 1000
Rn TO ID
1000
-------
LEVEL 21.8 ( JUN 74
03/360
DATE 77,111/0*.33,33
COMPILER OPTIONS • NAME* MAIN,OPT«00,LtNECNT»60,SIZE»OOOOK,
SOURCE,EBCDIC,NOLIST.NQDECK,LOAD,MAP,NOEPIT,ID,NOXREF
SUBROUTINE RPROO(IX,IFORM)
LOGICAL I03M,PRINT
COMMON/PARW/NC,NE,NO,GAMMA,BETA,MINORM,PR INT,IDSW
REAL'S FH(Z,3),FO(3)
COMMON/FORN8/PO.FH
REAL*4 LIMITC(300).LIMITECSOO),LIMITS(900),CENTRC(900),
1 •CENTRE(500),CENTRQ(500)
COMMON /XCLASS/ LIMITC,LIMITE,LIMITO,CENTRC,CENTRE,CENTRQ
CaMNON/TABL3/PM8(500),PBNQ(500),CPMQ(SOO),eP6E(500),CPMQE(500),
1 CPME(IOO)
COMMON/OENS/PLC(900),PLa(500),PLMET(500),PLEPS(500)
REAL*4 XNPC(500),XNPQ(500)
REAL*4 TABS(900,3)
00 10 HI,500
XNPC(I)*0.
XNPO(1)»0.
PEV»0.
00 1000 Hl.NC
00 1000 JM.NO
00 1000 KM.NE
PEV«PLMET(I)*PLQ(J)«PLEPS(K)
QME«CENTRC(I)«CENTRO(J)"CENTRE(K>
IF ( 3ME .58. GAMMA) SO TO 500
Nfl REDUCTION
IO*J
XC»CENTRCCI)*CENTRO(J)
00 200 ICiZ.NC
IF{ XC .LT. LlMlTCtlCU GO TO 250
CONTINUE
IC«NC+1
ICHC.l
XNPC(IC) • XNPC(IC) * PEV
XNPO(IQ) • XNPQ(IQ) + PEV
GO TO 1000
REDUCTION PROM
XQ«GAMMA/(CENTRC(I)'CENTRE(K))
DO TOO IQig.NO
IP( XO .LT. LIMITOdO)) GO TO 750
CONTINUE
IQ«NO*1
UN 0002
UN 0003
UN 0004
UN 0009
UN 0006
UN 0007
UN 0008
UN 0009
UN 0010
UN 0011
UN 0012
UN 0013
UN 0014
UN 0019
ISN 0016
UN 0017
UN oois
ISN 0019.
UN 0020
UN 0021
ISN 0022
ISN 0024
UN 0029
ISN 0026
ISN 0027
UN 0029
ISN 0030
ISN 0031
UN 0032
UN 0033
UN 0034
UN 0039
UN 0036
UN 0037
UN 0039
UN 0040
ISN 0041
UN 0042
UN 0043
UN 0044
UN 0046
UN 0047
UN 0048
UN 0049
ISN 0050
ISh 0051
10
e
c
c
c
200
290
C
c
c
500
700
750
900
990
C
1000
XCi GAMN4/CENTRECO
00 900 IC«»,NC
IFC XC .LT. LIMITC(IC)) GO TO 950
CONTINUE
IC«NC»1
XNPG(IG) • XNPC(IC) » PEV
XNPO(IO) • XNPO(IQ) + PEV
CONTINUE
PAfiE 002
ISN 0052
UN 0093
ISM nn$4
UN 0055
UN 0056
UN 0057
ISN 0059
UN 0061
ISN 0062
UN no63
UN 0065
ISN 0066
UN 0068
UN 0069
UN 0070
UN 0071
UN 0072
2500
2100
3000
c
c
c
nuTPtPT RESULTS I CLASS, XNPC, XNPn
DO 2500 I«l,500
TABsri.n • «.
Tt*S(I,21 • 0.
T»»S(I.3) • 0.
CONTINUE
IFfNQ .ST. NO NHAXlNO
IF(NC .GE. NQ) MM»X«MC
00 3000 I«1,NMA«
TASSd.l) • I
NC3 GO TO 2100
I XNPC(I)
IFf I .ST.
TA8SfI,2)
IFCI .ST. NO) GO TO 3000
TAP.Sd.3) • XNPgtl)
CONTINUE
MSITE
CALL T»BLE(TA8S,500,3,NMAX,3,FH,?,FO,5)
RETURN
FNH
B-45
-------
ueveu 2i.s ( JUN T» i
oa/i*o FORTIUN
O»TE T7.m/o»tjj,j,
CONRILE* riRTIONS . NAME* HAIN, OFTlOO.LIN£CNT«60, SIZE«0000« .
SOURCE, EBCDIC, NOUI3T.NOOECK, LOAD, MAR, NOEOIT, ID, NOXREF
ISN 0002
ISN 0003
ISN 000*
ISN 9003
ISN 0006
ISN 0007
ISN OOOS
ISN 0009
ISN 0010
ISN 0011
ISN 0012
ISN 0013
ISN 001"
ISN 0019
ISN noi6
ISN 0017
ISN 0013
ISN 0019
ISN 0020
ISN 0021
ISN 0022
ISN 002«
UN 0029
ISN 0026
ISN 0027
ISN 0029
ISN 0030
ISN 0031
ISN 0032
ISN 0033
ISN 0034
ISN 0039
ISN 0036
ISN 0037
ISN 0039
ISN 0040
ISN ooai
ISN ooai
ISN uoaj
ISN ooa«
ISN 00«6
ISN ooar
I3N OOaS
ISN float
SUBROUTINE RSNITCNCIC.IFORM)
REAL'S FM(J,3),FOC3>
COMMON /FORMS/FO.FH
CONMON/TA8L3/RN9(300),FiM9(3nO),CFHO(300),CP6Ef300)
1 C'**C (300)
,CPM9E(300)
REAL»« Ll"ITC(900)»LINITE<900),Ll"I70(SOO),C£NTRC(900),
1 CENTRE(300),CENTRO(900)
COMMON /XCLASS/ LIHITC. LIMIT*, LIMIT8.CENTRC, CENTRE, CENTR9
LOSICAL RRINT.IQSM
COMMON /FARM/ NC, NE, NO, 8AWMA, BETA , MINORM, MINT, IH3*
CONMON/OEN8/F\C(300) ,FlO(900) ,Rl."ET<300) ,RLEP3(900)
REAL*A XNRtf (300) , XNRO (900)
REAL** TABs(9oo,3)
00 10 Iil,300
XNFC(I) • ",
XNRQ(t) • 0.
10 CONTINUE
00 1000 !•!, NC
DO 1000 J*1,NQ
00 1000 (•I.Me
e
Ff VtFLHtT(l) «FL3( J) *FLEF3(K)
OME«C£NTRC{ I) *CEMTRO(J) (CENTRE (K)
IF ( QMS ,SE. SA«MA) 90 TO 300
C
C NO JWJTCM
C
IO«J
XC«CENTRO(J)*CENTRC(I)
00 200 IC*2iNC
IF (XC.LT.LIMITCUCM SO TO 250
200 CONTINUE
IC«NC*t
230 IOIC»1
XNRCUC) • XNRC(IC) * REV
KNFQ(IO) • KNRO(la) • FEV
SO TO 1000
C
C SWITCH FR083
c
900 XOF»ETA.C£NTRO(J)
00 700 I9«?,N9
IF( XO ,L7. LI"ITOfI8)) SO TO 730
700 CONTINUE
IO>NO*1
730 IO«tO«l
IC« 9£TA.CeNT»C(I)«CENT»0(J)
00 900 ICF2.NC
IF( XC ,L7. LlMITCtlC)) 60 TO 990
900 CONTINUE
IC»NC«t
990 IC«IC.l
XNPC(IC) • XNFC(IC) * FEV
ISN 0030 XNRIJ(IO) • XNFQ(IQ) * FEV
C«»« ENO OF LOQR
ISN 0031
1000 CONTINUE
PAGE 002
ISN 0032
ISN OA33
ISN 0034
UN 0033
UN 0036
ISN 0037
ISN
Oflbi
o"*«
006!
go»r
0068
UN 0070
I S " ; n T i
J300
2100
JOOO
»E3ULTS
00 2304 t»1>900
H8SC1.1J • I
T4D3CI.25 • 0.
T»»3a.X1 • 0.
CONTINUE
IF (U9 .ST. NO NMAXiNO
IF CMC .St. «0) NWAXlNC
00 3000 I»1,WMA»
IF ( I .ST. WC) SO TO ?100
Tusti.j) • iwFctn
IFC I .ST. N01 SO TO 3(100
. XN»Q
«UITE
T»B|.E(TA»S.300i3|NH»X,3.FM,g,FOf3)
E-,0
B-46
-------
SUBROUTINE INPUT(KEYS,N,1C,IFORM,TITLE,K,*)
t****************************»****f*********i
c IBM 360 E. REIFENSTEIN FORTRAN iv
C VERSION 1 720623
REAL*8 NAME/'INPUT'/
INTEGER KEYS(N),IC,IFORM,K,TITLE(13),JF,KEY(3),
X . . KEYW(5)/'PARA'.'COMM1,"COMP",«ENDJ','99991/,
X BLANK/' V
C********************»****»*****************»*********»*»******»»***
C
10 REAO(5,5010,ENO=800) KEY,1C,IFORM,TITLE,JF
5010 FORMATC3A4,2I3,2X,12A4,2A2)
C
IF (ic) 20,49,22
c
30 IC=-IC
REWIND 1C
C
22 CALL PAGE
CALL LINES(4,«2S)
25 WRITE (6,6025) 1C,TITLE
6025 FORMAT(/T21,'TAPE',12,T31,'LA8EL=', 12A4,A2//)
IFUF.NE.BLANK) CALL INE(1C,.TRUE.)
C
REAO(IC,5010,ENO=800) KEY,K,IFORM,TITLE,JF
GO TO 50
C
49 IC=5
C
50 DO 60 K = l,5
IF(KEY(1).EQ.KEYW(K)) GO TO(100,200,300,400,10),K
60 CONTINUE
C
oo so K=I,N
IF(KEY(1).EO.KEY8(K)) GO TO 90
80 CONTINUE
C
CALL ERRXt60,NAME)
C
90 IFUC.E0.5) CALL PAGE
MRITE(6,6090) KEY,TITLE,1C
6090 FORMAT(/T2,3A4,T21,12A4,A2,T81,'(UNIT I,I2,')1/)
CALL LINES(3,*95)
C
95 RETURN
C
100 CALL INPARMdC,TITLE,JF)
GO TO 10
C
200 CALL INE(IC,.TRUE.)
GO TO 10
C
300 IFUC.EQ.5) CALL PAGE
WRITE(6,6300) TITLE,1C,IFORM
6300 FORMAT(/T21,12A4,*2,T81,'(UNIT ',12,')'//T21,'COMPUTATIONS ',
X 'PERFORMED BY ROUTINE «,I5/)
C
CALL LINES(5,*350)
350 CALL COMP(IC,IFOHM)
GO TO 10
C
800 CALL EKRM(800,NAME,&400)
400 RETURN 1
END
1PRINT ERTLTXLOC
B-47
-------
// MSGLEVEL=1,CLASS=8
/tk EXEC FORTHC,PARM.FORTs'OPTCsa,LOAO'
//FORT.3YSLIN 00 OSN=£RT 46 10.P9990000.ERTLIB (TABLE) rOISPsQLD, SPACES
//FOHT.3Y3IN DO *
SUBROUTINE TA8L£(X,NR,NC,KR,KC,FH,KH,FO,KD)
C IBM 360 E.REIFENSTEIN FORTRAN IV
C ENVIRONMENTAL RESEARCH ANO TECHNOLOGY, INC. ,WALTHAM, MASS
C
C VERSION 23 LEVEL 71075 (SPECIAL CHARACTERS)
C INPUTS--
C XsARRAY TO BE TABULATED (NH.NC)
C NR3MAX NUMBER OF ROWS (ROrt-OIMENSION OF X IN MAIN)
C NC=MAX NUMBER OF COLUMNS (COL-DIMENSION IN MAIN)
C KRsNUMBER OF ROMS TO BE PRINTED
C KCsNUMBER OF COLUMNS TO 8E PRINTED
C FHsARRAY OF 8-flYTE HEADING FORMATS (DIMENSIONED (KC,KH))
C KHsNUMBER OF HUMS OF COLUMN HEADINGS
c FD*ARRAY OF S-BYTE OATA FORMATS(DIMENSIONEO(NC))
C KD=NUM8E» OF ROMS BETWEEN HORIZONTAL LINES
c METHOD—COMPUTES OBJECT-TIME FORMATS FOR COLUMN HEADINGS, VERTICAL
C ANO HORIZONTAL LINES, AND TABULATED DATA.
c •»»•****»««•»*•*»»*•«»•««**•**»•*«***•***«*»*»«»*«***•**»***•*«*•«
REAL«4 X(NR,NC)
REAL*8 FH(NC,KH) ,FO(NC)
REAL*« TABdlJ/'TarAU'f'TlSrAlrS'TaBrAl.'.'Tai.Al,',
X 'T54,A1,','T67,A1,', 'T80,A1,», ' T93 , A 1 , ' , ' T 1 06 , A 1 , ' ,
X ITH9,AJ,','T132,A1,'/.TT
REAL*6 FMT(e3)/' Cf21*' ' , ' IX) • /,GMT (23) / ' ( ' , 31* ' ',MX)'/f
X HMTC23)/' C ,31»' ', (1X) '/,FF/'2X,A8, '/,GG/' • / , HH/ • 3A4 , A 1 , • /
INTEGER VLINE/'I'/,TLINE/' = '/,CROSS/l*l/,H8AR(3)/3*'-— '/,
X TBAR(4)/4»'===='/
IF(KC.GT.IO) KC=10
C BLANK OUT OLD FUKMATS
00 5 1=2,22
FMT(I)sGG
GMT(I)=GG
5 HMT(I)sGG
C COMPUTE- NEW FORMATS
K «(10-KC)/2+l
TT»TAB(K)
HMT(2)sTT
J=2
DO 10 1=1, KC
FMTUJsTT
GMT(J)=TT
FMT(J+1)=FF
GMT(J*l)sFD(I)
HMT(I+2)=HH
KSK»1
10 TTsTAB(K)
20 FMT(J)»TT
GMT(J)=TT
1 = 0
WRITE COLUMN HEADINGS
30 CALL LINES(KH+2,»35)
35 WRITE(6,HMT) TLINE, (T8AR , J=l , KC)
00 ao K=1,KH
40 wRITE(6,FMT) vLlNfc , (FH ( J , K) , VLINE , J = l , KC )
50 *HITE(6,HMT) CROSS, (MB AS , CH033 , J=l ,KC)
CALL LINES(KO+1,A30)
DO bU K=l ,KD
1 = 1*1
*RITE(b,SMT) VLINE,(X(I,J),VLINE,Jsl,KC)
IF(I.GE.KR) GO TO 70
60 CONTINUE
SO TO 50
70 CALL LINE3(K-KO,&75)
75 «»ITE(6,HMT) CROSS, (HBAH, CROSS, J = l ,KC)
RETURN
END
B-48
-------
1.4 Program Flow Chart
1 SUBROUTINE CLBSSl1C.1FORH)
REALM LlHITC(SOO) .LlttlTE(SOO) .LlfllTQlSOO) .CENTRCI500).
CENTRE!500).CENTRQl500)
REALM L1H1T(500.3).CENTER(500.3)
EOU1VALENCE! LIMIT!1.1).LIHITC11 ))
EQUIVALENCE (CENTER! 1.1).CENTRCI1 ))
connoN/xcLASs/LiniT.CENTER
LOGICAL PRINT.IOSM
COnnON /PARK/ NN(3).GArmA.BETA.HlNORM.IPRINT.IOSH
REAL«8 KEYS!1J/'NORH'/.NAHES! 3)/'C8NC'.'EPS*.'O1/.NAME/'CLASS1/
REfiL-8 EIGHTS/'8888'/.NINES/'9999*/.BLANK/' '/
RERL-8 NAHER.KEYH
REALM OATA(6)
REALM LOMLIH
JOSM=.TRUE.
10 '
Rl
IREAOC5.7000I KEYH.NAHER I
7000 ^
1 FORMAT (R4.6X.fl41 |
IF CKEYH .£0. EIGHTS)
I GO TO 10
PG 1 OF
B-49
-------
r
CflLL TXLOCtNRflES.3.KEYM.Il.-»100)
I CO TO 200
100
CflLL ERRXI IQQ.NflflE)
I C INPUT CLflSS LIMITS I
20
MOX=1
NQ=NN(I 1 )
HR1TEI6.7010) KCYH
PG 2 OF 6
3-50
-------
7010
IFQRHRT CQ CLPSS LIMITS OF '.B4i I
210 v
[RERD (5.70051 KEYM.DRTR |
7005 ^
j FQRnRTlR4.6X.6G10.5n
PC 3 OF 6
B-51
-------
ICflLL ERRXlZSO.NflHEM
HR1TE 16.7015) OflTfl
7015
FORMflTtTll.61G1Q.4.1QX))
< 00 350 lsl.6 >
LlHlTlNOX.iljsOWTfllI )
350
t
I
CONTINUE
GO TO 210
>**T
PG 4 OF S
3-32
-------
1C CBLCULflTE CENTER VPLUE FOR ERCH CLflSS |
360 fr
< DO 375 1=1.NO >
I LOHLlHrLlMITl1.11 ) |
rHlLlHsLiniTlNO.nl > H1NORH
CENTER!I.11)= (LOMLlH»MlLini/2. 1
I CONTINUE 1
PC 5 OF 6
B-53
-------
[GO TO 10
C*3
1000
0
RETURN
PG 6 FINflL
5-54
-------
SUBROUTINE HETOSlIC.1FORH)
1NTECER-4 ICLRSSI6.16.8)
connoN /ncTO/ ICLRSS
RERL-4 NINES/'9999V.BLRNK/- V.KEYM
RERL»8 NRHE/'METOV
COHHON/OENS/PLC(500).PLQ( 500).PLNETl500).PLEPSl500)
RERL-4 VRLUE16)
LOGICAL 10SH.PRINT
r
i
i
COnHON/PRRH/ NN(31.BETR.CRNHR.H1 NORM.PR1NT.IOSH
JOSNr.TRUE.
< DO 50 1=1.500 >
_SO i
JPLHET(I) = 0
I
CONTINUE I
IRERD cs.70001 KEYH.IST.JH.VRLUE |
7000 G
IFORHRT (R4.ix.i2.i3.6Gio.5)
IF ( KEYM .EO. NINES)
PC 1 OF
B-55
-------
i
i
i
i
i
i
i
fl2
1
I CO TO 1000
< DO 275 1=1.6 >
I 1C = ICLflSSH .JN.IST)
PUHET(IC) = PLHETUC) * VfllUE(l)
MRITE16.8000) VffLUEd 1.IC.PLHETHC)
FORUWTl ' PROS OF '.G10.4.T31.'IS flOOED TO CLflSS
T61 .'RESULTING IN TOTflL PR08 OF '.CIO.4)
{CONTINUE |
PG 2 OF
B-3b
-------
i GO TO 10
Ol
1000
0
I
RETURN j
END"
B-57
PC 3 FINflL
-------
SU8ROUT1NE RSMITCHIIC.1 FORM)
REflL-8 FH(2.3).FOl3)
COMMON /FORHS/FO.FH
soo ) .PBMQ( soo ) .CPMOI soo ) .CPGEI soo ) .CPMOEI soo
CPME(SOO)
RERl-4 LIMITCI 500).LIHITEl SOO).LIHIT0( 500) .CENTRCl 500).
CENTRE ISOO).CENTROt500)
COMMON /XCLflSS/ L1HITC.UNITE.L1MITO.CENTRC.CENTRE.CENTRO
LOG1CPL PRINT.IOSM
COMMON /PflRM/ NC.NE.NO.GPMMR.BETR.HINORM.PRINT.IOSH
COMMON/OENS/PLCI 500) .PLOl 500) .PLHET ( SOO) .PLEPSI 500)
REflL•4 XNPC1500 J.XNPO(500)
REflL-4 TABS!500.3)
< DO 10 1=1.500 >
XNPC111:0.
XNPOI1) = 0.
CONTINUE I
< 00 1000 Isl.NC > - - -
< DO 1000 Jsl.NO > - - -
6
< 00 1000 K=i.NE > - - -
> 4
> 4
> 4
P£V=PLHETl I )«PLOJJ)-PLEPS(K)
OME=CENTRCt1)»CENTROt J)»CENTRE(K
-_
PG 1 OF
B-53
-------
I GO TO 500
I c MO suTrcH
I XC=CENTRO(J)»CENTRC11)
< DO 200 1C=2.NC >
ICOTO 250
00 6
I CONTINUE |
PG 2 OF 7
B-59
-------
250
XNPCI1C) s XNPCt1C) * PEY
XNPQ(IQ) = XNPO(IO) * PEV
| GO TO 1000
|C SM1TCH PROBS
500
XO=8ETfl«CENTROI J)
< DO 700 10=2.NO >
XC= BETB»C£NTRCt1)-CENTRQ(J)
T
PG 3 OF
B-60
-------
< DO 900 1C=2.NC >
XNPC11C) = XNPC(IC) * PEV
XNP0110) s XNPOIIO) «• PEV
Cmmm END OF LOOP I
1 .1 .1 - - -
Rfl3
^1000 v
1 CONTINUE"]
PRINT RESULTS . CLOSS .XNPC . XNPO |
< DO 2500 1 = 1.500 > - - - >5
T
PG 4 OF
B-61
-------
TABS!1.1)
TP8SU.2)
TflBSl1.3)
I
0
0
4 - - -
< DO 3000 isi.
PG 5 OF 7
62
-------
I TflBSll.2) = XNPC(l) I
2100 i'
1 CO TO 3000
r
I TRBSl1.3) = XNPOtI ) |
5 - - -
3000 i t
_ ,
CONTINUE I
1C HR1TE
PC 6 OF 7
B-63
-------
CALL TBBLElTR6S.500.3.NnfiX.3.FH.2.F0.5)
PG 7 FINRL
-------
SUBROUTINE HETCLRSSI 1C . IFORm
INTEGERS 1CLOSS16.16.8).IORTR(3.6)
connoN/riETO/ i CLASS
REALM NINES/' 9999V .EIGHTS/' 8888V .CLAS/'CLAS V .KEYM
REAL-8 NAME/'HETCLASSV
LOGICAL 10SH
IOSM = .TRUE.
r
i
i
i
r
i
i
i
< DO 5 K= i. 5>
6
< DO 5 J=1.16 >
^
< DO 5 I=lT6>
1 ICLRSSC1.JJU = 0
10 ! >
REOD15.700Q) KEYM.1CL
7000 6
FQRnQT(fl4.6X.110)
IFIKEYH .EO.EIGHTS)
| GO TO 10
PG 1 OF
B-65
-------
ICflLL ERRXCIQ.NflHE) |
[WRITE (6.70101 ICL |
7010
FORMflTl '0' .T21 .'HET CLflSS ' . 110.5X.'CONTRINS HET CONDITIONS : V)
100
REflO(S.700S) KEYH.10PTB
7QQS
FQRMPT(fl4.6X.6l 12.IX.13.IX.12.IX))
PG 2 OF 4
B-66
-------
IF I KEYH .EQ. NINES)
< DO 200 1=1.6 > - - -
\ 1U= IDRTRU.I)
PC 3 OF 4
B-67
-------
IOIR= IOPTRI2.1)
ISTR8=1DRT«(3.I )
ICLRSSt1U.10IR.1STRB) = ICL
3 - - -
P4R5
200
CONTINUE
WRITE (6.7015) IDPTfl
7015
FORMRTlTll.61 12.IX.13.1 X.I 2.6XJ )
I GO TO 100
iop
p
1
RETURN
PG 4 F1NRL
•orf
-------
SUBROUTINE INPRRHI 1C.TITLE.JF )
RERl»8 NRME/'INPflRM1/
LOG1CRL PRINT.IOSM
COMMON /PRRM/ NC.NE.NO.GflMMR.BETfl.HI NORM.PRINT.10SH
NflMEL1ST/INPUT/ NC.NE.NO.GflMNR.BETR.HINORM.PRINT.IOSM
BETOLDsBETR
REROl5.1NPUT.ENO=800)
1F( BETR .NE. BETOLO)
I RETURN
800
I CBLL ERRX(800.NflnE) I
I STOP |
TNO"
PC 1
F1NBL
B-69
-------
BLOCK DATA
REAL'S TITLE16)
REAL"4 OATEI31.VERS
TiTLE.iCODE.VERS.LEVEL.DATE.iRUN.NPAGE.NLOO
DATA TITLE/'ERT PROS'.'ABILITY '.'ANALYSIS'.' OF SCS '.'METHODS'
' •/.NPAGC/O/.NLQG/9/.IRUN/O/
REAL-8 FH(3.2).FO(3)
COHHON /FORMS/ FO.FM
DATA FO/'F8.2.'.2»'F8.6.'/.FH/'CLASS'.'CONC.'.'EHISS.'.
' =' .' PROS.'.' PROS.'/
connoN/TABLS/pnoi soo) .PBMOI soo) .CPHOI soo i .CPGEI soo i .CPHOEC soo).
CPHE1500)
DATA PnO/500«0./.PenO/SOO«0./.CPnO/500-0./.CPO€/500-0./.CPnOE/SOOi
o./
DATA CPHE/SOOiO./
REAL»4 LiniTC(SOO).LiniTE(SOO).LiniTQ(500).CENTRC(SOO).
CENTRE!500).CENTROI500)
connoN /XCLASS/ LIHITC.LIHITE.LIHITO.CENTRC.CENTRE.CENTRO
DATA Llf1ITC/SOO«0./.LlHITE/SOO«0./.Ll«ITO/SOO«0./
DATA C£NTRC/500»0./.CENTRE/SOO«0./.CENTRQ/SOO»0./
c
I LOGICAL PRINT.JOSH |
PG 1 OF
3-70
-------
COntlON/PflRM/ NC.NE.NO.GWinR.BETR.HINORll.PRINT.IOSN
ORTR NC/0/.NE/O/.NQ/O/.GflnnR/O./.BETR/O./.HlNORn/O./.IOSM/.TRUE./
LL
J
COMMON/OENS/PLC i soo) .PLOI sooi .PLMETI soo i .PLEPSI soo i
ORTR PLC/500-0./.PLO/500-0./.PLMET/500»0./.PLEPS/500«0./
PG 2 F1NBL
B-71
-------
PROBflBlLlTY flNflLYSIS OF SCS METHODS |
OflTfl 1COOE/48/.VERS/1.1/.LEVEL/73151 I/
C PR08B81LITY TECHNIQUES DEVELOPED BY R.J. HORN flNO PROF. SCHHEPPE
C PROGRAMED BY RJ HORN
C 15/11/73
INTEGER KEYS17)/'HETO'.'METC'.'DENS'.'CLflS'.'RNOS'.'RSHI'.'RPRO'/
INTEGER TITLEU3)
CflLL HEflORt1COOE.VERS.LEVEL)
1
j C REflD KEYMORD CPROS |
10 ^r
Blfc*
fCffLL lNPUTlKEYS.7.1C.!FORn.TlTLE.K.->800) |
PI
GO TO 1100.200.300.400.500.800.700).K|
100
r
CPLL HETDSIIC.IFORM)
| GO TO 10"
PG 1 OF
-------
200
I CBLL METCLBSSlIC.lFORni |
I GO TO 10
Oi
300 fr
TCRLL DENSITY (1C. I FORHTj
| GO TO 10
R4
400
ICBLL GLOSSnc.iFORM) |
| GO TO 10
500
CBLL RNOSC5(1C.1FQRH) |
' C1
I CO TO 10
600
I CRLL RSH1TCH1IC.lFORni
PG 2 OF
B-73
-------
I CO TO 10
fl7
700
1
CELL RPRODC IC.IFQEfl)
i ZZj
ICQ TO 10
800
I HR1TE16.6800) |
6800
FORMRTI-Q END OF PROGftPtT )
ISTOPI
PC 3 FINBL
3-74
-------
SUBROUTINE DENSITYl1C.IFORH)
connoN/DENS/ PLCIsoo) .PLOIsooi .PLHETC soo) .PLEPSIsoo
LOGICAL PRINT.IOSN
COHMON/PflRH/ NNOl.GAnnR.BETR.HINORH.PRINT.lOSH
RERLM PH500.3)
EQUIVALENCE (PLOI1).PL!1 .1 ))
RERL-8 NAME/1DENSITY'/
RERL-8 EIGHTS/'8888V.NINES/19999V.BLRNK/1 '/
RERL«8 KEYH
REPL-8 KEYSOJ/'O'.'MET1 .'EPS'/
RERL-4 OflTR(6).NRMER
IOSM:.TRUE.
10
I RERO(5.7000) KEYM.MftHER I
FORnPT(B4.6X.R4)
IFIKEYM .EO. EIGHTS)
I GO TO 10
PC 1 OF
B-75
-------
IFIKEYW .£0. NINES)
I
ICRLL TXIOC[KETS.3.KEYM.K.+1001
CO TO 200
100
CflLL ERRXI100.HPHE)
20
PG 2 OF 4
J-76
-------
jNOXrl |
IHRITE 16.7010) KEYH I
7010
|FQRHPT('0'.Til.'PROBABILITIES FOR CLRSSES OF '.R41
250
94
REflD(5.7005) DPTff
MR1TE16.7015)
< DO 300 1=1.6 > - - -
PL(NOX.K)=DRTA( I )
NOX;NOX*1
PC 3 OF
B-77
-------
3 - - - >
I GO TO 250
7005
I FQRHflT (10X.6C10.5)
7015
.61010.4.1 OXH j
fl5
1000
RETURN
PC 4 F1NPL
B-78
-------
I SUBROUTINE COHPl 1C . 1FORH )
| RETURN |
"END"
PC 1 F1NRL
B-79
-------
SUBROUT1NE METOSlIX.I FORM)
INTEGERS ICLRSS16.16.8)
COMMON /METO/ ICLflSS
REflL«4 NINES/'9999 V.SLflNK/' '/.
RERL»8 NftME/'METO1/
COHHON/OENS/ PLCl 500) .PLO( 500 J .PLMEK 5001 .PLEPSl 500 J
REPL>4 VRLUEI6)
LOCICPL 10SU
riOSMs.TRUE. |
< DO 50 1=1.500 >
50
I PLflETU )=Q. I
CONTINUE
REflO(5.700Q) KEYH.lSTBB.lOlR.VflLUE
7000
FORHffT (fl4.1X.I2.13.6G10.S)|
IF ( KEYM .EO. NINES)
PG 1 OF
8-30
-------
R2
I GO TO IQOO"
1
< DO 275 I si.6 >
I 1C = ICLBSSi1.1D1R.1STR6)
I
I PLflETllcrVPLHETUC) + VPLUE(H
275 2
I CONTINUE I
'
GO TO 10
1000
E
I
RETURN |
PG 2 F1NRL
R-81
-------
SUBROUTINE RNOSCSl1 C.I FORM)
LOGICAL IOSH.PRINT
COf1WJN/PARH/NC.NE.NO.Gflnn«.8ETfl.HlNORH.PRINT.IOSH
REALM LIMITCISOOJ.LIHITEISOO) .LIHI T0( 500 1 .CENTRCl SOO ) .
CENTRE! 500).CENTROt500 )
COMMON /XCLASS/ LlMITC.LlHITE.LIHITO.CENTRC.CENTRE.CENTRO
RERL-4 TR8S(500.3)
RERL»8 FHI3.2J.FD13)
connoN/FOtns/Fo.FH
COMMON/OEMS/ PLCI sooi .PLOI soo) .PLHETi sooi .PLEPSI soo)
NflrNC
< DO SO 1=1.500 >
50
= o. j
< DO 1000 1 = 1.NO > - - - 02
V
< DO 1000 Jsl .Nfl > - - - O2
|CONCzCEMTROlI)»CENTRCU)
PG 1 OF
B-82
-------
I GO TO 500
400
0
I
CONTINUE |
6
K=NC*M
500 V
q t
1K=K-1
|PLC(K) = PLCtK) » PLO( 1 )»PLHET( J>
1 .1
PC 2 OF 3
B-83
-------
R3
1
NZ=NC
EP"
i < DO 2000 1 = 1.NZ >
' y
I TflBSl1.2)=0.
I TRBSC1.3laQ.
1 2000 v
\ TRBS11.1)=1 |
r < DO 30001 1 = 1. MQ >
i
' - 3000
| TQBS11.3)=PLQ11) j
< DO 40001 1 = 1.NC >
- - 4000
j TflBSt 1 .2) = PLCfTTl
ICflLL TflBLEC TB6S.500.3.NZ.3.FH.2.FD.5)
| RETURN |
"END"
PG 3
FINflL
5-84
-------
SUBROUTINE RPRODIIX.IFORM )
LOGICAL 10SW.PRINT
COHnON/P«RH/NC.NE.NQ.GW1Mfl.BETR.HINORrt.PRINT.IOSH
RERL-8 FH(2.3).FO(3)
comiON/FORMS/FO.FH
RERL»4 L1H1TCI 500).L1HITEI 500l.LiniTOl 500J.CENTRCI5001.
CENTRE I 500).CENTROI500)
I COMMON XXCLBSS/ L1HITC.LlHlTE.L1H1TQ.CENTRC.CENTRE.CENTRQ |
6
connoN/TRBLS/pnoi soo) .PBWOC soo) .CPHOI soo i .CPCEI soo i .CPMOEI soo i.
CPflElSOO)
COnnON/DENS/PLCl 5001.PLOI500).PLMET1SOO).PLEPSI500)
REPL»4 XNPCISOO).XNPO(SOO)
RERL-4 TRBSI500.3)
< DO 10 1=1.500 >
~"^
XNPC(1)=Q.
< DO 1000 1=1.NC > - - - 0 4
V
< DO 1000 J=1.NO > - - - > 4
_ 6
< DO 1000 Krl.NE > - - - >4
PEV=PLHET(1)«PLO(JI»PLEPS(K)
OnE=CENTRClIJ-CENTROlJ1-CENTRElK)
PG 1 OF
B-85
-------
I GO TO 500
^••^••^^^•M^M^MM
I C NO REDUCTION |
XCsCENTRCt I 1"C£NTRO(J1
< DO 200 1C=2.NC >
I GO TO 250
00 6
I CONTINUE!
PG 2 OF 7
-------
Jni
250
XNPC11C) = XNPCC1C) * PEV
XNP0110) = XNPOC10) » PEV
I GO TO
REDUCTION PROS
500 fr
I X0=OffHHR/1CENTRC11 )»CENTRE(K ) 1
< 00 700 10=2.MO >
i
|GO TC
. .....-...--. 7QQ J
T
r
| CONTINUE |
£
| IO=NO*1 |
750 i
t
1 10=10-1 |
^
| XC= Gfin«R/CENTRElK) |
PC 3 OF
B-87
-------
< DO 900 IC=2.NC >
XNPCl1C) = XNPCl1C) » PEY
XNP0110) = XNPOl10) * PEV
1 .1 .1
fl3
1000
CONTINUE
OUTPUT RESULTS : CLflSS.XNPC.XNPO
< 00 2500 1 = 1 .500 > - - - OS
PG 4 OF
B-i
-------
TABS!1.1)
TABS!I.2)
TABS! 1.3)
0
0
0
4 - - -
| MftAXsNC I
< 00 3000 Isl.NflAX > - - -
I TBBSd.l ) = 1
T
PG 5 OF 7
B-89
-------
I
I GO TO 3000
ITflBSC1.3l = XNPQI1
5 - - - t>
3000 tt
CONTINUE
I C
PC 6 OF 7
B-90
-------
ICflLL TOBLElTflBS.500.3.NHflX.3.FH.2.FD.5)
IRETURN |
TNO"
PC 7 FlNflL
B-91
-------
APPENDIX C
SAMPLE CASES OF PROBL
-------
APPENDIX C
SAMPLE CASES OF PROBL
The following examples have been taken from the original study (EPA
1976a) and isolate the effect of changes in each of the pertinent
variables which influence reliability. These variables include: R,
the geometric mean of the error ratio R; a, the standard deviation of
the error ratio distribution; y= the threshold value of the predicted
maximum concentration above which some operational process adjustment is
made; and 3, the ratio of the sulfur content of the low sulfur fuel to
the sulfur content of the high sulfur fuel used in a fuel switch SCS.
Example 1 - What is the effect on SCS reliability of changing the value
of a for the error ratio R?
Reduction of the value of a for the Error Ratio R is a desirable
objective of every SCS operation. If a could be made negligibly small,
the SCS could be perfectly reliable with a minimum loss of production or
fuel costs for the source. A nonzero value of a results from the
presence of unbiased errors in meteorological forecasting, estimation of
emissions, or modeling results. A reduction in a would be expected from
any of the following system improvements.
• Additional or improved meteorological data used in predicting
the meteorological parameters which are input for air quality
forecasts. Unless R is very near 1.0 or the system is operating
near the predictability limit for each parameter, some improve-
ment through added meteorological support might be atmospheric
sounding data, on-site wind measurements, NWS teletype or
facsimile circuits, a wind field generator model, a faster data
reduction system, or simply more frequent observations of
important meteorological data.
• More experienced or more capable meteorological personnel.
Because personnel gain experience as the system is operated,
the a of the system should become smaller with time.
C-l
-------
• An improved model. As a forecasting model is updated through
system experience, a reduction in a is to be expected.
• An improved emission schedule forecast system. This improvement
might be gained by more thorough production planning or it
might involve more careful fuel or materials analysis, better
emissions monitoring, or better plant process monitoring.
Table 1-1 summarizes the results of this sample analysis. Note
that all SCS operating parameters are the same for each SCS option except
that a is varied. The first column in the summary table describes the
six SCS options and the NO SCS option (for comparison). The second
column contains the frequency of violations of a 1-hour standard of 0.5 ppm
expected to occur with the indicated control strategy. The third column
contains the fraction of low cost fuel (higher sulfur content) which can
be used. The remaining fraction of fuel must be more expensive (lower
sulfur content) fuel. The fourth column contains the fraction of the
time that full production is possible assuming that the SCS process
curtailment is the only constraint.
Clearly, any of the six SCS plans reduces the frequency of violations
by at least a factor of 2 but, interestingly, no more than a factor of
3.4. By improving forecast accuracy for the fuel switching cases, SCS
reliability is noticeably improved. Since the fuel switching constant
3 = 0.25 is overly conservative in most cases, nearly every switch action
results in concentrations below standards. Therefore, improved accuracy
of prediction (reduced a) results in fewer potential violations escaping
control. Since the switch threshold y = 0.5 is exactly the standard,
there is no conservatism in the process curtailment forecasts. Although
improved forecast accuracy reduces the magnitude of violating concen-
trations, the number of violations remains the same. These examples
indicate that some conservatism is desirable for an efficient SCS
strategy. Ways of including conservatism are discussed later.
Improved forecast accuracy can have possible economic and social
benefits despite the probable added expense. For the fuel switching
examples, use of valuable low sulfur fuel is reduced from 0.25 to 0.23,
and finally to 0.19 of the total fuel used as forecasting accuracy is
improved. Meanwhile, SCS reliability is also improved. Note that full
C-2
-------
TABLE 1-1
EFFECTS ON SCS RELIABILITY OF CHANGING THE VALUE OF a
FOR THE ERROR RATIO R
Each SCS plan below has the following parameter values:
Fuel switching fraction 6 = 0.25
Switching threshold y = 0.5
Geometric Mean of Error Ratio R = 1.0
Width of Error Ratio distribution a is variable
Total Frequency
SCS Control Strategy of Violations
NO SCS
0.16432
Fraction of Low
Cost Fuel
1.000
Fraction of
Time at Full
Production
1.000
SCS #1
FUEL SWITCHING
a = 0.5
a. 06605
0.754
1.000
SCS #2
FUEL SWITCHING
a = 0.4
0.06291
0.768
1.000
SCS #3
FUEL SWITCHING
a = 0.2
0.04875
0.808
1.000
SCS #4
PROCESS CURTAILMENT
a = 0.5
0.08194
1.000
0.918
SCS #5
PROCESS CURTAILMENT
a = 0.4
0.08216
1.000
0.948
SCS #6
PROCESS CURTAILMENT
a = 0.2
0.08216
1.000
0.961
C-3
-------
production is assumed to be possible regardless of fuel type. For the
process curtailment cases, the percentage of full production is increased
as forecast accuracy improves. Meanwhile, SCS reliability is maintained
at the same level.
Example 2 - What is the effect on SCS reliability of changing the value
of R~ for the error ratio R?
The geometric value of the error ratio, R, is less than 1.0 if
concentrations are characteristically underpredicted, greater than 1.0
if concentrations are characteristically overpredicted, and 1.0 if
there is no systematic bias in prediction. It is easy for a system to
achieve a value of IT = 1.0 by simply reducing each forecast value by
the required amount to bring the mean of past values to 1.0. It is
generally desirable, however, to intentionally operate an SCS conser-
vatively to prevent a high frequency of violations which are near but
higher than the standard. The limits on reliability of a nonconservative
SCS were illustrated in the previous example analysis. One method of
operating a conservative SCS is to maintain an error ratio mean R greater
than 1.0.
An air quality forecast model which overpredicts provides a means
of achieving R greater than 1.0. Most air quality models overpredict
because "worst-case" conditions such as persistent meteorology and
conservative plume- rise are assumed.
Similarly, meteorological and emission predictions used for air
quality projections are often chosen to be "worst-case" forecasts. For
example, predicting fumigation conditions for all clear mornings would
produce a value of R greater than 1.0, but may be necessary to prevent
contravention of standards on those several mornings when inversion
breakup is a problem.
The sample analysis that follows is designed to investigate the
effect of changing R on SCS reliability, leaving all other SCS parameters
unchanged. Table 1-2 includes the results of the operation of six
hypothetical SCS schemes and the NO SCS case.
C-4
-------
TABLE 1-2
EFFECTS ON SCS RELIABILITY OF CHANGING THE VALUE OF R"
FOR THE ERROR RATIO R
Each SCS plan below has the following parameter values:
Fuel switching fraction = 6 = 0.25
Switching threshold = y = 0.5
Geometric mean of error ratio R is variable
Width of error ratio distribution a = 0.5
Total Frequency
SCS Control Strategy of Violations
Fraction of
Low Cost Fuel
Fraction of Full
Production
NO SCS
0.16432
1.000
1.000
SCS #1
FUEL SWITCHING
R = 1.0
0.06606
0.754
1.000
SCS #7
FUEL SWITCHING
R = 1.5
0.00876
0.521
1.000
SCS #8
FUEL ^WITCHING
R = 2.0
0.00370
0.413
1.000
SCS #2
PROCESS CURTAILMENT
R = 1.0
0.08194
1.000
0.918
SCS #9
PROCESS CURTAILMENT
R = 1.5
0.01306
1.000
0.836
SCS #10
PROCESS CURTAILMENT
R = 2.0
0.00000
1.000
0.609
C-5
-------
Again, each of the six SCS plans reduces the frequency of violations
by a considerable amount. The increased conservatism of air quality
prediction, manifested in increased values of R, re'duces the frequency^
of violations of the standard for both fuel switching and process
curtailment. For fuel switching, 43 of every 44 violations can be
eliminated using an SCS with R = 2.0.
The economic penalty for the indicated improvements in air quality
is shown in the final two columns of Table 1-2. With R = 2.0, lower
sulfur fuel is required 59% of the time for operation of the fuel-switching
plan. For process curtailment, a negligible violation frequency is
accomplished by reducing maximum possible production by 39%. Unlike
reducing a, increasing R above 1.0 has no compensating economic savings.
Example 3 - What is the effect on SCS reliability of changing the value
of the switch threshold y ?
The previous sample analysis investigated the improvement in SCS
reliability effected by conservative air quality forecasting. Another
method of improving SCS reliability is through the use of a switch
threshold less than the standard. Similar to making conservative
predictions, this control technique compensates for tendencies to under-
predict since most underprediction errors will result in "violations"
of the threshold which are still below the standard.
Table 1-3 displays the results of the sample analysis for six
hypothetical SCS plans with switch thresholds of varying values.
Systematic improvement in SCS reliability is evident for both the
fuel-switching cases and the process-curtailment cases as the switch
threshold is made a smaller fraction of the air quality standard.
Systematic reduction in economic benefit manifested in fractional
fuel usage data and fraction of full production data is also evident.
Similar to maintaining the value of R" greater than 1.0, a conservative
switch threshold is a simple tool for improving SCS.reliability; an
overall loss of plant efficiency is a probable effect of the control
strategy.
C-6
-------
TABLE 1-3
EFFECTS ON SCS RELIABILITY OF CHANGING THE VALUE OF
THE SWITCH THRESHOLD y
Each SCS plan below has the following parameter values:
Fuel Switching Fraction g = 0.25
Switching Threshold y is variable
Geometric Mean of Error Ratio R = 1.0
Width of Error Ratio Distribution a = 0.5
Total Frequency
SCS Control Strategy of Violations
Fraction of Fraction of Full
Low Cost Fuel Production
No SCS
SCS #1
Fuel Switching
Y = 0.5
SCS #11
Fuel Switching
Y = 0.4
SCS #12
Fuel Switching
Y = 0.3
SCS #2
Process Curtailment
Y = 0.5
SCS #13
Process Curtailment
Y = 0.4
SCS #14
Process Curtailment
Y = 0.3
0.16432
0.06606
0.03500
0.01562
0.08194
0.05641
0.02557
1.000
0.754
0.615
0.526
1.000
1.000
1.000
1.000
1.000
1.000
1.000
0.918
0.873
0.801
C-7
-------
Example 4 - What is the effect on SCS reliability of changing the fuel
switching fraction 3?
Although choice of a fuel switching fraction 8 is most likely
determined by the availability of fuel types, it is interesting to
observe the effect of changing the value of 8. One can hypothetically
achieve any value of 3 by blending fuels of known sulfur content, but
engineering problems prohibit this generality in most cases.
Three SCS plans with values of 6 of 0.25, 0.30, and 0.40 were
investigated. No appreciable change in SCS reliability or in plant
production was observed. Apparently, the value 6 used in all three
cases is very conservative; that is, each time a switch is implemented
to a lower sulfur content fuel a greater than necessary reduction in
concentrations is achieved. Therefore, increasing the value of S>
toward 1.0 has no effect on violation frequency for values of 8 less
than 0.5.
Example 5 - What is the effect on SCS reliability of maintaining a
conservative value of R for the error ratio R and changing
the value of y?
The preceding examples indicate that significant improvement in air
quality can be expected from any one of many reliable SCS plans. It is
not possible to define which SCS is both sufficiently reliable for
acceptance by control agencies and economically practical for acceptance
by plant operators. It is likely that some combination of the preceding
sample SCS systems would be optimum for most operations.
Furthermore, it is conceivable that an operating SCS will require
updating due to demands for more SCS reliability or due to demands for
more cost-effective operation by the plant management. In this even-
t
tuality, it is likely that some combination of the preceding SCS changes
would be optimum for the particular operation.
It is, therefore, important and interesting to observe the effects
of more than one parameter change on SCS reliability. Table 1-4 includes
six sample SCS plans that observe the effects of changing the switch
threshold v and employing a conservative mean value of the Error Ratio R.
C-8
-------
TABLE 1-4
EFFECTS ON SCS RELIABILITY OF OPERATING WITH A CONSERVATIVE
VALUE OF R" AND CHANGING x
Each SCS plan below has the following parameter values:
Fuel Switching Fraction g = 0.25
Switching Threshold y is variable
Geometric Mean of Error Ratio R" = 1.5
Width of Error Ratio Distribution a = 0.5
Total Frequency
SCS Control Strategy of Violations
No SCS
0.16432
Fraction of
Low Cost Fuel
1.000
Fraction of Full
Production
1.000
SCS #15
Fuel Switching
Y = 0.4
0.00471
0.450
1.000
SCS #16
Fuel Switching
Y = 0.3
0.00370
0.395
1.000
SCS #17
Fuel Switching
Y = 0.2
0.00370
0.372
1.000
SCS #18
Process Curtailment
Y = 0.4
0.00353
1.000
0.784
SCS #19
Process Curtailment
Y = 0.3
0.00000
1.000
0.664
SCS #20
Process Curtailment
Y = 0.2
0.00000
1.000
0.572
C-9
-------
Comparing SCS Number 7 and the three fuel-switching plans in
Table 1-4, it is clear that increased conservatism yields only small
improvement in reliability until the SCS reaches its limit of reli-
ability under the fuel-switching plan. Further improvement would
require the plant to cease operations 0.57% of the time, or 52 hours per
year. For process curtailment a comparison of SCS Number 9 and the
three plans included in Table 1-4 indicate continuous improvement in SCS
reliability with decreasing value of the switch threshold. Values of y
less than 0.5 are unnecessary since only a negligible frequency of
violations is expected at a value of y = 0.5.
Note that SCS Number 19 expects less than 0.1 violations per year
and achieves more than 66% of full production. Considering no other
complexities in evaluating SCS reliability, SCS Number 19 accomplishes
most acceptable reliability with maximum plant production of all SCS
plans considered in these examples.
Example 6 - How can emission error be incorporated into the analysis?
Each of the sample analyses considered so far in this section
considers the error ratio R to be some hypothetical log-normally dis-
tributed function. No attempt has been made to simulate the effects of
each component of SCS reliability. The following sample analysis will
consider SCS schemes that have meteorological error distributed like the
Error Ratios of the preceding examples, but that also have emission
errors. According to the discussion in Section 3,
R = RW ' RQ • Si
For these examples, we assume R^. = 1.0, therefore
R = «W ' RQ
iv'e will assume that R,^, has a log-normal distribution with R~ = 1.0 and
-.. - 0.5. Furthermore, we will assume that
C-10
-------
that is, that the error in emission rate Q is measured simply by the
ratio of predicted Q to the observed Q for that time.
Then,
R = R
Q0 w
Q
It is reasonable to expect that ^j*- has either a normal or a "top-hat"
distribution. The example below considers both of these possibilities.
The hypothesized distributions for RW and R_ are combined to form a
distribution for R. Figure 1-1 illustrates the three distributions of
^e- used. They are designated as Q functions 1, 2 and 3.
Table 1-5 summarizes the results of the analysis using the combined
Error Ratios. The frequency of violations for all six sample SCS plans
is greater than the frequency of violations for the corresponding SCS
with no emissions error (SCS Number 1 or SCS Number 2) . Improvement in
SCS reliability is achieved as a of the distribution is reduced. The
"top-hat" emission error distribution is associated with a reliability
intermediate between the two normally distributed emission error functions.
C-ll
-------
Q FUNCTION *1
r
y
\
Normal Distribution
er=O,2
\
\
0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5
Q FUNCTION -2
Normal Distribution
3ar=O.2
Q FUNCTION "3
0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5
Q
1
"Top
-hat"
i
Q
Oistri
'butio*
f)
-^
0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5
Q
Figure 1-1 Three Frequency Distributions of Ratio Qp/Qo
C-12
-------
TABLE 1-5
INCORPORATION OF EMISSIONS ERROR INTO
THE RELIABILITY ANALYSIS
Each SCS plan below has the following parameter values:
Fuel Switching Fraction 6 = 0.25
Switching Threshold y = 0.5
Geometric Mean of Error Ratio R~ = 1. 0
Width of Error Ratio a = 0.5
Total Frequency Fraction of Fraction of Full
SCS Control Strategy of Violations Low Cost Fuel Production
No SCS
SCS #21
Fuel Switching
Q Error 1
0.16432
0.07079
1.000
0.765
1.000
1.000
SCS #22
Fuel Switching
Q Error 2
0.06837
0.764
1.000
SCS #23
Fuel Switching
Q Error 3
0.06943
0.766
1.000
SCS #24
Process Curtailment
Q Error 1
0.08582
1.000
0.920
SCS #25
Process Curtailment
Q Error 2
0.08397
1.000
0.921
SCS #26
Process Curtailment
Q Error 3
0.08523
1.000
0.921
C-13
-------
TECHNICAL REPORT DATA
fPlease read hiunictions on tlif rei-crtc be/ore completing/
. REPORT NO.
PA-450/3-78-039
3. RECIPIENT'S ACCESSIONING.
. TITL'E A\D SUBTITLE
Case Study Analvsis of Sunnlementary Control System
eliability"
5. REPORT DATE
August 1978
6. PERFORMING ORGANIZATION CODE
S) H. Lqan, ti. riotmaqle, • J . Lague, H. McCann, and
8. PERFORMING ORGANIZATION REPORT NO.
. Doucette
PERFORMING ORGANIZATION NAME AND ADDRESS
nvironmental Research and Techno!oqy,
596 Virqinia Road
oncord, MA 07142
Inc.
10. PROGRAM ELEMENT NO.
2AF 643
11. CONTRACT/GRANT NO.
EPA Contract
No. 68-02-2090
2. SPONSORING AGENCY NAME AND ADDRESS
S. Environmental Protection Anency
)ffice of Air, Noise and Radiation
Iffice of Air Ouality Planninn and Standards
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final Technical Report
14. SPONSORING AGENCY CODE
5. SUPPLEMENTARY NOTES
'Yfirouqh a supplementary control system (SCS), SO,
6. ABS
emissions from a facility are
temporarily curtailed when meteoroloqical conditions conducive to high ambient SO-
:oncentrations exist or are anticipated. This report describes a case study demonstra-
tion of SCS reliability analysis techniques presented in "Technioue for Supplementary
;ontrol System Reliability Analvsis and Upgrading" (EPA-450/2-76-015). A user manual
is also provided. A primary objective of this study is to discuss the reliability
malysis techniques and their applicability to the problem of estimating SCS reliability
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lOENTIFIEHS/OPEN ENDED TERMS C. COSATI I Iclil/Croup
Mr Pollution
Sulfur Dioxide
Meteorology
Atmospheric Diffusion
Atmospheric-Models
Air Pollution Control
Supplementary Control
Sys terns
13B
. DISTRIBUTION STATEMENT
el ease Unlimited
19. SECURITY CLASS f Tilts Report/
None
21. NO. OF PAGES
222
20. SECURITY CLASS (TH
None
22. PRICE
|A Form 2220-1 (9-73)
------- |