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TABLE OF CONTENTS
VOLUME XIII
Technique for Supplementary Control System Reliability Analysis
and Upgrading. MDAD. 3/76. OAQPS No. 1.2-037. ':
I Control Strategy Preparation Manual for Photochemical Oxidant.
CPDD. 1/77. OAQPS No. 1.2-047.
J Control of Volatile Organic Emissions from Existing Stationary
Sources - Volume I: Control Methods for Surface-Coating
Operations. ESED. 11/76. OAQPS No. 1.2-067.
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EPA-450/2-76-015
March 1976
(OAQPS 1.2-037)
GUIDELINE SERIES
TECHNIQUE
FOR SUPPLEMENTARY
CONTROL SYSTEM
RELIABILITY ANALYSIS
AND UPGRADING
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
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A TECHNIQUE FOR SUPPLEMENTARY CONTROL SYSTEM
RELIABILITY ANALYSIS AND UPGRADING
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March 1976
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g OAQPS No. 1.2-037
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Source Receptor Analysis Branch
Monitoring and Data Analysis Division
Office of Air Quality Planning and Standards
Research Triangle Park, N.C.
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This document does not constitute a general endorsement of
supplementary control systems as a control alternative. It is
intended only to assist the SCS user and the responsible control I
agencies in those limited situations where legislation, EPA or
the courts permit its use.
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 - as supplies
permit - from the Air Pollution Technical Information Center,
Environmental Protection Agency, Research Triangle Park, North
Carolina 27711; or, for a fee, from the National Technical Infor-
mation Service, 5285 Port Royal Road, Springfield, Virginia 22161. |
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PREFACE
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The purpose of this document is to emphasize the key factors
J that affect the reliability of a supplementary control system (SCS)
and to present an analytical concept applicable to the analysis of
SCS reliability. Examples are presented that demonstrate the type
of information obtainable through application of the concept.
Except for relatively minor changes, Sections 2, 3 and 4 were
extracted from the final report prepared by Environmental Research
and Technology, Inc., under EPA Contract No. 68-02-1342. Credit
for that report is gratefully extended to Dr. Bruce A. Egan, ER&T
project leader under that contract. A follow-on effort by ER&T is
underway to supplement this document with a manual that will enable
I the user to apply the reliability analysis concept presented herein.
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TABLE OF CONTENTS
Page
PREFACE
I 1. SUMMARY 1-1
m 2. FACTORS AFFECTING RELIABILITY 2-1
2.1 Introduction 2-1
I 2.2 Air Quality Monitoring Reliability and Upgrading 2-1
2.2.1 Sampling and Information Transfer Errors 2-2
| 2.2.2 Example Analysis to Optimize the Siting 2-3
of Air Quality Monitors
2.3 Meteorological Forecasting Reliability and Upgrading 2-7
2.3.1 Introduction 2-7
2.3.2 Criteria for Assessing Meteorological 2-8
Forecasting Reliability
| 2.4 Air Quality Modeling Reliability and Upgrading 2-15
- 3. RELIABILITY ANALYSIS CONCEPT 3-1
3.1 Introduction 3-1
3.2 Relevant Probability Theory 3-1
3.3 Reliability Analysis 3-6
| 3.3.1 The Basic Concept 3-6
_ 3.3.2 A Mathematical Application of the Concept 3-11
" 3.4 Isolating Component Error 3-14
4. EXAMPLE RELIABILITY ANALYSIS 4-1
4.1 Test Case Conditions and Assumptions 4-1
I 4.2 Dependence of SCS Reliability on Various 4-3
Influencing Factors
5. REFERENCES 5-1
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I 1. SUMMARY
m Through a supplementary control system (SCS), stack emissions
of pollutants are temporarily curtailed when meteorological conditions
are conducive to ground-level concentrations in excess of an ambient
air quality standard. This document addresses the reliability of an
I SCS. Reliability is defined herein as the ability of an SCS to prevent
M ambient pollutant concentrations from exceeding ambient standards.
The intent of this document is to present the fundamentals of a
fl mathematical concept that can be applied to the reliability analysis
and upgrading (improving the reliability) of an SCS. Also presented
| are hypothetical examples that demonstrate the type of information
that can be obtained through application of the concept. Specific
procedures for applying the concept will be presented in a user manual
to be published about the end of 1976.
The reliability analysis concept, presented in Section 3, requires
f the analysis of source, meteorological and air quality data collected
_ concurrently during several months or more of SCS operation. Applica-
" tion of the concept, as demonstrated in Section 4, can yield information
on (1) the overall reliability of an SCS and (2) the degree to which
reliability can be improved by adjusting key system parameters.
In general, the true reliability of an SCS will be known only
after a year or more of system operation in conjunction with a well-
planned air quality monitoring program. Nevertheless, an assessment
fl of system reliability should be made as early as possible in the
development phase of an SCS to pinpoint sources of error and to provide
a basis for further development and refinement of the system.
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The reader should be aware of related documents concerning SCS.
Probably of most interest to anyone concerned with the technical M
aspects of supplementary control systems will be the "Guidelines for
Evaluating Supplementary Control Systems" (EPA, February 1976). That
document provides detailed guidance for the design and development of m
an SCS. "Guidelines for Enforcement and Surveillance of Supplementary
Control Systems" (EPA, September 1975) provides guidance to the control I
agency in the surveillance and enforcement of such systems. "Review-
ing New Stationary Sources" (EPA, 1976a) is one of several documents I
providing basic guidance in pollutant dispersion modeling, which is «
an essential tool in the development of an SCS. "Guidance for Air
Quality Monitoring in the Vicinity of Large Point Sources" (EPA, 1976b) I
provides information useful for air quality monitor siting in the
vicinity of a facility proposing to use SCS. |
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2. FACTORS AFFECTING RELIABILITY
2.1 Introduction
There are four generalized components of an SCS in which
uncertainty can exist. These components are: (1) air quality
monitoring; (2) meteorological forecasting; (3) emissions fore-
casting; and (4) air quality modeling. The meaning of the first
three components is self-evident. Air quality modeling implies
the algorithms and methodology which are used to relate emission
rates, other source data, meteorological inputs and topographic
factors to current and future air quality in the vicinity of the
source. Components 1, 2, and 4 are considered individually in
this section with respect to their (general) effect on overall
SCS reliability. Emission forecasting is discussed in Example 6
of Section 4.
g 2.2 Air Quality Monitoring Reliability and Upgrading
Every Supplementary Control System must have a monitoring
network to verify that the required air quality is being main-
tained through the operation of the SCS. Also, real-time air
quality monitoring data must be available as an input to the deci-
sions to curtail emissions. In addition, monitoring data are used
during the development phase of the SCS and whenever the forecast
models are calibrated and periodically upgraded.
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The following sources of uncertainty in a monitoring system
will contribute to a degradation of system reliability: 9
Instrumentation accuracy limits
Percentage data capture statistics
Information transfer errors
t Insufficient and/or inappropriate sampling locations.
Section 2.2.1 provides a brief discussion of the first three m
items. The last item is addressed in more detail in Section 2.2.2. *
2.2.1 Sampling and Information Transfer Errors
Proper choice of SOp monitoring instruments depends
on many factors. A primary requirement is that the air quality
monitors provide continuous SCL data. For purposes of evaluating a
system for an SCS application, it is also important to consider sen- I
sitivity, lag time and response time, interferences, accuracy,
calibration drift, and maintenance requirements.
The lag time of a monitoring network is the time between ;
the occurrence of the concentration and the time that this value is
displayed for use by SCS personnel. With telemetered data, short
term averages (e.g., 2-minute averages or instantaneous concentration
values less than 2 minutes old) are usually available for examination
before a 1-hour or 3-hour averaging period has transpired. In these
cases, the lag time is no constraint on the system. For systems which
require analysis of strip charts, manual data handling, or chemical
analysis, the lag time between collection and display of the data
severely constrains the potential uses of the systems. m
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j The percentage of useful data capture depends upon the
_ combined downtime of the sensors and associated data capture and
transmission components. Sensor downtime includes time periods of
ft instrumentation calibration and maintenance as well as identifiable
data sets of inaccurate measurements. A well designed system will
| attempt to minimize these sensor downtime contributions by providing
_ automatic instrument calibration, remote sensing of possible instrument
malfunctioning and generally, remote control of the instrumentation.
Thus, real-time monitoring and telemetry of information provides
mechanisms for substantially enhancing data capture. If the system
jj involves telemetry such as telephone line usage, the percent data
capture will depend additionally upon the downtime of this telemetry
system and the remote recording devices. If the system requires any
real-time data processing, the downtime of the data processing
equipment must also be considered.
* 2.2.2 Example Analysis to Optimize the Siting of Air Quality
I Monitors
The question of sufficient number and spacing of monitors
1 is difficult to assess in general because every site has peculiar
_ meteorology, terrain, and land use. Monitor locations should, in
* general, be chosen to monitor the highest concentrations in the
vicinity of the source. They should not be significantly influenced
by minor local sources.
P An analysis methodology designed to assist in determining
_ the best distribution of monitors for SCS applications is presented in
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"Guidance for Air Quality Monitoring in the Vicinity of Large Point «
Sources" (EPA, 1976b). The analysis provides an estimate of the
percentage of air quality violations expected to be directly observed
by any monitoring network. Through this analysis, the improvement
in the monitor network anticipated by the addition of one or more |
monitors can be assessed and the concomitant improvement in SCS _
reliability can be weighed against the increased cost and effort.
An example application of a similar methodology is discussed in the
following paragraphs.
In the example analysis, the emission rate and other g[
source statistics were those of two stacks at an actual source under _
full load conditions. A dispersion model appropriate for application
to the source was then utilized to compute concentration versus down-
wind distance for each of a wide range of possible stability-wind
conditions. A stability-wind rose from a nearby airport was used to £
determine the frequency of occurrence of each condition.
Given the above data, it was then possible to deter-
mine, for each wind direction sector, the downwind distance at which
the maximum number of occurrences of concentrations above a specified
threshold level can be expected to occur. Such information is presented I
in Table 2-1, which provides a ranked listing of 25 monitor locations
considering all wind directions. The location is defined by an
azimuth (wind direction) and a radial distance (distance downwind).
The monitors are ranked by the proportion of the time that each
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TABLE 2-1
Optimum Monitor Locations Ranked by Expected Frequency of
Monitored Values Exceeding the Concentration Threshold
CONCENTRATION THRESHOLD = 0.20 ppm
OPT1H4L MONIT3P1NC.
MONITMH *
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monitor will observe concentrations above the 0.20 ppm threshold.
The improvement in the fraction of observed violations is indicated
in the cumulative capture frequency in column 5. For this example,
the total percent frequency of occurrence of values above 0.20 ppm
is 23.29%. Thus, with 25 receptors 90.06% (20.976/23.29) of all
observed concentration values greater than 0.20 ppm would be observed.
Clearly, the use of this many monitors would be a very expensive and
yet not a foolproof way of assuring that required air quality is
being maintained. It is interesting to note that by adding the 17th
monitor to a network including the best 16 locations, an order of m
magnitude less improvement in important data capture is gained than
when the second monitor was added to the first. I
From the previous example, one can deduce two general
results:
1. For any reasonable number of sensors, a relatively
high percentage of significant peak values may go unobserved.
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2. Using monitoring alone as the only guide to decisions
concerning emission curtailments in an SCS could result in a signifi-
cant number of undetected violations of the short-term standards *
given that violations are expected to occur.
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2.3 Meteorological Forecasting Reliability and Upgrading
2.3.1 Introduction
The purpose of every SCS is to avoid violations of
| air quality standards by reducing emissions during periods when
_ weather conditions are not conducive to adequate dispersion of
the pollutants. Identification of these poor dispersion periods
must be accomplished with some advance notice since there exist
practical limits to the speed with which emission reduction orders
| can result in lower emissions from the stack. Furthermore, there
is a significant "transport time" before the emissions can travel
from the stack to the point of maximum ground-level impact. The
requirement for advance warning of impending poor dispersive
periods forces the supplementary control system to include some
£ form of meteorological forecasting. Some conditions, such as
_ inversion breakup fumigation, demand advance forecasting. Moni-
tored air quality levels alone would provide no advance warning
W of such conditions.
The principal role of meteorological forecasting for
I an SCS is to provide a basis for the appropriate SCS response to
anticipated poor dispersion conditions. After the SCS has been
operative and meteorological forecasts and observed concentration
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levels have been recorded, analysis of the data can verify the
meteorological conditions which accompany poor air quality, and
point to ways of improving the meteorological forecast system.
2.3.2 Criteria for Assessing Meteorological Forecasting
Reliability |
The following factors are essential to a meteoro- _
logical forecasting system and provide a framework with which to *
discuss the reliability of this important SCS component:
The spatial and temporal scales of the forecasting
procedures must be appropriate for the requirements of the SCS.
The relationship between errors in meteorological
parameter forecasts and errors in predicted concentration levels
must be understood. I
Verification of all aspects of the meteorological
forecasting system must be a part of the SCS.
These criteria are considered in detail below.
Spatial and Temporal Scales of Forecasted Conditions J
Meteorological forecasting for the estimation of air
quality is categorized by space and time scales. Forecasting for
time scales of 24 hours or more requires the prediction of synoptic
scale (hundreds to thousands of kilometers) meteorological events.
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For example, it entails the prediction of the movement and location
of stagnating anticyclones with their associated light winds and
poor dispersion characteristics. Short time periods require
detailed forecasts on smaller spatial scales. In determining
the reliability of meteorological forecasting for an SCS, it is
necessary to consider forecasts on temporal scales of 1 to 24-hours
and on spatial scales of several thousand square miles to within
a few thousand feet of the pollutant source.
The "weather" variables which the meteorologist must
forecast are those which influence the dilution capacity of the
lower atmosphere. As direct forecasts and measurements of the
turbulent components of the wind are frequently unavailable,
related parameters become the forecast requirement. These include
wind speed and direction, atmospheric stability, cloudiness,
precipitation, and mixing depth.
8 The reliability of any weather forecast is never
M perfect and in general depends on several diverse and often
highly variable factors. A 6-hour forecast of cloud cover is
V usually more reliable than a 24-hour forecast of the same event.
Local effects are important. The onset of a sea breeze circu-
| lation in coastal areas can be in opposition to the wind flow
_ normally associated with a weather system where there is no large
body of water nearby. Similarly, the diurnal variation in tempera-
I ture is different in urban areas compared to rural areas.
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Meteorological Forecasting Errors vs. Air Quality
Forecast Errors
The reliability of a forecast for air quality is a
function of the reliability of forecasting the meteorological |
parameters which dictate the ensuing air quality. First, «
consider wind speed and direction. For an isolated source
unaffected by terrain, the wind direction may be unimportant as I
possible high pollutant concentrations may occur in any downwind
direction from the source. Two examples when wind direction is I
important are plume downwash, which may occur with strong winds _
from particular directions, and terrain modified winds which might
produce high concentrations at a particular critical location.
The predictability of wind direction is generally good, especially
with well-defined synoptic systems. The predictability decreases f
with time and is often lower in areas with complicated terrain _
features. When an anticyclone is over the station, wind direction "
can be variable and, hence, difficult to predict.
Wind speed usually is more difficult to forecast.
It varies diurnally with high speeds during the day, when there I
is a transfer of momentum from higher levels to the surface boundary
layer, and with low speeds at night. Wind speed depends on the
intensity of the pressure gradient, insolation, surface roughness,
terrain channeling, and other local factors. The reliability of
wind speed forecasts also decreases with length of forecast time. I
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The stability of the lowest kilometer of the atmos-
phere broadly describes its turbulent characteristics. An unstable
atmosphere is characterized by thermal convection, turbulence, and
good mixing. A stable atmosphere is characterized by weak turbu-
lence and poor mixing.
M Temperature measurements in the vertical are usually
the best indicator of stability. If continuous temperature measure-
I ments in the vertical (e.g., on a meteorological tower) are avail-
able, then atmospheric stability can be accurately estimated.
| Temperature typically varies diurnally, with changing air mass and
f with local effects.
When a vertical temperature profile is unavailable,
I the prediction of stability is indirect and, hence, less reliable.
The stability, however, may be estimated by the prediction of
jj cloud cover, wind speed, type of air mass over the region, ground
_ cover (e.g., snow cover, proximity to large bodies of water) and
time of day.
The atmospheric mixing height is defined as the depth
of the surface layer of the atmosphere through which complete
P vertical mixing occurs, and is thereby a function of the vertical
temperature structure of the atmospheric boundary layer. Local tem-
* perature sounding data provide an excellent basis for the estimation
of the mixing height. The predictability of the mixing height depends
upon the predictability of such factors as the vertical distribution
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of temperature in the lowest few kilometers and the presence and
height of subsidence inversions associated with synoptic scale
anticyclones. The afternoon mixing height is identified by the
height of the intersection of the dry adiabatic lapse rate from the |
surface maximum temperature with the observed or predicted vertical . _
temperature profile. Pollutants trapped in a shallow mixing layer
could result in high ground-level concentrations.
The prediction of maximum temperature is routine and
generally quite reliable. The reliability of a temperature forecast |
decreases with time and is affected by cloud cover, wind speed and
direction, time of year, and local effects.
The forecasting of meteorological parameters is strongly
related to the predictability of synoptic scale weather systems. The
prediction of the growth and movement of cyclones and anticyclones I
is routinely performed by forecasters in the National Weather Service
(NWS) and in private industry. At present, forecasts of synoptic m
scale weather are made in a "man-machine mix" mode. Completely
objective numerical forecasts provide guidance to the meteorologist
who prepares the "best" forecast. I
Even if meteorological forecasts are available from a
nearby NWS station, forecasting for a supplementary control system
will require additional on-site meteorological information. Pilot
balloons, radiosondes, and on-site wind and temperature sensors are
important sources of forecast inputs. It is obvious that the mix of
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NWS guidance, on-site data collection, and forecasting experience
| and skill are important for meteorological forecasting reliability.
M The reliability of these predictions varies with geographical area,
temporal length of forecast, and large-scale weather patterns. It
I is difficult to assess the absolute reliability of these predictions
as one must consider the unique meteorological and engineering needs
| of each proposed SCS. For example, the time requirements necessary
_ to change fuel usage or to reduce fuel load at a power plant will
* dictate the minimum forecast time scale and, hence, will enter into
H the assessment of forecast reliability.
To assess the reliability of a forecasting capability
in reference to air quality, a basic understanding of the relation-
ship between pollutant emissions, atmospheric dispersion potential,
and ambient pollutant concentrations is assumed. This knowledge
should be gained by an extensive dispersion analysis and meteorology-
air quality monitoring program in which their relationship is modeled
and observed over an extended time period. An understanding of the
relationship between pollutant emissions, dispersion potential and
air quality is a primary prerequisite in any SCS.
Verification of Meteorological Events
During the development of an SCS there should be a
continuous review of the forecast accuracy through verification
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of the predicted meteorological parameters. Verification of these
forecast meteorological parameters is relatively simple. Pre-
dictions are compared to observations to determine forecast |
accuracy. The verification program should indicate the average M
reliability of meteorological forecasts for different time periods
and different initial conditions. For example, at a certain pollutant 8
source, plume downwash is expected with northeast winds above a
certain wind speed, U . When the wind speed exceeds U , high |
v* C
ground-level S02 concentrations are measured. The verification
program must then demonstrate the ability to forecast strong winds
from the northeast. If this pollution source were located in the
Boston area the relative frequency of northeast winds is low, about
8 percent; and, hence, the predictability of this wind direction J
may be lower than the predictability of more frequent wind direc- _
tions. However, if this meteorological event is the only weather
condition with a high pollution potential, then the verification ft
program must emphasize the predictability of strong northeast winds.
Accurate prediction of other wind directions may be unimportant. |
Forecasting light northeast winds may be very difficult but is also _
unimportant as related to air quality prediction since downwash or
other situations conducive to air quality problems do not occur.
The air quality-meteorology relationship, specific to
the locale under consideration, must guide the verification program |
and must also guide the assessment of forecasting reliability.
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The verification program should thereby emphasize the predicta-
bility of those meteorological conditions that produce the highest
air pollution potential. It is important to ascertain the relia-
bility of those predictions - especially the probability of
occurrence of adverse meteorological conditions that were not
predicted.
NWS and U.S. Air Force aviation forecasters routinely
predict winds, sky cover, visibility, precipitation, and tempera-
ture for a 24-hour period at a specific location. If verification
statistics for several years are available for the location in
question, the predictability of the meteorological parameters im-
portant to air quality can be assessed. (Verification statistics
are indicative of the relative reliability of forecasts at a parti-
cular locale.)
2.4 Air Quality Modeling Reliability and Upgrading
Several types of air quality models have been developed to
predict ambient pollution levels resulting from pollutant emission
sources. These models fall into two general categories: (1)
I deterministic-atmospheric dispersion models which calculate
concentrations based upon physical relations between emission
and meteorological parameters and effluent plume dispersion; and
(2) statistical or empirical models based upon the determination
of statistical relations between emission rates, meteorological
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conditions, etc., and air quality levels. Models based upon
multiple applications of a Gaussian plume equation to calculate
the pollutant concentration at a receptor or models based upon I
the numerical solution of a conservation of pollutant mass
equation are of the former type and will be primarily addressed I
in this section.
The reliability of a model is defined by its ability to
predict ambient pollutant concentrations based upon given meteoro- ff
logical conditions and emission parameters. The best method for
the evaluation of prediction model accuracy is thorough analysis |
of the accuracy resulting from a large data set of predictions
with the model. Mith a sufficiently large data set, the model
reliability can be assessed over all weather conditions and V
observed emission rates. Such an evaluation procedure results
in three benefits: (1) the model is immediately useful for £
operational application; (2) the expected accuracy of short-term
forecasts can be evaluated; and (3) threshold pollutant concen- *
trations for the reliable operation of an SCS can be determined.
To assess the reliability of an atmospheric dispersion model
for a particular locale, i.e., an isolated SCS, a basic under- |
standing of the relationship between meteorology, emissions, and
pollutant concentrations must be established. This can be deter-
mined through a joint meteorology-air quality monitoring program
and a model validation program.
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* Of interest to the maintenance of air quality standards is
I an indication of the maximum "underprediction" observed during
the time the verification program has been in operation. For
| example, a predicted 24-hour S0? average of 0.05 ppm in com-
f parison to an actual observation of 0.10 ppm represents a marked
underprediction and certainly should be accounted for in the
design of the SCS.
For some applications a comprehensive verification program
| may be unnecessary. If it has been determined that high pollutant
_ concentrations rarely occur or occur only under certain well
defined weather conditions, then the model validation study need
only concentrate on the occurrence of those particular adverse
weather conditions and source emissions which cause high pollu-
tant concentrations. The model reliability, then, must most
carefully be established for the emissions and meteorology that
will produce concentrations above a specific threshold level.
Because of the differences in the characteristics of the models
it is difficult to establish general analysis criteria applicable
to all model types. Therefore, each type of model is considered
individually below.
Gaussian Plume Models
The empirical plume equation most frequently used to estimate
the down-wind dispersion of a pollutant from an elevated continuous
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point source is the bi -normal Gaussian plume equation:
exp -
Q is the source strength;
u is the mean horizontal wind speed;
a ,a are the standard deviations of the distributions of concen-
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where C is the pollutant concentration at height, z
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trations in the y (cross-wind) and z (vertical) directions, I
and are functions of downwind distance, x, atmospheric
stability, and averaging time; and |
h is the effective source height. «
The Gaussian form of a plume equation is convenient because
of its simple analytical form. The Gaussian dispersion equation I
and its application to various source configurations is discussed
in "Reviewing New Stationary Sources" (EPA, 1976a). |
The causes of errors in point source model calculations may be g
broadly grouped into three categories: inaccuracies in the repre-
sentation of the atmospheric transport and dispersion process by
the model, errors in the emissions data and errors in estimating
meteorological parameters. |
Gaussian point source models also generally assume that wind speed
and direction are constant throughout the area. Model calculations
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8 are particularly sensitive to errors in wind direction as
non-centerline pollutant concentrations decrease exponentially
away from the centerline. Wind direction persistence informa-
I tion is especially important for estimating concentrations over
time periods of a few hours.
The effective height (h) of a stack, which determines the
M centerline height in the Gaussian plume model, is computed as the
sum of the physical stack height and the plume rise due to the
8 vertical momentum and buoyancy of the effluent. Plume rise is
related to the dimensions of the stack, effluent characteristics
| such as temperature and heat flux, the wind speed above the stack,
_ and atmospheric stability. Uncertainties in these parameters will
affect the plume rise calculation. Several formulae (see Briggs
I 1969 for a review) have been developed to describe plume rise.
Deciding which equation is applicable to a particular source is
| difficult and, at best, uncertainty by a factor of two in estimates
of the plume rise is likely on any one occasion.
If a stack is located on a building and its efflux velocity is
low or if the stack is not tall enough with respect to nearby
buildings, plume downwash could occur, resulting in high ground-level
| pollutant concentrations. The following parameters are important for
_ aerodynamic downwash: the strength of the undisturbed wind, stack
height, effluent exit velocity and buoyancy, and the dimensions and
spacing of local obstructions to the wind. These parameters will
2-19
m
I
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I
I
determine the likelihood of downwash. In turn, their reliability I
will affect the reliability of the pollutant concentration calcu-
lation.
To eliminate some of the uncertainties of the Gaussian plume
model a comprehensive model validation program should be instituted
for the point source of interest. The primary objective of the Q
validation effort is to assure that the model adequately predicts
concentrations over the time and space scales of interest and over B
the range of expected source emissions.
Model validation implies a detailed investigation of the model
results and a comparison of those results with measured values in I
order to identify and evaluate discrepancies. If the model results
compare well with the observed data, the model may be used without "
modification. On the other hand, if systematic discrepancies are
found, the investigation may suggest alterations of model parameters
or of the model mechanics which would improve the representativeness I
of the model.
The procedures for validating models will differ somewhat from
application to application depending upon the nature and purpose of
the study and depending upon the quality of the available data.
Ideally, validation should consider individual weather conditions I
or emission rates depending on the length of the data base. For
example, the error for stable atmospheric stability may be greater I
than for neutral stability. Winter emission rates associated with
2-20
I
I
-------
I
I
space heating needs may be positively correlated with cool northerly
winds. Neglect of this mechanism often causes models to overpredict
I pollutant concentrations during other weather conditions. The
validation procedure will normally require a thorough study of the
implications of model assumptions and the performance of "sensitivity"
studies for various input parameters.
Numerical Simulation Models (Conservation of Mass Models)
Gaussian-type models tend to ignore spatial and temporal varia-
tions in meteorological conditions by assuming that wind speed, wind
direction, and dispersion parameters are uniform in both the vertical
B and horizontal directions. Large spatial and time variations, however,
are generally found in nature and especially in areas with irregular
terrain. Numerical dispersion models which attempt to simulate air
pollution phenomena associated with vertical and horizontal variations
in meteorological parameters are being developed.
The numerical advection - diffusion models are based on solutions
to a conservation of mass equation for a trace material in a con-
tinuum fluid. The tracer equation may be written
I
2-4 = v (UC) + V ' KVC + Q
M
-
a L
§ 2-21
I
I
-------
meteorological forecasts.
2-22
I
I
where
C is the concentration
U and K are wind velocity and turbulent diffusivity generally
varying with space and time, and
Q is the emission rate per unit volume. I
For general wind and diffusivity fields the continuum equation
must be solved numerically by finite difference techniques.
In general, the sources of error in a numerical dispersion
model are four: (1) emissions data; (2) specification of the wind
field; (3) specification of the turbulent diffusivities; and I
(4) errors resulting from the numerical approximations.
Statistical Air Quality Prediction Models
If an adequate historical data bank of pollutant concentrations |
and meteorological observations is available for a region, it is _
possible to construct a statistical model relating observed concentra- *
tions to various meteorological parameters. Because statistical
models do not consider changes in emission parameters, they are
only useful for the prediction of concentrations for short time |
periods. For short period predictions as is necessary for an SCS, _
such models, developed from a sufficient data base, can provide the *
necessary predictions with a minimum of computation.
In common with Gaussian plume models, statistical models rely
upon meteorological forecasts for short period predictions. The J
accuracy of all types of models depends upon the accuracy of the _
I
I
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I
3. RELIABILITY ANALYSIS CONCEPT
I 3.1 Introduction
This section presents a mathematical concept that involves
| the analysis of source, meteorological and air quality data collected
m concurrently during an extended period of SCS operation. The analysis
is designed to yield information on overall system reliability. It
also provides information useful in system "upgrading" (improving
system reliability).
| Section 3.2 describes the probability theory underlying the
_ analysis concept. Section 3.3 describes the concept and Section 3.4
presents examples of its application.
3.2 Relevant Probability Theory
Throughout this document the concept of a frequency distribu-
tion is used. A frequency distribution is a representation of the
fraction of the time a variable quantity assumes each of the possible
values in its range. A frequency distribution of ground level con-
I centrations downwind of a source provides much information about the
characteristics of the source emissions.
The analysis model presented in this section is based upon
studies of the frequency distributions of air quality levels from
point sources whose contributions dominate the concentration fields.
I
I
I
I
Figure 3-1A illustrates two typical concentration distributions.
3-1
-------
I
I
The first would be the case of a single receptor where the wind is
often blowing in a direction other than from source to receptor so
concentrations are most often near zero. The second is representa- I
tive of a distribution of 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 cate-
gories 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 fre-
quency of concentration values exceeding C . To satisfy the air
quality standard the sum of the frequencies for values of concen-
tration to the right of C must be less than F .
Thus, from a compliance view point, a more useful distribution m
is the cumulative frequency distribution associated with each of
the frequency distributions discussed above. In this case, the sum
of the frequencies of all values greater than the abscissa value is
plotted as the ordinate. Figure 3-1B illustrates the cumulative |
frequency distributions associated with the distributions of Figure M
3-1A. The sum over the frequency distribution of occurrence for
concentrations greater than C can now be read directly from the I
ordinate of the graph.
3-2 I
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re 3-1 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.)
3-3
-------
I
Since the range of concentration values is continuous, the
step function presentation of the cumulative frequency distri-
bution can be replaced by a smooth function as illustrated in I
Figure 3-1C. Using the graphs of Figure 3-1C, it can be simply
stated that the goal of any control procedure is to reduce the
locus of F at the abscissa value C below the dashed line repre-
senting F . When it is obvious which frequency distribution of
the three presented in Figure 3-1 is being discussed, the term
distribution will be used for convenience in this document.
The cumulative frequency distribution can be used to illustrate
the effects of any control procedure. Figure 3-2A represents a
hypothetical distribution of maximum ground level concentrations.
Since the locus of F is above the dashed line at C = C , the source I
is exceeding the standard. Assume the graph of F represents the
uncontrolled conditions. Direct application of a constant emission
control which reduces emissions uniformly by 50% (say, changing
from 2% to 1% sulfur fuel or installing 50% efficient removal devices)
would move every value of F from the abscissa value C to the abscissa
value C/2 to yield the graph illustrated in Figure 3-2B. The graph
of F has been reduced, as required, below FS to satisfy the air
quality requirements.
I
An alternative to a constant emission control system such as
discussed above would be an SCS capable of changing the tail of the I
graph to F to reduce F* to values below F for C >_ C . Figure 3-2C
3-4 I
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A single source of S02 is responsible for observed
concentration levels;
Without an SCS, emissions are independent of meteoro-
logical conditions;
With an SCS, emissions are controlled according to rules
which depend on predicted meteorological conditions;
> Error in air quality prediction (as defined later) is
independent of meteorological conditions. (Section 4.3
discusses how this assumption can be relaxed.)
I
Consider the following definitions relevant to understanding
. the model:
c(x,t): concentration at time t and location x
C(t): max c(x_,t); maximum concentration over all x
locations at time t
| x; downwind location of C(t)
_ C : air quality standard
Q(t): emission rate without SCS
M(t): meteorological function relating the maximum concen-
tration C(t) to source emission rate Q(t) and which
| will include the effects of stack height, wind
conditions, mixing depths or any other pertinent
meteorological inputs
R(t): The error ratio of concentration prediction defined
as follows:
I
I
I
I
-------
I
With or without an operating SCS, the observed maximum
concentration CQ is related to the actual emission rate
Q through the meteorological function M as follows: I
I
CQ = 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:
C = Q ' M ' R at time t
From the above, the error ratio can be defined as
from the forecast concentration C .
The value of Q depends on the SCS control strategy being
C
The observed maximum concentration under SCS control is given by
C = Q ' M where 0_ is the SCS controlled emission rate determined
I
used. Two examples of possible control strategies are:
(1) Fuel Switching
i 4 4* f* ^ ^B
n - 4 P " T (Strategy 1)
yc ~ ^ 6Q if Cp > Y I
where 6 is a constant (less than one) which 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 I
quality levels attempted to be maintained.
3-8 I
I
-------
I
I (2) Process Curtailment
|
c
I
I
I
y/cp q if cp > y
(Strategy 2)
I In general, the threshold y 1^ set below standards to provide a
margin of safety.
I The functions Q, M, and R require more careful des-
_ cription. Q(t) can be a well defined quantity if emission monitors
* are used or if emission rate is simply related to the production
rate. 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 moni-
toring record, M(t) could be estimated from the ratios of measured
maximum concentrations C (t) and known emission rates Q(t), Where
| a shorter monitoring record exists with an extended meteorological
data bank, M could be the output of a statistical model; e.g., M =
a-jin.] + a2m2 + -- + anmn where m-| , m^, -- mn are meteorological
parameters such as stability or air mass characteristics and a-,, a
an are regression coefficients determined from the available
I air quality data. By knowing the distributions of the m. 's, the
statistical data of the shorter monitoring period can be combined
with the longer period meteorological distributions. This is
3-9
-------
I
frequently the case since meteorological data has been collected
at many locations by the National Weather Service for periods up
to a century. Finally, where little site monitoring data exists,
outputs from air pollution dispersion models can be used in con-
junction with the meteorological data to construct M. I
The function R(t) may be determined from historical
real-time monitoring and forecasting data. Since the function R
will depend upon the unique forecasting difficulties for each SCS
scheme, initial estimates of R must be made during the design and
initial testing of the SCS. The upgrading of an SCS as time 8
proceeds will involve periodic re-evaluations of this function.
Given the functions Q(t), M(t) and R(t) over an appro-
priate time period, frequency of occurrence distributions can be
readily derived for the various magnitudes of the observed or
estimated values of Q, M and R. Thus, the time history data are |
transformed into frequency of occurrence distributions. For purposes
of future estimations, the frequency of occurrence distributions
become expected probability density functions. I
When the frequency distributions for Q, M and R as defined
above are determined, they may be utilized to generate information |
useful in the reliability analysis and upgrading of an SCS. For _
example, it would be useful to generate the following information
(Section 4 presents several examples): I
1. The number of violations to be expected without and
with any SCS scheme. |
3-10 I
I
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I
2. The percentage of production lost if the SCS
I scheme is a load reduction program.
3. The percentage use of high and low sulfur fuel in
a fuel switching SCS program.
4. The dependence of the number of violations, pro-
duction lost and/or percentage use of high and low
I sulfur fuel upon the implementation threshold (y),
model calibration, meteorological forecasting skill,
I and/or the difference in sulfur content of the two
switching fuels.
3.3.2 A Mathematical Application of the Concept
I This sub-section presents a mathematical approach that
may be used to apply the concepts presented in Section 3.3.1.
Define PX as the probability density function for the
variable X. Then the probability of the variable X having a value
between a and b is
I
I
Px U)
m Assume that there exist probability density functions for M and
Q, and we wish to generate a frequency distribution for C when
I 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
| 3-11
I
-------
PC(C = A) = FPQ (Q = e) ' PM (M = A/e)
+ PQ (Q = 2e) ' PM ((M = A/2e) +
+ PQ (Q = ne) ' PM (M = A/ne) +-
or
A.
Pc (A) = P0 (c) ' PM
Jo
I
I
I
or, in the limit as Ae approaches 0
P (C = A) = | Pq (Q = 5) ' PM (M = A/c) d£
I
I
dc
Expressing the operator above by *,
WQ '
I
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 M
and Q. Therefore, the frequency distribution of ground-level
concentrations for an uncontrolled plant can be determined from 8
determinations of M and Q.
Once PC is known, the graphs corresponding to Figure |
3-1B can be displayed, and the probability of violating standards M
is directly known.
3-12 |
I
-------
I
Consider next the case when the SCS is operating.
I In this case C = Q ' M where subscript c denotes the functional
c c
value when the SCS is operating. Q is no longer independent of
\+
meteorology since the operation of the SCS depends on meteorolo-
gical forecasting.
P~ will, therefore, also be generally dependent upon
P., and will vary for different control strategies. For computer
solutions to the correlated integration, the dependence of these
I quantities upon each other can be readily simulated.
Assuming that the error ratio R is independent of M
I and of Q and given PR, P^., and PQ it is possible to use the control
strategy rules for determining Q to numerically evaluate P~ under
the SCS control.
I In this case C = M ' Q ' R. The value of Q is
determined in each case from the predicted value of concentration
I
I
C and from the strategy (e.g., strategy 1 or 2). From the resulting
I
distribution of Q , the value of PC is obtained from the equation
IP = P * P
KCc HQc KM
Note the parallel nature of this equation and the equation for Pp.
This means that the existing frequency distribution of
ground level concentrations 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.
3-13
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I
3.4 Isolating Component Error I
This section proposes a method for isolating the error induced _
by three of the major components of an SCS--meteorological fore-
casting, emission forecasting, and air quality modeling. The
individual errors can then be assessed and combined (e.g., by
utilizing the concepts presented in Section 3.3.2) to estimate I
the overall system reliability.
For the first part of this analysis, assume that emission
forecasting uncertainty is negligible. Given that assumption,
the method requires that the following three (maximum) concen-
tration values be recorded for each forecasting time during a period I
of several months or more of SCS operation:
t The model predicted concentration using predicted meteoro-
logical parameters. (This concentration value is the basis
of the SCS control action which will affect concentrations T
hours later.) |
The model predicted concentration using observed meteorolo-
gical parameters.
The maximum concentration recorded by the monitoring network.
The procedure combines the above recorded data in a way that I
isolates the error in air quality forecasting due to meteorological
forecasting uncertainty from the error due to model uncertainty.
Recall the formulation developed in Section 3.3.1 for ground
level concentration:
The observed maximum concentration is assumed to be C = Q ' M. I
3-14 I
I
I
-------
I
I The predicted maximum concentration is assumed to be C =
Q ' M ' R where the Error Ratio R is the ratio
" R = Cp/Co
I R is a function which contains contributions from all sources of
_ error and uncertainty which prevent a perfect air quality forecast
(C = C ). These sources of uncertainty arise from each component
I of the SOSmeteorological forecasting, emissions forecasting, and
air quality modeling. Consider the following formulation of R:
I
I
I
I
I
" Rq ' Rw ' "m
where R , R , and R^ are the error ratios for emissions prediction,
meteorological (weather) forecasting, and air quality modeling
respectively.
In the absence of emission source uncertainty,
= Rw
Define the following model predicted concentration values.
The predicted concentration using predicted meteorological para-
meters is given by:
Cp (Q,Mp) = Q ' Mp = Q ' M ' R.
3-15
-------
I
This concentration value is the basis of the SCS control action I
which will affect concentrations T hours later. The predicted
concentration using observed meteorological parameters is given by:
Cp (Q,M0) « Q ' MQ |
C is the maximum concentration recorded by the monitoring I
network.
I
Hence,
CP (Q."p) CP (Q.MQ)
"
I
That is, the error ratio R can be expressed as the product of «
two ratios. The first ratio is the quotient of two model predictions
using the same model, the same source emissions and different meteoro-
logy. It is an error ratio isolating the effect of meteorological
forecasting on the net error ratio, R. The second ratio is the |
quotient of two concentration values based on the observed source _
emissions and observed meteorological parameters. The numerator
is a model prediction, and the denominator is a monitored concen- I
tration value. It is an error ratio isolating the effects of model
accuracy on R. The first ratio satisfies the requirements for R I
w ^*
and the second ratio satisfies the description of Rm, so that _
w m K
3-16
.
I
-------
I
I
where
C_ (Q,M ) C (Q,M
I
I In practical operation of the SCS, C (Q,M ) will be computed
or determined at every forecast time and recorded. Then T hours
I
_ simple matter to determine the value C (Q,M ), using the observed
* meteorological parameters. If these three values are recorded at
later the value of C will be recorded. Simultaneously, it is a
every forecast time and every forecast verification time, the
ratios R , R , and R can be routinely computed.
| To consider the possibility of uncertainty in emissions
_ forecasting, define the following additional model predicted con-
* centration values. The predicted concentration using predicted
meteorological parameters and predicted source emissions is given
by:
Cp < W = Qp Mp = Q M R
* This concentration value is the basis of the SCS control action
which will affect concentrations T hours later. The predicted
concentration using predicted source emissions and observed
I meteorological parameters is given by:
| CP
I 3-17
I
-------
I
C (Q0»M0) is the predicted concentration using observed "
source emissions and observed meteorological parameters. I
It is clear that,
I
CP (VV
p p' o
CP
Cp(W
p o ' o
Co
= R
I
i
I
That is the error ratio R can be expressed as the product of three
ratios. Similar to the case with no source error, the first
and last ratios represents RW and Rm, respectively. The second
ratio is a quotient of concentration predictions using the same I
meteorological parameters and the same model but different source
emissions. It is an error ratio isolating the effects of source |
emission uncertainty and errors on the Error Ratio R.
The presence of source emission errors requires that four
concentration ratio values, RW, Rm, R and R be determined for I
each time. The distribution of R which is generated is available
for verification and upgrading of the SCS by means of the procedures |
described in Section 3.3 and applied in Section 4.
Finally, the distribution of the error ratio, R must be
determined for each SCS application. A preliminary estimate of the I
character of the ratio can be made from data collected from an
existing air quality monitoring/forecasting network (AIRMAP - |
operated by Environmental Research and Technology, Inc.). The AIRMAP _
network for the Boston area consists of S0? monitors which continu-
ously monitor and record air quality levels. Experienced forecasters
3-18
I
-------
I
I
predict 24-hour average concentration levels at each receptor
I for the time period beginning 12 hours after the time of the
_ forecast. A one year record of both observed concentrations and
predicted concentrations for each day of 1973 was available.
I Maximum predicted concentrations and maximum observed concentra-
tions were compared for each day to generate the distribution of
I R for this potential SCS network.
_ Figure 3-3A illustrates the resulting distribution of R for
* the Boston AIRMAP network. The median value of R is nearly 1.0
indicating no significant bias in prediction. Also, the frequency
of R values approaches zero as R approaches either zero or values
I much larger than 1.0. Figure 3-3B is the same distribution with
_ R represented on a logarithmic scale. The distribution is nearly
log-normally distributed. For the example analyses which follow
in Section 4, a log-normal distribution of R will be assumed.
It should be noted that the R distribution derived from the
I Boston AIRMAP system is for a metropolitan area and may not be
_ applicable to a region characterized by an isolated source.
However, it was the best available for the examples presented in
Section 4. The use of this specific R distribution in the example
applications is based on the assumption that one could predict air
I quality levels resulting from isolated source emissions with
accuracies comparable to those associated with predicting air quality
I
I
levels at specific receptors in a multiple source region.
3-19
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Error Ratio R (log scale)
(b)
Figure 3-3 Distribution of the Error Ratio R for the Boston AIRMAP Network I
1
3-20 _
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1
1
1
1
1
1
1
1
1
1
1
4. EXAMPLE RELIABILITY ANALYSIS
4.1 Test Case Conditions and Assumptions
The reliability analysis concepts presented i
have been applied* to several example hypothetical
control systems. The examples are designed to ill
utility of the analysis technique as well as to il
n Section 3
supplementary
ustrate the
lustrate the
dependence of the reliability of an SCS upon the various indepen-
dent parameters which influence SCS reliability.
The source data and the meteorological inputs
are appropriate
to an actual source. However, because we wish only to isolate and
illustrate the effect on reliability of changes in
the SCS structure,
the inputs have been simplified. Assumed input information is
given as follows:
The source is a single 828-ft. stack.
The meteorological data are based on a 5-year stability-wind
rose from a nearby airport. Estimates of
the frequency of
inversion conditions and of inversion break-up fumigations
are only approximate.
Terrain is essentially ignored except for
stability-wind rose.
From the source data and the meteorological i
its effect on the
nputs detailed
above, the Meteorology Function M and the Emissions Function Q can
be defined. At any time, the Meteorology Function
a Gaussian point-source dispersion model for unit
*Plans are underway to document, in the form of a
computer program that was utilized in the examples
section (see Preface).
4-1
is predicted by
S0? emissions.
user manual , the
presented in this
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The distribution of M is determined from the stability-wind rose.
The maximum downwind model prediction for each weather condition
is assigned the corresponding frequency from the stability-wind
rose and the frequency distribution of M is constructed. The
Emissions Function Q is assumed for these examples to be constant I
and equal to the full load emissions to simulate conditions in the
absence of an SCS. The frequency distribution of Q is, therefore,
very simple. The probability of full load is 1.0 and all other
values have probability zero.
Specification of the SCS is based upon several parameters. A I
range of values for each parameter is considered in the examples
below to represent a wide range of possible SCS operations. I
Two SCS types are examined: (1) a single option switch plan,
and (2) a continuous option plan. The single option plan is
representative of fuel switching. Implementation of the SCS reduces I
emissions by the fraction B in all cases. The continuous option
switch plan is representative of process curtailment. Implementation |
of the SCS reduces emissions by exactly that fraction necessary to m
bring the maximum ground level concentration below a prescribed
threshold. These two SCS types were chosen for study from an I
infinite set of SCS types which can be investigated by this pro-
bability analysis technique. |
The distribution of the Error Ratio R is assumed to be a log- .
normal distribution, well specified by a geometric mean value R
and by the standard deviation of the distribution a. I
4-2
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I The characteristics of the distributions for R were chosen
to be similar to the observed distribution of R described for
the AIRMAP network in Section 3.4. The log-normal shape and the
I width of each sample distribution are similar to those corres-
ponding to this distribution. Error Ratio will be carefully
specified for each example below.
As described in Section 3.4, the Error Ratio R can be expressed
as the product of three ratios, R , R , and R . The majority of
examples below consider the total function R without considering
the individual component contributions separately. However, for
I one set of examples, R = R ' R where both R and R have a
M significant probability of being different from 1.0. In this case,
the distributions of R and R are both considered.
I Each SCS, regardless of type, is assumed to have a switch
threshold. If the predicted value of the maximum ground-level
| concentration is projected to exceed the switch threshold, the
SCS emission reduction action is initiated. Obviously, the
highest acceptable switch threshold is the air quality standard.
I Because of uncertainty in air quality forecasts, the switch
threshold, y. is usually some fraction of the standard.
4.2 Dependence of SCS Reliability on Various Influencing Factors
I The following examples have been provided in order to isolate
the effect of changes in each of the pertinent variables which
I influence reliability. These variables include: R~, the geometric
mean of the error ratio R; a, the standard deviation of the error
4-3
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ratio distribution; y, the threshold value of the predicted maximum
concentration above which some operational process adjustment is
made; and e, the ratio of the sulfur content of the low sulfur fuel I
to the sulfur content of the high sulfur fuel used in a fuel
switch SCS. I
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 I
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 non-zero value of o »
results from the presence of unbiased errors in meteorological
forecasting, estimation of emissions, or modeling results. A I
reduction in a would be expected from any of the following system
improvements: |
Additional or improved meteorological data used in pre-
dieting the meteorological parameters which are input I
for air quality forecasts. Unless R is very near 1.0
or the system is operating near the predictability limit
for each parameter, some improvement through added
meteorological support is expected. Among the possible
improvements in meteorological support might be atmos-
pheric 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 para- _
meters. I
More experienced or more capable meteorological personnel.
Because personnel gain experience as the system is operate
the a of the system should become smaller with time.
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An improved model. As a forecasting model is updated
through system experience, a reduction in a is to be
expected.
t An improved emission schedule forecast system. This
I 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 4-1 summarizes the results of this example 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 vio-
lations 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
I 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
I 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
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4-5
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Table 4-1
Effects on SCS Reliability of Changing the Value of o for the
Error Ratio R
Each SCS plan below has the following parameter values:
Fuel switching fraction 3 = 0.25
Switching threshold y = 0.5
Geometric Mean of Error Ratio R = 1.0
Width of Error Ratio distribution a, is variable
SCS Control Strategy
NO SCS
SCS #1:
FUEL SWITCHING
o = 0.5
SCS #2:
FUEL SWITCHING
o = 0.4
SCS #3:
FUEL SWITCHING
a = 0.2
SCS #4:
PROCESS CURTAILMENT
o = 0.5
SCS #5:
PROCESS CURTAILMENT
a = 0.4
SCS #6:
PROCESS CURTAILMENT
o = 0.2
Total Frequency
of Violations
0.16432
0.06605
0.06291
0.04875
o.oa2!6
0.08216
0.08216
Fraction of Low
Cost Fuel
1.000
0.754
0.768
0.808
1.000
1.000
1.000
Fraction of
Time at Full
Production
1.000
1.000
1.000
1.000
0.918
0.948
0.961
4-6
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below standards. Therefore, improved accuracy of prediction
I (reduced a) results in fewer potential violations escaping control.
Since the switch threshold y - 0.5 ppm is exactly the standard, there
| is no conservatism in the process curtailment forecasts. Although
I improved forecast accuracy reduces the magnitude of violating
concentrations, 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 .25 to ,23 and finally to .19 of the total fuel used
J as forecasting accuracy is improved. Meanwhile, SCS reliability
_ is also improved. Note that full production is assumed to be
possible regardless of fuel type. For the process curtailment
cases, the percentage of full production is increased as forecast
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accuracy improves. Meanwhile, SCS reliability is maintained at the
same level .
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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 I
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 R^ = 1.0 by simply reducing each
forecast value by the required amount to bring the mean of past I
values to 1.0. It is generally desirable, however, to intention-
ally operate an SCS conservatively 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 m
meteorology and conservative plume rise are assumed.
Similarly, meteorological and emission predictions used for
air quality projections are often chosen to be "worst case" fore- |
casts. 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.
4-8
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I The example analysis which follows is designed to investi-
m gate the effect of changing R" on SCS reliability, leaving all
other SCS parameters unchanged. Table 4-2 includes the results
I of the operation of six hypothetical SCS schemes and the NO SCS
case.
| Again, each of the six SCS plans reduces the frequency of
f violations by a considerable amount. The increased conservatism
of air quality prediction, manifested in increased values of R",
I reduces 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 4-2. With R~
I = 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 ?
I The previous example 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
4-9
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Table 4-2
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
SCS Control Strategy
NO SCS
SCS #1:
FUEL SWITCHING
R = 1.0
SCS #7
FUEL SWITCHING
R = 1.5
SCS #8:
FUEL SWITCHING
R = 2.0
SCS #2:
PROCESS CURTAILMENT
R = 1.0
SCS #9:
PROCESS CURTAILMENT
R = 1.5
SCS #10:
PROCESS CURTAILMENT
R = 2.0
Total Frequency
of Violations
0.16432
0.06606
0.00876
0.00370
0.08194
0.01306
0.00000
Fraction of Low
Cost Fuel
1.000
0.754
0.521
0.413
1.000
1.000
1.000
Fraction of Full
Production
1.000
1.000
1.000
1.000
0.918
0.836
0.609
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I conservative predictions, this control technique compensates for
tendencies to underpredict since most underprediction errors will
result in "violations" of the threshold which are still below the
standard.
Table 4-3 displays the results of the example analysis for
six hypothetical SCS plans with switch thresholds of varying value.
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
I also evident. Similar to maintaining the value of R" greater than
1.0, a conservative switch threshold is a simple tool for improv-
ing SCS reliability; but an overall loss of plant efficiency is
a probable effect of the control strategy.
Example 4 - What is the effect on SCS reliability of changing the
I fuel switching fraction e ?
Although choice of a fuel switching fraction 3 is most likely
determined by the availability of fuel types, it is interesting to
I observe the effect of changing the value of 3. One can hypothetically
achieve any value of 3 by blending fuels of known sulfur content,
| but engineering problems prohibit this generality in most cases.
| 4-11
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TABLE 4-3
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 B = 0.25
Switching Threshold Y is variable
Geometric Mean of Error Ratio R = 1.0
Width of Error Ratio Distribution a = 0.5
i
SCS CONTROL
STRATEGY
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
TOTAL FREQUENCY
OF VIOLATIONS
0.16432
0.06606
0.03500
0.01562
0.08194
0.05641
0.02557
FRACTION OF
LOW COST FUEL
1.000
0.754
0.615
0.526
1.000
1.000
1.000
FRACTION OF
FULL PRODUCTION
1.000
1.000
1.000
1.000
0.918
0.873
0.801
4-12
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Three SCS plans with values of 3 of 0.25, 0.30, and 0.40,
respectively 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
I greater than necessary reduction in concentration is achieved.
Therefore, increasing the value of e toward 1.0 has no effect on
violation frequency for values of 6 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
B air quality can be expected from any one of many reliable SCS plans.
It is not possible to define which SCS is both reliable enough for
acceptance by control agencies and economically practical enough
for acceptance by plant operators. It is likely that some combination
of the preceding example SCS systems would be optimum for most
operations.
Furthermore, it is conceivable that an operating SCS will
require upgrading due to demands for more SCS reliability or due to
I demands for more cost effective operation by the plant management.
In this eventuality it is likely that some combination of the
I preceding SCS changes would be optimum for the particular operation.
| 4-13
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It is, therefore, important and interesting to observe the
effects of more than one parameter change on SCS reliability.
Table 4-4 includes six example SCS plans which observe the effects I
of changing the switch threshold -y and employing a conservative mean
value of the Error Ratio R. I
Comparing SCS number 7 and the three fuel switching plans in
Table 4-4, it is clear that increased conservatism yields successively
smaller increments of improvement in reliability until the SCS reaches
its limit of reliability under the fuel switching plan. For process
curtailment a comparison of SCS number 9 and the three plans included I
in Table 4-4 indicate a greater improvement in SCS reliability with m
decreasing value of the switch threshold. Values of y less than 0.3
are unnecessary since only a negligible frequency of violations is I
expected at a value of y = 0-3.
Note that SCS number 19 expects less than 0.1 violations per |
year and achieves more than 66% of full production. Considering no g
other complexities in evaluating SCS reliability, SCS number 19
accomplishes the most acceptable reliability with maximum plant B
production of all SCS plans considered in these examples.
Example 6 - How can emission error be incorporated into the analysis? |
Each of the example analyses considered so far in this section
considers the Error Ratio R to be some hypothetical log-normally *
distributed function. No attempt has been made to simulate the
effects of uncertainties in the individual components of the SCS.
The following example analysis will consider SCS schemes which have |
4-14
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TABLE 4-4
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 6 = 0.25
Switching Threshold T is variable
Geometric Mean of Error Ratio R = 1.5
Width of Error Ratio Distribution 0" = 0.5
SCS CONTROL
STRATEGY
No SCS
SCS #15:
Fuel Switching
Y = 0.4
SCS #16:
Fuel Switching
Y = 0.3
SCS #17:
Fuel Switching
Y = 0.2
SCS #18:
Process Curtailment
Y = 0.4
SCS #19:
Process Curtailment
Y - 0.3
SCS #20:
Process Curtailment
Y = 0.2
TOTAL FREQUENCY
OF VIOLATIONS
0.16432
0.00471
0.00370
0.00370
0.00353
0.00000
0.00000
FRACTION OF
LOW COST FUEL
1.000
0.450
0.395
0.372
1.000
1.000
1.000
FRACTION OF
FULL PRODUCTION
1.000
1.000
1.000
1.000
0.784
0.664
0.572
4-15
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meteorological error distributed like the Error Ratios of the
preceding examples, but which also have emission errors. According
to the discussion in Section 3, I
R = Rw ' RQ ' RM
For these examples, we assume R = 1.0, therefore
R = RW ' RQ
I
We will assume that RW has a log-normal distribution with RW =
1.0 and a = 0.5. Furthermore, we will assume that
V^ '
I
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, g
QD *
W Hi
It is reasonable to expect that ^ has either a normal or a
0 ^1
"top-hat" distribution. The example below considers both of '
those possibilities. The hypothesized distributions for RW and RQ
are combined to form a distribution for R. Figure 4-1 illustrates
CIP
the three distributions of *- used. They are designated as Q
functions 1, 2 and 3.
4-16
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Q FUNCTION #1
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x
X
y
V
/
/
s
^
0
Normal Distribution
\
\
a
\
\
=0.2
V
^
«te
Q FUNCTION #2
0.6 07 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5
Q
1
1
1
1
1
1
1
Q
Normal Distribution
3cr=0.2
Q FUNCTION #3
06 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5
Q
"TOP
-hat"
Q
Distn
'buffo
n
0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5
Q
Figure 4-1 Three Frequency Distributions of the Ratio Q / 0
^p c
4-17
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Table 4-5 summarizes the results of the analysis using the
combined Error Ratios. The frequency of violations for all six
example 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 B
distribution is reduced. The "top-hat" emission error distribution is
associated with a reliability intermediate between the two normally
distributed emission error functions. «
4.3 Further Applications of the Probability Analysis of SCS Reliability
It is likely that in many applications the Error Ratio R will
not be independent of the meteorology function M. If conditions of
very predictable strong winds are responsible for many high S02 |
levels, for example, it would be incorrect to use an Error Ratio R _
derived from more difficult to predict light wind cases. A different
Error Ratio for each of several meteorological categories is likely.
The probability analysis should be performed separately for each
category; then the resulting frequency distributions can be added I
together.
It is also possible that several process curtailment actions
are available for use but that a continuous option plant is not
practical. This would be the case for an operation with integral
units which can be either shut down or operated at full capacity.
Such an SCS is easily investigated by the probability analysis.
Generally, SCS plans would have M functions which are not
independent of the Q functions. The principal cause of this
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TABLE 4-5
INCORPORATION OF EMISSIONS ERROR INTO
THE RELIABILITY ANALYSIS
Each SCS plan below has the following parameter values:
Fuel Switching Fraction 0 = 0.25
Switching Threshold y = 0.5
Geometric Mean of Error Ratio R~ = 1.0
Width of Error Ratio a = 0.5
1
1
1
1
1
1
V
1
1
SCS CONTROL
STRATEGY
No SCS
SCS #21:
Fuel Switching
Q Error 1
SCS #22:
Fuel Switching
Q Error 2
SCS #23:
Fuel Switching
Q Error 3
SCS #24:
Process Curtailment
Q Error 1
SCS #25:
Process Curtailment
Q Error 2
SCS #26:
Process Curtailment
Q Error 3
TOTAL FREQUENCY
OF VIOLATIONS
0.16432
0.07079
0.06837
0.06943
0.08582
0.08397
0.08523
FRACTION OF
LOW COST FUEL
1.000
0.765
0.764
0.766
1.000
1.000
1.000
FRACTION OF
FULL PRODUCTION
1.000
1.000
1.000
1.000
0.920
0.921
0.921
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dependence is plume rise which is determined by both wind and _
stability (meteorology) and by heat flux through the stack *
(emissions). The probability analysis would require modifications 8
to handle this interdependence of M and Q. For a given emission
source this would require the specification of different M functions |
(incorporating the effects of differences in plume rise) for each _
significantly different source emission rate category.
For the examples in this Section, heat flux through the stack tt
has been assumed to be fairly constant regardless of load. It is
instructive to investigate in some detail the effect that changes |
in emission rate can have on ground-level concentration.
For a 36 day period in March and April of 1971, S0» emission
rates, flue gas rates, and exit temperatures were compared for the
828-ft example stack. Exit temperatures are very constant, and flue
gas rates are not a strong function of emission rate. A linear I
regression analysis to relate heat flux and emission rate for the
stacks indicates that heat flux is reduced by just 8.0% when
emissions are reduced by 50%. Many processes contribute effluent
to the stack and effluent characteristics vary according to the
stage of each process.
For power plants, on the other hand, the volumetric flow rate is
a strong function of emission rate. Since exit temperatures vary by I
only about 10% over the range of possible power plant loads, heat flux
is also strongly related to emission rate. In fact, the heat flux is
nearly proportional to emission rate over the range of possible loads. I
4-20
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Assuming the plume rise formulation of Briggs (1969), the
effect of changing emission rates on maximum ground-level concen-
trations can be assessed. Using a standard Gaussian diffusion model,
I maximum short-term concentrations were compared for the example plant
under full load and half load conditions. An 8.0% reduction in heat
flux was assumed. Under each weather condition, the maximum concentra-
tions under half load conditions was no more than 53% and no less than
50% of the concentrations under full load conditions. A linear "roll-
| back" of concentrations with emissions seems appropriate in this case.
m For a typical power plant, a 50% reduction in heat flux is expected
to accompany a 50% reduction in emissions of S02. Under each weather
I condition, the maximum concentration predicted by the diffusion model
under half load conditions was no more than 81% but no less than 61%
I of concentrations under full load conditions. Csanady (1973) developed
M a generalized technique of comparing emission reduction with maximum
concentration reduction when heat rate is linearly related to emission
I rate. The hypotheses of the technique are most applicable to a point
source under unstable atmospheric conditions. Figure 4-2 illustrates
| the result of this technique when heat rate is assumed proportional to
_ emission rate. Maximum concentrations under half load conditions are
expected to be 63% of concentrations under full load conditions. The
effect of other fractional load reductions can be estimated from
Figure 4-2. Clearly a linear roll-back of concentrations with emissions
| is not valid in this case.
4-21
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c 1.8
g
? 1.6
c
CD
u 1.4
o
0 1.2
CD
o> 1.0
TJ
§ 0.8
o
C9 n c
0.6
E
1 °'4
X
o
S 0.2
0
Figure 4-2
y
1
/
/
-oad
/
'
Red
/
uctio
'
n
/
LOQ(
i Inc
/
^
reast
/
1
1
1
1
1
1
1
1
1
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
1
Effects of Emission Reduction on Maximum Ground Level
Concentrations when Heat Rate through the Stack is
Proportional to Emission Rate
1
1
4-22
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5. REFERENCES
1. Smith, M.(editor), "Recommended Guide for the Prediction of the
Dispersion of Airborne Effluents," Second Edition, American Society
of Mechanical Engineers, New York, N.Y. (1973).
2. Anderson, G.E., "Mesoscale Influences on Wind Fields," Journal of
Applied Meteorology, Vol. 10, pp. 377-381 (1971).
3. Slade, David (editor), "Meteorology and Atomic Energy," Atomic
Energy Commission (1968).
4. Briggs, G.A., "Plume Rise," Critical Review Series (TID-25075),
Atomic Energy Commission, Division of Technical Information, Oak
Ridge, Tennessee (November 1969).
5. Csanady, G.T., "Effect of Plume Rise on Ground Level Pollution,"
Atmospheric Environment, Vol. 7, pp. 1-16 (1973).
6. Forrest, J., and L. Newman, "Ambient Air Monitoring for Sulfur
Compounds," Journal of Air Pollution Control Association, Vol. 23,
No. 9, pp. 761-768 (1973).
7. Montgomery, T.L., et. al., "Controlling Ambient SO " Journal of
Metals, pp. 35-41, (June 1973). ^
8. Peters, M., "Report of Investigation at American Smelting and
Refining Company, El Paso, Texas," Air Pollution Control Services,
(1971).
9. Shepard, D.S., "A Load Shifting Model for Air Pollution Control
in the Electric Power Industry," Journal of Air Pollution Control
Association, Vol. 20, No. 11, pp. 756-761 (1970).
10. TVA Press Release (June 24, 1973).
ll. U.S. Environmental Protection Agency, "Guidelines for Enforcement
and Surveillance of Supplementary Control Systems," Volumes 1 and 2,
EPA-340/1-75-008, U.S. Environmental Protection Agency, Washington,
D.C. (September 1975).
12. U.S. Environmental Protection Agency, "Guidance for Specifying
Primary Standard Conditions under ESECA," OAQPS No. 1.2-035, U.S.
Environmental Protection Agency, Research Triangle Park, N.C.
(October 1975).
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13. U.S. Environmental Protection Agency, "Guidelines for Evaluating M
Supplementary Control Systems," EPA-450/2-76-003, OAQPS No. 1.2-036,
U.S. Environmental Protection Agency, Research Triangle Park, N.C.
February 1976).
14. U.S. Environmental Protection Agency, "Legal Interpretation and
Guideline to Implementation of Recent Court Decisions on the Subject
of Stack Height Increase as a Means of Meeting Federal Ambient Air
Quality Standards," Federal Register, Vol. 41, No. 33, pp. 7450-
7452, (February 18, 1976).
15. U.S. Environmental Protection Agency, "Reviewing New Stationary |
Sources," Guidelines for Air Quality Maintenance Planning and
Analysis, Volume 10 (in preparation), OAQPS No. 1.2-029, U.S.
Environmental Protection Agency, Research Triangle Park, N.C.
(1976a).
16. U.S. Environmental Protection Agency, "Guidance for Air Quality
Monitoring in the Vicinity of Large Point Sources," (in preparation) |
OAQPS No. 1.2-012, Supplement B, U.S. Environmental Protection
Agency, Research Triangle Park, N.C. (1976b). «
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