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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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3
4
5
6
7
ft
9
10
11
12
13
Itt
15
16
17
IS
19
20
21
22
23
21
25
«INO DIRECTION
9
ft
11
12
10
7
t>
1)
2
5
3
14
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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
 I
I
I
                                        2-15

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                                                                              I
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.
                             2-16                                             I

                                                                              I

                                                                              I

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 I

 *               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
I
I
I
2-17

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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-
                                                                                I
                                                                                9
                                                                                ^

where C is the pollutant concentration at height,  z
                                                                                I
        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             ™
                             2-18                                               I

                                                                                I

                                                                                I

-------
I
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

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 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

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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

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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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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

                                                                              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

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                                                                                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

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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

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                                                                               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

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     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 SOS—meteorological  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

-------
V. \*J
Oi n
.IU
o
c
O)
CD
L-
u.
0.05








i_r






0.2 0.4





L_


0.6



••••
«••



_n



08 0



~i n
L_

i





f^™™i
l-Tl^r-H
1






~» —







1
1
1
1
1
. 1
.2 1.4 1.6 1.8 2.0 2.2 2.4
Error Ratio R *
0.15

0.10
o
c
CD
CT
CD
Ul
0.05

f















Lr
0. 0.2























•«••





u
1
L









0.5



(a)


P
J













i



in
'l
1

k























1
1
1

1

1
1
.0 2.0 5.0 10.0 20.0 I
Error Ratio R (log scale) •

(b)
Figure 3-3 Distribution of the Error Ratio R for the Boston AIRMAP Network I















1
3-20 _
1

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1
1
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




-------
                                                                             I
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
                                                                            I
                                                                            I

-------
I
I

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
I

-------
                                                                                I
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.
                                                                               I

                                                                               I

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 I

 •               •   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
I
I
I
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

-------
I

          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
I
I
I
I
I
         accuracy improves.  Meanwhile, SCS reliability is maintained at the
         same  level .


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                                                                              I
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
                                                                             I
                                                                             I

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1

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
 I
 I

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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
  I
  I
  I
  I

  I
  I
 I
 I
 I
 I
 I
 I
 I
 I
 I
I
I
                           4-10

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1
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

I

I

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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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                                                                           I
     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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                                                                            I
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
                                                                           I

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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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                                                                          I
     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              •
                                4-18
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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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                                    4-19

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                                                                        I
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 •
1
1

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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).
                              5-1

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                                                                            I
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).                          «
                              5-2
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