EPA-450/3-74-022-a
July 1973
[WEIGHTED SENSITIVITY ANALYSIS
OF EMISSIONS DATA:
VOLUME I -
BACKGROUND AND THEORY
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Water Programs
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
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EPA-450/3-74-022-a
WEIGHTED SENSITIVITY ANALYSIS
OF EMISSIONS DATA:
VOLUME I -
BACKGROUND AND THEORY
by
F. H. Ditto, L. T. Gutierrez,
T . H . Lewis, and L . J . Rushbrook
IBM Corporation
18100 Frederick Pike
Gaithersburg, Maryland 20760
Contract No. 68-01-0398
EPA Project Officer: John Bosch
Prepared for
ENVRIONMENTAL PROTECTION AGENCY
Office of Air and Water Programs
Office of Air Quality Planning and Standards
Research Triangle Park, N. C. 27711
July 1973
&.
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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, Environ-
mental Protection Agency, Research Triangle Park, North Carolina 27711, or from
the National Technical Information Service 5285 Port Royal Road, Springfield,
Virginia 22151.
This report was furnished to the Envrionmental Protection Agency bv the IBM Corpo-
ration, Gaithersburg, Maryland 20760, in fulfillment of Contract No. 68-01-0398.
The contents of this report are reproduced herein as received from the IBM Corpora-
tion. The opinions, findings, and conclusions expressed are those of the author and
not necessarily those of the Environmental Protection Agency. Mention of company
or product names is not to be considered as an endorsement by the Environmental
Protection Agency. .
Publication No. EPA~450/3-74-022-a
11
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WEIGHTED SENSITIVITY ANALYSIS OF EMISSIONS DATA
CONTENTS
PAGE
SECTION I - INTROUCTION
Project Background 1-1
Project Objectives 1-3
Summary of Results 1-4
SECTION II - GENERAL ANALYSIS
Hierarchial Structure of Emissions Data 2-1
Weighted Sensitivity Analysis 2-14
Confidence Level for The Emissions Inventory 2-31
SECTION III - NUMERICAL ANALYSES
Analysis of the Standard Tree 3-1
Analysis of Alternative Trees 3-18
SECTION IV - WEIGHTED SENSITIVITY ANALYSIS PROGRAM (WSAP)
Program Abstract And Run Description 4-2
Flow Charts 4-15
Input-Output Description 4-23
Test Data 4-27
Operating Instructions 4-28
Suggestions, Warnings and Changes 4-30
Program Listing 4-31
Appendix IV-A - Driver Table 4-32
Appendix IV-B -- Label Table 4-37
111
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PAGE
SECTION V - CONCLUSIONS 5-1
REFERENCES
APPENDIX A - THEORETICAL ANALYSIS
APPENDIX B - NUMERICAL ANALYSES OF THE NATIONWIDE EMISSION REPORTS
APPENDIX C - APPLIED ANALYSIS FOR THE VIRGINIA STATE CAPITAL AQCR
APPENDIX D - WSAP USERS MANUAL (UNDER SEPARATE COVER)
APPENDIX E - USAP2 PROGRAM DOCUMENTATION
APPENDIX F - SCCS PROGRAM DESCRIPTION
IV
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TABLES
PAGE
2.1 VALUES OF & FOR SELECTED PAIRS (A,1-C) 2-33
3.1 WEIGHTED SENSITIVITY ANALYSIS OF OHIO STATE 3-2
EMISSIONS REPORT WITH 6=5%
3.2 WEIGHTED SENSITIVITY ANALYSIS (av) OF POINT 3-20
K
FUEL COMBUSTION SUBTREES RESTRUCTURED BY
CLASSES OF FUELS
CHARTS
005 WSAP OVERALL SYSTEM FLOW 4-14
006 GENERAL PROGRAM FLOW - WEIGHTED SENSITIVITY 4-15
ANALYSIS PROGRAM
FIGURES
2.1 NEDS DATA IN TABULAR FORMAT 2-2
2.2 NEDS SOURCE CATEGORIES IN TREE FORMAT 2-7
2.3 NEDS DATA IN TREE FORMAT 2-20
2.4 RELATIONSHIP BETWEEN (T v AND Q V/Q 2-27
K K
3.1 FUEL COMBUSTION SUBTREES RESTRUCTURED BY 3-19
CLASSES OF FUELS
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PREFACE
The project described in this report was performed under the
auspices of the Environmental Protection Agency in conformance with
Task Order No. 1, BOA68-01-0398.
The work performed as the Weighted Sensitivity Analysis of
Emissions Data project proceeded with unusual effectiveness because
of the excellent support provided by the Technical Project Monitor,
Mr. John Bosch, and his associates. During the course of the project,
Mr. Bosch gave much valuable assistance and guidance which led to the
timely and successful completion of the project. Because of these
efforts, it was possible to develop additional programs beyond those
originally contemplated. The support of Mr. Gerald Nehls to provide
basic and test data from the NEDS data was greatly appreciated and
directly contributed to the capability to extend the study to include
the SCC summarization program.
VII
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WEIGHTED SENSITIVITY ANALYSIS (WSA) OF EMISSION INVENTORIES
The IBM contractual report on weighted sensitivity analysis
(WSA) allows users to Quantitatively analyze the effects of potential
inaccuracies in their air pollution source/emissions inventories.
This enables the user to quantify the amount and direction of future
resources he must allocate to maintain a piven accuracy for his
entire emissions inventory. The WSA is one of a series of manage-
ment tools provided by EPA to effectively interpret emission and
source inventories of air pollutant emitters.
WSA is based on the format used and data contained in the
National Emissions Data System (NEDS), the official air pollution
data base used by EPA. Because a number of States are patterning
their emission inventories according to NEDS, the WSA with subse-
quent modifications is also expected to be useful to non-EPA users,
especially to the pollution control agencies using the Comprehensive
Data Handling System (CHDS).
The primary objective of WSA is to calculate the maximum allowable
variation in emissions for each of the component sub-categories of
the emission inventory. This is accomplished by the user first
specifying an acceptable error in the total emissions of any
criteria pollutant for the geographical area of interest (County,
AQCR, State, U. S.). (This is referred to as 8 in the WSA report.)
Vlll
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USA then applies standard statistical techniques to the NEDS inven-
tory for that geographical area and delivers an "allowable" error
for over 100 sub-categories comprising all components of the emission
inventory.
WSA calculates the maximum variance in emissions for each sub-
category in order to maintain the previouslyspecified error for the
total inventory. It must be emphasized that WSA does not estimate the
actual or existing emission errors for each sub-category: this can only
be accomnlished by accessing the rew data files of NEDS and estimating
the errors due to emission calculations on an individual point and
area source basis. An EPA contract is currently underway to perform
this function (Source Inventory and Emission Factor Analysis; SIEFA)
which will be complementary with WSA and will provide users with an
integrated system for error analysis.
:"-our major assumptions were required for the successful development
of WSA;
1. The "on-paper" inventory represents the "real-world" emissions.
The necessity of this assumption is apparent: analysis of any data base
presupposes that that data base is correct. Any analytical tool becomes
more useful to users as the data which it utilizes become more complete.
2. The allowable errors calculated for each sub-category are
assumed to be independent of each other. This assumption was necessary
> develop -he WSA analysis and is justified because any error
interdeperdencies between sub-categories (e.g. population biases) are
IX
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considered to be minor compared to the numerous other causes of
emission errors for a given sub-category. It should be noted that
the sub-category errors are considered to be independent and not the
sub-category emissions.
3. Sub-category errors are considered to be random in nature.
It is felt that this assumption is, in general, a valid one and USA
was designed with this definition. As described in the WSA report,
however, there is a capability to "fix" sub-category errors when
known by the user. In this manner, biased or random errors for an
individual sub-category can be inserted into WSA whenever they are
available. (In such cases, WSA recalculates allowable errors for the
remaining sub-categories.)
4. WSA assumes that the distribution of component errors is
unknown. This provides for a conservative estimate of the confidence
limits to be attached to the 0's (defined in the WSA report as overall
errors). There are no known means of estimating the distribution of
emission inventory errors although SIEFA will eventually provide such
a mechanism; thus the assumption of a normal error distribution seems
inappropriate at this time.
It must be emphasized that in analyzing a small subset of
inventory data the user should reevaluate the validity of the above
WSA assumptions for his project before relying on the technique.
John C. Bosch
EPA Project Officer
NADB/OAQPS/OAWM/EPA
Research Triangle Park, N. C. 27711
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Section I
INTRODUCTION
This final report documents the work performed under contract
BOA 68-01-0398, "Weighted Sensitivity Analysis of Emissions Data".
It presents a body of analytical techniques appropriate for determining
accuracy requirements of component parts of an emissions inventory so
as to insure (at a given confidence level) an overall acceptable accuracy
in the total inventory. Selected numerical analyses are presented to
illustrate application of the techniques to Nationwide Emissions Report
(NER) data at different levels of aggregation. Contract work included
development of the necessary software to implement the results of the
analysis. The results are believed to constitute a significant step in
the development of techniques for making reliable forecasts of air
pollutant emissions, and have already been applied for such purposes
to emissions in region 5 of the State of Virginia. A report on that
application i& also included in the present document.
PROJECT BACKGROUND
In 1969, NAPCA established a project called "Projected Growth Data
for the Air Quality Control Regions"; in support of this project the
U.S. Department of Commerce, Office of Business Economics (OBE) , prepared
the document, "Economic Projections for Air Quality Control Regions,"
CFB195805) in June 1970, in ample time to support the nationwide preparation
of state air quality control implementation plans.
1-1
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The preparation of these projections entailed the application of
sophisticated techniques by expert econometricians and the utilization
of esoteric methodologies by specialists in the Regional Economics
Division of QBE.
Although these projections were the best possible, there was no way
of predetermining their accuracy or relating economic projection errors
to predicted air pollutant emission errors. On the basis of the QBE
report's nationwide projections to 1970, the error in projected gross
national product was just under 6%, the error in the projected population
was 0.75%. The significance of these errors with respect to projected
emissions is unkown.
The National Source Inventory Section of EPA processes and publishes
data on point and area source emissions of air pollutants, and is respon-
sible for determining the quality of the data used. The emissions inventory
is a basic requirement of states' implementation plans and provides EPA
with a valuable management tool in the decision-making process associated
with the administration of air pollution control activity. It is no
longer satisfactory _to merely provide an inventory; it i£ necessary to
quantitati vely state in statistical terms error existent in^ a_ specified
inventory. This being the case, the National Source Inventory Section
actively sought development of statistical methodology to establish the
quality of emissions data.
The methods of weighted sensitivity analysis were chosen as the
most flexible approach to develop the necessary techniques, and the
Federal Systems Center of IBM Corporation was engaged to perform the
necessary theoretical and numerical analyses, as well as to develop the
necessary software and its documentation.
1-2
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PROJECT OBJECTIVES
It is appropriate to summarize at the outset the objectives sought
in undertaking the project, as mutually agreed upon between EPA and IBM.
The goals to be achieved in the project, as stated in the work scope,
were as follows:
1. Analysis
In this activity, a methodology is to be formally derived
whereby accuracy requirements of component parts of an emission
inventory can be calculated so as to insure an overall acceptable
accuracy in the total inventory. The techniques of weighted
sensitivity analysis are to be applied in the performance of this
task.
2. Program Development
In this activity, a FORTRAN computer program for weighted sensi-
tivity analysis is to be designed, coded, tested and debugged.
The resulting software will provide a means to evaluate the
maximum permissible errors in emissions data with sufficient
flexibility to be applicable to both source categories and
geographical areas, for a given maximum permissible error of
the nationwide inventory. Complete compatibility with NEDS will
be assured.
3. Numerical Validation
In order to demonstrate the adequacy of the analysis and the
usage of the computer program, three sample analyses shall be
oerformed (using 1970 nationwide emissions data) to indicate
the maximum error in source categories and subcategories (nation-
wide) for three different nationwide inventory maximum errors to
be provided by EPA.
1-3
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SUMMARY OF RESULTS
Project objectives and requirements as set forth above have been
fully achieved. Furthermore, significant developments in both analysis
and programming beyond the original goals have been accomplished. A
summary of the addtional results obtained is as follows:
1. Refinement of the theoretical weighted sensitivity analysis to
distribute both percentage and physical errors in emissions
according to their respective weightings.
2. Extension of the analysis to cover the case where one or more
of the error components in a given level are to be fixed by the
analyst.
3. Modification and/or extension of the software to implement
developments 1 and 2 as part of the deliverable program.
4. Parameterization of the software to allow the analyst to apply
the program to alternative hierarchial configurations of the
emissions data.
5, Extension of the software to permit application of the weighted
sensitivity analysis to emissions data at the SCC level of
aggregation.
6. Preparation of a comprehensive set of numerical analyses to
demonstrate applicability of the technique and adequacy of the
computer program. Numerical analyses were conducted for different
areas (e.g., county, state, AQCR, U.S.), for different emissions
data configurations (e.g., point and area fuel combustion emissions
restructured by fuel usage).
7. Consolidated application of weighted sensitivity analysis
techniques and Chebyshev's inequality to establish confidence
levels for emission inventories.
1-4
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Section II
GENERAL ANALYSIS
The section presents the techniques developed for weighted sensi-
tivity analysis and its application to emissions data as contained in
the National Emissions Data System (NEDS) reports. The presentation
will be focused on the application of the analytical technique to emissions
data, rather than the theoretical development of the technique itself.
The reader interested in the latter is referred to Appendix A for a full
discussion of the theoretical analysis. An annotated numerical example
is also included in this section, to provide insight on how the propagation
of random error throughout the inventory is accounted for in the application
of the weighted error formulae.
HTE8ARCHIAL STRUCTURE OF EMISSIONS DATA
The reports of the National Emissions Data System (NEDS) constitute
the primary source of data for this project. In fact, the weighted
sensitivity analysis technique introduced below was specifically developed
for the treatment of random error in these sets of data, although it can
also be applied to any other set of data processing the same properties.
Figure 2.1 displays a sample nationwide emissions report from NEDS.
Emissions as of April 19, 1973, are listed by source categories for five
classes of air pollutants: particulates, sulfur oxides, nitrogen oxides,
hydrocarbons and carbon monoxide. The source categorization is uniform
for other area reports, i.e., county, AQCR, and state emissions reports.
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From the viewpoint of analysis, the most important property of
these sets of data is their hierarchial nature. In fact, the tabular
source categorization of the NEDS reports can be best understood if its hier-
archial structure is explicitly recognized. This can be effectively done
by converting the tabular format of Figure 2.1 to a tree format, as shown
in Figure 2-2. Taking the grand total of the very bottom of the table in
Figure 2.1 as the starting point or highest level, the tree unfolds back
hierarchially through four and sometimes five successively lower levels
of aggregation, the lowest level being the elementary emissions data
for each segment of the tree.
The tree format of Figure 2.2 provides a convenient, systematic
representation of an emissions inventory for analysis purposes. Each
node of the tree, together with the branches coming out of it, constitutes
a level of error propagation in the inventory. Therefore, the weighted
sensitivity analysis must be applied hierarchially, starting with the
allowable error for the grand total (i.e., the overall allowable error),
so as to compute allowable errors for each one of the branches which, if
satisfied, insure that the overall allowable error is not exceeded.
Figure 2.2 displays the tree of source nodes and branches, numerically
annotated to facilitate the discussion. Thus, for example, node 1.1 (fuel
combustion-point) has two branches denoted as 1.1.1 and 1.1.2 (external
combustion and internal combustion, respectively). The emission quantity
(in tons/year) associated with each branch throughout the tree is of course
read from the appropriate total, subtotal or elementary data item in the
NEDS table of Figure 2.1. This is illustrated in Figure 2.3, which displays
a segment of the tree with the actual particulate emission quantities for
each branch. For example, 3416197 tons/year of particualte emissions is
shown as originating from electricity generation through external fuel
2-6.1
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1. Point Sources
Grand Total
2. Area Sources
Figure 2.2 NEDS source categories in tree format
2-7
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combustion at point sources. Observe that the summation of the emissions
associated with their node. This relationship will be the basis for the
weightings to be used below in computing allowable errors for each branch
of the tree.
WEIGHTED SENSITIVITY ANALYSIS
In this project, the mathematics of sensitivity analysis were directed
to the development of accuracy requirements for the component parts of an
emissions inventory such that a given accuracy requirement for the overall
inventory is satisfied. The objective of sensitivity analysis is to deter-
mine the effect (changes) on some measure of performance due to changes in
each component that makes up the measure of performance. In the simplest
case the measure of performance is the sum of component measures. In the
case of an emissions inventory, it was shown above that the total emissions
for a given source class is always equal to the sum of the emissions from
the source subclasses in that class. Furthermore, since each one of these
emissions have been independently measured, it follows that the overall
squared error for the source class is a linear function of the squared
errors of the source subclasses.
This analysis is based on statistical linear models and their appli-
cation to represent propagation of error in sets of data (References 1,2,5).
For clarity of presentation, the discussion in this subsection will be
focused on the main analytical results, their statistical interpretation,
and their practical implications. Detailed mathematical derivations of
all formulae are given in Appendix A.
2-19
-------
Fuel Combustion
Point Sources
13624732
5073194
Industrial Processes
8410250
Solid Waste Disposal
141280
Other
8
Grand Total
17132475
Fuel Combustion
Area Sources
3507743
1952109
Solid Waste Disposal
617275
Transporta tion
718081
Miscellaneous
220278
Figure 2.3 NEDS data in tree format
2-20
-------
Electric Generation
3416197
Industrial Fuel
1562142
External Combustion,
5070238
,Comm-Inst. Fuel
89158
iOther
2741
Fuel
Combustion (Point)
5073194
Electric Generation
1151
Industrial Fuel
1429
Internal Combustion
Comm-Inst Fuel
29056
53
.Engine Testing
323
Other
0
Figure 2.3 (cont.)
2-21
-------
Anthracite Coax
19246
Bituminous Coal
3314900
Lignite
27872
Residual Oil
27500
Electric
Generation (Point)
3416197
Distillate Oil
3519
Natural Gas
20348
Process Gas
46
Coke
Bagasse
Solid Waste/Coal
240
Figure 2.3 (cont.)
2-22
Other
2527
-------
The basic theoretical development proceeds as follows. The
linear model
(1)
where
Q£ = air pollutant produced by source subclass K
100 (F~^ = percentage error associated with Q
/v
Q =2.%
Kil
100 O = percentage error associated with Q
N = number of subclasses in the source class
is postulated as an appropriate model to analyze propogation of error
throughout the emissions inventory, for hte reasons stated above. For
example, with reference to the external combustion node of Figure 2.3,
we would have
QTL = 3416197 tons/yr.
Q2 = 1562142 tons/yr.
Q3 = 89158 tons/yr.
Q, = 2741 tons/yr.
^ *
Q = T Qv = 5070238 tons/yr.
/ R
K-i
2-23
-------
Dividing both sides of equation (1) by Q &
(2)
The objective of this analysis is to obtain &£ for each class k
according to some value of Q (error in total) . As a first approxi-
mation we can assume that each term in Equation (2) contributes the
same amount to the total.
/V
(3)
whence
e
where N is the number of source classes.
As a second approximation, the analysis can be modified to recognize
the fact that each source class k contributes to the total error an
amount proportional to its relative physical contribution to the total
pollutant emission Q, as given by the ratio QK/Q. Analytically, it is
only necessary to note that
2-24
-------
Q
Therefore, from equation (2):
K-l
(5)
Equating both sides of ea. (5) term-by-term is equivalent to assuming
that each term contributes to the total an amount proportional to
(6)
whence
-------
either by changing O or by regrouping the source classes, which changes
Q/QK . The latter method is particularly useful in that it allows modifi-
cation of 0~K without changing & . A useful policy for regrouping the
source classes is to assemble the classes with the smallest emissions into
one or more classes; however, this policy should be applied with some
discretion in order to have groups or classes that can be successfully
forecast.
In order to illustrate the application of the technique, let £? *
5% for the external combustion node of Figure 2.3. The allowable errors
for the component branches as computed from equation (7) are as follows:
5070238
5 37.70%
89158
, I/ 5070238
(f =5/ 215.04%
' 2741
2-26
-------
100
70
60
50
30
20
10
O =5 '>e
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 O.R 0.9 0.10
QK/Q
RELATIONSHIP BETWEEN &* AND 0/0
K kK
Figure 2.4
2-27
-------
The allowable errors in physical units are:
-+ 208046.39 tons/year
-+ 140748.99 tons/year
0"~3&3 - + 33612.56 tons/year
=+ 5894.24 tons/year
The analysis demonstrates that, to obtain a known level of precision
in the total emissions for a source class, not all source subclasses need
to be measured with the same precision. Furthermore, the analysis shows
that the probable error of the sum of emissions is less than the sum of the
probable error of the component emissions. In fact, it is the square root
of the weighted sum of the squared probable errors of the components, as
can be readily observed by solving equation (1) for $ to obtain
K-i
(8)
Figure 2.4 displays the resulting relationship between 3£ and Q^/Q
in graphic form. When Q is a very small fraction of Q, the allowable
K.
value of Gjv is much larger than the allowable overall error Q ,
increasing exponentially as Q^/Q approaches zero. On the other hand,
approaches O asymptotically as Q^/Q approaches one. In general,
2-28
-------
C7< £ £> » k = 1,.., N, with the equality sign holding only in the
limiting case where there is only a single source subclass. Naturally,
if there is a single source subclass, QK = Q and 0~^ must be equal to
(5 if the latter is to be satisfied. Otherwise, the component emission
errors 0]<. will be allowed to have values greater than the overall
emission error O . With respect to Figure 2.4, it is also interesting
to note that the shape of the function is invariant to the value of
0 , i.e., perturbing the value of & would merely shift the horizontal
asymptote of the curve. This conclusion has a significant practical
implication, i.e., for any given value of & , the ^ 4 can be allowed
to have values greater than O . This conclusion has significant
impact in determining the required accuracy of measurement of emission
rates, and emission factors for individual source classes. In turn, these
conclusions are useful in allocating resources to the determination or
measurement of various emission parameters. Hierarchial application of
the technique to the complete emissions data tree will result in (Jj^ *S
much greater than the grand total © as the computations proceed to
successively lower levels of aggregation. Sample numerical analyses
for complete emission inventories will be presented in the next section.
In the case where one or more of the
-------
where
(9)
and
G
(10)
in the general case where ^. is unknown for k = 1, 2, ..., m and fixed
for k = m + 1, ..., N. Even assuming ^ - + 0 for k = 1, ..., ra, there
is, of course, a maximum value that ^, can be fixed at for k = m + 1,
..., N and still satisfy a given overall error Q . This upper bound
is also shown in Appendix A to be given by the formula
(11)
2-30
-------
These extensions of the basic weighted sensitivity analysis will
provide the analyst valuable guidance in performing the hierarchial
error analysis of the emissions inventory so as to retain the integrity
of the allowable error at the grand total level of emissions.
CONFIDENCE LEVEL FOR THE EMISSIONS INVENTORY
The weighted sensitivity analysis technique presented in the previous
section serves to compute accuracy requirements for the component parts of
an emissions inventory so as to insure that a given accuracy requirement
for the overall inventory is not violated. By using Chebyshev's inequality
it is possible to go one step further and establish in formal probabilistic
terms the confidence level for the inventory, i.e., what is in fact the
probability that the actual overall error in emissions will not exceed
£ .
Chebyshev's theorem (Reference 3) states that if a probability
distribution has mean Q and standard deviation & , the probability
of obtaining a value which deviates from the mean by more than A.
-v-l
standard deviations is less than /(. . Symbolically, in percentage
error terms
(12)
2-31
-------
where Q is the measured grand total emissions, as before. It is
important to note that Chebyshev's result is distribution-free. In
other words, inequality (12) applies regardless of what probability
distribution is associated with the emissions data. This is eritif.aj t
important because the actual probability distributions of the various
emissions are generally unknown.
Letting cA - /^LJ , inequality (12) becomes
r~
' ^
(13)
and the fraction G/pC gives a percentage confidence level for the
inventory, i.e., the probability that the actual percentage error exceeds
<-X is less than L: ^/;A . As a numerical example, if it is desired to
attain a 95% confidence level that the percentage emissions error will be
within a 20% interval of the true value, then setting
01'
and applying the weighted sensitivity analysis technique to compute the
(/"" S results in a set of precision requirements which, if satisfied,
insure that the 95% confidence level for the emissions inventory has been
attained. Using the same technique, Table 2-1 summarizes the required value
-------
Confidence Level
l-C
90%
95%
99%
Q)
4J
c
M
o
B
0)
u
o
1.58%
1.12%
0.5%
10%
3.16%
2.24%
1.0%
20%
6.32%
4.47%
2.0%
Table 2.1 Values of© for selected pairs (ot,l-C)
2-33
-------
of for selected trade-offs between confidence level and accuracy of the
for selected trade-offs between confidence level and accuracy of the
emissions inventory. For example, (9 must be set at 2.24% to attain
95% confidence level for the overall inventory error to be within 10%,
6,32% for 90% assurance of it being within 20%, etc.
In summary, the analysis of random error in emissions data should
be undertaken as a two-step procedure: first, establish the desired
value of the overall allowable error G> as a trade-off between confidence
level and acceptable error interval, by means of Chebyshev's theorem;
second, compute the required values for all component errors C'X so
as to preserve the integrity of & , using the weighted sensitivity
analysis technique.
2-34
-------
Section III
NUMERICAL ANALYSES
This section presents a sample numerical analysis for a complete
emissions data tree, using the Ohio State Emissions Report with emissions
as of February 23, 1973 as sample data. The discussion will cover
numerical analysis of both the nominal hierarchy or tree (as in Figures
2.1 and 2.2) and some alternative trees.
During the project, weighted sensitivity analyses were run for each
of the nine values of overall error B in Table 2.1, and for each of the
following summaries: county emissions report (Franklin County, Ohio),
AQCR emissions report (Metropolitan Columbus, Ohio), state emissions
report (Ohio) and nationwide emissions report (United States). Complete
numerical analyses for the nationwide emissions report (with emissions
as of April 19, 1973) using three different values of 0 are reproduced in
Appendix B of this final report. Other numerical analyses conducted
during the project are available as computer printouts. The annotated
numerical analysis given in this section is presented to illustrate the
application of the techinique from the analyst's viewpoint.
ANALYSIS OF THE STANDARD TREE
A complete weighted sensitivity analysis for the Ohio State Emissions
Report (with emissions as of February 23, 1973) is tabulated in Table 3.1.
3-1
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3-14
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3-16
-------
The table displays the av's which result from setting 0 = 5% for each
Jx
of the five classes of air pollutants. For clarity of presentation,
Table 3.1 is structured so as to give the Q^'s and a 's in adjacent
K K
columns for the five pollutants, with the source breakdown on the left
following the standard NEDS categorization of emissions sources as
shown in Figure 2.1 and Figure 2.2. Each grouping of emission sources
in the table is labeled by line number and title (refer to Figure 2.1)
as well as by node (refer to Figure 2.2).
These numerical results fully illustrate the characteristics of the
weighted sensitivity analysis as discussed in the previous section.
Starting at the grand total (highest) level of aggregation, the formula
of equation (7) is applied in a hierarchial fashion, working through nodes
and branches down to elementary emissions data. It is possible to
appreciate a significant relaxation of precision requirements as the
analysis progresses from top to bottom of the hierarchy. It is also
possible to appreciate the effect of the weightings as allowable errors
are allocated in proportion to the relative dominance of the various
emissions in any given group. With reference to the relationship between
the weightings QV/Q and the allowable errors
-------
ANALYSIS OF ALTERNATIVE TREES
There are two types of structural changes which can be of interest
in working with the emissions data tree of Figure 2.2. On the other
hand, it may be desired to eliminate a node of the tree. For example,
the fuel combustion subtrees of Figure 2.2 could be restructured by classes
of fuels, thus eliminating two intermediate nodes and permitting a direct
analysis of fuel combustion emissions broken down by type of fuel combusted
regardless of what activity the fuel was consumed for. On the other hand,
it may be convenient to aggregate the branches of a given node into a
smaller number of branches. This could be useful, for example, to reduce
forecasting effort by consolidating into a single forecast sources with the
smallest emissions so that the new error requirement can still be satisfied.
The first case is illustrated in Figure 3.1 and the numerical results
are summarized in Table 3.2 for the modified point sources subtree. In
order to obtain the Ov's of Table 3.2, the 0 for each of the fifteen types
K. K
of fuels first had to be computed by summing the emission contributions from
usage of that fuel in all branches of the subtree. The results are indicative
of the predominance of bituminous coal users as the source of air pollutants
released through fuel combustion, and therefore the need for better forecasting
and control of these sources.
3-18
-------
fuel combustion
point sources/
fuel combustion
anthracite coal
/
bituminous coal
I
liguite
i
residual oil
/
distillate oil
f
natural gas
process gas
coke
wood
liquid petroleum gas
vbagasse
^solid waste/coal
ygasoline
ydiesel fuel
Vother
same as above
area sources
Figure 3.1 Fuel combustion subtrees
restructured by classes of fuels
3-19
-------
antracite coal
bituminous coal
liguite
residual oil
distillate oil
natural gas
process gas
coke
wood
liquid pet/gas
bagasse
solid waste/coal
gasoline
diesel fuel
other
Particulates
e -9.U
274.06
9.22
199.98
583.06
172.96
89 52
730.90
»o-»s R^
3617.77
Sulfur
Oxides
0 -5.60
98.75
5.64
78.19
312.23
1679.44
66 81
3418.35
3197.57
Nitrogen
Oxides
& -8.39
190.58
8.65
96.26
133.08
40.39
14D 88
900.82
SOA 57
557.21
Hydrocarbons
6 =52.12
1409.35
60.02
429.84
650.95
118.11
1879.13
0-1 f. f.-)
J-LD . Oi
1699.74
Carboi
Monoxi<
0-112.8
737.34
114.49
5861.77
10000.00
2894.92
6178.84
2215.54
Table 3.2 Weighted Sensitivity Analysis (ov) of Point
K
Fuel Combustion Subtrees restructured by classes of fuels
3-20
-------
The second case can be Illustrated with reference to source hierarchy
[1.2] in Table 3.1, particularly the carbon monoxide column. The dominant
Q 's correspond to primary metals (6269525 tons/yr) and the petroleum
K.
industry (2907030 tons/yr). Consolidating carbon monoxide emissions frora
all other industrial processes into a single group yields the following
results:
QK (tons/yr) <7R (%)
primary metals 6269525 7.40
petroleum industry 2907030 10.87
other industrial processes 250957 37.02
The results above were computed, of course, using the same
0=6.04%. The value of a for the aggregated "other industrial processes '
K.
is not very rsstrictive and could be an indication that detailed forecasts
of carbon monoxide emissions for specific industries other than primary
metals and petroleum are not necessary to preserve the integrity of the
emissions inventory. Generally speaking, forecasting effort can be
reduced by regrouping the source classes with the smallest emissions
into one or more classes, however, this policy should be applied with
some discretion in order to have groups or classes which are meaningful
and which can be successfully forecast.
3-21
-------
Section IV
WEIGHTED SENSITIVITY ANALYSIS PROGRAM (WSAP)
This section documents the software developed to implement the
weighted sensitivity analysis technique. The program provides a means
to evaluate (hierarchially) the maximum permissible errors in emissions
data for source categories when given the maximum permissible errors
for the total emission inventory. The system is coded in FORTRAN IV
for the IBM System/360. The material below is structured in consonance
with EPS's outline for software documentation.
4-1
-------
Program Abstract
Program Name: WSAP Programmer: L. J. Rushbrook
Program Written for: John Bosch Section/Branch: National Air Data
Language: Fortran IV Size: 66K
Normal Execution Time: 7 sees for summary (state, county) Class A
Input: Control Cards 1, Data Cards 0, Tape: 1, Disk: 0
Explanation: The single control card contains the percent error of
the total emission (Theta) for each of the five pollutants. The input
tape is a NEDS print tape.
Function: To provide a means of evaluating the maximum allowable error
in emission data (Sigma) for source categories when given the maximum
allowable error for the total emission inventory (Theta). The techniques
of weighted sensitivity analysis are employed.
Output: Cards 0, Tape 0, Disk 0, Printer 1
Explanation: The "Weighted Sensitivity Analysis Program" report is
printed according to the hierarchical structure of the NEDS report and
lists the tons of emission (QK), the percent of allowable error
and the amount of allowable error for each pollutant.
Programmed Diagnostics:
RUN TERMINATED: Invalid control card, invalid tape, tape read error.
SUMMARY PROCESSING TERMINATED: Input line not acceptable to program,
negative pollutant field on input.
4-2
-------
RUN DESCRIPTION:
This program provides a means to evaluate the maximum permissable
errors in emission data for source categories when given the maximum
permissable error for the total Emission Inventory. The techniques of
weighted sensitivity analysis are employed.
The system is coded in Fortran IV for the IBM System 360.
The program reads the "National Emissions Data System" print tape,
stores the entire amount of data for one report (state, county) in memory,
and under the control of a driver table selects the lines of the report
to calculate the allowable errors (o' ) and the amount of allowable error
K
(cr Q ) for each pollutant. The output is according to the hierarchical
Jx Ix
structure of the NEDS report that is designed into the Driver Table and
lists the amount (Q), the percent of allowable error sigma (o) and the
K.
amount of allowable error (oxQ ) for each pollutant. The formula used
K K
for the computation is:
where o = percent allowable error for a given source
K.
9 = percent allowable error for total emission
Q = amount of emissions for a given source
Q * z^Qv f°r a particular category.
4-3
-------
Method:
Figure 1 and 2 in Section 2 describe the overall system flow and the
General Program flow.
A. Initialization of the Driver Table (IDRIVR)
At compile time the Driver Table is initialized. This
table (IDRIVR) determines the hierarchical level for process-
ing by selecting the lines of data to be processed from the
standard National Emissions Data System input tape. The table
contains values that control processing actions by specifying
hierarchical headings, source class labels and references to
data for processing within each hierarchy.
The Driver table is a series of sub-tables which corre-
spond to one hierarchical level or sublevel. One sub-table
thus represents the data to process for a given Theta (0 or a).
There are 33 sub-tables within IDRIVR. Normally, all 33 sub-
tables will be used to process each state or county.
The contents of IDRIVR is a continuous stream of 3 digit
numbers containing indicators and line numbers related to the
standard "National Emissions Data System" report.
The indicators are of two types. One type is depicted by
a numerical value greater than 799. The other indicator is a
positional relationship within the sub-table and is a numerical
count of the number of line numbers immediately following the
indicator on which the program must act for this event.
See Appendix A for a layout of the Driver Table (IDRIVR)
and an example of its use. A clear understanding of this table
is essential to understanding the program.
4-4
-------
B. Initialization of the Titl« Table
At compile time the Title Table (ITITL) is initialized
to the values shown in Appendix B. It is a 2 dimensional
array (8,238) containing the 32 character title of each
possible line on the NEDS report. These titles are
positioned precisely as they are on the NEDS report and each
is identically spelled.
C. Setup
A parameter card is read which contains the maximum
permissable error (#) for each pollutant in the total emission
inventory. It is a five digit number of two decimal places.
Its maximum value is 999.99. These 5 theta (0) values, one
for each pollutant, are stored in array TH and are used to
compute the sigmas (07,) of the lower levels.
Ix
Table TDATA is set to 0. This table will contain the
amount fields to be read from tape, the calculated allow-
able errors «T) and its allowable amounts (CT*QK).
K. K.
D. Read One NEDS State (county)
The NEDS tape is read until the first line is found.
Each record is scanned until the words "National Emissions
Data System" is found and this record or line is assigned
line number 1. All succeeding lines are assigned the values
2-237. Blank lines are ignored.
Lines 1-6 are stored as read in IHEAD and used as is
for the header of the report.
-------
Lines 8, 9, 10 contain the columnar headings for the 5
pollutants and are stored in IPOLL. Only the 13 characters
each of pollutant name are stored.
Lines 11-237 constitute data lines and are used to build
the amount (QK) field of table TOATA.
Since the program which generates the NEDS tape suppresses
(fails to output) all lines in which the 5 pollutant amounts
are each zero, the lines of data on the NEDS tape will rarely
equal the maximum number of lines (237) for a standard report.
To circumvent this problem table ITITL contains all the titles
for each line (11-237) of the standard NEDS report.
Progression of the read in routine is by line number
(11-237) down the ITITL table. The routine will compare the
standard line title in ITITL with the NEDS input line title.
If equal the NEDS data for each pollutant is stored in the
TDATA array, the line counter is incremented and another line
is read from the NEDS tape. If unequal no data is stored
(the amount fields in TDATA remain zero) the line counter is
incremented and the next title in ITITL is compared to the
NEDS input title. This procedure repeats itselt until line
238 is reached in the ITITL table. At this time the complete
state or county has been stored in TDATA in the standard NEDS
sequence and the Driver Table (IDRIVR) is ready to select
lines for processing.
A change in the NEDS print program (a spelling or word
repositioning change) will cause that word to never find its
match in the WSAP program and insufficient data will be loaded.
4-6
-------
To detect this possibility an error check is made at line 233,
the "GRAND TOTAL" line. It is assumed that all NEDS reports
have an entry for "GRAND TOTAL" (line 233). When line 233 is
reached a match between NEDS and WSAP (on "GRAND TOTAL") is
mandatory or WSAP will print an error, fall to process the
summary (state or county) and go on to the next state. The
number of errors detected during the run is printed on the
first line of the last page of the run. If this number is
not 0 the report is incomplete.
r
E. Process One State or County
The IDRIVR table contains 33 sub-tables. The program
will start with sub-table 1 and continue through until table
33 or the last table is processed. The counter KTS is used
to indicate the table desired (table separators encountered)
and the array JTSTBL contains the start position in the IDRIVR
table for each of the 33 sub-tables. The contents of KTS are
used as the index for JTSTBL to determine the start point for
the proper table in IDRIVR.
The first entry of the sub-table is checked for a table
separator (>799) or the end of table (999). If neither, the
start point for IDRIVR is stored in KJTS and is used to cal-
culate the start points of the other key positions in the
IDRIVR sub-table (see Appendix A).
The IDRIVR table is now used to drive the program. It
determines what to do and which line number in the TDATA
table or ITITL table to do it to. By using the indicator
and line numbers in the IDRIVR table the calculation of
and a x QK begins. The line number to act on in the TDATA
table (QK) is found in the IDRIVR table. This line number
4-7
-------
(NN) in IDRIVR is used as |he TDATA index [TOATA(NN) ] to
find the amount (QK) . TDATA is a 3 dimensional array hence
Sigma for:) is calculated and placed next to the amount (QK)
K
in TDATA and Sigma (0£) x the amount (QK) is placed next to
sigma in TDATA.
After all the calculations have been made for each pol-
lutant the report for this sub-table is printed in pollutant
sequence.
The sub-table report requires the following:
1. A main header
This consists of lines 1-7 of the NEDS report.
2. A sub-table title describing the hierarchical level of
the sub -table.
This title is obtained from the ITITL array using
the offset (line numbers) found in the IDRIVR
array entries IH.
3. Type of pollutant
This is taken from line 8 of the NEDS report.
A. Theta (#ora) used in this calculation
Obtained from input 6 or from a a in TDATA as
directed from IDRIVR entries IDH.
4-8
-------
5. Labels for data lines
These labels are taken from the ITITL array as
directed by the IDRIVR table entries IL.
6. Calculations
Data is obtained from TDATA array as directed by the
IDRVR table entries ID.
9
After printing the report for this sub-table the next
sub-table is processed and printed. This cycle continues
until all 33 sub-tables have been processed.
A new state (county) is read in from the NEDS tape and
the main cycle repeats until an end of file is reached on the
tape.
F. Major Program Tables
BYTES
B5 (5) 5x4 20
Stores BETA OS) for 5 pollutants.
IDRIVR (720) 720x4 2,880
A continuous stream of 3 digit numbers
representing indicators and line numbers
used to drive the program. Initialized
at compilation. See Appendix A.
IHEAD (33, 7) 4x231 924
Contains characters 2-133 of the first
7 lines, excluding blank lines, of the
NEDS report tape. The carriage control
character is not stored. Format is 33A4
for each line.
4-9
-------
BYTES
IPOLL (15, 3) 54x4 180
Stores the columnar headings for each of
the 5 pollutants (lines 8, 9, 10 of NEDS
report).
ITITL (8, 237) (4x8)x237) 7,584
Stores the row title for each of the 237
lines of the Standard NEDS table. Initialized
at compilation. See Appendix B.
JTSTBL (50) 50x4 200
Contains the start points for each sub-table
in IDRIVR. Start point is determined by the
Table Separator indicator (an integer greater
than 799) in the IDRIVR table.
Q5 (5) . 20
Stores Q for 5 pollutants.
TDATA (3, 5, 237) 4x15x237 14,220
(data, pollutant, line number)
Contains the 3 amounts (QK,a , axQK) for
each of the 5 pollutants for each of the
237 lines.
TH (5) 5x4 20
Stores the input theta for each pollutant.
THETA5 (5) 5x4 20
Stores active THETA (0) for 5 pollutants.
-------
TN5 (5) 5x4
Stores pollutant fields from NEDS tape.
QTHETA (5) 5x4 20
Stores (Q/100)* Theta for each active pollutant
in the sub-table used in printing total line.
Total bytes 26,108
FORMULAE USED
The formulas utilized at the various levels in the
hierarchical structure of the NEDS file are:
N
Q Total Emission: Q -
Beta:
Sigma: O - tf/Q/QK" - &f /QK~
0 a Percent error contained in the total emission Q.
K = A particular source class for level.
Each pollutant (maximum of 5 per run) will have its own
values for the above variables. The initial input 0 applies
to its pollutant at the highest level (IDRIVR table 1). The
a of the preceding level then becomes the B for the active
level .
RESTRICTIONS
The input theta (on card) must be positive and no greater
than 999.99.
4-11
-------
The maximum sigma internally generated is 10,000. Any-
thing higher defaults to 10,000.
OPTIONS
Five input thetas must be inserted in the parameter card
for use by IDRIVR Table 1. A 0.00 theta entry for a pollu-
tant will cause that pollutant to be bypassed in processing
and printing for each table.
i
ACCURACY
All internal calculations are made in floating point
and converted to fixed point for printing.
4-12
-------
FLOW CHARTS
4-13
-------
art 005 WSAP OVERALL SYSTEM FLOW
4-14
-------
Chart 006 GENERAL PROGRAM FLOW WEIGHTED SENSITIVITY ANALYSIS PROGRAM
4-13
-------
Chart 007 WSAP (SHEET 1 OF 7)
I 2 » 3 4
c
/READ THCTA /
CARDS /
/PRINT TH6TA /
CARDS /
~
.YES / PRINT:ERROR /
> »/ INVALID THETA /
' / CARD /
4-16
-------
Chart 008 WSAP (SHEET 2 OF 7)
i » a
PR I NT! ERROR
INVALID THETA
CARD
* / -( END J
/PR I NT NORMAL /
/ END OF FILE /
*/ TERM 1 NAT I ON /
/ ^ I
IN /
INCREMENT LINE
CTR (KLINE) BY
1
4-17
-------
Chart 009 WSAP (SHEET 3 OF 7)
I « 2
/ PR I NT: ERROR /
-*/ ABNORMAL EOF /
/ TERM /
BQ05
/PR I NT:ERROR /
*EAD ERROR ON /
C'"gg /
/PRINT:ERROR /
ABNORMAL EOF /
TERM /
60 Q 5
/ PRINT:ERROR /
*/ READ ERROR ON /
/ LINE X /
4-18
-------
Chart 010 WSAP (SHEET 4 OF 7)
/PR INT I ERROR /
IN TITLE NE I
ITFTL TITLE /
/PR I NT! ERROR /
DLLUTANT FIELD/
<0 I
4-19
-------
Chart Oil WSAP (SHEET 5 OF 7)
CALC START AND
END VALUES FOR
EACH TYPE ENTRY
IN IDRIVR
92
/=R 1 NT HEADER /
LINE Ml OF /
WSAP REPORT /
I
93 *
/PRINT LINES /
-8 (LINES I-7 /
OF NEDS) /
/DR INT OR I VER /
TABLE USED /
(LINE 9) /
/PRINT /
HIERARCHIAL /
SOURCES OF /
REPORT /
STORE TDATA
SIGMA IN THETA5
AS PROCESSING
THETA
4-20
-------
Chart 013 WSAP (SHEET 6 OF 7)
I
RESET OR
INCRI
I DR 1 VR
:MENT
INDEX
CTR
NO
CALC Q -= SUM QK
RESET OR
1NCR
1DRIVR
:MENT
INDEX
CTR
SIGMAK =
BETA / SORT (QK I
SIGMAJ = THETA
SORT ((Q'Q/AA)
/ I Q J ) 1
/PR INT
MAX
POSS
ERROR
SIGMA
POSSIBLE
4-21
-------
Chart 014 WSAP (SHEET 7 OF 7)
I 2
/ PRINT TOTAL / /ITl
/ LINE /-4 Bl /
/ / V^X
/ PR I NT QK . /
-»/S 1 GMA , S I GMA ' QK/
/PR I NT QK , /
(DT^lfe^-^OR /
SIGMA, QKI /
/PR INT;ERROR /
IN TITLE NE /
ITITL TITLE /
/PR I NT I ERROR /
XLUTANT FIELD/
' ° I
/PR I NT: ERROR /
ABNORMAL EOF /
" " /
C
4-22
-------
INPUT-OUTPUT DESCRIPTION
A. Input
1. Card Input
The first and only card is the Theta (0) card which con-
tains the percent error in the total emission for each pollu-
tant . It has the .following format:
Comment
Card identifier
0 Pollutant 1
Q Pollutant 2
0 Pollutant 3
0 Pollutant 4
0 Pollutant 5
All N's must be an integer (0-9) and the decimal point must
be present.
A 0.00 theta will cause that pollutant to be bypassed in
processing and printing.
Col
1-5
6
7-12
13
14-19
20
21-26
27
28-33
34
35-40
Contents
THETA
blank
NNN.NN
blank
NNN.NN
blank
NNN.NN
blank
NNN.NN
blank
NNN.NN
4-23
-------
2. National Emissions Data System (NEDS) Print Tape
The description of this NEDS tape can be found in the
EPA library as it is generated by another program. Program
is presently set up for:
LRECL - 133
BLKSIZE - 2660
RECFM - FBA
LABEL - 1
DENSITY - 1600 BP1
B. Output
The printed report will be in IDRIVR hierarchical table order
(table 1 through table 33). Table 4.1 is a sample of the output.
4-24
-------
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4-25
-------
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-------
TEST DATA
The test input is a National Emissions Data System print tape for
4 states (Illinois, New Jersey, Ohio, Texas). Run date for the tape is
April 3, 1973 for emissions as of February 23, 1973. A listing of the
tape is furnished with the program listing and the original test tape
is delivered with the program.
The following test checks have been made:
1. A 0.00 input Theta cancels processing and printing for
that pollutant.
2. An invalid Theta card. THETA missing in columns 1-5.
3. No Theta card present, hopper empty.
4. A no match between input line title and the standard line
title in ITITL array.
1. All mathematical calculations have been checked for
validity.
2. All IDRIVR tables are correct.
3. The ITITL table agrees with the NEDS test tape.
4. The report is printing correctly, including the printing
of dashes for sigma if it equals zero.
4-27
-------
OPERATING INSTRUCTIONS
KEYPUNCH INSTRUCTIONS:
Prepare the THETA parameter data and punch the card to the follow-
ing format:
Comment
B for Pollutant 1
0 for Pollutant 2
0 for Pollutant 3
0 for Pollutant 4
9 for Pollutant 5
All N's must be an integer 0-9 and the decimal point must be
present.
A 0.00 theta will cause that pollutant to be bypassed in processing
and printing.
INPUT-OUTPUT COORDINATOR INSTRUCTIONS:
Obtain the NEDS report tape for processing.
Col
1-5
6
7-12
13
14-19
20
21-26
27
28-33
34
35-40
Contents
THETA
blank
NNN.NN
blank
NNN.NN
blank
NNN.NN
blank
NNN.NN
blank
NNN.NN
-------
CONSOLE INSTRUCTIONS:
Mount NEDS tape
Insert THETA card in hopper
Run WSAP program.
4-29
-------
SUGGESTIONS, WARNINGS AND CHANGES
SUGGESTIONS:
Improvements to be added:
WSAP has been modified to incorporate the following in
WSAP 2:
o Ability to load the ITITL table from cards.
o Capability to load the IDRIVR table from cards.
o Capability to load a known sigma at any category
level for any pollutant from cards.
4-30
-------
PROGRAM LISTING
The program listed is given under separate cover, together with
the users' manual for WSAP. The driver and title tables are given in
this section as appendices IV-A and IV-B.
4-31
-------
APPENDIX IV-A
DRIVER TABLE (IDRIVR)
The IDRIVR table is a continuous stream of 3 digit integers which
controls the selection of data for processing within the WSAP program.
It consists of 33 sub tables that correspond to the hierarchical levels
in the NEDS report.
Each sub table begins with a Table Separator indicator (an integer
greater than 799). Following the Table Separator is a series of
indicators and line numbers.
Each indicator is an integer which tells the program how many
following table entries there are concerning this event. These entries
are the actual line numbers in the ITITL table and the TDATA table where
the program must go to obtain the data for processing and printing. The
ITITL table provides Titles for headings and data lines while the TDATA
table provides the amount (QK) , sigma and sigma X QK fields.
The number of line number entries in each subtable is variable but
the number of indicators and their relative positions within each sub-
table are fixed.
By calculating the start position of a desired subtable and the
start position for each event within the subtable the Driver table
can now provide control information (line numbers) to the program.
The following pages provide a more detailed description of the
IDRIVR table.
4-32
-------
APPENDIX IV-A (continued)
Layout of Driver Table (IDRIVR)
JTS Table Separator indicator. It is an integer greater than
799 and identifies the beginning of a new table. A 999
entry is used to denote "end of tables".
NH Count of following (IH) line numbers used for report
header information. (1 entry number)
»
IH Line numbers used to obtain the heading label information
in ITITL. (Nil entries)
NDH Count of following (IDH) line numbers used to obtain 9
(or
-------
APPENDIX IV-A (continued)
Example use of IDRIVR Table stream for 1 sublevel
IDRIVR
POSITION
1
2
3
4
5
6
7
8
9
10
11
12
13
POSITION
VARIABLE
NAME
KJTS
KNH
KIH
KNDH
KIDH
KNL
KIL
KND
KID
KJTS
KNH
IDRIVR
DATA
801
1
233
1
237
2
235
236
2
235
236
802
1
DATA
VARIABLE
NAME
JTS
NH
IH
NDH
IDH
NL
IL
ND
ID
JTS
NH
COMMENT
Table separator, Begin
Table 1
There is 1 label item next
Use label on line 233 of
ITITL
There is 1 6 line item next
Use on line 237 of TDATA
as 9
There are 2 lines of label
data next
Use label on line 235 of
ITITL
Use label on line 236 of
ITITL
There are 2 lines of amt.
data next
Use the 5 pollutant amts.
on line 235 of TDATA
Use the 5 pollutant amts.
on line 236 of TDATA
Table separator - Begin
Table 2
If IDH were 799 the input Theta would be used instead of the
sigma on line 237 of the TDATA table.
4-34
-------
APPENDIX IV-A (continued)
By using the data in the IDRIVR subtable example on the preceding
page the program calculates the following variables.
KJTS =
KNH -
NH
KIH -
IH
KNDH »
NDH «
KIDH »
IDH <=
KNL =
NL
KIL -
IL -
KND =
ND
KID =
ID -
JTSTBL (KTS)
KJTS + 1
IDRIVR (KNI!)
KNH + 1
IDRIVR (KIH)
KIH + NH
IDRIVR (KNDH)
KNDH + 1
IDRIVR (KIDH)
KIDH + NDH
IDRIVR (KNL)
KNL + 1
IDRIVR (KIL)
KIL + NL
IDRIVR (KND)
KND + 1
IDRIVR (KID)
Value
1
2
1
3
233
4
1
5
237
6
2
7
235
9
2
10
235
Once the above variables are calculated for any given IDRIVR
sub table (1-33) the processing of data for that table can begin.
4-35
-------
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rv ^i r cr1 -' "-1 cv. r-i " rri otj <.-< r c i j ir-, r
! j_ ai cr Oi ; fv r r^ ac t -< r LI
r- c
at
i (« ^c u. r~ c r>: c\.
» f| p- r-' c n:>TLn
r irj u p o' cr { ri
f\i
cr <. r- ic ex c r- o vi ^t ^-. ^j ^-< ^ »- ui -< 01 i rj vj u . cr f. u «' <*
fi cc~ if' cj c\ CM u -a r- >i vT i u- a
vt f> x c r<. n p- r
( re, r r> u C' rvi (
'A r- I i f ( t I r- t\) r
i t r n CM r\i
a <
' >j 0.1
a. m rn a.
«> ^- <*i 10
r>:r\,fM(\
on a. cr
rvi r- rM LT\ ir
^-4 ro -j r^
'11
4-36
-------
APPENDIX IV-B
LABEL TABLE
LABEL
NO.
c
1"
11 n h I rrMJ|_ if X- * X * * >t^ *
i° i v T F P N ^ i CCPE'I^MCN
J f< _ . l..tlJ.C.Lli.!.[.M-..f:.U.f L.JLA
1 & A N 71- R * M T r r c A L
i - r> iTi.N1 p rt;s rrAi
1 "/ ri^TILMTrrU
\f . »fcir L ^ L r r i
r.t FC cr.^F^T ITN (PC I\T i
A.Mf-^riTf- r [ A L
p ntv ir^L5_ crai.
i i r N T T r
___________ -1.I1C1 AL_J1LL ___________
C 1 5 T 1 1 I. A T f r II
p p c r E ^ ^ CA<;
f r_bx
p £f A $ C C
i£! J £___M 5..T P / C C A L .
f T (- F P
__ Tf TH .(f'trr, r_FM .
r L ^ T P I A I F ( . F t
.^ N "f hE A C T T r rr AI_
APT A cp,)prF5
P r \ ;\ T s C L ' P C C S
0 M L N f N C L S r r H
ftp FA <:CUR<~F
PfINT <:r
CIL
4-37
-------
LABEL TABLE (cont.)
; <-
- f-
K "7
M
71
77
/ -3
7 <-
PC I
? c T FL I
A r< F
pr T
SCLRCFS
' Tl
r i ' P r F c
A p c /\ c, (- ( i (, r c
prTMsripr
c fj r f f c c r \ c
f f K_L
y» p p /> <;fi , (,T r
PC T^ T sn CC
v r r n
L TCI 1C
f A c c r
PC IK T Sfli,pC CS
|- P r
°LLM .SCLPCE5
T/»L(Of'Lc>TRTrr
! I r L I r P F T (.> r i c
4-38
-------
LABEL TABLE (coat.)
cf TC7«L (COv-IKST)
S7 APFA SOJPCES
c ",^ " pr'NTsruprFS
__S_ c LLLLL_ _lf.£ JAIJL
}".' T r T /»I ( F X T c ^ N A I ffVP)
1 ~ i .* P r _A _ c r L _P r r s _
l"3 fMFrNM r ( f~( 51 ir\ _(pr _IN_T
i:^ r | r r T <- H" TNT-^jirv
J.11. H_LL1 LLJL.U,L_ C_LL
n
"I'l
1 1
~ 1
" f-
~c.
I '
1 1
1 /
1 ^
I c
r I F
r f(-
Tf T
T N f I S T c
r. y
r'Tc
nt-
Q r i
M
^ L ( F-" i r c f f- N )
JAl Fl, PI
T HI ATF f1 IL
cii^rAS
FR
1 * r i r <; c i
1 1 c C It- E R
1?" TCTAL
121 FNGTNf--1FSf {NT.
12? AIPTftAFT
12? CThEP
''^ TCTAl (FNH TFSTNGI
1 ?r; - P-IhFR IPDLNT.1 .. _
I??1- TTTAt ( T N T F P \ A I CQMP)
121 TTT.AL (FUEL CCV.BUST T r^J
1 ?° ARF ft ^CUKCF«:
12° PTIAT SrUPC£S-- ^
l^n T\jrHJSTPIAL PTTFSS (POTNTI
131. ****** *********** *.** *_£.*# * *
113 FOOC/AGF ICLLTUPAL
1 34 PRI WARY MFTAL
135 . SEcr*rApy VET.US
-I?7. _.. PE
i°p wrnr
Ml LEATHER PRODUCTS
I'-*? TFXTILF VAMIFATTIIP
Mf TfTAL (INCLSTRIJU
M6 SOLin WASTE DISPOSAI
147 ********************
4-39
-------
LABEL TABLE (cont.)
140 nrVFRM^FM (PCINT)
149 MUNICIPAL INCINERATION
15<- fpc\ BURNING
lc? TlT/si f n
]<=4 PN _ A_PF^
17A PCTNT
177 f r TNT 5PUPCFS
|>P AUTP pnnv TNCINEPATTCN
179 . _ - PC1M . SCUB.CE.S ____ -
18C PAIL CAP PURNINf,
181 PC TNT
182 TTHER
!.?? . . . EC TNT
1 **> TCT/!L { TNCl
|_P_C ___ _ __ a p c A
PC IKT SftJRCF
TTT/a (fClin V»A«;TF P T
r PCTM
JL_I£ *A1F CPTATICK ( A P
LIGHT VH-t f !_£ S
L££
TCTAL (GASCL
TIE5FL
4-40
-------
LABEL TABLE (cont.)
VEt-ICl ES
JLfLL. iUfihMV.
PA II
TCTM. (HFTSFl )
! O' A F T
^LUJL
"CIVIL
<~FJ
CCAI.
2}
T r T y L (a i a r P /» F T j
AIULLi.
f I TL'V IKfi
TTFSJLJLLJl!
^ F c IC t. A L fit
f- As c LJAf
TFTAL (VES^El
fAS HANFLJAC FVAP
TFT
nC***<*«<4444**4**
FTP
.2/1
2/F
2 7c
f
2? ]
^i
/ B 4
5 7 C
/ 7 /
227
?36
C r^S^FLCTIF^
FTCK HANF! TNC/STRING
TFTAI. fwi5CELLANfriJS>
fTHFQ (FflM)
f } ANT TF TM
***3t*>J^j}*«4
." K F / S f IF r E ^
r-CIM S F 1. r r F S
TFT /«t
4-41
-------
Section V
CONCLUSIONS
A weighted sensitivity analysis methodology has been developed in
this contract to establish the statistical quality of emission inventories.
A summary of the results, including developments beyond the original scope
of work, is given in Section I of this final report. Section II presents
a detailed explanation of the methodology, and the complete theoretical
development is documented in Appendix A. Section III and Appendix B pro-
vide numerical analyses to illustrate the application of the technique and
demonstrate the adequacy of the software. The latter is fully documented
in Section IV, which is structured in consonance with EPA's outline for
software documentation. The program.listing and user's manual is to be
delivered under separate cover.
The utility of the methodology that has been developed is manyfold.
It is consistent with activity forecasting requirements and serves to es-
tablish percentage error requirements for source categories so as to satisfy
given error bounds for the overall emissions inventory at a given level of
statistical confidence. It provides results useful for planning air pollu-
tion control enforcement activity. For example, suppose that for a given
source class k,
5-1
-------
is the allowed error quantity (in physical units) that satisfies a, , and
suppose that field measurements indicate that the actual error quantity is
some value &., ?£; then, the fraction
immediately gives the percentage reduction in error quantity which is
necessary to comple with o, , and appropriate corrective action can be
planned accordingly.
The versatility and wide range of applicability of the technique is
further illustrated in Appendix C to this final report, which shows an
application of the technique to assist the Commonwealth of Virginia's
State Air Pollution Control Board in achieving an approvable implementation
plan for attaining secondary standards for particulate matter by 1975.
The formulation of the weighted sensitivity analysis presented in this
report possesses a high degree of generality. It can be applied to compute
component error requirements for inventories of emissions (or any other
kind of) data which exhibit a hierarchial (tree-like) structure, as exempli-
fied by NEDS reports. A concrete case of interest could arise by multi-
plying the hierarchial table of emissions data (i.e., the table of Q,'s)
K
by some set of "effect" factors such as the health effect factors provided
by Walther [Reference 4]. Denoting the effect factor by f, and the resulting
effect as E , E = ^v^v ^or eac^ source in a given category, with E = K
IT - 1
k giving the total effect for that category. In this case, the
ratios E /E provide weightings analogous to Qk/Q in the standard application
KL
of the technique, i.e., it can be readily extended to perform weighted
sensitivity analysis on the contributions of the major air pollutants and
their sources by effect as well as by weight or mass. Additional prospective
extensions of the analysis are its application to emission factors and to
emissions data at the SCC level of aggregation.
5-2
-------
REFERENCES
[1] Baird, D. C., Experimentation: An Introduction to Measurement
Theory and Experiment Design, Prentice-Hall, Inc., Englewood
Cliffs, N. J., 1962
[2] Mendenhall, W., Introduction to Linear Models and the Design and
Analysis of Experiments, Wadsworth Publishing Co., Inc., Belmont,
California, 1968
[3] Miller, I. and J. E. Freund, Probability and Statistics for Engineers,
Prentice-Hall, Inc., Englewood Cliffs, N. J., 1965
[4] Walther, E. G., A rating of the major air pollutants and their sources
by effect, Journal of the Air Pollution Control Association, vol. 22,
no. 5, May 1972
[5] Worthing, A. G. and J. Geffner, Treatment of Experimental Data,
John Wiley & Sons, Inc., New York, 1943
S-3
-------
Appendix A
THEORETICAL ANALYSIS
This appendix documents the theoretical development of the basic
weighted sensitivity analysis technique for emissions data and its
various extensions. These analytical developments are based on well-
known theory [References 1, 2, 5] and well-established assumptions. Sec-
tion II of this final report provides a descriptive discussion of the
assumptions adopted, their statistical interpretation, and their practical
implications. Concise mathematical notation will be used for the theo-
retical analysis in this appendix.
A.I Weighted Sensitivity Analysis
The objective of sensitivity analysis is to determine the effect
(changes) on some measure of performance due to changes in each component
that makes up the measure of performance. In the simplest case the measure
of performance is the sum of component measures. Let T be the total mea-
sure of performance and C be the K component. Then,
K.
k=/
A-l
-------
and any change in T (4T) due to changes in each of the components (AC )
K.
would be related to these component changes as
H
I 44
(A-2)
However, each component may be dependent on one or more primitive parameters
so that, for example,
Cv - Cv (X) (A_3)
(A-4)
if X is a column vector, then with the gradient operator defined as
,
v ^^>,M-xrj""^>/M) (A-s)
\
/
the propagating change formulation takes on the form
(A-6)
A-2
-------
For this exposition we shall use the single variable notation with the
understanding that, should multivariable parameters be considered, then
the partial derivatives must be thought of as gradients. The relationship
of changes indicated in Equation A-2 is valid for deterministic changes.
However, if the changes are uncertain or stochastic, the changes must be
indicated by a statistical measure of dispersion (e.g., variance, standard
deviation) rather than by differentials. Thus,
rf
u,7)
where v(») is the statistical variance (the square of the standard devi-
ation) and the component variances are assumed to be uncorrelated with
each other. Let
(A.8)
and 100 6 is the percent error or deviation of T. Similarly, let
"
where Q < ^ $ I
-------
or
(A-ll)
where 100 C../T is the percent of C., in T. Equation A-ll relates the
K. K.
error in T to the errors in each of the components , with all errors
represented as fractions (or percentages); moreover, these component
errors are weighted according to the contribution of each component
measure to the total measure of performance.
Because of this weighting it becomes possible to assess the significance
of each component as it relates to the confidence (or error) of the total
measure of performance.
The following subsections exhibit the application of this method of analysis
to emissions data as well as some numerical examples.
A. 2 Application to Emissions Data
This analysis is based upon Equation A-10. Let C be replaced by
K.
Q , where Q designates the emissions (e.g., in tons/year) of a specific
K K.
air pollutant produced by source class K. Also, let o be the error
K.
(replacing y ) in Q . Similarly, let Q replace T for total emissions
K. K
with error 6 . Then in analogy with Equation A-10 we have
K-'
A-4
-------
where
Q--
By division we obtain
K-/
The objective of this analysis is to obtain a for each class K according
K.
to some value of 0 (error in total). As a first approximation we can
assume that each term in Equation A-14 contributes the same amount to
the total. Thus,
l/N = (QK/Q)2 ( V#)2 (
whence,
(QR/Q)]
where N is the number of source classes.
We can interpret Equation A-16 as indicating the present error allowable
(a) in forecasting emissions from source class K given the percent
K.
error allowable (Q ) in forecasting total emissions, o v can be modified
JV
either by changing Q or by regrouping the source classes, which changes
N and Q^ simultaneously.
K.
A-5
-------
As a second approximation, the analysis can be modified to allow each
source class k to contribute to the total error an amount proportional
to its relative physical contribution to the total pollutant emission
Q, as given by the ratio Q, /Q. Analytically, it is only necessary to
note that ,
i.e., the summation of all the weightings Q,/Q must necessarily add up to
K.
one. Since, from Equation A-14,
/< -
it follows that:
or, in expanded form:
&- a i a»
ZT T *"' T ""
&
Arbitrarily, equating both sides of the equation term by term yields
Q./a = (Q,
A-6
-------
or, more concisely:
Qk/Q = (Qk/Q)2
for each source class k. This revised formulation assumes that each
term contributes tc
from equation A-18
term contributes to the total an amount proportional to Q /Q. Then,
K.
(Qk/Q)(
-------
A.3 Extension to account for fixed errors
Refer back to equation (A-14) and consider the equations
if J . 'r~ I vn apriori, '
Cl _
_1 / }
c
A-8
d,
with reference to (A-21) J^- (A-25)
-------
whence
./
so that
D = &-& / a
Substituting (A-27) into (A-24) yields
/ -' N
Q
* __ J=^ <> ^ _ > ±£J/J£; (A-28)
-. ^ - /- \ ^ / V <9
or
- /v
/^ / *. \ x^ .
c\Li-b) -&j
with the assumption that
/-/>3-^'j"]^
A-9
(A-26)
(A-29)
(A-30)
for ki«j
-------
get
0
i\
G«
f (~v if unknown for K = 1, 2, , m, hut O i^. known fo-" j = m + ., ,
';!ron CA- ?0) beco^^ s ,,,,/
/v
We del inn D. to satisfy
(A-33)
A-10
-------
where
(A-36)
Equating (A-33) and (A- 34) then subtracting (A-35) for j - m + 1, --- , N
yields
N
x- - f r\ \ r rr- X-
Let
(A-38)
and
/O
with reference to (A-34)
(A-39)
7
-*-
(A-40)
A-ll
-------
whence ^
so that
or
A-12
P - 7 - Q ^ ft (A-42)
Substitution of (A-38) and (A-39) into (A-37) yields
with the assumption that
(A"45)
-------
we get
* ,.' «3 (i-o-A.
<£ ''
or
Equation (A-47) constitutes a generalization of equation (A-19) to
cover the case where one or more of the errors associated with the
subclasses of a given source class are to be fixed by the analyst. Even
assuming zero error for the other components, however, there is of
course a maximum value that can be attached to the fixed errors and
still satisfy a given overall error for that class. For a given Q , the
offer bounds that the ak's to be fixed can assume can be derived as
follows.
Consider that 00. It is
also always true that the quotient Q/Qk>0. Therefore the product
in equation (A-47) can assume a nonnegative value if and only if
1 - D - Q/>0. This implies that 1 - Q>D, or, in expanded form
or,
/v . /v .
^ _/\ '> . ^-^_» \ J / ,
- Q ^ Z_ Try^y 4- ^ (A-49)
A-13
-------
since
and, in the limit:
-
(A-52)
(A-53)
<7" "^ (A-54)
is the lower bound on & for all the \j , j = m + 1, , N which are
known apriori.
alternatively, from (A-53) :
note that
A-14
-------
fYYV
^T
<3-£_4
A--/
(A-57)
hence
£_\^r Q< 7
^ I > 7T - 2 (A-59)
G-ZaJ^, *
k-i
and therefore:
6_ N "
r
' A
K.
letting
Q
and substituting (A-61) into (A-60):
- / ^ . x > / rr V
(A-62)
A-15
-------
or, assuming each term contributes to the total an amount proportional
to Q /Q:
(A-63)
(A-64)
(A-65)
and,
/ ... A/
' J (A-66)
are upper bounds on (j,j=m+l, ...,N, which can be fixed and still
satisfy if a.,j=l, ...,m are assumed to be zero. Equation (A-66)
provides the analyst with valuable guidance in the apriori selection of
values for one or more of the subclass errors in a source class.
A-16
-------
TECHNICS REPORT DATA
/ - , fPtetue read Inunctions OH the reverie before completing)
1. REPORT NO.
EPA-450/3-74-022-a
2.
4. TITLE AND SUBTITLE
Weighted Sensitivity Analysis of Emissions Data
Volume I - Background and Theory
7. AUTHOR(S)
F. H. Ditto, L. T.
L. J. Rushbrook
9. PERFORMING ORG "\NIZATION NAME Afv
IBM Corporation
18100 Frederick Pike
Gaithersburg , Maryland 207
12. SPONSORING AGENCY NAME AND ADC
Environmental Protection
Research Triangle Park, N
Gutierrez, T. H. Lewis
ID ADDRESS
60
IRESS
Agency
orth Carolina 27711
3. RECIPIENT'S ACCESSION-NO.
5. REPORT DATE
July 1973
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
68-01-0398
13. TYPE OF REPORT AND PERIOD COVERED
Final Report
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
This report presents a body of analytical techniques appropriate for determininj
accuracy requirements of component parts of an emissions inventory so as to insure
(at a given confidence level), an overall acceptable accuracy in the total inventory.
Selected numerical analyses are presented to illustrate application of the techniques
to Nationwide Emissions Report data at different levels of aggregation. The results
are believed to constitute a significant step in the development of techniques for
making reliable forecasts of air pollutant emissions, and have already been applied
for such purposes to emissions in Region 5 of the State of Virginia. A report on
that application is also included in the present document.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
Weighted Sensitivity Analysis
Emissions
NEDS
Data Systems
Industrial Classifications
Pollutants
13. DISTRIBUTION STATEMENT
Release Unlimited .
b. IDENTIFIERS/OPEN ENDED TERMS
V
19. SECURITY CLASS (This Report)
Unclassified
20. SECURITY CLASS (This page)
Unclas s i f i ed
c. COSATI Field/Group
21. NO. OF PAGES
125
22. PRICE
EPA Form 2220-1 (9-73)
;A-17
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