EPA-450/3-77-006
March 1977
EMISSION DENSITY
ZONING
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
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EPA-450/3-77-006
EMISSION DENSITY ZONING
by
Frank H. Benesh, Phillip D. McLellan,
Michael T. Mills, and Robert Patterson
GCA/Technology Division of GCA Corporation
Bedford, Massachusetts
Contract No. 68-02-1376
Task Order No. 26
EPA Project Officer: John L. Robson
Prepared for
ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
March 1977
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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 - in limited quantities - from the
Library Services Office (MD-35), Research Triangle Park, North Carolina
27711; or, for a fee, from the National Technical Information Service,
5285 Port Royal Road, Springfield, Virginia 22161.
This report was furnished to the Environmental Protection Agency by
GCA/Technology Division of GCA Corporation, Bedford, Massachusetts,
in fulfillment of Contract No. 68-02-1376, Task Order No. 26. The contents
of this report are reproduced herein as received from GCA/Technology
Division of GCA Corporation. The opinions, findings, and conclusions
expressed are those of the author and not necessarily those of the Environ-
mental Protection Agency. Mention of company or product names is
not to be considered as an endorsement by the Environmental Protection
Agency.
Publication No. EPA-450/3-77-006
11
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ABSTRACT
Emission density zoning is an air quality control strategy whereby
all parcels of land within an air quality maintenance area, excluding
public rights of way and reserved open space, are assigned maximum legal
emission allowances for particulate matter and sulfur oxides, expressed
in terms of mass' of pollutant per time period per lot area. The subject
of this publication is the development of criteria for (a) partitioning
an air quality maintenance area into component areas, (b) the setting of
emission density limits for all land uses in each component area and,
separately, all major emission sources, and (c) the revision of the emis-
sion density limits as conditions change. The criteria are then trans-
lated into a generalizable decision model, a linear program, for setting
the emission density limits. The criteria and model are tested in two
air quality maintenance areas, Baltimore and Louisville.
iii
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CONTENTS
Page
Abstract ill
List of Figures viii
List of Tables xi
Sections
I Introduction and Summary 1
Introduction 1
Organization of the Report 5
Summary of Project 6
Findings and Limitations 7
II Criteria for Partitioning AQMAs 12
Introduction 12
Air Quality Goals 13
Land Use Goals 20
Administrative Goals 22
III Criteria for Setting EDZ Limits 24
Economic Goals 25
Air Quality Goals 27
Land Use and Environmental Planning Goals 31
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CONTENTS (continued)
Sections
Administrative Goals 33
IV Criteria for Revising EDZ Limits 35
Criteria for Revising Limits Without an Emission Rights
Market 36
Criteria for Revising Limits With an Emission Rights
Market 37
V Specification of Decision Model 40
Maximization of Emissions (Model No. 1) 43
Minimization of Control Costs (Model No. 2) 48
Alternative Formulation of Control Cost Minimization
(Model No. 3) 49
Land Value (Model No. 4) 50
Variants of Model No. 1 52
VI Guidelines and Model Implementation Considerations 56
Resource Requirements 57
Linear Programming Considerations 58
Guideline for Executing the EDZ Model 62
VII An Example of the Emissions Maximization Formulation in
the Baltimore AQMA 95
Data Compilation 95
Execution of MPS 100
Optimal Solution to Sulfur Oxides Maximization 103
Particulate Matter Example 115
VIII An Example of the Emissions Maximization Formulation in
the Louisville AQMA 119
vi
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CONTENTS (continued)
Sections Page
Data Compilation 119
Execution of MPS 123
Particulate Matter Example 123
Sulfur Oxides Example
IX References 140
Appendixes
A An Introduction to Linear Programming 144
B Provision for Short-Term Standards in Air Quality Constraint 148
C The SO -PM Feasibility Constraint 160
D Specification and Utilization of Control Cost Parameters 169
E The Application of the Emission Density Setting Model in an
Attainment Situation . 178
vii
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LIST OF FIGURES
No. Page
1 Offset Gridding 15
2 Receptor Locations Outside an AQMA 19
3 Test City Example Output 72
4 ROWS Section of SOX Emissions Maximization Program 98
5 COLUMNS Section of SOX Emissions Maximization Program 99 .
6 RHS Section of the SOX Emissions Maximization Program 101
7 BOUNDS Section of SOX Emissions Maximization Program 102
8 MPS Control Program 104
9 ROWS Section of SO Optimal Solution 105
10 COLUMNS Section of SO Optimal Solution 106
11 Slack SO Levels (micrograms per cubic meter) 109
X
12 Status of Bounds on Emission Density Limits, Current
Light Industry 110
13 Status of Bounds on Emission Density Limits, Future
Light Industry 111
14 Status of Bounds on Emission Density Limits, Current
Heavy Industry 113
15 Status of Bounds on Emission Density Limits, Future
Heavy Industry 114
16 Slack TSP Levels in Baltimore (micrograms per cubic meter) 116
17 Status of Bounds on Emission Limits, Current Light Industry 117
viii
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LIST OF FIGURES (continued)
No. Page
18 Louisville AQMA Component Area Grid System 120
19 Numbering of Louisville AQMA Component Areas 121
20 Slack SOX Levels (micrograms per cubic meter) 126
21 Projected SOX Concentrations (microgram per cubic
meter) 127
22 SOX Levels Attributed to EDZ Sources (microgram
per cubic meter) 128
23 SOX Levels Attributed to non-EDZ Sources
(micrograms per cubic meter) 129
24 Status of Bounds on Emission Limits, Current Light Industry 130
25 Status of Bounds on Emission Limits, Future Light Industry 131
26 Status of Bounds on Emission Limits, Current Heavy Industry 132
27 Status of Bounds on Emission Limits, Future Heavy Industry 133
28 SOX Emission Density, Base Year (tons per day per
square kilometer) 134
i
29 SOX Emission Density, Design Year (tons per day
per square kilometer) 135
30 SOX Emission Density, All Sources at Upper Limit
(tons per day per square kilometer) 136
31 Construction of Feasible Region 146
32 Determination of Optimal Solution 146
33 Location of TSP Monitoring Stations and Associated Geometric
Standard Deviation 154
34 Hypothetical Relationship Between SO and PM Emissions 161
X
35 Plot of Baltimore Heavy Industrial Point Source PM Emission
Rates Versus SOX Emission Rates (tons/year) 164
ix
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LIST OF FIGURES (continued)
No. Page
36 Plot of Baltimore Heavy Industrial Point Source PM Rates
Versus SOX Emissions Rates, Sources With Emissions Less
Than 100 Tons/Year 165
37 Plot of Baltimore Light Industrial Point Source PM Emission
Rates Versus SOX Controlled Emission Rates (tons/year) 166
38 Plot of Baltimore Commercial Point Source PM Emission Rates
Versus SOX Controlled Emissions Rates, Excluding Coal
Burning Sources (tons/year) 167
39 Scheduel of Emission Reductions Versus Control Costs for
Prototypical Heavy Industrial Point Source 174
40 Plot of Linear Approximation of the Control Cost - Emission
Reduction Schedule 175
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LIST Of TABLES
No^ Page
1 Definitions of Variables Used in Section V 44
2 Control Cost and Emission Schedule, Example of Prototypical
Heavy Industrial Point Source 51
3 Problem Characteristics and MPS Timing Estimates, Emissions
Maximization Linear Programming 60
4 Requisite Data for Preparing an Emissions Maximization
Linear Program 62
5 Test City Base Year Emission Inventory, SO (tons/day) 67
X
6 Test City Land Use Inventory (square kilometers) 68
7 Calculation of the Right-Hand Side 69
8 1974 TSP Concentrations Recorded at Monitoring Stations
in the Baltimore AQMA 150
9 1974 SO Concentrations in the Baltimore AQMA 156
x
10 1980 to 1990 Projections of Growth in Manufacturing
Earnings ($000) 170
11 Emission Reductions and Associated Control Costs 173
xi
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SECTION I
INTRODUCTION AND SUMMARY
INTRODUCTION
Emission density zoning is an air quality control regulation whereby
a maximum legal rate of air pollutant emissions is prescribed for certain
parcels of land. The limits are expressed in terms of mass of pollutant
per time period per lot area. The maximum legal rate, or emission density
limit, would vary with the location and the planned use of the land parcel.
The concept of an emission density strategy is not new. An early
discussion of its potential was published by the National Air Pollution
Control Administration in 1968.29 Subsequently, John Roberts and Edward
Croke of Argonne National Laboratory contributed greatly to a definition
of an EDZ control strategy, its,potential, and its limitations.30*31
Emission density related control strategies, similar but not the same
as those contemplated in this report, have been implemented in Chicago,
Illinois and Louisville, Kentucky.26'32
In concept, it is very similar to the typical use of density and
bulk regulations in land use zoning. Each parcel of land is assigned
a permitted use; e.g., residential, commercial, and the permitted uses
have associated maximum densities. For example, a residential zone may
have a maximum density of two dwellings per acre; i.e., a minimum lot
size of 1/2 acre. Similar restrictions are placed on commercial and
office zones, frequently in terms of a floor area ratio (FAR), which
specified the maximum amount of building floor area per lot area. For
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example, a four-story building covering one-half of the lot would have
a FAR of two.
Land-use zoning is usually applied to all areas of the city, both
developed and undeveloped. Developed; i.e., currently built on, land
can expand or redevelop up to the maximum permitted density and use for
its zoning class. One land use may have differing maximum permitted
densities in various areas of the city; e.g., for residences, one may
find areas zoned for a minimum lot size of 2 acres and other areas in
the same city zoned for 1/2-acre lots. Emission density zoning could
also be implemented in this manner, such that all areas of the region
are controlled and that similar land uses have different maximum emis-
sion densities, depending on their location within the city.
This report describes the criteria for setting the emission density
limits in a metropolitan region, a model for setting the limits, and
examples of the application of the criteria and model. The region
considered is an air quality maintenance area1 because this is convenient
for air quality planning purposes (though other regions could be em-
ployed) . The model sets emission density limits for a grid network of
squares called component areas. It is assumed that either all the land
use within a particular category in a component area will have identical
emission density limits, or that a local jurisdiction will reassign
emission density limits reflecting local planning goals but not increas-
ing the total permitted emissions within the component area.
In a manner similar to land-use zoning, the emission density zoning
model described in this report is based on a land use plan. It adopts
the amount and configuration of land use for a specified future date,
called a design year, and sets a pattern of emission density limits that
achieve an adopted objective. The emission density limits are suf-
ficiently high on every parcel of land to permit development as contemplated
in the land use plan. However, in some areas they would be so stringent as
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to permit only certain types of the broad category of development out-
lined in the land-use plan, to require the application of emission control
techniques, or to require development of a lesser density; i.e., the same
kind of development on a larger parcel of land. In other areas, the po-
tential development will not be so restricted.
This dependence on a region's land-use plan, as well as specific
implementation concerns, requires the substantial involvement of city
and regional planners as well as air pollution control engineers in the
setting of emission density limits and the implementation of an emission
density zoning ordinance.
It is possible (and, in fact, may be desirable) that emission density
zoning be implemented with the provision for transferable emission rights.
This would be similar to transferable development rights in conventional
zoning. A market for transferable emission rights is attractive in that
it will allow the pattern of set emission limits to change with changes in
growth patterns, yet still maintain the National Ambient Air Quality
Standards (NAAQSs). Transferable emission rights may be necessary to ensure
the legal and political acceptability of emission density zoning. The En-
vironmental Protection Agency's proposed Emission Offset policy (41 FR
55524 and 55558) almost certainly will stimulate development of such a mar-
ket. The required new institutional mechanisms, however, are not considered
in this report.
Emission density zoning, as contemplated in this report, would in-
clude the following procedures:
• Each compartment area and, separately, each major stationary
source, will be assigned emission density limits by the
regional authority that are the maximum densities of
annual* emissions of sulfur oxides (SOX) and particulate
matter (PM).
Annual emission density limits, to be effectively enforced, probably
will require translation into daily limits.
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• Except for major stationary sources, all land of the same
land use category in a component area, as specified in
land use plans and/or zoning ordinances, will be assigned
the same emission density.
• Every parcel of land in the region, excluding public
rights-of-way and reserved open space, will have a fixed
emission density limit.
• Local jurisdictions may reallocate but not increase emis-
sion limits within a component area as local plans, zoning,
or planning goals change. Local jurisdictions may reallo-
cate emissions among component areas under their authority
subject to the constraints discussed in Section IV of this
report.
• A market for transferable emission rights among industrial,
and perhaps commercial, sources may be instituted according
to the procedures described in Section IV of this report.
• Variances may be granted by a regional authority subject to
the limitations described in Sections III and IV.
Brail26 has defined four types of emission quota strategies, viz.
• Emission Allocation Planning - (jurisdictional emission
quotas) under which the air pollution control agency
allocates permissible emission quotas by local govern-
ment jurisdiction within its region. No attempt is made
directly to apply the emission quota to new stationary
sources.
• Floating Zone Emission Quotas - in which a limitation
on pollutants generated within an area of a specified
size which can be drawn about any specific location
within the metropolitan area.
• District Emission Quotas, a step down from emission
allocation planning, a strategy which limits the amount
of pollutants to be emitted during some time period from
a planning district within a jurisdiction.
• Emission Density Zoning in which the emissions of a
pollutant be limited to prescribed levels for a selected
unit area.
The subject of this report does not fit neatly into any of the above
categories. The output of the decision model does provide unique emission
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density limits for every major point source; thus it may be called emis-
sion density zoning. It also provides emission density limits for every
area source. The area source emission density limits are uniform for all
land use of a particular category within a component area; i.e., grid
square. Thus, the emission density limits for a specific land use within
a component area can be summarized as an emission quota for that land
use, an approach similar to district emission quotas. Moreover, in the
contemplated implementation scenario, the total emissions in a municipality
are treated as a jurisdictional emission quota which the municipality
would be free (and encouraged) to reassign. Thus the subject of this
report is a decision model for setting emission density limits, the con-
templated implementation of which may include elements of emission allo-
cation planning and possibly district emission quotas. If desired, the
model can be used as a means of setting jurisdictional emission quotas
or district emission quotas without assigning emission density limits.
ORGANIZATION OF THE REPORT
The remainder of this section is devoted to a summary of the report.
The following three sections of this report describe the criteria for
partioning a region into component areas, setting emission density limits,
and revising the emission density limits at a later date as conditions
change. Next, Section V describes the specification of a mathematical
model, a linear program, for setting the emission density limits. Sec-
tion VI describes a step-by-step procedure for executing the model.
Sections VII and VIII illustrate the application of the criteria and model
in two example regions, Baltimore and Louisville.
There are several appendixes. The first is a brief introduction to
linear programming and should be read first by the reader unfamiliar with
the technique. The second and third discuss two refinements of the model,
the consideration of short-term air quality standards and the consideration
of a functional relationship between sulfur oxide and particulate matter
emission rates. Appendix D discusses the estimation of control costs for
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future emission sources, which is necessary for an alternate formulation
of the emission limit setting model. Appendix E discusses the application
of the model if attainment is a problem (i.e., air quality standards are
currently being violated).
SUMMARY OF PROJECT
Criteria for partioning a region into component areas for the pur-
poses of setting emission density limits were developed. This partioning
of a region very closely approximates the process of gridding an air
quality control region (AQCR) for the purposes of dispersion modeling.
More attention, however, is given to minimizing the number of large grids
spanning jurisdictional boundaries.
Criteria for setting emission density limits in component areas were
developed and translated into a generalized mathematical model. The model
was tested in two air quality maintenance areas (AQMAs), Baltimore, Mary-
land and Louisville, Kentucky. Criteria were also developed for revising
the emission density limits due to unforeseen growth or changes in commu-
nity land use plans.
The model for setting emission density limits is in the form of a
linear program. The simplest formulation of the model is one that maxim-
izes the aggregate regional emissions of air pollutants subject to the
constraints that the NAAQSs are not violated and the emission density limit
set for each source be in a feasible range. The maximization of emissions
is assumed to be loosely associated with minimizing the conflict between
maintaining the NAAQSs and regional economic growth. The opportunities
for other formulations of the model are presented; among them is the mini-
mization of control costs of firms complying with emission density limits.
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The model for setting emission density limits (EDLS) is based on and
assumes the validity of the land use element of the comprehensive plan for
the region. The emission density zoning (EDZ) model does not alter the
location of development within the broad categories of the plan. The emis-
sion density limits set by the model do place additional constraints on the
nature of development at any one location. Within a broad category of
development; e.g., light industry, the pattern of emission density limits
identifies those locations in the region planned for such development that
can more easily accommodate development with high emission rates and those
areas that are more suited for low emission rates. In other words, the
model identifies the optimal pattern of "carrying capacities" that maximizes
the total emissions in the region (while maintaining the NAAQSs).
FINDINGS AND LIMITATIONS
The emissions maximization formulation of the model was tested in
two AQMAs. In each AQMA it was executed twice, once for particulate matter
and once for sulfur oxides, the two pollutants that are principally from
stationary sources. (Pollutants such as carbon monoxide, which is gener-
ated primarily by mobile sources; e.g., the automobile, are not well-
suited to control by emission density zoning.) Overall, the testing of
the model was successful.
The model, however, assumes attainment of the NAAQSs; i.e., the air
quality in the region is currently below the standards. If this is not
the case, control strategies must first be developed to restrict the
emissions of existing sources so that attainment of the NAAQSs is achieved.
Moreover, the model assumes that if the region develops according to the
land use plan and all future development employs the best available emis-
sion control technology while building facilities at the lowest develop-
ment density economically feasible, the NAAQSs can still be maintained.
The model operates, then, on the middle ground between the extremes of
future development without additional controls (which is assumed to violate
the NAAQSs) and requiring all future development to adopt the most stringent
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controls (which is assumed not to violate the NAAQSs). The model can be
revised to accommodate situations outside this range.
Several problems may confront a user of the model. First, the size
and complexity of the linear program increases rapidly with the number
of emission sources; i.e., component areas. For metropolitan areas
roughly the size of'Baltimore or larger, the computer resources required
to solve the linear program can become quite large; i.e., over an hour
of computer time. In such cases it is possible to solve a series of
smaller problems. One can solve the problem for a sample; e.g., 10 per-
cent, of the receptors (locations at which air quality is calculated), and
then use the solution to that problem as a starting point to solve the
linear program with a full complement of receptors (or a dense field of
receptors near those receptors projected to approach the NAAQSs).
Second, the user of the model must be able to specify the maximum
emission density that can be expected in each land use category as well
as the minimum emission density that is economically feasible and still
compatible with development according to the land use plan. This is a
critical data item; one can expect to devote a significant amount of man-
power (several man-months) to compiling it. Many emission density limits
will be set at one of these limits.
Third, the general pattern of emission density limits that can be
expected implies that the land use plan must have addressed urban sprawl.
In the model tests that were conducted, emission sources on the periphery
of the region were set at their upper limits and sources at the center
of the region were set at their lower limits. This pattern means that:
• Capacity expansion of existing sources at the periphery
is favored over those in the center of the region.
Centrally located sources cannot expand their capacity,
and hence increase emissions, without reducing their
emissions from current activities. Suburban sources
are not so limited.
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• The permitted emission densities on undeveloped land,
within a specified category, are higher on the periphery
of the region and lower'in the center. This would seem
to encourage development away from the center of the
region unless there are more overwhelming locational
advantages at the central location.
While such a pattern of emission density limits does not affect the amount
of land planned for specific uses, it confers on peripheral locations a
decided advantage. The congruence of this phenomena with other planning
goals must be examined. A more balanced allocation of emission limits may
be desirable, facilitating additional development at central locations at
the expense of a lesser aggregate amount of permitted emissions in the
region. It is this attempt at balance that the control cost and land
value formulations of the decision model address.
Implementation Considerations
There are several considerations that will be faced by an agency
implementing EDZ. One should first note that EDZ cannot be used to
control natural and transported particulate matter, and emissions from
nontraditional sources. Background pollution, auto exhaust, reentrained
road dust, fugitive dust from construction, demolition, and quarrying and
dust from unpaved areas and other urban activities fall into this difficult-
to-control category. The contribution of background and nontraditional
sources to each receptor must be projected for the design year. If the
EDLs are met by every controlled source, it is still possible to violate
the NAAQSs if the noncontrolled EDZ sources actual emissions are greater
than was projected.
Implemention of EDZ will require substantial intergovernmental coopera-
tion. A close working relationship between the staffs of the regional air
pollution control agency and the regional planning agency is necessary —
more so than in other aspects of air quality maintenance planning. More-
over, EDZ must be integrated into the regional planning process and must
influence the transportation plan, water resource management plan, and land
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use element of the regional plan. The EDZ limit setting model computes an
"optimal" set of EDLs without considering their effect on mobile source
pollutants, water pollution, housing quality, core area revitalization,
conversion of agricultural land, and other regional goals. This means
that the regional plan must have already dealt with these issues. The EDZ
model will then optimize the potential emission density pattern within the
limits of the regional plan. The 208 and transportation plans must be
based on, and be compatible with the regional plan.
Cooperation among and within regional agencies is not all that is
required. EDZ also requires the involvement and commitment of local
governmental units. Ideally, the municipalities in the region will
internally reallocate the regionally-specified EDLs so that they will
reflect local planning goals, and will include the implicit municipal
emission quota as a constraint in subsequent revisions of the local land
use plan. At a minimum, the municipality must include compliance with
the EDL as an additional criterion when issuing building and occupancy
permits. For example, the EDZ ordinance might require a certificate
signed by a professional engineer stating an estimated average daily
emission rate to accompany all permit applications. The municipality
could then check compliance with the maximum permitted emission density
as it now does for compliance with the maximum permitted development
density. If the municipality is unwilling to cooperate in administering
EDZ, a scenario like the one postulated earlier may be unfeasible. An
unexamined issue is how one might require or force a municipality to
administer EDZ.
If municipality-based administration of EDZ is unfeasible, a regional
or state agency will have to administer it. This is less desirable,
because it is likely that only sources above a certain threshold size
could be checked for compliance. This limits the effectiveness of EDZ.
A possible loss of flexibility in a regionally-administered system, and
a possible lack of integration with local planning, also appear to make
a regional system less desirable.
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Another issue is how to ensure compliance with the EDL once a
facility is operating. Most of the physical changes in a facility that
would alter its emission rate can be controlled through the building per-
mit process. There are, however, at least two other actions that alter
emission densities and may be more difficult to control. An industrial
facility may desire to increase its hours of operation. It may then
not be in compliance with its EDL. More traditional emission control
for point sources, administered by the regional agency, are thus still
necessary in conjunction with EDZ. Also, a facility may change its land
holdings, thereby changing its emission density. Some mechanism must
be designed either to prevent a source from selling vacant land used only
to satisfy EDZ, or to reduce the EDL on the land that was transferred to
a new owner. A transferable emission rights market may alleviate this
problem.
The legal basis for emission density zoning is unclear. While there
appear to be no substantial issues raised if emission density zoning is
implemented as a maintenance strategy,26 a specific implementation
strategy has not been reviewed. For example, because emission density
zoning is patterned after land use zoning, should emission density
limits for the same land use category in a component area differ among
parcels? In conventional zoning, the regulations must be uniform for
each class and kind of building within a district.
Finally, the political considerations inherent in assigning emis-
sion density limits should be noted. First, as previously mentioned, the
issue of balance between the center city of a region and suburban loca-
tions must be addressed by the implementing agency. Second, the assign-
ment of emission densities to component areas and, hence, the allocation
of emissions to local jurisdictions constrains the zoning prerogative of
the jurisdiction. Though the local jurisdiction may be permitted to
reallocate emission rights among districts within its boundaries, the
total emissions permitted from within a grid cell is essentially fixed.
Third, emission density zoning, by assigning limits according to a regional
land use plan, can become a substantial tool for implementing the plan.
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SECTION II
CRITERIA FOR PARTITIONING AQMAs
INTRODUCTION
Emission density zoning (EDZ) requires the partitioning of an air
quality maintenance area into smaller units. Such divisions are common
in air quality studies, most notably in connection with air quality model-
ing. When an array of square or rectangular units is used, one refers
to this array as a "grid system" comprised of "grid cells" or "grid squares."
The problem in partitioning any area for EDZ is to choose the sizes
of grid cells, and the spatial arrangement of grid cells and receptors,
to account for various concerns of EDZ. So that these concerns may be
better defined, the overall goals of EDZ are broken down into three
categories with particular relevance to the gridding problem. These
categories are maintenance of air quality standards, adequate considera-1
tion of existing and future land use patterns, and administration of EDZ.
There is, of course, some overlap among these categories, but the dis-
tinctions provide a useful framework for discussion of the gridding problem.
In the following discussion the specific concerns within each of these
categories are presented, along with the specific gridding objectives
suggested by them. Criteria for meeting each objective will then be
presented.
Attention should first be drawn to EPA's Guidelines for Air Quality
Maintenance Planning and Analysis, hereafter referred to as the Guidelines.
12 3
Volumes 7, 8, and 13 are particularly relevant to the gridding concerns
of EDZ, and the user should be familiar with the techniques described in
12
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them. Volume 7 presents methods for projecting pollutant emissions by
counties, and Volume 13 describes how these emissions can be allocated
to subcounty areas. Volume 8 presents a semiautomated (computerized)
procedure for constructing an area source emissions inventory grid, based
on population densities. A manual overlay gridding technique is also
presented in Volume 13.
As noted previously, an EDZ analysis assumes the"existence of studies
such as those described in the Guidelines. If the grid system for the
air quality analysis and the concurrent emission inventory are prepared
in a manner compatible with the requirements of EDZ, a substantial
amount of effort will be saved.
AIR QUALITY GOALS
The need for air quality maintenance planning is based on the likeli-
hood that growth and development will lead to a violation of air quality
standards. The key to maintenance planning with EDZ is to identify
existing and potential problem areas and to set emission density limits
in these areas sufficient to maintain air quality. Analyses of emission
inventories and air quality monitoring data and estimates of growth in
emissions are sources of this information. It is also necessary to relate
emissions to ambient concentrations through the use of a diffusion model
4
such as the Air Quality Display Model (AQDM). Thus any grid system must
meet the requirements of the diffusion model used to determine this rela-
£
tionship. For example, AQDM requires that all area source grid cells
be squares, and that all receptor locations have positive coordinate values.
*
AQDM is the only model currently capable of producing the source-receptor
file (described in Section III)~used as an input to the decision model.
However, the Climatological Dispersion Model (CDM)5 is being modified to
generate such a file, and may be recommended by EPA for future applica-
tions. CDM currently imposes certain requirements on the grid system,
and these requirements are likely to remain in force for any revised ver-
sions. These requirements are as follows: large grid cells must be in-
tegral multiples of the smallest grid cell in the array; the grid system
outline must be rectangular; and, all grid cells must be squares. These
13
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Grid cell side lengths should be between 1 and 8 km, as this size
range ?llows for resolution of most data normally used for air
quality planning. Furthermore, grid cells should be of sizes that can
be easily aggregated or subdivided. The easiest way to obtain a grid sys-
tem that meets these requirements is to use side lengths of 1, 2, 4, or
8 km for all grid cells. The best method for preparing such a grid sys-
tem is to overlay an array of 8 km x 8 km cells on the study area, and
then to subdivide these cells according to the criteria presented below.
It is recommended that the Universal Transverse Mercator (UTM)
coordinate system be used for grid registration since this system is
widely used for other air quality planning purposes.
These considerations can be summarized in the first criterion for
partitioning an air quality maintenance area:
1. Grid cells shall be squares with side lengths between
1 and 8 km, based in the UTM coordinate system. Addi-
tionally, they shall be of sizes that are easily aggre-
gated and subdivided. In order to comply with this
criterion, side lengths of 1, 2, 4, and 8 km are strongly
recommended.
The grid system is the means for spatially allocating existing and
projected area source emissions for modeling. Thus, grid sizes must be
chosen that give adequate resolution of emissions. "Adequate resolution"
simply means that the grid size must be small enough to prevent under-
estimating concentrations, but not smaller than the scale of the data and
requirements also mean that any offset between grid cell boundaries (see
Figure 1) must be an integral multiple of the side length of the small-
est grid cell. In fact, the user should avoid offsets whenever possible,
as they can lead to the use of small, inefficient dummy cells to "fill
out!1 the rectangular boundary. If it is necessary for the user to fill
out an existing grid system with zero-emission dummy cells to make it
rectangular, the added grid cells should be as large as possible; e.g.,
even larger than the 8 km x 8 km limit imposed in the criteria. CDM's
requirements strongly suggest use of the 1-2-4-8 gridding system
described in the text.
14
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Figure 1. Offset gridding
15
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modeling efficiencies will allow. Thus the higher the area source emis-
sion density, the smaller the grid size required to provide resolution.
Emission densities correspond to the intensity and type of develop-
ment in an area. Industrial land uses typically emit more pollutant
per hectare than residential or commercial uses, the high-rise residential
development typically has a higher emission density than single-family
houses on large lots.
In preparing the grid the user need not know actual emission den-
sities. Instead, he may use other values as proxies, such as the values
used to allocate emissions in maintenance planning analyses.8 The most
common such value is population. Emission densities for several land
uses are considered to be directly related to population densities.
One obvious exception to this relationship is industry. Industrial
emissions are more typically related to employment, process volumes, or
value added. However, since industrial emission densities are among the
highest of any land use type, gridding can be simplified by applying the
smaller grid sizes to heavy industrial areas. The user should keep in
mind that a large part of industrial emissions may be point source emis-
sions, which need not be reflected in the grid.
The following criteria are based on these considerations and allow
the user to prepare a grid system that reflects likely emission densities.
2. Areas having an existing or projected population density
greater than 2,000 persons per square kilometer should be
contained in grid cells no larger than 1 km x 1 km.
3. Areas having an existing or projected population density
between 1,000 and 2,000 persons per square kilometer should
be contained in grid cells no larger than 2 km x 2 km.
4. Areas having an existing or projected population density
between 200 and 1,000 persons per square kilometer should
be contained in grid cells no larger than 4 km x 4 km.
16
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5. Areas containing heavy industrial sources* that are not in-
dividually itemized in the emission density limit setting process
should be contained in grid cells no larger than 2 km x 2 km.
The relationship between emission density and grid size also holds true
for concentrations. High-concentration areas (i.e., those areas where
concentrations are near the air quality standard) may be identified from
isopleth maps based on monitored or projected concentrations at selected
receptor points. Resolution of emissions is especially important in
these areas, as great care must be taken in locating any new sources
there. Therefore:
6. Areas in which existing or projected pollutant concen-
trations are 90 percent or more of the applicable air
quality standard shall be contained in grid cells no
larger than 2 km x 2 km.
Problems can still arise in areas having lower concentrations. It
is possible that a given grid cell may have an existing or predicted con-
centration low enough to allow for a substantial amount of development.
However, the spatial distribution of emissions within the cell may lead
to a "hot spot" problem if all the development is clustered in a small
area. Thus, if the cell is larger than 1 km x 1 km, it should be sub-
divided to reflect emission patterns more accurately. This requires that
emissions be allocated to the grid cells. Then:
7. If the projected emission density of a grid cell in the
system produced by criteria 1 through 6 is higher than
the median value for the air quality maintenance area,
and if by subdividing the cell into four equal parts
and reapportioning emissions to the resulting
cells, 40 percent or more of the total emissions for the
original cell can be assigned to a smaller cell, the sub-
division shall be incorporated into the grid system. This
criterion clearly cannot apply to 1 km x 1 km grid cells.
For example, defined as Standard Industrial Classification (SIC)
categories 26 through 33.9
17
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The "hot spot" situation just described highlights the importance
of another concern, the location of receptor points. Clearly a strategy
like EDZ requires detailed information on emissions and concentrations
throughout the air quality maintenance area. Therefore:
8. A model receptor point shall be located within each grid
cell, preferably at the center. If an existing monitoring
site is located within a grid cell, that site can be sub-
stituted for the receptor point to lower modeling costs.
One other consideration for receptor location must be mentioned.
Because one of the goals of EDZ is maximizing the use of the assimilative
capacity of the air, the decision model may tend to set higher emission
density limits in grid cells near the outer edge of the air quality
maintenance area. This happens because emission sources located in those
areas have a smaller cumulative impact on air quality within the air
quality maintenance area than those located in the center of the grid
system. This is an undesirable outcome, as it may cause violations of the
NAAQS if sufficient industrial development is planned for along the bound-
ary of the AQMA, and regardless of the type, of development, it may cause
a violation of the allowable PSD increment in the county adjacent to the
AQMA. To be able to control this possibility, the receptor grid should
be extended into the adjacent areas, as shown in Figure 2. Therefore:
9. In AQMA's where there is or may be substantial industrial
development near the AQMA boundary, or where the adjacent
area is a Class II or Class I PSD area, a row of receptor
points shall be added at regular intervals around the out-
line of the grid system at a distance of not less than
4 km. It is recommended that these receptors be placed
at what would be the center points of 8 km x 8 km grid
cells, as illustrated in Figure 2.
Another air quality goal related to model receptor location is pro-
tection of sensitive receptors. The issues involved in identifying these
receptors and setting air quality standards for them are presented in
Prevention of Significant Deterioration.
18
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8 km —*|
i r
~r
I
\
X
X
-AQMA GRID
BOUNbARY
•"
X
^
RECEPTORS
Figure 2. Receptor locations outside an AQMA
19
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Section III. If the user decides to protect sensitive receptors, receptor
points representing them must be included in model runs. However,
increasing the number of receptor points increases the cost and complexity
of modeling. Therefore:
10. A receptor point shall be placed at the location of each
sensitive receptor designated as "protected" by the
implementing authority. Receptor points located under
previous criteria may be substituted if they are located
within 1 km of the sensitive receptor.
A final air quality goal with relevance to both gridding and re-
ceptor location is prevention of significant deterioration. As currently
proposed, significant deterioration regulations will effectively require
air quality standards more stringent than the NAAQSs to be met in desig-
nated areas. The standard will depend largely on the area's classifica-
tion. Therefore:
11. A single grid cell shall not contain areas with different
classification for significant deterioration requirements,
unless at least one receptor point is located within each
area.
It is quite likely that by following the above criteria, so many
receptors are identified that in a large AQMA the computer resources
necessary to execute the linear program for setting emission density
limits may become prohibitive. Techniques for modifying the receptor
grid to overcome this problem are discussed in Section VI.
LAND USE GOALS
From the discussion of air quality goals it is clear that land use
patterns must be considered in the gridding process. Land use patterns
serve as a proxy for emissions, and projections of future emissions must
be based on future land uses. Furthermore, land use plans represent
community preferences about development. For EDZ to be meaningful it must
be implemented in a way that reinforces and is consistent with the land
use plan; the grid system should reflect the patterns in that plan.
20
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For the purposes of setting and administering emission limitations,
the ideal grid would have a single land use in each cell. Otherwise, a
single-number emissions limit must be translated into emissions limits
for a number of source types, unless the community has no particular
land use preferences in a given grid cell. Given the scale of most urban
development and the size range of grid cells, isolating land uses with
the grid is not practical. Ranking of land uses by their air quality
impacts might be possible, but in most cases emissions result from a
combination of activities. Considering these combinations, rather than
individual land uses, in the gridding process will give better informa-
tion about emissions, at least in urbanized areas.
However, it may be desirable in some cases to consider plans more
explicitly, and to grid so as to separate incompatible land uses. An
example might be a planned industrial area bordered by low density housing.
While undue expansion of the industrial area can be effectively prevented
with a low emissions ceiling for a large grid cell containing both uses, .
location of facilities within the cell is not directly addressed. If
the cell were subdivided so that the two areas were placed in separate
grids, limits could be set that would directly reinforce the desired
development patterns.
"Incompatible land uses" must be identified from their differential
air quality impacts, arid not simply from the kinds of activities they re-
present if such a strategy is to be successful. Further, such a decision
is most appropriately made by local jurisdictions. One obvious category
of land uses to be included is sensitive environmental areas. If such
areas are not otherwise protected, they can be separated from other land
uses by grid boundaries, and appropriate emission limits can be set to
prevent development of them.
Another feature of some plans is their consideration of natural
boundaries to development, such as water bodies. Such boundaries can
simplify gridding based on land use patterns. Grid cell subdivision is
not necessary if an effective boundary already exists.
21
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12. When the user judges it necessary he may separate in-
compatible land uses with grid boundaries. The deci-
sion should be based on applicability of other criteria,
likelihood of conflicts over land use that may be re-
solved in a way detrimental to air quality goals, and
the presence of natural boundaries that effectively
limit the spread of a given land use.
ADMINISTRATIVE GOALS
EDZ can be implemented and enforced through any of a number of agency
structures, and will require substantial interagency cooperation. Careful
consideration of grid placement can help reduce the potential for such
conflicts. In the California situation cited by Brail, et al.,26 local
jurisdictions were concerned with whether emissions limits assigned by
the State Air Resources Board would be set for local jurisdictions or for
grid cells. In such a situation it would clearly be desirable for each
grid cell to be wholly contained within a single jurisdiction. Again,
given the size range of grid cells this is neither efficient nor feasible.
Rather, it may be desirable to identify areas of high conflict potential
and to subdivide grid cells in these areas to fit jurisdictional boundaries
as closely as possible.
For example, such a situation was encountered in the Louisville test
of these criteria. The Indiana Port Commission has planned construction
of an industrial area and port facility on the Clark County, Indiana shore
of the Ohio River, located within the Louisville Interstate air quality
maintenance area. The Kentucky shore and an island in the River opposite
the proposed site are used for recreational purposes, and Kentucky is
opposed to development of the facility.10 It would clearly be desirable
to have grid boundaries conform to state boundaries in this case, but the
grid scale makes it unlikely. Emission density limits can be set for any
grid cell spanning the state boundaries, based on both states' regional
land use plans. Once these limits have been set, allocation of emissions
to each portion of the grid cell may be done on the same basis. Disputes
22
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between the states might then be settled by some negotiating procedure.
The point is simply to facilitate such negotiations by subdividing grid
cells in such areas to the smallest allowable size.
13. If a single grid cell spans jurisdictional boundaries
and the potential for conflicts between jurisdictions
over land uses in the grid cell is high, the cell shall
be subdivided until each grid cell is contained as
nearly as possible within a single jurisdiction.
A second general administrative goal is to simplify the process of
regridding in response to developments in the air quality maintenance
area. First, the need to regrid will be minimized by meeting the grid-
ding criteria in the first gridding effort. Second, the criteria must
also be observed for any regridding effort, and hence provide guidance
as to when regridding is necessary; e.g., for obtaining adequate resolu-
tion of emissions. Finally, selection of grid sizes that can be aggre-
gated or subdivided easily will make regridding simpler.
14. Grid boundaries shall be redrawn whenever changing condi-
tions cause any of the criteria to be violated.
In any administrative situation minimizing costs is important. Since
the criteria are designed to simplify the process of implementing EDZ,
meeting them should help minimize costs. Since cost (especially modeling
costs) is partly dependent on the number of grid cells, unnecessary
subdivisions should be avoided. For example, the gridding technique in
Volume 13 of the Guidelines requires that the user subdivide grid cells
until each portion of the air quality maintenance area for which alloca-
tion data are available is contained as nearly as possible within a single
grid cell. This may be unnecessary for achieving adequate resolution
of emissions for EDZ. Therefore:
15. A cluster of adjoining grid cells may be aggregated if
the resulting cells do not violate any of the previous
criteria.
23
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SECTION III
CRITERIA FOR SETTING EDZ LIMITS
The relatively long-term nature of air quality maintenance requires
that those measures used to ensure maintenance be as compatible as
possible with overall community goals. Air quality is oftentimes not as
tangible'an objective as other public desires and is thus open to per-
haps closer scrutiny than more tangible desires such as more jobs. It
is for these reasons that considerations other than air quality must
also be included in setting EDZ limits.
The following discussion has two objectives. First, the criteria
that planners are likely to require are identified. Secondly, these
criteria are expressed in terms compatible with the decision model used
to set emission density limits. Four groups of goals from which cri-
teria can be developed have been identified and are discussed in turn.
These are economic goals, air quality goals, land use and environ-
mental planning goals, and administrative goals.
The discussion assumes the reader's familiarity with the basic ter-
minology of linear programming, as this is the technique used to set emis-
*
sion density limits. Some criteria have thus been formulated as objec-
tives or constraints.
*
The reader unfamiliar with linear programming is referred to Appendix A,
which is a brief introduction to the subject.
24
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ECONOMIC GOALS
The economic goals of any region are, in the general sense, well
known and often stated. In a word, prosperity is sought. Economic
prosperity is typically identified with high levels of employment, stable
prices and tax levels, and a diversity of economic activity. EDZ is likely
to influence the location, density, amount, and type of industrial activity
in the region. Therefore, criteria in this area must be established.
Emission density limits can affect urban development either by pre-
cluding certain types of activity altogether or by necessitating controls
for new establishments. Therefore, accounting for these impacts will
require two kinds of information. First, the user must have some idea
of the amount of growth expected to occur during the period covered by
the maintenance plan, and how the growth will be distributed across the
air quality maintenance area. The best sources of this information are
the land use element of the comprehensive regional plan(s) applicable to
the air quality maintenance area, and local plans and zoning. These plans
and regulations reflect community preferences and expectations about
growth, and the emission density limits should reflect the amount and
location of growth called for in them. To accomplish this, the user
must define a value for the projected maximum emissions (without EDZ)
from a given site for the last year of the planning period. These val-
ues can then be used in the decision model in various ways, depending
on the formulation the user selects.
In most instances the user cannot determine exactly which industry or
other development will locate where in a region. For example, most plan-
ning and zoning schemes include only one or two industrial land use cate-
gories; e.g., heavy and light, or general and permitted. Therefore, the
user should select those categories within each land use category that
are expected to show the most growth as prototypes for calculations of
future emissions.
25
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With this information, emission density limits can then be set by
maximizing the aggregate emission loading in the region, given the pro-
jected land-use growth. Emission density limits would thus be set, while
keeping within the bounds of minimum and maximum feasible rates that will
allow the development specified in the land-use plan, in a manner that
allows the greatest amount of emissions consistent with the NAAQs. One
assumes that facilitating the maximum emission loading in a region is
loosely synonomous with facilitating the maximum amount of economic growth
consistent with the NAAQSs. Note, however, that in some areas whose eco-
nomic base consists of little high emission density industry, it may not
be true that maximizing potential emission loading will help economic
growth.
The second kind of information that may be required is control costs.
These costs vary by industry, process, and control efficiency, and should
also be estimated for prototype industries. They are most useful when
expressed in their incremental form; i.e., the cost per unit of emission
reduction. If resources permit this information to be obtained, emis-
sion density limits can be set that will reflect the cost of controls for
the projected level of activity. Such costs would be expected to vary
with the location of activity within an air quality maintenance area,
simply because the degree of control needed for a given source would vary
from location to location. Thus emission limits can be established that
represent the least control cost development pattern from an air quality
maintenance perspective, given a desired or projected level of economic
and demographic activity.
Economic goals can thus be summarized in the following criterion.
1. Emission density limits shall reflect the costs of emission
controls associated with the desired level and location of
economic activity for a community, or shall reflect the maxi-
mum amount of emissions in the region consistent with the
NAAQSs.
26
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AIR QUALITY GOALS
For the purposes of this report EDZ has as its primary goal the
maintenance of NAAQSs for particulate matter and sulfur oxides. Emis-
sion density limits must be set low enough so that predicted concentra-
tions of these pollutants do not exceed the standards. This means that
the user must know the relative air quality impact of each existing and
potential source at every receptor point in the air quality maintenance
area. This impact is determined by the location of the source relative
to the receptor and by the variables that influence the atmospheric dis-
persion of pollutants.
However, emissions from inventoried sources in an air quality main-
tenance area are not the only components of concentrations at a given
receptor point. Background concentrations resulting from sources outside
the air quality maintenance area are one component; fugitive emissions that
are not inventoried within the air quality maintenance area are another.
These values must be accounted for before emission density limits can be
set.
Existing background and fugitive components are often assumed to be
accounted for by "statistical" calibration of the model. Calibration is
accomplished using simple linear regression, so that predicted concentra-
tions are adjusted by the formula
/>,
X = A + BX (1)
where X is the predicted concentration.
The statistical validity of the calibration process is discussed in two
monographs by Brier.16,17
27
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• * ('-I. t
12
Calibration is discussed elsewhere in more detail, and the user
should refer to these discussions if he is unfamiliar with the technique.
The intercept A should include the background and fugitive concentration
components, and can simply be subtracted from the standard being used to
set emission limits for the pollutant in question.
Future background and fugitive components may be larger or smaller than
existing values. The user must attempt to estimate the changes in these
values and to adjust the concentration standards accordingly. Projected
increases would have to be subtracted from the standards, but decreases
might be held in reserve by the implementing agency as a safety factor.*
In any case a safety factor or reserve should be available for several
reasons. Unusual meteorological conditions or unanticipated increases in
background or fugitive emissions could lead to violations of the standards.
Error in the modeling process could lead to underprediction of concentra-
tions. Finally, changes in the land use plan are likely to occur over
time. In order to avoid rerunning the decision model for small changes,
the implementing authority should have a reserve concentration increment
available so that variances can be granted. This point is discussed in
more detail in Section IV.
In summary, the primary air quality constraint can be expressed as:
.J.k,* £ (Ej,k,£,m aj,k,m> lXi>£ - b^ - fi)£ - pi>a - r^
- s for all i,A
At this time there is no approved methodology for inventorying fugitive
emission let alone projecting them. As methodologies are developed, they
should be used. Background concentrations are best estimated by regional
air quality planners familiar with the area and a specific methodology is
not given here. To the extent that these components of the emission inven
tory are omitted, the calibration intercept may account for them. If sub-
stantial sources are uninventoried, it may be prudent to project the cali-
bration intercept to the design year by the population forecast to account
for growth in these sources.
The variable definitions shown in Table 1 are employed.
28
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This states that the emissions at a source and the transfer coefficient
between that source and a specified receptor, summed over all sources,
shall not exceed a certain critical value. The critical value is cal-
culated by subtracting the concentration at the specified receptor due
to emission sources not in the EDZ limit setting model from a desired
air quality standard. There would be a similar constraint equation for
each receptor.
The transfer coefficient, t. . , „ is derived from executing AQDM.
!> J >K» *•
This relates annual emissions to annual mean concentrations (i.e., long-
term standards). It is sometimes referred to as x/Q or the coupling coef-
ficient. A method for considering short-term standards is discussed in
Appendix B.
There may be state or local air quality standards in an air quality
maintenance area that are more stringent than the NAAQSs. These can simply
be entered in place of the NAAQSs in the formulation if they are expressed
in the same way for the same pollutants. State and local ambient air .
quality standards may be expressed for different averaging times and with
different definitions of violations; e.g., a 4-hour particulate concentra-
tion standard not to be exceeded more than once a month. State and local
agencies should have sufficient experience with such standards to be able
to make them compatible with the model. Another air quality goal to which
EDZ must be applied is prevention of significant deterioration. This ef-
fectively means that more stringent air quality standards must be met in
13
designated areas. The standards as currently proposed are expressed in
terms of an allowable concentration increment for each designated area of
a certain class. The implementing agency might want to phase the use of
this increment over time to prevent its being rapidly used up in a way that
limits development opportunities. Thus, the standard on which emission
limits are based would represent that portion of the allowable increment
to be used during the period in question.
29
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Yet another potential air quality goal that may or may not be codified
is protection of sensitive receptors, namely persons, plants, or materials
whose susceptibility to air pollution warrant their protection with more
stringent air quality standards. Previously, a criterion was presented
requiring model receptor points to be located at any sensitive receptor
that the user would want to protect. Concentration limits sufficient
to protect these receptors could then be assigned to these points in the
process of setting emission limits. The process would involve several
steps. First, the user would have to define which receptors would be
protected, as the number of possibilities could be large. Then
concentration limits sufficient to protect the designated receptors
would have to be established. These could be based on information about
pollutant effects, or, if such information is difficult or costly to ob-
tain, on some arbitrarily defined "safe" value; e.g., the significant
deterioration increment for a Class I area. Whatever the method used, the
standard selected would simply be used in place of the NAAQS for the des-
ignated sensitive receptors. In deciding which sensitive receptors to
include, the user should keep in mind that increasing the number of re-
ceptor points increases the cost and complexity of modeling, and that any
tightening of air quality standards will impose additional costs on the
community.
2. Emission density limits shall be sufficient to maintain the
NAAQSs and any standards based on significant deterioration
requirements and community air quality objectives. The stan-
dard shall be adjusted to account for background concentra-
tions, fugitive emissions, and a safety margin selected by
the implementing authority.
A final technical issue involved in setting limits is the question
of stack heights. Clearly, the user will not know exact stack heights
for future sources and must thus make certain assumptions. The usual
practice is to assume a standard stack height for all area sources of a
given type (i.e., industrial and nonindustrial types), which applies to
existing and future sources. For future point sources the following
criterion should apply:
30
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A conservative stack height for all future point sources
shall be assumed for modeling purposes, based on state
and local minimum-stack-height regulations and on exist-
ing sources of the same category in the base year emis-
sion inventory.
LAND USE AND ENVIRONMENTAL PLANNING GOALS
The comprehensive planning process normally involves consideration
of several sets of goals, which, when taken together, define the desired
development pattern for a community. These goals include those on eco-
nomic development and housing, public service, environmental quality,
and transportation.
Because EDZ is a factor in land-use decisions, and especially in
industrial location decisions, it will affect travel patterns in an air
quality maintenance area. It is -necessary to account for this effect
in setting emission density limits. Land use plans normally account in
some way for travel patterns, especially those resulting from work trips.
Future land uses shown in plans are determined in part by access to
transportation. There may be a transportation control plan that imposes
a limit on travel. Emission density limits can be set to account for
these concerns if they are reflected in the land use plan.
EDZ affects land use patterns because different land uses have dif-
ferent emission characteristics. Emission density limits must thus be
set for each land use type in each grid cell. Furthermore, the land use
types for which limits will be set must be those defined in planning and
zoning documents, as these are the categories for which future locational
information is available. This allows the user to tailor the emission
limits to conform to the land use pattern presented in the plan.
Tailoring of emission limits can be accomplished in two steps. First,
in each formulation of the limit setting model, the emission limit is
weighted by the land area available to each source category in a grid cell,
31
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based on the regional land use plan. Secondly, the emission limits must
reflect the emission characteristics of the given land uses. For example,
in the emissions maximization model (Model No. 1 of Section V), if emis-
sion limits were based on planned areas alone, a residential area might
receive a higher limit than an industrial area in the same grid cell.
This situation can be prevented by setting minimum emissions for each
land use type in the grid cell based on the planned or projected activity
levels for that land use. These minimum emissions would correspond to the
minimum feasible emissions constraint used in Model No. 1.
Furthermore, certain land uses might be prevented from locating in
an area by setting maximum limits low enough to make control costs pro-
hibitive. If, for example, a residential area is to be protected against
industry, a limit might be set low enough to preclude any industrial loca-
tion there. If no development is to be allowed in a given area in order
to protect certain resources, emissions from that area would not be al-
lowed to increase at all.
EDZ can also be used to aid in the attainment of environmental goals
expressed in the land use plan. For example, water quality management
might be aided, as development types and densities relate to waste loads
entering streams. Water quality planning information might be used to
place a limit on the amount of development occurring in various locations
in a basin over a given period, depending on the phasing of construction
of treatment facilities. EDZ limits could then be set to reflect the cor-
responding level of development.
These concerns can be summarized in the following criteria:
4. Emission density limits shall be set for individual land
use types within a grid cell. The land use types selected
shall be those for which future location data are available;
i.e., existing planning and zoning categories. Since the
numbers and definition of these categories are likely to
vary from municipality to municipality, for uniformity and
modeling efficiency they should be placed within broader
groups. A suggested grouping follows:
32
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rural/open space
low density residential
high density residential
commercial/office
institutional/service
light industry
heavy industry.
5. Emission density limits shall reflect development patterns
congruent with the land use and environmental planning
goals of the community, which are expressed as land use
or development plans or as policy statements. This may
be accomplished by setting limits that bar certain sources;
i.e., land use types, from a given area, or encourage their
location in other area.
ADMINISTRATIVE GOALS
Some administrative concerns of EDZ have been mentioned previously,
such as reserving a concentration safety margin to avoid model reruns.
A major administrative goal that was mentioned previously in relation to
gridding is conflict minimization. The implementing agency will have to
balance some competing interests in the process of setting limits. By
meeting the other criteria presented in this section, the agency can
hopefully enter the goals of these interests into the decision model.
Some issues will remain to be resolved. One goal that should be ad-
dressed directly is minimum interference with growth patterns. This goal
is partly met by using emission limits to reinforce the land use plan.
However, it is possible that the decision model could set very different
emission density limits for similar land uses in adjoining grid cells.
The user should guard against this by requiring that a cluster of parcels
of a given land use type has the same emission density limit over its
whole area.
This might be expressed as a model constraint in the following way:
33
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Ej,k,*,m - V-.k,i,. - ° I for certain A and J; (3)*
or as a criterion.
6. When continguous areas of the same land use type are
contained within separate grid cells, emission density
limits for the two areas shall be equal.
The user must manually identify each j and A. If any grid cell has no
area in a particular land use class, it cannot be identified in this con-
straint. That is, where a. , = 0 or a... . = 0, the constraint is
meaningless. j'k'm J+A*k»m
34
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SECTION IV
CRITERIA FOR REVISING EDZ LIMITS
Once emission density zoning limits have been set (i.e., emissions
quotas have been allocated to grid cells) and implemented, several
conditions may arise that require the revision of the prescribed emission
limits. These conditions can be categorized as
• those arising from unexpected community growth
• those arising from significant changes in community
goals (e.g., transportation and land use plan revisions)
• those arising from unexpected changes in the techno-
logical, administrative, or economic precepts of the
emission density limit setting decision model; e.g.,
changes in fuel prices, changes in state or federal
regulations, or unplanned closings or openings of major
emission sources.
The differences in the scope and influence of these conditions suggest
the application of different methods of revising emission density limits.
In general, small changes can be accommodated through variance proceedings;
only in the event of major changes in these conditions should the limits
be revised globally.
In addition, whether a market is instituted for the exchange of emis-
sion rights will significantly limit the frequency and extent of emission
limit revisions. A market for emission rights will depend on a stable in-
ventory of emission limits to be orderly and fair.
Criteria for revising limits with and without an emission rights
market are outlined separately below.
35
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CRITERIA FOR REVISING LIMITS WITHOUT AN EMISSION RIGHTS MARKET
In defining the original set of emission density limits, one will
use the best information available on existing emission sources, commu-
nity growth plans, control costs, etc. However, it is almost certain
that this information is imperfect. One should expect unforeseen and
undesired hardships imposed on individual firms. For an emission den-
sity zoning control strategy to be equitable, and perhaps legal, one
must be able to ameliorate these hardships by revising the emission
density limits in individual cases; i.e., by granting of variances.
To be able to grant a variance without violating the air quality stan-
dards, a reserve is required. Therefore,
1. The emission density limits shall be set with a reserve
concentration at each receptor.
2. To provide for orderly community growth and unanticipated
individual hardship situations, a quasi-judicial air pol-
lution control board or similar institution shall be em-
powered to grant variances to emission density limits
from time to time. Variances could be granted either
to individuals for specific sites or to municipalities
for allocation among sites in component areas. An in-
dividual would need the endorsement of the appropriate
municipality. In each calendar year, up to 10 percent
of the remaining reserve at each receptor could be al-
located in such a manner.
3. Changes in conditions that lower emission levels will be
treated on an individual basis, with the reduction in
emissions in a particular component area accruing to the
air quality reserve at each receptor.
A revision to the transportation and land use plans may alter the
configuration of the emission sources. If the revised plans are based on
new demographic and economic projections, the total quality of projected
emissions may change as well. If these changes are significant, it will
be necessary to revise the emission density limits globally.
36
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4. After a significant revision in the transportation and land
use plans, the emission density limits will be redefined ac-
cording to the criteria for setting emission density limits.
5. Existing emission densities at the time of a plan revision
will be used as a lower bound on the redefined emission den-
sity limits.
Aside from individual variances, unplanned closings of major sources,
and plan revisions, other unexpected changes in the technological, ad-
ministrative, or economic assumptions of the emission density limit set-
ting process may occur. For example,
• a New Source Performance Standard that was promulgated
or projected to be promulgated may be rescinded, or
• (in the event the control cost minimization objective
function is employed) changes may occur in the costs of
various control devices or in the relative prices of fuels.
Such unexpected changes may alter the optimal mix of emission density
limits. If the changes are of a large magnitude, it would be desirable
to revise the limits globally. If the changes are small or affect only a
small number of sources, it would be less disruptive to grant variances
to the appropriate sources. While the threshold between the two possible
reactions would have to reflect the experience of the control agency,
6. Sensitivity analysis should be used when a change in the
assumptions that were used in setting the limits occurs.
If the sensitivity analysis indicates a significant, say
more than 20 percent, change in the optimal solution for
more than 10 percent of the sources, then the limits should ,
be reset according to criteria 4 and 5. Otherwise, the
sources could be treated on an individual bases according
to criterion 2.
CRITERIA FOR REVISING LIMITS WITH AN EMISSION RIGHTS MARKET
The ability of a private or public emission rights market to provide
for orderly community growth, changes in fuel prices, and variances
37
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from original limits in individual cases markedly limits the revisions
in emission limits that would have to be implemented by a control agency.
In fact, only when a major revision is made in the land use plan would
a control agency have to consider the global redefinition of the EDZ
limits. That redefinition would be accomplished according to the cri-
teria outlined previously. Otherwise, one could depend on the market
to provide for the requisite changes in emission limits, subject to the
following criteria.
1. Emission rights may be transferred between parcels within
a component area on a one-to-one basis.
2. Emission rights may be transferred between parcels in
different component areas according to the following
relationship:
the smallest over all i (A)
where Ae is the change in emissions in the new component area
Ae is the change in emissions in the old compartment area
X
t , is the transfer coefficient from source x to
x' receptor i
t ^ is the transfer coefficient from source y to
receptor i.
This is based on the identity,
lAey fcy,i I " lAex tXfll
In other words, there is some increase in emissions Ae
in component area y, whose resulting increase in con-
centration at receptor i will exactly balance the reduc-
tion in concentration at receptor i due to the decrease in
emissions at x. If, over this set of emission increases,
S(Ae ), the smallest value of Ae , the amount, AS ,
v y ' y' y
is permitted to be transferred to component area y,
then concentrations at all receptors will not increase
due to the transfer. The corresponding Aex is sub-
tracted from the old component area.
38
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3. After a transfer between component areas according to
criterion 2, the incremental decrease in concentrations
at receptors other than the binding receptor; i.e., the
receptor i for which Ae is the smallest, would accrue
to the control agency as a reserve.
For each receptor i, except for the binding receptor(s),
this reserve would be
Ri =
A. To facilitate orderly community growth, portions of the
reserve at each receptor (the sum of the initial reserve
that was set aside when emission density limits were first
set and any increment due to transactions of emission
rights between component areas) should be auctioned in a
public market at appropriate time intervals. For example,
50 percent of the remaining reserve could be sold every
10 years or after a major change in the transportation or
land use plans.
A control agency could publish a matrix of minimum values of the
tv j/t . ratios. A source wishing to buy emission rights then could
x, i y,i
search for high values in the appropriate row (or column) to find the
potentially best bargin. On the other hand, a source wishing to sell
emission rights could search for high values in the appropriate column
(or row) to find the potentially best prospective purchaser.
39
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SECTION V
SPECIFICATION OF DECISION MODEL
The selection of a decision model for setting emission density limits
in an AQMA must rest with the individual agency implementing an EDZ main-
tenance strategy. The choice of a particular model will represent the
resolution of the tradeoff between a specific agency's concerns and avail-
able resources. Four candidate formulations are described in the follow-
ing sections. These formulations differ in their objective functions;
i.e., exactly what is being maximized or minimized. The possibility of
other objective functions is discussed. Next, several variants of the
first formulation, emissions maximization is described. While each
variant does maximize emissions, they each treat the constraint set
slightly differently.
The simplest model is the maximization of emissions. This formula-
tion is the most inexpensive model formulation to implement in terms of
both data requirements and computer time. Given the community goals
expressed in the land use element of the regional plan, it will allocate
emission rights to component areas in a pattern that maximizes the aggre-
gate emission loading in a region and still maintains ambient air quality
standards. The assumption implicit in this formulation is that the
maximization of emissions is closely related to the maximization of eco-
nomic activity permitted by the NAAQSs. Within the limits of the upper
*
and lower bounds on emission density limits , the maximization of emissions
implicity values emissions from different land use categories in the same
That is, the zero cost and technological constraints.
For example, light industry and commercial land use.
40
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component area Identically. That is, if both sources are not at their
upper or lower bound, several alternate optimal solutions are possible
since the transfer coefficients are identical.
More significantly, in the case of one binding receptor (which was
the case in the Baltimore TSP test run and was closely approached in the
other tests), the emissions maximization formulation implicitly values
emissions from different areas of the region, weighted by the reciprocal
of their transfer coefficients as having equal value. An example will
clarify this condition. Assume two emission sources, whose emission
density limits, in tons per year per acre, are E.. and £„. Their transfer
coefficients (X/Q) to a certain receptor are, respectively, 0.5 and 0.1
ym/m3/ton/year and their areas of the emission sources are both 2 acres.
Mathematically, the linear program may be stated as
Maximize emissions, E = 2 E..+ 2 E- (7)
such that (0.5) (2) EX + (0.1) (2) E2 <. S
where S is the desired NAAQS. In the maximization of emissions then, the
linear program will implicitly value 5 tons of emissions from source 2 as
equivalent to 1 ton of emissions from source 1 for the purposes of meeting
the air quality constraint. The linear program would assign a higher
emission density limit to the second source regardless of the control
cost schedules (or other costs) of the two emission sources. The remain-
ing three decision models attempt to value the emissions from various
sources according to the location and type of emission source.
The premise behind the control cost minimization formulations (the
second and third models) is that for two emission sources with equal
transfer coefficients (x/Q) to a critical receptor, the emission source
with the higher incremental control costs should be required to meet a
less stringent standard. The goal of this formulation is to set a pattern
of emission density limits such that, if the region is developed to the
41
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levels specified in the regional land use plan, the individual source's
incremental control cost of reducing the ambient air concentration at a
critical receptor would be identical with that of all other sources. With
suitable constraints, the minimization of control costs is equivalent to
maximizing emissions weighted by control costs. It is an attempt at a
cost effective approach to setting EDZ limits.
The final model is the maximization of emissions weighted by land
value (model no. 4). There are several reasons why it may be preferred
to the second and third models. First, land value represents the upper
bound on control costs, and in some situations may be easier to obtain
than other control cost data. An individual source is faced with several
options in complying with an EDZ ordinance. One, of course, is the instal-
lation of control equipment in addition to that required by other existing
regulations. Another possibility is the reduction of the emission density.
This means, in effect, that some of the site must remain comparatively
underutilized (not developed to the firm's desired emission generating
capacity). The cost of the underutilized land, therefore, is one form of
control cost facing the firm. However, because there appears to be no
clear theoretical justification for using maximum control cost — land
value — as opposed to average or minimum control cost in the model, some
users may prefer the second or third model. Second, because land costs
tend to be higher in the center of a metropolitan area, this formulation
will not exhibit the tendency of the emissions maximization formulation
to set high emission density limits on the urban fringe. (Model No. 1
does this because the critical receptors tend to be in the center of the
metropolitan area.) Even though the land use plan may restrict intensive
development on the urban fringe, the emissions maximization model, as
opposed to model no. 4, will encourage near suburban industrial develop-
ment to the detriment of expansion of existing core city industrial
facilities and redevelopment of core city industrial sites. Third, model
no. 4 may reduce the potential desruption of existing land use patterns
caused by the introduction of EDZ. The relative value of a parcel is
taken as a partial indicator of that parcel's rightful share of the bundle
42
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of emission rights available to the region. High value property would
receive higher emission limits than low value property, other things
being equal. Model no. 4, therefore, would perturb the already existing
value ranking of land as determined by market forces the least, and pre-
sumably change the location and timing of future development the least.
This is done at the expense of the total emissions in the region.
Aside from the four models described below, others are possible. The
user is limited only by the resources and ingenuity of the implementing
agency. The models would be basically the maximization of emissions
weighted by some parameter; e.g., control cost, land value. Within this
format, other formulations can easily be specified if they more adequately
reflect the goals of the community and if the requisite data are available.
The four models are presented below. Variable definitions are shown on
Table 1.
MAXIMIZATION OF EMISSIONS (MODEL NO. 1)
Maximizing emissions is relatively the most straightforward formula-
tion of-an objective function. The most specious relationships to specify
are the SO -PM feasibility constraints, which ensure that a very stringent
X
emission density limit for one pollutant and a relatively lax unusable limit
for the other pollutant are not set in the same cell. The linear program
may have to be run several times as this approximation is fine tuned. The
necessity of this constraint and the estimation of its parameters are dis-
cussed in Appendix C. The formulation of Model No. 1 is as follows:
Maximize emissions = E Z Z £ E. . . _ a.« i, _ (8)
j k Am j'k'*'m j'k'm
43
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Table 1. DEFINITIONS OF VARIABLES USED IN SECTION V
SUBSCRIPTS
i = receptor index
j = grid square or point source index
k = land use class index
Si = pollutant species index
1. particulate matter
2. sulfur oxides
m = current and growth index
1. existing sources
2. future sources
n = 1,2 . . . for each potential emission rate (tons/year)
PARAMETERS
ai k m = t*ie lan(* area of emission source j,k,m for existing sources
' ' (m = 1) , obtained from base year land use inventory, and
for future sources (m = 2) , obtained from land use plan
^1 i ~ t*ie Pr°Jected concentration at receptor i of pollutant i
' due to background
c, . = the incremental control cost incurred to reduce emissions
' 'm from land use category k. Obtained from execution of IPP.a
c. = the cost of land for land use type k in grid square j; or for
3» point source j
i
c = the control cost incurred at source j to emit at the emis-
' sion rate indexed by n, i.e., at emission rate e
J j*1*11
ei o n = for each source j, the set of possible emission rates,
J' ' indexed by n
e. , ^ = the maximum feasible future emission density after application
of existing and planned regulations for existing sources
(m = 1), obtained from AQMP projection; for future sources
(m = 2) , obtained from floor area ratio and emission factors
e . .• . = the minimum feasible design year emission density (defined
j,fc,J6,m Qnly for m . 2)
. = the base year emission density (defined only for m = 1) , ad-
J. . >m justed for current and pending emission control regulations.
E. , ,, = the emission density limit, the variable that is set by the
j,K,x,,m settlng model
44
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Table 1 (continued). DEFINITIONS OF VARIABLES USED IN SECTION V
f. » = the projected concentration due to fugitive emissions for
' receptor i (usually defined only for £ = 1)
s. ,, = the projected concentration at receptor i of pollutant H
' due to mobile sources
r. ., = safety margin or reserve
p. ^ = the projected concentration at receptor i of pollutant £
' due to power plants and other sources not considered in the
emission limit model
t. . ....... = the transfer coefficient, the incremental air quality impact
' at receptor i of source j, land use class k, for pollutant £.
Obtained from AQDM
p^, v, = coefficients relating the minimum possible levels of particu-
late matter emissions for a given sulfur oxide emission level,
and the converse
X. „ = the reverse calibrated standard, pollutant £, receptor i
1, X,
Z. „ = a zero-one variable
j > ^j n
The Air Quality Implementation Planning Program (IPP) determines control
costs for point sources given emission limits. See TRW Systems Corp.
Air Quality Implementation Planning Program. 2 volumes. Environmental
Protection Agency, Research Triangle Park, North Carolina. November,
1970.
45
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subject to:
nlr quality constraint: I Z t.
£ (E
for all
* r
i,£
,
attainment constraint:
m | for all j,k,£; for m = 1
proximity constraint:
- E.j+A kj£ - 0 | for certain A and j
zero cost constraint:
for all j,k,£,m
technological constraint: E
> e°in „ | for all j,k,£,m
— j,K,x,,m
SO -PM feasibility
constraint: E.
-Pk
1 vk
for
PM in
each first term
for £ = SOX in
each second term
for all j,k,m
The objective function is the sum of the total emissions in the
region; i.e., the sum of the products of each source's emission density
limit and its area. The first constraint is the air quality constraint.
The sum of the products of emissions at each source and its transfer
coefficient represents the ambient concentration at the specified receptor
due to sources controlled by EDZ. This must be less than the NAAQS after
subtracting the concentration due to mobile sources, fugitive dust, power
plants, background, etc. There is a separate constraint equation for each
receptor and pollutant.
46
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The attainment constraint indicates that an existing source shall not
have an emission density limit assigned to it that is less than its exist-
ing emission density (after considering compliance schedules and other
planned emission controls). This places the maintenance burden on future
sources and capacity expansion of existing sources. The possibility of not
doing so is discussed in Appendix E. There is a separate constraint
equation for each existing source.
The proximity constraint allows one to require emission density limits
in adjoining component areas to be identical. It permits one to set
identical emission density limits for all the grid cells in a political
subdivision; e.g., municipality, township, to facilitate the administration
of EDZ.
The zero cost constraint specifies an upper bound on the emission
density limit for each source. The upper bound is the maximum emission
density that may be expected for that source in the absence of EDZ. It
implies that no control equipment beyond what is already required by
other regulations would be installed; hence, it is the point where the
firm incurs no additional costs due to EDZ.
It is necessary to include an upper bound on all sources; otherwise,
the linear program will assign an excessively high and unusable emission
density limit at a few sources that have the smallest transfer coefficients
•ff
to the critical receptors. In similar manner, the technological constraint
specifies the minimum emission density for each source that is technologi-
cally or economically feasible.
*
This occurred by accident in preparing the Louisville TSP test case.
Several sources had their upper limits omitted. The linear program maxi-
mized emissions by setting most sources at their lower limit and assigning
an emission density limit of 2456 tons/day/km^ at one source that had no
upper limit! In the same run, several sources also had their lower limits
omitted by mistake. Their emission density limits were set at zero.
47
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MINIMIZATION OF CONTROL COSTS (MODEL NO. 2)
The minimization of control costs is formulated as follows:
Minimize C = I. I. I c, „ 1 a. . eTT 0
k*m k'£'m j j'k'm \J>k>*>m
subject to:
air quality constraint: Z Z t Z (E
| for all i.X,
attainment constraint: E. , . > e. , I for all j,k,&; for m = 1
j,K,x.,m j,K.,x,,m
proximity constraint: E. , 0 - E..A , g = 0 | for certain A and j
~
zero cost constraint: E..0,m
technological constraint: EJ i. p > e™^ | for all j,k,Jl,m
It should be noted that this is equivalent to maximizing emissions
weighted by control costs, viz.,
Maximize E' = Z Z Z c,, „ „ Z a. ,, m E. . „ ,iriN
k H m j J.k*^1" (10)
subject to the same constraints.
The major difficulty in using this formulation, as well as the next
one (Model No. 3), is the specification of the control cost parameter,
GV o ™» fc^e incremental annualized cost per ton per day of an emission
iiC y X* y ni
48
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reduction at each source. A method for specifying the parameter is dis-
cussed in Appendix D. However, the estimation of control costs of future*
emission sources is tenuous at best. If, in a given application, they
cannot be estimated with some confidence it may be prudent to use the
simpler emissions maximization formulation.
ALTERNATIVE FORMULATION OF CONTROL COST MINIMIZATION (MODEL NO. 3)
Rather than forcing control cost to be a linear parameter, one can
recognize its nonlinear and discrete nature. Through the use of inte-
ger programming, one can directly minimize control costs, control costs
being defined as a set of costs associated with each of the possible
emission levels. The formulation is as follows:
Min C' = Z Z Z c. 4 n Z. £ n (11)
j H n
subject to:
= 1 I for
single emission level
per source
for
air quality constraint: Z Z t. . „ e. • Z. i
j i»J»* j>*»n j,£,n I
j n ......
- Xi,£ " bi,£ ~ fi,* " ri,£ - Pi,£ - Si,£ I
for all i,£
Z is a zero-one variable which is constrained to add to one for each
source. Therefore, for the set of Z's for a single source and pollutant,
in the solution to the linear program all Z's except one will be zero.
49 '
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The emission density associated with the nonzero Z is the limit for that
source and pollutant. In the case of the sample point source for Balti-
more discussed in Appendix D, the set of emission rates (not emission
densities) and associated control costs are shown in Table 2.
The advantage of this formulation is that it allows the emission
density limits to be set at specified levels that are related to certain
control devices, as was not the case in the prior control cost formulation.
In most contexts, we believe this is not that great an advantage and does
not outweigh the higher per run cost associated with integer programming
(as much as 10 times that of linear programming).
LAND VALUE (MODEL NO. 4)
The minimization of the value of additional land required to be pur-
chased in order that the same level of economic activity be maintained
is not feasible, viz.,
max
min Z E E c^
j k 4
(12)
since one cannot take the reciprocal of the decision variable, E, in the
objective function in an ordinary linear program.
An alternative formulation is the minimization of the cost of excess
land that must be owned by a firm to comply with EDZ, viz.,
... _ „ _ r land max land
jk'm Cj'k aJ.k.* eJ.k»*.* " 'j.fc
max
50
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Table 2. CONTROL COST AND EMISSION SCHEDULE,
EXAMPLE OF PROTOTYPICAL HEAVY
INDUSTRIAL POINT SOURCE
Cost
dollars
0
6,876
13,752
20,628
22,769
24,910
27,051
39,122
51,193
63,264
75,410
87,556
99,702
122,203
135,116
157,617
170,530
193,031
205,944
299,791
393,638
487 ,485
581,322
675,179
Emissions
(64 J> >
J»i»n'
tons per year
6,852
5,952
5,052
4,152
3,927
3,702
3,477
3,081
2,685
2,289
1,959
1,629
1,299
1,224
939
864
579
504
219
193
166
140
113
86
Source: Derived from data in
Appendix D
51
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Equivalently, one can maximize emissions weighted by the cost of
land, viz. ,
maximize E E E E c.&? a. , E. , „ ,,,^
J' J.k.m "j.k.Jl.m (14)
subject to:
air quality constraint: E E t. . , E (E * a )
j k i.J.k,* m j,k,£,m j,k,ni
| for all i,£
i
attainment constraint: E. , . > e. u „ „ | for all j,k,«,; for m = 1
j,K.,x,,m — j,K,x,,ni
proximity constraint: E, . - E . - 0 | for certain A and j
K.x.m ' J
zero cost constraint: E. , « <_ e!?8? « _ | for all j,k,£,m
technological constraint: E-i k £ m — ^^ Si \ for a11 J»k»&»m
and perhaps the SOx~PM feasibility constraint.
VARIANTS OF MODEL NO. 1
Variant 1A - Municipal Aggregation
The proximity constraint allows one to require the linear program to
set emission density limits such that the limits in certain specified
component areas (grid squares) are equal. Where this is done to a
limited extent, model no. 1 is the most straightforward approach. However,
one may desire to use the proximity constraint more extensively. For ex"
ample, it may be desirable for emission density limits to be assigned by
municipality; i.e., a municipality would be assigned one emission density
limit which could then be allocated among land use categories. If there are
-------
100 municipalities in a urban area and several component areas in each
municipality, using the proximity constraint of model no. 1 becomes a
cumbersome process.
An alternative approach is to define a composite transfer coefficient
for the municipality. After calculating the transfer coefficients for each
component area, one would determine the average transfer coefficient for
each municipality, or preferably an average of the component area transfer
coefficients weighted by the area of that land use in the component area.
Specifically,
aj,k>m
a
j km J
for all !,«, (15)
where the summation is taken over all component areas in the municipality
and the area, a. , is the area of the land use in that portion of the
J ,tc,m,
component area that is also in the municipality. Model 1 can then be used
directly, where j, instead of representing a grid square index, becomes a
municipality index. Note that in this variation, the proximity constraint
could be redefined to allow one to set identical emission density limits
in adjacent municipalities.
The use of this variant is most suited to an urban area that has many
small suburban municipalities; e.g., Boston or Minneapolis-St. Paul.
Even in these areas, it would be advisable to divide the core city into
several sectors or to retain the component area gridding in the core city.
Variant IB - Census Tract Component Areas
While the use of grid squares as the basic geographical unit for com-
piling data is well suited for the requirements of dispersion modeling,
the use of a square grid is both an awkward basis for compiling the emis-
sion and land use inventories as well as for administering a set of emission
53
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density limits. If an approach such as variant 1A, municipal aggregation,
i.a conteii,, uted, even the accuracy of the dispersion model output is com-
promised when the average municipal transfer coefficient is calculated.
In addition, an unwieldly data item should be necessary; viz., the amount
of each grid square that is in each municipality.
An alternate approach is the use of census tracts as the component
area. This allows one to compile a more accurate emission and land use
inventory in less time, as well as simplifying the use of variant 1A since
census tracts generally follow political boundries. The only difficulty:
with this approach is the question of dispersion model accuracy. We are
unaware of the answer to this question. It should be noted that AQDM
has been successfully run several times in this manner with the coordinates
of the centroid of the census tract used as the center of a pseudo grid
28
square.
Variant 1C - Constant Emission Density Limits
The logical extrapolation of 1A would be to set one emission density
limit for each land use category in the region. That is, the proximity
constraint would be used for every component area. The advantages of this
*
approach are significantly smaller linear programming costs and, later,
a much simpler task of administration. It will definately allow less
total emissions in the region, and therefore potentially constrain growth
to a greater extent. •
Though possible to simply add a proximity constraints for each grid
square and land use, it is equivalent to reformulate model no. 1 without
the grid square and point source index j, viz.,
Maximize emissions = E L E E, „ E a. , (16)
kt£,m k**'m j j'k'm
About 10 percent of the costs of executing model no. 1.
54
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subject to
air quality constraint: £ £ £ t.
4 ' k m j
E,
k,
~ P
i,£ i,
for all i,X,
and corresponding attainment, zero cost, and technological constraints.
One problem with this approach is the definition of the upper and
lower bounds. For future sources (m=2) it presents no problem. There are
however, at least three options on how current sources (m°l) may be
treated
1. Use the same upper and lower bounds for current sources
as future sources. While this is the simplest approach,
it will certainly lead to many nonconforming uses where
the emission density limit for a current source is less
than its present emission density. This will be espe-
cially true of large point sources.
2. Set a constant emission density limit for all area
sources, as in equation (15), but treat each point source
separately as in the original formulation, equation (8).
This should lead to only a moderate increase in program-
ming costs and eliminate most of the nonconforming uses.
3. Set a constant emission density limit only for future
area sources. Existing area sources and point sources
would be treated individually, with unique upper and
lower bounds. This will eliminate all nonconforming
uses, but it will only eliminate about half of the
linear programming costs and cause the administration
of the emission density limits to be almost as complex
as the original emissions maximization, Model No. 1.
55
-------
SECTION VI
GUIDELINES AND MODEL IMPLEMENTATION CONSIDERATIONS
This section first reviews emission inventory considerations and
technical considerations of the linear program. Subsequently, a guide
for executing an EDZ limit setting model is presented and illustrated
using test city of the AQDM manual."*
All of the formulations of the emission density limit setting model
require significant amounts of information on base year and projected de-
sign year emissions. These data must be summarized in a way that usually
would not be available if the emission inventory is prepared without the
requirements of emission density zoning in mind. However, if sufficient
foresight is used when the emission inventory is prepared, the inventory
can meet the requirements of the emission density limit setting model
while incurring a negligible increment in cost.
The following considerations should be observed.
• The grid square network used for the subcounty allocation
of emissions should also observe the criteria in Section II
for partioning an air quality maintenance area. In
practice, the grid system that one would devise using
CAASE^ will require only minor modification. Most of
the modifications would be implemented in the absence
of EDZ in the interest of accurate dispersion modeling.
The exception to this would be modifications resulting
from the criterion of subdividing grid squares spanning
jurisdictional boundaries.
56
-------
The emission inventory must be prepared using the source
classes for which emission density limits are contemplated.
Most emission inventories use only three stationary area
source classes* i.e., residential, commercial, and indus-
trial; it is probable the emission density zoning regula-
tion would utilize a more detailed classification scheme.
Since the emission density limit setting model also re-
quires the base year and planned land use of each source
category in each grid square, this imposes no additional
data requirements. The land use data can be conveniently .,
used for the subcounty allocation of the emission inventory.
In summary, the gridding of the AQMA must meet the additional criteria
discussed in Section II, the land use and emission inventories (both cur-
rent and projected) must have the same classification scheme, their geo-
graphical basis must be the gridded component areas, and the classification
scheme must be the same as (or more detailed than) the categories contem-
plated for the administration of EDZ.
RESOURCE REQUIREMENTS
If the emission inventory is prepared with the requirements of EDZ
in mind, it will require a negligible increase in resources committed
to its preparation.
If one attempts to use the emission density limit setting model with
a pre-existing inventory, the inventory must be modified to reflect the
cited considerations. This will likely require the splitting of grid
squares and a disaggregation of the emission source classes. The methods
one is prone to use will probably lead to a more inaccurate inventory than
if the emission inventory had originally been compiled with EDZ in mind.
It will also require a moderate amount of time and resources; e.g., it
required 1 man-month and an hour of computer time to modify the inventory
for the Baltimore example discussed in the subsequent section. Finally,
in modifying an existing inventory, care must be exercised that the
resulting emission inventory is compatible with the land use inventory.
57
-------
In summary, the compilation of data for input into the linear programs
will be simpler and involve fewer problems if the emission inventory is
developed being cognizant of the requirements of emission density zoning.
The land use inventory and plan will, in most cases, already exist.
The resources required to summarize it on the geographical basis of the
component areas will vary widely, depending on the form and scale of the
inventory and plan. A typical situation is where the inventory is shown
on a series of Prismicolor maps. One common approach is to prepare an
acetate overlay of the grid system and, by planimeter or random dot grid,
determine the amount of land use in each grid. It should also be noted
that if the land use inventory has been summarized by census tract, con-
sideration should be given to using the census tract as the component
area.
Beside the land use inventory and the emission inventory, sufficient
data must be compiled to determine the upper and lower bounds on each
emission density limit. Of the three items, this can require the largest
resource commitment. It is, as noted earlier, absolutely necessary and
its accuracy is, in addition, critical, as many of the emission density
limits may be set at either their upper or lower limits. It will require
several man-months to acquire the necessary information with sufficient
accuracy.
LINEAR PROGRAMMING CONSIDERATIONS
Considering the size; i.e., number of sources, of a typical air qual-
ity maintenance area, it is apparent that for all but the smallest the
linear program to set emission density limits is a significant computer
problem. The computer time required to solve a linear program is diffi-
cult to predict even if the time required for a similar problem is known.
There are, however, several rules of thumb describing the importance of
various parameters of the problem in determining solution time, viz.,
58
-------
"The most important factor is the number of ordinary
function constraints. In fact, computation time tends
to be roughly proportional to the cube of this number,
so that doubling this number may multiply the computation
time by a factor of approximately 8. By contrast, the
number of variables is a relatively minor factor. Thus
doubling the number of variables probably will not even
double the computation time. A third factor of some
importance is the density of the table of constraint
coefficients (i.e., the proportion of the coefficients
that are not zero) because this affects the computation
time per iteration. One common rule of thumb for the number
of iterations is that it tends to be roughly twice the num-
ber of functional constraints."^5
Setting aside Model No. 3, which was not tested here, it should also
be noted that the EDZ problem is an atypical linear program. The matrix
has a density of almost 100 percent. That is, almost every single vari-
able — each of which is an emission 'density limit for a particular
pollutant and source — appears with a nonzero coefficient — the trans-
fer coefficient — in every one of the air quality constraints. (The
attainment, zero cost, and technological constraints are handled as
upper and lower bound statements, and are not included in the matrix.
The feasibility and proximity constraints, if used, would reduce the
density.) A more typical linear programming problem has a density of
20 percent to 40 percent. In other words, more variables are omitted
from each constraint than are left in. General purpose linear program
computer application packages, such as MPS,18>19 are designed for the
more typical problem and can be expected to be inefficient in solving
20
a problem such as that posed by EDZ. A linear program code more
appropriate than MPS for this type of problem could not be located.
The extent of the inefficiency using MPS instead of a special purpose
code could not be estimated.
With these caveats in mind, the Central Processing Unit (CPU) time
and Execute Channel Program (EXCP) count required for the execution step
of MPS are presented in Table 3 for several emission maximization
linear programs. The information processing requirements increase
59
-------
Table 3. PROBLEM CHARACTERISTICS AND MPS TIMING ESTIMATES, EMISSIONS
MAXIMIZATION LINEAR PROGRAMMING
Application
Problem
characteristics
Machine
Rows (Including object)
Columns
Elements
Dens Ity
Iterations
Invert calls
Execute step CPU time
EXCPS
Core
Test run of MPS
on teat city of the
AQDM Manual4
IBM 370/158
18
43
774
71.66
0
0
2.91 seconds
68
25 6K
County example
Air Quality Analysis
Workshop21.b
IBM 370/195
237
121
28,914
34.07
65
1
20 seconds
2,092
400K
Sulfur oxide
example,
Baltimore
IBM 370/158
53
2256
119,568
99.74
1,514
20
20 minutes
23,200
44 8K
Partlculate matter
example,
Baltimore
IBM 370/158
53
2256
119,568
99.74
2,253
22
17.8 minutes
18,950
448K
Sulfur oxide
example #1
Louisville
IBM 370/158
103
629
64,787
86.04
442
25
*•- 3 minutes
~ 1000
448K
Particulate matter
example,
Louisville0
IBM 370/158
103
629
64,787
86.04
419
4
~2 minutes
~ 1000
44 8K
Sulfur oxide
example #2
Louisville0
IBM 370/158
257
629
161,653
71.07
404
5
12 minutes
8556
448K
*Ihe input matrices were all 100 percent dense, however the introduction of a slack variable in every constraint affects the final
density.
Dual problem solved.
CInfe«slble solution reached.
-------
dramatically with the size of the problem; one who is formulating a
linear program for a large air quality maintenance area should exercise
caution so that the problem does not exceed the resources of the user.
If a problem is too large, one effectively has two options for simplify-
ing it, viz., reducing the number of rows (receptors) or the number of
columns (sources). (Reducing the number of feasibility or proximity
constraints would have the same effect.)
To reduce the number of columns, one essentially has to (a) aggre-
gate or remove land use categories or (b) aggregate component areas. A
substantial reduction in the number of columns can only be accomplished
by the former method. Some of the more homogeneous or low emission
density source categories can be removed from the model. For example,
the emission density limits for the residential source categories can be
set a priori and removed as variables from the linear program. Their
contribution to ambient air quality at each receptor would have to be
subtracted from the standard in a manner similar to background or mobile
source contributions. Alternatively, one can collapse or aggregate the
land use categories. For example, the commercial and institutional
categories could be combined. This is feasible either if they have
approximately the same upper and lower bounds on feasible emission den-
sities; or if component areas tend to have one or the other category of
land use, or neither, but not both.
An alternative to reducing the number of columns is reducing the
number of receptors. This is less preferable, because one does not know
where critical receptors will be located. The sensitivity of the optimal
solution to the number and location of receptors has not been completely
investigated. The Louisville sulfur oxides test run was executed for
two receptor sets. A different solution was reached, as discussed in
Section VIII.
61
-------
GUIDELINE FOR EXECUTING THE EDZ MODEL
Presented below are step-by-step instructions for preparing input
for and executing an emissions maximization linear program for one pollu-
*
tant using MPS. Familiarity with MPS is assumed. Data, as described in
Table 4, are assumed to have been compiled:
Table 4. REQUISITE DATA FOR PREPARING AN EMISSIONS
MAXIMIZATION LINEAR PROGRAM
Base year and design year emission inventory for all emission
sources. The stationary area source emission categories must be
identical to those contemplated for regulation by emission density
zoning. The subcounty allocation must be done on a grid system
that is compatible with the component area criteria of Section II.
Base year land use inventory and design year land use plan that
is compatible with the emission inventory in terms of grid network
and subcounty allocation. The land use should be in terms of net
land area, not gross land area; i.e., it should be in terms of lot
area.
Lot area and land use classification of all major point sources.
Meteorological data, air quality, and stack height data necessary
for executing AQDM for the base year and design year.
This includes estimates of stack heights of future sources.
Maximum permitted floor area ratios and minimum feasible floor
area ratios (for nonindustrial development) for each land use in
each component area — obtained from the land use plan, zoning
ordinance, and discussions with the regional planning agency.
The guideline is divided into three sections, viz., right hand side,
columns, and bounds, corresponding to discrete data elements required for
the MPS input.
See the Mathematical Programming System/360 Application Description
for an overview of MPS.
62
-------
Right Hand Side Section
1. Execute AQDM with the calibration option for the base
year emission inventory and the air quality monitoring
stations.
2. Determine the desired ambient air quality standard, in
terms of an annual arithmetic mean for each receptor
to be used in the EDZ model. These may be the long-
term NAAQSs, a controlling long-term standard reflecting
the short-term NAAQS,* or ambient air quality levels
reflecting PSD or local regulations.
3. Adopt a suitable safety margin or reserve at each
receptor. Subtract this from the standard. The reserve
should be based, in part, on the validity of the AQDM
calibration.
4. Reverse calibrate the standard at each receptor in the
EDZ model', i.e., subtract the intercept from the results
of step 3, then divide by the slope.
5. Execute AQDM with the source-receptor file option for the
design year emission inventory.+
6. Using the source-receptor file and the design year emis-
sion inventory, calculate the contribution of each source
not in the EDZ model to each receptor. Sources not in
the EDZ model are those sources in the design year inven-
tory for which emission density limits are not being set.
They may include:
• background
• fugitive emissions
• fugitive dust emissions
« power plants
• mobile sources
Sum the contributions for each receptor.
See Appendix B.
The version of AQDM utilized in this study produces an uncalibrated
source-receptor file. If the version used produces a calibrated file,
Step No. 4 is not necessary. The version of AQDM utilized also produces
a unit emission source receptor file. If this is not the case, the trans-
fer coefficients must be divided by the emission rates.
63
-------
Subtract the vector of non-EDZ source contributions
(step no. 6) from the vector of reverse calibrated
standards (step no. 4). The result is a column vector
that is the right hand side (RHS) of the air quality
constraint.
Columns Section
8. For each plant that is treated as a major source in EDZ;
i.e., it remains in the source-receptor matrix, and has
more than one paint, develop a source-receptor contribu-
tion for each plant by averaging the individual contribu-
tions for each point within the plant weighted by the
emissions from each point.
9. Reduce the source-receptor matrix by deleting each row
that is a non-EDZ source. Take the transpose of this
matrix. AQDM provides, for each receptor, the contribu-
tion from each source; MPS requires, for each source, the
contribution at each receptor.
10. Using the land use inventory, land use plan, and point
source lot area, compute the amount of each component
area taken up by:
a. current land use, by category, excluding point
source land use, and
b. planned growth in land use, by category, excluding
point source land use.
11. Using the results of steps no. 9 and 10 construct a vector
for each emission source', i.e., current area source,
future area source, point source, that consists of:
• the area of that source
• the product of the area of the source and its trans-
fer coefficient (obtained from the transposed source
receptor file) to receptor no. 1
• the product of the area of the source and its
transfer coefficient to receptor no. 2
(and so on for each receptor)
(and so on for each receptor)
(and so on for each receptor)
64
-------
• the product of the area of the source and its trans-
fer coefficient to the ifch receptor.
This is the columns input to MPS; i.e., the constraint
matrix.
12. Determine, as discussed in Appendix C, whether an
SOx-PM feasibility constraint is necessary. If
one is required, the computed parameters are added
to the end of the column vectors and RHS vector.
13. For each proximity constraint required, a 1 and_-l
must be added to the ends of column vectors of the
appropriate sources, and zeros must be added to the
end of the column vectors of all other sources and
the RHS vector.
Bounds Section
14. All necessary input to MPS has now been prepared except
for the BOUNDS section; i.e., the minimum and maximum
feasible values for each emission density limit. The
importance of these parameters is critical; many of the
emission density limits will be set at one or the other
of these values. For existing sources, the lower bound
is their current emission density which is computed by
dividing their total annual emissions by their land
area. For point sources, the lower bound is the smallest
of their current emission density and their projected
design year emission density excluding capacity expansion.
15. The emission density upper bound on existing sources
should be defined from the AQMP projections.^'^ Note
that this is projected growth for existing sources.
16. The emission density upper bound for nonindustrial future
sources is obtained by multiplying the maximum permitted
floor area ratio of the land use in a specific component
area and the land use based emission factor, 2 after
applying existing control regulations.
17. The emission density lower bound for nonindustrial future
sources is obtained by multiplying the minimum feasible
floor area ratio and the most controlled land use based
emission factor.
18. Upper and lower bounds for industrial future sources are
obtained by considering the dirtiest and cleanest indus-
try that can be expected to locate in each industrial land
use category. ....,__ .
65
-------
19. The data must now be formatted for input to MPS. Consult
the following sections for examples of input data, MPS
control programs, .and sample output.
Example of Guideline
An example of the guideline is illustrated for sulfur oxides using
A
test city of the AQDM manual as a sample problem. The test city emis-
sion inventory was modified to show emission classes, as shown in
Table 5. An assumed land use inventory is presented in Table 6.
1. The AQDM execution of test city, as shown on page C-9 of
the AQDM manual, yields a calibration of
y = 0.2 + 0.5132 x
2. Applying the average geometric standard deviation of
1.93, one calculates the annual mean equivalent to
the short-term standard, viz.,
m = 80.9 = 365 (1.93)0*5 ln i'93"2'62
(see equation 25). Therefore, the long-term standard, 80 yg/m3,
is controlling.
3. For the purposes of this example, no safety margin is
assumed.
4. Reverse calibrating,
155.49 = (80 - 0.02)70.5132
5. As shown in the AQDM manual.
6. Source No. 2, assumed to be a power plant, is the only
non-EDZ source. The product 6f its projected emission
rate by its uncalibrated transfer coefficient (x/Q) to
each receptor yielded the second column on Table 7.
7. As shown in Table 7, the vector of non-EDZ source
contributions (in this case, due solely to source no. 2)
is subtracted from the reverse calibrated standard,
yielding the third column in Table 7, the right-hand side.
8. Of the three remaining point sources; i.e., source no. 1,
3 and 4, none have multiple emission points.
66
-------
Table 5. TEST CITY BASE YEAR EMISSION INVENTORY,
SO (tons/day)
Source
no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Light
residential
-
-
-
-
0.130 '
0.120
-
0.140
0.094
0.250
-
-
0.252
0.250
- .
0.200
0.260
0.230
-
0.270
Medium
residential
-
-
'-
-
-
-
-
-
-
-
1.244
-
-
-
0.750
0.300
-
-
0.510
0.530
- .
High-rise
residential
-
-
-
-
-
-
-
-
-
-
0.622
-
-
-
-
-
-
-
-
-
-
Conerclal
-
-
-
-
-
-
-
0.017
-
1.244
-
0.378
-
-
-
-
-
-
.
-
Light
Industry
-
-
-
10.500
-
-
0.250
-
-
-
-
0.208
-
-
-
-
-
-
-
-
H««vy
Industry
130.000
-
21.120
-
-
-
0.250
-
-
-
-
0.312
-
-
-
-
-
-
-
-
-
Other
-
150.51
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
67
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Table 6. TEST CITY LAND USE INVENTORY (square kilometers)
Score*
Bo.
1
2
3
4
5
6
7
I
9
10
11
12
13
14
15
It
17
18
19
20
21
Base year land use Inventory
Light
residential
15.00
15.54
22.50
15.27
14.06
10.38
14.06
7.38
13.24
13.24
9.00
Medium
residential
44.55
17.50
10.30
17.50
12.25
High-rise
residential
5.46
Cooerclal
0.80
13.64
5.39
Light
industry
0.0809
11.67
7.50
Heavy
industry
0.8094
0.0202
4.94
11.25
Transportation,
open space,
and utilities
1.4165
2.50
2.44
4.99
2.48
2.50
2.50
34.76
6.25
4.49
2.50
7.50
5.70
2.49
2.49
7.50
12. 75
16.00
Total,
excluding
vacant
17.50
17.98
21.60
24.98
18.57
16.56
98.41
25.00
20.26
16.56
25.00
23.58
15.73
15.73
25.00
25. 80
25.00
Vacant
7.50
6.21
3.32
0.0
6.43
8.44
1.59
0.0
4.74
8.44
0.0
0.0
9.27
9.27
0.00
0.00
0.00
Planned land use, design year
Light
residential
-
6.21
-
-
6.11
8.44
-
-
3.12
8.44
-
-
9.27
9.27
-
-
-
Hediua
residential
-
-
-
-
-
-
1.11
-
-
-
-
-
-
-
-
-
-
High-rise
residential
-
-
-
-
-
-
0.14
-
-
-
-
-
-
-
-
-
-
Comercial
-
-
-
-
0.32
-
0.34
-
1.62
-
-
-
-
-
-
-
-
Light
industry
-
-
2.33
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Heavy
Industry
0.0
-
-
0.99
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Ideal.
excltt£l3£
poinc S3UZZKC
25 .CC
21.13
24.«
24.98
25. OC
25.90
vn.se
15.-3O
25. 30
25.90
25.90
23.58
25.08
25.03
25.00
25.08
2v ae
ON
oo
-------
Table 7. CALCULATION OF THE RIGHT-HAND SIDE
Standard
155.49
155.49
155.49
155.49
155.49
155.49
155.49
155.49
155.49
155.49
155.49
155.49
155.49
155.49
155.49
155.49
155 . 49
Concentration
due to source no. 2
2.58
3.08
4.28
5.58
5.58
1.78
2.18
5.88
8.98
1.58
4.18
11.18
0.88
1.18
1.58
1.58
4.08
Right-hand
side
152.9
152.4
151.2
149.9
149.9
153.7
153.3
149.6
146.5
153.9
151.3
144.3
154.6
154.3
153.9
153.9
151.4
69
-------
9. The transfer coefficients from source no. 2 to each
receptor are deleted from the source receptor matrix.
The transpose is taken.
10. The land use inventory, Table 6, already presents
the information in the required format.
11. For example, the first source has an area of 0.8094
square kilometers, and its transfer coefficients to
the first two receptors are 0.1607 and 0.5067 pg/m3
per ton/day, so the beginning of the first vector
would be
• 0.8094
• 0.1301
• 0.4101
12. The SO -PM feasibility constraint is assumed to be
unnecessary.
13. The proximity constraint is assumed to be unnecessary.
14. The lower bounds for the current sources are their cur-
rent emission density. For example, the first source
has a current emission rate of 130 tons per day and
an area of 0.8094 square kilometers. Its lower bound
would be 160.6 tons per day per square kilometer.
15. For example, based on the AQMP analysis, assume source
no. 1 plans to increase its capacity by one-third.
Its upper limit would therefore be 213.6 tons per day
per square kilometer.
16. For example, assume the maximum permitted development
density for light residential land use is 1/2 acre
lots, or two dwelling units per acre. Multiplying
by the appropriate land use based emission factor,22
assume this product yields an emission density of
0.0197 tons per day per square kilometer.
17. Assume for light residential land use, the minimum
expected development density is 1-1/2 acre lots. If
the emission factor remains the same, the lower bound
would be one-third of the upper bound calculated in
step 17, or 0.00657 tons per day per square kilometer.
70
-------
18. For example, assume the range of expected floor area
ratios for light industrial development is 0.30 to
0.36, that light industrial sources are currently
required to have a 75 percent control efficiency and
the maximum feasible control efficiency is 90 percent.
Also, based on an analysis of the expected industrial
development, assume that the average expected emission
factor is 0.0674 tons per day per square foot of floor
area (658 kg/day/m2). Therefore the upper and lower
bounds would be computed as follows:
(0.3) (0.9) (0.0674) = 0.01821
(0.36) (0.75) (0.0674) = 0.02604
19. The format requirements for MPS are illustrated in
Section VII.
Based on the data developed in this sample program, a MPS input data file
was prepared and executed. The output of this execution is shown in
Figure 3 which includes a listing of the MPS control program. The system
used in this example consists of 8-digits, viz.,
Column Index
1-3 Source number, sources 1 to 4 are point sources
Source number, sources 5 to 21 are area sources
4-6 Unused, all zeros
7 Land use, 2 = light residential
3 = medium residential
4 = high rise residential
5 = commercial
6 = light industry
7 = heavy industry
8 Current or future source, 1 = current
2 = future
The interpretation of the output is explained in Section VII.
71
-------
//GC35EKHR JOL> (GCA02. JOB 34* .DI SP= (NEW .PASS >
XXSYSP9INT DD SYSOUT=A
XXSYSUDUMP OD SYSOUT=A
XXSYSABS DD SYSOUT=A
XXSYSPUNCH OD SYSOUT=R
//MPSI .SYSIN DO »
IFF2361 ALLOC. FOR GC35EKHR MPSI
IEF237I 243 ALLOCATED TO STF.PLIB
IEF237I 340 ALLOCATED TO SCRATCHl
IFF237I 341 ALLOCATED TO SCRATCH2
IEF237I 342 ALLOCATED TO SCRATCH3
IEFP37I 343 ALLOCATED TO SCRATCH4
IEF237I 344 ALLOCATED TO SYSMLCP
IEF237I 6O2 ALLOCATED TO SYSPRINT
IEF?37I 603 ALLOCATED TO SYSUDUMP
IEF237I 60« ALLOCATED TO SYSABS
IEFP37I 73? ALLOCATED TO SYSPUNCH
1EF?37I 70? ALLOCATED TO SYSIN
1EFI4?! - STEP WAS EXECUTED - COND CODE OOOO
IFF2B5I SYS 1.MPS.SYSTEM KEPT
IEFP8SI WL SER NOS= RESPAG.
IEF285I SYS77I2-5.T09I51 I .RVS77.GCSSEKHR.ROOOOOO 1 DELETED
IF.F28!il VOL SER NOS= PPDO03.
I = F?8-SI SYS77125.TOQ151 1 . RV677 .GCS5EKHR . HOOOO 00 ? DELETED
IFF28S! VOL SFO NOS= KEM002.
IFFaSSI SVS77]?S.TO"151 1 ,RV877.GCa5FKHR.ROOOOO03 DELETED
IFF285I VOL SER NOS= BSD003.
IEF2B5I SYS7712S.T091S11.RV877.GCaSEKHR.R0000004 DELETED
IEF2R5I VOL SER NOS= BSD002.
1EF?85I SYS77125.TO91511.RV877.GC35EKHR.ROOOOOOS PASSED
IEF285I VOL SER NOS= MDS444.
1EF373I STTP /MPSI / START 77125.09IS
1EF374I STEP /MPSI / STOP 77125.0916 CPU OM IN 01.63SEC STCR VIRT 25fiK
XXMPS2 EXEC PC,M=EXECUTOR.CONO = ( 4 ,LT .MPSI )
XXSTEPL1B DD DSN=SYS1.MPS.SYSTEM,DISP=SHR
XXSYS«LCP OD UNIT=2314.DSN=*.MPSI.SYSMLCP.DISP-(OLD.DTLETE)
XXPROHFILF OD UNIT=2314,SPACF=(CYL.(tPRI?)..CONTIG)
Figure 3. Test city example output
72
-------
IF.F6531 SUBSTITUTION JCL - UN 1 T=231 4 . SPACE=(C YL .( 5 ) . . CONT 16 )
XXMATRIXl ID UNIT=231«.SPACE«=(CYL.(EPOI2>..CONT?G>
IEF6531 SUBSTITUTION JCL - UN IT=231« . SPACE=(C YL .( 5 > . .CONT IGI
XXETA1 OD UNIT=2314.SPACE=«CVL.ftPRI2»..CONTIG>
IEF653I SUBSTITUTION JCL - UN IT=231 4 . SP ACE=(CYL .< 5 ) . . CONT 1 G >
XXSCRATCH1 DO UNI T=23I4 . SPACE = < CVL. « CPR I 2 ) . .CONTI G)
IFF653I SUBSTITUTION JCL - UNIT=23I 4 . SPACE=»CYL. < 5 ) • t CONT IG )
XXSCRATCH2 DO UNI T=2314 ,SPACE=(CYL. ( EPf» I 2) . .CONTI G»
IEF653I SUBSTITUTION JCL - UNIT=23I4. SPACEMCVL .< 5 > ..CONT IG)
XXSYSPRINT OD SYSOUT = A
XXSVSUDUMP DO SVSOUT=A
XXSVSABS DD SVSOUT=A
XXSVSPUNCH DD SYSOUT=B
//MPS2.SYSIN DD *
IEF236I ALLOC. FOR GC35FKHR MPS2
IEF237I 243 ALLOCATED TO STEPLI8
IFF237I 34« ALLOCATED TO SYSMLCP
1EF237I 3« 1 ALLOCATED TO PROBFILE
IEF237I 34(S ALLOCATED TO MATRIX!
IEF237I 340 ALLOCATED TO ETA1
IEF237I 343 ALLOCATED TO SCRATCHI
IEF237I 341 ALLOCATED TO SCRATCH2
IEF237I 602 ALLOCATED TO SYSPRINT
IEF237I 603 ALLOCATED TO SYSUDUMP
IEF237I 604 ALLOCATED TO SVSABS
IEF237I 732 ALLOCATED TO SYSPUNCH
IEF?37I TO2 ALLOCATED TO SYSIN
IEFI42I - STEP WAS EXECUTED - COND CODE 0000
1EF285I SYS I .MPS. SYSTEM KEPT
IEF20S1 VOL SER NOS= RESPAG.
IRF2B51 SYS77125.TO9151 1.RV877.GC35EKHR.ROO00005 DELETED
IEF2B5I VOL SER NOS= MDS444.
IEF285I SYS7712S.T09I51 I .RV877.GC95EKHR.ROO0001 I DELETED
lEF?^! VDL SFR NOS= KEM002.
IEF?B«iI SYS77125.T09I51 I . RV877. GC3SEKHR.HOOOOOI 2 DELETED
IEF?B5I VOL SER NOS= PPD002.
IEF28SI SYS77I2S.TOOI5I1.RV877.GCS5EXHR.ROOOOOI3 DELETED
IEF285I VOL SER NOS= PPDO03.
IFF285I SYS77125.TO915I l.RV877.GC3)5EKHH.ROOOObl4 DELETED
IEF285I VOL SFR NOS= BSD002.
IEF2S5I SYS77I25.TO9I5II.RVB77.GC85EKMR.ROOOOOI5 DELETED
IEF28SI VOL SER NOS= KEMO02.
1EF373I STEP XMPS? / START 77125. O9I6
IEF374I STFP /MPS2 / STOP 77125.0917 CPU OMIN 02.9ISEC STOR VIRT 2S6K
IEF3751 JOB /GCaSEKHRX START 77125.0915
IEF376I JOB XGCSSEKHR/ STOP 77125.0917 CPU OMIN 04..54SEC
Figure 3 (continued). Test city example output
73
-------
CONTROL PROGRAM COMPILFR - MPS/3K) V."-«l 1
0001 • PROGRAM
0002 INITIALZ
OO65 MOVE(XDATA.«TESTCITY«)
0066 MOVE
OO67 CONVERT!'SUMMARY•)
O068 BCOOUT
0069 SETUP»'BOUND*."EM1SL«)
O0.7O MOVE(XOBJ.*EMISS'>
O071 MOVEfXRHS.*SO?«)
DOT? PRIMAL
OO73 SOLUTION
OO74 RANGE
0075 EXIT
0076 PEND
EXTCUTOR. MPS/360 V?-MU
CONVERT TESTCITY TO PBF ILF
TIME = 0.01
SUMMARY
I- ROWS SFCT1ON.
0 MINOR CTROR(S) - 0 MAJOR ERROR(S).
2- COLUMNS SECTION.
O MINOR BRROR(S) - 0 MAJOR ERROR(S).
3- RHS'S SECTION.
SO?
0 MINOR ^RROR(S) - 0 MAJOR ERROR IS).
5- BOUNDS RfTCTION.
EMISL
0 MINOR E(?POR(S) - 0 MAJOR ERRORfSI.
Figure 3 (continued). Test city example output
74
-------
FXFCUTOR. MPS/360 V2-M11
NUMBER OF ELEMeiTTS BY COLUMN ORDER
PACE
77X135
19
26
33
4O
47
54
O010O071 .
OO80O021.
01200061.
OI6OOO31 .
00600022.
011000*2.
.. .18
...18
...ta
.. .18
...18
...18
O03OOO71....18
OO9O0021....16
012OOO71 ....13
01700021 ....18
OO7OOO62....1S
01 100052.. ..I 8
OOAOO061 .
OO9OOOS1 .
O130OO2I .
0180 OO 21 .
00 70 007? .
01300022.
. .. 18
... 16
...18
...18
...18
...18
OOSOOO21..
0100O02I..
OI3OOO5I ..
O19O0031..
OO9OOO22..
0130005?..
..18
..18
..18
. .18
..ta
..18
OO60O021 ..
O110O031..
0140O021 ..
02OOO031 ..
OO90OOS2..
OI40O022..
..18
..18
..18
..18
..IB
..18
OO70OO6I.... 18
Ol 1OOO41.. .. 18
O15O0031.. ..18
O210OO21.. ..18
01000022. ...18
O17OOO22....I8
00700071 .. .. 18
Ol lOOOSi .. .. 18
016OOO21 .. .. 18
OO5OOO22.. .. 18
Ol 1OOO32-. .. 18
O1OOOO22.. ..18
Figure 3 (continued). Test city example output
-------
EXECUTOR. MPS/36O V2-MI1 PAGE 3 - 77X125
NUMBER OF ELEMENTS BY ROW ORDER. EXCLUDING BUS'S. INCLUDING SLACK ELEMENT
1 N EMISS ....43 L ROOI ....43 L ROO2 ....43 L ROO3 ....43 L ROO'4 ....43 L RODS .,..43 L ROO6 ....43
8 L ROO7 ....43 L RO08 ....43 L ROO9 ....43 L R010 ....43 L RO11 ....43 L R012 ....43 L RO13 ....43
15 L RO14 ....43 L ROiS ....43 L ROI6 ....43 L RO17 ....43
PROBLEM STATISTICS - 18 ROWS. 60 VARIABLES. T74 ELEMENTS. DENSITY = 71.66
THESE STATISTICS IMCLUDE ONE SLACK VARIABLE FOR EACH ROW.
0 MINOR ERRORS. O MAJOR ERRORS.
Figure 3 (continued). Test city example output
-------
EXECUTOR.
8CDOUT - USING PBF ILE
TIME = 0.24
MPS/360 V2-MI1
NAME
ROW?
N BOSS
L ROOI
L ROO2
L RO03
L BOO*
«. 0005
L "0 O6
L POO7
L Rooe
L ROO9
L R01O
L ROM
L BO I 2
L ROI3
L RO 1 4
L BO 1 5
L R016
U RO17
COLUMNS
OOIOO07I
OO 100071
00100071
OOIOOO71
OO10OO71
00100071
O010OO71
00100071
OOIOO071
00300071
00300071
OO30O071
00300071
O03O0071
00300071
0030007)
00300071
003OOO71
00400061
004OOO6I
00400O6I
004OOO61
00400061
O0400061
00400061
OO400061
00400061
00500021
OOSOOO21
00500021
0050OO?!
00500021
00500021
EXECUTOR
TESTCITY
EHISS
R002
BOO 4
R0a6
R008
B010
ROI2
BO14
R016
EMI SS
B002
R004
R006
BOOB
R01O
B012
BOI4
B016
EHISS
BOO 2
R004
ROO6
BOOS
B010
P012
RO14
BOI6
EMISS
BOO?
B004
B006
B00.8
BO10
MPS/36O V2-M11
.8O940
.41010
. 2463O
.O648O
.18700
.06850
.1O20O
.07357
.O6475
.02023
.OO209
.O1018
.oooes
.OO3II
.OD064
.00230
.OO091
.00183
.08094
.Ol 301
.04932
.OO476
.02028
.00376
.01086
.00598
.0071 1
15.00000
9.09SOO
3.63200
2.322OO
3.36600
1.72200
R001
RO03
ROO5
B007
ROO9
RO1 I
ROI3
B01S
B017
B001
ROO3
BOOS
ROOT
B009
RO1 1
H013
•R015
R017
B001
R003
BOOS
RO07
ROO9
BO 11
R013
BOIS
R017
BOOl
R003
RODS
ROO7
RO09
BO 11
.13010
.451 1O
.1957O
.0676O
.teiae
.1O81O
.059T3
.O709O
.06749
.00199
.00323
.01221
.00112
.OO5O3
.00230
.00062
.00149
.0017*
.OO84T
.03519
.02473
.OO569
.01883
-O1O07
.00367
.00736
.OO647
7.5930O
4.55700
2.877OO
1.886OO
2.51300
1.886OO
Figure 3 (continued). Test city example output
77
-------
EXECUTOR.
MPS/3f-0
OOS00021
O050O02I
005000?!
00600021
OO600021
00600021
00600021
OO600021
00600021
00600021
00600021
0060O021
007000ISI
00700061
00700061
00700061
00700OA1
007O006I
007O0061
00700061
007OO061
O0700071
OO7O0071
00700O71
00700071
0070OO71
00700071
O0700071
00700071
OO7OOO71
OOBOOO21
00800021
008OOO21
00800021
00600021
OOBO0021
00800021
00800021
008000?!
OO9O0021
00900021
009O0021
O09OOO21
O09O0021
009OOO21
00900021
00900021
0090O02I
009O0051
00900051
OO9OOO51
O0900051
OO900OSI
00900051
R012
ROI 4
R016
EM1SS
ROO2
R004
RO06
RO08
ROIO
H012
R014
RO16
EMISS
0002
ROO4
R006
R008
0010
R012
ROI 4
R016
EMISS
R002
R004
R006
R008
R01O
R012
RO14
R016
EMISS
ROO2
R004
R006
ROOB
ROIO
0012
R014
ROI ft
EMISS
ROO2
POO*
ROO6
ROOfl
ROIO
R012
ROI4
ROl*)
EMISS
R002
R004
ROOC.
RODS
ROIO
I.8390O
1.31100
1.25400
I5.5400O
7.87200
4.728OO
1.24300
3.606OO
.19900
.95800
.4123O
.2430O
1 .67000
.876OO
7.109OO
.68600
2.92400
.54130
1 .5660O.
.86220
1.0260O
- 4.938OO
.79400
3.0OBOO
.29O30
1.23700
.22910
.6626O
.3649O
.43400
22.50000
2.324OO
I 1.3200O
.98100
3.4610O
7.1 IOOO
2.781OO
1.00800
2.03400
15.270OO
I. 18300
2.421OO
.50690
1.20200
.47O30
1.72500
.464 1O
1. I 12OO
. - .8O36O
.06228
.I274O
.O266R
.06324
.02475
R013
R015
RO17
9O01
R003
R005
R007
RO09
R01 1
ROI3
R015
RO17
ROO1
R003
R.O05
R007
R009
R01 1
no 13
RO15
R017
ROO1
ROO3
RO05
ROO7
R009
R011
RO13
ROI5
ROI7
R001
RO03
RO05
RO07
R009
ROI I
"013
R015
R017
ROO1
RO03
ROO5
RQ07
RO09
ROI 1
0013
RO15
0017
R001
R003
R005
R007
ROO9
ROI 1
1 .36800
1.1970O
1 .2660O
2.498OO
8.66000
3.7570O
1.29700
3.4B9OO
2.076OO
1.1*700
I .1MOO
1.30000
1 .??000
5.0 C30O
3.5t>*OO
.82020
2.715OO
1.45100
.5297O
.5192O
.93330
.5165O
2.147OO
I.50800
.34710
1.149OO
.61420
.22420
.45030
.395OO
I.766OO
3.501OO
13.58OOO
1 .24200
S.589OO
2.56300
.6930O
1.65400
1.958OO
.9039O
I.56300
7.606OO
-6397O
2.32100
1.I59OO
.29310
.6794O
1.3680O
.O4757
.08229
.40030
.03367
.122^0
.06099
Figure 3 (continued). Test city example output
78
-------
MPS/36O V7-MII
0090O051
00900051
OO90OO51
01000021
010O0021
O1OOOO21
0100OO?!
010OOO21
Ol 0000?!
010000?!
01OOOO?!
O10OOO21
01 IOOO31
01 1OOO?I
01 100031
01 1OOO31
01100031
01 10O031
01 1OOO31
01 10O031
01 1OO031
01 10OO41
01 100041
01 10OO41
01 100041
01100041
Ol 100041
01 1O0041
01100041
Ol 10OO4I
01 IOO051
01 100051
01100051
01100051
01 10OO51
O11OOO51
01 100O5I
01 100OFS1
01 100051
01200061
01200O61
01200061
O12OO061
O12OOO61
012OOO61
012000*1
01200061
0120O061
012OO071
01200O7I
012O0071
01200071
OI20O071
012OOO71
R012
9014
R016
EMISS
0002
R004
R006
ROO6
WO10
3012
R014
ROlft
EMISS
ROD?
0004
R006
R008
ROIO
R012
R014
ROI6
EMISS
R002
ROO4
R006
RO08
ROIO
R012
R014
RO16
EMISS
R002
R004
RO06
Rooe
ftOlO
RO12
P014
R016
EMISS
R002
ROD 4
R006
ROO8
ROIO
ROI2
Pt>14
R016
EMISS
RO02
POO 4
ROO6
ROOS
ROIO
.09080
.02443
.osaso
14.06000
4.137OO
2.51200
7.27300
4.O61OO
2.599OO
2.813OO
?.O85OO
2. 1 15OO
44.55000
I5.56OOO
6.6S10O
7.190OO
13. 6300 O
3.S8100
10.06000
5.15400
6.OOOOO
5.45500
1.90500
.81440
.88150
1.669OO
.43850
1.232OO
.IS311O
.73470
13.64OOO
4.7620O
2.03600
2.20400
4. 173OO
1.09600
3.079OO
1.578OO
1.83700
- 7.50OOO
1.25OOO
1. 12OOO
.59700
3.272OO
3.3300O
1.6870O
.34880
.66780
11.25000
1.8750O
3.93OOO
.8955O
4.90600
. 499SO
ROI3
R015
ROI7
R001
ROO3
ROOS
ROO7
R009
R01 1
R013
R015
RO17
ROOI
RO03
ROOS
RO07
RO09
R01 1
R013
R015
R017
ROOI
R003
ROOS
R007
ROO
-------
FXECUTOP.
MPS/360 V2-W1I
01200O71
012OOO71
01200071
013000?!
013000?!
01300021
01300031
01300021
01300021
0130OO?!
OI30OO2I
013OOO?!
013000S1
0130OO51
Ol 300051
013000S1
01300O51
01300051
013O0051
01300O51
01300051
O14OOO?!
01AOOO?!
O140OO21
OI400O21
OI4OOO21
OI4O0021
014000?!
014000?!
0140O021
01500031
01500031
OI500O31
01500031
01500O3I
01500O31
01500031
015OO031
01500031
016OOO?!
OI6OO02I
016000?]
OI6O002I
016OOO21
OI600O?!
O160O021
0160OO?!
016O0021
01600031
016OOO31
01600031
01600031
01600031
01600O3I
ROI 2
RO1A
R016
EMISS
R002
ROOA
R006
ROOB
ROIO
ROI 2
R014
B016
RMI51S
R002
0004
ROO6
»OO«
OO1O
ROI 2
R014
R016
EM1SS
ROO2
ROO4
ROO/S
ROO8
ROIO
ROI?
POI4
R016
EMISS
ROO?
R004
R006
ROOS
ROIO
R012
ROJ4
ROI 6
EMISS
ROO2
ROO4
ROO6
ROOB
ROIO
ROI?
RO14
R016
EMISS
ROO2
ROO4
ROO6
ROOB
ROIO
2.83100
.97310
I.302OO
1O. 36000
I.3O6OO
2.T74OO
.747TO
1.98700
.41S4O
1.Q19OO
.39T7O
.05640
5.36500
.6774O
1.43800
.38770
I. 03100
.2154O
.99510
.2062O
.4959O
- I4.06OOO
2.83600
1 . 1150O
5.81100
2.51300
7.27300
3.212OO
4.19500
3.76500
- 17.50OOO
2.03400
4.17600
.2730O
6.09QOO
1 .3930O
9.81400
1.034OO
2.72700
7.37500
.86O7O
1.58000
.48970
1.66200
.44S4O
3.218OO
.32670
.59300
10.50000
1.22500
2.25000
.69720
2.36700
.63840
ROI 3
R015
9017
R001
R003
ROOS
ROO7
RO09
ROI 1
R013
R015
ROI7
RO01
ROO3
ROOS
ROO7
ROO9
ROI I
RO13
RO15
R017
ROO I
ROO3
ROOS
ROO7
R009
ROI 1
ROI3
ROI 5
ROI 7
R001
ROO3
ROOS
ROOT
R009
R011
ROI 3
RO1S
R017
ROOI
QOO3
ROOS
ROOT
R009
ROI 1
R013
ROI5
R017
ROOt
ROOS
ROOS
RO07
ROO9
ROI I
.3A340
.117300
1.409OO
.8 1520
2.0S40O
4.2950O
.694 TO
5.3720O
.«876O
.38730
.S7?20
I.4230O
.4??TO
1.O6SOO
2.22700
.36O2O
2.78500
.5I21O
.20080
.296 TO
.737TO
3.9TOOO
1.54400
I .2ISOO
2.69000
2.018OO
4.05600
2.6O200
3.9ISOO
2.81300
2.03400
3.7S20O
2.979OO
1.93700
4.3?eOO
6.81800
.7735O
1.40700
4.4OIOO
.71460
1-2070O
1.73TOO
.6018O
2.57100
1.188OO
.24930
.43660
1 . 15OOO
1.01700
1.718OO
2.501OO
.85660
3.660OO
1.69200
Figure 3 (continued). Test city example output
80
-------
EXECUTOR.
MPS/360 V2-M11
01600031
OI6OOO31
01600031
017000?!
01700O21
01700021
OI7OOO21
017000?!
01700O21
017OOO21
01 7OOOPI
0170OO21
01600021
OIBOOO21
01800031
018OOO?!
0180OO?!
01S00021
oisooo?!
OI80O021
0180OO21
01900O31
OI900O3I
01900031
01900O31
O1900O31
OI900O31
OI9OOO31
OI900O31
O1900O31
02000031
02000O31
02OOOO31
0200OO31
0?OOOO31
02000031
02000031
07000031
O200OO31
O2100021
02100021
0210O02I
021000?!
07100021
O2I00021
02100O21
OP10002I
02100021
005O0022
005O002?
OOSOOO2?
OO50OO22
00500022
OO50O022
R012
RO14
R016
FMISS
R008
R004
ROO6
nods
R01O
RO1?
R01A
R016
6MISS
ROD?
R004
ROOft
ROOS
RO1 0
R01?
RO14
ROlft
EMISS
RO02
ROO4
R006
ROO8
RO10
RO12
R014
HOlft
EMISS
R002
RO04
R006
ROOS
ROtO
R012
R014
RO16
EMISS
R002
ROD 4
0006
a oo e
RO10
RO12
R014
R016
EMISS
ROO2
BO04
R006
R008
ROIO
4.5S2OO
.46520
.8442O
13.24000
2.20600
2.83600
3.73800
1.0480O
5.469OO
I.9O100
«. 79900
3.8240O
I3.24OOO
2.7S70O
1.239OO
3.362OO
1.45300
3.53600
2.3640O
6.8480O
4.80200
17.50000
3.442OO
2.912OO
3.39500
3.53000
3.46500
3.08700
3.3S5OO
t 1.64OOO
12.25000
2.04200
2.62500
1.47OOO
3.5340O
1.47000
3.67SOO
1.597OO
6.2400O
9.0000O
.74970
1.38600
.72000
1.90400
.72000
3.06000
.783OO
1.52800
7.SOOOO
4.S4900
1.8I6OO
I.1610O
1.6830O
. .»61OO
R013
R015
"017
R001
R003
ROOS
ROO7
ROO9
'JO 11
ROI3
R015
R017
9001
R003
ROOS
RO07
R009
R011
ROI3
R015
R.OI7
R001
R003
ROOS
ROOT
RO09
RO1 1
ROI3
R01S
R017
ROOI
ROO3
ROOS
ROO7
R009
R011
R013
R015
t«OI7
ROOI
R003
ROOS
R007
R009
ROI 1
R013
R015
0017
ROOt
R003
ROOS
R007
ROO9
RO11
.35*90
.62I6O
1 .6370O
2.7600O
1.2360O
.70940
1. R6000
1 .14100
2.36IOO
7.997OO
4.800OO
3.024OO
?.«06OO
.7346O
2.2290O
1 .05IOO
2.3290O
2.54000
8.800OO
3.82400
2.82600
3.6400O
1 .6380O
3.332OO
1.92OOO
5.O94OO
2.I74OO
9.056OO
6.34600
I .884OO
2.45000
2.227OO
1 .93IOO
2.52700
5.063OO
.94200
2.40200
8.16700
.69210
I .260OO
1 .63600
.92610
2.14300
2.040OO
.69210
.882OO
4.00OOO
3.79700
2.27900
I.A39OO
.9428O
1.256OO
.94280
Figure 3 (continued). Test city example output
81
-------
MPS/3M) V2-M11
00500022
00500022
O050OO22
00600022
00600022
O060OO22
00600022
OO600O22
OO60O022
006OOO?2
00600022
006OOO22
OO7000I42
O0700O62
00700062
O070006?
00700062
O0700062
0070O062
00700062
007O0062
0070O072
O0700072
OO70O072
007OOO72
OO700072
O07OO072
007OOO72
00700072
00700072
00900022
O09OOO22
OO9OO022
OO90OOP2
009OO022
009O0022
00900O22
0090OO22
009O0022
00900052
00900052
009O0052
009O0052
00900O52
00900052
0090O05?
009O0052
00900052
010OOO22
01000O22
010O0022
01000O?2
01000022
01000O??
ROI2
ROI4
R016
EMISS
R002
«004
ROO6
R008
0010
R012
R014
R016
EMISS
R002
R004
ROO6
R008
ROIO
R012
R014
R016
EMISS
R002
R004
R006
RO08
P01O
ROI2
R0t4
9016
EMISS
R002
ROO4
R006
R008
ROIO
RO1?
R014
R016
EMISS
R002
R004
R006
ROO8
ROIO
R012
R014
R016
EMISS
R002
R004
ROO6
R008
ROIO
.91950
.65550
.627OO
6.21000
3. 147OO
1.88900
.49680
1.44IOO
.47940
.78250
.56450
.4968O
- 2.33300
.37510
1.42100
.13720
.5846O
. 1O83O
.31310
.17240
.2O510
.98750
.15880
.6017O
.0581O
.24750
.04582
. 1325O
.07298
.08680
- 6.1O7OO
.47330
.9686O
.20280
.48060
.18810
.69010
. 1 857O
.4446O
.32140
.02491
*O5O97
.01067
.02529
.00990
.03632
.O0977
.0234O
- 8.43800
2.46700
1.50700
4.364OO
2.43700
1.559OO
R013
ROIS
R017
R001
RO03
R005
R007
RO09
P011
R013
R015
0017
ROOI
R003
RO05
R007
R009
R01 I
R013
ROIS
R017
R001
R003
RODS
ROO7
ROO9
ROII
ROI3
ROIS
RO17
ROD I
R003
RODS
ROO7
R009
R01 1
R013
ROIS
RO17
R001
R003
ROO5
R007
R009
R011
RO13
901 S
ROI7
R001
R003
RODS
ROO7
0009
ROII
.6840O
.S9850
.63300
.99860
3.46100
1.5O2OO
.5185O
1.39500
.82970
.4S83O
.34400
.51980
.244OO
1.01400
.7I87O
.16400
.54890
.29020
.10890
.2128O
.I 8660
.10330
.42940
.30170
.06942
.22980
.12280
.O4463
.09006
.O79OO
.36150
.62340
3.04300
.25590
.93130
.46350
.11730
.27180
.54780
.01903
.03291
.16010
.01347
.04901
.08439
.02931
.01430
.02800
3.492OO
1 .4680O
1.2I2OO
1.78SOO
1.92700
2.237OO
Figure 3 (continued). Test city example output
82
-------
EXECUTOR.
MPS/360 V2-N11
0100O022
0100002?
01OOO022
01 100032
01 100032
01100032
01 100O32
01 100032
01 100032
01 100O32
01 100032
Ol 1OOO32
Ol 10004?
Ol 100042
01 10004?
01 10004?
01 10004?
01 10004?
01 100042
01 IOOO42
01 10O042
01 IOOO1?
01 IOOOS2
01 1OOO52
01 10OOS2
01 100 OS2
01 100OS?
01 100052
01 1OOO52
01 100052
O130OO??
01300O22
013O0022
01300O22
0130002?
01300022
013000P2
01300022
0130002?
01300O52
01300052
01300052
013000S2
01300052
OI30005?
O13000S?
O1300O52
01300052
01400022
0140002?
014OOO2?
014OOO??
0140O022
0140002?
RO12
1014
R016
EMISS
ROD?
POO*
RO06
ROO8
R010
R01?
001 4
9016
EMISS
RO02
ROO4
ROO6
ROOfl
R010
ROI2
ROI4
R016
EMISS
P002
0004
ROO6
ROO8
ROIO
R012
R014
R016
EM1SS
RO02
R004
RO06
POOS
ROIO
R012
RO14
ROI6
EMISS
RO02
R004
R006
BOOS
ROIO
RO12
RO14
R016
EMISS
RO02
RO04
RO06
ROO8
ROIO
1.6BSOO
I.2S1OO
1.26900
1 .1 I4OO
. 3890O
.16630
.18000
.34090.
.O895T
.2515O
.12B9O
. 15O1O
. I364O
.04763
.02036
.02204
.04173
.01097
.03080
.01578
.Ol 837
.34090
.11900
.OS09O
.05509
. IO43O
.02741
.07698
.03944
.O4592
3. 1 15OO
.39190
.83200
.22430
.59650
. 1 2460
.5757O
.11930
.28690
1.615OO
.20320
.43140
. 1 1 630
.30930
.06460
.29850
.06185
.I487O
8.43800
1.70200
.66910
3.487OO
1.50800
4.36400
R013
R01S
R017
ROOI
R003
POOS
ROO7
P009
P01 1
R0»3
ROI5
R017
ROOt
R003
POOS
ROO7
R009
ROM
P013
R015
R017
ROOI
R003
ROO5
ROO7
POO9
ROM
ROI3
RO15
RO17
ROOI
R003
POOS
POO 7
ROOQ
ROI I
ROI3
R015
RO17
ROOI
POO3
R005
ROO7
ROO9
ROI 1
R013
POI5
R017
ROOI
POO 3
RO05
RO07
ROO9
not i
I.IS9OO
1.347OO
1.23400
.251 1O
.27540
.16810
.25470
.2713O
.25950
.08666
.1396O
.14110
.03O74
.03378
.07058
.03118
.03321
.0317T
.O1O6O
.OI7O9
.01778
.076*4
.08427
.0514*
.07793
.08301
.079*0
.026*9
.04271
.04319
.244SO
.61610
I.288OO
.2084O
I.61100
.29620
.1162O
.17160
.42680
.12680
.31940
.66800
.1O80O
.835*0
.15360
.O6O24
.08899
.22130
?.382OO
.9265O
.729OO
I.614OO
I.21100
2.434OO
Figure 3 (continued). Test city example output
83
-------
f?XECUTOB.
MPS/360 V2-M11
RHS
01400022
01400O22
01*00022
01 700022
OIT00022
017OOO22
017O0022
01700022
017O0022
01700022
01700022
017OOO?2
O18OOO22
0180O022
0180O022
01800022
OIB00022
01800O22
01800022
01600022
01800022
S02
S02
SO2
SO?
SO 2
SO 2
SO2
SO 2
SO 2
R012
0014
R016
EM1SS
R002
R004
ROO6
RO08
R010
R012
R014
ROI6
EMISS
ROO2
R004
R006
R008
R01O
R012
R014
R016
ROOI
RO03
R005
R007
R009
R01 I
R013
R015
0017
1.92700
2.517OO
2.2S9OO
- 9.265OO
1.54400
.50960
2.61600
.73380
3.8280O
1.33000
6. 15900
2.67700
9.265OO
1.93000
.86720
2.35300
1.0170O
2.4760O
1.65500
4.79400
3.36100
152.9000O
151.20000
I49.400OO
153.300OO
146.50000
151.30000
154.60000
153.90OOO
151.40000
ROI3
R015
POI7
ROOI
R003
ROO5
ROOT
R009
RO1 1
R013
ROI5
R017
ROOI
R003
R005
R007
R009
R011
ROI3
R015
R017
R002
ROO4
R006
R008
R010
R012
RO14
ROI6
1 .56100
2.349OO
I .6B800
1 .93200
.86540
.49660
I.3020O
.79860
1 .6530O
5.59800
3.3600O
2.11 700
1 .824OO
1 .544OO
.51420
1 .5600O
.7356O
1 .6310O
1 .77800
6.16000
2.67TOO
152.400OO
149.90OOO
153.70000
149.600OO
153.90OOO
1 44.3OOOO
154.30000
153.30000
BOUNOS
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
EMISL
EMISL
EMISL
EMISL
FMISL
EMISL
EM JSL
EMISL
EMISL
EMISL
EMISL
EXISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMTSL
EMISL
EMISL
PMISL
OO100071
0010O071
00300071
00300071
O04O0061
OO400O61
00500021
005O0021
OO60OO21
00600021
OO70OO61
00700061
007O007I
OO700O71
008OO021
00000021
00900021
00900021
00900051
009OOOS1
01000021
01000021
160.60000
213.60OOO
1044.OOOOO
2088.00000
129.700OO
194.SOOOO
.00737
.00958
.00657
.00854
.01821
.O2367
.O43O4
.OS595
.00529
. 0068R
.00520
.00677
.01745
.02269
.0151 1
.01964
Figure 3 (continued). Test city example output
84
-------
FXECUTOH.
V?-M1I
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
CO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
LO
UP
FMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EM1SL
FMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
FMISL
EMISL
EMISL
EMISL
EMISL
EMISL
EMISL
01100031
01100031
01100041
01100041
011O0051
01100051
O120O061
012O006I
01200071
012O0071
013OOO21
013OOO21
01300051
01300051
01400021
01400021
01500031
O1500O31
01600021
01600021
OI60003I
0160OO31
01700021
01700021
OIBOOO21
OIS00021
0190O03I
01900031
02000031
02000031
02100021,
02100021
00500022
OO50O022
00600022
006OOO22
00700062
OO700062
00700O72
00700072
OO9 00022
0090002?
OO9OO052
OO9OOO52
01000022
01OO0022
01100032
0110003?
01IO0042
O110O042
01100052
OI1000S2
01300082
0130002?
.02374
.03086
.09693
.12600
.O77S4
. IOO8O
.02357
.03064
.02353
.03O58
.02063
.02682
. 05967
.07757
.01511
.01964
.03643
.04 736
.02305
.02997
.02429
.03158
.01 669
.O2I70
.Ol»77
.01 920
.02477
.03280
.03670
.047RI
.02555
.03322
.00657
.01970
.00657
.01970
. 0 1 82 1
.02604
.02663
.06155
.00657
.01970
.01152
.02836
.00657
.01970
.03643
.03940
.06494
.15750
.05195
.12600
.00657
.01970
Figure 3 (continued). Test city example output
85
-------
EXECUTOR.
MPS/360 V2-N1I
LO EMISL
UP EMISL
LO EMISL
UP EMISL
LO EMISL
UP EMISL
LO EMISL
UP EMISL
ENOATA
OI30OO52
0130OOS2
OI4OO022
0140O022
01700022
017OOO22
01000022
OI80OO22
.03998
. 09696
.OO657
.01970
.O0657
.0197O
.00657
.01970
EXECUTOR.
SETUP PBPILE
TIME ° 0.28
BOUND = EMISL
MPS/360 V2-M11
MATRIX1 ASSIGNED TO MATRIX!
ETA1 ASSIGNED TO ETA1
SCRATCH1 ASSIGNED TO SCRATCHl
SCRATCH2 ASSIGNED TO SCRATCH2
MAXIMUM PRICING NOT REQUIRED - MAXIMUM POSSIBLE
NO CYCLING
POOLS
H.REG-BITS MAP
WORK REGIONS
MATRIX BUFFERS
ETA BUFFERS
ROWS (LOG.VAR.t
COLUMNS (STR.VAR.)
774 ELEMENTS - DENSITY = 71.66 -
BE1
9
3
5
R SIZE
168
3504
7152
CORE
92
1512
IOS12
35760
TOTAL NORMAL .FREE.
18
42
17 1
0 0
FIXED BOUNDED
0 0
0 42
3 MATRIX RECORDS (WITHOUT RHS'S)
PRIMAL OBJ = EM1SS
TIME = 0.3O MINS.
SCALE = .
SCALE RESET TO 1.00000
OPTIMAL SOLUTION
RHS = SO2
PRICING 7
FXECUTOR. MPS/360 V2-M11
SOLUTION (OPTIMAL)
TIME = O.31 MINS. ITERATION NUMBER = 0
...NAME...
FUNCTIONAL
RESTRAINTS
BOUNDS....
...ACTIVITY...
242.15117-
DEFINED AS
EMISS
SO?
EMISL
Figure 3 (continued). Test city example output
86
-------
EXECUTOR.
SECTION I - BOWS
MPS/360 V2-M11
NUMBER ...ROW.. AT
.ACTIVITY...
SLACK ACTIVITY
1
2
3
4
S
6
7
8
<»
to
1 1
12
1.1
14
15
16
17
IS
ewiss
ROOI
RO02
RO03
RO04
POOS
R006
9007
ROO8
ROO9
R010
R011
R012
R013
R014
R01S
R016
ROI7
BS
BS
BS
BS
BS
BS
BS
BS
BS
BS
RS
BS
BS
BS
BS
BS
SS
BS
242.15117-
34.81524
97.17264
112.48956
85.86729
74.34O54
18.32188
19.60387
53.47604
55.87774
16.92212
32.34656
31.85386
15.89226
20.3751 1
2I.5302S
81.17437
21.53262
242.15117
118.08476
55.22736
38.7IO44
64.O3271
75.05946
135.37812
133.69613
96.12396
9O. 62226
136.97788
118.95344
112.44114
138.70774
133.92489
132.36975
I3P. 12563
129.86738
.LOWER LIMIT.
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
.UPPER LIMIT. .DUAL ACTIVITY
152.
152,
151
149
140,
153
153,
149,
146
153,
151,
144,
154
154,
193
183
151
NONE
,«OOOO
,4OOOO
,2OOOO
,9OOOO
,40000
,TOOOO
,30000
,60000
.SOOOO
,90000
,30000
,30000
.6OOOO
,30000
,90000
.30OOO
,40000
i.ooooo
Figure 3 (continued). Test city example output
87
-------
M°S/36O V2-M11
SECTION 2 - COLUMNS
r*\ji* r>C rf
19
?0
?1
22
?3
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
4fl
49
SO
51
52
S3
54
55
56
57
SB
59
60
. v-ni_ vimn .
O010007I
O0300071
OO400O61
O0500O21
OO600021
00700O61
00700O71
OOBOO021
O090OO21
OO90OO51
OIOOO021
01100031
Ol IOOO41
O110OO51
OI20O061
OT2OOO71
O13OOO21
013OO051
OI4QOO2I
O15OOO31
O16OOO21
OI6OOO3I
O17OOO21
01800021
0 190OO31
OPOOOO31
021OO021
00500022
00600022
00700062
OO7OOO72
OO9OOO22
O090O052
010OOO22
OI10O032
O110OO42
O I1OO052
013OO022
O1300O52
OI4OOO22
01700022
01BOO022
n i •
UL
UL
in.
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
Ut-
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
213.60000
2O88.00OOO
194.50000
.O09S8
.OOR54
.02367
.05595
.00688
.00677
.02269
.01964
. 03O86
.12600
.10080
.03064
. O3OS8
.02682
.07757
.01964
.O4736
.02997
.03158
.O2170
.01920
.03220
.O4781
.03322
.01970
.01970
.02604
.06155
.0197O
.02836
.01970
.03940
.15750
.126OO
.0197O
.09696
.01970
.OI970
.01970
INPUT COST..
.80940-
.O2O23-
.08094-
15.OOOOO-
15.54000-
1 1.670OO-
4.93800-
22.5000O-
15.27000-
.BO360-
14.06000-
44.55OOO-
5.45500-
13.64000-
7.5OOOO-
I 1.25OOO-
10.38000-
5.385OO-
14.06000-
17.5OOOO-
7.37500-
1O.50000-
13.240OO-
13.24OOO-
17.50OOO-
12.25OOO-
9.0000O-
7.SO 000-
6.21000-
2.33300-
.98750-
6.1O700-
i32140-
8.43800-
1.11400-
.13640-
.3409O-
3.1150O-
1.61500-
8.43800-
9.2650O-
9.26500-
O LIHIT.
I6O.60OOO
1044.00000
129.70000
.00737
.00657
.01821
.04304
.00529
.OO52O
.01745
.01511
.02374
.09693
.07754
.O2357
.O2353
.02063
.05967
.01511
.03643
.023O5
.O2429
.01669
.01477
.•O2477
.03678
.O2555
.00657
.O0657
.01821
.02663
.00657
.01152
.00657
.03643
.O6494
.OS19S
•OO657
.03998
.00657
.00657
. 00657
.UPPER LIMIT.
213.60000
2088.00000
194.5000O
.00958
.00854
.02367
.05595
.O06B8
.00677
.02269
.01964
.03086
.12600
.IO08O
.O3064
.03 058
.O2682
.07757
.01964
.04736
.02997
.03158
.0217O
.01920
.O322O
.04781
.O3322
.O197O
.01970
.02604
.06155
.O197O
.02836
.01970
.03940
. 157SO
.1260O
.01970
.09696
.01970
.O197O
.01970
COST.
.80940-
.02093-
.08094-
IS.OOOOO-
15.S400O-
11.67000-
4.938OO-
22.SOOOO-
15.27OOO-
.8036O-
14.060OO-
44.55000-
5.4S5OO-
13.64OOO-
7.50OOO-
I 1.25000-
I0.38OOO-
5.38500-
14.06000-
17.5OOOO-
7.375OO-
10.50000-
13.2400 O-
13.24OOO-
17.500OO-
12.25OOO-
9 . OO OO 0—
7.500OO-
6.2IOOO-
2.33300-
.98750-
6.1O7OO-
.32140-
A.4380O-
1 .114OO-
.13640-
.3*090-
3. I1SOO-
1.6150O-
8.438OO-
9.26500-
9.26SO0-
Figure 3 (continued). Test city example output
88
-------
RANGE
TIMfi =
EXECUTOP.
MPS/360 V2-MI1
0.32 KINS. ITERATION NUMBER
...NAME...
FUNCTIONAL
RESTRAINTS
ROUNDS....
...ACTIVITY...
242.15117-
OEFINED AS
EMISS
SD2
EM ISC
Figure 3 (continued). Test city example output
89
-------
VO
O
EXECUTOR. MPS/36O V2-M11
SECTION 2 - COLUMNS AT LIMIT LEVEL
.COLUMN. AT ...
19 OO10O071 UL
20 OO3O0071 UL
21 OO4O0061 UL
22 OO5O0021 UL
23 OO6O0021 UL
24 OO70O061 UL
25 OO7OOO71 UL
26 O08OOO21 UL
27 OO9OOO2I UL
28 OO90O051 UL
29 010OOO21 UL
30 01100031 UL
31 01100041 UL
32 0110OO5I UL
33 01200061 UL
34 O12OOO71 UL
PAGE 20 -
213.59991
2O87. 99921
194.49992
.00958
.00854
.02367
.05595
.O0688
.OO677
.02269.
.01964
.O308A
.126OO
.10080
.O3O64
.030-58
.80940-
.02023-
.08O94-
1S.OOOOO-
15.54000-
I 1.6700O-
4.9380O—
22.SOOOO-
15.2700O-
.80360-
I4.O600O-
44.55003-
5.45500-
13.64000-
7.5OOOO-
11.25001-
• • U.*J"C. ^ l_ 1 >" * i •
..UPPER LIMIT.
160.59995
213.59993
1O43.9996O
2087.99954
129.69996
194.49994
.OO737
.00958
.OO657
.OO854
.O1821
.02367
.O43O4
.O5595
.00529
.OO688
.00520
.OO677
.01745
.02269
.0151 1
.01964
.O2374
.03O86
. O9693
.12600
.07754
.10080
.02357
.O3064
.02393
.O305*
l_LJ Ht T «\_ 1 I V I 1 I
UPPER ACTIVITY
INFINITY-
299.41330
INFIN1TY-
8235.37408
INFINITY-
1294.54006
INFINITV-
6.O7985
INFINITY-
4.47856
INF1NITY-
7.65435
INFINITY-
IS. 08596
INFINITY-
5.534O8
INFINITY-
9.87522
1NF1N1TY-
187.53O70
INFINITY-
13.36925
1NF1NITY-
3.54679
INF1NITY-
28.84294
INFINITY-
1 1.58417
INFINITY-
21.57657
INFINITY-
14.39454
* • * \J ri i f t.w -» • • •
...UNIT COST..
.80940
.8O94O-
,O?O23
.O2O23-
.08094
,03094-
15.OOOOO
IS.OOOOO-
I5.54OOO
I5.54OOO-
1 1.67OOO
. 1 1.67OOO-
4.93800
4. 9380 O-
22.500OO
22.50000-
15.27000
15.270OO-
.80360
.80360-
14.O6OOO
14.O6OOO-
44.S50O3
44.55OO3-
5. 4550 0
5.45500-
13.640OO
13.64OOO-
7.500OO
7.5OOOO-
11. 2500 I
11.25001-
• •ur-r-t-r* \JLJ .a I ••
..LOWER COST..
1NFIN1TY-
INFINITY-
1NF1NITY—
INFINITY-
*
INFINITY-
INFINITY-
*
1NFINITY-
INFINITV-
INFIN1TY-
INFINITY-
INFINITV-
INFINITY-
INFINITY-
INF1NITV-
INFIN1TY-
INF1NITY-
i_i FI i it nu
PROCESS.
NONE
RO03
NONE
RODS
NONE
ROO3
NONE
R002
NONE
ROO3
NONE
R003
NONE
R003
NONE
RO05
NONE
R005
NONE
ROO5
NONE
R002
NONE
R003
NONE
R003
NONE
ROO3
NONE
R009
NONE
f* 1
AT
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
Figure 3 (continued). Test city example output
-------
EXECUTOR. HPSX36O V2-HII
PAGE 21 - 77/125
VO
35 O13O0021 UL
36 O130O051 UL
37 01400021 Ul.
38 OI5OOO31 UL
39 016O0021 UL
40 O160O031 UL
01700021 Ut.
42 OISOOO21 UL
43 01900031 UL
44 O2OOO031 UL
45 O210O02I UL
46 OO500022 UL
47 OO60OO22 UL
48 OO70O062 UL
49 OO7O0072 UL
SO O 090 0022 UL
51 OO9OOO52 UL
026B2
07757
O1964
O4736
O2997
031S8
O2I7O
01920
O322O
04781
O3322
O197O
O197O
02604
06155
0197O
O2836
• • r*r~\j i ^_u ^> • • » » * h
..l
10.380OO-
5.38500-
14.O6OOO-
1 7. SO 000-
7.375OO-
10.50001-
13.24OOO-
13.24000-
17.SOOOO-
12.25000-
9.OOOOO-
7.5OOOO-
6.21 OOO-
2.3330O-
.9875O-
6.1O700-
.32140-
,U Wt." k. •""*•» *
JPPER LIMIT. l
.02O63
.O2682
.05967
.O7757
.01511
.01964
.O3643
.O4736
.02305
.02997
.O2429
.03158
.O1669
.021 7O
.O1477
.O1920
.02477
.03220
.04 781
.02555
.03322
.OO657
.01970
.00657
.01970
.01821
.O26O4
.O2663
.06155
.00657
.01970
.01 132
.O283*
JPPER ACTIVITY ..
INFINITY-
16.89619
INFINITY-
32.61697
INFINITY-
IB. 85338
INFINITY-
ID. 36 464
INFINITY-
32.10157
INFINITY-
22.56383
INFINITY-
IS. 24216
INFINITY-
IS. 06121
INFINITY-
10.66693
INFINITY-
IS. 84 798
INFINITY-
3 O. 75579
INF1N1TY-
1 2.I6O24
INFINITY-
1 1.20445
INFINITY-
38.202OO
1NFINITY-
90.21 162
INFINITY-
24.68596
IMFINITT-
468.SS680
..UNIT COST.. .,
10.38OOO
1O.38OOO-
5.38SOO
5.385OO-
14.0600O
14.06000-
17.5OOOO
17.50OOO-
7.37500
7.37500-
IO.SO001
10.50001-
I3.24OOO
13.24000-
13.24OOO
13.240OO-
17.50000
I7.5OOOO-
12.2SOOO
12.25000-
9.OOOOO
9.OOOOO-
7.50OOO
7.SOOOO-
6.21OOO
6.21000-
2.33300
2. 3330 O-
. 98 75 0
.9875O-
6.I07OO
6. 10700-
.32140
.32140-
.LOMER COST..
INFINITY-
•
INFINITY-
•
INFINITY-
INFINITY-
•
INFINITY-
•
INFINITY-
•
INFINITY-
•
INFINITY-
INFINITY-
•
INFINITY-
»
INFINITY-
•
INFINITY-
•
INFINITY-
•
INFINITV-
INFINITY-
INFIN1TY-
INFINITV-
PBOCESS.
NONE
ROO9
r*JME
R009
NONE
R010
NONE
RO03
NONE
R003
NOff
R003
NONE
ROI4
NONE
ROI5
M3NE
ROO3
NONE
ROO3
NONE
9003
NONE
R002
ROO3
NONE
ROO3
NO»«
ROO3
NONE
R005
NOME
no 05
AT
UL
UL
UL
UL
UL
OL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
Figure 3 (continued). Test city example output
-------
N)
EXECUTOR. MPSX36O V?-«ll
NUMBER .COLUMN. AT ...ACTIVITY.
52 OIOOO022 UL
53 O1IO0032 UL
S4 01100042 UL
55 O1IOOOS2 UL
56 O1300022 UL
57 OI3O0052 UL
S8 01400022 UL
59 01700022 UL
6O O18OOO2S UL
PAGE
22 - 77X125
VITY... ..INPUT COST.. ..LOWER LIMIT. LOWER ACTIVITY ..
..UPPER LIMIT. UPPER ACTIVITY ..
.01970 8.438OO-
.O394O 1.1140O-
.I575O . 1364O-
. I26OO .34O90-
.OI970 3.11500-
.09696 1.61500-
.OI97O 8.4380O-
.O197O 9.26500-
.01970 9.26500-
.00657
.0197O
.03643
.O394O
.O6494
.1S75O
.05195
. T260O
.O0657
.01970
.03998
.O9696
. OO6S7
.0197O
.OO6S7
.01970
.00657
.O197O
INFINITY-
22.40614
INFINITY-
14O.6OOI1
INFINITY-
1148.15377
INFIN1TY-
459.48789
INF1NITY-
56. 27 J 83
1NFINITY-
108.57464
INFINITV-
3.1.40781
INFINITY-
21.76427
INFINITY-
2 1 .SO 029
.UNIT COST..
.UNIT COST..
B. 43800
8. 4380 O-
1. 1140O
1.1I40O-
.1364O
.13640-
.34O9O
.34O9O-
3.11500
3.115OO-
1.615OO
1.6I5OO-
8.43800
8. 4380 O-
9.26500
9.265OO-
9.265OO
9. 26 SO 0-
.UPPER COST.. LIMITING AT
.LOWER COST.. PROCESS. AT
. NONE
INFINITY- ROO2 UL
. NONE
INFINITY- ROO3 UL
NONE
INFINITY- ROO3 Ut
INFINITY- ROO3 UL
. NONE
INFINITY- ROO9 UL
NONE
INFINITY- ROO9 UL
NONE
INFINITY- ROIO UL
. NONE
INFINITY- DO 14 UL
NONE
INFINITY- HOIS UL
Figure 3 (continued). Test city example output
-------
CXIFCUTOR. NPS/36O V2-N11
SECTION 3 - ROWS AT INTERMEDIATE LEVEL
23 - 77/125
VO
LO
CR ...OOW.. AT ...ACTIVITY... SLACK ACTIVITY ..LOWE" LIMIT. LOWER ACTIVITY .
..UPPER LIMIT. UPPER ACTIVITY .
2 ROOI BS 34.81525
3 R002 BS 97.17264
4 RO03 BS 112.46056
5 ROD* BS 85.86728
6 RODS BS 74.34O55
7 R006 BS 18.32188
8 R007 BS 19.60387
9 RO08 BS 53.47604
10 ROO9 BS 55.87773
11 R010 BS 16.92212
12 ROll BS 3?. 34656
13 R012 BS 31.P5886
14 R013 BS 15.89226
15 RCM4 BS 20.37511
16 R015 BS 21.53O24
17 R016 BS 21.17438
118.08475 NONF
152.S9999
55.22736 NONE
152.39999
38.71043 NONE
151.2000O
64.O3271 NONE
149.89999
75.O5945 NONE
149.39999
13S. 37811 NONE
153.7OOOO
133.69612 NONE
153.29999
96.12395 NONE
149.59999
9O. 62225 NONE
146.4999S
136.97787 NONE
153.89999
118.95343 NONE
151.29999
112.44113 NONE
144.29999
138.70773 NONE
154.59999
133.92488 NONE
154.29999
132.36975 NONE
153.89999
132.12561 NONE
153. 20999
34.76538
34.81525
97.11289
97.17264
1 1 2.44411
112.48956
82.67134
85.86728
61.59331
74.34055
18.28894
18.32188
19.6O3I1
19.6O387
53.45291
53.476O4
55.84799
55.87773
16.88917
16.92212
32.29O71
32.34656
31.75159
31.85886
15.81873
15.89226
2O. 29421
?O. 37511
2 1.44934
21.53O24
21.08789
21.1 7438
..UNIT COST.. ..UPPER COST.. LIMITING
..UNIT CO.ST.. ..LOWER COST.. PROCESS.
1.97524
INFINITY
1.64871
INFINITY
1.79428
INFINITY
1.64112
INFINITY
1.65684
INFINITY
1.93318
INFINITY
4.37377
INFINITY
2.29216
INFINITY
1.78317
INFINITY
1.93318
INFINITY
2.41951
INFINITY
1.78317
INFINITY
1.65 SOS
INFINITY
1.50430
INFINITY
1.50406
INFINITY
1.50344
INFINITY
00500022
NONE
OOSOOO22
NONE
OO6OOO22
NONE
OO400O61
NONE
OO3OOO71
NONE
OIOOOO21
NONE
Ol IOOO32
NO ft
O120OO61
NONE
012OOO61
NONE
O14OOO21
NONE
O2 00 OO 31
NONE
01 5O OO 31
NONE
O17OOO22
NONE
01700022
NONE
01800022
NONE
O19OOO31
NONE
AT
AT
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
Figure 3 (continued). Test city example output
-------
EXECUTOR. MPS/36O V2-M11 PAGE ?» - 77/125
NUN3ER ...»0».. AT ...ACTIVITY... SLACK ACTIVITY ..LOWER LIMIT. LOWER ACTIVITY ...UNIT COST.. . .UOPER COST.. LIMITING AT
..UPPER LIMIT. UPPER ACTIVITY ...UNIT COST.. ..LOVER COST.. PROCESS. AT
18 R017 OS 21.5326? 129.86737 HONE 21.4*25* l.»999« O2OOOO31 UL
151.39999 21.53262 INFINITY NONE
Figure 3 (continued). Test city example output
-------
SECTION VII
AN EXAMPLE OF THE EMISSIONS MAXIMIZATION
FORMULATION IN THE BALTIMORE AQMA
The emission density limit setting model was executed in two AQMAs,
Baltimore, Maryland and Louisville, Kentucky-Indiana. The emissions
maximization formulation was executed for both pollutants in the Baltimore
AQMA and the Louisville AQMA. The Baltimore example is discussed in this
section; the Louisville examples are discussed in Section VIII.
DATA COMPILATION
The emission inventory and land use inventory available for the
Baltimore AQMA were not compatible; in addition, neither geographic system
for which the data were compiled was consistent with the component area
criteria of Section II. Consequently, a new grid system was prepared.
The emission inventory was reallocated to the new grid system; the land
use inventory and plan were compiled by grid square using acetate overlays.
During the latter stages of the preparation of this report it was dis-
covered that an error was made in the partitioning of industrial area
source emissions in Baltimore into the light and heavy industrial land
use classes. For each grid square the inventoried industrial emissions
were partitioned into light and heavy industrial emissions by the light
and heavy industrial land use, weighted by the mean emission densities
of light and heavy industrial point sources. Through a programming error
the mean plant emission densities were calculated for general commercial
and light industrial rather than for light industrial and heavy industrial
sources. Since the emission densities for the general commercial plants
were much lower than for the light industrial plants, the heavy industrial
95
-------
Point source lot areas were obtained by consulting real estate tax assess-
ment records; estimates of floor area ratios were developed from discus-
sions with the staff of regional and local planning agencies.
After the required data had been developed the preparation of the
input proceeded as described in Section VI. A total of 2256 emission
sources in 524 component areas were identified. There were seven land
use categories, consistent with those specified in the regional plan
and local zoning ordinances, viz:
• low density residential
• medium density residential
e high density residential
• local commercial
• general commercial
• light industrial
• heavy industrial
There was an average of 4.3 emission sources, area and point, in each
component area.
All power plants and incinerators were classified an non-EDZ sources,
as well as all mobile sources and the miscellaneous emission sources on
NEDS area source card 5. All point sources in the emission inventory
that were larger than 25 tons per year were treated as point sources in
the EDZ model; those less than 25 tons were assigned to the appropriate
area source. A 10-meter stack height was assumed for all nonindustrial
sources. Based on an examination of the point source inventory, a
65-meter height was assumed for all industrial area sources.
area sources were assigned a disproportionally high percentage of the to-
tal industrial area source emissions, leaving effectively a single indus-
trial land use, namely, heavy industrial. For the Louisville simulation
this error was corrected. This error does not invalidate the usefulness
of the test; however, it is less representative of Baltimore and more of
a similar city with a light industrial base that has a very low mean emis-
sion density.
96
-------
To facilitate the manipulation of the emission and land use inven-
tories by computer, an eight-digit identifier was constructed for each
source. It consisted of the following:
digits 1-3 the component area index number
4-6 point source identification number,
(zero if an area source)
7 land use category (values of 2 through 8 and
corresponding to the seven land uses
noted above)
8 current-future emission source identi-
fier (1 = current, 2 = future growth)
18
The input to the MPS execution step consists of four discrete sets of data:
the ROWS section, the COLUMNS section, the RHS section, and the BOUNDS
section.
The ROWS section is shown in Figure 4. The rows section is pre-
ceded by a name card with a user specified problem name. Shown is EDZBAL
(emission density zoning - Baltimore). Following the name card is the rows
card indicating the beginning of the ROWS section. Following that is a
record for each row indicating the type of row and the user specified name
of the row. The first row is the objective function, called EMISS (emis-
sions). The N indicates it is the objective function. Subsequent records
are included for each receptor. The L indicates that the constraint is a
"less than or equal to" type. The name of each row is the receptor number.
The COLUMNS section, shown in Figure 5, contains, for each source,
a vector consisting of first, the area of the source (the objective func-
tion parameter) and second, for each receptor, the product of the area of
the source and its transfer coefficient to that receptor. Thus the first
source shown in Figure 5 is the current low density residential land
97
-------
NAME EDZBAL
ROWS
N EMISS
L RQOl
L R2
L R523
L R524
Figure 4. ROWS section of SOX emissions
maximization program
98
-------
COLUMNS
00100021 EMISS
00100021 R001
00100021 R002
-0.5440E 00
0.3076E 00
0.2950E 00
00100021 R524
00100032 EMISS
00100032 R001
0.1690E-01
-0.2400E 00
0.1357E 00
02101761 R524
03501861 EMISS
03601861 R001
0.3730E-02
-0.1919E 02
0.5622E 00
Figure 5. COLUMNS section of SOX emissions
maximization program
99
-------
use in component area 1. It has an area of 0.544 square kilometers.
3
With a transfer coefficient of 0.5654 yg/m /ton/day, the value of the
element in the matrix is 0.3076 (0.5654 x 0.5440). Since there are 524
receptors and 2256 emission sources, there are 1,184,400 ((524 + 1) *
2256) records in the COLUMNS section.
The RHS section, shown in Figure 6, contains the right-hand side
constraint value (i.e., upper limit on air quality) for each row (i.e.,
receptor). The vector is given a user specified name, in this case, S02.
The BOUNDS section, shown in Figure 7, contains the lower and
upper bounds on emission density for each source; this vector is also
given a user specified name, in this case EMISL. For example, the first
source shown, source No. 12200181, has a lower limit of 0.122 and an
upper limit of 2.249. The BOUNDS section contains two records for each
source, or 4512 records. It is followed by an ENDATA card.
The SO -PM feasibility constraint was found to be unnecessary based
on the analysis in Appendix C. If it had been required, it would have
been added to the columns section. The proximity constraint was also not
employed to simplify the testing. If used, it too would have been added
to the columns section.
EXECUTION OF MPS
The problem, as compiled above, contained more matrix elements than
had been expected. We had estimated that there would be fewer emission
sources per component area. To reduce the problem to a more manageable
size, the number of rows (i.e., receptors) was reduced. This was done
*
The linear program actually run was a minimization. Hence the minus sign
for the area, which in effect led to the minimization of the negative of
emissions, equivalent to maximizing emissions.
100
-------
RHS
S02 R001 0.1215E+3
S02 R002 0.1214E+3
S02 R003 0.1213E+3
S02 R050 0.1180E+3
Figure 6. RHS section of the SOX emissions
maximization program
101
-------
BOUNDS
LO EMISL
UP EMISL
LO EMISL
UP EMISL
12200181 0.1220E+00
12200181 0.2249E401
03500361 0.7936E-02
03500361 0.1090E+00
UP EMISL
ENDATA
49400082 0.3048E+01
Figure 7. BOUNDS section of SOX emissions
maximization program
102
-------
by using an option in MPS to use a subset of the constraint equations.
It is not recommended that this option be normally employed, for it is
relatively inefficient. The number of constraint rows; i.e., receptors,
was reduced to a set of 52.
Because it was unnecessary to include the SOX-PM feasibility con-
straints, the maximization of particulate matter and sulfur oxide emis-
sions could be solved independently. Therefore two separate linear
problems could be executed, one for each pollutant.
The control program for MPS used in this example is shown in Fig-
ure 8. The CONVERT command reads the input data, converts it to
binary, and stores it on a temporary disk file. In this example, it is
also using a masking option to use only those rows that end in the digit
five. SETUP takes certain sections of the problem and places them in a
working file. CRASH is a procedure to obtain a starting point that con-
tains fewer infeasibilities. It is an attempt at solving the linear
program more efficiently. PRIMAL is the command that solves the linear
program. SOLUTION outputs the optimal solution (see the example output
in Figures 9 and 10) and RANGE is a postoptimal procedure that calculates
how sensitive the final solution is to changes in the right-hand side of
the air quality constraint and to changes in the land area of each source.
OPTIMAL SOLUTION TO SULFUR OXIDES MAXIMIZATION
After presenting information on the characteristics of the problem
and an iteration log, the output of MPS presents the optimal solution to
the problem and the sensitivity of the solution to changes in the param-
eters. The solution is described in two sections. The first is the rows
*
Through the use of the masking option on the CONVERT command.
+The number of rows was thus 53, 52 constraints and the objective function.
103
-------
PROGRAM
INITIALZ
MOVE(XDATA,'EDZBAL')
MOVE(XPBNAME,'PBFILE')
CONVERT('SUMMARY','RMASKS','R**5', 'EMISS',' ')
SETUP('BOUND'.EMISL1)
MO VE(XOBJ,'EMISS')
MOVE(XRHS,'S02')
CRASH
PRIMAL
SOLUTION
RANGE
EXIT
PEND
Figure 8. MPS control program
104
-------
EXECUTOR.
SECTION 1 - ROWS
MPS/36O V2-HII
77/01O
o
Ul
NUMBER
2
3
: 4
5.
6
7
8
9
10
11
12
13
14
15
16
17
! 20
! 21
22
23
24
26
26
i 27
i 28
29
30
31
32
— if-
35
36
37
38
2.9
40
42
; 43
. . .ROM. .
R005
RO1S
R02S
R035
R045
R0o5
R065
R075
RO85
R095
R105
R115
R125
R135
R145
R155
R16S
R175
R18S
R195
R205
R215
^225
R235
R245
R2S5
R265
R275
R285
R295
R305
R315
— R32S
R33S
R345
R355
~R36S
R375
R385
R395
R4O5
R415
R425
R435
R445
R45S
R475
AT
BS
BS
BS
. UL
UL
BS
BS
.-BS_
BS
BS
BS
BS
BS
UL
BS
UL
BS
BS
BS
UL
BS
BS
UL
BS
UL
BS
BS
bS
BS
BS
BS
BS
bS
UL
__BS_ _
UL
BS
US
BS
as
BS
BS
BS
BS
BS
BS
. . .ACT IV1TY. . .
0*3.66417-
26.46435
44.7399O
59.57467
119.90000
118.50000
101 .92672
1 14.33388
48.7740
-------
EXECUTOR•
SECTION 2 - CULUMNS
MHS/360 V2-M11
PAGE
5O -
77/010
NUMBER
54
55
56
57
• 58
59
60 .
61
62
63
64
65
66
67
66
69
70
71
72
73
74
75"
76
77
78
79
80
81
82
— 83""
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
9*
100
101
102
.COLUMN.
" '00 10*0031
00200021
O020O022
00200051
"00300021
00300O31
00300051
00400021
00400022
O04000S1
00400071
005OO021
00500022
00300051
O05O0071
00600021
00600051
00600071
O0600O82
O070O021
OO700O22
00700051
00700071
O070008i
00800021
00800022
00800051
OO800071
"6090O02 1 '.'
00900022
01 O00021
010OOO22
"01 SOOT/51
01 100021
01100022
01100031
Ol 10O051
01 100061
01 100072
O1200021
0120002?
01200031
01200052
O12OOO61
O120OO71
01200072
Ol JOOO21
O13OO022
A r . . . AC
„ .jJi
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
UL
.06_900
.12900
.06900
.069OO
.28200
.06900
.12900
.28200
.06900
.06900
.28200
.3O600
.06900
.06900
.2U200
.3O600
.06900
.28200
.30600
3.0480O
.06900
.26200
.30600
3.04800
" ~.0~6900 '"
.06900
.28200
.30600
— .069W
.06900
.06900
.06900
V2"8200 ~"
.06900
.06900
. 12*OO
.28200
.50dOO
.3OoOO
.06900
.06*00
.12900
.28200
.5O600
.30*600 " -"'
.30600
.06*00
.06*00
:>UT COST.. ..LOWER LIMIT. ..UPPE* LIMIT. .REDUCED COST.
.5*400- .0145? .06900 .=-2o59-
.24000-
2. 1760O-
3.80800-
.72OOO-
.59840-
.24000-
.2-000-
1.08600-
13.60000-
. 4800O- -
.09600-
1.36000-
2.99200-
.24000-
.24000-
1.25100-
.O96OO-
.09600-
.04800-
2.720OO-
2.17oO6-
.4*000-
.04600-
.04600-
1.36000-
2.72000-
. 24OOO-
.0360O-
1.3600O-
2.99200-
2.1760O-
4.216OO-
.T20T)0-
1.63200-
3.80800-
.24OOO-
".24000-
2.496OO-
.46COO-
1.63200-
I 14400-
.48000-
.41600-
' .04600-
,43200-
.81600-
8.7040O-
.03458
.00767
.02300
.00361
.O1387
.03375
.Ol 167
.01645
.02300
.00604
.00625
.02300
.02300
.02667
.00625
.01463
.04200
.01354
.09500
.00728
."52300
.01208
.O2600
.09500
.01669
.02300
.01O42
.01667
".0*300
.02300
.01466
.O2300
.03633
.00619
.02300
.01500
.00042
.00168
.02600
.01060
V02"300
.02569
.04200
.01442
" V0~2"600
.02600
.02300
.02300
. 1?900
.O69OO
.069OO
.282OO
.O69OO
. 12900
.28200
. 06900
.06900
.28200
.30600
.06900
'""- V06900 "
.28200
.30600
. O6900
" .28200 "" "
.30600
3.04800
.0690O
. 069OO
.2820O
.30600
3.04800
.0690O
.06900
.28200
.30600*
i'06$"00
.06900
.06900
.06900
.28200
. 069OO
. 069OO
.12900
I 50800
.oObOO
.06900
I 12900
.28200
.3O80O
.30600
.30600
.06900
.06900
.1O820-
1 .6*739-
2.97054-
.56164-
.45371-
.18197-
.18197-
.8O390-
10.04a62-
.35465-
.07099-
1.00678-
2.21484-
.17766-
.17780-
.89957-
.O6903-
.O69I4-
.03457-
1.86742-
I033O1-
.03301-
.93136- "
1.86278-
.16436-
.O247O-
2ll0994-
1 .42907-
2.76CJ95-
.07882-
1 .04305-
2.43357-
.15338-
.13338-
1.59520-
.30776-
1.O4886-
.09255-
.30851-
.26737-
.03093-
.27961-
.490O9-
5.31220-
Figure 10.
COLUMNS section of SO optimal solution
X
-------
sections, shown in part in Figure 9, which lists for each row an
internal variable number, the row name, its status (BS indicates the row
is in the basis and not binding, UL indicates the row is binding and at
its upper limit), the row activity (the ambient air quality at each re-
ceptor), the slack activity, the lower and upper limits as assigned by
the user, and the dual activity. Of most interest is whether a row is
at the upper limit, and the level of slack activity; i.e., unused tol-
erance for SO or the difference between the NAAQS and the projected con-
X
centration at the receptor. As can be seen in Figure 9, nine receptors
are at their upper limit. The lower limit for all receptors is zero;
i.e., ambient air quality is constrained to be nonnegative.
The second section of the solution output is the columns section, a
portion of which is shown in Figure 10. For each column (source), the
internal variable number, the column name (source index number), its
status, the column activity (assigned emission density limit in units of
2 2
tons/km /day), its objective function parameter (area in units of km ),
The dual activity is the value of the dual variable in the dual problem.
The dual can be interpreted as minimizing the marginal value of the air
quality standards used in the primal right-hand side, that is, minimizing
the rate at which total emissions may be increased by increasing the
standards. The value of the dual variables are sometimes called shadow
prices, and can be thought of as the maximum unit price one should be willing
to pay to increase the allocation of that resource; i.e., the air quality
standard. The shadow prices provide a convenient ranking of the importance
of each receptor. If one receptor is found to have a very high shadow
price, any non-EDZ sources (e.g., power plants) that have a significant
contribution to the ambient air quality at that receptor should be examined
for the possibility of additional emission controls, thereby increasing
the right-hand side value for the receptor. Also, if the receptor is a
sensitive receptor (thus with a lower total concentration than the NAAQS),
the desirability of maintaining its status should be reassessed.
107
-------
the lower and upper limits assigned by the user, and the reduced cost
of the associated variable. Of most interest is the activity column,
which indicates the emission density limit assigned to the source.
Interpretation of Solution
Tables of numbers such as those shown in Figures 9 and 10 are diffi-
cult to interpret, especially in a large problem such as the one at
hand. For this reason, the output of MPS was routed to a disk file.
The more interesting values were retrieved and displayed graphically using
27
SYMAP. The most interesting parameter in the rows section of the so-
lution output is the slack air quality, or the difference between the
standard and projected ambient concentrations at each receptor. These
values are plotted as a contour map shown in Figure 11. Immediately
apparent from the figure is that all the binding receptors are grouped
together in the center of the city or to the east over the Chesapeake Bay.
One would suspect, therefore, that emissions would be allocated by the
linear program to sources most distant (and therefore with smaller transfer
coefficients) from this grouping of binding receptors. This is obvious
from inspecting the spatial distribution of the emission sources that
are either at their upper or lower limit, or are unconstrained; i.e., at
neither limit. Figures 12 and 13 show, respectively, the status of each
grid square component area for current and future light industrial
sources. In both figures, those component areas on the periphery of the
region tend to be binding at the upper limit while those sources at the
*
The reduced cost is the rate of increase in the objective function, total
emissions, per unit increase in the emission density limit. At optimality,
an increase in a source currently at its upper limit will cause the total
emissions to increase, an increase in a source at its lower limit will
cause the total emissions to decrease, and an increase in a source in the
basis will cause no change in total emissions. See the section on sensi-
tivity analysis for more detail on these relationships.
108
-------
Figure 11. Slack SO levels (micrograms per cubic meter)
A
109
-------
LEGEND.
L AT LOWER LIMIT
* AT UPPER LIMIT
Figure 12. Status of bounds on emission density limits, current
light industry
110
-------
LEGEND.
L AT LOWER LIMIT
• AT UPPER LIMIT
Figure 13. Status of bounds on emission density limits, future
light industry
111
-------
center of the region tend to be binding at the lower limit. The same
pattern is evident in Figures 14 and 15 which show the same information
for heavy industrial sources.
Three critical insights to the emission density maximization for-
mulation as applied to sulfur oxides in Baltimore can be stated, viz:
• The critical (i.e. , binding) receptors tend to be in the
center of the region.
• The emission density limits for most sources will be set
at either the upper or lower limit.
• The emission density limits for future industrial sources,
which have identical bounds, will be higher on the periphery
of the region. There is then a possible sprawl inducing
potential inherent in simply maximizing emissions.
Sensitivity Analysis
The remainder of the output provided by MPS is a sensitivity analysis
of the optimal solution. The problem is, however, so constrained that
much of the analysis is of little interest. First, the maximum ambient
air quality at each of the binding nine receptors can be changed only
3
slightly (less than 0.3 yg/m ) before the optimal solution changes; i.e.,
an emission source not at an upper or lower limit in the current solution
reaches that limit.
The second part of the sensitivity analysis indicates how much the
assigned emission density limit at binding sources can change if the land
area of that source were changed. It also indicates how the value of the
objective function will change. In general, the model is fairly insensi-
tive to changes in the area of an emission source. The area of most
sources could change by a factor of two or more before the emission den-
sity limit on another source is affected. The emission density limit of
a source whose area is changed is greatly altered, of course.
112
-------
LEGENDi
L AT LOWER LIMIT
• AT UPPER LIMIT
Figure 14. Status of bounds on emission density limits, current
heavy industry
113
-------
LEGENDi
L AT LOWER LIMIT
• AT UPPER LIMIT
Figure 15. Status of bounds on emission density limits, future
heavy industry
114
-------
The third part of the sensitivity analysis indicates how the maximum
ambient air quality at unbinding receptors can change without altering the
3
optimal solution. This analysis shows that a slight change (0.1 yg/m )
in the ambient air quality of a nonbinding receptor will cause an emis-
sion source to reach an upper or lower limit.
The final section of the sensitivity analysis indicates how much the
area of an emission source not at an upper or lower limit may change
without altering the optimal solution. The emission density limit for
2
such sources can change only slightly; i.e., less than 0.2 tons/day/km ,
before another emission source currently at its upper or lower limit is
forced to change its emission rate.
PARTICULATE MATTER EXAMPLE
In a similar manner, a linear program was executed to maximize par-
ticulate matter emissions in the Baltimore AQMA. Baltimore currently is
recording violations of the annual particulate NAAQS. To allow the
linear program in this example to reach a feasible solution, attainment
was assumed. Total suspended particulate levels were assumed to be
20 yg/m3 less than they are in the base year.
The optimal solution to the problem was very similar to that for the
sulfur oxide example. However, in this case there was only one critical
receptor, located in Baltimore City. A contour plot of slack TSP level
is shown in Figure 16.
A plot of the status of the emission density limits is shown on
Figure 17 for current light industry. In this example most of the
sources are at their lower limits and only a few sources at the northern
edge of the region are at their upper limits. In contrast with the sulfur
In other words, a uniform rollback of 20 percent of the emissions at all
current sources was assumed.
115
-------
Figure 16. Slack TSP levels in Baltimore (micrograms per cubic
meter)
116
-------
LEGENDi
L AT LOWER LIMIT
• AT UPPER LIMIT
Figure 17. Status of bounds on emission limits, current light
industry
117
-------
oxide example, there was relatively less room for growth in emissions in
the particulate matter example. Almost all sources had their emission
limits set at the specified lower limit to allow for all the development
contemplated in the land use plan. The particulate matter example does,
however, support the observations made at the conclusion of the preceding
interpretation section. In this case:
• There is one critical receptor at the center of the region.
• Sources at the periphery of the city tend to have their
limits set at the specified upper bound and those nearer
the center of the city (and the binding receptor) are set
at the lower bound.
118
-------
SECTION VIII
AN EXAMPLE OF THE EMISSIONS MAXIMIZATION
FORMULATION IN THE LOUISVILLE AQMA
DATA COMPILATION
The emission inventory had been prepared on a census track basis.
Though it would have been possible to use census tracts as component
areas; to fully test the criteria of Section II it was decided to prepare
a new grid system and reallocate the emission inventory to this grid
system. The new grid system is shown in Figures 18 and 19.
Each county in the AQMA; i.e., Clark, Floyd, and Jefferson, had a
prepared land use plan. However, the plan was presented on a different
scale map in each county, respectively, 1 in. = 5000 ft, 1 in. = 500 ft,
and 1 in. = 6500 ft. Clark and Floyd counties also had land use inven-
tories compiled on colored base maps — of differing scales, 1 in. = 2000 ft,
and 1 in. = 500 ft. Jefferson County's land use inventory was compiled
by census tract. Jefferson County's land use inventory was reallocated
to the grid square system by measuring the percentage of each census
tract in a grid square. The remaining two land use inventories and the
land use plans were transferred to the grid system by preparing an acetate
overlay of the appropriate scale and measuring the amount of each land
use category in a particular grid. This process took 2 man-months.
Point source lot areas were obtained by consulting real estate tax
assessment records. This required 1 man-week.
119
-------
Figure 18. Louisville AQMA component area grid system
120
-------
Figure 19. Numbering of Louisville AQMA component areas
121
-------
To conserve resources, light and medium density residential land use
was treated as a non-EDZ source, their emission density limit was es-
tablished a priori and their projected contribution to each receptor was
subtracted from the right hand side. Their emission density limits were
set two geometric standard deviations larger than the geometric mean emis-
sion density of each class. The remaining land use was partioned into
three categories, viz.,
• Commercial, consisting of high rise residential,
commercial, office, and institutional land uses.
• Light industrial
• Heavy industrial
All power plants and incinerators were classified as non-EDZ sources,
as well as all mobile sources and the miscellaneous emission sources on
NEDS area source card 5. All point sources in the emission inventory
that were larger than 25 tons per year were treated as point sources;
those less than 25 tons were assigned to the appropriate area source. The
same stack heights used in Baltimore; i.e., 10 and 65 meters, were assumed.
Following these procedures, a total of 629 emission sources in 248
component areas were identified; thus, there were an average of 2.5 emis-
sion sources in each component area. This is 59 percent of the average
in Baltimore and can be attributed to the deletion of the two residential
classes and the aggregation of high rise residential, commercial, office
and institutional into one category.
AQDM was executed to determine the calibration coefficients. However,
the calibration was poor; consequently, the linear programs were executed
on uncalibrated data. It is thought that the poor calibration can be
attributed, at least in part, to questionable monitoring data.
The lower bound for existing sources was set at their current emis-
sion density. Point sources, whose emission density was expected to
122
-------
decline in the desing year (1990) due to current regulations, had their
lower limit set at this projected emission density (which does not include
capacity expansion). The upper bound for existing sources was set at
their projected 1990 emission density, based on the projected emission
inventory. Sufficiently detailed floor area ratios could not be readily
obtained for future nonindustrial sources. Consequently, their upper and
lower bounds were determined in the same manner as future industrial
sources. The upper and lower bounds for all future sources, therefore,
were set by estimating the smallest and largest emission density that
could be expected in each land use class. This was determined by analyzing
the distribution of existing emission densities in each class, which was
found to approximate a log-normal distribution. The mean was selected
as the lower bound and the sum of the mean and two standard deviations
was selected as the upper bound.
The input to the MPS execution step was identical in format to
Baltimore. The feasibility and proximity constraints were also not used.
EXECUTION OF MPS
MPS was executed three times, once for particulate matter and twice
for sulfur oxides. The sulfur oxide maximization was run once with
40 percent of the total receptors and once with a full compliment of
receptors. The control program was similar to that illustrated in the
Baltimore example.
PARTICULATE MATTER EXAMPLE
The linear program reached an infeasible solution in the particulate
matter example. That is, with all sources at their lower limits, the
NAAQS was still violated. Emissions at this point included the projected
1990 emissions from non-EDZ sources (power plants, mobile sources, etc.),
the existing emissions from current sources, no capacity expansion at
123
-------
existing sources, and complete development of the vacant land according
to the land use plan with a moderately stringent emission density limit.
Assuming the validity of the dispersion model and the emission inventory,
several options present themselves, viz.,
& Apply additional control strategies at non-EDZ sources.
o Require reductions in the emission density of existing
sources covered by EDZ.
• Rerun the EDZ model with a smaller lower limit for
future sources.
All three are viable strategies in the present case. Non-EDZ sources
generally account for half the particulate concentration at most receptors.
There are several large point sources included in the emission density
limit setting model with significant contributions to receptors projected
to violate the NAAQS. Finally, a more stringent lower limit on future
sources could be considered.
SULFUR OXIDES EXAMPLE
Optimal Solution - 40 Percent Sample
The sulfur oxide example of the emissions maximization formulations was
first run with a 40 percent random sample of total receptor set. There-
fore, 102 receptors were utilized. The optimal solution to the emissions
maximization had a total of 238.8 tons per day of sulfur oxide emissions.
Two receptors, R083 and R087, were at their upper limit; i.e., at the
NAAQS. Thirty-six sources were set at their upper limit, two at neither
bound, and the remainder at their lower limit.
Interpretation of Solution - 40 Percent Sample
The slack air quality is shown in Figure 20. As was the case in
Baltimore, the two binding receptors, along with four others that are
close to the standard are in the core of the metropolitan region. (This
124
-------
is the area with the symbol '.' in Figure 20. The opposite of slack
air quality is shown in Figure 21, which is the total projected sulfur
oxide concentrations. It is interesting to note the contribution to
ambient air quality from EDZ sources and non-EDZ sources. This is shown
in Figures 22 and 23, respectively. The values represented in Figure 23
are, of course, the amount that was subtracted from the NAAQS to obtain
the right-hand side.
Reviewing the pattern of emission density limits set at the upper
limit, the lower limit, or unconstrained, Figures 24, 25, 26, and 27, the
same pattern is discerned as was the case in Baltimore; sources at the
core of the region tend to have their emission density limit set at their
lower bound, those on the periphery tend to have theirs set at the upper
limit. In addition, note that for some component areas, a current source
is set at the upper limit while a future source of the same category is
set at the lower limit. Since the transfer coefficients for two such
area sources would be the same, the emission density limits could be
traded off between current and future sources and still remain at the
optimal solution — so long as total emissions from the component area for
that land use category remained unchanged.
The emission densities in the Louisville AQMA for the base year, the
design year, and the design year with all sources at their upper limit are
shown in Figures 28, 29, and 30.
Sensitivity Analysis - 40 Percent Solution
/
As discussed in the Baltimore example, the sensitivity analysis is
presented in four parts, viz., rows (receptors) at the limit level,
columns (sources) at the limit level, rows at an intermediate level,
and columns at an intermediate level.
The first part indicates how the optimal solution would change if the
value of right-hand side were increased or decreased. For example, at the
125
-------
Figure 20. Slack SO levels (micrograms per cubic meter)
X
126
-------
Figure 21. Projected SO concentrations (microgram per cubic meter)
X
127
-------
Figure 22. SOX levels attributed to EDZ sources
(micrograms per cubic meter)
128
-------
..r
Figure 23. SOX levels attributed to non-EDZ sources
(micrograms per cubic meter)
129
-------
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LLLLLLU.LLLL
U.U.LLLLLLULL
LLLLLLLLLLU.L LLI
LLLU.LLLLLLLLL U.IU.L N. tXMM •
ULtLLLLLLLULLL ^J j
LLIU.H.LLLLLLL, LL^ttL *• *M LLL «MT
LLIULULLLLLLLL LLt I4.L •» «•» LLL «••
I.LI LLLLLLLLt-LL * . /
txl U.LLLLIL1.I.U. ^ • ~^*+^ 97
LEGEND*
L AT LOWER LIMIT
« AT UPPE«
Figure 24. Status of bounds on emission limits, current light industry
130
-------
- —
rf..
j psssss
V ^ralwrnmB
t ' • iwpnftDMifiarmn
• fmBsmmnmmn
J Ben«RBfwnanen LLI
I raeieeeeBaoea LLI
* ' BPPOBttBBMBHP LL
I " BafUlMMBtMiBQR LL
1 LLLLLLLLLLLLL LLI
1 " — r LLLLLLLLLLLLL IL1
* — ••!••!. — — y LLLLLLLLLLLLL LLI
t LLLLLLLLLLLLL LLI
\ LLLLLLLLLLtLL
1 LLLLLLLLLLLLL LLI
1% LLLLLLLLLLLLL LLI
& LLLLLLLLLLLLL LL
\ LLLLLLLLLLLLL LLI
\ LLLLLLLLLLLLL Lt
.^LLLLLLL
^~ LLLLLLL
v. f *^ LLLLLLL *
1 • I LLLLLLL LL LLL Uf
• - ^^ LL LLL LLL LLL/LL
I j LL LLL LIL LUt LL
> *J -v /
L :('
i J
1 i L
/•
^
LLLLLL
LLL LLLLLL
/ . LLL .LLLLLL
9 LL LLL LLLI LL
I—— ••"/ LLLLLL
I UU LLL * ' LLL LLLLLL
I UU LLL LLL LLLLLL
1 LLLLLLLLLLLLL LL
1 LLLLLLLLLLLLL LL
1 LLLLLLLLLLLLL LL
L
/
y
^^r
+^r
^ s~
ALL X
-LLL /
XLL/
ALL/
4.L< LLLLKLL
JLLL LLLLLLL
.LLL LLLLUL
.LUL LLLLUL
A.m-
.L|L
3 \
/ ^LLLLLLLL LLLLLL
' XLLLLLLLL LLLLLL
*tt^^LLL LLLLLL
LLLLCkLL LLLLLL
LLLLLLLLLLLLL
LLLLLLLLLLMM.
LLLLLLLLLLLLX^
LLLLLLLLLLLLL
LLLLLLLLLLLLL
LLLLLLLLLLLLL
LLLLLLLLLLLLL '
LLLLLLLLLLLLL
LLLLLLLLLLLLL
LLLLLLLLLLLLL
LLLLLLLLLLLLL
LLLLLLLLLLLLL
LLLLLLLLLLLLL
LLLLLLLLLLLLL
LLLLLLLLLLLLL
LLLLLLLLLLLLL
LLLILLL LLLLLL
LLLLLLLLLLLLL
LLLLLLLLLLLLL
LLLLLLLLLLLLL
LLLLLLLLLLLLL
LL LLL LLLLLL
LL LLL LLI LIL
LLLLLLLLLLL
1 LLLLLLLLLLLLL LLLLLLLLLLLLL ^
i LLLLLLLLLLLLL LL
LLIL^rWUJL LL
»* LLLLLLLLLLLLL LL
X LLLLLLLLLLLLL LL
* ^ LLLLLLLLLLLLL LL
/ x'
» X""
L. '^
LEGEND:
L AT LOWER LIMIT
»-AT UWtfi LIMIT
B IN BASIS ( UNCONSTRAINED 1
LLLLL LLLLLL S
.LLLLLLL LLL f
XflMi^^^U. ^T
LLLLLLLLLLIT* ^m* .
LLLLLLLLLCL
LLLLLLLLLLL
\.
k
I
I
jl
Figure 25. Status of bounds on emission limits, future light industry
131
-------
LEGEND:
L AT LOWER LIMIT
»AT UPPER LIMIT
Figure 26. Status of bounds on emission limits, current heavy industry
132
-------
LLU.l-LU.LLLk
LLLLLLLLLLLL
LLLLLLLLLLLL
LLLLLLLLLLLL
LLLLLLLLLLLL
LLLLLLLLLLLL
LLLLi
. JLLLLLLLLLL
"LLLLLLUO.LLLLL
LtLLLLLLLLLLLL
J/
.-.J
LEGENDt
L AT LOWER LIMIT
• AT UPPER LIMIT
Figure 27. Status of bounds on emission limits, future heavy industry
133
-------
r
~n
.•.•U'UJLUVfc"llllll"'««
EfmmimmmiimmmiE;
•^;3i
:>S
/:
:S:
1
b.;
-J
MINIMUM
MAXIMUM
.00000
.00055
.00055
.00554
.00554
.02770
.02770
.27702
Figure 28. SOX emission density, base year (tons year
day per square kilometer)
134
-------
MINIMUM
MAXIMUM
.00000
.00035
.00055
.00554
.00554
.02770
.03770
.27702
.27702
.83106
Figure 29. SOX emission density, design year (tons per
day per square kilometer)
135
-------
I -
MINIMUM .00000
MAXIMUM .oooss
,00055
.00554
.00554
.02770
.02770
.27702
XX
XX
.27702
,83106
HH
MH
.83106
1.20000
Figure 30. SOX emission density, all sources at upper limit
(tons per day per square kilometer)
136
-------
upper limit the first receptor, R083, has an upper bound in the problem
of 61.98 micrograms per cubic meter. (The concentration at this receptor
due to non-EDZ sources is thus 80 - 61.98, or 18.02.) . The upper bound
on this receptor could be changed to any value between 61.97 and 62.03.
The total emissions; i.e., the objective function, would decrease or
increase, respectively, at a rate of 0.66 tons per day per unit change
in the receptor's upper bound. At the values 61.97 or 62.03, emission
source 9404021 (a light industrial point source) currently in the basis
would have its emission density limit set at, respectively its lower or
upper bound. For changes in the receptor's upper limit beyond 61.97 or
62.03, the rate of change of the objective function would be different
and other emission sources besides 9404021 would be affected. Similar
information is given for the other receptor at its upper limit.
The second part provides similar information for each column at the
limit level. For example, the first source given is 200012 (a commercial
area source, future development) is at its upper bound, 0.18790 tons per
square kilometer per day, in the optimal solution. It has a planned area
of 1.94 square kilometers. The sensitivity analysis indicates that if
its area were reduced to 1.15 square kilometers its emission density limit
would be set at 0.42 tons per square kilometer. Total regional emissions
would decline 0.80 tons per day per unit decrease in this source's emission
density limit. Any change in this source will affect the emission density
limit of source 9404021, currently in the basis. If source 200012's emis-
sion density limit were set below 0.42 tons per square kilometer, source
9404021's emission density limit would be set at its upper bound. Similar
information is presented for all of the emission sources.
The third part indicates the sensitivity of the solution to changes
in the ambient concentrations at receptors not at their upper limit. The
first receptor is at 33.47 micrograms per cubic meter in the optimal
solution. Its upper bound is 72.6 micrograms per cubic meter. However,
the upper bound can be changed down to 33.40 before an emission source
whose emission density limit currently at its upper bound will be forced
to change.
137
-------
The last part provides information on sources not at their upper or
lower bound. For example, source 9494921 is currently in the basis with
an emission density limit of 18.1 tons per square kilometer. Its upper
and lower bounds are 18.4 and 15.5, respectively. It can however, change
only between 18.2 and 18.0 before another source, currently at its upper
or lower bound, will be affected.
The examples given above are typical of the sensitivity of the solu-
tion to the right hand side and bounds of all the receptors and sources.
As was the case in Baltimore, it is highly sensitive.
Solution - 100 Percent Sample
The emissions maximization was also executed for the full complement
of receptors to determine the sensitivity of the optimal solution to dif-
fering receptor sets. With the full receptor set, the linear program
failed to reach an optimal solution. That is, with all sources set at
their lower limit, the NAAQS is still exceeded. Two receptors, not in-
cluded in the 40 percent execution, showed projected ambient concentra-
tions of, respectively, 10 and 6 yg/m3 in excess of the standard. Several
receptors in the vicinity of these receptors; i.e., 1 kilometer distant,
that were included in the 40 percent execution showed projected concentra-
tions of 15 to 20 yg/m3 less than the standard. Inspection of the emis-
sion inventory indicated several point sources with low stack heights in
the immediate vicinity of these two receptors.
Unlike the infeasible particulate matter example, in which nearly half
or the receptors over a broad area exceeded the NAAQS, the infeasible
100 percent sulfur oxide example is due to a hot spot with most receptors
well below the NAAQS. The appropriate action would be to prepare a sum-
mary of each source's contribution to the two receptors and review the upper
and lower bounds on the emission density for each significant source.
Some form of source specific emission limits may well be appropriate.
In conclusion, several observations can be made.
138
-------
The same pattern of emission density limits set in
Baltimore by the emissions maximization formulation
were set by this model in Louisville; i.e., more
stringent emission density limits in the center of
the region and less stringent ones on the periphery.
It is possible that even though the NAAQS is currently
being attained, the standard may be violated due to
planned growth even if all growth is at the specified
lower emission density limit. In such cases, the
linear program will reach an infeasible solution. The
emission density of any one or all three classes of
sources must then be reduced; viz., non-EDZ sources,
existing EDZ sources, and planned future development.
The model can be sensitive to the number and location of
receptors. In the extreme, an infeasible solution may
be reached with a full complement of receptors when a
feasible solution is reached with a subset of receptors.
If the receptor locations are valid, an analysis of
source contributions to the receptors exceeding the
standard should be used to further define the problem.
To conserve resources, it may be appropriate to run the
model with a subset of receptors. When a satisfactory
optimal solution has been achieved, the model must then be
rerun with all receptors. The preliminary optimal solu-
tion can serve as a starting point for the rerun with all
receptors.
139
-------
SECTION IX
REFERENCES
1. Guidelines for Air Quality Maintenance Planning and Analysis.
Volume 7: Projecting County Emissions. U.S. Environmental Pro-
tection Agency, Office of Air Quality Planning and Standards,
Research Triangle Park, North Carolina. January 1975.
EPA 450/4-74-008.
2. Guidelines for Air Quality Maintenance Planning and Analysis.
Volume 8: Computer-Assisted Area Source Emissions Gridding Pro-
cedure. U.S. Environmental Protection Agency, Office of Air
Quality Planning and Standards, Research Triangle Park, North
Carolina. September 1974. EPA-450/4-74-009.
3. Guidelines for Air Quality Maintenance Planning and Analysis.
Volume 13: Allocating Projected Emissions to Sub-County Areas.
U.S. Environmental Protection Agency, Office of Air Quality
Planning and Standards, Research Triangle Park, North Carolina.
November 1974. EPA-450/4-74-014.
4. Air Quality Display Model. TRW Systems, Inc. Prepared for U.S.
Department of Health, Education and Welfare, Public Health Service,
National Air Pollution Control Administration, Washington, D.C.
November 1969. 2 vols: PB-198~299 and PB-198~300.
5. Busse, A. D. and J. R. Zimmerman. User's Guide for the Climato-
logical Dispersion Model. Prepared for U.S. Environmental Pro-
tection Agency, December 1973. EPA-R4-73-024.
6. Guidelines for Air Quality Maintenance Planning and Analysis.
Volume 13. Op. cit. p. 133.
7. Ibid. See also: Guide For Compiling A Comprehensive Emission
Inventory (Second Edition.) U.S. Environmental
Protection Agency, Office of Air Quality Plan-
ning and Standards, Research Triangle Park,
North Carolina, p. 7-10 (APTD-1135)
140
-------
8. Guidelines for Air Quality Maintenance Planning and Analysis.
Volume 13. Op. Cit. Chapter 2.
9. Kennedy, A. S., et al. Air Pollution/Land Use Planning Project,
Phase II Final Report, Volume III: An Economic Comparison of Point
Source Controls and Emission Density Zoning for Air Quality Manage-
ment. U.S. Environmental Protection Agency, Office of Air Quality
Planning and Standards, Research Triangle Park, North Carolina.
May 1973. EPA-450/3-74-028c.
10. Pertinent Excerpts from the Preliminary Final Environmental Impact
Statement. Clark Maritime Center, Jeffersonville, Clark County,
Indiana, Ohio River Mile 597. U.S. Army Corps of Engineers,
Louisville District, Kentucky. No date given.
11. Guidelines for Air Quality Maintenance Planning and Analysis.
Volume 13. Op. cit. p. 134.
12. Air Quality Display Model. TRW Systems, Inc. Op. cit. p. 2-1
to 2-3.
13. Brown, Barbara D. and C. S. Lipaj. Implications of a Prevention
of Significant Deterioration Policy on State Growth Management.
(Presented at 69th Annual Meeting of the Air Pollution Control
Association. Portland, Oregon. 1976.) p. 3-4-
14. Larsen, R. I. A Mathematical Model for Relating Air Quality
Measurement to Air Quality Standards. U.S. Environmental Pro-
tection Agency, National Environmental Research Center. Re-
search Triangle Park, North Carolina. November, 1971. AP-89.
15. Larsen, R. I. An Air Quality Data Analysis System for Inter-
relating Effects, Standards, and Needed Source Reductions -
Part 2. J Air Pollut Contr Assoc. 24(6). Pittsburgh, Pennsylvania.
June, 1974.
16. Brier, G. W. Validity of the Air Quality Display Model Calibra-
tion Procedure. U.S. Environmental Protection Agency, National
Environmental Research Center. Research Triangle Park, North
Carolina. PB-218 716. March, 1973.
17. Brier, G. W. Statistical Questions Relating to the Validation
of Air Quality Simulation Models. U.S. Environmental Protection
Agency, National Environmental Research Center, Research Tri-
angle Park, North Carolina. EPA-650/4-75-010. March 1975.
18. IBM Corporation. Mathematical Programming System/360, Version 2,
Linear and Separable Programming — Users Manual (360A-CO-14x).
White Plains, New York, GH20-0476-2. October, 1971.
141
-------
19. IBM Corporation. Mathematical Programming System/360 — Applica-
tion Description Manual. White Plains, New York, 6H20-0136-4.
November 1969.
pUFfa; ••- T . • I1 .
20. Personal Communication, Laurel Slate, IBM Corporation, White Plains,
New York.
21. Cirrillo, R. R. et al. Air Quality Analysis Workshop: Volume 1 -
Manual. U.S. Environmental Protection Agency, Office of Air
Quality Planning and Standards, Research Triangle Park, North
Carolina. EPA-450/3-75-080a. November 1975.
22. Benesh, F. H. Growth Effects of Major Land Use Projects -
Volume II: Compilation of Land Use Based Emission Factors.
U.S. Environmental Protection Agency. Office of Air Quality
Planning and Standards, Research Triangle Park, North Carolina,
EPA-450/3-76-012b. September 1976.
23. Baumol, W. J. Economic Theory and Operations Analysis.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey. 1972.
24. Vajda, S. Readings in Linear Programming. John Wiley and Sons,
Inc., New York, 1958.
25. Killer, F. S. and G. J. Lieberman. Operations Research. Holder-
Day, Inc., San Francisco, California. 1974.
26. Brail, R. K. et al. Emission Density and Allocation Procedures
for Maintaining Air Quality. U.S. Environmental Protection
Agency, Office of Air Quality Planning and Standards, Research
Triangle Park, North Carolina. EPA-450/3-75-079. June, 1975.
27. Laboratory for Computer Graphics and Spatial Analysis, SYMAP
Manual. Graduate School of Design, Harvard University, Cambridge,
Massachusetts, October, 1971.
28. Personal Communication with Mr. Dave Lueck, Division of Air Pollu-
tion, Kentucky Department of Natural Resources and Environmental
Protection, Frankfort, Kentucky.
29. Williams, J. D., et al. Air Pollution Emissions Related to Land
Area - A Basis for a Preventive Air Pollution Control Program.
National Air Pollution Control Association, Durham, North Carolina.
APTD-68-11. July 1968.
30. Roberts, J. J. and E. J. Croke. Land Use as an Organizational
Basis for Regional Air Resource Management. Proc 2nd Int Clean
Air Congress, edited by H. M. Englund and W. T. Berry, Academic
Press, New York. p. 1247. 1970.
142
-------
31. Roberts, J. J., E. J. Croke and S. Booras. A Critical Review of
the Effect of Air Pollution Control Regulations on Land Use Plan-
ning. J Air Pollut Contr Assoc. (25)5. Pittsburgh, Pennsylvania.
1975.
32. Guidelines for Air Quality Maintenance Planning and Analysis.
Volume 3: Control Strategies. U.S. Environmental Protection
Agency, Office of Air Quality Performance Standards, Research
Triangle Park, North Carolina. July 1974. EPA 450/4-74-003.
33. 1972 OBERS Projections. U.S. Water Resources Council, Washington,
D.C. April 1974.
143
-------
APPENDIX A
AN INTRODUCTION TO LINEAR PROGRAMMING
\
Linear programming is a mathematical technique whereby a linear
function of several variables is maximized (or minimized) when the vari-
ables are subject to various constraints. The linear function that is
maximized is referred to as the objective function; it is usually some
kind of economic or policy objective such as profit, output, or, in the
problem at hand, the maximization of the emissions of air pollutants or
the minimization of costs imposed on sources of emissions. For example,
the objective function of a linear program that maximizes emissions
would be:
maximize emissions, E' «= a, E, + a. E0 . . . . + a E (17)
1122 n n
where E, , E .... and E are the variables (the emission density limits
12 n
in tons per day per acre) and a , a , and a are the constants (the lot
area of each emission source). All the E's are of the first power, which
is necessary to characterize the relationship as a linear equation.
Each of the variables, E , E .... and E , are subject to some
12 n
constraint. In the problem at hand, the air quality at a specified recep-
tor must not exceed a specified level. Specifically:
t a E + t a E + t a E < S (18)
111 222 n n n —
where t., t., .... t are the transfer coefficients relating unit emissions
12 n
at each source to the ambient concentration at the receptor. The sum,
144
-------
over all sources, of t a E must be less than or equal to the
n n n
standard.
It is useful to consider the graphic solution to a simple problem
with two emission sources and two receptors. Assume the maximum ambient
concentrations desired at receptor 1 is 12 jig/m^ and at the second receptor,
o
8 mg/m . The areas and transfer coefficients are as follows:
Source 1
Source 2
Area, acres
6
7
Transfer coefficie
To receptor no. 1
0.33
0.43
yg/m
at, ,
tons /year
To receptor no.
2
0.33
0.14
The maximization problem would then be formulated as:
Maximize: 6 E + 7 E (19)
Subject to: 2 E. + 3 E <_ 12
2 E1 + E. < 8
j. z —
V E2 i °
In Figure 1 the two constraining equations are shown. All points to the
left of the inequality:
2 El + 3 E2 - 12
(20)
are possible (feasible) combinations of E and E . Similarly, points to
the left of the second constraint(inequality are feasible.
The hatched region in Figure 31 is the set of points that are feasible
under all constraints; it is the feasible region. Clearly, not all of
these points will maximize emissions.
145
-------
(0,8)
2E, + E2 < 8
= (0,4)
2E, + 3E,
-------
The family of objective functions is shown in Figure 32. Each line
is the set of points with constant amounts of aggregate emissions. Con-
sider the objective function for which total emissions, E, equals 18.
This line contains many feasible points, all of which give us 18 tons
per year of emissions. But the line E = 24 is better, because it contains
points with 24 tons per year. Best of all is the line E = 32. Here there
is only one point in the feasible region, D, and this is the optimal
solution. The optimal solution is to set an emission density limit of
3 tons per year per acre for emission source No. 1 and 2 tons per year per
acre for emission source No. 2. At any other combination of emission
limits, either the desired ambient air quality levels of 12 and 8 micro-
grams per cubic meter would be violated or the sum of emissions over the
two sources would be less than 32 tons per year.
For a more detailed and comprehensive treatment of the subject, the
reader is referred to any standard text on the subject, such as:
• W. Baumol. Economic Theory and Operations Analysis23
S. Vajda, Readings in Linear Programming*1*
F. Hiller, G. Lieberman, Operations Research25
These references also note more advanced texts.
147
-------
APPENDIX B
PROVISION FOR SHORT-TERM STANDARDS
IN AIR QUALITY CONSTRAINT
The air quality constraint in the emission density limit setting
model, equation (8), viz.,
'i.J.k.i (EJ,k,*,m «Jikfm> 1 Xi>
s, „ | for all !,«, (21)
1, X.
states that the sum, over all sources, of the product of the emissions
from each source and a transfer coefficient between that source and a
specified receptor i shall not exceed the air quality standard at that
receptor. The transfer coefficients, derived through the execution of
AQDM, relate the effect of annual emissions at a specific source to the
ambient concentration at a specified receptor i. Thus, through the use
of this relatively straightforward constraint, it is possible to set a
pattern of emission density limits such that the annual ambient air qual-
ity standards, expressed as arithmetic means, are not violated.
One problem with this formulation, however, is that the annual stand-
ard for particulate matter, 75 yg/m^, is an annual geometric mean. For
the receptors in the EDZ model that are monitoring stations, it is possible
*
The variable definitions of Section V are employed.
148
-------
to convert the geometric mean to an expected arithmetic mean that is
equivalent to the annual particulate matter standard, if one assumes a
log-normal distribution, viz,
2 *
m = m exp (0.5 In s ) (22)
where m = arithmetic mean
m = geometric mean
s = geometric standard deviation
O
For example, the geometric standard deviation at the St. John's
College monitoring station in the Baltimore AQMA is 1.5 (see Table 8),
Substituting in Equation (22), one obtains
m = 81.4 - 75 exp (0.5 In2 1.5)
(23)
Ignoring the effects of calibration, one would substitute 81.4 in
place of X- o f°r the. *• corresponding to the St. John's College receptor
i, x,
and the H corresponding to particulate matter.
The question remains, however, of how to treat the majority of the
receptors in the EDZ model that are not monitoring stations and therefore
have an unknown geometric standard deviation. If a geographic pattern
existed among the observed geometric standard deviations, it would be
For the convenience of the reader familiar with A Mathematical Model for
Relating Air Quality Measurements to Air Quality Standards,14 EPA Publica-
tion AP-89, the indicated equations in this appendix correspond to rear-
rangements or combinations of the following equations in AP-89.
Equation number AP-89
22
24
25
26
149
-------
Table 8. 1974 TSP CONCENTRATIONS RECORDED AT MONITORING STATIONS IN THE
BALTIMORE AQMA
Monitoring stations
St. John's College
Anne Arundel Co.
Overlook School
Anne Arundel Co.
Arundel High School
Anne Arundel Co.
Glen Burnie Public Works
Anne Arundel Co.
Route 176 & 170
Anne Arundel Co.
Harwood High School
Anne Arundel Co.
Fire Dept. HQ
Baltimore
Sun Ave. Fire Dept.
Baltimore
NE Police Station
Baltimore
Number of
observations
53
53
56
62
53
48
107
79
100
Maximum
24-hr
135
184
169
196
182
137
282
324
175
Second
highest
126
136
115
162
153
119
253
317
143
Arithmetic
mean
51
66
52
80
65
47
117
148
60
Geometric
mean
47
60
47
65
58
43
102
134
53
Geometric
standard
deviation
1.5
1.5
1.6
2.7
1.6
1.5
2.0
1.6
1.6
-------
Table 8 (continued). 1974 TSP CONCENTRATIONS RECORDED AT MONITORING STATIONS IN
THE BALTIMORE AQMA
Monitoring stations
NW Police Station
Baltimore
SE Police Station
Baltimore
SW Police Station
Baltimore
3001 Eastern Blvd.
Baltimore Co.
Fort McHenry
Baltimore
1030 Linwood Ave.
Baltimore
Sewage Disposal Plant
Baltimore
Ft. Howard VA Hospital
Baltimore Co.
Garrison Police Barracks
Baltimore Co.
Number of
observations
91
73
140
53
54
58
52
114
47
Maximum
24 -hr
198
309
309
172
228
265
291
182
123
Second
highest
151
287
294
113
221
263
266
154
122
Arithmetic
mean
74
120
96
57
114
108
126
55
55
Geometric
mean
68
106
86
49
103
95
113
50
49
Geometric
standard
deviation
1.5
1.7
1.6
2.1
1.6
1.7
1.6
1.6
1.7
-------
Table 8 (continued). 1974 TSP CONCENTRATIONS RECORDED AT MONITORING STATIONS IN
THE BALTIMORE AQMA
Monitoring stations
Catonsville Library
Baltimore Co.
County Office Bldg.
Harford Co.
Dundalk
Baltimore Co.
Essex
Baltimore Co.
Whiteford
Harford Co.
Simpsonville
Howard Co.
Goucher College
Baltimore Co.
Carrol Co. Hospital
Carrol Co.
Number of
observations
47
53
108
53
58
61
76
52
Maximum
24 -hr
141
130
203
158
96
145
135
227
Second
highest
91
122
176
155
86
116
110
122
Arithmetic
mean
51
56
84
69
39
51
54
50
Geometric
mean
46
51
76
63
35
46
48
43
Geometric
standard
deviation
1.6
1.5
1.6
1.5
1.6
1.6
1.7
1.7
Ui
S3
Source: SAROAD data system.
-------
possible to use that pattern to assign deviations to the receptor grid
in EDZ. A plot of the location of the monitoring stations and geometric
standard deviations is shown in Figure 33. In our view a convincing
pattern does not exist. If a pattern does not exist, an alternative
is to use the mean of the recorded data, in this case 1.67. Substituting
in equation (22), one calculates a value for the expected arithmetic mean
3
of 85.54 yg/m . Therefore,
every receptor in the grid.
3
of 85.54 yg/m . Therefore, this value would be used as the standard at
In this example, the observed geometric standard deviation, obtained
*
from SAROAD printouts, was utilized. In the actual execution of the
decision model it is more appropriate to compute the geometric standard
deviation using the following formulae.
Sg = (c/m> (2A)
where c is the maximum 24-hour observations, and
z is the z deviate of the normal distribution corresponding
to a frequency calculated by
f = 1 - ±~^- (25)
where n = the number of valid 24-hour observations.
The use of formulae 24 and 25 allows the calculation of a geometric
standard deviation from the top half of a distribution, which most closely
fits the frequencies associated with the standard.
*
Storage and Retrieval of Aerometric Data.
153
-------
Ai.r
CARROLL COUNTY
HARTFORD COUNTY
Al.B
ANNE ARUNOEL COUNTY
Ai.e
Figure 33. Location of TSP monitoring stations and associated
geometric standard deviation
154
-------
The assumption of a log-normal distribution also allows the consid-
eration of the 24-hour standards in the emission density limit setting
model. The ability to make this assumption is critical, in that there
is no other way to consider the short-term standard and maintain a rela-
tively simple EDZ model which would be easily implemented.
The treatment of the short-term standards would proceed in a manner
analogous to the estimation of an arithmetic mean equivalent to the geo-
metric mean particulate standard. For example, in the case of sulfur
dioxide, the average geometric standard deviation measured in the Baltimore
AQMA is 2.76 (see Table 9). Assuming log normality, the second highest
24-hour concentration would be related to the arithmetic mean as follows.
z - 0.5 In s ,„,..
C2ndmax=msg g (26)
The appropriate z deviate would be 2.62. The 24-hour sulfur dioxide
standard is 365 yg/m3. Accordingly, rearranging Equation (26) to solve
for m,
m = 365 s °'5 ln sg - 2'62 (27)
O
Substituting 2.76 for s , one obtains an arithmetic mean of
o
42.7 yg/m . Since this is more stringent than the annual standard of
o
80 yg/m , it would be used in Equation (21) for x. „ where £ corresponds to
»
sulfur oxides.
The use of the second highest 24-hour concentration in a year as the
"design value" means that the standards will be violated (second highest
concentration exceeding standard) on the average of every other year.
As an alternative, it has been suggested-^ that the annual maximum con-
centration be used as the design value. If this is done, the ambient
short-term standards would probably be violated in 1 year out of 8. A
Z deviate of 2.94 would be used instead of the 2.62 used above.
155
-------
Table 9. 1974 SO CONCENTRATIONS IN THE BALTIMORE AQMA
Monitoring stations
St. John's College
Anne Arundel Co .
Arundel High School
Anne Arundel Co.
Glen Burnie Public Works
Anne Arundel Co .
Route 176 & 170
Anne Arundel Co.
Harwood High School
Anne Arundel Co.
Calvert & 22nd Sts.
Baltimore
3001 Eastern Blvd.
Baltimore
Number of
observations
51
50
53
55
49
51
43
Maximum
24 -hr
152
150
162
121
61
120
65
Second
highest
74
92
118
64
58
109
33
Arithmetic
mean
20
23
30
18
13
26
8
Geometric
mean
9
13
17
11
8
13
5
Geometric
standard
deviation
3.4
3.2
3.1
2.9
2.9
3.6
2.3
Ui
-------
Table 9 (continued). 1974 SO CONCENTRATIONS IN THE BALTIMORE AQMA
Monitoring stations
Fort McHenry
Baltimore
1030 Linwood Ave.
Baltimore
Sewage Disposal Plant
Baltimore
Ft. Howard VA Hospital
Baltimore Co.
Garrison Police Barracks
Baltimore Co.
Catonsville Library
Baltimore Co.
County Office Bldg.
Harford Co.
Number of
observations
54
55
52
108
44
45
61
Maximum
24 -hr
169
106
284
76
41
49
80
Second
highest
166
102
262
68
31
26
65
Arithmetic
mean
77
24
70
18
9
8
19
Geometric
mean
64
13
50
11
6
5
12
Geometric
standard
deviation
2.0
3.1
2.4
2.7
2.5
2.3
2.6
-------
Table 9 (continued). 1974 S() CONCENTRATIONS IN THE BALTIMORE AQMA
X
Monitoring stations
Dundalk
Baltimore Co.
Essex
Baltimore Co.
Whiteford
Harford Co.
Simpsonville
Howard Co.
Goucher College
Baltimore Co.
Carrol Co. Hospital
Carrol Co.
Number of
observations
108
56
58
59
73
48
Maximum
24 -hr
169
110
35
54
117
54
Second
highest
156
98
28
39
60
48
Arithmetic
mean
33
29
7
12
18
14
Geometric
mean
16
20
5
9
11
9
Geometric
standard
deviation
3.7
2.6
2.3
2.3
2.7
2.6
Ul
00
Source: SAROAD data system.
-------
In a similar fashion, the annual arithmetic mean equivalent to the
24-hour particulate standard can be computed. Using Equation (27), one
obtains
m = 150 s °'5 ln Sg - 2'62 (28)
O
Substituting 1.67 (the average in Baltimore) for s , one calculates a
O
value of 44.6 for the expected arithmetic mean equivalent to a 24-hour
standard of 150 yg/m3. As this also is more stringent than the expected
arithmetic mean, 85.5, equivalent to the annual standard, the value of
44.6 yg/m3 would be used in equation (21) for x. „ where K, corresponds to
i, x,
particulates.
159
-------
APPENDIX C
THE SO -PM FEASIBILITY CONSTRAINT
x
The sulfur oxides emission density-particulate matter emission density
feasibility constraint is based on the premise that sulfur oxide emis-
sion densities and particulate matter emission densities are not inde-
pendent. The utilization of this constraint in the decision model will
avoid the assignment of a certain emission density to a component area
for one pollutant and the subsequent assignment of an emission density
for the other pollutant that is so stringent that the emission density
for the former pollutant could never be utilized.
Assuming that the respective emission rates are not independent, more-
over, that they are linearly related, one could expect to obtain a scatter-
gram such as that shown in Figure 34. The regression line estimating this
relationship, PM = a + b SO , is shown as a solid line. The intercept,
-\ A *
a, and the slope, b, are estimated values; one can compute a confidence
interval for the regression line. In particular,
(29)*
For a given sulfur oxide emission rate, X , one would then constrain
the particulate matter emission rate, Y , to be greater than or equal to
*
See, for example, J. Johnston, Econometric Methods, McGraw-Hill. 1972.
160
-------
(0
2
O
to
I
UJ
s
0.
-PM
SOX EMISSIONS
S°X,
Figure 34. Hypothetical relationship between
SO and PM emissions
x
161
-------
the lower boundary. However, since X appears underneath the radical, this
cannot be easily employed in a linear program. It is an expedient approx-
imation, though of no statistical meaning, to use the confidence interval
for the mean of Y given the mean of X. Specifically,
1 '
e/2
(30)
The dotted lines in Figure 34 show what the extremes of this interval
may look like. The constraint equation would then be
j,k,m
(3o)
which reduces to
a -
iff
j,k,m
(31)
denoting the slope term in parentheses as y, , and the term in brackets
a k
as y, , this can be expressed as
K.
b a
j,k,£=l,m ~ yk Ej,k,Jl=2,m - pk
(33)
which is the first SO -PM feasibility constraint in the emissions maximi-
X
zation decision model described in Section V.
In the execution of the model, one would specify the confidence level
of the interval by selecting a specific t, say 80 percent.
See Johnson, op. cit.
162
-------
As was stated previously, the necessity of this constraint depends on
the existence of a relationship between sulfur oxide and particulate matter
emissions, after the application of existing regulations. If such a
relationship does not exist, then this constraint is superfluous. The
setting, in a specific component area, of a relatively high sulfur oxide
emission density and low particulate matter emission density, or the
converse, would only encourage those sources that have such emission
characteristics to locate in that component area.
The existence of such a relationship would have to be tested for each
time EDZ is implemented in an AQMA. Whether it existed would depend on
the characteristics of the emission sources in an AQMA of a particular
land use category and the homogeneity of these sources. One should note
that this independence may exist only for some of the land use categories.
An inspection of the point source emission inventory in Baltimore and
Louisville would suggest that, in these AQMAs, emission rates for the
two pollutants are independent in the case of the heavy industrial land
use category. Sulfur oxide and particulate matter emission rates for
this category are plotted in Figure 35. Each asterisk represents one
point source and a number represents the position of multiple sources.
The lack of a linear relationship between sulfur oxide and particulate
matter emission rates is adequately documented by the correlation coeffi-
cient. Figure 36 shows the relationship between emission rates for all
heavy industrial point sources emitting less than 100 tons per year.
No linear relationship is evident. (In fact, it could be more accurately
described as a hyperbolic or reciprocal relationship, rather than linear.)
Light industrial point source emission rates are plotted in Figure 37.
Again, there is little linearity evident. Figure 38 shows the relation-
ship between emission rates for noncoal burning commercial point sources.
2
The R is 0.7, which would suggest a relationship exists. The regression
line has been drawn in as a solid line; however, it appears to have been
greatly influenced by a half dozen relatively large sources. A more
appropriate regression line is shown as a dashed line.
163
-------
SCATTfRSR*"! 0
45000.00
40500.00
36000.00
31900. OU
27000.00
Z250B.OO
11000.00
13500.00
9000.00
HOT. 00
0.0
P 100*4) PM (ACROSS) SOX
361.35 1084.05 1B06.TS 252*. 45 3252.15 3*74.85 46*7.5
* :
•
-.-..-- - - -
*
i* •
»999*7 55 * • •
r •• •••• ' • --
•
i
i
i *
5 5420.25 6142.95 6*65.65
«
I
I
I
1
' ' '— •'•" " ' «
I
-'- ' I
1
+
• r
i
i
t
i
»
4SOOO.OO
40SOXT.OO
36000.00
" **W**"W
27000.00
i
------ — -- • - --j -• - -
i
t
i
• "• - •-• "i
»
•' •" ' ~ " . ~ 7 '
I
I
I
' - " T~
I
*
. - •-• I
I
I
I
I
I
9 »»
0.0 722.70 1445.40 2161.10 2890.30 1M1.50 4336.20 50S8.90 5781.60 6504.10 7227.00
STATISTICS..
CORRELATION IRI- 0.00819 R SQUARED - O.OOOOT SIGNIPICANCt
STO ERR OF EST - 1343.95656 INTERCEPT (A) - 72.00005 SLOPE
-------
SCATTERSRAN Of IDOMNI P«
J.OO 15.00
2S.OO
(ACROSS) SOX
35.00 65.00
75.00
•5.00
20.00
lO'.OO
•* *• * *~
*
•
*
2 2
3
6
* «
13
14
14 .
I*
44
12
I
I* ...
I
»Z . i
[•
13
iV
[ 3 — • * " ~—
12 2
• 2
19
19 2
13
[*2
•a
13
19 2
13 2
13 3
48
19
1922
192 44 4
19*962256 2 t
»99«93 "28 *
o.o 10.06
1
r
i
i
i
i
i
t
i
i
I
i
i
i
i
i
i
i
i
' t ' "
i
i
i
i
i
I
i
i
i
i
i
,
i
i
i
i * .
i
i •
2 I •
2 I
I
I
2 2 I
2 t 2
« 61
9 I
* 24 13
22 2 I •
20.00 30.00 40.00 50.00 60.00
.
•
.:
7
i
4
..
... ... _
2
1
I
I
• I
' . *
70.00 10.00 90.00 100.0
90.00
STATISTICS..
CORRELATION CHI-
STD ERR OF EST -
PIOTTEO VALUES -
0.0673*
14.499S5
1075
It SQUARED
INTERCEPT (A) -
EXCLUDED VALUES-
0.00453
6.20879
>2
SIUUFICANCI
SLOPE IB)
. MISSING VALUES
0.019*3
0.10946
. _ 0
Figure 36. Plot of Baltimore heavy industrial point source PM
rates versus SOX emissions rates, sources with emis-
sions less than 100 tons/year (note: '9' indicates
9 or more observations)
165
-------
Of COOK*I M (ACKOSII SOX _
67.41 101.35 317. JS 471.II 607.0S 741.9« 876.89 IOII.T5 1144.6» IMI.tS.
84O.OO
756.00
672.00
588.00 "
504.00
420.00
'
336.00
252.00
.
168.00
84.00 <
1
0.0 •
1
1
*
.
3
3
3
» *
2 4
3
9» 2
94» 2 39
994927 4
.0 134.90 269.80 404.70
I I
t
I
I
I
I
I
I . .
I ._'.
I
I
I
I
I
I .
I
I
. I . — _. ._. .
i . .. .T. :
i
i
i
t
i
i
i
i
i
i
i . .
i
.1 ... . ...
i
i
i
i
i
i
2 T *
I
I
I
* I .
I . 5.
539.60 674.50 809.40 944.30 1079.20 1214.10.. 134.9.
_..
.".
.
10
M4.00
J«4.00
J36_.00
84.00
STATISTICS..
CORRELATION («)-
STD ERR OF EST -
PLOTTED VALUES -
0.61210
53.08410
1007
R SQUARED
INTERCEPT (A) -
EXCLUDED VALUBS-
0.37467
5.66194
.0
SIGNIFICANCE
SLOPE (ft)
MISCINC VALUES -
0.00001
0.26243
0
Figure 37. Plot of Baltimore light industrial point source PM
emission rates versus SOX controlled emission rates
(tons/year) (note: '9' indicates 9 or more observations)
166
-------
SCATTERGMN Of IOOHMI
m.os
is.oe
22.50
17.10
JJupo
*.»S 10.15 M.T9 «».»» 42. S» 7».«5
27.10
55.60
20 125.10 U».00
STATISTICS..
CORRELATION -
STO ERR OF EST -
PLOTTED VALUES -
0.83675
1.67332
i»»
0 SQUARED
INTERCEPT (A) -
EXCLUDED VALUE5-
O.TOOIS
0.94229
0
SIGNIFICANCE
SLOPE IB)
MISSING VALUES -
_
o.ooooi
0.14413
0
Figure 38. Plot of Baltimore commercial point source PM emission
rates versus SOX controlled emissions rates, excluding
coal burning sources (tons/year) (note: '9' indicates
9 or more observations)
167
-------
In summary, a relationship between emission rates should be tested
for on a sample from the base year emission inventory, stratified
according to the land use categories contemplated for emission density
regulation. If one exists, it is prudent to include a feasibility con-
straint, as discussed above, in the decision model.
168
-------
APPENDIX D
SPECIFICATION AND UTILIZATION OF CONTROL COST PARAMETERS
Both formulations of the control cost minimization objective func-
tion (i.e., model nos. 2 and 3 of Section V) require an estimate of
incremental control cost functions for future emission sources. The
ability to estimate these functions is limited by two problems — the
need to forecast adequately the nature of future emission sources and the
need to estimate control cost functions that can be used in the linear
programs. The discussion below is limited to industrial sources, as the
control cost linear programs would likely be applied only to that source
category.
At best, one can identify those areas that are planned for heavy and
light industry. Within each of these categories, regional employment pro-
*
jections would give some indication of the most likely SIC code categories,
probably, at best, on the two-digit level. One could either use the
industry with the largest employment growth or, within the top 5 or 10
categories, the heaviest polluting industrial category as a prototype
heavy (or light) industry. Using this prototype, one would endeavor to
estimate the incremental control costs.
For example, in Baltimore the U.S. Water Resource Council projections,^
shown below in Table 10, indicate that primary metals (SIC code 33) and
chemicals (SIC code 28) are the two industrial categories that will experience
*
Standard Industrial Classification.
169
-------
the largest absolute growth. One could use the control costs associated
with the primary metals industry as the "c" parameters for future heavy
industrial sources. On the other hand, most of the growth in SIC code 33
may represent the utilization of existing capacity and the capacity ex-
pansion of existing sources. In such a situation, it would be appropriate
to use another industrial class.
Table 10. 1980 TO 1990 PROJECTIONS OF GROWTH
IN MANUFACTURING EARNINGS ($000)
Heavy
26
27
28
29
30
31
32
33
industry
28,000
55,400
65,500
1,400
85,100
20
22
23
24,
34,
35
36
371
37
21,
Light
25
19
ex 371
30-32,
industry
12,300
11,000
12,700
12,500
65,300
69,700
26,800
28,000
10,700
38, 39 58,700
Source: Reference 33.
For the purposes of this example, we will assume that it is more
appropriate to use SIC code 28, which is Chemicals and Allied Products.
However, projections more detailed than two-digit SIC codes are needed
to develop a control cost parameter. Unless more detailed employment
projections are available, it would be consistent with AQMP emission pro-
jection methodologies to assume the characteristics of future sources to
be similar to those of existing sources. Therefore, one would review the
emission characteristics of existing heavy industrial point sources to
develop the incremental cost of emission reductions. Given the specific
characteristics of several prototypical sources, the control cost element
of the Implementation Planning Program (IPP) package could be utilized to
estimate the costs of an emissions reduction.
170
-------
One would
1. Develop projections of regional industrial growth by at least
two-digit SIC code. The OBERS projections or equivalent or
superior projections available locally can be used.
2. For each two-digit SIC code, estimate the percentage of future
growth occurring from:
a. the utilization of existing industrial capacity
b. capacity expansion of existing sources
c. construction of new industrial facilities.
This information can be derived from the regional economic
projections and a survey of existing point sources conducted
for the AQMP emission projection.
3. Rank order the existing point sources in each two-digit SIC
code by their emission density after application of existing
and projected regulations.
4. For both the heavy and light industrial categories, deter-
mine the probable two-digit SIC codes for new industrial
facilities, based on the results of Step 2.
5. Identify prototypical point sources in the heavy and light
industrial categories by selecting the existing point source
with the highest emission density in the fastest growing
two-digit SIC code. If, in either the heavy or light in-
dustrial category, growth in more than one two-digit SIC
code is expected to contribute significantly to the con-
struction of new industrial facilities, identify a proto-
typical point source for each one.
6. For each of the two or more prototypical point sources and
for the expected capacity expansion at existing sources,
execute the control cost segment of the IPP package and
identify the annualized control costs for possible levels
of emission reduction beyond existing and projected
regulations.
The costs of specific levels of emission reduction cannot be directly
used in equation (9). There is, however, a more complex formulation of
a control cost minimization that employs integer programming, discussed
in Section V, in which they can be used.
171
-------
Before reviewing the specification and use of the cost parameter, it
is convenient to develop a specific example. In the Baltimore AQMA, it
was assumed that SIC code 28 was the fastest growing heavy industrial
category. The first SIC code 28 point source in the Baltimore inventory
is the Glidden Durkee paint plant, SIC code 2816. The particulate matter
emission sources are summarized in Table 11. Table 11 also shows the
various levels of emission reductions available by installing control
equipment and the annualized cost of that equipment. The possibility of
tandem devices is ignored. Based on this information, a schedule of
control costs and emission reductions was prepared and is shown in
Figure 39.
To use this information to specify the cost parameter, it is necessary
to develop a linear approximation. A possible one is shown in Figure 40.
Three line segments are shown with slopes of 13.86, 68.93, and 3528.08.
Since the control cost — emission reduction schedule cannot be adequately
approximated with a single line segment, one is faced with several cost
parameters that could be used in the objective function.
The only feasible way to accomplish this, given the control cost
minimization formulation in equation (9), is through successive solu-
tions to the linear program.
For example, in the case of three future heavy industrial sources of
the same area, one would first execute the following linear program.
Max E' = 13.86 a-,^ EI + 13.86 &2 E2 + 13.86 a.j E3 (34)
subject to:
air quality constraint: £ t. . a. E; £ S. | for all i
.: i>J J J 1
172
-------
Table 11. EMISSION REDUCTIONS AND ASSOCIATED CONTROL COSTS
u>
Source and control device
Calcination kilns (three)
Uncontrolled
Low efficiency cyclone
Medium efficiency cyclone
Lou efficiency scrubber
Medium efficiency scrubber
High efficiency scrubber
High temperature fabric filter
Rotary dryers (three)
Uncontrolled
Low- efficiency scrubber
-Low temperature fabric filter
Ball mills (three)
Uncontrolled
Low temperature fabric filter
Boilers (five)
-Distillate oil
Natural gas
Ore sulfation (eight)
Uncontrolled
Total uncontrolled emissions
Device
efficiency
0
60
75
80
90
98
99
0
80
99
0
99
Particulate
emissions,
tons/year
1,500
600
375
300
150
30
15
333
66
3
400
it
29
2.5
1
6,852
Capital
cost, $
0
15,700
15,700
60,000
60,000
60,000
114,000
0
11,100
6,900
0
6,200
0
0
Annual
operating
cost, $
0
5,042
7,183
24,508
38,379
58,211
31,113
0
11,956
11,340
0
11,347
0
93,847
Total annualized
cost, ignoring
tax effects, $
0
6,876
9,017
31,158
45,388
65,220
44,431
0
13,252
12,146
0
12,071
0
93,847 .
Emission
reduction
0
900
1,125
1,200
1,350
1,470
1,485
0
267
330
0
396
0
26.5
Average
control cost
per ton
reduction, S
0
7.64
8.02
26.27
33.62
44.37
29.92
0
44.63
36.81
0
30.48
0
3,541.40
-------
1700,000
8600,000 -
8500,000 -
o 8400,000 -
o
K
u 8300,000 -
8200,000 -
8100,000 -
1000
2000 3000 4000 5000
EMISSION REDUCTION, ton/year
6000 7000
Figure 39. Schedule of emission reductions versus control costs
for prototypical heavy industrial point source
174
-------
8675,179 -
o
u
o
a:
I-
o
o
$205,944 -
$63,264 -
4563
EMISSION REDUCTION, tons/year
6633 6766
Figure 40. Plot of linear approximation of the
control cost - emission reduction
schedule
175
-------
technological constraint: a E > 0
J J ~
zero cost constraint: a. E. <^ 4563
for all j
If, in any source j, the upper bound on E. was binding, it may be
possible to achieve a further emission reduction at that source. However,
the incremental cost would no longer be 13.86; it would be 68.93. There-
fore, one would rerun the program, substituting the parameters of the
second line segment. In this instance, suppose the upper bound on the
third E. was binding; one would then rerun the linear program as follows.
Max Ef = 13.86
+ 13.86
+ 68.93
E3 + 63264
(35)
subject to:
air quality: £ t. . a. E. < S. | for all i
• 1>3 J 3 — •*•
technological
constraints
al El —
a2 E2 -
a3 E3 > 0
al El ^- 4563
zero cost
constraints
a
—
< 6633 - 4563 = 2070
The technological and zero cost constraints are specified for the nodes of
a line segment on Figure 40, plot of linear approximation of the control
cost-emission reduction schedule.
176
-------
While one could use ordinary linear programming and rerun the model
until all the upper and lower bounds were not binding or until the opti-
mum solution did not change, it is expedient to use a spatial formula-
tion of linear programming that will do this all at once; viz., separ-
able convex programming.18
177
-------
APPENDIX E
THE APPLICATION OF THE EMISSION DENSITY SETTING MODEL IN AN
ATTAINMENT SITUATION
The models described in Section V and illustrated in Sections VII
and VIII assume that all current emission sources, after the applica-
tion of current or pending emission control regulations, will not be
required to further reduce their emission rates under emission density
*
zoning. Emission density zoning is thus a technique for managing
growth, both in terms of new emission sources and expansion of existing
ones, as contemplated by air quality maintenance planning. Attainment
of the NAAQSs is assumed.
In regions where the NAAQSs have not been attained or in those re-
gions where the current ambient air quality levels are so close to the
NAAQSs so as to preclude growth without reductions in emission levels of
current sources, the models described in Section V are not applicable.
The former situation will be apparent; the latter may not be so obvious.
It is possible that the linear program will be unable to find a feasible
solution; that is, if the region experiences the growth contemplated
in the land-use plan, the NAAQSs will be violated, even if all new sources
emit at minimum levels and current sources do not expand. To achieve
the NAAQSs it is necessary that current sources reduce their emission
rates beyond that contemplated by existing emission control regulations.
*
Specifically, note the attainment constraint of Model No. 1 on page V-3.
This is what happened in the Louisville particulate matter test case.
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It is possible to implement emission density zoning in such a
situation, though EDZ is more commonly thought of as a maintenance
strategy than an attainment strategy. One has two options. The first
is to impose additional emission control regulations on existing sources.
If sufficient reductions are imposed it will then be possible for the
linear program to find a feasible solution.
Alternatively, one can impose emission density limits that require
existing sources to reduce their emission rates. To set such emission
density limits in a model such as described in Section V, the lower
bound on the emission density limit of existing sources should be set at
a lower value. As formulated in model no. 1, the attainment constraint,
viz.,
Ej,k,£,mle5?I?*,m I for a11 J.k.*; for » - 1 (36)
restricts the emission density for current sources to be greater or equal
bfl SG '
to e , their current value adjusted to show compliance with applicable
regulations. This base or floor for current sources must be respecified
at a lower yet still feasible value.
It is unlikely that one would set the minimum emission levels for
current sources as low as those of future sources. With older plant and
equipment, current sources would find it more difficult to meet such
standards as new development. Also, the options of locating on a site
with a higher emission density or purchasing additional land are not as
easily available to the current emission source as they are to a future
source.
Within the range between the current emission density and the lower
limit that is used for future sources, one must specify a lower bound.
The most straightforward way of doing this is to:
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a. Catalogue the possible emission reductions for each
current source category. This would basically be
various types of control equipment, process modifi-
cation or fuel switching.
b. Convert the maximum emission reduction to a minimum
emission density. This would have to be done separately
for each component area and point source, as densities
of development will differ.
c. Use this value as the e ase parameter of equation (36).
This method has two shortcomings. The first is that the cost of
control is not considered if the emissions maximization formulation of
the model is utilized. The second is that it is assumed that emissions
can be abated to any point down to the minimum level. Neither short-
coming is particularly serious, the former can be resolved by using the
control cost formulation of the model, the latter is not serious since
most sources will have emission density limits set at their lower or
upper bounds.
However, combining the attainment and maintenance problems into one
model sidesteps the issue of how much emissions growth will be permitted
at new sources and, concurrently, how much emissions reduction will be
required at existing sources. If it is not the intent or policy to
treat the two classes of sources identically, it is more satisfactory to
separate the two problems and treat the trade-off between growth and
current sources openly.
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TECHNICAL REPORT DATA
(Please read Inunctions on the reverse before completing)
. REPORT NO.
EPA-450/3-77-006
2.
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
EMISSION DENSITY ZONING
5. REPORT DATE
March 1977
6. PERFORMING ORGANIZATION CODE
7.AUTH0R(s)
Fran|< H< Benesh> phil
Mills, Robert M. Patterson
) Michael T.
8. PERFORMING ORGANIZATION REPORT NO.
GCA-TR-77-01-G
9. PERFORMING ORGANIZATION NAME AND ADDRESS
GCA Corporation; GCA/Technology Division
Burlington Road
Bedford, Massachusetts 01730
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
Contract 68-02-1376, TO 26
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Protection Agency; Office of Air Quality
Planning and Standards; Strategies and Air Standards
Division; Land Use Planning Office
Research Triangle Park, North Carolina
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
Emission density zoning is an air quality control strategy whereby all parcels of
land within an air quality maintenance area, excluding public rights of way and
reserved open space, are assigned maximum legal emission allowances for particulate
matter and sulfur oxides, expressed in terms of mass of pollutant per time period per
lot area. The subject of this publication is the development of criteria for
(a) partitioning an air quality maintenance area into component areas, (b) the
setting of emission density limits for all land uses in each component area and,
separately, all major emission sources, and (c) the revision of the emission density
limits as conditions change. The criteria are then translated into a generalizable
decision model, a linear program, for setting the emission density limits. The
criteria and model are tested in two air quality maintenance areas, Baltimore and
Louisville.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Area emission allocations
Flux Density
Land Development
Land Use
Linear Programming
Particulates
Planning
Regional Planning
Sulfur Oxides
Urban Planning
Zoning
Air Pollution Control
Air Quality Maintenance
Emission Density Zoning
18. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (ThisReport)
UNCLASSIFIED
21. NO. OF PAGES
192
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
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