United States
Environmental Protection
Agency
Environmental Sciences Research
Laboratory
Research Triangle Park NC 27711
EPA-600/4-79^010
February 1979
Research and Development
v>EPA
Commuter
Exposure
Modeling
Methodologies
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the ENVIRONMENTAL MONITORING series.
This series describes research conducted to develop new or improved methods
and instrumentation for the identification and quantification of environmental
pollutants at the lowest conceivably significant concentrations. It also includes
studies to determine the ambient concentrations of pollutants in the environment
and/or the variance of pollutants as a function of time or meteorological factors.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/4-79-010
February 1979
COMMUTER EXPOSURE MODELING METHODOLOGIES
by
Patricia B. Simmon
Robert M. Patterson
SRI International
333 Ravenswood Avenue
Menlo Park, California 94025
Contract 68-02-2754
Project Officer
William Petersen
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Trianale Park, North Carolina 27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
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DISCLAIMER
This report has been reviewed by the Environmental Sciences Research
Laboratory, U. S. Environmental Protection Agency, and approved for
publication. Approval does not signify that the contents necessarily
reflect the views and policies of the U. S. Environmental Protection
Agency, nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
11
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ABSTRACT
Two methodologies for modeling commuter exposures are proposed:
computer-oriented approach and a manual approach. Both modeling metho-
dologies require that major commuter routes, or pathways, be identified
and that the traffic on the remainder of the roadway network be treated
as background pollutant sources. Since the majority of pathway exposure
is expected to result from emissions on the pathway itself, the emissions
and dispersion of non-pathway source pollutant are handled in a simple
fashion. Pathway traffic undergoes a more sophisticated treatment, in
that congestion and delay due to signalization are accounted for and
emissions are computed accordingly. The methodology used to simulate
the dispersion of pathway emissions utilizes three separate dispersion
treatments, according to whether the roadway is limited-access, non-
limited access, or a street canyon.
The numerical and manual models will each consist of three distinct
modules that treat traffic, emissions, and dispersion. The numerical
model is designed to compute exposures on a network of pathways for either
a short-term, worst-case commute or for the commutes during an average year.
Annual or short-term commuter exposure statistics will be produced by
the numerical model. The manual methodology relies on a number of graphs
and nomograms to produce exposures for a single commute on one or more
commuter routes. The input data requirements of each modeling methodology
is discussed. The data required for model evaluation and the availability
of data bases both for model input and for evaluation purposes are also dis-
cussed. A critical evaluation of the modeling approaches is also presented,
including discussions of development costs, model deficiencies, and model
accuracies.
111
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CONTENTS
Abstract ill
Illustrations
Tables X
I Introduction i
II Numerical Commuter Exposure Model 3
A. General 3
B. Definition of the Modeling Approaches 5
1. Commuter Pathways 5
2. Non-Pathway Sources 8
C. Traffic Modeling 13
1. Uninterrupted Flow 13
2. Interrupted Flow 27
D. Emission Modeling 35
1. Emissions on Pathways 36
2. Non-Pathway Emissions 45
E. Dispersion of Pathway Emissions 47
1. Dispersion of Pathway Emissions 47
2. Dispersion of Non-Pathway Source Emissions 57
3. On-Roadway/In-Vehicle Concentration Relationship. . . 63
F. Commuter Exposure Statistics 65
1. Short-term Statistics 65
2. Annual Statistics 66
3. Graphical Display of Statistics 68
4. Summary of Model Output ,q
G. Summary of Numerical Methodology 72
III Manual Commuter Exposure Model 77
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A. General .......................... 77
B. Definition of the Modeling Approaches ........... 79
1. Commuter Pathways .................. 79
2. Non- Pathway Sources ................. 79
C. Traffic Modeling ..................... 8!
1. Uninterrupted Flow ................. , 81
2. Interrupted Flow ................... 84
D. Emission Modeling ..................... 92
1. Emissions on Pathways ................ 92
2. Non- Pathway Emissions ................ 96
E. Dispersion Modeling .................... 101
1. Dispersion of Pathway Emissions ........... 101
2. Dispersion of Non-Pathway Source Emissions ...... 107
F. Summary of Manual Methodology ............... 108
IV Data Specification ....................... 109
A. Input Data
1. Numerical Model ................... 109
2. Manual Model ..................... 124
B. Data Required for Evaluation of the Model ......... 128
C. Data Base Availability .................. 131
V Critical Evaluation of Modeling Approaches ........... 133
A. Development Costs
B. Model Deficiencies
C. Model Accuracies
1. Method for Determining Relative Error ........ 139
2. Application of the Method to Traffic Parameters . . . 141
3. Results of Sample Applications ............ 144
4. Accuracies of Emissions and Dispersion Algorithms . . 148
References ............................. 152
vi
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LIST OF ILLUSTRATIONS
1. Sample Commuter Pathway Network With Grid Overlay 10
2. Flowchart of Pathway Traffic Modeling Procedure 14
3. Relationship Between V/C Ratio and Operating Speed, In One
Direction of Travel, On Freeways, Under Uninterrupted Flow
Conditions 18
4. Relationships Between V/C Ratio and Operating Speed, In One
Direction of Travel, on Multilane Rural Highways, Under
Uninterrupted Flow Conditions 21
5. Relationships Between V/C Ratio and Operating Speed, Overall for
Both Direction of Travel, On Two-Lane Rural Highways With Average
Highway Speed of 50 Mph, Under Uninterrupted Flow Conditions.... 21
6. Relation Between Demand, Capacity, and Congestion 27
7. Typical Relationships Between V/C Ratio and Average Overall
Travel Speed, In One Direction of Travel, On Urban and Suburban
Arterial Streets 29
8. Operating Speed Related to Level of Service, Route Type, Volume/
Capacity Ratio and Ring 29
9. Service Volume of a Signalized Intersection Approach 31
10. Flowchart of Pathway Emission Modeling Procedure 37
11. Illustration of a Limited-Access Roadway Segment Showing Parameters
Used in Dispersion Computations 48
12. Schematic of Cross-Street Circulation Between Buildings 53
13. Flowchart of Pathway Dispersion Computation Procedure 55
14. Illustration of Integration Technique for Non-Pathway
Concentrations 60
VI1
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15. Flow Chart of Non-Pathway Source Traffic, Emissions, and
Dispersion Computation Procedure 62
16. Flowchart Showing How Annual Histogram Data is Generated 67
17. Simplified Flowchart for Numerical Commuter Exposure Model 74
18. Nomograph for Finding the Extent (Vehicles) of the Primary
A
Backup, N, and the Total Backup, N, From Demand Volume, Capacity,
and Time for Congested, Uninterrupted Flow 82
19. Nomograph for Finding Average Delay per Vehicle 83
20. Two-Way Street CBD, Fringe, OBD and Residential Capacities 85
21. One-Way Street CBD, Fringe, OBD and Residential Capacities 86
22. Graphical Estimation of the Number of Vehicles Per Hour Stopping
at a Signalized Intersection 87
23. Intersection Delay Per Vehicle 88
24. Graphical Estimation of Delay at Signed Intersections and Toll
Booths 89
25. Graphical Estimation of Queue Length As a Function of Lane
Capacity and Intersection Delay with a Minimum Queue Length of
40 Meters Assumed 91
26. Relationship Between Emission Rate and Emission Density and
Demand Volume 93
27. Graphical Calculation of Carbon Monoxide Emissions 94
28. Graphical Calculation of Acceleration/Deceleration Emission Rate,
g/m-sec, Given Acceleration/Deceleration Emissions From Figure 27
and the Cycle Length, Cy 97
29. Graphical Calculation of Idle Emission Rate, g/veh-sec, Given
Idle Emissions From Figure 27 and PC 98
y
30. Graphical Calculation of Cruise Emission Rate, g/m-sec, Given
the g/veh-mile From Figure 27 and the Volume 99
31. Normalized On-Roadway Concentration Versus Wind/Roadway Angle for
Various Stabilities and rr Values for an Infinite Line Source..103
zo
viii
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32 . Finite Line Source Geometry , 104
33. Variation of the Normalized CO Concentration With Roadway Length,
Stability, Wind/Road Angle, and Terrain Roughness 106
ix
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LIST OF TABLES
1. Locale Types 12
2. Example of Weekday Diurnal Traffic Cycles on Freeways in the
San Francisco Bay Area 15
3. Examples of Weekday Diurnal Traffic Cycles on Non-Freeway Streets
in the San Francisco Bay Area 16
4. Combined Effect of Lane Width and Restricted Lateral Clearance on
Capacity and Service Volumes of Divided Freeways and Expressways
and Two-Lane Highways with Uninterrupted Flow 19
5. Average Generalized Adjustment Factors for Trucks on Freeways and
Expressways, and Two-Lane Highways Over Extended Section
Lengths 20
6. Vehicle Group Designations 41
7. Value of the Constants a and b for Various Stabilities 58
8. Numerical Commuter Exposure Model Output 70
9. Dispersion Algorithms Used in Numerical Commuter Model 75
10. Minimum Roadway Length of an "Infinite" Line Source 102
11. Input Data Requirements for the Numerical Commuter Exposure
Model 110
12. Numbers Associated With Each Combination of Wind Speed Class,
Wind Direction Class, and Stability Class 121
13. Definition of Value Intervals of Wind Direction, Wind Speed, and
Stability Classes 123
14. Data Requirements for the Manual Commuter Exposure Model 125
15. Model Deficiencies 137
16. Relative Error and Sensitivities for the Freeway Backup Case.... 145
17. Relative Error and Sensitivities for the Signalized Intersection
Case 146
x
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18. Relative Error and Sensitivities for the Toll Booth Case 147
19. Relative Error and Sensitivities for Street Canyon
Concentrations 151
xi
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I INTRODUCTION
Commuters are exposed to pollutants at levels high enough to cause
widespread concern, and this concern has been heightened by studies
indicating that commuters are exposed to more roadway-generated
pollutants than any other group. The results of preliminary studies of
the commuter exposure problem are recognized as first order
approximations. To more accurately assess the exposures to which
commuters are subjected, the areawide concentration patterns that occur
during commute hours must be determined. Such patterns depend on factors
such as meteorological conditions, traffic volume distributions in
space and time, roadway characteristics, distributions of vehicle types
and models, vehicle operating characteristics, intersection signalization,
and vehicle emissions. These factors must therefore play an important
role in a model that can simulate commuter emission patterns and the
subsequent action of the atmosphere in dispersing the emissions.
This report proposes the elements of a commuter exposure model. Two
approaches have been formulated to predict pollutant concentration patterns
arising from vehicular sources: (1) an approach involving numerical
techniques, and (2) an approach involving simple charts and nomograms.
The manual approach is a simplified version or subset of the numerical
approach.
The basic modeling methodology is comprised of four parts, each of
which is concerned with one aspect of commuter exposure modeling. The
first part of the methodology—the definition of the modeling area—will
be executed by and requires the judgement of the user. The remainder of
the methodology-treating traffic, emissions, and dispersion—will be
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executed on a computer (in the case of the numerical model) or by the
user with the aid of worksheets, tables, and nomograms (in the case of
the manual model). The methodologies recommended for defining the
modeling area and simulating traffic, emissions, and dispersion are
described in detail for the numerical model in Section II and for the
manual model in Section III. The formulations presented could apply to
almost any inert pollutant, but it was assumed, as the general commuter
modeling methodology was being developed, that carbon monoxide was the
pollutant of primary concern.
Because of the flexibility gained through the use of a high-speed
computer, the numerical methodology will allow computation of both annual
average and short-term, worst-case commuter exposure statistics. The
manner in which the statistics are developed is discussed in Section II,
and a presentation of the types of output available with each modeling
approach appears in the sections of this report that deal with the
numerical and manual methodologies.
The content of Section IV concerns the specification of data. The
data input requirements of the two modeling approaches are given, and
the data needed to evaluate the models are discussed. The availability
of existing data bases is also examined.
The final section of this report contains an evaluation of the two
modeling approaches. Items such as development costs, both in dollars
and time, and the deficiencies and accuracies of the model are investigated,
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II NUMERICAL COMMUTER EXPOSURE MODEL
A. General
The basic numerical commuter exposure modeling methodology is
separated into three distinct parts that consider traffic flow, emissions,
and atmospheric dispersion. When the code for the model is written,
separate modules treating each of these topics should be maintained, to
facilitate model updates necessitated by improved technology. The modeling
approaches are defined in Subsection II-B. The techniques to be used to
compute the parameters relating traffic, emissions, and dispersion are
described in Subsection II-C through TI-E. Subsection II-F contains a
detailed discussion of the output of the numerical model and how it will
be formulated from model computed statistics, while Subsection II-G is
a summary of the numerical methodology as a whole. In this subsection,
a more general discussion of model ouput, and its effect on the design
of the methodology itself, is presented.
Naturally, the information desired by the model user plays a key
role in the design of any model. Basically, two types of statistics are
of interest to the commuter exposure modeler: (1) so-called short-term
statistics, concerning a single commute during worst-case meteorology:
and (2) annual statistics, which describe average exposure or the frequency
of occurrence of exposure throughout a year. The numerical model method-
ology is designed so that it may produce either type of statistic.
In both the annual and short-term modes, the model allows the user
to compute exposures for the "average" commuter on each of the pathways.
(The "average" commuter is the driver who commutes mostly during the peak
travel period.)
The differences in the way the model will compute annual and short-
term exposures concern the consideration of the time period of the commute.
Annual statistics require computations for each of various meteorological
and traffic condition combinations, so it is assumed that the meteorology
and the traffic volumes on the pathways do not change during the commute
period. That assumption reduces the number and complexity of the required
computations, because it eliminates the need to contend with time sequences
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of meteorology and traffic during the commute period. The annual exposure
statistics developed under the methodology will be "average," in the'sense
that the traffic and meteorological conditions used in the computations
are the average prevailing conditions during a commute.
For an in-depth, worst-case analysis, the model should be us.id in
the short-term mode, in which both traffic and meteorology will be allowed
to vary with time. If the average commute on a pathway lasts longer than
one hour, the traffic volumes and meteorological conditions may change for
the next hour.
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B. Definini.ti.on of the Modeling Approaches
The crux of the commuter exposure modeling problem is defining the
modeling area. Ideally, the definition of the modeling area should be
the same for the numerical and graphic models. As a minimun, the definition
for the graphic model should be a subset of that for the numerical model.
The modeling area should coincide with the Standard Metropolitan Statistical
Area (SMSA) or the Air Quality Control Region (AQCR) bounding the urban
core. Such a practical choice has been made because those areas usually
encompass the region that influences and is impacted by the urban core,
and because a wealth of requisite data is routinely available for them.
Generally, the SMSA and AQCR boundaries are the same.
This section describes a methodology for defining the modeling area
in terms of the two important types of emission sources in a commuter
exposure model: (1) line sources, or commuter pathways; and (2) non-
pathway sources (the "background source effects") from the remaining
roadway network.
1. Commuter Pathways
The most critical aspect in defining the modeling area is
choosing the appropriate commuter pathways. The commuter exposures that
are calculated and the statistics that are derived all depend directly
on the pathways that are defined.
Fortunately, the major commuting pathways, or "commuting
corridors," are well-defined and recognizable if one is familiar with the
modeling area. Often, just the physical size of the roadway, or, more
properly, its capacity, will identify it as a commute route. The commuting
pathways are also corridors of development, fostered largely by the access
to the urban core that the route provides.
From a methodological standpoint, however, it is suggested that
the user of the commuter exposure models seek advice in defining the
major commuting routes. The local transportation department, the metro-
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politan transportation planning authority, or the council of governments
should be able to provide this assistance. The remainder of this dis-
cussion provides the criteria that should be presented to the transportation
expert to help him help the model user in defining the commuting pathways.
a. Origin-Destination Zones
A key part of the transportation planning process is the
estimation of trends of demand for transportation services. Estimates
of demand are based on a knowledge of existing demand, and on known and
planned land-use and demographic characteristics of the planning region.
Tools that help quantify this demand are the origin-destination survey
and the additional data that can be generated from the survey results.
Typically, the region is divided into subareas, or zones.
They are of variable size, depending on population density and other
demographic characteristics, and on the roadway network. The zones are
smaller and denser in the urban core than in outlying areas. For example,
the transportation planning region for Pittsburgh encompasses about 9000
square miles and contains approximately 900 zones. However, about 100
of them are in the downtown, "Golden Triangle," area of the city.
In simplest form, the origin-destination data will supply
the daily trips between zones. Thus, they may be broken down by trip
purpose, by trip purpose pairs indicating the direction of flow (home-
work, work-home), and by time of day. For the commuter exposure TLodel,
trips to and from work are the main ones of concern in defining the
commuting routes. Fortunately, work trips have the most tractable sta-
tistics. They are likely to vary the least from one weekday to the next
and they occur during fairly well-defined time periods. They are relatively
insensitive to weather and travel conditions. Additionally, even if the
trip is identified only as a work trip, it can be assumed to be from home
to work in the morning and from work to home in the evening. The origin-
destination data are usually presented as a matrix, with an accompanying
map indicating the zones. The matrix elements are the numbers of trips
between origins and destinations.
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The purpose of origin-destination data for commuter exposure
modeling is to define the commute pathways. Accepted accuracy for the data
is +_ 20 percent, so they should not be used to generate traffic volumes.
Their utility lies in showing the spatial flow of home-work and work-home
trips. Once the spatial flow is known, the key roadways can be determined,
and traffic volumes can be taken from volume flow maps.
Given fairly comprehensive origin-destination data, it would
be tempting to try to model all commuters. All of the work-related trips
are identified, and one could 'seemingly define routes for them and model
the exposures. But the futility of doing so becomes readily apparent when
the Pittsburgh example is considered: the toal number of possible origin-
2
destination pairs is 900 , or 810,000. Even as few as 100 zones would
yield 10,000 combinations. While not every combination will produce a
work-related trip, the percentage is large enough to render such an
approach impractical.
b. Definition of Commute Pathways
For commuter exposure modeling to be a manageable problem,
a reasonable number of major commuting routes or pathways must be defined
even though a plethora of origin-destination data is available. The
number of pathways will be a function of the size of the modeling area,
but it should be about 25 or less. Those routes will generally have the
highest number of vehicle miles traveled (VMT) by commuters. Again it
is recommended that the advice of a transportation planner or traffic
engineer familiar with the area be sought when the routes are defined.
It is recognized that the commute pathways defined in such
a manner will not carry all commuters. However, the method described
here should include a great majority of the commuters who are at risk of
experiencing high exposures on the order of the air quality standards.
Most of the extensive commuting will be done along the defined pathways,
both in time and distance, and the pathways will by definition carry high
volumes of traffic. Although their total number may be close to that on
the pathways, the commuters "missed" will, on the average, be traveling
shorter times and distances on less heavily traveled roads. They are not
considered to be at risk to high pollutant exposures during their commute.
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Commuting trips do not begin on the commute pathways as
defined here, but rather, on local surface streets and "collectors."
Often, they will not even begin in the same zone that they are in when
they enter the pathway. To handle the exposure during the approach to
and departure from the pathway, minor pathways should be used that are
representative of the travel to and from the route.
c. Characteristics of Pathway Sections
Two types of roadways are candidates for commute pathways:
expressways and arterials. A pathway may be composed of both. The Highway
Capacity Manual (HCM) defines an expressway as "a divided arterial highway
for through traffic with full or partial control of access and generally
with grade separations at major intersections." (A freeway is defined
as an expressway "with full control of access.") The term arterial is
intended to have the meaning that the HCM applies to a major street or
highway: "an arterial highway with intersections at grade and direct
access to abutting property, and on which geometric design and traffic
control measures are used to expedite the safe movement of through traffic.'
The other descriptors that characterize the pathways
pertain to physical location and include street canyons and cut, fill,
elevated, and at-grade sections. For on-roadway concentration calculation,
the second group may be taken together. That is discussed later in this
section.
2. Non-Pathway Sources
a • Definition of Grid System
Non-commute pathway pollutant emissions will be treated
on a grid square basis. The modeler will overlay the study area with a
grid system, and the grid squares will have dimensions of 2 km by 2 km.
The coordinate system used to define the grid must be
consistent with the system used to define commuter pathway coordinates.
Grid squares will be defined by their lower left corner coordinates, and
the input data required can be abbreviated for sections of the study area
in which grid square descriptors have the same value.
8
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The grid square coordinates, and other grid square descrip-
tors described in the next two sections, need be input to the model for
only those squares through which commuter pathways pass. Figure 1 illu-
strates a typical commuter pathway network, overlaid by a grid system.
The shaded grid squares are those for which input data are required.
b. Apportionment of Vehicle Miles Traveled on ttie Primary Network
The primary street network is defined as those roadways
carrying a major amount of the total vehicle miles traveled (VMT) on the
entire roadway network of a metropolitan area. In general, the primary
network can be considered to be those streets for which average daily
traffic (ADT) values are available. For the commuter exposure model,
the primary network will not include roadways that are commuter pathways.
Because the major part of the concentration on a commuter
pathway is expected to result from vehicles traveling on the pathway
itself, the part of the concentration resulting from the other non-pathway
roadways in the vicinity can be approximated. The approximation to be
used in the model will consist of an aggregation of primary network
emissions into grid squares, with the assumption of a uniform emission
rate across the square. This approach will save the user the considerable
effort that would be required if each roadway in the primary network, and
its associated characteristics, were used as model input.
Therefore, once the grid system is defined, the user must
apportion the total VMT of primary network streets among the grid squares
and input that information for the appropriate squares. The recommended
approach for the apportionment is the following. A volume flow map
showing the ADT on the major roadways in the study area should be overlaid
with the grid system. The length of the portion of each roadway that lies
in the grid square should be multiplied by the number of vehicles traveling
on that roadway each day, yielding the VMT on the portion of the roadway
that lies in the grid square. This procedure should be followed for each
portion of roadway in the grid square; the total VMT in the grid square
will be the sum of the individual roadway VMTs. The measurement of
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TT
FIGURE 1. SAMPLE COMMUTER PATHWAY NETWORK WITH GRID OVERLAY
(DATA MUST BE INPUT FOR SHADED SQUARES )
10
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roadway lengths and volumes need not be exact, because the primary network
emissions and dispersion treatments involve a number of approximations.
The VMT for each grid square through which a commuter
pathway passes will be input to the model and used to generate an emission
rate for the square. Care should be taken so that the VMT on commuter
pathways is not included in the VMT of a grid square.
In general, the results of the foregoing procedure will
be used to compute emissions from the primary network. However, the
model will allow the user to input an average daily emission rate for
each grid square, in lieu of VMT. This option would be used when gridded
emissions for the study area are readily available from another source
or when the user has access to the projections generated by the Federal
'Highway Administration's (FHWA) battery of computer programs. In the
latter case, the user may opt to run the APRAC-2 emissions module, which
takes the FHWA historical traffic files as input (deleting, of course,
the commuter pathways), to produce a gridded emission inventory. The
values from this inventory may be used as input to the commuter exposure
model. For further details on the APRAC-2 emissions module, see Ludwig,
et al.2
c. Apportionment of Secondary Network VMT
The secondary traffic network consists of all streets not
in the primary network or commuter pathways. The approach used for
assigning secondary traffic to grid squares assumes that the ratio of
secondary traffic to primary traffic varies by locale (or by land use).
For instance, virtually all of the streets in the Central Business District (CBD)
are likely to be important enough to be included in the primary traffic
network. Similarly, very little traffic in rural areas is likely to be
found off the major roadways. In residential and industrial areas, a large
fraction of the the total traffic may use secondary streets. The user
estimates the ratio of secondary to primary traffic for each locale type.
The locale type of each grid square or group of grid squares for which data
are required also will be input. The model will allot secondary network VMT
11
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on the grid squares in proportion t.o the product of the VMT on the primary
network in that square and the ratio of the secondary to primary traffic
associated with the locale type of the square. A list of locale types
appears in Table 1.
Table 1
LOCALE TYPES
1. Central business district
2. Commercial areas in the core of the city,
or suburban centers
3. Residential areas
4. Industrial areas
5. Rural and miscellaneous
If gridded emissions are input directly, as discussed in
the previous section, secondary network emissions should be included in
that inventory.
12
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C. Traffic Modeling
Traffic modeling along commuter pathways requires the handling of
two separate traffic flow regimes: uninterrupted flow and interrupted
flow. Travel on expressways is generally uninterrupted, although during
a backup, the flow can become severly constrained to the point of becoming
"stop and go." Interrupted flow describes travel on arterials with traffic
signals at the intersections.* The following discussion details those
elements of the computer exposure model that describe the traffic flow.
Figure 2 is a flowchart illustrating the traffic modeling procedure.
1. Uninterrupted Flow
The characteristics of uninterrupted flow can be obtained from
two parameters, demand volume (v) and free-flow capacity (c) of the road
segment. Both will be required inputs to the model. Demand volume may
be obtained from volume flow maps or tabulated volume data available from
the local transportation agency. Ideally, hourly data should be available,
but often only the average daily traffic (ADT) or annual average daily
traffic (AADT) can be obtained. In the latter cases, factors must be
applied to arrive at estimated hourly volumes during commuting periods.
Those factors should be obtained from the local transportation agency so
that they are representative of the area. If they are unavailable,
national average values should be used. As an example, Table 2 shows
the percentage of weekday AADT by hour, land use type, and direction of
travel on freeways in the San Francisco Bay Area. Table 3 supplies the
same data for nonfreeway streets.
Seasonal adjustment factors are also needed to define how the
AADT changes with season (winter incudes December-February, spring includes
March-May, etc.). These data should be obtained for the local area under
consideration.
The commuter exposure model will allow the input of hourly
volumes directly, ADT, AADT, and the appropriate correction factors.
•"Intersections that have stop signs are not considered since they will
not be presert for the main traffic flow on an arterial, commuter pathway.
13
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INPUT VOLUME AND
CAPACITY SERVICE
VOLUME DATA FOB RE
MAIMING APPROACHES
COMPUTE SIGNAL
PARAMETERS FROM
CAPACITY SERVICE
AND DEMAND VOLUME
CALCULATE QUEUE
LENGTHS AND DELAY
COMPUTE CAPACITY FROM ROAD-
WAY PHYSICAL AND TRAFFIC
MIX DATA. AND FROM SIGNAL
DATA AS APPROPRIATE
No
COMPUTE HOURLY VOLUME
FROM ADT OR AADT USING
APPROPRIATE SEASONAL
AND DAILY FACTORS
CALCULATE TRAVEL
TIMES IN THE CRUISE
MODE, AND IN THE
OTHER MODES COMBINED
COMPUTE SPEED FROM V/C
AND SPEED RELATION-
SHIPS FOR ROADWAY
TYPE AND SIGNALIZATION
AS APPROPRIATE
1
SPEED - 20 MPH FOR
UNINTERRUPTED FLOW.
10 MPH FOR INTERRUPTED
FLOW. COMPUTE NUMBER
OF VEHICLES IN BACKUP
AND AVERAGE DELAY
FIGURE 2. FLOWCHART OF PATHWAY TRAFFIC MODELING PROCEDURE
14
-------
Table 2
EXAMPLES OF WEEKDAY DIURNAL TRAFFIC CYCLES ON
FREEWAYS IN THE SAN FRANCISCO BAY AREA
Hour
Ending CBD
(local
time) NB"1"
00
01
02
03
04
05
06
07
08
09
010
Oil
012
013
014
015
016
017
018
019
020
021
022
023
Total
.017
.010
.006
.004
.004
.007
.022
.057
.055
.044
.044
.050
.057
.053
.059
.078
.110
.099
.060
.045
.033
.035
.028
.024
1.001
SB
.014
.007
.004
.004
.006
.016
.062
.097
.075
.052
.051
.054
.049
.056
.063
.067
.072
.064
.047
.039
.027
.027
.026
.022
1.001
Commercial
NB SB
.013
.004
.004
.002
.003
.005
.033
.127
.130
.066
.048
.043
.047
.042
.045
.051
.070
.073
.055
.042
.031
.026
.020
.017
.998
.012
.006
.004
.001
.001
.005
.026
.079
.086
.049
.039
.040
.043
.046
.052
.071
.091
.103
.074
.048
.035
.033
.029
.025
.998
Residential
NB SB
.007
.003
.002
.001
.000
.009
.077
.175
.131
.056
.045
.041
.039
.042
.041
.057
.059
.059
.045
.048
.032
.021
.023
.013
1.001
.017
.005
.003
.001
.001
.001
.009
.041
.049
.034
.032
.034
.035
.035
.043
.070
.163
.181
.101
.051
.028
.024
.025
.017
1.000
Industrial
NB SB
.009
.006
.004
.003
.005
.011
.055
.094
.072
.059
.032
.058
.054
.058
.059
.070
.083
.068
.051
.039
.033
.034
.023
.018
.998
.012
.006
.004
.003
.004
.C08
.047
.069
.053
.052
.055
.056
.052
.061
.063
.073
.088
.097
.067
.041
.029
.026
.018
.019
~ 1.003
Rural
EB WB
.022
.011
.007
.005
.005
.007
.019
.053
.045
.045
.045
.047
.043
.050
.053
.070
.099
.101
.095
.045
.036
.039
.033
.025
1.000
.011
.006
.005
.004
.007
.023
.110
.117
.083
.061
.054
.049
.045
.046
.050
.050
.065
.058
.042
.037
.021
.019
.021
.017
1.001
These data are from Seattle; others are San Francisco Bay Area Locales.
Directions:
NB
SB
EB
WB
Northbound
Southbound
Eastbound
Westbound
15
-------
Table 3
EXAMPLES OF WEEKDAY DIURNAL TRAFFIC CYCLES ON
NONFREEWAY STREETS IN THE SA1I FRAI1CLSCO BAY AREA
Hour
Ending
(local
timet
00
01
02
03
04
,05
06
07
08
09
010
Oil
012
013
014
015
016
017
018
019
020
021
022
023
Total
CBD*
NBf SB
.013
.006
.003
.004
.002
.003
.017
.035
.036
.039
.048
.067
.104
.068
.070
.071
.095
.081
.057
.048
.046
.039
.028
.020
1.000
.015
.008
.006
.004
.004
.007
.027
.061
.052
.040
.050
.059
.078
.081
.070
.066
.077
.072
.049
.043
.047
.036
.026
.021
0.999
Comercial
EB WB
.008
.004
.003
.002
.002
.007
.036
.101
.081
.051
.052
.057
.064
.066
.061
.065
.068
.052
.052
.052
.045
.028
.025
.018
1.000
.014
.007
.005
.003
.002
.002
.010
.031
.041
.038
.046
.055
.068
.060
.064
.073
.097
.121
.081
.058
.035
.038
.031
.019
0.999
Residential
NB SB
.006
.003
.002
.002
.003
.015
.078
.149
.077
.059
.052
.051
.052
.049
.058
.071
.056
.052
.055
.043
.021
.017
.017
.011
0.999
.021
.010
.005
.003
.002
.003
.009
.033
.036
.034
.040
.053
.057
.064
.067
.074
.099
.079
.052
.036
.032
.039
.027
.019
1.002
Industrial
EB WB
.015
.007
.005
.004
.002
.004
.024
.086
.057
.049
.051
.053
.057
.064
.067
.074
.099
.079
.052
.036
.032
.039
.027
.019
1.002
.010
.004
.004
.002
.005
.018
.066
.103
.079
.001
.057
.057
.056
.056
.061
.062
.079
.065
.054
.031
.019
.018
.016
.016
0.999
Rural
EB WB
.007
.002
.002
.001
.012
.012
.056
.161
.091
.058
.058
.055
.045
.052
.062
.066
.064
.059
.054
.032
.017
.012
.019
.015
1.001
.016
.009
.005
.002
.004
.003
.017
.054
.046
.037
.051
.052
.048
.051
.057
.073
.127
.125
.063
.035
.030
.040
.031
.022
0.998
*These data are from Seattle, others are San Franciosco Bay Area Locales.
Directions:
NB
SB
EB
WB
Northbound
Southbound
Eastbound
Westbound
16
-------
Typical values of the correction factors will be built into the model as
default parameters. The user of the model will then be able to tell the
model the form of data that are being input, and will also have default
correction factors available if necessary.
The capacity of a roadway is defined in the Highway Capacity
Manual as "the maximum number of vehicles which has a reasonable expectation
of passing over a given section of a lane or a roadway in one direction
(or in both directions for a two-lane or a three-lane highway) during
a given time period under prevailing roadway and traffic conditions".
Usually, capacity pertains to a one-hour period. Capacity will vary
along segments of a commute pathway because of physical characteristics,
the makeup of the traffic, weather conditions, accidents, and so forth.
For the commuter exposure model, capacity can be estimated by
the following techniques. If the local transportation agency can provide
better estimates, such as from field study results, those data should be
used. The Highway Capacity Manual gives the following maximum uninterruped
flow capacities under ideal conditions for various types of roadways:
Highway Type Capacity
Multilane 2,000 per lane
Two-lane, two-way 2,000 total (both directions)
Three-lane, two-way 4,000 total (both directions)
The capacity, C, of a multilane roadway is computed with the
following equation:
C = 2000 MWf T;
the capacity for one direction of a two-lane roadway is computed with the
equation:
C = 1000 WfT
where
M = number of lanes moving in one direction
Wf = adjustment factor for lane width from Table 4
T = truck factor from Table 5 .
17
-------
The entries in Tables 4 and 5 will be included in the model.
The user will be provided the option of entering capacity directly, or
the type of roadway, lane width, lateral clearance, and percentage of
trucks for each segment so that the appropriate factors can be called in
the model.
Once volume and capacity are known for a freeway or expressway,
the speed at which traffic moves may be determined. Figures 3 and 4 show
the relationships between the ratio of volume to capacity and the operating
speed in one direction of travel and under uninterrupted flow conditions
for freeways and expressways and for multilane rural highways. Figure 5
depicts similar relationships for both directions of travel on two-lane
rural highways. The equations to those curves will be functions or will
be in subroutines in the model. Given volume and capacity, the operating
speed would then be calculated for use in calculations of emissions and
travel or exposure time.
FREEWAYS AND EXPRESSWAYS
0.1
0.2 0.3
0.4 0.5 0.6
WC RATIO
0.7
0.8 0.9 1.0
SA-4429-3
FIGURE 3 RELATIONSHIPS BETWEEN V/C RATIO AND OPERATING SPEED, IN ONE
DIRECTION OF TRAVEL, ON FREEWAYS AND EXPRESSWAYS, UNDER
UNINTERRUPTED FLOW CONDITIONS
18
-------
Table 4
COMBINED EFFECT OF LANE WIDTH AND RESTRICTED LATERAL CLEARANCE
ON CAPACITY AND SERVICE VOLUMES OF DIVIDED FREEWAYS AND
EXPRESSWAYS AND TWO-LANE HIGHWAYS WITH UNINTERRUPTED FLOW
Distance from
Traffic Lane
Edge to
Obstruction
Adjustment Factor ,,Wf, for Lane Width and Lateral Clearance
Obstruction of One Side of
One-Direction Roadway
12-ft
lanes
11-ft
lanes
10-ft
lanes
9-ft
lanes
Obstructions on Both Sides
of One-Direction Roadway
12-ft
lanes
11-ft
lanes
10-ft
lanes
9-ft
lanes
Four-Lane Di vided Freeway, One Direction of Travel
6
4
2
0
1.00
0.99
0.97
0.90
0.97
0.96
0.94
0.87
0.91
0.90
0.88
0.82
0.81
0.80
0.79
0.73
1.00
0.98
0.94
0.81
0.97
0.95
0.91
0.79
0,91
0,89
0.86
0.74
0.81
0.79
0.76
0.66
Six- and Eight-Lane Divided Freeways, One Direction of Travel
i
6
4
2
0
1.00
0.99
0.97
0.94
0.96
0.95
0.93
0.91
0.89
0.88
0.87
0.85
0.78
0.77
0.76
0.74
1.00
0.98
0.96
0.91
0.96
0.94
0.92
0.87
0.89
0.87
0.85
0.81
0.78
0.77
0.75
0.70
Two-Lane Highway, One Direction of .Travel
6
4
2
0
1.00
0.97
0.93
0.88
0.88
0.85
0.81
0.77
0.81
0.79
0.75
0.71
i
0.76
0.74
0.70
0.66
1.00
0.94
0.85
0.76
0.88
0.83
0.75
0.67
0.81
0.76
0.69
0 62
0.76
0.71
0.65
0.58
19
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Table 5
AVERAGE GENERALIZED ADJUSTMENT FACTORS FOR TRUCKS
ON FREEWAYS AND EXPRESSWAYS, AND TWO-LANE
HIGHWAYS OVER EXTENDED SECTION LENGTHS
Pt, Percentage
of Trucks (%)
1
2
3
4
5
6
7
8
9
10
11
14
16
18
20
Factor, T, For All Levels of Service
Level Terrain
Rolling Terrain
Mountainous Terrain
Freeways and Expressways
0.99
0.98
0.97
0.96
0.95
0.94
0.93
0.93
0.92
0.91
0.89
0.88
0.86
0.85
3.83
0.97
0.94
0.92
0.89
0.87
0.85
0.83
0.81
0.79
0.77
0.74
0.70
0.68
0.65
0.63
0.93
0.88
0.83
0.78
0.74
0.70
0.67
0.64
0.61
0.59
0.54
0.51
0.47
0.44
0.42
Two-Lane Highways
1
2
3
4
5
6
7
8
9
10
12
14
16
18
20
0.99
0.98
0.97
0 96
0.95
0.94
0.93
0.93
0.92
0.91
0.89
0.88
0.86
0.85
0.83
0.96
0.93
0.89
0.86
0.83
0.81
0.78
0.76
0.74
0.71
0.68
0.64
0.61
0.58
0.56
0.90
0.82
0.75
0.69
0.65
0.60
0.57
0.53
0.50
0.48
0.43
0.39
0.36
0.34
0.31
20
-------
MULTILANE RURAL HIGHWAYS
0.1 0.2 0.3 0.4 0.5 0.6
FIGURE 4 RELATIONSHIPS BETWEEN V/C RATIO AND OPERATING SPEED, IN ONE
DIRECTION OF TRAVEL, ON MULTILANE RURAL HIGHWAYS, UNDER
UNINTERRUPTED FLOW CONDITIONS
2-LANE RURAL HIGHWAYS
70
60
f"
100% WITH 1,500 ft SIGHT DISTANCE
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
FIGURE 5 RELATIONSHIPS BETWEEN V/C RATIO AND OPERATING SPEED, OVERALL FOR
BOTH DIRECTIONS OF TRAVEL, ON TWO-LANE RURAL HIGHWAYS WITH AVERAGE
HIGHWAY SPEED OF 50 MPH, UNDER UNINTERRUPTED FLOW CONDITIONS
21
-------
The methodology described so far applies to uninterrupted flow
on freeways and expressways. It is possible for the flow to become con-
strained to the point of being stop-and-go on expressways and freeways,
either because of a particularly high demand volume or because capacity
is reduced for some reason. The following discussion presents a method
for calculating the number of vehicles that would be influenced by a
traffic backup when volume exceeds capacity. A method for calculating
average exposure time is also given.
When the demand volume exceeds capacity, a backup builds up
in the congested area at a rate equal to demand minus capacity:
dn
— = q-s q > s
where n = size of backup (vehicles)
q = demand volume over a suitable averaging time, (vehicles/sec)
s = capacity of the particular section of the road on which the backup
occurs (vehicles/sec)
t = time (sec)
The backup increases and reaches a size, N, at some time, t', measured
from the time that the backup begins (q > s), when q = s:
N = (q-s)t'.
The total number of vehicles affected by congestion includes N plus those
entering the backup after capacity exceeds demand (s > q), but before the
backup dissipates. The backup is relieved at some time, t", measured from
the time when q = s; (t" = t-f), satisfying
st" - N - qt" = 0
t" = —
s-q s > q.
The total number of vehicles affected is
N = N + qt"
}N _ sN - qN + qN
= N +
s-q s-q
22
-------
Note that the numerator is evaluated for the time that q > s, while the
denominator is evaluated during s > q. Note also that q is the demand
volume over a suitable averaging time that is representative of the
transiency of the backup.
The "delay", or time spent traversing the backup, is a function
of the length of the backup and the average travel speed:
D = D(n,v).
Assuming each vehicle occupies a constant k meters,
kn
D = ,
v
and assuming that the average speed is constant, then the change in delay
to vehicles entering the backup at different times is
dD = dn,
and the total delay for all vehicles is
ten
dn.
Calling the total delay D, we have
/kn
D = I dn.
v
For q > s, n = (q-s)t and dn = d£(q-s)t] = (q-s)dt, since q and
s are
also assumed constant. Then
k(q-s)2t2
2v
rx
where T = N/(q-s). The average delay is D/N, or D/ /(q-s)dt
k(q-s)2t2
2v
avg
(q-s)t jT
10
2v
23
-------
or
k(q-s)T
2v
kN
2v.
The average delay when s > q is calculated in the same manner.
In this case, the number of vehicles in the backup is
n = N - (s-q)t
and dn = -(s-q)dt.
Then
/kn
D = /—
J v
dn
N
0
=-/u [N-(S-
T'
and the total delay can be calculated from
K)
(s-q)dt
D=- fcN(s-q)t
22
+ k(s-q) t
T"
2v
T"
where T" is the time for the backup to dissipate. Since T" equals N/(s-q),
the total delay for vehicles arriving when s > q is
= kN2 _ kN2
v 2v
2v
The average delay per vehicle is
kN'
2v(N-N) .
The total delay when q > s equals the total delay when s > q.
delay for all vehicles is then
D (all vehicles) = |^ + ^ f
avg \^v 2v
The average
24
-------
As an example, consider the data below, giving five-minute
demand volumes on a roadway with a capacity of 2000 vehicles/hr, 167
vehicles/five minutes, or .55 veh/sec:
Five-Minute Increment Demand Volume
1
2
3
4
5
6
7
8
9
10
167
200
200
210
180
190
180
150
110
100
In increment 1, demand equals capacity, and no backup occurs,
In increments 2-7, demand exceeds capacity. The average demand is 1160
vehicles/1800 sec, or .64 veh/sec.
The number of vehicles backed up during this period is then
N = (q - s)t'
= (.64 - .55) 1800
= 160 vehicles.
During the next 15 minutes, the additional vehicles backed up equals
qN (.40X160) _ ... ...
= —— —— - 411 vehicles.
s-q .55 - .40
The total is
160 + 411 = 571 vehicles.
N
The time for the backup to clear up is given by t" =
s-q
160
.55 - .40
= 1029 seconds = 17.1 minutes.
Assuming that vehicles in the congested area are able to maintain an
average speed of 20 mi/hr, and assuming a time headway of 1.8 sec, each
vehicle "occupies" 16 meters. The time for the 160th vehicle to pass
through the congested area is
25
-------
C160 vehicles)(16m/vehicle)
(20mi/hr)(0.447m/sec/mi/hr) = 286 sec<
= 4 min, 46 sec.
Assuming a 2-second headway yields
C160)d8m/vehicle)
(20)(0.447) = 5 mn' 22 SeC'
This example shows that, first of all, the calculation of the
total queue length produces a conservative estimate. During the last
three five-minute increments, 360 vehicles approach the congested area,
while the calculation indicates that 411 vehicles enter the backup. Also,
the time for the congestion to break up is presented as 45 minutes, while
the calculated time is 30 + 17.1 minutes, or 47.1 minutes. This extended
time and the conservative calculation of the number of vehicles affected
are directly related.
Figure 6 indicates that the maximum time for a vehicle to pass
through the congested area is just under five minutes. The calculated
values of 4.8 and 5.4 minutes agree reasonable well with this time.
The "delay", or the time for vehicles to traverse the backup is,
for q > s,
*
= 8(.64 - .55)218002
(20)(.44704)
= 22906 vehicle sec
or 143.2 sec average per vehicle;
for s > q *
8C.55 - .40)21Q292
(20)(.44704)
= 22906 vehicle sec
or 55.7 sec/average vehicle
The average over the life of the backup is
2(22906)
(160 + 411)
= 80.23 sec average per vehicle
* Some of the numbers in this equation have been rounded.
26
-------
The equations presented above for backup conditions occurring
when demand volume exceeds capacity will be included in the commuter
exposure model. That is important for modeling worst-case exposures,
as well as for providing a more realistic indication of overall commuter
exposure. The example calculations apply to one lane of traffic; a
four-lane expressway with similar conditions in each lane would have a
backup involving 2,284 vehicles.
200 r
150
100
50
°7:00 7:'
Demond >copocity - 30 min
10
7:20 7:30 7:40 7:50 8:00
2,000 r
«»
I ',500
I 1,000
500
Duration of congestion * 45 min^*
/V£]167 vehicles
,''5min
p^ Copocity ' --«2,000 vpn
7.00 7:10 7:20 7:30 7-40 7:50 8:00
T.'me, A.M.
3
FIGURE 8 Relation between demand, capacity, and congestion.
2. Interrupted Flow
Interrupted flow pertains to traffic conditions when movement is
routinely stopped, or interrupted, for a finite period of time. For
the purposes of a commuter exposure model, only two causes of interrupted
27
-------
flow need be considered: signalized intersections and toll booths. At
those two locations of interrupted flow, traffic goes through mode changes
from cruise to deceleration, idle, acceleration, and back to cruise.
Emissions, and hence concentrations, and times of exposure are influenced
by those mode changes.
Comparisons of emissions estimates made using the Modal Analysis
Model and the FTP methodology have shown good agreement except at low
average route speeds. That is to be expected because as the average
route speed increases, more driving time is spent at or near the average
route speed, and there are fewer changes of driving mode. At lower speeds,
however, there is an increasing array of mode and speed combinations that
can produce the same average speed, and the FTP methodology does not fully
account for that. As a result, the commuter exposure model will include
traffic modeling capabilities for both average route speed and mode changes
for interrupted flow conditions. The average route speed methodology will
be used outside of the CBD, while the modal methodology will be used inside
of the CBD. The reason for this choice is that speeds are likely to be
lowest and mode changes most frequent within the CBD, and the difference
among emission estimates most pronounced. Although the use of the average
route speed/FTP methodology for interrupted flow conditions outside of the
CBD does not provide the spatial detail that the modal treatment can give,
that is not crucial for a commuter exposure model, because exposure is
time-integrated along the pathway. Using an average route speed temporally
smooths emissions instead of concentrations.
Average route speed will be an input parameter. The local
transportation agency should be able to offer advice on average route
speed estimates for interrupted flow portions of pathways. As a default,
the curves in Figure 7 should be fit to equations for inclusion in the
model. The curves rely on volume-to-capacity ratios as input, and they
estimate an average speed for coordinated and uncoordinated traffic signals.
As a comparison with Figure 7, which is based on national data, Figure 8
shows site-specific curves specifically for the Washington, B.C. metro-
politan area. If a transportation agency cannot supply average speed data,
they may be able to provide curves similar to those in Figure 8, but based on
data from the local region.
28
-------
URBAN AND SUBURBAN ARTERIALS
0 . 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
FIGURE 7 TYPICAL RELATIONSHIPS BETWEEN V/C RATIO AND AVERAGE OVERALL TRAVEL
SPEED, IN ONE DIRECTION OF TRAVEL, ON URBAN AND SUBURBAN ARTERIAL
STREETS
FIGURE 8 OPERATING SPEED RELATED TO LEVEL OF
SERVICE, ROUTE TYPE VOLUME/CAPACITY
RATIO AND RING
29
-------
A more thorough analysis is warranted for CBD pathway segments.
Calculations must be made of driving mode changes, the proportion of
vehicles changing modes, and the length of time spent in the different
modes. Basically, that requires a calculation of queue lengths and delay
at intersections. The parameters required are demand volume, capacity,
and the traffic signal parameters of cycle length and the length of the
green phase. Queue length and delay data can then be used to calculate
modal emissions.
Ideally, capacity, volume, and signal parameters will be obtained
from the local agency and input directly to the model. However, given
the demand volumes on the intersection approaches, the geometry of the.
intersection, and the composition of the traffic as described below, first
the capacity and then the signal parameters (and then queue length and
delay) can be calculated. The following discussion explains how this
may be done. The commuter exposure model will call on the user to supply
capacity, but will have the default option of performing the remaining
calculations of signal parameters.
Any at-grade intersection approach has a capacity that represents
the maximum number of vehicles that can be accommodated, given the par-
ticular geometry, environment, and traffic characteristics and controls.
The capacity service volume of an intersection approach is the maximum
number of vehicles that can pass through the intersection during one hour
of green time. The number of vehicles that can clear the intersection
from an approach during one hour of elapsed time can be calculated by
multiplying the fraction of the total cycle time that the signal is green
. by the capacity service volume.
The capacity service volume in vehicles per hour of green is
determined using the nomograph, Figure 9. The user must know the percentage
of trucks and buses, left turners, right turners, the location within the
metropolitan area, the size of the metropolitan area, and whether or not
the intersection is located in the CBD. The nomograph provides a solution
for a two-way urban street with parking. The solution for that type of
interesection is the most conservative estimate of capacity in the Highway
Capacity Manual. If a street has no parking within 250 feet of the
interesection, eight feet can be added to the curb-to-center line width
30
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TAIU I Mf • M(nO»OUtAN SIZI AND H*« MOUt PACTOI AOJUSTMlNT
o
I
MinofOu'AN
AMAK*. (1000- 1)
Qrv 1000
1000 ,
750
MO
J7J
MO
175
100
71
«A« HOU« rAcroi
0.70
1.00
fl.»7
O.N
O.»l
O.l»
O.M
O.M
O.M
0.77
0.75
1 SJ
I.Q2
o.w
0.9J
0.»3
0.91
O.U
c.»:
o.e
O.M ! O.U | 0.90
l.tfli .14
1.07 .11
1.04 | .39
1.01 .06
O.M | .03
O.W ! .00
0.« ! 0.»7
0.90 ' 0.74
0.17 1 O.»l
.!»
.1*
.13
.11
.01
.05
.02
O.W
O.W
O.f] 1 1.00
.14 .M
.Jl ' .77
.11 .23
-IJ
.12
.10
07
.04
1.01
.»
.17
.14
.11
.Of
.0*
77/s
77s
20
*y /.
lu
tf>
1200 >
u
800 |
u
SA-4439-2S
FIGURE 9 SERVICE VOLUME OF A SIGNALIZED INTERSECTION APPROACH
31
-------
(Wa) and a conservative solution will still result from use of the
nomograph.
The approach capacity, C, is determined by multiplying the
capacity service volume by the G/Cy ratio for the approach. The green
phase time, G, and cycle time, Cy, are determined by Webster's "Traffic
Signal Settings". Webster's equations provide enough cycle time for
the vehicle demand volume to proceed through the intersection; however,
the user must ensure that G for each phase is long enough for pedestrian
crossings. To determine Webster's optimum cycle length, the critical or
maximum volume to capacity service volumes must be determined for each
phase. The maximum volume to capacity service volume for phase i is
written as
Max [v.,./Cs. .1
• L i'j i,ji
and refers to those V/Cs ratios for approaches or lanes of approaches on
which traffic moves on phase i. For example, if approaches 1 (i=l) and
3 (i=3) to an intersection move on phase 1 (j=l) of a signal, then
Max [v. ./Cs. .1 = Max fvi /Cs V /Cs, 1 ,
£ I i,J i,jJ L 1,1 1,1 3,1 3,U
and if phase 1 above is a left-turn phase, and phase 2 controls through
and right-turning traffic on Approaches 1 and 3, then
Max [V. ./Cs. .1 = Max [v /Cs , V /Cs 1
i L X'J J-.JJ I !>2 l>2 3>2 3'2J •
In the above example, V is the left-turn volume demand for Approach 1
J-) *•
and Cs is the capacity service volume for left-turning traffic from
1 > •'•
Approach 1; similarly, V is the through and right-turning volume demand
J- > ^
for Approach 1 and and Cs is the capacity service volume for through
1 > ^
and right-turning traffic on Approach 1. The optimum signal cycle length
is determined using the following equation:
(9 Np + 5)
Cy =
1 - Z Max fV. ./Cs. .
all i i
32
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where
Np = the number of amber intervals per signal cycle during which
there is no simultaneous green phase.
9 = a constant representing a weighted lost time in which three
seconds of amber time and three seconds of start-up time are
assumed.
. » t.T_
V. . = the volume on the i approach that moves during the j signal
green phase.
Cs. . = the capacity per hour of green to vehicles on the i approach
1>J • j • u -th • i u
moving during the j signal phase.
The green phase length is a fraction of the signal cycle time minus the
total amber time. A three-second amber time is assumed for all green
phases. (A three-second amber time is usually adequate for roadways with
a speed limit less than or equal to 35 mi/hr. A four-second amber time
is applicable for speeds of 35 to 50 mi/hr, and a five-second amber time
is applicable beyond 50 mi/hr.) The green phase length of phase j is
given by the following equation:
r I
Max iv. ./Cs. .1
G. = Cy l ' Ma}, n,r^ i- - 3
all j i
'j ^y I Max [V. ./Cs. .T
' ' ' i.JJ
where
• Max IV. ./Cs. . is the maximum V/Cs ratio on all approaches i
i I i.J i.JJ
moving on green phase j .
• 3 is an assumed 3-sec amber time
_Z . V. ./Cs. . is the sum of the V/Cs ratios that control
the green phase durations.
The approach capacity is found by multiplying the approach
capacity service volume by the appropriate green to cycle ratio and summing
for all applicable phases. Since an approach is considered to be one
direction of flow into an intersection, separate left-turning, through,
33
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and right-turning signal phases affecting one approach should have their
capacities added together to determine the total capacity of an approach.
The capacity of an approach is given as follows:
C. = E Cs. . Gj/Cy
where j are those green signal phases that allow traffic to move on
intersection approach i.
Examples of controllers for which this methodology is applicable
are three-and four-phase controllers, which have a preceding left-turn
green indication, three-and four-phase controllers with one or two left-
turn phases, and eight-phase controllers with possible overlapping left-
turn and through phases (i.e., multiple phases) on all opposing approaches,
Usually the signal cycle time is the sum of the green phase times and
amber times for all phases. When overlapping phases occur, the cycle
time is the sum of the left turn and through phases plus amber time, when
there is no simultaneous green indicator. The capacity of an approach is
the sum of the capacities for each through or turning movement on the
approach.
Once capacity, volume, and the signal parameters are known,
the proportion of vehicles that stop for a signal is given by
1-G/Cy
1-V/Cs
where G = length of the green phase
Cy = signal cycle length
V = hourly demand volume
Cs = capacity service volume per hour of green.
The number (N) of vehicles subject to queueing delay is:
N =
3600
while the maximum length of the queue (Lq, m) is:
Lq = 8N/M
where 8 is the distance (meters) occupied by each queued vehicle and M
34
-------
is the number of lanes in the approach. On the average, a stopped vehicle
waits one-half the length of the red phase, so the average delay to those
vehicles is
D = 0.5 (Cy-G).
For toll booths, the methodology is different because all
vehicles must stop and wait to be served. The average number of vehicles
waiting to leave a toll booth is computed from classical queueing theory as
V
N ~ C-V.
The queue length in meters is
_ 8N
The average delay for vehicles at a toll booth is the queue
length (vehicles) multiplied by the average service rate, or inverse of
capacity:
D = 3600 N
C •
Note that this applies to all vehicles because all must stop.
The methodology presented in this section has been demonstrated
for air pollution work in a number of studies. While there are other
more complicated methods of handling traffic flow modeling, the approach
recommended here has been found to be quite suitable for air pollution
work.
When the commute paths enter the CBD, and the queueing calcula-
tions are applied, single routes must be chosen for each commute path,
terminating at a reasonable location. This could be a central point in
the CBD, or there could be a separate terminus for each path, such as
locations of relatively high employment density within the urban core.
For paths not going to the CBD, the end points should be clear because
they had to have been identified already in order to support a commute
path not involving the CBD.
35
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D. Emissions Modeling
The model user will have the option of inputing emission rates for each
pathway segment and grid square directly or of having the model compute
the emission rates. If emissions are to be computed, two types of emissions
treatments are required of the commuter exposure model: a treatment based
on the average route speed, and one that considers the effects of driving
mode changes on emissions. The first treatment is given by the familiar
FTP procedure. The second treatment will use the "Automobile Exhaust
Emission Modal Analysis Model," or modal model. Emissions modeling along
pathways requires both treatments; FTP-based emissions estimates are
suitable for non-pathway sources.
1. Emissions on Pathways
Figure 10 is a flowchart illustrating the modeling procedures
for pathway emissions. FTP emission factors will be used for pathway
segments that are freeways, expressways, or arterials outside the CBD.
The FTP methodology requires the following input parameters as a minimum:
altitude, state (California or other), calendar year, vehicle model year
mix, and vehicle type mix. Vehicle mix data may be obtained for a given
location from state or county agencies or from R. L. Polk, or national
average data may be used.
The basic FTP emission factors assume an average route speed
of 19.6 mi/hr, an ambient temperature of about 75°F, and 20 percent cold-
starting, 27 percent hot-starting, and 53 percent hot-transient vehicles.
When conditions depart from these assumed values, a combined speed-
temperature-cold start correction factor will be applied. All other FTP
correction factors (e.g., air conditioning, trailer towing) will be
assumed to have a value of unity.
For the purposes of the commuter exposure model, it will be
assumed that no vehicles are operating in the cold-start mode while
they are on freeways, expressways, or pathways outside of the CBD. While
cold-start emissions might affect background concentrations by their
impact on network-wide emissions, travel to the pathways in the morning
is assumed to take place on roadways having relatively low on-roadway
concentrations. In the evening, vehicles are assumed to be warmed up by
the time they leave the CBD or enter a freeway or expressway.
36
-------
FREEWAY
OR
XPREiJSWAY
APPLY FTP
EMISSION FACTOR
BASED ON SPEED
APPLY MODAL EMISSION
FACTORS TO FIND
CRUISE AND EXCESS
EMISSIONS FACTORS
USE MORNING
AND EVENING
VOLUMES TO
COMPUTE AM
AND PM
EMISSION RATES
USE VOLUME
TO COMPUTE
EMISSION RATE
APPLY TEMPERATURE
AND COLD START COR-
RECTION FOR EVENING
EMISSION FACTOR
APPLY TEMPERATURE
AND COLD START
CORRECTION
ADD EMISSION
FACTORS FOR
TWO DIRECTIONS
USE MORNING AND
EVENING VOLUMES TO
COMPUTE AM AND PM
CRUISF AND EXCESS
EM'SSION RATES
USE VOLUME TO
COMPUTE CRUISE
AND EXCESS
EMISSIONS RATES
TIME AVERAGE CRUISE AND
EXCESS EMISSIONS RATES
FOR AM AND FOR PM
TIME AVERAGE
CRUISE AND EXCESS
EMISSIONS RATES
ADD EMISSION
FACTORS FOR
TWO DIRECTIONS
FIGURE 10. FLOWCHART OF PATHWAY EMISSION MODELING PROCEDURE
37
-------
When there are no cold-starting vehicles, the combined cold-
star t-tetnperature-speed correction factor loses its temperature dependence
and become a function of speed only. To reduce repetitive calculations,
the model will compute emission factors for speeds of 10 to 60 mi/hr in
increments of 5 mi/hr; estimates of speed will be rounded to the nearest
5 mi/hr. That is well within the accuracy of the speed estimation procedures,
Therefore, 11 FTP emission factors, corresponding to 11 speeds,
will be computed for pathways for both the short-term and annual modes
of model operation. A computer program of the FTP methodology is available
from EPA; it can be adapted for use in the commuter model.
The mechanics of model operation will proceed in the following
way. For each non-CBD, freeway, or expressway segment of a pathway, the
following equation will be used to compute emissions:
= EV
Q (3600)(1609)
where Q - emissions rate, g/m/sec
E = FTP emission density, g/vehicle-mi.
V = demand volume, vehicles/hr
3600 = sec/hr
1609 = m/rai
The emission density, E, will be chosen from the previously computed
table, according to average route speed. To compute the average emission
rate over a segment having congested flow, it is convenient to break the
emissions into two components: (1) those occurring during normal flow,
E, and (2) the excess over normal flow emissions that occurs during
congested flow, E'-E, where E' represents the emissions during congested"
flow. The component of total emissions due to uncongested flow is given
by the above expression for Q, with E chosen according to the average
route speed on the uncongested portion of the segment. The component
due to congested flow is
n, (E'-E) N
Q = — , g/m/sec
1609 T
38
-------
/%
where E' corresponds to an average route speed of 20 mi/hr and T is the
duration (sec) of the backup. The average emission rate over the
pathway segment is calculated as
T T n O '
Q*vg = Q + 3600 L ' 8/m/sec
where L = segment length, mi
Lq = backup length, mi
= 0.01 N.
Substituting for Q and Q' and reducing, the expression for Qavg ^s
EV + (E'-E)N Lq/L
Qavg " (1609M3600)
In the annual mode, the model will compute two emission rates,
using the volumes of the morning and evening commutes. In the short-term
mode, the model will compute only one emission rate, appropriate to the
volume of the hour during which the "average" commuter travels the segment.
Travel on arterials within the CBD is characterized by interrupted
flow and low speeds, and a modal emissions treatment should be used. This
is available through an adaptation of EPA's modal model.
The modal model determines an instantaneous emission rate, e(t),
which is a function of vehicle speed, v, and acceleration, a. Since speed
and acceleration are functions of time, the emission rate function can be
expressed as
e(t) = 4 [v(t), a(t)] .
Acceleration to or from a given speed is assumed to be a perturbation
to the steady-state emission rate, and two equations ar§ used to describe
the emission rate:
2 2 2 2 ? 2
eA(v,a) = b1 + b2v + b a + b^av + b v + b,a + b av + bga v + b a v (A)
and
eg(v,o) = b1Q + bnv + t>12v2, (B)
where the first equation describes the non-zero acceleration emission
rate and the second describes emission rates for steady speeds. Note
that the idle emission rate equals the coefficient b .
39
-------
Inputs to the modal model include calendar year, vehicle model
year mix for various locations (low or high altitude, California or outside
California) and second-by-second speed data for the driving sequence being
modeled. The two preceding equations are solved for each second, the
results are taken as one-second integrated emissions, and the model output
is the total emissions over the driving sequence. Eighteen vehicle groups
can be included in the vehicle mix; deterioration as a function of calendar
year is included in the emission calculations. The 18 groups are listed in
Table 6.
Second-by-second speed profiles are inconvenient input data for
roadway air-quality modeling. As a result, the basic modal model has been
Q
modified to accept and calculate more appropriate parameters. Patterson
modified the model to accept inital and target speeds and acceleration or
deceleration as inputs, and to calculate an emission density (g/m) over
successive eight-meter lengths of roadway. The distance of eight meters
was chosen for convenience because it is the average distance occupied by
9
a queued vehicle. Time was entered from traffic modeling data. Sandys
used the median speed during deceleration or acceleration as the basis
for a modal emission calculation that was assumed to be an average value
for the mode. Inputs were speed, and acceleration or deceleration. In
other work, Patterson computed emissions during acceleration and decel-
eration in a one-step process by integrating the instantaneous emission
rate over time. That approach yields almost the same result as using the
median speed, but it recognizes the nonlinear speed dependence of the
fifth, seventh, and ninth terms of the instantaneous emission rate equations.
Modeling the effects of modal emissions is facilitated through the
introduction of the concept of excess emissions. Excess emissions are
those that occur over and above those that would have occurred had the
vehicle not stopped. The acceleration or deceleration parts of excess
emissions are then the difference between the acceleration or deceleration
emissions given by equation (A) and the cruise emissions calculated by
equation (B). Similarly, the idle part of excess emissions is the difference
between the idle emissions, given by the coefficient bin of equation (B),
and the cruise emissions. The emissions during acceleration or deceleration
40
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Table 6
VEHICLE GROUP DESIGNATIONS
Group 1 - 1957-1967 Denver
Group 2 - 1957-1967 low-altitude cities (non-California
1966, 1967)
Group 3 - 1966, 1967 California
Group 4 - 1968 low altitude cities (49-state)
Group 5 - 1969 low altitude cities (49-state)
Group 6 - 1970 low altitude cities (49-state)
Group 7 - 1971 low altitude cities (49-state)
Group 8 - 1968 Denver
Group 9 - 1969 Denver
Group 10 - 1970 Denver
Group 11 - 1971 Denver
Group 12 - 1972 Denver
Group 13 - 1973, 1974 Denver
Group 14 - 1972 California
Group 15 - 1973, 1974 California
Group 16 - 1972 low-altitude cities (49-state)
Group 17 - 1973, 1974 low-altitude cities (49-state)
Group 18 - 1975 low-altitude cities (49-state)
41
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are found by assuming that acceleration is constant, converting speed to
a function of time, v = at, substituting in equation (A), and integrating
over the time, T, to come to a stop or to reach cruise speed:
T
Total acceleration _or . A (v(t) )dt .
deceleration! emissions J A.
o
The cruise emissions that would have occurred had the vehicle not stopped
are found by integrating e over
T/2
Cruise emissions = I e (v(t),o)dt, grams.
o
For one vehicle, the acceleration and deceleration parts of the excess
emissions, E.n, are, assuming acceleration equals deceleration:
T T T/2
r r
E.
AD
= AA(v(t),a)dt + I e (v(t),-a)dt - 2 j es(v(t),o)dt
Idle emissions must be added to EAr. to arrive at the total excess emissions.
AD
The values for total excess emissions, E , in units of g/m/sec. are cal-
t
culated as
(E»r> N b1nD DVP
AD 10
-CT~ 3600
The cruise emissions component may be calculated by
e V/3600
E
C v 1609.344/3600
where 1609.344 is the number of meters in a mile. For calculating con-
centrations, note that the total excess emissions, E will be averaged
E
over the queue length. The cruise emissions component occurs at all
points along the roadway.
Operationally, the values of E will be calculated once and
stored for inital and target speeds of 0 to 30 mi/hr in increments of 5 mi/hr.
Acceleration and deceleration may be taken to be a constant 2.5 mi/hr/sec,
o 2
based on work by Patterson0 and Ludwig . The inital speed for deceleration
42
-------
and the target speed for acceleration will generally be the same across an
intersection. If the two speeds differ, the lower speed may be chosen to
provide a conservative estimate when choosing a value for E based on speed.
Once emissions are calculated with the modal treatment, they should
be averaged for each link or pathway segment. To do this, the total excess
emissions (excess per vehicle times the number stopping), E£ , are multiplied
by the queue length, the cruise emissions are multiplied by the link length
and the results are added and divided by the length of the link. This can
be expressed as :
E
avg
E Lq + Ex
where E = average emissions on link, g/io/sec
Lq = queue length, mi
x = link length, mi
E = excess emissions per stopping vehicle, g/m/sec
tli
E = cruise emissions per vehicle, g/m/sec.
The discussion on FTP emissions estimates mentioned the exclusion
of cold-start (and therefore temperature) corrections, because vehicles
were assumed to be wanned up on a freeway, expressway, and non-CBD
arterial segments of the pathways. In the evening, vehicles leaving
the CBD cannot be assumed to be warmed up, and correction factors must
be applied to the emissions estimates. The EPA methodology for cor-
recting modal emissions for cold-starts and temperature involves the
use of the FTP combined speed-temperature-cold-start correction factors.
A modal correction factor is found by taking the ratios of the FTP
combined correction factors. The numerator of the ratio is the FTP
correction factor computed for the temperature and percentages of cold-start,
hot-start, and hot-transient vehicles of interest and the roadway's average
route speed. The denominator of the ratio is the FTP correction factor
43
-------
for the the same temperature and average route speed, but with completely
warmed-up vehicles. The commuter exposure model will compute this ratio
for the input percentage of cold-starting vehicles. If the model is in
the annual mode, the percentage of cold-starts will be for the evening
commute in the CBD, and an annual average temperature for the evening
commute period. If the model is in the short-term mode, the percentage
refers to the single commute being analyzed, and the average temperature
of that commute.
For both modes of operation, the correction factor will be
computed for speeds from 0 to 30 mi/hr in increments of 5 mi/hr. Then, for
each pathway segment, the correction factor for the appropriate average
route speed will be used.
Another factor that must be considered for the modal model is
a combined calendar-year/heavy-duty vehicle correction factor. The modal
model is applicable to vehicles through 1975, and a correction must be
made for later years. Also, because the modal methodology considers only
light-duty vehicles, a factor that accounts for the vehicle type mix must
be included, A correction factor to account for all of these considerations
could be developed by: (1) making a number of computations for various
conditions with the modal model using the future year deterioration factors;
and (2) using the FTP methodology to compute ratios of composite emissions
to light-duty vehicle emissions for various vehicle type mixes for different
calendar years. A large number of computations would be involved, but
similar factors have been developed with the use of the previously accepted
FTP methodology. The correction factors developed in this way would be
stored in the model and applied to estimates of modal emissions.
The user will have the option of inputing emission rates for each
payment segment directly, and if that option is exercised, the emissions
module described above will be bypassed. The direct input option may be
particularly useful if a pollutant other than carbon monoxide is to be
modeled.
44
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2. Non-Pathway Emis s ions
Unless non-pathway emissions are input indirectly, emissions
from primary and secondary traffic in the grid squares will be computed
with the use of the latest FTP methodology. As mentioned under the
discussion of pathway emissions, the methodology requires the following
parameters :
• Calendar year
• Model year mix
• Vehicle type mix
• Average route speed
• Ambient temperature
• Percentage of cold-starting, hot-starting, and hot-transient
vehicles.
The calendar year, the vehicle type mix, and the model year mix will be
input and fixed over the time period over which exposures are to be computed
(up to one year). For non-pathway emissions, the standard FTP average route
speed of 19.6 mi/hr will be assumed in computing the combined speed-temperature-
cold start correction factor. All other correction factors in the FTP
methodology will be assumed to be unity for non-pathway sources.
When the commuter exposure model is in the annual mode, average
annual morning and evening temperatures will be used in the combined
correction factor. A table of percentages of cold-starting, hot-starting,
and hot-transient vehicles, varying according to time of day (morning or
evening), and locale type, will be stored in the model and used in computing
the factors. The emissions module will be called once, and it will compute
10 emission factors: for the morning commute's temperature and five cold-
start percentages (for the five locale types); and for the evening commute's
temperature and five cold-start percentages. The model will enable the
user to compute morning and evening emission rates for each grid square
by: (1) choosing the emission factor appropriate to the time of day and
the grid square's locale type, (2) multiplying the factor by the VMT of
the grid square, (3) multiplying the total by the percentage of the daily
VMT appropriate to the average hour of the commute, and (4) dividing the
total by the area of the grid square.
45
-------
When the model is in the short-term mode, the average temperature
and cold-start percentages (for each of the five locale types) specific
to the commute being analyzed will be input to the model. The emission
module will compute an emission factor for each locale type, and the
model will compute an emission rate for each grid square in the same
manner as described previously for the annual mode of operation.
When daily gridded emissions are input directly, they must be
converted to emission rates for the average commute hour. In the annual
mode, percentages of daily traffic appropriate to the average morning
and average evening commute hour will be applied to the daily rate for
each square, in order to produce gridded morning and evening emissions.
For the short-term mode, the percentage of daily traffic appropriate to the
average hour of the commute being analyzed will be applied to each gridded
emission rate.
46
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E. Dispersion Modeling
1. Dispersion of Pathway Emissions
a. Limited-Access Roadways
To compute the dispersion of pollutants from limited-access
roadways, a semi-empirical approach will be followed, patterned after the
ROADMAP model of Dabberdt. The model formulation is based on the treat-
ment of pollution dispersion as the vector sum of two components:
(1) dispersion occurring along the horizontal wind component oriented
perpendicular to the roadway; and (2) dispersion along the horizontal
wind component parallel to the roadway. It is assumed that there is no
vertical transport by a non-zero mean vertical wind component. Figure 11
illustrates the coordinate system for a one-way road.
The two-component dispersion formulation can be written as:
XTU
iXnu
JXV
where
i = unit vector normal to roadway
j = unit vector parallel to roadway
U = vector wind speed (m/sec)
u = wind component normal to roadway (m/sec)
v = wind component parallel to roadway (m/sec)
Q = line source emission rate (g/m-sec)
X = total pollutant concentration (g/m )
X = concentration from lateral dispersion (g/m )
n
X = concentration from longitudinal dispersion (g/m ).
When 9 is introduced as the angle between the longitudinal axis of the
line source and the wind vector, then
u = D sin 6. and
v = U cos 6.
Substituting and squaring both sides,
XTU
QI
2
X U sin 6
n
Ql
2
+
xp u cos e
QI
47
-------
\
\
\
FIGURE 11. ILLUSTRATION OF A LIMITED-ACCESS ROADWAY SEGMENT SHOWING
PARAMETERS USED IN DISPERSION COMPUTATIONS
48
-------
For convenience, the first right-hand term in the above equation is
designated the "perpendicular" term and the second, the "parallel" term.
The form of the perpendicular term is specified in analogy
to the Gaussian line source equation for a perpendicular wind,
X U
n
A
V2/if"
a
z
exp
[-• (- * •')!
2 I a J
L \ «/.
where o" ~ vertical Gaussian dispersion function (m)
Z
z = height of the receptor above grade-level (m)
z' = height offset from plume rise (m).
The term z1 serves as a height-modifier to represent the possible
change in the height of the plume centerline as a function of distance
downwind. This offset could result either from the aerodynamic influence
(i.e. shelterbelt) of the traffic stream or from the buoyancy effect
of vehicular waste heat emissions.
The parallel dispersion term was formulated to represent the
general features of the Gaussian point source equation when the latter
is integrated for a wind aligned parallel to a semi-infinite line
source. The resulting formulation may be thought of as a type of ex-
panding-box model whose sides and top are given as exponential functions
of height (z) and cross-roadway distance (x) . The form chosen assumes
the same functional dependence on height as the perpendicular term, but
a different cross-roadway dispersion representation (f ) ,
XpU
exp
-1
2
' z + z' 1
i °Zj
2"
49
-------
where a = a _ + a., x 1 ,
z' = z' + a, x b2
° b
f - a3 (c3 * 25) 3
and W = roadway width (m).
The parameters that this dispersion treatment will require,
either as model input, or from the traffic and emissions portions of the
model, are the pathway segment emission rate, roadway width, wind speed,
wind direction, and atmospheric stability. All other parameters in the
dispersion formulation can be incorporated in the model of the preceding
variables, those that vary with time are emissions, wind direction, wind
speed, and stability. Concentration can easily be normalized with respect
to wind speed. Thus, wind-speed-normalized concentrations on limited-access
roadways will be a function of emissions, wind direction, and stability.
b. Non Limited-Access Roadways
The dispersion of pollutants emitted by vehicles on non-
limited-access roadways will be computed by a technique taken from the
12
CALINE 2 model. "The technique is similar to the limited-access roadway
dispersion treatment described in the previous subsection, but is more
suitable for modeling dispersion on non-limited access roadways because
it does not include terms (that are in ROADMAP) that describe the enhanced
vehicle waste heat emissions, mechanically induced turbulence, or the
"shelterbelt" effect present on freeways. Because of these terms, it is
doubtful that ROADMAP could accurately predict concentrations at locations
where low speed driving controlled with signals is practiced. The concen-
tration is separated into cross-wind and parallel wind components. The
major difference in the formulations is in the consideration of the parallel
wind components. The parallel wind model in CALINE 2 assumes that the road-
way is divided into a series of square area sources as wide as the roadway.
The concentration downwind of the area source is computed as if the emissions
50
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originated from a virtual source upwind of the area source. The distance
from the center of the area source to the virtual source is set so that
the model is forced to assume a uniform concentration within a mixing
cell over the roadway.
The equation used to compute the normalized concentration
from each area source is:
Y U
P
^
*p We os2 9
— i ^
a c
y z
1 ^ y
exP 1 ~ o a
1 y
where
P
U
^
w
concentration from parallel dispersion (g/m )
wind speed (m/sec)
line source emission rate (g/m/sec)
roadway width (m)
angle between wind direction and roadway
y = perpendicular distance between receptor and roadway
edge plus an initial dispersion parameter (m)
. z = height of the receptor above grade-level (m)
a = horizontal dispersion function (m)
y
o = vertical dispersion function (m).
The number of area sources used is equal to one-half mile
divided by the width of the roadway. The concentrations from each area
source are summed to give the parallel component, which, in CALINE 2, is
then corrected by a stability-dependent factor that increases the line
source length to five miles. Correction factors for roadways of different
lengths will be derived and incorporated in the commuter exposure model.
The cross-wind or normal component of concentration is
given by:
exp
51
-------
o
where X = concentration from normal dispersion (g/ra ).
The parallel and crosswind components are summed to give
the total concentration when 6 is non -zero.
As in the dispersion treatment for limited-access roadways,
wind speed normalized concentration will be a function of emissions, wind
direction, and stability.
A note should be made here concerning the use of CALINE2
for computation of dispersion on non-limited access roadways. It appears
that a further update of the model, to be called CALINE3, will soon be
released. This model should be examined for its potential applicability
to the commuter exposure model.
One of the problems encountered with virtually all existing
dispersion models is that they do not predict concentrations on the road-
way. The ROADMAP and CALINE2 models were chosen for this application
because they can predict the concentration at the edge of the roadway or
in a mixed cell over the roadway. The effects of this limitation should
be examined using actual data gathered in a field program designed to study
this problem.
c. Street Canyons
Dispersion on a roadway with tall buildings on both sides
is greatly influenced by the presence of the buildings. The street-canyon
dispersion treatment to be used in the commuter exposure model is basod
13
on the empirical street-canyon model developed by Johnson et al. and
modified by Ludwig et al. . Their studies give evidence of a helical air
circulation in street canyons, as illustrated in Figure1 12. The concen-
tration arising from street-canyon emissions on the leeward side of buildings
is given by:
\~
52
-------
where
X = concentration on leeward side of street (g/m )
X/
Q = line source emission rate (g/m/sec)
K = empirically derived nondimensional constant=2?
U = wind speed (m/sec)
x and z = horizontal and vertical distance of the receptor
relative to the center of the traffic lane (m)
L = dimension representing vehicle size ~ 2 m.
The concentration on the windward side of the street is given by:
KG, (H-z)
where
X.. =
w W(U+0-5)H
Xw = concentration on windward side of street (g/m )
H = average building height (m)
W = street width (m).
BUILDING
MEAN
WIND
IU)
BACKGROUND
CONCENTRATION
TRAFFIC
LANE
-W-
FIGURE 12 SCHEMATIC OF CROSS-STREET CIRCULATION BETWEEN BUILDINGS
53
-------
In the commuter exposure model, the concentration on the
roadway will be assumed to be the average of the concentration on the
windward and leeward sides of the street. Since the receptor is on the
roadway, x and z are zero.
Substituting, and combining the above equations gives:
KQ,
2 |(U+0.5)LQ WCU+0
1
.5)J
2(U+0.5)
Since W is usually considerably larger than L , the 1/W term
is small in comparison with the 1/L term. Considering this, the concen-
tration relationship resembles that of a box model.
Thus, concentrations in street canyons are described by the
time-dependent parameters of emissions and wind speed.
d. Computation of Concentration Statistics
The three dispersion methodologies discussed previously
will be used to compute exposures resulting from pathway sources when the
commuter exposure model is run in either the short-term or the annual mode.
The differences in the mechanics of model operation between the modes are:
(1) the number of meteorological and traffic conditions for which exposures
are computed; and (2) the treatment of a commute as a time period with fixed
meteorology and emissions, or as a period during which meteorology and
emission rates may vary with time. The following discussion explains the
mechanics of dispersion computations for the two modes of operation. The
flowchart in Figure 13 illustrates the dispersion computation procedure
for pathway sources.
When the commuter exposure model is run in the short-term
mode, it will make computations of concentrations resulting from pathway
sources in the following manner. Beginning with the first segment of the
54
-------
H
_ jo
—
a'os
Idf
is-:
•" I-
I COMPUTE CONCEN-
TRATION (LIMITED
ACCESS TREATMENT)
ON SEGMENT USING
WIND DIRECTION.
SPEED. AND
STABILITY OF
APPROPRIATE HOUR
o
>
cc
o
o
CO
«—
u
OC
D
55
-------
first pathway, it will determine whether the segment is a limited-access
roadway, a street canyon, or a non-street-canyon, non-limited-access roadway,
Using the input wind speed, wind direction, and stability, and the emission
rate generated by the emissions module, the appropriate dispersion treatment
will be used to compute the concentration on the segment. (If the segment
is a street canyon, only the wind speed and emission rate are required.)
Then, the concentration is multiplied by the travel time on the segment
to yield an exposure on the segment. The model will repeat the procedure
for each segment of a pathway and sum the segment exposures to produce a
pathway exposure. When each new segment of a pathway is encountered, the
model will check the travel time on the pathway before the start of the
segment, and use the meteorology appropriate to the hour during which the
segment will be traveled. The model will cycle through all pathways and
calculate an exposure from pathway sources for each pathway.
When the model is run in the annual mode, it will attempt
to produce exposure statistics representative of the various meteorological
conditions and emissions that occur during a typical year. If a model
individually computed the morning and evening computer exposures for each
day of the year, for several years, to ensure a representative "average"
year's statistics, a very large number of computations would need to be
made, at considerable cost. To avoid that, the numerical model is designed
to compute exposures only once for each combination of conditions.
The parameters that determine the concentration and vary
with time are wind speed, wind direction, atmospheric stability, and
emissions. Concentration can be normalized with respect to wind speed (in
the street-canyon treatment, with respect to wind speed plus 0.5). Thus,
separate computations need be made only for various combinations of wind
direction, stability, and emissions. Let wind direction be divided into
16 classes, stability into five classes, and emissions into morning and
evening values. All combinations of those classes make up 160 cases.
Morning and evening emission rates and travel times will
be passed from the traffic and emissions portions of the model to the
dispersion portion. It will compute exposure in the following manner.
56
-------
As in the short-term mode, it will begin with the first segment of the
first pathway and determine the segment's roadway type. If the roadway
type is limited-access or non limited-access and not a street canyon, the
appropriate dispersion treatment (of the preceding two) will be used to
compute wind-speed-normalized concentrations on the segment for each of
the 160 cases. If the segment is a street canyon, there is no dependence
on wind direction or stability, so normalized concentrations will be computed
for two cases: morning and evening emissions. Once the set of normalized
concentrations is computed, each concentration will be multiplied by the
appropriate travel time on the segment (morning or evening) to produce a
set of exposures on the segment. The model will repeat the procedure for
each segment of a pathway and sum exposures from all non-street canyon
segments of the pathway for each of the 160 cases. Two other sums will
be created for the pathway: the sums of exposures on street-canyon segments
for morning and evening commutes. Those exposures must be stored separately
because they are normalized by wind speed plus 0.5, instead of just wind
speed, as on the non-street-canyon segments. The model will cycle through
all pathways and produce a set of exposures from pathway sources for each
pathway. The 162 values for each pathway (160 exposures for non-street-
canyon parts of the pathway plus the values for the two street-canyon
exposures), along with the 10 exposure values for each pathway resulting
from non-pathway sources (described in the next section) will be used to
develop the annual commuter exposure statistics.
2. Dispersion of Non-Pathway Source Emissions
It is expected that the portion of the total pathway integrated
concentration (exposure) that results from non-pathway sources will be
small in comparison to the portion resulting from traffic on the commuter
pathways themselves. Therefore, a very simple emissions and dispersion
treatment will be used, both to reduce computational time on the computer
and to simplify the data required to be input by the user.
The line-source emissions on non-pathways have been aggregated
into area source emissions from grid squares, according to the methodology
previously presented. The approach to be used to compute the concentrations
57
-------
along the commuter pathways resulting from the area source emissions is the
so-called Hanna-Gifford dispersion treatment. The basic assumption of
the treatment is that the area source strength in a metropolitan area varies
by less than a factor of 10 over distances of a few kilometers. That
assumption permits the horizontal cross-wind dispersion component to be
neglected in comparison with the vertical component. If the area sources
are a gridded system, with grid spacing of one to 10 km, the concentration
in grid 0 can be calculated according to the formula:
• V? 'c^ {". *E Qi
l-b
"• Vf SPbT <«.*£«,- [(H'U1-" - (21-1
where X = concentration in grid 0
Q = emission rate
U = wind speed
Ax = grid spacing
N = number of upwind grid squares
a,b = constants, dependent on stability
and the subscript i refers to the upwind grid squares, with zero denoting
the central square, 1 denoting the square next upwind, and so forth.
The equation can be simplified by taking advantage of the fact
that the influence on X of source areas far upwind from the central area
is small due to the rapid decrease of terms multiplying Q. as i increases
Making the assumption that Q. ss Q , the equation can be approximated in
i o
the following manner:
CO
X = __o
U
where
C =4/~
L-b)
and D = city size. The values of a and b for various stability regimes
are shown in Table 7.
58
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Table 7
VALUES OF THE CONSTANTS a AND b FOR VARIOUS STABILITIES
Stability £ b
Very unstable 0.40 0.91
Unstable 0.33 0.86
Neutral 0.22 0.80
Estimated Pasquill's 0.15 0.75
"D" (average)
Stable 0.06 0.71
Thus, for any point on a pathway, the approximated form of the
equation can be used to compute the concentration from area sources. The
coomuter model will compute those concentrations on a pathway-by-pathway
basis. For a given pathway, the model will take the first segment and
determine which grid squares contain the segment end points. The coor-
dinates of the midpoint of the segment will be generated, and the grid
square in which the midpoint is located will be determined. For each of
these grid squares, a concentration normalized by wind speed will be
calculated according to the relationship discussed above. Concentrations
would be calculated, for example, for the point P.. , P- (the midpoint),
and point P., in Figure 14. The traffic model will have generated the
times at which the average vehicle reaches PI , P , and P . From them,
two travel times can be derived: (1) the travel time from PI to P~,
T , and (2) the travel time from P to P_, called I . Thus,
Tl= C2 ' Cland T2 = '3 - V
The normalized integrated concentration over the segment (the exposure)
is given by:
i= r3 x
u J u
dt.
59
-------
LU
O
z
5
£
o
UJ
UJ
-2-
O
I
cc
O
u.
UJ
g
z
o
LU
CC
o
111
z
U.
LU
CC
D
O
60
-------
Through a stepwise integration, the following relationship results:
i . *- dt + r *-
u / u / u
1 Xl X2 3
= 2 iTTl+r (Tl+T2)+lTT21.
This normalized exposure applies to only one segment of a pathway. The
model will compute similar exposures for all segments of a pathway, and
sum the results to yield the normalized pathway exposure resulting from
non-pathway sources.
When the model is in the annual mode, wind-normalized exposures
on all pathways will be computed for five stability classes and two times
of day (morning and evening). Thus, 10 exposure values will be stored
for each pathway for use in developing the statistics that will describe
commuter exposure.
When the model is in the short-term mode, the exposure on each
pathway for the input wind speed and stability will be computed using the
model-generated emission rate.
Figure 15 is a flowchart showing the treatment of traffic,
emissions and dispersion from non-pathway sources.
61
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READ X OF DAILY TRAFFIC FOR AVERAGE
HOUR OF AM AND PM COMMUTES
READ SECONDARY TO PRIMARY
VMT RATIO FOR LOCALE TYPES
READ GRID SQUARE COORDINATES.
LOCALE TYPE, PRIMARY VMT
COMPUTE SECONDARY VMT AND ADD
TO PRIMARY VMT FOR EACH GRID
CALL EMISSIONS MODULE;
COMPUTE EMISSION
FACTORS FOR 10 CASES
(COMBINATIONS OF 5 LO
CALES AND PM TRAFFIC
DETERMINE AM AND PM
EMISSION RATES
IN EACH GRID
CALL EMISSIONS
MODULE; COMPUTE 5
EMISSION FACTORS
(FOR 5 LOCALES)
DETERMINE EMISSION
RATE IN EACH GRID
1ft COMMUTE PATHWAY
1« SEGMENT OF PATH
NEXT
SEGMENT I
LOCATE GRID SQUARES IN WHICH
END AND MIDPOINT OF SEGMENT LIE
COMPUTE WIND SPEED NORMALIZED
CONCENTRATION AT EACH END AND
AT MIDPOINT OF SEGMENT FOR 10
CASES (COMBINATIONS OF AM AND
PM EMISSIONS AND 5 STABILITIES)
_L
INTEGRATE NORMALIZED
CONCENTRATIONS ALONG SEGMENT
FOR EACH OF THE 10 CASES
COMPUTE CONCENTRATION AT
EACH END AND AT MIDPOINT OF
SEGMENT USING WIND SPEED AND
STABILITY OF APPROPRIATE HOUR
INTEGRATE CONCENTRATION
ALONG SEGMENT
SUM INTEGRATED NORMALIZED
CONCENTRATIONS OVER PATHWAY
FOR EACH OF THE 10 CASES
SUM INTEGRATED CONCEN-
TRATIONS OVER PATHWAY
FIGURE 15.
FLOW CHART OF NON-PATHWAY SOURCE TRAFFIC. EMISSIONS. AND DISPERSION
COMPUTATION PROCEDURE
62
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3. On-Roadway/In-Vehicle Concentration Relationship
A search of the literature has yielded a limited amount of
information about the relationship between the concentration on the road-
way and the concentration within a vehicle. Several papers > > ^
discuss in-vehicle concentrations, but only two references'^, 20 could
be found that presented measurements of concentrations both inside and
outside a vehicle. In one study1^ the pollutants measured were 03, CO,
NO, and NOX; measurements were made on only one vehicle with the windows
closed and the air conditioner set on maximum or normal for most of the
time. The study concluded that concentrations of CO, NO, and NOV inside
X
a vehicle are about equal to that on the outside, while the 63 inside
concentration was a factor of 3 or 4 lower than the outside concentration,
due to decay of 63 on the surfaces within the vehicle. The other study
discussed measurements of particulate lead; levels inside the vehicle
were approximately three-quarters of the levels outside the vehicle.
Therefore, since so little work has been directed toward
establishing a data base suitable for deriving on-roadway/in-vehicle
relationships, both the numerical and manual commuter exposure models
will assume the concentrations at the two locations are identical. The
commuter model will be of most use in predicting carbon monoxide exposure,
and one of the studies discussed above found inside and outside CO con-
centrations to be about equal.
Even if the assumption is made that all of the pollutant outside
the vehicle will find its way inside the vehicle, a question still remains
concerning the time response of the inside concentration with respect to
changes in the outside concentration. Evidently, the response is very
rapid, since both concentrations have been found to be approximately the
18
same. Further reinforcement to this theory is given by Chaney, who
measured concentrations within a vehicle with the windows closed and the
fan on maximum. He often found a distinct increase in CO concentration
when his vehicle was passed by another vehicle. The increase occurred
a few seconds after the passage of the vehicle.
63
-------
When a good body of data becomes available, on-roadway/in-vehicle
concentration relationships will be able to be established. They will most
likely depend on the state of the windows (closed or open), the state of
the fan, air conditioner and heater, the vehicle model, and whether there
is smoking occurring in the vehicle. It appears that for CO, inside and
outside concentrations will be similar. However, it is expected that in
some vehicles, with the windows closed and no ventilation system in
operation, inside concentrations, while responding to perturbations in
outside concentrations, in effect will be filtered.
If on-roadway/in-vehicle concentration relationships were
available, and assuming the correction factor would be directly propor-
tioned to concentration, application of the relationships could be made
in one of two places in the model. If the relationships were a function
of model year, they would need to be applied in the emissions module,
before the individual emission factors for each model year are weighted
by the fraction of travel for each model year. If the relationships
were not model year dependent, they could be applied after concentrations
have been calculated, but before exposure statistics are tabulated.
64
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F. Commuter Exposure Statistics
The exposures to be computed for each pathway for each mode of model
operation were discussed in the previous sections. In addition to the
exposures, the model will store the total travel time or times on each
pathway and the average number of commuters using the pathway. The
commuter exposure statistics to be developed by the model from the
previously computed values and the manner in which the model will compute
those statistics for each mode of model operation are outlined in the
following paragraphs.
1. Short-term Statistics
When the model is run in the short-term mode, commuter exposures
will be output in three forms. One type of output is a list of the exposure
on each pathway for the input worst-case meteorological and traffic condi-
tions and the average and standard deviation of pathway exposure. The
other two outputs are data that can be used to construct a histogram.
The range of exposures found on all pathways will be divided into several
classes. For each class two parameters will be listed: (1) the percentage
of the commuting population (commuting vehicles mutiplied by the average
number of commuters per vehicle) treated by the model that experience
exposure levels in the class; and (2) the probability of experiencing the
exposure levels in the class (i.e., the percentage of time commuters are
exposed to the levels of the exposure class).
The first form of output will be found by simply adding the
exposures on each pathway resulting from pathway and from non-pathway
sources, listing the results, and taking the average and standard deviation
of the values. These numbers will describe the spatial variation of
exposures. The histogram data will be produced by: (1) assigning a
range of exposure values to be included in each exposure class ; (2)
determining in which class the total exposure value on each pathway lies
and assigning the pathway's commuters and travel time multiplied by
commuters (commuter minutes) to that class; and (3) tabulating the number
of commuters and the commuter-weighted travel times in each class.
65
-------
Dividing the number of commuters associated with each class by the total
number of commuters on the pathway network yields the percentage of
commuters exposed to each range of exposure values. Dividing the commuter-
minutes associated with each class by the total commuter-minutes on the
pathway network gives the probability of occurrence of the exposure levels
in each class.
2. Annual Statistics
Two forms of annual statistics from which histograms can be
made will be produced by the model when it is in the annual mode. In
addition, subsets of those statistics may be output at the user's dis-
cretion. The two kinds of annual histogram data that will be generated
are: (1) the percentage of commuters exposed to various classes (ranges)
of exposure; and (2) the probability of experiencing various classes of
exposure (i • e., the percentage of time commuters are exposed to various
classes of exposure).
The manner in which the model will produce both of those types
of statistics is illustrated graphically in Figure 16. The model will
begin with the first pathway. As stated previously, several normalized
exposure will have been computed for each pathway: 160 normalized exposures
arising from non-street-canyon pathway sources (for 16 wind directions,
five stabilities, and morning and evening emission rates); two normalized
exposures resulting from street-canyon sources (for morning and evening
emission rates); and ten normalized exposures resulting from non-pathway
sources (for five stabilities, and morning and evening emission rates).
The model will take the first of the 160 cases (one combination of wind
direction, stability, and morning or evening emissions) and multiply
the exposure by one of six wind speed values. Next, the normalized street-
canyon exposure for the corresponding time (morning or evening) will be
multiplied by the same wind speed plus 0.5. Finally, the normalized non-
pathway source exposure for the corresponding time and stability will be
multiplied by the wind speed, and all three exposure values will be summed.
The model will determine the exposure class in which this total exposure
value lies, and it will multiply the pathway travel time by the number of
66
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1rt PATHWAY
1st CASE
1«t WIND SPEED
MULTIPLY NORMALIZED CASE EXPOSURE BY WIND SPEED,
CHOOSE APPROPRIATE STREET CANYON EXPOSURE FOR PATH-
WAY(AM OR PM) AND MULTIPLY BY WIND SPEED PLUS 0.5; :
MULTIPLY NON-PATHWAY SOURCE EXPOSURE FOR PATHWAY
(AM OR PM, APPROPRIATE STABILITY) BY WIND SPEED ; ADD ALL THREE
DETERMINE EXPOSURE CLASS
WEIGHT NUMBER OF COMMUTERS ON PATHWAY
BY FREQUENCY OF OCCURRENCE OF METEOR -
OLOGICAL CONDITIONS (AM OR PM)
±
ADD TO COMMUTER SUM FOR CLASS I
±
WEIGHT TRAVEL TIME ON PATHWAY BY FRE-
QUENCY OF OCCURRENCE OF METEOROLOGICAL
CONDITIONS (AM OR PM) AND
NUMBER OF COMMUTERS ON PATHWAY
ADD TO COMMUTE-MINUTES SUM FOR CLASS
Yw
NEXT CASE
Yes
Yes
ADD WEIGHTED NUMBER OF COMMUTERS
FOR ALL EXPOSURE CLASSES
DIVIDE NUMBER OF COMMUTERS IN
EACH CLASS BY TOTAL COMMUTERS
ADD WEIGHTED COMMUTE-MINUTES
FOR ALL EXPOSURE CLASSES
DIVIDE COMMUTE- MINUTES IN EACH
CLASS BY TOTAL COMMUTE-MINUTES
c
END
FIGURE t6. FLOWCHART SHOWING HOW ANNUAL HISTOGRAM DATA ARE GENERATED
67
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commuters on the pathway. It then will weight both the number of commuters
(commuting vehicles multiplied by the number of commuters per vehicle)
on the pathway and the pathway commuter-minutes by the frequency of
occurrence of the case's wind speed, wind direction, and stability for
the emission time period (morning or evening). The two weighted numbers
will be stored for the exposure class. The model will then cycle to the
next wind speed and repeat the procedure, then to the next case (of the
160) for each wind speed, and so forth. For each pathway, the weighted
number of commuters will be summed for each exposure class, as will be
the weighted commuter-minutes. Finally, the percentage of commuters in
each exposure class will be found by dividing the number in the class by
the total commuters; percentages of commuter-minutes (probabilities) will
be found similarly.
If the user desires one or more subsets of the preceding infor-
mation, he may request it with model input. For example, if pathway X is
of particular interest, the user can input a flag and the pathway number
to produce either or both types of histogram data for pathway X only.
One othar type of output will be available when the model is
in the annual mode. If information about the variation with meteorology
of exposure on a particular pathway is desired, the user will input a
flag, the pathway number, and the meteorological conditions of interest,
and the model will list the morning and evening exposures on the pathway
for each combination of meteorological parameters.
3. Graphical Display of Statistics
Histograms provide a convenient means of depicting the statistics
generated by the model, with the added feature that a subroutine can be
easily added to the model to generate the plots on a line printer.
Classes of exposure or dose will be plotted on the abscissa, while the
percentage of commuters or commuter minutes will be plotted on the ordinate.
For the annual statistics, it is more convenient to plot the
results in a format analogous to a wind rose, with a separate plot for
each set of meteorological and other conditions. In this case, each
spoke will be associated with a pathway by numbering. Directionality
68
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will not be implied. Spoke width, expanding radially, will be associated
with exposure or dose class, and the length of a spoke at each width will
give the percentage data. The characteristics of each pathway relative
to other pathways for each set of conditions will be easily discernible
from such plots.
Alternatively, plots may be made for each pathway with the
spokes referring to different conditions. This will serve to pinpoint
the less desirable conditions for each roadway.
4. Summary of Model Output
The various types of model output generated by the numerical
commuter exposure model have been discussed in the preceding paragraphs.
Table 3 contains a summary of model output for both the short-term and
annual modes of operation.
A final note should be made regarding the interpretation of the
statistics generated by the model. As discussed previously, the commuter
pathways do not account for all of the commuting in the modeled region.
The number and complexity of the commuting routes in most metropolitan
areas render a computer simulation of the complete commuting picture nearly
impossible. Given this initial limitation for all cities, the model
nevertheless can consider a larger percentage of the total commuters in
some cities than it can treat in other cities. The percentage of commuters
treated by the model is dependent not only on the size of the modeling
area and the numbers of actual commuting routes in the area, but also on
the user's choice of routes and the number of routes defined. For most
cities sufficient data are available from which the user can determine
the total number of commuters in the area and thus the percentage of the
total commuters traveling on the commute pathways the user has defined.
In interpreting model-produced statistics, the user should remember that
the statistics only apply to this percentage of the commuters. In additl::
the user knows that commuters traveling on the pathways by definition have
relatively long commutes, and hence are at risk of high exposure. By th e
same token, the commuters "skipped" by the suggested method for pathway
definition are those commuters with short home-to-work trips or having
69
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Table 8
NUMERICAL COMMUTER EXPOSURE MODEL OUTPUT
Output in Short-Term Mode of Model Operation
List of exposures on each pathway
Average and standard deviation of exposures on pathways in modeled region
Percentage of commuters in each of several exposure classes
Probability of experiencing exposure levels in each of several exposure
classes
Output in Annual Mode of Model Operation
Percentage of commuters in each of several exposure classes (for all
pathways)
Probability of experiencing exposure levels in each of several exposure
classes (for all pathways)
"'Percentage of commuters in each of several exposure classes (on any
single pathway)
""'Probability of experiencing exposure levels in each of several exposure
classes (on any single pathway)
"'Pathway concentration associated with different meteorological conditions
Pollution roses (see text on graphical display of statistics)
^'Optional output
70
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non-centralized places of employment. Thus, the commuter exposure
statistics developed by the model will be biased toward high exposure
levels.
71
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G. Summary of Numerical Methodology
The details of the numerical commuter exposure modeling methodology
have been discussed in the previous sections. The following is a summary
of the overall model structure.
The first step in the application of the model involves the definition
of the area to be modeled. To describe the pollutant concentrations to
which the commuter is exposed, one must quantify the sources of the pollutant
and prepare them for input to the model. The model user must prepare two
types of data that will define the pollutant sources (i.e., traffic).
First, the network of pathways on which the majority of commuters will
travel must be identified. Computational problems would result if a large
number of pathways were defined, so the user must choose only those pathways
that are heavily traveled, and on which commuters are likely to experience
high levels of exposure. Each pathway will be broken into a number of
segments, according to roadway type. If a pathway has an abrupt change
of direction, additional segments should be defined so that each segment
approximates a straight line. Various parameters describing each of the
segments will be input to the model.
The other type of traffic data that will be required by the model
concerns motor vehicle pollutant sources that do not travel on the pathways.
Since the majority of pathway exposure will result from traffic on the
pathways themselves, information concerning non-pathway pollutant sources
need not be extremely detailed. Therefore, the user will overlay the
study area with a grid system and will assign the total vehicle miles
traveled on the non-pathway street network to the grid system. This
information, along with the locale (land use) type of each grid square,
will be input to the model. The user will have the option of inputting
gridded emission rates, rather than traffic data, directly if such data
are available.
The numerical model will be capable of producing two kinds of output,
one giving annual statistics, and the other describing short-term, worst-
case exposure for a single commute. When the model is to be used in the
annual mode, the user will input meteorological data in the form of two
72
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joint frequency distributions, describing the average morning and average
evening hour of the commute. The frequency distributions will describe
the joint frequency of occurrence of wind speed, wind direction, and
stability over an average year. For the short-term mode of model operation,
the user will input the meteorological conditions of each hour of the
commute being analyzed.
Given the data described above as model input, the model will compute
commuter exposures in the manner illustrated in Figure 17. First, calcu-
lations will be made of exposures resulting from pathway sources. For
freeway, expressway, and non-CBD arterial segments of pathways, average
route speed will be used to compute FTP emission rates on the segment;
travel time will also be computed. On CBD arterials, the effects of
signalization and congestion will be accounted for, and modal emissions,
as well as travel time, will be computed for each segment. In the annual
mode of model operation, emission rates for both the morning and evening
commutes on each pathway will be calculated; in the short-term mode, a
single emission rate on each pathway will be found (but traffic volume
will be allowed to vary with time and to affect emissions).
Normalized exposures on each segment will be computed from emission
rates, through the use of different dispersion on methodologies according
to whether the segment is a street canyon; limited access; or non-limited
access, non-street canyon. Table 9 lists the dispersion algorithms used
for each roadway type. In the annual- mode, 160 wind speed normalized
exposures will be produced for each non-street-canyon segment, corresponding
to all combinations of 16 wind directions, five stabilities, and two emission
rates (morning and evening). On street-canyon segments, exposure is not
a function of wind direction or stability. Therefore, only two normalized
exposures will be produced for each segment, corresponding to morning and
avening emissions. In the short-term mode, one exposure for eac^ segment
will be computed, using the meteorology appropriate to the hour during
which the segment is traveled.
Next, calculations for non-pathway sources will be made. If gridded
emissions are input directly, the model will simply convert daily emissions
to average hourly emissions for each grid square (morning and evening
73
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READ BASIC INPUT DATA
Yet
No
DETERMINE AM AND PM AVERAGE ROUTE
SPEED, TRAVEL TIME, AND NUMBER OF
COMMUTERS FOR EACH PATHWAY SEGMENT
DETERMINE AVERAGE ROUTE SPEED,
TRAVEL TIME, AND NUMBER OF
COMMUTERS FOR EACH PATHWAY SEGMENT
No
ATHWA
EGMENT EMISSIONS
READ DIRECTLY
DETERMINE WHICH PATHWAY SEGMENTS
THE AVERAGE COMMUTER
TRAVELS DURING WHICH HOUR
COMPUTE AM AND PM
EMISSION RATES ON
EACH PAGHWAY SEGMENT
No
COMPUTE NORMALIZED INTEGRATED
CONCENTRATIONS ON EACH PATHWAY
FROM STREET CANYON PORTIONS OF
PATHWAY FOR AM AND PM EMISSIONS
COMPUTE NORMALIZED INTEGRATED
CONCENTRATIONS ON EACH PATHWAY
FROM NON-STREET CANYON PATHWAY
SEGMENTS FOR 160 CASES (COMBINATIONS
OF 16 WIND DIRECTIONS, AM AND PM
EMISSIONS, AND 5 STABILITIES)
ATHWA
EGMENT EMISSIONS
READ DIRECTLY
COMPUTE EMISSION
RATE ON EACH
PATHWAY SEGMENT
COMPUTE INTEGRATED CONCENTRATION
ON EACH PATHWAY FROM PATHWAY
SOURCES FOR INPUT METEOROLOGICAL
AND TRAFFIC SEQUENCES
No
Ye*
GRIDDED
EMISSIONS INPUT
DIRECTLY
7
GRIDDED
EMISSIONS INPUT
DIRECTLY
DETERMINE VMT
IN EACH GRID
DETERMINE AM
AND PM EMISSIONS
IN EACH GRID
CONVERT DAILY
EMISSIONS TO AM
AND PM EMISSIONS
IN EACH GRID
DETERMINE VMT
IN EACH GRID
DETERMINE
EMISSIONS IN
EACH GRID
CONVERT DAILY
EMISSIONS TO
EMISSION RATES
DURING COMMUTE
PERIOD IN
EACH GRID
COMPUTE NORMALIZED INTEGRATED
CONCENTRATIONS ON EACH PATHWAY FROM
NON-PATHWAY SOURCES FOR 10 CASES
(COMBINATIONS OF 5 STABILITIES AND
AM AND PM EMISSIONS)
COMBINE CONCENTRATIONS FROM
NON-PATHWAY AND STREET CANYON-AND
NON-STREET CANYON PATHWAY SOURCES
FOR EACH PATHWAY; DEVELOP VARIOUS
STATISTICS (CUED BY MODEL INPUT);
AND PRINT RESULTS
COMPUTE INTEGRATED CONCENTRATIONS
ON EACH PATHWAY FROM NON-PATHEWAY
SOURCES FOR INPUT METEOROLOGICAL
AND TRAFFIC SEC'JENCES
SUM INTEGRATED CONCENTRATIONS ON
EACH PATHWAY FROM PATHWAY AND
NON-PATHWAY SOURCES
COMPUTE VARIOUS STATISTICS (CUED BY
MODEL INPUT) AND PRINT RESULTS
END
J
c
END
FIGURE 17. SIMPLIFIED FLOW CHART FOR NUMERICAL COMMUTER EXPOSURE MODEL
74
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values for the annual mode, single values for the short-term mode). If
traffic data are input, the model will compute the values described above
from the traffic and locale data. Once gridded data on emissions are
available, the model, in the annual mode, will compute morning and evening
wind speed normalized integrated concentrations, for each of five stabilities,
on each pathway. In the short-term mode, an integrated concentration for
each pathway will be produced.
The model now will have computed the exposure values, for each segment,
needed to develop annual or short-term commuter exposure statistics. In
the annual mode, the appropriate non-street canyon, street canyon, and
non-pathway exposures for each segment will be multiplied by wind speed
and combined. Segment exposures will be summed for each pathway. As
appropriate, each of the pathway exposures will be weighted by either the
morning or evening frequency of occurrence of the meteorological conditions
used to compute the exposure value. Those exposures will then be used in
the development of various annual statistics describing commuter exposure
In the short-term mode, the model will simply combine pathway and non-
pathway exposures for each segment and sum over the pathway. The resulting
pathway exposure will be used to develop short-term, worst-case commuter
exposure statistics.
76
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Ill MANUAL COMMUTER EXPOSURE MODEL
A. General
The manual commuter exposure modeling methodology is similar to
the numerical methodology in terms of the individual methodologies of
the three model components, traffic, emissions, and dispersion. The
major difference between the manual and numerical models is in the degree
of complexity of the commuting with which each model can deal. Because
the numerical model is executed on a computer, a large number of compu-
tations may be made rapidly. On the other hand, manual model computations
are made at best on a desk calculator; a large number of computations
would, be both time-consuming and prone to error. Therefore, the
commuting situations that can be analyzed with the manual model are
limited. While the numerical model can produce annual or short-term
commuter exposure statistics for a number of pathways, the manual model
is, practically, limited to the analysis of a short-term, worst-case
commute on one pathway or a small number of them. Since the generation
of enough pathway exposures to produce exposure statistics is time-
prohibitive with the manual model, its value may lie in use as a screening
tool for planning. If application of the manual model indicates a
potential problem, the numerical model can be applied to analyze the
situation in greater detail.
The manual model will be comprised of a series of worksheets, instruc-
tions for completing each worksheet, and a number of charts, tables, and
nomographs similar to those presented in the following sections. To apply
the manual model the user will follow the procedure outlined below. The
user will read the instructions concerning definition of the modeling area
and gather the necessary information to define pathway and non-pathway
sources. The next step will be to fill in the first worksheets with the
necessary traffic information. Each worksheet will have a series of
instructions that detail the nature of the information required for the
worksheet and a source of such information. In some cases the source
will be one of the charts, tables, or nomographs included in the user's
guide to the model. In other cases, the information must be obtained
from a local or state agency.
77
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Once the traffic worksheets have been completed, some of the para-
meters computed will be transferred to the emissions worksheet, and the
emissions worksheets will be filled out according to their instructions.
Finally, the pathway segment emission rates (from the emissions worksheets),
along with the number of computers on the pathway and the segment travel
times (from the traffic worksheets), will be entered on the dispersion
worksheets. The user also will enter the meteorological parameters and,
following the dispersion worksheet instructions, use the appropriate
tables and figures to complete the worksheets. The output of the dis-
persion worksheets will be the pathway exposure.
The following sections describe the manual methodology for defining
the modeling approach, and treating traffic, emissions, and dispersion.
The approach assumes that computations are made for a single commute,
with meteorology and traffic held constant over the commute.
78
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B. Definition of Modeling Approach
As discussed for the numerical model, proper definition of the
modeling area is vital to having a tractable problem. In general, the
definition of the modeling area for the manual model will be the same
as for the numerical model.
1. Commuter Pathways
The commuter pathways may be defined in the same manner as for
the numerical model. It may be desirable to choose considerably fewer
pathways, ranked by traffic flow conditions, because the manual compu-
tations will be by necessity somewhat cumbersome. The number of path-
ways to be analyzed will depend on the resources available to do the
manual modeling. Again, the local transportation agency should be
called for assistance in choosing pathways and determining their
characteristics.
2. Non-Pathway Sources
As for the numerical commuter model, non-pathway sources consist
of the vehicles traveling on all of the roadways in the study area other
than commuter pathways. In the manual model, the emissions and disper-
sion from non-pathway sources will be treated in the same manner as they
would be for the numerical model. The user will overlay the commuter
pathway (or pathways) being analyzed with a 2-km-by-2-km grid system.
Primary traffic network VMT (excluding the pathway) will be apportioned
to the grid squares as described for the numerical model. Secondary
network VMT will be computed by the user. It will be equal to the
primary network VMT of the grid square multiplied by the ratio of
secondary to primary traffic associated with the locale type of the
square. The user will combine primary and secondary VMT for each grid.
In the numerical model, it is necessary to consider all grid
squares through which commuter pathways pass, even though the dispersion
treatment does not use all grid squares. Since the model is a black
box to the user, the grid squares that are used cannot easily be deter-
mined. It is simply more efficient to require input for all grid
79
-------
squares. However, in the manual model, all computations must be made
by hand, so those grid squares that will be used will be familiar to
the user. Therefore, the VMT for all grid squares through which pass
commuter pathways need not be computed. Those grids for which infor-
mation will be required can be identified once the user understands how
dispersion computations for non-pathway sources will be made.
80
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C. Traffic Modeling
Traffic modeling in the manual model will use the same formalism
as in the numerical model. However, the manual use of graphs and
nomographs as well as hand calculations will be substituted for calcu-
lations performed by the computer.
1. Uninterrupted Flow
Derivation of volume, capacity, and average speed may be accom-
plished in the same manner as that described for the numerical model,
for pathway segments that have uncongested flow. The only difference
is that the user will hand-calculate capacity based on the type of
roadway and adjustment factors being considered, rather than have the
option of letting the model perform the computation.
Congested segments may be modeled by nomographs, as shown in
Figures 18 and 19. The nomographs are based on equations presented in
the section of this report that discusses the numerical model. In
Figure 18, the user enters the nomograph with the length of time that
demand (volume) exceeds capacity, selects the appropriate value of
demand volume minus capacity, connects that point with the volume-to-
capacity ratio for the time that capacity exceeds demand, and finds the
**
total number of vehicles in the backup," N, from the bottom left-hand
scale. The number of vehicles backed up while demand exceeds capacity,
N, is read from the abscissa.
Figure 19 may be used to find the average delay per vehicle
(time to traverse the portion of the roadway on which the backup occurs).
*
The values of N and N must be known. The user enters the top left-hand
scale at N, connects that point horizontally with the solid line, then
/\
moves vertically to the value of N from among the family of curves on
the bottom graph. The average delay per vehicle is then read from the
bottom left-hand scale. The dashed lines on Figures 18 and 19 show the
procedure for the example presented for the numerical model.
81
-------
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82
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1000
TOTAL VEHICLES IN BACKUP, N
1,000,000
10,000
100,000
1,000,000
FIGURE 19. NOMOGRAPH FOR FINDING AVERAGE DELAY PER VEHICLE,
SPEED = 20 MPH. HEADWAY = 1.8 SECONDS.
83
-------
2. Interrupted Flow
Average route speeds for interrupted flow outside the central
business district (CBD) may be obtained through the use of Figure 7;
reference is made to the discussion in the numerical model section of
this report.
For calculating the interrupted flow within the CBD, the starting
point is again to find the capacity service volume, Cs, and the demand
volume, V, on the intersection approaches. Capacity service volume may
be found using the nomograph presented for the numerical methodology,
or alternatively, the simpler nomographs given in Figures 20 and 21 may
be used. The green time-to-signal cycle ratio, G/Cs, must be hand-
calculated using the numerical model methodology. Ideally, values of
these parameters may be obtained from the local transportation agency.
Once known, the values may be used with Figures 22 and 23 to
calculate the number of stops and the average delay per vehicle.
Figure 22 is a graphical presentation of the signalized intersection
queueing equations given for the numerical model. The user must know
the capacity service volume of the intersection approach, Cs, the
demand volume, V, and the green time-to-cycle length ratio. The dashed
line on the figure shows the procedure for finding the number of
vehicles stopping per hour.
Figure 23 is based on equations similar to the delay equation
of the numerical model, except it results in the calculation of
average delay for all vehicles on the intersection approach. The user
must calculate the capacity of the approach under signalization,
GCs/Cy. That is merely the capacity service volume per hour of green,
Cs, multiplied by the fraction of the time that the signal is green,
G/Cy. Denoting that as C, the user must also supply the degree of
saturation, S, found by taking the ratio of the demand volume to the
capacity, V/C.
Figure 24 may be used to find the average delay per vehicle at
toll booths. Again, it is based on the toll-booth-delay equation in the
84
-------
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When the peak hour factor Is known
me Table to determine the adjustment,
when peak hour factor is not known
use population directly.
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WAY STRE£T
85
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FIGURE 21. ONE WAY STREET CBO, FRINGE. OBD AND RESIDENTIAL CAPACITIES
86
-------
LLI
O Z
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4000
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O -p
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SOLUTION OF: N = V
1 - G/Cy
1 - WC,
EXAMPLE*: C, = 3000 Vehicles Per Hour
V = 1500 Vehicles Per Hour
G/Cy =0.6
N = 1200 Stops Per Hour
'Follow clashed line.
NOTE: If V/S > G/Cy, intersection is over capacity
and all vehicles stop.
NUMBER OF STOPPING VEHICLES (Veh/Hour)
8e888888§"
nwv\^
o
o
in
cs
8
Ul
GREEN/CYCLE
RATIO (G/Cvl
ffW/////
DEMAND VOLUME (V)
(Vehicles Per Hour)
i I I I I
FIGURE 22. GRAPHICAL ESTIMATION OF THE NUMBER OF VEHICLES PER HOUR STOPPING AT A
SIGNALIZED INTERSECTION
87
-------
CORRECTION
CYCLE LENGTH
UPPER LIMIT
ONE CYCLE
LENGTH
30 50 70 90 110
CYCLE LENGTH - seconds
200
400
600
&
u 800
| 1000
o"
o
1400
2000
2800
4400
o •-
o 6
X
X
X
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§
10
§
300
500
700
1200
1600
2400
3200
DEGREE OF SATURATION
where: S » V/C • degree of saturation
V « demand volume
Cs * capacity service volume
G/Cy - green to cycle time ratio
C " GCj/Cy - capacity under signalization
FIGURE 23 INTERSECTION DELAY PER VEHICLE
88
-------
1000
SOLUTION OF: D
EXAMPLE*:
3600(V/C){1/(C-V)|
V
C
V/C
0
800 VEHICLES PER HOUR
1000 VEHICLES PER HOUR
OS
15 SECONDS
•FOLLOW DASHED LINE
I 10°
•o
c
o
tu
Q
uu
o
INTERSECTION APPROACH OR TOLL
BOOTH GATE CAPACITY (vehicles per hour)
tr
tu
10
03 0.4 OS 0.6 0.7
VOLUME/CAPACITY RATIO (V/C)
OS 1.0
SA-3935-12
FIGURE 24 GRAPHICAL ESTIMATION OF DELAY AT SIGNED INTERSECTIONS
AND TOLL BOOTHS
89
-------
numerical model description. Queue lengths, in vehicles and in meters,
can be found through the use of Figure 25 once the average delay is
known.
90
-------
INTERSECTION DELAY
(Seconds Per Vehicle)
40
100 200 300 400 500 600 700 800 900 1000 1100 1200 1300
AVERAGE LANE CAPACITY (Veh/Hr/Lane) C
DC EXAMPLE*: LANE CAP. -°- =- 800 VEH/HR
450L DELAY = 90 SEC
QUEUE LENGTH = 160 METERS
SOLUTION OF: Xr
Number of Lanes
•FOLLOW THE DASHED LINE
FIGURE 25 GRAPHICAL ESTIMATION OF QUEUE LENGTH AS A FUNCTION OF LANE
CAPACITY AND INTERSECTION DELAY WITH A MINIMUM QUEUE LENGTH
OF 40 METERS ASSUMED
91
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D. Emissions Modeling
The treatment of emissions in the manual modeling methodology will
be based on the same methods used for the numerical model. Again, the
FTP and modal model treatments are applicable.
1. Emissions on Pathways
When there is uncongested flow, the following equation gives
the relationship between the emission rate and the emission density
and demand volume:
Q-
(3600)(1609)
Figure 26 illustrates how a graph of the equation might appear.
The user of the manual model will have to develop values of the
emission density, E, based on speed, altitude, state, calendar year,
and vehicle mix. The user's guide to the manual model should include
tables giving values of E for a nationwide average vehicle mix and
ranges of the other parameters. The user could then use those values,
if necessary.
When there is congested flow outside the CBD, values of emission
density for both the free-flow and congested portions of the pathway
segment must be found by the model user. An average emission rate will
be computed by the user from the relationship presented and discussed
in the numerical model section of this report.
Within the CBD, the modal emission treatment is applicable.
Figure 27 can be used to find the acceleration and deceleration
emissions, E , idle emissions, E,., and cruise emissions, E,,. The
procedure for the emissions calculation is demonstrated by the dashed
lines on the graph. They indicate that the emissions from deceleration
and acceleration, with a cruise speed of 30 mi/hr, total 6.2 kg per
1,000 stops. Using the example of Figure 22, 1,200 stops/hr,
and a cycle length of 90 sec, the excess emissions from deceleration
and acceleration would be:
92
-------
FIGURE 26 RELATIONSHIP BETWEEN EMISSION RATE AND EMISSION DENSITY AND
DEMAND VOLUME
93
-------
CRUISE
(At Cruise Speed)
SPEED CHANGE
(Per 1000 Stops
From Cruise
Sp*ad)
15
20 25 30 35 40 45 50
CRUISE SPEED — miles per hour
55 60 65
I I
I I
10 20 30 40 50 60 70 80 90 100 110 120 130
INTERSECTION DELAY PER VEHICLE — seconds
NOTE: Dashed lines Illustrate calculation procedure.
SA-3935-5
FIGURE 27 GRAPHICAL CALCULATION OF CARBON MONOXIDE EMISSIONS
94
-------
6.2 kg
1000 stops
1200 stops
3600 sec
1000 g
1 kg
— 8 m
1200 stops
3600 sec
90 sec
cycle
= 0.0086 g/m/sec.
That can be expressed as
AD
where E
8
E/8Cy,
emissions per stop, g (= kg/1000 stops)
a constant, representing the length of a stopped
vehicle, m
cycle length, seconds.
Continuing to use the data from Figure 22, one finds the delay per
vehicle from Figure 23 to be about 15 seconds. From Figure 27, idle
emissions of 4 kg/1,000 vehicles/15 sec are indicated. Excess emissions
from idling are thus:
4 kg
(1000 veh)(15 sec)
8m
m
1200 stops
3600 sec
i
1500 veh
1 hr
/
/
90 sec
cycle
15 sec
veh
1 hr
3600 sec
1000 g
1 kg
= 0.0069 g/m/sec
or
8PC
g/m/sec
where
proportion of vehicles that stop.
Finally, cruise emissions at 30 mi/hr are 27 kg per 1,000 vehicle-miles
traveled, according to Figure 27. That is equivalent to 27 g/mi;
95
-------
EC is thus:
27 g
vehicle mi
1500 veh
3600 sec
30 mi
3600 sec
1 mi/hr
0.447
—
sec
0.007 g/m/sec
or
EV
^ (3600^)(.44704)
= 1.726 X 10~7 EV
where V = demand volume, vehicles/hr.
As an alternative to the calculations of E^, E^ and EC> Figures
28 through 30 may be used. Those figures are used with Figure 27 and
present graphical solutions to the equations presented in this section
for calculating E^, Ej, and EC in g/m/sec.
2. Non-Pathway Emissions
As in the numerical methodology, the manual model methodology
will use FTP emission factors (emission density). The user will supply
the emission factors corresponding to the cold-start percentages (for
each of the five locale types) and the average temperature of the commute
being analyzed. The user should assume the FTP average route speed of
19.6 mi/hr, and that all other correction factors are unity.
To compute an emission rate for the grid squares, first the
daily VMT in the grid must be converted to VMT for the average hour of
the commute. The conversion will be made by multiplying the daily VMT
by the percentage of VMT during the average commute hour. (The percent-
age should be available for the area being analyzed from the local
transportation agency.) The average hourly VMT will be multiplied by
the appropriate emission factor, and the product will be divided by the
96
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dots apmoA/6 — g
97
-------
•V
I
UJ
0.025 0.05 0.075 0.1 0.125 0.15
E| — g/nv«ac
FIGURE 29. GRAPHICAL CALCULATION OF IDLE EMISSION RATE, G/VEH-SEC,
GIVEN IDLE EMISSIONS FROM FIGURE 27 AND PCy.
98
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160
140 I-
°-°1 0.02 0.03 0.04 0.05 0.06
Ee-
FIGURE 30. GRAPHICAL CALCULATION OF CRUISE EMISSION RATE. G/M-SEC,
GIVEN THE G/VEH-MILE FROM FIGURE 27 AND THE DEMAND VOLUME.
99
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area of the grid to yield the grid-square emission rate. The user will
make this computation for each grid square needed in the dispersion
computations.
100
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E. Dispersion Modeling
1. Dispersion of Pathway Emissions
The consideration of the dispersion of pathway emissions in
the manual model will differ somewhat from that in the numerical model.
As in the numerical model, a distinction will be made between dispersion
on long, limited-access roadways, non-limited-access roadways, and street
canyons. However, concentrations will be computed in the manual model
through the use of charts and nomographs.
a. Long, Limited-Access Roadways
Long, limited-access roadway segments are those segments
on which the emission density is both uniform and continuous for a mini-
mum length of road. For the purposes of commuter exposure modeling, the
minimum length is a function of atmospheric stability and wind/roadway
angle. Table 10 lists minimum roadway lengths. The user will follow the
dispersion computation procedure described in this subsection for all
limited-access segments longer than the appropriate minimum length
value in Table 10. If the segment is shorter than the minimum length, the
procedure described in the next subsection should be followed.
If a roadway segment meets the minimum length criteria,
the concentration on the segment, normalized by wind speed, U, and
emission rate, Q, can be determined from a set of curves such as those in
Figure 31. The normalized concentration is read on the ordinate from
the curve corresponding to the appropriate stability and initial disper-
sion, and for the wind/roadway angle of the segment. When the normalized
concentration is multiplied by the emission rate and divided by the wind
speed, the result is the concentration at a point on the roadway. To
compute the exposure on the segment, one multiplies the concentration
by the segment travel time.
b. Non-Limited-Access Roadways
For roadway segments that do not meet the criteria for long,
limited-access roadways, and that also are not street canyons, a dispersion
methodology for finite line sources will be used. Figure 32 illustrates
the geometry of the finite line source. The concept of a reference plane
is introduced in this dispersion treatment. The reference plane is marked
101
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104
-------
by a line perpendicular to the roadway and located 20 m downwind of the
receptor plane. The term Yu denotes the upwind distance along the road-
way axis from the reference plane to the upwind edge of the queue; Yu is
set equal to zero if the upwind end of the queue is downwind of the refer-
ence plane. The term Yd is the upwind distance (measured along the
roadway axis) from the reference plane to the downwind end of the queue.
It is also set equal to zero if the downwind end of the queue is downwind
of the reference plane.
21
The HIWAY dispersion model was used to generate a series
of nomograms that depict the dependence of the normalized concentration
on variations in wind/roadway angle and the length (Yu) of the finite
line source measured from the reference plane to the upwind edge of the
line source. Figure 33 illustrates these curves for specified combina-
tions of stability and a
J zo
For finite line sources, the concentration from the local
roadway source can be considered as the sum of two components: (1) the
finite line source as represented by the excess emission rate, emitted
over the finite length of the queue (Lq); and (2) an infinite line source
representative of the nonstopping vehicles passing through. Accordingly,
a dual analysis is required — one for each component. The excess
emissions component is found by: (1) obtaining the normalized concentra-
tion for the "maximum queue" from Figure 33 using the distance Yu; (2)
obtaining the normalized concentration for the "imaginary queue" from
Figure 33 using the distance Yd; (3) subtracting the result of (2) from
the result of (1); and (4) multiplying the difference by the excess
emissions rate and dividing by the wind speed.
Once the two components of the pathway concentration
(finite and infinite) are found and summed, the pathway segment exposure
can be computed. The exposure is equal to the concentration multiplied
by the travel time along the segment.
The procedure described in this subsection requires the
user to select a receptor location on the segment. The receptor should
be located such that the concentration computed for that location is an
105
-------
SIGMA ZO - 1.5 m STABILITY - 0
SIGMA ZO - 1.5 m STABILITY - 6
1200
2000
SIGMA ZO » 1.5 m STABILITY - F
3000
SIGMA ZO - 5.0 m STABILITY - D
SIGMA ZO - 5.0 m STABILITY = E
1400
o
q
d
I
a
3
FIGURE 33
VARIATION OF THE NORMALIZED CO CONCENTRATION WITH ROADWAY LENGTH,
STABILITY, WIND/ROAD ANGLE, AND TERRAIN ROUGHNESS
106
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"average" for the segment. The instructions for the manual commuter
exposure model should include nomograms to aid the user in choosing the
receptor location. The nomograms would be produced by making a large
number of computer computations for various roadway and queue lengths,
stabilities, wind/roadway angles, and values of 0 , and charting the
zo
results.
c. Street Canyons
The manual model will use the same technique for
computing exposures in street canyons as was used in the short-term
mode of the numerical model, only the computation will be done by hand.
See the discussion of street canyon dispersion in the numerical model
section of this report.
2. Dispersion of Non-Pathway Source Emissions
The dispersion of non-pathway source emissions will be
calculated with the same methodology as described for the numerical model,
operating in the short-term mode. The concentrations at each of the three
points shown in Figure 14 will be hand-calculated and weighted for
travel time, as discussed previously. Once those points have been located,
it is easy to identify the grid squares (in which the points lie) for
which input data will be needed.
107
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F. Summary of Manual Methodology
The first step in the application of the manual model is to select
the pathway or pathways to be analyzed. Next, the pollutant source data
must be prepared for both pathway and non-pathway sources. For pathways,
information on volume and other aspects of traffic is gathered for each
segment. To quantify non-pathway emissions, a grid system that overlays
the pathway is defined, and the non-pathway vehicle miles traveled in some
of the grids through which the pathway passes are tabulated.
Each segment of a pathway will be treated individually. For freeway,
expressway, and non-CBD arterial segments of pathways, average route speed
will be found and used to compute a FTP emission rate on the segment;
travel time will also be computed. On CBD arterials, the effects of
signalization and congestion will be accounted for, and modal emissions,
as well as travel time, will be found from nomographs.
The normalized concentration on each segment resulting from pathway
sources will be computed using different dispersion methodologies, according
to whether the segment is a street canyon; limited-access; or non-limited-
access, non-street canyon. The exposures on the segment is found by
multiplying the concentration by the travel time on the segment.
To determine the pathway exposure resulting from non-pathway sources,
the VMT in each grid square is converted to an emission rate through the
use of FTP emission factors. The user then computes a concentration at
three points on each segment, and weights the concentrations by the travel
times between points to compute an exposure for the segment.
The exposure on a pathway is found by summing the pathway and non-
pathway source exposures for all segments of the pathway. If more than
one pathway is considered with the manual methodology, the user may develop
commuter exposure statistics for the worst-case commute.
108
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IV DATA SPECIFICATION
Three topics pertaining to data are discussed in the data specifica-
tion section of this report. First, the input data required to use both
the numerical and manual commuter exposure models are defined. Secondly,
the data required for model evaluation are delineated, and finally, the
availability of data bases is discussed.
A. Input Data
1. Numerical Model
The types of data that will be required for execution of the
numerical commuter exposure model are listed and described in Table 11.
The table also contains information on preferred units, data value limits,
and typical values.
The data will be entered on eight types of cards. Type 1
contains general information about the computer simulation to be run,
such as a heading, the date, and various run flags. The next two card
types contain traffic information about each commute pathway segment.
One of each of these card types will be input for each segment of each
pathway. Card types 4 and 5 contain information required for emissions
computations. Information on non-pathway sources will be input on card
type 6 (one card for each grid source), and meteorological data will
appear on card type 7. Card type 8 contains several output flags which
will cause additional output of the specific types requested to be printed,
In Table 11 card types 5 and 7 are shown with two formats. The user
will select the format appropriate to the specified mode of model
operation (annual or short-term).
109
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115
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a. Card Type 1
The data to be entered on the card type 1 are general in
nature. First is an alphanumeric heading, which may be up to 20 charac-
ters long. The heading may say anything the user would like to have
printed at the beginning of model output. Next, the data and size of the
city being modeled will be input. Finally, two flags will be set,
specifying the desired mode of operation for the model (annual or short-
term) and whether non-pathway emissions are to be entered directly or
calculated by the model.
b. Card Type 2
Some of the data on card types 2 and 3 are direct traffic
engineering parameters, and some are flags that are operationally impor-
tant to running the model. The inputs describing the traffic volume data
format are in the latter category.
The data listed for card type 2 will be needed for analysis
of uninterrupted traffic flow. The user must identify the pathway and
segment by number, and provide data on the demand volume, number of lines,
lane capacity, lane width, and the endpoint coordination of the segment.
Flags are available to convert demand volume given as ADT or AADT to
hourly values. Capacity may be entered directly if known, or a default
input of 2,000 veh/hr will cause capacity to be calculated from lane
width, percent trucks (input elsewhere), and number of lanes data.
Similarly, speed may be entered if known, but a zero value will cause
speed to be calculated from the capacity restraint relationships. The
endpoint coordinate of the segment may be entered in any convenient,
consistent units and then converted to miles by a conversion factor
specified by the user.
At the end of card type 2 are two flags concerning data
on intersections. The first describes the existence and type of intersection
116
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(including interrupted flow on expressways); the second is a flag that
denotes whether or not the user is supplying the intersection data.
c« Card Type 3
Card type 3 will supply the intersection data. When the
user supplies these data, the model skips to the cycle-length input and
reads the remaining data. Left-turn, and through and right-turn signal
phases are allowed by the model.
To calculate the signal parameters, inputs will be required
for each of the three phases for the two critical approaches to the
interesection. (Those are the approaches with the highest volume-to-
capacity ratios from north-south and east-west directions). The inputs
will be the capacity service volume (vehicles per hour of green) and the
demand volume for each phase on each approach. Approaches without a
separate left-turn phase are considered through entering a zero for the
corresponding capacity service volume.
If the model is to calculate the signal parameters, the
cycle length and green phase times should not be entered. However, the
segment approach volumes must still be entered to accommodate the rare
case when the segment is not a critical approach.
The final inputs on card type 3 need be entered when back-
ups on expressways occur (when a flag value of 3 is entered as the next-
to-last entry on card type 2). The required data will be the demand
volume and the time during which demand exceeds capacity. During the
remainder of the one-hour period, the demand volume from card type 2 will
be used.
d. Card Type 4
The distributions of model year and vehicle type needed to
compute mobile source emissions are entered on card type 4. The fraction
117
-------
of the annual travel by each of 20 model years, beginning with the
calendar year being modeled and followed by the 19 previous model years,
is entered on this card. Finally, the fractions of the annual travel
driven by light-duty vehicles, light-duty trucks, heavy-duty gasoline-
powered trucks, and heavy-duty diesel trucks will be input.
e. Card Type 5
The type of data to be entered on card type 5 depends on
the mode of operation of the model. A description of the data required
for both the annual and short-term modes of operation is given in Table
11.
For the annual mode, the model will require the entry of
the annual average percentage of cold-starting and hot-starting vehicles
for the evening commute. Commuting vehicles usually begin the evening
commute in the CBD; therefore, the percentage should refer to the CBD.
The annual average temperatures for the morning and evening commute
periods will be entered next. Those temperatures, along with the percen-
tage of cold-starting and hot-starting vehicles, will be used by the
model in computing emission factors. The next data entered on card type
5 (annual mode) will be the percentages of the average daily VMT during
the morning and evening commutes. Those values will be used in the
computation of non-pathway source emissions.
For the short-term mode of operation, the input data on
card type 5 are similar to those for the annual mode, but the data are
for only one commute. The percentages of cold-starting and hot-starting
vehicles refer to the commute time of interest. The percentages should
apply to the locale in which most of the commute vehicles begin their
trips. The temperature entered on card type 5 should be an average
temperature during.the commute being analyzed. Next, the number of hours
the commute lasts should be entered, and then the percentage of the average
daily VMT during each hour of the commute should be input.
118
-------
For either mode of model operation, the average number of
occupants for all vehicle types should be input.
f. Card Type 6
Data describing the grid squares will be entered on card
type 6. One card should be input for each grid square through which a
pathway passes. The first data to appear on card type 6 are the
coordinates of the southwest corner of the grid square. The next entry
will depend on whether the model is to compute non-pathway source emissions
or whether emissions are to be input directly. If the model is to compute
non-pathway source emissions, the next input will be the average daily
VMT in the grid square, followed by the locale type associated with the
grid square. If emissions are to be input directly, the average daily
emission rate for the square should be entered in lieu of the grid square
VMT and locale type.
g. Card Type 7
The meteorological data are entered into the model on card
type 7. As with card type 5, different formats and data will be used for
the two different modes of model operation.
For the annual mode, the joint frequency distribution of
wind direction, wind speed, and atmospheric stability should be entered.
The distributions consist of the fraction of the time that each combina-
tion of wind direction, speed, and stability occur. There are 16 wind
direction classes, 6 wind speed classes, and 6 stability classes.
For the short-term mode, values for wind speed, wind
direction, and stability should be entered for each hour of the commute
of interest. The number of values of each of those parameters that is
entered should correspond to the duration of the commute as it appears on
card type 5.
119
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h. Card Type 8
Card type 8 is an optional data card. If the model user
elects to utilize one or more of the optional output features of the
commuter exposure model, card type 8 should be included. If only some
of the options available are to be used, zeroes should be entered for all
remaining inputs on the card.
The first set of input values on card type 8 will consist
of the numbers of those pathways for which the user wants the percentage
of commuters on each of the pathways in each of several exposure classes
to be printed. The output can be obtained for up to five pathways.
The next set of input values will contain the numbers of
those pathways for which the user wants the probability of the commuters
on each of the pathways experiencing exposure levels in each of several
exposure classes to be printed. As many as five pathway numbers can be
input.
The next values to be entered on card type 8 will allow
the user to observe the variation of exposure on a specific pathway with
meteorological conditions. First, the number of the pathway of interest
will be entered. Next, the number associated with a particular combina-
tion of wind direction class, wind speed class, and atmospheric stability
class will be entered. The model will allow up to 10 sets of meteorolo-
gical conditions to be input. The number associated with each combination
of meteorological conditions will be taken from Table 12. The definitions
of the" value intervals for the wind direction, wind speed, and stability
referred to in Table 12 appear in Table 13.
The final input on the card will be a flag for the graphics
package. If the flag is set to a value of one, a graphics package will
be called that will plot the "pollution roses" discussed in Section II-F-3,
120
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2. Manual Model
The types of data that will be required for execution of the
manual model are listed in Table 14. Many other data elements will be
required, but they will appear on the worksheets or will be taken by the
user from the tables, nomograms, etc. in the User's Guide for the manual
model.
The requirements for traffic data for the manual model are
essentially the same as for the numerical model except that the various
flags are not needed. Table 14 lists the necessary data. (The data are
described in the previous discussion of inputs for the numerical model.)
Emission data will be taken by the user from the appropriate
figures in the User's Guide. The meteorological parameters that will be
required by the model are also listed in Table 14, and were described in
the previous discussion of numerical model inputs.
124
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B. Data Required for Evaluation of the Model
The commuter exposure model outlined in this report can be evaluated
in more than one way. One method of evaluation is to determine the
adequacy of the simulation in terms of the reliability of the results.
To evaluate the overall model from an air pollution standpoint, data
describing the model ouput, commuter exposure (time-integrated concentra-
tion), is needed. Ideally, such data would be obtained by having a
statistically significant sample of commuters carry a personal monitor
that could time-integrate the concentration to which the commuter is
exposed. The readings from the personal monitors could be compared with
model calculations to arrive at a quantitative measure of overall model
performance.
Another way of evaluating model performance, and one through which
insight into model inadequacies could be gained, is to individually
evaluate the major modules of which the model is comprised. One method
of evaluating individual modules is to compare the output of each major
module with empirically derived data. The three major modules that should
be analyzed individually are the modules that treat traffic, emissions,
and dispersion. The following paragraphs contain a discussion of the
data requirements of an evaluation of each of these modules.
For evaluation of the output of the traffic module, the following
parameters are needed. For pathway segments that have uninterrupted and
uncongested flow, the average route speed on the segment will be required to
evaluate the output of the traffic module. For pathway segments on which
flow is uninterrupted but congested, the length and duration of the
backup will be needed, in addition to the average route speed. For
pathway segments that have interrupted flow, the cruise speed, queue
length, signal cycle parameters, average delay time, and rates of
acceleration and deceleration are required.
128
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The performance of the emissions module in simulating roadway
emissions is difficult to test empirically. In the commuter exposure
model, the currently-accepted EPA methodologies are used to compute
emissions. It is assumed that these methodologies represent the state
of the art in emissions simulation.
The output of the dispersion module is the pollutant concentration
on each pathway segment. A single concentration is computed for each
pathway segment and, when multiplied by the travel time on the segment,
is assumed to represent the time-integrated concentration for the segment.
To evaluate the output, two questions must be asked: (1) Does the single
concentration computed for the segment correspond to the actual average
concentration on the segment? (2) Is the variation of concentration
along the segment such that an integration of the measured concentrations
can be represented by the product of the travel time on the segment and
the computed "average" concentration? Such an analysis requires measure-
ment of on-roadway concentration at frequent intervals on each pathway.
The evaluation of the dispersion module discussed above would indeed
be an analysis of the performance of the dispersion module alone if the
inputs to the dispersion module accurately represented the emissions and
meteorological conditions on the pathway segment. However, the emission
rate used by the dispersion module is obtained from the emission module.
Because an evaluation of the emissions module output would require an
effort considered beyond the scope of a typical model evaluation study,
for carbon monoxide the dispersion module must be evaluated in conjuntion
with the emissions module.
This problem can be eliminated, however, if the measurements
recommended for use in the evaluation of the dispersion module could be
made for a tracer gas released at a known rate from a test vehicle. The
known emission rate would be entered into the dispersion module, along
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with site-specific meteorological parameters. The output of the dispersion
module then could be tested against measured concentrations of the tracer
gas to determine the reliability of the dispersion modeling procedure.
One other part of the model that should be evaluated is an assumption
made in the commuter exposure modeling methodology, specifically, that
on-roadway and in-vehicle concentrations of carbon monoxide are equivalent-
This theory is based on limited studies and is used in lieu of any
evidence to the contrary. An evaluation of the commuter exposure model
should include further investigation of the relationship between concen-
trations of carbon monoxide on the roadway and inside the vehicle.
Simultaneous measurements should be made inside and outside various
vehicle types, models, and makes, under different conditions, such as
with windows up and down, the air conditioner on and off, vents open and
closed, and smoking being or not being practiced inside the vehicle.
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C. Data Base Availability
The commuter exposure modeling methodologies were designed so that
the input data required would be routinely available from federal, state,
and local agencies. The numerical model will be most applicable to major
metropolitan areas, with the exception that the New York and Los Angeles
areas would require special procedures due to their size and complexity.
In general, the larger is the urban area to be modeled, the more detailed
are the available data.
The traffic information required on card types 2, 3 and 5 in Table
11 is generally available from the state department of transportation or
the local transit district. Instructions on how to define the commute
pathways from various types of data appear in Section II-B-1 of this
report. Section II-B-2 contains a discussion of how the grid system
should be defined and how the traffic input for card type 6 should be
obtained.
Perhaps the weakest data are those that concern the commute pathways
of individual or even small traffic groups of commuters. These data are
simply not available. The best that can be done is to deal with commuters
in the aggregate, and to work with major commuting routes that are used
by a majority of commuters for a majority of their trips, at least in
terms of exposure.
The distributions of vehicle model year and vehicle type required
on card type 4 may be available for the local modeling area from the
traffic agencies. If these data are not available, the model will have
the national average distributions in storage, and those distributions
may be used as default variables.
The percentages of cold-starting and hot-starting vehicles required
on card type 5 should be determined according to the method described by
22
Midurski, et al. The meteorological data called for on card types 5
131
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and 7 can be obtained from the National Climatic Center (NCC) in Asheville,
N.C. If the model is to be run in the annual mode, the joint frequency
distribution can be produced by the NCC STAR program from a historical
meteorological record for any first-order weather station.
The data required for model evaluation are described in the preceding
section. In general, most of these data are not available. The authors
of this report know of only one study in which personal monitors were
carried, and in that study, data were not taken outside the vehicle in
which the commuter was riding.
The data required to evaluate the individual modules of the model
do not exist. However, measurements in the automobiles of a few commuters
over a number of commutes (and commute paths) could be made with a
relatively modest effort. While such measurements would not be ideal for
discerning the accuracy of the individual modules of the model, they
would provide an indication of overall model performance. Concurrent
traffic count and signal data would provide more confidence in the study
results.
Some indication of model performance can be gained through use of
existing data. Where local monitors are already in place near commuting
routes, their data would provide a reference for model calculations. In
that case, the accuracy of the dispersion models in predicting on-roadway
concentrations, and the relationship between on-roadway and in-vehicle
concentrations, would still be questionable.
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V CRITICAL EVALUATION OF MODELING APPROACHES
Following is a critical evaluation of the modeling approaches
presented in Sections II and III of this report. The costs of developing
each of the models are detailed, and the deficiencies and accuracies of
the methodologies are discussed.
A. Development Costs
To detail the costs of developing the commuter exposure models, a
breakdown of the tasks to be accomplished should be presented. The
following list shows the tasks in-developing the numerical model:
(1) Formulate the structure of the numerical commuter exposure model
code.
(2) Design a User's Guide that will describe the model and its
operation.
(3) Write the computer code of the numerical model.
(4) Write the User's Guide.
(5) Produce monthly, interim, and final reports that fully describe
the model development.
The cost of accomplishing these tasks in the development of the numerical
model is estimated at approximately 2,300 person-hours and $83,000. This
cost includes labor and direct costs, such as computer time, materials
and supplies, communications, travel, and report costs. The labor costs
were estimated according to SRI's currently approved overhead rates.
Development of the manual model would consist of the following tasks:
(1) Formulate the structure of a manual commuter exposure model.
(2) Develop the tables, worksheets, nomograms, and so forth, needed
to use the model.
133
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(3) Write a User's Guide that describes and illustrates application
of the manual model.
The cost of accomplishing these tasks, in conjunction with or
following the development of the numerical model, is estimated at 1,000
person-hours and $33,000.
134
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B. Model Deficiencies
In most instances the commuter exposure model uses state-of-the-art
technology to simulate the traffic, vehicle emissions, and pollutant
dispersion affecting commuters in an urban area. The areas in which
improvements are needed to state-of-the-art techniques are well known and
have been widely discussed. For example, the use of a Gaussian distribu-
tion to represent the variation in pollutant concentration usually assumes
a steady-state condition for periods of up to one-hour in duration. Of
course, wind direction and speed and many other descriptive parameters
can vary considerably during such a time period. Thus, the assumption
of a steady-state is not always valid and ideally should be replaced by
a treatment that can accommodate high frequency variations in basic
descriptive parameters. Deficiencies of this sort are well known, and
as the state of the art progresses, they will be eliminated.
The model deficiencies discussed here are those relating to assump-
tions made in formulating the methodology that, while not ideal, were
necessary to produce a practical, useful model of a reasonable size and
moderate running costs. To keep the modeling problem tractable, certain
assumptions were necessary. In designing the methodology, care was
taken that such assumptions would have a relatively minor effect on the
model output.
Table 15 contains a list of model deficiencies. First, and most
important, is that the model does not treat all commuters. Short commutes
and commutes on less popular routes are not treated. While ideally all
commuters would be treated, the number of origin-destination zone pairs
in a major metropolitan area needed to define all commute routes is far
greater than can be reasonably handled. Another possible model deficiency
is the method by which commute routes are defined. The method is only
semi-objective. If the model user is familiar with the areas to be
135
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modeled and is experienced in traffic modeling, he will undoubtedly make
better choices of commute routes than would a less experienced person.
The suggestion that the local transportation agency be contacted for
help in selecting the commuting routes mitigates this somewhat.
To keep the calculation of annual average exposures within reasonable
computational bounds, no peaks (other than diurnal) are allowed in the
traffic distribution. If the volume input to the model is annual average
daily traffic (AADT), the lack of peaking characteristics will not be
a problem. However, if average daily traffic (ADT) is input, the lack
of weekly and seasonal peaks could affect the annual average exposures.
This effect can be alleviated by adjusting ADT to AADT using seasonal
factors when computing annual average exposures. Another model assumption
is that the acceleration and deceleration rates have a constant value,
although the effects of this are expected to be minor. Single, constant
rates may be chosen that reflect the average emissions from a distribution
of rates.
Three assumptions are made relating to the computation of emission
rates. The assumptions are necessary to keep the number of model compu-
tations and the computer storage required at realistic levels. First,
an annual average ambient air temperature is used where the model is in
the annual mode. Next, in the morning all vehicles on the commute routes
are assumed to be in a warmed-up mode of operation. (The vehicles reached
this state while traveling to the beginning of the commute route.)
Finally, when computing pollutant concentrations resulting from non-pathway
sources, fixed cold-start and hot-start percentages are assumed for the
morning and evening commutes for each locale type.
Four possible model deficiencies are related to the simulation of
atmospheric dispersion. The use of the Gaussian dispersion formulations
presented precludes treatment of fumigation or stagnation conditions.
136
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Table 15
MODEL DEFICIENCIES
Not all commuters are treated
Semi-objective method of commute pathway selection
No seasonal or weekly traffic distribution
Constant acceleration and deceleration rates
Assume annual average ambient air temperature
All morning commute vehicles assumed hot-running
Cold-start and hot-start percentages fixed for each
locale type for morning and evening commutes
Gaussian dispersion treatments cannot treat fumigation or
stagnation
Non-pathway dispersion treatment does not allow variation of
grid square emission rates
No provision for effects of precipitation
On-roadway and in-vehicle concentrations assumed equal
137
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The Hanna-Gifford dispersion treatment used to compute concentrations
resulting from non-pathway sources assumes that the emission rate in
grid squares adjacent to the receptor square is the same as the emission
rate in the receptor grid square. Another factor which has been ignored
in the commuter exposure modeling methodology is the effect of precipi-
tation. Undoubtedly some scavenging or rainout would occur. Finally,
on-roadway and in-vehicle concentrations have been assumed to be equal.
The state of the windows, air conditioner, heater, and so forth in the
vehicle would affect this relationship.
138
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C. Model Accuracies
A number of equations are presented or derived for the traffic
module of the commuter exposure model. These relate "independent" traffic
parameters to other, dependent parameters. The dependent or predicted
parameters are in turn used in the emission calculations, and the output
of the emissions module is then used in dispersion computations. A
method is presented below that investigates the relative accuracies or
relative errors of the predicted traffic variables as functions of the
relative errors of the independent traffic variables. A discussion of
the accuracy of the emissions and dispersion modules of the model is
presented at the end of this subsection.
1. Method for Determining Relative, Error
Define the relative error of a variable , x, as
E -!*
x
X
where E is the relative error, S is the standard deviation of x, and
x x '
x is the mean of x. In stating that the value of x is 5 + 10%, the 10%
is the relative error expressed as a percent.
In general, if z = f(x , x , .... x ), then
l / n
Sx x (C)
J1
where p is the point at which the derivatives are evaluated, assumed to
2
be the mean or observed value. Note that S = S Assuming that
x.x x.
the errors are independent yields
0, i
139
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If z = xy then
2 2 ? 22
= (y)2 s/ + (x)2 Sy2.
_2
Dividing by z and taking the square root gives
s /s 2 s 2
Sz t/Sx . Sy
V:
or E = ? E + E
z
The same relation holds for division.
For z=x+yorz=x-y,
Dividing by z,
S = S + S
z x y
s Js2
_z W^L. .
= T +
s2
y , or
-2 .2
z z
3 -2 S .2
x x y y , and
_— _ i ' *—
-2 -2 _2 .2
x z y z
E* =VV (?) + V f1' (E)
140
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Finally, note the assumption that z = f(x , x , ..., x ).
12 n
While this is not, in general, a strict equality, it provides a best
estimate of z.
The sensitivity of the relative error in z to a change in the
relative error in the other variables can be easily evaluated. Taking
V2 2 22
A E + B E
x y
where A = x/z or 1
and B = y/z or 1,
then
?>E A E
_ z __ x
BE ~ E
X Z
2
and SE BE
3E ~ E
y z
In general,
» K2E
oE x.
_ z _ i
3E = E
Xi
\
where K is the relative weighting as defined above.
2. Application of the Method to Traffic Parameters
Six basic equations were introduced for the traffic module to
predict queue lengths and delay times.
These are
Queue length of a freeway backup
(q-s)t' (G)
l-q'/s
141
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Associated delay
D=^
vN
Queue length at a signalized intersection
N . i-G/cy V_GZ
1-V/Cs 3600
Associated delay
D = O.S(Cy-G) (j)
Queue length at a toll booth
V
N = (TO
C-V ^ }
Associated delay
3600 N
D - -y- (L)
The equations for the propagation of errors and the sensitivities of the
resultant errors are derived below for the freeway backup case. Relation-
ships for the other two cases are not presented but are derived similarly.
a. Example - Freeway Backup Case
Given
l-q'/s
sqt'-s t'
s-q'
142
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then
~\2 /^-v2
2 /BN\ 2
st'
s-q1
2
2 I2
sqt'-s t1
. (s-q1)2 J °
2
Dividing by N and reducing, this becomes
v 2
,s-q' V8,
2 r 2 T
s\ 2q'st'-s t'-qq't'
LCs-q1)2J
1/2
The sensitivity of this relative error in N to changes in the relative
errors in the independent variables can be calculated using equation (F)
/ . \
= /st^N 1 _3.
\s-q'/ N2 Efl
2 r 2
2q'st'-s t'-qq't'
L (s-q1)2.
"sqt'-s2t'1 /£^
. (s-q')2 J \N,
fal
EN
143
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The relative error and sensitivity relationships for equations (H) through
(L) are derived in the same manner.
3. Re suits of Sample Applications
The results of applying the relative error and sensitivity
relationships derived for equations (G) through (L) are presented in
Tables 16, 17, and 18. The specific numerical results should be interpreted
with caution, since they depend on the values and relative errors assigned
to the independent variables. However, doubling the relative error in
all of the independent variables doubles the relative error of the
predicted values. The sensitivities will remain unchanged. Such
statements cannot be made when the values and relative errors of the
independent variables are varied at random. The numerical results are
quite useful, however, for examining the general propagation of errors
and the sensitivities of the predictive equations.
From Table 16, the relative error in the prediction of the
number of vehicles involved in the freeway backup is 117%, while the
relative error in the delay prediction is 85%. The error in predicting
N is most sensitive to the error in s, the roadway capacity, and next
most sensitive to q, the over-capacity demand volume. This is encouraging,
since the roadway capacity is the parameter that can most likely be
estimated with the least, error. Reducing the relative error in this
parameter from 1070 to 57, would improve the relative error in N by 337, in
this example. The relative error in the delay prediction, E , is most
sensitive to the relative error in the over-capacity demand volume. This
unfortunate result implies that the relative error in D is difficult to
improve because it is so highly sensitive to a transient condition.
Turning to Table 17, the relative error in the queue length
prediction is 427,, and the relative error is 367, for the associated delay.
Again, both depend on the conditions assumed for the example. Both
144
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Table 16
RELATIVE ERROR AND SENSITIVITIES FOR THE FREEWAY BACKUP CASE
ht1 (g-s)rs-q'
,
l-q'/s ~
q = 0.64 veh/sec E = 10%
q
s = 0.55 veh/sec E = 10%
s
q1 =0.40 veh/sec E , = 10%
t1 = 1800 sec E
t' = 10%
h = 1.8 sec EL = 10%
h
N = 594 veh D = 79.5 sec
Efi -1.17 ED=0.85
=117% = 85%
rr~ » 4.34 - — = 5.96
oE 3E
q q
iT
h
145
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Table 17
RELATIVE ERROR AND SENSITIVITIES FOR THE SIGNALIZED INTERSECTION CASE
°Ev
0.94
3ECs
= 0.24
G = 60 sec E = 107,
G
Cy = 90 sec E = 107.
Cy
V = 600 veh/hr E - 107.
Cs = 1200 veh/hr E,, = 107,
Cs
N = 10 veh/cycle D = 15 sec/veh
E = 0.42 ED = 0.36
= 42% = 367,
5EN 5ED
^-,4 -=1.11
Cy Cy
146
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Table 18
RELATIVE ERROR AND SENSITIVITIES FOR THE TOLL BOOTH CASE
N = — D - 3600V
C-V ~ C(C-V)
V = 400 veh/hr • E = 10%
C = 1200 veh/hr • E = 10%
C
N = 0.5 veh D = 1.5 sec
EN = 0.21 ED = 0.29
=21% = 29%
SE 9E
• '•«
• IM
147
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relative errors are most sensitive to the relative error in the cycle
length, the parameter that generally can be known with least error.
Improving the relative error in the cycle length from 10% to 57. leads to
E of 317. and E of 247,.
Table 18 lists the results for the case of a toll booth. E is
N
equally sensitive to the relative errors in volume and capacity with a
nearly one-to-one relationship. E , on the other hand, is more sensitive
to E and less sensitive to E than is E .
c v N
l
Finally, the dependence of all of these results on the absolute
values assumed for the dependent variables should be reemphasized. The
results are not absolute but rather indicate general dependencies, and'
they must be interpreted accordingly. For any specific case, an exact
investigation of relative error and sensitivity requires calculations '
using the values of the parameters for that case. This can be accomplished
easily using equations (C) through (F) to find the proper relationships
and then applying these with the specific parameter values.
4. Accuracies of Emissions and Dispersion Algorithms
The emission module will take the average route speed computed
by the traffic module, and use speed, ambient air temperature, the
percentages of cold-starting and hot-starting vehicles, and the vehicle
type and age distributions to compute emission rates. Error in any of
these parameters will produce error in the computed emission rate. The
magnitude of the relative error is difficult to determine. The method
presented in the preceding sections could be applied to the emission
rate equation. However, the complexity of the emissions equation is such
that the resulting equation representing relative error would be ungainly.
An assessment of the accuracy of the emissions estimation procedure
employed in the commuter exposure model can be made more readily by relying
on EPA estimates of the accuracy of their procedure.
148
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In assessing the accuracies of the dispersion algorithms the
same problem that was encountered in examining the accuracy of the
emissions module appears: the complexity of the algorithms. However,
there is one parameter, the source emission rate, that is directly
proportional to segment concentration. Therefore, a given error in
emission rate will produce the same amount of error in concentration.
The effects of error in other parameters are in some cases
considerably more subtle. For example, the model accepts atmospheric
stability expressed as a Pasquill-Gifford class. The dispersion algorithms
do not use the class number directly, however; the number determines the
values of constants used in the computation of the horizontal and vertical
dispersion coefficients. Another such input parameter is wind direction.
The direction from which the wind is blowing is used by the model to
determine the x- and y- distances from source to receptor in a coordinate
system with the origin at the source and the x-axis along the direction
of the wind. The x- and/or y- distances appear in the relationships for
rr and
-------
The empirically-derived equation used to represent on-roadway
concentrations in street canyons contains only three dependent variables;
the equation is simple enough to apply the method presented in Subsection
V-C-1.
The equation for concentration, X, is
KQ.
X =
2(U+0.5)
To simplify application of the method, the assumption is made that the
street width, W, is considerably larger than the dimension representing
vehicle size, L . The above equation then reduces to
o
KQ,
X =
2L (WO. 5)
o
Applying equation (C),
s 2
2 s 2
K
2L (WO. 5)
o
V
r -«% ;
2L (U+0.5)'1
o
Dividing by X and reducing,
U
1/2
U
Table 19 contains the results of applying the relative error
and sensitivity relationships for a given set of variable values. The
results shown in Table 19 are intended as an illustration of the method
and should not be interpreted as general in nature.
150
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Table 19
RELATIVE ERROR AND SENSITIVITIES FOR STREET CANYON CONCENTRATION
X
2L (13+0.5)
Lo = 2 m *\ \
U = 4m/sec SEQ EX
K = 7
aEu L^-5).
X = 38.9,j,g/m
EX - 0.13 - m SE
^- °-75
E = o.io = 10% SE
Qje j?
E = 0.10 = 10%
u
151
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References
1. Highway Capacity Manual, 1965. National Academy of Sciences, Highway
Research Branch, Special Report No. 87.
2. Ludwig, F., P. Simmon, R. Sandys, J. Bobick, L. Seiders, and R. Mancuso,
1977. "Users' Manual for the APRAC-2 Emissions and Diffusion Model,"
Final Report EPA Contract No. 68-01-3807, SRI International, Menlo Park,
CA.
3. Drew, D.R., 1968. "Traffic Flow Theory and Control," McGraw-Hill Co.,
New York
4. "Modal Program Guide", an update to "Automobile Exhaust Emission Modal
Analysis Model," 1974. U.S. EPA Report No. EPA-460/3-74-005, 75 pp.
5. "Mobile Source Emission Factors, Final Document", 1978. Environmental
Protection Agency, Office of Transportation and Land Use Policy,
Washington, D.C.
6. "Existing Transportation Systems in the Washington Metropolitan Area,"
1976. Metropolitan Washington Council of Governments.
7. Webster, F.V., 1958. "Traffic Signal Settings," Road Research Technical
Paper No. 9, Road Research Laboratory, HMSO, England.
8. Patterson, R.M., and F.A. Record, 1974. "Monitoring and Analysis
of Traffic and Carbon Monoxide Concentrations at Oakbrook,"
EPA-450/3-74-058, U.S. Environmental Protection Agency, Research
Triangle Park, N.C.
9. Sandys, R.C., P. Buder (Simmon), and W.F. Dabberdt, 1975. "ISMAP:
A Traffic/Emissions/Dispersion Model for Mobile Pollution Sources,"
SRI International, Menlo Park, CA.
10. "Mobile Source Carbon Monoxide Hot Spot Guidelines Volume II:
Rationale and Example Applications," 1977. Draft Report, EPA
Contract No. 68-02-1376, Task Order 22, GCA/Technology Division,
Bedford, MA.
152
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11. Dabberdt, W.F.; 1977. "Air Quality On and Near Roadways: Guidelines
for Estimating Air Quality for Alternative Roadway Configurations,"
Federal Highway Administration Contract DOT-FH-11-8125, SRI International,
Menlo Park, CA.
12. Noll, K.E., T.L. Miller, and M. Claggett, 1976. "A Comparative Analysis
of EPA HIWAY, California, and CALINE 2 Line Source Dispersion Models,"
submitted to Transportation Research Board, Washington, D.C.
13. Johnson, W.B., W.F. Dabberdt, F.L. Ludwig, and R.J. Allen, 1971.
"Field Study for Initial Evaluation of an Urban Diffusion Model for
Carbon Monoxide," Comprehensive Report CRC and Environmental Protection
Agency (EPA) Contract CAPA-3-68 (1-69), SRI International, Menlo Park, CA.
15. Hanna, S.R. 1971. "A Simple Method of Calculating Dispersion from
Urban Area Sources," J. Air Pollution Control Assoc. 21, p Ilk-Ill.
16. Mayron, L.W., and J.J. Winterhalter, 1976. "Carbon Monoxide: A
Danger To the Driver?," J. Air Pollution Control Assoc., 26, p 1085-1088.
17. Cortese, A.D., and J.D. Spengler, 1976. "Ability of Fixed Monitoring
Stations to Represent Personal Carbon Monoxide Exposure," J. Air
Pollution Control Assoc., 26, p. 1144-1150.
18. Chaney, L.W., 1978. "Carbon Monoxide Automobile Emissions Measured
From the Interior of a Traveling Automobile," Science, 199, p 1203-1204.
19. Petersen, G.A., and R.H. Sabersky, 1975. "Measurements of Pollutants
Inside an Automobile," J. Air Pollution Control Assoc., 25, p. 1028-1032.
20. Sevan, M.G., D.M. Colwill, and L.E. Hogbin, 1974. "Measurements of
Particulate Lead on the M4 Motorway at Harlington," Transport and
Road Research Laboratory Report 626, Transport Systems Department,
Environment Divison, Crowthorne, Berkshire, England.
21. Zimmerman, J.R., and R.S. Thompson, 1975. "User's Guide for HIWAY,
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22. Midurski, T.P., and A.H. Castaline, 1977. "Determination of
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No. 68-02-1376, Environmental Protection Agency, Research Triangle
Park, N.C.
154
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/4-79-010
2.
3. RECIPIENT'S ACCESSIOr*NO.
4. TITLE AND SUBTITLE
COMMUTER EXPOSURE MODELING METHODOLOGIES
5. REPORT DATE
February 1979
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Patricia B. Simmon and Robert M. Patterson
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
SRI International
333 Ravenswood Avenue
Menlo Park, California 94025
10. PROGRAM ELEMENT NO.
1AA601 CA-04 (1977)
11. CONTRACT/GRANT NO.
68-02-2754
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory - RTP, NC
Office of Research and Development
U. S. Environmental Protection Agency
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final 9/77 - 10/78
14. SPONSORING AGENCY CODE
EPA/600/09
15. SUPPLEMENTARY NOTES
16. ABSTRACT
Two methodologies for modeling commuter exposures are proposed:
computer-oriented approach and a manual approach. Both modeling methodologies
require that major commuter routes, or pathways, be identified and that the
traffic on the remainder of the roadway network be treated as background
pollutant sources. Since the majority of pathway exposure is expected to
result from emissions on the pathway itself, the emissions and dispersion of
non-pathway source pollutant are handled in a simple fashion. Pathway traffic
undergoes a more sophisticated treatment in that congestion and delay due to
signalization are accounted for and emissions are computed accordingly. The
methodology used to simulate the dispersion of pathway emissions utilizes three
separate dispersion treatments, according to whether the roadway is limited-
access, non-limited access, or a street canyon.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
* Air pollution
* Vehicular traffic
* Personnel
* Exposure
* Mathematical Models
13B
051
06T
12A
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report/
UNCLASSIFIED
21. NO. OF PAGES
167
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
155
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