STANFORD RESEARCH INSTITUTE
Final Report
September 1970
A PRACTICAL, MULTIPURPOSE URBAN
DIFFUSION MODEL FOR CARBON MONOXIDE
By: F L. LUDWIG
ALBERT E. MOON
WARREN B. JOHNSON
ROBERT L. MANCUSO
Prepared for:
COORDINATING RESEARCH COUNCIL, INC.
30 ROCKEFELLER PLAZA
NEW YORK, NEW YORK 10020
NATIONAL AIR POLLUTION CONTROL ADMINISTRATION
411 WEST CHAPEL HILL STREET
DURHAM, NORTH CAROLINA 27701
CONTRACT CAPA-3-68
CONTRACT CPA 22-69-64
SRI Project 7874
Approved:
R. T. H. COLLIS, Director
Aerophysics Laboratory
RAY L. LEADABRAND, Executive Director
Electronics and Radio Sciences Division
Copy No.
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ABSTRACT
This report describes the development and current status of a receptor-
oriented diffusion model that can be applied to urban areas to give the fol-
lowing outputs: (1) carbon monoxide (CO) concentration isopleths for a given
set of meteorological conditions and times of day, (2) sequences of hourly CO
concentrations at specific locations for given sequences of meteorological
conditions, and (3) climatological summaries of CO concentration for specific
locations if an historical record of meteorological data is available. The
model can be used to obtain the frequency distributions of concentrations aver-
aged over various time intervals for specific hours of the day or days of the
week.
Model inputs are traffic volumes on major streets and highways in the
urban area, atmospheric stability,, mixing depth, and wind speed and direction.
Traffic volumes can be obtained from either past measurements or forecast
values. Methods are described for obtaining atmospheric stability and mixing
depth from conventional (i.e., airport) hourly meteorological measurements and
twice daily radiosonde data. Meteorological parameters are assumed uniform
throughout the urban area. When the airport winds are calm the model uses a
small finite value of wind speed and the last observed wind direction.
The concentrations calculated with the model are compared with observations
of CO concentration from Continuous Air Monitoring Program (CAMP) stations. Al-
though the agreement is not good—the model generally calculates concentrations
lower than those observed—improvement is obtained by empirical corrections.
Possible reasons are given for the disagreement between calculations and obser-
vations, and a field measurement program is described that the authors feel
will help to define the sources of the discrepancies and provide the infor-
mation necessary for their correction.
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SUMMARY
If city planners and highway planners are to include air pollution
effects among the factors to be considered in the urban and highway de-
sign processes, then some method must be made available that will allow
them to estimate the magnitude and nature of the effects that will arise
from implementation of various plans. This report describes the results
of the first year's efforts to develop a method for determining the air
pollution consequences of various city and highway planning alternatives.
The approach taken has been that of the numerical model, i.e., a scheme
for calculating air pollution concentrations from information about air
pollution sources and meteorological conditions.
The long-term objectives of the program are to develop a model that
will accurately calculate the concentrations of any pollutant at virtually
any point in any city, if meteorological conditions and pollution sources
are known. The objectives include being able to calculate the statistical
distributions of concentrations at a point, as well as single values
appropriate to some specific set of conditions.
During this first year we limited ourselves to developing a calcu-
lational scheme for carbon monoxide concentrations, largely because this
pollutant is relatively nonreactive, permitting us to focus our efforts
on the meteorological side of the problem. After this is in hand, work
to extend the model to chemically active pollutants will be in order.
The model as presently developed incorporates diffusion submodels based
upon both Gaussian and uniform (to the top of the mixing layer) vertical
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monoxide at any point in a city using readily available meteorological
and traffic data. Techniques have been developed to estimate,, from ob-
served quantities, those model inputs that are not directly observed.
The model can provide statistical summaries and estimates for individual
situations. The model has been applied to five different cities (St.
Louis, Washington, Chicago, Cincinnati, and Denver) in several different
ways to demonstrate its versatility. This report contains examples of
the following different types of calculations:
(1) Maps of concentration isopleths for the five cities,
based on calculated concentrations at 625 points
(25 * 25 grid). Inputs were specific observed meteoro-
logical conditions from 1964 or 1965 weather records
and historical, diurnally corrected 1965 average
traffic data.
(2) Week-long sequences of calculated hourly concentrations
at single points in each of the five cities. Inputs
were historical average traffic data and hourly
meteorological observations.
(3) Maps of concentration isopleths for St. Louis based on
forecasts of 1980 traffic, two hypothesized levels of
exhaust emission control, and specific meteorological
conditions corresponding to those used for a 1964
case.
(4) Ten different concentration frequency distributions for
a location in St. Louis, based on a five-year (1960-64)
meteorological record and historical average traffic
data. The frequency distributions presented include
those of
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• Concentrations during all hours
• Concentrations during weekday, Saturday, or
Sunday hours
• Concentrations at the following hours: 0800,
1200, 1800, or 2400 local time (includes day-
light savings time corrections)
• 8-hour and 12-hour averages of concentration.
(5) The same ten frequency distributions based on St. Louis
traffic forecasts and the same five-year meteorological
record.
(6) The median and 90-percentile values of hourly concen-
trations at nine St. Louis locations, based on the same
data as Item (4).
(7) The median and 90-percentile values of hourly concen-
trations at nine St. Louis locations, based on the same
data as Item (5).
When the concentrations calculated by the model are compared with
those measured at Continuous Air Monitoring Program (CAMP) stations, the
agreement is found to be generally poor, with observations usually
higher than calculations. There are many possible sources for the dis-
crepancies, but each falls into one or more of three categories:
(1) Inadequate input data for the model
(2) Inappropriate assumptions used in the modeling
(3) Unrepresentative or inaccurate CAMP observations.
The consequences of several possible sources of error in the first
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to its various inputs. The inputs include source strength (determined
from traffic data)^ wind speed and direction (measured at the local air-
port), atmospheric stability (determined from conventional airport
meteorological observations), and mixing depth (determined from airport
radiosonde temperature measurements). The calculated concentrations
are directly proportional to source strengths, but, in general, sources
nearest the receptor are the most important in determining the calcu-
lated concentration.
Calculated concentrations are inversely proportional to wind speed.
Stability changes can cause large changes in calculated concentration,
particularly when the mixing layer is deep. If the air is relatively
unstable so that mixing proceeds rapidly and if the mixing layer is
relatively shallow, then calculated concentrations are almost propor-
tional to the mixing depth used. As the stability and mixing depth in-
crease, the sensitivity of the model to changes in the mixing depth
becomes less and less.
The possible sources of error that can be included in the category
of inappropriate assumptions include those that would arise from taking
airport meteorological observations to be valid throughout the city.
from the assumption of Gaussian dispersion, and from our handling of the
calm-wind case. The report concludes that local values of input meteoro-
logical parameters would provide an improvement over the present assump-
tion of uniform meteorology. The Gaussian dispersion assumption is also
discussed, and it is concluded that the dispersion rates used may not be
seriously in error, but further study is needed. As presently constituted,
the model takes a measured (airport) calm to correspond to an urban wind
of small finite speed (1 m/s) from the most recently measured (airport)
direction. Better methods of treating this difficult case are being
sought.
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The only CO data available for checking our model in the five
cities to which it was applied are the CAMP station data. The model
evaluation thus depends upon the representativeness and accuracy of
these data. Some of the CAMP stations are located near parking lots
or large buildings, where aerodynamic effects are likely to be a signi-
ficant factor. All measure CO concentrations at single points rather
than over areas comparable to the spatial resolution of the model.
These factors could contribute importantly to differences between ob-
served and calculated concentrations. Other possible sources of error
include water vapor interference and the relatively poor precision
(1 ppm) of the observations.
Attempts have been made to correct some of the model's discrepancies
using a least squares statistical method in conjunction with St. Louis
CAMP Station observations. These attempts focused on errors that might
arise because of differences between winds observed at the airport and
those in the city, and on errors that might come from poor estimates of
the fractions of the total daily traffic that occur during individual
hours. After the statistical adjustments have been made, the model can
reproduce the high concentration parts of the observed frequency dis-
tribution of independent data with good accuracy. Its performance on
individual hourly values is slightly better than "predictions" based
upon a long-term mean value of concentration. The model also performs
about as well as "persistence," i.e., assuming that concentration has
the value observed 24 hours earlier-
The report concludes with a discussion of our plans for a program
of field measurements that should help to define the most serious sources
of discrepancies between observed and calculated concentrations. This
measurement program should also provide much of the information neces-
sary to correct the discrepancies.
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Meteorological and CO measurements are planned for several loca-
tions and at several heights above street level in and around downtown
intersections in San Jose and St. Louis. These should help define the
characteristics of aerodynamic flow effects around buildings and oi
differences in meteorology between the airport and the downtown area.
When combined with the detailed traffic data available from downtown
San Jose, these data should also provide a test of the accuracy of the
relationship used to determine CO emissions from traffic data. Study
of the detailed traffic data should provide intormation on the probable
representativeness of historical traffic data, which are based on very
limited counting periods. We also plan field measurements of CO con-
centrations at various points in the vicinity of the St. Louis CAMP
Station. These should serve as a check on the accuracy and representa-
tiveness of the available CAMP data.
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CONTENTS
ABSTRACT iii
SUMMARY v
LIST OF ILLUSTRATIONS xv
LIST OF TABLES xix
I INTRODUCTION 1
A. Scope and Objectives 1
B. Fundamental Concepts 3
II ELEMENTS OF THE BASIC MODEL 5
A. Spatial Partitioning of Emissions 5
B. The Gaussian Model 7
C. The Box Model 9
D. Transition from Gaussian to Box Models 9
E. Required Inputs for the Basic Model 10
F. Simplifying Assumptions 11
III DETERMINATION OF THE INPUTS 15
A. Emission Inventory Design 15
1. General 15
2. Calculation of Primary Network Emissions
Using Historical Data 22
3. Calculation of Secondary Traffic Emissions
Using Historical Data 24
4. Calculation of Emissions Using Forecast
Traffic Data 25
B. Meteorological Inputs 28
1. Gaussian Standard Deviation Function 28
2. Stability Category 30
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3. Mixing Depth 32
4. Wind Speed and Direction 33
IV ORGANIZATION AND APPLICATIONS OF THE SYNOPTIC AND
CLIMATOLOGICAL MODELS 37
A. Introduction 37
B. The Synoptic Model 38
1. Description 38
2. Applications 40
C. The Climatological Model 58
1. Background 58
2. Description 59
3. Applications 62
V TESTING AND IMPROVING THE MODEL 77
A. Sensitivity Tests 77
1. Source Strength 78
2. Wind Speed 80
3. Wind Direction 80
4. Location of the Receptor 81
5. Stability and Mixing Depth 83
B. Use of Observations to Improve the Model 88
1. Introduction 88
2. Attempted Improvements 89
3. Example 93
VI DISCUSSION AND FUTURE PLANS 99
Appendix A—PRINCIPAL SOURCES OF CO IN URBAN AREAS 107
Appendix B—THE URBAN TRANSPORTATION PLANNING PROCESS .... 113
Appendix C—METHODS FOR DETERMINING STABILITY CATEGORY. . . . 121
Appendix D—METHODS FOR DETERMINING MIXING DEPTH 129
Appendix E—INCREASING THE SPATIAL RESOLUTION FOR EMISSIONS
IN THE FIRST SEGMENT 143
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Appendix F—TREATMENT OF EXTRAURBAN SOURCES AND
STREET EFFECTS 147
Appendix G—PROGRAM FOR PREPROCESSING OF THE DATA FOR THE
CLIMATOLOGICAL MODEL 155
Appendix H—THE EQUIVALENCE OF CERTAIN COMBINATIONS
OF STABILITY AND MIXING DEPTH 161
Appendix I—CONTINUOUS AIR MONITORING PROGRAM STATIONS. . . . 167
ACKNOWLEDGMENTS 177
REFERENCES 179
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ILLUSTRATIONS
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Diagram of Segments Used for Spatial
Partitioning of Emissions
Figure 7
Figure 8
F i gur e 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Computer-Generated Display of Traffic
Links in a 24-by-24-Mile Central Portion
of the Primary Network for Washington, D.C..
Hourly Distribution of Trips in
Washington, D.C
Hourly Distribution of Traffic for Two
Facility Types in St. Louis
Simplified Schematic Diagram of Traffic Link
Assignment Subroutine Used for the Five
Segments Closest to the Receptor
Illustration of the Grid-Point
Transformation Technique Used for Computing
the CO Emissions within the Four Most
Distant Segments
a Functions Used in the Model
z
Simplified Flow Chart for Synoptic Model
Calculations
Simplified Flow Chart for Concentration
Calculations
Calculated Washington, D.C., Concentration
Patterns
Calculated St. Louis Concentration Patterns
0700-0800, 15 October 1964
Calculated Concentration Patterns Based on
Forecast of 1990 St. Louis Traffic ....
Calculated St. Louis Concentration Patterns
for Two Grid Sizes
16
18
18
20
Calculated Carbon Monoxide Concentrations
(PPM) for Chicago
21
31
39
41
43
44
45
47
48
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Figure 15 Calculated Carbon Monoxide Concentrations
(PPM) for Cincinnati
Figure 16 Calculated Carbon Monoxide Concentrations
(PPM) for Denver
Figure 17 Observed and Calculated CO Concentrations
at the St. Louis CAMP Station, 18-24
January 1965
Figure 18 Observed and Calculated CO Concentrations
at the St. Louis CAMP Station, 19-25
October 1964
Figure 19 Observed and Calculated CO Concentrations
at the Washington, B.C., CAMP Station,
19-25 October 1964
Figure 20 Observed and Calculated CO Concentrations
at the Cincinnati CAMP Station, 14-20
December 1964
Figure 21 Observed and Calculated CO Concentrations
at the Chicago CAMP Station, 20-26
July 1964
Figure 22 Observed and Calculated CO Concentrations
at the Denver CAMP Station, 19-25
April 1965
Figure 23 Simplified Flow Chart of Climatological
Model ,
Figure 24 Simplified Flow Chart for a Program to
Determine Ten Different Frequency
Distributions
Figure 25 Calculated St. Louis CAMP Station CO
Concentration Frequency Distribution for
1965 Traffic Conditions; Weekday, Saturday,
and Sunday Hours
Figure 26 Calculated St. Louis CAMP Station CO
Concentration Frequency Distribution for
1965 Traffic Conditions; 0800, 1200, and
1800 Hours
Figure 27 Calculated St. Louis CAMP Station CO
Concentration Frequency Distribution for
1965 Traffic Conditions; 1-Hour, 8-Hour,
and 24-Hour Averages ,
49
50
51
52
54
55
56
57
63
65
67
68
69
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Figure 28 Spatial Variations of Calculated St. Louis
Median and 90 Percentile Concentrations
for 1965 Traffic Data
Figure 29 Calculated St. Louis CAMP Station CO
Concentration Frequency Distribution
for 1990 Traffic Conditions; Weekday,
Saturday, and Sunday Hours
Figure 30 Calculated St. Louis CAMP Station CO
Concentration Frequency Distribution
for 1990 Traffic Conditions; 0800, 1200,
and 1800 Hours
Figure 31 Calculated St. Louis CAMP Station CO
Concentration Frequency Distribution
for 1990 Traffic Conditions; 1-Hour,
8-Hour, and 24-Hour Averages
Figure 32 Spatial Variations of Calculated St. Louis
Median and 90 Percentile Concentrations
for 1990 Traffic Conditions
Figure 33 Effect of Wind Direction on Concentrations
Computed for the Washington, D.C., CAMP
Station
Figure 34 Effect of Moving Receptor Point
Figure 35 Normalized Concentration as a Function
of Stability and Mixing Depth
Figure 36 Diurnal Emission Patterns for St. Louis. .
Figure 37 Observed and Calculated Frequency
Distributions for Five Months of
Independent Data
Figure D-l Schematic Representation of the Diurnal
Temperature/Time Interpolation of Mixing
Depth
Figure G-l Simplified Flow Chart of Program for
Converting Holzworth's Mixing Depths
to Hourly Values
Figure G-2 Simplified Flow Chart of the Data
Processing Program Used with the
Climatological Model
70
71
72
73
74
82
84
86
94
98
140
158
159
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Figure 1-1 St. Louis CAMP Station 171
Figure 1-2 Cincinnati CAMP Station 172
Figure 1-3 Chicago CAMP Station 173
Figure 1-4 Washington CAMP Station 174
Figure 1-5 Denver CAMP Station 175
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TABLES
Table I
Average Speeds for Washington, D.C.,
Table II
Table III
Table A-I
Table C-I
Table H-I
Table H-II
Percentage Increase in Calculated CO
Concentration Resulting from the Doubling
of Emission Rates in Different Segments. . . .
Results of Model Calibration
Percent CO Contribution by Source Category . .
Stability Categories .
Values of (x/Q). . for Unit Wind Speed . . .
79
96
110
124
164
166
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I INTRODUCTION
A. Scope and Objectives
There is a need for an objective, practical method of simulating
the current and future impact of motor vehicles on air pollution in
urban communities. Such a technique could be used to assess current
concentration patterns of primary vehicular pollutants in cities, and
to predict the effects of exhaust emission controls and expressway
routings on future concentration patterns. This report describes our
progress in developing a simulation model designed to meet these ob-
jectives. Further refinements of this model are indicated and will be
made in the course of our continuing study. In this sense, the model
is not yet a completely finished product, and any present applications
should be carried out with caution.
In developing the model, we have been aided considerably by pre-
vious urban diffusion modeling studies, which have been reviewed and
*
summarized by Wanta (1968), Stern (1969), Moses (1969), and Neiburger
(1968). An investigation of carbon monoxide diffusion in Washington,
D.C., by Ott et al. (1967) and Clarke's (1964) model could be considered
prototypes for the model described here.
For simplicity, the modeling effort has been restricted to carbon
monoxide (CO), since (1) the gas is relatively inert in the atmosphere
*
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*
with no known significant natural sources or sinks in urban areas,
(2) motor vehicles are known to be the most important source of the CO
in urban air, and (3) CO is an important pollutant in terms of health
effects.
Our goal has been to develop a versatile, practical model to pre-
dict street-level CO concentrations at any point in a city. Calculations
of the following types can be made using the model:
(1) Hourly concentrations as a function of time, for veri-
fication use and possible operational applications, and
(2) The frequency distribution of concentrations for
selected averaging times, including statistical pre-
diction of the frequency of occurrence of specified
high concentrations for planning purposes.
To improve the accuracy of the model, we have developed calculation
schemes to assess the concentration contributions resulting from diffu-
sion on various scales, including the treatment of:
(1) Extraurban transport and diffusion, mainly from upwind
cities, and
(2) General intraurban diffusion from arterial and feeder
streets.
Too little is yet known about the effects of nearby buildings and
streets to permit these influences to be included in the model, but
*
Although evidence is mounting that such sources and sinks may be found
in the biosphere (Swinnerton et al., 1969; Went, 1966; Robinson and
Robbins, 1967). Concentrations arising from such sources could be in-
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studies currently underway should substantially add to our knowledge in
this area.
In developing the model we have attempted to:
(1) Bring together into a single model the best features
of previous efforts and supplement these with original
contributions where necessary.
(2) Maintain simplicity unless additional complexity is
required to achieve greater accuracy, and is clearly
justified in terms of the accuracy of the available
input data and the resulting increased computing
costs.
B. Fundamental Concepts
Our plan has been to develop the model around individual pieces,
or "modules." These modules were to be organized in different ways to
accomplish different objectives. In computer programming terms, this
means that several subroutines were used in the program. This approach
has been useful, although it has been applied differently than originally
anticipated. The same general organization is used in all the applica-
tions, but modules are changed to reach the different objectives. This
characteristic has allowed us to change different aspects of the model,
and to experiment with a minimum of disruption of the overall system.
The organization of this report reflects the modular nature of the
diffusion model it describes. We have chosen to describe the basic
model and then the various forms that the subunits of that model have
taken. Much of the detailed description of the subunits is confined to
the appendices of this report. Results obtained with the model are also
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the available input information, and of the data available to verify the
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II ELEMENTS OF THE BASIC MODEL
A. Spatial Partitioning of Emissions
Our diffusion model is a modified form of the receptor-oriented
model developed by Clarke (1964). The concentration at the receptor
is considered to be due only to emissions located within logarithmically
spaced segments, such as shown in Figure 1. This arrangement of seg-
ments allows more precise selection of effective emissions near the re-
ceptor. The closest segment extends from the receptor to 125 m, roughly
comparable to the size of a city block, and the farthest segment extends
to 32 km, approximately the diameter of a large city.
The 22.5° sector width is convenient and fits reasonably well the
angular plume widths, between ±2 a points, predicted by Gifford's (1961)
model for slightly unstable conditions. The sector width is expanded
to 45° within the closest 1 km to allow for the large initial lateral
dispersion observed during the St. Louis tracer studies (Pooler, 1966;
McElroy, 1969).
Because nearly all urban carbon monoxide emissions are from internal
combustion vehicles (see Appendix A), the model assumes emissions to be
at ground level. Furthermore, the emissions within each segment are
assumed to be uniformly distributed. Thus the total emission from all
the highway links and parts of links that lie within a segment is averaged
over the area of that segment. The emissions from the smaller and resi-
dential streets are also included. The methods for determining emissions
are described in a later section of this report. Here, it is sufficient
to note that each upwind segment is assigned an average emission rate
-2 -1
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16km
8
RECEPTOR
POINT
1000m
500
EXPANDED VIEW OF
ANNULAR SEGMENTS
WITHIN 1 km OF
RECEPTOR
250
125
RECEPTOR
POINT
TA-7874-1S
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The small size of the segments near the receptor provides good spatial
resolution for the close sources, where such resolution is important.
For farther areas the detailed location of individual sources is not
very important because diffusion processes during transport intermingle
the individual emissions before they reach the receptor. The sacrifice
of resolution at greater distances simplifies the calculations, but
does not substantially affect the results.
B. The Gaussian Model
Gifford (1961) has developed a generalized diffusion model to
describe the plume from a continuous ground-level point source, assuming
perfect reflection at the ground. In its simplest form, the ground-
level concentration from a ground-level source is given by
Q / 2 2
c = - exp -
where
3
C - ground-level concentration (g/m )
Q = source strength (g/s)
u = average wind speed (m/s)
y = lateral (crosswind) distance from the plume axis (m)
a , Q = lateral and vertical standard deviations of plume con-
y z
centration (m); these parameters are functions of distance
between the source and the receptor and of atmospheric
stability.
When Eq. (II-l) is integrated over y, we obtain the following basic form
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1/2
-1 -1
In this formulation Q has the units g m s
L
Estimates of c as a function of atmospheric stability and pollu-
z
tant travel distance or time have been proposed by Gifford (1961) and
Smith and Singer (1966), and urban observations of this type have been
*
reported by Pooler (1966) and McElroy (1969). We have used Gifford' s
values, but the model is flexible and can use any set of functions that
can be reasonably approximated, over the intervals between segment
boundaries, with expressions of the form
b. .
a = a r 1J , (II-3)
z ij
where r is the travel distance, the subscript i refers to annular seg-
ments upwind of the receptor point (see Figure 1), and j refers to dif-
ferent stability classes. The determination of stability class is
discussed later in the report. The a functions are generally well
z
approximated by this set of power functions.
Substituting Eq. (II-3) into the line-source equation and inte-
grating with respect to r from r = r to r gives the contribution to
i i+1
th
the calculated concentration from the i segment area source tor
stability class j:
*
Gifford's work is a modification of that by F. Pasquill (1961). The
Gifford-Pasqui11 curves are based upon data from open country, and
probably underestimate the diffusion in urban areas. We are examining
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0.8 ,
b
(l-
\
u a. . x
b =1 (II-4)
ij
where r. and r. are, respectively, the distance to the downwind and
th
upwind boundaries of the i segment. In this expression Q is the
th -2 -1
average emission rate from the i segment and has the units g m s
This basic Gaussian model applies when there is no effective limitation
to vertical mixing or when the cloud has not spread sufficiently to be
affected by such a limitation.
C. The Box Model
When the layer into which the pollutants are being dispersed is
restricted, then they will tend to become uniformly distributed in the
vertical after sufficient travel has taken place. Under these conditions,
the "box" model is used. According to the box model, the concentration
arising from a uniform area source ii
by (see Miller and Holzworth, 1967):
th
arising from a uniform area source in the i annular segment is defined
r - r
i+l i
r , (n-5)
uh
where h is the depth of the layer into which the pollutants are mixed.
D. Transition from Gaussian to Box Models
We have chosen to change from the Gaussian model to the box model
at that point where the two (in their respective line source formulations)
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source is:
C = Q /uh . (11-6)
L
Setting the right-hand sides of Eqs. (II-2) and (II-6) equal to each
other, and solving for r gives:
\1/bi '
r = (0.8h/a 1 1J . (II-7)
T \ ij/
In Eq. (II-7), r is that value of r for which the box and Gaussian
models give equivalent results. At this distance, we change from Eq.
(II-4) to Eq. (II-5) in calculating concentrations. The part of an
annular segment downwind of r is treated according to the Gaussian
model, and the part that is upwind, according to the box model. If the
transition occurs in segment i, then r is substituted for r in the
Gaussian equation and for r. in the box equation.
E. Required Inputs for the Basic Model
Equations (II-4) and (II-5) are the basis of the model. In order
to use these equations to calculate the concentration at a receptor,
the values of certain input variables are required. These inputs are:
(1) The wind direction
(2) The average transport wind speed
(3) The average emission strength within each of the upwind
segments
(4) The depth of the mixing layer
(5) The variation of a with travel distance.
z
-------
The last item requires that we select some empirically or theo-
retically determined function that describes the dependence of a on
z
distance for the meteorological conditions for which we are calculating
the concentration. As will be discussed later, these functions may be
conveniently approximated in the form given by Eq. (II-3).
None of the necessary inputs are routinely measured, except wind
speed and direction. To satisfy the requirement that the model be
generally applicable in a variety of cities, we have had to develop
methods of deriving the model inputs from readily available information.
Section III of this report describes the ways in which the inputs can be
determined from conventional traffic data and from routine meteorological
measurements.
F. Simplifying Assumptions
Before proceeding to the next section, it should be noted that two
broad simplifying assumptions have been made with regard to the meteoro-
logical data. First, the meteorological inputs have been taken to be
uniform throughout the urban area, and second, they have been assumed
to remain constant during the travel of the pollutants between source
and receptor. For example, it may take two hours for pollutants to
travel to the receptor from the farthest segment, but we assume that the
meteorological parameters such as stability and mixing depth have re-
mained constant at the value they have when those pollutants arrive at
the receptor. The assumption of horizontal uniformity of the meteoro-
logical factors is made, in large part, because it represents the best
available estimate of the situation. Winds are seldom measured at more
than a very few locations in an urban area, so we must generally make
do with a single measured wind. There appears to be no reason, in
principle, why the emission segments upwind of the receptor could not
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be laid out along a wind trajectory, if the trajectories were known and
the added complexity were warranted by improved results.
Variations of mixing depth and stability almost certainly occur
through a city, but at present there are seldom, if ever, sufficiently
detailed data to determine such variations. As a matter ot tact, the
measurements required to determine a mixing depth are usually made at
some distance outside the urban area. A similar situation exists with
the information required for stability estimates. We must therefore
assume the estimates of mixing depth and stability are typical oi the
area, although we do make some adjustments to account for the gross
effects of urbanization.
The assumption that diffusing pollutants have been subjected,
throughout their trajectory, to the conditions prevailing at the time
of their arrival at the receptor is justified when the quality of the
input data is considered. We have already conceded our inability to
determine the spatial changes. In general, we would expect the temporal
changes to be comparable with the spatial, so treating one without
treating the other could constitute an unwarranted complexity. Though
the winds are measured hourly, as are the data from which stability is
determined, mixing depths must be interpolated between values estimated
at half-day intervals. Again the principle of consistency suggests that
added complexity to account for changes in conditions during the travel
period of the pollutants is unwarranted.
One other factor that concerns the assumption of temporal constancy
of inputs is the relative importance of emissions at different distances
to the observed concentrations at a point. Calculations with the model
indicate that contributions of emissions to the concentration at a point
decrease with increasing distance, other things being equal. Thus, the
nearby sources, with correspondingly short travel times, are the major
-------
factors in determining the concentration. The short travel times from
these sources minimize the likelihood of substantial change in the
meteorological parameters. This factor alone is probably sufficient to
justify the simplification of taking meteorological factors to be con-
stant during the time that pollutants travel from their source to the
receptor.
-------
Ill DETERMINATION OF THE INPUTS
A. Emission Inventory Design
1. General
The emission inventory for the model consists entirely of the
emissions from vehicular sources, since these sources are responsible
for almost all urban CO emissions (see Appendix A). The inventory of
vehicular emissions has two components: (1) primary network link
emissions from vehicles traveling on the network of major arterial
streets and freeways, and (2) secondary background emissions from
vehicles traveling over the less densely traveled local and feeder
streets.
The primary network links for which the emissions are computed
are the sections of major arterial streets and freeways between inter-
sections with other major arterials and freeways. The average length
of the links on the primary network is approximately one mile, although
the links may be much shorter in densely traveled downtown areas, and
more widely spaced in outlying areas. Figure 2 illustrates the network
used for the Washington, D.C., area. Computer-generated displays of
the links, like that in Figure 2, are very useful for detecting errors
in coding.
Traffic volumes on links vary hour-by-hour over a day and are
different for weekend days than for weekdays. Further, there are
smaller seasonal variations. Highway engineers and planners average
these variations into a quantity that they call average daily traffic
(ADT).
-------
TA-7874-18S
FIGURE 2 COMPUTER-GENERATED DISPLAY OF TRAFFIC LINKS IN A 24-BY-24-MILE
CENTRAL PORTION OF THE PRIMARY NETWORK FOR WASHINGTON, D.C.
-------
For use in the synoptic model, the emissions must be expressed
as hourly averages, so the average daily traffic is expressed as a func-
tion of time. The amount taken to occur within any given hour is based
on the hourly distribution of trips compiled by the traffic study
agencies of many areas. A typical weekday diurnal pattern of trips is
shown in Figure 3. There are, however, limitations to the accuracy of
the assumption that the traffic on each link is distributed like the
hourly trip pattern. We know that trips taken during the morning and
evening peak hours are longer than those taken during other times of
the day, and that the pattern of use of different kinds of streets in
different parts of the city is different, as shown by the comparison in
Figure 4 of hourly volume on a freeway and a downtown arterial in the
St. Louis area. It is preferable to use the data on hourly distribution
of trips, rather than hourly traffic volume, because it is easier to use
and more widely available. In Section V of this report, an hourly
traffic pattern has been determined on the basis of statistical compari-
sons of calculated concentrations and those measured at the Continuous
Air Monitoring Program (CAMP) Station in St. Louis. That diurnal pattern
clearly reflects the traffic in the central city area around the CAMP
Station.
Urban transportation studies generally do not explicitly survey
or forecast weekend travel. This is because peak traffic loads on most
of the facilities in the area occur on weekdays during the morning and
evening commute hours. Urban highway networks are therefore designed
to handle these peak loads. Because of this preoccupation with peak
weekday traffic, little weekend travel data is available. It is known,
however, that peak loads occur on certain rural or suburban roads used
for travel to recreational areas during weekends, and that the traffic
patterns on Sunday vary significantly over time and space from weekday
patterns.
-------
04 08 12 16 20 24
HOUR OF DAY — LST
TA-7874-14
FIGURE 3 HOURLY DISTRIBUTION OF TRIPS IN WASHINGTON, D.C.
12
10
w
O
<
cc
LU
u
cc
HI
I
II I I I I I I
RADIAL EXPRESSWAY
CIRCUMFERENTIAL ARTERIAL
I I
00
04
08 12 16
HOUR OF DAY — LST
20
24
TA-7874-1S
FIGURE 4 HOURLY DISTRIBUTION OF TRAFFIC FOR TWO
FACILITY TYPES IN ST. LOUIS
-------
Data that show weekend travel patterns are based upon a very
limited sample—from five permanent locations in Nashville, Tennessee
(Institute of Traffic Engineers, 1965). These data show that total
Saturday traffic is about the same as the average daily traffic (ADT),
and that total Sunday traffic is about 70 percent of ADT. Hourly traffic
flows are also available from these counting stations. From these data,
diurnal traffic patterns for Saturday and Sunday have been prepared and
used in the diffusion model operation.
In order to calculate the contribution of the emissions from
traffic links within the five closest segments, the links are first
identified with the segments through which they pass. Then the length
of the link that lies within a given segment is determined. The compu-
tational scheme developed for making these determinations is illustrated
in Figure 5. For these calculations, the segment boundaries are taken
as straightline fits to the curved boundaries illustrated in Figure 1.
The coordinate system is transformed to one that originates at the re-
ceptor and is oriented in the upwind direction.
The emissions within the four segments farthest from the re-
ceptor are calculated by a different technique than that used for the
closer segments. The outermost segments are larger than those nearby,
and it was felt that the spatial resolution achieved by the link assign-
ment technique was not necessary when the emissions were to be averaged
over the entire large area, of each outer segment. The scheme that was
developed requires less computation time than the link assignment method.
Before other computations begin, the city is divided into a
grid of one-mile (1.6 km) squares. The traffic link data are used to
determine the average daily CO emission in each of these squares. This
is accomplished by dividing each link into small increments, less than
0.08 km long. The average daily emission from each of these small pieces
-------
READ IN X, Y, 6
COMPUTE SIN e. COS 6
READ IN TRAFFIC LINK DATA
* • * »
x,, Vr x2, y2, V, f, L
TRANSFORM AND ROTATE COORDINATES
x = (x* X) cos 6 (y* Y) sin 0
y = (x* X) sin 6 + (y* Y) cos 0
T
RECEPTOR
POINT
CHECK FOR LINK FALLING WITHIN
DIFFUSION SECTOR; DETERMINE AREA
SEGMENTS CONTAINING END POINTS
1
LOCATE INTERSECTIONS OF LINK
WITH BOUNDARIES DIVIDING
AREA SEGMENTS
LOCATE INTERSECTIONS OF LINK
WITH SIDE BOUNDARIES OF
AREA SEGMENTS
LOCATES A's
LOCATES B's
COMPUTE PROPORTIONATE LINK LENGTH
FALLING WITHIN EACH AREA SEGMENT
COMPUTE AND ACCUMULATE CO
CONCENTRATION CONTRIBUTION FROM
LINK TO EACH AREA SEGMENT
REPEAT FOR OTHER LINKS
RECEPTOR
POINT
TB-7874-4
FIGURE 5 SIMPLIFIED SCHEMATIC DIAGRAM OF TRAFFIC LINK ASSIGNMENT SUBROUTINE
USED FOR THE FIVE SEGMENTS CLOSEST TO THE RECEPTOR
-------
is determined by assuming emissions are spread uniformly along the link.
Then, the emissions from all the small pieces of link within a square
are added together to give total daily emissions for that square. This
total is paired in the computer memory with the coordinates of the point
at the center of the square. These calculations are done only once for
the city. <
A trapezoidal grid system is used in the four outer emission
segments. As the location of the receptor changes or the wind direction
changes, these trapezoidal grids are superimposed on different parts of
the fixed city emission grid described in the preceding paragraph.
Figure 6 shows a superposition of a movable trapezoidal grid (marked by
+ 4- + + +
Small section of fixed emission grid
(crosses). The CO emission per unit
area is initially computed at these
grid points from traffic link data.
Eighth segment of diffusion sector
and movable trapezoidal grid (circles).
Emission values for segment grid are
interpolated from the values of the
fixed emission grid (crosses).
TA-7874-77
FIGURE 6 ILLUSTRATION OF THE GRID-POINT TRANSFORMATION
TECHNIQUE USED FOR COMPUTING THE CO EMISSIONS
WITHIN THE FOUR MOST DISTANT SEGMENTS
the circles) on the fixed city grid (marked by the crosses). The average
emissions at each point on the trapezoidal grid are determined by inter-
polation between the values at the points on the fixed grid. The average
of the emission values determined for the points on the trapezoidal grid
defines the emission rate for the segment.
-------
A technique similar to that just described was used to determine
the emissions due "to traffic on the secondary streets. The average
secondary emissions were determined for squares two miles (3.6 km) on a
side (see Section III-A-3). The secondary emissions were then determined
from the value on the fixed two-mile grid for each of the nine movable
segments, using basically the same superimposed-grid technique just
described. However, for the small segments near the receptor, the trape-
zoidal grid was replaced by a single point at the segment center. Once
the emissions due to the secondary traffic were determined, they were
added to those already determined, either directly (for the first five
segments) or indirectly (for the outermost segments), from the primary
traffic link data.
Traffic data sources and the data handling varied with the use
of the model. Data obtained from measurements of past traffic were used
as inputs to produce comparisons with the CAMP Station data. Traffic
forecasts were used to calculate pollution concentrations for future
years. The traffic data were obtained and treated as described below.
2. Calculation of Primary Network Emissions Using Historical Data
Historical data for the network description, the node coordi-
nates, and link distances are obtained from highway and street maps.
The network is described by assigning numbers to the intersections, or
nodes, of the network and by identifying the pairs of nodes that are
connected by links. The coordinates of the nodes establish the locations
of the traffic links in the network. Link distances are measured along
the links, rather than as the shortest distance between the nodes, al-
though, as noted in the preceding section, the assignment of the emissions
assumes that the link is a straight line between the nodes.
-------
Historical link-volume data are obtained from traffic depart-
ments in the cities, towns, and counties in the region being studied.
These agencies sample traffic volumes by means of portable counting
units and a few fixed installations. Their observations may be almost
continuous, or as infrequent as once every two or three years. Because
traffic varies according to seasonal, weekly, and daily cycles, an ob-
servation of volume for one day must be adjusted for the weekly and
seasonal fluctuations. The resultant corrected value is recorded as the
average daily traffic (ADT) for that location.
The emission rate, e (g/vehicle-mile), is determined from the
equation
8
e = c SM (III-l)
where S is the average speed over the link, in mi/hr, and c and 3 are
constants. For vehicles in use before exhaust control systems, c = 1121
and 3 = -0.849, as determined by Rose et al. (1964) from observations on
a number of vehicles in several locations.
Link speeds for use in the emission rate calculation are de-
termined from averages for peak and off-peak travel hours on various
kinds of route facilities. Speed data were obtained from the traffic
survey. For example, speeds used in the Washington, D.C., area were
based upon the study by Wilbur Smith and Assoc. (1958) and are shown in
Table I.
For other locations, the peak traffic hour speeds were taken
as equal to 80 percent of the off-peak speeds. Peak-hour speeds were
generally assigned to the four heaviest traffic hours of the day.
-------
Table I
AVERAGE SPEEDS FOR WASHINGTON,, D.C., HIGHWAY FACILITIES
Facility Type
Suburban Freeway
Downtown Freeway
Suburban Arterial
Downtown Arterial
Local or Feeder Street
Average Speeds
(mi/hr )
Peak Traffic Hours
(0700-0900, 1600-1800)
42
33
30
24
10
Off-Peak Traffic Hours
(0000-0700, 0900-1500,
1800-0000)
48
39
36
30
12
Accuracy of the historical data is limited by the frequency
with which it is recorded and by the accuracy of the factors used to
correct it to average daily traffic. However, since locations with
/
heaviest traffic are generally monitored most often, the most confidence
may be placed in data of highest volumes.
3. Calculation of Secondary Traffic Emissions
Using Historical Data
The number of vehicle-miles traveled on streets not represented
by the primary network is computed from an estimate of the total vehicle-
miles traveled in the area and the total vehicle-miles on the links of
the primary network. The local street mileage is taken to be the dif-
ference between the two. It is distributed over the study area by esti-
mating the relative density of local streets as opposed to parks, open
spaces, or streets already coded, for each four-square-mile area in a
two-mile-by-two-mile grid covering the area. The emissions from the
local street travel in a given square are assumed to emanate uniformly
-------
from that square. Although the emission per mile per vehicle is high
on these local streets because of low speeds, the overall contribution
is small because of the small number of vehicles on these local streets.
4. Calculation of Emissions Using Forecast Traffic Data
Most urban areas in the United States have completed or are
conducting an area-wide transportation study to determine traffic de-
mands and transportation facility needs for future years, e.g., 1980 or
1990. Such studies are required for participation in federal highway
programs. An important result of these studies is a design of a future
traffic network for the area and a forecast of the traffic volumes on
the links of this network. The procedure for conducting these studies
has been highly developed and partially standardized (see Appendix B).
The emission inventory components of the model are designed so that the
network description (including link length and facility types), link
volume, and link speed data of the widely used traffic-planning com-
puter programs, in magnetic tape form, can serve as input for the diffu-
sion model. In most cases, the only manual step required will be the
measurement and coding of node coordinates for the network.
Traffic forecasts include travel on both primary and secondary
networks. The primary network links are usually represented in the
analysis just as they appear on the street map. However, local or
feeder streets are represented in the traffic forecast analysis as
connectors between the assumed center of population of a traffic zone,
where all traffic in that zone is assumed to originate, and points on
the primary network. The vehicle-miles on connector links therefore
approximate those expected on local streets, but the traffic is concen-
trated on a few links, rather than spread over a broad area. This is
compensated for in the model by averaging the emissions from these links
-------
over a background grid. The connector links never explicitly appear in
the spatial positioning process where individual links are analyzed.
Accuracy of the forecast traffic data is difficult to estab-
lish. One study that sought to appraise the accuracy of earlier fore-
casts was unsuccessful in finding a case where the planning recommendations
had been followed sufficiently closely to make the actual situation
equivalent to the conditions for which the forecast was made (Highway
Research Board, 1968). Checks made to establish the adequacy of cali-
bration of the forecasting models are usually considered successful if
the forecast for present conditions gives link volumes in wide corridors
within 10 to 20 percent of counted volumes. Variations between the
volumes on individual streets within the corridor may be much wider since
the models do not distinguish between parallel routes as readily as do
drivers.
Historical emission rates were computed from a formula derived
from emission data taken from actual highway driving. Comparable data
for the 1966-70 model vehicles are not available. It was therefore
necessary to develop a baseline of performance for the 1968-70 autos in
order to apply the proportional controls for future model years. The
controls used in the 1968-70 era improved emission performance for
acceleration, deceleration, and idle conditions more than for steady
cruise conditions. Since the acceleration, deceleration, and idle con-
ditions are more prevalent at the lower average speeds, the greatest
reduction in emissions due to new control devices is realized for the
lower average speeds.
To determine the approximate nature of the improvement, data
on an engine with and without emission controls (Beckman et al., 1967)
have been used together with data on driving conditions encountered on
various types of roads. These driving data were collected by SRI for
-------
an earlier project. A computer program was developed to determine the
carbon monoxide emissions per mile versus average speed for route seg-
ments sampled in the road-test data.
One hundred thirty-nine emission values were calculated from
emission data presented by Beckman et al. (1967) and from actual obser-
vations of speeds, speed changes, and stops for a variety of road types
and traffic congestion conditions. Regression analysis was used to
examine the relation between emissions and average speed, both with and
without controls. The following power function proved to be the best
fit for 1969 model year automobiles:
-0.48
e = 245 S , (III-2)
where e is the carbon monoxide emission in grams per mile, and S is the
average speed on the network link in miles per hour.
Increasingly stringent regulations on exhaust emissions will
require further reductions in CO emissions from automobiles. The best
estimates of future levels of controls are that allowable emission
values on the test cycle will be reduced from the equivalent of 34 grams
per mile (1.5 percent by volume) in 1969, measured on the federal test
cycle, to 4.5 grams per mile on the test cycle for 1980 and later model
year automobiles. These values were derived from estimates provided by
Mr. Seward of the Ford Motor Company and from work done at NAPCA (Rose
and Krostek, 1969). Although it has been shown that emissions at lower
speeds were reduced more than at higher speeds for the 1969 controls,
the best estimates of future emission control performance is that
emissions will be reduced by the same amount under all engine perfor-
mance conditions. Therefore, a proportional reduction of the emission
model coefficient, equal to the ratio of the allowable emission values
-------
in 1969 and 1980, has been applied to the 1969 emission model to make
it applicable to post-1980 automobiles. The resulting emission model
for 1980 and later model year automobiles is:
-0.48
e - 34 S (III-3)
where e and S are as defined before.
B. Meteorological Inputs
1. Gaussian Standard Deviation Function
The Gaussian model requires that we know how the standard
deviation, o , of the vertical distribution of the concentration Iron a
z
line source changes as the pollutants travel downwind. There are
several authorities for these functions (see Slade, 1968). In one
approach different functions are given for different atmospheric sta-
bilities. In the other approach, a single function is specified, con-
taining parameters whose values may depend on the stability or turbulent
mixing conditions.
There are several criteria for the selection of one set oi
functions over another. First, the functions should describe dittusive
behavior as accurately as possible. For our model, they must be capable
of being accurately approximated by power functions over the intervals
defined by the boundaries of the model's emission segments. Finally,
and very importantly, the proper function or parametric values lor a
given atmospheric stability must be easily determinable from routine
meteorological observations. With regard to the last item, it is
preferabie that the functions be determinable Irom observations made
at short intervals, rather than from those made only once or twice a
day. The observations should also be made within the environs of the
-------
city being studied. Thus functions dependent upon hourly suri'ace meteoro-
logical observations are preferable to those based on the twice-daily
upper air observations.
Several authors have given estimates of a as a function of
z
atmospheric stability and the distance that a cloud or plume has traveled
(e.g.., Hilsmeier and Gifford,, 1962; Smith, 1968; Pooler, 1961). On the
basis of the criteria presented earlier, we have selected a set of curves
developed by Gifford (1961) from Pasquill's (1961) work. In this pre-
sentation^ atmospheric turbulent conditions are divided into six cate-
gories, and a curve of O versus distance traveled is given for each of
Z
the six. Methods for selecting the proper stability category have been
developed; these are discussed in the next section.
After selecting the Pasquill-Gifford curves, they were approxi-
mated by power functions as required by the model. The behavior of the
cloud has not been defined by Pasquill or Gifford for distances less
than 100 m. Pooler (1966) and McElroy (1969) have found that there is
an initial rapid mechanical mixing of pollutants released from ground
level sources in urban areas. To approximate this effect the pollutants
were assumed to mix immediately upon release to the point where a was
z
equal to its value at 125 m according to the Pasquill-Gifford curves.
It then remains constant at that value throughout the first segment.
Using this assumption, the Pasquill-Gifford curves were extended to very
short travel distances.
For those conditions where there is rapid mixing, a quickly
becomes very large. The Pasquill-Gifford curves do not extend lo values
of O greater than 3 km. Because the box model will generally be in
z
effect for such large values of 0 , and because the ground level con-
z
centrations accompanying these large o 's will, in any event, be very
-------
small-, it was felt that the curves could be arbitrarily extrapolated
beyond a values of 3 km without serious consequence to the calculated
z
results.
Figure 7 shows the a curves used for the calculations with
z
the model. For the first segment (i = 1, r < 125 m), a is a constant
for each stability type, j. Beyond that the Pasquill-Gifford curves
have been approximated by the power law representations—shown as
straight line segments on the log-log plot.
Although the model currently is based on the Pasquill-Gifford
specification of a as a function of travel distance, it would be a
z
simple matter to change to another specification should that be desired.
All that is required is a new set of constants, the a 's and b 's in
ij ij
Eq. (II-3), to describe the new functions. As long as the new functions
are described by exponential expressions, the rest of the basic model
remains the same.
2. Stability Category
Once we have a set of a functions, we must be able to select
z
the proper one for the calculations. Methods were sought for determining
atmospheric stability from conventional meteorological measurements. To
be useful, any method chosen had to define stability in a way that was
consistent with the definitions used originally to determine the a
z
functions. Other sets of a functions might require different approaches
z
than those given in this section. '
Two methods of stability determination have been used with
this model. One was developed from Pasquill's criteria by Turner (1964)
for use with another model and was simply cast in computer-compatible
form for these studies. Turner's technique was used for the examples
-------
CO
10J
8
6
10
8
6
10
i = 1
EXTREMELY
UNSTABLE
SLIGHTLY
UNSTABLE
MODERATELY
UNSTABLE
NEUTRAL
SLIGHTLY
STABLE
MODERATELY
STABLE
— 2
^4^5^6-^-^S^-^
10"
r, DISTANCE FROM SOURCE — m
10=
TA-7874-46
-------
of synoptic calculations given in later sections. Because this method
was rather complicated, we returned to the original definitions of
stability used by Pasquill to classify his data and developed a some-
what simpler approach directly from these. This technique was used for
the climatological examples presented in later sections. The two methods
generally, but not always, give the same stability category for a given
set of data. The methods are described in more detail in Appendix C.
3. Mixing Depth
To apply the box model it is necessary to know the depth to
which the pollutants will be mixed. Considerable effort was expended
to find a method of estimating mixing depth that required only surface
meteorological observations. Our attempts started with the assumption
that the daytime mixing depth should be closely related to the amount
of heat added to the lower layers of the atmosphere and to the resulting
change in temperature during the period of heating. When mixing depths
were determined by these methods and compared with mixing depths deter-
mined from temperature soundings, it was found that the two sets of
values were virtually uncorrelated. For this reason we were forced to
use upper air data, either directly or indirectly, to determine mixing
depth. We had hoped to avoid the use of these extra data for reasons
of simplification. At this time, that does not seem feasible.
Two methods have been devised for calculating mixing depth.
They are described in detail in Appendix D. The method used for the
synoptic calculations presented in later sections of this report uses
the morning temperature sounding taken by the nearest U.S. Weather
Bureau station. This sounding, when combined with the afternoon maximum
temperature, allows us to calculate an afternoon mixing depth. Early
morning mixing depths make use of a simple model of the mixing layer
-------
over urban areas proposed by Summers (1966) and an empirical relation-
ship among city size and urban and rural nighttime temperatures developed
by Ludwig (1970). A single value of mixing depth is assumed to apply
throughout the urban area, although mixing depth variations have been
observed by Clarke (1969) and Bornstein (1969), and modeled in limited
fashion by Summers (1966) and Leahey (1969).
The other method, which has been used with the climatological
model, is basically the same, but makes use of preprocessed mixing depth
data obtained from Mr. George Holzworth of the National Air Pollution
Control Administration. Use of Mr. Holzworth's tabulations simplifies
the data processing.
Neither method discussed above provides values of mixing depth
for all hours of the day, so interpolation must be used. Again, two
methods were employed. For the climatological model, mixing depth was
interpolated on the basis of time between its early morning and its
afternoon values. The synoptic model interpolated hourly mixing depths
on the basis of observed hourly temperatures for daylight hours and on
the basis of time for the premidnight evening hours. Both interpolation
schemes assumed that mixing depth remained constant during the hours be-
tween midnight and dawn. The reasons for this are discussed in Appendix
D. In general, all the methods gave consistent, though not identical,
results.
4. Wind Speed and Direction
The wind velocity is the only input parameter that is available
as a routine measurement. However, these observations are mostly taken
at airports, where the surface roughness and atmospheric stability are
generally quite different than within the built-up part of the city. It
is known that these different conditions cause variations in wind speed
-------
and direction between the outskirts (where the airports are located)
and the center of "the city. Available measurements of these wind
variations, however, are fairly meager.
In one study, Graham (1968) found an urban/rural average wind
speed ratio for Ft. Wayne of 0.67 at 15-m height and 0.64 at 60 m. These
observations also show the wind direction over the city to be backed by
10° to 15° from that at the outskirts. In Nashville, Schnelle et al.
(1969) found the roof-level wind speed (U ) to be related to the airport
r
wind speed (U ) as
a
U = 0.33 U + 1.0 m/s , (III-4)
r a
where the overbars refer to daily averages. These results are mostly
for daytime conditions. At night the wind speed at low levels over the
city is likely to be higher than that at the airport, due to the greater
mechanical and thermal mixing and the presence of convective local cir-
culations over the city.
In view of the uncertainties in our knowledge of the modifica-
tion of the airflow by the city, we have used the airport surface wind
velocity measurements directly as the transport wind input for the model.
Particularly for daytime use, this may not be a bad approximation. Al-
though the airport surface wind is generally higher (in daytime) than
the urban "surface" wind, the appropriate input for the model is a mean
wind in the layer between from 50 to 100 m above the surface. Since the
wind speed increases with height, a higher wind speed than that at the
urban "surface" is appropriate, and the higher airport wind may help
compensate for this.
-------
*
At any rate, we have used airport winds directly in the model
trials, with the idea of correcting the winds for urban effects later by
using a statistical technique to adjust the wind input for the best
agreement between observed and calculated CO concentrations. The re-
sults of this "calibration" procedure are given in Section V-B.
A further point of some importance is that the present model
cannot handle the case of calm winds (which are fairly common at air-
ports) without some adjustments. The nocturnal urban circulation for
the stagnation case has been reasonably well documented (e.g., Pooler,
1963; Hilst and Bowne, 1966; Clarke, 1969) and takes the form of a con-
vective cell driven by the urban heat island. On this basis, and taking
into account the fact that most anemometers will not respond to very
light winds, we assume in the model a minimum speed of 1.0 m/s for an
airport wind reported as calm. We assume further that the wind direc-
tion is the same as the most recently measured direction. Other
approaches to this problem are possible, but they require the develop-
ment of special models, which was beyond the scope of this first-year's
work.
* o
In terms of direction, to the nearest 10 or sixteenth point of the
compass, as appropriate for the different model configurations.
t
In some of the early calculations, a minimum speed of 2.0 m/s was used.
-------
IV ORGANIZATION AND APPLICATIONS OF THE SYNOPTIC
AND CLIMATOLOGICAL MODELS
A. Introduction
The synoptic model takes the data for a single hour, calculates
and displays concentrations for one or more points within the city for
that hour, and then proceeds to the next hour. This is repeated on an
hour-by-hour basis for some limited time period of interest. The tem-
poral changes of concentration for a specific location can be compared
with the measured values during the same period. The climatological
model provides the statistics of CO concentration for different loca-
tions and various averaging periods.
It was originally planned that the two models would employ signifi-
cantly different approaches. The synoptic model was to calculate con-
centrations, in sequence, using hour-by-hour meteorological observations,
whereas the climatological model was to use meteorological statistics to
determine the frequency of occurrence of different CO concentrations.
As the work has proceeded, the constraints imposed on the clima-
tological model, particularly by the requirements for the statistics of
the concentrations averaged over periods longer than an hour, have caused
the climatological model to become very much like the synoptic model.
The two models are discussed in the following sections: first the
synoptic, then the climatological model. This order is important be-
cause the climatological model eventually developed through simplifica-
tion of the synoptic model. In its final version, it appears that the
climatological model could very serviceably replace the synoptic model
with little sacrifice in accuracy.
-------
B. The Synoptic Model
1. Description
The organization of the synoptic model is shown in Figure 8.
In this flow chart it is assumed that the traffic data for the city are
already stored and that the inputs consist of the meteorological
parameters and the city population and latitude. These items are neces-
sary for the application of the subroutines for computing stability
category and the mixing depth. The calculations start by determining
the afternoon and early morning mixing depths from the appropriate
sounding. Then the meteorological parameters for the starting hour are
read and the stability class determined. Mixing depths are interpolated
by the appropriate method, concentrations are calculated, and then the
next hour's data are read.
The calculations referred to in the box with the double out-
line in Figure 8 are performed using the basic models. The appropriate
form of the model, Gaussian or box, must be applied in each oi the up-
wind segments. Thus, the Gaussian formula, Eq. (II-4), is used for all
segments up to the distance, r , that marks the transition to the box
model. The box model, Eq. (II-5), is used for those segments beyond r .
If r occurs in segment N, then the model is summarized by the following
equation
C = -
1
u
/
N-l
/ Q
^^^j i
\
/ l-ta 1-b \"
I i i i-j I
O.SIr J - r J I
\ i+1 i /
i-< i \
a .( 1 - b I
r - r
N+l T
h
i r\
+ QN
/ 1-b 1-b \
1 il ill
O.Slr J - r J 1
\ T N /
a. .(l - b. \
-
\
9
E-
Qi
i=N+l
r - r
i+1 i
h
"
(IV-1)
-------
READ POPULATION. LATITUDE. INITIAL TEMPERATURE
SOUNDING, DATE, MAXIMUM AND MINIMUM TEMPERATURES,
AND LAST OBSERVED WIND DIRECTION
CALCULATE INITIAL VALUES OF AFTERNOON AND NIGHT
MIXING DEPTHS (SEE APPENDIX)
READ HOUR OF DAY. CEILING HEIGHT, CLOUD COVER,
TEMPERATURE. WIND SPEED, AND DIRECTION
IF WIND IS CALM ASSIGN SPEED THE VALUE 1.0 m/s AND
USE THE LAST OBSERVED DIRECTION
DETERMINE STABILITY CLASS
IS
IT
DAY'
HAS SUNSET OCCURRED WITHIN THE PAST HOUR?
DETERMINE MIXING DEPTH
FROM AFTERNOON VALUE
BY TEMPERATURE INTER-
POLATION
DETERMINE MIXING DEPTH
FROM AFTERNOON VALUE
BY TEMPERATURE INTER-
POLATION
READ NEXT MORNING'S
SOUNDING AND MAXIMUM
AND MINIMUM TEMPERATURES
DETERMINE MIXING DEPTH
BY INTERPOLATION (ON
BASIS OF TIME) BETWEEN
NIGHT VALUE AND VALUE
AT FIRST HOUR AFTER
SUNSET
USE
NIGHT
MIXING
DEPTH
CALCULATE AFTERNOON
AND NIGHT MIXING DEPTHS
CALCULATE CONCENTRATION
FOR ONE OR MORE POINTS
AND DISPLAY RESULTS
STOP
TA-7874-13 R
FIGURE 8 SIMPLIFIED FLOW CHART FOR SYNOPTIC MODEL CALCULATIONS.
Using radiosonde data, Turner's stability index and temperature interpolation.
-------
This equation can be expressed in simplified fashion as
9
!.rM • (iv-2)
ij
In the simplified version the terms Ex/Q]. . refer to the appropriate
square-bracketed terms in Eq. (IV-1).
The application of the equation to the calculation of concen-
tration is shown in the simplified flow chart of Figure 9. This flow
chart is a description of the calculations required in the box with the
double outline in Figure 8.
2. Applications
The synoptic model, as described above, has been used in two
different types of application. In one type, concentration is calcu-
lated for a single hour at 625 points in a square grid covering all or
a selected area of a city. These 625 values are then used for an iso-
pleth analysis. The other application presents the calculated CO con-
centrations at hourly intervals for a week.
We have taken advantage of computer techniques for objective
contour analysis and graphical display. In this work.we have used
*
special subroutines called "CONTOOR" and "GRAPH 4" with the CDC 6400
computer and the CDC 280 cathode-ray tube (CRT) peripheral display
system. The CONTOOR subroutine furnishes objective isolines describing
the CO concentration distribution over an urban area, on the basis of
the grid point values calculated by the diffusion model. These automatic
graphical techniques expedite trial and evaluation procedures.
^
These subroutines were developed, respectively, by S. Briggs and
B. Sifford of Stanford Research Institute.
-------
FROM PROGRAM IN FIG. 8
J
CALCULATE POINT OF TRANSITION FROM
GAUSSIAN TO BOX MODEL
IS ANNULAR SEGMENT ENTIRELY BEYOND
(Upwind of) TRANSITION POINT?
CALCULATE AND
STORE VALUE OF
THE CONCENTRATION-
TO-SOURCE STRENGTH
RATIO (x/Q) FOR THE
SEGMENT ON THE
BASIS OF THE BOX
MODEL.
IS SEGMENT ENTIRELY INSIDE
(Downwind of) TRANSITION POINT?
HAVE ALL ANNULAR
SEGMENTS BEEN TREATED?
CALCULATE AND STORE
X/Q FOR THE
SEGMENT ON THE
BASIS OF THE
GAUSSIAN MODEL.
CALCULATE x/Q FOR THAT
PART OF THE SEGMENT
INSIDE THE TRANSITION
POINT ON THE BASIS OF
THE GAUSSIAN MODEL
AND BEYOND THE
TRANSITION POINT ON
THE BASIS OF THE BOX
MODEL. SUM AND STORE
AS x/Q FOR THE SEGMENT.
CALCULATE THE AVERAGE
SOURCE STRENGTH FOR
EACH SEGMENT. MULTIPLY
BY THE APPROPRIATE
X/Q AND SUM OVER
ALL SEGMENTS.
PROCEED TO NEXT
RECEPTOR POINT.
PRINT RECEPTOR LOCATION
AND SUM OF CONCENTRATIONS
FROM ALL SEGMENTS, PLUS
THE CONCENTRATION
FROM OUTSIDE THE CITY
(Background level).
HAVE ALL RECEPTOR POINTS
BEEN TREATED?
RETURN TO PROGRAM
IN FIG. 8
FIGURE 9 SIMPLIFIED FLOW CHART FOR CONCENTRATION CALCULATIONS.
Corresponds approximately to the box with the double outline in Figure 8.
-------
A sample product of these techniques is given in Figure 10(a).
Here the GRAPH 4/280 display of the CQNTOOR objective analysis is super-
imposed upon the primary traffic network for Washington, B.C. The corre-
spondence between the CO concentrations and road density is evident.
The calculations used the values of wind, mixing depth, and stability
shown in the figure. The objective contouring may be compared with a
manual analysis of the identical data, presented in Figure 10(b). Dif-
ferences between the two patterns were traced to plotting and drawing
errors by the analyst. The hand analysis is smoother, but the objective
analysis is substantially faster, cheaper, and more accurate.
Figure 11 shows two concentration patterns calculated for the
meteorological conditions in St. Louis during the 0600-0700 hour of 16
October 1964. The difference between these two cases is in the traffic
data used. Figure 11(a) illustrates the results based on historical
traffic data. Figure 11(b) shows those results obtained using emissions
based on the traffic forecast process when 1965 demographic data were
*
used as an input. Comparison of the two cases shows that the traffic
"forecast" yields a slightly lower peak CO concentration. This may arise
because the forecast program distributes traffic over a different network
of highways and arterials.
Figure 12 provides examples of analyses based on 1990 forecast
*
traffic. For easy comparison with the 1965 case the same hour of the
day and the same meteorological conditions have been used for the calcu-
lations. Figure 12(a) shows the forecast concentrations for cars without
any emission control devices, i.e., like the 1964 cars. Comparison of
*
The traffic forecasts were obtained on magnetic tape from the Missouri
State Highway Department.
-------
-10
-12
0700-0800 LSI
WIND 270° M m I"1
MIXING DEPTH 200m
NEUTRAL STABILITY
-12-10-8-6-4-2 0 2 4 6 8 10 12
DISTANCE EAST OF CAMP STATION — miles
TB-7874-9S
(a) MACHINE ANALYSIS
12,
10
0700-0800 LST
WIND 270°/4 m r1
MIXING DEPTH 200m
NEUTRAL STABILITY
I
N
-12
-12 -10
_8 -6 -4 -2 0 2 4 6 8 10 12
DISTANCE EAST OF CAMP STATION — miles
TB-7874-8S
(b) SUBJECTIVE ANALYSIS
FIGURE 10 CALCULATED WASHINGTON, D.C., CONCENTRATION PATTERNS
-------
12 r
-12
-12 -10 -8 -6 -4 -2 0 24 6 8 10 12
DISTANCE EAST OF CAMP STATION — miles
TA-7874-25S
(a) BASED ON HISTORICAL TRAFFIC DATA
-12
FIGURE 11
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
DISTANCE EAST OF CAMP STATION — miles
TA-7874-60
(b) BASED ON SIMULATED FORECAST TRAFFIC DATA
CALCULATED ST. LOUIS CONCENTRATION PATTERNS 0700-0800,
15 OCTOBER 1964
-------
o
I-
Q.
<
o
LL
O
DC
O
z
111
o
z
co
D
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10
DISTANCE EAST OF CAMP STATION — miles
(a) WITHOUT EXHAUST EMISSION CONTROLS
12
CO
Q_
<
CJ
I
cc
12
10
8
6
4
2
0
-2
LU e
O ~b
I -8
-10
-12
O.5
-12 -10-8-6-4-2 0 2 4 6 8 10 12
DISTANCE EAST OF CAMP STATION — miles
TA-7874-61
(b) WITH EXHAUST EMISSION CONTROLS
FIGURE 12 CALCULATED CONCENTRATION PATTERNS BASED ON FORECAST OF 1990
ST. LOUIS TRAFFIC. Meteorological conditions same as in Figure 11.
-------
this pattern with that in Figure 11(a) shows a very large increase in
«
forecast concentrations. Figure 12(b) shows the results for the case
where the hypothetical emission control (as described in Section III)
has been applied. The significant reduction in CO concentrations is
readily apparent.
By choosing different grid point spacing, the spatial resolu-
tion of the model can be changed. Figure 13 illustrates this. The two
halves of the figure show analyses of CO concentrations in St. Louis for
the same hour. In Figure 13(a) the grid point spacing is 1 mile; in
13(b), 0.1 mile. Both are centered on the CAMP Station. The figure
shows that the model is capable of providing concentration patterns in
considerable detail. It is limited in its spatial resolution, however,
by the size of the emission segments, particularly those nearest the
receptor.
The model has been used to obtain concentration patterns in
five different cities. Examples have already been shown for Washington
and St. Louis. Figures 14, 15, and 16 show results obtained for Chicago,
Cincinnati, and Denver. These figures are all based on 1965 historical
traffic data. They show, as do the other figures, the expected high
concentrations downwind of congested downtown areas and major arterials.
Results of trials using the synoptic model to calculate hourly
concentrations continuously for a week are presented in Figures 17 and
18. To provide a true test of the model's capabilities, weeks were
selected during which a variety of concentration magnitudes were ob-
served, as shown by the dashed curves in the figures. These figures
and those that follow do not necessarily show examples of the best agree-
ment between calculations and observations, but are representative of the
kinds of results achieved. In an attempt to treat the effects of nearby
sources more accurately, the closest diffusion area segment was divided
-------
Q-
<
o
I
DC
O
•
LU
O
CO
1500-1600 CDT
15 OCTOBER 1964
WIND 310°/1.5m s"1
MIXING DEPTH 1670m
UNSTABLE
-8-6-4-2 0 2 4 6 8 10 12
DISTANCE EAST OF CAMP STATION — miles
TA-7874-26s
(a) 1-MILE (1.6 km) GRID SPACING
-1.2
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 1.2
DISTANCE EAST OF CAMP STATION — miles
TA-7874-24S
(b) 0.1-MILE (0.16 km) GRID SPACING
FIGURE 13 CALCULATED ST. LOUIS CONCENTRATION PATTERNS FOR TWO GRID SIZES
-------
-20
-15
-10 -50 5 10
DISTANCE EAST OF CITY CENTER — miles
15
TA-7874-62
FIGURE 14 CALCULATED CARBON MONOXIDE CONCENTRATIONS (PPM) FOR CHICAGO.
(0700-0800 LST, wind 270°/4 ms~1, mixing depth 200 m, neutral stability)
-------
-12 -10
-6-4-20 24 6
DISTANCE EAST OF CAMP STATION — miles
10
TA-7874-73
FIGURE 15 CALCULATED CARBON MONOXIDE CONCENTRATIONS (PPM) FOR CINCINNATI.
(0700-0800 LST, wind 270°/2 ms~1, mixing depth 200 m, slightly stable)
-------
-12 -10
-6 -4-20 2 4 6
DISTANCE EAST OF CAMP STATION — miles
10 12
TA-7874-63
FIGURE 16 CALCULATED CARBON MONOXIDE CONCENTRATIONS (PPM) FOR DENVER.
(0700-0800 LST, wind 315°/2 ms~1, mixing depth 400 m, slightly stable)
-------
o.
o.
o
o
o
o
E §
X
UJ
o
m o
25 -
20
Q 15
10
OBSERVED -
CALCULATED
Q.
UJ
Q
4000
2000
- tt 400
200
S 20
— uj
o Q.
10
10
.,. ••««».•.,
20
WON
40
TUBS
60
WED
80 100 120 140 160 HOURS
THURS-4— FBI -I- SAT -|« SUN —-I
FIGURE 17
ST. LOUIS, MO. DATA [JANUARY 18-24. 1965)
TA-7874-47
OBSERVED AND CALCULATED CO CONCENTRATIONS AT THE
ST. LOUIS CAMP STATION, 18-24 JANUARY 1965. The
meteorological inputs to the model are also shown.
-------
o.
a
1
o
o
o
o
4000
J £ 2000
X
i
Q
o
o
UJ
Ld
Q.
Q
2
5
in
i
400
200
0
20
10
0
10
o
z
i!
20
MON
40
TUES
60
WED
80
THURS
100
120
140
FRI -!•" SAT —*+
ST. LOUIS. MO. DATA (OCTOBER 19-25. 1964)
160 HOURS
SUN —|
TA-7874-49
FIGURE 18 OBSERVED AND CALCULATED CO CONCENTRATIONS AT THE
ST. LOUIS CAMP STATION, 19-25 OCTOBER 1964. The
meteorological inputs to the model are also shown.
-------
into two sections for these calculations (see Appendix E). One segment
extends from the receptor to 62.5 m in range, and the other extends from
62.5 out to 125 m. The calculations also include estimates of the ex-
traurban background, i.e., contributions from emissions outside the
city, made with the model described in Appendix F. Figures 17 and 18
also show the values of the meteorological inputs to the model, either
as observed or as calculated.
The CO observations during the January period (Figure 17) were
anomalously high, and the model generally gives underestimates for this
*
week. A variety of weather conditions prevailed; cold fronts passed
St. Louis on the evenings of 17, 19, and 23 January. The poorest per-
formance of the model occurs on 19, 21, and 22 January, when the wind
was generally southerly. This suggests that the high observed concen-
trations may be caused by the nearby sources on the adjacent streets,
since the St. Louis CAMP Station is located on the northwest corner of
an intersection.
Weather conditions during the October period (Figure 18) were
not so variable, and more typical CO concentrations were observed. In
contrast to the January period, the predicted concentrations are often
too high. The worst agreement occurs when the airport winds are reported
as very light or calm. For these calculations, the model used a minimum
wind speed of 2 m/s and, as noted earlier, the last observed wind direc-
tion. It is probable that much of the prediction error is due to this
uncertainty in winds.
The possibility of water vapor interference as a source of some of the
discrepancy between observed and calculated concentrations is discussed
in Section VI of this report.
-------
Many additional calculations of the type illustrated in Figures
17 and 18 for St. Louis have been carried out for Washington, B.C.;
Cincinnati, Ohio; Chicago, Illinois; and Denver, Colorado. Some ex-
amples of these are given in Figures 19 through 22. Prevailing meteoro-
logical conditions are also shown in Figures 20 through 22. It can be
seen that a wide variety of meteorological situations are represented.
In general, the agreement between calculations and observations leaves
much to be desired. The measurement program to be conducted during the
coming year should help us to identify the sources of the discrepancies
and to make corrections.
40 60 80 100 120 140
MON -|-» TUES »[• WED -|« THURS -| • FBI—• | • SAT—-|
WASHINGTON, D. C. DATA (October 19-25, 1964)
160 HOURS
•SUN-
TA-7874-48
FIGURE 19 OBSERVED AND CALCULATED CO CONCENTRATIONS AT THE
WASHINGTON, D.C., CAMP STATION, 19-25 OCTOBER 1964
-------
O> UJ
V OL
5
o
UJ
0.
§
0
20
10
x
UJ
Q
•.-^ .«•""•" """
1,1,
^ 0
=! 8
CD -J
20
140
|— MON •
SAT
CINCINNATI. OHIO DATA (DECEMBER W-20. 196^)
160 HOURS
SUN -~\
TA-7874-50
FIGURE 20 OBSERVED AND CALCULATED CO CONCENTRATIONS AT THE CINCINNATI
CAMP STATION, 14-20 DECEMBER 1964. The meteorological inputs to the
model calculations are also shown.
-------
o.
Q.
O
O
O
o
o
o
35
30
25
20
15
10
OBSERVED
CALCULATED
4000-
2000-
x
5
p 400
o
LU
Q:
Q
Q 20°
0
20
Q
UJ
bj
CL
in
E Q
10
" ^ 0
8 ™ 10
§
o
o
o
80 100 120 140
-THURS-4— FRI -I' SAT
CHICAGO. ILL DATA (JULY 20-26. 1964)
160 HOURS
SUN -—I
TA-7874-51
FIGURE 21 OBSERVED AND CALCULATED CO CONCENTRATIONS AT THE CHICAGO
CAMP STATION, 20-26 JULY 1964. The meteorological inputs to the model
calculations are also shown.
-------
DENVER. COLO. DATA (APRIL 19-25. I965)
160 HOURS
SUN
TA-7874-52
FIGURE 22
OBSERVED AND CALCULATED CO CONCENTRATIONS AT THE DENVER
CAMP STATION, 19-25 APRIL 1965. The meteorological inputs to the model
calculations are also shown.
-------
C. The Climatological Model
1. Background
There are two different approaches to calculating climato-
logical summaries of the concentration of carbon monoxide at a site.
The most commonly used approach starts with a joint frequency distribu-
tion of all the meteorological variables that affect the concentration.
For our model there are five variables: wind speed and direction, time
of day, mixing depth, and stability. There would be 24 categories of
time, and 16 of wind direction. Six categories each for wind speed and
mixing depth, and five categories for stability would probably provide
sufficient resolution for climatological purposes. With these numbers
of categories, the joint frequency distribution would have 69,120
entries.
As will be shown in a later section, some combinations of
stability and mixing depth are essentially equivalent to others. By
combining equivalent categories it should be possible to reduce the
number of categories by about a third to a half. This reduction would
make the indexing of the variables slightly more difficult but would
reduce the number of entries in our joint frequency table to about
4
4 X 10 . If only eight wind-direction categories were used, this number
4
could be halved to about 2 X 10 .
The method that has been described above gives the frequency
distribution of hourly values of CO concentration. To obtain the fre-
quency distribution of the 8-hour or 24-hour average values requires
some statistical model, such as Larsen's (1969). Since there is some
uncertainty about the validity of Larsen's model (e.g., McGuire and
Noll, 1970) we felt that it might be better to approach the problem
more directly. If the individual calculated hourly values of concen-
tration are available, in sequence, it is possible to use "running mean"
-------
type operators to get the distribution of concentrations averaged over
periods greater than an hour.
We have already shown that a very large number of categories
have to be considered for the conventional approach using the joint fre-
quencies of the input parameters. In fact, the number of categories
could be very nearly as large as the number of hours in a five- to ten-
year period. Thus, it seemed reasonable to consider the possibility of
calculating hourly values in sequence. This approach, which is described
below, was found to be practical and was adopted.
2. Description
a. Simplifications
To calculate a long series of concentrations economically
requires some simplification of the model. It is possible to represent
the source strengths of the segments as the product of a time-dependent
factor and a time-independent factor. Thus
. ^ <. +.
i,d,t t i
where
th th
Q = the source strength of the i segment, in the d
i)d>t th -2 -1
direction, for the t hour. (gm m s )
Q = the average daily source strength, based on total
i,d
traffic and average speeds on the different roads
-2 -1
within the segment. (gm m s )
-------
th
P - a factor that gives the source strength for the t
hour, based on daily distribution of traffic, and
changes in average speed during peak hours. P is
assumed to be independent of the location in the
city. In some of the previously presented synoptic
applications, P has assumed different values for
different road types.
To further limit the number of conditions to be considered, mixing
depths have been classified into seven categories (<100 m, 100-200 m,
200-400 m, ..., >3200 m). With these simplifications, the model can be
written as follows:
9
p
t V >
c = —
where
C - CO concentration at the receptor
u = wind speed
th
CX/Q) . = ratio of the CO concentration received from the i seg-
ment to the emissions in that segment (for unit wind
speed). The values of these ratios depend on stability
class, j, and mixing depth class, m.
The values of
-------
9
Xj m d ~X/'~' Qj - ' (IV~5)
1=1 ->">™
Then, for a given receptor site, all possible values of X can be
calculated and stored in a 5 X 7 X 16 (stability type X mixing depth
category X direction) array. These values need only be calculated once
for each receptor. These numbers, when combined with the 24-item list
of P values, provide the information necessary to calculate concentra-
tion at a given receptor. The storage space required is less than 600
numbers. The operating equation for the climatological model is
(P \
t\
— . (IV-6)
u /
b. Preprocessing of the Meteorological Data
Equation (IV-6) can be applied most easily when we have
converted the usual meteorological observations to a sequence of records
of time (t), stability (j), mixing depth category (m), direction on a
16-point compass (d), and wind speed (u). This preprocessing of the
data is described in Appendix G. Five years (1960-1964) of St. Louis
meteorological data have been condensed and recorded on magnetic tape.
These five years of data constitute a reasonably stable climatological
description of that city, although anomalies of this duration do
occasionally occur. Five years of data are used partly because
Holzworth's tabulations of mixing depth cover only a five-year period,
and partly because longer periods of record would increase the calcu-
lation time disproportionately to the small increase in climatological
accuracy. Although it is quite possible in principle to use radiosonde
data from the National Weather Records Center to extend the period of
-------
record, their data are not universally available on magnetic tape for
all U.S. stations, and the processing of large quantities of punched
cards presents practical difficulties.
3. Applications
The preprocessed data are used as the climatology of the city.
The effects of changes in the transportation network or of emission con-
trols are then assessed by determining a set of values of Q . which
i,d
are used to calculate X . The five-year meteorological data se-
j,m,d
quence is used with Eq. (IV-6) to determine a sequence of CO concentra-
tions. A simplified flow chart showing this process is given in Figure
23.
In Appendix H it is shown that there are different combinations
of stability and mixing depth that give the same value of (X/Q) for
i,j,m
all the upwind segments. Because this is the case, we were able to re-
duce the stored number of values of (y/Q) . This results in a corre-
i,J,m
spending reduction in the required number of values X , from 560 to
j,m,d
400 per site. The simplified model makes it feasible to calculate a
sequence of CO concentrations for each of a number of points in the city.
Once this is done, these sequences can be treated as though they were
sequences of real observations. Thus, it is possible, without resorting
to a statistical model, to calculate any of the statistical parameters
that can be determined from sequences of real hourly observations. This
includes the frequency distribution of 8-hour averages, 24-hour averages,
or the frequency distribution of any special subset of the data.
As noted above, the output of the climatological model can be
treated in any way that observed data can be treated. This means that
the potential number of outputs is virtually unlimited. For purposes
of illustration, a computer program has been written to determine ten
-------
yes
(
START
No
INPUT THE FOLLOWING DATA:
1. Q for 9 upwind segments d), 16 wind directions (d), and n number of city locations
2. (X/Q). . for upwind segments, stability classes (j), and mixing categories (m)
3. P 's for different hours of day (t) and days of week (w)
t,w
4. Determine, and store values of X for n city locations
J.m.d
Read first record: year, month, day, and m, j, u, and d for 24 hours
Determine if it is a daylight savings time month
Determine the day of the week code: w 1 is weekday, w 2 is Saturday, and w 3
is Sunday
Adjust t to account for daylight savings time and set u < 1.0 m/s to 1.0 m/s
Calculate
p t,W
u
or t 1,24 and fo
9 / Y \
S ( X I n
U/ .
1 = 1 M, m
,
r n number of city locations
+ extraurban contribution
,d
r
Record year, month, day of week, and C for 24 hours and n city locations
i
r
Read next record: year, month, day, m, j, u, and d for 24 hours
TA 7874-41 R
FIGURE 23 SIMPLIFIED FLOW CHART OF CLIMATOLOGICAL MODEL
-------
different frequency distributions based on the output from the cliraa-
tological model:
(1) All hours, a frequency distribution based on
the total five-year set of hourly calculated
concentrations
(2) All weekday hours
(3) All Saturday hours
(4) All Sunday hours
(5) All 0800 hours
(6) All 1200 hours
(7) All 1800 hours
(8) All 2400 hours
(9) 8-hour means; frequency distribution of the
averages of the values calculated for all 8-
hour periods in the five-year sequence
(10) 24-hour means; same as (9), except for 24-
hour averages.
A simplified flow chart for the program used to calculate the
above frequency distributions is shown in Figure 24. This program also
computes cumulative distributions, and determines median (50 percentile)
and 90-percentile values by log-linear interpolation between the points
calculated on the cumulative distributions.
We used the climatological model to calculate a five-year
sequence of CO concentrations at nine locations, including the CAMP
Station in St. Louis. For these calculations, a constant 0.25 ppm
background concentration was added, based on the observations of
-------
SET FREQUENCY 0 FOR FACH DATA SUUTYPF
AND EACH LOCATION WITHIN THE CITY
READ FIRST 24 HOURLY VALUES OF
CONCENTRATION FOR EACH LOCATION
DETERMINE SUM OF CONCENTRATIONS TOR
HOURS 1 THROUGH 2-1 AND 17 THROUGH
'14 FOR EACH LOCATION
READ AND DETERMINE CONCENTRATION CLASS
(• 0 25 ppm . 0 76 - 0 5 ppm , >64 p»m )
FOR NEXT HOUFtLY CONCENTRATION
ADO 1 TO FREQUENCY IN PROPER CLASS FOR
TYPE I DISTRIBUTION (See Tax!)
IS IT SATURDAY
IS IT A
WEEKDAY '
I YESING
ADD 1 TO FREQUENCY
IN PROPER CLASS FOR TYPE
2 DISTRIBUTION (See Texl)
ADD 1 TO PROPER
CLASS FOR TYPE 3
DISTRIBUTION (S«e Text!
ADO 1 TO PROPER
CLASS FOR TYPE A
DISTRIBUTION (See Text!
ADD CONCENTRATION TO 24-HOUfl SUM AND SUBTRACT
VALUE FOR 2-5 HOURS EARLIER ADD CONCENTRATION TO
8-HOUR SUM AND SUBTRACT VALUE FOR 8 HOURS EARLIER
DIVIDE 21- AND 0-HOUR SUMS BY 24 AND 8
RESPECTIVELY AND DETERMINE THE CONCENTRATION
CLASS OF THE RESULTING AVERAGES
ADD 1 TO THE FREQUENCIES IN THE PROPER CLASSES
FOR THE TYPE 9 AND 10 DISTRIBUTIONS ISei- Text)
YES
YES
*
ADD 1 TO FREQUENCY
IN PROPER CLASS FOR
TYPE 7 DISTRIBUTION
(Sue Te*ll
ADD 1 TO FREQUENCY IN
PROPER CLASS FOR TYPE
6 DISTRIBUTION ISce Text)
ADD 1 TO FREQUENCY IN PROPER
CLASS FOR TYPE 8 DISTRIBUTION
(See Ten)
I
a
a —
IS IT END OF FILE
SUM THE FREQUENCIES IN EACH CONCENTRATION
CLASS TO DETERMINE TOTAL NUMBERS OF
OCCURRENCES FOR EACH DISTRIBUTION
TYPF AND LOCATION
DETERMINE RELATIVE CUMULATIVE FREQUENCIES
if. TOTAL PERCENT OF OCCURRENCES LESS
THAN EACH OF THE CLASS BOUNDARIES
FOR EACH DISTRIBUTION TYPE AND LOCATION
DETERMINE MEDIANS AND ")0 PFRCENTILF. VALUES
BY LOG LINEAR INTERPOLATION BETWEEN CLASS
BOUNDARIES, FOR EACH DISTRIBUTION
TYPE AND LOCATION
PRINT STATISTICAL RtGULFS
TA-7874-64
FIGURE 24 SIMPLIFIED FLOW CHART FOR A PROGRAM TO DETERMINE TEN DIFFERENT
FREQUENCY DISTRIBUTIONS
-------
Robinson and Robbins (1967). The calculations used traffic emissions
appropriate to 1965. We then applied the program diagrammed in Figure
24 to these results and obtained frequency distributions of the types
enumerated above for each of the nine sites.
Figure 25 shows the calculated St. Louis CAMP Station fre-
quency distributions for weekday, Saturday, and Sunday hours. The figure
shows the expected decrease in the frequency of the higher concentrations
on the weekend, and the corresponding increase in the lower concentra-
tions. Figure 26 shows the frequency distributions of concentrations at
0800, 1200, and 1800 Local Standard Time. The greater frequencies of
high concentrations at 1800 are quite evident. The 0800 also shows a
considerably greater number of occurrences of concentrations above 2 ppm
than does the 1200 distribution. Figure 27 shows the frequency distri-
butions of concentrations averaged over three different time intervals,
1-hour, 8-hours, and 24-hours. Qualitatively, the results are just as
expected. The mode remains the same, between 1 and 2 ppm, but the spread
of the distributions decreases appreciably with increased averaging time.
The output of the program can also be used to determine spatial
variations of certain statistical parameters. For example, Figure 28
shows the variation of the median and 90-percentile values for nine sites
along a north-south line passing through the St. Louis CAMP Station. As
expected, the highest values are calculated for the downtown area, where
the CAMP Station is located.
The calculations described in the preceding paragraphs were
repeated using the emissions based on the 1990 traffic forecast for
St. Louis. The results are displayed in Figures 29 through 32. As was
evident in Figure 12, the hypothesized emission controls result in a
decrease in CO concentration from 1965 to 1990, although the amount of
traffic increases. Some of the same qualitative features are seen in
-------
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TA-7874- 93R
FIGURE 25 CALCULATED ST. LOUIS CAMP STATION CO CONCENTRATION FREQUENCY
DISTRIBUTION FOR 1965 TRAFFIC CONDITIONS; WEEKDAY, SATURDAY,
AND SUNDAY HOURS
-------
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TA-7874-S4R
FIGURE 26 CALCULATED ST. LOUIS CAMP STATION CO CONCENTRATION FREQUENCY
DISTRIBUTION FOR 1965 TRAFFIC CONDITIONS; 0800, 1200, AND 1800 HOURS
-------
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TA-7874-59R
FIGURE 27 CALCULATED ST. LOUIS CAMP STATION CO CONCENTRATION FREQUENCY
DISTRIBUTION FOR 1965 TRAFFIC CONDITIONS; 1-HOUR, 8-HOUR, AND
24-HOUR AVERAGES
-------
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ill i i
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DISTANCE NORTH OF ST LOUIS CAMP STATION — miles
TA-7874-56F
FIGURE 28 SPATIAL VARIATIONS OF CALCULATED ST LOUIS MEDIAN AND 90 PERCENTILE
-------
INTERVAL
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TA-7874-65
FIGURE 29 CALCULATED ST. LOUIS CAMP STATION CO CONCENTRATION FREQUENCY
DISTRIBUTION FOR 1990 TRAFFIC CONDITIONS; WEEKDAY, SATURDAY,
AND SUNDAY HOURS
-------
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TA-7874-67
FIGURE 31 CALCULATED ST. LOUIS CAMP STATION CO CONCENTRATION FREQUENCY
DISTRIBUTION FOR 1990 TRAFFIC CONDITIONS; 1-HOUR, 8-HOUR, AND
24-HOUR AVERAGES
-------
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0.7
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DISTANCE NORTH OF ST. LOUIS CAMP STATION — miles
FIGURE 32 SPATIAL VARIATIONS OF CALCULATED ST. LOUIS MEDIAN AND
90 PERCENTILE CONCENTRATIONS FOR 1990 TRAFFIC CONDITIONS
with emission controls
-------
the 1990 frequency distributions at the CAMP site as were seen in those
based on 1965 emissions. Figure 29 shows that the higher concentrations
occur more frequently on weekdays than on weekends, and Figure 30 shows
that higher concentrations are more likely at 1800 than at 1200 or 0800.
These results are certainly as expected, considering that we have not
changed the diurnal or weekend values of P used in Eq. (IV-6). If
there were a foreseeable change in working hours, a change in these
values might be justified.
Figure 31 for 1990 corresponds to Figure 27 for 1965. Again
we see the reduction in the spread of the frequency distribution as the
averaging period is increased. In this case the change is not so pro-
nounced because there are so few high concentration cases in the dis-
tribution of the hourly values.
Figure 32 shows the change in the 1990 median and 90-percentile
concentrations along a north-south line through the CAMP site. The
scales on this figure are different than those on the corresponding
figure for 1965, Figure 28. Some of the pronounced features of the 90-
percentile curve may be artifacts caused by the log-linear interpola-
tion used to determine the values. It suggests that smaller class
intervals should be used when we know that the calculated concentra-
tions will not reach high values. Regardless of the artifacts, the
data show that the concentrations remain very nearly the same along
this line for several miles through the downtown area.
-------
V TESTING AND IMPROVING THE MODEL
In the preceding sections, the design of the basic model was pre-
sented along with the techniques used to determine its inputs, and
examples of the types of output that the model is capable of producing.
In this section, we will discuss the way in which input accuracy affects
the accuracy of the resultant outputs, i.e., the sensitivity of the
model. We will also present the results of an attempt to "calibrate"
the model by comparing its output to the observed concentrations.
A. Sensitivity Tests
It is important to know the effects in output values caused by
changes in the inputs. If a very small change in a certain input re-
sults in a large change in the output, then the model is very sensitive
to that input and we will be required to provide values of the input
that are very accurate, if we are to avoid large errors in the output.
On the other hand, if large changes in an input have little effect on
the output, then little effort need be expended to achieve high input
accuracy for that particular variable. Of course, sensitivity is not
likely to remain constant over the whole range of values that a par-
ticular variable can assume. Thus it is possible that for certain com-
binations of parametric values, the model output will be totally
independent of the changes in one or more inputs. This, as will be
seen in this section, occurs with this model, and we have referred to
it in earlier sections. This characteristic has allowed us to treat
several different combinations of variables as though they were the
same.
-------
In the following we will discuss the inputs to the model and try
to illustrate their interdependence and their effects on the output.
1. Source Strength
If source strength were to increase or decrease by some factor
uniformly throughout the city, then the resultant change in the calcu-
lated concentration would be quite straightforward. The calculated
concentration would increase or decrease by the same factor. Similarly,
if our emission estimates were uniformly in error, then that error would
show proportionally in our calculations.
A more realistic situation would be the case where the
emissions are poorly estimated for individual upwind segments of the
model. In this case the change in the output will depend not only on
the relative magnitude of the error in emission, but also on the seg-
ment in which the error occurs and on mixing depth and stability. The
relative effect also depends on the average emission rates in other
segments.
To test the effects of errors in the different segments, cal-
culations were made for a case where the true source strength was taken
to decrease linearly away from the receptor and to reach zero at 32 km
upwind. For a site at the center of the city, this is probably a
reasonable approximation of the distribution of emissions. To test the
sensitivity of the model to changes in source strength in the different
segments, we doubled the emissions (relative to those specified by the
assumption of a linearly decrease with distance) in one segment at a
time. The results of these calculations are given in Table II. This
table shows the percentage increases in the total calculated concentra-
tions that result from the doubling of the source strength in the
individual segments. Four stability types and two different mixing
depths are represented in the table.
-------
Table II
PERCENTAGE INCREASE IN CALCULATED CO CONCENTRATION RESULTING
FROM THE DOUBLING OF EMISSION RATES IN DIFFERENT SEGMENTS
Stability
Class*
1
2
3
4
1
1 2
3
4
Mixing
Depth
(m)
50
50
50
50
3000
3000
3000
3000
Segment with Doubled Emission
1
1.4
2.1
3.1
4.5
26.9
22.3
14.6
9.8
2
1.0
1.5
2.1
3.3
17.8
15.9
10.2
7.3
3
1.5
1.6
2.2
3.7
15.2
16.0
10.4
8.2
4
3.0
3.0
3.0
4.3
9.1
14.4
11.1
9.4
5
5.9
5.8
5.7
5.5
3.5
11.2
11.7
11.2
6
11.2
11.1
10.8
10.1
3.6
6.6
12.3
13.4
7
20.1
20.0
19.4
18.1
6.4
4.0
12.5
15.5
8
31.0
30.6
29.8
28.0
9.8
5.3
11.4
16.1
9
24.8
24.4
23.9
22.4
7.8
4.4
5.7
9.1
1 = Extremely unstable
2 - Moderately unstable
3 = Slightly unstable
4 = Neutral.
For the low mixing depth case (50 m) there is a general in-
crease in the contribution caused by changes in source strength as one
progresses toward the segments farthest from the receptor. The box
model is employed for most of the calculations when the mixing depth is
low, and it specifies that the contribution from a segment is propor-
tional to the upwind distance subtended by that segment. Since the
outer segments are considerably larger than the nearby segments, their
contribution is consequently greater. This effect is suppressed in the
larger mixing depth cases where contributions from the nearer segments
are mixed through a shallow layer compared to those from the further
segments.
The table indicates that for some combinations of stability
and mixing depth, appreciable uncertainties can be introduced into the
calculations by uncertainties in the specification of source strength.
-------
Other factors to be considered include the possibility that errors in
specifying emissions may be compensating and therefore not so important.
Finally, errors in emission values due to improper location of
highway links are much more apt to be large, relative to the total source
emission in the smaller, close segments, than they are in the large
outer segments. When the mixing depth is low, Table II shows that errors
in nearby source strengths cause relatively small errors in the calcu-
lated concentration. It is only for the larger mixing depths that the
errors in the nearby segments produce large relative errors in the cal-
culated concentrations. However, for large mixing depths the concentra-
tions tend to be lower and of much less importance to planners.
2. Wind Speed
Of all the inputs, the most straightforward effect on the model
output comes from wind speed. Since both the Gaussian and box models
yield concentrations that are inversely proportional to the wind speed,
then the overall model will also have this characteristic regardless of
where the transition occurs between the two submodels. As the model is
presently constituted, observed wind speeds less than 1 m/s are not used,
so for observed wind speeds less than this value the model output would
not change. For higher wind speeds the calculated concentrations will
vary inversely as the wind speed, providing the other parameters remain
invariant.
3. Wind Direction
With regard to model sensitivity, wind direction and source
strength are closely related parameters. Variations in wind direction
only change the values used for the emissions in the segments upwind of
the receptor, so the effects of changes of segment source strengths dis-
cussed earlier can, to some extent, be interpreted in terms of wind
-------
direction effect. However, this requires that we know something of the
changes in source strength as a function of direction from the receptor.
If the receptor is located at the edge of the city, then changes in wind
direction can shift the emissions in the segments from large to small as
the wind shifts from the city to the countryside. Such changes would be
likely to occur in almost all the segments, for such a case.
For locations near the center of the city, the farther and
larger segments are not likely to change much with direction because
the large numbers of streets within the larger areas will tend to smooth
out the fluctuations. However, for the nearby segments that may on the
average contain only a few streets, the variations are likely to be
large. Since the nearby segments contribute appreciably to the calcu-
lated concentrations, we may expect substantial variations.
To provide an example of the kinds of changes that might be
expected to arise from changes in wind direction, some sample calcula-
tions have been made; they are illustrated in Figure 33. Two sets of
meteorological conditions are shown; we can see that the relative
changes are about the same in both cases. There is about a 3:1 dif-
ference between the largest and the smallest calculated concentrations.
The calculations were made at 22.5° increments, and it can be seen that
the largest difference between adjacent directions amounts to about 60
percent. Thus, it seems reasonable to estimate that an error in wind
direction specification of 22.5" could result in errors as large as a
factor of two.
4. Location of the Receptor
Another factor that is closely related to source strength is
the accuracy with which we can specify the location of the receptor
relative to the traffic links. The arguments are essentially the same
as those given above for direction, i.e., moving the receptor relative
to the links changes the location of the various upwind segments, and
hence changes the source strengths used for the calculations.
-------
Q.
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to
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50
100 150 200 250
WIND DIRECTION deq from N
300
350
TA-7874-6R
FIGURE 33 EFFECT OF WIND DIRECTION ON CONCENTRATIONS COMPUTED FOR
THE WASHINGTON, D.C., CAMP STATION. (0700-0800 LST, neutral
-------
A study was made to determine the sensitivity of the model to
errors in the location of the receptor. The study was conducted by
moving the coordinates of the receptor point from its original location
in increments of 0.1 mile and determining the effect of the displacement
on the concentration. Increments of 0.1 (0.16 km) mile were chosen be-
cause this is the coding precision for most of the areas studied, al-
though in crowded central areas, coordinates have been coded to the
nearest 0.01 (0.016 km) mile. Figure 34 shows changes in the calculated
CO concentration arising from displacements of the receptor in the down-
wind (x) and crosswind (y) directions. The initial location corresponds
to the Washington, D.C., CAMP Station. In this area, with its dense
network of major streets, concentrations are fairly sensitive to the
location of the receptor relative to the streets. Outside the densely
packed downtown area, the sensitivity to location is much less.
The figure shows that changes in calculated concentration of
more than a factor of two do occur within 0.1 mile (0.16km). However,
for a precision of location of about 0.01 mile (16 m), the changes would
be limited to a few tens of percent or less, regardless of wind speed.
The model would probably be more sensitive to these errors for the cases
of low mixing depth and high stability.
5. Stability and Mixing Depth
Stability and mixing depth interact to determine which of the
two submodels are used for the calculation of the contribution of
emissions from a given segment. To determine the effects on the model
output of variations in stability and mixing depth, calculations were
made using two different configurations of carbon monoxide emission.
In the first case, source strengths were assumed to be the same in all
nine segments of the model. It was assumed that there were no emissions
-------
Q.
Q.
z
o
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RECEPTOR LOCATION DISPLACEMENT (X)
(a) ALONG-WIND
a.
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RECEPTOR LOCATION DISPLACEMENT M mi
(b) CROSS-WIND
FIGURE 34 EFFECT OF MOVING RECEPTOR POINT
(Washington, D.C., CAMP Station; 0700-0800 LST, wind 270°/4 ms
neutral stability, mixing depth 200 m)
1.0
TA-7574-5R
-1
-------
beyond the outer boundary of the last segment, 32 km from the receptor.
The results of calculations for this source configuration and for
various combinations of stability and mixing depth are shown in Figure
35(a). The results have been normalized to represent unit wind speed
and unit source strength. In this figure we see that all the results
are essentially the same for low values of mixing depth, regardless of
stability. For very shallow mixing layers, the box model is used for
almost the entire distance upwind of the receptor. Since the box model
results are independent of stability, the fact that the results converge
at small mixing depths is to be expected.
The neutral and slightly unstable cases shown in Figure 35(a)
are unaffected by mixing depth for the larger values of the parameter.
This too is quite reasonable because mixing of the emitted material
proceeds rather slowly under the more nearly stable conditions and the
mixing is uninhibited by the top of the mixing layer, if it is suffi-
ciently high. In such cases, the Gaussian model is used for the con-
centration calculations throughout the entire 32-km upwind distance.
The results of Gaussian model calculations are independent of mixing
depth.
For the moderately unstable and extremely unstable cases the
box model is used in the calculations, for at least some segments, for
mixing depths to 3000 m. However, the number of segments for which the
box model is applicable decreases with increasing mixing depth, so that
calculated concentrations become less dependent on mixing depth as that
parameter increases. This is reflected in the continual approach of the
slope of the curves toward zero. It also suggests that the 4000 m upper
limit that was placed on mixing depth, in some applications of the model,
will have very little effect on the results.
-------
oo
05
1000
800
600
400
200
a
O 100
80
60
40
20
10
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MODERATELY UNSTABLE
EXTREMELY UNSTABLE
(a) UNIFORM SOURCE STRENGTH
I II I I I I I I I I I I
50 100
500 1000
T 1 1—I I I I I
MODERATELY UNSTABLE
EXTREMELY UNSTABLE
(b) SOURCE STRENGTH DECREASING
LINEARLY FROM RECEPTOR
I I I I I I I I I I I
50 100
MIXING DEPTH — m
500 1000
TA-7874-38
FIGURE 35 NORMALIZED CONCENTRATION AS A FUNCTION OF STABILITY AND
-------
As noted before, the assumption of a uniform source strength
over the city is probably less realistic than an assumption of a source
strength that decreases from the center of town to its edge. We recal-
culated the cases used for the curves in Figure 35(a), but used a source
strength that linearly decreased from two units at the receptor to zero
32-km upwind. The results of these calculations are shown in Figure
35(b). Again, the results have been normalized to represent unit wind
speed and unit average source strength. Qualitatively, the two source
configurations produce similar results. However, the dependence on
mixing depth is less for all cases. This is because the mixing depth
dependence is the result of those parts of the calculation based on the
box model. The Gaussian model is used for calculations of concentrations
due to emissions from segments close to the receptor. The box model, if
used at all, applies to the farther segments. In this source configura-
tion the emission rates in the more distant segments are less than those
in segments close to the receptor. Thus, the contributions that the box
model makes to the results are smaller than those for the uniform area
case. This decreases the effect of mixing depths upon the normalized
concentrations.
The results displayed in Figure 35(a) suggest that for some
values of mixing depth, the results obtained from the model are nearly
independent of stability. For certain stability types, changes in the
mixing depth produce no changes in the results, if the mixing depth is
sufficiently large. We have made use of this latter fact in the de-
velopment of the climatological model. It allows us to consider certain
combinations of stability and mixing depth to be identical with certain
others. As noted earlier, this simplifies calculations and reduces the
amount of computer memory required.
-------
B. Use of Observations to Improve the Model
1. Introduction
The formulation of the model given in earlier sections of this
report was based entirely on empirical and theoretical considerations
of traffic emissions, and meteorological diffusion and transport. No
adjustable constants have been used. It is clear that the accuracy of
this model could be improved if we were to make some use of observed
carbon monoxide concentration data. In this section we will discuss a
method whereby this information can be incorporated into the model. In
developing a method, we have attempted to make statistical adjustments
with as little damage to the physical basis of the model as possible.
If the model is to be useful in a variety of cities, it should be de-
veloped from sound physical principles, rather than by purely statistical
means. The physical phenomena underlying the model will remain the same
from city to city, but we cannot assume the same to be true of the
statistics. Of the inputs to the model, source strength, wind speed,
and wind direction have been chosen as the most amenable to study
through the use of statistical comparison with observed CO concentra-
tions. Mixing depth and stability were discarded, partly because neither
is amenable to statistical correction. Both are involved in the model
in such nonlinear fashion that they cannot be isolated from the rest of
the model for statistical treatment. Also, model results are not very
sensitive to mixing depth under most conditions, as was shown in the
preceding sensitivity analysis, so that if the mixing depth is specified
incorrectly, it may be less serious than an incorrect wind speed or
source strength, which are directly related to the output.
In considering source strength, we have assumed that it is
directly related to the total daily traffic and to the average speeds,
but there is uncertainty about how the emissions are distributed through
-------
the day. This uncertainty inseparably includes considerations of the
proportionality of emission rates and traffic amounts. As will be seen
in the following sections, uncertainties in source strength can be mini-
mized by statistical techniques.
We know that wind speed has a very significant and direct
effect on concentration. We also know that the transport wind that
moves and dilutes pollutants in the city may be different than the air-
port wind that we have used for our calculations. The relationship be-
tween the two winds can be determined so as to minimize the differences
between calculated and observed concentrations.
Finally, wind direction probably plays a part in determining
the background concentrations entering the segment farthest from the re-
ceptor and in determining the aerodynamic effects of structures near the
measuring point. The gross effects of wind direction at a given loca-
tion can be checked through comparison of calculated and observed
concentrations.
In the following section an approach to the "calibration" of
the model is presented along with some results. This approach is by no
means the only one possible, but we feel that it has a sound physical
basis, and encouraging results have been achieved.
2. Attempted Improvements
As was shown in Section IV-C, the model can be most simply
expressed in the following form
(V-l)
-------
where
C = calculated concentration due to emissions within the city
X = the sum of the products of average daily emissions in the
j,m,d
upwind segments and the dilution ratios for the segments;
depends on stability (j), mixing depth (m), and wind
direction (d)
th
P = a factor used to give source strengths for the t hour,
based on the daily distribution of traffic and changes in
average speed during peak traffic hours
u = wind speed.
a. Background Concentration
The above equation can be related to the observed concen-
tration C for a given time by the following
C = C + e
o
= x- ,, — I + en , (v-2)
j,m,d \u I 1
where e is the error in specifying the concentration. If we assume
that part of the error arises from a background concentration 13 entering
the farthest upwind segment of the model, then Eq. (V-2) can be written
c = c + 3 + e
(p \
;T + » + «2 •
-------
In this formulation (3 is a constant, although it can be made a function
of wind direction; e is the error remaining after the background has
£i
been added to C.
b. Wind Speed
Let us assume that effective urban transport wind speed
u is not correctly represented by the wind measured at the airport, u
a
and that the true value of its reciprocal can be approximated by a linear
expression depending upon the reciprocal of the measured wind speed at
the airport, i.e.,
1 b
- = a + — , (V-4)
u u
a
where a and b are constants to be determined, and u is the measured air-
a
port wind, assumed to have a minimum value of 1 m s . Assuming the
dilution factor 1/u to be a linear function of the dilution due to the
airport wind makes it much easier in practice to minimize errors than if
we assumed a linear relation between the winds themselves.
Making the substitution in Eq. (V-3) gives
\ P
/ t
au +
c = x '• + 3 + e , (v-5)
o j,m,d u
a
where e is the residual after adjustments have been made.
The problem is then to use the observed data to determine
the values of the constants. To do this we used the conventional approach
and minimized the sum of the squares of the residuals. This procedure
gives the following equations:
-------
X P \
J;I";d 1 = EC (V-6)
Ua
2
P
(3Sx P + aSx p + bS J'm' = EC x. P (v-7)
j,m,d t j,m,d t I u I o j,m,d t
pE. J^Zt) + .flp^L* | + bEM^I = Ef ° J'°'d 1 , (v-8)
\ Ua . - - a
where N is the total number of cases over which the summations are per-
formed. The above simultaneous linear equations were solved for 3, a,
and b using a standard matrix inversion computer program. This minimizes
the root-mean-square error for the hypotheses represented in Eq. (V-5),
and for the available data set.
c. Diurnal Distribution of Emissions
The values of P have been specified for the model on the
basis of only a few measurements in a limited number of cities. After
the wind speed corrections have been made, it is a simple matter to
correct the values of each of the 24 values of P to minimize the total
differences between observed and calculated values. After a new set of
P values has been calculated, they can be used to recalculate the a, b,
and 3. This iterative procedure has been used on a set of St. Louis data
(see the examples given in Section V-3); the correlation and root-mean-
square error were found to stabilize after four repetitions.
d. Wind Direction
The wind direction effect could most easily be included
in the background constant term. The data could be stratified according
-------
to wind direction and values of (3 calculated for each case. The average
of these 3 values (weighted by the number of occurrences of each wind
direction in the data set) would be the same as the value of (3 calcu-
lated from the procedure outlined in the preceding sections. We have
not had sufficient data to stratify according to wind direction, so the
example that follows has not considered that correction.
3. Example
The approach to calibration outlined on the preceding pages
has been applied to data from St. Louis. The earliest CO concentration
records that we have available from the CAMP Station in St. Louis were
for the month of March 1964. The records were fairly complete for the
rest of that year. This provided us with ten months of concentration
data that were concurrent with values that had been calculated using
the climatological model. We chose to determine the calibration con-
stants on the basis of the available odd-numbered months and to use the
even numbered months as independent data for checking the results.
To determine if there was an annual variability to the values
of the constants &, b, and $, they were calculated separately for the
weekdays in each of the odd numbered months. There appeared to be no
regular changes in a and b, but |3 did seem to have a seasonal change.
The seasonal change was incorporated into the corrections. For the
independent months, values of 3 were interpolated between those found
for the odd numbered months. The resulting calibrated equation is
0.07 u + 1.4
C = P X + 0 , (V-9)
u t j,m,d m
a
-------
where
P = the adjusted traffic emission factors determined
statistically
3 = background concentration adjusted for monthly variations.
m
The adjusted values of P are shown in Figure 36. This figure
also shows the values of P derived from trip data. The corrected curve
shows greater midday emission and lower night emissions than had been
0.10 —
Statistically
determined
10 15
HOUR OF DAY
TA-7874-70
FIGURE 36 DIURNAL EMISSION PATTERNS FOR ST. LOUIS
-------
originally postulated. This probably reflects the traffic conditions
in the downtown area near the CAMP Station. Downtown areas attract
considerable traffic during operating hours but very little at night.
This is reflected in the very rapid increase in the value of P at the
beginning of the business day and the corresponding rapid decrease at
its end.
The performance of the model was considerably improved by the
derived constants. Table III shows the correlation coefficient and
root-mean-square errors of the calibrated and uncalibrated models for
the ten months studied. The table also shows the values of (3 used for
m
each month. With these calibration factors included, the model predicts
the hour-by-hour concentrations for the independent months with a root-
*
mean-square error of 3.1 ppm.
The correlation and root-mean-square error resulting from the
use of "persistence" values have been calculated for the weekdays of the
five independent months. For these calculations, the observed CO con-
centration at the CAMP Station was compared with the concentration ob-
served during the same hour of the preceding weekday. The correlation
was 0.64, with a root-mean-square error of 3.0 ppm, so the calibrated
model performed very nearly as well as persistence. Of course, the per-
sistence method cannot be used with forecast traffic data to estimate
conditions in future years.
* / 2
Root-mean-square error - ~\ /[2(C - C ) ]/N
y o c
where
N - number of cases
C = observed concentration
o
C — calculated concentration.
c
-------
Table III
RESULTS OF MODEL CALIBRATION
CD
CT)
Month
(1964)
Calibration Months
March
May
July
September
November
Independent Months
April
June
August
October
December
(ppm)
4.2
5.6
7.0
5.6
4.2
4.9
6.3
6.3
4.9
3.5
Uncalibrated
Correlation
Coefficient
0.45
0.29
0.26
0.27
0.45
0.28
0.32
0.16
0.26
0.39
Root— Mean-Square
Error
(ppm)
5.5
6.2
8.8
5.7
5.9
6.9
8.1
5.0
4.7
5.4
Calibrated
Correlation
Coefficient
0.59
0.61
0.63
0.58
0.61
0.58
0.50
0.63
0.53
0.61
Root-Mean-Square
Error
(ppm)
2.0
2.2
2.3
3.8
3.4
2.3
3.7
3.2
3.3
-------
A second comparison is also available for judging the model's
performance. We can compare it to climatology. The root-mean-square
difference between the observed concentrations and the mean concentra-
tion is the standard deviation of the observed values. For the inde-
pendent data this is 3.5, somewhat greater than the model's root-mean-
square error of 3.1. As with persistence, the concentration climatology
is not a useful tool for estimating future conditions.
One final check can be made of the performance of the cali-
brated model. We can see how well it reproduces the frequency distri-
bution of observed concentrations. This has been done for the independent
weekday hours used in the above calculations; the results are shown in
Figure 37. In this figure, cumulative frequencies are plotted on a log-
probability graph. On such a graph, log-normal distributions appear as
straight lines. It can be seen that both the calculated and observed
distributions differ somewhat from the ideal log-normal. For the high
percentile values, the two frequency distributions agree quite well.
Between the 50 percentile and the 99.9 percentile, the agreement between
the observed and calculated concentrations is generally within 25 percent.
It is the high percentile concentrations that are of greatest importance
to planners, and for these the calibrated model appears to perform very
well.
-------
1
0.5 1
10 30 50 70 90 95 98 99
PERCENT OF HOURLY VALUES < ORDINATE VALUE
99.9 99.99
TA-7874-69
FIGURE 37 OBSERVED AND CALCULATED FREQUENCY DISTRIBUTIONS FOR FIVE MONTHS
OF INDEPENDENT DATA
-------
VI DISCUSSION AND FUTURE PLANS
This report has presented an approach to modeling urban CO concen-
trations that meets most of the established objectives. The model can
calculate hourly concentrations at one or many points in a city. It
can determine frequency distributions and other statistical information
about CO concentrations. Source strengths can be determined from esti-
mates of traffic, either historical or forecast, but assumptions have
to be made about the CO emissions to be expected from the automobiles
of the future. The meteorological inputs for the model can be deter-
mined from readily available weather data.
The model is quite versatile, in that a wide variety of parameters
can be calculated without the need for esoteric input data. In these
respects the model is satisfactory, but its performance has been dis-
appointing in one most important respect. For those few places from
which data are available, the hourly concentrations calculated with the
model and those observed are generally in poor agreement.
The discrepancies between observed and calculated concentrations
may be due to many different causes. In general, these causes can be
divided into three categories: (1) inadequate or inaccurate input data
for the model, (2) invalid assumptions used in the formulation of the
model, and (3) unrepresentativeness or inaccuracy of the CAMP observa-
tions. Specific examples that fall into these categories are discussed
in the following paragraphs.
The first category of observation/calculation discrepancy is errors
in input data. Errors in source strength specification immediately come
to mind as an example in this category. Source strength errors can
-------
arise from erroneous or unrepresentative historical traffic data, or
from inaccurate relationships between average speeds and emission rates.
Such errors can come from anomalous traffic situations such as accidents
or large sporting events, or from assuming an incorrect distribution of
the total daily traffic among the individual hours of the day. The re-
sults given in Figure 36 suggest that there may be significant dif-
ferences between the assumed and the actual distributions in central
St. Louis. The calculated concentrations are directly proportional to
the emissions from traffic, so inaccuracies in its specification can
contribute substantially to the differences between observed and model
results.
Meteorological observations from a single station, usually at the
airport outside the city, are used for the inputs to the model. Except
for wind, these observations are not used directly, but are transformed
to give the basic inputs to the model, i.e., stability type and mixing
depth. Thus the sources of potential input error are twofold. First
the meteorological observations themselves may not represent conditions
in the city, and secondly the methods used to transform the observations
into values of mixing depth and stability may not be totally appropriate.
The sensitivity analyses in the report have shown some of the effects of
such errors on the calculated concentrations. Wind speed and calculated
concentration are inversely proportional. The relationship among mixing
depth, stability, and concentration is more complicated. For unstable
conditions and small mixing depths, the calculated concentration is al-
most inversely proportional to mixing depth, other things being equal.
For large mixing depths, calculated concentration increases quite
rapidly with increasing atmospheric stability. In any event, the re-
sults achieved with the model can be quite sensitive to the inputs, so
inaccuracies in their specification represent potentially important
sources of the discrepancies between model results and observations.
-------
The second category for possible causes of the discrepancies be-
tween calculations and observations includes those that might arise from
any invalid assumptions used in the formulation of the model. The first
assumption made is that the Gaussian model provides a reasonably accurate
description of the diffusion of pollutants from sources near the receptor
and the next is that the rates for this Gaussian diffusion can be defined
by the Pasquill-Gifford empirical functions based on data from nonurban
areas. While it would be difficult to change the model to remove the
Gaussian assumption, it would be quite easy to use other functions to
describe the diffusion rates. Because of increased mechanical and ther-
mal turbulence in cities we might expect the diffusion to proceed more
rapidly than given by the Pasquill-Gifford functions, which would mean
that the presently calculated concentrations are biased to the high side
by this effect. However, the presence of large buildings in downtown
areas restricts the volume into which the pollutants can mix, and such
an effect might counteract those caused by increased turbulence.
Another assumption that is included in the model in its current
form is that of uniform meteorology throughout the urban area. It is
certain that winds in cities are not uniform, and the same is true of
mixing depth (e.g., Clarke, 1969). The stability index also changes
between the edges of a city and its center. It may be that these factors
are not so serious as it first appears because the results that have been
achieved with the model seem to indicate that sources close to the re-
ceptor are the most important in determining concentrations. If this is
indeed true, then wind, stability, and mixing depth close to the receptor
are very important, but their values at greater distances are much less
so. This would mean that different values of the inputs could be used
for different receptor locations, but the basic form of the model would
not have to be changed to accommodate changes of the parameters with
distance upwind of each individual receptor point.
-------
One of the most serious remaining weaknesses of the fundamental
model is the assumption that it can be applied to calm conditions (if
such conditions ever actually exist) by assuming that some slight
organized air movement is present. After we identify and correct other
possible sources of discrepancy between observations and calculations,
it may be feasible to develop a better method for treating this important
special case. Studies of air motions within cities during calm and near
calm conditions would probably be of some help.
The third possible source of error is unrepresentative observations
of CO concentrations. Before discussing examples, the term should be
defined. for our purposes, a representative observation is one that has
very nearly the same value as most of those that would have been obtained
if the measurements had been made simultaneously at many other points in
the same "general area." For studies with this model, the general area"
to be considered should have dimensions comparable to the resolution of
the model, or about 100 to 200 m. Thus, we would consider observations
to be unrepresentative of an area if significantly different results
were likely to be obtained by moving the instrument to some randomly
chosen points within about 200 m of its original location. This defini-
tion of representativeness implies that a monitoring station should be
located at a point where its surroundings are reasonably uniform for
about 200 meters in all directions. Such locations are virtually im-
possible to find in most cities. The CAMP Stations that served as data
sources for the examples given in this report are probably located about
as well as is possible (see Appendix I), but their locations cannot be
considered "representative" in the above defined sense. The readings
from these stations are likely to be biased or otherwise made unrepre-
sentative by the presence of parking lots, traffic signals, and the
aerodynamic effects of large nearby buildings.
-------
The accuracy of the available observations of CO concentration is
somewhat limited by the precision to which observations are reported.
Values are given to the nearest part-per-million, resulting in an un-
certainty of about 0.5 ppm.
Interferences from other atmospheric constituents are also possible
with the instruments. The most likely interferent is water vapor, so
the usual measurement procedures either remove the water vapor itself
from the air to be analyzed, or else neutralize its infrared absorption
interference with optical filters. Nevertheless some questions of
possible interference remain. For instance, at the Washington CAMP
Station it has been found that the removal of CO from ambient air by
Hopcalite does not produce the anticipated readings of zero ppm when the
CO-free air is analyzed; instead, the instrument indicates CO levels of
*
2 to 3 ppm. If the instruments consistently indicate CO concentrations
higher than those actually present, then the actual discrepancies between
observed and calculated concentrations would be somewhat smaller than
presently indicated. However, only a small portion of the disagreement
can be explained by CO measurement errors.
A continuation of the work described in this report is currently
underway. It is directed toward determining the source of the dis-
crepancies discussed above. The major portion of the program will be
devoted to field measurements of carbon monoxide concentrations and
meteorological parameters within urban areas. Results from the earlier
experimental studies of diffusion through cities (e.g., Stanford
*
Letter to W. B. Johnson, dated 10 October 1969, from C. E. Couchman,
Chief, Air Pollution Division, District of Columbia Department of Public
Health.
-------
University Aerosol Laboratory, 1953 a, b, c, d; Perkins,, 1962; Pooler,
1966; Hilst and Bowne, 1966) will continue to be used for the further
development and refinement of the CO model, along with the new data to
be obtained. Although these previous studies are generally limited to
point and line-source releases of tracers and their determinations of
diffusion in the vertical are limited, they should be useful in refining
the Gaussian model for urban applications.
To test the representativeness of CAMP Station measurements, we
plan to measure CO concentrations at various locations around the St.
Louis CAMP Station using a mobile instrument. Mobile measurements will
also be made in other areas of St. Louis and San Jose in order to study
the small-scale spatial variability of concentration.
Other studies of spatial variability are also planned. These will
involve CO, wind, and temperature measurements around downtown inter-
sections in St. Louis and San Jose at several levels from rooftop to
about ten feet above street level. These studies should help to relate
rooftop concentrations, which we believe are better represented by the
model, with concentrations at lower levels, where measurements are
usually made and where most people are exposed to the pollutants. The
observations should also help to determine the nature and importance of
aerodynamic effects caused by airflow around buildings and through the
street canyons. These measurements will test the validity of using
airport meteorological data to represent conditions throughout a city.
Additional observations of temperature profiles and mixing depth varia-
tions across the urban area will check the methods we have used for
estimating mixing depths.
Another input that will be tested during the program is the rela-
tion of observed traffic to the rate at which CO is generated. It is
planned to use the detailed traffic data available from a relatively
-------
dense, computer-monitored network of sensors in downtown San Jose. By
knowing the details of the traffic flow near the CO measuring stations,
it should be possible to test the validity of the relationships between
traffic and CO generation that have been used with the model.
-------
Appendix A
PRINCIPAL SOURCES OF CO IN URBAN AREAS
-------
Appendix A
PRINCIPAL SOURCES OF CO IN URBAN AREAS
The model considers only the mobile sources of carbon monoxide.
The literature was surveyed to determine the importance of other sources
of CO. Table A-I shows the fraction of total CO emissions arising from
various sources for nine individual American cities and a 28-city average.
The table shows that transportation CO emissions range from about 77 to
99 percent of the total for the different cities. According to Mason's
(1969) data, about 98 percent of the CO emissions due to transportation
are from motor vehicles.
San Francisco is the only city shown in the table that has non-
transportation emissions greater than ten percent of the total. The
major nontransportation source in the San Francisco Bay Area was incin-
eration. As of 1 January 1970, incineration has been banned in the Bay
Area. If we assume that the other CO sources remained the same, but all
CO generated by incineration was eliminated, then the San Francisco Bay
Area CO emissions from transportation would be about 92 percent of the
total. This is very nearly the same as the other cities shown.
Inasmuch as more than 90 percent of the CO in urban areas is
generated by traffic, we ignore fixed sources in our model. In the
future we may treat some of the diffuse sources (such as space heating)
in the same way that we now treat residential area streets. Very strong
individual point sources, if they exist, may have to be treated separately
at a later time. For now, we feel that inclusion of the more than 90
percent of the total CO emissions arising from traffic will give results
-------
Table A-I
PERCENT CO CONTRIBUTION BY SOURCE CATEGORY
City
Washington, D.C.
Area, 1965-1966
Los Angeles Metropolitan
Area, 1967
Boston, Massachusetts
Area, 1967
San Francisco
Bay Area, 1967
Pittsburgh Metropolitan
Area, 1967
Cleveland Metropolitan
Area, 1967
Kansas City Metropolitan
Area, 1966
Metropolitan
Baltimore
Hartford-Springfield
Area, 1967
Average of 28 Major
Metropolitan Areas
Category
Transportation
98.7
98.2
91.3
77.2
92.1
94.3
95.2
95.7
94.2
91.5
Industry
—
—
—
6.5
—
2.0
—
1.2
1. 1
2.6
Incineration
0.8
1.8
8.4
16.3
1.0
2.1
4.3
1.8
3.8
1.9
Power Plants,
Space Heating,
and Other Sources
0.5
—
1.2
—
6.9
1.5
0.5
1.3
0.9
4.0
References
NAPCA
(1968a)
NAPCA
(1968b)
NAPCA
(1968c)
NAPCA
(1968d)
NAPCA
(1969a)
NAPCA
(1969b)
NAPCA
(1969c)
NAPCA
(1969d)
NAPCA
(196 9e)
Mason
et al.
-------
that are quite consistent with the accuracies of the other input
parameters.
Other potentially important nontraffic sources of carbon monoxide
are the airports. Carbon monoxide emissions at airports are comparable
with those of surrounding communities (Bastress, 1969). Increased air
traffic may increase these levels. One of the problems to be considered
in the modeling of airports as CO sources is that they do not constitute
a ground level source. Much of the emission occurs in a volume above
the area occupied by the airport. For this reason, the box model would
seem appropriate to the treatment of emissions from an airport regardless
of its distance from the receptor.
The distribution of airport emissions through the mixing layer
appears to minimize their contribution to ground level concentrations.
However, this should be checked and if airports contribute significantly
to ground level concentrations, they should be added to future versions
of the model.
-------
Appendix B
THE URBAN TRANSPORTATION PLANNING PROCESS
-------
Appendix B
THR URBAN TRANSPORTATION PLANNING PROCESS
The purpose of this appendix is to describe the urban transporta-
tion planning process so that its capabilities and limitations may be
assessed, and to show how data generated in the planning process can be
used as inputs to the urban diffusion model.
1. Background
The first major urban transportation planning effort was undertaken
for the Detroit area by the Detroit Metropolitan Area Transportation
Study (DMATS) in the early 1950's. Dr. Douglas Carroll and his staff
developed many of the concepts and the methodology that are still used.
The Carroll study team staffed subsequent studies in Chicago, Pittsburgh,
and New York. The methods and techniques have been developed and re-
fined in the succeeding years, strongly aided by increasingly efficient
data processing equipment. It is a requirement of the Federal Aid
Highway Act of 1962 that every community with a population over 50,000
have a transportation plan to participate in federal highway programs.
2. Structure of a Transportation Study
A transportation study produces a plan for future transportation
facilities. A five-step process is generally followed: (1) inventory.
(2) model development, (3) forecast, (4) system design, and (5) system
evaluation. There is considerable iteration and feedback among these
steps, as described below.
-------
3. Inventory
Three kinds of data are collected:
(1) Complete descriptions of present transportation
facilities
(2) Numbers of trips presently taken, their purposes, and
demographic data that may serve as trip-predicting
variables
(3) Descriptions of land uses in the study area.
The study area is divided into small "traffic zones, and the trip-
taking and land use data are collected for the traffic zones. Traffic
zones are usually related to census tracts, with one or more tracts in
each traffic zone. Census tracts are used because they provide the
most readily available historical and forecast data on population, in-
come, and other demographic variables.
The transportation system inventory is a description of the local
highway network of major arterial streets and freeways. A map of the
highway network is prepared. The network is described by the inter-
sections, or nodes, and the characteristics of the links that connect
the nodes. For example, traffic capacity, observed speed, observed
volume, and type of facility are recorded for each link in the network.
Public transportation facilities are described by their frequency of
service, kind of equipment, capacity, and current patronage.
The trips taken at the present time are determined from a household
survey in each traffic zone. Households are asked to report the number
of trips taken by household members on a specified day, the purpose of
the trips, and the destinations. Household income, number of persons in
the household, ages of household members, and number of automobiles are
also determined.
-------
Land use and employment in each traffic zone are determined from
planning agencies,, surveys, and in some cases from field observations.
4. Model Development
To develop the model, the data collected in the inventory are re-
lated in such a way that trips between zones can be predicted from demo-
graphic and land-use data. Three submodels are used: the trip
production model, the trip attractions model, and the trip distribution
mode 1.
The trip production model relates the number of trips originating
in a zone to characteristics of the zone, e.g., population, average
household income, etc. The trips are characterized by their purpose,
e.g., to work, to social or recreational activity, to health or medical
treatment, etc. The trip production model is a statistical regression,
concerned only with the number of trips that originate in the zone, not
their destinations.
The trip attraction model relates the number of trip destinations
in a zone, by purpose, to zone characteristics, e.g., land use, total
employment, etc. The trip attraction model is concerned statistically
only with the number of trips that end in a zone, not their points of
origin.
The trip distribution model describes the relation between trip
productions and attractions: i.e., the number of trips between each
zone pair. The distribution model describes the number of trips between
each zone pair by a formula of the form:
, k
t = p a /d .
ij i J iJ
-------
where
t = the number of trips from zone i to zone j
ij
p = the number of productions in zone i
i
a = the number of trip attractions in zone j
j
d = the impedance between zones i and j, usually expressed
ij
as the travel time between the zones, but occasionally
as distance or cost
k = an exponent that depends upon the travel characteristics
of the area's residents.
Because of its form, the trip distribution model is commonly called the
"gravity" model. The exponent k is determined from the frequency dis-
tribution of trips between zone pairs as revealed by the household
interview data.
5. Forecast
In the forecast step, the land use, employment, population, and
income are forecast for some future year. The travel in that future
year is forecast from these variables, using the models developed in
the previous step. The demographic variables must be forecast for each
zone. Frequently, this is done by allocating overall population and
income projections among the zones, using models that have been developed
for that purpose.
Future land use may be a function of the transportation system
adopted, so there is feedback between the transportation system design
and the land use forecast. Further, zone-to-zone travel time will be
influenced by the transportation system, so there must be iteration
between the forecast and the design. The division of trips between
-------
private automobiles and public transit is estimated by using a model
based on relative time and cost.
6. System Design
In the system design step, alternative changes to the existing
transportation system are postulated. These must meet the forecast
travel demand. They may include addition of freeway links, increase in
capacity of arterials or freeways by widening, or the addition of new
public transportation facilities. A network description is prepared
for each of the alternatives.
7. System Evaluation
In the system evaluation step, the costs of the alternative systems
are determined and compared. Costs include the costs of construction,
costs of rights-of-way, costs of equipment, annual maintenance and
operating costs, and user and community costs. User costs include those
of operating, parking, and owning an automobile; the costs of accidents;
transit fares; and the value of all travelers' time. Community costs in-
clude disruption, noise and emission pollution, and the cost of limited
access to employment and other opportunities. Because these costs occur
at different times, and the expenditure patterns may be different for
different alternatives, future costs are discounted according to com-
pound interest formulas to obtain comparable values for all outlays.
Costs that cannot be expressed in dollar terms are described qualitatively
The heart of the evaluation process is the series of computer pro-
grams that make up the traffic assignment model. This model is capable
of determining the minimum time path between zone pairs for a given
transportation network and can assign zone-to-zone trips to the links
along that minimum path. Thus, the total traffic volume on each link
-------
is predicted. This defines the needed capacity, the traffic speed, and
finally the total travel time and vehicle operating cost. The diffusion
model uses link volume and link speed outputs. These are obtained
directly from the magnetic tape outputs of the traffic assignment pro-
grams. The network descriptions are also on magnetic tape. Thus, it
is possible to forecast future pollution concentrations from the fore-
cast traffic. The pollution forecasts will provide additional informa-
tion for the transportation planners to evaluate alternatives.
-------
Appendix C
METHODS FOR DETERMINING STABILITY CATEGORY
-------
Appendix C
METHODS FOR DETERMINING STABILITY CATEGORY
This appendix discusses two methods for determining stability
category for use with the model described in this report. One of the
methods has not been presented elsewhere in the literature.
1. Turner's Method
Turner (1964) developed criteria for determining stability from
routinely available meteorological data. His procedure estimates the
stability class on the basis of cloud cover, ceiling height, wind speed,
and solar elevation. In his paper, Turner presents a series of compu-
tational steps that effectively constitute the flow chart for a computer
program. His model requires the following inputs: cloud cover, ceiling
height, wind speed, and, if daytime, solar elevation. The parameters,
other than solar elevation, that are required for the application of
Turner's stability determination method are all available from routine
hourly meteorological measurements. For application of Turner's approach
with the synoptic model, an approximate formula was used to determine
solar elevation. The approximation assumes that the earth has a circular
orbit and that the station lies at the center of its time zone. With
these simplications the following useful relation is obtained:
f * /12 - H\
L sin 8 sin $ + cosl— It
a = arcsinjsin 6 sin $ + cos(———Jcos 6 cos $ | (C-l)
and
/2rr(N + 10)
365
5 = arctan -tan 23.5° cosl — )| (C-2)
-------
where
Ot - the solar elevation
5 = the solar declination
$ = station latitude
H = the hour of the day (24 is midnight)
N - the number of days since 1 January.
2. Method Based More Directly on Pasquill's Classifications
In the work that Pasquill (1961) did to determine the spread of a
plume with distance traveled, atmospheric conditions were classified
according to prevailing insolation strength and wind speed, for daytime
conditions, and according to cloud cover and wind speed for night condi-
tions. His classification scheme, which Turner also used in developing
his method, is summarized in Table C-I. The table, as presented here
Table C-I
*
STABILITY CATEGORIES
Surface Winds
(knots)
S3
3-6
6-10
10-12
>13
Daytime Insolation
Strong
1
1
2
3
3
Moderate
2
2
3
3
4
Slight
2
3
3
4
4
Night Clouds
>5/10
5
4
4
4
4
^4/10
5
5
4
4
4
1 = extremely unstable, 2 = moderately unstable,
3 = slightly unstable, 4 = neutral, 5 = slightly stable.
-------
has been changed slightly from the form presented by Slade (1968). First,
that table contains some cases where the stability falls between the
accepted classes; these have been assigned to a single category. Second
the moderately unstable case in the original table has been redefined as
slightly unstable and the two slightly unstable cases have been rede-
fined as neutral. We feel this is more appropriate to urban conditions,
where very stable conditions are uncommon. In the original scheme, no
categories were defined for the near-calm wind cases at night. We have
assumed such cases to be slightly stable over an urban area.
The next problem was to define an objective method for determining
the strength of insolation. The strength of the insolation depends on
the solar elevation, the cloud cover, and the atmospheric turbidity.
The latter factor is not routinely measured and was ignored because its
attenuating influence should be small compared to cloud cover. The
following equation approximately describes the flux density of solar
energy on a horizontal surface:
Insolation strength = k(l - AN)sin a (C-3)
where
k = a proportionality factor, depending on the solar constant,
and atmospheric transmission
A = the average albedo or reflectance of the clouds
N = the fraction of the sky obscured by cloud
a. = the elevation angle of the sun.
Of course, this equation applies only to an average insolation over an
area sufficiently large that the effects of the irregular distribution
of clouds are minimized.
-------
A reasonable value of A would be 0.5, so that Eq. (C-3) becomes
Insolation = k(l - 0.5 N)sin a . (C-4)
Of necessity,, we assume that k is constant, i.e., the insolation is
proportional to (1 - 0.5 N)sin a. This term can assume values from U
to 1. If we divide that interval in three equal parts, corresponding
to Pasquill's three insolation categories, we then have the following
relationships:
Slight Insolation: 0 < (1 - 0.5 N)sin a ^ 0.33
Moderate Insolation: 0.33 < (1 ~ 0.5 N)sin a < 0.67
Strong Insolation: (1 - 0.5 N)sin a > 0.67.
These simple expressions are used to determine the insolation type. When
combined with the wind speed information, they give the stability classi-
fication more directly than does the scheme devised by Turner (1964).
This method also seems somewhat more consistent with Pasquill's original
specification of the stability types.
In using Table C-I and the insolation expressions given above, it
is still necessary to determine the solar elevation for the time of day;
cloud cover and wind speed are measured parameters. To economize on
calculation time, the subroutine using this scheme to preprocess the
data (see Appendix G) does not calculate a, but uses a table of values
of sin a obtained by means of Eq. (C-l). Values are given for each
month of the year and each hour of the day. The five cities studied in
this report are all within ±3° of 40° north latitude, so a single table
for that latitude has served for all calculations.
The procedure for determining stability has been improved by using
"opaque" cloud cover. This is a regularly recorded parameter. In
-------
determining the opaque cloud cover, the very thin semitransparent clouds
are ignored. Thus, the assumption of an average cloud albedo of 0.5 is
probably more accurate when applied to these types of cloud than when
applied to the total cloud cover.
-------
Appendix D
METHODS FOR DETERMINING MIXING DEPTH
-------
Appendix D
METHODS FOR DETERMINING MIXING DEPTH
One of the model's required inputs is mixing depth. The most
commonly used method for determining the top of the mixing layer for
afternoon conditions is to assume that it is at the height where the
potential temperature on the morning sounding is equal to the afternoon
surface maximum potential temperature (e.g., Miller and Holzworth, 1967).
This is the method used with the synoptic model. Potential temperature,
9, is defined as
R/c
0 = T(1000/p) P (D-l)
where
T = temperature (°K)
p = pressure (mb)
R/c = the ratio of the gas constant for air to its specific heat
P
at constant pressure (0.287).
*
To determine afternoon mixing depth, the morning sounding from the
nearest radiosonde station and the afternoon maximum temperature were
used. Potential temperature is calculated for the surface maximum tem-
perature first, and then for each of the successively higher reported
*
For this model we used the pressures and temperatures at the significant
levels, Deck 505, available from the National Weather Records Center,
Asheville, North Carolina.
-------
radiosonde levels until the potential temperature at some level exceeds
the surface maximum value. The pressure where the surface maximum and
upper level potential temperatures are equal is determined by linear
interpolation between values for the reported levels. If we assume a
constant average temperature T, through the mixing layer, then we can
use the thickness equation (e.g.,, Panofsky, 1957) to convert the pressure
at the top of the layer, p , to height
h
h = ln(p /p ) (RT/g) = 29.3 T ln(p /p ) . (D-2)
\ o h' \ o h/
In this equation, g is the acceleration of gravity, p is the surface
pressure, and T is taken to be the average of the temperatures at the
surface and the top of the mixing layer.
The estimation of nighttime mixing depth over the city for use with
the synoptic model is based on Summers' (1966) model of the urban heat
island and Ludwig's (1968, 1970) empirical relationship between rural
lapse rates and the intensity of urban heat islands. If we assume T to
be a linear function of the logarithm of pressure (very nearly the same
as Summers' assumption of T as a linear function of height), then the
temperature T at some height h outside the city is given by:
T =T + — Alnp K, T + p — In — (D-3)
h o dlnp ' '
where T and p are the rural surface temperature and pressure, respec-
o o '
tively, p is the pressure at h, and p is the average of p and p .
h oh
If air moving into a city is heated from below to the extent that
complete mixing takes place through a depth h, then the temperature at
height h will remain T , and the lapse rate below h will become adiabatic
h
The dry adiabatic lapse rate y (in pressure coordinates) is given by
-------
Y = - 0.287 — K, 0.287 —
d pc p p
(D-4)
where T and p are absolute temperature and pressure, and T and ^ are
their average values within the layer from the surface to height h.
For the urban situation, Eq. (D-3) becomes
/v
T = T + p Y ln|—
h u d \p ,
(D-5)
where T is the surface air temperature in the center of the urban area.
u
Subtracting Eq. (D-5) from Eq. (D-3) gives:
Tu - TQ = p|ln( —1|[— -
(D-6)
Substituting Eq. (D-4) into Eq. (D-6) gives:
T - T =
u o
o/J
_ dT
p — - 0.287 T
dp
(D-7)
Ludwig (1970) has shown that the urban-rural temperature difference
(T - T ) can be approximated within about ±2° C by the following
u o
equation:
1/4 / dT
T - T = $ 0.0633 - 0.298 —
u o \ dp
(D-8)
where $ is the population of the urban area and dT/dp is expressed in
"C/mb. The equation is based on 85 sets of data from 18 different
cities. Substituting Eq. (D-8) into Eq. (D-7) gives:
ln(p /p
\ h c
dT\
0.0633 - 0.298 —
dp/
p — - 0.287 T
dp
(D-9)
-------
The value of dT/dp is determined from the lowest portion of the morning
sounding (using the differences in temperature and pressure at the sur-
face and the first significant level above the surface; "p and T are the
averages of the pressures and temperatures at these points.
To convert ln(p /p ) to mixing depth, we use Eq. (D-2). Making
h o
that substitution gives
— 1/4 / dT
29.3 T $ 10.298 — - 0.0633
h = * — . (D-10)
_ dT —
p — - 0.287 T
dp
This is the- equation that was used to determine the predawn values
of urban mixing depth from 1200 GMT soundings.
The above equation has an idiosyncracy that should be noted. For
increasing positive values of dT/dp, h becomes larger, as it should, but
at some point where dT/dp is approximately adiabatic, h becomes infinitely
large. If dT/dp increased further still, h becomes negative. This be-
havior arises because of the assumption that the observed rural lapse
rate is less than the adiabatic rate. Large positive lapse rates are
quite rare in the early morning hours, so the assumptions are not
seriously misleading. However, it is necessary to provide for the
eventuality in the computer program. This has been done by assigning a
large positive value to h whenever the above equation yields a negative
value. The value chosen was 4000 m. This same value was also assigned
to h whenever the equation gave a positive value larger than 4000 m.
This assignment of a maximum mixing depth will not affect the cal-
culations, except for moderately or extremely unstable conditions, and
according to the stability classification system used (see Appendix C),
such stabilities cannot be assigned at night.
-------
We have also used the 4000-m maximum mixing depth for afternoon
calculations in order to limit the amount of radiosonde data necessary
to apply the program. As is shown in Section V of this report,, this has
very little effect on the results.
Inspection of the mixing depth equation given above indicates that
there is a minimum positive value that h can assume, given a fixed city
size and fixed values of p and T. This minimum occurs when dp/dT is
5
infinitely negative. For a city of 9 X 10 population, an average
pressure of 925 mb, and an average temperature of 280" K, the minimum
nighttime urban mixing depth should be about 79 meters.
This number appears reasonable considering that the heat generated
by the city, and the mechanical mixing produced by the airflow over its
rough surface probably set a lower bound on urban mixing depths. From
this it follows that daytime mixing depths are also likely to have some
minimum value in the city. We have arbitrarily chosen 50 meters as that
minimum, although there is no minimum intrinsic in the procedure used
to determine afternoon mixing depths. This choice seems to be physically
reasonable. However, its main function is to prevent h from assuming a
value of zero, which could give an infinite calculated concentration.
The use of radiosonde soundings for mixing depth computations is
time-consuming and expensive on the computer. This is particularly true
for climatological applications where large amounts of data are required.
The sounding data are not universally available on magnetic tape from the
National Weather Records Center, and several years of punched-card data
are very cumbersome to process. Fortunately, Holzworth (1967) has calcu-
lated forenoon and afternoon mixing depths for a large number of U.S.
cities, using the morning (1200 GMT) temperature soundings. Mr. Holzworth
has been very cooperative and has allowed us to use his tabulations of
mixing depth for several stations. His tabulations generally cover the
-------
period 1960-1965,, and most U.S. radiosonde stations are represented.
These data are considerably more convenient as a source for mixing-depth
computations than the original radiosonde data. This body of data does
require some modification for use with the diffusion model. These ad-
justments are described below.
The afternoon mixing depths given in Holzworth's tabulations were
determined by the conventional method described at the beginning of this
appendix, so we have taken his tabulated values and used them without
change.
Holzworth determines his forenoon mixing depth from the intersec-
tion, on a thermodynamic diagram, of the morning sounding and an adiabat
passing through a surface temperature 5° C greater than the observed
early morning minimum temperature. Thus, his forenoon mixing depth, h
(meters), can be related to the morning vertical temperature gradient
dT/dZ by the following approximation, which is exact if dT/dZ is con-
stant to the height h , and if the surface radiosonde temperature is
the minimum temperature:
3 1
where (dT/dZ) is the adiabatic temperature gradient, -9.8 X 10 "C m~
£L
Substituting and simplifying, Eq. (D-ll) becomes:
dT s° C - (9.8 X 10~3 °C/m)h
The gas law and the hydrostatic equation can be combined to give:
dZ RT
-------
Using Eq. (D-13) we can reduce Eq. (D-12) to the following
|~9.
^
RT9.8 X 10~3 (°C/m)h - 5"
~ - - - - . (D-14)
Pghf
Virtually all cities in the U.S. are located at altitudes such that
the atmospheric pressures in the lowest layers are between about 850 mb
and 1000 mb. Thus, we introduce an error of less than 10 percent,
assuming p to be constant and equal to 925 mb.
Similarly, temperature can be assumed constant and equal to 280° K
without introducing errors greater than about 10 percent. Substituting
these, and the values for the constants gives:
dT / -2 \ C
— & 8.7 X 10 - 44/h — . (D-15)
dp \ f/ mb
We have already shown that the early morning mixing depth, h, over
the city can be related to this low level lapse rate. Recalling Eq.
(D-10)
h=
— 1/4 / dT
29.3 T $ 0.298 — - 0.0633
_ dT —
p — - 0.287 T
dp
where f is the population of the urban area. Using the same values of T
and p as used in the development of Eq. (D-15) and substituting from
that gives:
1.1 X 10 + 307 h
1/4 f
h = $ - — — meters . (D-16)
4. 1 X 10 + 0.02 h
For those cases of importance, where h would be less than about
4
10 m, the term 0.02 h in the denominator will be very small compared
4
to the constant 4.1 X 10 and can be ignored. Then Eq. (D-16) becomes:
-------
h « $ (2.6 + 7.5 X 10 h I meters . (D-17)
f /
This equation was used to convert Holzworth's tabulated forenoon mixing
depths to values appropriate to the early-morning hours for use with the
climatological model.
Equation (D-17) has the same characteristic as Eq. (D-10), in that
there is a minimum value that h can have. It is, as expected, the same
as found with Eq. (D-10), if the conditions are the same.
As with the methods based on radiosonde data, we have assigned the
same minimum and maximum values of mixing depth, when appropriate, to
those obtained from Holzworth's tabulated values.
The two methods described above provide values of mixing depth for
only two hours of the day, one in the early morning, predawn hours and
one for the time of the afternoon temperature maximum. To obtain values
for other hours of the day, interpolation must be used. Two schemes have
been employed with the model. The first approach combines time and sur-
face temperature interpolations. The second uses time only as the basis
of the interpolation. The time-temperature interpolation has been used
with radiosonde data to obtain mixing depths for the examples that
illustrate the use of the synoptic model in this report. The time-only
interpolation was used with Holzworth's mixing depths in the examples
that illustrate the climatological model.
When the temperature interpolation scheme was used, the following-
equation gave mixing depths from the first hour after sunrise through
the first hour after sunset:
(T - T N
min
T - T
max min,
Ifh - h ) t h (D-18)
f\ d n/ n
-------
where
h = mixing depth
h and h - mixing depth at time of maximum temperature and at
d n
time of the morning sounding
T, T . T = current, maximum, and minimum temperature.
max min
Temperature interpolation during the day is reasonable because the top
of the mixing layer is usually marked, on a thermodynamic diagram, by
the intersection of the morning sounding and the adiabat passing through
the current surface air temperature. If the slope of the morning
sounding is constant up to this height, the change of mixing depth will
be very nearly proportional to the change of surface air temperature.
From the second hour past sunset through midnight, the mixing depth
is interpolated by time. At the first hour past sunset it has the value
given by the above equation. At midnight it has the value of h deter-
mined from the next morning's soundings. Observations presented by
Ludwig and Kealoha (1968) for Dallas and Ft. Worth, Texas, show that the
urban heat island develops rather quickly in the evening and then tends
to stabilize about midnight. If the urban heat island and the urban
mixing layer are related, as suggested by Summers' (1966) model, then
the mixing depth should also reach its early morning value by the middle
of the night as does the heat-island intensity. For this reason the
early morning value of mixing depth is assumed to apply from midnight
until the first hour past sunrise on the next day.
Figure D-l gives a schematic representation of the results of
applying the temperature-time interpolation to a typical day's data.
The second interpolation scheme, based on time alone, has many of
the same features as the hybrid approach described above. For instance,
-------
0.
LU
Q
CJ
Z
X
I
SUNRISE
SUNSET
TIME OF T
max
CONSTANT
INTERPOLATION BY
SFC TEMPERATURE
I I I I I
INTERPOLATION CONSTANT
j BY TIME
I I I
8 10 12 14 16
LOCAL TIME
18 20 22 24
02
04
TA-7874-28S
FIGURE D-1 SCHEMATIC REPRESENTATION OF THE DIURNAL TEMPERATURE/TIME
-------
the early morning mixing depth, h , is used throughout the hours from
midnight until sunrise. We have assumed that the afternoon mixing
depth, h , occurs at 1400 local standard time. The hourly mixing depths
h, are interpolated for the hours between sunrise and 1400 using the
following equation
H - H
sr
sr
where
H = current hour of the day
H = the first integral hour after sunrise, determined from
sr
tables of solar elevation angle, e.g., 0600, 0700, etc.
From 1400 local standard time until midnight, a similar interpolation is
used between h and the mixing depth for the following morning.
d
The advantage to using a time-based interpolation is that an hourly
sequence of mixing depths can be determined from either soundings or from
the Holzworth tabulated data without concurrently handling the hourly
surface temperature data.
-------
Appendix E
INCREASING THE SPATIAL RESOLUTION
FOR EMISSIONS IN THE FIRST SEGMENT
-------
Appendix E
INCREASING THE SPATIAL RESOLUTION
FOR EMISSIONS IN THE FIRST SEGMENT
For the first segment, which covers the upwind area from the re-
ceptor to a distance of 125 m, the Gaussian model is used. As noted in
the text, the standard deviation, a } in this segment is presumed to
z
remain constant, so the exponent, b. .is zero in the exponential repre-
•"v 3
sentation of cr } and the Gaussian equation becomes:
Z
0.8 • 125 100 El
C . = - Q = - — (E-l)
Lj u a 1 u a A
where
C . = the concentration due to remissions from the first seg
ment, for j type stability (gm m )
Q = the average source strength in the first segment
(gm m s )
a = a constant for the first segment, for j type stability
lj
(m)
E = the emission rate in the first segment (gm s )
-2
A = the area of the first segment (m ).
If we divide the first segment in two, part A extending to 62.5 m and
\
part B from 62.5 to 125 m, then
a = a = a (E-2)
lj Aj Bj
-------
A = A + A (E-3)
1 A B
A = A /4 (E-4)
A 1
A = 3A /4 (E-5)
B 1
E = E + E . (E-6)
1 A B
It follows that
(E E \
A B
62.5 h 62.5
A A
A is /
u a A \ A 3 B
100 12E +=• E I . (E-7)
If we let
then we can use Q as an effective source strength for the first seg-
AJD
merit, replacing Q in Eq. (E-l), and we obtain the same results that we
would had we divided the nearest segment into two parts. By using the
effective source strength, Q , we do not have to add to the numbers of
Ar>
segments treated in many stages of the calculations.
-------
Appendix F
TREATMENT OF EXTRAURBAN SOURCES AND STREET EFFECTS
-------
Appendix F
TREATMENT OF EXTRAURBAN SOURCES AND STREET EFFECTS
1. Introduction
In an earlier report (Johnson, et al., 1969) we discussed submodels
to account for the amounts of carbon monoxide arriving from outside the
city and for the aerodynamic effects associated with airflow around
buildings and through street canyons. For completeness, the submodel
used to account for CO concentrations resulting from extraurban sources
is described below. This model was used in the calculations that illus-
trated the use of the synoptic model in the text of this report. A
constant background was used for many of the calculations with the
climatological model. In the text it was shown that a background could
also be accounted for on the basis of statistical modeling, using ob-
served CO concentrations. At this time the statistical model appears
to give the better results, if adequate data is available. If not, the
model described in this section would be preferred.
Because of a number of problems encountered in applying the em-
pirical street effects submodel on a general basis, it was judged in-
adequate for our purposes and has not been incorporated into the
diffusion model. No attempt was made to include street and building
effects directly in the calculations used as examples in this report.
2. Extraurban Model
The development of the following model accepts, a priori, the
assumption that the treatment of extraurban transport and diffusion
should be considerably more gross than the treatment of nearby sources.
-------
The first problem to be faced in the development of an extraurban
diffusion model is that there is no convenient way of knowing the upwind
trajectory of the air arriving at a city. We can either determine the
trajectory from past and present meteorological data or we can assume
that the air has come from somewhere within a very large upwind segment.
This latter approach is much more practical.
We apply the box model to a quadrant centered on the upwind direc-
tion and extending from 32 to 1000 km upwind of the receptor. The source
strength is assumed to be constant in time and space throughout the
sector, and is estimated from yearly fuel consumption for those states
(Federal Highway Administration, 1966) and Canadian provinces (Dominion
Bureau of Statistics, 1968) whose centers fall within the sector. To
determine the total emission rate within the area, we use the total
amount of motor vehicle fuel consumed and the conversion factor:
3
1 gallon of fuel yields 1.32 X 10 grams of carbon monoxide. If the
7
yearly (3.15 X 10 s) consumption of fuel within the quadrant extending
to 1000 km is given by F, then the average CO emission rate Q in the
11 2
area (7.86 X 10 m ) is given by:
Q = 5.32 X 10 F (g m~ s~ ) . (F-l)
The extraurban model input for a given city includes a table of 16
values of F, one for each wind direction used. A different table is
used for each city. An average wind direction is used based on the
direction observed with the highest hourly wind speeds.
According to the box model, the concentration C from some upwind
segment is
r - r
2 I
- - , (F-2)
-------
where r and r are the distances to the outer and inner segment
6 3
boundaries (in this case 10 and 32 X 10 m), u is the wind speed, and
h is the depth of the layer through which the material is mixed. Sub-
stituting Q from Eq. (F-l) and the values of r and r gives the following
equation for concentration from extraurban sources, C :
e
5.15 X 10" 1 F
C - . (F-3)
e uh
The afternoon mixing depth is used in Eq. (F-3) because the pollu-
tants are likely to have traveled for long enough periods that they will
have had time to be mixed through the depth of the afternoon layer. We
are aware that the local mixing depth will not necessarily be appro-
priate to the region upwind of the city, but more detailed treatment of
this problem does not seem to be warranted. To approximate the normal
increase in wind speed with height in the lower atmosphere, we have
taken the average transport wind velocity through the depth of the mixing
layer to be 1.5 times the maximum airport winds for the day.
In addition to the material generated within the segment extending
to 1000 km, the general "worldwide" background is included. Robinson
and Robbins (1967) have estimated this to be about 0.2 ppm (about
-4 -3
2.4 X 10 g m ) at sea level in the midlatitudes of the northern
hemisphere. This value is added to that calculated from Eq. (F-3) to
give the total extraurban concentration, which generally amounts to a
few tenths ppm. In applying the synoptic model, the extraurban con-
tribution was calculated once for each 24-hour period. The same value
was used from one midnight to the next.
-------
3. Street Effects Model
Because of the finite spacing of sources within a city, area-source
simulation such as is used in the intraurban model is best applied at
scales above a certain lower limit. This minimum spatial scale can be
considered to be on the order of a city block, hence the choice of 62 m
as the finest resolution in the intraurban model. For shorter source-
receptor distances, an alternative technique is needed.
Additional complications arise because, contrary to the usual
situation in nonurban diffusion studies, the scale of the largest urban
roughness elements (buildings, etc. ) is very large compared to the local
scales of emission and reception. This means that the aerodynamic
effects of structures become important.
Models that do not include the effects of microscale diffusion will
normally undercalculate concentrations in comparison with those measured
at CAMP Stations, which are often located near streets. For example,
the model used by Ott, et al. (1967) gave average concentrations that
amounted to 36 percent of the CAMP average.
The street effects have great importance for two reasons. First,
they must be considered if we are to use existing data to verify the
performance of our model. Most available observations are taken near
streets in downtown areas where local effects are likely to be signifi-
cant. The second reason for the importance of the street effects is
that they contribute substantially to those concentrations to which
large parts of the population are exposed.
Current knowledge about street effects on CO concentrations is
based largely upon the extensive measurements of Georgii, et al. (1967)
in Frankfurt/Main, Germany; McCormick and Xintaras (1962),, Schnelle,
et al. (1969), and Rouse (1951) have also made experimental contribu-
tions in this area.
-------
Georgii's experiment involved extensive measurements of CO concen-
trations and wind speeds at different levels above three different
streets in built-up areas, along with occasional traffic counts. A
major finding was that the CO concentrations on the leeward sides of
buildings were considerably higher than those on the windward sides
implying a helical cross-street circulation component in the opposite
direction from the roof-level wind. In addition, the averaged data
showed that (1) the vertical concentration profiles on either side of
the street assume an exponential form, (2) the mode of air circulation
above the street apparently changes when the roof-top wind speed exceeds
about 2 m/s, and (3) the concentrations are exponentially related to
traffic density. Examination of the measurements reported by Schnelle,
et al. (1969) also indicates general agreement with (1) and (2) above;
their data are insufficient for verifying (3).
Georgii's observations show that the roof-level concentrations
differ only slightly from windward to leeward sides of the street-side
buildings. It is reasonable to assume that the urban background con-
centrations calculated by the intraurban model are approximately equiva-
lent to roof-level concentrations. The effect of the street is to
increase incoming roof-level concentrations by a factor that depends
upon the receptor location relative to the wind direction, the height
above the street, the wind speed at average roof level, and the traffic
density.
A street effects submodel, empirically derived from Georgii's
observations, was discussed in an earlier report (Johnson, et al., 1969).
Because of a number of problems encountered in applying the empirical
model on a general basis, it has not been incorporated into the
diffusion model.
-------
The statistically derived adjustments to the model discussed in
the text would probably account for much of the aerodynamic effects
associated with buildings and streets, but those parts of the results
that were directly attributable to street effects would not be easily
separated from those due to other causes. Also, statistically derived
results could not be transferred with any confidence to other locations.
Because of the importance of the street effects, a program of field
measurements is planned. The results of this program should provide
the data necessary for the development of an adequate model of CO
diffusion on the microscale in a city.
-------
Appendix G
PROGRAM FOR PREPROCESSING OF THE DATA
FOR THE CLIMATOLOGICAL MODEL
-------
Appendix G
PROGRAM FOR PREPROCESSING OF THE DATA
FOR THE CLIMATOLOGICAL MODEL
The preprocessing of the meteorological data for use in the clima-
tological model is done in two steps. First, the Holzworth tabulated
values of mixing depth for afternoon and forenoon are processed to give
a series of hourly values. The equations used have been enumerated in
Appendix D to this report. Figure G-l shows a simplified flow chart
of the program used for converting Holzworth's mixing depth tabulations
into a sequence of hourly values.
After the magnetic tape records of hourly mixing depth are produced,
they are merged with conventional hourly meteorological records ob-
tained from the National Weather Records Center. The methods used to
convert solar elevation, opaque cloud cover, and wind speed to stability
index have already been discussed in Appendix C to this report and
need not be repeated here. The organization of the preprocessing is
summarized in the simplified flow chart in Figure G-2. The magnetic
tape record of the condensed historical meteorological data that results
from this program is then used as the climatological basis for calculating
extended sequences of CO concentrations.
-------
START
INPUT CITY POPULATION
READ STATION, DATE, AND HOLZWORTH'S VALUES OF
FORENOON AND AFTERNOON MIXING DEPTH
DETERMINE PRE-DAWN MIXING DEPTH FROM
HOLZWORTH'S FORENOON VALUE — See Discussion in Text
NO
YES
IS THIS DATE IN
THE SAME MONTH
AS THE PREVIOUS
DATE ?
NO
DETERMINE SUNRISE HOUR FOR CURRENT MONTH
FOR HOURS FROM 0100 TO LAST PRE-DAWN HOUR,
LET THE MIXING DEPTH EQUAL THE PRE-DAWN VALUE
FOR HOURS BETWEEN FIRST POST-DAWN AND 1400,
LINEARLY INTERPOLATE BETWEEN PRE-DAWN AND
AFTERNOON VALUES ON THE BASIS OF TIME
READ NEXT DAY'S DATA
DETERMINE NEXT DAY'S PRE-DAWN MIXING DEPTH
FOR HOURS FROM 1500 TO 2400 INTERPOLATE BETWEEN
AFTERNOON MIXING DEPTH AND NEXT DAY'S PRE-DAWN
VALUE ON THE BASIS OF TIME
RECORD DATA AND MIXING DEPTH FOR ALL
24 HOURS ON MAGNETIC TAPE
IS IT THE END OF THE DATA FILE ?
YES
TA-7874-71
FIGURE G-1 SIMPLIFIED FLOW CHART OF PROGRAM FOR CONVERTING HOLZWORTH'S
MIXING DEPTHS TO HOURLY VALUES
-------
START
READ IN TABLES - STABILITY INDEX AS A FUNCTION OF RADIATION INDEX AND WIND SPEED
(SEE TEXT) AND SINE OF THE SOLAR ELEVATION AS A FUNCTION OF MONTH AND HOUR.
READ MONTH, DAY, YEAR, HOUR, WIND SPEED, WIND DIRECTION, AND OPAQUE CLOUD COVER
FROM SURFACE-OBSERVATION TAPE AND MIXING DEPTH FROM HOLZWORTH-BASED DATA (SEE TEXT).
DETERMINE RADIATION INDEX FROM MONTH, TIME OF DAY, AND OPAQUE CLOUD COVER.
DETERMINE WIND-SPEED CATEGORY.
READ STABILITY CATEGORY FROM TABLE, AS A FUNCTION OF RADIATION INDEX AND
AND WIND-SPEED CATEGORY.
PUT WIND DIRECTION IN 16-POINT FORM.
DETERMINE MIXING DEPTH CATEGORY 1 : h<100m, 2 : 100
-------
Appendix H
THE EQUIVALENCE OF CERTAIN COMBINATIONS
OF STABILITY AND MIXING DEPTH
-------
Appendix H
THE EQUIVALENCE OF CERTAIN COMBINATIONS
OF STABILITY AND MIXING DEPTH
As was noted in the discussion of the climatological model in the
text of this report, it can be simplified to the following form:
P 9
t
u
i=l '""'"
where
_3
C - CO concentration at the receptor (gm m ).
P = A factor that gives the source strength for the t
hour, based on daily distribution of traffic, and
changes in average speed during peak traffic hours.
u - Wind speed (m s ).
th
- Ratio of the CO concentration received from the i
segment to the emissions in that segment (for unit
wind speed). The values of these ratios depend on
stability class, j, and mixing-depth class, m.
- th
Q = Average daily source strength in the i segment, and
the d direction upwind of the receptor, based on
the total daily traffic and the average speeds on
the different types of roads within the segment
(gm m s ).
-------
It is the term (v/Q) that is of interest here. It will be shown
' i,J,m
that, for some combinations of j and m, the values are independent of
stability and mixing depth.
First, the mixing depth class will be defined. Table H-I shows
the mixing depth intervals for each class and geometric mean, h , for
each of the classes.
Table H-I
MIXING DEPTH CLASSES
m, Mixing
Depth Class
1
2
3
4
5
6
7
Mixing Depth Interval
(meters)
<100
100-200
200-400
400-800
800-1600
1600-3200
>3200
hm, Geometric
Mean of Depth
*
70.7
141
283
566
1131
2262
4525
For classes 1 and 7, the geometric mean was
calculated as though the classes were bounded.
We can calculate the values of (v/Q) for all the combinations
i,j,m
of j and m. These values are based on the Gaussian model for those seg-
ments totally inside that distance where the Gaussian and box models
give the same ground level concentration. For those segments wholly
beyond that distance, the box model values are used. For the segment
in which the transition occurs, (x/Q) is based on a combination of
i,j,m
the two models, as discussed in Section II of this report. Values of
were calculated using the values of h shown in Table H-I
m
-------
and the exponential approximations of the Pasquill-Gifford curves of
the vertical standard deviation as discussed in the text. These values
of (x/Q) . are presented in Table H-II.
The values in Table H-II are those that are used in the climato-
logical model. Inspection of the table shows that there are rows that
are identical. For instance, the rows of (x/Q) values are identical
i,j,m
when the stability class, j, is 5 and the mixing depth class, m, has any
value from 3 through 7. The same is true for stability class 4, except
that for i = 9 and m = 3 the value differs slightly from the values
found for m > 3. In applying the climatological model, this slight dif-
ference was ignored.
The last column of Table H-II gives a type number that was assigned
to each row. Rows with the same type number have been taken to be
identical for purposes of applying the model. Inspection of the last
column shows that the number of rows that need to be considered separately
has been reduced from 35 to 25. When this fact is employed in the appli-
cation of the model, it results in a reduction of required memory space
of about 28 percent. This allows for much more efficient use of the
computer.
-------
Table H-II
VALUES OF (v/Q)
FOR UNIT WIND SPEED
Stability
Class, j
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Mixing
Depth
Class,
m
1
1
1
1
1
2
2
2
2
2
3
3
3
3
3
4
4
4
4
4
5
5
5
5
5
6
6
6
6
6
7
7
7
7
7
Segment, i
1
4.60
6.89
10.38
16.11
23.0
4.60
6.89
10.38
16. 11
23.0
4.60
6.89
10.38
16. 11
23.0
4.60
6.89
10.38
16.11
23.0
4.60
6.89
10.38
16. 11
23.0
4.60
6.89
10.38
16. 11
23.0
4.60
6.89
10.38
16.11
23.0
2
3.04
4.92
7.22
11.91
16.67
3.04
4.92
7.22
11.91
16.67
3.04
4.92
7.22
11.91
16.67
3.04
4.92
7.22
11.91
16.67
3.04
4.92
7.22
11.91
16.67
3.04
4.92
7.22
11.91
16.67
3.04
4.92
7.22
11.91
16.67
3
3.60
4.99
7.49
13.48
18.96
2.62
4.99
7.49
13.48
18.96
2.61
4.99
7.49
13.48
18.96
2.61
4.99
7.49
13.48
18.96
2.61
4.99
7.49
13.48
18.96
2.61
4.99
7.49
13.48
18.96
2.61
4.99
7.49
13.48
18.96
4
7.07
7.07
8.24
15.74
22.50
3.54
4.60
8.08
15.74
22.5
1.96
4.55
8.08
15.74
22.5
1.58
4.55
8.08
15.74
22.5
1.58
4.55
8.08
15.74
22.5
1.58
4.55
8.08
15.74
22.5
1.58
4.55
8.08
15.74
22.5
5
14.14
14.14
14.14
19.17
27.6
7.07
7.07
8.79
19. 17
27.6
3.54
4.03
8.75
19.17
27.6
1.77
3.60
8.75
19.17
27.6
0.955
3.60
8.75
19.17
27.6
0.67
3.60
8.75
19, 17
27.6
0.604
3.60
8.75
19.17
27.6
6
28.3
28.3
28.3
28.5
34.9
14.14
14.14
14.14
24.2
34.9
7.07
7.07
9.65
24.2
34.9
3.54
3.54
9.65
24.2
34.9
1.77
2.38
9.65
24.2
34.9
0.884
2.88
9.65
24.2
34.9
0.442
2.28
9.65
24.2
34.9
7
56.6
56.6
56.6
56.6
56.6
28.3
28.3
28.3
31.5
47.1
14.14
14.14
14.16
31.1
47.1
7.07
7.07
10.89
31. 1
47. 1
3.54
3.54
10.9
31.1
47.1
1.77
1.83
10.89
31.1
47.1
0.884
1.28
10.89
31.1
47. 1
8
113.2
113.2
113.2
113.2
113.2
56.6
56.6
56.6
56.6
67.4
28.3
28.3
28.3
42.0
67.4
14. 1 4
14. 14
14.50
9
226.
226.
Type
1
2
226. ; 3
226.
226.
113.2
11X2
113.2
113.2
113.2
56.6
4
5
6
7
8
9
10
11
I
56.6 | 12
56.6
60.5
100.3
28.3
28.3
28.3
42.0 59.3
67.4
7.07
7.07
12.97
42.0
67.4
3.54
3.54
12.97
42.0
67.4
1.77
1.77
12.97
42.0
67.4
100.3
14. 14
14. 14
16.37
59.3
100.3
7.07
7.07
16.3
59.3
100.3
3.54
3.54
16.3
59.3
100.3
13
14
['•>
16
17
18
14
15
19
20
21
14
15
22
23
21
14
15
24
25
21
14
15
-------
Appendix I
CONTINUOUS AIR MONITORING PROGRAM STATIONS
-------
Appendix I
CONTINUOUS AIR MONITORING PROGRAM STATIONS
The only generally available carbon monoxide measurements that can
be used to verify the performance of the diffusion model are those
taken at the stations of the Continuous Air Monitoring Projects (CAMP).
This appendix has been included to provide some information about the
sites at which the measurements were taken. In this program we have used
data from the stations in St. Louis, Cincinnati, Chicago, Washington
and Denver. These stations are pictured in Figures 1-1 through 1-5. All
are located in or near the downtown sections of their respective cities.
The individual sites have certain characteristics that make their
measurements not entirely comparable to the computations made with the
model. As can be seen from Figure 1-1, the St. Louis site is adjacent
to a parking lot that has considerable in and out traffic during business
hours. This traffic, which is not included in the model calculations,
undoubtedly influences the measured CO concentrations.
The location of the Cincinnati CAMP Station, also in a parking lot
(Figure 1-2), is similar to that of the St. Louis station, but there is
probably less in-and-out traffic during the day at the Cincinnati site.
The Cincinnati parking lot is near a theater, so that anomolously high
measurements may occur at times when there are public events at that
theater.
The Chicago site represents a different type of problem. Figure
1-3 shows that the station is situated just at the foot of a tall
building. The airflow around that building is likely to be considerably
-------
different than the airport wind used for the computations. For example,
airflow around the building may cause the measurements to reflect the
high emission rates on the adjacent street, although the airport wind
may indicate that those emissions would be swept away from the site.
These aerodynamic effects are to be investigated during the coming year.
The Washington and Denver CAMP Stations (Figures 1-4 and 1-5) are
probably better located than the others, being somewhat farther away
from tall buildings and parking lots. However, their measurements may
not be entirely free of such interferences.
-------
FIGURE 1-1 ST. LOUIS CAMP STATION
-------
FIGURE 1-2 CINCINNATI CAMP STATION
TA-7874-73
-------
FIGURE 1-3 CHICAGO CAMP STATION
-------
FIGURE 1-4 WASHINGTON, D.C., CAMP STATION
-------
FIGURE 1-5 DENVER CAMP STATION
TA-7874-76
-------
ACKNOWLEDGMENTS
We are grateful for the able assistance of the following individuals
at Stanford Research Institute: the late Mrs. Shirley Reid, who secured
and supervised the reduction of the traffic data; Mr. Hisao Shigeishi,
who programmed much of the model and carried out computer trials;
Miss Joyce Kealoha, who assembled and cataloged our library of urban
pollution model studies, and who helped with numerous other aspects of
the work; Mr. Elmer Robinson, who aided in planning the model develop-
ment; and Mrs. E. Cox, Miss S. Hanson, Miss M. Ray, and Mrs. D. Orr, who
have typed the reports required on this project.
We also thank the members of the CRC-APRAC Urban Diffusion Project
Group for their guidance and suggestions, and for supplying useful tech-
nical information.
The assistance of Messrs. Charles Hosier and George Holzworth of
NAPCA and of Messrs. V. Hagarty and D. Galloway of the National Weather
Records Center are gratefully acknowledged for their cooperation in
supplying us with special and conventional meteorological data.
Finally, we thank all the state and local traffic agencies that
were so cooperative in supplying historical or forecast traffic data.
The following personnel and agencies provided such information for St.
Louis: Messrs. J. R. Turner and R. Weldinger, Missouri State Highway
Department; Mr. C. Sweet, St. Louis Land Use and Transportation Study;
and Mr. R. L. Grady, St. Louis Department of Streets. For the Washington,
D.C., metropolitan area, traffic data were supplied by: Mr. L. E. Brett,
Jr., Virginia Department of Highways; Mr. W. C. Scruggs, Arlington
County Traffic Engineering Division; Mr. D. E. Tyler, District of
-------
Columbia Bureau of Administrative Services; and Mr. G. W. Cassell,
Maryland State Road Commission. For Chicago traffic data, we acknowledge
the assistance of Messrs. E. W. Campbell and J. Miller, Chicago Area
Transportation study; and Mr. H. R. Handley, Illinois Division of
Highways. Mr. C. Ball, Denver Regional Council of Governments, and the
Colorado Department of Highways provided Denver traffic information.
Messrs. C. Ball and A. H. Hessling, Ohio-Kentucky-Indiana Regional
Transportation and Development Plan, provided traffic data for the
Cincinnati area.
-------
REFERENCES
Bastress, E. K., 1969, Nature & Control of Aircraft Engine Exhaust
Emissions, APCA No. 69-190.
Beckman, E. W., W. S. Fagley, and Jorma O. Sarto, 1967: "Exhaust
Emission Control by Chrysler—The Cleaner Air Package," Air
Pollution—1967 (Automotive Air Pollution), Hearings before the
Subcommittee on Air and Water Pollution of the Committee on Public
Works, United States Senate, Ninetieth Congress, First Session,
Part 1, pp. 411-424.
Bornstein, R. D., 1969: Observations of the urban heat island effect
in New York City, J. Appl. Meteorol., _7, 575-582.
Clarke, J. F., 1964: A simple diffusion model for calculating point
concentrations from multiple sources, J. Air Poll. Cont. Assoc.,
14, 347-352.
Clarke, J. F., 1969: Nocturnal Boundary Layer over Cincinnati, Ohio,
Mon. Wea. Rev., 97, 582-589.
Dominion Bureau of Statistics, 1968: Canada Year Book, 1968, Ottawa,
Canada, 815 pp.
Federal Highway Administration, 1966: Highway Statistics for 1966,
U.S. Government Printing Office, 186 pp.
Georgii, H. W., E. Busch, and E. Weber, 1967: Investigation of the
Temporal and Spatial Distribution of the Immission Concentration
of Carbon Monoxide in Frankfurt/Main, Report No. 11 of the Institute
for Meteorology and Geophysics of the University of Frankfurt/Main
(Translation No. 0477, NAPCA).
Gifford, F. A., Jr., 1961: Use of routine meteorological observations
for estimating atmospheric dispersion, Nuclear Safety, £, 48.
Gilman and Co., 1959: St. Louis Metropolitan Area Traffic Study,
Prepared for City and County of St. Louis by W. C. Gilman & Co.,
55 Liberty Street, New York, New York.
-------
Graham, I. R., 1968: An analysis of turbulence statistics at Fort Wayne,
Indiana,. J. Appl. Meteor., Tj 90-93.
Highway Research Board, 1968: Comparative Analysis of Traffic Assignment
Techniques with Actual Highway Use, Report No. 58, National
Cooperative Highway Research Program.
Hilsmeier, W. F. and F. A. Gifford, Jr., 1962, Graphs for estimating
atmospheric dispersion, USAEC Rpt ORO-545, Weather Bureau, Oak
Ridge, Tennessee.
Hilst, G. R. and N. E. Bowne, 1966: A Study of the Diffusion of Aerosols
Released from Aerial Line Sources Upwind of an Urban Complex, Final
Report, Vols. I and II, prepared for U.S. Army Dugway Proving
Ground, by the Travelers Research Center, Inc., Hartford,
Connecticut.
Holzworth, G. C., 1967: Mixing depths, wind speeds and air pollution
potential for selected locations in the United States, J. Appl.
Meteor., £, 1039-1044.
Institute of Traffic Engineers, 1965: Traffic Engineers Handbook,
Washington, D.C.
Johnson, W. B., Jr., F. L. Ludwig, and A. E. Moon, 1969, 'Development
of a Practical, Multipurpose Urban Diffusion Model for Carbon
Monoxide," Paper presented at Symposium on Multiple-Source Urban
Diffusion Models, Chapel Hill, North Carolina, 28-30 October 1969.
Larsen, R. I., 1969: A new mathematical model of air pollutant
concentration, averaging time and frequency, J. Air Poll Cont.
Assoc., 19, 24-30.
Leahey, D. M., 1969: A model for predicting the variation of pollution
within the urban heat island, APCA paper No. 69-107.
Ludwig, F. L., 1968: Urban temperature fields, paper presented at WMO
Symposium on Urban Climates and Building Climatology, Brussels,
15-25 October 1968.
Ludwig, F. L. , 1970: Urban air temperatures and their relation to
extraurban meteorological measurements, paper presented at January
1970 Meeting of Amer. Soc. Heat., Refrig. and Vent. Eng., San
Francisco.
-------
Ludwig, F. L. and J. H. S. Kealoha, 1968: Urban Climatological Studies,
Final Report,, Contract CD-DAHC-20-67-C-0136 (Work Unit 1235A)
Stanford Research Institute, Menlo Park, California.
Mason, D. V., G. Ozolins, and C. B. Morita, 1969: Sources and Air
Pollutant Emission Patterns in Major Metropolitan Areas, APCA
69-110.
McCormick, R. A. and C. Xintaras, 1962: Variation of carbon monoxide
concentrations as related to sampling interval, traffic, and
meteorological factors, J. Appl. Meteor., 1, 237-243.
McElroy, J. L., 1969: A comparative study of urban and rural dispersion,
J. Appl. Meteor., 8, 19-31.
McGuire, T. and K. Noll: Relationships Between Concentrations of
Atmospheric Pollutants and Averaging Time, paper presented at llth
Conf. on Methods in Air Pollution and Industrial Hygiene, U. of
California, Berkeley, 30 March-1 April 1970, 13 pp.
Meade, P. J., 1960: Meteorological Aspects of the Safety and Location
of Reactor Plants, World Meteorological Organization, Tech. Note
No. 33.
Miller, M. E. and G. C. Holzworth, 1967: An atmospheric diffusion
model for metropolitan areas, J. Air Poll. Contr. Assoc., 17,
46-50.
Moses, H., 1969: Mathematical Urban Air Pollution Models, Report No.
ANL/ES-RPY-001, Argonne National Laboratory, Argonne, Illinois.
National Air Pollution Control Administration, 1968a: Report for
Consultation on the Washington, B.C., National Capital Interstate
Air Quality Control Region, U.S. Dept. of HEW.
National Air Pollution Control Administration, 1968b: Report for
Consultation on the Metropolitan Los Angeles Air Quality Control
Region, U.S. Dept. of HEW.
National Air Pollution Control Administration, 1968c: Report for
Consultation on the Metropolitan Boston Intrastate Air Quality
Control Region, U.S. Dept. of HEW.
National Air Pollution Control Administration, 1968d: Report for
Consultation on the San Francisco Bay Area Quality Control Region,
U.S. Dept. of HEW.
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National Air Pollution Control Administration, 1969a: Report for
Consultation on the Metropolitan Pittsburgh City Intrastate Air
Quality Control Region, U.S. Dept. of HEW.
National Air Pollution Control Administration, 1969b: Report for
Consultation on the Greater Metropolitan Cleveland Intrastate Air
Quality Control Region, U.S. Dept. of HEW.
National Air Pollution Control Administration, 1969c: Report for
Consultation on the Metropolitan Kansas City Intrastate Air Quality
Control Region, U.S. Dept. of HEW.
National Air Pollution Control Administration, 1969d: Report for
Consultation on the Metropolitan Baltimore Intrastate Air Quality
Control Region, U.S. Dept. of HEW.
National Air Pollution Control Administration, 1969e: Report for
Consultation on the Hartford-Springfield Interstate Air Quality
Control Region (Connecticut-Massachusetts), U.S. Dept. of HEW.
Neiburger, M., 1968: Diffusion Models of Urban Air Pollution, WMO
Symposium on Urban Climates and Building Climatology, Brussels,
15-20 October 1968.
Ott, W., J. F. Clarke, and G. Ozolins, 1967: Calculating future carbon
monoxide emissions and concentrations from urban traffic data,
PHS Publ. No. 999-AP-41, National Center for Air Pollution Control,
Cincinnati, Ohio.
Panofsky, H., 1957: Introduction to Dynamic Meteorology, Pennsylvania
St. U., University Park, Pennsylvania, 243 pp.
Pasquill, F., 1961: The estimation of the dispersion of windborne
material, Meteorol. Mag. (London) 90, 33-49.
Perkins, W. A., 1962: Some effects of city structure on the transport
of airborne material in urban area, paper presented at Air over
Cities Symposium, R. A. Taft Sanitary Engineering Center, Cincinnati,
Technical Report A62-5, pp. 197-205.
Pooler, F., 1963: Airflow over a city in terraine of moderate relief,
J. Appl. Meteorol., 2, 446-456.
Pooler, F., 1961: A prediction model of mean urban pollution for use
with standard wind roses, Intern. J. Air and Water Poll., 4, 199-211.
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Pooler, F., 1966: A tracer study of dispersion over a city, J. Air
Poll. Contr. Assoc., 11, 677-681.
Robinson, E. and R. C. Robbins, 1967: Sources, Abundance, and Fate of
Gaseous Pollutants, Prep, for Amer. Petroleum Inst. Final Report
Proj. PR-6755, Stanford Research Institute, Menlo Park, California.
Rose, A. H. and W. D. Krostek, 1969: Emission Factors, U.S. Dept. of
Health, Education and Welfare, National Air Pollution Control
Administration, p. 5.
Rose, A. H., R. Smith, W. F. McMichael, and R. E. Kruse, 1964:
Comparison of Auto Exhaust Emissions from Two Major Cities, U.S.
Public Health Service, Cincinnati, Ohio.
Rouse, H., 1951: Air tunnel studies of diffusion in urban areas,
Meteor. Mono., _1, 39-41.
Schnelle, K. B., F. G. Ziegler, and P. A. Krenkel, 1969: A study of the
vertical distribution of carbon monoxide and temperature above an
urban intersection, APCA Paper No. 69-152.
Slade, D. H. (Ed.), 1968, Meteorology and Atomic Energy U.S. Atomic
Energy Commission, Div. Tech. Info., Oak Ridge, Tennessee.
Smith, M. (Ed.), 1968, Recommended guide for the prediction of the
dispersion of airborne effluents, Amer. Soc. Mech. Eng., New York.
Smith, M. E. and I. A. Singer, 1966: An improved method of estimating
concentrations and related phenomena from a point source emission,
J. Appl. Meteor., 5_, 631-639.
Smith, Wilbur and Associates, 1958: Transportation Survey—National
Capital Region, prepared for National Capital Planning Commission
by W. Smith and Assoc., 495 Orange Street, New Haven, Connecticut.
Stanford University Aerosol Laboratory and The Ralph M. Parsons Co.,
1953a: Behavior of aerosol clouds within cities, Joint Quarterly
Report No. 3, January-March 1952, Contracts DA-18-064-CML-1856 and
DA-18-064-CML-2282, DDC No. AD31711, January.
Stanford University Aerosol Laboratory and The Ralph M. Parsons Co.,
1953b: ibid., Joint Quarterly Report No. 4, April-June 1953, DDC
No. AD31508.
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Stanford University Aerosol Laboratory and The Ralph M. Parsons Co.,
1953c: -ibid.,, Joint Quarterly Report No. G, Vol. I, October-
December 1953,, DDC No. AD31510.
Stanford University Aerosol Laboratory and The Ralph M. Parsons Co.,
1953d: ibid., Joint Quarterly Report No. 6, Vol. II, October-
December 1953, DDC No. AD31711.
Stern, A. C., 1969: The Systems Approach to Air Pollution Control,
Pub. No. 216, Dept. of Environ. Science and Engineering, Univ. of
North Carolina, Chapel Hill, Presented at Clean Air Conference,
Sydney, Australia, 21 May 1969.
Summers, P. W., 1966: The seasonal, weekly, and daily cycles of
atmospheric smoke content in central Montreal, J. Air Poll. Contr.
Assoc., I6_, 432-438.
Swinnerton, J. W., V. J. Linnenbom, and C. H. Cheek, 1969: Distribution
of methane and carbon monoxide between the atmosphere and natural
waters, Environ. Sci. and Tech., 3^, 836-838.
Turner, D. B., 1964: A diffusion model for an urban area, J. Appl.
Meteor., 3_, 83-91.
Wanta, R. C., 1968: Meteorology and air pollution, Chap. 7 of Air
Pollution, Vol. 1, 2nd Edition, A. C. Stern, Ed., Academic Press,
New York, 187-227.
Went, F. W., 1966: On the nature of Aitken condensation nucleii, Tellus,
18, 549-556.
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