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U. S. ENVIRONMENTAL PROTECTION AGENCY

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PROCEEDINGS
OF
SYMPOSIUM
ON
MULTIPLE-SOURCE
URBAN DIFFUSION
MODELS
Editor: Arthur C. Stern
Sponsors: National Air Pollution Control Administration
and North Carolina Consortium on Air Pollution
U.S. ENVIRONMENTAL PROTECTION AGENCY
Air Pollution Control Office
Research Triangle Park, North Carolina, 1970
For sale by the Superintendent of Documents, U.S. Government Printing Office
Washington, D.C., 20402 - Price $1.73

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The AP series of reports is issued by the Air Pollution Control Office to
report the results of scientific and engineering studies, and information of
general interest in the field of air pollution. Information reported in this
series includes coverage of APCO intramural activities and of cooperative
studies conducted in conjunction with state and local agencies, research insti-
tutes, and industrial organizations. Copies of AP reports are available free of
charge to APCO staff members, current contractors and grantees, and non-
profit organizations — as supplies permit — from the Office of Technical
Information and Publications, Air Pollution Control Office, Environmental
Protection Agency, Research Triangle Park, North Carolina 27709
Air Pollution Control Office Publication No. AP-86

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PREFACE
This symposium was conducted under the terms of a contract between the
Meteorology Division of the National Air Pollution Control Administration
(NAPCA) and the Department of Environmental Sciences and Engineering,
School of Public Health, University of North Carolina at Chapel Hill (UNC).
The contract officer for the sponsor was Mr, Lawrence E. Niemeyer, As-
sistant Director, Division of Meteorology, NAPCA. The responsible officer
for the University was Arthur C. Stern, Professor of Air Hygiene. The sym-
posium was held from October 27 to 30, 1969, at the Carolina Inn on the
University campus. On December 4, 1970, the functions of NAPCA were
transferred to the Air Pollution Control Office (APCOI of the Environmental
Protection Agency. All references to the former, therefore, now refer to the
latter.
Although UNC was the contractor, it was agreed that the symposium would
be sponsored by the North Carolina Consortium on Air Pollution, com-
prising: Duke University; North Carolina State University; the Office of Man-
power Development, NAPCA; Research Triangle Institute; and the University
of North Carolina at Chapel Hill. The detailed planning for the symposium
was done by a steering committee representing the members of the Con-
sortium and the contract officer.
All the papers, both invited and volunteered, that were presented during the
symposium, are included in this volume. In addition to the invited partici-
pants, some attendees were selected from persons who responded to the
public announcement of the symposium. Almost all papers were preprinted
and distributed to participants in advance of the meeting. Although there
was open discussion after every presentation except the Keynote and Ban-
quet speeches, the only discussions incorporated in the Proceedings are those
subsequently submitted in writing.
Questions from the floor and authors' responses do not appear unless those
same questions and answers were also included in the written discussion.
Every author questioned was given an opportunity to submit a rebuttal. The
nature of such an arrangement made it necessary, for the sake of coherence,
to incorporate all discussion in a separate chapter, divided into two sections:
speaker-directed discussions and discussions submitted by the participants.
iii

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Particular thanks are given to the graduate students in Air Pollution in my
department at UNC, who acted as floor monitors during the symposium —
particularly to Harvey Jeffries and Douglas McKay, who managed the audio-
visual arrangements throughout the symposium. The registration of partici-
pants and the preparation of the symposium program and information kits
were ably handled by the Continuing Education Department of the School
of Public Health, UIMC. I am especially appreciative of the excellent services
of my secretary, Martha Davis, for her help in the preparation and conduct
of the symposium and in the coordination of these proceedings.
Arthur C. Stern
Chapel Hill, N. C.
November 1970.
iv

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STEERING COMMITTEE
Dr. Jay Apple, Director, Institute of Biological Sciences, North Carolina State
University.
Dr. Robert Barnes, School of Forestry, Duke University.
Mr. James L. Dicke, Meteorologist, Office of Manpower Development, Air Pol-
lution Control Office.
Dr. James S. Ferrell, Department of Chemical Engineering, North Carolina
State University.
Dr. Kenneth Knoerr, School of Forestry, Duke University.
Dr. Harry Kramer, Director, Office of Manpower Development, Air Pollution
Control Office.
Mr. Lawrence Niemeyer, Assistant Director, Meteorology Division, Air Pollu-
tion Control Office.
Professor Arthur C. Stern, Department of Environmental Sciences and Engi-
neering, School of Public Health, University of North Carolina at Chapel
Hill.
Mr. James J. B. Worth, Associate Director of Engineering, Research Triangle
Institute.
SESSION CHAIRMEN
Mr. James J. B. Worth, Associate Director of Engineering, Research Triangle
Institute.
Dr. Lester Machta, Director, Air Resources Laboratories, National Oceanic and
Atmospheric Administration.
Mr. Robert A. McCormick, Director, Meteorology Program, Air Pollution Con-
trol Office.
Dr. Kenneth Knoerr, School of Forestry, Duke University.
Dr. Walter J. Saucier, Department of Geosciences, North Carolina State Univer-
sity.
v

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CONTENTS
1.	John T. Middleton
Keynote Speech: Diffusion Modeling for Urban Air Pollution
Abatement and Control	1_1
2.	Heinz H. Lettau
Physical and Meteorological Basis for Mathematical Models
of Urban Diffusion Processes	2-1
3.	Frank Pasquill
Prediction of Diffusion over an Urban Area—Current Practice
and Future Prospects	3-1
4.	Kenneth L. Calder
Some Miscellaneous Aspects of Current Urban Pollution
Models	4-1
5.	Warren B. Johnson, Francis L, Ludwig, and Albert E. Moon
Development of a Practical, Multi-purpose Urban Diffusion
Model for Carbon Monoxide	5-1
6. John J. Roberts, Edward J. Croke, and Allen S. Kennedy
An Urban Atmospheric Dispersion'Model	6_1
7. Glenn Ft. FiUst
Sensitivities of Air Quality Prediction to Input Errors and
Uncertainties	7-1
8. Shin'ichi Sakuraba in collaboration with M. Mariguchi and I.
Yamazi
Elevation of Tracer Cloud over an Urban Area	8-1
9. Heinz G. Fortak
Numerical Simulation of the Temporal and Spatial Distri-
butions of Urban Air Pollution Concentration	9-1
VI

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10. LiauJ. Shieh, Ben Davidson, and J. P. Friend
A Model of Diffusion in Urban Atmospheres: SO2 in Greater
New York	10-1
11.	James R. Mahoney, William 0. Maddaus, and John C,
Goodrich
Analysis of Multiple-Station Urban Air Sampling Data	11-1
12.	Morris Neiburger
Banquet Speech: Progress + Profits + Population = Pollution	12-1
13.	Arthur C. Stern
Symposium Summary: Utilization of Air Pollution Models	13-1
14.	Discussions	14-1
15.	Appendix: Attendance List	15-1
vii

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PROCEEDINGS
OF
SYMPOSIUM
ON
MULTIPLE-SOURCE
URBAN DIFFUSION
MODELS

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AUTHOR
JOHN T. MIDDLETON, Acting Commissioner of the Air Pollution Control Office,
was Professor and Director of the University of California State-wide Air Pollu-
tion Research Center where his pioneer studies of the environment as a regulating
factor in disease development in agricultural crops enabled him to first recognize
photochemical air pollution as an adverse economic factor to California agricul-
ture in the mid-1940's.
Or. Middteton has served in the past as: Chairman, California Motor Vehicle
Pollution Control Board; member. Governor's Interagency Committee on Air Pollu-
tion, and Executive Task Force on Waste Management; consultant, U. S. Public
Health Service, Office of Science and Technology, and the World Health Organi-
zation; and as a Director for the Air Pollution Control Association.
Dr. Middteton has a B.S. from the University of California and a Ph.D. from the
University of Missouri.

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Keynote Speech
1. DIFFUSION MODELING FOR AIR POLLUTION
ABATEMENT AND CONTROL
JOHN T. MIDDLETON
Acting Commissioner, Air Pollution Control Office
Environmental Protection Agency
I am very pleased to be with you this morning, and to have the chance to talk
to you about the urgent need for developing systematic solutions to one of the
most ironic incongruities we face in this country today, the problem of air
pollution.
Some months ago, we received from the National Aeronautics and Space
Administration photographs of portions of the United States taken from
Apollo 8 as it streaked toward the moon. NASA sent us these particular
photographs because one of the more interesting phenomena they featured was
the pall of air pollution hanging over a number of large urban areas. Here, it
seems to me, is the irony for our time, a spaceship, carrying men to the moon
and back, capturing with its cameras our tragic failure to prevent the contami-
nation of the earth's most precious resource, the air that all of us breathe.
Of all the threats to our environment, air pollution is potentially the most
dangerous; certainly it is the most difficult to solve. We cannot replenish the air
as we replenish soil and trees; and we cannot purify the air, as we do water,
before we use it. We must breathe the air as it comes to us-and each day it
comes to us more heavily laden with the by-product wastes of our industri-
alized society.
Today, this Nation is paying billions of dollars each year for the dubious
privilege of living with—rather than controlling—air pollution. Air pollution
soils, corrodes, and damages a wide variety of structures in our cities and
towns—from the despoiling of our homes to the corrosion of suspension
bridges that span our rivers. It threatens forests and farmlands as well. It
constitutes a national health hazard of greater significance than many may
appreciate. It contributes to the rising incidence of such important respiratory
diseases as lung cancer, asthma, bronchitis, and emphysema. Emphysema is the
fastest growing cause of death in America today.
1-1

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The ways in which we seemingly may be changing our environment through air
pollution are endless; and they are international, as well as national, in their
dimensions. An acid tongue of combustion products from the industrialized
area of Western Europe is transported over the southern part of Scandinavia;
and, particularly in the winter months when combustion activities are high, the
acidity of rainfall in the area increases substantially. The ability of the soil to
accommodate these international acid rains is certainly limited, and the con-
sequent effects on vegetation and the ecosystem can only be guessed at.
Man introduces 10,000,000 tons of nitrogen into the atmosphere annually.
This is comparable to the input of the natural nitrogen cycle. The main source
of nitrogen contamination is inorganic agricultural fertilizers. The nitrates in
the rivers and drinking water of some Illinois towns are now approaching the
upper safe limit of 10 parts per million set by the Environmental Control
Administration. As agriculture expands to keep the pace with world food
needs, the problem of nitrates in water supplies will become more serious.
Although we are not sure of the health effects of the current levels of lead in
our environment, we do know that a person's body burden of lead corresponds
roughly to the levels in his environment and that those levels are going up as
the use of the principal source of lead, the automobile, continues to increase. |
have yet to see any data that show any useful purpose served by lead in the
body.
The toxicity of mercury compounds has also been well established. The
inhalation of only small amounts of mercury or its derivatives can result in
exaggerated emotional response, muscular tremors, and gingivitis. This poison-
ing has occurred in most of the major industries that use mercury. Vegetation
has been damaged when kept in a greenhouse painted with a mercury fungi,
cide, and fish in some Swedish lakes have absorbed and concentrated methyl
mercury from pesticides to such a high degree that fishing in those lakes has
been prohibited.
Estimates differ about the potential effects on world temperature and climate
due to increased atmospheric carbon dioxide and particulate concentrations.
Estimates also differ on how much air pollution can affect precipitation ancj
condensation. Questions are also being raised about the ultimate effect of
man's conversion of energy to heat. The opinions differ about the details of
processes involving temperature trendy climate, melting of polar ice caps, see
level, photosynthesis, and the distribution of fish, to name a few.
There are, of course, many other examples. The point is, that when man alters
the balance of Nature, it is like tossing a pebble into a pond: the resulting
ripples spread out concentrically from the entry point until they touch every
point on the shore. Continued small alterations of our environment may have
drastic effects later, effects we cannot foresee now.
Today we stand at a point in our scientific progress where our capacity
1-2

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enhance-or to degrade—the quality of our environment is almost literally
beyond reckoning. From the standpoint of our sheer survival as a nation and a
people, it is essential that the talent and imagination of all of us—and especially
of the scientific community—be engaged in enhancing it.
If it is obvious that one way to halt the contamination of the air we breathe is
to prohibit automobiles* stop the generation of electricity, and shut down
industry—it is just as obvious that this way is impossible. Air pollution is woven
throughout the fabric of our daily lives. It is a by-product of the way we build
our cities. It is a waste, left over from the ways we transport ourselves and our
goods, and from the ways we generate the energy to heat and light the places
where we live and work. It is part and parcel of the ways in which we produce
and package a multitude of manufactured goods, and, among other things, the
ways in which we use those goods and dispose of the remains.
The problem of air pollution, then, affects not one segment of society, but all
segments. To deal adequately with such a problem has implications for
thousands of daily decisions that are made in every activity of our busy
modern life.
Air pollution is a direct threat to human health and welfare that no responsible
person can put aside; but it is also a social, political, and economic problem.
We will not truly come to grips with air pollution unless we derive our remedies
from a careful consideration of what is truly in the public interest.
Here, then, is perhaps the most challenging frontier of our space-age society.
Air pollution, like the other problems of our environment, is no longer the
private preserve of the professional engineer, either in government or out. It is
rather a problem that requires attention from all facets of our society if we and
our institutions are to survive its solution. Governments at all levels must rise
above their jealous disputes as to what jurisdictional rights are being violated
by whom, and work together side by side as regional partners in a public
enterprise that no single government possibly can carry off alone. The manu-
facturer will have to look beyond his assembly line and take responsibility for
the performance of his product in the hands of the sometimes neglectful
consumer. The industrialist is going to have to take responsibility for his use
and misuse of those resources which sustain not only the industrial revolution
in this country, but also our very lives. The scientist, hardly last and hardly
least, must provide the technical solutions to those by-product problems that
have unfortunately accompanied the modern miracles his science has created.
In the Clean Air Act, as amended, the Congress has attempted to give NAPCA*
the legislative apparatus that we need to remove the malignancy of air pollu-
tion. This Act requires that we carefully consider all the ramifications of every
step we take—and every step we do not take—in the control process. The Act
charges us to protect the public in those places where air pollution has reached
acute proportions and to prevent the problem from occurring in those places
•Now APCO.
1-3

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where fresh air is still enjoyed. On the other hand, the Act reflects an
awareness that air pollution is the result of many of the activities that sustain
our modern way of life. It says that we must optimize use of currently
available technology to control and abate air pollution without disrupting these
activities.
The Federal government has the responsibility for setting the machinery of the
Clean Air Act in motion. Under the Act, the Department of Health, Education,
and Welfare is required to draw the boundaries around each urban area of the
country where we believe air pollution is a problem. So far we have drawn the
boundaries around 20 major urban areas, and by the end of next summer we
expect that we will have drawn the boundaries for a total of 57 air quality
control regions, involving all the 50 states, the District of Columbia, Puerto
Rico, and the Virgin Islands.
Last February we issued to the states criteria and control technique reports on
two of the major families of air pollutants, the sulfur oxides and gross
particulate matter. The states are now on notice to use this information in
developing air quality standards for the regions we have designated and to
design plans for implementing the standards.
It is at this later stage of the Clean Air Act procedure, the regional implemen-
tation plan, that the technique of diffusion modeling plays such an important
role. I would like in the time remaining to me this morning to discuss that role
in more detail.
In 1958, the year of the First National Air Pollution Conference, there
appeared to be some element of doubt at least in the minds of some people as
to whether there was indeed an air pollution problem. .. At that time.
NAPCA's meteorologists were already engaged in developing an empirical
diffusion equation. Weather Bureau wind summaries and an IBM 650 computer
were used to furnish mean monthly sulfur dioxide concentration distributions
for an entire urban area. The data from Nashville, Tennessee was used to test
the model. Although the absolute magnitude of the concentrations could not
be verified, patterns that were predicted and observed were generally similar
for the 5-month test period. This was the first step by NAPCA scientists,
indeed the first by any group following Frenkiel's pioneering effort in 1955, to
delineate mathematically transport and dispersion processes on an urban scale.
We have come a long way since 1958, and NAPCA's Division of Meteorology
has not been alone in its modeling efforts. In recent years its work has been
complemented by modeling work conducted by meteorologists at New York
University, the University of California at Los Angeles, the University of
Florida, and ESSA's Air Resources Laboratory. Studies have also been con-
ducted by Travelers Research Center and the Stanford Research Institute.
Work also goes on abroad. There has been diffusion modeling by scientists in
Germany, Hungary, Japan, England, and Canada. Some of their developments
1-4

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will, I understand, be presented at this symposium, and that is good. The need
for abatement of air pollution is a strong international tie.
As we proceed with the implementation of the Clean Air Act, the meteo-
rologist will be called upon more often to provide a mathematical description
of the transport of air pollution in the research, survey, and operational phases
of control activities. In essence, the meteorologist is charged, because of time
limitations and paucity of air quality measurements, with the chore of pre-
senting convincing evidence of the magnitude and frequency of pollution
transport and dilution. The diffusion models we have been discussing are the
yardsticks for furnishing quantitative determinations of ambient air concen-
trations of pollutants. These determinations must be credible enough to satisfy
the members of other scientific and technical disciplines, as well as represen-
tatives of legal, economic, and political interests. These models should also be
flexible enough to assimilate feedback from source emissions for obtaining
solutions to both chronic and acute pollution problems.
Future diffusion models that incorporate air pollution climatology are ex-
pected to be used more frequently in long-range air-resource-management
programs for the evaluation of future air quality and source locations with
regard to projected emissions rates and population distributions. In order to
interpret the relationships between proposed or existing source emission
standards and ambient air quality standards, we need a quantitative account of
the meteorological processes that cause pollutants to be diluted, chemically
changed, or dispersed between source and receptor. Our hope is that by
applying diffusion models to calculate the integrated effects of multiple
sources of the same pollutant, we will be able to interpret the relationships
between proposed or existing source emission standards and ambient air
quality standards.
The advantages of this computer age technology have already been recognized
by responsible segments of commerce and industry, and more recently by
community planning agencies. In the words of Jimmy Durante, "everybody
wants to get into the act."
Another application of diffusion models will come with the evaluation of the
effectiveness of individual control or abatement procedures for a given source
or complex of sources. By use of appropriately programmed models, such an
assessment may be made without the need for an intricate and dense network
of air quality measurements taken at the right place in the right time at the
right season. Using diffusion models, the meteorologist can greatly reduce the
time and cost of such evaluations by answering the questions of what actually
constitutes "the right place, length of time and season." Moreover, under
operating situations one may expect that the short-term-period diffusion model
will be employed to determine the amount of emission decrease required to
meet air quality standards. Such models will also be helpful in the strategic
1-5

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deployment of mobile air quality and meteorological monitoring units during
air pollution alert situations.
So far as a warning scheme is concerned, the heart of any effective air pollution
control strategy will be meteorological forecasts that can provide the necessary
lead times and guidance required to deploy and implement abatement and
control devices. The sine qua non of such forecasts is the capability of
meteorological techniques to forecast meteorological conditions within the
urban boundary layer on urban scales appropriate to the air pollution problem.
There are some meteorologists, and I must agree with them, who suggest that
the utility of present diffusion models is limited by the inability to make
accurate forecasts of wind and temperature profiles. I think it is abundantly
clear that the accurate description within the planetary boundary layer of the
profiles of wind, temperature, and moisture and their variability in time and
space as a function of surface conditions and of synoptic-scale features is a
fundamental requirement for improved meteorological services not only to air
pollution problems, but also to many other interests. We have an urgent need,
it seems to me, for greatly improved mesoscale forecasting from the national
weather sen/ices.
I do not ask for a doctoral dissertation on a weather forecast; all I ask is that
we be supplied with the facts that we need to do our job, the facts that you
gentlemen need to make your diffusion models more efficient. I think we agree
that the quality of your results depends upon the information you start with.
To alleviate to some degree the inadequacies in mesoscale observations and
forecasts in the United States, we are supporting the Environmental Science
Services Administration program of low-level soundings in five urban areas. The
program provides for a full-time meteorologist to concentrate on mesome-
teorological-scale forecasts in these five metropolitan areas, particularly as they
relate to air pollution. Hopefully, ESSA will be able to assume responsibility
for such services in these five cities and to extend them to an additional 15
cities in the next fiscal year.
The programs that we are supporting in the National Air Pollution Control
Administration to improve our knowledge in the atmospheric sciences area
may seem to some of you at first glance to be a far cry from the usual business
of a Federal regulatory agency. A closer look, I think, will reveal (1) that these
and other research programs in NAPCA are a vital link in the control process
and fully congruous with the fundamental thesis of the Clean Air Act and (2)
that our efforts to control air pollution should be derived from a careful
evaluation of the latest scientific evidence of the effects of air pollution on
health and welfare. This systematic approach to control, this linking of the
control effort to scientific evidence of the need for control, seems to me to
lend a vitality to the research area that it might never otherwise acquire. I am
hopeful that the research programs we have found it necessary to support
1-6

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NAPCA, in order to give us that information so vital to the planning of our
control program directions, will stimulate other agencies and institutions to
begin to explore this as yet largely untouched area of the meteorological
sciences.
In this regard, diffusion models such as have been developed up till now, and
the generations of models yet to come as we refine, expand, and develop our
techniques, can play a vital role in our attempt to systematically apply air
pollution control theory on a regional basis. For this reason, I wish all of you
Godspeed in your deliberations at this symposium.
1-7

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ABSTRACT
Diffusion processes in the volume of air above a geographical area can
be described in spatial detail with two- and three-dimensional vector
models drawn from boundary layer and fluid dynamics concepts. A
simpler scalar model, in particular, can directly account for temporal
trends in average pollutant levels due to simultaneous diffusion of
mass, energy, and momentum from multiple sources.
By an application of climatonomy, the qualitative box model of scalar
diffusion is expanded quantitatively with fluid dynamic equations. The
theoretical model has been applied to prediction of both long-and
short-range, thermal and particulate pollutant trends in large and small
cities. The use of the box model to evaluate aerodynamic momentum
drain over the built-up area of a city is also described. City types are
specified in terms of their aerodynamic roughness parameter with a
formula based on results of micrometeoro/ogicai experiments. Knowing
only the horizontal pressure gradient in the lower troposphere the
model makes it possible to estimate the characteristic wind speed for a
specific city type.
In comparison with Davenport's power law, a Universal Wind Spiral
Theory described here has the advantages of yielding quantitative
estimation of directional shear and surface roughness effect on the
wind profile. Examples of scalar and vector application of the latter
law to thermal pollution are discussed.
author
HEINZ H. LETTAU is Professor of Meteorology and Civil Engineering at the
University of Wisconsin, where his current research is directed toward modeling
earth-air interaction processes. His model of the hydrological cycle for restoring
the level in water sheds was one of the earliest attempts at environmentsI
modeling. He has been a research scientist at the Geophysics Research Director-
ate U.S. Air Force, Cambridge, Massachusetts; Fellow of the American Meteoro-
logical Society; corresponding member of the Bavarian Academy of Science;
member of the NAPCA Research Grants Advisory Committee, and is main editor
of the two-volume Exploring the Atmosphere's First Mile, 1957.
Dr. Lettau received his Ph.D. in geophysics from the University of Leipzig in 193T.

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2. PHYSICAL AND METEOROLOGICAL BASIS
FOR MATHEMATICAL MODELS
OF URBAN DIFFUSION PROCESSES
HEINZ H. LETTAU
University of Wisconsin at Madison
INTRODUCTION
t shall discuss some general aspects of processes taking place in the atmo-
spheric boundary layer when wind passes over urban terrain. Emphasis will
be on simultaneous diffusion of mass, energy, and momentum with special
consideration of aerodynamic resistance due to roughness of urban surfaces
and resulting feedback on the diffusion potential of the urban atmosphere.
I shall start with an illustration familiar to you. Figure 2-1 shows what I
would like to call the "vector model" of diffusion from multiple sources.
This illustration comes from a report by Moses1 demonstrating the conven-
tional approach that assigns one grid to the sources and another grid to the
receptors, with a composite of "plumes" in between. The merits of this basic
model for the study of the details of complex urban diffusion processes are
obvious, and I trust that its implications and desirable refinements will be
competently discussed by other participants at this Symposium.
Let me contrast the vector model with a "scalar model" (Figure 2-2) in
which the volume of "city-air" is somewhat crudely defined. Pollutant
emission is attributed to a quasi-uniform area source at the tower boundary.
The major flushing agency is horizontal air motion, additionally supported
by vertical eddy flux at the level h* that tops the volume. If no other city is
immediately upstream, the wind enter's the volume relatively clean but leaves
it loaded with emission products. The level h* may coincide with an
inversion of temperature, in which case vertical exchange through this level
will be of minor importance. Such scalar or "box-models" of urban diffusion
have been mentioned occasionally in the literature. They cannot be used for
the study of spatial detail, but produce interesting, specific results, if em-
phasis is placed on time-series (either short- or long-range trends). Moreover,
the box-models permit discussion of similarities between air diffusion and
other natural processes such as the loading of a watershed by precipitation,
discharge into river channels, and losses by evapotranspiration. It is not my
2-1

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SCHEMATIC
SOURCE GRID
A.

C.
dA
POLLUTANT
ISOPLETHS
0.6 ppm
POLLUTANT ISOPLETHS
SCHEMATIC
RECEPTOR GRID
Sources are located ot A, B, C and D of source in ventory grid. A section of the
monitoring grid is given by squares 15, 16 and 17. Ihe concentration enclosed
by the 0.6 ppm isopleth of source B and 0.3 ppm isopleth of source D contribute
a concentration exceeding 0.9 ppm for square 15. See hatched area. Diagram as
published by Moses,^
Figure 2-1. Illustration of conventional or vector model of urban
diffusion.
2-2

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intention, however, to discuss the descriptive concept of an "air shed."2 I
prefer instead to consider a basic similarity between air pollution dispersal
and the hydrologic cycle that permits me to utilize a theoretical solution of
the water balance equation recently described by Lettau,3
Parameter Considerations
Before moving to that point, let me insert a general statement: The entity of
transport and flux processes must be taken into account in fluid dynamics
problems. Thus, in atmospheric boundary layer studies we should not restrict
our consideration to transport of mass (either intentionally or inadvertently
loaded on the moving fluid} but should investigate concurrent generation and
dissipation of both momentum and energy. The scalar model (Figure 2-2}
has the advantage over the more specialized vector model of Figure 2-1, that
it can, without alteration, express a city area as a heat source (essentially
due to the combustion of fuels), as well as a momentum sink or negative
momentum source (due to the efficiency of buildings as aerodynamic rough-
ness elements). A coherent consideration of the transport and flux of mass,
momentum and energy in any atmospheric boundary layer is also a logical
starting point for the discussion of mechanical and thermodynamic feedback
since the horizontal dimensions involved in urban boundary layer structure
are comparable to meso-meteorological and synoptic-scale atmospheric pro-
cesses.
Aerosol Effects on Sunlight Absorption-Example
Let me begin discussion of the combined aspects of long-term trends and
feedback on meteorological phenomenon, by considering the attenuation of
sunlight by pollutants in the volume of city air.
McCormick and Ludwig4 have recently discussed climatic modification by
atmospheric aerosol. Let me illustrate my approach with Figures 2-3 through
2-5,* taken from a recent publication by K. and H. Lettau.5 A common
Y0n some" graphs the word "climatonomy" wilt appear. This word is also found in the
title of the references by Lettau3 and K. and H. Lettau. It is a new term that we use
at the University of Wisconsin to indicate a systems approach to problems of climate.
System in engineering problems is conventionally used to encompass the following
components: (1)a process. (2) an input to the process, or a forcing function, (3) an
output from the process, or a response function, (41 feedback, and (5) control of
inputs or management of the system. Typical of climatonomy is the use of a mathe-
matical-physical model of a specific atmospheric process, such as the response of a
climatic element to a defined forcing function, which may be an insolation cycle Qr
another defined input like pollutant emission. The climatonomic approach considers
physically significant parameterization of the problem so that, even though control or
management may not be possible, one could reasonably and realistically answer such
questions as what response can be predicted if, for reasons beyond control, the inter),
sity of the forcing function, and/or the value of a response-controlling parameter,
would be halfed, doubled, or increased by any specified multiplication factor. A char-
acteristic result of a climatonomic case study is documented on Figures 2-4 and 2-5.
2-4
-------
scheme appears on all three graphs. It is intended to bring out the contrast
in attenuation of insolation by typical aerosol between a big city [repre-
sented by Kew (London), England] and that of an extremely dry desert
[represented by the Pampa de la Joya, Peru], We selected these data from
the published literature because the measurements include not only direct
sunlight or "beam radiation" but also scattered or diffuse light. Note that
external conditions (sun's elevation angle, optical air mass, etc.) happen to
be such that the attenuation of beam radiation was nearly the same at both
stations.
In Figures 2-3 to 2-5 the upper horizontal line represents the atmosphere-
space border, across which solar rays enter the atmosphere and reflected
light ("earth-shine") returns to space. The lower horizontal line represents
the earth-air boundary, at which the attenuated solar beam and the diffuse
light scattered down from the sky arrive. The dashed arrows show the sun-
light that is reflected by the ground and attenuated in the air before entering
space; part is scattered back down and part is absorbed. Numbers along, and
at the tips of the arrows show fractions of scattering and absorption as
decimal fractions of the unit incident-extra-atmospheric irradiation. These are
always separated into downward and upward components. Numbers above
and below the braces indicate combined radiation intensities as decimal frac-
tions of the unit solar radiation budget.
Figure 2-3 shows that beam attenuation was nearly identical in both cases
with reductions from 100% to 61.8% in Kew, and to 61.9% in La Joya. The
city air absorbs 22.5 percent and scatters 15.7 percent (5.2% outwards and
10.5% downwards), or about 2/3 of the absorption. The desert air on the
other hand absorbs 14.3 percent and scatters 7.9% + 15.9% = 23.8%, about
5/3 of the absorption. Figures 2-4 and 2-5 suggest that the assumed aerosol
increase, first by an arbitrary factor of two and then of five, leads to
extinction of direct sunlight in both locations. This means that the sun,
although visible in the sky, will not throw a shadow. Obviously, the "gloom
at noon" under the opaque smog of the city where only 26.9 percent of the
incoming energy reaches the ground will be more frightening than under the
strongly-scattering, mineral-particle-containing desert dust where 55.6 percent
of the energy reaches the ground. If an aerosol increase by a factor of five is
possible, what can be done to control the increase once the factors are
known? Let us discuss it first with the aid of the box (scalar) model of com-
munity air pollution.
2-5
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1. KEW, ENGLAND, MAY 1948, AFTER ROBINSON (1963)
1.000	0.129
0.Z5Z
0.(18	0,110
0/728 ~
-0.109
0.619
2. LA JOYA, PERU, JULY 1964, AFTER STEARNS (1966)
1.000	0.175
0.619
0.119 -0-145
D.JOi
0.663
Figure 2-3. Shortwave radiation budget —air over city versus air
over desert.
1. KEW; AEROSOL ABSOflPT. TO SCATT. - 1.66	2- LA JOYA; AEROSOL ABSORPT. TO SCATT. - OJO
Figure 2-4. Shortwave radiation budgets for city versus desert
after aerosol increase by factor of 2. Other conditions same as $ri
Figure 2-3. {Note: no change in ratio of scattering to absorption
efficiency)
2-6
-------
1. KEW; SMOG DENSE ENOUGH TO OBSCURE SUN
1.000	0.H7
0.133

0.267
/
1
1
lv
f
0.024 J


0.002

OPAQUE
SMOG
*
1
r Y

0.014
0.624
0.000
0.269
0.269 -O.MO
	/
2. LA JOY A; DUST DENSE ENOUGH TO OBSCURE SUN
1.000
0.269
0.275
0.229
0.456
Figure 2-5. Shortwave radiation budget- city versus desert-after
aerosol increase by factor of 5.
BOX MODEL OF URBAN AIR DIFFUSIONS
Qualitative answers can be readily provided by a schematic "budget box"
such as the one illustrated in Figure 2-6. It is assumed that the source
strength of pollutant release per unit area of the lower boundary is the same
for two cities of different size; and two different flushing rates are applied
to both cities. These rates could correspond to two weather situations, one
with relatively strong versus one with relatively weak winds. The particle
loading of a comparable unit volume of air is illustrated in Figure 2-6 by the
number and arrangements of "dots" carried by the outgoing air current,
which in each case equals the number of "dots" released by the area source
into the volume of city air. Obviously, a small city with a weak flushing rate
would be no worse off than a big city with a good flushing rate. For
example, an innocent activity like the burning of leaves could be well
tolerated in a small city, but could generate intolerable smog conditions once
the city became large.
Quantitative answers require consideration of the basic fluid dynamics equa-
tions. Let
s = specific admixture to air, (g meter"3)
V=iu + jv + kw (meter sec 1)
S = strength of internal source, or .sink if negative,
of considered admixture (sec-1 meter-3)
v = molecular diffusion coefficient (meter2 sec-1)
2-7
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SMALL	LARGE
CITY SIZE
Figure 2-6. Schematic illustration of effects of city diameter
and atmospheric flushing rate on pollutant concentration in box
model of urban diffusion; assumes uniform area source of pol-
lutant and removal from city volume by horizontal air motion
only. Dots M indicate output of pollutant sources to city air
volume. Arrows indicate ingoing (shaded) and outgoing
(white) volumes of air per unit time. Forcing function, Q.
The principle of conservation yields
|i + v.vs - s . S	(1)
Eddy fluctuations are removed from the instantaneous values by time averaging
and by introducing s - s' = s, S - S1 = 5, and V - V4 = V, whereupon
the primitive Equation (1) transforms into
+ V.V s + V.VV _ vv2? = S	(2)
It appears legitimate to neglect molecular diffusion, the eddy fluxes in the
horizontal direction, and the transport by mean vertical motion, in comparj
son with vertical eddy flux and the transport divergence by mean horizontal
wind components. This amounts to saying that
[(w ?>2 + (iT5T)x + (v'VJy - i>V2 5]<€(IT 3)x + (Vl)y +(«^)2]
(3)
where subscripts denote partial derivatives with respect to the three indeperi
dent spatial variables (x,y,z).
2-8
-------
From Equations (2) and (3). the simplified version of the primitive equation
becomes
|f + (U 5}k + (v 5)v - S - (w1?),	(4)
It is characteristic for thfi box model of urban diffusion that we are
primarily interested in representative area averages over city diameter D (m)
and thickness h* (ml of the boundary layer [Figure 2-2). Let such an
average of any function, 0 or representative function value,  be denoted
by the following symbol:
f f * dx dz	<55
n u h* D
The area source is represented by the boundary value (v?y)0 tnat is the
vertical eddy flux of pollutant at height, z = 0. Actually existing dependen-
cies on the cross-wind coordinate, y could be readily incorporated in the
defining Equation (5) but may be suppressed for the purpose of this basic
discussion.
In air pollution climatonorny, the forcing function is the effective strength
of the area source, G (per meter5, per unit time), a function only of time, t,
G(t> = [|«)„] + [h*5]	M
that is. the effective release qualified by effective internal sources. The
response function is the bulk value of pollutant concentration in the voiume
of city air, q {m 31, also a function or>(y of time, where
q(t) = [§]	(6b)
With the aid of q and 0, the controlling process of horizontal advectton is
expressed by a bulk value of wind speed, U* (m-secT1)
U*(t) = ~ [ 
-------
Horizontal advection will significantly control the flushing frequency, espe-
cially when the lev/el h* coincides with a "lid" such as an inversion layer.
The transformation of Equation (4) with the aid of Equations (5) through
(6d), yields the equation governing the box model of urban diffusision,
Which is the equivalent of the governing equation of evapotranspiration
ctimatonomy, see Lettau.3 For further transformation let us introduce the
reduced source strength or quasi-equilibrium value of pollutant concentra-
tion, q* (rrf3):
* _	(8a)
q h*f*
and a dimensionless time (f) which serves as the new independent variable,
f = / f* dt ; or,	{8b,
dt1 = f* dt
In its final form the characteristic equation of the box model, or the
governing equation of air pollution climatonomy, may be written as an
ordinary differential equation,
-gSj- = q* ~ q	(9a)
which is solved by	,
q = e"*' [q0 + / e1' q* dt']	(9b)
0
where q0 is the initial value of concentration at time t = 0. Representative
values of a parameter having the physical units of seconds per meter were
estimated for a variety of cities by Holzworth,7 and I suggest that for
practical applications, Holzworth's theoretical jlative pollutant concentra-
tion can be identified with 1/h*f* in Equation (8a).
Prediction of Pollutant Trends by Box Model
It is evident that Equation (9a) and its solution, Equation (9b), correspond
to an initial-value problem only if q* is a quasi-constant. In reality, even foi-
time-independent source strength, Q, the value q# will vary considerably
because, according to Equation (8a), it is controlled by the atmospheric
flushing frequency, which changes with the weather. An example of practical
numerical application of the theory is illustrated in Figure 2-7.
2-10
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FORCING FUNCTION - POLLUTANT RELEASE

DAYS
Figure 2-7. Calculated trends of pollutant concentration in response to indicated forcing function for
day-to-day variation of atmospheric flushing parameters. Calculation by box-model for three different
city diameters to demonstrate adverse effects of urban sprawl.
-------
Over a period of 5 days, the area source is assumed to have the same daily
average rate on which is superimposed a semi-diurnal variation with peaks at
the hours of 8 am and 6 pm. While the first and fifth day have normal wind
speed conditions, the second day is stormy and the third and fourth days,
relatively calm. The bulk value U* according to Equation (6c) is depicted in
the middle part of Figure 2-7, showing slight diurnal variation with one peak
per day induced by the normal insolation cycle. To bring out the effect of
f#-dependency on the city diameter-see Equation (6d)-three D-values were
employed, 10 mi for a moderately large city, 20 mi for one of intermediate
size, and 40 mi for a metropolis.
For practical numerical evaluation of the model, a fixed time-interval At
equal to 2 hr, was employed for the calculation shown on Figure 2-7. For
any period beginning at time tj and ending at time tj + A t, representative
values were assumed for source strength, Qj, {the forcing function) and for
atmospheric parameters. Representative values qj* and fj* were thus ob-
tained with the aid of Equations (6c) and 6d). Knowing qj at time tj, the
concentration, A t later is q( + 1 and was calculated numerically using the
following version of Equation (9b), with f,* At = At|:
qj+, = e~Ati [Qi + q*(eAt'}-1) ] = q* + (q, - q*) e"Ati (10)
The numerical calculation may begin at time to with an arbitrary initial
concentration value q0. The only prerequisite is that the chosen q0 has the
same order of magnitude as a typical q* value for the city under considera-
tion. For example, all three q-series shown in the lower part of Figure 2-7
begin with q0 = 1 (in relative units) and are continued for a total of 120
hours, which means 60 steps in At. We see that within a few time steps the
three q-functions align themselves to the individual forcing functions quali-
fied by the respective flushing frequencies. A characteristic tendency toward
lagging and smoothing-out details of the forcing function is evident as a city
gets larger. The three curves on the lower part of Figure 2-7 are self-explan-
atory. The important feature is that, other factors being the same, the larger
city must suffer considerably more than the smaller city during periods of
nearly stagnant air. This follows as the direct result of reduction of the
flushing rate in proportion to city diameter. The buildup of pollutant levels
during a calm weather spell in a large city is more severe, and last for longer
periods than in a smaller city. This quantitative result of numerical calcula-
tion supports the qualitative statements made previously in connection with
the discussion of Figure 2-6.
While the box model excludes the possibility of investigating spatial detail of
pollutant distribution, the emphasis on temporal variations is applicable to a
number of important problems. Before we begin to talk about long-range
trends, let us discuss another application of the box model to relatively
2-12
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FORCING FUNCTION - POLLUTANT RELEASE
NJ
—fc
GJ
DAYS
Figure 2-8. Trends of pollutant concentration in response to week-end lull of forcing function, calcu-
lated for constant diurnal cycle of atmospheric flushing parameter. Response function illustrated for
city diameters of 10 miles and 30 miles, but normalized (to equal daily mean value) to bring out
smoothing effect of larger city.
-------
short-range fluctuations. Specifically, we refer to a time-variation on the
forcing function caused by the weekday versus weekend cycle. While on
Figure 2-7 the forcing function remained the same from day-to-day, Figure
2-8 schematically depicts a weekend decrease of emission. Two cities of
different D-values were assumed, and the response functions normalized to
bring out the damping and lagging predicted for the larger metropolitan area.
Direct measurements documenting diurnal peaks and weekend lulls that
compare with the theoretical results shown on Figures 2-7 and 2-8 have been
reported for a number of cities.
Examples of observed weekly cycles in a variety of pollutants including
carbon monoxide, sulfur dioxide, smoke, and oxidants are discussed by
McCormick and Xintaras;6 W. Johnson;7 Schuck, Pitts, and Wan;8 Harris,
Huffman, and Weiland;9 and others.
Obviously, any application of the results of air pollution climatonomy,
represented by Equations (9b) or (10), requires information not only on
the input normally available from source inventory of urban emitters, but
also on the atmospheric parameters defined in Equations (6c) and |6d).
Applicability will be limited if, for instance, the parameter h\ the mixing
depth, is unsatisfactorily known. In principle h* for downwind change in
surface roughness and energy supply could be determined from the dynamic
and thermal aspects of boundary layer development given the state of the
lower atmosphere at the upwind edges. At the present time, however, it
appears more practical to rely on statistical-climatological evaluation of
meteorological measurements in the urban area. Reference is again made to
Holzworth.10
Application of Box Model to Thermal Pollution
Equations (7) and (9a) permit an evidently steady state if q = q.* This is
used to predict the order of magnitude of the effect of thermal pollution in
the air of a metropolis. New York City is a self-explanatory example of an
urban complex for which heat input and pertinent atmospheric parameter
values have been reported (Table 2-1).
It follows that the reported heating rate of 39 calories per second per square
meter, or about 0.2 langley per minute, will raise the average temperature of
the volume of city air approximately 2° C above its surroundings. Such a
temperature-volume average suggests that the excess may reach 4 to 5 C at
the center of the city and roof-top or stack levels. According to Bornstein,11
this value is not uncommonly encountered in temperate zone cities such as
New York.
It is evident that fuel combustion represents only one among several causes
of the urban heat island. Atmospheric feedback, from city structures and air
2-14
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Table 2-1 EXAMPLE OF AIR POLLUTION CLIMATOIMOMY -
LEVEL OF THERMAL POLLUTION IN NEW YORK CITY,
CALCULATED FROM INPUT AND PARAMETER VALUES
Element
Symbols
Numerical values
References
Area source— fuel
Q,
39 cal nrf2 sec"1
Bornstein11
combustion in winter
Q/cpP
0.13° Cm sec-1
Holzworth10
Parameter value
1/h*f*
16 sec nrf1
Holzworth1 0
Predicted excess of
Q/cpP h*f*
2.1° C
Climatonomy
air temperature


Equation (7)
(quasi-equilibrium)


for dp. q
9t
pollution, to dynamics of the lower atmosphere also involves both insolation
and terrestial or long-wave radiation, and the soil moisture budget. Petersen1 2
gives more detailed documentation.
To the best of my knowledge there have been no previous attempts to use
the box model of urban diffusion for the calculation of thermal pollution
levels. The application documented in Table 2-1 is, however, a logical step
and it conforms with the philosophy outlined in my introductory remarks
regarding the desirability of a simultaneous treatment of transfer of masses,
momentum, and energy in boundary layer problems.
AERODYNAMIC ROUGHNESS AND
MOMENTUM DRAIN IN URBAN AREAS
Having shown examples of the application of the box-model to diffusion of
mass and thermal energy, we can now apply it to the drain of momentum
encountered by the wind in its passage over a city.
First, it will be necessary to determine the representative aerodynamic
roughness length, zQ (cm), of the urban area. I propose to use a formula
that has been derived from a series of out-of-doors micrometeorological
experiments done over a period of years at the University of Wisconsin.
In late winter, hundreds of commercial bushel baskets were distributed over
a section of level, almost undisturbed ice on Lake Mendota. Changes in the
vertical wind profile as a function of the roughness modification upwind of
an anemometer mast were analysed. The z0 value of the undisturbed ice
(about 0.01 cm) was increased systematically and in a controlled fashion to
nearly 10 cm. It is established13 that the z0 value can be predicted using
similarity concepts if we know the effective height H (cm), of the roughness
elements; their silhouette area seen by the wind, a (m2) and their lot area,
2-15
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A (m2). Lot area refers to the total area of the test field divided by the
number of elements.
z0 = H a / 2A	(11)
The factor 1/2 approximates the average drag coefficient of the roughness
elements. A set of urban background data for use in Equation (11) js
summarized in Table 2-2. The values are arbitrary within an order of
magnitude. More specific information will be required for actual case studies
of specified urban boundary layers. The same applies to the data in Table
2-3, where the estimated z0 values for three building types were considered
in a pilot study intended to show how the characteristic wind speed U can
be determined for a specific city type, knowing only the overall atmospheric
dynamics represented by the intensity of the horizontal pressure gradient in
the lower troposphere. U can be predicted and, in turn, used to obtain the
velocity, U*, in Equation (6c).
Table 2-2 AERODYNAMIC ROUGHNESS LENGTH CALCULATED
FROM EQUATION (11) FOR ESTIMATES OF
BUILDING CHARACTERISTICS IN AN URBAN AREA
Building type (schematic)
Low
Medium
High-rise
Building height (approximate)
4 m
20 m
100m
Assumed lot area
2000 m2
8000 m2
20000 m2
Assumed silhouette area
50 m2
560 m2
4000 m2
Calculated Zq
5 cm
70 cm
1000 cm
Table 2-3. APPLICATION OF LOGARITHMIC LAW
TO WINDSPEED CALCULATION3
Zo
G (m/sec)
log10(G/z0f)
C
U (m/secT"3*
5
5
6.00
0.0378
3.3 —
70
5
4.85
0.0475
2.9
1000
5
3.70
0.0590
1.9
5
20
6:60
0.0342
12.8
70
20
5.46
0.0420
10.5
1000
20
4.30
0.0538
6.8
^indspeed U calculated from Equation (12) at level of 150 meters for given surface
roughness (zq), given geostrophic speed (G) and subsequent geostrophic drag coefficient
(C); derived from universal relationship between C and scaling factor for atmospheric
boundary layers, Ro0 = G/z0f
Roq ¦ surface Rossby number
f = Coriolis parameter = 1.0 x 10"4 sec'1 for these calculations assuming 43°
geographic latitude.
2-16
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To follow the procedure, take the calculated or estimated geostrophic speed
G (cm sec-1) as the ambient flow. Geostrophic speed is independent of
roughness. Then, the surface Rossby number, Ro0 = G/z0f, where f =
Coriolis parameter (sec-1) can be calculated for a given z0. Lettau14 was
the first to demonstrate that this Ro0 serves as a scaling factor for atmos-
pheric boundary layer structure and that it plays a role equivalent to the
role of the Reynolds number that is used in engineering flow problems to
determine the friction factor. The factor C, named the "geostrophic drag
coefficient,"14' 15 was shown to be a unique valued function of Ro0 for
thermally neutral states of the lower troposphere. If height z(cm or m) is
restricted to the lowest part of the boundary layer, a first approximation
value for U(z) in the model is provided by the logarithmic law, which can be
written as
U(z) =5.5 C G log10 (1 + z/z0)	(12)
Application of Equation (12) is determined by the Karman constant and the
natural-to-common logarithm conversion factor. Note that z0-effects appear
both directly, under the logarithm, and indirectly, through its Ro0 depen-
dency in the coefficient, C.
Tables 2-4 and 2-5 are self explanatory. Although the calculated values of
the parameter 1/h*f* are comparable with actual conditions,10 it must be
remembered that h* in Table 2-4 was arbitrarily kept constant at 300 m.
Nevertheless contribution of the three essential factors (1) lowering of
overall wind speed, (2) increase of city diameter, and (3) change from low-
to high-rise buildings, can equivalently increase the net pollutant concentra-
tion. The last two effects favoring the increase of relative pollutant concen-
tration (or the value of 1/h*f*) could be of interest to the city planner.
Table 2-5 presents a result of air pollution climatonomy, comparable with
the example shown in Table 2-1. The box model of urban diffusion applied
to momentum predicts that for the conditions of a big metropolis such as
New York City the average wind speed could be 2 m sec-1 lower than in a
comparable situation over open country. The "negative area source," or
momentum drain due to the increase of surface roughness, is estimated to
equal a ground drag difference of 1.5 dynes cm"2, based on geostrophic drag
coefficients and the relationship defining surface stress r0 as pC2 G2, where
p indicates air density. Obviously, if the number of high-rise buildings in a
central city is increased and the lot area is not enlarged, the resulting z0
increase will favor stagnant air and the likelihood of pollution episodes. That
effect is additive to the city-diameter effect. (Figure 2-7).
2-17
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Table 2-4. ESTIMATE OF BOX-MODEL PARAMETER 1/h*f*
FOR TWO DISTINCT CLASSES OF AMBIENT (GEOSTROPHIC) SPEED
AND THREE CITY SIZES WITH TWO BUILDING TYPES3
Geostrophic speed,
m/sec
City diameter,
km
Building typeb
1/h*f* c
sec/m
20
4
Low
1
20
4
High-rise
2
5
4
Low
4
5
4
High-rise
7
20
20
Low
5
20
20
High-rise
10
5
20
Low
20
5
20
High-rise
35
20
80
Low
21
20
80
High-rise
39
5
80
Low
80
5
80
High-rise
140
aCompare Tables 2-2 and 2-3.
bSee Table 2-2.
cFor h* = 300 meters.
Table 2-5. EXAMPLE OF AIR POLLUTION CLIMATONOMY:
LOSS OF AIRFLOW MOMENTUM OVER AN URBAN AREA3
Element
Symbols
Numerical value
References
Momentum area sink
A T0
1.5 dynes cm-2
Geostrophic
(by aerodynamic roughness)
A T0P
0.13 m2 sec"2
drag coefficient
Parameter value
1/h*f*
16 sec rrf1
Holzworth1 0
Predicted speed deficit
A T0 /ph*f *
2.0 m sec"'
Climatonomy
Steady-state


Equation {7)
aAssuming an ambient (geostrophic) speed of 10 m/sec, an Aerodynamic Surface
Roughness z0 of 100 cm (hence, C = 0.050) for the City, and 5 cm (hence, c = 0.035) f
the Upwind Region, and a Parameter Vafue of 1/hf* = 16 sec/m (Momentum Dra^1*
Conditions in New York City*	lri
2-18
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WIND PROFILE OVER CITIES
Boundary layer concepts lend themselves readily to application in urban
diffusion problems. To emphasize this, let me use the results of one of the
bushel basket experiments performed on the ice of Lake Mendota (Figures 2-9
and 2-10). The experiment was designed to study both control of surface
roughness (Rossby number) and effect of thermal stratification (Richardson
number). A total of 420 bushel baskets were used, half of them painted
white, the other half, black. A lot area of about 2 m2 was selected in a
layout of two adjacent fields, 21 m cross wind, and 20 m downwind. The
albedo values measured were 0.15 for the black and 0.65 for the white
obstacles. The albedo of the aged snow on the ice averaged about 0.52. In
the March sunshine, the effective heating of the field with the black obsta-
cles was estimated at 0.07 langley min-1, and that of the field with the
white baskets at 0.03 langley min-1, giving relatively differential heating rate
of 0.04 langley min-1.
Figure 2-9 illustrates the analysis of wind profile observations at a variety of
x-positions for the anemometer mast, in the form of velocity defects (AV)
and vertical motion computed for two-dimensional mean flow with the aid
of the continuity equation. The velocity defeats and updrafts are more
pronounced for the black than for the white field. Temperature measure-
ments suggested that the difference in Richardson numbers between black
and white fields varied from about —0.005 to +0.005. For cases of relatively
strong changes in vertical shear, however, it is questionable whether the
Richardson number retains its significance as a scaling parameter.
Figure 2-10 shows the momentum balance for adjacent "budget boxes" in
the x-z plane between the surface and 1.6 m. All values are in dynes cm"2,
double arrows refer to transport by mean (organized) velocity components
(u and w), thin arrows show the eddy flux, p(u' w1), in the vertical direction
at z=0 and z=1.6 m. The black field drains 2.9, and the white field 2.3
dynes cm"2, and the loss due to transport to higher layers amounts to 3.0
and 1.8 dynes cm-2, respectively. These values indicate an increase in the
mixing depth due to Richardson number effects, similar to the dynamic
roughness effect in boundary layer development over cities in Equation (11).
Further experiments of this type are desirable.
Although the horizontal scale of our out-of-doors or free air experiments is
significantly larger than the scale of wind tunnel studies, the similarity to the
prototype of boundary layer structure over urban areas is still incomplete
because on the larger, real scale the effect of Coriolis forces appears, causing
directional shear of horizontal air motion. The two dimensionality of actual
wind profiles over cities is not accounted for by the power-law V ^ z a,
frequently suggested for transport of material in the lower troposphere in
urban pollution studies; reference is made to Davenport17 and Turner.18 In
2-19
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I	1	1	1	1	I	I	1	I	I	I	I	I	I	I
•20	-10	0	10	20	30	40	50
x, meters
BUSHEL BASKET EXPERIMENT ON MENDOTA ICE	MARCH 23,1963	11:17 -14:45 CST
V: Undisturbed velocity	W: Completed vertical motion	&V: Velocity Defect
o WHITE BASKETS (11:17 • 12:45)	¦ BLACK BASKETS (13:32 • 14:45)
Figure 2-9. Analyzed results of micrometeorological experiment by Stearns and Lettau on March 23,
1963, using fields of bushel baskets on ice of Lake Mendota. Mimicks conditions found in boundary
layer development over city. Undisturbed wind profile, extreme left. Vertical profiles of velocity de-
fects and calculated vertical motion plotted for different mast positions at indicated downwind dis-
tances. Note stronger momentum drain and deeper mixing layer over black obstacles illustrating pos-
sible Richardson number effect.
-------
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BUSHEL BASKET EXPERIMENT ON MENDCTA ICE MARCH 23,1963 11:17 -14:45 CST
Figure 2-10. Budget boxes showing horizontal momentum balance for experiment illustrated
in Figure 2-9. Double arrows represent budget contributions due to mean components u and
w; single arrows, contributions due to eddy flux in vertical direction, including surface
stress.
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addition to the disregard for directional shear, the power law has two other
disadvantages: (1) at low elevation the logarithmic law (which alone expres-
ses the surface roughness effect rationally) is not approached as an asymp-
totic case, and (2) at high elevation, there is no asymptotic approach to the
gradient or high geostrophic wind. Clearly, these two shortcomings mean
that the power law is merely an interpolation formula, with difficulties
expressing upper and lower boundary conditions. More realistic models of
wind profile structure in atmospheric boundary layers are available in the
literature. Let me restrict discussion to one of my earlier contributions to
this problem. It concerns a universal wind spiral theory of the barotropic
(thermally neutral) lower atmosphere.13 The tabulated functions for the
wind and stress components that this model generates are universally appli-
cable to a wide range of external conditions. In order to verify a wind or
stress spiral in the atmospheric boundary layer for a special case, the only
scaling factor needed is the surface Rossby number. Figure 2-11 illustrates
Figure 2-11. Universal Wind Spiral Theory verified for three values
of surface roughness (Rossby numbers, Roq) characteristic of urban
areas. Calculated for thermally neutral atmosphere. Normalized to
geostrophic speed (Vg). Symbols: z0, aerodynamic roughness length,
(meters); f, Coriolis factor (1.0 x 10"4meters sec"1 for 43° surface
latitude); Roq, Vg/zgf.
2-22
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1,000
Figure 2-12. Comparison between Universal Wind Spiral Theory
and Fower Law treatment of vertical profiles of normalized hori-
zontal wind speed (V/Vg). Symbols: Vg -geostrophic speed; f =
Coriolis factor of 1.0 x 10"4 meters sec "1; 27 - surface stress:p -
air density; C = geostrophic drag coefficient; C h * height coef-
ficient; H r effective height of roughness elements (centimeters);
z • geometric height; a = silhouette area seen by the wind (meters2).
2-23
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verification for three different Rossby numbers that correspond to the
urban z0-values shown in Tables 2-2, 2-3, and 2-4, a geostrophic speed of 10
m sec-1, (denoted by the symbol Vg in Figures 2-11 and 2-12, and a Coriolis
parameter f = 1.0 x 1CT4 sec 1 (for 43° geographic latitude).
The two parts of Figure 2-11 illustrate scalar and vector wind ratios,
normalized relative to geostrophic speed. For scalar wind speed, plotted
linearly against a geometric scale in height, straight sections at small height,
indicate that the logarithmic law is an asymptotic case. The scalar and vector
graphs also document an asymptotic approach to the gradient wind at high
elevations. There are reports in the literature of wind direction changes of
the order of 10 degrees, at heights of about 60 m, between upwind and
downwind towers. For reference see Graham's19 analysis of data from Fort
Wayne, Indiana.
Figure 2-12 compares the power law17 profile with the scalar wind profile
derived from the Universal Wind Spiral solution.15 The latter provides all the
necessary numerical scale factors, including the geostrophic drag coefficient
C, and the height coefficient CH, as unique-valued functions of the surface
Rossby number. The power law is deficient in this respect and its applica-
tion, with the assumptions listed on the lower part of Figure 2-12, is
arbitrary or empirical.
SUMMARY
I hope to have convinced some of you that fluid-dynamical boundary-layer
concepts are promising physical and meteorological bases for mathematical
models of urban diffusion processes; and that mass, momentum, and energy
transfers and transports can be effectively handled by a systems approach
with: defined forcing functions, parameterization of response functions, and
feedback and control functions. Much detailed research still has to be done,
especially with regard to the combined feedback processes of turbulence
generation by surface roughness and heating over urban areas.
2-24
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REFERENCES
1.	Moses, H. Mathematical Urban Air Pollution Models. National Center 1or Air
Pollution Control, Chicago Dept. of Air Pollution Control, Argonne National
Laboratory. Argonne, III. ANL/ES-RPY-001. April 1969 . 69 p.
2.	Lieber, H. Controlling Metropolitan PoHutfon Through Regional Airsheds: Admini-
strative Requirements and Political Problems. J. Air Pollution Control Assoc.
}8:86-93, February 1968.
3.	Lettau, H. Evapatrainspiration Climatonomy. 1. A New Approach 1o Numerical Pre-
diction oi Monthly Euapotranspiration Runoff and Soil Moisture Storage. Mon.
Weather Rev, 97:691-699, October 1969,
A. McCcrmick, R. A. and J. H, Ludwig. Climate Modification by Atmospheric Aero-
sols. Science. 756(3780}: 1358-1359, June 9, 1967,
5.	Lettau, H, and K. Lettau. Shortwave Radiation Climatonomy. Tellus, 21 \208-222,
February 1969.
6.	McCormick, R. A. and C. Xintaras. Variation of Carbon Monoxide Concentration as
Related to Sampling Internal, Traffic and Meteorological Factors. J. Appl. Mete-
orol. ?(21:237-243. June 1962.
7.	Johnson, W. This Symposium, Chapter 5.
8.	Schuck, E. A., J. N, Pitts, Jr., and J. K. S. Wan. Relationships Between Certain
Meteorological Factors and Photochemicaf Smog. Int. J. Afr Water PoNution.
f0:689-711, October 1966.
9.	Harris, D. N., J. R. Huffman, and J. H. Weiland. Another Look at New York City's
Air Pollution Problem. J. Air Potlution Control Assoc. 75:406-410, June 1968.
10.	Holzwvorth, G. C. Mixing Depths, Wind Speeds and Air Pollution Potential for Se-
lected Locations in the United States. J. Appl. Meteorol. S{6): 1039-1044, Decem-
ber 1967.
11.	Bornstein, R. D. Observations of the Urban Heat Island Effect in New York City.
J. Appl. Meteorol. 7(41:575-582, August 1968.
12.	Petersen, J. T. The Climate of Cities (A Survey of Recent Literature!. National Air
Pollution Control Administration. Raleigh, N. C. Publication Number AP-59. 1969.
48 p.
13.	Lettau, H, Note on Aerodynamic Roughness-Parameter Estimation on the Basis of
Roughness ETennent Description. J. Appf. Meteorol. 5:828-832, November 1969,
14.	Lettau, H. H. Wind Profile, Surface Stress and Geostrophic Drag Coefficients in the
Atmospheric Surface Layer, In: Advances in Geophysics, Landsberg, H, E. and J,
Van Mieghem {eds.l Vol. 6 New York, Academic Press, 1959, P. 241-257,
15.	Lettau, H, H. TNeoneticat WjjkJ Spirals in The Boundary Layer of a Barotropie At-
mosphere. Bettr. Phys. Altnos. 3513/4): 195-212, 1962,
16.	Lettau, H. H, Problems of Mjcrometeorotogical Measurements |Qn Degree of Con-
trol in Out-of-Doors Experiments). In: The Collection and Processing of Field Data;
A CSIRO Symposium, Bradley, E. F. and 0. T. Denmead (eds.). New York, Inter-
science Publishers, 1967. p. 3-40.
17.	Davenport, A. G. The Relationship of Wind Structure to Wind Loading. In: Pro-
ceedings of International Conference on Mnd Effects an Suitdings and Structures.
National Physical Laboratory, Teddington, England, June 26-28, 1963. London, H.
frf. Stationery Office, 1965,
18.	Turner, D. G. Workbook of Atmospheric Dispersion Estimates. National Air Potlu-
tion Corwof Administration. Cincinnati, Ohio. PHS Publication Number 999-AP-26.
Revised 1959, 84 p.
19.	Graham, I. R. An Analysis of Turbulence Statistics at Fort Wayne, Indiana. J.
Appl, Meteorol. 7(11:90-93, February 1968.
2-25
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APPENDIX - GLOSSARY OF SYMBOLS
a	silhouette area of roughness element
A	lot area of roughness element
C	geostrophic drag coefficient
CH	height coefficient
D	city diameter
f	Coriolis parameter
f*	flushing frequency of volume of city air
G	ambient air flow, gradient wind, or geostrophic wind
h*	upper boundary, or thickness, of volume of city air
H	effective height of roughness elements
q	average pollutant concentration for box model
q*	quasi-equilibrium value of average pollutant concentration for box
model
q0	initial value of q at t = 0
q(t)	response function, of air pollution climatonomy
Q	area source of pollutant emission
Q(t)	forcing function of air pollution climatonomy
s	specific admixture to air
S	strength of internal source (sink, if negative) of considered admixture
t	time
t'	dimensionless time
At	time interval
U*	bulk value of windspeed
V	velocity vector = i u + i v + k w
Vg	geostrophic windspeed
(w1 s1) vertical eddy flux of admixture
x	downwind coordinate
y	crosswind coordinate
z	height
z0	aerodynamic roughness length of urban area
v	molecular diffusion coefficient
p	air density
0	function
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ABSTRACT
The method currently in practical use in the United Kingdom Meteoro-
logical Office for predicting levels of air pollution from source
strengths and meteorological data is reviewed briefly. A study of
6-hour average S02 concentrations in the town of Reading, recently
published by the British Petroleum Research Centre, shows that, while
the overall average may be predicted reasonably well by the foregoing
method, the individual predicted values have targe deviations from
those observed.
Some aspects of the theoretical and empirical basis for the estimation
of the diffusive spread of material are considered-particularly the
applicability of the gradient-transfer approach and the indications of
Lagrangian similarity arguments regarding the effects of surface rough-
ness and thermal stratification.
The vertical spread for neutral flow over a roughness typical of urban
areas predicted on Lagrangian similarity is found to be compatible with
that recently estimated from tracer experiments in St. Louis, Missouri,
for evening, when neutral thermal stratification was indicated by tem-
perature observations in the city. It has to be admitted, however, that
the actual flow conditions were most unlikely to have been in equilib-
rium with the urban terrain over the whole depth of spread of the
tracer. Furthermore, there is some indication of substantially greater
spread during the day even when similar (neutral) stratification pre-
vailed in the city; this feature remains to be explained.
Elementary aspects of the influence of the urban heat island in aug-
menting vertical spread are considered. Examination of the St Louis
data reveals some evidence to support the expected augmentation, but
there is no obvious support for the notion that vertical spread into a/j
initially stable atmosphere is controlled solely by the urban heat input
as in Summer's model.1
Finally, brief consideration is given to the prospects of and require-
ments for improvement in the systems for predicting air pollution.
author
Frank Pasaui„ took an Honours degree in physics at the University of Durham
1935 and was awarded the D.Sc. in 1950. He Joined the United Kingdom
. ¦ / nffire in 1937 and since 1954 has held a special appointment f0r
teorologtcal Office m 7937 *n	Meteorological Office's recently
ZZLTmth of Mutlon ,»d ,urbuIM	.»»«*«* H.
is author of the hook Atmospheric Diffusion.
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3. PREDICTION OF DIFFUSION
OVER AN URBAN AREA - CURRENT PRACTICE
AND FUTURE PROSPECTS
FRANK PASQUILL
Meteorological Office, Bracknell, England
INTRODUCTION
There are three basic components in the development of any system of
estimating the concentration of air pollution solely from a knowledge of the
sources and of the meteorological conditions. The first is a theory within
which the relations between the spread of the material and the properties of
the airflow are at least implicit, if not entirely explicit. Secondly, for opera-
tional use, this theory must then be expressed in a suitable form (so-called
diffusion formula or dispersion formula) giving the concentration of pollu-
tant in terms of the source-strength and meteorological parameters. Finally,
there is the requirement for observations of the levels of air pollution pro-
duced by known sources, against which the theoretical system can be tested
and from which generalizations and predictions may then be made. It hardly
needs to be said that the effective union of these components has proved to
be a slow and complicated process, in which considerable care is still needed
to distinguish the essential features and to avoid unrewarding expenditure of
research effort.
The first purpose of the present paper is to note the stage reached In the
United Kingdom in the provision and testing of prediction systems in prac-
tice. Although it is evident that for urban situations there are complexities
that seem intractable to precise theoretical analysis, it is nevertheless impor-
tant to extract as much guidance as possible from basic ideas about the
diffusive action of idealized airflow. Only by such a process can we derive
the greatest benefit from such practical experience as is now available, and
hence make the most sensible appraisal of the further work required. Ac-
cordingly, the second purpose of the paper is to recall the basic concepts
and to note some ideas and results that seem likely to be particularly rele-
vant to future development. From this point, attention is turned specifically
to the factors determining the average rate of vertical spread in urban airflow
and then, briefly, to the prospects of achieving significant improvements in
the ability to predict the distribution of air pollution from specified sources.
3-1
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CURRENT PROGRAM IN UNITED KINGDOM
In the Meteorological Office of the United Kingdom, the practical estimation
of pollutant concentrations from specified sources currently follows lines
that were formulated some 10 years ago, largely under the stimulus of the
accident at the Windscale Works of the Atomic Energy Authority. Although
this system does not contain any specific application to urban conditions, it
is nevertheless relevant to our present considerations in two respects. It has
been widely used as a basis for examination and comparison of many
measurements, including some of air pollution in urban conditions. Also, it is
now in the process of a revision that has a bearing on the extension to urban
conditions.
The details of the current system are set out and discussed in two articles2*3
and here it is proposed to do little more than emphasize a few crucial
features:
1.	The original aim was to provide a practical system with which, as far as
possible, crosswind and vertical spread of material could be estimated
from data on the corresponding fluctuations of the wind.
2.	For the case of short-range vertical spread from a ground level source,
and, in general, when data on wind fluctuation were not available, broad
estimates of spread were provided for categories of atmospheric stability
specified in terms of surface wind speed and state of sky.
3.	The broad estimates for short-range spread, < 1 kilometer (km).refer to
level, unobstructed terrain with rather small aerodynamic roughness, z0
about 3 centimeters (cm). (Standard notation is foliowed-see end of
paper for list.)
4.	The broad estimates for longer range, partially based on experimental
data, automatically include some influence of the minor topographical
and urban features present in the area of Central Southern England.
5.	No means of quantitatively allowing for either major topographical fea-
tures or urban influences were provided, though some qualitative appre-
ciation of the effect of topography was briefly attempted in the latter of
the two publications.
6.	As far as the magnitude of spread was concerned, no distinction was
drawn between surface and elevated sources.
In operational use, the system has been limited and inadequate in a number
of respects; so far, no attempts have been made to allow for these inade-
quacies beyond the expression of rather broad qualifications and specula-
tions.
Experimental and observational work on the distribution of air pollutants is
carried out in the United Kingdom by the Warren Spring Laboratories, the
Central Electricity Research Laboratories, and the British Petroleum Re-
search Centre. It appears, however, that the only study published so far on
3-2
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the use of diffusion formulas in prescribing urban air pollution is the one
carried out by the last-named organiiation in the town of Reading. That
study included extensive measurements of the sulphur dioxide concentration
distribution and detailed estimation of the source inventory over a 15-month
period during 1'3S4- arid 1965. Aspects of the study have been discussed in
papers by Marsh arid Foster4; Marsh, Bishop, and Foster"1; and Marsh and
Withers.6 The last of these publications compares the observations with
estimates derived from the source inventory and meteorological data, using a
number of methods, including these used in the Meteorological Office ar.d
referred to above.
The pollution data consisted of sulphur dioxide concentrations averaged over
6-hour sampling periods, for 40 sites in and around the town. Continuous
records were available for wind direction, wind speed, air temperature,
humidity, and the intensities of the vertical and lateral components of tur-
bulence. The wind speed and turbulence measurements were made at a
height of 14 meters (m) in a relatively open space, 10Q m or more from
buildings, about 10 m high, and about 700 m from the taller buildings in the
center of the town. For the source distribution, three categories of fuel-
burning installations were considered—domestic heating, industrial and com-
mercial installations tor space-heating, and processing plants, Domestic
(space-heating) sources were divided into 251 housing areas with a diameter
of roughly 400 m, and the strength of source in each area was based en
official estimates of the average fuel consumption in private houses. Installa-
tions burning more than 10 tons of fuel per year ware considered
individually.
For evaluation of the diffusion formulas. Marsh and Withers6 defined 67
area sources that were tr-eated as individual sources if their centers were
farther than 1000 m from the sampling site, and 7 major sources, that were
treated as individual sources regardless of distance. If the center of an area
was less than 1000 m from the sampling site, the individual housing areas or
installations were also treated as individual sources. In some of the calcu-
lations, the housing areas and source areas were treated as equivalent line
sources. For the domestic sources, a standard height of 15 m was adopted,
but for individual sources the effective heights were estimated from the
chimney height and the plume rise calculated from the CONCAWE empirical
formula.7
Marsh and Withers7 give an extensive series of comparisons of observed and
calculated concentrations from which we shall reproduce only a selection
that most directly reflects on the present point of interest. The calculated
concentrations were obtained in three ways:
1. Using the familiar Gaussian form for the distribution from a point
source with the standard deviations (of particle displacement) cry and
ot obtained from wind fluctuation data.
3-3
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2 As in (1.) but with ay and oz obtained from the broad estimates of
spread.
3. From a regression of the observed values against a parameter invol-
ving the air temperature (as representing the variation of effective
overall source strength) and the reciprocal of the wind speed.
The selection of comparisons, in which the observed concentrations have
been corrected for 'background' concentration using measurements made up-
wind of the town, is given in Table 3.1
In Marsh and Withers' analysis, attention is focused primarily on the root-
mean-square (r.m.s.) differences between the observed and calculated 6-hour
average concentrations. In Table 3-1, these r.m.s. differences are always large
and are of similar magnitude to the corresponding overall mean of the obser-
ved concentrations. Furthermore, the r.m.s. differences expressed relative to
the observed mean are lowest for the regression method and highest for the
broad estimates of spread. On this basis, Marsh and Withers conclude that
diffusion formulas do not provide a satisfactory basis for calculating the
pollution in a town and that a regression equation directly representing
observations is to be preferred.
Table 3-1. COMPARISON OF OBSERVED AND CALCULATED S02
CALCULATIONS AT SIX SELECTED SITES IN READING, ENGLAND6

Method of
calculation
Mean of 6-hour
concentration,
ng m 3
r.m.s.difference
between calculated
and observed C


Obs. C
Calc. C
r.m.s.
obs. c

a. Wind fluctuation
68
38
84
1.2
All periods8
b. Broad estimates
of spread
(stability categories)
68
88
132
1.94

c. Regression on tem-
perature and wind
68
-
68
1.0
119 selected
periods**
a.	Wind fluctuation
b.	Regression on tem-
perature and wind
66
66
53
63
57
0.95
0.86
a Methods a. and b. tollow rasquur
b Steady wind direction and speed (6 a.m. to 12 noon and 12 noon to 6 p.m. onlvl
for which most confident estimates of emission were made.	' ' *'
3-4
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It is not entirely surprising, however, to find that the 'regression method',
which uses the actual observations, provides the least scatter between ob-
served and calculated valuer On the other hand, it is encouraging, that the
'wind fluctuation' method provides independent estimates with individual
departures that are not very much larger than those of the regression
method. Also, the fact that the least agreement in the individual 6-hour
values is provided by the broad estimates of spread is not surprising, since
the latter refer to aerodynamically smoother terrain and, as will be seen
later, the rougher nature of the terrain is reflected in the wind fluctuation
measurements. Finally, Marsh and Withers are inclined to attach little signifi-
cance to the overall mean concentration. In view of the very wide range of
the component values, it is particularly interesting that the observed and
calculated mean values are as close as they are, and that their agreement is
even closer when occasions are selected for greater reliability in wind and
emission estimates. Before discounting the agreement on the score of the
discrepancies in individual values, it would seem desirable to examine in
more detail the significance of, and possible reason for, such discrepancies.
(This point will be referred to again in the final discussion.)
BASIC CONCEPTS
IN THEORETICAL ESTIMATION OF DIFFUSION
The theoretical treatment of diffusion in a turbulent fluid has developed
along three main lines.
1.	The gradient-transfer relation, in which the eddy transfer of material
across a plane is represented as a product of the gradient of material
(normal to the plane) and an eddy diffusivity, K.
2.	Statistical theory, involving statistical descriptions and laws for the
velocities and trajectories of typical particles in the fluid.
3.	Dimensional analysis and similarity theory.
Discussion will be confined to some specific features that seem to have
particular relevance to future development of methods for estimating urban
air pollution.
Applicability of Various Approaches
The fundamental validity of the gradient-transfer approach has always been
regarded as a matter of debate, and it Is important to make clear the circum-
stances in which it is most acceptable. Any qualitative basis for the method,
as is involved in the classical 'mixing length' theory or in direct analogy with
kenetic theory of molecular motion, inevitably implies the notion that the
physical scale and effective range of action of the turbulent elements be
small compared with the domain over which the diffusible material is spread.
Obviously, this condition may be expected to be approached as the spread
of the material increases with time or distance of travel from the source.
3-5
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Consistent with this physical idea is the formal result from statistical theory
that, in the limit of long time, T, the spread of particles in homogeneous
turbulence is proportional to TVs, as in the Fickian (constant K) solutions of
diffusion.
Recognition of the existence of the foregoing parabolic law is confused by
two practical features of atmospheric flow. The first is the width of the
spectrum of eddy motion, which is such that diffusive spread over di-
mensions larger than all effective eddies may not be achieved in practice.
The second is the lack of homogeneity in the atmosphere regarding such
properties as mean wind speed and direction, and the intensity and scale of
turbulence. No demonstration has yet appeared for the existence of the
parabolic relation in horizontal spread. There is, however, evidence in
Hogstrom's8 experimental study using an elevated source, of a close
approach to this relation for vertical spread in stable conditions. This seems
entirely consistent with the idea that, in such conditions, the vertical scale of
the eddies will be significantly limited. It is not unreasonable to expect this
limitation in vertical scale to be effective irrespective of stability, provided
the cloud or plume of material is not clear of the ground (i.e., as from an
elevated source). In other words, vertical diffusion from a source that is
effectively at ground level may reasonably be expected to be in accordance
with the gradient-transfer theory, without necessarily leading to the parabolic
law, since the effective K must then be expected to be a function of height.
On the other hand, it is evident that the early stages of spread in the
horizontal, or in the vertical, when the source is elevated, cannot generally
be attributed to a constant diffusivity or to a function only of position in
the flow. In these cases, the statistical theory appears to be a preferable
alternative.
The Lagrangian similarity theory was originally put forward as a means of
predicting the variation of a continuous point-source concentration with
distance downwind. Since crosswind diffusion is implicity involved, there is
some controversy regarding the fundamental validity of the approach, but
this qualification does not apply to vertical spread. In any case, there is a
basic restriction of the height range over which the horizontal shearing stress
is effectively constant.
General Explicit Form for K
Well-known forms for K have been specified for two limiting conditions, i.e.,
for the constant-stress layer, when, for vertical momentum transfer
K = ku.x / 0 (f)	C )
= ku»z, at small (f)	(2)
3-6
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and for particle spread in the limit of long time in homogeneous turbulence
(3)
Invoking dimensionally acceptable and empirically determined relations be-
tween the variables ctw, u*f tL, tE, Xm, and z, Equations (2) and (3) may be
reduced to a common form
where Am is the equivalent wavelength for peak nS(n) in the spectrum of the
vertical component.
Invoking a further relation between ow, Xm, and e (see Pasquill9), this may
be further transformed to
Note that equations (4) and (5) allow K to vary with height in an arbitrary
way, according to the variation with height of the properties 
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inapplicable, and in which the statistical theory is more appropriate (notably
the calculation of crosswind spread or of vertical spread at relatively short
range from an elevated source), the effects of roughness and stratification are
reflected in the magnitudes of aw and tL. Even for the case of vertical
spread from a ground level source at relatively short range, however, the
gradient-transfer method is complicated by the logarithmic form of wind
profile applicable in neutral conditions; the Lagrangian similarity theory now
seems to provide an approach that is neater analytically and more satisfying
physically.
For neutral flow, the Lagrangian similarity theory provides the following
relation between the mean height reached by successively released particles
(Z) and the mean horizontal distance that they have travelled in a given
time, (X).
y =-j^ [In-— —1 + H-Inc}]	(6)
It has been argued that the dimensionless constant b is identical with von
Karman's constant, k, and there is some observational evidence for this.11
On the other hand, the constant c has not yet been well-determined. This
constant is, in fact, the ratio of the mean horizontal velocity of the particles
to the mean fluid velocity at the height Z, and in the earlier forms of the
treatment was assumed to be unity. Since it seems likely to be between Vi
and 1 [a recent theoretical estimate by Chatwin gives 0.56], the re-
maining uncertainty in its precise value is not particularly important. Given
the constants b and c, and a specification of the characteristic aerodynamic
roughness through z0, Equation (6) can provide the magnitude of vertical
spread as a function of distance.
In the testing and practical use of Equation (6), there are two other com-
plications not yet mentioned, which, fortunately, seem unlikely to be of
major importance in terms of the expected accuracies. 1.) Most published
results on vertical spread have been expressed in the form of r.m.s. spread,
ctz or of 'height of cloud', conventionally defined as the height at which the
concentration or dosage is one-tenth of the gound-level value. Conversion
from 2 to one or the other of these more useful forms requires the shape of
the vertical distribution to be specified. In practice it is customary to assume
the simple Gaussian form. While there is no obvious reason to prefer any
other form in the case of crosswind spread from a point source or vertical
spread from an elevated source, there is some doubt about its suitability jn
the case of vertical spread from a ground-level source. On theoretical
grounds, the exponent s in the exponential form, exp(- bz ), seems likely to
be somewhat less than the Gaussian value of 2.0; and experimentally deter-
mined values lie in the range 1.1 to 1.5.l4-,s
Measurements of vertical spread of air and the associated concentration Qf
3-8
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material from a continuous source refer to particles that have all travelled to
a specified position at a distance x downwind from the source. On the other
hand, in the foregoing theoretical result, the vertical spread is related to the
mean of all distances travelled by all particles in a particular but otherwise
unspecified time. In practice, the assumption is made, so far without any
formal or observational demonstration, that the two specifications of vertical
spread are identical when x = X.
Finally, it should be noted that although Equation (6) has a fairly con-
vincing theoretical background, it has so far been tested in a limited way,
only for diffusion over surfaces with very small z0 (1 cm to 3 cm).
Turning to the effect of thermal stratification, it may be noted that an
extension of the Lagrangian similarity theory to stratified conditions has
been developed and, to some extent, tested.16 Here again, there are con-
troversial features, with specific respect to the vertical spread.12 Neverthe-
less, the notion that the effect of stability on properties of vertical spread is
somehow characterised by the Monin-Obukhov length-scale has considerable
appeal, and could be used as the stability parameter in correlating measure-
ments of vertical spread. The writer has recently been reviewing this
possibility ir relation to the prairie grass measurements at O'Neill, Nebraska,
in 1956, also with the objective of assigning values of L to the qualitative
stability categories referred to earlier in thj^ paper, A reasonably close cor-
relation between cz and Panofsky's	has already been demon-
strated12 (Figure 3-1)r but L' (as distinct from L} has the complication of
being a function of height even in the constant-stress layer. A completely
satisfactory assessment of the values of L, to be associated with the prairie
grass data, has not yet been achieved. At present, the most reasonable assess-
ment is based on assuming Ri as a working approximation in unstable
conditions. This suggests that the minimum value of |L| in the particular
prairie grass data summarized by the writer2 was between 3 and 4, and that
the values of ]l_| to be associated with stability categories A, B, and C are
roughly 1, 3, and 10.
ESTIMATE OF EFFECT OF URBAN ROUGHNESS
Although the concept that the enhanced roughness in an urban area would
cause an increase in vertical spread, as compared with open and relatively
smooth country, seems to have been accepted, no theoretical estimate of the
magnitude of the effect has yet been offered. For relatively short distance of
travel, we can easily make such an estimate from the Lagrangian similarity
treatment for neutral conditions. In Equation (6), b = k = 0.4; if c is 0.6. it
then remains to specify the roughness length, z0, for an urban area.
Davenport11 quotes a value of 3 m for z0, derived from wind profile obser-
vations by Jensen, in the center of Copenhagen, and by Shiotani and
3-9
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DISTANCE DOWNWIND, km
— — FROM LAGRANGIAN SIMILARITY THEORY,
Zq = 3m (upper curve), 0.03m (lower curve) c = 0.5
	 EARLIER SEMI-EMPIRICAL CURVE FOR OPEN COUNTRY2
Points from Louis dispersion slody experirn«Ms No. 16 24 (®r 35 (Aj,
37 O' 42 O i 43 Hi- Open points for daytime, solid for evening experiments.
Figure 3-1. Vertical spread Z as a function of distance from a
source near ground level.
3-10
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Yamamoto, in the suburbs of Tokyo. In a later paper on the wind profile
and spectrum of wind speed in London, Ontario, Davenport18 gives a
further estimate of 2.3 m. An independent rough indication is provided by
Marsh's 19 measurements of turbulence in the rather open site near the
centre of Reading. These give ow/tr - 0.17 at a height of 14 m in neutral
conditions. Adopting the value 1.25, which now seems to be well established
for the ratio ow/u*, and substituting in the usual form ku/u# = ln(z/z0) for
the wind profile, we obtain z0 = 0.7m. This may be an overestimate since no
allowance has been made for a zero-plane displacement in the wind profile.
There is, however, probably another underestimation arising from the fact
that aw was measured over an area more open, and hence, smoother than
the town in general. On the whole, it would appear that values in the range
1 to 3 m may be taken as typical for modern urban complexes.
Equation (6) has accordingly been evaluated for distances in the range 0.2 to
5 km, using z0 = 3 m and, for comparison with relatively smooth open
country, = 0.03 m. The results are shown graphically in Figure 3-1. Note
that the difference of 100-fold in roughness length brings an increase in
vertical spread that ranges from 4-fold at the shortest distances to just over
2-fold at 5 km. The growth of vertical spread with distance may be
approximated by a simple power lawZ a Xp ; the curve can be fitted at the
greater distances with p equal to 0.85 for zQ = 0.03 m and 0.72 for zQ = 3
m. For comparison, the corresponding section of the semi-empirical curve for
vertical spread in neutral conditions in open country2 has been reproduced
in Figure 3-1, after converting from a 'height of cloud' to Z, assuming a
vertical distribution of the form exp (-bz~is). As already pointed out, this
empirical curve corresponds to a z0 of about 0.03 m, and is remarkably
consistent with the Lagrangian similarity prediction. This latter agreement is
not entirely new, having already been demonstrated for a distance of 100
m,12 but here is additionally verified over the considerable range of distance
up to 5 km. In view of the magnitude of vertical spread at the extreme
distance, however, implying diffusion over some hundred of meters, i.e.,
outside the likely depth of the constant-stress region, the extension of the
range of agreement may be rather fortuitous.
No useful direct measurements are yet available for vertical spread over an
urban area, but indirect estimates have recently been published by McElroy
and Pooler20 on the basis of a tracer study in St. Louis, Mo. The St. Louis
'dispersion study' was carried out from 1963 to 1965, using a point source
of fluorescent particles (zinc cadmium sulphide) near ground level. In each
of about 40 experiments, the source was maintained for about 1 hour, and
measurements of total dosage at the surface were obtained on three nearly
circular arcs at distances between about 1 and 10 km. (A few vertical
distribution measurements were made from a tethered balloon but, evidently,
these did not provide any definitive information.)
3-11
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By an application of mass conservation, McElroy and Pooler derive values of
equivalent a2 from the observed surface distribution of dosage and the
amount of tracer emitted. In certain stages of their calculation, a Gaussian
distribution in the vertical is assumed and, in adjusting the values for
comparison with the Z of Figure 3-1, a correction has been included on the
assumption that the vertical distribution was actually of the Jorm exp
(-bz1,5). Actually, the effects of transforming from az to Z and of
correcting for the shape of the vertical distribution are both small and
largely compensatory, and the net adjustment is less thanJO percent; so
that, for practical purposes, the magnitudes adopted for Z are essentially
those given for az in Table 2 of McElroy and Pooler. The data for
effectively neutral conditions, in which the bulk Richardson Number, RiB/
was within the range ±0.01, i.e., those of experiments 16, 24, 35, 37, 42,
and 43 are plotted on Figure 3.1. Note that the data from the four 'evening'
experiments are all above the zQ = 0.03 m curve, and their average trend is
obviously more in accordance with, though slightly lower than, the curve for
z = 3 m. Closer examination of the variation with z0 suggests that the best
fit to the evening data would occur with a z0 of about 1 m. In considering
this result, it must be remembered that the theoretical treatment assumes
horizontal uniformity and that the flow over the city is in equilibrium with
the surface characteristics, at least over the height range encompassed by the
vertical spread of the tracer. The values of Z/x range from about 0.06 at 1
km to about 0.04 at 5 km from the source. The corresponding ratio of Z to
the upwind extent of flow over urban terrain is presumably smaller (since
the source was not located at the upwind edge of the city) but it seems
unlikely that it could be less than say, 0.03, at the longer sampling distance.
Since the currently suggested ratio of the height of the new equilibrium
layer to the fetch over a new terrain is <0.01, the vertical distributions of
the tracer cannot be assumed to have been entirely within the equilibrium
layer.
Also, most of the estimates of vertical spread from the two 'daytime'
experiments are substantially larger than those from 'evening' experiments.
In considering this difference, it is to be noted that McElroy and Pooler used
rather different procedures in deriving their oz. They assumed a Gaussian
distribution from the start, with a wind constant with height for 'daytime'
experiments. For the evening experiments, the wind was assumed to have a
simple power law variation with height and an equivalent 'height' of cloud,
h, was evaluated on the assumption that concentration was constant up to h
and then fell to zero. The height, h, was converted to an 'equivalent
Gaussian' az by writing
TL	T	<7>
h x0 ue -	^ °z x° d
3-12
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and assuming that the effective mean wind speeds, ue and ud, were the
same. Since udi is strictly a mean of the wind distribution over the real
height of the cloud weighted according to the concentration, it follows that,
if the cloud distribution did extend above h (as it would in a Gaussian
distribution), ud > ue, and the az derived from h would be an overestimate,
suggesting that the discrepancy between the 'evening' and 'daytime' results
could be a consequence of the difference in analytical procedure.
The tentative conclusion is that, in evening conditions with neutral thermal
stratification within the city, the enhancement of the average vertical spread
by urban roughness is consistent with similarity theory. In practice, this
vertical spread is about two to four times that normally ascribed to neutral
conditions over level, unobstructed, open country. In daytime conditions,
however, which are apparently identical as regards thermal stratification in
the city, the vertical spread implied by surface concentration downwind of a
source appears to be substantially greater than can be accounted for by
roughness. The reason for this discrepancy is not yet evident.
EFFECT OF URBAN HEATING
There is abundant evidence that the temperature regimen within an urban
area is measurably different from that in open country. Mid-urban air
temperatures are known to reach values higher than those in surrounding
rural districts, by amounts ranging from a few tenths to several degrees
Centigrade, the maximum effect (in UK cities) being found on calm clear
nights in summer. There are probably two important contributions in the
production of this heat island. The first is concerned with the natural heat
transfers; the balancing of the net supply or loss by radiation must be
provided predominantly by ground conduction and turbulent transfer in the
air; whereas in vegetated areas, the loss of heat by evaporation is an
important and, at times, controlling contribution. As a consequence, surface
temperatures may reach appreciably higher values in towns and cities than in
country districts. Cities also have a second 'man-made' supply of heat that
will contribute to enhance urban temperatures.
It is to be expected that the urban heat island will affect both the horizontal
airflow pattern and the vertical mixing over a city, especially when the
airflow is naturally weak. This, in turn, may affect the distribution of
pollution. Summers1 has proposed a model of urban air pollution based on
the concept that, with a stable incident airstream, the effective depth of
mixing over a city is essentially determined by the heat released in the city
from domestic heating and industrial operations.
In the first instance, it is useful to note the magnitudes of heat transfer that
are likely to be involved. Summers estimates that, over the densely built-up
area of Montreal, the heat output from space-heating and industrial activities
3-13
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is, on the average, about 4x Iff3 cal cm"2 sec"1 and points out that in
winter this amounts to an appreciable fraction (about one-fourth) of the
heat received from the sun. In open country, even with strong insolation, the
rate of transfer of heat from the surface by turbulent and convective transfer
is probably not much larger than the urban heating rate quoted by
Summers-for example, measurements of turbulent heat flux by Swinbank21
range up to about 8 x 1CT3 cal cm"2 sec"1. On the other hand, on clear
nights the turbulent transfer of heat to the surface is probably only about
1CT3 cal cm"2 sec-1.
It is probably a reasonable assumption that, in the absence of unnatural heat
supplies, the turbulent transfer of heat over a city would be larger than over
open country by day, and of similar or smaller magnitude by night. The net
effect of also including a fraction (say half) of the unnatural output of heat
might, therefore, range from a modest increase in the (upward) turbulent
heat flux, H, during the day and a marked decrease, or even reversal, of the
(downward) heat flux at night. A first-order estimate may then be attempted
by regarding the effect on the rate of vertical spread as characterised by the
length-scale, L, which is proportional to u.3/H. From the trend of the
prairie grass data on short-range vertical spread (see Figure 1 of Pasquill12),
it seems that a substantial reduction or reversal of the downward H (hence
of 1/L) at night is likely to be more effective in proportionately increasing
vertical spread than a corresponding increase of the upward H during the
day.
The St Louis data on vertical spread have been classified by McElroy and
Pooler20 in terms of qualitative stability categories equivalent to those
defined by the writer,2 as well as in terms of Richardson number and wind
gustiness. The former classification provides an opportunity to examine the
effect of urban heating in the following way.
Figure 3-2 (reproduced from McElroy and Pooler's20 Figure 10) shows the
mean curves of oz against distance, for the various stability classes. Here,
classification D, for example, is not representative of effectively neutral con-
ditions; rather it represents the net effect of an incident neutral atmosphere
plus any effect of urban heating. Plotted on the same diagram are two mean
curves for RiB = ±0.01, one reproduced from McElroy and Pooler's Figure 2,
the other based on evening data only. If the latter curves are taken to
represent neutral conditions in the urban airflow, then their departures from
the McElroy and Pooler curves represent the net effect of natural atmos-
pheric thermal stratification and urban heating. For comparison, we may use
the 'open-country' curves of the writer's2 Figure 2, here referring the curves
to the D(1) curve as one truly representative of naturally neutral conditions.
Table 3-2 has been constructed from Figure 3-2 and the corresponding
3-14
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Figure 3-2- Vertical spread from ground-fevef source in St
Louis, Missouri.
Table 3-2, PATIO OF oz TO ITS VALUE iN EFFECTtVEL Y NEUTRAL CONOITIOMS,
FOR OPEN CQUMtRY STAWUTV CATEGORIES B TO F
Vertical j	f	°t 10 value m effectively neuxrai conditions
distance,

tar staUilitv canecore-si.
km
Locaticri
B
C I
0 1
E - F

St. Leu is*1
4.5


0.7
1
St. Louis0
4.0
2 A
1.S
0.6

Open country
3.2
1.9
1.0
0.5

St. Louis3
9
3.4
1.0
0.3
10
St. Louis0
11
4.1
1.2
0.4

Open country
6
»
t.0
0.3
a Ustrvg McEltoy a™3 PootWs cutud lot Rig j 0.01 in riteii Fl9u*e 2.
b Uslrg data for Rig * 0.01 (n ^vertl rig conditions only.
3-15
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curves for open country to display the apparent effect of natural stability in
the two cases at distances of 1 and 10 km. The figures in the table are the
ratios of az to its value in effectively neutral conditions. A modification of
the effect of natural stability by urban heating should result in larger ratios
over a city tlhan over open country. For tine shorter distance, this effect is
evident consistently at all stabilities, but, for the longer distance, it is mare
obvious in the B and C than in the D and E-F categories, Thus, the specu-
lation above thai the effect of urban heating ml^ht be expected to be more
obvious in naturally stable than in unstable conditions does not seem to be
supported by the fig J res, which, in fact, irr p y a difference at the larger
distance and ro obvious differeice st the rfoorte>- distarce. Reiated ta this, is
the fact that in Figure 3 2 the slopes of the E-F and D curves are apparently
quite different from the slopes of the curves for effectively neutral con-
ditions within the city. A possible implication is that the artificial sources of
neat ast in two ways. Those producing haat at low level may lead to en-
hanced m xirc st low level iheree, a: short distances from tfve source of
material}, whereas those effective in heating relatively high laysrs (elevated
sources arid rising plumes) may rainforce the stability that is ultimately
restrictive as regards vertical spread to greater bie-iflhts (i.e., at longer dis-
tances from the source of material I. Such a restriction 'would not apply to
material released with the heat; however this type of release presumably was
not the ca&e in tfve tracer experiments under consideration.
As regards categories E-F and D, the temperature gradient data for St. Louis
(obtained from 40- and 150-m levels on a 'downtown' television tower and
represented in ftiB) provide additional evidence. Of the five E-F cases, three
have specified values of Ris, which are + 0.14, — 0.03, and + 0,12. From
these there is no strong indication of a general elimination of the stable
classffication, consistent with the indication in Table 3-2 that at the longer
distance the influence of urban heating had not brought the vertical spread
in E-F conditions near the magnitude expected in effectively neutral condi-
tions. On the otha- hard, for those occasions when a D classification is
indicated consistently at al\ three of tfie meteorological sites employed
(McElroy and Pooler's Table 3,10 the values for Ria are in the range -0,05
fa 0, i.e., no positive valuss, suggesting conversion to somewhat unstable
thermal stratification in the urban airflow, which is generally consistent with
Table 3-2.
It would be unwi'5£ to attach too much significance to these results 3ione,
bearing in Tirol the cartsiderable scatter ir the data that fed to the cluybs
on Figure 3-2, and the qualitative nature of the stability classification. In
particular, there is some doubt about the precise comparability of the
present urban and open country curves when so classified.
At this point, some comment on	model1 for vertical spread in the
3-16
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flow over an urban area of an initiafly stable atmosphere seems desirable.
The essentiaf principle of this mode* *'s that any heat released into the
atmosphere from domestic and industrial processes is instantaneously mixed
in the vertical, generating a growing layer with a dry adiabatic temperature
lapse rate (or constant potential temperature) extending from the ground.
This layer is identified with the mixing layer tor pollutants, and the corres-
ponding assumption of uniformity of concentration with height provides an
easily deduct tile cetet«w\	rait oi emission of pollutant, wind speed,
and distance afongwind.
JnitiaUy Summers adopts linear profiles of temperature and wind, but for
much of the ultimate analysis he eliminates the wind variation. The analysis
can easily be generalized, using power law forms for the height-dependence
of temperature and wind and also for the variation o1 heal input with
downwind distance, x, from the upwind edge of the city. Taking for the
potential temperature distribution
6(z) = sz° at x < 0
- ah" at x > 0, 0 < z < h
= az° at x > 0,	z > h
for the wind distribution
U « b 2a = ~a I
a _	,a
Li
uniform in the horizontal both upwind of and directly on the urban area,
and for the surface heat input from urban processes
q(x) = cxT per unit area and unit time
conservation of heat requires
t + ^
not
h c: U~1 + a + P X 1 + a + p	(11)
Simplification to the case of p = t, a - 7 = 0 gives
h a Uj"W xI/3	(12)
as obtained by Summers, while more realistic values, say 0.3 for a and p,
give a result that is only slightly different
La. h a uf°'« x0,6	(131
As a matter of practical interest, three exampfes of stable temperature and
wind profiles observed near midnight at Cardington, England, have been
3-17
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analysed, by numerical integration, to get the heat required to convert to
uniform potential temperature over various depths. The results are displayed
in Figure 3-3. Of particular interest is the fact that over a considerable range
there is, on the average, a fairly close fit to a relation
which for uniform heat input implies h « xv\ as predicted by the simple
The heat input required to produce a value of h similar to the vertical spread
of tracer material observed in St. Louis has been considered nominally for
these cases where conditions of stability prevail |E-F). If we take the total
vertical spread of the tracer cloud to be, say 2az, this gives, according to
Figure 10 of McElroy and Pooler20, a value of about 350 m at 10 km
downwind from the source. Assuming uniform heat input, Figure 3-3 in-
dicates that such a value for h at 10 km would require 7.4 x 10~3 cal cm'2
sec"1, not unlike, though somewhat larger than, the figure of 4 x 10"3
estimated by Summers1 for Montreal. Moreover, the temperature data al-
ready discussed for St. Louis imply that mixing to the stage of uniform
potential temperature did not extend over the full depth of the tracer-cloud.
In other words, the extent of vertical mixing is not determined solely by the
urban heat input as implied in Summers' model but, as implied by the
analysis of urban roughness, is probably controlled to a large extent by the
surface roughness of the area.
CONCLUSIONS AND FUTURE PROSPECTS
In order to predict levels of air pollution in any condition of terrain, one
must distinguish between two main classes of meteorological conditions—
those in which the airflow is relatively well defined, with geostrophic wind
speeds, say > 5 m sec-1 and those in which the wind is calm or very light
and the general pattern of flow is not under any large-scale control. For the
second class, the foregoing treatments are almost certainly inappropriate and
a special approach recognizing the local and individual character of the flow
pattern would appear necessary. For the first class, however, the preceding
discussion suggests that the 'idealized' (open-country) treatment may be
extended to urban situations to give at least a crude specification of the
effect of increased roughness and, to some extent, the effect of urban
heating on the general rate of vertical diffusion and the consequent average
level of concentration from an array of sources. There are, of course, still
many deficiencies in the system and it would be unrealistic to expect further
improvements to appear rapidly.
Current and foreseeable investigations of the turbulent properties and
(14)
model.
3-18
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Co
co
Figure 3-3. Heat input required to adjust 2300 temperature profile
(Cardington-Engfand) to uniform potential temperature e(h) through
layer 0-h.
-------
diffusive action in the upper parts of the planetary boundary layer seem
likely to be quite relevant to the matter of vertical diffusion at medium
range over an urban area. With increasing height in the boundary layer. it
seems clear that the character of the turbulent motion will have progressively
greater dependence on buoyancy effects and progressively less dependence
on the aerodynamic character of the surface. The latter feature is, to some
extent, reflected in the theoretica) results discussed earlier, in which the
proportionate effect of a change of roughness on Z decreases with distance
of travel. When vertical spread is large, whether as a result of instability or
of long-distance travel, observations of turbulence at the greater heights will
be particularly meaningful.
The continuous evolution of the boundary layer in response to changing
surface roughness and surface heating is a matter attracting increasing atten-
tion in meteorological studies. Such studies should bring further insight both
into the process of modification of an airstream as it leaves rural sur-
roundings and flows over an urban area and into the analogy of the modifi-
cation of an initially stable airflow by an urban heat input with the temporal
modification of the nocturnal boundary layer by the sun's heat early in the
morning. Except for complications that may arise from the particular varia-
tions of the heat input in time or space, and from the effects of wind shear
in the advective case, we may take as equivalent to u ^ . Reference to
existing information on the diurnal development of the vertical temperature
profile may well be rewarding, but it is also evident that special observations
on these evolutionary aspects are desirable. Examples that spring to mind
immediately are the post-dawn evolution of the turbulence profile and the
formation of an evening 'heat plume' over a large urban complex.
It may appear that much could also be done directly to improve our know-
ledge of the turbulent and diffusive structure over an urban area. Amid the
complexities that are inevitably present, the problem is to isolate the con-
trolling features and subject them to theoretical analysis and critical obser-
vation. For certain purposes, tracer experiments have an immediate appeal in
that they provide a direct answer to the ultimate questions, but they may
involve expensive repetitions unless supported and generalized by a rational
theoretical approach. Thus it would seem no more than common sense to
ensure, by examinations of the kind described previously, that the maximum
information is extracted from a preliminary experiment, such as that con-
ducted in St. Louis, before planning and embarking on repetitions or ex-
tensions. One of the outstanding prerequisites for the theoretical specifica-
tion of the rate of vertical mixing is the provision of characteristic profiles
of the intensity and scale of turbulence. For the effective vertical diffusivity.
we recall that such a specification is provided by data on any two of the
quantities tjw. e, and Xm, and it would clearly be a step of major importance
to extend to the higher parts of the boundary layer the generalizations that
3-20
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are now available for these same quantities in the lower layers. The experi-
mental program now evolving at the Cardington station of the Meteorological
Office is expected to provide such data, ultimately. It will be characteristic
of open country with variable but relatively minor roughness from both
natural and urban features. It would, of course, be valuable if at least some
of the simpler observations were to be carried out over rougher terrain and
specifically over a major urban complex. Measurements of the relatively
high-frequency contribution to the intensity of turbulence, from which to
derive estimates of e, seem particularly worthy of consideration.
In the meantime, the attention of the Meteorological Office is focused on
the exercise of making the most realistic estimates of the K profile, commen-
surate with the limited theoretical understanding and observational data
currently available on the effects of natural thermal stratification and rough-
ness. The intention is then to examine the consistency of these profiles with
the independent data available on the vertical spread of windborne material
over medium (10 km) and long distances (100 km). This exercise is an
essential part of the previously mentioned revision and extension of the
practical system for estimating pollutant concentration, and will be reported
in detail elsewhere.
Most of this discussion has been concerned with the general rate of vertical
mixing in the atmosphere and as such is meaningful only in relation to
spatial integrals of pollutant concentration. As regards the detail of the
variation of concentration in space and time, it is obvious, even from a
consideration of relatively ideal conditions of diffusion, that there are ad-
ditional (imitations to be faced. From general estimates such as those
provided by the writer,2 it is easily demonstrated that the estimated concen-
tration arising from a point source, at a given position relative to the source,
may change by several-fold as a consequence of a 5- to 10-degree change in
the assumed wind direction, especially in neutral and stable conditions. It
would obviously be unrealistic to expect any better precision in specifying
the effective wind direction from the observations available in an urban
experiment such as that reported by Marsh and Withers.6 From this uncer-
tainty alone, it should not be surprising that the individual 6-hour dosages in
that experiment deviated widely from the corresponding calculated values.
Discrepancies introduced in this way and from other uncertainties, notably
those in the magnitude of the spread and in the strengths of the sources, can
be reasonably expected to contain a large random element. It would be of
interest to examine whether there is, nevertheless, some measure of agree-
ment in the statistical distributions of pollutant concentration as measured
and as calculated (i.e., the frequency of occurrence of various levels of
concentration in space or time). It may be significant in this connection that
in Marsh and Withers' analysis6 (Table 3-1) the r.m.s. differences between
calculated and observed values are not greatly in excess of the r.m.s.
3-21
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distributions would be desirable, however, and if successful, would be an
iicouragirg pointer to the prospects of pred.ct.ng more than the averse
level of pollutant concentration.
addendum
Since this paper was completed, Mr. Marsh has followed up the suggestion
made in the last paragraph and has derived frequency distributions of observed
and calculated 6-Hour concentrations for three of the sites in the Reading
experiment I am grateful to Mr. Marsh for his permission to reproduce the
combined data here, in the form of a plot on a log-normal scales (F igure 3-4).
Figure 3-4. Marsh's reanatysis of Marsh and Wither's data.®
Reading sites 1, 5, and 11; all periods-
The observed and calculated distributions are rou#,lv .n ajreement and
conform fai.'Y «> *	^ °	Th° f>«
r, ™e most of the range, the broad estimates of spread provide better
that, over m , itout Furthermore - and probably most important
TTowers that the calculated distribution provided a statistical estimate of
- it appears	concentrations (say the concentration exceeded
£ rfeTpe^	>.	-"Id be satisfactory for many
3-22
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practical purposes. Obviously, a great deal of further work arid discussion are
required on this point, and the matter is, of course, taken further in Dr.
Fortak's paper. It seems to me, however, that there is already some reason
to anticipate that a useful statistical prediction of the probability distri-
bution of pollutant concentration in an urban area is realizable in practice.
3-23
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references
1	Summers P. W. An Urban Heat Island Model; Its Role in Air Pollution Problems
' with Applications to Montreal (abstract only). In: Proceedings 1st Canadian Con-
ference Micrometeorology. 1967. 435 p.
2	Pasquill, F. The Estimation of the Dispersion of Windborne Material. Meteorol.
Mag. 30(10631:33-49, February 1961.
3	Pasquill, F. Meteorological Aspects of the Spread of Windborne Contaminants. In:
Seminar on the Protection of the Public in the Event of Radiation Accidents,
Geneva, November 18-22, 1963. Geneva, World Health Organization, 1965. p.
43-53.
4	Marsh, K. J. and M. D. Foster. An Experimental Study of the Dispersion of the
Emissions from Chimneys. In Reading - I. The Study of Long-Term Average Con-
centrations of Sulphur Dioxide. Atmos. Environ. 7(5):527-550, September 1967.
5.	Marsh, K. J., K. A. Bishop and M. D. Foster. An Experimental Study of the
Dispersion of Emissions from Chimneys. In Reading - II. A Description of the
Instruments Used. Atmos. Environ. 7(51:551-559, September 1967.
6.	Marsh, K. J. and V. R. Withers. An Experimental Study of the Dispersion of the
Emissions from Chimneys. In Reading - III. The Investigation of Dispersion Cal-
culations. Atmos. Environ. 3(31:281-302, May 1969.
7.	The Calculation of Atmospheric Dispersion from a Stack. Stichting CONCAWE.
The Hague, Netherlads. August 1966. 57 p.
8.	Hogstrom, U. An Experimental Study on Atmospheric Diffusion. Tellus. 7©
(21:205-251, May 1964,
9.	Pasquill, F. The Vertical Component of Turbulence at Heights up to 1200 Metres.
Atmos. Environ. /(4):441-450, July 1967.
10.	Busch, N. E. and H. A. Panofsky. Recent Spectra of Atmospheric Turbulence.
Quart'J. Roy. Meteorol. Soc. 94(400):132-148, April 1968.
11.	Readings, C. J. and D. R. Rayment. The High-Frequency Fluctuation of the Wind
in the First Kilometre of the Atmosphere (in press). Radio Science. 1969.
12 Pasquill, F. Lagrangian Similarity and Vertical Diffusion from a Source at Ground
Level. Quart J. Roy Meteorol. Soc. 92(392) .185-195, April 1966.
13.	Chatwin, P. C. Dispersion of a Puff of Passive Contaminant in the Constant Stress
Region. Quart. J. Roy. Meteorol. 94(4011:350-360, July 1968.
14.	Pasquill, F. Atmospheric Diffusion. London, D. Van Nostrand Co., Ltd., 1962. 297
P.
15.	Elliott, W. P. The Vertical Diffusion of Gas from a Continuous Source. Int. J. Air
Water Pollution, 4(1/2):33-46, June 1961.
16.	Gifford, F. A. Diffusion in the Diabetic Surface Layer. J. Geophys. Research.
67(81:3207-3212, July 1962.
17.	Davenport, A. G. The Spectrum of Horizontal Gustiness Near the Ground in High
Winds. Quart. J. R. Meteor. Soc. 87: 194. 1961.
18 Davenport, A. G. Instrumentation and Measurements of Wind Speed Spectra in a
City. Proceedings of the First Canadian Conference on Micro-meteorology. Part III.
Department of Transport. Toronto, Canada. 1967. 361 p.
19. Marsh, K. J. Measurements of Air Turbulence in Reading and Their Relation to
Turner's Stability Categories (in press). 1969.
20	McElroy, J. L. and F. Pooler, Jr. St. Louis Dispersion Study, Volume II - Analysts.
National'Air Pollution Control Administration. Arlington, Va. Publication Number
AP-53. December 1968. 51 p.
21	Swinbank, W. C. The Exponential Wind Profile. Quart J. Roy. Meteorol. Soc.
90(3841:119-135, April 1964.
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ACKNOWLEDGMENT
This paper is published with the permission of the Director-General of the
United Kingdom Meteorological Office.
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APPENDIX - GLOSSARY OF SYMBOLS
b, c	dimensionless constants in the Lagrangian similarity treatment,
k	von Karman's constant (0.4).
H	vertical eddy flux of heat.
K	eddy diffusivity; subscripts M and H refer to momentum and heat
respectively.
pCp T u3
L	Monin-Obukhov length scale, — ^ ^
q	rate of heat input from urban processes.
Ri	Richardson number; subscript B denotes 'bulk' form using tempera-
ture difference over specified height interval.
S(n)	spectral density of wind component variance at frequency n.
tL,tE	Lagrangian and Eulerian integral time scales.
T	time of travel from source; absolute temperature.
u	mean wind speed in x (alongwind) direction,
u*	friction velocity.
X	mean distance of travel of particles in a given time.
Z	mean displacement of particles in vertical (z) direction.
z0	roughness parameter in wind profile.
6	rate of dissipation of turbulent kinetic energy per unit mass.
\m	equivalent wavelength ( = u7nm) at which nS(n) is maximum.
p	air density.
a	standard deviation; subscript w refers to vertical component of wind-
y and z, to particle spread in respective directions.
0	Monin-Obukhov universal function.
x	distance downwind
0	potential temperature.
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abstract
The basic structure of many current urban pollution models is
examined from the point of view of underlying assumptions and
ohvsica/ basis. Initial attempts to extend steady-state models to vari-
able conditions and long-term predictions are indicated, with a brief
discussion of stochastic simulation of the concentration patterns and
average seasonal and annual distributions. In view of the complexity of
most computer-oriented models, a sensitivity analysis is recommended
to identify the input parameters that most critically affect the concen-
tration predictions.
author
KENNETH L. CALDER obtained honors degrees in physics and mathematics at
the University of London before joining the British Meteorological Office at its
Porton Research Establishment in 1936. He left Proton in 1949 to accept an
appointment with the U. S. Army Chemical Corps as Chief of the Meteorology
Research Division at Fort Detrick. In 1968 Mr. Calder transferred to the Air
Resources Laboratory of NOAA where he currently serves as Chief Scientist to
the Division of Meteorology of the National Air Pollution Control Adminis-
tration.
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4. SOME MISCELLANEOUS ASPECTS OF CURRENT
URBAN POLLUTION MODELS
KENNETH L. CALDER
Air Pollution Control Office, NO A A *
INTRODUCTION
The last decade has witnessed an unprecedented interest and concern with
the development of mathematical-physical models for predicting air pollution
concentrations in an urban environment. It is not surprising that, in most of
these efforts, we see the underlying influence of the pioneering thoughts of
Francois Frenkiel on the subject, and it is fitting that he can be with us at
this symposium. The ever increasing current interest in urban pollution
modeling derives, of course, from its obvious potential value in nearly all
practical problems involving quantitative consideration of air quality relative
to the sources of pollution. These include air pollution abatement strategies,
the forecasting of the occurrence of undesirable levels of urban pollution,
and problems of urban planning for the future. Each one of these topics
constitutes a large well-recognized area of study that is being vigorously
investigated by many groups, although these matters lie outside the scope of
the present symposium.
As a newcomer to the field of urban pollution modeling who was at-
tempting, with no little trepidation, to select an appropriate topic for a
paper to be presented before experts, I was primarily influenced by two
considerations. First, was the knowledge that the fundamental physical and
meteorological aspects of the subject would certainly be covered at the sym-
posium in an authoritative fashion by Drs. Lettau and Pasquill. Second, was
the fact that several quite comprehensive general papers and bibliographies
on urban diffusion modeling have recently been written. Here it will suffice
to mention the article by Wanta in Stern's book1 and two comprehensive
review articles prepared this year by Turner2 and Moses.3 With these recent
articles, still another review seemed out of place for this meeting. Under
these circumstances, it seemed more worthwhile to mention miscellaneous
questions that come to mind in reading accounts of some of the currently
'National Oceanic and Atmospheric Administration, U. S. Department of Commerce.
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available models-and, more particularly, those developed in the past few
years by members of a U. S. air pollution meteorological team under the
direction of Mr. Ft. A. McCormick. The somewhat fragmentary observations
contained in this paper are made at a time when a rapidly expanding effort
in modeling gives optimism for expecting a second generation of improved
models to become available in the near future. While it is appreciated that
the present paper raises a lot more questions than it answers, it is certainly
not done with the feeling that the problem is so hopelessly complicated as
to defy useful analysis. Instead, it is believed that an explicit recognition of
some of the difficulties will lead to more mature appreciation of the limita-
tions of modeling techniques among those who may be wanting to apply
them. This recognition of the difficulties is also a prerequisite to the devel-
opment of improved urban pollution models.
A MULTIPLE-SOURCE URBAN POLLUTION MODEL
In the following discussion, we shall be concerned almost exclusively with
modeling the effects of a chemically stable gaseous pollutant that is released
from a stationary source in a city. Sulphur dioxide that results from the
combustion of sulphur-containing fossil fuels in domestic, commercial, and
industrial operations is normally regarded as the classical example. We shall
also restrict attention to physically based models of the pollution distribu-
tion. These are explicitly constrained by the law of the conservation of
matter, in contrast to empirical models that are based on statistical correla-
tions established between observed concentrations of pollutant and simul-
taneously observed meteorological parameters, and that do not involve
considerations of material balance.
Steady-State Equation
The starting point of the majority of urban pollution models is the postula-
tion of a quasi-steady state. Thus, in spite of the obvious long-period varia-
bility of diffusion and meteorological conditions over an urban area, it is
assumed that this variability can be treated as though it resulted from a
sequence of different steady-state situations. The sequence interval may be
some relatively short-term period—perhaps only of the order of an hour.
During each "steady-state period," it is further assumed that a unique hori-
zontal mean wind direction can be defined for the entire urban area, and
that if this is used to define the x-axis of a rectangular coordinate system,
with y-axis also horizontal, and z-axis vertical, then the mean concentration
at a receptor location at ground level (x, y, 0) resulting from an elevated
continuous point source (0, 0, z0), release of pollutant, of constant strength
Q, per unit time has the function form Q R (x, y; z0)-
For a "given" meteorological situation, R denotes a fixed, i.e., nonstochastic.
4-2
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function, independent of the location of the origin of the coordinate system,
i.e., is the same irrespective of the horizontal location of the source. Further-
more, R does not depend on the horizontal mean wind direction that defines
the orientation of the coordinate system relative to the urban area. The
assumption that the form of R is independent of the source location, is
tantamount to the more formal statement that the concentration distribution
function is invariant under arbitrary horizontal translations of the source-
receptor pair. This might conceivably be a reasonable approximation over a
very extensive area of uniform, level, open countryside. Considering, how-
ever, the edge effects that inevitably are associated with the relatively small,
finite size of all cities, and the rather obvious horizontally inhomogeneous
nature of the buildings and their distribution, the above assumption can only
be a very crude approximation for an urban diffusion environment. The
same comment would seem to apply with equal force to the assumption that
the form of R is unaffected by the direction of the airflow over the city.
The specific functional form of R(x, y; z0) that is used in the so-called
Gaussian plume dispersion models is, for x > o,
e*p[-y" { cr/ll.SI + o;J(x.S) }]
R(x,y; z0) =	1	J			U	(1)
rr U ov (x,S) az(x,S)
with R = 0 for x < 0, i.e., no upwind travel of material,
U = a representative, constant, and spatially uniform, wind
speed;
S = atmospheric stability category first introduced by Pasquill.4
Here S = 1 may denote extremely unstablity and S = 6,
extreme stablity, and
ay(x,S),az(x,S) = horizontal and vertical diffusion functions—the horizontal
and vertical standard deviations of the Gaussian concentra-
tion distribution at distance x from the source. These dif-
fusion functions are normally assumed to be parameterized
by the stability category and are assumed independent of
release height.5
In addition, in some models, a crude attempt may be made to allow for the
known fact that diffusion in the vertical direction is frequently limited, such as
when the pollutant is trapped between the ground surface and a stable layer
aloft. When this occurs, a uniform vertical distribution of concentration would
be expected throughout the effective mixing layer for sufficiently large values
of x. One simple method of approximately allowing for this was suggested by
Pasquill.6 If the mixing layer is of height L, then Equation (1) is used for
downwind distances, x, such that az(x,S) < ViL. When az(x,S) = L, the
4-3
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~ .~im, hecomes approximately uniform with height and of a
resulting concentrati	- L At greater distances than this, the ground*
magnitude appropriate to o,by vertica| dHfusion and the aqua-
level concentration no ^ ^^ 0z = L = constant and with the appro-
HUM w~--
priate value of oy x,	scheme based on the atmospheric stability
In the original diffusion pr • ^ ^ diffusion functions ov(x,S) and ffz(x,S)
categories suggested by Pasqu ^	experjmenta, data 0n diffusion
were tentatively esta^'shJh	was thus no allowance for the possible div
over open level coufi^'	topography. With some minor modifications,
turbing effects of bulW"*	^ .|n an urban diffusion model and has
Turner5 has utilized these	for objective determination of the stability
indicated both a w°rk^ * jve method of adjusting the values to allow for
category and a crude	the results of ad hoc experimental diffusion
urban conditions. More recen Y	^,itan St. Louis, Missouri, have
studies made with tracer", and MeHmy. These studies h«.
been reported by McElroy	^ crosswind diffusion in cities,
shown that, for	. open country, soon converges to the latter
although initially 9reaterJ	, diffusion occurs in the city than in open
value. Significantly greater	under meteorological conditions,
country; and it ismo* P	^ quantitative aspects of the urban
As is to be expected, n	. ^ ^ reso,ved atthough it « encour-
point-source diffusion P	experiments have generally confirmed the
aginfl «•"«	aspects of the simple Gaussian model,
appropriateness of «least son.
j> Cnurce App^'ca^on
Area :*>ur	in the preceding discussion, it .s now only
With all the provisions mer,^ca, formu,ation of a multiple-source urban
a smalt step to a formal m	^	,, choose the x-axis of the
pollution model. For any ^ ^ horjzonta, mean wind direction tor
rectangular eoordinate	^ ^ urban pollution emission be regarded es
the urban area.	distributed, area source such that Q(x0, yQ, zG) dx^
a steady, horizontally o ||utant emitted per unit time at an "effective"
dy0 * the total amot.	Qf ^ ^ ^ ^^nding the point
height, *o 8 ^ here that the function Q(x0, y0. *<>) can be specific
(x0, Yo). >« U imP*l„rooriate emission inventory techniques for the enthr*
on the basis of app * J ~ oo ^ ~°°
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The area source concept has been justified as an appropriate idealization in
urban diffusion modeling when there are too many sources (e.g., from
domestic heating units) to be considered individually. It has sometimes been
used, however, (e.g.. Turner5) even when larger commercial and industrial
sources are included in the emission inventory. For the primary purpose of
reducing the computational effort, a single effective height of emission is
sometimes selected, also. More realistically, large pollution emitters, like
power plants with tall stacks, are treated as individual elevated point sources,
and the effective height is calculated from the actual height plus the plume
rise associated with upward momentum of discharge and thermal buoyancy
effects. Consideration of plume rise is a somewhat controversial topic and far
from straightforward, although it becomes an important element in realistic
pollution models. A comprehensive and, hopefully, definitive, critical review
of the subject has recently been prepared by Briggs.9 [We note that the
point source situation may be regarded as covered by Equation (2) by the
formal device of the Dirac delta function. Thus, for a continuous point
source at height z0, of strength, q, per unit time, and with horizontal
coordinates (a,b), we have Q (x0, Yo, z0) = q 6{x0 — a) 6 (y0 — b) so that
Equation (2) gives x = q R(x-a, y-b; z0).
The integral of Equation (2) has to be evaluated by numerical methods, of
course, once the source function Q (x0, yo, z0) and the diffusion function
R (x - x0, V — Yo; zo) have been specified. The calculations that are
involved are normally so extensive that they necessitate use of a high-speed
computer. Various and somewhat arbitrary devices have been used in the
past for the approximate numerical integration, with no proper study of the
errors incurred. For example. Pooler,10 in developing a multiple-source S03-
prediction model, used a source inventory for Nashville, Tennessee, based on
1-mile-square area sources; then replaced each square {with a single excep-
tion) with a point source at its center. Again, Turner5 assumed that 1-mile-
square area sources could be approximated by appropriate Gaussian-
distributed, line sources oriented crosswind and passing through the center of
each area. These approximations appear to be very crude and consideration
of more sophisticated integration techniques should be worthwhile in the
future.
It is, perhaps, obvious that an urban pollution model of the type we are
considering, which requires as a quantitative input, a source-strength func-
tion, Q tx0, yo, zo). cannot yield concentration predictions that are more
accurate than the pollutant source inventory itself. Unfortunately, the latter
may be quite crude and is frequently based on indirect reasoning. The
accuracy may also be expected to diminish rapidly as the time period over
which the emissions are averaged becomes shorter. Sulphur dioxide, pro-
duced by the burning of coal and oil for space heating, for example, requires
indirect estimation (see, e.g., Turner11) of diurnal and day-to-day variations
4-5
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„f fuel coemption. The estimations are made by using such empirical
concepts as "heating-degree-days" (the depression of a suitably defined daily
ZpLure below some limit like 66° F). While an annual emission mven-
tTv derived from the total annual consumption where fuel has a known
sulohur content may be quite accurate, large errors can be expected in daily
hourly inventories. These are probably unavoidable due primarily to the
tan. that in general, no adequate records of fuel consumption with fine
enough resolution in time and space are available. This fact, itself, could
Impose an intrinsic limitation on the accuracy of urban pollution models as
applied to short-period predictions.
EXTENSION OF MODEL TO VARIABLE CONDITIONS
AND LONG TIME PERIODS
The basic model of the preceding discussion relates to meteorological and
emission conditions that can be regarded as steady-state and that have
Drevailed for a sufficiently long period of time to perm.t full development of
the concentration fields associated with the individual sources. In consider'^
extension of the model to variable conditions, we will assume that the
steady-state assumption is normally an adequate working approximation for
time periods of the order of an hour, and that the general nonsteady-state or
variable situation can be resolved into a succession of steady-states of this
duration In general, both the pollutant source distribution and the meteoro-
logical conditions must be regarded as varying between consecutive periods.
Quasi-Steady-State Applications
Since the x-axis for Equation (2) is determined by the mean urban wind
direction while the source distribution is specified in a coord.nate system
that is fixed relative to the city, and is also desirable for the concentration
distribution it will be necessary in utilizing Equation (2) to use the standard
formulas for rotation of coordinate axes. In addition to the mean urban
wind direction the change in meteorological conditions occurring between
r-nnsecutive 1-hour periods should reflect changes of the mean wind speed,
U the stability category, S, and the height. L, of the mixing layer, because
these all will affect the concentration function R(x, y; z0). It is then evident
that bv repeated applications of Equation (2). each with an appropriate set
of hourly parameter values, and an emission distribution estimate; we can
simulate the pollutant concentration changes occurring at any receptor loca-
tion over any specified period of time.
Precisely one such urban pollution model was developed by Turner5 for the
i hiir riioxide pollution in Nashville. Tennesee. This analysis was based on
an emission inventory prepared for mile-square areas forming a rectangular
17 b 16 miles Source strengths and meteorological parameters were
*en estimated by 2-hour periods (instead of the 1-hour period above). The
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mean wind direction, to 16 compass points, and wind speed, to 0.1 meters
per second {m sec-1), were estimated from instrumental records at several
wind stations in the area. The corresponding 2-hour stability category, S, was
obtained by using an objective technique proposed by Turner (in this model,
no allowance was made for a finite mixing height, i.e., L = °°). In terms of
these inputs to the model, 2-hour S02 concentration values were first
estimated at a number of receptor locations at 1-mile intervals. From the
2-hour values, average 24-hour concentrations were then obtained. Com-
parison of the calculated 24-hour concentration values with those obtained
by actual chemical sampling during a number of test periods occurring
throughout a 1-year period showed quite reasonable agreement. In fact.
Turner showed that even for 2-hour periods the calculated values were in fair
agreement with corresponding observed values.
It is evident that, in principle, the above approach could be used to provide
elaborate information on the characteristics of the concentration distribution
in terms of forecast or observed meteorological and emission variations. If
frequency statistics are available for the relevant meteorological parameters,
then a probabilistic model is possible and the actual frequency distribution
of the pollution concentration at a receptor can be estimated. (It should be
noted that this is strictly true only if temporal variations of the source
strength function, i.e., Q (x0, y0, Zo). of Equation (2), are disregarded.
Otherwise, it would be necessary to know the joint frequency function for Q
and the meteorological parameters.)
Thus, after calculating the concentration values for alt possible combinations
of the three meteorological parameters: wind direction, wind speed, and
stability category, and for simplicity assuming L = °°, i.e., diffusion is un-
limited in the vertical direction, we can get the frequency of occurrence of a
particular concentration value from the sum of the joint frequencies of all
the combinations of meteorological parameters that give rise to this concen-
tration value. If hourly observations of wind direction are rounded off to the
nearest 10 degrees, and there are, say, ten classifications of wind speed, then
with only five possible stability categories, we obtain 36 x 10 x 5 = 1800
possible combinations; hence, 1800 meteorological situations for which the
integral of Equation (2) has to be evaluated numerically for each receptor
location of interest.
Since each of the meteorological "parameters" in reality has a continuous
distribution, this use of only a finite number of combinations will, of course,
mean that the real ensemble of diffusion situations is only being approxi-
mated in the mathematical simulation. Such extensive computation can
quickly involve prohibitive time, even with present high-speed computers.
Nevertheless, extensive calculations designed to characterize the concen-
tration frequency distribution relating specifically to ground level SO^ for
the urban area of Bremen, Germany, have already been reported by
4-7
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Professor Heinz Fortak.12 We shall probably hear the latest news of this
pioneering effort later at this symposium. It might be noted that the same
approach could be used to provide probabilistic information on the two-
dimentional concentration distribution, where the joint frequency distribu-
tion for concentrations at two of more receptor locations couid be deter-
mined by the same enumerative procedure.
Ori the basis of extensive air pollutant concentration data for several pollu-
tants and several U. S. cities, Larsen3 3 has been abfe to show that the
empirical frequency distribution of concentrations is closely approximated
by the logarithmic-normal distribution. With the possibility discussed above
for stochastic simulation, it would be of considerable interest to see whether
the iog-normal distribution can be generated by appropriate mathematical
simulation.
A less ambitious objective than the determination of a concentration fre-
quency distribution is that of determining just the long-term average value
over some specified period—usuafly a month, season, or year. Although this
can obviously be obtained in calculations of the type just considered, much
simplification is possible when interest is restricted to average values. This
simplification is achieved by a change in the order of integration and summa-
tion, In the previous consideration of an aggregate of 1800 possible meteoro-
logical situations corresponding to wind directions Oj (i = 1-2,3, ., ,36), wind
speeds, Uj dx0dy0	45)
"~00	"CO
so that C is now expressed as a single integral that would have to be
evaluated numerically, Although the sum in Equation (4) apparently involves
4-3
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1800 terms, considerable simplification arises from the physically obvious fact
that, for a given source-receptor pair, it is only a limited range of wind
directions that realty contributes to the concentration at the receptor. For
example, Meade and Pasquill,14 in their paper analyzing the average dis-
tribution of S02 pollution around Staythorpe power station in England,
have shown that, with the assumption of a Gaussian type concentration
distribution given by Equation (1), the average concentration at a receptor,
produced by a fixed-point source and corresponding to all possible wind
directions, can be approximated by a simple analytic formula. This actually
involves only the wind direction frequency for the single wind sector (10
degrees in our example) that contains the source-receptor direction. In this
case, the sum in Equation (4) would reduce to a double sum extending over
all combinations of wind speed and stability category and would involve
only 10 x 5 = 50 terms.
Multiple-source urban pollution models that essentially utilize this simplifica-
tion and provide estimates of long-term average concentrations have been
proposed by Pooler10 and, more recently, Martin and Tikvart.15 The Pooler
model mentioned previously for the average monthly S02 concentrations at
Nashville, Tennessee, is an example for which sampling data from an exten-
sive air pollution study were available. Pooler disregarded atmospheric
stability changes and, in effect, considered only a single stability category.
The meteorological frequency function only involved consideration of wind
direction and wind speed and was obtained from monthly summaries of
hourly observations at the airport. In addition, the Pooler model assumed no
limitation of vertical diffusion, i.e., the mixing height, L = °°. The source
inventory was based on 1-mile-square areas; then, for each receptor location
in the numerical integration over the entire urban area, each square (with a
single exceptional case) was replaced by a point source at its center. A
reasonably close agreement was obtained between calculated and observed
patterns of average monthly S02 concentrations.
The model proposed by Martin and Tikvart1 s differs only in its details and
actually incorporates the simple Meade-Pasquill averaging formula. The mete-
orological frequency function involved the additional variable of stability
category, S, and was thus established in terms of an array of 480 possible
meteorological combinations from the long-term records of hourly meteoro-
logical observations that are normally available from Weather Bureau sta-
tions. A difficulty arising here is that the long-term records refer to airport
locations and not to the nearby urban area that is of primary interest. In
addition, a finite mixing height, L, was assumed, and a crude procedure
proposed in an attempt to reflect the functions major diurnal changes. The
calculations for both the above models become so extensive that they re-
quire the use of a high-speed computer. This is so in spite of the drastic
mathematical approximations that have been adopted in order to simplify
numerical evaluation of the surface integrals involved.
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Instantaneous Gaussian Puffs Approach
The preceding models are all based on the postulated equivalence of the
general long-term variable situation to a sequence of different quasi-steady
states. This assumption allows model development in terms of the relatively
simple steady-state concentration formula of Equation (1). To more accu-
rately portray the general nonsteady-state situation, it will be necessary to
regard the pollution emission from any point source as resulting in a series
of "instantaneous puffs" that may follow different trajectories and have
different rates of diffusion. Such a basis for a more general type of urban
diffusion model in cases where meteorological conditions could not be re-
garded as constant and uniform for the whole urban area was explicitly
indicated by Frenkiel16 in his now classic paper. Such a modeling procedure
implies the ability to specify separately the trajectory in space of every puff
center and the puff concentration distribution at any time relative to the
puff center. A sophisticated urban pollution model of this character, based
on the assumption of a three-dimensional Gaussian distribution of concen-
tration in the individual instantaneous puffs, was recently proposed by the
late Professor Ben Davidson17 and his associates at New York University.
The Gaussian puff approach has also been applied by Start and Markee18 to
the calculation of average concentrations resulting from a prolonged point-
source release of pollution in a valley where the winds underwent a marked
diurnal cycling. Start and Markee also indicated the potential application of
their model to urban air pollution problems. A further detailed application
of the Gaussian puff concept to urban pollution modeling has been made
recently at the Argonne National Laboratory under a contract supported by
the National Air Pollution Control Administration, and a paper on this work
is to be presented at this symposium. Models that utilize the Gaussian instan-
taneous puff rather than the steady-state Gaussian plume distribution of the
continuous point source obviously possess greater flexibility and may well
mark the advent of the second generation of urban air pollution models.
Increased flexibility is, of course, only bought at the price of the very
sophisticated knowledge required to predict, for an urban environment, both
the trajectories in space and the diffusive spreading of the individual puffs.
In principle, the important meteorological situation corresponding to the
"calm" wind condition, which approximates the situation frequently encoun-
tered in episodes of high urban air pollution, could be discussed in terms of
the Gaussian puff-type model. This is not possible in terms of the Gaussian
plume of Equation (1), for which wind speed U = 0 represents a degenerate
case.
SOME MISCELLANEOUS QUESTIONS
Prediction Limitations
The preceding discussion may have pointed to some of the difficulties of
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urban pollution modeling. In the past, most theoretical attempts to model
the diffusive conditions in an urban environment have been based simply on
a judicious adjustment—guided perhaps by a few ad hoc tracer experiments—
of our knowledge of what happens in the much simpler situation over open,
level country. Nevertheless, a reasonable agreement has been obtained be-
tween the predicted and observed concentration values in a number of dif-
ferent comparisons. In view of the somewhat tenuous nature of the physical
basis of these models, however, it should be emphasized that they need to
be applied with proper caution and, where possible, only by professional
meteorologists fully conversant with the practical aspects of urban atmos-
pheric diffusion. In a slightly different connection, this point has been
emphasized by Scorer19, who says: "There are NO universal formulae which
can be used to describe what will happen to pollution emitted into the air,
and this needs to be said because formulae have been so misused in the past
by people who have been secretly frightened of realities and have dispensed
according to the prescription of the most fashionable wizard. Responsibilities
cannot be so easily shed. Pollution problems are certainly local, almost per-
sonal/' It seems, however, to be a point worth reemphasizing, particularly in
view of the current urgent demands for urban models to provide a quanti-
tative basis for a variety of critical management decisions relating to urban
air quality. It seems likely that any major improvement beyond the present
somewhat empirical approach to urban diffusion modeling wilt require a
much improved understanding of the dynamics and thermal structure of the
continuously developing urban boundary layer. Detailed observational studies
of the structure of the urban boundary layer of the type described recently
by Clarke and McElroy20 may provide the basis for such understanding. In
any case, it should be evident that present models are based on some ideal
assumptions and that considerable departures from the model predictions can
be anticipated in the presence of any special local phenomena such as lake
breezes and mountain-valley effects.
Parametric Sensitivity Analysis
In spite of the conceptual simplicity of the urban pollution models that have
been discussed, the superposition of the effects produced by a large number
of pollutant souces and their evaluation for complex sequences of meteoro-
logical conditions involves such large computational effort that, in most
cases, it can only be handled with a high-speed computer. Under these cir-
cumstances, the more general features of the models may be obscured by the
massive details of particular applications. At the present time, there appears
to be a real need to study the sensitivity of the concentration predictions to
variations in inputs to the models. In some cases, large variations in input
may have little effect on output. With others, the reverse may be true. It,
therefore, appears desirable to conduct a sensitivity analysis for some of the
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current models in order to identify the sensitive parameters and the condi-
tions under which they are sensitive.
Two typical questions that come to mind, on which a sensitivity analysis
would throw some light, relate to the degree of accuracy and detail that is
necessary for an urban pollutant emission inventory, and the accuracy re-
quired to specify the concentration field corresponding to a single source.
Ad hoc tracer diffusion experiments in cities, of the type described by
McElroy and Pooler,7 are difficult and expensive to perform. Since they
must, to some extent, reflect localized conditions, they may not add signifi-
cantly to the predictive accuracy of the model in general urban situations
after a certain stage of specification is reached.
The sensitivity analysis is also valuable from a rather different point of view.
Because it is not very difficult to identify a large number of the possible
sources of error and unrealistic simplifications in existing models, in a quali-
tative way, there is a temptation to make rather arbitrary and simple adjust-
ment for these in order to improve the agreement between computed and
observed concentrations. This can be a dangerous procedure because, until a
good understanding of the response of the model to its many inputs exists,
there can be no guarantee that the adjustments necessarily reflect a real
expression of improved physical understanding. Thus the apparently improved
agreement could be fortuitous. In the above sense, some recently proposed
models may already be over-complicated. We mention here the recent
notable revelation by Dr. Frank Gifford of NOAA Atmospheric Turbulence
and Diffusion Laboratory at Oak Ridge, that, at least for the calculation of
isopleths of annual-average air quality in terms of a typical urban source
inventory, the calculations can be organized and simplified to such an extent
that they can be carried out quickly and easily by hand.
Of those models for which accounts have appeared in the open literature,
the only other one specifically developed in a simple enough form to permit
calculation from a source inventory without the aid of an electric computer,
is that of Clarke.21 At a time when computer-based models can be expected
to proliferate rapidly, Dr. Gifford's recent success can serve as a reminder
that simple models should not be overlooked since they might still be of
great value.
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REFERENCES
1.	Stem, A. C, (ed.), Air Pollution. Vol. 1, 2d ed. New York, Academic Press, 1968.
694 p,
2.	Turner, D. B. Workbook of Atmospheric Dispersion Estimates—Past, Present, and
Future. Presented at meeting of Mid-Atlantic State Section of the Air Pollution
Control Association. Philadelphia, APCA 9946. June 1969. 17 p.
3.	Moses, H. Mathematical Urban Air Pollution Models. National Center for Air Pollu-
tion Control, Chicago Dept. of Air Pollution, Argonne National Laboratory.
Argonne, III. AIML/ES-RPY-001. April 1969. 69 p.
4.	Pasquill, F. The Estimation of the Dispersion of Windborne Material Meteorol. Mag.
30(10631:33-49 February 1961.
5.	Turner, D. B. A Diffusion Model for an Urban Area. J. Appl. Meteorol. 3(1):83-91,
February 1964.
6.	Pasquill, F. Atmospheric Diffusion. London, D. Van Nostrand Co. Ltd., 1962.
297 p.
7.	McElroy, J. L. and F. Pooler, Jr. St. Louis Dispersion Study, Volume II — Analysis.
National Air Pollution Control Administration. Arlington, Va. Publication Number
AP-53. December 1968. 51 p.
8.	McElroy, J. L. A Comparative Study of Urban Rural Dispersion. J. Appl. Meteorol,
8( 1): 19-31, February 1969.
9.	Briggs, G. A. Plume Riser A Critical Survey. Air Resources Atmospheric Turbulence
and Diffusion Laboratory, Oak Ridge, Tenn. U. S. Atomic Energy Commission,
Division of Technical Information. USAEC Critical Review Series. Publication
Number TID-25075. 1969. 81 p.
10.	Pooler, F., Jr. A Prediction Model of Mean Urban Pollution for Use with Standard
Wind Rose. Int. J. Air Water Pollution. 4(3/4): 199-211, September 1961.
11.	Turner, D. B. The Diurnal and Day-to-Day Variations of Fuel Usage for Space
Heating in St. Louis, Missouri, Atmos. Environ. 2:339-351, July 1968.
12.	Fortak, H, G. Rechneriscbe Ermittlung der SO2 — Grundbelastlung aus Emissions-
daten — Anwendung auf die Verhaltnisse des Stadtgebietes von Bremen. Institute
for Theoretical Meteorology. The Free University of Berlin. 1966.
13.	Larsen, R. I. A New Mathematical Model of Air Pollutant Concentration Averaging
Time and Frequency. J. Air Pollution Control Assoc. 7.9:24-30, January 1969.
14.	Meade, P. J. and F. Pasquill. Study of Average Distribution of Pollution Around
Staythorpe. Int. J. Air Pollution. 7(1-21:60-70, October 1958.
15.	Martin, O. O. and J. A. Tikvart. A General Atmospheric Diffusion Model for
Estimating the Effects of One or More Sources. Presented at 61st Annual Meeting
of the Air Pollution Control Association, APCA-68-148. St. Paul. June 1968. 15 p.
16.	Frenkiel, F. N. Atmospheric Pollution and Zoning in an Urban Area. Sci. Monthly.
52:194-203, April 1956.
17.	Davidson, B. A Summary of the New York Urban Air Pollution Dynamics Research
Program. J. Air Pollution Control Assoc. 77:154-158, March 1967.
18.	Start, G. E. and E. H. Markee, Jr. Relative Dose Factors from Long-Period Point
Source Emissions of Atmospheric Pollutants. In: Proceedings of the USAEC Me-
teorological Information Meeting, Chalk River Nuclear Laboratories, September
11-14, 1967, Mawson, C. A. (ed,). Atomic Energy of Canada, Ltd. Chalk River,
Ontario. Report Number AECL-2787. 1967. p. 59-76.
19.	Scorer, R. S. Air Pollution. New York, Pergamon Press, Inc. 1968. 151 p.
20.	Clarke, J. F. and J. L. McElroy. Experimental Studies of the Nocturnal Urban
Boundary Layer. In: Proceedings of WMO Symposium on Urban Climates and
Building Climatology, Brussels, Belgium, October 15-25, 1968.
21.	Clarke, J. F. A Simple Diffusion Model for Calculating Point Concentrations from
Multiple Sources. J. Air Pollution Control Assoc. 74/347-352, September 1964.
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5. A PRACTICAL MODEL FOR CARBON MONOXIDE
ABSTRACT
This paper reports our progress in the development of essentially two
different types of diffusion models for carbon monoxide (CO):(1)a
"synoptic" model, which calculates hour-to-hour concentrations, for
vertification studies and possible operational use, and (2)a "climato-
logical" model, which calculates arithmetic mean concentrations and
frequencies of extreme concentrations, for planning use. The design of
these two models, as well as the results of limited evaluation trials of
an early version of the synoptic model are described.
The synoptic model design is based upon a modification of Clark's1
receptor-oriented model, and emphasizes practicality, generality and
completeness. The present version of the model includes provision for
handling extra-urban as well as intra-urban sources. In addition, a
"street submodel" is being developed. Based largely upon experimental
work, it converts the intra-urban background to street-level concen-
trations. When incorporated, this should substantially improve the
agreement between calculated and observed values at the Continuous
Air Monitoring Projects (CAMP) Stations.
The climatological model is similar in basic form to the synoptic model
but uses the joint frequency function for all combinations of specified
classes of the input parameters, derived from a large body of hourly
meteorological data. The arithmetic mean concentration thus obtained
is then used in statistical relationships, derived by Larsen2 from carbon
monoxide (CO) concentration data, to calculate the magnitude of
high-percentile and maximum concentrations for any averaging time.
Alternately, such calculations can be performed directly using die
predicted concentration joint frequency function.
Implementation of the model required the development of an objective
technique for converting traffic data to a time- and space-dependent
CO emission inventory, as well as methods for estimation of die
meteorological variables appropriate to the urban area from routinely
available (airport) weather data. The accuracy of these methods effec-
tively establishes an upper limit to the model prediction accuracy.
Sample computed area-wide concentration patterns and time-varying
point concentrations for St. Louis and Washington, D.C., are presented.
As expected, the preliminary calculated concentrations are, for the
most part, lower than those observed at the CAMP Stations, reflecting
the need for incorporation of the street submodel into the program.
The need for better treatment of light-wind conditions is also indicated
by these evaluation trials; possible improvements are discussed.
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AUTHORS
WARREN ft JOHNSONJR., Manager of Environmental Meteorology Program, at
SRI received a 8.S. degree in electrical engineering from Texas A&M in 1957 and
M.S. and Ph.D. degress in meteorology from the University of Wisconsin in 1962
and 1965. At the University of Wisconsin, under Professor H. H. Lettau and
subsequently at ESSA's Atmospheric Turbulence and Diffusion Laboratory in Oak
Ridge, Tennessee, Dr. Johnson studied atmospheric boundary layer problems. At
SRI, he has been developing Hdar {laser radarf techniques for studying the behavior
of pollutants in the atmosphere.
FRANCIS L. LUDWG, Meteorologist, Environmental Research Department, at
SRf received B.A. and M.A. degrees in meteorology from UCLA in 1957 and
1958, respectively. While at UCLA he participated in studies of Los Angeles air
pollution problems. Since coming to SRI in 1959, Mr. Ludwig's interest has
centered on atmospheric aerosols and urban meteorology.
ALBERT E. MOON, Senior Operations Analyst, Management Systems Division,
at SRI received B.S. and M.S. degrees from the University of Texas in 1951 and
1952. He worked on the design of electrical and electronic control systems. He
received a degree of Master of Business Administration from the Harvard Grad-
uate School of Business Administration, in 1964 shortly before joining Stanford
Research Institute. Since that time, he has evaluated public and private invest-
ments, including benefit-cost of mass transit systems in Los Angeles and San
Mateo County, California.
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5. DEVELOPMENT OF A PRACTICAL,
MULTIPURPOSE URBAN DIFFUSION MODEL
FOR CARBON MONOXIDE
WARREN B. JOHNSON, F. L. LUDWIG, AND ALBERT E. MOON
STANFORD RESEARCH INSTITUTE
INTRODUCTION
Scope and Objectives
There is a need for an objective, practical method of simulating the current
and future impact of motor vehicles upon air pollution in urban communi-
ties. Such a technique could be used to assess the characteristics of current
concentration patterns of primary vehicular pollutants in cities, as well as to
predict the effects of exhaust emission controls and expressway routings
upon future concentration distributions. We are currently engaged in the
development of a simulation model of this nature, and this paper reviews our
progress midway through the first year's effort. In this task, we have been
aided considerably by previous urban diffusion modeling studies, which have
been aptly reviewed and summarized by Wanta,3 Stern,4 Moses,5 and
Neiburger.6 An investigation of carbon monoxide (CO) diffusion in Washing-
ton, D.C., by Ott et a!.1 could be considered a prototype for our study.
For simplicity, this initial modeling effort is restricted to CO, since (1) the
gas is relatively inert in the atmosphere with no known significant natural
sources or sinks in urban areas/ (2) motor vehicles are known to furnish
large percentages of the CO in urban air (discussed in a subsequent section
of this paper), and (3) CO is believed to be an important pollutant in terms
of health effects. Later, it is planned to extend the model developed for CO
to piiotoreactive, automobile-generated pollutants.
*Research sponsored by the Coordinating Research Council and the National Air Pollution
Control Administration (Division of Meteorology).
tEvidence is mounting, however, that such sources and sinks may be found in the bio-
sphere (Swinnerton,® Went,® and Robinson and Robbins.10).
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Our goal is to develop a versatile model that can predict both urban back-
ground and street-level CO concentrations at any point within a city. Cal-
culations of the following types are required:
1.	Hourly concentrations as a function of time, for verification, use, and
possible operational applications (with the "synoptic" model).
2.	Long-term average concentrations and statistical predictions of high (and
maximum} concentrations for planning purposes (with the "climato-
logical" model).
We are aiming to complete a practical model that is convenient to use,
economical to run, generally applicable to most cities, and, of course, ac-
curate. To achieve the latter, we are attempting to develop capabilities for
assessing concentration contributions resulting from diffusion on various
scales, including the treatment of:
1.	Extra-urban transport and diffusion, mainly from upwind cities.
2.	General intra urban diffusion from arterial and feeder streets.
3.	Local (microscale) diffusion within streets.
Fundamental Concepts and Assumptions
Our basic approach has been to develop individual components of the model,
and then to arrange these components into submodels, which can be appro-
priately combined to suit particular needs. This procedure affords maximum
flexibility.
Other key elements in our rationale have been to
1.	Bring the best features of previous efforts together into a single model.
2.	Maintain simplicity until additional complexity is shown to be clearly
required to achieve greater accuracy, and is justified by the accuracy of
model inputs,
3.	Strike an appropriate balance between the complexity of the model and
the computing costs (program running time).
Input data requirements for the model include two major types, traffic and
meteorological. For the synoptic model, it is necessary to assume that diur-
nally adjusted, average daily traffic data (which are all that are available on a
network basis) are compatible with hour-to-hour (synoptic) meteorological
data.
EMISSION INVENTORY DESIGN
Introduction
Estimates of vehicular emission of carbon monoxide range from 98 percent of
the total for the Washington, D.C., area1 1 and 91 percent in Los Angeles,1 2 to
75 percent in the San Francisco Bay region.13 (The latter estimate is for
automobiles only.) Hence, the principal effort thus far (discussed in
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detail below) has been to model the mobile sources. Significant fixed
sources, such as airports, will later be included in the emission inventory.
The inventory of motor-vehicle CO emissions is represented as a primary
network of the major arterial streets and freeway links, plus a secondary
background of emission from vehicles on the many local streets that are not
included in the primary network.
Two kinds of data are used for the emissions inventory, (1) historical data,
to re-create past conditions for comparison with recorded concentration
measurements for model verification; and (2) forecast data, to estimate
future concentrations.
Calculation of Primary Traffic Network Emissions Using
Historical Data
Figure 5-1 illustrates the primary network used in the Washington, D.C.,
area.* The amount of travel on the major network is in excess of 90 percent
of the total travel in the metropolitan area. Emission from each straight
segment, or link, of the network is determined from the emission per
vehicle-mile and the number of vehicle-miles traveled on the link.
CO emission, e (grams per vehicle-mile), is determined from the equation
e - c/Sp	(1)
where S is the average speed over the link, in miles per hour (mi hr-1), and c
and 0 are constants. For vehicles in use before exhaust control systems were
used, c = 103 and (3 = 0.8, as determined by Rose et al.14 from observations
on vehicles in several locations. For conditions where a majority of vehicles
have exhaust-control devices, alternative values will be used for the coeffi-
cients.
To define the network and compute the emissions, the following input data
are needed:
•	Network description
•	Node coordinates
•	Link distances
•	Link volumes
•	Link speeds
Historical data for the network description, the node coordinates, and
the 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
•Computer-generated displays of this nature are very useful for examining the accuracy of
the coding of the traffic links.
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the network. Link distances are measured along the links, rather than as the
shortest distance between the nodes, although the assignment of the emis-
sions assumes that the link is a straight line between the nodes.
Figure 6-1. Computer-generated display of traffic links in 24-by
24 mile central portion of primary network for Washington, D. C.
Historical link-volume data are obtained from traffic departments in the
cities, towns, and counties of the region being studied. These agencies sample
traffic volumes by means of portable counting units and a few fixed
installations. The frequency of their observations may vary from almost
continuously to as infrequently as once in two or three years. Because traffic
varies according to seasonal, weekly, and daily cycles, an observation of
volume for one day must be adjusted for the weekly and seasonal fluctua-
tions. The resultant corrected value is recorded as the average daily traffic
(ADT) for that location.
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For use in the synoptic model, the emissions must be expressed in hourly
averages, so the average daily traffic must be allocated among the hours of
the day. Allocation can be accomplished using data on the hourly distribu-
tion of trips, which are compiled by the traffic study agencies of many
areas. A typical diurnal pattern of trips is shown in Figure 5-2. 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
o.
tc
y-
>-
_j
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Figure 5-3. Hourly distribution of traffic for two facility types
in St. Louis.50
different times from different source locations affect the concentration at a
given time at a given receptor point. For example, with a 2-m sec"1 wind,
the average concentration at a receptor point from, say, 0800 to 0900 Local
Standard Time (LST) will result from emissions generated in the hour from
0700 to 0800 at a location 7.2 km upwind, and from 0600 to 0700 at a
location 14.4 km upwind, and so on. A computational loop in the model
uses wind speed to determine the displacement in time needed for each
emission computation.
Link speeds for historical data are determined by using averages for peak and
off-peak travel hours on the various kinds of route facilities in the area. Data
for the average speeds are obtained from the traffic survey. Speeds used in
the Washington, D.C. area were based upon the study by W. Smith and
Assoc.1 6 shown in Table 5-1.
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
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Table 5-1. AVERAGE SPEEDS FOR WASHINGTON, D.C., HIGHWAY FACILITIES
(mi hr-11
Facility type
Peak traffic hours
(0700 to 0900, 1600 to 1800)
Off-peak traffic hours
(0000 to 0700, 0900 to 1500,
1800 to 0000)
Suburban freeway
42
48
Downtown freeway
33
39
Suburban arterial
30
36
Downtown arterial
24
30
Local or feeder street
10
12
monitored most often, greatest confidence can be placed in data with highest
volumes. In addition, very few data are available for Saturdays and Sundays,
since traffic planners are concerned with recording peak demands, and peak
demands on streets usually occur on weekdays. This lack of data impedes
efforts to run weekly cycles, however, because peak traffic usually occurs on
weekdays, peak pollution concentrations from motor-vehicle emissions also
usually occur on weekdays.
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 distributed over the study area by
estimating the relative density of local streets as opposed to parks, open
spaces, and primary streets, for each 4-square-mile area in a 2-mile by 2-mile
grid covering the area. The average emission from the local street travel in
each square is then assumed to emanate uniformly from that square. Al-
though the emission per mile is high because of low speeds, the overall
contribution is small because of the small fraction of the total area travel
that is carried out on these local streets.
Calculation of Future 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 demands and transporta-
tion facility needs for a specific future. Such studies are required for par-
ticipation in Federal highway programs. Two important outgrowths of these
studies are: (1) a design for a future traffic network for the area and (2) a
forecast of the traffic volumes on the links of the network. The procedure
for conducting these investigations has been highly developed and partially
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standardized. We are designing the emission inventory components of the
model so that the magnetic tape form of network description, link volume,
and link speed data, of widely used traffic-planning computer programs can
serve as input for the diffusion model. In most cases, the only manual step
required will be the measurement and coding of node coordinates for the
network.
Accuracy of the forecast data is difficult to establish. One study that sought
to appraise the accuracy of earlier forecasts was unsuccessful in finding a
case where the planning recommendations had been followed closely enough
to make the actual situation equivalent to the conditions that were fore-
cast.' 6 Checks made to establish the adequacy of calibration of the fore-
casting 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 with-
in the corridor may be much wider since the models do not distinguish
between parallel routes as readily as do drivers.
INTRA URBAN TRANSPORT AND DIFFUSION SUBMODEL
Spatial Partitioning of Emissions
Our diffusion model is a modified form of the receptor-oriented model de-
veloped by Clarke.1 As shown in Figure 5-4, we use logarithmic spacing of
the area segment boundaries to permit more precise location assignment for
RECEPTOR
POINT
EXPANDED VIEW OF
ANNULAR SEGMENTS
WITHIN 1 km OF
RECEPTOR
TB-7874-ls
Figure 5-4. Diffusion model area-source configuration.
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emissions near the receptor and to tend to equalize the contributions from
each segment to the concentration at the receptor point. The closest segment
extends from the receptor to 125 meters, roughly comparable to the size of
a city block, while the farthest segment extends to 32 kilometers, approxi-
mately the diameter of a large city.
The 22.5° sector width is convenient and fits reasonably well the angular
plume widths {between ±2a points), predicted by Gifford's17 model, for
slightly unstable conditions. The sector width is expanded to 45° within the
closest 1 kilometer to allow for the large initial lateral dispersion observed
during the St. Louis tracer studies.1 8,19
Emissions from the line sources (links) in the traffic network are assigned to
one of the nine area-segments as shown by Figure 5-5. To simplify these
computations, the segment boundaries are taken as straight-line fits to the
curved boundaries illustrated in Figure 5-4. The computations transform the
rectangular node coordinates into polar coordinates originating at the recep-
tor points and then determine whether all or part of a link falls within a
given segment. The link is assumed to be a straight line connecting the
nodes. Where part of the link is within a segment, an equivalent fraction of
the link emission is included in the computation. The total emission within
TA-7874-4*
Figure 5-5. Schematic of traffic link assignment subroutine.
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each segment is assumed to be uniformly distributed and consists of the
total emission from all the links and parts of links that lie within that
segment, plus the secondary traffic emission in the segment.
As previously discussed in this paper, the secondary traffic emission is
described in a 2-mile-square grid system. The values at the centers of the
squares represent the average emissions over the squares. The secondary
emission assigned to each segment in the diffusion model is computed by
locating the center of the area segment, then interpolating among the four
adjacent secondary emission grid centers. The value thus determined at the
center of the segment is assumed to prevail over the entire segment.
The contributions of each area segment to the concentration at the receptor
point are computed separately and then totaled. The calculation of pollutant
concentrations from each of these individual segments is based on a com-
bination of two simple mathematical models, the Gaussian and the "box." A
similar approach has been employed by Miller and Hol2worth.20
Basic Gaussian Model
Gifford1 7 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, for the ground-level concentration, the
equation is
C = ¥0% u exP (-V2f2°y)	{2]
where
C = ground-level concentration (g m~3l
Q = source strength (g sec-1 )
u = average wind speed (m sec"1)
y = lateral {crosswtnd] distance from the plume axis (m)
°y> °z< = lateral and vertical standard deviations of plume concentration
(m); these parameters are functions of source-receptor distance
and atmospheric stability.
This equation takes the following basic form for ground-level concentrations
emitted from a ground-level line source:
2^ 1,2
C = 0L [f) (uo,r'	(31
In this formulation QL has the units g rrT' sec-1
Estimates of o2 as a function of atmospheric stability and pollutant travel
distance or time have been proposed by Gifford1 7 and Smith and Singer,21
and urban observations of this type have been reported by Pooler'8 and
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McElroy.19 At present, we are using Gifford's* values, but the model is
flexible and can use any set of functions that can be reasonably approxi-
mated, over the intervals between segment boundaries, with expressions of
the form:
Where r is the travel distance, the subscript i refers to annular segments
upwind of the receptor point (see Figure 5-4), and j refers to the stability
classes. The oz functions are, thus approximated by a series of power
functions, each appropriate to some upwind distance interval and stability
class. This allows us to select different representations for different distances,
if we choose. Short ranges, in particular, may require special treatment to
account for the initial rapid mechanical mixing found in urban areas.18'19
We are testing two ways of handling this initial dispersion: (1) adding 25
meters to oz over all distances, as suggested by Pooler1 8 and by McElroy;1 9
and (2) using a value of oz throughout the closest segment corresponding to
Gifford's values at a distance of 125 meters.
Substituting Equation (4) into the line-source equation and integrating with
respect to r from r = r( to r = ri+1 gives the contribution for stability class j
from the /th segment area source GA:
where rj and ri + 1 are, respectively, the distance to the downwind and
upwind boundaries of the /th segment. In this expression GA has the units (g
m"2 sec-1). 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.
Transition from Gaussian to Box Model
When the layer into which the pollutants are being dispersed is restricted,
they will tend to become uniformly mixed at a sufficient distance from the
source. Under these conditions, the box model is used. The concentration
arising from the uniform area source in the /th annular segment is
where h is the depth of the layer into which the pollutants are mixed.
"Gifford's work is a modification of that by F, Pasquill (unpublished) and Meade11 The
Gifford-Pasquill curves are based upon data from open country, and probably under-
estimate the diffusion in urban areas. We are examining possible improvements on this
point.
oz = aVl r
(4)
b«j 1 (5)
(6)
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We have chosen to change from the Gaussian model to the box model at
that point where the two equations (in their respective line source formula-
tions) give equal concentration values. The distance to that point, rT, is
given by:
The part of the annular segment inside rT is treated according to the
Gaussian model, and the part that is outside, according to the box model.
For this application rT is substituted for ri + 1 in the Gaussian equation and
for rj in the box equation.
Determination of Model Inputs
The model requires meteorological inputs of mixing depth, stability, and
wind speed and direction. At present, the model uses winds observed at the
nearest airport. Central urban daytime wind speeds above the buildings are
known to be on the order of 30 to 40 percent less than airport speeds, and
a correction for this effect is planned, but not yet incorporated into the
computations.
The case of calm winds cannot be handled by the model without some
adjustment. At present, the model assumes that a wind that is reported as
calm has a speed of 2.0 m sec-1 and that its direction is the same as the
most recently measured direction. Other approaches to this problem are
possible, but they require special models to be developed for the calm-wind
case, as will be discussed later.
The stability and the mixing depth are not directly measured quantities and
require estimation methods. We are using Turner's23 criteria for determining
stability from routinely available data. This procedure estimates the stability
class on the basis of cloud cover, ceiling height, wind speed, and solar eleva-
tion. The stability class is used to select the Gifford-Pasquill oz function.
Following Turner, we are using five stability classes ranging from "very
unstable" (Class 1) to "slightly stable" (Class 5}, eliminating the "stable"
and "very stable" classes. These conditions are known to occur very seldom
over cities because of the heat-island effect. Mixing depth over the urban
area is determined for nighttime cases from Summers'24 simple model of the
urban heat island and from an empirical relationship involving heat island
intensity, city population, and low-level rural (airport) lapse rate, as dis-
cussed in detail in Appendix A.
Afternoon mixing depth is determined from the height of intersection of the
morning sounding and the dry adiabat passing through the maximum tem-
perature for the day. Other daytime values are interpolated on the basis of
the observed hourly temperatures (see Appendix). The model currently uses
a uniform mixing depth throughout the area.
1/b.j
(7)
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Model Limitations and Prospective Refinements
The simple model that has been outlined here has a number of limitations.
Refinements are possible, but one must first determine whether such refine-
ments are warranted in view of the limitations of the available meteoro-
logical and traffic data in terms of accuracy and representativeness. In
addition, the increased prediction accuracy must be worth any additional
computing costs. We are currently considering several potential model refine-
ments in this context.
Suitability of Input Parameters
The model currently takes the airport wind speed to apply over the entire
urban area. We plan to adjust this value to give a more realistic wind speed
over the city. Graham25 found an urban/rural average wind speed ratio for
Ft. Wayne of 0.67 at 15 meters height and 0.64 at 60 meters. In Nashville,
Schnelle et al.2b found the roof-level wind speed, Ur, to be related to the
airport wind speed, Ua, as
Ur = 0.33 Ua + 1.0 m sec-1
where the overbars refer to daily averages. Graham's observations also show
the wind direction over the city to be backed by 10° to 15° from that at
the outskirts, which could also warrant a correction to the airport data.
These results are mostly for daytime conditions. At night the wind speed
over the city may be higher than that at the airport.
Incorporation of nonuniform meteorological parameters over the city would
be more complex. Spatial variations in nocturnal mixing depth have been
observed by Clarke57 in Cincinnati, and Bornstein28 in New York, and
modeled in limited fashion by Summers24 and Leahey,29 The desirability of
inclusion of such effects is under study. Efforts are also being made to
improve the form of the traffic data to include (1) diurnal volume patterns
for each road type, and (2) weekend data.
Nonsteady Conditions
The steady-state nature of the model is a more important limitation. The
reasonably uniform spatial distribution of the traffic network, however, helps
to offset this situation. Wind direction changes from hour to hour are
included simply by switching to a new diffusion sector in the model, which
serves reasonably well for strong winds on the order of 30 km hr_1, or 8 m
s""1 (the diffusion sector extends to 32 km). A special feature of the model
accounts for the finite travel time of emissions under light wind conditions
(see page 5-2), but no provision is made for directional changes in trajec-
tories, as observed by Angell et a/.30 and Hassetal.31 from tetroon flights.
We are considering a modification that would calculate the contribution of
5-13
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each previous hour's emission to the concentration at the receptor for a
given hour, and would accommodate wind directional changes by relocating
the apparent receptor point and diffusion sector with respect to the traffic
network.
The Stagnation Case
The most important pollution situation, the stagnation with very light winds,
is virtually impossible to treat with our present model. The nocturnal urban
circulation for this case has been reasonably well documented32'33 and
takes the form of a convective cell driven by the urban heat island. One
approach that we are considering for night hours involves treatment of the
circulation as that of a height-limited, ground-based "thermal" or vortex
ring, symmetrically oriented over the urban area. The wind field would be
taken as convergent toward the center of the city. Allowing for recirculation,
a time-dependent concentration distribution would be calculated by means
of a cylindrical version of the box model (which might be called a "pan"
model). A critical parameter would be the entrainment rate for clean air at
the top and circumference of the "pan," which might be estimated on the
basis of convection theory.34'35 A more realistic treatment would allow
superposition of this circulation upon a weak gradient flow, giving the
buoyant heat plume observed by Clarke.27
DIFFUSION SUBMODELS FOR OTHER SCALES
Microscale (Street) Diffusion
Because of the finite spacing of sources within a city, area source simulation
such as is used in the intra-urban 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 125 m as the finest resolution
in the intra-urban 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 usually located near streets. For example, the model used
by Ott eta/.1 gave average concentrations that amounted to 36 percent of
the CAMP average.
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A "street submodel" that can be used to calculate curbside CO concentra-
tions is currently under development. The effort thus far has been based
largely upon the extensive measurements of Georgii36 in Frankfurt/Main,
Germany, although the work of McCormick and Xintaras,37 Schnelle et
aI.,26 and Rouse38 have also been considered.
Georgii's experiment involved extensive measurements of CO concentrations
and wind speeds at different levels above three different streets in built-up
areas, along with occasional traffic counts. One 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 rooftop wind
speed exceeds about 2 m sec1, and (3) the concentrations are exponentially
related to traffic density. Examination of the measurements reported by
Schnelle et a/.26 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 concentrations calculated
by the intra-urban model are approximately equivalent to roof-level concen-
trations. The effect of the street is to increase incoming roof-level con-
centrations 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.
Georgii's averaged data for a traffic density of 1400 vehicles per hour {the
mean traffic density during his experiment) are well approximated by the
empirical relationships
C
— = exp [(0.55) (1 - z/zj]
Cr
c.
	 = exp [(0.87 + 0.098 ur) (1 - z/zr)],	(8)
Cr
where Cw and CL are concentrations on the windward and leeward sides of
the street-side buildings,
Cr =	rooftop concentration (g rrf3)
ur =	rooftop wind speed (m sec-1)
zr =	average rooftop height (m), and
z =	receptor height (m).
5-15
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The windward concentration ratio (Cw/Cr) turns out to be approximately
independent of wind speed. This is apparently because the wind effect at
this more exposed location is mostly absorbed by changes in Cr. On the
leeward side, the concentration ratio increases with increasing wind speed,
reflecting the relatively greater effect of sheltering at street level as the wind
increases.
Although changes in traffic density, thus emission rate, in the adjacent street
are not reflected directly in these equations, some justification for their
application exists if it is assumed that the local traffic at a given time is
always proportional to that in the city as a whole. For this case, the traffic
changes will be reflected in the rooftop concentration, Cr, calculated by the
intra-urban model, and hence, in Cw and CL.
An additional problem in applying the above empirical results is that of
defining leeward and windward cases on the basis of receptor location, street
orientation, and wind direction. The problem is compounded further when
the receptor is located at the corner of a street intersection, as is frequently
the case with CAMP stations, tn addition, in the vicinity of many inter-
sections are buildings with widely varying heights, as well as open spaces
such as parking lots. These complications make it difficult to apply the
empirical relationships on a general basis. Additional work is necessary
before treatment of microscale effects is incorporated into the model.
Macroscale (Extra-urban) Diffusion
In addition to considering sources in the immediate urban area, the model
also takes into account the background pollution that is transported from
one urban area to another. We have accepted, a priori, that the treatment of
extra-urban transport can and should be considerably more gross than the
treatment of nearby sources.
The first problem to be faced in the development of an extra-urban 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. The latter approach
seems more practical, particularly if we ever hope to apply the model to
climatological data. Even the synoptic problem of trajectory determination
by objective means seems too complicated to be warranted.
We apply the box model to a quadrant centered on the upwind direction
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 consumption39 for those states and
Canadian provinces whose centers fall within the sector. To determine the
total emission rate within the area, we use the total amount of motor vehicle
5-16
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fuel consumed and the conversion factor: 1 gallon of fuel yields 1.32 x 103
grams of carbon monoxide. If the yearly (3.15 x 10^ sec) consumption of
fuel within the quadrant extending to 1000 kilometers is given by F, then
the average CO emission rate Q in the area {7.86 x 1011 m2) is given by:
Q = 5.32 x 1CT17 F (g nrf2 sec-1).	{9)
The model input includes a table of 16 values of F, one for each of the
wind directions used. This table is changed for each city. According to the
box model, the concentration C from some upwind segment is
Zq (r2 " l"i )\
L " V	/	(io)
uh
where r2 and rj are the distances to the outer and inner segment boundaries
(in this case 106 and 32 x 103 m), u is the wind speed, and h is the depth
of the layer through which the material is mixed. Substituting Q from
Equation (9) and the values of rj and r2 gives the following equation for
concentration from extra-urban sources, Ce:
Ce - 6.16 X 1
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SYNTHESIS OF BASIC MODEL TYPES
The previous sections have described the individual portions or components
of the diffusion model. Here we discuss the organization of these com-
ponents into models capable of furnishing the desired outputs.
Synoptic Model
The synoptic model is designed to take the data for some hour, calculate
and display point concentrations or concentration [sopleths within the city
for that hour, and then proceed to the next hour. This is repeated until the
time period of interest has been covered on an hour-by-hour basis. The
temporal changes of concentration for a selected location can be compared
with the measured values during the same period.
The organization of the model is shown in Figure 5-6. 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 those parameters neces-
sary for the application of the stability and mixing depth subroutines (see
Appendix A). The calculations start with determination of the afternoon
(maximum) and night (minimum) mixing depths from the appropriate
sounding. Then the meteorological parameters for the starting hour are read
and the stability class determined. Mixing depths are calculated by different
methods according to whether it is day or night. Concentrations are cal-
culated and then the next hour's data are read.
The diurnal variation of mixing depth estimated by the model is schemat-
ically illustrated in Figure 5-7. A constant, the night (minimum) mixing
depth, is assigned to the hours from midnight until the first hour after
sunrise. This value is based on the morning temperature sounding. The day
values are interpolated between the night (minimum) and afternoon (maxi-
mum) values on the basis of surface temperature (see Appendix A). The
mixing depth from sunset to midnight is interpolated by time between the
sunset and the new night (minimum) value based on the next morning's
temperature sounding. This process makes the transition to the night mixing
depth somewhat smoother.
The meteorological data used with this model consist of hourly surface
observations and 1200 Greenwich Mean Time (GMT) (eariy morning) upper-
air soundings, both on punched cards in edited form.
The traffic data are stored in the computer in the form described in an
earlier section. Each traffic link is identified by the location of its endpoints.
Data regarding length, daily traffic volume, and type (arterial, freeway, etc.)
are associated with each link. This information, when combined with hour of
the day, receptor location, wind direction, etc,, is converted by the emission
model to appropriate source strengths.
Sample results of calculations with the synoptic model are presented later in
this paper.
5-18
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READ POPULATION. LATITUDE INITIAL TEMPERATURE
SOUNDING DATE MAXIMUM AND MINIMUM TEMPERATURES.
AND LAST OBSFRVEO WIND DIRECTION
CALCULATE INITIAL VALUES OF AFTERNOON AND NIGHT
MIXING DEPTHS ISEE APPENDIX)
READ HOUR OF DAY CEILING HEIGHT ClOUO COVER
TEMPERATURE WIND SPEED. AND DIRECTION
IF WIND IS CALM ASSIGN SPEED VALUE > 0 oV» AND
USE THE LAST OBSERVED DIRECTION
DETERMINE STABILITY CLAPS
~r
(y)

HAS SUNSET OCCURRED WITHIN THE PAST HOUR'
~T~
©
DETERMINE MIXING DEPTH
FROM AFTERNOON VALUE
BV TEMPERATURE INTER
POLATlON (SEE APPENDIXI
IS IT BEFORE
MIDNIGHT'
DETERMINE mixing depth
BV INTERPOLATION ION
BASIS Of TIME) BETWEEN
NIGHT VALUE AND VALUE
AT flftST HOUR AFTER
SUNSET

USE

NIGHT

MIXING

DEPTH
DETERMINE MIXING DEPTH
FROM AFTERNOON VALUE
BV TEMPERATURE INTER-
POLATION (SEE APPENDIXI
READ NEXT MORNING'S
SOUNDING AND MAXIVUM
AND MINIMUM TEMPEPATURES
CALCULATE AFTERNOON
AND NIGHT MIXING DEPTHS
ISEE APPENDIXI
©
_L_
IS THERE
MORE DATA
~r
(i)
CALCULATE CONCENTRATION
FOR ONE OR MORE POINTS
AND DISPLAY RESULTS
SET MIXING
DEPTH 50 m
Figure 5-6. Flow chart of synoptic model calculations.
5-19
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Figure 5-7. Modeled diurnal variation of mixing depth (schematic).
Climatological Model
Our computational work, thus far, has been limited to calculations of
hour-to-hour concentrations with the synoptic model, based on hourly mete-
orological observations and average daily traffic data adjusted for diurnal
conditions. We also are developing a capability to calculate average concen-
trations, as well as high-percentile and maximum concentrations over various
time periods. That capability requires what we have termed a climatological
model. In this section we discuss how we plan to proceed in this task,
drawing upon recent work by Larsen,2 Larsen and Burke,40 and Martin and
Tikvart.41 A simitar approach has been used by Frankel.42
Basically, a two-step procedure is involved: (1) an arithmetic mean concen-
tration (C), for a 1-hour averaging time is calculated from the diffusion
model, and (2) either the statistical relationships developed by Larsen40 are
applied to this value to yield estimates of high-percentile and maximum
concentrations, or else the predicted concentration-joint-frequency function
is used for direct estimate.
Calculation of Arithmetic Mean Concentrations
Computation of C at a point requires a different treatment of the input
data, as suggested by Martin and Tikvart.41 This computation requires a
large body of hourly meteorological data, preferably for a period of at least
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a year. The discrete joint probability density function f(xlf x2,.. .xk) is
tabulated* for all combinations of classes of hourly values of the model
input parameters Xj to xk. By definition,
n n ' " n	^Xl- x2 . -Xk) = 1	H2)
n, n2 nk
where the n's denote the number of class intervals for each parameter.
The judgment as to the number of classes to be established for each
parameter must be based on a compromise between expected accuracy and
required computing time. The latter can become critical when the diffusion
model, C(X|, x2, ... xk), is used to compute C at several hundred receptor
points, where the calculations at each point take the form
C - 2 2 f(x,, ...xk) C(xi, x2, ...xk)	(13)
ni n2 nk
Here the concentration computed for each combination of parameter classes
is weighted by the probability of occurrence of that combination, and all
such fractions are summed to give the average (arithmetic mean). The
quantity (N) of individual concentration computations for each point is
determined by the size of the k-dimensional joint-density-function array:
N = n, x n2 x ...x nk
Obviously the number of parameters, as well as the number of classes,
affects the computing cost.
For our study, the traffic input is currently identified uniquely by the time
of day, since available detailed data are only sufficient to establish the
diurnal cycle. As indicated by Figures 5-2 and 5-3, the source emissions can
be adequately represented by five time classes, two during peak and three
during off-peak traffic periods: 0000 to 0600, 0700 to 0900, 1000 to 1500,
1600 to 1800, and 1900 to 2300 LST. Wind speed is divided into 6
categories, wind direction into 16, and stability into 5. At times it may be
feasible to reduce the number of classes for wind direction to 8.
The remaining parameter, mixing depth h, is the most difficult to obtain,
since its determination requires a morning temperature sounding (see Appen-
dix A). Frankel42 handled this problem by adjusting Holzworth's1 s'43'44
climatotogical mixing-depth values on the basis of the stability class, effec-
tively eliminating mixing depth as a separate parameter in the joint proba-
bility function. This seems to be a logical, if rather inexact approach.
Deletion of the requirement for temperature soundings has a considerable
computational advantage. To simplify his model. Pooler4 s also used the
principle of minimizing the number of variables, by eliminating stability and
'Special computations and tabulations of this nature are available from the National
Climatic Center, Asheville, N. C.
5-21
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taking the vertical diffusion parameter to be a function only of wind speed.
We are currently searching for a relationship between mixing depth and
other meteorological parameters. Since obtaining this relationship on the
basis of physical reasoning alone does not appear promising, we plan to
analyze 4 months (1 month per season) of surface and radiosonde data for
both Washington, D.C., and St. Louis. The mixing-depth values computed by
the method developed for the synoptic model (see Appendix A) will then be
stratified by time classes and correlated with the other meteorological para-
meters, particularly stability. If the correlations are significant, the result
should be a general empirical expression for mixing depth for each time
class. If not, we will resort to the best alternative, adjustment of climatologi-
cal values.
If the planned number of classes and parameters are feasible, we will end up
with the following computation:
5 5 6 16
C = 2 2 2 2 fltj.S,. Uk,0m ) C(tj, Sj( Uk, 0m ). (14)
j=l j=l k = l m = l
This amounts to (5 x 5 x 6 x 16) = 2400 concentration calculations for each
point. Since the diffusion model orientation is constant, for each point, the
traffic links need only be scanned once, saving computer time.
Calculation of High-PercentHe and Maximum Concentrations
The arithmetic mean concentrations (C) for a 1-hour averaging time, ob-
tained by the method just described, can be used to calculate estimates of
high-percentile and maximum concentrations by means of Larsen's2 statis-
tical model.* Larsen analyzed 3 years of concentration data for seven
pollutants from CAMP stations in six cities, and found that
1.	Concentrations are approximately log-normally distributed for all pollu-
tants, in all cities, and for all averaging times.
2.	The median concentration (50 percentile) is proportional to a power of
the averaging time.
These conclusions were derived mainly from the concentration data from the
important region above the median concentration.
Larsen discussed certain significant applications of these general findings.
Since arithmetic mean concentrations, C, for all averaging times are equal,
and since the concentration distribution is log-normal, the geometric mean
concentration Cg, for any averaging time t can be calculated from:
(Cg)t = C/(Sfl)t 05 lnt.	(15)
"Such calculations could also be performed directly using the predicted concentration
joint frequency function, if the latter were based upon a sufficiently large body of
Meteorological data.
5-22
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C is available from the diffusion model calculations, and (Sg}t, the standard
geometric deviation for a given averaging time, may be obtained for CAMP
station measurements of carbon monoxide from the tabulations by Larsen
and Burke.40*
The concentration (Cp)t associated with any percentile p, of the frequency
distribution, for any averaging time t, may be calculated from
(Cp}t = (Cg)t (Sg)tq	(t6)
where the number of standard deviations, q, is found from tables of the
standardized cumulative normal distribution, where:
p/100 =	fq e**12 dx	(17)
\[2tT ~oo
The maximum concentration during a 1-year period for an averaging time to
t hours is designated by {Cmax)t; it is given by
(Cmax)t = (Cg)^ (Sg)^1 tm	(18)
where values of m as a function of Sg are those tabulated by Larsen.2
Using these relationships and the arithmetic mean concentrations furnished
by the diffusion model, we can calculate, for any averaging time, (1) the
concentration expected for any percentile and (2) the maximum concentra-
tion expected once a year. It is also straightforward to generalize (2) above
to the calculation of maximum concentrations expected once during any
given period.
PRELIMINARY RESULTS TO DATE
Status
At the present time the basic designs for both the synoptic model and the
climatological model are fairly complete. The synoptic model, less the street
and extra-urban submodels, is programmed and running. Traffic data for
Washington, D.C., and St. Louis have been coded, and data for three other
cities are in the process of reduction. We are currently evaluating the model
output in terms of its sensitivity to parametric changes and its response to
design refinements. Sample results of some of these trial computations with the
synoptic model are presented here, to furnish an idea of its eventual capabili-
ties. The other models and submodels and necessary input data are in the
preparation stages.
•The values of (Sg>i.hr for CO measured at the CAMP Stations in eight cities range
from 1.44 to 1.95, with a mean of 1.63. Application of the model to non-CAMP cities
will require an estimate of Sg or its calculation using CO data. The probable factors
having the greatest effect upon Sg are (1) the receptor siting, and (2) variability of the
meteorolog cal parameters. Consideration of these factors could allow estimation of Sg
for any city, iased upon those calculated for the CAMP cities.
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Analysis and Display Techniques
To facilitate model development, we are taking advantage of modern com-
puter techniques, particularly objective contour analysis and graphical
display. In this work we are using special subroutines called CQNTOOR and
GRAPH 4* with the CDC 6400 computer and the CDC 280 cathode-ray
tube {CRTI peripheral display system. The CONTOOR subroutine furnishes
objective isolines describing the CO concentration distribution over an urban
area on the basis of a grid of point values calculated according to the
diffusion model. The GRAPH 4/280 combination permits such contour
analyses (or the results of any other calculations - see Figure 5-1, page 5-4) to
be displayed on the CRT and photographed. This facility significantly expe-
dites the trial and evaluation procedure.
Figure 5-8. Calculated intra-urban concentration distribution
of carbon monoxide (ppm) over Washington, D. C. - computer
generated contour analysis and display.
"These subroutines were developed by S. Briggs and B. Sifford of Stanford Research
Institute, respectively.
5-24
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GRAPH 4/280 display of the CONTOOR objective analysis is superimposed
upon the primary traffic network for Washington, D.C. Good correspondence
between the CO concentrations and road density is evident. The analysis was
based upon concentrations over a 25 x 25 section grid of 625 points, as
calculated by an early version of the diffusion model from simulated mete-
orological data. The objective contouring compares well with a manual
analysis of the identical data, presented in Figure 5-9. Differences between
the two patterns were traced to plotting and drawing errors by the analyst.
The smoother hand analysis may look better, but the objective analysis is
substantially faster, cheaper,* and more accurate.
DISTANCE EAST OF CAMP STATION, miles
TB-7874-8S
Figure 5-9. Same as Figure 5-8, but hand contoured.
"Computer costs for the diffusion calculations in Figure 10 were about $20. The objective
was an additional $5.
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Model Sensitivity and Evaluation Trials
Figure 5-10 illustrates the type of tests of model sensitivity to parameter
changes that are in progress. (This and all subsequent graphs were also
produced by the GRAPH 4/280 system.) Tests of this nature are helpful in
the refinement of the model design. The figure shows that the highest
concentrations at the Washington CAMP station should occur for west winds,
all other parameters being equal.
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DISTANCE EAST OF CAMP STATION, miles
TA-7874-25S
Figure 5-11. Calculated intra-urban CO concentration distribution
(ppm) for St. Louis area during early morning.
the morning near the junctions of freeways on the western side of St. Louis.
The same data as Figure 5-12 were used earlier in an attempt to furnish an
idea of the capability of the basic intra-urban model to compute detailed
concentration patterns over small areas. Those results are given in Figure
5-13, where the horizontal scale has been decreased by a factor of ten, and
the box size is now only 2,4 x 2.4 miles, still centered on the CAMP station.
The concentration pattern shows a large spatial variability that is related to
the distribution of downtown streets represented by the underlay.
The results of trials using the synoptic model to calculate hourly concentra-
tions continuously for a week are presented in Figures 5-14 and 5-15. To
provide a true test of the model's capabilities, weeks with a variety of
5-27
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DISTANCE EAST OF CAMP STATION, miles
TA-7874-26s
Figure 5-12. Same as Figure 5-11, but for late afternoon.
observed concentrations were selected. To account for a suspected instru-
mental zero-calibration problem, the observations, indicated by the dashed
curves in the figures, have all been adjusted downward by 1 ppm. In an
attempt to more accurately treat the effects of nearby sources, the closest
diffusion area segment was divided into two sections for these calculations.
One segment extends from the receptor to 62.5 m in range, and the other
extends from 62.5 out to 125 m.
The CO observations during the January period (Figure 5-14) were anom-
alously 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 performance of the model
occurs on 19, 21, and 22 January, when the wind was generally southerly.
5-28
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TA-7874-24S
Figure 5-13. Same as Figure 5-12, but scale reduced by a
factor of ten to give detailed CO concentration pattern in
central portion of St. Louis business district.
This suggests that the high observed concentrations are 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 were not so variable, and
more typical CO concentrations were observed. In contrast to the January
period, the predicted concentrations are mostly too high. The poorest agree-
ment occurs when the reported airport winds are very light or calm. For
these cases, the model uses a wind speed of 2 m sec-1 and the wind
direction last observed. It is probable that much of the prediction error is
due to this uncertainty in wind direction, part of the general difficulty
encountered in applying airport observations to urban areas. Better results
5-29
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might be achieved for very light-wind conditions if a symmetrically conver-
gent urban circulation, driven by the heat island effect, were included in the
model.
No agreement was expected between the calculated and observed weekend
values, since no weekend traffic distribution has yet been incorporated into
the model. It is interesting, however, to note the low concentrations ob-
served on Sundays, and the late peak in the observed concentration at about
1100 on Saturday, 23 January (Figure 5-14), probably due to shopping
traffic.
0 20 40
I-*—Won Tues-
18 Jan 19 Jan
60 80
_Wed—-U-Thiirs-
20 Jan
160 hours
Sun—-1
22 Jan 23 Jan 24 Jan
TA-7874-34s
Figure 5-14. Hourly predicted and observed CO concentrations
at St. Louis CAMP station for period 18-24 January 1965.
5-30
-------
19 Oct 20 Oct 21 Oct 22 Oct 23 Oct 24 Oct 25 Oct
1964
TA-7874-23S
Figure 5-15. Same as Figure 5-14, but tor period 19-25 October
1964.
SUMMARY AND CONCLUSIONS
The model design described here is believed to be a realistic and practical
approach toward developing capabilities for accurate and economical calcula-
tion of: (1) hour-to-hour CO concentrations, using synoptic weather data,
and (2) average, high-percentile, and maximum concentrations, using climato-
logical weather data and forecast traffic data. The simplified model design
makes full use of several previous modeling efforts, with the incorporation of
necessary and appropriate modifications. Unique features of this model
include (1) an objective treatment of the traffic data to give a time- and
space-dependent emission inventory, (2) a technique for estimating hourly
values of mixing depth, and (3) a method (under development) for calculat-
ing street-level concentrations. So far we have not used adjustable "cali-
bration" constants in the model.
Final evaluation of the model must be deferred until all the sub-models, and
any necessary refinements are incorporated. To date the preliminary evalua-
tion trials have been instructive in showing model performance, Two
5-31
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expected results are already apparent: (1) agreement with observed (CAMP)
values depends critically upon proper treatment of microscale effects, and
(2) the steady-state model in its present form gives poor results for light-
wind conditions.
Since the model is designed to be general, only routinely available input data
are used. This means reliance upon airport weather data and rather gross
traffic data, placing an upper limit on the accuracy obtainable with the
model. The substantial effort expended in the development of techniques, to
estimate the required model input variables, using such largely inappropriate
input data, underscores the need for additional, routine, pollution-oriented,
meteorological and traffic measurements within cities.
ACKNOWLEDGMENT
This research was jointly sponsored by the Coordinating Research Council
under Contract No. CAPA 3-68 (1-68) and by the National Air Pollution
Control Administration under Contract No. CPA 22-69-64. We are grateful
for the assistance of the following individuals at Stanford Research Institute:
Mrs. Shirley Reid, who secured and supervised the reduction of the traffic
data; Robert Mancuso and Hisao Shigeishi, who programmed the model and
carried out the computer trials; and Elmer Robinson, who aided in planning
the model development.
We also thank the members of the CRC-APRAC Urban Diffusion Project
Group for their guidance and suggestions, and for supplying useful technical
information.
5-32
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APPENDIX
DETERMINATION OF MIXING DEPTHS
FOR USE WITH SYNOPTIC MODEL
F. L. Ludwig
Initial attempts to estimate mixing depths tor the synoptic model from surface
observations only, were unsuccessful. The method finally chosen for estimating
daytime mixing depths follows the commonly accepted approach20 and re-
quires knowledge of the early morning temperature sounding. The maximum
afternoon mixing depth (hmax) is calculated as the height at which the dry,
adiabatic lapse rate from the maximum surface temperature (Tmax) intersects
the morning sounding. The calculations of mixing depth are made in pressure
coordinates, and then converted to heights with the hydrostatic equation and
the gas law.
For nighttime hours, a minimum mixing depth (hn) is estimated as follows. For
daylight hours other than the time of maximum temperature, the mixing depth
hj is obtained by linear interpolation between hma)< and hn, according to the
temperature T:
The estimation of nighttime mixing depth over the city is based on Sum-
mers'24 model of the urban heat island and Ludwig's48,49 empirical relation-
ship between rural lapse rates and the intensity of urban heat islands. If we
assume T to be a linear function of the log of pressure {very nearly the same as
Summers' assumption of T as a linear function of height), then the tempera-
ture, Th, at some height, h, outside the city is given by:
where T0 and p0 are the rural surface temperature and pressure, respectively,
ph is the pressure at h, and p is the average of p0 and ph.
(A-1)
dT
Th = T0 + _— Alnp
dlnp
(A-2)
5-33
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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. The dry, adiabatic
lapse rateyd (in pressure coordinates) is given by
7d
TR
PCp
T
0.287 -
P
T
0.287 —
P
(A-3)
where R and cp are the gas constant and specific heat at constant pressure for
dry air, T and p are absolute temperature and pressure, and T and p are the
respective average values within the layer from the surface to height, h. For the
urban situation, Equation (A-2) becomes
Th Tu + P td
In
Ph
Po
(A-4)
where Tu is the surface air temperature in the center of the urban area.
Subtracting Equation (A-4) from Equation (A-2) gives:
dT
Tu - T0 = p
dp
- 7a
Substituting Equation (A-3) into Equation (A-5) gives:
Tu - T0 =
Pti
dT
~dfT
0.287 T
(A-5)
(A-6)
Ludwig48 has shown that (Tu - T0) can be approximated within about 2° C
by the following equation:
Tu - T0 = p,/4 ^0.0633 - 0.298	(A-7)
where P is the population of the urban area and dT/dp is expressed in °C per
millibar. The equation is based on 85 sets of data from 18 different cities.
Substituting Equation (A-7) into Equation (A-6) gives:
In
Ph
Po
= P
/	dT1
(0.0633 - 0.298 —
1 /4	\	d|D/
- 0.287 T ^
(A-8)
5-34
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The value of dT/dp is determined on the basis of the lowest portion of the
morning sounding between the surface and the first reported level above the
surface; p and T are the averages of the pressures and temperatures at these
points.
To convert Inf— ) to mixing depth, we can use the thickness equation.
YV
If temperature is assumed equal to T throughout the layer then:
/Ph\ RT
h = -In — 	 = -29.3 T In	
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and Related Phenomena from a Point Source Emission. J. Appl. Meteorol. 5<5):
631-639, October 1966.
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22.	Meade, P. J. Meteorological Aspects of the Peaceful Uses of Atomic Energy- Part
1, Meteorological Aspects of the Safety and Location of Reactor Plants. World
Meteorological Organization. Geneva, Switzerland. Publication Number 97 TP41.
Technical Note Number 33. 1960. 33 p.
23.	Turner, D, B. A Discussion Model for an Urban Area. J. Appl. Meteorot. 3(1):
83-91, February 1964.
24.	Summers, P. W. The Seasonal, Weekly, and Daily Cycles of Atmospheric Smoke
Content in Central Montreal. J. Air Pollution Control Assoc. 75:432-438, August
1966.
25.	Graham, I. R. An Analysis of Turbulence Statistics at Fort Wayne, Indiana, J.
Appl. Meteorol. 7(1):90-93, February 1968.
26.	Schnelle, K. B., F. G. Ziegler, and P. A. Krenkel. A Study of the Vertical
Distribution of Carbon Monoxide and Temperature Above an Urban Intersection
(APCA Paper No. 69-152). 1969. 65 p.
27.	Clarke, J. F. Nocturnal Urban Boundary Layer Over Cincinnati, Ohio. Mon.
Weather Rev. 37(8):582-589, August, 1969.
28.	Bornstein, R. D. Observations of the Urban Heat Island Effect in New York City.
J. Appl. Meteorol. 7(41:575-582, August 1968.
29.	Leahey, D. M. A Model for Predicting the Variation of Pollution Within the Urban
Heat Island (APCA Paper No. 69-107). 1969. 45 p.
30.	Angell, J. K. et al. Tetroon Trajectories in an Urban Atmosphere. J. Appl.
Meteorol. 5(5):565-572, October 1966.
31.	Hass, W. A. et al. Analysis of Low-level, Constant Volume (Tetroon) Flights Over
New York City. Quart. J. Roy. Meteorol. Soc. 93(398):483-493, October 1967.
32.	Pooler, F., Jr. Airflow Over a City in Terrain of Moderate Relief. J. Appl.
Meteorol. 2(4):446-456, August 1963.
33.	Hilst, G. R. and N. E. Bowne. A Study of the Diffusion of Aerosols Released from
Aerial Line Sources Upwind of an Urban Complex. Travelers Research Center, Inc.
Hartford, Conn. Final Report. Vol. I. Contract DA 42-007-AMC-37(R). 1966. 241
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34.	Turner, J. S. The Motion of Buoyant Elements in Turbulent Surroundings, J, Fluid
Mech. 7ff:1-16, May 1963.
35.	Lilly, D. K, Models of Cloud-topped Mixed Layers Under a Strong Inversion. Quart
J. Roy. Meteorol. Soc. 94(401 ):292-309, July 1968.
36.	Georgii, H. W., E. Busch, and E. Weber. Investigation of the Temporal and Spatial
Distribution of the Emission Concentration of Carbon Monoxide in Frankfurt/
Main, Frankfurt/Main University, Institute for Meteorology and Geophysics.
Report Number 11; Translation Number 0477, NAPCA. 1967. 66 p.
37.	McCormick, R. A. and C. Xintaras. Variation of Carbon Monoxide Concentrations
as Related to Sampling Interval, Traffic, and Meteorological Factors. J. Appl.
Meteorol. 1[2) :237-243, June 1962.
38.	Rouse, H. Air Tunnel Studies of Diffusion in Urban Areas. Meteorol. Monogr.
7(4):39-41, November 1951.
39.	Highway Statistics for 1966. Bureau of Public Roads. Washington, D. C. 1968..
186 p.
40.	Larsen, R. I. and H. W. Burke. Ambient Carbon Monoxide Exposures. Presented at
62d Annual Meeting of the Air Pollution Control Association. New York.
(NAPCA) June 22-26, 1969. 38 p.
41.	Martin, D. O. and J. A. Tikvart. A General Atmospheric Diffusion Model for
Estimating the Effects on Air Quality of One or More Sources. Presented at 61st
Annual Meeting of the Air Pollution Control Association, for NAPCA, St. Paul.
June 1968. 18 p.
42.	Frankel, M. L. Regional Air Pollution Analysis—Phase I. TRW Systems Group.
Redondo Beach, Calif. Status Report. Sales Number 11 130 000, 1965. 467 p.
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43	Holzworth G C Mixing Depths, Wind Speeds and Air Pollution Potential for
Selected Locations in the United States. J. Appl. Meteorol. 6[6): 1039-1044,
December 1967.
44	Holzworth G. C. Large-scale Weather Influence on Community Air Pollution
Potential in the United States. J. Air Pollution Control Assoc, 79:248-254. April
1969.
45	Huber M. J., H. B. Boutwell, and D. K. Witheford. Comparative Analysis of
Traffic Assignment Techniques with Actual Highway Use. Highway Research
Board. Washington, D. C. National Cooperative Highway Research Program Report
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46	Miller, M. E. Forecasting Afternoon Mixing Depths and Transport Wind Speeds.
Mon. Weather Rev. 55:35-44, January 1967.
47	Ludwig, F. L. Urban Air Temperatures and Their Relation to Extra-urban Meteoro-
logical Measurements. Presented at Meeting of the American Society of Heating,
Refrigerating, and Ventilating Engineers for Stanford Research Institute. San
Francisco. January 1970.
48	Ludwig, F. L. Urban Temperature Fields. In: Proceedings of WMO Symposium on
Urban Climates and Building Climatology, Brussels, Belgium, October 15-25, 1968.
To be published by World Meteorological Organization, Geneva, Switzerland. In
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49	Ludwig, F. L. and J. H. S. Kealoha. Urban Climatological Studies. Stanford
Research Institute. Menlo Park, Calif. Final Report. Contract OCD-DAHC-
20-67-C-0136. (Work Unit 1235A). March 1968. 191 p.
50. Gitman and Co. St. Louis Metropolitan Area Traffic Study. Prepared for City and
County of St. Louis. New York. 1959. 154 p.
5-38
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6. AN URBAN DISPERSION MODEL
ABSTRACT
A computerized, multiple-source, atmospheric dispersion model de-
signed for operational use in air resource management has been formu-
lated and programmed for the IBM 360-75 system. This "integrated
puff" model provides a more realistic physical simulation of the pro-
cesses of smoke plume dispersion than has hitherto been employed,
since it provides for simulation of near-zero wind speed conditions,
models three-dimensional wind vector variation and atmospheric diffu-
sion, including upwind-downwind diffusion, and permits variation of sta-
bility and mixing layer depth with time.
This paper describes the development and preliminary validation testing
of the model with data from a 3-year, computerized inventory of
sulfur dioxide air quality data recorded by the receptors of the Chi-
cago, Illinois, telemetered air monitoring system.
A detailed, 2-year inventory of Chicago coal and oil burning S01
emission sources was acquired, data storage formats were designed, and
computer algorithms were developed to generate hourly average esti-
mates of emissions from major utility, industrial, residential, commer-
cial, and institutional sources. Small emitters were aggregated into
square-mile area sources.
The model consists of a series of algorithms assembled around a kernel
that represents the transport and diffusion of pollutant species from
point and area sources according to a Gaussian distribution in three
dimensions. This kernel, which represents a three-dimensional puff of
smoke, is integrated according to a time-series of piecewise constant
wind vectors and piecewise constant atmospheric stability parameters
to simulate the transient behavior of a continuous smoke plume.
Smoke plume rise and downwash phenomena are simulated.
The model is incorporated in a master air pollution data management
system, which is employed to store, retrieve, process, analyze, and
display emission, meteorology, and air quality data. This system is used
to study micrometeorofogical dispersion, to form and input data ar-
rays, and to validate its own theoretical predictions against recorded air
quality data.
At present, the model is in the early stages of validation and has been
tested against 1 month of hourly-average S02 data from five Chicago
air quality monitoring stations. A statistical sample of approximately
2300 data points is presently available. The ratio of standard deviation
-------
to mean values for all hourly S02 predictions is 0.93. For 6-hour
average predictions, this ratio is 0.64 and for 24-hour average predic-
tions it drops to 0.43. Over 66% of the 24-hour average S02 pre-
dictions are within ±0.05 part per million {ppm} of observed values
and approximately 90% are within ±0.1 ppm of actual dosages.
Hourly time series plots of observed and actual S02 concentrations
indicate that the model is sufficiently accurate to test selective hypo-
theses about the model itself and to evaluate urban air resource
management strategies.
authors
JOHN J. ROBERTS, the lead engineer for the development of computerized
mathematical models of atmospheric diffusion processes for the Chicago Air
Poilution Systems Analysis Program. CAPSAP is an interdisciplinary, environmen-
tal science research and development program supported by the Department of
Health, Education and Welfare, the Atomic Energy Commission and the City of
Chicago. It is directed towards the development of physical and economic
mathematical models for use in air resource management planning and air
pollution systems analysis. Dr. Roberts is a major participant in the Argonne
study of the design and implementation of episodal and long-range emission
control programs. He recently organized a program of research to develop
numerical models of hydrothermal plumes from power plants and has also been
associated with the Argonne-U.S. Navy magnetohydrodynamic research program.
Dr. Roberts received a B.E.E. from Rensselaer Polytechnic Institute in 1958 and
then spent four years teaching in the U.S. Navy Nuclear Power program. He
received a Ph.D. in nuclear engineering at the University of California, Berkeley,
in 1966.
EDWARD J. CROKE is the director of the CAPSAP. Prior to joining Argonne
National Laboratory in 1963, as a systems analyst for the NASA refractory metal
nuclear rocket program, he was with the James Forrestal Research Center at
Princeton, and was later propulsion systems project officer for the Agena Satel-
lite program of the Air Force Systems Command.
He holds a B.S.E. in physics from the University of Illinois and an M.S.E. from
Princeton in 1960. He has subsequently pursued postgraduate studies in geophy-
sical sciences, operations research, systems analysis and management sciences at
the University of Chicago and Northwestern University.
ALAN S. KENNEDY received an M.S. in mathematics at Washington University
in 1962. He joined the Applied Mathematics Division of Argonne National
Laboratory in 19$3 and has continued his studies toward a Ph.D. in operations
research at Northwestern University.
From his study of data management problems associated with an operational air
pollution control department, he developed a system of storage, retrieval, and
analysis of air quality„ meteorological, and emission data for CAPSAP.
-------
6. AN URBAN ATMOSPHERIC
DISPERSION MODEL
JOHN J. ROBERTS, EDWARD S. CROKE
and ALLEIM S. KENNEDY
Argonne National Laboratory
INTRODUCTION
A computerized, multiple-source, atmospheric dispersion model has been
formulated and programmed for the IBM 360-75 system. This "integrated
puff" model provides a more realistic physical simulation of the processes of
smoke plume dispersion than has hitherto been employed, since it provides
for simulation of near-zero wind speed conditions, models three-dimensional
wind vector variation and atmospheric diffusion, including upwind-downwind
diffusion, and permits variation of stability and mixing layer depth with
time.
A source-oriented model is essential for the development of optimal incident
control strategies and long range abatement plans. For example, a prelimi-
nary version of the integrated puff model was programmed and subsequently
employed to develop a prototype optimal control model for an urban power
plant network.1 That prototype model will be used in combination with
Chicago's emission inventory data as the primary analytical tool in the
performance of a series of air pollution system-analysis studies including:
1.	Cost-effectiveness analysis of alternative control strategies for specific
source aggregates such as power plants, the food processing industry,
the steel industry, asphalt batching, etc.
2.	Development of rapid-response, automated optimal incident control
strategies for the urban power plant network, optimal gas allocation to
dual fuel sources, process emission control, etc, based on operations
research techniques.
3.	Development of long-range air pollution abatement plans oriented
around the computer simulation of the city, with projections of its
population, fuel use, production and transportation network growth
*Work jointly sponsored by the National Air Pollution Control Administration, the
Atomic Energy Commission, and the Chicago Department of Air Pollution Control.
6-1
-------
patterns, so that emission control legislation, zoning ordinances, etc.,
can be tested on a simulation of Chicago urban area of the future, and
cost-effectiveness studies can be performed to evaluate the economic
impact of pollution abatement measures.
The model described in this paper has several aspects in common with earlier
efforts2,3'4 (e.g. Koogler, 1967; Turner, 1964; Clarke, 1964):
1.	An emission inventory is developed; large emitters are considered as
point-sources and smaller residential commercial and industrial emitters
homogenized as area-sources on a standard grid.
2.	A mathematical algorithm (typically based on the representation of
turbulent diffusion by a Gaussian distribution) is used to describe the
advection and diffusion of plumes from each of the sources or source
areas.
3.	Contributions from individual plumes are summed and sometimes in-
tegrated over time to give pollution doses at arbitrary locations.
4.	The model is validated by statistical comparison with field measure-
ments taken by an array of monitors.
5.	While the results of the validation study may indicate a refinement of
certain physical assumptions (such as the plume rise formulation) or
inclusion of additional sources (such as distant power plants), no
further improvement by linear regression or similar curve fitting tech-
niques is permitted; that is, the model is not tuned to a particular
receptor or city. This last point is particularly important if the model
is to be used in the development of incident control strategies and
long-range urban planning.
The essence of an air pollution dispersion model as a collection of algorithms,
a set of assumptions and subsequent calculations for every stage of the analy-
sis, from the compilation of the emission inventory to the validation of the
results, is discussed briefly in the following sections.
DEVELOPMENT OF AN EMISSION INVENTORY
A major task element of the Chicago Air Pollution Systems Analysis program
was the development of an inventory of hourly average emissions for the
power plants and industrial, residential, commercial, and institutional S02
sources that are the primary contributors to Chicago's sulfur oxide air
pollution problem.
Figure 6-1 shows the location and distribution of the largest individual coal
and oil burning sources of sulfur oxides, while Figure 6-2 shows the source
density of residential emitters. They were too numerous to inventory indivi-
dually. Figure 6-3 depicts, by source category, the distribution and magni-
tude of Chicago's S02 emitters.
6-2
-------
A MULTIPLE RESIDENCES ,
« COMMERCIAL ESTABLISHMENTS
O INDUSTRIAL PLANTS
INDUSTRIAL PLANTS WITH DUAL..,
FUEL CAPABILITIES
| PUBLIC UTILITY POWER PLANTS
~ TELEMETERING STATIONS
Figure 6-1. Map of major Chicago sources and TAM stations.
6-3
-------
TONS OF EMISSIONS PER YEAR
i	1 0 - 200
r—i 200 - 500
mm 500 - 1,000
¦¦ 1,000 - 1,500
Mi 1.500 - 2,500
Figure 6-2. Sulfur dioxide from residential space heating, 1968.
6-4
-------
380
370
373,120
r
60-
53,551
2 m en
ir> c
40
30
20
10
9,123
1
44,287
22,239
14,974
14,903
P51" s
±n\ n
s=
Is
m
ill
tn
O Q
O UJ
1OC
t-cc.
Z LLl
ujsc:
Q O
¦ LJ f
3-i
to
Sg
V)_
UJ -J
K
4 ^
t-O
OO UJ
2(^>
UJ.
o
o
o
I—
oo
o i
o
E -»—
= U
o :
o
20,009
826
25

22
	 — »¦.¦¦¦¦¦.« m-*m > m — -		
—i _j _j _j _j _i _i	_i	J3
<* «tQ 
-------
The Chicago Air Quality Monitoring System
Chicago operates a network of eight telemetered air monitoring (TAM)
stations that continuously and automatically record 5-minute, average S02
concentrations at 15-minute intervals throughout the day. The data recorded
by these stations during 1966 and 1967 are typical of a cfty that is charac-
terized by a highly unhomogeneous SO? source distribution and density.
Table 6-1 provides a summary of the air quality situation of Chicago as
recorded by the network of TAM stations.
Since the source density, type, and distribution in the immediate vicinity of
a receptor may, under certain meteorological conditions, dominate the am-
bient air quality recorded, it is of value to examine the record of the eight
TAM stations from the standpoint of their proximity to Chicago's S02
sources. This exercise is particularly useful, since it provides an indication of
what types of sources are likely to have the predominant effect on the
recorded air quality, and therefore serves as an indicator of the level of
effort that should be expended to develop a detailed emission inventory.
Moreover, an understanding of the distribution of sources relative to each of
the monitoring stations that provide the data required to validate the
Chicago atmospheric diffusion model explains certain of the results predicted
by the model. Table 6-1 shows the distribution of 1-hour S02 dosages re-
corded at the eight TAM stations.
Table 6-1. TOTAL NUMBER OF RECORDED 1-HOUR S02 DOSAGES (1966-67)
TAM station
Total dosage, ppm
0.2
0.3
0.4
0.5
1
182
59
18
5
2
618
203
70
30
3
3210
1838
975
483
4
1990
966
491
268
5
525
207
84
45
6
364
169
94
65
7
934
332
122
35
8
206
51
15
6
TAM Station 1
TAM station 1 is located near the northwestern limits of Chicago in an area
characterized by residential neighborhoods of relatively recent construction,
and a limited amount of light industrial development. Heating plants in this
sector of the city are predominantly natural-gas fired and relatively little
coal or oil is consumed by industrial or commercial sources. TAM 1 is thus
sited in a relatively cfean section of the city, insofar as sulfur oxide
6-6
-------
emissions are concerned. This conclusion is borne out by the fact that
recorded high ambient S02 concentrations at TAM 1 are at least one order
of magnitude less frequent than at monitoring stations located nearer to the
urban core area.
TAM Station 2
Station 2, located in the northeast sector of the city approximately 1.5 miles
from the lakeshore, is in a mixed industrial-residential area that contains a
large concentration of high-rise gas-fired residential structures. The prevailing
southwesterly wind flow tends to transport S02 from the central utility-
industrial cluster into this area, but average dosages tend to be relatively low
because of the comparatively large transport distances involved. This is
evidenced by the relatively high ratio of low to high concentrations recorded
at TAM 2 compared to TAM 3 or TAM 4 where localized coal and oil
burning sources are more significant. The nearest major S02 source to TAM
2 is a moderate sized coal fired power plant located approximately 1.5 miles
southwest.
TAM Station 3
This receptor is centrally located atop a large office building in the Chicago
loop business district. It is not only surrounded by a cluster of targe
commercial and institutional space-heating sources, but it is also situated
directly northeast of a major concentration of industrial plants and a line
formed by the three largest power plants within the city limits. Since the
prevailing wind flow is southwesterly, a high incident frequency due to this
industrial-utility concentration and to local space heating effects is to be
expected at TAM 3. As indicated in Table 6-1 this station is, in fact, located
in the most polluted sector of the city.
TAM Station 4
TAM 4 is located in the south-central Hyde Park area of Chicago within 1
mite of Lake Michigan. The immediate area is characterized by a row of
highrtse apartments sited along the lakefront, a large concentration of old
coal- or oil-fired low-rise, six-flat apartment buildings and a single major
source — the University of Chicago steam plant. TAM 4 is approximately 5
miles southeast of Chicago's central industrial-utility complex. As indicated
in Table 6-1, the frequency of high, recorded S02 concentrations at TAM 4
is second only to that of TAM 3. Statistical analysis of TAM 4 air quality
data has indicated that the air quality in this area is very strongly correlated
with ambient temperature — a finding that indicates the Hyde Park area is
largely self-polluted by local, residential space-heating sources.
6-7
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TAM Station 5
TAM 5 is situated approximately 6 miles inland in the south central sector
of the city. It is approximately 3 miles south of the centra! industrial-utility
complex, atop a school building in a neighborhood of low-rise apartments
and single family dwellings. Residential buildings in the TAM 5 area are
somewhat newer than in TAM 4, and gas tends to predominate over coal and
oil for space-heating purposes. TAM 5 is nearer to the central industrial-
utility cluster than any of the other monitoring stations; however, only a
few large sources are located southwest of the site. This fact, combined with
the relatively low level of residential emissions in its immediate vicinity,
results in comparatively modest number of high S02 concentrations recorded
there.
TAM Station 6
Station 6, in the extreme southeast of the city, is sited in a residential area
located approximately 5 miles west of a second large concentration of
Chicago industrial and power plants. Immediately adjacent to the Chicago
source-cluster is the Gary-Hammond industrial complex. Since the receptor is
also located within one mile of the southwest city limits of Chicago, it is
exposed to emissions from two areas for which an emission inventory is not,
at present, available. According to the data presented in Table 6-1, TAM 6 is
located in one of the less polluted areas of the city. This conclusion is
consistent with the fact that the metropolitan region southwest of the city is
relatively free of large S02 sources, and that east winds, which would bring
in S02 from the south Chicago-Gary-Hammond area, are comparatively
infrequent in the midwest Great Lakes region.
TAM Station 7
TAM 7 is sited atop a school building within 0.5 mile of the western city
limits and almost 7 miles directly west of the central business district. The
immediate neighborhood is predominantly residential, although a few large
industrial plants are located within 2 miles of the receptor in the northeast
and southwest directions. The station is approximately 6 miles northwest of
the central industrial-utility cluster.
A detailed emission inventory for the regions immediately west and south of
this receptor is not yet available, since these areas lie outside the Chicago
city limits. It is known, however, that the area west of TAM 7 is a mixed
residential, light-industrial sector in which gas heating predominates, while
the highly industrialized city of Cicero, Illinois, lies immediately south of
TAM 7, within 2 miles of the receptor.
Although the relative scarcity of southeasterly winds minimizes the influence
6-8
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of the central Chicago source-cluster on TAM 7, the area experiences signifi-
cant S02 concentrations with moderately high frequency, making it the
third or fourth most frequently polluted site.
TAM Station 8
Like the TAM 6 receptor, TAM 8 is located in a residential neighborhood
near one of the southwestern extremities of Chicago's irregular western
border. Two relatively large industrial plants lie within 1 mile northeast of
the site; however, the area itself is relatively free of significant S02 sources.
Since the western city limits are within 0.5 mile and the southern city
limits are within ^ mile, emission data for virtually the entire southwestern
quadrant, relative to TAM 8, are not available.
As indicated in Tabfe 6-1 the TAM 8 receptor is sited in one of the least
polluted areas of the city.
Power Plants
Electric power for the Northern Illinois region is provided by a network of
15 power generating stations, of which six are located in the Chicago metro-
politan area. These six coal-fired plants, shown in Figure 6-1 account for
approximately 65% of the sulfur oxides released into the Chicago atmo-
sphere. Table 6-2 indicates the relative contribution of each plant in terms of
its annual fuel consumption.
Table 6-2. RELATIVE CONTRIBUTION8 OF NORTHERN ILLINOIS POWER PLANTS
TO CHICAGO S02 CONCENTRATION
Plant designation
S02
Amount, tons yr"'
% of Chicago total
Crawford
107,954
18,97
Ridgeland
100,540
17.67
Fisk
73,438
12.90
State Line
70,606
12.42
Northwest
10,566
1.86
Calumet
10,016
1,76
Total
373,120
65.58
aln terms of annual fuel consumption
Of these installations, four: the Fisk, Crawford, Ridgeland, and State Line
plants are capable of partial or total conversion from coal to natural gas
during periods when the latter fuel is available at "dump" or "interruptible"
rates.
6-9
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Because of the extremely large emission rates associated with the urban
power plants and because of their complex, but relatively consistent diurnal
emission cycle, the acquisition of the most accurate body of emission data
available constituted a high-priority task in the emission inventory. Fortu-
nately, the Chicago utility maintains excellent records of plant operation.
These were provided for the period January 1966 through December 1967,
The data array required was:
1.	Hourly power generation, in megawatts (Mw), tor each generator unit
of each power plant, including an indication of whether the power was
generated with coal or gas,
2.	Monthly coal and natural gas consumption rates for each boiler-genera-
tor combination.
3.	Monthly average coal-sulfur-content analyses for each plant.
4.	A set of boiler-turbine-generator efficiency curves for each generator
unit. These presented efficiency vs. power output for each unit.
5.	A set of stack temperature vs. output curves for each plant.
6.	A physical description of each plant layout, including the relationship
between boilers, turbines, generators, and stacks, stack heights, etc.
The above information was combined in a computer algorithm for calcula-
tion of the hourly fuel consumption and S02 emission rates for each stack
of each plant of the system. Details of the computational procedure are
provided in the program progress reports.5
The resultant body of power plant emission data was stored in the master
data file of the Air Pollution Information and Computation System (APICS)
from which it could be retrieved and automatically input to the dispersion
model. The details of the APICS system are described by Kennedy and
Anderson,6 and in the program progress reports.5, 7
Industrial Sources
There are over 2500 relatively large coal and oil burning industrial plants in
the City of Chicago, which are responsible for approximately 10 percent of the
average annual sulfur oxides emitted within the city limits. The 100 largest
plants account for over 83 percent of the total industrial emissions, and the
largest 50. for over 64 percent.
The inventory of industrial emissions was derived from four sources;
1,	Department of Air Pollution Control Survey. A Comprehensive annual
average inventory compiled in 1963 by the Chicago Department of Air
Pollution Control was computer processed to establish industrial S02
emissions on a square-mile basis. Within any given square-mile sector,
industrial emissions were assumed to be uniformly distributed,
2.	Argonne National Laboratory Field Survey. Detailed fuel consumption
and physical and operating cycle data for the 50 largest S02 sources
6-10
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were obtained through a field survey system designed by Argonne and
implemented by Laboratory and city engineers. This involved a pro-
gram of site visitations and personal or telephone interviews with plant
personnel.
3.	Natural Gas Utility Records. The 1966-67 natural gas consumption and
fuel costs records for all dual fuel plants among the 50 largest S02
sources were obtained from the local, natural gas supply utility.
4.	Fuel Supply Records. The Midwest Coat Producer's Institute, an organ-
ization of wholesale coal suppliers, provided records of the average
annual coal consumption by major industrial sources during 1966-67.
Industrial sources that were not sufficiently large to be included among the
largest 50 emitters were aggregated into uniformly distributed square-mile
area-sources. All plants in this category were assumed to have a stack-height
of 150 feet.
Industrial Source Simulation Programs
The 50 largest sources of S02 were treated as individual point sources. A
detailed analysis of the diurnal, weekly, and seasonal operating pattern of each
of these pfants, 5n combination with fuel consumption records, gas-use
patterns, and such characteristics as process-vs. space-heating fuel-use practices
was incorporated into an industrial-plant-emission-simulation computer algo-
rithm (PLANTSIM) to generate an operating-shift-oriented emission estimate
for each plant.
The data file for large industrial sources is designed to include enough
information about each plant to characterize its "expected" emission pattern
by operating-shift for each day throughout the year. For this purpose "shifts"
are defined as follows:
Shift 1: 12 midnight to 8 am	(00001 to (0800)
Shift 2:	8 am to 4 pm	(08001 to (1600)
Shift 3:	4 pm to 12 midnight (1600) to (2400)
Up to three daily emission patterns may be assigned to each plant. These are
as follows:
1.	W — weekday or normal operation.
2.	S — Saturday.
3.	H — Sunday or special holidays.
Finally, a monthly weighting is provided to allow for variation due to
seasonal patterns, etc. Each plant requires two computer cards; (1) a source
identification card, and (2) a source emission card. An example of each is
shown in Figures 6-4 and 6-5 respectively. A description of each item on the
cards is provided in Table 6-3 and Table 6-4.
6-11
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no.

NAME (125 CHARACTERS MAX INCL. BLANKS)

TYPE

GRID

COORDINATES

?.Ta.cx oax& '

WORK SCHEDULE
1
2
3

4



y
HGT.
%
M6T,
%
HCT
%
HGT.
%
M
T
w
T
F
5
$
1 3

5 Z9

31 34

36 59

41 45
46 50

52 M
53 56
sr 54
6ti 61
u>
N»
li
65 66
67 69
TO 71

7i
74
75
76
77
78
79
f

CAMPBELL SOUP 2&5C ME11 M SHEET

MU

ora

1.1
•IS

I7i
25
\n
K
3«
50



H
¦
V
M
N
s
H


















	












































I
1


















f i
! 1




J

i
i




Figure 6-4. Sample of source identification card.
Figure 6-5. Sample of source emission card.
-------
Table 6-3. SOURCE I.D. CARD
No.
Item
Description
1
Source no.
Plant sequence number
2
Name
Plant name (not to exceed 25 characters including blanks),
address included if sufficient space available
3
Type
Standard industrial code
4
Grid
City of Chicago square-mile number
5
Coordinates
x- and y-coordinates relative to standard City of Chicago-
coordinate-system
6
Stack data
Four stacks maximum (1, 2, 3, 4)
HGT — Stack height, (feet)
% — The percent of total emission emitted from each stack
7
Work schedule
Each day of week assigned one of the following:
W — Weekday
S — Saturday
H — Sunday or holiday
Table 6-4. SOURCE EMISSION CARD
No.
Item
Description
1
Source no.
Plant sequence number
2
Max space htg load
Maxium hourly thermal requirements for space-heating
3
Max process load
Maximum hourly requirements for process
4
Monthly fuel use
weighting
Achieves monthly variation in process fuel use. Each month
assigned weight (0, 1,...,9) s average percent (0%, 10%,
...,90%) of maximum process fuel used during month
5
Shift-fuel-use
weighting
Within each day pattern (W, S, H), weight (0%, ...99%)
assigned to each shift, = average percent of current monthly
process fuel used during shift
6
% Sulfur-coal
Average percent of sulfur in coal
7
Avg % coal
Average percent of thermal load due to coal (0 implies coal
not used)
8
% Sulfur oil
Average percent sulfur in oil
9
Avg % oil
Average percent of thermal load due to oil (0 implies oil
not used)
10
% Gas SP HTG
Percent of space heating thermal requirements that can be
supplied by gas
11
% Gas process
Percent of process thermal requirements that can be sup-
plied by gas
12
Avg gas temp
Average ambient temperature (°F) at which dual fuel plant
receives gas on"interruptible" supply contract
13
Gas price
Gas rate (cents per therm) for dual fuel plants
6-13
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The PLANTSIM code is completely general. Large, individual space-heating
sources or major institutional sources such as coal-fired water-pumping sta-
tions can be treated in exactly the same manner as industrial plants. In the
case of heating plants, the process-load portion of the operating cycle input
is zeroed and emissions are calculated solely on the basis of temperature. A
special-purpose plant such as a pumping station may be treated as an
industrial plant that consumes fuel according to a characteristic processing
cycle. Individual power plants that have a repeatable diurnal operating cycle
may also be simulated by PLANTSIM; however, power plants that are a part
of a regional power grid may not have a consistent and repeatable emission
pattern, since such plants are likely to engage in power-load transfer among
plants - on at least a seasonal, if not a weekly or diurnal basis.
All sources treated in PLANTSIM are assigned individual physical stack
heights based on the field survey data.
PLANTSIM Computations
When the temperature, T, is between-10° F and 55°F, a linear relationship
for the space-heating thermal load Ls is assumed. This is expressed as
follows:
Ls-LJ,ax	(-10 < T < 55)
Then the total thermal load is
L = Ls + LP ,	{2)
where Lp, the process load, is determined from the appropriate month, day,
and shift factors. The amount of load due to coal, Lc, and due to oil, L°, is
then determined, and the SO2 emission due to each source is calculated as
folJows:
Lc (TH* hr*1) x 10s (Btu TH"1)
1. C(tons/hour) =
2. 0(kgal/hr)
12000 (Btu lb"') x 2000 (lb ton"1)
SO2 (TH hr"') = C(tons hr"1) x 3.68 x Sc(%)
L°(TH) x 10s (Btu TH-1)
18000 (Btu lb"1) x 8000 (lb kgal~!)
SO° (TH hr-1) = Olkgalhr"1) x 157.0 x S°(%)
Thus, the total S02 emission is
S02 = SO2 +¦ SO°	(3)
"Therms
6-14
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When the ambient temperature is such that a dual fuel interruptible plant is
likely to be receiving natural gas, the amount of S02 produced is corres-
pondingly reduced.
In order to facilitate data storage according to a uniform and consistent
format, each plant is assumed to have four stacks. For plants having less
than four stacks, zeros are filled-in for non-existent stacks. The following
parameters are associated with each stack:
1.	S02 emission in pounds per hour
2.	Heat emission in therms per hour.
These parameters are determined by weighting the total SO2 and heat
emissions for the plant by the percentage emitted from each stack. The heat
emission, H, is assumed to be 15 percent of the thermal input.
Example
Consider the example of the Campbell Soup Company shown in Figures 6-4
and 6-5 and assume that emission data are required for the following set of
conditions:
January
temperature 30°F
weekday pattern
first shift
Then,
Ls =
Lp =
L =
Lc =
L° =
C =
so2 =
H =
For Stack 1
SO^' =
H(1,=
500155 ^ 30J = 200 TH hr"1
(.70) (.60)5000 = 2100 TH hr"1
2300 TH hr-1
2300 TH hr"1
0
2300 x 10s 'v
= 10 tonshr
12000 x 2000
10 x 36.8 x 2.8 = 1000 lb hr"1
(.15)2300 = 345 TH hr"1
(.25)1000 = 250 lb hr-1
(.25)345 = 85 TH hr"1
6-15
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For Stack 2
SO^ = (.25)1000 - 250 lb hr"
(2\
H = (.25)345 = 85 TH hr"
For Stack 3
S0^3) =	(.50)1000 = 500 lb hr"1
H{3) =	(.25)345 = 170 TH hr"1
For Stack 4
S0^4) =	0
H(4) =	0
Residential Space-Heating Sources
Residential space-heating sources account for approximately 15 percent of
the annual total emissions for the city. The inventory of coal- and oil-fired
residential space-heating sources was derived primarily from data supplied by
the market research organization of the local natural gas supply utility. This
information was in the form of a city-wide, field-sampling survey of space-
heating sources categorized by fuel use and by the number of dwelling units
per building surveyed. For the purposes of the emission inventory, the
survey data was aggregated into two groups - moderate sized residential
structures of 19 dwelling units or less and large apartment complexes of 20
or more dwelling units.
Since residential sources are generally too numerous to treat individually, the
two building size categories described above were treated as uniformly
distributed square-mile area sources. The source density per square mile for
each category was assigned on the basis of the natural gas utility market
research data.
The operating cycle of the moderate sized heating plants was based on a
55°F degree-day proration of a seasonal average fuel consumption modified
by an empirical function5 that represents the daily cycle of automatic
stoking during waking periods followed by a hold-fire and cool-down during
sleeping periods. This cycle was simulated by a "Janitor Function" that
maintains heating sources on an automatic stoking cycle between 6 AM and
11 PM on days having a minimum night ambient temperature in excess of
5°F. For nights with a minimum temperature below 5 F, the automatic
stoking period was assumed to begin at 3 AM. This pattern was derived
through an interview survey of building superintendents and heating plant
operators. A hot water heating baseload equal to 10 percent of the daily
6-16
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heating fuel use was assumed for all residential buildings in this category.
Hourly-average emissions were assumed to be distributed uniformly through-
out the automatic stoking period and were assumed to be constant during
the hold-fire period. All moderate-size residences were assigned a uniform
physical stack height of 50 ft.
Large residential buildings were considered to operate on an automatic
stoking cycle at all times. Fuel use and S02 emissions were based on a 55°F
degree-day proration and a hot water heating baseload equal to 10 percent of
the daily heating-fuel use was assumed. AIJ buildings in this size category
were assumed to have a 200 ft physical stack height — an assumption based
on a sensitivity analysis of the effect of stack height on the ground level air
quality, and on surveys of actual building sizes.
The hourly-average emissions for large si2e residential buildings were assumed
to be distributed uniformly throughout the stoking period.
Commercial and Institutional Sources
Commercial and institutional sources account for about 8 percent of the
total emissions in Chicago. Fuel use and S02 emission data for large
commercial and institutional sources such as office buildings, water-pumping
stations, educational institutions, etc., were derived from a computer analysis
of a comprehensive inventory developed in 1963 by the Chicago Department
of Air Pollution Control, combined with the results of a field survey of
major sources conducted in 1968 by Argonne National Laboratory and the
Department of Air Pollution Control.
With a few notable exceptions, the commercial and institutional sources are
too small and numerous to treat individually. They are therefore aggregated
as area sources, uniformly distributed throughout each square mile of the
city. The square-mile source-density is based on the 1963 inventory.
Virtually all sources in this category burn fuel primarily for space and hot
water heating and operate on art automatic stoking cycle. Emissions from
these sources were therefore calculated in exactly the same way as in the
case of the large residential sources.
Certain commercial and institutional plants are sufficiently large to warrant
inclusion as individual point sources. Among these are the five Chicago
pumping stations and a number of apace-heating plants that are associated
with extremely large buildings. An operational analysis of the pumping
stations was conducted in order to define their diurnal emission cycle. They
were then treated in essentially the same manner as the large industrial
plants. Individual large commercial heating plants were treated in a manner
similar to the large residential structures. The validity of the latter assump-
tion was established through a detailed survey of the operating cycles of
6-17
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most of these sources, which included, among others, the large University of
Chicago heating plant, the Union Station, the Chicago Merchandise Mart, and
the Chicago Housing Authority complexes.
METEOROLOGICAL AND AIR-QUALITY DATA
Chicago's TAM Networks
In January 1966, the Chicago Department of Air Pollution Control (DAPC)
began recording wind speed and direction and sulfur dioxide levels at eight
telemetered air monitoring (TAM) stations (starred locations on the map,
Figure 6-1). These continuous measurements are integrated over 5-minute
periods; 15-minute averages are then telemetered to the DAPC office where
they are recorded. Tape records of these 15-minute observations have been
reduced to hourly averages. Thus, atthough the accuracy of data from some
of the aerovane sites is limited by 15- to 30-foot masts and/or close
proximity to taller buildings or smoke stacks, the procedure for developing
hourly averages is excellent. This is in contrast to special airport data where
the aerovane sites are excellent, but only brief hourly observations are
recorded.
In the dispersion model, the wind speed and wind direction from the TAM
aerovane nearest to the dose-point is used to determine the trajectory of all
plumes sensed at that point. This temporary assumption will eventually be
eliminated by using all eight stations to develop a wind field for the city. In
contrast to single city-wide values of wind speed and direction from the
nearest airport, the data from a local aerovane is sensitive to special circula-
tion patterns such as lake breezes.
Airport Data
Tapes containing hourly standard weather data from Midway Airport and
Glenview Airport (15 mi north of Chicago) have been obtained from the
National Climatic Center.
Argonne Meteorological Data
The observing station at Argonne National Laboratory (25 mi southwest of
Chicago) was specifically designed to measure parameters controlling diffu-
sion: atmospheric stability, wind speed and direction at five levels up to 150
ft., net and solar radiation, etc. The hourly averages stored there on mag-
netic tape, are the only stability records available in the Chicago area.
Unfortunately, the data are for a shallow layer taken in an open, grass
covered field. Transformations relating these data to the urban environment
are currently underway.
6-18
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Upper-Air Data
Radiosonde observations from the U.S. Weather Bureau RAWIN station at
Peoria, Illinois (140 mi southwest of Chicago) and Green Bay, Wisconsin
(180 mi north of Chicago) have been obtained from the National Climatic
Center. These data have been extrapolated to estimate the height of the
mixing layer in Chacago (see below).
Atmospheric Stability
Turbulent diffusion of pollutant species is represented in the model by a
Gaussian puff kernel with dispersion coefficients aX|(T), ayj(T), oZj(T);
where T is the travel time and i, the atmospheric stability index. The
classification system proposed by Turner3 has been employed using weather
data from Midway Airport.
Height of Mixing Layer
The mixing layer defines a zone within which pollutants can be diluted. The
height of this layer is probably the most critical parameter in determining
ground level S02 concentrations resulting from emissions from tall stacks.
With a high lid (> 2000 ft) plumes from power plants tend to travel far and
disperse widely before touching ground. With a sharp temperature inversion
beneath the physical stack-height, plumes will travel in stable air, which
greatly inhibits vertical diffusion, and touch ground far from the local urban
area. High ground-level concentrations occur in the intermediate range of
mixing-layer heights where the plumes are trapped beneath the lid and
disperse rapidly to the ground in unstable air. Figures 6-6 and 6-7 show
vertical profiles of temperature and sulfur dioxide measured by an instru-
mented helicopter at a point 4 miles downwind of a major industrial area in
Chicago. The sharp inversion at 2300 ft (700 m) has clearly defined a ver-
tical mixing zone within which S02 levels are nearly uniform.
Except for the low level rural temperature profiles measured at Argonne, no
vertical soundings are available for the Chicago area during the period from
January 1966, when the TAM network became operational, to January
1969. This is the period during which meteorological air quality and emis-
sion data have been accumulated at Argonne. It was therefore necessary to
design a scheme for estimating the height of the mixing layer from historical
weather data. (In July, 1969 the Weather Bureau in the Chicago Air Quality
Control Region began a program of daily balloon soundings at 0600 and
1200 from Midway Airport. This data will be available for future validation
studies of the dispersion model and will also be used to validate the objec-
tive mixing-layer height estimate described in this section.)
The computerized objective mixing-layer depth estimates are based on an
interpolation scheme between two rawinsonde stations. Green Bay, Wiscon-
sin, and Peoria, Illinois. The soundings are usually taken at 0600 and 1800
6-19
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1,400
38
0.2 0.3
S02, ppm
±
±
40
46
J
48
42	44
TEMPERATURE, °F
Figures 6-6 and 6-7 (superimposed) Vertical profile
of SC>2 concentrations and temperature in Hinsdale,
Illinois, April 11, 1969 at 10:20 am. (D. Nelson,
Argonne National Laboratory).
Central Standard Time (CST). The mandatory and significant levels for each
station are merged to form a single pressure-temperature array for each
sounding. The Chicago rural (Argonne) temperature profile is formed either
by "shifting" one of the two to the Argonne surface temperature or by
interpolation between the Peoria and Green Bay soundings. If only one
station is in the same air mass as Chicago, the sounding from that station is
transposed without changing its shape, to the Argonne surface temperature
6-20
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at sounding time. If both Peoria and Green Bay are in the same air mass as
Chicago (as determined by inspection of the daily weather map), then a
linear interpolation is performed. This procedure forms a pressure-tempera-
ture array for the 0600 and 1800 rural profiles.
The next step is to compute the hourly rural profiles using temporal
weighting. The profile for any hour is a linear interpolation in time between
the bracketing 0600 and 1800 rural soundings.
The hourly urban mixing depth and mixing depth indices are now computed.
The height of the mixing layer is defined by the intersection of a dry
adiabat from the urban surface temperature with the constructed Argonne
rural temperature profile. In the Chicago case mixing-layer heights calculated
by this objective procedure are compared with more subjective estimates
provided by a local meteorological consulting firm. While actual magnitudes
differed, there was a good agreement in terms of diurnal trends. Calculated
values agreed very closely with data from two helicopter soundings but, in
both cases, the inversions were above 2000 ft and therefore not in the
critical range where plume trapping could occur.
Pollution concentrations from a given source are evaluated in this model by
forming a convolution sum of two time-series: (1) piecewise (hourly) con-
stant stack emissions, and (2) a discrete transfer function based on the
mathematical representation of an integrated puff. The latter is found by
integration of a Gaussian kernel representing advection according to a time
series of piecewise constant wind vectors and three-dimensional dispersion
according to a time series of piecewise constant classes of atmospheric
stability. (For example, results indicate that one of the more important
types of short-term pollution incidents, the morning fumigation, which is
characterized by low winds (up to 6 mph) and by a sharp transition from
stable stratification to strong vertical mixing, is simulated successfully.)
Details of the development of the kernel and limitations on its range of
applicability are discussed in the following sections.
Dispersion Kernel
For a steady mean wind, U, in the downwind x-direction, with y and z
representing unbounded crosswind and vertical dimensions, a normal distribu-
tion yields the following Green's Function:
TRANSPORT OF AIRBORNE POLLUTANTS
X(t, t') =
Q(t')
+
(2?r)3/2 ctx (t - t') ay (t - t') oz (t - t')
6-21
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where x(t t') is the concentration at time, t due to an instantaneous release,
Q at time t' and position (0,0,0)8'9. The dispersion coefficients ax. ay, o2,
are assumed to be functions only of the delay time T = t - t' and the
atmospheric stability class".
Assume Q(t) a piecewise constant over a fundamental time interval, A (e.g.,
A = 1 hour)' then, for the special case of a steady wind in the x-direct'ion,
the concentration i(x,y,z,m) at time t = mA can be found by a convolution
of the piecewise constant emissions with a series of integrals (the discrete
transfer function) evaluated over m periods of duration A:
X(*.Y,z,m)
» f
~ h 1 + 1 I
h=l	J
nA
exp-
(t«-1) A
(x - uT)'
2 o*
2a.
(2ff)
3/2
Z2
2^7_
ox(T) ffy(T) oz(T)
dT (5)
^ Qm-n
n=l
+ 1 Gn
This is represented schematically in Figure 6-8 by the buildup of SO^ due to
three (m = 3) consecutive 2-hour (A = 2) piecewise constant emissions.
TWO-HOUR
EMISSION PERIOD
I NO. 1
I STACK _
~Q2Gl
TWO-HOUR
EMISSION PERIOD
I STACK N0'2
TWO-HOUR
!EMISSION PERIOD
X(x) = Q1G1 (x)
X(x) = Q2g1 W + QlG2 W
Q1G2
X(x) - Q3G1 (x) + Q2G2 (x) + Q1G3 (x)
Q2G2
Figure 6-8. Buildup of SC^as superposition of consecutive 2-hour
releases for case of steady wind in x-direction.
6-22
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Equation (5), the contribution from an individual source to the concentra-
tion at time mA, must then be summed over all sources.
Equation (5) can be generalized to account for variation (piecewise constant)
in wind direction, wind speed, and atmospheric stability:
m
[x-A 2 Uj-um_n + 1 (T-A(n-I) ) ]2
j = m-n + 2
na	
2ah (T)
m
Ey-A 2 vrvm_n + j (T-A(n-1) )
exp- (+	J°m-n + 2 '	
2ah2 (T)
z2
{n-1)A	2oz2(T)
(6)
(2tt) ah (T) az(T)
where variations in wind velocity are represented by the piecewise constant
series [uj]™ and [vj]{". Note that this result is contingent upon the
assumption of ax = oy = uh, a horizontal dispersion coefficient. There are
valid arguments (to be reviewed in a later section) why this assumption is
questionable, except perhaps, for very low wind speeds. From a computa-
tional standpoint, the puff appears circular if ax = ay, and consequently,
since its x,y shape is independent of wind direction, the generalization of the
kernel to accommodate variations in wind direction is greatly simplified. The
propagation of a circular puff for varying wind speed and direction is easily
visualized by the schematic of Figure 6-9.
In simulating lake breezes and unusual urban circulations, continuity in the
wind field and conservation of the mass of pollutant require introduction of
a vertical velocity component. This component as well as the horizontal
quantities u and v will be hightly dependent upon space and time variations.
Equation (6) considers only time dependence of the wind, although one can
use different sequences [uj]™ and [vj]™ depending upon the location of
the dose point. Using the lake breeze and, in particular, a dose point near
the confluence,as an example, we must allow for two converging streams and
a vertical motion which is highly space dependent. The algorithms presented
in this paper are not yet expressed in a manner sufficiently general to handle
this space dependence. However, it seems relatively straightforward to ap-
proximate a three-dimensional velocity field with the three components
u(x,y,t). v(x,v,t) and w(x,y,t) and restate the basic algorithm.
Variable Atmospheric Stability
Postulating variations of a with a travel time T and requiring continuity of o
at each time step,3 we might describe a three step process by the paths
shown in Figure 6-10.
6-23
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Figure 6-9. Three-hour propagation of circular puff from an in-
stantaneous release. Assumption: 
-------
Figure 6-10. Three-step variations in atmospheric stability
class, exact method (500 sec, crcontinuous).
T, sec
Figure 6-11. Three-step variations in atmospheric stability
class by approximate method (A = 500 sec, T continuous,
- °5 + A o"4 + A 0-3).
6-25
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Associated with each puff are functions of time, ah(t) arid a?(t), that could,
in principle, be calculated according to the procedure of Figure 6-10. This
procedure requires calculation of a psuedo-time for travel within each new
stability class. Although the stability class does not change every hour, a
computer program based on hourly steps must provide a general algorithm
for handling this situation. Unfortunately, the process in Figure 6-10 appears
devoid of any simple algorithm suitable for economic programming on the
computer. The problem is that the dispersion coefficient o should be kept
continuous in spite of the fact that we are forced to employ a set of discrete
functions.
An approximation to the "continuous a" scheme of Figure 6-10 is proposed
iri Figure 6-11 for which the time of flight is continuous and the value of cr(t}
is determined by adding changes in a. A comparatively simple algorithm can
be written to implement the procedure shown in Figure 6-11. The two
procedures are compared in Table 6-5 where a tolerable error is incurred by
the "approximate" method of Figure 6-11 as opposed to the "exact"
method of Figure 6-10. For this comparison, we allowed a single change in
stability class at the beginning of period 2.
Table 6-5. EXACT METHOD* VERSUS APPROXIMATE METHODb
FOR DETERMINING ATMOSPHERIC DISPERSION COEFFICIENT
(A = 5000 sec; a At 10,000 sec)
Atmospheric stability classc
Dispersion coefficients
<7y(m)d

Period t
Period 2
Exact
Approx.
Exact
Approx,
4
5
2000
1900
200
230
5
4
1900
1700
200
220
3
5
2400
2500
1000
1100
5
3
2500
2100
1100
1120
a Figure 6-10
b Figure 6-11
*1 Piecewise constants (see section—Transport of Airborne Pollutants)
"m" indicates number of discrete transfer functions (periods]
to which a is applied [see section—Dispersion Kernali
6^26
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Dispersion Cofficients
The integrated puff model is similar to earlier dispersion models in that a
Gaussian distribution with appropriate dispersion parameters is the funda-
mental assumption. Although the puff model is closer to physical reality, it
is still dependent and quite sensitive to these dispersion coefficients.
There are a number of sets of functions for cy and az with either downwind
distance or time-of-flight as the independent variable, and, for the most part,
resultant curves are in mutual agreement. Some modifications (for example,
by Turner10 in the St. Louis study) have been made to account for greater
instability over a city, since most curves are based on experiments over level
rural terrain. Recent field experiments in St. Louis by McElroy and Pooler11
support these modifications; although their estimates of the coefficient of
vertical diffusion may be excessive if applied to smoke plumes, because their
data was obtained by tracer releases at ground level.
The choice of the function ax (j,t) required for the integrated puff model is a
serious consideration. Data from field experiments on instantaneous and
steady releases12, 11 have been processed to yield dispersion coefficients
which fit the plume model, where concentration:
0 exp-	~ -iU
x = 	—	(7)
2n ay o2 U
Extensive horizional measurements were employed to determine oy statis-
tically; and oz by inferrence. Clearly the introduction of an additional
dispresion coefficient ax with a corresponding change in the basic equation
will alter the analysis of the experiments and thus the conclusions regarding
the magitude of dispersion coefficients.
Another concern is the assumption ax=aywhich results in the advecting/dif-
fusing circular puff discussed and shown in Figure 6-9. Although rot strictly
correct, it is convenient to consider ox as the superposition of two compo-
nents: (1) horizontal turbulence due to eddies of a scale smaller than the
puff size, and (2) upwind/downwind elongation due to vertical shear. Thus,
wbiJe the assumption ox=av may be reasonable for unstable and neutral
conditions of atmospheric stability, it may be inappropriate in situations
where the effect of wind shear is magnified by the existence of a stable
atmosphere that inhibits vertical mixing.13,14 However in these cases, smoke
plumes from major emitters will probably not touch ground within the
urban area.
The dispersion coefficients used to obtain the resiilts presented here obey
the sets of functions
av.i (0, cZti(t); t = 1,5
6=27
-------
from the equation proposed by Turner'0 for use in his St. Louis model
(Figures 6-12 and 6-13 tor i = 1 to 7!. Furthermore, it is assumed that ax ~ °y •
Plume vs. Puff Calculations
Equation (5) which, for constant Q, expresses the steady-state concentration
according to the integrated puff formulation; wjll in general not agree with
the plume model equation 17) evaluated at T = x/u. However, on the
centerline (y = 0, £ = 0) the two equations yield almost identical results for
j > 1 mph.
The linear plots of az (T) and jy 
-------
6-12 and 6-13 can be approximated by the linear relations: ax = oy = aT;
oz = 7T. Substitutions of these functions into Equation (4) for y = z = 0
yields the following:

OO
oL
J o
/ (X-UT)2)
8XP" j 2 oz2 (T) J
(2tt)3/2 ax
a>
N
b
Figure 6-13. Sets of vertical dispersion coefficients Qx> j (t), for atmos-
pheric stability classes i = 1 to 7; used in St. Louis model by Turner.10
T = plume travel time.
6-29
-------
Figure 6-14, Linear plot of 
-------
-------
Table 6-6. CALCULATED VALUES OF CENTER LINE3 PLUMEb -
PUFF CONVERSION FACTOR. F,c FOR
SELECTED VALUES OF r IN STABILfTY CLASSES 3, 4, 5d
DURING FIRST FEW HOURS OF TRAVEL TIME
¦¦
Stability class horizontal wind speeds, mph

r = u/\/2 a
U)
"4
U5
F
10
12
8
7
1.00
1
1.2
0.8
0,7
1.03
0.?
0.8
0.5
0.4
1.10
0.5
0.6
0.4
0.3
1.22
0
0
0
0
OO
t Y = z * 0	x
b Plume Equation (4) evaluated at T = ~
c Equation (9) = PF
d See Figure 6-15
with dispersion coefficients expressed as functions of travel time T = (x/u)
goes to zero. This is in contrast to the plume formula based on dispersion
coefficients as functions of travel distance x. This function becomes infinite
as u 0. In contrast to these two versions of the plume equation, concen-
trations estimated by the integrated puff model in Eq. (5) approach an x~2
distribution as u -»¦ 0.
Effective Stack Height
The effective stack height H, is the height above ground which best defines
the centerline of the pfume. The plume is assumed to originate as a point
source at an altitude H feet above ground at the location of the stack. If
aerodynamic downwash causes the plume to break up and mix rap/dly
downward in the vicinity of the stack, H may be set equal to the actual
physical height, Hs. Observations of a local utility indicate this phenomenon
occurs frequently for wind speeds greater than 15 mph. Otherwise a plume
rise AH is added to the physical stack height Hs, so that:
H = Hs + AH	<10)
where AH is estimated as described below:
Smoke plume rise calculations in this model are based on a plume rise
formula derived from observations at TVA stations and other power
plants15. {The momentum term in the original formulation is omitted in the
following equation since its contribution is generally negligible compared to
thermal buoyancy.)	1/2
AH = 		—	(11)
U
6-32
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where AH = plume rise (ft)
Qs = heat emission rate from stack (Btu hr*1)
U = wind speed (mph) at the height of the stack
K = 0.870 (unstable-Class 3), 0.354 (neutral-€1 ass 4), 0.222
(stable—Class 5}
Values of the heat emission rate may be approximated by a fixed percentage
of the total heat rate {heating value of the fuel times the fuel rate), The
percentage depends on the type and efficiency of the burning and heat
exchange equipment but may be categorized as follows:
Power plant — 12%
Large industrial, commercial - 20%
Small industrial, commercial and residential — 35%
The mean wind at the physical stack height, Hs should never be used in the
plume rise Equation 111). In evaluating the dispersion kernel (Equation 6},
wind at the effective stack height H, corresponding to the plume centerline,
is used. In each case, the desired value for the wind speed will be usually
greater than that measured at a local airport or TAM station (typically at 30
ft to 100 ft above the ground!. Equation {12} provides a correction term
for altitudes up to 1000 ft. The exponent P >s dependent on the stability
class, as shown in Table 6-7,
U {at height z2) = U (at height ZjJCz^/zj	(12)
	Table 6-7. EXPOMENT FOR WIND PROFILE LAW16	
Stability Class	P
stable (5)		0.5
neutral |4)		0.2
unstable (3)		0,2
The experimental data in the reference cited, indicated a slightly more
uniform vertical wind speed profile for unstable than for neutral conditions,
but the model is not sensitive to this distinction.
Four restrictions placed on the use of Equation (11) are listed in Table 6-8.
Table 6-8. RESTRICTIONS ON PLUME RISE FORMULA (Equation 11>
Mixing-layer height
Hm
Low wind speeds
U
Stability class and
Coefficient K
a.	Effective stack height H, cannot be
greater than mixing-lave' height,
H^, if stack is beneath mixing layer;
i.e. H < if Hs < Hpn
b.	If Hs > Hm, assume Hm = 00 with
ptume rise and dispersion accord-
ing to stable atmospheric conditions
1 f U estimated to be
< 4 mph, value 4mph
used in Equation [11}
H tfie physical stack
height, Hs > 200 feet,
K =0.354 (neutral
used even though the
stability index indicates
unstable conditions.
6-33
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The restrictions on mixing-layer height in Table 6-8 are based on the assump-
tion of an impenetrable atmospheric layer (lid) at height Hm. The effluent
from a stack which emits its plume just beneath the lid will probably pene-
trate into the stable layer rather than obey the assumption ol perfect
reflection at the lid. Unfortunately, there do not appear to be any data that
describe this situation.
The restriction in Table 6-8 limiting the minimum wind speed to be used in
Equation (11) reflects the fact that the equation is an empirical one in
which the parameters n and m in an equation of the form AH = K Qns Um
were found by multiple linear regression. A comparison of Equation (11)
with TVA data17 indicates good agreement down to wind speeds of about
6 rrph. Below this, the (l/u) factor in the equation causes an over-estimation
of the plume rise. An arbitrary restriction has been made, therefore, on a
minimum value of U in Equation (1T).
The restriction on stability class and coefficient K, occurs because, for plume
rise calculations, the vertical variation of temperature at heights greater than
200 feet is best characterized by a neutral lapse rate, even though unstable
conditions may exist in the first few hundred feet above ground.
A single value of plume rise is also ascribed to each of the three classes of
area-sources (previously discussed) whenever the wind is less than a critical
wind speed. With winds Jess than6mph, low-rise residential buildings are
assumed to have an effective stack height of 100 feet; high-rise residential
and commercial buildings, 300 feet; and industrial area-sources, 300 feet.
The model proves to be insensitive to these assumptions as long as the initial
value of az (oz0) is greater than or equal to 100 feet.
Finite Geometry
The fundamental puff kernel has been defined for z from (-«>,+«>) with z=0
on the plume axis. If we assume perfect reflection at the ground, the
concentration C, at time m, at a receptor position (x,y,z), due to a single
source at position (x',y',z',) is:
C = x
-------
In order to avoid this abrupt transition and simultaneously, to allow for
time-dependent (piecewise, constant, hourly) values of Hm multiple reflec-
tions between ground and the inversion are represented by pairs of image
sources. For example, the first image source above the lid is the reflection
about Hm of the actual source; the second image source above the lid is the
reflection about Hm of the first below-ground image (Figure 6-16). Depen-
ding upon the lid height and the time of travel, up to five pairs of images
may be required to adequately represent a condition of uniform vertical
mixing in an urban area.
~I	• l2
Figure 6-16. Multiple reflections of pollutant between stable layer
and ground, represented mathematically by two sets of image
sources. Image G-j reflected above lid at L2, Image Li reflected
below ground at G2. S = first image source, reflection of actual
source.
6-35
-------
Since the lid height may vary during the lifetime of each 1-hour puff,
algorithms have been formulated to allow for specification of a different
effective lid height for each hour m, look-back time n (Equation (5), and
source J. For example, in Figure 6-17 the height of the mixing layer is
steadily decreasing during the three 1-hour periods. Calculations of concen-
trations due to stack emissions during the first hour (m=t) would be based
on lid height Hm, for m=1, n=1, and the lid height Hm2 for m=2, n = 1 and
2. Concentrations due to stack emissions during the second hour (m=2)
would be based on lid height Hm2 for m=2, n=1, and on Hm3 for m=3,
n=2. Concentrations due to stack emissions during the third hour (m=3)
would be based on an infinite lid with diffusion coefficients corresponding
to stable atmospheric conditions.
Figure 6-17. Variable mixing-layer heights.
Area Sources
Earlier studies have emphasized the importance of residential coal use in
determining ambient S02 levels. For example, at Hyde Park (TAM-4) S02
levels of 0.2 to 0.3 p'pm for southwest winds 6 to 9 mph can be attributed
almost entirely to space-heating by coal-fired boilers in three-story build-
ings.19
The realistic modeling of residential zones characterized by multiple-sources
too numerous to represent by individual plumes is therefore critical to the
6-36
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success of a source-oriented dispersion model for Chicago. For the Chicago
grid system these so-called area-sources can be visualized in one of two
modes:
1.	For winds less than a critical speed the individual emissions resemble
plumes. For three-story buildings, visual observations indicate that a
representative plume rise for wind speeds less than 6 mph is about
equal to the building height, i.e., approximately 50 feet.
2.	Above the critical wind speed, mechanical turbulence, primarily down-
wash, destroys the plume slightly above the rooftop level.
Similar arguments apply to high-rise, commercial, and industrial area-sources
previously described. In the first case, we might approximate the area-source
as a uniform horizontal sheet of small thickness Az located at z = 100 feet.
In the second mode, it is reasonable to assume uniform mixing over the
volume of the building.
The integrated puff model is ideally suited to the task of synthesizing these
source configurations. In contrast to the plume equation, limited to cross-
wind and vertical coordinates, thereby representing a two-dimensional front,
the puff incorporates the downwind coordinate and thus represents a three-
dimensional cloud of pollutant.
The area source is approximated by a psuedo point source. This is similar to
algorithms employed in plume models; but as mentioned above, the more
sophisticated puff kernel results in a volumetric source rather than a two-
dimensional wave front. In addition to giving a more realistic description of
downwind dispersion, the puff model can, therefore, directly evaluate the
effect of the area-source upon the area itself.
The volumetric source is synthesized by specifying three initial dispersion
coefficients: ctx0, ay0 and ctz0. These are then associated with times tx, ty,
and tz which are the solutions to:
tfxo = MUxh tjy0 = oy(i,ty), az0 = az(i,tz)	(14)
where a(i,t) is the family of functions describing the dispersion coefficients
at time, t, for stability class, i. A virtual source is thus defined at upwind
distances 5X = utx and £y = vty from the center of the area (see Figure 6-18).
The choices of ax0, ay0 and oz0 as well as the effective source height, z,
depend upon the representative building height for each square mile and the
mode of initial transport: plume or downwash. The transport equation
(Equation 6) is then modified with x -5X replacing x, y -Sy replacing y,
and T + tx, T + ty, T + tz replacing T in the appropriate locations.
For a square-area source of side length, n the value of ayo is defined by
ay0 = n/2.4	(15)
6-37
-------
Figure 6-18. Volumetric synthesis P, of area source of bui (dings of
height z, at upwind distances of and &y; from center of area
source (x, y).
This insures that the concentration will be independent of position aiong a
line on the downwind side ol a row of identical area sources $ Figure 6-19).
U
Figure 6-19. Choice of OyQ = n/2,4, insures uniform concentrations
along line A-A for row of identical area sources.
6-38
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AN INTEGRATED SYSTEM FOR
AIR RESOURCE DATA MANAGEMENT AND
DISPERSION MODEL DEVELOPMENT
The preceding sections of this paper have described the array of emission
inventory, meteorology and air quality data that was acquired and processed
in order to test and validate the diffusion model. This computerized file
containing nearly 3 years of hourly-average data for a wide variety of pa-
rameters, represented a singularly valuable resource, but at the same time,
it presented a formidable problem in data management. The development of
the "integrated puff" model required that this data file be exploited in two
ways:
1,	Analysis of statistically significant subsets of this array of data could
be expected to yieJd information concerning the relative significance of
many of the parameters and phenomena that were modeled. Moreover,
the insights into the micrometeorological characteristics of the Chicago
metropolitan area obtained through analysis of this data should serve
as a guide to the interpretation and evaluation of the output of the
model.
2.	Time series arrays of emission-inventory data, and raw and processed
meteorology data were required as inputs to the puff model, while a
corresponding array of measured sulfur oxide concentrations had to be
merged and compared with puff model output in order to analyze and
validate its theoretical predictions against real-world data. The tatter
represented a major and laborious task if it was done manually.
An automatic data management system was clearly required in order to
achieve these objectives. This need was met by the development of a master
Air Pollution Information and Computation System (APICS) designed to
automate the entire process of data storage, retrieval, manipulation, analysis,
and display, associated with the dispersion model development effort.
The APICS system consists of the IBM PL-1 data storage and retrieval code
nested in a series of operational subroutines and computational codes
tailored to the analysis of air pollution data. With this system, the data
stored in the master file can be partitioned in any way desired. Any
combination, array or subset of emission, meteorology and/or air quality
data can be formed and retrieved. The selected data array can be accessed
through a FORTRAN subroutine which allows the user to manipulate the
array in any desired way. For example, the analyst may form a new data
array which consists of products of components of the original array raised
to some power, etc. Standard subroutines for computing atmospheric stabi-
lity, smoke plume rise, etc., are included as options in this system.
The array of data in the master file may be analyzed with a multivariate
6-39
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linear regression analysis code or a discriminant analysis code, both part of
the system and the results may be displayed as tables, histograms or CAL-
COMP plots.
The air pollution data management system described above provides a
uniquely powerful tool for the development and testing of the dispersion
model. The emission simulation model previously described and the disper-
sion model algorithms previously described have been incorporated into the
APICS system, so that the testing and validation process, conducted with a
3-year computerized inventory of hourly-average meteorology and sulfur
dioxide air quality data, is totally automated. Meteorology and emission data
from the master data file are input to the dispersion model, and sulfur
dioxide concentrations are calculated; these results are compared with the
corresponding measured air quality data and displayed in a single operation
within the Argonne, IBM 360-75 computer. The sensitivity of the model to
variations of critical meteorological parameters and the effects of modifi-
cations in the structure of the model itself can be tested. When the dis-
persion model development effort is completed in the early part of 1970, a
manual of operations for the APICS system as well as for the dispersion
model itself will be prepared for general use.
RESULTS, CONCLUSIONS, and PROJECTIONS
TAM Stations
The month of January, 1967 was chosen for an initial comparison of the
model with recorded sulfur dioxide data. Five TAM stations were selected
representing a wide range of geographical and emission features (Figure 6-1).
TAM 1, situated in a low-density residential area in the northwest corner of
the city, sees little S02 unless southeasterly winds carry plumes from the
power plants and other industries 11 miles away.
Prevailing southwest winds are responsible for high concentrations occasion-
ally observed at TAM 2. This station is also influenced by the high-rise
concentration along the lakeshore during northeasterly winds, especially
during lake breeze conditions.
TAM 3 generally records the highest sulfur dioxide levels in the city. It is
situated in the midst of coal-burning commercial buildings (for example.
Union Station, several blocks to the west emitted 8 x 106 pounds of S02
per year until it recently shifted to gas). Furthermore, southwest winds,
sweeping up the "industrial corridor," along which three power plants and
major industries are located, cause extremely high pollution concentrations
downtown, especially when vertical ventilation is limited by an inversion.
Peak hourly averages greater than 1 ppm have been recorded.
TAM 4 is situated along the lake at the edge of over 20 square miles of
6-40
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coal-burning three-story residences. Studies of the frequency of air pollution
incidents in Chicago from January 1966 to December 1967 indicate that this
station has the highest number of midwinter short-term air pollution inci-
dents (6 hrs to 24 hrs duration). For example, in January 1966 and January
1967, TAM 4 had a total of thirty 6-hour periods for which S02 levels
exceeded 0.4 ppm. The corresponding figures for TAMS 1,2, and 3 are 0,1
and 8. Furthermore, plumes from the industrial corridor 7 miles northwest
are often sensed at TAM 4.
TAM 5 is similar to TAM 1 except that northerly winds are responsible for
occasionally high S02 levels. Other TAM stations (6 through 8) were not
included in this initial validation effort because they are situated on the
borders of the city, and no inventory has yet been assembled for the areas
of Cook County immediately outside the city limits or for the Gary-Ham-
mond, Indiana, industrial zone.
Ninety-seven station-days (2328 hourly values) were studied for the month
of January 1967 at TAM stations 1 through 5. A station malfunction on any
particular day eliminated that station from the data set for that day. Mal-
functions, either due to sensor or transmission difficulties, were
automatically logged on the original Chicago air quality tapes.
Computer Requirements
The model has been programmed for the IBM -360 computer. Since each
hourly time step for each source and each receptor involves a numerical
integration, some effort has been expended to:
1.	Limit the number of integrations by employing a preliminary test to
estimate whether or not a particular ptume is likely to contribute to a
given dose point (for example, there is no reason to evaluate the
contribution from a stack located 5 miles downwind of the receptor).
2.	Approximate integrals, where possible, by the mean value theorem.
3.	Lump distant area sources together.
As presently constructed, the model run with hourly time steps requires
between 0.5 and 0.75 minute of computer time per station-day. Thus the
run for five TAM stations for the 97 station-days in the month of January
1967 required less than 2 hours. Recent analytical work (see Plume vs. Puff
Calculations page 6-28) indicates that dispersion coefficients can be approx-
imated by the linear relationships ay = aT, az = 7T where a and 7 are
constants. Under these circumstances, the integral (Equation 6) can be
evaluated in closed form. It is anticipated that run time with this modifi-
cation will be approximately equal to that required for a standard plume
model.
6-41
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Statistical Results
There are numerous statistical tests that have been applied to source-orien-
ted, pollution-dispersion models. The importance attached to any particular
test clearly depends upon the intended use of the model.20 One of the more
standard presentations involves evaluating the percentage of calculated values
within a given tolerance of the corresponding observed values. This is
equivalent to a scattergram, but less dazzling and more easily interpreted
Table 6-9 lists these percentages for each TAM station and for the citywide
collection. Hourly data and 2-hour, 6-hour, and 24-hour averages are evalu-
ated in terms of five criteria.
Table 6-9. STATISTICAL EVALUATION OF INTEGRATED PUFF MODEL DATA:
PERCENTAGE OF CALCULATED POLLUTANT CONCENTRATIONS WITHIN
DESIGNATED TOLERANCE LIMITS OF SAMPLE DATA®


TAM si
ations
Item
avg.
1 2
3
4
5
1-5
Mean l^0t)S)

0 06 ppm
0 .12 ppm
0.33 ppm
0 ,15 ppm
0,06 ppm
0.14 ppm
(^obs ^calc) „ ino%
Mobs

10%
i 16%
t 14%
3%
9%
* 7.4%
Sib dev. (obs calc)
i
0.09 ppm
0.10 ppm
0.20 ppm
0.13 ppm
0 10 ppm
0 13 ppm
Sid dev/mean

1.7
0 88
0.62
0 84
1.6
0.93
% • 0 025 ppm
1
58%
37%
12%
?6%
45%
35%
% • 0.05 ppm
i
69%
63%
23%
53%
71 %
57%
% '0.1 ppm
i
84%
81 %
47%
79%
89%
77%
No, data poims
1
288
576
432
408
624
2328
Std. dev. (obscalc)
2
0.08
0.09
0 18
0.11
0.09
0.12
Std. dev/mean
2
1.3
0.78
056
0.77
1.5
0.83
% ' 0.025 ppm
2
58%
40%
15%
29%
45%
37%
% ' 0 .05
2
70%
66%
27%
52%
70%
58%
% 1 0.1 ppm
2
83%
83%
49%
81%
88%
78%
No, data points
1
144
288
216
204
312
1164
Std dev lobs caic)
6
007
0.08
0-14
0 08
0 07
0.09
Std, dev,'mean
6
11
65
0.42
0.58
12
0.64
% ' 0 025 ppm
6
56%
36%
10%
32%
46%
36%
% ¦ 0 05 ppm
6
67%
66%
29%
54%
72%
j 59%
% 0 1 ppm
6
90%
88%
j 56%
85%
91%
: 83%
IMo data points
6
48
96
72
68
104
388
Sid dev (obs-calcl
24
0.04 ppm
0.05 ppm
0.10 ppm
0.07 ppm
0.04 ppm
' 0.06 ppm
Std, dew/mean
24
0.71
0 44
0.30
0.45
0.70
; 0.43
% -0.025 ppm
24
25%
46%
17%
59%
58%
43%
% > 0.05 ppm
24
75%
62%
39%
77%
77%
66%
% • 0.1 ppm
24
100%
96%
67%
88%
96%
90%
No. data points
24
12
24
28
17
26
97
'• Chicago, Uo uiry, 1967
6 42
-------
Monthly and daily predictions are in excellent agreement with observed
values. Marsh and Withers21 indicate that, for their Reading, England, model
as well as for others in the literature, the ratios of the standard deviations
{observed-calculated) to the observed means are all higher than 1.1. From
Table 6-9 the corresponding value for 24-hour averages is 0.43. It is 0.64 for
6-hour averages and 0.93 for 1-hour averages.
Results for individual TAM stations vary, depending primarily upon the
monthly mean. For example, almost all values for TAMS 1 and 5 fall within
±0.1 ppm since the means are only 0.06. For the same reason, however, the
ratios (aob$.ca|C)/ Mobs are high for these stations.
Figure 6-20 (a and b) shows daily averages at TAMS 1 to 5 for January
1967. Six-hour averages are presented in Table 6-9 because 6 hours is the
minimum practical time step for the implementation of incident control
strategies.22 On a citywide basis 59 percent of the calculated 6-hour values
are within ±0.05 ppm and 83 percent within ±0.1 ppm. The results for
6-hour averages are also presented in Figure 6-21. Assuming the solid lines
delineate a region of successful predictions, then 59 percent of the calcula-
tions are "correct", the skill score (based on chance) is 0.42; the model
explained 52 percent of the variants in the observed data set. For 24-hour
averages this statistic is 74 percent.
Tables 6-10 and 6-11 illustrate the use of the model in evaluating the
frequency of short-term air pollution incidents. The contingency tables are
based on the following air pollution "war game" rules:
1.	A threshold S02 level is defined for a given averaging period.
2.	If the model predicts that this level will be exceeded, then action is
taken.
3.	If action is taken and the observed average is greater than the thresh-
old /ess a tolerance {here .025 ppm), then incident is said to have
actually occurred.
4.	If no action is taken and the observed average is less than the
threshold plus a slight tolerance (here 0.025 ppm), then an incident is
said not to have occurred.
When compared to chance, the model is significant at better than the 99.9%
confidence level and the skill scores for this air pollution war game range
from 0.64 to 0.80, Skill scores are defined by the ratio (V-VVCT-V1)
where V is the number of correct estimates (here yes*yes + no*no cases), T
the total number of cases, and V1 the value of V expected by some means
other than the model under evaluation. (For example, instead of chance, a
simpler plume mode) might be used.) It is worth noting, also, that in terms
of incident control policies; taking serious actions, such as temporarily
curtailing industrial production is costly. Air pollution cost-benefit studies
conducted at Argonne show that as much as $10 million per day can be
6-43
-------
o>
I
-£»
O
t-
BC
O
o
o
a.
0.20
0.10
0
0.20
0.10
0
0.40
0.30
0.20
0.10
0
STATIONS
TAM-2
j_ » ^
i —
-O- "O-
I I I I
M M M M
I I I I I
M M U M M.
--rv-




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0.20
0.10
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£ 0
STATIONS
TAM-1
M M
TAM-2
-o- -
i r
t~i—r
_i
"O"	-9. M M M M M MM
--O- -o- -y— -TST
-¦O" --O-
_2_

--0--
LlJ
O
O
O
TAM-3
0,40
— M
-o~
M M
0.30
| 0.20
iJ 0.10
£ o
>-
—J
a 0.20
g 0.10
£ o
>¦
0.20
0.10
0
TAM-4
--o- -
--o-
mmmmmmm mm
TAM>5
M M M M M
TT-	°
! r j —n r t i i" i T i~r "T r
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
DAY
Figure 6-20b. Daily pollutant concentration averages, Chicago, January 16 to 31, 1967.
"M", missing data.
-------
a 0.5
0.4
CsJ
O
t/)
o
LU
>
C£
LU
CO
o
0.3
0.2
0.1



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1



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2
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)
3


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2
2
3

3
I
3
3


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7




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3 I
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4



1
15
10
8
5
5
3
4
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1


2
21
16
41
iJ
6
1


1
68
^9
4
2

2




0.1	0.?	0.3
ESTIMATED S02t ppm
0.4
2 0.5
Figure 6-21. Six-hour pollutant averages, Chicago, January 1967.
Table 6-10. FREQUENCY OF 24-HR INCIDENTS FOR STATIONS 1-6
JANUARY 1967
Symbol
Threshold
Tolerance
Skill score
(Based on chance)
X
0.1 ppm
0.025
0.76
V
0.2 ppm
0.025
0.73
z
0.3 ppm
0.025
0.75
CONTINGENCY

Predict


Yes
No

Y
x 44
x 9
O
e
V 17
V 6
c
s
z 9
z 1
c

x 3
x 41
u
r
N
V 3
V 71

o
z 3
z 84
6-46
-------
Table 6-11. FREQUENCY OF 6-HR INCIDENTS FOR STATIONS 1—5
JANUARY 1967
Symbol
Threshold
Tolerance
Skill score
i Based on chance)
X
0.1 ppm
0.025
0.76
y
0.2 ppm
0.025
0.64
z
0.3 ppm
0.025
0.80
CONTINGENCY

Predict


Yes
No
O
c
Y
e
s
x 145
y 62
z 32
x 32
y 28
z 10
c
u
r
N
0
x 14
y 20
z 6
x 197
y 278
z 340
involved in lost wages
practice, the tolerance
insure that the model
and 6-10
and production for a city
used above would have to
scores significantly better
such as Chicago. Thus, in
be enlarged sufficiently to
than shown in Tables 6-9
Hourly Time Series
Figure 6-22 is a sample of strip charts for January 1967 showing hourly wind
speed, wind direction, temperature (all measured at Midway Airport), atmo-
spheric stability class, and the mixing height as estimated by the objective
method previously described. Figure 6-23 is a sample of strip charts also for
January 1967 showing smoothed hourly values of observed {solid lines) and
estimated (dotted lines) sulfur dioxide for TAMS 1-5. For readability, the
hourly values have been smoothed by the formula: X(n) = 1/4(X(n-1) +
2X(n) + X(n+1) where n is the hour number. They are then approximately
equivalent to 2-hour averages. Missing data is denoted by an "M".
This appears to be the first paper which presents time series such as these.
They clearly show that the model, which, statistically, looks very promising,
has its exceptionally good and equally disappointing moments. The model as
presently constructed has a number of strong points: among them a disper-
sion kernel that can respond fn a physically realistic way to transients in
wind direction, wind speed, source strength, and mixing-layer height, and
which synthesizes area sources exceptionally well; and industrial inventory
that estimates seasonal and daily shift patterns, based on an emission inven-
tory procedure geared to a boiler-room superintendent; an objective, mix-
ing-layer height-estimation technique, which, although suffering from the
6-47
-------
C5
¦fck
00
DAY
DAY
Figure 6-22. Stripchart of hourly values of (top to bottom ordinates) atmospheric stability
classification, estimated mixing-layer height, temperature at Midway airport, and wind speed
and direction, January 1 to 16, 1967.
-------
o
•
4*.
CD
DAY
DAY
Figure 6-22 (continued). Stripchart of hourly values of (top to bottom ordinates) atmospheric
stability classification, estimated mixing-layer height, temperature at Midway airport, and wind
speed and direction, January 17 to 31, 1967.
-------
6 12 18 24 6 12 18 24
TIME, hours
observed,	estimated M-missing data.
Figure 6-23. Sample of smoothed hourly values of SO2 concen-
trations at TAM stations 1 to 5, January 1 and 2, 1967.
6-50
-------
0.40
0.30
0.20
0.10
0
0.30
0.20
0.10
0
0.60
0.50
0.40
0.30
§. 0.20
S* 0.10
CO
0
0.40
0.30
0.20
0.10
0
0.40
0.30
0.20
0.10
0
6 12 IB 24 6 12 18 24
TIME, hours
	observed,	estimated M-missing data.
Figure 6-23 (continued). Sample of smoothed hourly values of SO2
concentrations at TAM stations 1 to 5, January 3 and 4, 1967.
TAM 1





*






'/\
\
\
1 .


BOTH
ARE-
0.0


V









TAM 2









M



M









f\TAM3lA
. i \ X \
f !\

v\
\\


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A *
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11
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1
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1 \
1
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!/
1
i
v I
A



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V
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k
1

/
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A
TAM 4

r




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\





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TAM 5



















V r.
r \\


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b —


v' V
SS><

6-51
-------
0.40
0.30
0.20
0.10
0
130
0.20
0.10
0
0.60
0.50
0.40
% 0.30
cf 0.Z0

0.10
0
0.40
0.30
0.20
0.10
0
0.40
0.30
0.20
0,10
0 g 12 18 24 6 12 18 24
TIME, hours
		 observed,	estimated. M-missing.
Pinure 6-23 (continued). Sample of smoothed hourly values of S02
concentrations at TAM stations 1 to 5, January 5 and 6, 1967.
TAM 1


n







r







V

M





/
•




TAM 2









M


M











TAM 3




T
1 l
f 1

i[\


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t
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V 1
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N	
6-52
-------
0.40
0.30
0.20
0.10
0
0.30
0.20
0.10
0
0.60
0.50
0.40
g. 0.30
o.
0.20
c/>
0.10
0
0.40
0.30
0.20
0.10
0
0.40
0.30
0.20
6 12 18 24 6 1 2 18 24
TIME, hours
observed, 		estimated. lift-missing.
Figure 6-23 (continued). Sample of smoothed hourly values of SO2
concentrations at TAM stations 1 to 5, January 7 and 8, 1967.
TAM 1

















M


M










TAM ?
TAM 3




/*¦

/





t
1
/
1
L
i
1
(





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	V








TAM 5
6-53
-------
0.40
0.30
0.20
0.10
0
0.30
0.20
0.10
0
0.60
0.50
0.40
0.30
0.20
0.10
0
0.40
0.30
0.20
0.10
0
0.40
0.30
0.20
0.10
0
TAM1








Ml











M









TAM 2
V
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i
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— _ «¦

m — *T,'


H- v-
12 18 24 6
TIME, hours
observed,	estimated.
12 18 24
M-missing.
Figure 6-23 (continued). Sample of smoothed hourly values of SO2
concentrations at TAW stations 1 to 5, January 9 and 10, 1967,
6-54
-------
-------
0.40
0.30
0.20
0.10
0
0.30
0.20
0.10
0
0.60
0.50
0.40
£ 0.30
A
^5 0.20
0.10
0
0.40
0.30
0.20
0.10
0
0.40
0.30
0.20
0.10
0
6 12 18 24 6 12 18 24
TIME, hours
—		 observed,	estimated. M-missing.
Figure 6-23 (continued). Sample of smoothed hourly values of SO2
concentrations at TAM stations 1 to 5, January 13 and 14, 1967.
TAM 1
















M



M










TAM 2
If V"*
f \
\
lx

\


-J


- v

\


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6-56
-------

0.40

0.30

0.20

0.10

0

0.30

0.20

0.10

0

0.60

0.50

0.40
e
0.30
a-

cS1
0.20
t/j


0.10

0

0.40

0.30

0.20

0.10

0

0.40

0.30

0.20

0.10

0
TAN) 1
















M



M










TAM 2



			—L.
1
,k

I
\





P
V
1
\
\

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—





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—n—
/ \
1A /







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y v






—






r



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/"\
/ \.
/
y>
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*









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-^1




-
6 12 18 24 6
TIME, hours
observed,	estimated.
12 18 24
M -missing.
Figure 6-23 (continued). Sample of smoothed hourly values of SO2
concentrations at TAM stations 1 to 5, January 15 and 16, 1967.
6-57
-------
0.40
0.30
0.20
0.10
0
0.40
0.30
0.20
0.10
0
TAM 4
t
f
~—
'
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/
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/ \
/ \


/
f \





v"~'
\
\









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/







1
v/
V

\



/
/
Vy


\


-—-






6 12
observed,	estimated.
18 24 6
TIME, hours
12
18 24
M -missing.
Figure 6-23 ( continued). Sample of smoothed hourly values of SC>2
concentrations at TAM stations 1 to 5, January 17 and 18, 1967.
6-58
-------
6 12 18 24 6 12 18 24
TIME, hours
	 observed,	estimated. M - missing.
Figure 6-23 ( continued). Sample of smoothed hourly values of SO2
concentrations at TAM stations 1 to 5, January 19 and 20, 1967.
6-59
-------

0.40

l).3U

0.20

0.1U

0

0.30

0.20

0.10

0

O.tiO

0.50

0.40
F
0.30
a.

esi
0.20
c/>
0.10

0

0.40

0.30

0.20

0.10

0

0.40

0.30

0.20

0.10

0
TAM 1


f\



	



! \

A
4- 1
A



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1 /¦>
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A
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0.462
TAM 2


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TAM 4
















M



M










TAM 5
















M



M


|






observed,
12 18 24 6
TIME, hours
	estimated.
12
18 24
M-missing.
Figure 6-23 (continued). Sample of smoothed hourly values of SO2
concentrations at TAM stations 1 to 5, January 21 and 22, 1967.
6-60
-------
0.30
0.20
0.10
0
0.30
0.20
0.10
0
0.60
0.50
0.40
0.30
o.
cCi 0.20
o
oo
0.10
0
0.40
0.30
0.20
0.10
0
0.40
0.30
0.20
0.10
° 6 12 16 24 6 12 IS 24
TIME, hours
		observed,	esti mated. M - mi ssi ng.
Figure 6-23 (continued). Sample of smoothed hourly values of SO2
concentrations at TAM stations 1 to 5, January 23 and 24, 1967.
TAM 1




/
1
{





"t~
1
\
\





f
' /
r\

TAM 2

/
\
-
ll *
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TAM 3
























M



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|













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M



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6-61
-------
0.30
0.20
0.10
0
0.30
0.20
0.10
0
0.60
0.50
0.40
e 0.30
3
cvi 0.20
o
«/>
0.10
0
0.40
0.30
0.20
0.10
0
0.40
0.30
0.20
0.10
° 6 12 18 24 6 12 18 24
TIME, hours
	-observed,-	estimated. M - missing.
Figure 6-23 (continued). Sample of smoothed hourly values of SO2
concentrations at TAM stations 1 to 5, January 25 and 26, 1967.
TAM 1








M



M










TAM 2








A

/\











' ¦¦
TAM 3







1
J

1 V






t
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v.
		
s
6-62
-------
0.30
0.20
0.10
0
0.30
0.20
0.10
0
0.60
0.50
0.40
e 0.30
CL
&
* 0.20
° 0.10
0
0.40
0.30
0.20
0.10
0
0.40'
0.30
0.20
0.10
0
6 12 18 24 6 12 18 24
TIME, hours
	observed,-	estimated. IKI- missing.
Figure 6-23 (continued). Sample of smoothed hourly values of SO2
concentrations at TAM stations 1 to 5, January 27 and 28, 1967.
TAM 1








M



M










TAM 3






'V




/r
ft
it
1
*

l\\





\
\
\

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1

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M



M










6-63
-------
0.30
0.20
0.10
0
0.30
0.20
0.10
0
0.60
0.50
0.40
t 0.30
GL
£ 0.20
ts>
0.10
0
0.40
0.30
0.2(1
0.10
0
0.40
0.30
0.20
0.10
° 6 12 18 24 6 12 18 24
TIME, hours
	observed,	estimated M-missing.
Figure 6-23 (continued). Sample of smoothed hourly values of SO2
concentrations at TAM stations 1 to 5, January 29 and 30, 1967.
TAM 1


	
	




M

M










TAM 2














s-
	j


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r ~~


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M



M










6-64
-------
0.30
0.20
0.10
0
0.30
0.20
0.10
0
0.60
0.50
0.40
§. 0.30
A
0.20
-------
obvious problems of extrapolating vertical temperature profiles over dis-
tances greater than 100 miles, correlates well with subjective estimates of
diurnal trends; and an overall system of data storage, retrieval, and analyses
designed to meet the operational requirements of an urban air pollution
control administration. Weak points are also evident; most significantly, a
poor determination of the wind field, which should be improved by deriving
an hourly wind map but which, in any event, is limited in Chicago by the
accuracy of the TAM aerovanes. Under certain circumstances the model is
also extremely sensitive to meteorological parameters—both observed and
derived. (For example, when the height of the mixing-layer approaches the
physical stack-height of a major power plant, the calculation of ground-level
concentrations due to that plant may vary by a factor of 10 or more,
depending upon whether the plume is assumed to travel above or to be
trapped beneath the lid.) There are also further refinements that should be
made in the model; major point sources and area sources outside the city
limits must be included in the emission inventory; the local effect of the
topography of city center on the mixing-layer height and the effective
atmospheric stability should be included; plume rise formulations might be
modified to synthesize a gradually ascending plume; the run-time can be
greatly reduced if the equations can be integrated analytically.
The sample strip charts give clear evidence of many of these items. The
results, magnitudes, and trends appear to be sufficiently consistent to test
selected hypotheses, about both the model and the air pollution meteorology
of the urban area. The following is a list of topics for which the hourly time
series of meteorological and air quality variables give evidence.
The Importance of Residential and Commercial
Heating Sources and Low-Lying Industrial Sources
The importance of residential and commercial heating sources and low-lying
industrial sources can be seen easily by an overall comparison of ambient S02
levels at the five stations with emission maps (Figures 6-1 and 6-2). The model
predicts station means for January to within plus or minus 20 percent.
The Importance of Wind Direction
January 9 and 10 at TAM 4 are days of almost constant temperature (28°F),
wind speed (15 mph), and mixing-layer height (2000 ft). Vet the S02 level
rose steadily from below 0.1 ppm on January 9, to 0.2 on the 10th, as The
wind swung from 220° (comparatively low residential emissions) to 270°
(significantly higher residential emissions) to 300° (high residential emissions
plus the distant industrial area). On the same two days, TAM 2 saw
approximately the reverse trend of upwind source concentration. TAM 3, on
January 27, responded to a gradual shift in wind direction from NE to NW.
6-66
-------
Large Point Sources are Assumed to Touch Ground —
But Do Not
The Crawford power pfartt (III in Figure 6-71, as opposed to others with
different stack configurations, is regularly predicted to reach ground level
whenever its plume centerline passes over TAM 5 (4 mi south), but it is
consistently barely detected (for example, TAM 5, Jan. 5, 10, 27, 29).
Large Point Sources Trapped Beneath a Lid
Cause Very High Concentrations Downwind
For example: TAM 1, Jan. 1, 4, 5
TAM 3, Jan. 15 (note dropping lid had little difference
on TAM 2)
TAM 2, Jan. 21, 23
Periods of Very Low Winds
Winds of < 5 mph occur on the following occasions:
Jan 3 (0300-0800) - 5 (1300-1600) - 13 (0600-0900)
18 (1000-1300) - 21 (2000-2200) - 23 (1800-2400)
24 (0000-0900) - 25 (1800-2400)
Almost uniformly, the model yields satisfactory predictions of trends and
magnitudes of SO2 levels during these critical periods of low winds and
potentially high SOs levels.
Transition Hours—Sunrise and Sunset
From 0600 to 1000 and from 1500 to 1900 are diurnal periods of significant
change in the dispersive capacity of the urban atmosphere. During these
periods the model is influenced by changes in atmospheric stability and
mixing-layer height. The model appears capable of simulating the corres-
ponding diurnal trends in S02 level; although, occasionally the sensitivity of
the relationship between assumed lid height and physical stack height of
upwind point sources causes large discrepancies between predicted and ob-
served concentrations (example TAM 4, Jan. 6).
The Emission inventory
This should be extended beyond the city limits. For example, TAM 5 is
consistently under-predicted when winds are from the SW. The receptor is 4
mi from the Cicero residential/commercial area. Approximately 20 mi to the
southwest is the Ronrteoville Power Plant which regularly emits more than 2
x 10s pounds SOi per hour. For a southwest wind at 10 mph, the pfume
concentration on the ground at TAM 5 is approximately 0.03 ppm with no
lid present. Examples of under-predictions at TAM 5 during SW winds:
January 11, 12, 13 (midday) January 9, 19 (all day)
6-67
-------
Abrupt Changes in Windspeed and Direction
On January 23 (1800), January 24 (0700), January 28 (2300), and January 29
(1300) abrupt changes in wind speed and direction were simulated with
acceptable accuracy.
6-68
-------
REFERENCES
1.	Croke, K. and A. Kennedy. An Air Quality Control Program for Large Industrial
Sources in the City of Chicago. Presented at 62d AnnuaI Meet mo of the Air
Pollution Control Association. New York. June 22-26, 1969.
2.	Koogler, J. B, et at A Multivariate Model for Atmospheric Dispersion Predictions.
J. Air Pollution Control Assoc. 77:211-214, April 1967.
3.	Turner, D. B. A Diffusion Model for an Urban Area. J. Appl. Meteorol. 3(11:83-91,
February 1964.
4.	Clarke, J. F. A Simple Diffusion Model for Calculating Point Concentrations from
Multiple Sources. J. Air Pollution Control Assoc. 14:347-352, September 1964.
5.	Croke, E. J. et at. Chicago Air Pollution System Model; Second Quarterly Progress
Report. National Center for Air Pollution Control, Chicago Dept. of Air Pollution
Control, Argonne National Laboratory. Argonne, III. ANL/ES-CC-002. May 1968.
160p.
6.	Kennedy, A. and J. Anderson. A Computerized Information and Computation
System for Environmental Studies. Presented at 62d Annual Meeting of the Air
Pollution Control Association. New York. June 22-26, 1969.
7.	Pasquill, F. The Estimation of Diffusion from Meteorological Data. In: Atmospheric
Diffusion. London, D. Van Nostrand Co. Ltd., 1962. p. 179-204.
8.	Slade, D. Estimates of Dispersion from Pollutant Releases of a Few Seconds to 8
Hours in Duration. Air Resources Laboratories. Washington, D. C. Technical Note
39-ARL-3. 1966.
9.	Croke, E. J. at al. Chicago Air Pollution System Model; Fourth Quarterly Progress
Report. National Center for Air Pollution Control, Chicago Dept. of Air Pollution
Control, Argonne National Laboratory. Argonne, III. ANL/ES-CC-004. March 1969.
10.	Private communication with D. B. Turner. Bureau of Criteria and Standards,
National Air Pollution Control Administration. 1968.
11.	McElroy J. L. and F, Pooler, Jr. St. Louis Dispersion Study, Vol.lt Analysis.
National Air Pollution Control Administration. Arlington, Va. Publication Number
AP-53. December 1968. 61 p.
12.	Cramer, H. E. et a). Meteorological Prediction Techniques and Data System.
Geophysics Corporation of America. Bedford. Mass. GCA Technical Report Number
64-3-G, March 10, 1964. 252 p.
13.	Bowden, K. F. Horizontal Mixing in the Sea Due to a Shearing Current. J, Fluid
Mech. 21:83-95. January 1995.
14.	Cramer, H. E, and R. K. Dumbauld. Experimental Designs for Dosage Predictions in
CB Field Tests. Geophysics Corporation of America. Bedford, Mass. GCA Technical
Report Number 68-17-G. 1968
15.	Carson, J. E. and H. Moses. The Validity of Currently Popular Plume Rise
Formulas. In: Proceedings of the USAEC Meteorological Information Meeting,
Chalk River Nuclear Laboratories, September 11-14, 1967. h/lamori, C.A. led.).
Atomic Energy of Canada, Ltd. Chalk River Ontario. Report Number AECL-2787.
1967 p. 1-20,
16.	DeMarrais, G, A. Wind-speed Profile at Brookhaven National Laboratory. J. Mete-
orol. 75(21:181-190, April 1959.
17.	Carpenter, S. G. et at. Report on Full-Scale Study of Plume Rise at Large Electric
Generating Stations. Presented at 60th Annual Meeting of the Air Pollution Control
Association. Cleveland, June 11-16, 1967.
18.	Turner, D. B. Workbook of Atmospheric Dispersion Estimates. National Center for
Air Pollution Control. Cincinnati, Ohio. PHS Publication Number 99S-AP-26. 1967.
84 p.
19.	Croke, E. J. et a/. Chicago Air Pollution System Model; Third Quarterly Progress
Report. National Center for Air Pollution Control, Chicago Dept. of Air Pollution
Control, Argonne National Laboratory. Argonne, 1(1. ANL/ES-CC-003. October
1968. 254 p.
6-69
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20.	Moses, H. Mathematical Urban Air Pollution Models. National Center for Air
Pollution Control, Chicago Dept. of Air Pollution Control, Argonne National
Laboratory. Argonne, III. ANL/ES-RPY-001. April 1969. 69 p.
21.	Marsh, K. J. and V. R. Withers. An Experimental Study of the Dispersion of the
Emissions from Chimneys in Reading - III. The Investigation of Dispersion Calcula-
tions. Atmos. Environ. 3(3):281-302, May 1969.
22.	Croke, E. J, et at. Chicago Air Pollution System Model; First Quarterly Progress
Report. National Center for Air Pollution Confrol, Chicago Dept. of Air Pollution
Control, Argonne National Laboratory. Argonne, III, ANL/ES-CC-001. February
1968. 106 p.
ACKNOWLEDGMENT
The authors of this paper wish to acknowledge with gratitude the significant
contributions of Messrs. J. Norcs and L. Conlev of Argonne National Labora-
tory and Mr. J. Lin and the late Mr. R. Votruba of the Chicago Department of
Air Pollution Control.
The advice and counsel of Mr. D. B. Turner of the National Air Pollution
Control Administration, Mr. H. Moses of Argonne National Laboratory, and
the late Dr. B. Davidson of New York University were also of great value to the
atmospheric dispersion model development program.
6-70
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APPENDIX - GLOSSARY OF SYMBOLS
C	concentration of pollutant at a receptor point
G„	derivative of discrete transfer function representing value of
curve at point of intersection, n
H	effective stack height (centerline of plume)
Hm	height of mixing layer, lid height
Hs	actual, physical height of stack
AH	plume rise height
i	atmospheric stability class
K	constant, conversion coefficient
LP	process load
L5	space-heating thermai load
m	number fundamental time intervals over which discrete trans-
fer function is integrated
n	iteration integer; or "look back" time
P	exponent describing stability class
G(t)	piecewise constant pollutant release function
r	dimensionless number used to simplify Equation (8)
T	delay time = (t -1')
T	puff travel time
U	steady mean wind velocity
[UilJUvj]?1, constant series for variations in horizontal wind velocity
V	number of correct estimates
V'	value of V predicted from a different model
X	concentration at time t, due to instantaneous release, Q at
time t' and position (0,0,0)
x	horizontal wind distance, downwind
y	horizontal wind distance, crosswind
z	vertical wind distance
Az	approximate, of area-source thickness
6-71
-------
Z	effective source height
a	parameter used to define a in terms of T, units: *en9t^
time
5X 5y	upwind distances
A	fundamental time increment
ah	horizontal dispersion coefficient
an (t)	d ispersion coefficient as function of time
ax	dispersion coefficient in x-direction
6-72
-------
ABSTRACT
Analyses of tracer-dispersion data in Japan, especially those of vertical
concentration profiles, indicate that the tracer-cloud height generally
increases with the downwind distance. The increase is larger over an
urban area than a rural area. When the tracer crosses over a hill, it rises
remarkably. Over a complicated topography the rise of tracer-cloud is
larger than over a flat terrain, a circumstance well reflected in the
surface concentration pattern. When the tracer-cloud height varies
greatly with the downwind distance, the surface concentration
decreases uniformly downwind in spite of the elevated source.
AUTHOR
SHIN'ICHI SAKURABA is Chief of the Applied Meteorology Laboratory,
Meteorological Research Institute, Tokyo. He is currently involved with tracer
studies of medium range atmospheric dispersions in littoral, industrial areas of
Japan, in connection with the nation's air pollution control program. In other
meteorological work he has been concerned with atmospheric turbulence up to
the 500-meter level and plume rise from a high stack
-------
7. SENSITIVITIES OF AIR QUALITY PREDICTION
TO INPUT ERRORS AND UNCERTAINTIES
SHIN'ICHI SAKURABA*
Meteorological Research Institute, Tokyo
INTRODUCTION
In earlier dispersion-data analyses, the height of the tracer cloud was usually
assumed to be constant; this frequently resulted in an over-estimate of the
vertical dispersion parameter, especially over an urban area or a sloped
terrain. When vertical concentration profile data are available at one or two
points downwind, tracer-cloud height can be estimated from the
surface-concentration analysis. Some dispersion data in Japan are analyzed
along this line
RELEASE TIME AND SAMPLING TIME IN DETACHED
PLUME EXPERIMENT
In field studies of atmospheric dispersion made in urban areas of Japan, the
drum-impactor was used at two points downwind to measure the travel time
of the tracer cloud, the time-concentration curve and eventually the total
time, TDr required for the passage of a detached tracer-plume. In these
experiments the sampler, which measured the concentration, was actuated
before the dispersing tracer arrived and was deactivated after the last of the
tracer was assumed to have passed, so the real sampling time, T, of the
sampler is usually equal to TD. However TD or T is not always equal to the
release time, r, of tracer.
Table 7-1 shows the result of experiments fn 1968.
*tn collaboration with M. Moriguchi and I. Yamazi
7-1
-------
Table 7-1. COMPARISON OF RELEASE TIME,7", AND TOTAL TIME TD
OF DETACHED PLUME DISPERSION8



frequency




Location of experiment
experiments
Tq=7
TD > r
To < T
Toyama	
8
5
3
0
Wakayama	
8
5
3
0

13
5
1
7
Total	
29
15
7
7
aJapan, 1968.
Here r was usually 30 min and TD = t shows the case for ITD - r I
smaller than 5 min. It is noteworthy that the total frequency of TD > t is
the same as that of TD < r , though the total number of cases is small.
Figures 7-1 and 7-2 show the time-concentration curves at x = 2.5 km and x
= 5.0 km respectively, x being the downwind distance, t is 27.5 min and
the source height, h, is 150 meters (m) The ordinate is 1 minute
concentrations in relative units and the abscissa is time. The increase of TD
with the downwind distance is small. These cases are listed as TD = r in
Table 7-1.
Figures 7-3 and 7-4 show the examples of TD > r when r is 26 min and h =
200 m. In Figure 7-3 the concentration curve of surface-source tracer
released simultaneously with the 200-meter source is also shown by black
circle. In case of h = 200 m, TD is 48 min at x = 1.5 km and 72 min at x
= 5.0 km. The elongation of TD with the downwind distance is remarkable,
and in these cases it may happen that TD exceeds the sampling time T .
Figure 7-5 shows an example TD < r when r = 30 min and h = 150 m.
Now it is important to investigate the mechanism of how the time width,
TD , of detached plume elongates or contracts with the downwind distance
x , since the analysis of surface concentration data composing most of
dispersion-experiment data depends exclusively on such mechanisms.
In case of Figures 7-3 and 7-4 half-hourly pilot balloon observations were
made at the source x = 0 ( P| ) and x = 3.8 km ( ?2 ). The wind direction
was due west and the piba) station; P2, was east of the source. The two
drum-impactor sites Dj, and D2,were also east of the source as follows:

P.
(source)
D,
P2
d2
X
o
1.5
3.8
5.0 km
7-2
-------
TOYAIVIA (JULY 24, 1968)
D-l
h = 150 m, Td - 15:16-15:44 - 28 min
JS

e
=3
150
a>



'¦M
JS

0>

k—
100
z

o

h-


»
£ 100
•x
oc
Ui
u
o
o
50
TOYAMA (JULY 24, 1968)
D-2
h -150 m, TD -15:35-16:05 - 30 min
x = 27.5 min,jj,=2.4msec*l,X =5.0 km












	Oil

-	i
	I	


15:20 15:30 15:40 15:50
CLOCK TIME
16:00
16:10
Figure 7-2. Same as figure 7-1 out for x = 5.0 km.
7-3
-------
1,000
a>
>
ts
2 - 0.8, jl 1.6 m see**
h - 0 mf To = 12:20-12:52 = 32 min, t 12:00-12:30 30 min
= 1.25 m sec-1




I


<
A
1/
'v


L>"
12:10 12:20 12:30 12:40 12:50 13:00
CLOCK TIME
Figure 7-3. Time-concentration curve at x 1.5 km. Tq>t
60
<1
oc
d>
UJ
o
O
o
30
CO
o>
AUGUST 7,1968 (WAKAYAMA)
X - 5.000 m
h = 200 m T = 12:42-13:40 58 min
TD = 12:42-13:54 72 min
x = 12:01-12:27 26 min
Jij = 1.3Tji2 = = 1*5 m sec*1


J\
M

/\

	

/Vs
/
h




N

12:40 12:50 13:00 13:10 13:20 13:30 13:40 13:50
CLOCK TIME
Figure 7-4. Same as Figure 7-3 but for X= 5.0 km.
7-4
-------
AUGUST 26,1968 (OITA)
X=2.6 km
TD =11:07-11:25 (18 min)
v= 10:30-11:00 (30 min)
300
250
| 200
J2
o 150
i—
•x
ai
v—
| 100
o
o
50
0
11:00 11:10 11:20 11:30 11:40
CLOCK TIME
Figure 7-5. Time-concentration curve at X = 2.6 km. Tq < t.
The tracer was released at 12:01, ending at 12:27. The wind speeds at 200 m
level at P, and P2 are as follows:
P.
P
3

Windspeed

Windspeed
Time
(m sec-1)
Time
(m sec 1)
12:00
2,4
12:00
1.3
12:30
0.9
12:30
1.3


13:00
1.3
-

1



-





./
J




7-5
-------
According to the drum-impactor data, the transport speed of the tracer is;
Speed, m sec 1
Part of tracer cloud
x, km
2.3
0.8
2.0
1.1
front
rear
front
rear
1.5 to 5.0
0 to 1.5
This, compared with pibal data, suggests that the elongation or contraction
of Td occurs by the windspeed difference between the front-part and the
rear-part of tracer cloud.
Next we will try to compute TD based on pibal data. If the front of tracer
flows with the speed 2.4 m sec"', it will reach D, at
12:01 + 1500 m/2.4 m sec 1 = 12:11
and P2 at
12:01 + 3800 m/2.4 m sec ' = 12:27
The corresponding arrival time of the rear
12:27 + 1500 m/0.9 m sec"1 = 12.55 ( D, )
12:27 + 3800 m/0.9 m sec'1 = 13.37 { P2 )
The calculated TD is, at Di
12:11 - 12:55 = 44 min.
While the observed TD is
12:12 - 13:00 = 48 min.
From P2 on, the tracer speed is 1.3 m sec"1, so the arrival time at D2 is
12:27 + 1200 m/1.3 m sec*"1 = 12:42 (front)
13:37 + 1200 m/1.3 m sec'1 - 13.52 (rear)
TD - 70 min
The observed TD at D2 is
12:42 - 13:54 = 72 min.
7-6
-------
The coincidence is good, supporting the view that the elongation or contrac-
tion of a detached plume is due to the windspeed difference at its front and
rear. The sampling time T, by the way, and the estimated or observed TD in
this case are as follows:
X
0.6
1.5
3.0
5.0 km
T
33
48
57
58 min
Td
33
[48]
68
[72] min
Here the numeral in brackets shows the observed value. Evidently samplers
at 3 km and 5 km downwind were stopped before the tracer passed by.
AVERAGE CONCENTRATION AND DISPERSION EQUATION
The dispersion equation for a continuous point source is:
q- C(x, y,z) = / [ay(x), a2(x), h, y, z]
(11
and the equation of mass continuity is
C dy dz = Q
// ¦
(2)
The notations are customary ones. In dispersion-data analysis we must refer
to Equation 1. Some kind of average concentration conforming to Equation
1 must then be introduced to compensate for having only the exposure data,
especially when TD is not equal to r, or when TD is not known.
Let C be the instantaneous concentration. The exposure, E, and the average
concentration, C are
E =
I
/
C dt
(3)
C 
-------
Case 1. TD - T
This corresponds to the case when the sampler has captured all the tracer
materia! passing by, which is usually the case with the dispersion experiment.
Then, from the equation of mass continuity,
j dt J £ uCdydz = Qr	(5)
Qr shows the total mass of tracer released. Dividing by T,
u C dy dz = Q r/T	(6)
II
where
„ T
u C = _J	 / uCdt ^ u C (T)
-/•
t/
cm = — / cdt
So Equation 6 becomes
ff =
C (T) dy dz = Q r/T = Q'	(7)
The dispersion equation corresponding to Equation 7 should be
T
uC(T)/Q'= uC (T) 7 = /	(8)
Equation 7 shows that the source intensity corresponding to the average
concentration C(T) is not Q, but Q'. 0 coincides with Q' only when T =
T.
Equation 8 may be simplified, by introducing the concentration C, defined
by
7-8
-------

E = / Cdt = / C'dt	(9)
and the corresponding average concentration C (r);

C (r) = -J C' dt	(10)
Namely Equation 8 becomes
u C (r) / Q = f	(11)
Equation 11 does not contain T explicitly and is convenient for the con-
centration analysis.
Cds& 2. Tq > T
This is a rather rare case and sampling time does not cover the whole range
of the time concentration curve. Such an example was already shown (Figure
7-4). The best estimate for the equation of mass continuity in this case, is
/ dt //u
which yields:
C dy dz = Q r rr	(12)
1 D
- TD _
u — C (t) / Q = f	(13)
T
Equations 11 and 13 will be used later in the surface-concentration analysis.
Estimation of tracer-cloud height
based on surface-concentration analysis
Since 1967 the vertical measurement of tracer material has been made at
two points downwind, from which the center-line height, 1 , of the tracer-
cloud as well as the vertical dispersion parameter, oz, is derivable. Examina-
tion of 45 vertical concentration profiles, made it clear that ~z varies
7-9
-------
remarkably with the downwind distance, and in turn seriously affects the
surface concentration pattern. In the sea breeze layer, in which most disper-
sion experiments were conducted, 1 generally increases with the downwind
distance. The increase is larger over an urban area than a rural area, and over
a sloped area than a flat area. Next we wilt examine the possibility of
estimating, z from the surface concentration.
We will begin with the dispersion equation:
C (Cx, y, z) = / [av(k) , az(x), z(x), y, z]	(14)
z is the center-line height of the tracer cloud or the gravity-center height of
concentration and a function of downwind distance x.
C/O is:
TD _
C/Q - — C(r)/Q	(15)
T
as proved in the previous section, and Tq/T is in most cases unity.
To determine 1 (x) from Equation 14, the transport speed u . the source
intensity Q , the horizontal dispersion parameter ay and the vertical disper-
sion parameter o, must be known. The determination of cry is simple and
needs no special comment; u may be accurately determined by the drum-
impactor record. At one or two points downwind we have the concentra-
tion-profile data, or z and az. Then Q is determined from the Equation 14,
with the concentration data The constancy of Q may also be checked if the
concentration-profile data are available at two points downwind. It was
found that Q is almost constant down to at least 5 km, as far as the
elevated-source dispersion is concerned.
Now, from Equation 14 ,
j Ca/Q - / lay(x),a^(x), z(x), 0, 0]	(16)
Ca = C(x,0,0,) is the axial concentration at the surface. We already have z and
ut at one or two points downwind. Then, from oz , the corresponding
Pasquill stability could be determined. If the Pasquill stability thus deter-
mined is fairly constant over the downwind distance concerned, the estima-
tion of z (x) from Equation 16 becomes possible. It was made clear from
the measurement of oz at two points downwind that in the case of elevated
sources the Pasquill stability can be regarded constant down to about 5 km
distance, even over an urban area. It is important to rote here that the
Pasquill stability decided from the observed a, should be adopted.
7-10
-------
In the following sections we will give some examples of z (x) over an urban
area analyzed along the line stated in this section.
Yokohama experiment
Figure 7-6 is the sampling network of the Yokohama experiment. Two
sources, 60 m and 113 m high, were placed at the Negishi industrial area, at
the southern extremity of Yokohama City. From the 60-meter source to 1.6
km arc, the terrian is flat. Beyond the 1.6 kilometer arc, there is a tableland
about 50 m high bounded by a cliff (see Figure 7-10). Beyond the 3.5
kilometer arc is the central part of Yokohama City. In the experiment
of July 26, 1967, two fluorescent particle tracers were released from a 60-
meter source and 113-meter source simultaneously. The tracer drifted in the
southerly wind; hit the tableland; crossed over it; and flowed over the
congested area of Yokohama City.
Figure 7-6. Network of Yokohama experiment.
7-11
-------
The concentration-profile sounding was made at two sites, one at x - 2.3 km
on the tableland and the other at x 4.8 km near the coast of Yokohama
Port, the downwind distance x being measured from the 60-meter source.
Figure 7-7 shows the concentration-profile at x 2.3 km The analysis is usually
made, assuming the Gaussian distribution of concentration in the vertical.
The profile in Figure 7-7 does not lend itself to such an analysis; however, it
is certain that z is larger than 250 m, the highest level of sounding.
JULY 26, 1967 (YOKOHAMA)
10:00-^0:30
h 60 m x = 2.3 km Z = 295 m crz - 51 m (D)
0.09,	1				 +
0.08 h
0.07
0.06
CO
e
« 0.05
o 0.04
o
0.03
0.02
0.01
0.00
0 40 80 120 160 200 240 280
Z, m
Figure 7-7. Concentration profile at X - 2.3 km. source height 60
meters,
7-12
-------
Figure 7-8 shows two soundings: one is at x = 4.8 km from the 60-meter
source and the other is at x = 3.7 km from the 113-meter source. In the
former I is 170 m and oz is 56 m, the Pasquill stability, E; , while in the
latter z is 175 m and u/ is 54 m, the Pasquill stability, D to E. In the
following the Pasquill stability E will be adopted to treat the dispersion from
the meter 60-meter source.
o h - 60 m
• h -113 m
0.08
0.07
0.06
0.05
E
<_>
0>
vp 0.04
o»
o 0.03
0.02
0.01
0.00
JULY 26,1970 (YOKOHAMA)
10:00-10:30
X 4.8 Km Z -170 m CTz^56m(E)
X 3.7 Km Z 175 m 0"z 54 m (D»E)
-
1
~ •

-

o
•
•
o

o
•
o
	 1
1.


0 40 80 120 160 200 240 280
Z, m
Figure 7-8. White circle same as Figure 7-7 but for x = 4.8 Km,
black circle, concentration profile at x= 3.7 km, source height,
113 meters.
7-13
-------
Figure 7-9 shows the result of the surface concentration analysis made with
the procedure stated in the previous section, The curve is the isoline of z, in
meters, when the Pasquill stability is E. The white circle shows only how the
JULY 26,1967 (YOKOHAMA)
10:00-10:30 h ^ 60 m ^ = 5.0 m sec-1
X (D) 0.8 1.6 (2.3) 3.5 (4.8) 5.0 km
Z (60) 50 70 (>250) 150 170 170 m
STABILITY, E
Figure 7-9. Surface axial concentration versus downwind distance
curve, case of Pasquill stability E. Labelled numeral shows tracer
cloud height, meters.
7-14
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normalized surface axial concentration varies with the downwind distance
and has no connection with z . The black circle shows the surface concen-
tration modified such that xy conforms to that in Pasquill stability E. This is
because xy and xz are usually different in Pasquill stability. In the case in
Figure 7-9, the Pasquill stability of xy is higher than E at x = 0.8 km and
1.6 km, while at x = 3.5 km and 5 km it is about the same; z can be read
from the black circles in Figure 9.
The result, depicted together with the topography in Figure 7 10 is sum-
marized as follows:
E
500
400
300
200
100
0
JULY 26. 10:00-10:30 (YOKOHAMA)
0.8 1.6
f [
i



¦ -r- |
1
- '
1
/•"


i

j


1

j


^	1

jmm


2.5	3.5
X, km
5.0
Figure 7-10. Tracer-cloud height variation with downwind distance
and topography in Yokohama experiment.
x	(0) 0.8 1.6 (2.3) 3,5 (4.8) 5.0 m
z	(60) 50 70 (>250) 150 (170) 170 m
Here z is estimated from the surface concentration, except for the bracketed
numbers which are the results of direct analysis of concentration profiles or
the source height.
An 0.8-km arc runs along a pier. The tracer released from the 60-meter
height flowed north, descended a little over a small canal ahead of the
0.8-km arc, and began to rise, passing over the industrial plant area between
the 0.8-km and 1,6-km arcs. Crossing the tableland beyond the 1.6-km arc it
rose remarkably, then descended over the congested area. The difference of
z between x = 0 and x = 5 km is 110 m. Because of such large variations of
z, the surface concentration decreases rather uniformly with the downwind
distance and does not have the value, characteristic of an elevated source.
7-15
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Mizushima experiment
Mizushima is an industrial area facing the Seto Inland Sea, and Figure 7-11
shows one example of the analysis in the Mizushima experiment. The
Pasquill stability is D, which is due to the concentration profile sounding at
x = 5.2 km; and the source height is 90 m,
x	(0) 1.0 2.0 3.0 5.0 (5.2) km
7	(90) 65 120 170 130 (130) m
The 1.0-km arc runs along a pier and there is a small canal ahead of this arc,
similar to the situation in the Yokohama experiment. The tracer flowing
north descended over the canal and began to rise significantly over the
congested plant area between x = 1.0 km and x = 3.0 km. Beyond the 3.0
km arc there follows the flat, rural area with scattered small towns. There
the tracer descends
Toyama experiment
The experiment was conducted at the western suburb of Toyama City,facing
the Japan Sea, a flat rural area extending to 5.0 km arc. The 150-meter
source was sited near the coast and the tracer flowed inland (Figure 7-121.
The tracer flowed horizontalily down to the 5.0 km arc and rose at the 8.0
km arc where there are hills. The Pasquill stability was D. The surface
concentration curve is typical of the elevated source, since z does not vary,
Kainan City experiment
Kainan, south of Wakayama City, is situated in a narrow valley surrounded
north and south by mountains about 150 to 400 m high and extends east-
west. The west end of the city is open to the sea. The 200-meter and
surface-sources were placed at the mouth of the valley. The tracer flowed in
over Kainan City with the west wind.
Figure 7-13 shows the concentration profile at x = 550 m; for the source
height of 200 m; z 154 m; and oz was 33 m; the Pasquill stability was C.
Figure 7-14 is the same profile, but for x = 1.5 km. Here the ordinate is the
ratio of the source to surface concentration and the abscissa is z / z ,
parameter £ being az / z . Figure 7-14 shows that z is 200 m and az is
126 m, when the Pasquill stability is B-C. Two kinds of Pasquifl stability
were used, B-C and C. In the other runs of the experiment the Pasquill
stability was all B-C, so in this case the same stability was also adopted.
7-16
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AUGUST 9,1967 (M1ZUSHIMA)
14:30-15:00 h^90m
X (0) 1.0 2.0 3.0 5.0 (5,2) km
Z (90) 65 120 170 130 (130) jn
Figure 7-11. Same as Figure 7-9 but for Pasquill stability D,
Mizushima experiment.
7 17
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JULY 24, 1958 (TOYAMA)
15:00-15:27.5 h . 150 m
X (0) 1.5 2.5 3.5 5.0 8.0 km
Figure 7-12. Same as Figure 7-11 but for Toyama experiment.
7-18
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AUGUST 7,1968 (WAKAYAMA)
12.00 h 2Q0m Z 154 m
cz 33 m X 550 m
-



-
•


¦


i -i.
0 8
0 160 240
Z, m
Figure 7-13. Concentration profile at X - 550 meters, source
height 200 meters. PasquiU stability C.
AUGUST 7,1968 (WAKAYAMA)
12:00
h 200 m Z 200 m
X 1.5 km o„ 126 m
Figure 7-14. Normalized concentration profile at X = 1.5 km,
Pasquill stability B-C, Wakayama experiment.
7-19
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Figure 7-15 is the final result of the analysis. The tracer descends about 50
m at the 0.6-km arc, resumes its initial height at the 1.5 km arc and then
begins to rise remarkably. At about 150 m east of the source there is a
building about 50 m high, which seems to have affected the lowering of
tracer to the 0.6-km arc. This is refiected in the concentration profile from
the surface-source released simultaneously with 200-m source (Figure 7-16) z
being 130 m at x = 1.6 km.
AUGUST 7,1968 (WAKAYAMA)
12:01-12:27 h 200 m
X (0) (O.G) (1.5) 3 5 km
Z (200) (154) (200) 250 >450 m
10*4
10-5
CVI
0
E=
cy
ro
O
10-6
10-7
0.1	0.5 1.0	5.0 10.0
DISTANCE, km
STABILITY B*C
Figure 7-15. Same as Figure 7-9 but for Pasquill stability B-C,
Kainan City experiment.
7-20
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AUGUST 7,1968 (WAKAYAMA)
12:00
h = 0 Z 130 m
X 1.5 km crz 126 m
2.0
1.5
K 1.0
M
0.5
0
0	0.5	1.0	1.5	2.0	2.5
Z/Z
Figure 7-16. Normalized profile of surface - source concentration
at X 1-5 km, Wakayama experiment.
The weather conditions such as stability and wind speed or profile were
almost the same as the case in Figure 7-12. The big difference is in the
terrain. The Pasquill stability is certainly much affected by the topography.
Oita experiment
There are many examples to show that the tracer-cloud released from the
surface-source rises more or less over an urban area. One example is picked
out here from the Oita experiment.
The surface source was near the coast and the tracer flowed over Oita City.
The concentration profile at x = 2.6 km is shown in Figure 7-17; 2 is 65 m
and the Pasquill stability is D. Figure 7-18 is the result of the analysis:
7-21
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AUGUST 27,1968 (OITA)
12:00
h 8m	Z 65 m
X 2.6 km 
-------
AUGUST 27,1968 (OITA)
10:00-10:30 h 0 m
X (0) 0.6 1.5 (2.6) 3.0 5.0 km
Z (0) 45 65 (65) 80 140 m
DISTANCE, km
Figure 7-18. Surface axial concentration versus downwind distance
curve, Pasquill stability D.
7-23
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APPENDIX - GLOSSARY OF SYMBOLS
A, B, C, D, E Pasquill stability ratings
C	instantaneous tracer concentration
C	average tracer concentration
Dj , D2	drum-impactor sites
E	exposure time
H	source height
Pi	pibal station, i
Q	source intensity
Qt	total mass of tracer released
t	time
T	real sampling time
TD	total time required for passage of a detached tracer plume
u	transport speed
x	horizontal (downwind) distance from source
~l	centerline height, or gravity-center height
£	az/z
oy	horizontal dispersion parameter
°z	vertical dispersion parameter
t	tracer release time
7-24
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ABSTRACT
With the advent of computer-oriented simulation models of the physi-
cal and chemical system that produces varying levels of air quality, it is
both possible and desirable to assess the model's sensitivities to errors
and uncertainties in the input variables. From such analyses, it is
possible to derive more explicitly the levels of accuracy that must be
observed in the specification of the inputs for source strengths and
distributions, wind velocity, horizontal and vertical diffusion rates, and
pollutant chemical reactions or physical decay and loss rates, if the air
quality predictions derived from these inputs are to remain within
useful limits of accuracy and uncertainty.
For the present report, a single case study is utilized to test the
sensitivity of the Travelers Research Corporation Regional Model to
random and systematic errors in the source-strength input and to
systematic errors in the remaining input variables. It has been found
that random errors in the source strengths do not produce comparable
errors in the air quality prediction. Beyond this, and in order of
decreasing sensitivity, the TRC model has been found to be highly
sensitive to systematic regional wind-direction errors and moderately
sensitive to systematic errors in source-strength estimates, decay or loss
rates, and vertical diffusion rates. The model is insensitive to errors in
lateral diffusion rates, at least for the multiple-source distribution
encountered in Connecticut. These sensitivites are quantified for the
case studied.
The case used for the sensitivity analyses also provided an opportunity
to determine the effect of changes in the input variables on the
verification of the model, since observations of SO2 were available
from the verification program. Significant improvements in the TRC
model verification, over that obtained from the original, independantly
chosen, input variables, were found when either the source strengths or
the decay or loss rates were adjusted appropriately. This result suggests
the need for much better understanding of the decay and loss of
airborne SO2.
author
DR. GLENN R. HILST, a native of Kansas, holds degrees from MIT and the
University of Chicago. He has worked in association with the General Electric
Company, Argonne National Laboratory, and The Travelers Research Center on
various facets of air and water quality control and environmental safety. Dr. Hi/st
is presently editor of the Journal of Applied Meteorology.
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8. ELEVATION OF TRACER CLOUD
OVER AN URBAN AREA*
DR. GLENN R. HILST'
The Travelers Research Corporation
INTRODUCTION
The advantages of a capability to simulate the physical and chemical behav-
ior of the air quality system are so obvious as to require no further emphasis
here. The very existence of this Conference and the reports we have heard
on the state-of-the-art for simulation modeling (within useful limits of
accuracy) also speak to these advantages, even the need for an ability to
evaluate alternative air quality control strategies before massive and costly
programs are instituted. This is the ultimate utility of simulation modeling;
happily, along the way, these modeling attempts also provide us with the
possibility of unusually clear recognition of where our ignorance, errors, and
uncertainties lie. It is on this facet of simulation modeling of air quality
systems that I should like to focus.
In particular, our work at Travelers Research Corporation (TRC) now per-
mits us to make a preliminary assessment of (1) just how faithfully the TRC
Regional Model simulates the real-world air quality system in Connecticut
and (2) the sensitivities of that model's air quality predictions to errors and
uncertainties in the input parameters and variables. I shall discuss these two
topics in reverse order.
At the outset, let me emphasize that these studies have utilized only the
TRC Regional Model; therefore, the results are limited to that particular
version. Since the basic methods employed by the model are quite conven-
tional and common to most modeling efforts, it is reasonable to assume that
~The work reported here was supported as an in-house program development effort by
TRC. The TRC Regional Model was developed under a grant from the Connecticut
Research Commission, however, and the verification data used here were obtained
under joint support from the Connecticut Research Commission and the National Air
Pollution Control Administration.
tThe very substantial assistance of Mr. Charles R. Case, Computer Operations, and the
advice and counsel of Dr, G. D. Robinson, Mr. N. E. Bowne, and Dr. R. R. Hippler
are gratefully acknowledged.
8-1
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the sensitivities found are appropriate to other models that also purport to
predict air quality with a similar time and space resolution. 1 leave this
extension to your own good judgment.
TRC REGIONAL MODEL
The model whose sensitivities and predictive capabilities are under study here
has been reported on extensively over the past 2 years. Verification of the
model was undertaken in a 1968-69 study that is the subject of a report by
the TRC staff4 and a preliminary paper by Bowne/ both of which are just
now becoming available.
In brief, the TRC model is designed to predict ground-level concentrations of
a semiconservative pollutant emitted from multiple sources within a region
of the order of 5,000 square miles. The model is capable, in principle, of
resolving those concentrations on an hour-by-hour basis, with a space resolu-
tion of 5,000 feet. Since the design of the model is quite general with regard
to time and space resolution, the only real limitations on these features are
(1) computer capacity and speed, (2) ignorance regarding the appropriate
decay and toss of a pollutant over great distances of travel, and (3) a very
large degree of uncertainty regarding the transport and dispersion processes
over very short distances of travel. As presently configured, the model fits
nicely into the IBM 360/40 and requires about 10 minutes of that com-
puter's time to provide a 100-point prediction of any single air quality
pattern.
The TRC model employs the conventional Gaussian diffusion representation
of dilution of the pollutant {with a simple exponential decay) from each
individual area or point source that could contribute to the concentration at
the point (or small area) and time of interest. These sources are identified by
computing the prior trajectory of the air resident over that point at the time
of interest and by noting the lateral dispersion appropriate for the traverse
from the source to the point of interest. Chronological variations in the wind
field and atmospheric dispersion are accounted for by changing the input
variables at 2-hour intervals.
The basic equation used is shown in Figure 8-1; the total concentration at
(x, y, 0) is obtained by summing over all appropriate source locations
(£*?,?)¦ Except for the transporting wind velocity field, which defines |x -
£), 
-------
X (x,y,z I € ,17. i) =
Q U.T),f)
u(£,rj,£)
\	v	/ V
exp
Mx - O
exp
1	y ~"
2	v*-",
(J (X - o
y
A/~
B
V V
—V
c
V V
Closs of error
Terms of equation
Nature of error
and uncertainty
affected
and uncertainty
Source strength
A
Both random and systematic likely
Decay or loss
B
Largely unknown - tendi to be systematic
D i s pers i on
C, D
Tend to be systematic
Positional
A, B, C, D
Both random and systematic likely
oo
CJ
Figure 8-1. Classification of input errors and uncertainties for model sensitivity tests.
-------
X	= the decay or loss coefficient for the pollutant under consi-
deration.
ay(x-|) = the standard deviation of the cross-wind spread of the
pollutant eminating from £77 f.
tJi(x-£). = the standard deviation of the vertical spread of the pollu-
tant emanating from
These are the input variables that we can manipulate in seeking concurrence
between predicted and observed air quality levels and to which these pre-
dicted levels will be more or less sensitive. Our first study is an attempt to
quantify these sensitivities via the model itself.
POTENTIAL ERRORS AND UNCERTAINTIES IN THE
ESTIMATES OF INPUT VARIABLES
For a typical air quality pattern prediction, the TRC model requires approxi-
mately 200,000 input estimates. The probability of errors and uncertainties
in these input estimates is very high. Figure 8-2 is a pictorial representation
of the different mistakes that could be made for a single source situation
and, as noted in the figure, there are eight distinct sources of input error and
uncertainity. They are:
1.	Misplacement of source with respect to geography and elevation.
2.	Misestimation of source strength.
3.	Misestimation of wind speed at source.
4.	Miscalculation of trajectory of pollutant cloud or plume, due to er-
roneous or uncertain wind fields.
5.	Misjudgment of vertical diffusion of cloud or plume, including errone-
ous distribution functions, as well as parametric errors.
6.	Misjudgment of the lateral diffusion of cloud or plume, including
erroneous distribution functions, as well as parametric errors.
7.	Misestimation of decay or loss of pollutant.
8.	Misplacement of receptor or monitor.
This appears to be an exhaustive list; at any rate, it is a sufficient one for
our present purpose.
Figure 8-1 shows that, for sensitivity-analysis purposes, these eight sources of
error and uncertainty may be grouped into four convenient classes:
1.	Source strength estimates.
2.	Pollutant decay or loss estimates.
3.	Pollutant diffusion and distribution estimates.
4.	Positional errors and uncertainties.
Of these, the first three are self-evident and essentially independent of one
another. The fourth, however, in effect, affects all of the other estimates
since, as shown in Figure 8-1, each of the terms in the diffusion equation
8-4
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1.	SOURCE MISPLACED
2.	SOURCE STRENGTH MISESTIMATED
3.	WIND SPEED AT SOURCE IN ERROR	,
4.	TRAJECTORY MISCALCULATED	/
5.	VERTICAL DIFFUSION MISESTIMATED	jCT	//*
Figure 8-2. Sources of input errors and uncertainties in variables
utilized in air quality simulation models.
upon which the model is based depends upon the positions of the source
and the receptor. Errors and uncertainties in estimating the relative positions
of the source and the receptor, and in estimating the time of flight and path
between the two automatically involve errors in the estimates of the source
strength and the decay or loss and diffusion of the pollutant. For example,
if the transporting wind direction is misestimated, the receptor "sees" the
wrong sources, the time of flight is misjudged, and the diffusion is misesti-
mated. The only time when no "error" is involved occurs when the sources
and meteorological conditions are absolutely uniform over the region, a case
of less than trivial interest.
The nature of likely errors and uncertainties in the input parameters is of
considerable interest, particularly the distinction between random and sys-
tematic errors. In preparing source inventories, we fully expect a random
component of error since we can seldom even measure the output of a given
source precisely, and we know that most sources do not operate at a single,
steady emission rate. On the other hand, we should also expect some
systematic component of error, with a tendency for this component to be in
the nature of an underestimate. This is because of the high probability that,
amidst thousands and tens of thousands of sources, we will tend to overlook
some entirely, but will not be inclined to compensate with imaginary
sources.
8-5
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On the other hand, quite irrespective of the reality of simple exponential
decay or losses of the pollutant, the error in estimating this rate of loss is
apt to be systematic in nature. For the more complicated photochemical
reactions and product formation rates, for which I have not seen anything
more than rudimentary simulation models, a mixture of random and system-
atic errors may appear.
For short times of flight and averaging, we would expect, from the nature of
atmospheric diffusion, to see sizable random errors in the estimates of
vertical and lateral diffusion rates. Over longer distances and times of
averaging, however, when these local variabilities have been suitably smooth^
ed, any error should tend to become systematic. Since the model requires at
least 1-hour averages through these variations, our primary problem is pro-
bably with systematic over- or under estimates of diffusion.
The positional errors are of two kinds: (1) geographic misplacement, which
is largely a surveying problem (for fixed sources and receptors) and a
fixed-point referencing problem (for mobile sources and receptors), and (2)
advection or trajectory errors due to erroneous estimates of the wind field
and location within the wind field. Suppression of the geographical error
depends upon the precision one is willing to pay for in locating sources and
receptors; these errors are probably random in nature. The trajectory errors,
however, will depend upon the precision and spatial density of airflow
measurements at various altitudes in the lower levels of the atmosphere.
Although both random and systematic errors are probably present, the
requirements for maintaining mass continuity for our representation of these
flow fields operate strongly for systematic errors. The wind fields in adjacent
grid cells are not independent of one another; an error in one estimate is
reflected in neighboring estimates by this generally positive correlation,
through the equation of continuity.
Finally, 3s is evident from the choice of words in the last few paragraphs, we
recognize the conventional distinction between errors and uncertainties;
errors can be identified and corrected whereas uncertainties cannot be
corrected. Beyond this, the effects of these "mistakes" are indistinguishable
for our present purposes, and we shall refer to them simply as "errors." The
distinction between random and systematic errors is of much greater impor-
tance.
THE TESTS FOR SENSITIVITY
The objective of sensitivity tests is, of course, to measure the error in the
predicted quantity, in this case, pollutant concentration, as a function of
increasing errors in each of the input variables. The rate of change of the
predictand error as a function of the rate of change of the predictor error is
the measure of the sensitivity of the former to the latter. Since in air-auality
8-6
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pattern predictions (the regional problem) we are dealing with numerous
predicted values that range through several orders of magnitude, it is con-
venient to measure the relative error rather than the absolute error in the air
quality predictions.
Let
XT - the "true" concentration of a pollutant at a given station,
XE = the estimate of concentration after an input parameter error is
introduced.
Then
Xr-Xe
"Xt "
fractional error in X produced by the input error.
For N separate estimates, we have
and
1 VXl Xr	(1)
N t—i X T
i £(s?y -
where equations (1) and (2) specify the mean and variance of the fractional
error distribution, respectively. We have chosen these distributions and their
mean and variance (or the standard deviation,[(v')2]1/2) as the measures of
predictand errors. We should note that The value of (XT-XE) /XT must be
less than or equal to one, since Xe cannot be less than zero. Assumptions
with regard to the distribution functions for the fractional errors do not
arise in the present analysis, but with this latter constraint, we expect these
distributions to be skewed toward negative values of the fractional error of
X.
The technique used for assessing the fractional error in X was simply: to run
the model for a reasonable set of input parameters, solve for the concentra-
tion at 100 stations uniformly spaced over the Connecticut input parameters
in a stepwise fashion. The mean and standard deviations of the fractional
error in X were then constructed for each solution referenced on the original
or "true" solution.
In order to assure a systematic and controlled variation of the input-para-
meter error (and, incidentally, to conserve computer time), the following
error generator was employed:
8-7
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Let
XT = the original or "true" value of any input parameter;
XE = the erroneous value of the input parameter.
Then take
XE = XT (1 ± a + b),	(3)
where a is the fractional error in X due to random errors and b is the
fractional error in X due to systematic errors. Then
XT - XE
-b + a	(4)
and — b + a < 1 . In order to give a the character of a random variable, it
was assigned the values +|a|, o,-|a| with equal frequency and applied to
the collection of input variables, such as the source strength Q, on a random
basis. Likewise, a systematic error was generated by assigning a single value
to b .
It follows directly from Equation (4) and the assignments of a that
XT - XE \
—	— 1 = -b	(5)
and	(v'x)2 - ~ a2,	(6)
i.e., the mean and variance of the fractional input errors are specified sepa-
rately by a and b.
For the present sensitivity test, a random error analysis has been done only
for the source strength field, Q . Analyses of systematic errors have been
completed for all of the input parameters except windspeed. The measures
used are shown in Figure 8-3.
RESULTS OF SENSITIVITY TESTS
The situation chosen for these sensitivity tests was based on a real-world case
for which verification measurements of S02 levels over a 21-station network
covering Connecticut were available. The exact period was from 0600 to
0800 on October 30, 1968. (A 2-hour average was used in the verification
program in order to assure significant sampling of S02, hence this 2-hour
test period, rather than 1-hour.) The weather prior to the morning of
October 30th was mostly clear to partly cloudy, with NW winds at 4 to 6
meters per second (m sec-1 ). Surface temperatures during the night were in
the low 30's with some reports of frost.
8-8
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Prediction
error measure
Input error measure
Class
Random error
Systematic error
*T ~ XE
and
' Xrp ~	^
xT /
XT XE
Source
strength
Decay
Dispersion
Positional
1/2
'Q^ - Qr,
T E
Qm
Qt - 
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The source inventory for $Ga emissions in Connecticut is shown in Figure
8-4A. A summary of this inventory shows the following- frequency of emis-
sions in pounds per day per square mile (lbs dayH
rrii"2).
Emission rate (Q)
Source ceil area
lb day"* mf
100
10
1
1000
1000
100
10
1
Number of source c&tis
per 25 x 10* ft
27
98
82?
3,248
1,358
As is clear from the map and summary, the emissions of SDj over this
region are far from- uniform, but they do exhibit a pattern of rural land
usage in the northwest and northeast sections {with some notable local
anomalies} and an industrial feed and urbanized belt from southwest to
northeast through the central portion of the region. There is also a relatively
strong source region extending northward along the Thames River in the
southeast section of the region.
$02 EWSSIOHS,
Itffefl mi"?
• >i|3
21 » Ifjl
ua»>10
Figure 8-4A. Source inventory for SO2 emissions in Connecticut
used in TRC regional model.
3-10
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. 0.01-
.0,01-
FALLS VILLAGE
~\JT • t	| STAFFORD
THOMPSON VIL.LE *
,0.01
• SIMS BURY / WINDSOR
WINSTED	» I *

0,005
\	CHAPLIN
BOLTON	•
HAHTFORCr\ X •
( MORRtS DAM	t / /fP\^
I	• "V new Britain)J > , „
NEW MIL FORD
0.0) '
i t in 11 w t g ¦' g M ~	I	s
j i ( /
MIDDLE TOWN! I ! tNORW;
s
GREEINWIC
y
y NORWA

DANSURY
# \
FIE DO! IMG
NORTH S T 0N,I«GTON
0.05
: i , [• <• /ER
V V	\
0,02
¦a
0102
0.02
Figure S-4B. SOg concentrations predicted by t RO .iiodei for
0600—0800, October 30, 1968, from original, independently
specified input variables.
Figure 8-4 6, shows the pattern of SO* concentrations predicted by the
TRC model from the original choices of input parameters, {These choices are
listed in Table 8-1.5 The values of predicted S02 concentrations rang© from
0.003 ppm at North Stomngton in the southeast corner of the region to
0.11 ppm at New Haven in the south-central part of the region. The pattern
of concentrations shows the major axis of high concentrations extends from
Hartford to the coast near Deep River; New Haven is something of a local
anomaly.
Tai»l« 8-1, CHOICES OF INITIAL INPUT PARAMETERS
FOR TffC'REGi'ONAt MODEL USED TO ESTABLISH
REFERENCE CONCENTRATIONS FOR SENSfTfVfTY TESTS
Input parameter
Value or method of ch<
Source strength
c i*, i it source inventory for SO j, corrected for
diurnal variations and difrtfi days4
Wind field
320° at i m me3
Decay coefficient
0,231, Half-life of 3 br
Diffusion coefficients
Appropriate- to a partly-cloudy night with moderate
wind speeds11
a See Reference 3..
8-11
-------
Figure 8-5 shows the frequency distribution of predicted values of S02
concentration occasioned by this original choice of input parameters. This
distribution is quite typical, being strongly skewed toward large values of
XT . Note however that there are several values of XT < 0.005 ppm. Since
XT enters in the denominator of our measures of the mean and variance of
the fractional errors in X, these low values can lead to spuriously high
values of these measures. This situation led to no particular difficulty in the
sensitivity tests, but required special attention in the verification tests dis-
cussed in later sections. Examples of the distribution of (Xt-Xe;)/Xt are
shown in Figure 8-6, where they are pSotted for increasing values of the
random error in the source strength. As can be seen from Figure 8-6, the
distributions of tXT-XE) I XT are reasonably symmetrical near zero and
are well behaved. (The frequency distributions of (XT-Xe)/XT are
tabulated for each sensitivity test in Appendix A.)
Xt, ppm
Figure 8-5. Frequency distribution ot SO2 concentrations pre-
dicted by TRC model for 0600-0800, October 30, 1968, from
original, independently specified input variables.
8-12
-------
100
50
JV
¦1/2 100
/S_V
[ Q., ,
¦ 0.816
"7' /"
=ij
*r " *k|
50
= 0,283

50 -
,	. 0'
0.5 1.0 -1.0
1/2
/Ql1Q£\
\ <>r I
= 0,404
~l/5
fXr " x£
0,170

T
¦0.5
qt - 
-------
Sensitivity to Random Errors in Q.
Since the model prescribes that the concentration X is directly proportional
to the source strength Q, there must be a one-to-one correspondence
between systematic errors in Q and errors in X . In terms of our measures of
sensitivity.
[(XT - XE)/XT] = [(Qt " Qe>/Qt1,
and
(v*)2 = 0.
This result, which derives directly from the model, is shown in Figure 8-7.
Figure 8-7. Mean and standard deviation of errors in concentra-
tion predictions as functions of a random and systematic errors in
source-strength estimates.
8-14
-------
Random errors in Q produce a different result, namely
[(XT — XE) / Xj] - o,
but (v')2
is non-zero, i.e., while no systematic error in the prediction of concentration
is introduced by random errors in Q, the distribution of the fractional errors
in N is broadened as the random errors in Q increase. The calculated values
for this relationship are tabulated in Table 8-2 and plotted in Figure 8-7.
(The distributions of (XT - XE) /XT are shown in Figure 8-6.)
Table 8-2. CALCULATED VALUES OF MEAN AND STANDARD DEVIATION
OF (XT - XE) / XT AS FUNCTION OF THE RMSa ERROR IN Q (RANDOM)
(LIMITS ASSESSED AT THE 95 PERCENT CONFIDENCE LEVEL)



qt-qe
XT-XE
-------
sole criterion for source inventory accuracy. The latter must also be used to
determine abatement strategies, and the need for accuracy on this account
may be overriding. But, with this provison it is clear that concentration
predictions are much more vulnerable to systematic errors in the source
specification than they are to random errors in this input variable.
Sensitivity to Systematic Errors in
Decay Coefficient, X.
Although the physical reality of a simple exponential decay of S02 with
travel time has not been rigorously demonstrated, our experiences with the
TRC model show that a distinct improvement in S02 concentration predic-
tions is achieved with this corrective term. It is, therefore, at least of
practical interest to determine the sensitivity of X to variations in this
empirical input parameter. Our reference here is a half-life of 3 hours ( X =
0.231 hr"1).
The effect of varying systematically the decay coefficient, X , on the mean
and standard deviation of (XT — Xg) /XT is tabulated in Table 8-3 and
shown graphically in Figure 8-8.
Table 8-3. CALCULATED VALUES OF MEAN AND STANDARD DEVIATION
OF 
-------
0.6
0.4
0.2
r
0k
\
\
xo.
\
\
\
o
\
\
*t-xe\
XT /	\ A
-0.2
-0.4
-0.6
-0.8
*1.0
I
_—a—. ^ r / \
^	-A.	\
' \
\
\ / O
i_L__y	i	
\
©/
A
0.6
0.4
*0.6 *0.4 *0.2	u	0-2 0.4
(Aj-A£)t hours-1
I 1	I	I, I	I	I
0 1	1.5	3 8 °°
HALF-LIFE, hours
Figure 8-8. Mean and standard deviation of errors in concentra-
ration predictions as functions of systematic errors in estimate
of the half-life of pollutant.
8-17
-------
Sensitivity to Systematic Errors in
Lateral Diffusion Coefficient, ay .
As used in the TRC model, the lateral diffusion coefficient, ay , specifies the
relative contributions of the sources arranged across the prior trajectory of
the volume of air that is resident over the point at a time for which an air
quality assessment is desired. In principle, this is no different from the more
conventional practice of carrying a pollutant forward from each source point
or area and speading it laterally according to the Gaussian distribution
specified by oy.
More importantly, of course, the lateral spread of a pollutant emanating
from multiple sources quickly mixes pollutant with pollutant and tends to
produce a more or less uniform cross-wind concentration. It is not surprising,
therefore, that we have found the model's predictions of ground level
concentration to be quite insensitive to errors in the lateral diffusion coeffi-
cient. These errors are tabulated in Table 8-4 and shown graphically in
Figure 8-9. As can be seen, the mean error in (XT - XE)/XT is not
significantly different from zero and the spread of these errors, as measured
by (v')2 1/2 comparable to those produced by a random error in Q (Figure
8-7).
Table 8-4. CALCULATED VALUES OF MEAN AND STANDARD DEVIATION
OF (XT - XE) / XT AS FUNCTION OF SYSTEMATIC ERRORS IN
LATERAL DIFFUSION COEFFICIENT Oy
{LIMITS ASSESSED AT 95 PERCENT CONFIDENCE LEVEL)
OyT -OyE
/Xt-xe\
<~)» "J
°y T
\ xT J
-0.2
-0.003 ± 0.02
0.105 < 0.122 < 0.139
+0.2
0.007 ± 0.03
0.130 < 0.161 < 0.172
-0.5
-0.018 ± 0.03
0.138 < 0.161 < 0.183
+0.5
0.012 ± 0.03
0.138 < 0.161 < 0.183
-0.7
-0.032 ± 0.04
0.170 < 0.197 < 0.224
+0.7
0.014 ± 0.03
0.141 < 0.164 < 0.187
Sensitivity to Systematic Errors in
Vertical Diffusion Coefficient, o2
Vertical diffusion has been recognized as a critical component of air quality
prediction for some time, principally through the employment of measures
of the depth of the mixed layer? The inherent sensitivity of concentration
predictions to errors In oz derives directly from the basic diffusion equation
(Figure 8-2), since, for ground level concentrations, (z =0),
8 18
-------
°yT" OyE N
~WJ
Figure 8-9. Mean and standard deviation of errors in concentra-
tion predictions as functions of systematic errors in estimate of
lateral diffusion coefficients.
" ¦ (V) ^
is the fractional change in X as a function of the fractional change in oz .
Equation (7) indicates that the fractional error in X will be large when oz is
smalt relative to the source height, f , a situation that may extend to
considerable distances when vertical mixing is slow (stable conditions).
The tests of sensitivity of {XT—XE) / XT to fractional changes in ox are
tabulated in Table 8-5 and shown graphically in Figure 8-10. The extreme
sensitivity of X to a2 when o2 is small (a2T - ozE -*¦ ozT) is clearly evident
from this figure. For substantial overestimates of oz (azT - azE < 0), this
sensitivity behaves very similar to errors in ay.#
"The avoidance of the sensitivity to small values of oy is, in part, due to the fact that area
sources with a minimum dimension of 5,000 feet predominate in the model.
8-19
-------
Table 8-5. CALCULATED VALUES OF MEAN AND STANDARD DEVIATION
OF 
-------
between the "stretching" effect at the source and the time-of-flight effect in
the decay of the pollutant, errors in windspeed estimates tend to be com-
pensatory. Rather, the wind direction field over the region was simply
rotated the desired number of degrees from the originally chosen wind
direction, 320?
As might be expected, the errors produced by this input-error generation
were rather spectacular. They are tabulated in Table 6-6 and shown graphi-
cally in Figure 8-11. (One completely erroneous station contributed so
strongly to the variance of (XT - XE) /XT for 0T—0E = + 20° that this
point has been deleted.)
Table 8-6. CALCULATED VALUES OF MEAN AND STANDARD DEVIATION
OF (XT -,XE) / Xx AS FUNCTION OF SYSTEMATIC ERRORS
IN WIND DIRECTION,©
(LIMITS ASSESSED AT 95 PERCENT CONFIDENCE LEVEL)
0y - 0El
degrees
(VE)
1 i \ 1 ^ ^
-------
•40 -30 -20 -10
10 20 30 40

Figure 8-11. Mean and standard deviation of errors in concentra-
tration predictions as functions of systematic errors in estimate of
regional wind direction.
In studying Figure 8-12, it is well to keep in mind that the reference values
for the input parameters are arbitrarily chosen. These curves should not be
constructed as a universal or general representation of error sensitivity. With
this caveat, however, it is clear that the sensitivities of concentration predic-
tion to systematic input errors in the expected range of ± 0.5 may be ranked
as follows:
1.	Wind field directional errors.
Mean error < ± 50 percent; individual errors > 200 percent.
2.	Source strength errors.
Mean errors ^ ± 50 percent; individual errors < ± 50 percent.
3.	Decay rate errors.
Mean error < 40 percent; individual errors < ± 50 percent.
4.	Vertical diffusion errors.
Mean error < 25 percent; individual errors < ± 50 percent.
8-22
-------
W9
0.5 1.0
00
1
fO
u
Figure 8-12, Comparative summary of mean and standard deviation of errors in concentration prediction as
function of fractional systematic errors in each input variable. Sensitivity of model to errors is measured
by slope of curves.
-------
5. Horizontal diffusion errors.
Mean error < 5 percent; individual errors < 40 percent.
The greatest sensitivites are found when errors become so targe that input
parameters approach their singular or limiting values {0 for oz, and for \ )
but, assuming that prudence in the use of models will obviate this difficulty,
by far the most serious expected error is found when the wind direction
field is misestimated. Errors in the mean of the concentration prediction,
averaged over the region, approach ± 25 to 50 percent, and errors in
individual concentration predictions readily exceed 200 percent of the true
value when wind direction errors reach and exceed 20°.
Surprisingly, air quality predictions showed no particular sensitivity to ran-
dom source strength errors. As noted previously, however, this is probably a
function of the density of the multiple sources and deserves more rigorous
study from that point of view.
Finally, this whole study must be recognized as the case study that it is.
Because of the obvious importance of a clear and quantitative measure of
the accuracies and uncertainties of simulation predictions, this type of
analysis should be extended and generalized far beyond this first effort.
Insofar as these results pertain only to the TRC Regional Model, other
models should be similarly exercised and examined for sensitivities to input
errors and uncertainties.
A CASE STUDY OF SENSITIVITIES OF MODEL
VERIFICATION TO INPUT PARAMETER VALUES
Since direct observations of S02 concentrations are available for 21 stations
within Connecticut for the period used in the above sensitivity analyses, an
unusually detailed analysis of the sensitivities of the model verification to
changes in the input parameters arises as a welcome bonus in this study. This
is, of course, a single case and must be treated as such. The results are well
worth noting, however, (For a more general analysis of the verification of
the TRC Regional Model, see the 1969 TRC Staff Report.4)
For this analysis, we simply need redefine XT as the observed value of S02
concentration at any given station and Xe as the predicted value for that
station for any given set of input parameters, including the original set used
as the base reference for the sensitivity analyses. The mean and standard
deviation of (XT-XE)/XT constitute the test for goodness of fit or the
verification of the model's predictive capabilities.
The values of XT observed at the 21 verification stations and the fractional
error associated with each observation when compared with the predicted
values using the original input parameters (Table 8-1) are shown in Figure
8-24
-------
8 13. As can be seen from that figure, the fractional errors in the verification
of observed concentrations tend to cluster around zero, with the notable
exceptions of two stations for which the observed concentrations are very
low, 0.002 and 0.003 ppm (0.001 ppm is the threshhold level for the
measurement system used to monitor SOj). If these stations are eliminated,
the mean value of (Xx—XE)/XT is, in fact, zero, and there is a great
temptation to do exactly that. The temptation has been resisted, however,
primarily because there are several other observations of S02 in the < 0.005
ppm region that did not produce anomalous error values; one would be hard
pressed to justify their retention if the two bad actors were eliminated on
the grounds of unreliability of observation. Hence we retained all 21 sta-
tions.
0.06
Xj, ppm
0.04
0.02
°-4	-3 -2 -I	0	12
(*?)
Figure 8-13. Joint values of observed values of SO2 concentra-
tions and fractional error in values predicted by TRC model, using
original, independently specified values of input variables, for
period 0600-0800t October 30, 1968.
Using the original input variables described in Table 8-1, the verification
parameters tor the observed versus predicted values of S02 were
*"0642'
and
FF1'^ 1.225

I
r-
1 ¦— ¦ 1
1




•





«





M


-


• # •

—



O •





^ ^ ft


I
1 ..
T
•V. •/
1 1
1 .

8-25
-------
hardly an inspiring result. The question then asked was, "Could this verifi-
cation be improved by varying input parameters for the model?" Normally,
of course, input parameters must be chosen independently of the verification
data, but the question is valid for analytical purposes.
Knowing the general behavior of the model and the results of the sensitivity
analysis, we can immediately speculate that improved verification of the
mean value of (XT - XE) /XT can be obtained in any or all of three ways:
(1) reduce the source strengths uniformly by 40 percent (since in the mean,
concentration predictions were overestimated by this amount), (2) increase
the vertical diffusion rates by an amount that compensates the overestimate,
and (3) decrease the half-life of S02, so as to compensate for the overesti-
mate of X. in addition, we can test to see if systematic changes in either the
wind direction or the horizontal diffusion rate reduce the verification errors.
We are also vitally concerned with the individual station verification (since it
appears air quality assessment and control will be based on local values of
concentration, not the regional average). It is imperative, therefore, that the
range of verification errors.be reduced also, a feature that is measured by the
standard deviation of (Xx - XE) / XT , (v')3l/2. It would be desirable,
of course, to test all of the combinations and permutations of input para-
meters; and this is possible, given the time and resources to perform the
necessary iterative solutions of the model. The present analysis does not go
that far; rather, we have examined only one input variable at a time.
The effects of random variations in the source strengths on the verification
parameters are shown in Figure 8*14, (Values and confidence limits of (Xx-
XE) / XT and (v7)71" are tabulated for all input variables in Appendix B.)
Clearly, no improvement in the verification is achieved by this manipulation;
both the mean and standard deviation are at their minima with the original
source inventory.
The effects of systematic variation of the source strengths are shown in
Figure 8-15 and, as expected, a uniform reduction by 40 percent of all the
source strengths reduces the mean error in X to very near zero, and the
standard deviation of the fractional error In X is reduced to 0,75 from its
original value of 1.225. This is a distinct improvement; In fact, it is the best
result that could be obtained from single-input-variable manipulation. Exami-
nation of Figure 8-16, however, shows that an equivalent improvement could
be obtained by reducing the estimated half-life of SOj from 3-hours to
1-hour. The mean error for this case is also near zero and the standard
deviation is reduced to 0.860. Figure 8-17 shows that even a very substantial
increase in the vertical diffusion coefficients produces only a slight Improve-
ment in the mean error of concentration prediction, and no improvement at
all in the standard deviation of the fractional errors in X, as should have
been expected from the sensitivity analysis,
8-26
-------
0
—I 2.0
1.5
•1.0
- 1.0
FT 1/2
1.5 -
- 0.5
Qt /
Figure 8-14. 0600-0800, October 30, 1968, verification scores for
TRC model as a function of random errors in source strength speci-
fications.
The effects of variations of the horizontal diffusion coefficient and of the
wind direction are shown in Figures 8-18 and 8-19, respectively. Clearly, the
TRC model could not be more indifferent to the choice of horizontal
diffusion coefficients for this case. The model's sensitivity to the com-
pounded errors introduced by changing the wind direction is reiterated in
Figure 8-19, but the original choice of wind direction provides the best fit
for this verification test.
To summarize this case study, Figure 8-20 shows the maximum improve-
ments in the verification of the model that were achieved by varying, in
turn, the vertical diffusion, the decay rate, and the source strengths. Of
these, only the latter two provide a significant improvement in the verifica-
tion scores. (See Appendix B for confidence limits on (XT -Xe) /XT and
(v')2 1/2 for these tests.)
No sweeping conclusions can be drawn from this single case study, but it
seems unlikely that the source inventory for Connecticut is in error by a 40
percent overestimate. The other verification tests showed that mean concen-
trations were underestimated as frequently as they were overestimated using
the same source of inventory. Rather, this partial result seems to emphasize
the importance of better understanding of the decay and loss of S02.
8-27
-------
CO
ro
oo
~2~l/2
Figure 8-15. 0600-0800,October 30,1968, veri-
fication scores for TRC model as a function of
systematic changes in source strength specifica-
tions.
Figure 8-16. 0600-0800,October 30,1968, veri-
fication scores for TRC model as a function of
systematic changes in decay rate for SO2.
-------
-1.5 -
- 0 j
-ZJll	I	I	I	 Q
-IX -0.5	0	0.5	1.0T
OzT-OzE
-------
0.5
Oh
-0.5 h
(*?)

>
\r
/
/
/
/ *
2.0
1.5

V'
2~l/2
7
N./-k J

1.0
-1.5
0.5
-2.0
•0.2 -1.0
Bih
6 max
0.1
0 2
Figure 8-19. 0600-0800, October 30, 1968, verification scores for
TRC model as a function of systematic changes in regional wind
direction.
The empirical exponential decay and loss term used in the TRC model
operates to reduce concentrations most at those stations that are relatively
far removed from major source areas. The "effective" distance from each
station to the contributory sources for that station, Xe, may be calculated
from the model's estimates of X for two different values of X ,
y - u	|n XE3
e X3 - X,	XE1	<7>
a parameter that is expected to change with wind direction. For the present
case (NW winds), Xe ranges from 2 to 41 miles in Connecticut (Figure 8-21)
and clearly portrays both the rural and urban areas and the presence of local
sources in otherwise nonsource areas. For example, Danbury, Stamford,
Bridgeport, and New Haven are subject primarily to local sources of S02
with NW winds, while the Hartford-Middletown-Deep River axis of SOa
8-30
-------
ORIGINAL
INPUT
PARAMETERS


V
Figure 8-20. Summary of maximum Improvements In verification of
TRC model predictions of SO2 concentrations for period 0600-0800,
October 30, 1968, by independent manipulation of vertical diffusion,
decay rate, and source strength field,
8-31
-------
concentrations (Figure 8-5) represents the regional concentration of sources
in the Hartford-Middletown area. Similarly, the Norwich-Groton area consti-
tutes a regional source of S02. On the other hand, the New Milford-Morris
Dam and the Colchester regions are obviously far removed from the major
sources of S02 that affect them.
FIXED SAMPLING STATIONS
"I^TtHOMPSON VI L LE
i VFALLS » 1LLA GE'
t -•
WINSTED
•	SI MS BURY.
• m
MORRIS DAM
I •/ , NEW BRITAIN 1 0*
' / I s*\ # :
NEW MILFORD /	\	I	__<
| MIDDLET
/Thar'tford •
\v»'"V
TOWN I COLCHESTER NORWICH
1 WATERBURY meriden"vV\ V I* I \* i I I V
v,j' °Vv^)/ll>
v	/	/ N\ NORTH sT°NINGTON f
DANBURY \ I
• v	^ i
10	\l — ,
REDDING \lNEW HAVEN / MADISON
•	/ t in
i o
GREENWICH
Figure 8-21. Effective distance to SO2 sources for case of NW winds.
These results are, of course, more suggestive than conclusive at the present
level of analysis. If nothing else, however, they do point clearly to the
powerful analytical capabilities of a reasonably faithful simulation model. As
noted by one of my colleagues, these are indeed powerful, if expensive tools.
8-32
-------
REFERENCES
1.	Hilst, G. R. An Air Pollution Model of Connecticut. In: Proceedings the IBM
Scientific Computing Symposium on Water and Air Resource Management. York-
town Heights, N. Y, October 1967. IBM. Data Processing Division. White Plains.
1967. 251-274.
2.	Bowne, N. E. Simulation Model for Air Pollution Over Connecticut. J. Air Pollu-
tion Control Assoc. 79:570-574, August 1969.
3.	Hilst, G. R. J. E. Yocom, and N. E. Bowne. The Development of a Simulation
Model for Air Pollution over Connecticut, Vol. I. Travelers Research Center, Inc.
Hartford, Conn. Final Report to the Connecticut Research Commission. TRC
Report No. 7233-2798. 1967. 66p.
4.	Hilst, G. R. Verification by Observation of the Application of An Air Pollution
Model to the State of Connecticut (in press). Travelers Research Center, Inc.
Hartford, Conn. Final Report to the Connecticut Research Commission. TRC
Report No. 7242-365. September 1969.
5.	Bowne, N. E. A Mathematical Model of Air Pollution in the State of Connecticut.
Presented at 62d Annual Meeting of the Air Pollution Control Association. New
York. June 22-26, 1969.
6.	Holzworth, G. C. Estimates of Mean Maximum Mixing Depths in the Contiguous
United States. Mon. Weather Rev,
8-33
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APPENDIX A
Frequency distribution of errors in predicted concentration, (XT-XE)/XT,
for designated errors or values of variables.
(100-station sensitivity tests.)
Range of
Rms error in (Qj - Qg;)/Q-r
Value of half-life, A. (hr 1 )
-------
APPENDIX A (continued)
Range of

Fractional error in az, (ozT— <"zE
V°zT

(XT-XE)/XT
0.2
+0.2
0.5
+0.5
0.7
+0.7
0.860 to
0.959
1
1
1
1
1
1
0.760 to
0.859
0
0
1
0
1
0
0.660 to
0.759
0
0
2
0
0
0
0.560 to
0.659
0
0
1
0
2
0
0.460 to
0.559
0
0
2
0
0
0
0.360 to
0.459
0
0
4
0
1
11
0.260 to
0.359
0
1
9
19
3
15
0.160 to
0.259
2
8
18
22
3
20
0.060 to
0.159
7
27
8
15
7
13
0.040 to
0.059
38
52
25
38
24
37
-0.140 to -0.041
21
4
6
3
4
2
-0.240 to
-0.141
26
6
4
1
9
0
-0.340 to
-0.241
3
0
8
1
1
1
-0.440 to
-0.341
1
0
3
0
4
0
-0.540 to
-0.441
0
1
0
0
1
0
- 0.640 to
-0.541
0
0
3
0
4
0
-0.740 to
-0.641
0
0
0
0
4
0
-0.840 to
-0.741
1
0
2
0
2
0
-0.940 to
-0.841
0
0
0
0
3
0
<-0.940
0
0
3
0
26
0
Avg of <
0.940
0
0
-1.429
0
1.339
0
Largest (-) value
-
-
1.857
-
-2.333
-
Avg of (Xx-XE)/XT
-0.071
0.055
-0.236
0.120
-0.429
0.151
Std. dev. of
(X-j—Xg )/X-|-
0.164
0.130
0.240
0.155
0.776
0.168
8-35
-------
APPENDIX A (continued)
Range of

Fractional error in ay, 
-------
APPENDIX A (continued)
Range of
Systematic error in wind direction, ©, (°)
-------
APPENDIX B
The mean and standard deviation of fractional error in
verification of S02 predictions at 21 stations as
function of indicated changes in input variables.
(Confidence limits assessed at 95 percent level.)
Random Variation of Source Strengths, Q.
/Qt-QeY 1/2
/xT-xE\
—/j
V
V Qt /
V XT J
0
-0.642 ± 0.54
0.848 < 1.225 < J .60
0.082
-0.673 ± 0.055
0.865 <1.25 <1.64
0.163
-0.690 ± 0.57
0.903 <1.30 <1.70
0.409
-0.701 ± 0.59
0.937 <1.35 <1.77
0.923
-0.753 ± 0.63
1.07 <1.54 <2,02
Systematic Variation of Source Strengths, Q.
fOj - Qe\
fxr-xE\
~Vr'Ui
I Qt J
V XT /

-0.2
-0.961 ± 0.63
1.00 <1.44 < 1.90
0
-0.642 ± 0.54
0.848 < 1.225 < 1.60
+0.2
-0.323 ± 0.44
0.693 <1.00 <1.31
+0.4
0.027 ± 0.32
0.501 < 0.723 < 0.947
+0.6
0.331 ± 0.22
0.349 < 0.504 < 0.660
Systematic Variation of the Decay Rate for SO2,
(k T - *e), *
At-XjA

hr"1
\ xT /

-0.462
-0.013 ± 0.38
0.595 < 0.860 <1.13
-0.231
-0.230 ± 0.43
0.648 < 0.987 < 1.29
0
-0.642 ± 0.54
0.848 < 1,225 < 1.60
0.146
-1.18 ± 0.68
1.08 <1.55 <2.03
0.231
-1.70 ±0,82
1,29 <1.86 <2.44
*At = 0.231 hr"1 (3-hr half-life)
8-38
-------
APPENDIX B (continued)
Systematic Variation of Vertical Diffusion Coefficient, oz.
(uzT ~ °ze\
(x T-XE\
—7T~'
V ^ )
V XT )
V
0
-0.642 ± 0.54
0.848 < 1.225 < 1.60
-0.2
-0.596 ± 0.54
0.858 <1.24 <1.62
+ 0.2
-0.733+ 0.54
0.851 <1.23 < 1.61
-0.5
-0.483 ± 0.51
0.810 < 1.17 < 1.53
+0.5
-0.911 ± 0.69
1.09 <1.57 < 2.06
-0.7
-0.428 ± 0.54
0.858 <1.24 <1.62
+0.7
-1.06 t 0.67
1.06 <1.52 < 1.99
Systematic Variation of Lateral Diffusion Coefficient, oy
/
-------
APPENDIX C - GLOSSARY OF SYMBOLS
a	fractional error in X due to random error
b	fractional error in X due to systematic error
Q	source strength field, emission rate
Q{£ t?£)	source strength at x = £, y = r?, z = f
u	transporting wind speed that determines time of
flight from x to etc.
(v'f2	variance of fractional error distribution
, ,i2" 1/2
'v '	standard deviation of fractional error distribution
X	concentration
XE	erroneous value of any input parameter
XT	"true" value of any input parameter
A	decay or loss coefficient for pollutant under consi-
deration
Oylx - £),
o?(x — £) standard deviation of crosswind and vertical spread
respectively of pollutant from £ 7? f
©	wind direction
oy, oz	lateral and vertical diffusion coefficients
8-40
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9. TIME - SPACE MODEL FOR S02
ABSTRACT
A multiple-source diffusion modeI for the simulation and prediction of
long-term fcl/matological) ground-level sulfur dioxide concentrations in
urban areas is described. The computer input consists of data from an
emission source inventory together with statistics on relevant diffusion
parameters.
Because of the capacity of available computers, only a limited number
of the largest emission sources (approximately 150) can be treated
individually. Smaller industrial emission sources are treated as residen-
tial sources. These are represented by a large number of stacks (about
150) of the same dimensions, distributed over areas of 1 square
kilometer, for which the mean area emissions have been estimated.
The meteorological input consists of data on wind direction, wind-
speed, and Pasquill-Turner stability classes.*' 2 These parameters are
assumed to be spatially homogeneous throughout the metropolitan
area. Low-level emissions (residential'} are correlated with low-level
windspeeds and Pasquill-Gifford diffusion parameters}' 3 whereas high-
level emissions (industrial) are correlated with extrapolated windspeeds
and Brookhaven diffusion parameters.4 The program also uses corres-
ponding statistics for urban boundary layer depths and values for
parameters affecting absorption at the earth's surface.
The diffusion model used is basically Gaussian. It is modified, however,
such that turbulent diffusion is restricted exclusively to the depth of
the urban boundary layer. This is true for all sources having effective
emission heights less than the height of the upper limit of the bound-
ary layer. The rate of decay of sulfur dioxide is taken into account, as
well as the experimentally determined absorption at the earth's surface.
The model calculates fields of steady-state ground-level concentrations
that correspond to a given spatial distribution of emission sources and
to any possible combination of relevant meteorological diffusion para-
meters. Knowledge of frequency distributions of these meteorological
diffusion parameters permits the derivation of frequency distributions
of ground-level concentrations for any location within or outside of
the metropolitan area. The computerized experiments simulate fre-
quency distributions of ground-level concentrations for a great number
of regularly arranged grid points (up to 2500 with a mesh size of 500
by 500 meters) and for a variety of time periods (months, heating
-------
period seasons, year, etc.). The frequency d,str,butions are charac-
terized bv a limited number of parameters (mean, percentiles, etcJ.
Each parameter is plotted as a system of isograms on a map of the
metropolitan area.
Exoeriments to validate the modeI were conducted during the heating
period in 1967-68 at four continuously monitoring stations that had
been installed at special locations within the limits of the metropolitan
area of Bremen. During the sampling period, the assumption of a
sufficiently homogeneous wind field was validated by wind measure-
ments at the same locations. The calculated frequency distributions of
half-hourly mean values of concentrations generally agreed fairly weft
with those derived from observed values. Comparison, however shows
that the model does not simulate ground-level concentration fields in
the vicinity of industrialized areas very well, because uncontrollable
low-level emissions from industrial plants could not be taken into
account in the diffusion model.
AUTHOR
HEINZ G FORTAK is a professor of meteorology and Director of the Institute
for Theoretical Meteorology at the Free University of Berlin. His scientific
interests include: general hydrodynamics, turbulence, dynamic meteorology, and
oceanography.
-------
9. NUMERICAL SIMULATION
OF TEMPORAL AND SPATIAL DISTRIBUTIONS
OF URBAN AIR POLLUTION CONCENTRATION
HEINZ G. FORTAK
Institut fur Theoretische Meteorologie
der Freien Universitat Berlin
INTRODUCTION
Increasing industrialization in Germany during the 1950's led to great in-
terest in the problem of ascertaining minimum stack heights essential to
pollution control. In line, therefore, with its responsibilities in developing air
pollution standards and criteria, the Kommission Reinhaltung der Luft[Air
Pollution Control Commision] within the Association of German Engineers
[Verein Deutscher lngenieure(VD\)] established a research group on air
pollution meteorology in 1958. The group was expected to develop the
scientific basis for an approximate solution to the problem. The results of
research during the first period, based mainly on the work of Sutton,5 led to
a simple nomogram for estimating minimum stack heights.6, 7 The nomo-
gram is widely used for legal and administrative purposes, although, among
other shortcomings, very little is known about one of the most important
input parameters of the model and therefore of the nomogram. This para-
meter (in German, tmmissions-Grundbe/astung) characterizes the temporal
and spatial distributions (air loadings with time) of ground-level concentra-
tions of pollutants in the area in which the newly built stack is located. In
most cases the location is in an urban area already possessing a great number
of emission sources. It is extremely difficult to define such a measure. A
simple number constant in space and time, as proposed by the VDI,7 will
9-1
-------
not suffice for urban areas. Instead, such a parameter is dependent on
horizontal space coordinates and, ultimately, on time (e.g., season).
In view of the crucial dependence of minimum stack heights on this para-
meter, some means of predicting ground-level concentrations in urban areas
must be found before the stack-height problem can be solved.
Based on the work of Frenkiel,8 the multiple-source urban diffusion model
being described in this paper was developed by the author in 1962. It was
hoped that this model would be able to solve problems of the kind mentioned
above. After financial support for programming and computing time became
available, a number of simulation experiments were conducted from 1963
through 1965. A tentative report was published early in 1966.9 During that
time the first papers on urban air pollution modeling by Turner2 and
Clarke,10 although they aimed at the solution of the real-time prediction
problem, were of great help. Especially, the replacement of Pasquili's stabi-
lity categories' by Turner's2 proved to be quite useful.
The purpose of the diffusion model is perhaps understood best by a discus-
sion of Figure 9-1, which shows the logical structure of some features of the
urban air pollution problem. Assuming that sufficient input data are avail-
able, a mathematical multiple-source urban air pollution model should yield
a set of output data such as that indicated in Figure 9-1.
The most important of these data certainly is a real time short-term predic-
tion of concentrations for the entire urban area. Most authors in the field of
urban air pollution modeling were interested primarily in that problern.
Following Turner,2 they applied the well known steady-state theory 0f
transport and dilution to simulate and predict time series of concentrations.
Quite recently, Marsh and Withers'1 demonstrated the inadequacy of such a
procedure. The model of Davidson' 2 that applies a non-steady-state theory
should provide a means of solving the short-term prediction problem, as well
as the problem of time series simulation, more successfully. If this turns out
to be true, the very important feedback circuit, "warning system," can be
closed; i.e., appropriate control measures can be applied to the source-
emission input in order to reduce the predicted concentrations below a given
limit.
The problem of minimum stack heights and, more generally, that of city
planning is connected with the problem of simulation and prediction of
long-term {climatological) ground-level concentration fields. Here, time series
of concentrations are of minor interest; instead, statistics of observed or
calculated concentration fields for given long periods of time are important.
There is no doubt that for a given location and a given period of time only
the frequency distribution of ground-level concentrations forms the basis of
what could be called "air pollution climatology." Generally, these frequency
9-2
-------
REGIONAL
GEOGRAPHICAL
(AND OTHER) DATA
REGIONAL
METEOROLOGICAL
DATA
SOURCE
EMISSION
INVENTORY
ADVECTION OF
POLLUTANTS FROM
OTHER REGIONS
DISPERSION OF
POLLUTANTS IN THE
REAL ATMOSPHERE
OBSERVED
CONCENTRATIONS
AT A FEW LOCATIONS
STATISTICS OF
OBSERVED
CONCENTRATIONS
VALIDATION OF THE MODEL
STRATEGIC
PLANNING OF
OBSERVATION
SITES
MATHEMATICAL
MULTJPLE-50URCE
URBAN AIR POLLUTION
MODEL
SIMULATION
OF OBSERVED
CONCENTRATIONS
STATISTICS OF
SIMULATED OBSERVED
CONCENTRATIONS
SIMULATION
OF POSSIBLE
CONCENTRATION
fields
SOURCE
EMISSION
TRANSFORMS
AND
PLANKING


REAL-TIME
PREDICTION OF
CONCENTRATIONS
CONTROL CIRCUIT
¦'WAftNING SYSTEM"



r-»4
L
CONTROL CIRCUIT
¦MINIMUM STACK HEIGHTS"
"PLANNING"
.1
| SIMULATION AND !
I PREDICTION DP I
"l	LONG-TERM	.
¦ concent radons |
T
I
I
I
I
I
I
	J
CO
GO
Figure 9-1. Major elements of the urban air pollution problem connected with mathematical modelling.
-------
distributions vary from location to location within the urban area and with
time and season. Figure 9-2 shows a typical example of the frequency
distribution in winter of measured half-hourly mean values of sulfur dioxide
concentrations in Bremen.
100
_ 10
e
-------
intervals (for example, hours); data from source emission inventories; rele-
vant meteorological parameters, etc. From these data the model then calcula-
tes possible steady-state ground-level concentrations for each interval of time
and for a large number of grid points within the urban area. From the stored
concentration data, the frequency distribution of concentrations is obtained
for each grid point. If the frequency distribution is characterized by a set of
parameters (mean percentiles, etc.), these parameters are plotted as a system
of isograms on a map of the urban area. Such maps then may be used to
define the Immissions-Grundbelastung (ground-level concentrations), to solve
problems of city planning as well as problems of strategic planning obser-
vation sites.
From the very beginning the main concern of the investigation was to apply
the model to a real situation and to validate the model by suitable measure-
ments. For several reasons the city of Bremen was chosen for the first
mathematical experiments. Local authorities of the city of Bremen were
willing and able (in 1963) to collect information on source emissions, which
led to a very complete source emission inventory. The location of the city,
on fiat terrain and only 40 miles from the North Sea, is favorable in many
respects: the city is well ventilated throughout the year and, in addition, the
relevant meteorological fields are approximately homogeneous horizontally.
In addition, advection of pollutants from other regions can be neglected. The
input data, therefore, were well defined and relatively simple and allowed
the application of a simple model.
The steady-state theory of the transport and dilution of pollutants is based
on a number of simplifying assumptions: the relevant meteorological fields
are stationary and are horizontally homogeneous; dispersion is not limited in
the vertical direction; mean windspeed exceeds a certain lower limit; and the
earth's surface is flat and not absorbing. The well-known formula for the
spatial distribution of a pollutant1 then is:
As usual, h = hs + Ah is effective stack height, r = x/U is travel time, and
T = 1/7 is decay time.
Assuming that the plume standard deviations, ov and oz, are functions of
travel time, r, it can be shown that Equation (1) is a solution of the
following1 3 initial-value and boundary-value problem:
MATHEMATICAL MODEL
-------
0 : X -* -g 6 (y) 5 (h-Z)
(3)
Z = 0
dx
dZ
= 0
(4)
Z 00 : X 0	(5)
The initial condition, that is, Equation (3), expresses the fact that a point
source of strength, Q, is located at the effective stack height, h. The
boundary conditions show that there is reflection of the pollutant at the
earth's surface and further that dispersion is not limited in the vertical
direction.
It may be noted that Equation (1) has the character of Green's function in
the special boundary-value problem. Equations (2), (4), and (5). It seems
legitimate, therefore, to apply Equation (2) to problems connected with
boundary conditions different from those described by Equations {4} and (5)
Two important assumptions are in question; that of a non-absorbing ground
and that of unlimited vertical dispersion. Denoting by H the height of a
ceiling restricting dispersion to a limited layer of the lower atmosphere
(urban boundary layer), and denoting by a(r,y) the absorption coefficient of
the ground, the boundary conditions, Equations (4) and (5), can be replaced
by:
'*(¥)
Z = 0 : ^ m = alr.y)*	|S)
3y
z = H :	g = 0	(7)
Even if absorption is not a function of location, only mathematical, rather
than experimental, methods are suitable for solving Equation (2) together
with Equations (3), (6), and (7).' 4 In view of the uncertainties connected
with absorption at the ground, and with the functional behavior of plums
standard deviations for such cases, only experimental calculations were per-
formed with boundary-condition Equation (6).
Important for practical applications, however, is the assumption that disper-
sion is confined only to the urban boundary layer; i.e., the utilization of
boundary condition Equation (7) for the upper ceiling of the layer (Figure
9-3).
Standard methods1 5-1 7 allow the derivation of a modified version of Eq-
uation (1) so that it now describes dispersion in a boundary layer of depth H:
9-6
-------
Figure 9-3. Model assumptions.
(8)
is a Jacobian theta-function.
It can be shown that Equation (8) differs only slightly from Equation (1)
for H > 3h. If, however, the ceiling approaches the effective stack height,
i.e., if H -> h, then the ground-level concentration increases drastically.
So far only a single source has been considered. In an urban area, a large
number of such sources exist. In reality, all of them are point sources as far
as emissions are concerned. They may be divided into three groups. Group 1
consists of all industrial stacks, including those of power stations and
gasworks; Group 2 consists of stacks of small industries, contributing, say,
less than 0.02 percent each to the total output into the city; Group 3
consists of all domestic sources burning fuel for space heating.
Industrial emission sources of Group 1 are treated individually by applying
Equation (8). Since they are irregularly distributed over the urban area,and
9-7
-------
since Equation (8) applies to a source-oriented coordinate system, the trans-
formation of coordinates shown in Figure 9-4 is performed.
Figure 9-4. Transformation of coordinates from a source-
oriented system to a geographically fixed system.
If a denotes wind direction {|3 = 37r/2 — a) , P(x,y) a receptor point, arid
(^ TlJ the location of a point source, then the individual source distance in
wind direction, Xn , and the individual crosswind distance, Yn, of the
receptor point, p(x,y), are given by:
Xn	=	e*7 = (x-i;n) cos/EJHY-r^) sin|3	(9)
Yn	=	kfe-7) = - 4x-£n) sin 3 + {Y—] cosj3
where
y	=	i
-------
Now, source strength, wind speed, travel time, plume standard deviations,
and effective stack height are dependent on i^nrjn) and (Xn, Yn) , respec-
tively. Individual source strength is denoted by Q = Q{£nj?n) = Qn . Wind
speed relevant for transport and dilution of pollutants originating from the
source at (£n,i7n) is given by U = U(£n,i7n) . Travel time is indicated by t„
= Xn/Un, plume standard deviations by ov = oy (7n) = ay_n and oz =
0z(Tn) = oZln , and local effective stack by h = h(£n.Tjn) = hSi„ +
Ah(£n,7?n) . Introducing these new parameters and coordinates into Equation
(8), the ground-level concentration originating from emission source "n," i.e.,
Xn(*.V,z) . is obtained.
The concentration fields from all individual sources can be superimposed.
Contributions to the concentration at receptor point, P, come from all
upwind sources having coordinates, £n < x + y tan )3, rj0 < y + x/tan . If
N denotes the total number of upwind sources, the concentration P is given
by:
(10)
JL
2H
£	exp[-Trn]—^^]|03 (^;aiV 03(^;^jj
n=l Un	I \2H 2H7 \2H 2H2/)
It is obvious that computing time goes up tremendously with an increasing num-
ber of individual sources. It is impossible, therefore, to treat all domestic sources
of Group 3 individually. In this context one generally talks about area sources.
The source strength, Q, is replaced by a local source strength density (source
emission per unit area), q(£rj). Local relevant mean wind speed, U(lj tj), as
well as local plume rise, Ah(£ 17), are connected with the emission height
hs(^ T?) of /the area source. The coordinates, Xn,Yn, with respect to an
individual source are replaced by x,y which obey the same relations, in
Equation <9), as Xn and Yn do. If the sum in Equation (10) is replaced by
an integral, the contribution of all upwind area sources to the concentration
at receptor point, P, is given by:
(11)
x . ' /df	4^exp[-r?] exp [- tofa)
2H £ ^ x+y tan j3 77 < y+x/tan /} U(£ 17)
n/2tt Gy(r)
Superposition of concentrations, in Equations (10) and (11), gives the
steady-state concentration field at any location in space, (X,Y,Z), if indivi-
dual point sources as well as area sources act together in that urban area.
9-9
-------
Apart from the fact that source emission data for area sources, i.e., q(£rj)
are not available, the analytical integration of Equation (11) cannot be
performed. Numerical integration replaces the integral by a sum which
represents the area source by a dense, regularly spaced system of point
sources having source strength, q(£j,T7k}A£AT}. This, in fact, has been done in
the model. The selection of the area element, A£Atj, depends upon resolu-
tion and scale. In addition, the characteristics of dispersion as well as the
conditions of emission (emission heights) are important. In order to find a
satisfactory answer to that question, a number of mathematical experiments
was performed. An area source, 500 m by 500 m was represented by a
successively increasing number of point sources (Figure 9-5).
0*9
° a o
Figure 9-5. Simulation of an area source by the use of increasing
number of point sources distributed regularly over an area 500 x
500 meters.
As Figures 9-6 and 9-7 show, an area size of A = A£Atj = 56 m x 56 m
should be sufficient for the representation of an area source by a great
number of point sources under the conditions indicated in Figures 9-6 and
9-7.
In order to get the same degree of approximation for a wide range of
windspeeds and stability categories, the 500 m by 500 m area source must
be represented by at least 100 individual sources (A = A£Atj = 50 m x 50
9-10
-------
m) or better, by 144 individual sources (A=A|A77 % 42 m x 42 m|. This
corresponds roughly to the mean distance between individual stacks from
space heating units.
Figure 9-6. Successive approximation of area-source emissions
under unstable conditions by the use of an increasing number qf
point sources. (Relative crosswind SQg concentration prpfiles
taken at Xmax distance from center of area. Uniform emission
height is £5 meters; stability class, 2; wind speed, 3 meters per
second.)
9-11
-------
S02 CONCENTRATION PROFILES
Figure 9-7. Successive approximation of area-source emissions
under neutral conditions by the use of an increasing number of
point sources. (Relative crosswind SO2 concentration profiles
taken at Xmax distance from center of area. Uniform emission
height is 25 meters; stability class, 2; wind speed, 3 meters per
second.)
9-12
-------
METEOROLOGICAL DATA INPUT
A set of meteorological data consists of windspeed, wind direction (both
taken at anemometer level), and stability category. All three are hourly
values taken at the Bremen airport Observations of windspeed and wind
direction at four sites in the city during winter (1967-68) validated the
assumption that the airport observations are representative for the urban area
of Bremen, at least during winter, which is the most important period with
respect to air pollution in Bremen. Stability categories were computed using
Turner's scheme.2
It was discovered during simulation experiments that 36 wind direction
measurements (wind roses divided into 10-degree intervals) are necessary to
provide reasonable ground-level concentration fields. Windspeed was divided
into seven classes. Including five stability categories, a total number of 1260
combinations exist, of which, however, only about 600 are realized.
Frequency distributions of wind data were calculated for each stability
category for a variety of periods (months of the year, seasons, years, and
five to ten years). Figure 9-8 shows a typical example of a long-term
distribution.
Data on plume standard deviations for urban areas were not available during
the years of experimentation. Therefore, the well-known Pasquill-Gifford
values1,3 were used for low emission heights (space heating), whereas the
Brookhaven values 4> 18 were applied in a slightly modified version to high
industrial stacks (Figures 9-9 and 9-10). The results of the St. Louis disper-
sion study indicate that utilization of those values given in Figures 9-9 and
9-10 inevitably lead to a systematic overestimation of ground-level concentra-
tions.19 This trend was, in fact, apparent when the results of calculations
were compared with those obtained by observations.
Finally, the problem of mean windspeed, U, which is relevant for the
transport and dilution of pollutants, was solved in the usual manner. Wind
observations were extrapolated from anemometer level to physical stack
height for each stack by means of a power-law - prof ile assumption. This
extrapolation was assumed to be a function of stability and was made by the
use of parameters taken from the literature (Figures 9-8, 9-9, and 9-10).
EMISSION SOURCE INVENTORY
All emission sources, as mentioned earlier, were classified in three groups. All
individual stacks (Group 1) with emission rates greater than 1 kilogram
9-13
-------
N
Figure 9-8. Frequency distribution of wind direclion and wind-
speed for Bremen, 1954 to 1959. Stability class: 4 (neutral),
Isopleth numbers represent hours per period.
sulfur dioxide (SOa) per hour were treated individually. The record con-
tained: geographical location, physical dimensions of the stack, output by
volume, exit velocity, exit temperature, and, finally, emission data that
included maximum emissions and mean winter and summer emissions. In
addition, data were obtained whenever possible on daily variations in emis-
sions and emissions during holidays.
Effective stack heights were calculated by applying Stumke's empirical for-
mula,20 similar to the well-known COMCAWE-formula, which is applicable tQ
all types of stacks in Bremen.
Group 1 emission sources, consisting of 136 stacks, contributed 75 percent
to the total emission rate in Bremen during winter 1965 (Table 9-1), Spatigl
distribution per square kilometer is given in Figure 9-11 for these sources.
8-14
-------
STABILITY CLASSES:
2	=UNSTABLE
3	- SLIGHTLY UNSTABLE
4	- NEUTRAL
5	- SLIGHTLY STABLE
6-STABLE
1,000
5,000
(Tx,m
Figure 9-9. Crosswind-plume standard deviations.
100
10.
LOW-LEVEL
EMISSIONS
30
STABILITY CLASSES:
2	=UNSTABLE
3	- SLIGHTLY UNSTABLE
4	- NEUTRAL
5	- SLIGHTLY STABLE
6	=STABLE
HIGH-LEVEL
EMISSIONS
Ox.m
Figure 9-10. Vertical-plume standard deviations.
-------
nv

563 24
20
0
BREMEN 1962
GRID: 1 km x 1 km
^P'T
107
tHsX'
i»t K"t;: i-H.aV—>
ti,.. ,J4 ,:jl
V ¦ ; ! 1 1 : i j i M
;i 'so?f; It i
* 520 . i?3'. i-j.
i 1«
\ ' ; *'60' I f"¦ "t" "t—|~~t" fi
) : ' • '2i1 1 M '
v ¦ • I - I ! i-
ift
•--H. '
\
lr
M
! U
88
/ \J^
i?»;
_ ,38 7ftil 0-
23(24
.rl-
12 2
L _...
35
25S
170 40
4
25
\L^
1" " I
i-2! i
'Zr
Figure 9-11. Spatial distribution of mean winter time industrial
emissions.
Table 9-1. STATISTICS FROM 1965 EMISSION-SOURCE INVENTORY
OF BREMEN

Number of
Total emissions,
kg SOj hr"1
Percent of total
emissions
Source
stacks
Summer
Winter
Summer
Winter
Industries and power plants
136
1,423
4,715
99
75
Small industries
425
46
116
1
2
Space heating
-
-
1,458
-
23
Total
561
3,469
6,289
100
100
9-16
-------
A large number of individual stacks from small industries contributed less
than 0.02 percent each to the total emission rate, i.e., Jess than 1 kilogram
S02 per hour. They contributed only 1 to 2 percent altogether and,
therefore, were not treated individually. Instead, the same technique was
used as that applied to emissions from space heating (Figure 9-12).
V

BREMEN 1962
GRID: 1 km x 1 km
i'J jiif
6,1:1 1 1 1
i13 i11 o 1 ! ;
u -L-.
:.Y
y
X

Figure 9-12. Spatial distribution of mean winter time industrial
emissions from small industries.
Although it contributed less than 25 percent to the total emission rate, space
heating is the dominant factor in air pollution in Bremen because of tow
emission heights.
Emissions from space heating were obtained in the following way. The
spatial distribution of dwelling units in Bremen, which number about
200,000 was known very well. Further, the total amount of coal and fuel oil
consumption during heating periods was known. From the sulfur content of
the fuels, the total fuel consumption, and the total number of dwelling
units, a mean emission rate of 8 grams SOj per hour per dwelling unit was
obtained. This is the amount that would have been emitted daily during the
heating period if the daily mean temperature had remained constant. In
several experiments, a relationship between daily mean temperature and daily
emission was used to make emissions from space heating a function of time.
9-17
-------
A mean emission height of 25 meters was assumed for downtown emissions
and 15 meters for suburban emissions. The corresponding effective stack
heights were calculated by a simpler method than that used for tall stacks.
Emissions from space heating were treated as "area sources" as described
earlier A grid produced areas 500 m by 500 m. The number of dwelling
units in each area was counted. Multiplying by 8 grams S02 per hour (or the
corresponding, temperature-corrected value) gave the mean emission rate for
that area (Figure 913). This amount was then divided by the number of
individual stacks (from 81 to 144) representing the area source.
1
1
V
* 3
l


5 2I
s|
8
4
4
14]2 1
1
6 [15| 9 { v"
BREMEN 1962
GRID: 1 km x 1 km

©f

Q J	t ^4 , ( 1 V
3>:»;^ t T>
L'l'L
Figure 9-13. Spatial distribution of mean heating period in-
dustrial emissions from space heating, kg SC^/km^hr.
The fact that area sources are represented by a large number of individual,
equivalent stacks simplifies the calculations a great deal. The distribution of
dwelling units in Bremen is such that only about 250 areas, 500 m by 500
m, are covered with dwellings. Since the density of these dwellings varies
spatially, the emission rates of the 250 types of stacks, in general, differ
from each other. Their physical dimensions and their plume rise values,
however, are equal, or are grouped into only two categories (downtown and
suburban). With the shift of calculated concentration fields from one point
source location to the other within an area of 500 m by 500 m, the
computing time is very much reduced.
9-18
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RESULTS OF SIMULATION EXPERIMENTS
An inventory of all possible steady-state ground-level concentration fields
forms the basis of simulation experiments. This inventory was obtained by
calculating concentration fields for all possible combinations of meteorolo-
gical parameters. It has already been noted that about 600 such combina-
tions, representing given weather situations, can occur in Bremen. This
number depends, of course, on the classification of windspeed and wind
direction used. If one calculates the concentrations at the points of a grid (a
grid distance of 500 meters) about 600 numbers have to be stored at each
grid point. Since the computer program was written for a grid of 2500
points, a total number of 1.5 million numbers have to be stored. If the
source inventory is assumed to be time-dependent (heating period, non-
heating period, etc.), the number of concentration values to be stored
increases considerably.
The use of concentration field inventory data together with frequency
distributions of relevant meteorological parameters permits the derivation of
frequency distributions of concentrations for each point on the grid. Other
statistics, as well, can be obtained quite simply, such as S02 wind roses.
Figures 9-14 to 9-17 demonstrate this clearly. Sulfur dioxide wind roses were
calculated for the four sites where monitoring stations were later installed.
These figures, together with Figures 9-11 to 9-13, show the possibility of
identifying large emission sources by means of S02 wind roses. It may seem
that this is by no means an easy task because emission sources with quite
different emission heights work together with meteorological factors having
complicated frequency distributions. It may be noted that the simulated SO^
wind roses coincide considerably well in structure with those obtained by
measurement.
Among the many experiments performed, the investigation of the influence
of boundary layer thickness on ground-level concentration was the most
interesting. The upper ceiling was lowered from 500 m to 25 m. In cases in
which the ceiling reached the effective height of an individual stack, this
effective height was reduced with the decreasing height of the ceiling until it
reached two-thirds its original value. This stack was then thrown out of the
inventory on the assumption that the plume would penetrate the ceiling
Figures 9-18 and 9-19 show how the isogram patterns change and they also
show the tremendously increased concentrations that result if the depth of
the mixing layer is approximately equal to the effective height of space
heating emissions. Figure 9-20 demonstrates this behavior for a specific
location in downtown Bremen. It is obvious that this picture looks different
for different locations. Only mathematical experimentation of the kind
applied here can simulate the complicated behavior of ground-level concen'
trations.
9-19
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BREMEN, 1967-68
O INDUSTRY :::3 RESIDENTIAL AREAS
— .2 km • MEASURING SITES
i—¦ = Q.l mg S02/m3
•3
I	yv
N	' \
V.	I®
GT3
O


—eza
\pJr Q i i ^
0 '
Figure 9-14. Calculated heating-peri od-SC>2"Wind rose for
Site 1 in downtown Bremen.
Figure 9-15. Calculated heating-period-S02 wind rose for
Site 2 in downtown Bremen.
920
-------
Figure 9-16. Calculated heating-period-SOg-wind rose for
Site 3 on the outskirts of Bremen.
¦ °/j
EZZ7
\ & i	>
^ui/Zqs ro=r~
S31IS DNIUflSV3W • uii| I
swav ivutraaissa rzi AnisnaHi
mm 'N3N3ija
Figure 9-17. Calculated heating-period-S02-wind rose for
Site 4, in close proximity to an industralized area.
9-21
-------
Figure 9-18. Calculated field of ground-level-SC>2concentration
in mg/m3 for a special meteorological situation and a boundary
layer thickness of 100 meters.
Figure 9-19. Calculated field of ground-level-S02 concentration
in mg/m^ for a special meteorological situation and a boundary
layer thickness of 25 meters.
9-22
-------
o
o
cs
o
(/)
LU
CJ
o
h-
<
{£ 0.5
z
1.0
INDUSTRY
0.0
101
l.ll.l
102
CEILING HEIGHT, meters
Figure 9-20. Variations in ground-level concentrations of SO2
in downtown Bremen as a function of boundary layer thickness.
As mentioned in the introduction, frequency distributions of ground-level
concentrations were of chief interest from the beginning of this investigation.
The method for obtaining these for desired periods of time is straightfor-
ward. It must be stated, however, that the derived distributions are not
complete because up to now no theory exists for explaining the dilution of
pollutants under calm weather conditions. These cases, therefore, were ex-
cluded from the statistics as were cases with limited boundary layer depths.
Neither source of error, however, plays an important role in Bremen. The
frequency of calm conditions as well as the frequency of low-level inversions
was small during all periods of time investigated.
Stored data on fields of steady-state concentrations (Figure 9-21) form the
basis of statistics of this kind.
Steady-state concentration fields, together with frequency distributions of
meteorological parameters, can be used to calculate frequency distributions
of concentrations for each grid point. These distributions were characterized
by a set of three parameters:
1. The percentage of time (in hours) for which ground-level concentra-
tions exceeded a given value (0.1 milligram S02 per cubic meter).
F igure 9-22 shows the pattern of this parameter for the heating period
of 1962. As seen, only 20 percent of the period concentrations in
downtown Bremen were below 0.1 milligram S02 per cubic meter.
9-23
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2.	The mean concentration for the period. Figure 9-23 shows the pattern
of this parameter. Typically, the pattern of the mean concentration
shows little structure and does not contain much information.
3.	An upper percentile; for example, the 97.5th percentile. The numbers
in Figure 9-24 indicate that for only 2.5 percent of the time (in hours)
concentrations exceeded that value given by the respective number.
The following Figures, 9-25 thru 9-27 show the corresponding pattern for a
nonheating period in which only industrial sources are contributing emis-
sions.
It might be possible to define Imissions-Grundbelastung with the help of
these maps of characteristic parameters. This investigation is one step for-
ward in this direction.
VALIDATION OF THE MODEL
During the heating period of 1967-68, four monitoring stations were in-
stalled at specially chosen locations. The locations were planned as stra-
tegically as possible. First of all,, an attempt was made to place all stations
on a mean concentration isogram (Figure 9-23). Second, an attempt was
9-24
-------
Figure 9-22. Percentage of cases (hours) for which ground-
level concentrations exceeded 0.1 mg SO/nA Winter 1962.
Figure 9-23. Mean ground-level-S02 concentration in mg/m3.
9-25
-------
Figure 9-24, 97.5th percentile S02concentrations in mg/m3.
Winter 1962.
Figure 9-25. Percentage of cases (hours) for which ground -
level concentration exceeded 0.1 mg SC^/m3- Summer 1962.
9-26
-------
:r&
BREMEN 1962
INDUSTRY
	[2 km
RESIDENTIAL AREAS
MEASURING SITES
\I
Figure 9-26. Mean ground-!evel-S02 concentration in mg/m^.
Summer 1962.
Figure 9-27. 97.5 percentile of ground-level-S02 concentrations
in mg/m3. Summer 1962.
9-27
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made to locate stations in areas as diverse as possible. Station 1 was located
in a "normal" downtown area, surrounded mainly by residences. Station 2
was located in the very center of the city on an island. It was surrounded,
however, on all sides by the water of the river Weser and of the waterworks.
Station 3 was located on the outskirts of the city, separated from downtown
Bremen by a large park with tall trees. Station 4 was located in the near
vicinity of a large plant.
The monitoring stations measured half-hourly values of S02 concentrations.
From these values, frequency distributions were derived for every month of
the period and for the period as a whole. At the same time, mathematical
simulation of the same distributions was performed using the latest version
of the emission source inventory and utilizing meteorological statistics for
the sampling period. Figures 9-28 through 9-31 show comparisons of ob-
served and calculated frequency distributions. The simulation of Station 1
(downtown "normal" area) is quite satisfactory, as indicated in Table 9-1.
For Station 2 (waterworks on the Weser island), the model obviously
overestimates the concentrations systematically (Figure 9-29). Overestimation
may occur for one or both of two reasons: absorption at the water surfaces,
or an insufficient spread as a result of improperly chosen urban plume
standard deviations. The same holds for Station 3 (separated from downtown
Bremen by a large park), where the filtering effect of the park was not taken
into account.
At Station 4 (in the vicinity of a large plant), the reverse is observed. The
model systematically underestimates the concentrations. Since emissions
from iow-level sources of space heating are small in the neighborhood of that
station, low concentration values could be expected. The comparatively high
concentrations that actually occur have their origin in uncontrollable low-
level emissions, which could not be taken into account, from the nearby
plant.
Table 9-2 summarizes the observed and calculated mean concentrations for
each monitoring station.
Finally, it can be stated that it is worthwhile to invest more effort in
diffusion modeling, for simulation may one day be a very important tool in
city planning.
9-28
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99.98,
99.9 |
99.5
CUMULATIVE FREQUENCY POLYGON
AND FREQUENCY HISTOGRAM
SITE NO. 1, UBEftLANDWERK NORO-HANNOVER
HEATING PERIOD, 1967/64

J	; . J I ¦ - I| 1 i Mjy'
; ;^Jjr 97.5th PERCENTILE ?
i	*"
1 ,>^90th PERCENTILE

LEGEND
--- OBSERVED
— COMPUTED
0.05
0.02
0.01
0.6 0.1 1.0
AVERAGE GROUND-LEVEL CONCENTRATION, mg/m3
Figure 9-28. Comparison between observed and computed
frequency distributions of ground-level concentrations in
downtown Bremen.
CUMULATIVE FREQUENCY POLYGON
AND FREQUENCY HISTOGRAM
SITE NO. 2, WASSERTURM WESERINSEL
HEATING PERIOD, 1967/68
.
PI
ij.'.U.
	 ) .<
Jj":r ' ' . V- ,
:	PERCEiifiiX
:*«—~onih pporrNTii f -
0.4 0.S 0.S 1.0
AVERAGE GROUND-LEVEL CONCENTRATION, mf/«|3
Figure 9-29. Comparison between observed and computed
frequency distributions of ground-level concentrations in
downtown Bremen.
9-29
-------
AVERAGE GROUND-LEVEL CONCENTRATION. mt »3
Figure 9-30. Comparison between observed and computed
frequency distributions of ground-level concentrations on
outskirts of Bremen.
95.98			
CUMULATIVE FREQUENCY POLYGON
99.9 AND FREQUENCY HISTOGRAM
59.5
91
95
90
SO
o 60
3 so
| «
£ 30
20
10
4
2
1
0.5
0.2
SITE NO. 4, PUMPENSTATION RIEDEMANNSTRASSE
HEATING PERIOD > 1967/68	, . ^
»VED ,

LEGENO
	 COMPUTED
	OBSERVED
¦ '>¦1.1:. •,
o.o5:
%r
I	-t-
^¦1- ^ |
'''' ' " '	L
"WCJ '
.K1H?E2
0.02
0.6 0.8 lj
0.04 0.06 0.08 0.1	0.2	0.4
AVERAGE GROUND-LEVEL CONCENTRATION,/*^
Figure 9-31. Comparison between observed and computed
frequency distributions of ground-level concentrations in an
industrial district.
9-30
-------
Table 9-2. OBSERVED AND CALCULATED MEAN S02 CONCENTRATIONS
IN BREMEN; HEATING PERIOD, 1967-1968
Site
1
2
3
4
Calc.
Obs.
Calc.
Obs.
Calc.
Obs.
Calc.
Obs.
November
0.14
0.11
0.15
0.10
0.14
0.08
0.05
0.10
December
0.10
0.08
0.12
0.08
0.10
0.06
0.03
0.07
January
0.10
0.10
0.12
0.13
0.09
0.08
0.04
0.08
February
0.09
0.08
0.12
0.08
0.07
0.06
0.04
0.08
March
0.08
0.07
0.10
0.04
0.07
0.05
0.04
0.07
April
0.09
0.07
0.11
0.05
0.06
0.05
0.05
0.07
May
0.05
0.06
0.07
0.03
0.04
0.03
0.03
0.05
Total
0.09
0.08
0.12
0.08
0.08
0.06
0.04
0.08
9-31
-------
references
1	Pasquill, Frank. Atmospheric Diffusion. London, D. Van IMostrand Co. Ltd.,
1962. 297 p.
2	Turner, D. B. A Diffusion Model for an Urban Area. J. Appl. Meteorol.
91, February 1964.
3	Gifford, F. A. The Problem of Forecasting Dispersion in the Lower Atmosphere.
AEC Division of Technical Information Extension. Oak Ridge, Tenn. 1961.
4	Singer I. A. and M. E. Smith. Atmospheric Dispersion at Brookhaven National
Laboratory. Int. J. Air Water Pollution. JO. 125-135, February 1966.
5,	Sutton, O. G. Micrometeorology; A Study of Physical Processes in the Lowest
Layers of the Earth's Atmosphere. New York, McGraw-Hill, 1953. 333 p.
6.	Verein Deutsche Ingenieure. VDI-Forschungsheft 483, Ausgabe B. Band 27, 1961.
7 Ausbreitung iuftremder Stoffe in der Atmosphare Zusammenhang zwtschen emis-
sion und immissiort Schornsteinhohen in ebenem, unbebautem Geiande. Verein
Deutscher Ingenieure, VD/Kommission Reinhaitung der Luft. Germany. VD|
2289. June 1963. 7p.
8.	Frenkiel, F. N. Atmospheric Pollution in Growing Communities. In-. Annual Re-
port of the Board of Regents of the Smithsonian Institution, Publication 4272,
1956. Washington, D. C. Government Printing Office. 1957. p. 269-299.
9.	Fortak, H. G. Rechnerische Ermitttung der S02 — Grundbetastung aus Emission-
sdaten - Anwendung auf die Verhaltnisse des Stadtgebietes von Bremen, institute
for Theoretical Meteorology, The Free University of Berlin. 1966.
10.	Clarke, i. F. A Simple Diffusion Mode) for Calculating Point Concentrations from
Multiple Sources. J, Air Pollution Control Assoc. 74347-352, September 1964.
11.	Marsh, K. J. and V. R. Withers. An Experimental Study of the Dispersion of the
Emissions from Chimneys in Reading — III: The Investigation of Dispersion
Calculations. Atmos. Environ. 3I3):281 -302, May 1969.
12.	Davidson, B. A Summary of the New York Urban Air Pollution Dynamics Re,
search Program. J. Air Pollution Control Assoc. 17:154-158, March 1967.
13.	Frenkiel, F. N. Turbulent Diffusion: Mean Concentration Distribution in a Flow
Field of Homogeneous Turbulence. In: Advances in Applied Mechanics, von Mi$6S(
R. and T. von Karman (eds.), Vol. III. New York, Academic Press Inc.. 1953. p.
61-107.
14.	Fortak, H. G. Einbeziehung der Sinkgeschwindigkeit und partiellen Absorption am
Erdboden in die A usbreitungsrechnung, speziell im Falls nicht-FlCKscher Off-
fusion. Institute for Theoretical Meteorology, The Free University of Berlin. 1964.
15.	Fortak, H. Zur allgemeinen Berechnung von Suspensionsverteitungen in turbutenten
Stromungen. Gerlands Beitr. Geophys. 66(11 '.65-78, 1957.
16.	Stumke, H. Vorschlag einer empirischen Forme! fur die Schornsteinuberhoburtg.
Staub (Dusseldorf). 2^:549-556. December 1963,
17.	Fortak, H. G. Ausbreitung von Staub und Gasen um eine kontinuierliche Punkt-
Quelle in einer bezuglich Windgeschwindigkeit und Austausch geschichteten Atmo-
sphare. Verein Deutscher Ingenieur. VDI-Forschungsheft 483. 1961.
18.	Singer, 1. A. and M. E. Smith. Relation of Gustiness to Other Meteorological
Parameters. J. Meteorol. 10(2) :121-126, April 1963.
19	McElroy, J. L. and F. Pooler, Jr. St. Louis Dispersion Study, Vol. II - Analysis.
National Arr Pollution Control Administration. Arlington, Va, Publication Number
AP-53. 51 p.
20	Fortak, Von Heinz. Sinkstofftransport in Geraden Kanaten als Randwertprobiem.
Acta Hydrophysica. 4(11:26-48, 1957.
9-32
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ACKNOWLEDGMENT
In the course of the research, a number of members of the Institut fur
Theoretische Meteorologie der Freien Universitat Berlin contributed to this
work, in many ways, mainly in programming and organizing. Especially, the
author wishes to thank the following for the valuable cooperation, without
which these experiments could not have been performed: R. Bleck, J.
Schwirner, H. Buttner, H. Woick, and P. Lenschow.
9-33
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APPENDIX - GLOSSARY OF SYMBOLS
a(r,y)	absorption coefficient of the ground
h	effective stack height
hs	actual stack height
Ah	plume rise
H	height of dispersion ceiling
N	total number of upwind sources
P(x,y)	receptor point
q(£ 17}	local source-strength density
Q	source strength
T	decay time, 1/y
U	wind speed
(Xn,Yn)	source distance in downwind and crosswind directions, respectively
a (3	wind direction angle coefficients
A	source area
(£n rTjr}	location of a point source
7T	3.14
oyraz	standard deviations of plume spread in y and z directions, respec-
tively
7	travel time
X	concentration
9-34
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ABSTRACT
A source-oriented three-dimensional model of diffusion and transport
based upon the statistical concept of turbulent diffusion was developed
for application to an urban area. A simple algorithm was found for
computing the concentration field from time-dependent continuously
emitting area sources of different scales. The model was applied to the
New York City metropolitan region by introducing known specific
meteorological conditions and the known pollutant (S02J source distri-
bution as input data. The validity of the model has been verified in a
preliminary manner. The results appear promising, giving concentration
fields computed on spatial scales down to 0.2 mile.
AUTHORS
Until his death in 1968, BEN DAVIDSON was Professor of Meteorology at New
York University, a consultant to both the U. S. Weather Bureau and Brook haven
National Laboratory, and chairman of the working group on sites for wind power
installations of the World Meteorological Organization. He has also been on the
University of Chicago Review Committee for the Radiological Physics Division of
Argonne National Laboratory and on the Air Pollution Training Grants Com-
mittee. Most of his research was concerned with turbulence diffusion, local wind
circulations, and urban air pollution models.
L/AU JANG SHI EH, a staff member of the Internationl Business Machines Cor-
poration Palo Alto Scientific Center, received his Ph. D. in Meteorology at NYU
in 1969 for work done with Dr. Oavidson. He also holds an M.S. from NYU and
a B.S. from National Taiwan University, Formosa.
JAMES P. FRIEND is the director of the U. S. Department of Health, Educa-
tion, and Welfare Air Resources Engineering Training Program at NYU, where he
is Associate Professor of Atmospheric Chemistry. He is a member of the ad hoc
committee for Air Pollution Manpower Affairs, NAPCA, and holds a S.B. in
chemistry from Massachusetts Institute of Technology, and an M.S. and Ph. o.
in chemistry from Columbia. His principal research is in the area of stratospheric
aerosols and mathematical models of air pollution dynamics.
-------
10. A MODEL OF DIFFUSION
IN URBAN ATMOSPHERES:
SO2 IN GREATER NEW YORK
LIAU J. SHIEH, BEN DAVIDSON,
AND JAMES P. FRIEND
New York University
INTRODUCTION
The essential components of a model of dispersion and transport of pollu-
tants in an urban atmosphere are (1) distribution and strengths of sources of
pollutant in space and time, {2) a set of meteorological conditions as
functions of space and time, (3) a mathematical formula (algorithm) repre-
senting the physical concepts of dispersion and transport, and (4), in com-
bination with the formula of (3), an expression for the removal (decay,
settling, or absorption on surfaces) of the pollutant.
The model described below was developed in the Urban Air Pollution
Dynamics Research Project at New York University. It was a task of the
project, not only to develop the model, but to provide sufficient data so
that the model could be tested. The pollutant chosen was sulfur dioxide
(S02) and the urban region was a 50 by 50 mile square containing greater
New York City. Commensurate with the requirements implied by the pre-
vious paragraph, the project provided a survey of S02 emissions throughout
the area. Also, during specific test periods of 2 to 5 days duration, it
provided wind, temperature, and S02 concentration measurements at several
points within the area. Helicopter-borne instruments were used for vertical
soundings of temperature and S02 concentrations.
The model of diffusion and transport in urban atmospheres was fashioned
Contribution No. 84, Geophysical Sciences Laboratory of the Department of Meteorol-
ogy and Oceanography, New York University. This research was sponsored by the U. S.
Department of Health, Education, and Welfare under Grant No. AP 00328-04.
10-1
-------
from the statistical theory of turbulent diffusion. In that theory, concentra-
tion profiles in diffusing plumes are represented as Gaussian distributions. An
attempt was made to maintain generality within the Gaussian framework of
the theory. The formulated theory was thus applicable in three dimensions
to non-isotropic and time-dependent motions of the atmosphere. The model
constructed on the basis of the theory was made to accept as data (1) any
specified time and space distributions of area and point source strengths,(2)
specified meteorological parameters (wind, temperature, thermal stability,
diffusivity, and height of inversion layer) as functions of time and space, and
(3) the (initial) field of pollutant concentrations over the region at any given
time. The output of the model consists of fields of pollutant concentrations
in three dimensions at 2-hour intervals after the initial time.
DATA
As used here, the term "data" refers to quantities entered into the computa-
tional scheme as input.
A summary of the meteorological and S02 source and concentration data
obtained in the Urban Dynamics project was given by Davidson1 and will be
given in complete detail by Davidson et a/.2
Meteorology
Winds for the various trial periods were obtained from a fixed network of
stations in the Greater New York region and from analyses of data obtained
from pibal ascents at three or four fixed sites plus a reference ascent at JFK
airport made on a continual basis throughout each trial period. Scudder3
analyzed stream-line patterns derived from various wind data and noted char-
acteristics ranging from essentially straight streamlines, through curved in-
flected ones, to sharp discontinuous ones. He also found high wave number
patterns. These patterns generally depend upon the strength of the prevailing
synoptic wind field, time of day, and insolation. Evidently the combined
effects of land-sea, land-river, urban-rural, and other contrasting topograph)*
cal features produce complicated mesoscale wind flow patterns.
In view of the observed complexity of flow over the New York City area It
is clear that a realistic model of diffusion and transport must be capable of
incorporating space-and time-dependent winds. Turbulent diffusion processes
are treated in the model by the statistical theory of diffusion. Transport of
the pollutants is based on the average trajectory of parcels according to the
analyzed wind field. This trajectory method was studied and verified by
Druyan.4
Bornstein5 frequently found temperature inversions at elevations of 200 to
300 meters over the metropolitan area in nighttime and early morning hours,
when the inversion was at ground level in rural areas. This is the heat island
10-2
-------
effect due to release of heat from urban surfaces. The air beneath the
inversion generally exhibited vertical temperature gradients ranging from
isothermal to adiabatic.
As Davidson1 pointed out, "the diffusive consequences of the temperature
structure over the urban area are enormous. One would expect good vertical
diffusion below the elevated inversion, but virtually zero diffusion through
the base of the inversion."
The model includes this thermal stratification effect by treating the observed
elevated inversion layer as a physical barrier to diffusion of the pollutant.
The height of the inversion at all points at all times is entered as data in the
computational scheme. The meteorological network and the grid used in
model computations are shown fn Figure 10-1.
Figure 10-1. Meteorological grid system and observational
network.
10-3
-------
SO2 Emissions
A comprehensive source survey was conducted in the 50 by 50 mile-square
region shown in Figure 10-1, and a portion of it is shown in Figure 10-2.
Two types of sources were delineated: (1) area sources representing emis-
sions from fuel combustion used for space heating and production of hot
water and (2) continuous point sources representing industrial emissions
from electrical power generating plants, large hospital heating plants, large
industrial heating plants, and chemical plants.
Messrs. P. Halpern and L. Randall* have analyzed the diurnal and daily
variations of S02 emission rate for area sources. Their findings have been
directly incorporated into the model:
¦ 0J ^DD + a3llf	<»
where Qday is the daily total output of S02, Qyear the annual total output,
and DD is the number of degree days for the date of interest. The diurnal
variation of the area-source strength was found to depend upon atmospheric
temperature in the manner shown in Figures 10-3 and 10-4.
The survey of point sources was conducted by Messrs. Kaiser, Simon, and
Ingram.* The most complete data were available for electric power genera-
tion plants. For other sources most of the important parameters such as
stack height, heat emission rate, and diurnal variation of source strength
were not available. Hence, assumed values of these are used in the rnodel.
Total output of SO, was, however, obtained for each source.
The model treats the point source emissions in a straightfoward manner
using the equations for a continuous elevated point source emitting a Gaus-
sian plume.
Initial S02 Concentrations
In all model computations to date the initial concentration of S02 has been
taken as zero everywhere. Experience has shown that under steady wind and
emission conditions the concentrations computed at the end of the first time
step (At = 2 hoursl are greater than or equal to 90 percent of the finaJ
steady values.
theory and algorithm
The model is based on the statistical theory of turbulent diffusion. In this
theory it is hypothesized that the concentrations in a cloud of trace material
(called pollutant in this paper) emitted from an instantaneous point source
"Members of the research staff. New York University.
10-4
-------
*5 -4-3-2-10 1
MILES EAST OF BATTERY
o
6l
Figure 10-2- $C>2 source inventory (tons mi"2 year~1).
-------
i i r
i i i i—i—r
MEAN DAILY TEMP. 20"to 29° F.
MEAN DAILY TEMP. 30" to 394 F.
	i—r
14
12
10
8
6
4
2
0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200 2400
CLOCK TIME
Figure 10-3. Diurnal variation of SO2 output during days with
mean temperature ranges of 20° to 29° F and 30° to 39° F.
16
14
^ 10
a.
o 8
_j
< c
(- 6
o
1-
d 4
D 2
0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200 2400
CLOCK TIME
Figure 10-4. Diurnal variation of SO2 output during days with
mean temperature 40° to 49° F, and >60° F.
I
I	r i i I II 1 1
1 1 —MEAN DAILY TEMP. 40° to 49°F
r—-J 	MEAN DAILY TEMP. 50° to 59 °F-
! i —MEAN DAILY TEMP. i 60" F
¦ 1

1 1
1
1
1
1
1
r


1 1

—
l-J
	1
—


—
I
1 1 1 1 1 i 1 1

10-6
-------
are given by a three-dimensional Gaussian distribution. Empirical data sup-
porting the use of such an hypothesis were found by Sutton,6 Frenkiel,7
Ogura,8 and others. Application of the theory to the atmosphere was studied
by many investigators, e.g., Batchelor;9- 10 Hay and Pasquill;11 Cramer,
Record, and Vaughn;12 Barad and Haugen;13 and Lin and Reid.'4
Models of urban atmospheric diffusion using statistical diffusion theory have
been formulated for several specific urban areas—in one case a whole state,
Connecticut—under various simplifying assumptions concerning area-source
representations, and temporal and spatial uniformity of meteorological con-
ditions. The pertinent features of these models including the regions repre-
sented and the assumptions made were recently reviewed by Moses15 and
will not be further discussed here.
In addition to the diffusion mechanism, the transportation of pollutant is
affected by large-scale flow, which is taken here as mean wind. It is assumed
that, as the material is released from a point source, it is dispersed and the
whole cloud is simultaneously transported along a trajectory given by the
mean wind field.
With the above assumptions the equation for the concentration distribution
in three dimensions in a moving medium from an instantaneous point source
with non-isotropic diffusion is represented by:
Q(t)
C
-------
Standard Deviation of Diffusing Cloud
Numerous schemes have been proposed for determining formulas and for
determining the o's in Equation (2). Most of these are based on G.I. Taylor's16
original work. Among the investigators are Sutton/' Holland,17 Kellogg,1 8
Frenkiel and Katz,19 Gifford,20 Gifford and Pack,21 Inoue,22 and
Hogstrom.2 ^
Pasquill,24, 25 using experimental data, formulated a set of rules for deter-
mining oy and oz for different atmospheric conditions. These have been
widely used in estimating concentrations in diffusing plumes.
It is generally considered that the diffusion coefficients (i.e., the o's) relating
to a non-isotropic, non-homogeneous atmosphere depend upon atmospheric
thermal stability, dynamic wind field, aerodynamic effects of roughness
elements in the boundary, and the time of exposure of the plume to these
conditions.
In the present model development a modification of the approach presented
by Singer and Smith26 was adopted. This method was judged to be well
suited for a computational method using Equation (2) as the basis for an
algorithm. The standard deviations of the diffusion cloud are given by:
"x -
°0x
+
au (t- t')p
(3a)
°y =
a0y
+
au (t - t')p
(3b)
-------
metropolitan New York area. Figure 10-5 shows an example of computed
S02 concentrations in the midtown Manhattan region for a = 0.2 at two
different wind speeds. The points plotted are measured S02 concentrations.
0.3
JAN. 30,1966 •HIS - 1242 (312 13 mph)
¦1339 * 1434 (315°-16 mph)
A1436» 1539 (315 °* 16 mph)
MILES
u =15 mph
a=0J
1
B'WAY
C.P.W.
5TH AVE 3RD AVE
E.E.
Figure 10-5. Computed SOg concentrations in 79th Street
Manhattan with « = 0.2 for two different wind speeds.
Since an inversion layer aloft is considered to be impenetrable by S02
injected below it, the value of az is taken as constant when an inversion
stratification is present. With the height of the base of the inversion layer as
H (mi), the relationship, following Gifford,27 is estimated as:
H
ffz =	15)
if crz as computed by Equation (3c) is greater than H/2.
Continuous Point Sources
Integration of Equation (2) over the time interval [0,*»] has been shown by
Frenkiel28 to give the following expression for the mean concentration from
a continuous point source at ground level:
10-9
-------
c (x, y, z) _ 1
Q	2n oy az u
exp -
2a.
2a,2
<6)
where u is the mean wind speed. The equation applies for uniform flow in
the x-direction. For emission from a source at height K (mi) above the
ground and considering the ground as a perfect reflector of pollutant Equa-
tion 16) becomes	^
C 
-------
/ Q (t'>
C{x,x0, v-v0( z-z0,t,t0) = I ——	—-
J {2irr2 o2[x~\')
^o
¦I
x--a
t r x-x0 -u • (t-t*> -x' -i
• exp i- %	
| L ox(t-t*) J
T V-Vo -v -	I
	 Hdx'dy'dt'	110)
L	Oy {t~t') jj
where:
C = concentration (g crrf3)
Q(t') = source strength (g cm-2 sec-1}
t = time (sec)
{t-t') = time since emission (sec>
(x',y'} = point of retease measured from {x0,y0).
A schematic diagram representing the space referring to any point (x'py'| and
{t—1'| is given in Figure 10-6.
/
y'=-b
1
Ox (t-t') ¦ Gy(t-t')
10*11
-------
	LL
*o
x =0
x0 + x' +u(t-t')
	1	L
x
X-X0-u(t-t')-X'
y - 0 MEAN pollutant concentration contributed from
AREA-SOURCE; SUMMATION OF CONTRIBUTIONS OF ALL x
y' AND t' FROM INFINITE INDIVIDUAL PUFFS.
Figure 10-6. Schematic diagram showing how plume is com-
puted from area source.
In order to simplify the integration of Equation (10), the following condi-
tions were set:
(1)	a = b;
(2)	t0 = 0. t = 2 hours;
(3)	v = w = 0;
(4)	u is constant over (0, t);
(5)	atmospheric stability and turbulent intensity are constant over (0, t)
(6} Q(t') = Q, a constant;
(7) x0 - Yo = 0.
In other words, the integration of Equation (10) is over a 2-hour interval
during which emission rates and atmospheric conditions are steady, and over
an area centered at the origin and oriented with one side parallel to the
wind, These conditions along with the transformations:
10-12
-------
x - u(t-t') - x'
ffx(t-t')
(11)
and
Y =
y-y
ov (t-t')
(12)
reduce equation (10) to:
2 hr
§-/
1
(2rr)l/i a,(t-t')
exp

1
y/2v
x - u • (t-t') + a
ax(t-t')
/
x-u • (t-t') -a
Ox (t-t')
exp
m
dX
V + a
ov (t -1')
s/2n
; /
exp
[-t]
dY) dt'
y-a
av(t-t')
(13)
In order to prevent accumulation of large errors in the double integration, a
polynominal representation of the Gaussian probability function was applied
for the integration over X and Y. To perform the integration over t', a
refined two-part interval was used in a complicated application of Simpson's
Rule. This prevented further undue accumulation of errors.
The integration in Equation (13) was carried out according to the procedure
10-13
-------
above for values of u, a, and a, within their possible limits; for various values
of x, y, and z; for p= 1; and for z0 = 100 ft., the assumed roof top level
characterizing metropolitan New York residential and small office buildings.
At this point in the development it can be stated.
		 = f(x,y, z, z0,a, p, u,a,t,t0).	(14)
Qa rea
It is to be noted that (x, y) now represents the distance from the center of
the area source.
Adaptation of Continuous Area Source Solution
In order to apply the result of the integration in Equation (10), represented
by Equation (14), to the model, it is necessary to adopt the assumptions
equivalent to those stated above. The 2-hour interval (0, t) is equivalent to
the emission interval, At, over which contributions from the various sources
are summed in the model. Emissions and meteorological conditions over the
entire urban region are assumed to remain steady over the interval, At.
The are no actual data to support a non-zero value for w, and the theoretical
knowledge of mesoscale phenomena, which would permit its calculation from
other meteorological variables, is limited. It therefore seems reasonable to
assume w = 0 everywhere in the region.
The assumption of v = 0 is equivalent to stating that the square area source
elements have one side parallel to the mean wind. On the basis of computa-
tions on a simple grid, errors resulting from this assumption are judged to be
small. With the above assumptions, Equation (14) can be used as the basis
for modeling multiple area sources in urban localities. The quantity C/QAroa
is a tabulated function and could not be conveniently used in a numerical
model in which a large number of area sources are considered. A set of
conditions (some of which are approximations) that gave simple representa-
tions of the area source solutions and required reasonable computation time
and memory storage capacity was found. The representations also preserved
the features of the exact integration, with the conditions:
1 _ |£- = 0; 0  This is commensurate with the notion that
mechanical mixing dominates atmospheric turbulent diffusion in the
vicinity of buildings and other bluff objects (see, for example,
Halitsky.31) It was found empirically that oQz = 0.01 mile gave a
reasonable approximation to the condition of uniform concentration
between the ground and rooftop height, z0.
2. In view of (1) the computed S02 concentrations at z = z0 = 100 ft
was used to represent those at ground level.
10-14
-------
3. For It — t') > At, and p = 1 the area source solution is approximated
by a pseudo-Gassian distribution. The manner in which this is done
will be discussed below.
. Cu
^Area
f(u). This condition will also be discussed below.
Using conditions <1) and (2) above, the solutions for area source emissions,
Equation (14) becomes:
Q
		 = f(x, y,a, p, u,a,t, t0)	(15)
'Area
Examination of the results of the integration in Equation (13) reveals that
for (t—t') > At the spatial concentration distribution approaches a shape
that might be approximated by a Gaussian distribution, and the maximum
concentration is far less than when (t—t') < At, An example of this is shown
in Figure 10-7. It follows then, that the computation of the concentration
field resulting from any area source can be divided into two formats, For
(t—t') < At, i.e., during the interval in which the portion of the plume under
study has been emitted from the source, one set of grid lines of the area
sources is assumed to be parallel to the mean wind and the concentration
field is computed directly from the tabulated value of C/QArea based on a
chosen value of a, and p = 1 (Taylor's hypothesis). For (t—t') > At, i.e.,
for portions of the plume that were in the atmosphere at the beginning of
interval, At, the field of concentration from an area source is represented in
the following manner:
The distribution of concentrations is first assumed to be Gaussian. Then it is
replaced by a simple uniform distribution within a rectangular parallelepiped
with dimensions related to the o's of the Gaussian distribution. This process
is represented by the equality:
oo oo oc
III

V 3/2
\ah
-oo -co -oo
+0+ (•'}
(2tt) o^Oy az
g(t)
(4)3 axoyoz
for -2ox < x <2 ax, -2 oy < y < 2 oy, -2 o, < z < 2 az
dxdydz
115)
where g(t) is the total source output of a 2-hour period (g of S02). The
dimensions of the parallelepiped are 4erx , 4oy , 4ot . Accurate representa-
tions of the o's in equation (16) were found to be the expressions;
10-15
-------
io;
T 10*2
o
e
o
cy
o
It = 2.0 hr
u = 8.00 mi. hfl
a = 0.2
AREA SIZE 1.0 x 1.0 mi
CTOZ=0.01
10 20 30 40 50 60 70
x, miles
Figure 10-7. Time history of a plume from a continuous area-
source.

a
Z
®z0
=	a0x	+	a u (t -1') + % a + Vt. u (-t')
=	o0y	+ au(t-t') + % a
=	oQz	+ a u (t -t')
=	o0y
(17)
With the above conditions (3) the dependency of the tabular function
C/QArea on p and the time, t and t0, are removed and:
C/QArea = f(x, y, d. U, a).
<18)
10-16
-------
Figure 10-8 illustrates the nature of this function for different values of the
parameters.
x, miles
Figure 10-8. Downwind distribution of pollutant from area-
sources .parameterized by values of a.
Finally, by studying the integrated solution of Equation (13), it was found
that:
^— = f{x, y, a, a).	(18)
uArea
This is condition (4) above and is illustrated in Figure 10-9. This was a
significant finding for it enables the model to handle a number of different
source grid dimensions, a, while including the effect of various wind speeds.
Using all of the conditions discussed above, Equation (10) can be summed
over all time intervals of duration At to obtain the contributions to the
concentration of all "puffs" (each emitted during a different interval) at the
point (x—x0, y-y0) from an area source located at (x0ly0). The result is:
10-17
-------
Figure 10-9. Illustrating that Cu/Q is independent of wind speed.
-------
nAt t-nAt+At
C(x-x0, y-y0, "At) =J"
t=nAt t-nAt
f 2(N-n+1)-1 A
?QL~i—At
IO'rri3/2 ft tn A* *'\
(2jt) 2 crz (nAt-t')
ox (nAt-t') ay (nAt-t')
* dx'dy' dt'
(20)
in this equation, N is the number of time intervals from the beginning of all
emission to the present. When n = 1, the exact solution to Equation (10) is
used, while for all of the remaining terms the center of gravity of the puff is
advected according to the wind, and the pseudo-Gaussian distribution of
Equations (16) and {17) are applied to compute the spatial distribution of
concentrations. Finally, to complete the model construction, Equation (20)
is summed over all x0 and y0 to obtain the concentrations contributed to a
point (x,y) by all continuous area sources. This summed equation plus an
equivalent one for point sources plus the tabular function Equation (19)
represent the algorithm for the multiple-source model of dispersion and
transport.
To complete the model, a value of a, remained to be fixed, a grid represent-
ing area source emissions to be constructed and the computation grid to be
specified. Based upon the parametric studies mentioned in earlier values of a
in the range 0.1 to 0,25 were chosen, depending upon the thermal stratifica-
tion.
Condition (4), in the preceeding section permitted simultaneous use of
several different vafues of a, the dimension of the area-source grid. Figure
10-10 shows the area-source grid. The values of the dimension a used were
0.5, 1.0, 2.0, and 5.0 miles. The grid size at any particular location depends
upon the source strengths and their spatial distributions, and on topographi-
cal and geographical factors. Generally the smallest grid size occurs in the
central portion of the region where the annual emissions per unit area are
the highest (Figure 10-2).
MODEL CONFIGURATION
10-19
-------
Figure 10-10. Area-source grid. Shaded areas represent zero emissions. Grid size depends on source
strengths and spatial distribution, geographical and topographical factors.
-------
Two computation grids (referring to x,y) with mesh sizes of 0.2 by 0.2 mile
and 1.0 by 1.0 mile were used. The time interval, At, was 2 hours.
COMPUTATIONS AND VALIDATION
The computer methodology used in the computations representing the mode!
is described elsewhere.8
The model was used to compute surface concentration patterns of S02 for
the two test periods March 8-9, 1966, and November 15-16, 1966.
The computations were carried out by a CDC 6600 computer. The portion
of the program dealing with winds and trajectories required 3 minutes of
computer time for 24 time steps (48 hours) for source grid system consisting
of 712 points (565 area sources and 148 point sources). The diffusion
portion of the program computed the concentration field at more than 2000
points for each of the 24 time steps in a total computer time of 19 minutes.
Some exemplary results are shown in Figures 10-11 to 10-18, maps of
concentration fields of S02 over Manhattan for various times during the test
period, each using a 0.2 by 0.2 mile computational grid. Isolines with values
(ess than 0.1 ppm are dashed. Zero time was at 00 hours on March 8 and
November 15. Figure 10-19 is a map of a larger area computed for the same
time as Figure 10-14, but using a 1.0 by 1.0 mile computation grid. It is
clear that the coarser grid computation may miss several important small-
scale features.
10-21
-------
0800 MARCH B , I 966
Figure 10-11. Predicted SO2 concentration field (ppm), 0800
March 8, 1966, 0.2 x 0.2 mile computational grid.
10-22
-------
Figure 10-12. Predicted SO2 concentration field {ppm), 1000
March 8, 1966, 0.2 x 0.2 mile computational grid.
10-23
-------
Figure 10-13. Predicted S02 concentration field (ppm), 1800
March 8, 1966, 0.2 x 0.2 mile computational grid.
10-24
-------
Figure 10-14. Predicted SOg concentration field (ppm), 1800
March 9, 1966 , 0.2 x 0.2 mile computational grid.
10-25
-------
Figure 10-15. Predicted SO2 concentration field (ppm), 1200
November 15, 1966, 0.2 x 0.2 mile computational grid. '
10-26
-------
Figure 10-16. Predicted SO2 concentration field (ppm), 2400
November 15, 1966, 0.2 x 0.2 mile computational grid.
10-27
-------
Figure 10-17. Predicted SO2 concentration field (ppm), 1200
November 16, 1966, 0.2 x 0.2 mile computational grid.
10-28
-------
Figure 10-18. Predicted SOg concentration field (ppm), 1800
November 16, 1966, 0.2 x 0.2 mile computational grid.
10-29
-------
o
CO
o
Figure 10-19. Predicted SO2 concentration field (ppm), 1800
March 9, 1966, 1.0 mile x 1.0 mile computational
grid.
-------
I	l_l	I	I	_L.	1	1	1	1——J	1	1
R.O. «.E.R'*A>AKI. COL. AVE. C.P.*.	it* AVE. PAflK AVL. MO ?ND 1STKMW E.E.
Figure 10-20. Observed and predicted variation of SO2 concentra-
tion along the 79th Street crosstown transect at the indicated
times.
A comparison of the computed results with observed concentrations is
shown in Figures 10-20 to 10-23 that are crosstown transects along 79th
Street, of the concentration of SO^ computed on a 0.2-mile grid. The lines
represent the computed quantities while the observations are plotted as
points.
I	1	L	J	I I	I	I	I	I	I	I	I
R.O. ».E,e,»A* MBT. COL. AYE C.P.I	51H AVE. PARK AVE. 3R0 TWO 1ST YORK E.E.
Figure 10-21. Observed and predicted variation of SO2 concentra-
tion along the 7 9th Street crosstown transect at the indicated
times.
10-31
-------
Figure 10-22. Observed and predicted variation of SO2 concentra-
tion along the 7 9th Street crosstown transect at the indicated
times.
0.4S
0.40
0.35
|0.30
|0J5(-
io
Ui
u
§0
&
"0.10
0.05
• OBSERVED DATA
|- MARCH 9,1966
0905 • 1042
• •
0.5
1.0 1.5	2.0
DISTANCE FROM HUDSON, miles
R.D. B'WAY COL. AVE,	5TH AVE. 3RD
1.1. I	,	I
2.5
3.0
1ST E.E.
, J	[	1	T	1	1	L—I	1—!	1
W.E. AMST. C.P.W.	PARK AVE. 2ND YORK
Figure 10-23- Observed and predicted variation of S02 con-
centration along the 79th Street crosstown
transect at the indicated times.
10-32
-------
While agreement is not perfect, the computed concentrations bear a discern-
ible relationship to the observed concentrations. Figure 10-24 shows a
transect for the same time as Figure 10-12, but it was computed using a 2.0
mile square area source grid over the entire region. It is evident that such a
course representation of the area sources causes severe smoothing and dis-
tortion of the computed concentration field.
K.D. *.E.6'WAYA'«T.C0L. AVE.C.P.*.	5TH AVE PARX AVE. 3RD 2ND 1ST YORK AVE.E.E.
Figure 10-24. Observed and predicted variation of SO2 concen-
tration along 79th Street crosstown transect, same period as Fig-
ure 10-12, coarse grid 2.0 miles x 2.0 miles.
An objective estimate of the relationship between computed and observed
concentrations for the two test periods is illustrated in Figure 10-25, a
scatter diagram of observed versus computed values. The mean of the
observed concentrations is 0.19 ppm, and the mean of the computed concen-
trations is 0.18 ppm. There are 121 data points in the diagram. The standard
error of estimate is 0.09 ppm.
The situation depicted in Figures 10-14 and 10-19 for 1800 hours March 9
arose because of a complex wind field with a region of convergence over
Manhattan Island. The wind field is shown in Figure 10-26. Because the S02
concentrations were computed using w = 0 everywhere, the values of concen-
trations shown are higher in the region of convergence than they would be if
provision were made for non-zero values of w. The concentrations in the
center of the convergence region are about twice as great as they should be.
A final point, illustrating the potential usefulness of the model, is seen in
Figure 10-27, which shows the 1000-hour, March 8 S02 concentration field
resulting from area source emissions only (compare with Figure 10-12).
10-33
-------
0	0.1 0.2 0.3 0.4 0.5
PREDICTED S02 CONCENTRATION, ppm
Figure 10-25. Plot of observed against predicted concentra-
tions of SO2. Mean observed and predicted concentrations,
0-19 and 0.18 ppm respectively. Standard error of estimate
is 0.09 ppm.
DISCUSSION
A mathematical model for computing concentration in a multiple-source
urban region has been developed. The model is three dimensional, accepts
input data of meteorological conditions and source strengths that are func-
tions of space and time; and computes pollutant concentration fields on a
fine mesh grid <0.2 mile-square) over a 50-mile-square region at any given
time The framework of the model is general enough so that the vertical
component of the wind could be included if it were known. To do this,
however, the part of the algorithm giving the integrated expression for a
continuous area source in tabular form (Equation 14) would have to be
modified.
The adaptation of the model for the computations of S02 concentrations in
the New York urban region involved assumptions of w = 0 and immediate
10-34
-------
uniform mixing of area source emissions between rooftop level and the
ground. No removal factor was included. S02 reaching the ground was
assumed to be reflected. These assumptions are, of course, possible causes of
error in the computed concentration fields. Other sources of error are:
coarseness of the meteorological observational network (Figure 10-1); poor
data for source strength and inventory, particularly for manufacturing plant
stacks; and unaccounted for topographical effects on dispersion.
Systems of the kind developed in this work are rarely amenable to a
posteriori error analysis. The algorithm is based upon semi empirical theory,
not derivable from known physical concepts. The sources of error as listed
above are generally not readily controlled, and the assessment of their
individual effects is difficult if not impossible.
The present status of the model is one of promising preliminary verification.
Certainly a new effort in obtaining high-quality test data for periods up to 3
or 4 days in duration would be desirable. With such data further parametric
studies could lead to improvement of the model.
Figure 10-26. Wind field 1800 March 9, 1966. Streamlines and
isotachs represented by solid and broken lines respectively.
Convergence zone over Manhattan Island, shaded.
10-35
-------
Figure 10-27. SO2 concentration field, predicted from area
sources only.
10-36
-------
references
1.	Davidson, B. A Summary of the New York Urban Air Pollution Dynamics Re-
search Program. J. Air Pollution Control Assoc. 77:154-158, March 1967.
2.	Davidson, B. et al. Mathematical Models of Urban Air Pollution Dynamics: Final
Report, Vol. 2. New York University. 1969.
3.	Scudder, B. Diagnosing the Mesoscale Wind Field over an Urban Area by Means of
Synoptic Data. New York University. M. S. Thesis. 1965.
4.	Druyan, L. M. A Comparison of Low-Level Trajectories in an Urban Atmosphere.
J. Appl. Meteorol. 7(4) :583-590, August 1968.
5.	Bornstein, R. Observations of the Urban Heat Island Effect in New York City. J.
Appl. Meteorol. 7(4):575-582, August 1968.
6.	Sutton, O. G. Theory of Eddy Diffusion in the Atmosphere. Proc, Roy. Soc., Ser.
A (London). 135:143-165, February 1, 1932.
7.	Frenkiel, F. N. Application of Statistical Theory of Turbulent Diffusion to Micro-
meteorology. J. Meteorol. 9(4):252-259, August 1952.
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Point. Meteorol. Soc. Japan J. 3.2(Series II), January 1954.
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Hundred Feet in the Atmosphere. J. Fluid Mech. 2:299-310, May 1957.
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Gases or Aerosols in the Lower Atmosphere. Massachusetts Institute of Tech-
nology. Cambridge. AFCRC-TR-58-239. 1958. 70 p.
13.	Barad, M. L. and D. A. Haugen. A Preliminary Evaluation of Sutton's Hypothesis
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1959.
14.	Lin, C. C. and W. H. Reid. Turbulent Flow, Theoretical Aspects. In: Handbuch der
Physik, Flugge, S. (ed ), Vol. 8/2, Berlin, Springer-Verlag, 1963. p. 438-523.
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Pollution Control, Chicago Dept. of Air Pollution Control, Argonne National
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16.	Taylor, G. I. Diffusion by Continuous Movements. Proc. London Math. Soc.
20(Series 2): 196-212, August 20, 1921.
17.	Holland, J. Z. and R. F. Myers. A Meteorological Survey of the Oak Ridge Area.
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nical Information Service, Final Report for 1948-1952. Report Number ORO-99.
November 1953. 584 p.
18.	Kellogg, W. W. Diffusion of Smoke in the Stratosphere. J. Meteorol. 73(3):
241-250, June 1956.
19.	Frenkiel, F. N. and I. Katz. Studies of Small Scale Turbulent Diffusion in The
Atmosphere. J. Meteorol. 73(4):388-394, August 1956.
20.	Gifford, F. A., Jr. Atmospheric Diffusion from Volume Sources. J. Meteorol.
72(3) :245-251, June 1955.
Gifford, F. A., Jr. Relative Atmospheric Diffusion of Smoke Puffs. J. Meteorol.
74(5) :410-414, October 1957.
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Advances in Geophysics, Landsberg, H. E. and J. Van Mieghem (eds.), Vol. 6. New
York, Academic Press, 1959. p. 117-138.
10-37
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22.	Inoue, E. On the Shape of Stack Plumes. National Institute of Agriculture Sci-
ences, Division of Meteorology, Meteorol. Res. Notes. Japan. Vol. 2, No. 5. 1960.
p. 332-339.
23.	Hogstrom, U. An Experimental Study on Atmospheric Diffusion. Tellus. 76(2):
205-251, May 1964.
Pasquill, F. The Estimation of the Dispersion of Windborne Material. Meteorol.
Mag. 90( 1063):33-49, February 1961.
Pasquil), F. Atmospheric Diffusion. London, D. Van Nostrand Co. Ltd., 1962. 297
24.
25.
26.
P-
Smith M E and I A Singer. An Improved Method of Estimating Concentration
and Related'Phenomena from a Point Source Emission. J. Appi. Meteorol. 5(5):
631-639, October 1966.
27	Gifford, F. A., Jr. Atmospheric Dispersion. Nucl. Safety. 7:56-62, March 1960.
28	Frenkie'l F N Turbulent Diffusion: Mean Concentration Distribution in a Flow
' Field of Homogeneous'Turbulence. In: Advances in Applied Mechanics, von Mises.
R. and T. von Karman (eds.), Vol. Ml. New York, Academ.c Press Inc., 1953. p.
61-107.
29	Brummage K. G. et. at. The Calculation of Atmospheric Dispersion from a Stack.
Stichting, CONCAWE, The Hague, Netherlands. August 1966. 57 p.
30	Simon C Plume Rise and Plume Concentration Distribution from Consolidated
" Edison Plant in New York City. New York University. Technical Report Number
68-15. 1968.
31. Halitsky, J. (unpublished report) Effect of Turbulence on Gas Diffusion Around
Obstacle's. New York University. 1965.
10-38
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APPENDIX - GLOSSARY OF SYMBOLS
a	dimensions of area-source grid
C	concentration
DD	number of degree days for date of interest
g(t)	total source output for a 2-hour period
h	height of stack from which pollutant is emitted
Ah	distance above stack through which plume rises by bouyancy
and exit velocity of stack gases
H	height of base of inversion layer
K	effective stack height
N	number of time intervals from beginning of all emissions to
present
p	data based parameter to describe intensity of turbulence
Q	source strength
Gh	heat emission rate
Gday	da'IV total output of SOj
Qyear	annual total output of S02
t	time
At	time interval
(t — t')	time since emission
u, v, w	velocities in x, y, z directions respectively
(x', y', z')	position of release
a	data based parameter to describe thermal stratification
ox, ov, az standard deviations of diffusing cloud in three dimensions respec-
tively.
10-39
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ABSTRACT
This paper presents a statistical approach to the analysis of multiple-
station air sampling data in urban (i.e., multi-source) areas. Measured
data values are considered to be composed of three contributions: an
urban scale constituent, a contribution due to sources in the vicinity of
the sampling station, and a contribution due to measurement and
analysis errors. The significance of correlation coefficients calculated
from paired data series and the influence of averaging several individual
data series prior to calculating correlations is examined.
The data base for the present study is limited, but the following
conclusions can be cited:
-The error contribution to the total variance in most field data series
is significant.
-Correlations among single station data series, and between data from
one station and an external predictor (such as a meteorological para-
meter), will be small in most cases. Errors and local phenomena in the
data from a single station mask much of the urban scale variability
that would correlate with most urban scale model predictors.
-An urban scale average, drawn from widely separated stations, is the
best index of large scale air quality patterns.
-A maximum expected correlation coefficient can be calculated from
the field data, and this value can serve as a criterion for the evaluation
of air quality model projections,
-Whenever possible, a double set of instrumentation should be op-
erated at one station within a sampling network. The redundant data
provide an excellent measure of the expected error variance in the field
observation.
authors
JAMES R. MAHONEY is Assistant Professor of Applied Meteorology at Harvard
University, School of Public Health, and staff consultant at Environmental
Research and Technology, Inc., Waltham, Massachusetts. He received a B.S.
degree in physics from LeMoyne College (New YorkI in 1959 and a PH.D. degree
in meteorology from Massachusetts Institute of Technology (M.l.T.) in 1966.
WILLIAM O. MADDAUS is Water Resources Systems Engineer at Engineering-
Science Inc., Oakland, California. He received a B.S. degree in civil engineering
from the University of California at Berkeley in 1967, and an M.S. in civil
engineering degree, together with a C,E, degree from M.l.T. in 1969.
JOHN C GOODRICH is a teaching assistant in City Planning at Harvard Univer-
sity Graduate School of Design, and staff consultant with Environmental Research
and Technology Inc., Waltham, Massachusetts. He received the B.S. in civil
engineering degree from Princeton University in 1966. and the Master of Re-
gional Planning degree from Harvard in 1969.
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11. ANALYSIS OF MULTIPLE-STATION
URBAN AIR SAMPLING DATA
JAMES R. MAHONEY, WILLIAM 0. MADDAUS
AND JAMES C. GOODRICH
Harvard University
INTRODUCTION
Air pollution control depends upon adequate current data and projections
describing concentrations of the important pollutants within the control
region. Average concentrations, temporal and spatial variability, and concen-
trations during poor ventilation conditions must all be known.
Recently a large investment in time, effort and financial expenditure has
been committed to the collection of multiple-station data in urban areas.
Within the United States, several of the largest cities have instituted con-
tinuous monitoring for important local pollutants:
-The Los Angeles County Air Pollution Control Department instituted a
program in 1947. Nine stations, all equipped to monitor carbon monoxide,
oxides of nitrogen, ozone, hydrocarbons, sulfur dioxide and particulates, are
operated throughout Los Angeles County.
—New York City recently activated a 38-station network, under the direction
of the Air Resources Department. Each station records concentrations and
surface meteorological data, and ten of the stations transmit data regularly
to a central, computerized facility.
—Chicago has an active monitoring and projection program, operated with
the cooperation of Argonne National Laboratories.
Many other cities have operated programs in response to local pollution
11-1
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problems. Pittsburgh, for example, has collected smoke shade data for more
than 40 years. Its monitoring program was instituted to support that city's
efforts to achieve a smokeless atmosphere.
In response to the requirements of the Air Quality Act of 1967, all of the
states are currently establishing monitoring networks within federally
designated air quality control regions. Ail of the data coliected is useful only
when it is properly analyzed and made available for study and decision-
making operations. This paper presents a brief analysis of the uses and
limitations of multiple-station air quality data collected in urban areas. The
illustrative examples cited are drawn from an analysis for a ten-station
SOj survey and a 20-station particulate survey conducted in the
metropolitan Boston region in 1966 by the Massachusetts Department of
Public Health.
The section headed "Design Specifications for a Multiple-Station System"
summarizes the elements required for adequate specification of a sampling
network. The section headed "Interstation Data Correlation Studies"
contains the results of several interstation correlation studies for the
Boston data. These results illustrate the degree of variability between
simultaneous observations in various parts of the same urban region. The
section captioned "Correlations between Air Quality Data and Meteoro-
logical Data" summarizes a correlation study of the same air quality data
related to local meteorological data. Such correlation statistics must be
developed to facilitate projections for special meteorological conditions and
for changes in local emission rates. The section captioned "The Use Of
Computer Generated Graphic Analyses for Air Quality Data" illustrates the
use of computer generated graphic displays for the presentation of regional
air quality data, and the concluding section contains recommendations for
the establishment and analysis of multiple-station air sampling networks.
DESIGN SPECIFICATIONS FOR A MULTIPLE-STATION
SYSTEM
Before a monitoring system can be established, several basic questions con-
cerning its purposes must be resolved. The system criteria can be developed
from an evaluation of the following topics. (Note that very similar specifica-
tions are required for the development of diffusion models intended to
provide urban area concentration data,}
1. Basic uses of the data. Information concerning long term (annual)
averages, monthly and seasonal variability, day-to-night variability,
background levels, and frequencies and magnitudes of peak values wjll
normally be desired. Also, observed concentrations during defined
periods of poor atmospheric mixing are usually required.
11-2
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2.	Spatial resolution. Is it sufficient to report an average for the entire
urban region, or for the "urban center" region? Will it be necessary to
describe the variability among sub-regions of the urban area, and will
an attempt be made to correlate local concentrations with local
emission data?
3.	Time resolution. Many instruments are capable of near-instantaneous
observations, and a number of observing systems are providing data at
5-minute intervals. With few exceptions, hourly records of
contaminant concentrations provide an adequate description of mean
values and variability in the urban atmosphere. Higher frequency
data reports usually contain significant noise caused by instrument
errors and transient changes in local concentrations. For many
purposes daily average values are adequate, and calibration
difficulties frequently appear when the results of 24-hour
observations are compared to corresponding averages of 24, one-hour
observations.
4.	Projections based upon the data. The required projections maybe
either short-term forecasts for a single-day or a several-day episode, or
long-term planning estimates, based upon expected changes in local
emission sources or rates. When projections are desired, the air quality
observations should be supplemented by surface and vertical profile
meteorological data. The accuracy requirements for all data become
more stringent when longer projections are prepared because small
errors in time tendencies or spatial gradients will be magnified by the
extrapolation process.
5.	Emergency action decisions based upon the data. Some redundancy in
measurements is desirable for the system if the output data is to be
employed as the basis for wide-ranging emergency decisions.
6.	Compatability with data from other regions. Although every reason-
able effort should be made to develop uniform data collection and
reporting programs, the physical variability within each urban area
and the rapid development of observing instruments make complete
standardization difficult.
When the purposes of the sampling network have been resolved, the detailed
requirements for the network can be estimated: How many observing points
are needed; how should they be located relative to one another and to the
local geography; what sampling frequency and accuracy are necessary? The
following sections are intended to provide some empirical information in
response to these questions.
11-3
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1NTERSTATI0N DATA CORRELATION STUDIES
When several observing sites are used to characterize air quality in an urban
area, the variations in the resulting data represent a mixture of instrumental
error, local {or transient) phenomena, and large scale variability in con-
taminant concentrations. The best use of the field data results when
estimates are available concerning the relative magnitudes of the observing
errors, local phenomena, and urban-scale phenomena.
This section describes an approach to such estimates, based upon correlation
studies and averaging techniques applied to the original field data. The
analysis proceeds from the formal definition of the correlation coefficient,
and it assumes that actual correlation statistics, calculated from field data,
represent useful approximations to the "true" statistics which would be
developed from very large data sets.
The illustrative examples cited in this section are drawn from the 1966
Boston Region Air Quality Study, conducted by the Massachusetts Depart-
ment of Public Health. A general description of this study and its results
appears in a state report;3 only the S02 and smoke shade (Coefficient of
haze, Coh) data are cited here.
Ten S02 observing locations were operated during the study period. These
ten sites and ten additonal sites were employed for the collection of smoke
shade data. The Boston region base map in Figure 11-1 indicates the
locations of all 20 sites.
In the case of the S02 data, four-hour air samples were obtained, and the
West-Gaeke method' was employed for all analyses. The monthly average
diurnal variability for the ten-station average SO? data is shown in Figure
11-2 for the months of February, March, September and November. The
observed diurnal pattern has the expected features: maximum concentrations
in the early morning hours, and minima in the late afternoon. For the
"winter" months, both the average concentrations and the average daily
variability are greater. (December and January data samples were unavaiiable
for use in the comparative study.) The November concentrations are prob-
ably higher than normal because of a prolonged stagnation episode between
November 21, and 25, that year. Concentrations in the mid summer months
were all lower than the September data illustrated in the figure, and no
diurnal pattern is evident for these months.
It should be noted that the concentrations observed on individual days
frequently do not follow the pattern of the monthly averages shown in
Figure 11-2. Mesoscale meteorological phenomena, having the time periods
of one day or less, mask the tendency for day-time mixing and nighttime
stability on many days.
11-4
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BOSTON METROPOLITAN AIR POLLUTION CONTROL DISTRICT (PRIOR TO 1969)
Figure 11-1. Boston region base map indicating the ocean
coast and the boundaries of the Boston Air Quality Control
Region prior to 1969.
11-5
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Figure 11-2. Average diurnal variability for the ten-station
Boston region SO2 data, 1966.
The statistical analysis of the S02 and smoke shade data is based upon
calculated correlation coefficients for data series from individual stations,
and groups of stations. The correlation coefficient R, for two data series x,
and Yj, having N members each, is
S[(Xj - 7) (yt ~ y)l
R * Ry'y VzilXi - W2] • 2 [ (y, - V)3]
where the overbar indicates the arithmetic average value for the series. The
summation limits are i = 1 through i = N in each case.
11-6
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For this discussion the symbol V indicates the variance of a series, and C
represents the covariance between two series:
SMx, - x)2]
V*	(y|	(2)
£[(X| - x) 
-------
But if the error contributions are random (i.e. uncorrected with the urban
plus local "real" variability, the Equation (7) reduces to
V* - + + VEX + CU Lx	{8)
A similar result is obtained for the time series represented	by the yt terms:
Vy = Vy + VLy + VEy + Cl, Ly	(9)
The covariance between series X| and y| is
Cx.y = S[(Ui+L^+E^U-I7-Eg) (U,+L^E^U-t7-E^)
N
= Vu + CLx.Ly + CU(Lx + Cl, Ly + CLx,Ey	^Qy
+ ClV.Ex + Cu.Ey + Cue* + CEX Ey
Again, if the error contributions are uncorrelated to the real contributions,
this becomes
C*,y ~ Vu + CLx>Ly + cu,l* + CUpLy	(11)
Now Equations (4), (8), (9) and (11) can be used to write the correlation
coefficient for the Xj and y, series as
(V^+CLX.Ly+Ctj ,Lx+Cu iLy)
Rx,y " (Vu+V1_x+VEx+Cu7x)"2(Vu+VLy+VE"y+CUiLy)TH~"
The remainder of this section is concerned with modifications of the general
form expressed in Equation (12).
Case 1. Data from two sampling instruments operating at same
site.
Two sampling instruments operated side-by-side can be used to estimate the
magnitude of random measuring errors associated with the instruments. In
this case the "urban" and "local" contributions to the measured concen-
trations are equal for each instrument. If the symbol T, represents the true
concentration at the observing site, then Tj = Ui + L(, and Equation (12)
reduces to the simpler, familiar form
Vt
R*.y ~ (VT + VEx)'* 
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If the magnitude of the error variance associated with each instrument is
assumed equal (i.e. Ex = Ey = E), then
R*.y = 
Thus, for two instruments operating at the same location, the correlation
coefficient for the paired data series represents the ratio of the "true"
variance to the total (true plus error) variance.
As an example of this analysis, two tape stain samplers were operated
side-by-side on the roof of a 50-foot-high building at the Harvard School of
Public Health during part of 1968. Coh data obtained from the instruments
operating on identical 2-hour sampling cycles during the months of June
through August are summarized in Table 11-1.
If a value of R = 0.75 is adopted from Table 11-1 as typical for the
sampling period, then the expected ratio of error variance to true variance
for these instruments can be calculated. Equation (14) can be rewritten as
Ve =,] - R.
or
VE = i
T
(15)
based on data of Table 11-1. This significant contribution due to measuring
errors must always be considered, particularly when the data from these
instruments are used to make projections, or to estimate local gradients in
concentrations,
Case 2. Data from two sampling instruments operated at different
sites within urban area.
For separated sampling sites, the general Equation (12) must be adopted as
the appropriate definition of the correlation coefficient for paired data
series. Two limiting cases of Equation (12) may be considered, but they
appear to be less interesting then the general case. In one limit, the "local"
contribution can be assumed to be perfectly correlated to the "urban"
contribution; this case reduces to Equation (14), discussed previously. In the
other limit, the "local" contributions can be assumed to be completely
uncorrected to one another and to the urban scale contribution (i.e.
Cu.l* = CUiLy = CLX,Ly = 0); in this case the "local contribution can
simply be considered as an additional error or "noise" term, and a form similar
to Equation (14) is again appropriate.
119
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An interesting approximation to Equation (12) can be developed from the
assumption that the urban and local scale contributions to the measured data
are uncorrelated (i.e. CU Lx = CUiLy = 0)-	error variances are
also assumed to be equal (VEx = VEy = VE), then
(V0 + CLJ£ Ly!
Rx'y = (Vu+VLx + VE),/a (Vu+V^y + Ve)I/2	16>
For this case the correlation coefficient represents approximately the ratio of
the urban-scale variance plus the covariance of the local contributions to the
total (urban plus local plus error) contributions.
Equation (16) is particularly interesting because the covariance term can be
either positive or negative. An interpretation of this equation is suggested by
the data illustrated in Figure 11-3. Monthly correlation coefficients for three
station-pairs for February through November, 1966 are illustrated in this
figure; the station locations are all indicated in the Boston base map, Figure
11-1. Stations 56 and 65 are central city locations, separated by a distance
of only three miles. The covariance term CLx Ly might thus be expected
to be positive for this pair. Conversely, stations 38 and 87 lie on opposite
sides of the urban area, and on opposite sides of the major SO^ emission
areas. A negative covariance term CLX Ly for the local contributions at
these stations is expected {i.e. when one station is upwind of the ma/or
sources, the other is downwind, and vice versa).
Equation (16) and the data of Figure 11-3 suggest the following interpreta-
tions:
a.	The error variances for the station data series may be approximately
one-half the magnitude of the real (urban scale plus local contributions)
variances.
b.	The urban scale contributions and the local contributions may be
approximately equal in the data series.
c.	For proximate station pairs (such as 56 and 65), and for station pairs with
similar orientations relative to the local maximum emission regions (such as
56 and 85), the covariance between the station data series is expected to be
positive. Calculated correlation coefficients for the data observed in condi-
tions a, b, and c would be in the range of 0.25 to 0.5. Such results are
obtained for most of the ten monthly calculations for both of these station
pairs, is illustrated in Figure 1V3,
d.	For station pairs on opposite sides of the major emission regions (such as
38 and 87), the covariance term CLx uy in Equation <16) is expected to
be negative. This would result in near-zero values for Rx y, because the
urban contribution variance term, VU( is always positive. Figure 11-3 con-
tains nine calculated monthly correlation coefficients for this pair of
11-10
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S02 STATION CROSS CORRELATION, MONTHLY DATA SERIES 1966
0.7
0.6
0.5
jjj
C 0-3
u.
g 0.2
o
| 0.1
3 o-o
UJ
{g -0.1
o
° -0.2
¦0.3
"°*4J F M A M i JASON
MONTH
STATION ANNUAL
CODE CODES AVERAGES
		56 + 65	Q.343
	 56 + 85	0.312
	 38 + 87	0.016
Figure 11-3. SO2 station correlation coefficients calculated
for monthly data series.
stations, arid the results are all small compared to the other station pairs.
The average of the nine available monthly values is very nearly zero.
It should be stressed that the illustration described here is only suggestive.
Many more data samples must be investigated to validate this statistical
determination of the scale of urban pollution phenomena.
Case 3. Use of averaged data to reduce error variance.
Because of the error contribution to the data record from a single observing
site, average values are frequently generated for use in model verification and
11-11
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projection applications, The averaging process can be carried out either along
the time dimension, grouping data from e single source, or spatially,
grouping data from separate observing sites operating simultaneously. In
either case the averaging process always reduces the error variance contribu-
tion to the calculated correlation coefficient for paired data series. The real
variance is also reduced by the averaging process.
An example of simple time averaging is provided by the tape stain data
collected from the two samplers operating together at the Harvard School of
Public Health. When the two-hourly data values are grouped into daily
averages, the correlation coefficients for the three sequential periods
described in Table 11-1 are 0.92, 0.95 and 0.94. The daily average values
from the two samplers contain very little error contribution.
Table 111. TAPE STAIN DATA COLLECTED AT HSPH, 1968
(2-HOUR SAMPLES)
Sampling
period
Average Coh per 10® ft
Number of
data pairs
Correlation
coefficient
Sampler A
Sampler B
6/21 -6/30/68
0.85
0.92
56
0.73
7/1 -7/10/68
0.72
0.68
93
0.73
7/11 - 8/6/68
1.00
7.01
269
0.78
When data from two or more observing sites are averaged, the correlation
coefficient for the averaged data represents an improved measure of urban
and local scale contributions, because of the reduction in random errors. The
reduction in variance for an averaged set of data can be illustrated as
follows, If Xj is defined as an average of two or more data series, then
1 M
Xi =	XU
1 M
= M ^,(U,+ L>>> + ^	(17>
where M is the number of stations entering into the averaging process. The
upper and lower limits for the variance Vx of the averaged data can be
calculated: If the local contributions L*tj are perfectly correlated to one
another, the upper t/m/t value is
VK = yU + VL* + CU.L* + M Ve*	<18>
If the local contributions are uncorrected, the lower limit value is
Vx - Vu + "fjj" IVt.* + Cu,lx + vex]	<19)
11-12
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In practice the actual variance calculated for a set of averaged data lies
between these two limits.
The variances enter the denominator of Equation (12) describing the con-
stitution of the correlation coefficient, and the limiting cases described above
suggest:
1.	When averages are calculated from stations that are relatively close
together, (a) the local contributions will be more highly correlated, (b)
relatively large values of Vx will result, and (c> the correlation
coefficient Rx.y wift be relatively small.
2.	When averages are calculated from stations widely separated from one
another, (a| the local contributions will be less correlated, (b) smaller
values of Vx will result, and (c) the value of Rx.y will be greater.
This pattern is illustrated in Table 11-2. The greatest correlation coefficient
results when the middle and outer suburban stations are averaged. These
stations are widely separated, and each is subjected to a variety of local scale
contributions that do not affect the others. The inner city stations are more
closely grouped, and the local scale contribution to these data is not filtered
effectively by the averaging process.
Table 11-2. CALCULATED CORRELATION COEFFICIENTS FOR GROUPS OF
TAPE STATION DATA, BOSTON, NOVEMBER 1 - 10,1866

Number of

Station Grouping
data pairs
ft
Station 45 vs station 47 		
120
0.11
Station 54 vs inner city average 	
120
0.39
Inner-citya average vs middle-suburban*5 average 	
120
0.65
Middle-suburban average yj outer-suburbanc average 	
120
0.82
alnner-city stations: 45, 47, 55, 56, 65, 66
^Middle suburban stations: 26, 29, 34, 38, 48, 74, 85,87
cOuter suburban stations: 9,13, 51,92, 99
Note that even for large groups of stations drawn from throughout the urban
region (the middle and outer suburban data), the correlation coefficient is
approximately 0.8. This value might be taken as an expected upper limit for
correlations between field data and air quality model data, even when the
field measurements and the model projections have been averaged to provide
urban scale comparisons. For point-by-point comparisons of model
projections and field data, significantly lower correlations must be expected.
11-13
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CORRELATIONS BETWEEN AIR QUALITY DATA AND
METEOROLOGICAL DATA
The time scale of several meteorological phenomena that influence urban air
quality is less than 1 day (e.g. diurnal changes in stability, front passage,
changes in "mean" wind direction, sea and lake breezes). The relationship
between meteorological parameters and air quality indices must therefore be
examined on a short-time period basis (e.g. 1-, 2-, 3-hour increments). This
time period limitation often prevents the use of time averaging as a device to
reduce the influence of errors in the data analysis. Spatial averaging, employ-
ing data from many stations, is , however, helpful in the examination of
meteorological effects upon air quality.
Up to the present time the meteorological information available for most
urban areas has been gathered at one primary observing site in each area. As
a result, the most appropriate air quality index is often an urban-wide
average value. Figure 11-4 illustrates the calculated correlations between
observed S02 concentrations and wind speeds observed at Logan Airport,
Boston during the 1966 study period. (Note that the ordinate scale in the
figure is reversed. The calculated monthly correlation between wind speed
and S02 concentration was always negative.) As expected, the ten-station
average data relate best with the wind data. For the three individual stations
illustrated, the correlation is lowest in the case of the coastal station number
48. Stations 56 and 65 are in urban-center locations.
In view of the error analysis developed in the preceeding section, it is likely
that the correlation between a single meteorological parameter and an index
of urban air quality may always be less than 0.5. This suggestion results
from three considerations:
1.	A single meteorological parameter (wind speed, stability, mixing depth)
only partially describes the dilution capacity of the urban atmosphere.
2.	The errors and the local influences reflected in the air quality observa-
tions are never completely filtered out of the data.
3.	The representativeness of the meterological data is unknown in most
cases. Usually a single observation, taken near the edge of the urban
area, serves to characterize the meteorology of the entire area.
Several other air quality-meteorology studies by the authors, similar to the
analysis summarized in Figure 11-4, have each resulted in correlation
coefficients less than 0.4 for all data periods. Multiple parameter
meteorological indices might result in larger correlations because of the
better description they provide of the local ventilation capacity of the
atmosphere. However, such indices were not considered in the present study.
11-14
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S02 VERSUS WIND SPEED CORRELATION, 1966
-0.7
¦0.6
¦0.5
*0.4
¦0.3
•0.2
¦0.1
0.0
+0.1
+0.2
+0.3
+0.4
T
10 STATION AVG. -0.317
	STATION 56
—0.200
J
M
M J
MONTH
Figure 11-4. SOg concentration versus wind speed correlation
coefficients calculated for monthly data series.
THE USE OF COMPUTER GENERATED GRAPHIC ANALYSES
FOR AIR QUALITY DATA
Spatial variability in air quality observations is most effectively displayed on
a geographic base map. This form of data presentation is desirable because
the observations can be related directly to emission patterns, to human
population, and to land-use distributions.
When the field data are stored in a computer-readable format (e.g., magnetic
tape, punched cards, disks) the use of computer generated graphical displays
of the data fields is particularly appropriate, with the advantages that:
—Maps can be produced rapidly and at minimum cost.
—The maps permit easy pattern recognition. Relationships between land use,
emissions and air quality are quickly evident, and suspicious data points are
often identified by the contour patterns.
11-15
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-The interpolation scheme for evaluation of variables away from the obser-
ving locations is objective and repeatable.
The Laboratory for Computer Graphics and Spatial Analysis, of the Harvard
Graduate School of Design, has adopted its SYMAP and SYMVU programs
for presentation of air quality data, and examples of these mapping tech-
niques are illustrated in Figures 11-5 and 11-6. In the two-dimensional-plan
view maps, illustrated in Figure 11-5, shading is proportional to concen-
tration. The left map is based upon an inadequate input data network, and
the widespread high concentration regions are unrealistic. The right map was
produced with the adoption of additional "background" data points, away
from the important emission regions.
The three-dimensional view shown in Figure 11-6 represents an air quality
(total suspended particulates) surface for Southern New England. The pro-
gram that produces this display can produce a similar display of the same
data for all possible lines of sight (i.e. all possible azimuth and elevation
angles) toward the surface.
These maps are illustrated here to underline the importance of pattern
display in the analysis of air quality field data. The mapping techniques are
important adjuncts to the statistical data treatments; both approaches are
useful for the analysis of urban scale concentration patterns.
RECOMMENDATIONS FOR THE ESTABLISHMENT AND
ANALYSIS OF MULTIPLE STATION AIR SAMPLING
NETWORKS
The data studies reported in this paper are limited, but they do offer a basis
for several recommendations concerning sampling networks:
1.	The intended purposes for the network data should be carefully
developed before establishment of expansion of an air sampling
network,
2.	At least one redundant set of sampling equipment should be employed
to evaluate the error contributions to the field data series which are
obtained. The extra sets of sampling equipment might be installed in a
mobile station and moved to each permanent field site on a scheduled
basis to provide calibration checks upon all field equipment. A mobile
unit could be used also, for special upwind-downwind studies near
major emission areas.
3.	Instead of equidistant spacing of sampling stations throughout an urban
region, arrangements involving two or more stations in neighboring
locations should be considered. Such arrangements may provide more
useful data concerning urban and local scale variability in pollution
concentrations.
11-16
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ARITHMATIC MEAN IS 75.07	STANDARDARD DEVIATION IS
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12.20 32.76
Figure 11-5a. SYMAP plot showing Southern New England
particulate concentrations for 1966. Insufficient network-
11-17
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2. THESE OCCUR IN I LOCATIONS.
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ABOVE
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11.11 11.11 11.11
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FREQUENCY DISTRIBUTION OF DATA POINT VALUES IN EACH LEVEL
Figure 11~5b, SYMAP plot showing Southern New England
particulate concentrations. Additional stations.
11-18
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S. NEW ENGLAND AIR QUALITY-PARTICULATES
AZIMUTH-330
WIDTH = 8.00
ALTITUDE =45
HEIGHT =2.00
Figure 11-6. Three-dimensional perspective view of the
Southern New England particulate surface for 1966.
-------
The following recommendations are concerned with data analysis techniques
for sampling networks.
4.	The best measure of urban scale concentrations is an average of
simultaneous data from stations throughout the region. This technique
minimizes both error variance and variance due to local sources. Cor-
relation analysis involving single-location field-observation series and
model projections (or meteorological parameters) will probably result
in maximum correlation values of approximately 0.5.
5.	When a large number of sampling stations are available, it is helpful to
calculate two urban-wide averages, from non-overlapping sets of
stations. The correlation coefficient for the two averages represents the
upper limit correlation expected from any comparative study involving
the field data. Examples of possible comparative studies include:
a.	Comparing time variability in the concentrations of two different
pollutants,
b.	Relating pollutant concentrations to meteorological parameters,
c.	Comparing model calculations with actual field data.
6.	When daily or longer-period data values are required, time averages of
shorter term observations will usually be more reliable than single, long-
period observations.
7.	Computer-generated graphic displays of air quality fields should be
employed as data analysis tools whenever practical. The repeatability
of the computer-controlled interpolation scheme is essential for con-
sistent interpretation of data. (As a corollary, it should be mentioned
that improved interpolation schemes, based upon emission data and
diffusion modeling, should be developed.)
The final recommendation represents a restatement of the theme for this
paper:
8.	All air quality observations include significant variability due to obser-
ving error and to the influence of sources near the observing site. All
data analyses, projections, and model comparisons should include an
evaluation of the error and local source contributions to the variability
in the measured data. Performance indices ("skill scores") for models
and projections must be judged relative to upper-limit correlation
figures developed from the field data.
11-20
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REFERENCES
1.	Selected Methods for the Measurement of Air Pollutants. Division of Air Pollution.
Cincinnati, Ohio. PHS Publication Number 999-AP-11. 1965,
2.	Goodrich, J. C. Regional Planning and Air Pollution Analysis and Control:
Methodology and Case Studies. Harvard University, Cambridge, Mass. MS. Thesis.
1969.
3.	Investigation and Study of Air Quality in the Metropolitan {Boston) Air Pollution
Controf District. Massachusetts Dept. of Public Health. 1968,
ACKNOWLEDGMENT
Mr. Maddaus carried out most of the Boston region correlation calculations,
and the data maps are drawn from a recent Harvard Masters Thesis by Mr.
Goodrich.2 Other calculations and evaluations have been provided by Mr. B.
A. Egan and Mr. E. I. White of the Harvard School of Public Health. The
Massachusetts Department of Public Health provided all of the Boston
Region data discussed in the paper.3
The preparation of this report was supported in part by the National Air
Pollution Control Administration, Consumer Protection and Environmental
Health Service, Public Health Service, U.S. Department of Health, Education,
and Welfare, under Grant Number 1 RQ1 APO1013-01.
11-21
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APPENDIX - GLOSSARY OF SYMBOLS
C	covariance between two series
E*	error contribution to X|
i	iteration integer
L*	constant contribution to X| from measuring site locality
M	number of measuring stations entering into an averaging process
N	number of members
R	correlation coefficient
U,	constant contribution to X, from urban area
V	variance of a series
Xj	measured pollutant concentration at i
Yi	point in measured time series
11-22
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AUTHOR
MORRIS NEtBURGER, a professor of Meteorology at the University of California
at Los Angeles has been a consultant for the Los Angeles County Air Pollution
Control Department, the State of California Department of Water Resources, and
the Public Health Service Community Air Pollution Program. He has been President
of the American Meteorological Society, the Society of Sigma Xi and the American
Geophysical Union. Atmospheric radiation and dynamics, cloud physics, and air
pollution have been his primary fields of research.
-------
Banquet Speech
12. PROGRESS + PROFITS + POPULATION
= POLLUTION
MORRIS NEIBERGER
University of California, Los Angeles
Thank you very much. Dr. Stern. Or perhaps I shouldn't thank you, for I
don't know why I let myself get into this situation. As I told the audience
the only other time I got roped into giving a banquet speech, "It reminds
me of Sam Goldwyn's comment, that anybody who pays good money to see
a psychiatrist ought to have his head examined." Anyone who voluntarily
undertakes to give an after-dinner talk at a technical conference certainly
renders his sanity suspect. For, on the one hand, since ladies are present he
has to be strictly non-technical, since being technical when ladies are present
is even worse than being obsecene, About the technical aspects—I might
mention that Francois Frenkiel saw me looking at a manuscript with
equations today and said in a voice filled with horror, "You're not going to
include equations in your talk tonight." When I replied "It will be only
equations; I'm not going to include any words, just symbols in equations,"
Irv Singer said, 'That's ah right, as long as you limit yourself to equations
my wife can understand." And when I asked what kind of equations his wife
understands, he said, "None." So, technical talk is out!
On the other hand, the men in the audience will be bored and feel cheated
if all they get for the price of the dinner ticket is some good food and a few
jokes and platitudinous remarks. They feel that at least they should come
away with some profound new ideas, stimulating insights that inspire them
to attack the subject of the conference with increased energy, and predic-
tions of the future of America and humanity that give them hope that their
efforts will not be in vain.
On top of this, as I said in my previous dinner speech, the talk should be
neither so humorous that the laughter is loud enough to awaken those who
are using the time for an after-dinner snooze, nor so serious that it arouses
thoughts that interfere with the digestive process.
12-1
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Obviously to succeed in this talk is impossible, so you may well ask: snce I
am aware' of its impossibility, why did I undertake it? There is a simple
answer The only condition under which Arthur Stern would invite ™ to
,he conference was if I agreed to be an after-dinner speaker.
So I Dromise that I will be only slightly technical, and not at all obscene,
although it is with some reluctance that I forgo the latter. Knowing that one
should always start an after-dinner speech with a little ,oke. I asked Dr. Claren-
bura who claims to know hundreds of them (though he says they are funny
only in Dutch), and he recited a limerick that was very apropos of my
subject as he will see when I give the title of my talk. I would like very
much to tell you this limerick; unfortunately, there are ladies present.
Besides, I have already forgotten it.
About the new ideas, stimulating insights, and hopeful predictions I'm afraid
that John Middleton, in his keynote speech for the conference, anticipated
all the ideas I had intended to present, so I'll have to be satisfied to say
things you already know, hoping that I can do so in ways that may possibly
be fresh to some of you.
While considering the title I should give to my talk, I was very impressed by
the slogan Walter Or Roberts enunciated a few weeks ago, namely, "After
the Moon, the Earth," and thought of stealing it as my topic. I certainly
concur with the view that now that we have achieved the goal of reaching
the moon we should divert a few billions from the space budget to augment
the few millions now budgeted to study and protect our earthly enviroment.
I have advocated making our federal expenditures more balanced in this
regard for a long time. I have restrained my kleptomaniac tendency to steal
Robert's subject, however, and following my pledge to Dr. Frenkiel, have
chosen for the title of this presentation the equation:
PROGRESS + PROFITS + POPULATION = POLLUTION
It is just eight years since the conference on Air over Cities was held in
Cincinnati, under the auspices of the Division of Air Pollution of the U.S.
Department of Health, Education, and Welfare, Public Health Service. At the
conference I chaired a session on dispersion and deposition of pollutants
over cities. In my introduction to the session I pointed out the deficiencies
in our knowledge of diffusion from multiple sources and area sources. I had
hoped that the papers being presented at the present conference would be
evidence of progress toward the elimination of these shortcomings. I fear
that such evidence is not clear. But whether or not the solution of the
problem has been attained, it is certainly true that the intervening 8 years
have seen a tremendous increase in the concern and attention paid to air
nollution Whereas 8 years ago, air pollution was still regarded as a minor
problem ' serious for only a few unfortunate communities such as Los
12-2
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Angeles; now, it competes with the Vietnam war, the racial question, and
the student protest movement for first place in the attention of the country.
Government bodies at all levels and civic organizations everywhere devote
large amounts of time and effort to combating it. Whereas, at that time, it
was regarded as an isolated problem, today it is recognized as an intrinsic
part of the complicated impact civilization and technology are exerting on
the environment.
In my talk this evening I wish to present some views about the root causes
of the air pollution problem, and the relationship of this problem to some
broader aspects of society. Just as education is frequently characterized as
being founded in the three R's, I suggest that the roots of air pollution and
other insults to the enviroment lie in the three P's: Progress, Profits, and
Population. These three P's represent fetishes, which are heretical to
question, like motherhood or patriotism. Unquestioning acceptance of them,
however, will in the long run, lead to catastrophe.
As a starting point, suggesting why I am concerned with the three P's, I shall
give an example from my home city. In Los Angeles the three P's are closely
correlated: the measure of Progress has been the increase in Population, the
expansion of industry, and above all, the Profits that have accrued to the
real estate developers.
Some 15 years ago I gave a talk to the members of the research committee
of the Los Angeles Chamber of Commerce. I told them that I did not know
whether or not the salubrious climate of Los Angeles would have been able
to destroy itself on its own; but with the energetic assistance of the Chamber
of Commerce it had been achieved. By advertising the wonders of the
Southern California climate and thereby attracting increasing numbers of
people and industries, they transformed the clear blue skies, sparkling sun-
shine, bright green vegetation and the year round invigorating air into a
murky brown smog that obscured the sun, withered the plant life, and
irritated the eyes, noses and respiratory tracts of the people. I recommended
to them that, until effective control measures were found, instead of trying
to attract still more people and industries, they should sharply apply the
brakes to the population growth of' the area, using every means at their
disposal to dissuade people and industries from moving to Los Angeles, and
persuading those who were already there to move away.
Needless to say, such a heretical recommendation did not receive a favorable
response from the Chamber of Commerce. Its promotional activities con-
tinued, for its primary motivation was and is the profits of its members, and
not the protection of its surroundings. Progress prevailed and smog became
more and more wide spread.
I have often been asked why the peak values of contaminant concentrations,
registered in those years, have not been exceeded. To this my half-joking
12-3
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reply has been that you can't get automobiles much closer together than
bumper to bumper. The tremendous increase in number of cars has meant
larger and larger areas of high traffic concentrations, but no increase in peak
concentrations of contaminants because the total emission in any given area
has not increased.
Of course, that is only part of the story. The other part is that we have not
yet had more severe meteorological conditions than those experienced in
1954 and 1955. One of these months, perhaps soon, a prolonged period of
very light winds and low inversion will occur, and with it will come
record-breaking levels of contaminant concentration, in spite of the measures
that have been taken so far to reduce emission of pollutants. We can only
hope that it will not be accompanied by a disastrous increase in illness and
mortality, If it is, it will be one more reward for the prevalence of the three
P's.
A great deal of attention has been paid, recently, to defining air quality
standards in various communities and states, as well as nationally. These
standards represent the maximum acceptable levels of concentration of
particular pollutants from the standpoint of health, safety, and well-being. In
some instances aesthetic considerations enter into the definition of standards
with respect to particulates in the atmosphere. But, as all those attending
this conference are aware, these air quality standards remain pious hopes
until they are utilized to set maximum allowable emissions from the various
types of sources. The multiple-source urban diffusion models that are the
subject of this conference, offer, as one of their applications, the possibility
of determining whether, under adverse meteorological conditions, the desired
air quality standards could be met with existing sources of emissions and if
not, how much reduction of emission rates would be required to achieve the
standards. The models could also predict the effects of increased emissions
due to expanding population, additional industrial sources, or the speading
and redistribution of the urban areas. In places where the air quality
standards are already exceeded frequently, the latter computations would
seem almost superfluous.
One principle, which I think, is readily evident, and which I therefore expect
to be confirmed by computation with these models, is the concept that
emission control standards must be expressed on a per-unit-area basis rather
than a per-source basis. This concept is most readily appreciated if one
considers the present practice of expressing the allowable emissions in terms
of the percentage of total concentration of effluent emitted from one source
or the total emission from each individual source. In the former instance, if
the rate of emission of the total effluent is increased, the permitted emission
of pollution is correspondingly increased. In both cases, if in a given
square-mile area the number of sources is multiplied, the total pollution
allowed is correspondingly multiplied. The pollution from one or two
12-4
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sources in an industrial plant emitting maximum allowable concentrations
might not exceed the air quality standards, tf the same plant constructs a
dozen more stacks, each emitting concentrations of contaminants indivi-
dually acceptable, the total effect might well be to produce concentrations
far in excess of the air quality standards. To prevent such excesses, the limit
must be expressed in terms of total emission per unit area, whether the
emission originates from one source or many.
This concept, which is so clear with respect to industrial stacks, applies
likewise to vehicles. It is not adequate to set the emission limit in terms of
individual cars without first estimating the consequences of this limit in
terms of the total emission from all cars expected to be operating in a given
area. As I pointed out before, and as has been experienced by drivers in all
cities, this number of cars has a maximum, which is frequently reached when
all lanes on all streets in the area are completely filled with bumper-to-
bumper traffic.
The area-limit concept also applies to domestic sources, but if the allowable
emissions are expressed on a per-capita basis there is no maximum simitar to
the automobile case, for modern apartment dwellings appear to have no
upper-bound on the density of population which can be concentrated on
small horizontal areas. While the vertical spread of high-rise apartments has
some effect of spreading the emissions upwards also; the net effect of an
increased number of people living in an area, is an increased amount of
waste produced which must be disposed of, inevitably increasing the amount
of pollution that enters the atmosphere.
I recognize that, at present, the limits to allowable emissions are not
expressed on a per-capita basis, however democratic this basis may seem.
Surely there is a sort of poetic justice in the idea that if I must share the
unpleasant consequences of pollution with everyone, I should be permitted
to contribute an equal share to everyone else's discomfort.
Whether or not the emission limits are expressed per-capita, it is self-evident
that the amount of pollution is closely related to population. Each addi-
tional person in a community adds to the requirements for electric power,
domestic heating, transportation, and waste disposal. If the pollution result-
ing is not proportional to the number of people, one may suspect that the
deviation from proportionality is in favor of a more rapid increase in
pollution than in population. Small towns generally have small pollution
problems, and large metropolitan areas have gigantic ones. When regions are
characterized by many metropolises their net pollution seems not merely
additive, but combined in some non-linear fashion.
I shall return to the problem of population on a national and world-wide
basis. Before considering it, however, I should like to expolore the effects of
progress and profit in more detail.
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Progress is often measured by the rise in the standard of living of the average
citizen, but it might also be measured by the increase in power, which is
associated with the rise in standard of living, or by the increase in number of
appliances and machines, which are used to produce the rise in standard of
living. Domestic cooling systems added to central heating, dryers in additon
to washing machines, color TV in addition to radios, hi-fi systems and tape
recorders, multiply the demand for power by a large factor. This increased
demand leads to construction of more and larger electric generating plants,
most of them using fossil fuel and emitting large amounts of contaminants
into the air.
The natural demand for these additional comforts of life is augmented by
intensive advertising campaigns by the manufacturers of the appliances and
by the utility companies that distribute the fuel and electricity. Insofar as
these industries are motivated by the purpose of rendering the lives of the
citizens more comfortable, the labors of the housewives easier, and every-
one's leisure more enjoyable, one would be led to commend them, while
regretting the degree to which they miss their goal by also contributing to
discomfort and illness with the pollution they introduce into the air. In
addition to these high motives, however, or, in some instances, instead of
them, the desire for profits enters strongly. Even when they know that
additonal thermal electric generating plants will augment already objection*
able levels of pollution, utility companies strive to increase the demand for
electricity, using all sorts of promotional gimmicks to get customers to con-
vert to all-electric homes, etc.
Two questions occur to me. One is whether the damage to the environment
and the discomfort to the people, resulting from technological advances,
should not be weighed against the conveniences produced in deciding
whether these technological advances really represent progress. Perhaps on
balance it would be preferable to forgo some of the benefits and be spared
the accompanying disadvantages. The second question is whether, assuming
the validity of asking the first, the decision about expansion of electric
generating plants, for instance, should be based, as it is for the most part
now, on whether expansion will yield a profit to the power companies.
Shouldn't the public's welfare come first?
The automobile industry is perhaps the outstanding instance in which the
desire for profits has dominated the public interest. Regretably, the recent
agreement of the Department of Justice to a consent decree in its conspiracy
suit against the auto makers has prevented the evidence in the case from
becoming available to the public. But the agreement of the manufacturers to
cease and desist, together with the fact that the court ruled that the
evidence be impounded so that it could be available in damage suits, strongly
suggest that they did indeed conspire to prevent and delay the development
of air pollution control devices for motor cars.
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Their motive has been stated clearly by Henry Ford II, in interviews quoted
in Fortune magazine and in newspapers. In these interviews he said that the
industry has too large an investment in equipment to make engine blocks,
transmissions, and other parts of the internal combustion engine, for it to
give a high priority to developing alternative power systems, such as an
electric car. The billions of dollars of machinery owned by the auto industry
act as a millstone, holding the people of our cities submerged in the
pollution exhausted from internal combustion engines.
The same eagerness for profit has, of course, been responsible for the auto
industry's failure to develop and introduce safety features until required to
do so by federal legislation. Similarly, the profit motive has been responsible
for the industry's disregard for such factors as the ease and costs of repairs
and the protection of the car itself from damage in minor collisions.
The auto industry appears to judge its progress by the size of engine it can
foist upon the public—500 cubic inches, this year. With the allowable
emissions presently measured per unit volume of exhaust, it is clear that the
increased cylinder capacity will represent increased amounts of pollution per
car, which when added to the increased numbers of cars will offset the
control measures. Pollution control considerations obviously did not enter
the decision to put these mammoths on the market and feature them in the
promotional advertising.
The internal combustion engine is, by its nature, an incomplete combusion
engine. The automobile industry's answer to the requirements to reduce the
products of that incomplete combusion, namely hydrocarbons and carbon
monoxide, has been to promote further combustion in the exhaust system,
where it produces no useful power. It has ignored the fact that, in that
process, increased amounts of oxides of nitrogen are emitted.
It seems to me that the solution to the problem is to abandon the intrin-
sically inefficient internal combustion engine, and to develop an essentially
pollution-free propulsion system in its place. It is inconceivable to me that
the technological ingenuity that got man to the moon cannot get him from
his home to work in a city without polluting the air.
The high rate of profit in the industry's operations can readily cover the cost
to industry of developing a smog-free engine. I do not have recent figures at
hand, but the American Institute of Management, in an article appearing in
The Corporate Director, in July of 1956, reported that General Motors' net
earnings, at the 1955 rate of profit, "were sufficient to recoup the com-
pany's entire net plant investment in 2 years." (Quoted by Ralph Nader in
The Progressive, September 1968.)
From the standpoint of the profit motive, it is hard to understand the past
reluctance of the auto industry to add air pollution control equipment to
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the internal combustion engines. The cost of this equipment has been added
to the price of the car and you may be sure that in arriving at the price, it
has been subject to the same profit margin as alt other parts of the car, so
that pollution control has increased the automobile industry's profits.
I have suggested that if the Federal, State, and municipal governments were
to adopt laws setting a date after which no vehicle injecting any hydrocar-
bons, carbon monoxide, or oxides of nitrogen into the atmosphere might be
sold in their jurisdictions, industry would accept the challenge and develop
new propulsion systems to meet that requirement. In the California State
Legislature, last year, such a bill was passed by the State Senate but was
killed in a committee of the Assembly. When it came before the Senate, the
lobbyists for industry apparently did not think anyone would take it seri-
ously but once it passed in that body, the lobbyists exerted great pressure to
prevent its consideration in the Assembly. Senator Petris plans to introduce
it again at the next session, but with industry alerted I have no hope of its
passage, even though the general public is more concerned about pollution
than ever before.
That it is necessary to develop completely smog-free vehicles is clear, since,
otherwise, whatever degree of reduction of emission is achieved, the increase
in number of vehicles will rapidly make up for it and the levels of pollution
of the atmosphere will continue to rise. Similarly, unless the emissions from
power plants are completely eliminated, the rising demand for electric power
due to population growth and increased per-capita use will offset individual
emission limits, and the deterioration of the atmosphere will continue. The
same applies, of course, to other industrial sources and to domestic sources.
This situation is true on a local and statewide basis and, also, on a national
and world-wide basis. The problems of urban areas in the more "advanced"
countries are particularly acute because of the concentrations of population
there. But the entire world is undergoing a population explosion, and in the
developing countries there is also a power or energy explosion, which will
increase as the people of Asia, Africa, and South America strive to attain the
same levels of comfort, convenience, and mobility as Americans and Euro-
peans have. Multiplying the world-wide population explosion by the prospec-
tive demands for power yields a potential for air pollution that staggers the
imagination. It dramatizes the urgency for the development of completely
pollution-free sources of energy and methods of transportation, and the need
for contol of population.
I have previously pointed out that, even now, we do not know whether, on
a world-wide basis, toxic contaminants are being put into the air faster than
the natural cleansing processes of the atmosphere remove them. We know
that pollution does not stay in the air; it is removed eventually. One way it
is removed, for instance, is by getting into our eyes and respiratory systems
12-8
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and irritating them, It is also incorporated into the clouds and falls out in
the form of rain, and it interacts with vegetation, and corrodes building
materials. The question is whether the processes of removal are able to keep
up with the rate of emission. We do know of one pollutant, though not a
toxic one, of which there is an accumulation in the atmosphere. Carbon dioxide
has been sampled long enough, and with enough accuracy, to show that the
total amount is increasing steadily year by year. If the same thing is
happening to toxic pollutants, such as carbon monoxide or nitrogen dioxide,
eventually, the entire atmosphere will become so toxic that it will be
necessary for people to go around in gas masks to survive. Alternatively, one
can visualize people living in air conditioned vehicles, dealing with a compli-
cated docking procedure similar to space vehicles, in going from building to
automobile and vice versa. People could never venture out of doors, where
they might be subject to "toxic fresh air."
Regardless of whether or not we are now putting toxic pollutants into the
air faster than they are being removed; if the number of sources, stationary
and vehicular, increases with the population and power explosion, that
situation certainly will be reached, unless sufficently stringent controls on
emissions per-source are put into effect, and unless the world population is
stabilized.
There are, of course, other urgent reasons for being concerned about world
population. To these is added the danger that the entire atmosphere wilt
become too toxic to breathe because of the sheer number of people adding
pollution to the air.
What is the solution? I believe that to find it, it is essential that we make
some fundamental changes in social attitudes.
tn the short run, of course, the present attempts to control sources of
emission must be strengthened. More and more stringent standards of emis-
sion from stationary sources and from vehicles must be adopted. Rather than
limiting the requirements by what is technically feasible, requirements should
be set at levels that challenge technology to meet them.
In the longer run we must revise our attitudes about Progress, Profits, and
Population. The concept of Progress must be amended to measure it in terms
of the true amenities of life, including the enjoyment of clean air. The
motivation of industry and commerce to maximize their profits must be
restrained by the requirements of the safety and welfare of the people.
Above all, we must take measures to limit population increase, and ulti-
mately, to stabilize the population of the world.
I am not at all hopeful that we will be successful in any of these tasks. The
concept that "bigger is better" is so ingrained in American attitudes that any
move toward smaller automobiles, fewer appliances, and less people per
12-9
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square-mile will be regarded as retrogress rather than progress. Unless we find
some way of having larger profits accrue to industry for building smaller
cars, producing less electricity, and, in general, contributing less to pollution;
industry and commerce will continue to enlarge their production of energy,
commodities, and smog. As for the control of population, since it depends
on the slow process of education about contraceptive methods and on
producing motivation for their use, the prospects are remote indeed.
The prospects will remain remote until the nature of the problem is recog-
nized. As I said at the beginning, I am encouraged by the increase in public
awareness and concern in the past few years. If this increased concern can be
focused on the roots of the problem, as typified by the three P's, there is a
chance that new attitudes will develop, and solutions will be found.
12-10
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author
ARTHUR C, STERN, a mechanical engineer, is Professor of Air Hygiene at the
University of North Carolina at Chapel Hill. He is the current President and
Chairman of the Board of the Triangle Universities Consortium on Air Pollution,
which involves Duke and North Carolina State Universities and the University of
North Carolina at Chapel Hill. From 1935 to 1968 he was associated with tfie
Federal Air Pollution Control Program, first in Cincinnati, Ohio, as the chief of
its Research and Development Program; later, in Washington D.C., as the Assis-
tant Director of NAPCA. He is perhaps best known as editor of the three-volume
work, Air Pollution.
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Symposium Summary
13. UTILIZATION OF AIR POLLUTION MODELS
ARTHUR C. STERN
University of North Carolina at ChapeI Hill
It would serve you poorly to have me now recite a series of abstracts of the
papers you have already read and heard, and of the discussion you have
heard and will be able to read in final form in the Proceedings of this
symposium. Rather, I can serve you best by assessing the impact of our
deliberations.
If any one statement could characterize this symposium, it is that this was
the one in which a "Gaussian" distribution was qualified by, "if that is not a
dirty word." Those who had incorporated in their models, diffusional pro-
cedures developed to a state of increasing sophistication over the past 5
years were here on the defensive against those who, looking ahead, foresee
newer procedures displacing them over the next 5 years.
This was the symposium at which people were first able to say to each
other, "You have an elegant model, but is it the one we need? Does it meet
our objectives for a model?" Yet statements of such objectives were alluded
to only peripherally by the speakers and discussers.
NEEDS AND OBJECTIVES IN MODELING
Perhaps, the reason a statement of our needs and objectives in modeling did
not come through loud and clear is that there is a complete spectrum of
needs and objectives and that no single approach can satisfy all these needs,
equally. We have heard of dimensional scales, ranging from the global scale,
noted by our banquet speaker, to that of the single city block, discussed by
several of you. Let us digress to look at the characteristics of these scales.
13-1
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They have a unifying feature in that, as the horizontal scale is changed, there
are corresponding changes in the vertical and temporal scales (Table 13-1).
Table 13-1. SCALES OF AIR POLLUTION SYSTEMS
System
Vertical scale
Temporal scale
Global
Atmosphere
decades
National
Stratosphere
years
State
T roposphere
months
Regional
Lowest mile
davs
City block
Heights of buildings
hours
The time scale in Table 13-1 can be interpreted to mean either the time for
effects to manifest themselves or the time inherent in taking effective,
corrective action.
Purposes Served by Models
Beclouding a statement of objectives is the fact that models serve two quite
diverse purposes. On one hand, models serve to test our understanding of
the physical nature of the atmosphere and the sources we are modeling. If
we can't model it, we don't understand it. A decade ago, we tended to say
that we understood these phenomena, but lacked the programming, com-
putational, and statistical capabilities to resolve the problem. Today, the
tables are turned; we have programming, computational, and statistical capa-
bility far beyond our needs, but lack the physical inputs and concepts to
fully exploit these capabilities. A model, thus serves to test these concepts
and inputs. In this application models need to resolve fine detail and to have
fine structure, otherwise they cannot test concepts and inputs.
On the other hand, models are used as an aid to decision making in air
pollution control, and city and regional planning, fn this application we
could not care less about fine structure and fine detail. In fact, fine structure
may obscure rather than elucidate, and we may have to seek ways to
surpress the structure in the output in order to make it effectively useable
for the decision-maker. It is small wonder that people talking about these
two aspects of model making may have some problems communicating with
one another.
Tactical and Strategic Models
Another thing that did not come through loud and clear in this Symposium
was the differing tactical and strategic roles {Figure 13-1) that models are
called upon to perform. Only by clearly delineating these differing roles and
13-2
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STRATEGY FOR
AIR POLLUTION CONTROL
SOURCES AND THEIR
CONTROL
POLLUTANTS
AND THEIR EFFECTS
TACTICS FOR
EPISODE CONTROL
AIR
QUALITY
STANDARDS
SOCIAL
POLmCAL
CQNSfOERAHONS
EMISSION
STANDARDS
EMISSION
ALLOCATION
AIR
QUALITY
CRITERIA
SOCIAL
AND
POLITICAL
^CONSIDERATIONS!
SOURCES
CONTROL
METHODS
POLLUTANT
HALF-
LIFE
ALTERNATE
PRODUCTS
AND
PROCESSES
COST
FUNCTIONS
POLLUTANTS
EMITTED
AIR
QUALITY
COST
EFFECTIVE-
NESS
DAMAGE
FUNCTIONS
AIR
POLLUTION
EFFECTS
TRANSPORT
AND
DIFFUSION
ATMOSPHERIC
CHEMISTRY
EPISODE
CONTROL
TACTICS
SOCIAL
AND
POLITICAL
CONSIDERATIONS
AIR
POLLUTION
POTENTIAL
FORECASTS
to
to
Figure 13-1. A model of air pollution system.
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recognizing their differing dimensional and temporal scales, can we plot a
rational path for future diffusion-model development. The tactical model, or
perhaps better stated, the model for the tactics of episode control, is
inherently regional in scale, limited to a vertical scale of the lowest mile and
a temporal scale of hours. In contrast to this, strategic models are best
developed on state or national scales, since economic decisions and trade-offs
inherent in the strategy of air pollution control are statewide, nationwide, or
even (as in the case of fuel oil and gasoline supply) worldwide in their
impact.
If a regional model is primarily tactical, rather than strategic, there are
implications as to its diffusional component to be considered. Here, I would
tike to read into this record a paragraph from a paper I presented in
Australia a few months ago.1
"Some of our regional air quality data systems may eventually prove to be
white elephants, or whatever other expression we use to signify possessions
entailing great expense out of ail proportion to their usefulness to their
owners. Some of these mistakes, which could have been avoided if the data
needs of the jurisdiction had, themselves, been subject to proper systems
analysis, are the result of a widespread misconception of the role of an air
quality monitoring network during an alert. In the United States, there is a
nationwide system for forecasting periods of high-meteorological-air-pollu-
tion potential, before they occur. The greater the extent and duration of the
stagnation that is forecast, the more likely the readings at scattered air
sampling stations in the area, the more representative the data from the
central station, and the less the necessity to interrogate a multiplicity of
remote stations. If the central station records the predicted rise in pollution
levels (particularly in hourly-average-time data) and a forward meteorological
forecast for a continuation of the stagnation is made, conditions exist for
taking corrective measures. The existence of short-averaging-time-telemetered
data from a multiplicity of stations would have corroborative value, but
would not be essential to the tactical decision-making process. During other
than extremely high-pollution situations, the data continually pouring out of
complex continuous sampling networks tend mainly to confirm, daily, what
is already known about diurnal and seasonal variation and about the effects
of wind direction and velocity. In most of these systems, more time and
effort are spent in keeping them operative, than in using the data acquired."
I will have more to say, later, about the data needs for strategic decision-
making.
Source- and Receptor-Oriented Models
We have also somehow or another, failed to make a distinction in our
discussion at this Symposium between source-and receptor-oriented models.
We have talked only about source-oriented models, but we all know that
13-4
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much work is under way on the receptor-oriented type. In the same paper
referred to above,1 I offered a rudimentary, statistical, air-quality receptor-
oriented, model and, again, will quote:
"Both Larsen2 and the author have discussed the properties of frequency
distributions of air quality data and of the so-called arrowhead charts (Figure
13-2) that display them. However, until now, these data and charts have not
been put to use to analyze the respective influences of source and weather
on their make-up. If we were able to separate the source factors subject to
human control, from the weather factors beyond such control, we would be
able to synthesize the distributions of air quality data that would result from
the application of specific control strategies. We would also be able to
compare them with air quality objectives, expressed in like format, to
determine which strategy comes closest to effecting a match.
AVERAGING TIME
ucofld	mtnul«	tax	lay	rohUi	ye*
AVERAGING TIME, hows
Figure 13-2. Arrowhead chart (produced by computer) for
concentration vs. averaging time and frequency for nitrogen
oxides in Washington, D. C. - - December 1, 1961 to Decem-
ber 1, 1964 2.
Figure 13-2 might have as its components, figures that look like Figures 13-3
and 13-4, respectively, the weather factors and the source factors. The
analysis of Figure 13-4 for its individual components would be the converse
of the emission inventory approach, in that the latter seeks to arrive at the
same result through synthesis, whereas the approach just outlined seeks to
13-5
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AVERAGING TIME
min hr
51015 3.0 1 ; 4 BIZ 1
day mo
2 4 7 1.4 t 3 3 g 1
L
WIND VELOCITY
WASHINGTON, D.C.
1961-1964
0.0001 oTooi O.'oi 0.1
10 100 I jOOO 10,000
AVERAGING TIME, hr
'RECIPROCA L
2i
. *-*-
1 00 x u°Z W
i"ZnC*
"~^Z zO
>¦ 30 vh
i_ co - x
"Zty V> = <
-10-1
J, >'D —
nxj**
is>^
1 0-2 * Z W Z
¦*a
o5
j
. I 0-3
alternate
FACTORS
FOP CHARTS
Figure 13-3. Weather factors in arrowhead chart.2
AVERAGING TIME
sec
t
8
&
>¦
o
LlI
to-
30-
50.
©. 70
. LU 90
a:
min hr day mo yr
5 101530 t 248 12 I 247 14 12361 3
Mxmiki
MINIMUM
TEMPERATURE
WASHINGTON, D.C.
1961-1964
0.0001 0.001 0.01
0.1 1 10 100
AVERAGING TIME, hr
~ RECIPROCAL
I 0
1,000 10,000
100
Z
o
10-1
• £!
UJ-J
tEP
=>D
h
-
i?<
Oa;a:
O-aw
u»-z
m
siS
ujjc:
u
&
10-3
ALTERNATE
FACTORS
FOR CHARTS
Figure 13-4. Source factors in arrowhead chart 2.
13-6
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arrive at it through analysis. The two approaches should tend to check and
reinforce each other, and thus improve our chances of determining the
relative influence of various source categories across the averaging-time spec-
trum. This should give us useful leads to control strategies."
Averaging-Time Considerations
Having just shown a model that looks at the broad spectrum of averaging
times, I would like to point out something we sometimes lose sight of,
namely, that the adverse effects of air pollution have inherently different
averaging times. The range is as follows:
Averaging
Effect	time
Corrosion 	year
Soiling		 . . month
I lealth 	 day
Visibility	hour
Vegetation damage	minute
Odor			minute
It follows that the ideal strategic model will resolve all these averaging times,
not just one of them. By the very nature of averaging time, once we resolve
a relatively short one, all longer ones become available to us. Strategic
models should, therefore, preferably resolve to averaging times, measurable in
minutes.
In contrast to this, tactical models, being primarily concerned with protec-
tion of the health of a regional population from the effects of stagnation,
need not resolve to such short averaging times.
CONCLUSION
In conclusion, let me repeat what our banquet speaker said last night. We
have come a long way in our ability to model urban air pollution since our
conference in Cincinnati on The Air Over Cities, a decade ago. We then
started developing first-generation transport and diffusion models for first-
generation computers. We are now developing second-generation models for
third-generation computers. The computers have gained a generation on our
use of them for modeling. It behooves us now to develop third-generation
models to take full advantage of the generation of computers available to us.
Yet, in doing so, let us heed the warnings we have heard at this symposium".
"It gains us naught, to apply better programming to inadequate physical
input data and inadequate physical concepts."
13-7
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REFERENCES
1.	Larsen, R. I. A New Mathematical Model of Air Pollutant Concentra-
tion, Averaging Time, and Frequency. J. Air Pollution Control Assoc.
19.24-30, January 1969.
2.	Stern, A. C. The Systems Approach to Air Pollution Control. In:
Proceedings of the Clean Air Conference of the Clean Air Society of
Australia and New Zealand, New South Wales Dept. of Public Health,
and New South Wales University, Vol. 2. Sydney, May 1969. p. 2.4.1. —
2.4.22.
13-8
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authors
DARRYL RANDERSON, Ph.D. is a research meteorologist with the National
Oceanic and Atmospheric Administration (NQAAl Air Resources Laboratory in
Las Vegas, Nevada, and is responsible for the development of prediction tech-
niques in forecasting atmospheric pollutant content.
RALPH C. SKLAREW, Ph.D. is a member of the Theoretical Sciences Division
of Systems:. Science, and Software, has engaged in applications of computer
techniques to modeling high altitude chemistry, and transport and chemical inter-
action of air pollutants. He holds a Ph.D. in physics from the University of
California.
LESTER MACHTA, Ph.D. is the Director of the NOAA Air Resources Labora-
tories, holds a Ph.D. in meteorology from the Massachussettes Institute of Tech-
nology. He has also worked for the U.S. Weather Bureau in the areas of radio-
active fallout, atmospheric trajectories, and air pollution.
D. BRUCE TURNER, on assignment from the NOAA Air Resources Labora-
tories, serves as senior meteorologist for the Bureau of Critera and Standards at
NAPCA. As a research meteorologist he was involved in developing dispersion
models for urban areas with NAPCA's Division of Meteorology. He is a graduate
of Carleton College and the University of Michigan.
J. E. CERMACK, Professor-in-Charge of the Fluid Mechanics Program at Colo-
rado State University, is director of the Fluid Dynamics and Diffusion Labora-
tory. He earned a Ph.D. from Cornell in engineering mechanics and was awarded
a NATO postdoctoral fellowship for study at Cambridge in 1962. He has
pioneered the development of special wind tunnels for simulation of the tower
atmosphere and directs a research program on low-level winds and diffusion over
urban areas and complex topographies.
HARRY MOSES, a Meteorology Group Leader at the Argonne National Labora-
tory, holds an M.S. from the University of Chicago, a Diplomate in Meteorology
from the University of Michigan and has been an Instructor at the University of
Chicago, where he was also a member of the Thunderstorm Project, 1945.
L. A. CLARENBURG, Commissioner of Environmental Hygiene of the Rijnmond
Authority in Rotterdam, has been head of the physical division of the chemical
laboratory of the Belguim National Defense Research Council. He received his
Ph.D. in theoretical chemistry in I960 at the University of Utrecht.
BURTON FREEMAN, Vice-President of Systems, Science, and Software, is one
of the founders of that company. He is an authority on large, computer code
application to radiation flow and hydrodynamics. Ha holds a Ph.D. in physics
from Yale.
DONALD H. PACK Deputy Director, NOAA Air Resources Laboratories
received his meteorology training at New York University, University of Chicago,
and the University of Puerto Rico, and has worked in forecasting, turbulence
and air pollution research.
ROBERT £ STEWART, Assistant Professor of Environmental Engineering, Uni-
versity of Florida, is the author of several papers on atmospheric and oceanic
diffusion. He received a Ph.D. from the University of Waterloo in J966.
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14. DISCUSSIONS
INTRODUCTION
The following discussions were submitted in writing to the editor, sub-
sequent to the Symposium. Attendees were given an open invitation to make
comments on the Symposium topic and all of their responses are included in
this chapter. Every author whose work was questioned was given an oppor-
tunity to read the question and to write a rebuttal if he felt one was needed.
The chapter is divided into two sections; the first includes the discussions of
Symposium papers and the second contains brief treatments of some addi-
tional approaches to multiple-source urban diffusion models.
RESPONSES TO INDIVIDUAL PAPERS
Lettau paper
Frank Pasquill
Regarding the effect on horizontal spread of the turning of wind with
height, I would like to refer to a matter that is discussed in more detail in a
paper that will shortly appear in the proceedings of a symposium on Recent
Research in Air Pollution held by the Royal Society in November, 1968.
Evidently, it is necessary to distinguish between the general distortion of a
plume and the ultimate contribution of this distortion to enhanced spread at
a given level. It turns out that there is a substantial time lag between these
two phenomena. Examination of field data for stable conditions, available at
the time of composing the foregoing paper, indicated that the effect on
spread at a given level was unimportant in relation to the spread produced
directly by the horizontal component of turbulence within about 5 km from
an elevated source and about 12 km from a ground source.
14-1
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Pasquill paper
Kenneth L Calder
It may be appropriate to emphasize that, with very few exceptions, alt urban
pollution models developed in the past decade have been derived, with only
minor modifications, from Dr. Pasquill's original broad estimates of spread
made nearly 10 years ago and, frequently, without any serious attempt to
modify his estimates for the effects of increased urban roughness or the
urban heating. It seems very difficult to break with these long-standing
affiliations with the Gaussian plume and ay(x), az(x), In fact, there may be
good reasons for not trying to, particularly since Dr. Pasquill now indicates
how some appropriate modifications in the original estimate might be made
to allow for urban factors. As Dr. G.D. Robinson has recently noted, it is
also much easier to keep track of the conservation of mass in terms of
modified Gaussian-plume (or puff] type models than in terms of theoretical
models derived from the eddy-diffusity concept.
If some pessimism may have been caused among urban pollution modelers
by Marsh and Withers' recent conclusions based on an attempt to model the
S02 concentration distribution in Reading, England, then I think that Dr.
Pasquill has provided the necessary antidote. Recognition of the random
errors inherent in urban pollution models, such as those arising from inac-
curate specification of wind direction, is very important. Dr. PasquUI's plea
for more consideration of the modeling aspects for probability distributions
of pollutant concentration, rather than just the spatial distribution of average
values appears to be very timely.
Darryl Randerson
In the development of the Gaussian plume models one of the fundamental
assumptions is that the diffusion is isotropic, so that the "exchange coeffi-
cients" do not vary spacially or temporally. Consequently, how do we justify
utilizing variable o values in the Gaussian plume models? Also, what
justification is given for varying the atmospheric stability when another basic
assumption of the model is that the atmosphere is neutrally stable?
Author's Reply
In my contribution to the general discussion I have included some general
comments on the principle and practice of the 'Gaussian' assumption in
dispersion models.
However, I must confess to being rather mystified by the emphasis in Mr.
Randerson's question. I have certainly not had the impression that the
assumption was necessarily prohibited either by nan-isotropic turbulence or
by non-neutral density stratification.
14-2
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Sin'ichi Sakuruba
In the analysis of St. Louis dispersion data I think the vertical spread was
overestimated. The tracer material, even if released from near the ground,
tends to be lifted bodily, especially over an urban area. In the St Louis case
the overestimation of vertical spread of concentration is unavoidable, if the
analysis is made assuming a constant height of the tracer-cloud. My inference
is based on the result of dispersion data analysis made in Japan using the
vertical concentration profile data.
Author's Reply
I am not sure whether Dr. Sakuruba's comment is offered primarily as an
explanation of the discrepancy in the predicted and estimated values of
vertical spread in daytime conditions or, generally, as a reason for question-
ing any apparent agreement. Clearly the mechanism to which he refers must
be included in the complex of uncertainty that applies to values of vertical
spread inferred from surface concentration, but there is, as yet, no quantita-
tive indication of the significance of the effect in the cases analysed.
Calder Paper
Ralph C. Sk/arew
Simple models, with universal applications, are much sought. Unfortunately,
the relationship between averaging time and spatial resolution limits practical
simplicity. A model so simple that the required calculations can be carried
out by hand must, of necessity, have only gross, spatial resolution and a
correspondingly long-period time average. In Dr. Gifford's model annual
averages do, in fact, correspond to a spatial resolution consistent with hand
calculational efforts. For abatement strategies and forecasting, where averages
over shorter intervals are needed, finer spatial resolution is required, resulting
in more lengthly computations.
A compromise may have been anticipated in two comments by Mr. Calder.
The form of the transfer function, R, depends upon the path traversed, not
just on the path length. Adopting this requirement and using a field or grid
model would incorporate path dependence and, as a secondary benefit,
eliminate the repetition of calculations necessary for each source-receptor
pair. The second comment concerns the possible benefits to be gained from
a parameter study with a large, complex model. A parameter study with
such a model would indicate simplifications possible for each specific appli-
cation. This, then, might become the third-generation model: a large, com-
plex, grid model whose simplified offspring are uniquely adapted to a class
of applications.
14-3
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Johnson, Ludwig and Moon Paper
Kenneth Calder
Dr. Johnson has indicated that the area-source simulation used in his intra-
urban model cannot be applied for very fine resolution of the concentration
pattern, say on a scale of less than a city block, and that for the latter an
entirely different modeling concept is necessary. This raises an important
general question regarding the ultimate uses of the model and just how much
knowledge of fine structure is really necessary, that is: what are the most
important spatial and temporial scales in regard to damage effect or inhala-
tion risk for the exposed population. Some clarification in terms of a system
analysis will be necessary if there is to be any guarantee that the urban-dif-
fusion modeling efforts are consistent with, and responsive to the characteris-
tics of the overall system model. The sensitivity of the overall model to the
urban diffusion model, when regarded as an input, should determine the
detail and accuracy required for the latter.
Response by W. B. Johnson*
Dr. Calder's remarks are very appropriate, and I fully agree that the temporaf
and spatial scales treated by a diffusion submodel should be compatible with
the objectives of any broader systems model of which it is part. The
fundamental, practical reason why the fine scale must be treated in our
model is that the only carbon monoxide {CO) data available for verification
consist of point measurements near streets and buildings. The most generally
available data are from Continuous Air Monitoring Program (CAMP) stations,
which are located at streetside, usually at intersections, ft is well known that
these data strongly reflect siting effects, so much so that intercomparisons
between cities are essentially meaningless.
We are attempting to design flexibility into our model so that different
versions of it can be used for different purposes. Some specific foreseeable
applications include the following:
1. Interpretation of the significance of existing air quality measurements
(correction for siting effects)
2 Estimation of current urban-wide air quality patterns (augmentation of
existing point measurements)
3.	Selection of optimum control strategies (when used with a suitable sys-
tems model, which includes economic considerations)
4.	Prediction of effects on future air quality of proposed or forecast changes
in source distribution and strength.
The temporal and spatial scales in .the completed model will be selectable to
fit each of these applications.
*1 would like to thank Mr. Wayne Ott of NAPCA and Mr. F. L. Ludwig of Stanford Research
I nstitute for sharing their ideas or> this subject with me.
14-4
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In general, simulation models should probably deal with the temporal and
spatial scales of pollutant concentrations that are most significant in terms of
health and other effects. The provision of such air quality criteria is the
domain of the medical and biological researchers and air quality management
officals. Present knowledge of the time scale factor is presumably reflected
in current air quality standards. However, the scale in space has not been
similarly treated, nor does the definition of air quality include any spatial
dimension. This situation is particularly serious when dealing with predomi-
nately ground-level sources, such as those of CO. Here, the location of a
point measurement of air quality is all-important. The problem could be
eased considerably if air quality were defined and measured in terms of line
or area integrals. At the very least, there should be standards prescribing that
point measurements be made at specific locations relative to local sources
and buildings. This would substantially facilitate model verification, as well
as air quality management.
Roberts, Croke, and Kennedy Paper
Kenneth L. Calder
Although this sophisticated model using superposition of instantaneous Gaus-
sian puffs will hopefully mark the advent of a new generation of multiple-
source pollution models, there may be some justification for the feeling that
the trend has yet to be established. That is to say, an acceptable degree of
agreement between the model predictions and observations may not be the
only criterion. What is frequenty surprising in some applications is the
closeness of the agreement in spite of the inherent inaccuracies of the model
inputs and the extreme nature of the physical idealization involved. It is
almost as though the condition for mass conservation, common to all
models, in itself provided a very strong rather than an extremely weak
constraint on the concentration field. Until it has been shown that such
extreme complication of the present type of model is absolutely necessary in
order to fit the practical observations with the required degree of accuracy,
and that this complication is supported by sound physical principles, a case
could be made for invoking Ockham's razor and continuing to use similar
models.
Author's Response
We agree with Mr. Calder that, while the initial validation of our urban
atmospheric pollution model is encouraging, there is as yet no demonstration
that success is contingent upon the use of the integrated puff transport
kernel. Because it is by nature a transient model, the integrated puff
approach is particularly well-suited to regions characterized by significant
diurnal cycling of windspeed and direction. For example, the work of Start
14-5
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and Markee,* with which we have recently become acquainted, indicates the
importance of a puff model in evaluating dosages from hypothetical radio-
activity releases in such regions. In this sense, Chicago may not be the
optimal city to test the transient aspects of the model although diurnal
variations in mixing-layer depth and periods of varying windspeed and
direction seem to be modeled adequately. As suggested by Mr. Calder, we
are currently investigating the sensitivity of our Chicago results to the choice
of transport kernel.
In reference to "the extreme complication" of the model, it is important to
note that the greatest demands on computer storage do not lie in the
necessity for numerical integration of the dispersion kernel but are tied to
the extensive efforts to establish seasonal and diurnal emission patterns and
then link these refined estimates with houriy weather data and hourly
estimates of mixing-layer depth to form the composite upon which the
integrated puff kernel operates.
Lester Machta
It is my view that uncertainties involved in predicting weather elements six
or so hours in advance raises serious questions about the usefulness of
forecasts of air quality made a similar time in advance. The verification of
low-level winds even in the simple terrain of suburban airports has not been
particularly good; one would imagine that forecasts of wind direction and
speed in a city setting would be even worse. Since the high-air-pollution
episode normally involves a weak windspeed, the problem is even further
complicated. Until it is demonstrated that forecasts of air quality can be
provided six or so hours in advance I would be very loathe to advise air
pollution control officials of such a possibility occuring in the near future.
Hi 1st Paper
Kenneth L. Calder
Dr. Hilst indicates that variations in windspeed were not considered in the
sensitivity analysis since the dilution effect at the source and the time-of-
flight effect in decay of poltutant would tend to cancel one another. This
argument is not clear since we are considering a function of the form u-1
exp | Xxu"1 J . With the trajectory analysis that is involved in the TRC
simulation model, it might be expected that the effects of errors in wind-
speed would be very complicated. If this is so, then I wonder about the
validity of the conclusions regarding the decay parameter for S02 that enters
the model in the combination Xxu*1. I personally would feel that juggling
•Start, G. E., and Markee, E. H. Jr., Relative Dose Factors from Long-Period Point Source
Emissions of Atmospheric Pollutants, AECL—2787, Proc. USAEC Met. Info. Meeting.
Chalk River, Ontario, 1967, pp 59-76.
14-6
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with the half-life of S02 and reducing it from 3 hours to 1 hour in order to
improve the agreement with observation is a rather risky business at this
stage of the game, before a full error analysis has been made for windspeed.
Finally, although Dr. Hilst says that the TRC model has been extensively
reported over the past 2 years, it is my feeling that the available accounts
may not be sufficiently detailed to allow independent application of this
model to other pollution problems. I would like to urge Dr. Hilst to publish,
as soon as possible, a full technical report so that others are able to utilize
this sophisticated model.
D. Bruce Turner
In additon to the eight errors listed by Dr. Hilst, I think there is a ninth,
which might be called grid-size error. This is most noticeable when calcula-
tions made at grid-points are compared with measurements made at non-
grid-point locations. Specific wind directions will cause individual pollution
plumes to affect the measurement station, yet pass between grid-points and
vice versa. This can be overcome by models able to calculate concentrations
for any point. Where this effect was noticed, the model being used made
calculations only at the center point of each grid square. This was because a
technique had been developed to determine the concentration at the center
point of an area-source square resulting from the emissions coming from
within that square, but was riot developed for points other than the center.
Even with a model restricted to making computation at the center of each
grid square this grid-size error can be made less noticeable if measurement
stations used for model validation are also located as close to the center of
grid squares as is practicable.
Sakuraba Paper
Frank Pasquili
The measurements of vertical spread described in Dr. Sakuraba's paper are
obviously of considerable basic value and will no doubt be widely studied.
However, one should be careful not to place a literal interpretation on the
description of the observed vertical spread in terms of the stability categories
that I have specified for use in the absence of more sophisticated data on
diffusive conditions. As I noted in my own paper in this symposium these
categories were specified for airflow, characteristic of a land surface with
small to moderate roughness. On the other hand, it seems likely that Dr.
Sakuraba's results also reflect the influence of sudden and appreciable
changes of roughness on an air stream passing from the sea over a rather
irregular coastline instead of the effect of stability differences alone.
14-7
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Fortak Paper
Kenneth L Calder
Dr. Fortak's discussion again emphasizes the point first raised by Dr. Pasquill
at this meeting, that while a calculated spatial field of short-period average
pollution concentration cannot be expected to agree very cfosely with that
actually observed, the statistics obtained from an ensemble of such calcu-
lated concentration fields may well be in close agreement with reality.
As a small but important detail I was interested to see that Dr. Fortak has
considered the numerical integration errors associated with the choice of grid
size for the area-source specification. His conclusion that an area size of the
order of 50 meters by 50 meters may be required for a satisfactory
representation of a large number of point sources, is noteworthy, since, I
believe, this is much smaller than the size used in some urban models
currently being recommended for operational use.
Sheih, Davidson, and Friend Paper
Kenneth L. Calder
One point I found rather confusing in Drs. Sheih, Davidson, and Friend's
paper was the initial statement that the model was derived from the statisti-
cal theory for turbulent diffusion, although later in the paper they stated
that the model was semi-empirical and not derivable from known physical
concepts. It would seem that the latter is a more true description since all
the adjustable parameters and constants of the model are apparently derived
by fitting observational data for sulfur dioxide in New York City. If this is
so, then agreement between the model predictions and actual observations
may be less impressive than for some other models where the parameter
values are estimated independently.
The considerable effort made in this study to develop an adequate method
for numerically integrating the emissions from a continuous area source is
noteworthy and in strong contrast to the crude procedures used in many
other models.
Mahoney, Maddaus, and Goodrich Paper
Harry Moses
One must bear in mind that the concentrations of a given pollutant such as
S02, at a given station, is a function of several variables. Windspeed is one
of these variables. It is possible in a multivariate system to find that several
of the individual independent variables correlate poorly with the dependent
variable, but when taken together, show a high multiple correlation.
14-8
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tt is also worth pointing out that the windspeed is a difficult variable to
define. For example, at some distances from an elevated source such as a tall
stack, an increase in windspeed is associated with an increase in pollutant
concentration on the ground, because the stack plume rise is reduced during
high winds, With a ground source an increase in windspeed results in lower
concentrations downwind because of increased turbulent mixing. One must
take such relations into account when using windspeed as a variable in a
regression type modef. Thus, it is not surprising to find that the zero order
correlation of pollutant concentration with windspeed or even the reciprocal
of windspeed is unimpressive, even though the windspeed has an ultimately
important influence on the pollutant concentrations.
GENERAL DISCUSSION
Vertical Circulations and Eddy Diffusion Coefficients
James P. Friend
Until a dynamic meteorological model of urban atmospheres can produce
circulations which are physically reasonable, attempts to incorporate circula-
tions having vertical motions into the present dispersion models are equiva-
lent to introducing new parameters to an already highly parameterized
system.
It has been suggested that solving a diffusion equation with eddy diffusion
coefficients (K's) would be more scientifically acceptable than application of
Gaussian plume formulas. It seems to me, with the present state of knowl-
edge, that this is equivalent to trading one set of parameters for another. We
simply have no known physical laws by which values of the K's can be
determined as functions of space, time, and meteorological conditions. There
has been a plea by Dr. PasquiU and others here for more research in
meteorological physics. One can do no better than to second that plea.
Perhaps the resulting knowledge will eliminate the need to apply either of
the two systems mentioned above.
Generalization of Vertical and Crosswind Spread
Frank PasquiU
i am, of course, primarily interested in the meteorological physics required
in the design of systems for the prediction of air pollutant concentrations
and in the need, which seems to be inevitable, for the adoption of some
generalization about the vertical and crosswind spread of material.
Some models appear to generalize about the standard deviation of particle
spread in vertical and horizontal directions, ay and oz, by using practical
14-9
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observations of the distribution of urban air pollutants. Although not unrea-
sonable, it should be emphasised that such a procedure cannot be accepted
automatically as justification for applying the model to flow and terrain
conditions other than those obtaining in the pollutant survey. For the most
useful generalization we must seek independent specifications of oy and oz
in terms of meteorological parameters that can either be measured at the
time in question or estimated from routine meteorological data.
The specification of ov and o2 may be explicit (as from the statistical
theory) or implicit (as from the gradient-transfer theory, and solution of the
so-called classical equation of diffusion}. It seems to be the view of some
participants in this symposium that there is something conceptually superior
in the use of the implicit classical diffusion equation. I find this view
surprising in light of the essentially empirical nature of this approach both in
principle and in application (i.e. no a priori specification of K is available to
us). On the other hand, I have not claimed (as stated in one contribution to
the discussion) that the K-approach is entirely unacceptable. In my own
paper, however, I do argue that the approach is physically plausible and
practically equivalent or superior to other approaches only for the case of
vertical spread from a source that is effectively at ground level.
Finally on this question of the specification of ay and Oz, it may be worth
remembering that, in general, the most accurate specification appears to be
possible for short ranges from continuous sources. On the other hand, the
greatest uncertainty still seems to apply to the spread of an individual
isolated puff.
Regarding the incorporation of estimates of spread in the prediction systems
I have two other comments to offer. The first concerns the term Gaussian,
to which there has been frequent reference in this symposium. It may be
recalled that the Gaussian distribution follows from the classical diffusion
equation only when K is constant and, consequently, the spread is propor-
tional to the square root of the time. This latter relation has not been
generally observed. Furthermore, the empirical support for the Gaussian
shape comes only from ensemble averages of time-mean crosswind distribu-
tions from continuous sources, or of vertical distributions from effectively
elevated sources. It has been noted, however, that the precise magnitude of
crosswind spread seems unlikely to be of prime consequence in the distri-
bution arising from a close network of multiple sources!
On the other hand, there is no real basis for assuming vertical Gaussian
distribution from a ground-level source—instead the theoretical and empirical
indications point to a shape between Gaussian and simple exponential.
Furthermore, there is no reliable guidance available on the distribution in a
puff. From all this it may seem rather irrelevant to attach great significance
to the assumption of Gaussian distribution. The Gaussian shape may be
14-10
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convenient to use, but a 'center-concentrated' plume with a linear fall-off of
concentration from the center may turn out to be just as satisfactory, in
practice, for passive plumes or puffs. (It seems that the distribution in a hot
plume or puff, initially dominated as it must be by the circulation and
entrapment induced by relative motion, may, however, have a distribution
much flatter than Gaussian).
My second comment concerns the suggestion that a 'sequential' puff repre-
sentation of a continuous source may be desirable. While in principle this
may seem preferable, permitting allowance for variable source strength and
widely variable wind direction and diffusive conditions, I find it difficult to
see how the approach can be advantageous in practice, unless it is in fact
possible to specify the trajectory and spread of an individual puff. On the
contrary, all experience points to the fact that the spreads of individual
puffs in the same general atrstream differ widely, and that reasonable
accuracy in specification can be expected only on the basis of an ensemble
average. In this context it does not seem to me to have been made clear how
the envisaged 'puff' predictions are expected to be superior to those that
would follow from considering the effects of continuous releases over arbi-
trary intervals of appreciable length.
Finally, there have been several references to pollutant movement within the
confines of a street, and indeed one of the papers has considered some
aspects thereof. It seems to me that there are two opposite extremes in the
types of estimates that might be attempted. On one hand; as already
in the general discussion, it may be possible to make a useful estimate by
considering, on an individual basis, the effective enclosed volume of air
available to accept the emission from some position in the street. It may be
useful to add to this the refinement of a ventilation coefficient defining the
rate at which this air is changed, so providing a more realistic estimate of the
rate at which the pollutant concentration might build up. At the other
extreme, for a statistical estimate of the effect over a complex of streets, it
might be possible to make progress by developing a two-layer model on the
following basis:
In the lower {street) layer one might reasonably assume that there is no
advection of the air flow and the pollutant but only a vertical exchange with
the upper (above roof) layer. Only in this upper layer can one reasonably
expect the spread to follow the 'laws' previously specified for plumes.
Essentially, the first requirement is to specify the distribution of sources in
the upper layer and in the lower layer. The latter must then be represented
as vertical fluxes at the boundary between the two layers. The concentration
at any position in the lower layer will be determined by the concentration
developed immediately overhead in the upper layer, by the local rate of
(vertical) ventilation of the lower layer and by the local emission rate in the
lower layer.
14-11
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Physical-Scale Model Advantages
J. E. Cermack
A basic deficiency appears in all of the numerical models of urban diffusion
presented in this Symposium—a deficiency of vital importance, particularly
for the "source-based" models. This deficiency is the unrealistic represen-
tation by Gaussian plumes of diffusion from sources located within the
urban complex. In particular, the diffusion of carbon monoxide from street-
level sources is dominated by local geometry of the city and local meteoro-
logical conditions. The only feasible approach to reaching some understand-
ing of this type of diffusion is through the study of physical models—scale
models of typical city complexes placed in flows simulating thermally strati-
fied atmospheres. Models on a scale of 1:200 to 1:1000 such as the 1:400
scale model of diffusion over Denver shown in a motion picture at this
Symposium permit detailed diffusion measurements which can lead to some
general conclusion on diffusion characteristics in city complexes. Utilizing
even a modest amount of knowledge gained in this manner, the design of
new numerical models should lead to gross improvement in their predictive
capability. Physical models can be utilized to great advantage for "receptor-
based" numerical models to help understand the relationship between source
location and receptor response. This can be accomplished for particular
urban settings under specified meteorological conditions.
In conclusion, I wish to emphasize that physical modeling of diffusion can
be of great assistance in the operational aspects of air pollution control. This
will be particularly true if the modeling is accomplished by a team composed
of specialists in fluid dynamics and atmospheric sciences working in a
meteorological wind tunnel of a type for which similarity of atmospheric
flows has been verified.*
Second Generation Models—Finite Difference Approximations
Darryf Randerson
Several of my colleagues have expressed concern about the limitations in the
Gaussian models and, consequently, forsee the advent of "second genera-
tion" prediction models. I would like to suggest that these new models will
not be Gaussian models and will be free of the restraints inherent in such
models. The new generation models will be both descriptive and conceptual
and may represent finite-difference approximations to initial-value problems
that arise in fluid dynamics. Special attention will be given to the calculation
of time-dependent fields so that micrometeorological phenomena can be
simulated in time and space and subsequently utilized to predict the
*Cermak, J. E. and Arya, S. P. S. Problems of Atmospheric Shear Flows and Their Labo-
ratory Simulation. Int. Jl. of Boundary-Layer Meteorology /: 3-23 January 1970.
14-12
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transport of effluvia over non-uniform terrain. Initial input for these new
models will be generated from information and knowledge collected from
past and future studies of urban meteorology. These new models will be
closely related to meteorological parameters, to chemical behavior of effluvia
in air and sunlight, to topographical effects, and to the generation of a
representative source term. Consequently, these models may become quite
complex; however, they should eventually lead to a rather fundamental
model for predicting the transport and diffusion of matter through the
atmosphere.
Tabluation Techniques
Harry Moses
A substantial amount of work has been carried out at the Argonne National
Laboratory on a method called the Tabulation Prediction Scheme. Since it is
relevant to the problem of developing and using multiple-source urban air
pollution models, I should like to describe it briefly and show how it may
be applied.
Description of Prediction Tables
This technique involves the use of a set of tables that show the relation
between air pollutant concentrations and those meteorological variables that
affect concentration levels. Hourly readings are used. The meteorological
variables are arranged in an ordered sequence. For each entry the associated
probability distribution of pollutant concentration is presented as shown in
Table 14-1. For each combination of meteorological variables, sulfur dioxide
-------
Table 14-1. TABULATION PREDICTION TECHNIQUE
Wind dir
degrees
Celling,
feet
Wind sp.
kt
Temp,
dagF
Hour,
CST
Percentile values of SO]{ppm) concentrations
Mean
St dev
-req
Min
25
50
75
90
95
98
99
Max
75 25
95-75
0-140
7000-"**
0-3
70-79
0- 3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0-140
7000-****
0-3
70-79
4-15
0.01
0.01
0.03
0.04
0.06
0.06
0.06
0.06
0.06
0.03
0,02
0.03
0.0183
6
0-140
7000-****
0-3
70-79
16-23
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.0
0.0
0.01
0.0
1
0-140
7000-****
0-3
80- 89
0- 3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0-140
7000-****
0-3
80™ 89
4—15
0.02
0.02
0.02
0.03
0.03
0.03
0.03
0.03
0.03
0.01
0.0
0.02
0.0050
2
0-140
7000-****
0— 3
80-89
16-23
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.0
0.0
0.02
0.0
1
0-140
7000-****
4-7
10- 19
0- 3
0.01
0.01
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.01
0.0
0.02
0,0047
3
0-140
7000-****
4- 7
10- 19
4—15
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0—140
7000-****
4-7
10- 19
16-23
0.08
0.08
0.10
0.12
0.12
0.12
0.12
0.12
0.12
0.04
0.0
0.10
0.0200
2
0-140
7000-****
4-7
20- 29
0- 3
0.02
0,02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.0
0.0
0.02
0.0
1
0-140
7000-****
4-7
20-29
4-15
0.09
0.10
0.15
0.20
0.21
0.21
0.21
0.21
0.21
0.10
0.01
0.15
0.0460
4
0-140
7000-****
4-7
20-29
16-23
0.05
0.05
0.07
0.10
0.27
0.27
0.27
0.27
0.27
0.05
0.17
0,12
0.0864
4
0-140
7000-****
4- 7
30-39
0- 5
0.01
0.01
0.03
0.04
0.05
0.06
0.08
0.08
0.08
0.03
0.02
0.02
0.0175
17
0-140
7000-****
4-7
30-39
4-15
0.01
0.02
0.04
0.09
0.13
0.15
0.28
0.29
0.30
0.07
0.06
0.06
0.0650
24
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The probability distribution of S02 concentrations, based on past history,
is given on the same line in the table as the combination of meteorological
variables. In practice, the assigned letters or numbers are converted to actual
ranges as shown in Table 14-1.
Applications of the Tabulation Prediction Scheme
The Tabulation Prediction Scheme may be used in at least three different
ways:
1.	As an adjunct to a source-oriented model.
2.	As a means for monitoring changes in the source distribution over an
area.
3.	As a receptor-oriented urban air pollution model.
Use with a Source-Oriented Model
Assuming that the sources remain constant for the same hour of the day, the
same season, and the same meteorological conditions, including air tempera-
ture, then the source-oriented model provides a single concentration value
for each point on the calculation grid over an urban complex. The Tabula-
tion Prediction Scheme shows that, historically, for example, during the past
two years, not a single value but a distribution of values has been observed.
The Tabulation Prediction Scheme thus provides a measure of the upper
limit of accuracy obtainable, at least at the monitoring stations, by the
source-oriented model. The source-oriented model may overcalculate in some
parts of a city and undercalculate in others. Similarly, systematic errors may
occur under some meteorological conditions such as different wind direc-
tions. The information provided by the tables of the Tabulation Prediction
Scheme could, thus, serve as a basis for judiciously adjusting the calculations
of the source-oriented models.
Monitoring Changes in the Source Distributions—The tables of the Tabula-
tion Prediction Scheme must be continuously updated if they are to be used
most effectively. One may accomplish this by comparing the distributions,
obtained during a 1- or 2-month period, with the values in the tables.
Appropriate tests for statistical significance may be used for this purpose.
Automatic updating would, of course, be accomplished on a computer.
As a part of the updating program one might apply triangulation techniques
to the data from two monitoring stations, to detect a significant change in
the source strength over a given area. In Figure 14-1, for example, station 1
shows an increase in a L 1, with respect to the base-line between stations 1
and 2. Similarly, station 2 shows an increase in the L 2. Such an analysis
indicates the area where the source inventory should be reexamined. When a
network of monitoring stations is available, the lines from each station,
indicating the direction in which a change in source strength occurred.
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Figure 14-1 Identification of change in source inventory by
triangulation techniques and tabulation prediction scheme.
14-16
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delinate the area to be investigated in order to update the source inventory.
This is yet another way in which this technique may be used with the
source-oriented model.
Use as a Receptor-Oriented Urban Air Pollution Model—In cities with a
network of pollutant monitoring stations, the Tabulation Prediction Scheme
may be used to develop a receptor-oriented model. For example, for a given
set of meteorological conditions, the 50th percentile SO2 value may be
determined from the tables, and lines of equal concentrations (isopleths)
may be drawn. Areas showing values of SO2 concentrations above a critical
predetermined value such as 0.3 ppm would be delineated. Similarly, 75 or
90 percentile charts may be drawn. In this way, the Tabulation Prediction
Scheme would serve as an urban air pollution model that would provide the
basis for action by a municipal air pollution control office to request public
utilities or other large users of coal to switch to gas where dual equipment
existed. The Tabulation Prediction Scheme was used in this manner in a
recent air pollution incident control test in Chicago, Illinois.*
A word of caution concerning the drawing of isopleths over a city where
there are an insufficient number of stations is appropriate. The heterogeneity
of pollutant concentrations over an urban complex coming from large,
widely distributed, discrete sources, must be considered in drawing isopleths.
For optimal use of the Tabulation Prediction Scheme information on the
lack of uniformity or "lumpiness" in the pollutant concentrations should be
obtained. Traverses with mobile air quality measuring equipment would
provide such valuable insight into the spatial distribution of pollutants.
Computerized equipment to provide isopleths of a given variable over an area
are described in the John, Ludwig, and Moon, and Mahoney, Maddaus, and
Goodrich papers. These could be adapted for effective use with the Scheme.
The Tabulation Prediction Scheme cables could be stored in a computer.
Using forecasts of hourly values of the pertinent meteorological variables,
prepared by a human forecaster as input, the computer can provide maps,
either on a cathode ray oscilloscope or on paper, of the 50th, 75th, 90th or
other percentile isopleths of a pollutant, for each hour of the forecast
period.
Although the Tabulation Prediction Scheme is easy to use, a considerable
amount of insight is necessary to develop an effective set of tables. The
selection of appropriate meteorological variables or even the division of each
variable into optimal group intervals requires a substantial amount of calcula-
tion. As an example: the levels of S02 in a residential area are closely
related to temperature; the lower the temperatures, the more coal is burned,
*Croke, Edward J. and Samuel G. Booras, The Design of an Air Pollution Incident Con-
trol Plan, APCA No. 69-99. Presented before the 62nd Annual Meeting of the Air Pollu-
tion Control Administration, June 1969. New York, N. Y.
14-17
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hence, the more S02 is produced. Hence, one is inclined to select tempera-
ture as one of the variables in the tabulations. The "cooling power," which
is a function of temperature and windspeed, must also be considered before
deciding whether this function, or the temperature, should be used.
In spite of the work and skill required to construct an effective set of tables,
their usefulness appears to be worth their cost. Every technique available
should be used to provide the air pollution control official responsible to the
public, with the best possible information to assist him in his decisions. The
combination of the Tabulation Prediction Scheme with the source-oriented
model results in a hybrid model, which appears to hold greater promise than
the purely source-oriented or receptor-oriented models.
Mathematical Refinements
B. E. Freeman
During the Symposium we have heard a comprehensive exposition of the
formulation and application of air pollution models to a number of urban
areas via the plume and puff approximations. While many of the participants
in the Symposium have pointed out shortcomings of these models and others
have called for a more complete treatment of physical phenomena in the
models, there has been no discussion of mathematical techniques to remedy
these dificiencies. Fortunately, considerable experience has been gained with
suitable methods of mathematical approximation which, in my mind, hold
out substantial hope of removing many of the objections to the existing
models. Clearly, it is not possible in these passing remarks to set out in
detail the methods, which have been developed and are now being improved.
Consequently, I shall attempt to summarize, briefly, the general character-
istics of one refined model, its advantages, and its prospects.
Before f turn to the model itself, let me add another objection to those
currently used; they are based on quasi-analytic solutions of linear equations
for the evolutions of pollutant concentration. Now, in fact, many of the
processes governing the fate of pollution are nonlinear; the reactions in-
volving the components of photochemical smog, the micrometeorology of
the urban basin, the modification of the eddy diffusion constants by the
heat island of the city, and many others. These processes can only be taken
into account in a mathematical framework more general than the plume and
puff models.
The tested and successful method employed in many field problems is the
grid or cell model, based on difference approximations to the partial differen-
tial equations governing the phenomena in question. In this approach, space
and time are divided up into cells and the dependent variables are approx*
imated through averages over the cells. If the cells are made to diminish in
14-18
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size in a suitably chosen manner, the solution of the difference equations
will approach that of the differential equations.
The difference-equation grid model is not a new technique. In fact, this
method was applied some 25 years ago by von Neumann to solve the
hydrodynamical problem of the behavior of a nuclear explosive—one of the
first applications of the digital computer. Since that time the difference-
equation method has become much more sophisticated. With advances in the
capacity and reliability of computing machinery and in numerical methods,
it has become possible to attack an increasing number of physical problems
—to mention only a few: astrophysicists model the evolution of the interior
of stars and the characteristics of the radiations from the atmospheres of the
stars; physicists describe nuclear explosion fireballs in the atmosphere and
duplicate the hypervelocity impact of pellets on plates. The technique has
been applied to the description of the natural enviroment, too. Of particular
relevance is the progress, in recent years, on the dynamical modeling of
global weather.
Now let me mention just a few of the characteristics of the model, that can
be developed in modular fashion by adding new physical phenomena as
warranted by our knowledge of them. First, the pollutants themselves are
followed in space and time. The governing equations are the conservation
equations for the several pollutant species necessary to describe urban pollu-
tion. The equations take account of the rate of change of the pollution
concentrations in all of the cells of the urban basin due to (,1) advection of
the pollutant to neighboring cells by the wind field, {2) spread of pollutants
through eddy diffusion, (3) injection of pollutants from the sources of
pollution within the urban area, (4) chemical reactions which may take place
within the cell, and (5) advection of pollutants from outside of the volume
of interest. Each of these processes is modeled by adding an appropriate
numerical term to some or all of the cells of the basin grid. The time history
of pollution in the basin then evolves by time increments that simulate the
actual temporal development. In such a field description of the pollutant
concentrations, there is no difficulty added in accounting for nonlinear
processes over linear ones.
With this model not only is it possible to take chemical reactions into
account, but by supplying the wind field, diffusion coefficients, and sources
in the usual way, the multi-source urban pollution application can also be
solved, as in present models.
In successive modules it will be possible to take account of processes
determining the wind field and the diffusion coefficients themselves. The
meteorological equations, for example, can be solved by difference approx-
imation, to predict the local modification of the wind field and thermal
stratification by topography, diurnal solar heating, and heat sources within
14-19
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the city. The formulation is also compatible with the incorporation of
models for the growth and decay of turbulence in order to evaluate eddy
diffusivity as a field quantity. While it is to be expected that the modeling
of the hydrodynamic equations will be quite expensive in computer time, in
contrast to the nominal computer use required by the pollution grid model;
some economics can be achieved by using implicit methods to increase the
size of the time increment interval.
As in the case of the numerical weather model, we can only conjecture what
the ultimate value of the grid model for air pollution will be. But to me it is
clear that substantial improvements in physical and mathematical verisimi-
tude can be achieved. As mathematical approximations are removed, the
challenge will lie in taking advantage of the growing volume of urban
pollution data to improve our understanding of the underlying physical
processes. Only this way can we hope to make air pollution models quanti-
tatively useful.
Consumer Applications
L. A. Clarenberg
I would like to approach the problem of multiple-source diffusion models
from the consumers' point of view, that is from the standpoint of a person
with some responsibility for the air quality in a region. After listening to the
lectures giver at this symposium I have the feeling that there may be a
discrepancy between the modet builders' aims and the consumers' needs.
The primary responsibility of an air pollution control authority is to see that
standards set for a pollutant are not violated. Air pollution standards specify
concentrations and corresponding percentages of the time these specified
concentrations may be exceeded. This brings forth a need for maps on which
iso-probability lines are drawn, that is lines of equal probability that a
specified concentration has been exceeded, permitting an immediate evalua-
tion of the air quality in a town or a region. The position of iso-probability
lines is affected only by long-term (1-year) changes.
The models we have been discussing, thus far, calculate the joint contribu-
tion of a number of fixed sources to the concentration at a fixed site, e.g. a
sampling station, for a given set of meteorological conditions. On a map the
location of the sampling station with respect to any one source can be
expressed exactly in terms of a downwind distance (x) and a lateral distance
(y). I would like to name this a "space frame," in which all subsequent
calculations are carried out. The result is a map covered with iso-concentr-
ation lines, pertinent to that particular set of conditions. For air quality
control these lines are of little value, since their positions on the map change
as meteorological conditions change. So, one might get the impression that
14-20
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model building has become a game—a word used by Dr. Roberts in this
context—being played for its own sake, however, one that loses track of
practical needs.
Turbulent diffusion is a process proceeding in time. Theories, describing the
diffusion of a puff, are worked out in a "time frame." This means that one
can predict the volume of a puff being transported through the atmosphere
after a lapse of time, t; one cannot predict the exact position of the center
of that puff relative to its origin. One can, however, predict the probability
of finding the center after a time, t, in any one position relative to the
origin.
If multiple-source urban diffusion models could be worked out in a pure
time frame; then the concentration in any one location could be found by
probability, for a given set of meteorological conditions, at the same time
giving accurate prediction. By repeating the calculation for a great number of
meteorological conditions and assigning the probability of occurrence, the
most probable concentration distribution, to each set of conditions. From it
is only a small step to produce iso-probability lines.
I have three reasons for advocating this idea. First, it seems to me that the
input of meteorological data becomes much easier. Second, if ever models
are to be made for pollutants other than sulfur dioxide—for example,
oxidants— in which case one can neither locate nor specify the sources
exactly, one would have to (as far as I can see) rely on "time-frame
models." Last, but not least, results would be in better compliance with
practical needs, especially when estimates of reliability are required for the
predictions.
Uses, Limitations and Accuracy of Models
James /?. Mahoney
A number of detailed, first generation, models for urban air contamination
have been discussed at this meeting. In each case it would be desirable to
have a statement of the specific uses, limitations and accuracy of the model.
Such information would facilitate both applications of existing models and
development of new models.
The following specific observations result from several of the technical
discussions during the Symposium:
— The uses and limitations of the diffusion models can be stated in terms of
the time and space scales appropriate for each model. Many of the early
models have been applied to a wide spectrum of scales, from near-instan-
tanous analysis to annual-average calculations in the time dimension, and
from a few meters to tens of kilometers in the space dimension. Obviously
14-21
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the grid size for input data and for calculations should reflect the scale of
the intended, model output data.
—	The greatest deficiency in the present models is the lack of detailed
meteorological data for the urban regions being described. It is futile to
refine existing emission data and to reduce grid size in most of the model
calculations when the windspeed and direction, atmospheric stability and
mixing-depth data are alt derived from a single observation site within the
region. The new observation networks in some major urban areas have
surface meteorological instruments at several sites; the data from such obser-
vations should be included in the model refinement process, whenever
possible. Significantly improved vertical meteorological observations are also
required for the development of improved models.
—	Current models lack descriptions of chemical and photochemical transfor-
mations involving the various pollutants. Realistic, dynamic chemical models
should be verified with detailed and extensive field observations; the first
examples of such information are just now becoming available.
—	Loss processes, particularly absorption and washout of pollutants, are not
sufficiently understood for incorporation into existing models, but current
field studies may provide some data on loss mechanisms that can be used in
refined diffusion models.
—	Model verification schemes, based upon comparisons with measured air
quality, must be analyzed carefully. Errors and small-scale phenomena, re-
flected in air quality observations at single sites, may be as important as
errors in the model input data. Whenever possible, model results should be
compared to time and/or space averages of observed air quality data.
—	It is possible that data from remote sensing instruments, presented in the
form of average concentrations over extended horizontal paths, may be
superior to data from individual observing sites for use in urban diffusion
models. The use of spatial average concentration data would reduce the
errors caused by locaf sources near the observing stations.
—	Current models neglect the initial field of observed concentrations in the
preparation of short-period (e.g. 1-day) forecasts. Model forecasts may
improve if the changes in concentration from a known initial field are
calculated as the predictive parameters.
—	Many current diffusion models are used to describe regions containing an
urban center and surrounding suburban and rural areas. When the spatial
gradients of the emission rates are large only in one section of the model
region (the central urban area), the use of grid telescoping in that limited
section can improve model accuracy without imposing excessive computation
time and data storage requirements.
—	The expense and the importance of urban air-quality monitoring programs
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in operation, or in development, justify a significant effort toward the
development of sophisticated advection-diffusion models that can make
optimal use of the data being collected.
Approach to a Universal Model
Robert E. Stewart
I am somewhat disappointed by the current method of attack for solving the
problem of urban air pollution prediction. 1 find that, for the most part, one
has to postulate "not so good" assumptions in order to make the particular
urban diffusion model fit the data. For example, the Gaussian distribution is
a special solution to the semi-empirical diffusion equation, provided the
standard deviations of concentration are related to their respective diffusion
coefficients as given by Batchelor.* This implies homogeneous turbulence.
Yet we stimpulate hypothetical, mathematical expressions for the standard
deviations and, perhaps, even for the velocity vector as well. That is to say,
we turn our backs on theory (ever so slightly) to arrive at a not-so-workable
solution. If we can justify this then I suggest that we go all out and assume
that the concentration field at a given time is a function of the important
variables involved (i.e., vertical-temperature and velocity gradients, turbulence
intensities, topographical parameters, stack conditions, pollutant parameters);
and conduct a series of planned experiments, based on similarity theory, to
arrive at a regression equation for urban areas. If we do have to revert to
this type of approach, let us consult with systems analysts and experimental
statisticians to arrive at a universally acceptable model.
In any event, it would be beneficial if a committee or a specialized group
were set up to develop guidelines for future approaches to source-inventory,
receptor-sampling, and urban diffusion modeling based on a review of the
existing state of the art.
User-Oriented Design
D. H. Pack
We have heard of many advances in simulating the emission of pollutants,
their transport and diffusion through the atmosphere, and the resulting
concentrations. Dr. Hilst has advised us to consider carefully the purpose of
any model during its design and not to expect all models to answer al)
questions.
It is profitable, I believe, to consider the use, and the users, of models in an
organized way.
•Batchelor, G.K. Diffusion in a Field, of Homogeneous Turbulence. I. Eulerian Analysis
Aust. J. Sci. Res. 2: 437-450. 1949.
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Suppose, for example, we set up the following table for model application:
Analyses
Prediction
Operations Scales of:
Meteorologists
Control Agencies
Planners
Time
Space
Information
Resources
A third dimension, scale, can be added for each combination of use and
user.
The ultimate urban model could conceivably be used in all combinations but
we must consider the paucity of information on sources and the deteriora-
tion of meteorological predictive skill with time.
It seems that, for some time to come, compromises will be necessary. To
acknowledge them, each model builder should fill in the above boxes (or
variants thereof) with his estimate of what the model will do and for whom
it will work best. In the process, current information input, computer
availability, and staff technical level should be considered among other
criteria.
Such an exercise may well show that many of the models are already very
successful. For unsuccessful models this approach can indicate where re-
search effort must be applied.
General Discussion
Here are some miscellaneous comments that I would like to make:
—	I would agree with Mr. Pack that the various models in use have been
designed for different applications.
—	Each researcher has verified his model in a slightly different manner
making intercomparison of models difficult. Several methods of verification
should be developed that could be used as standards for verification.
An additional problem in verification is that the concentrations calculated
from the model represent something quite different from the concentrations
measured by the sampling stations. In most models small sources are com-
bined and calculations are made from one, uniform, area source for each grid
square. The calculated concentrations are thus, more representative of an
area. But measured concentrations are made at a single sampling point and
are greatly influenced by nearby small sources especially those emitting at a
height nearly level with the sampler intake probe . This difference between
calculated and observed concentrations can be minimized by using the mean
concentration from 3 or 4 sampling stations located hundreds of meters
apart. The derived area-concentration may then be compared with the
D. Bruce Turner
14-24
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calculated concentration. An investigator will seldom expend his sampling
equipment in this way, however, due to the cost of establishing and servicing
stations.
-	It appears to me that there is a "communication gap" between the
researchers developing the models and those wanting to use them. There are
indications that the prospective user is confusing the researchers' goals for
the future uses of models with what can be done today. This may, in part,
be due to the fact that the model verifications are stated in terms difficult
for the laymen to understand readily.
-	The spatial variation of air pollution is extremely complex because of the
great number of air pollution sources in urban areas. Only the gross details
of this variation can be revealed by air quality sampling because cost and
manpower limit the number of samplers that can be applied. It is desirable
to complement air quality monitoring with dispersion modeling to obtain
isopleths of concentration. Since air quality is the product of the micro
enviroment, it is always possible to go to a smaller scale and find many more
details in the concentration field. Therefore, one has to decide on the space
scale suitable for the detail one wants to observe and conduct the emission
inventory, as well as the model computations, commensurate with that scale.
-	The models that have been presented at this symposium haven't con-
sidered photochemistry. There is a need to have dispersion models that can
be applied to reactive pollutants and their products. Since most models
presented here assume that the contribution to the concentration at a
receptor from each source can be determined independent of emissions from
other sources, I doubt if these models will be useful for other than
relatively unreactive substances. It appears that a different approach from
normally distributed puffs or plumes is required to model reactive sub-
stances.
-	A statement was made at this symposium to the effect that computer
technology was available that had not yet been used. I would like to disagree
with that statement because I know of a number of researchers who have
used computers that could be considered in the category with the largest and
fastest computers in this country, yet they have had to devise short cuts to
use these computers to make calculations of air pollutant concentrations at
reasonable cost and in a reasonable length of time. I believe that as advances
in computer technology become available, they will be put to use by
researchers formulating dispersion models.
-	There is certainly room for more simplified models, especially in the area of
community planning, where estimates of air quality for future decades is of
interest. Models whose calculations can be made with desk calculators, for ex-
ample, will find wide application when developed.
14-25
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-	A request was made to tailor dispersion model output to the user;
specifically, to determine how frequently a given pollutant concentration is
exceeded. Dr. Fortak's model for Bremen gives information of this type at
specific points. I can certainly see its utility to control officials and plan-
ners.
-	One item related to the success of dispersion modeling, which has not
been mentioned at this symposium, is the computation of plume rise above
the physical stack. Although several currently used plume rise equations do
rather well when averaged over a number of trials, we still need improvement
in hour-to-hour calculations of plume rise. Since many air pollution control
strategies emphasize the difference between elevated and low-level sources,
there is a critical need for models that can be used with equal reliability on
both low-level and elevated sources. This, of course, gets one into all the
difficulties involved in windspeed and direction, shear, and other measure-
ments pointed out by Dr. Lettau.
14-26
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15. APPENDIX
ATTENDANCE LIST
Dr. Donald D. Adrian
CivU Engineering Department
School of Engineering
University of Massachusetts
Amherst, Massachusetts 01003
Dr. Walter D. Bach, Jr.
Research Triangle Institute
Research Triangle Park, N. C. 27709
Dr. Eugene W. Bierly
Program Director of Meteorology
Atmospheric Sciences Section
National Science Foundation
Washington, D. C. 20550
Mr. F. T. Bodurtha
Senior Consultant
Environmental Control
Louviers Building
E. I. Du Pont de Nemours & Co.
Wilmington, Delaware 29898
Dr. W. A. Bowman
Lockheed Missiles & Space Co.
Huntsville Research and
Engineering Center
P. O. Box 1103 West Station
Huntsville, Alabama 35807
Dr. Ai Boyer
Officer-in-Charge of Meteorology
Air Management Branch, Sixth Floor
Ontario Department of Energy and
Resources Management
1 St. Clair Avenue West
Toronto 195, Ontario
Mr. Edward W. Burt
Meteorologist
Air Pollution Control
Office
3820 Merton Drive
Raleigh, N. C, 27609
Mr. Kenneth L. Calder, ESSA
Chief Scientist
Division of Meteorology
Air Pollution Control
Office
3820 Merton Drive
Raleigh, N. C. 27609
Dr. J. E. Cermak
Engineering Mechanics
Department of Civil Engineering
Colorado State University
Fort Collins, Colorado 80521
Dr. Jack Chaddock
Chairman
Mechanical Engineering Department
Duke university
Durham, N. C. 27706
Mr. Anton Chaplin
Litton Systems. Inc.
Applied Technology Division
354 Dawson Drive
Camarillo, California 93101
Dr. L. A. Clarenburg
Rijnmond Authority
Schiedam
The Netherlands
Dr. Alan Cole
Earth Sciences Department
Northern Illinois University
De Kalb, Illinois 60115
Dr. H. E. Cramer
Director
Environmental Sciences Laboratory
GCA Technofogy
P. O. Box 15009
Salt Lake City, Utah 84115
Dr. Gabriel T. Csanady
Meteorology and Space Science
Building
The University of Wisconsin
1225 West Dayton Street
Madison, Wisconsin 53706
Mr. Margaret Day
Manager, Research Systems Analysis
Meteorology Research, Inc.
464 West Woodbury Road, Box 637
Altaciena, California 91001
Mr. James L. Dicke
Meteorologist
Office of Manpower Development
Air Pollution Control
Office
Research Triangte Park, N. C. 27709
15-1
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Dr. Author Dodd
Meteorologist
Army Research Office
Duke University
Durham, North Carolina 27706
Dr. Rudolf J. Engelmann
Acting Chief
Fallout Studies Branch
Division of Biology and Medicine
U. S. Atomic Energy Commission
Washington, D. C. 20545
Dr. R. M, Felder
Department of Chemical Engineering
School of Engineering
North Carolina State University
Raleigh, N. C. 27507
Dr. Bruno Finzi-Contini
Istituto di Fisica Tecnica
Universita Degli Studi di Trieste
Facolta Di Ingegneria
Via Alfonso Valerio 10, Italy
Dr. Heinz Fortak
Institute fur Theoretische
Meteor alogia
Der Freien Universitat Berlin
1 Berlin 33
Thielallsee 49
Federal Republic of Germany
Dr. David Fraser
Department of Environmental
Science & Engineering
School of Public Health
University of North Carolina
Chape! Hill, N, C, 27514
Dr. Button Freeman
Vice-President
Systems, Science, 8i Software
P. 0. Box 1620
La Jolla, California 92037
Mr. FrancoisN. Frenkiel
Naval Ship Research and
Development Center
Washington, D. C. 20007
Dr. James P. Friend
Atmospheric Chemistry
Department of Meteorology and
Oceanography
School of Engineering and Science
New York University
Geophysical Sciences Laboratory
2455 Sedgwick Avenue
Bronx, New York 10468
Dr. J, Gavis
Department of Environmental
Engineering
The Johns Hopkins University
Baltimore, Maryland 21218
Dr, F. A. Gifford, Jr.
Director, Air Resources Atmospheric
Turbulence and Diffusion
Laboratory
U. S. Department of Commerce
Post Office Box E
Oak Ridge, Tennessee 37830
Dr. James Halitsky
Senior Research Scientist
School of Engineering and Science
New York University
University Heights, Bronx, N. Y. 10453
Mr. Harry Hamilton
Engineering and Environmental
Sciences Division
Research Triangle Institute
P. O. Box 12194
Research Triangle Park, N. C. 27709
Mr. Steven Hanna
Air Resources Atmospheric
Turbulence and Diffusion
Laboratory
Cheyenne Hall Building
P, O. Box E
Oak Ridge, Tennessee 37831
Dr. George Herbert
President
Research Triangle Institute
P. 0. Box 12194
Research Triangie Park, N. C. 27709
Dr. Glenn R. Hilst
Executive Vice-President
The Travelers Research Corporation
250 Constitution Plaza
Hartford, Connecticut 06103
Mr. G. C. Holzworth
Chief, Air Pollution Geophysics
Research Branch
Air Pollution Control
Office
3820 Merton Drive
Raleigh, N, C. 27609
Dr. Walter Hoydysh
School of Engineering & Science
New York University
Bronx, New York 10453
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Mr. Harvey Jeffries
Department of Environmental Sciences
and Engineering
University of Morth Carolina
Chapei Hill, North Carolina 27514
Mr. Robert M. Jimeson
Physical Sciences Administration
Air Pollution Control
Office
801. N. Randolph St.
Arlington, Virginia 22203
Dr. Warren B. Johnson, Jr.
Senior Research Meteorologist
Aerophysics Laboratory
Stanford Research Institute
Menlo Park, California 94025
Mr. Edward W. Klappenbach
Senior Meteorologist
City of Chicago Department of
Air Pollution Control
320 North Clark Street
Chicago, Illinois 60610
Kr. Kenneth Knoerr
School of Forestry
Duke University
Durham, N. C. 27706
Dr. Richard J. Kopec
Department of Geography
University of North Carolina
Chapel Hill, N. C. 27514
Dr. Hein2 H. Lettau
Department of Meteorology
University of Wisconsin
Meteorology and Space Science 8ldg.
1225 West Dayton Street
Madison, Wisconsin 53076
Mr. Oenis M. Lohman
Chief, Meteorology Section
Penn. Bureau of Air Pollution Control
P. O. Box 90
Harrisburg, Pennsylvania 17120
Dr. Lester Machta
Director, Air Resources Laboratories
Environmental Science Services
Administration
U. S, Department of Commerce
Silver Spring, Maryland 20910
Dr. James R. Mahoney
Assistant Professor of Applied
Meteorology
Harvard University School of
Public Health
Kresge Center for Environmental
Health
Department of Industrial Hygiene
665 Huntington Avenue
Boston, Massachusetts 02115
Dr. David B. Marsland
Department of Chemical Engineering
School of Engineering
North Carolina State University
Raleigh, N. C. 27607
Mr. Robert A. McCormick
Director Meteorology Program
Air Pollution Control
Office
3820 Merton Drive
Raleigh, N. C. 27609
Mr. Douglas L. McKay
Department of Environmental
Sciences and Engineering
University of North Carolina
Chapel Hill, North Carolina 27514
Dr, John T, Middleton
Commissioner
Air Pollution Control
Office
801 North Randolph Street
Arlington, Virginia 22203
Dr. David Moreau
Department of City and Regional
Planning
University of North Carolina
Chapel Hill, N. C. 27514
Mr. Paul Morgenstern
Environmental Sciences and Technology
Wafdin Research Corporation
359 Allston Street
Cambridge, Massachusetts 02139
Dr. William J. Moroz
Director
Center for Air Environment Studies
Pennsylvania State University
226 Chemicat Engineering II
University Park, Pennsylvania 16802
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Mr. Harry Moses
Argonne National Laboratory
9700 South Cass Avenue
Argonne, Illinois 60439
Dr. J, C. Mulligan
Mechanical and Aerospace Engineering
North Carolina State University
Raleigh, N. C, 27607
Dr. R. E. Mum
Meteorological Branch
Department of Transport
315 Bloor Street, West
Toronto, 5, Ontario
Dr„ C. R. Murthy
Physical Limnology Section
Department of Energy, Mines and
Resources
Canada Centre for Inland Waters
Great Lakes Division
P. O. Box 5050
867 Lakeshore Road
Burlington, Ontario
Dr. Charles O'Melia
Department of Environmental
Sciences and Engineering
University of North Carolina
Chapel Hill, N. C. 27514
Dr. Morns Neiburger
Department of Meteorology
University of California
Los Angeles. California 90024
Mr. Lawrence E. Nieneyer, ESS A
Assistant Director
Division of Meteorology
Air Pollution Control
Office
3820 Merton Drive
Raleigh, N.C. 27609
Mr. Donald H. Pack
Deputy Director
Air Resources Laboratory
Environmental Science Services
Administration
Silver Springs, Maryland 20910
Dr. Frank Pasquill
Meteorological Off ice
London Road
Bracknell, Berkshire, England
Mr. Francis Pooler
Chief, Boundary Layer Dynamic
Research Branch
Division of Meteorology
Air Pollution Control
Office
3820 Merton Drive
Raleigh, N.C. 27609
Dr. Parry I Randerson
ESSA-ARL
P. O. Box 14985
Las Vegas, Nevada 89114
Dr, John J. Roberts
Reactor Engineering Division
Argonne National Laboratory
9700 South Cass Avenue
Argonne, I llinois 60439
Dr. G. D. Robinson
Director, Environmental Physics
and Chemistry
The Travelers Research Corporation
250 Constitution Plaza
Hartford, Connecticut 06103
Dr. Shin'ichi Sakuraba
Meteorological Research Institute
Koenji Kita 4-35-8, Suginami-ku,
Tokyo,Japan
Dr. Walter J. Saucier
Department of Geosciences
North Carolina State University
Raleigh, N, C. 27607
Dr, Jabbar K. Sherwani
Department of Environmental
Sciences and Engineering
School of Public Health
University of North Carolina
Chapel Hill, N. C. 27514
Dr. L. J. Shieh
Scientific Center, ISM
2670 Hanover Street
Palo Alto. California
Mr. Conrad Simon
Senior Meteorologist
City of New York Department of
Air Resources
51 Astor Place
New York, N. V. 10003
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Mr. Irving A. Singer
Meteorology Group
Brook haven National Laboratory
Associated Universities, Inc.
Upton, Long Island,
New York 11973
Dr. Ralph C. Sklarew
Systems, Science and Software
P. O. Box 1620
La Jolla, California 92037
Mr. David Slade
Fallout Studies Branch
Division of Biology and Medicine
U. S. Atomic Energy Commission
Washington, D. C. 20545
Or. P. R. Slawson
Department of Mechanical Engineering
Faculty of Engineering
University of Waterloo
Waterloo, Ontario, Canada
Dr. William H. Snyder
Physical Scientist
Division of Meteorology
Air Pollution Control
Office
3820 Merton Drive
Raleigh, N. C. 27609
Dr. F, Y. Sorrell
Department of Engineering Mechanics
School of Engineering
North Carolina State University
Raleigh, N. C. 27607
Dr. Tom Stephens
Southern Research Institute
2000 9th Avenue, South
Birmingham, Alabama 35202
Prof. Arthur C. Stern
Department of Environmental Sciences
and Engineering
School of Public Health
University of North Carolina
Chapel HiN, N. C. 27514
Dr, Robert E. Stewart
Department of Environmental
Engineering
College of Engineering
University of Florida
Gainesville, Florida 32601
Dr. Gordon Strom
School of Engineering & Science
New York University
Bronx, New York 10453
Dr. John L, Sullivan
Environmental Engineering
Syracuse University
Syracuse, New York 13210
Dr, Hale Sweeny
Statistics Research Division
Engineering and Environmental
Sciences Division
Research Triangle Park, N. C, 27709
Dr. Peter A. Taylor
Department of Mathematics
University of Toronto
Toronto 5, Ontario, Canada
Mr. Joseph A, Tikvan
Meteorologist
Air Pollution Control
Office
3820 Merton Drive
Raleigh, N. C. 27609
Mr. Donald B. Turner
Meteorologist
Air Pollution Control
Office
3820 Merton Drive
Raleigh, N. C. 27609
Dr. Edward Ungar
Divisional Chief of Fluid and Gas
Dynamics
Battelle Institute
Columbus, Ohio 43201
Dr, Reginald I. Vachon
Mechanical Engineering Department
Auburn University
Auburn, Alabama 36830
Mr. E. A. Ward
TRW, Inc.
Washington Operal ions
1735 I Street, N. W,
Washington, D. C. 20006
Mrs. M. L. Weatherley
Warren Spring Laboratory
Ministry of Technology
Dudley House, Ended Street
London W. C. 2
England
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Dr. Willis L. Webb
Atmospheric Sciences Laboratory
White Sands Missile Range
White Sands, New Mexico
Dr. Allen H. Weber
Department of Geosciences
North Carolina State University
Raleigh, N, C. 27607
Dr. Larry Wendell
Atomic Energy Commission
Box 2108
Idaho Falls, tdaho 83401
Dr. Daniel Werner
Mechanical Engineering
Duke University
Durham, N. C. 27706
Dr. James J. B. Worth
Associate Director of Engineering
Research Triangle Institute
Research Triangle Park, N. C. 27709
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