V
EPA-600/4-76-055
November 1976
PROTECTION
AGENCY
JBALLAS
Environmental Moimorinl
UBRARY
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U S Environmental
Protection Agency, have been grouped into five series These five broad
categories were established to facilitate further development and application of
environmental technology Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields
The five series are:
1 Environmental Health Effects Research
2 Environmental Protection Technology
3 Ecological Research
4 Environmental Monitoring
5 Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL MONITORING series
This series describes research conducted to develop new or improved methods
and instrumentation for the identification and quantification of environmental
pollutants at the lowest conceivably significant concentrations It also includes
studies to determine the ambient concentrations of pollutants in the environment
and/or the variance of pollutants as a function of time or meteorological factors
This document is available to the public through the National Technical Informa-
'on Service, Springfield. Virginia 22161
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EPA-600/4-76-055
November 1976
URBAN AIR POLLUTION MODELING WITHOUT COMPUTERS
by
Michael M. Benarie
Institut National de Recherche Chimique Appliquee,
B.P.I - 91710 Vert-le-Petit, France
Visiting Scientist
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AMD DEVELOPMENT
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
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DISCLAIMER
This report has been reviewed by the Environmental Sciences Research
Laboratory, U.S. Environmental Protection Agency, and approved for
publication. Approval does not signify that the contents necessarily
views and policies of the U.S. Environmental Protection
does mention of trade names or commercial products constitute
or recommendation for use.
reflect the
Agency, nor
endorsement
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FOREWORD
The modeling of urban air pollution by mathematically oriented techniques
has for some time provided the primary quantitative basis for the development
of air quality management concepts and strategies. As such, the topic of air
quality modeling has high priority in the research program of the EPA.
The material of the present report formed the basis for a series of
three lectures given by Dr. M. Benarie, Chief of the Atmospheric Pollution
Service, Institut National de Recherche Chimique Appliquee, Vert le Petit,
France. The lectures were first given on 15-17 Sept. 1976 in Raleigh, N.C.,
as part of the "Continuing Seminar on Air Quality Research", which is a
joint activity of the Meteorology and Assessment Division, EPA and the North
Carolina State University. They were also repeated on 20-22 Sept. at
the Pennsylvania State University, University Park, Pa., under support of an
EPA grant with the Select Research Group on Air Pollution Meteorology at
P.S.U. The publication of this material as an EPA report is made in the
interests of wide dissemination of the information to air quality modelers.
Kenneth L. Calder
Chief Scientist
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
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PREFACE
The lecture material that is consolidated in this report represents an
abridged version of some selected chapters of a monograph entitled Urban Air
Pollution Calculation, by the same author. As the title indicates the
selection was oriented towards simple but nevertheless efficient methods.
The present discussion stresses the reasons why these methods are useful,
which are their recommended fields of application, and when they are to be
preferred to other kinds of calculation. As compared with the monograph
this abridgement differs primarily in the completeness of the coverage.
Here only about one tenth of the references are included and discussed.
The primary aim is to stress principles and only to present examples that
are really necessary. In contrast the monograph tends to be as complete as
possible, by providing comprehensive current information on references,
formulas, applications and validations.
The author would like to express his thanks to Mr. K. L. Calder who
kindly provided editorial assistance on the first draft of this report.
IV
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ABSTRACT
This report was the basis for a series of three lectures by the author
on urban air pollution modeling, and represents a condensed version of se-
lected topics from a recent monograph by him. The emphasis is on simple
but efficient models, that can often be used without necessitating a high-
speed computer. It is indicated that there will be many circumstances under
which such simple models will be preferable to more complex ones. Some
specific topics included in the discussion are the limits set by atmospheric
predictability, forecasting pollution concentrations in real time as for
pollution episodes, the simple box model for pollution concentrations, the
frequency distribution of concentration values including the log-normal dis-
tribution and averaging-time analysis, the relationships between wind speed
and concentration, and lastly the critical question of model validation and
the need to consider several indices of goodness-of-fit if pitfalls are to
be avoided.
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CONTENTS
Foreword iii
Preface iv
Abstract y
Figures vii
Tables viii
1. Introduction -1
2. Limits Set by Atmospheric Predictability 7
3. Forecasting Pollution 14
4. The Box Model 23
Short-term averages 23
Simple box model for long-term averages 28
5. Correlation with Demographic Parameters 31
6. Concentration Frequency Distribution 33
The log-normal representation 33
Averaging-time analysis 34
7. Wind and Concentration Relationships 38
8. Validation - Or the Ways to Delude Oneself 41
9. Conclusions 43
References 44
Addendum 71
VTl
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FIGURES
Number Page
1 Sulfur dioxide concentration as a function of the logarithm
of population density, in and around Paris, France. After
Pelletier (1967), with the permission of Laboratoire de
de THygiene de la Ville de Paris 51
2 Smoke concentration as a function of the logarithm of popula-
tion density, in and around Paris, France. After Pelletier
(1967), with the permission of Laboratoire de 1'Hygiene
de la Ville de Paris 52
3 Observed and experimentally predicted annual hourly CO concen-
tration distribution for San Francisco 53
4 Observed hourly wind-speed distribution for San Francisco
Federal Building, July 10-11, 1968 54
5 Observed and predicted hourly CO concentration distribution
for San Francisco, July 10-11, 1968 55
6 Observed and model-predicted annual hourly CO concentration
distribution for San Francisco 56
vm
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TABLES
'm~oer Page
1 Classification of urban air pollution concentrations, following
their purpose and accuracy requirements 57
2 bystematics of urban air pollution models based on the input
parameters 58
3 Tabulation prediction technique 59
4 Contingency table of the ozone prediction results on the training
set by Ruff (1974) 60
5 Breakdown of the episode forecasts for Rouen, France, after Benarie
(1971) and Benarie and Menard (1972) 61
6 Contingency table of forecast results obtained by Benarie (1971)
and Benarie and Menard (1972), with apparent meteorological
forecast error removed 62
7 Contingency table for the previous forecast results, overall results
for 549 cases 63
8 Multiplying factors to be applied to the 30-day running average to
obtain winter episode concentrations in Rouen, France 64
9 Comparison of observed, calculated and forecast data for seven
sampling stations in Rouen, France, in winter 1968/69 65
10 Predictions of hourly values of CO-concentration in ppm, in the
Los Angeles Basin, on September 29, 1969, by Hanna (1973) ... 66
11 Validation of the simple box model, according to Hanna (1971) and
Gifford (1972, 1973) 67
12 Data related to particle and SO pollution for U.S. cities. ... 68
/\
13 Distribution of selected cities by population class and particle
concentration, 1957 to 1967 69
14 Computed CO concentrations (17-hour day-averages, ppm) compared
with observed values for Sept 23, 1966 for the Los Angeles Basin 70
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SECTION 1
INTRODUCTION
It is not in the role of some latter-day follower of the machine-
smashers of the 1840's that I chose the title. At that time tailors fearing
unemployment destroyed the first sewing machines. I would like to speak
about "computer-less" methods and about "unsophisticated methods of modeling."
However, this will certainly not be done with any sense of glee that "see,
here the abacus outperformed the computer." The abacus will never do that.
My point of view is strictly that of the engineer. I consider the test of
the engineer to be the attainment of a given practical goal by the most
economical of the means available. The scientist and research worker on the
other hand seek to improve knowledge without consideration to cost, effort
and time, while the inventor labors to increase the available means. The
good engineer will happily use the output from the research worker or that of
the inventor, but his purpose is practical such as to build a bridge,
house, highway or gadget. He has to deliver the bridge, etc., on time and
meet specifications, while avoiding any suspicion of a gamble. On the other
hand, all research projects contain some element of a gamble. They verify,
validate, or prove some hypothesis; they compare or attempt to test or they
search for something as yet undisclosed by nature. At the outset, we always
hope for a positive answer, but a hope is only a gamble. On the other hand,
an engineer who "hopes" is truly a bad engineer. An engineer must deliver
his product in the same way as a manufacturer must do.
In our case, the product to be delivered mostly takes the form of infor-
mation. It is the result of a calculation or of some process akin to calcu-
lation. These calculations are usually undertaken in order to avoid the
unrealistically high cost of of full scale experiments. In the same way, it
is cheaper to calculate the strength of a beam than to shatter a real one;
it is also less expensive to calculate the impact of a power plant on an
urban area than first to build one and then see what happens.
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Before undertaking any urban air pollution calculations, the following
questions should be answered:
1. who needs the information and
2. what purpose has to be attained.
Table 1 presents a schematic outline of the answers to these questions.
The user has first to define his operational needs: If an annual arith-
metic mean is requested simply to check conformity with an air quality stand-
ard expressed as an annual mean, it would obviously be foolish to obtain it
from 8760 hourly estimates, when more direct and cheaper methods are avail-
able. High resolution—here as everywhere—costs money. This money and
labor are spent first in gathering the high-resolution input data, and then
in working out the fine details of the output. High resolution data do not
necessarily mean accurate or true data. Thus the first consideration we must
face before adopting some computationally sophisticated method—which, by the
way, rather often coincides with computer vs computer-less methods--, is
whether the quality and the quantity of the available input does in fact
justify the computational burden. On the other hand, some computationally
simple methods need high-grade input information. An obvious example is the
"persistence model" which without any calculations, when projected a short
time forward, wiTT give a fantastically good fit, because it already contains
a tremendous amount of accurate information. Needless to say, extra-
polation for a few years, or even a few days ahead, would be pointless.
The juxtaposition of "simple" box models, requiring little computing
effort, with mathematically and physically "sophisticated" models, that proba-
bly necessitate the use of large digital computers, does not necessarily mean
that one is better than the other. First of all it should be emphasized, as
Gifford (1973) pointed out, that "simple" is not the opposite of "sophisti-
cated," but of "complex." The antonym of "sophisticated" is "naive." Simple
urban air pollution models are not always naive, and may in fact be quite
sophisticated. Conversely, complex models can be quite naive, or can contain
naive assumptions.
Furthermore, if a complex- urban pollution model cannot estimate more
accurately than a simple one, say like the use of persistence, then its
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development is not profitable in applied studies (Gifford and Hanna, 1975).
This does not mean that the theoretical importance of a complex model is
diminished if it provides a better understanding of the underlying phenomena.
This leads directly to another question: Is there some fundamental
limit to the accuracy of the model computations? If there is such a limit,
then it is clearly pointless to use computational methods of much greater
precision as these only contribute to the proliferation of non-significant
figures in the estimate. Much of the discussion of the following section
will be concerned with the search for such limits.
Table 1 is an attempt to systematize computations on the basis of their
purpose. Another classification can be based on the amount and nature of
external - mostly meteorological - information, needed as input for the model.
Meteorological parameters have an overwhelming influence on the behaviour
of pollutants in the urban air. Among them, wind parameters (direction,
velocity and turbulence), and thermal properties (stability) are the most im-
portant. A classification of the models can be based on the method in which
this kind of input is generated. The following discussion will use "wind
field" as shorthand for all the dynamical and thermal properties associated
with the wind.
In some models, the wind field is assumed to be known or has to be fed
in by forecasting techniques. Mahoney (1971) has coined the word "driven"
for this kind of input.
In a second category of computations, a consistent wind pattern (in
the vicinity of the urban area), is either calculated from a full set of
meteorological model equations, or an actually observed wind field is used
as input
Finally, there are representations - also called models - that provide
statistical information on the occurrence of pollutant concentrations, and
which do not make use of wind or other meteorological parameters as input.
A further distinguishing feature, different from any of those discussed
above, appears in the nature of the model as to whether it is source - or
receptor-oriented. The distribution and the emission rate of pollutant
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sources are assumed to be known in "source-oriented models." Pollutant con-
centrations are then calculated from this source distribution over the entire
region of the model.
The opposite is true for the "receptor-oriented models": In their pure
form no assumptions are made about emissions, and only ambient concentration
is monitored at a number of receptor sites. Statistical or other inferences,
which may or may not be linked to meteorological information, are then
drawn - and possibly extrapolated - from the observed data.
Source-oriented models tend mostly to be explanatory and involve causal
relationships between the pollutant emissions and concentrations. Only ex-
planatory models can provide the necessary means to control the system and
produce desired changes in performance. Receptor-oriented models are gener-
ally descriptive and less directed toward establishing cause and effect
relationships.
Table 1 also distinguishes between short- and long-term objectives, i.e.
whether the result of the calculation is needed in the next few hours, or
in a few years. This aspect generally coincides with the distinction made
between computation of short-time concentration values or forecasts, and the
request for long-time averages. A typical, but rather arbitrary, separation
between these two classes, would be 24 hours. Anyway, the basic idea in the
30-minute averaging time computation and that for the seasonal or yearly
average, show enough difference for recognition of two quite distinct classes
for short- and long-time mean calculations.
The foregoing principles enable us to classify the main types of urban
air pollution "models," as shown in Table 2.
Examination of Table 2 shows that beyond the main classification cri-
teria (e.g. of short- or long-term averages; source- or receptor-oriented)
four kinds of models may be distinguished in terms of the type of information
they provide. This distinction may be termed "model character" and is de-
noted by letters from A to D in Table 2.
A. This letter denotes models which use either assumed or actually
observed values for the meteorological parameters.
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With assumed parameters, the plume and volume-element models give nu-
merical results, i.e., concentration values as a function of the space coor-
dinates. It is beyond the scope of the model to consider whether or when
the assumed set of meteorological descriptors will materialize. The results
are only as good as the input data. This category of models provides am-
bient concentration from inputs, and is analogous to the situation in chemical
engineering where content of a reactor is computed from reactants, stirring,
temperature, etc. The output is primarily a numerical value asssigned to a
space and a time coordinate. Usually, this kind of calculation justifies the
use of a computer, mainly when a larger set of computations is being made.
This is often the case in long-term calculations (plume combined with fre-
quency classes).
On the other hand, the "box model," which can conceptually be derived
from the principle of mass conservation, is an example of a model where the
use of a computer can often be avoided.
B. In forecasting pollution, the output from the calculation is ex-
pressed sometimes numerically, but more often by categories, by probabilities
or in some other convenient way as used in meteorology. The quality of the
forecast is limited by the atmospheric predictability.
C. Statistical description, in either of its forms, is a summary of
data already on record. Valuable for predicting trends or cycles, it is
of littla use for a true forecast (i.e., today's estimate of tomorrow's pol-
lution). For data-management, compilation and computation, the computer
is almost a necessity; for search and exploitation, it is only an advantage.
D. Finally, we have the description (which may also be termed "statis-
tical") or summarization of data already on record, mostly in form of graphs
or tables, and intended mostly for long-term inferences. The output is in
terms of a frequency not assigned to any time coordinate. Although the pre-
liminary tabulation is facilitated by use of a computer, the use of the re-
sulting tables or graphs is mostly computer-less.
The use of computer-less methods may be advisable, mainly in the follow-
ing situations:
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1. When relatively low resolution information (e.g., just an annual
mean) is sought.
2. When the available input information does not justify a complex
algorithm; when the range of error of a high precision calculation would still
be large because of observational inaccuracies. This case is rather more
frequent in air pollution than generally assumed.
3. When the predictability of the atmospheric motions sets an upper
limit to the predictions of the models.
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SECTION 2
THE LIMITS SET BY ATMOSPHERIC PREDICTABILITY
We shall distinguish between the conservation of the identity of air
parcels and our ability to simulate or compute the trajectory of these air
parcels.
Let us suppose that at a certain instant of time volume elements of air
can be marked by tracers, which are "ideal" balloons that are able to follow
every motion of the surrounding air, and the tracks of which can be observed.
Thus, each mesh cube is determined by eight balloons in the atmosphere. These
'mesh particles' will undergo a rapid change of their shapes during the fol-
lowing days, long bands will be stretching, and finally the development will
proceed to a chaotic state where the 'particles' have lost their identity.
All particles have the shape of a cube, i.e., as bounded by squares at
t = o. A particle will be said to have ceased to exist if one of the corner
points of the quadrilateral crosses one or both opposite sides during the
course of time.
Robinson (1967) found that a particle with mesh size equal to 300 km
should cease to exist within the period 12h < t < 75h. Egger (1973) using the
data of KAP (1968, 1969) on large-scale dispersion of clusters of particles
in the atmosphere, suggests 45h < t < 72h while using the data of EOLE
(Morel 1972; Larcheveque, 1972) he arrives at t«45h.
This estimate is one on an upper limit for atmospheric predictability.
No numerical forecast model however it is designed, can do better than this.
Our ability to predict is further limited by the following factors:
One of these arises from the finite representation of the atmospheric
fields in the models, which makes it impossible to describe scales of motion
below grid scale. Due to the nonlinearity of the hydrodynamic equations,
parts of the turbulent energy which is contained in the subgrid range, will
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appear under an alias in the larger scales, thus limiting the predictability
of these scales. "It is this last type of uncertainty that is generally felt
to be responsible for the limit of predictability of various scales" (Fleming,
1971). Another factor is the insufficient knowledge of the initial condi-
tions, such as errors in the raw data.
For planning purposes, we want to be able to calculate the influence of
different sources at specific sites, on specific locations of the urban area.
By using source-oriented models we attempt to establish a cause - to -
effect chain, between the emissions of a number of sources and the ambient
concentration at given locations. The main links of this chain are the
following:
1. Knowledge of the source strength.
2. Adequate definition of the meteorological parameters.
3. A reliable method for the calculation of the dispersion from
inputs 1. and 2.
4. Adequate knowledge of the pollutant losses (or formation] by
chemical or photochemical reactions.
Almost all these requirements can be subdivided into many parts. There-
fore in passing from source to ambient concentration a total of ten to twenty
elementary processes have to be estimated. Only a few of these can be cal-
culated free of error. Many can only be estimated roughly so that each
estimate may be tainted by large instrumental or theoretical uncertainties.
Almost all of these errors increase with decreasing wind velocity. A brief
summary of the facts is as follows:
1. Source strength : wind velocity has no influence on this factor.
2. The main meteorological parameters—wind velocity and direction—
are not monitored by currently available instruments when the wind velocity
sinks below 1 or 2 m s" . However, this is not only an instrumental diffi-
culty that could be remedied in the future. For the literature on turbulent
motion in the atmosphere is unusually scarce on the topic of the directional
variance of very light winds. This arises from the fact that the stability
of high building structures and the safety of aircraft is not affected by
such winds, and specialists in these areas of research have more immediate
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problems at the upper end of the scale. Theoreticians are embarrassed by the
lack of an exact approach and prefer to pass on to other topics. In contrast
the synoptic meteorologists are fully aware that light winds most frequently
are variable and with poorly-defined directions. The common observation of a
weathervane or of sailboats under such conditions, makes it unnecessary to
cite in detail the few available tetroon-flight experiments. These only add
very little to the already plentiful evidence. In the monograph of Lumley
and Panofsky (1964, p 151) which contains extensive information about
atmospheric turbulence, one only finds the following brief statement on the
subject of the standard deviation of the wind azimuth: "The unexpected fea-
ture is the tremendously large scatter and the frequently considerable values
of standard deviations in stable air. Further analysis of the observations
of inversions indicates that the largest standard deviations of azimuth occur
in light-wind conditions gradual azimuth drifts with periods of the
order of 20 minutes were observed in light-wind inversions. The origin of
these drifts is unknown. Their occurrence adds two difficulties to the esti-
mation of the lateral diffusion: first, they make lapse rate and wind speed
poor indicators of lateral wind fluctuations; secondly, even if the standard
deviation of azimuth is known to be large, it is not known whether these
large, but more or less local, standard deviations produce rapid spreading of
air pollution."
3. All known plume dispersion equations have a singularity near zero
wind velocity, and therefore their use at very low velocities becomes suspect.
4. The incomplete knowledge available about pollutant transformations
and sinks, is certainly not made any less important in the case of light winds.
Optimistically, we can only hope that these deficiencies in knowledge will
not increase the error under calm conditions.
Thus, even if low wind velocity did not influence the questions 1 and
4 above, its effect through the questions 2 and 3 would be so overwhelming
that source-oriented models would break down completely during light winds.
It can be conjectured from evidence concerning urban airflow and urban heat
islands that during conditions favorable to the formation of an urban heat
island, the source-oriented models will be of no use. In numerical terms,
this limit might be expected when the geostrophic wind diminishes to less than
9
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3 m s~ . Very probably, this is not a rigid limit, but varies with the city
size.
It should be emphasized that because of these arguments, we do not
speak about the usefulness of calculations based on plume-dispersion formu-
lae at very low wind speeds. The whole model concept, as being the causal
chain between pollutant source and ambient concentration, becomes meaningless
when the wind velocity falls below a certain value.
To express these considerations in the terminology of operational re-
search, one would say that we are dealing with a multi-nodal chain. At each
node, along with some information, we introduce more or less random noise.
Yet, just such a multi-nodal chain with noisy input could be used to simulate
the outcome of a throw at roulette. For suppose the torque applied to the
roulette wheel could be electronically monitored, and assume the same for
the velocity and the angle of the roulette ball. Then apply the known accu-
rate equations of the mechanics of rigid bodies. Do a few more steps of
computations and you have the final definitive system to beat Las Vegas.
Obviously, you will never be able to do that. But by the same logic,
multi-nodal models with the introduction of random noise at every step
will not indicate with accuracy tomorrow's pollutant concentration. On the
contrary, the more steps (nodes) that are used, the less accurate will be
the forecast of the outcome of any one individual occasion (calculation).
Sophistication may be a way to improve the precision of averages, of find-
ings about categories or to observe trends, but it seems of no use for
improving the accuracy of forecasts.
The strong statement should not be interpreted as saying that all so-
phistication is definitively to be rejected. As the body of this paper will
show, some very simple one- or two-step schemes show an honorable, if not
outstanding performance mainly in forecasting. On the other hand, if very
sophisticated, long-chain arguments must be bad, then there is some inter-
mediate length of operational chain which might give optimum results. Re-
search should be oriented towards methods which are intermediate between
utmost simplicity and noisy sophistication.
The roulette wheel is an example of a mechanical system beyond the
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reach of mechanical cause-to-effect calculations. But we shall try to develop
this concept gradually, uy considering a heavy beam supported by an axis of
low friction situated near to its center of gravity. If the latter is below
the axis, the device becomes a sensitive balance. Any perturbation of the
balance can be described analytically, in terms of oscillation and equilibrium
positions. If, however, the center of gravity and rotation axis are made to
coincide (they never actually do), the angular position at which the beam will
stop, can no longer be predicted analytically and the problem becomes one of
probability. Somewhere in the process of approaching the axis to the center
of gravity, the chain of causality has broken down and has been replaced by a
probability situation. Of course, I do not wish to discuss the fundamentals,
as these are well-known from the probability calculus; my purpose is only to
emphasize that a similar situation occurs in urban air pollution as for the
example of beam. When the chain of governing equations between cause and
effect becomes too long, and at each step rather unknown perturbations are
introduced then the use of calculus should be abandoned and a new probabilis-
tic approach should be attempted.
This is what occurs in urban air pollution, when the wind velocity sinks
below approximately 3ms; above this lower limit, atmospheric aerodynamics
is a powerful tool, but below or close to it, hydrodynamical equations are of
as much use as classical mechanics would be for calculting the face on which
a dice will fall. There are two distinct regimes in urban air pollution:
one for strong to moderate winds and another for light winds during calm con-
conditions.
The difference between urban air flow conditions with moderate and
strong winds and those during light winds, and also the fact that street ven-
tilation changes character when rooftop wind speeds fall between 2 and 5 m s~ ,
is already well-stressed in the literature.
Insofar as source-oriented models rely on classical analytical equations
and on a cause-to-effect chain, they will behave very poorly in warning sys-
tems or in episode control strategies, because generalized and protracted
pollution episodes occur mostly during moderate and light winds. On the con-
trary, plume-concepts can be quite useful to localize pollution effects due
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to point sources or groups, when the winds are above 3ms
By the same argument, source-oriented models, when used as a basis for
long-term averages, may be useful if treated with circumspection and provided
that light winds and calm periods only happen infrequently. However, when
meteorological taoles of the urban area of interest indicate that eyen only
5 to 10% of the winds are below 2 m s~ , then the validity of the concentra-
tion distribution as computed by a source-oriented plume model, should be
questioned. Numerically, these concentrations will be in gross error at the
higher levels, which—even if they occur with low frequencies—are the most
important ones, as regards effects.
Receptor oriented models, sometimes with some empirical keying to the
source inventory, can be used for warning systems, provided that meteorolo-
gical parameters are correctly forecast. The vital question is, what can
be reasonably expected from this kind of forecast.
Though nowhere clearly stated, a widespread belief prevails in air pol-
lution circles. It seems to say that for any two time intervals, character-
ized by unchanged emission rate and by approximately two score meteorological
parameters (such as wind direction and intensity, thermal gradient, cloudi-
ness, the situation of a given air parcel relative to a front, etc., etc.),
if all these parameters were equal then pollutant concentrations would also
be the same, for both time intervals.
By the same logic, it could be expected that if two or three score ap-
propriate parameters were identical, then the same form of cumulus cloud
would hover over the same quarter of the city. Of course, nobody would dare
to assert this as fact. Continuing in this vein, we should not expect that
pollution concentration forecasts will be fully accurate, all the time.
The following example may also emphasize what can be reasonably ex-
pected, as regards the accuracy of air pollution concentration computation.
The average deviation from scheduled arrival times at Paris airport, due to
weather conditions, was only six minutes, during 1973 (personal communica-
tion). Flights cancelled before departure, as well as delays due to techni-
cal or commercial reasons, are not figured in this statistic. Considering
that the average flight times were about three hours, this means that the
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"estimation" was done with 4% error. Now, these aircraft are driven by thou-
sands of horsepower, guio^d by exceptionally skilled crew, assisted on the
ground by other most competent people and the most powerful computers ever
built. If all this complex system results in a 4% relative error, then how
can we expect that the calculation of an air parcel's trajectory, driven by
its own buoyancy and some turbulent airflow only - instead of a jet engine -
should perform any better?
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SECTION 3
FORECASTING POLLUTION
Perhaps the least computerized branch of air pollution engineering re-
lates to the forecasting of pollution. We have to distinguish quite clearly
between forecast and calculation. The latter term is used to denote the
operation of taking some formula - e.g. plume, statistical time series or
anything else - and then substituting into this formula some assumed (e.g.
for the next winter season...) or meteorologically forecast parameters. The
forecast on the other hand is a process which used knowledge that is avail-
able today (e.g. past statistical record, to-day's pollution concentration,
to-day's meteorological forecast, etc.) to predict (a) a time (e.g., tomorrow;
or even a given hour...) and (b) a pollutant concentration for that time.
The upper limit of the time span is that for which a forecasting skill can
be demonstrated, and- might be for a few hours or a few days in advance. We
exclude from "forecasting" the climatological estimate of long-term averages,
although it is implied that they are often taken into account by the fore-
caster. In order to be termed a "pollution forecast," the pollution concen-
tration estimate must refer to a specific day or hour and not to a probabili-
ty of occurrence within a given time span.
Almost synonymous with "air pollution forecasting" are: "episode
forecasting" and "alert announcements." By "episode" and "alert," everybody
means a spell with above-average pollutant concentrations. However consider-
able confidence must exist as to "the likely duration of the spell and how
high the concentration may rise before calling an "alert." If by "episode"
we understand a relatively high, and not too-frequent pollution level, and
not just the fact of exceeding some hygienic or legal limit, then by defini-
tion an episode is a statistically rare event or an extreme occurrence.
Former experience about such events is generally scarce, and difficulties
increase when the episode level is set very high. If the level is set un-
reasonably low, so that it is often attained through stochastic fluctuations,
14
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then all predictive qualities will be suppressed by the noise. In terms of
the cumulative concentration frequency, it would not be sound practice to
attempt to forecast the upper 0.1 percentile of the concentrations. On
the other hand, concentration forecasts of either below or above the 50%
percentile would scarcely be considered as episode forecasts, but rather as
being air pollution concentration forecasts limited to two classes. Thus
the success or the skill in episode forecasting depends in very large measure
on the definition of an episode. Often instead of using the concentration of
a single pollutant to set the episode criterion, an "air pollution index" is
defined. This may be considered as a scheme that transforms the weighted
concentrations of several individual pollutants into a single number. OTT
and THOM (1976) found that 35 U.S. metropolitan air pollution agencies use
some form of air pollution index and no two indices are exactly the same.
Thus, an index value of 100 reported in Washington, D.C. means something
entirely different from a value of 100 reported in Cleveland, Ohio.
The goal of forecasting a numerical value for the concentration in air
pollution episodes is statistically more elusive than that of the day-to-day
prevision of the "episode." With stringent definition of the eoisode inten-
sity, 90% or more days are non-episode days even in winter. Hence, a random
guess, based on the average frequency of the non-episode days, will yield 80%
or more correct forecasts. If instead of a random guess, one decides to
forecast "non-episode" for each day, then 90% or more of the days will be
"correctly" forecast. As during non-episode days the concentration is rela-
tively low, a constant-value estimation near the ensemble average will
minimize the RMS error, without demonstrating any real skill of the method.
If concentration episodes are predicted exclusively, such spurious effects
cannot perturb the judgement on the method.
The difference between air pollution potential forecasting and episode
forecasting is that the first does not take into account pollutant emissions,
while the second is concerned with the emission-dispersion interaction. The
first is a weather forecast that is oriented towards ventilation-forecasting,
while the second is an air pollution forecast.
The difference is also one of scale. Air pollution potential forecast
2
concerns a large area on a regional scale, covering perhaps 200,000 km or
more, and extending in time over 24 or 48 hours. These scales are related
15
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to the controlling synoptic event, the warm core stagnating anticyclone
which, with the associated light winds and subsidence, reduces atmospheric
dispersion and enhances the accumulation of pollutants. Thus this forecast
requirement is primarily dependent on meteorological variables (W.M.O. 1972).
Urban episode forecast has a space-time scale where local circulations
(e.g. land-sea breeze, drainage winds, heat island effects, etc.) become very
important, especially during large-scale stagnation situations. The length
scales are from 10 to 100 km, the latter for large megalopolis areas. The
time scales of the prediction requirements range from a few hours to about
two days.
All forecasting represents a correlative evaluation of the post hoc -
ergo propter hoc type. It was observed that calm winds and restricted verti-
cal exchange are conducive to high pollution episodes. How many times was it
observed? Perhaps nobody cared to count and to make up a contingency table.
It is not necessary to be a scientist, nor even a grown up human in order to
link together two simultaneous or subsequent events into a predictive corre-
lation. Animals build up conditioned reflexes in the same way.
Air pollution levels expressed in such terms as "insignificant", "near
average" or "high" can be surprisingly well predicted by a skilled observer
who is familiar with the air pollution record of a site, has access to the
current weather forecast, and who is able to look out through the window.
Such "no cost, no computer" forecasts provided from 75% to 85% correct an-
swers (depending on the forecaster and the season) for the Rouen and Stras-
bourg (France) urban areas. Such performance equals or even surpasses that
of much more elaborate schemes described in the literature.
The opponent of the sophisticated would now exclaim with relish, that
simplicity has finally triumphed! This however, is not really the case.
The skilled observer here performed with a sophistication not equaled by any
computer program available at the present time: he recognized a pattern.
We do not have a computer able to identify a handwritten numeral, a signa-
ture or a face. Almost any human being can do these things. A computer
cannot even recognize the form "circle", unless pre-coded in color, contrast,
dimension, perspective, etc. The human is able to do these things automati-
cally. Thus the human outperforms the computer in a specific skill called
pattern or gestalt recognition. We do not necessarily have to relinquish
16
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the computer. We must simply chose the pattern elements, or in other words
the predictors, and the series or the program which will enable the computer
to perform objectively the same forecast which was made subjectively and
unconsciously by the skilled observer.
The pattern elements or prescriptors must be chosen in an economic
fashion. For not only is their observation expensive, but when the number
of prescriptor class combinations becomes large, thp number of cases included
in each category may be undesirably small, even for the longest stable re-
cords that are available.
When the prescriptors are of qualitative or discontinuous nature, they
can easily be divided into classes, and contingency tables become very useful.
The number of classes or groups should be small, and usually less than five
for each variable. Contingency tables can strictly only be used if it can
be assumed that the data are independent of each other, which is rarely the
case in air pollution climatology. The best way to test stability is to
generate a new multiple contingency table of similar size and then compare
the relative frequencies in the two tables. From such a comparison it
should be possible to determine how the system will work when used in actual
forecasting. When using a contingency table in forecasting, the actual pre-
dictor combination is determined first, and then the forecast will be the
predictand group that occurred with the highest frequency in the past. The
probability of the forecast can also be estimated.
MOSES (1969, 1970) has described the implementation of this method at
the Argonne National Laboratory. Called "the Tabulation Prediction Scheme,"
the places of the prescriptand values and the freauencies were reversed.
The column headings in the Table are the minimum, the 25, 50, 75, 90, 98, 99
cumulative percentiles and the maximum. The entries for each column then
give the respective pollutant concentrations: this can be seen in Table 3.
Also shown are the inter-quartile range, the difference in S0£ concentrations
between 75 and 95 percentiles, the mean, the standard deviation and the num-
ber of cases for each entry. A computer is not an absolute necessity for
this compilation, although it certainly makes it easier.
As is the case for any other empirical statistical model, the tables of
the tabulation prediction scheme must be continuously updated. The use of
this scheme in an air pollution incident control test in Chicago, 111. was
17
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demonstrated by CROKE and BOORAS (1970).
Although the tabulation prediction scheme is easy to use - it is possi-
ble to look up any set of meteorological conditions just as one would look up
a word in dictionary - a considerable amount of insight is necessary in order
to develop an effective set of tables. For fuller details on their selection
of variables, and construction of the tabulations and application, see CROKE
and ROBERTS (1971, p. 169-184).
This selection may also be performed by a computer. By choosing a set
of predictors, which may initially contain useless or redundant ones, an
adaptive pattern classifier, which is a device whose actions are influenced
by its past experiences, can be used to assign each pattern to a category
that has been a priori characterized by a set of parameters. First the pat-
tern is digitalized by a "preprocessor." If any of the dependent variables
prove to be misleading or irrelevant, then a technique must be devised for
their deletion.
RUFF (1974) used the adaptive pattern classification for the forecast of
ozone levels above 0.1 ppm at San Jose, California.
The following Tist of trial inputs were used as ozone predictors for San
Jose:
1. N02 - Selected because it reacts with sunlight to ultimately form
°3-
2. CO - While there may be significant photochemical reactions involv-
ing CO, evidence indicates that CO is a good indicator for automotive exhaust
pollutants, which are known to play an important role in photochemical smog
formation.
3. The time-rate of change of CO in the atmosphere as a measure of the
degree to which the primary pollutants are being dispersed.
4. Oo - The concentration of ozone in the early morning hours is
indicative of the amount of photochemical activity.
5. Percent sunshine, used along with temperature, to represent radia-
tion intensity.
6. Ventilation index computed at 0400 and 1600 hours daily. Low index
values imply that the temperature inversions exist with low wind speeds
that inhibit dispersion. High values indicate that the condition of the
18
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atmosphere is more conducive to thorough dispersion.
7. The daily average surface wind.
The time of prediction is another variable that must be considered. If
an accurate prediction is made in the early morning hours, such as at 4 a.m.,
then abatement action can be taken if necessary to reduce the amount of emis-
sions. On the other hand, a later prediction, such as one at 9 a.m. is not
as effective in curtailing the sources but can serve to warn the general
public to modify their physical activity. The approach will be to optimize
the predictor over a time period ranging from 2 a.m. to 10 a.m. in one hour
increments. Therefore, the model is predicting from twelve to three hours
in advance of the normal daily ozone peak.
Since the degree of photochemical smog is strongly dependent upon time
of year, the specific model is optimized over a limited period of three
months. Implied in this approach, is the fact that the time of year is it-
self one of the variables. In an attempt to hold this variable constant,
the training set consists of August to October data. The model is then
subsequently evaluated for September data. One further restriction is that
only week days are considered in the analysis. The rationale is that week
days are generally characterized by similar source emission patterns.
A special program was developed so that various combinations of input
variables could be tried in rapid succession. Results of the application of
this program showed that no single parameter exhibited a pronounced effect
on the classification accuracy.
The next step involved eliminating groups of variables. The best re-
sults correspond to the case where all N02 inputs were deleted. The predic-
tion distribution for 9 a.m. with all NO- inputs deleted, is shown in Table
4.
It should be emphasized that the results of Table 4 were obtained on a
development sample, the accuracy of the meteorological variables being 100%.
When used on independent data (September), prediction accuracies between 65%
and 95% were obtained, depending on the hour of prediction. The 7 a.m. pre-
diction, perturbed by the high pollutant peaks during the morning rush hour,
exhibits the lowest accuracy. The total number of cases - 7 days with _> .1
ppm 03, 11 days below this limit - does not allow a significant statistical
19
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analysis of the results.
If this is what the utmost sophistication and resort to a corpjte*- car
accomplish, one should perhaps look at the other end of the scale ^cr a set
of predictors as simple as possible (Benarie, 1971).
As an episode severity criterion any 24-hour concentration larger DV a
factor of at least 2.0 than the running average over the 3G previous ciaxs,
was selected. The 30-day running average was considered as a fair approxima-
tion of the actual seasonal average.
An essential condition in defining the predictors was their general avail
ability through broadcast, i.e., not limited to the users connected by tele-
type to the National Meteorological Service. This condition limits not only
the number and kind of predictors, but also the time of their availability.
The latter if determined by the radio or the press, is several hours behind
the information dispatched to the teletype user. Finally, to establish an
air pollution forecast it should also be meaningful to the non-meteorologist.
The rationale behind the choice of the main predictor was that 24-hour
calm inversion conditions are seldom conducive to pollution episodes. Ac-
cording to the theory of BOUMAN and SCHMIDT 11961), confirmed by the Dec.
1952 episode of London, England and the Dec. 1959 episode of Rotterdam,
Netherlands, and by LAWRENCE'S (1967) analysis of several London episodes
and KOLAR's (1967) discussion of several others, concentrations increase
proportionally with time at the beginning of an episode, and grow proportion-
ally to the square root of time afterwards. During the first 24-hour period
of calm winds, twice the value of the running seasonal (previous 30-days)
mean is seldom attained, although it occurs with high probability if calm
conditions persist for a second day or more. In this way, the predictor set
becomes of utmost simplicity:
1. The observation of an elapsed period of 24-hours during which the
mean ground level wind velocity was less than 3.0 m s" .
2. A forecast of a similar situation for tomorrow.
This simple rule was checked at Rouen, France, during two additional win-
ters (BENARIE and MENARD, 1972) from October to March, i.e. 540 forecasts,
and is shown in Table 5. It appears from this Table that of the average 13
episode-days per winter, on the average 8 are correct even when the occasions
20
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of incorrect meteorological forecasts are included. If the latter are ex-
cluded in order to reflect more closely the real merits of the method, then
out of 28 episode-days only 3 were incorrect, that is around 10%.
Table 5 shows a total of 18 false alerts, of which roughly one half are
due to incorrect meteorological forecasts, while the other half are due to
the prediction method itself. Research is in progress to determine predic-
tors which will optimize the ratio between the two kinds of errors. Obvious-
ly a "broad predictor" would hit all the real episode-days, although addi-
tionally set off a great number of false alerts; a "sharp-predictor" would
avoid false alerts, but miss a number of real episode-days. But as things
now stand, meteorological error is the cause of 17 incorrect episode fore-
casts, while methodological ("choice of predictor") error is responsible for
only 14 failures. Until meteorology becomes a much more accurate science,
the search for more accurate predictors would quickly become one of steadily
diminishing returns.
This situation appears even more clearly, if Table 5 is re-interpreted
as a contingency table, that contains not only the (necessarily restricted)
number of episode-days, but the whole forecast period. Table 6 is such a
display for 523 days when no meteorological error occurred, indicating the
skill score of the predictor choice. Table 7 contains the whole period of
540 days and provides the skill score for the effectiveness of the forecast-
ing program when the meteorological error is included.
The forecast method was further tested during the 1970-71 and 1971-72
winters, in Strasbourg, France (BENARIE, unpublished) and produced the same
skill score. Its application to other sites seems possible, since the fore-
cast criterion is not the absolute value of wind velocity or some other
locally influenced value, but the duration of the stagnation spell.
Furthermore, a semi-quantitative relation can be found between the
duration of the calm and the concentration increase. For the winter season,
at Rouen, France, the following concentration factors were obtained by re-
gression analysis of the 1968/69 data ( = development sample): Table 8.
In each case these factors multiply the 30-day running average concentration
recorded at the same station.
The factors relate to surface wind and its duration and thus may be
suitable for general application: they were foreseen in the theory of BOUMAN
21
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and SCHMIDT (1961) and confirmed by the Rouen data; they also check well with
observations from other cities (LAWRENCE, 1967; KOLAR, 1969). BRINGFELT (1971)
found in Stockholm, Sweden, that during stagnation periods lasting 3-5 days,
the average SCL-level becomes 2.3 times the winter mean. The factors figur-
ing in Table 8. were further checked and found adequate for two more winter
seasons in Rouen and Strasbourg, France. The temperature factor is less
general, as it is an emission factor that is related to climate and space
heating habits. These factors which depend on wind direction are completely
local and linked to the source-receptor configuration (Rouen).
The factors provided by Table 8 were further utilized to obtain the re-
sults shown in Table 9 for the 12 forecast episode-days of the test-set
represented by the 1968/69 winter season. Four of the 12 forecast episode
days did not materialize.
Meteorological forecasts not being sufficiently detailed to justify:the
breakdown into factors on the day before the episode forecast, an average
multiplying factor of 2.0 was applied in each case.
The RMS error of the values using the actual meteorological data observed
_2
during the episode-days is 82 yg m ; the mean for 7 stations and 12 forecast
_3
episode-days is 187 yg m , i.e. a relative RMSE of 0.43. For the true fore-
_2
cast values (third line in Table 9), the RMS error is 87 yg m , corresponding
to a relative RMSE of 0.46. These figures are comparable and rather below
those generally attained by other mathematical models in the more favorable
case of day-to-day pollution calculations. It should be kept in mind, that
most models break down just in the stagnation-episode conditions where this
simple method seems applicable.
Continuing to test two more winters (BENARIE and MENARD, 1972) which
were outside the development sample, the relative RMSE obtained was 0.66,
somewhat larger than previously, but still below that for some elaborate
forecasting systems.
22
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SECTION 4
THE BOX MODEL
SHORT-TERM AVERAGES
This concept is much too well known to require discussion of the details
which will already be familiar to most modelers. Only a few general ideas
and some results will be mentioned. A very thorough discussion of the box
model was given by LETT All (1970).
1. Firstly we remember that the box model may be considered as derived
from the idea of the continuity of mass of a volume element, as used in the
advective transport equation. If the volume element becomes large enough so
as to include the whole urban area, or at least a major part of it, and if
diffusion can be neglected, then we are concerned with the so-called box
model represented by the simple formula:
X = cQA/u (1)
where QA is the source strength per area unit and u the local wind speed.
This appraoch almost coincides with the intuitive idea which is to
assume that pollution coming from an area source is completely mixed within
a box, which has its base at the ground, and its top at the limit of vertical
mixing L; in this case L~ = c (SMITH, 1961). Here we have the basic form
of the box model. The product uL is the ventilation rate, i.e., the flush-
ing rate per unit width of the box. In fact, the general idea of using a
simple proportionality between emissions and concentrations goes back at
least to the Leicester survey (UNITED KINGDOM, 1945). SHELEIKOVSKII (1949,
p. 97) also derived an equation of the form of Eq. (1). He took as the
source strength for particulates emitted by domestic space heating, the pro-
duct of the population density by an emission factor. Thus his concept
belongs to the long-term box models.
2. Another way of considering the problem was developed by GIFFORD
(1970, 1972, 1973), GIFFORD and HANNA (1970, 1973), and HANNA (1971, 1973a).
23
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It involves the integration in the upwind direction of a cross-wind infinite
line-source diffusion formula. GIFFORD and HANNA used the Gaussian version,
but other formulations, such as those based on Lagrangian similarity theory,
could be used just as well. The results tend to be not very sensitive to the
particular diffusion model employed, since according to the simplifications
that are made, only vertical diffusion is involved. The usual simple power
law
az = Bxb /2\
where az is the standard deviation, x is the downwind distance, and B and b
constants, is used to represent the standard deviation of the concentration
distribution in the vertical. The receptor point is assumed to be located
at the center of a source square. The lateral dispersion is neglected, so
that the concentration at a receptor at any time can only be influenced by
the (sum) of the upwind sources (GIFFORD 1959, CALDER 1969: "narrow plume
hypothesis").
Based on this line of reasoning, GIFFORD and HANNA concluded that the
area-source component of a stable, non-reacting pollutant species would be
adequately described by the following formula:
x =
QA
A
f
( 2i
L
(3)
B ( 1-b) u
where x is the pollutant concentration at ground level, u is the mean wind
speed, x is the source inventory grid spacing, and QA the source strengths
in the (N H- 1) upwind source boxes, i = 0, 1, N. The total ambient
air quality then follows by combining the contributions from Eq. (3), toge-
ther with the point-source contribution and Q0 , the background concentra-
tion. Eq. (3) is closely related to several area source formulas based on
the Gaussian model, particularly the study by CLARKE (1964).
In fact, Eq. (3) actually takes into account N advective steps, and so
by itself does not correspond to the simple box, but rather to the multiple
box category. At present we are concerned with the application of Eq. (3)
to a series of upwind boxes. However, if the wind direction changes, 1...N
may also be interpreted as the contribution of the l...Nth direction multi-
plied by its class frequency.
On a statistical basis and without considering what happens upwind
(here we depart from the source oriented, deductive argument) HANNA (1971)
24
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concluded that Eq. (1) is a good approximation to Eq. (3) with:
c = (~Y |{2N + 1 ) Ax/2 I -iBd-b}) (4)
Equation (1) may be considered as a box model whose lid height increases
downwind, according to Eq. (4). Since the quantity (1 - b) is quite small
and the product B(l - b) only vanes slowly in the stability range ordinar-
ily encountered over cities, the assumption that C = constant for a given
stability condition is quite reasonable. According to GIFFORD and HANNA, C
can be assigned the approximate values 50, 200 and 600 for unstable, neutral
and stable conditions. Since az = Bx in Eq. (2), it follows that
c « x/az (5)
It should also be pointed out that by combining Eqs. (1) and (5) we
obtain
x/Qa = ( 1/oz) (*/u) (6)
The quantity u/x is essentially what LETTAU (1970) terms the "flushing fre-
quency" in his exposition of the role of the box model of urban diffusion.*
3. The statistical argument put forward by GIFFORD and HANNA - a third
way to come to the box model - changes the nature of Eq. (1) from source-
oriented into receptor-oriented, and at the same time the formula becomes
a description rather than a deduction. Nevertheless, it is included in this
section so as not to disrupt the discussion of the box model.
4. MILLER and HOLZWORTH (1967), HOLZWORTH (1972) also treated the city
source as a continuous series of infinitely long cross-wind sources. Verti-
cal concentrations follow a Gaussian distribution and average unstable con-
ditions are assumed. The normalized concentration X/OA 1'n these circum-
stances is given by HOLZWORTH as
x/QA = 4.0 (x/u) 0-115 (7)
for x/u 10.47 L1'13 (L = mixing height) and if n£ pollutants achieve uniform
vertical distribution. However,
X/QA - 3.61 z0.13 + JL._
*See addendum
25
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for x/u^.0.47 and if some pollutants achieve uniform vertical distribution.
In most cases, the term with 0.088 coefficient is very small and can be
neglected.
HOLZWORTH (1972) presents tabulated values of X/OA as a function of L,
u and x (= + the distance the wind travels across the city), for the two city
sizes of 10 and 100 km. The smaller the values of L and u, and the larger the
value of x, the smaller are the relative difference between the x/QAva^ues
from HOLZWORTH's model and those from the box model. Thus HOLZWORTH's
approach may be considered as a fourth way to converge towards the box model.
The approximation depends here also (as with GIFFORD and HANNA's deduction)
on the vertical mixing.
5. Finally, we may note that a test of the theoretical approaches will
depend on the empirical determination of
a. the vertical pollutant profiles and
b. the horizontal mass balance of the box.
These were experimentally checked by HALPERN et al (1971); sulfur dioxide
concentrations were obtained from helicopter soundings in the New York City
area and vertical wind profiles by using pilot balloon observations. The
data of HALPERN at a.1 confirm that the mass balance expressed by Eq. 1 be-
tween emissions and ambient concentrations is a fair approximation in urban
areas.
Also, we may note the calculation of CO-concentrations by HANNA (1973a)
and their comparison with the observations at eight stations in the Los Angeles
basin, for the period 5 a.m. - 4 p.m., on Sept 29, 1969. These are presented
in Table 10. The concentrations are set initially equal to the 5 a.m. ob-
served concentrations.
The correlations at each station are of the same order as for other more
sophisticated models. The overall correlation coefficient from 6 a.m. to
4 p.m. for all eight stations, is 0.43. Obviously, in the computation of
correlation coefficient the 5 a.m. figures -- where identity of the calculated
and observed concentrations was assumed -- were omitted. The correlation af
any given hour over the geographical extent of the Los Angeles basin is un-
certain. It seems that in this case, with eight "boxes" centered on the eight
26
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stations, the theoretical basis of the box model has been stretched too far.
In the first place, the single box model is not meant to provide spatial
resolution and in the second, when a multi-box is used, as here, advection
must also play a role. It seems that we have here an illustration of the
principle, that lengthening the deductive chain by introducing more sophis-
tication (Here in the quest for spatial resolution) does not necessarily im-
prove the results, because at the same time we introduce an increased amount
of noise. When hourly means are taken at each hour over the entire basin
(last column of Table 10), it is seen that the calculated concentrations
are mostly too high, by a factor of two or even greater. The correlation
in this column is 0.74, significant at the ]% level.
Eq. 1 has been validated by HANNA (1971), and GIFFORD (1972, 1973) on
short-time concentration values for several urban areas. Table 11 is a sum-
mary of these validation results. For the comparison of the box model per-
formance with other models, the references should be consulted. It is a
personal opinion of the author's, that only models with similar amounts of
detail, as regards the input and the output, should be compared (BENARIE,
1975).
The discussion, as so often happens between protagonists of (simple) box
models and others pleading for more elaborate ones yielding a finer space-
time resolution, somehow misses its point. An analogy with road maps may
perhaps help to clarify the situation. A general map, say of 1 : 1,000.000
scale will give the distances among various points almost as exactly the
ten sheets of 1 : 100,000 maps pasted together. This is because the higher
precision of the latter will probably be destroyed by matching errors. Thus
the low resolution map may win, because it achieves the desired purpose
( = distance measurement) by far more economical means. But when it comes
to the intermediate resolution -- the 1 : 1,000.000 map has nothing comparable
to offer. In the same way, it is not fair to compare calculations by simple
box (or other space or time average) models with average values given by
higher resolution models. Lf the user only needs averages then it would be a
waste of money to search for high-resolution input and compute expensively
detailed estimates, only then to lump them together. On the other hand, if
the user asks for high-resolution data, even the best quality average estimates
27
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will not satisfy his needs.
Notwithstanding the attempts to mathematicize it on a Gaussian or other
basis, the box model is really rooted in the statistical validations advanced
by HANNA and GIFFORD. Only further testing and comparison with observed data
can show just how "good" the concepts are.
HANNA (1973 b,c) proposed the extension of the simple box model to chemi-
cally reactive pollutants.
The model seems fairly successful in the prediction of hourly variations
of CO, hydrocarbons and NO. However, it is inconsistent in its prediction of
N02.
SIMPLE BOX MODEL FOR LONG-TERM AVERAGES
Integral Application of the Box Concept to an Entire Urban Area
It was pointed out by GIFFORD and HANNA (1973, where further references
may be found) that if Eq. 1 is applied to yearly or seasonal, i.e., long-
term averages, the estimates for the pollutant concentrations compare favor-
ably with those obtained from other models. Writing Eq. 1 as
QTOT n x
X = c -— -O.a)
Au
where QTOT is the total yearly, seasonal . . . pollutant emission of the
source
A is the area within which the pollutant is being emitted
uf is the yearly, seasonal . . . average wind velocity; and using pub-
lished average urban pollutant concentrations, GIFFORD and HANNA obtained
Table 12.
The average value of c_ from the particle data is 202, and that for S02
is 50. The authors believe that a large part of this difference is caused
by the fact that Q™,. for SOp generally contains a much larger fraction of
emissions from tall-stack "point" sources, such as steam-electric power
plants, than does QjOT for particles. Eq. l.a. is designed to account for
point-sources only to the extent that they are low enough to be considered
part of the distributed area-source component. If all the contributions from
strong, elevated point-sources were removed, the two c_-values would probably
28
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be closer together. However, the necessary source data to make this correc-
tion is not included in the published reports.
While this reason, as advanced by GIFFORD and HANNA, certainly contributes
to enhance the difference between the c_-values, there may also be others.
Thus SCL-averages used do not seem to be representative. For example, it is
-3
not likely that the average SCL concentration in Detroit would be 16 ug m .
Even the averages listed in Table 12 for Denver, Buffalo, Kansas City, Mil-
waukee, seem below the usual rural averages. Another reason for the dis-
crepancy may be the transformation of the SOp into sulfates, thus reducing
the monitored SO^-concentrations. It is possible that if all these input
errors could be removed, Eq. l.a. would perform even more generally.
GIFFORD and HANNA (I.e.) tested Eq. l.a. on the particulate pollution
of 15 additional U.S. cities, obtaining the same range of c_ values as pre-
viously. BENARIE (1975) used Eq. l.a. in a reverse way, calculating from
it the yearly average mixing height, since c_ can be interpreted as the ratio
of the transport distance from the city's edge to the average mixing height.
Very plausible values were obtained for SCL, for the French cities of Rouen,
Paris, Strasbourg, Lyon, Bordeaux and Marseille, as well as for the Japanese
cities of Tokyo and Osaka.*
The relative success of the simple box model for long-time averages must
be attributed at least partially to the fact that all box or cell concepts
are based on the idea of the infinite vertical diffusivity inside the cell.
Taking long-term averages, the diffusion time may be neglected when compared
to the averaging time. Thus at least this requirement is satisfied.
Multiple Application of the Box Concept to an Urban Area
It was pointed out earlier that the box concept is the extension of a
single volume element over an entire urban area. As such, it is not meant
to provide resolution,and its specific advantages are linked to the proper-
ties of low resolution, when this is all that is required. GIFFORD and HANNA
(1970) applied the box concept to a source pattern in the form of a 1 by 1
km grid. This is obviously a hybrid case lying between the multi-cell and
box concept, and with the inherent difficulty of allowing for the influence
of the upwind and neighbcring boxes. GIFFORD and HANNA (1970) adopted a
*See Addendum
29
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simple step-wise scheme for wind directions other than the cardinal ones,
while THUILLIER (1973) in a pragmatic way made a subjective estimation of
the relative contributions of the upwind boxes for each county-size box
and each of the possible patterns. These relative contributions were then
multiplied by the annual recurrence frequencies of the patterns to obtain a
set of annual average contribution weighing factors.
A comparative (model-to-modelj validation of this multi-box model (with
some modifications) and some plume models, was made in a very relevant paper
by TURNER, ZIMMERMAN and BUSSE (1972). A subsequent model-to-model and
model-to-observed comparison was made by STROTT (1974) for Frankfurt, Germany.
As with the previous model-to-model comparisons, the computed concentration
isopleths exactly reflect the emission inventory for the area sources -- a
rather obvious result, for which no modeling should be needed. Quantita-
tively, the multi-box model strongly overestimated the concentrations. It
seems that the box model should not be overstretched to yield simplicity and
resolution at the same time.
30
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SECTION 5
CORRELATION WITH DEMOGRAPHIC PARAMETERS
The basic box model Eq. 1 requires proportionality between pollutant
concentration and the source strength per area unit. If the wind speed is
averaged over a whole year or even a longer period, this mean value is sub-
ject to only relatively slight changes. Hence Eq. 1 may be written:
x =- QA = c' QA .(Kb)
where Q^ is the source strength per area unit
jj_is a long-term average of the wind speed.
Relation l.b. was found graphically by PEMBERTON et al (1959) to hold
between the smoke* in Sheffield, Engl., and the number of electors per acre
in the district surrounding the sampling site. The authors considered as an
index of population density the number of electors per acre. On the other
hand, they assumed that domestic heating accounts for the major part of smoke
pollution and hence, the source strength per area unit should be represented
by the "elector per acre" index. It should be noted that although PEMBERTON
et al did not express the graphical regression algebraically, the "box model"
was proven in this way two years before its first mention by SMITH, in 1961.
In the analogous graph for sulfur dioxide, PEMBERTON et al did not find a
correlation. This may be explained by the fact that sulfur dioxide showed
higher average concentration near heavily industrialized areas with low or
moderate population density. Consequently, the population density in Shef-
field was not a good index for sulfur dioxide source strength per area unit.
The situation is somewhat different in Paris, France, where the contri-
bution of industrial sources to area source strength, is relatively smaller
than for Sheffield. As PELLETIER (1967) pointed out — Figs. 1. and 2. —
both smoke and sulfur dioxide show a strong correlation with population
density. It may be noted that population density, as obtained from census
31
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figures, is just a first approximation to source strength, but it works out
well within reasonable limits, inside comparable demographic entities.
Thus, PEMBERTON's and PELLETIER's linear regressions are not transpos-
able directly to differently structured areas. The per capita pollutant
emission may vary between wide limits, depending on the fuel use, nature of
heating devices and other factors. Population density may have a different
meaning in different countries, because census survey is done within admini-
strative limits that are not well defined emissive entities at the time of
origin.
PEMBERTON's and PELLETIER's approaches are regression methods. Instead
of meteorological parameters an index of source strength per area unit was
considered as an independent variable, linked to population density.
Another good predictor of pollutant concentrations, is the total popula-
tion of the urban area. In the United States, concentrations of suspended
particulate matter were associated with urban population and this is pre-
sented in Table 13. Although this table does not fit a linear regression,
portions of it may be approximated linearly, as for example:
x(M9m-3) = 45logP-145 (9)
where log P is the common logarithm of the population.
This seems to represent fairly well the important 50,000 to 500,000 popula-
tion range. Thus we may have an extremely cheap way to estimate, within a
range of 50%, the yearly average of the particulate concentration of an urban
area, provided that climatology, fuel use, traffic conditions and population
density are about the same as in the Continental U.S. BOLIN et al (1971)
reported a similar relationship to Eq. 9 for Swedish cities.
Statistical correlations for 23 cities, ranging in population from
100,000 to 2 million, were run by CARTER (1973) and by CARTER and NELSON
(1973). Using the correlations between the pollutant emissions and the
demographic factors of population, number of passenger vehicles registered
by county, and the percentage of the work force employed in manufacturing, a
linear modeling technique describes the future air pollution emissions of a
city by size and the growth of the emissions.
32
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SECTION 6
CONCENTRATION FREQUENCY DISTRIBUTION
THE LOG-NORMAL REPRESENTATION OF CONCENTRATIONS
The histogram of urban air pollutant concentrations sampled over any
given time span (1 minute, 1 hour, 24 hours and so on) is quite skew. There
are only a few near-zero values, but afterwards the frequency increases
sharply, only to decrease again gradually towards the higher concentrations.
A large number of skew distribution functions known in statistics can be
fitted to such data: Poisson (WIPPERMAN, 1966), negative binomial (PRINZ and
STRATMANN, 1966), Weibull (BARLOW, 1971), exponential (BARRY, 1971, SCRIVEN,
1971), gamma ( = Pearson IV), beta (= Pearson I) and Pearson IV (LYNN, 1972).
None of these has enjoyed the practical success and the wide acceptance of
the lognormal distribution. POLLACK (1973, 1975) demonstrated that there is
a fundamental similarity among these distributions utilized to fit air qual-
ity data.
As early as 1958, it was empirically shown that cumulative frequency
distributions of suspended particulates at CAMP (urban) sites fit remarkably
well a straight line when plotted on log-normal paper (U.S.D.H.E.W., 1958).
Pronounced tendency towards log-normalcy of particulate concentrations was
also observed by ZIMMER et al (1959) and by GOULD (1961). LARSEN (1961)
extended this representation to carbon monoxide and ZIMMER and LARSEN (1965)
to carbon monoxide, hydrocarbons, nitric oxide, nitrogen dioxide, oxidant
and sulfur dioxide and to the main urban areas of the U.S.A. From this point
on, the lognormal plotting gained almost exclusively amongst the graphical
and functional representations of air pollution concentrations, and the num-
ber of papers and reports that make use of it is in the hundreds.
Considerable theoretical (GIFFORD, 1972; KNOX and PCLLACK, 1972; KAHN,
1973) and empirical (BENARIE, 1970) support exists for the lognormal distri-
bution, as the most appropriate for characterizing both reactive and inert
33
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pollutant concentrations for a wide range of averaging times. These argu-
ments were systematized and publicized by POLLACK (1973, 1975), although
overwhelming acceptance of the log-normal representation was a fact long be-
fore theoretical proofs became available. Some of the reasons for this
acceptance are:
1. The lognormal distribution is a relatively simple two-parameter dis-
tribution. Both parameters have easy-to-grasp physical meaning.
2. Convenient plotting paper and methods are available; the user does
not have to resort to lengthy numerical calculations. The two parameters are
easily read off the graphs.
3. The lognormal function has some mathematical properties (see AIT-
CHINSON and BROWN, 1969) which make its use very easy. Standard statistical
tests, mostly requiring a normal distribution of the population, may readily
be applied after the logarithmic transformation which is automatically pro-
vided by the plotting.
Inhomogeneous source distribution around the measuring site may lead to
deviations from the lognormal behavior (BENARIE, 1970). JOST et al (1974)
have attributed this reason for the occasional departures from lognormalcy
observed in Frankfurt, Germany.
Objections of a theoretical nature may be raised against the log-normal
representation of pollutant concentrations (BARLOW, 1971; MILOKAY, 1972;
MARCUS, 1972). These arguments mostly consider the extreme values, like zero
values of the pollutant concentrations. It should be realized that such
(theoretically important) concentrations are ordinarily below the sensitivity
threshold of the measuring instruments, which therefore introduces a thres-
hold parameter. The practical advantages of the log-normal representation
are full justification for its wide-spread use in air pollution engineering.
AVERAGING-TIME ANALYSIS
LARSEN (1964), ZIMMER and LARSEN (1965), LARSEN et al (1967), LARSEN
(1969, 1973, 1974) plotted by computer -- the first paper for a period of
one year, and the last for up to a seven-year period -- the concentration
frequencies as a function of averaging time for: carbon monoxide, hydro-
carbons, nitric oxide, nitrogen oxide, nitrogen oxides (NO + N02), oxidants
34
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and sulfur dioxide for the CAMP sites in downtown Chicago, Cincinnati, Denver,
Los Angeles, Philadelphia, St. Louis, San Francisco and Washington. These
plots have been called "arrowhead diagrams" by STERN (1969). They may be
characterized by the following properties:
1. Concentrations are lognormally distributed for all averaging times.
2. Plotted on a (log averaging time) - (log concentration) diagram, the
points representing a given percentile (frequency) are aligned almost on a
straight line.* Hence, at constant frequency, concentration is proportional
to averaging time raised to a constant power.
3. The 30 percentile is close to the arithmetic mean concentration.
The exponent (see above) is only a little different from zero, so that the
30 percentile and the arithmetic mean only vary slightly for all averaging
times.
4. For the longest averaging time calculated (usually one year), the
arithmetic mean, geometric mean, maximum concentration, and minimum concen-
tration are all equal (and thus plot as a single point).
5. For averaging times of less than one month, maximum concentration is
approximately inversely proportional to averaging time raised to an exponent.
The maximum concentration is that corresponding to the 1/n frequency point
(n = number of samples, e.g., 8760 hourly samples per year) on the linearly
extrapolated cumulative diagram.
Potential reasons for characteristic 1 above were cited by BENARIE
(1970), GIFFORD (1972), KNOX and POLLACK (1972) and KAHN (1973). Properties
2 and 3 are the most important experimental findings based on the analysis
of the CAMP-results mentioned above. Property 4 is a necessary consequence
of the averaging process. SINGAPURWALLA (1972) has cited possible reasons
for the property 5. McGUIRE and NOLL (1971) verified the relationship be-
tween maximum concentration and averaging time, for five different air pollu-
tants at 17 California sites in Los Angeles and San Francisco. The exponents
are wrthin the range observed by LARSEN.
*The f and the 1-f frequency loci are in fact asymptotes of parabolae.
The vertices of these parabolae are located at the one-year arithmetic
average point. The nearer to this point, the greater the deviation from a
straight line (Personal communication of Dr. LARSEN).
35
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The main consequence of this concept is to interrelate short- and long-
averaging times in a descriptive, statistical, and receptor-oriented way.
Therefore, in the systematics embodied by Table 2, the concentration fre-
quency distribution model belongs under both the headings short- and long-
term (however, receptor-oriented). But there may exist a possible source-
oriented extension, as noted by STERN (1969): 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 synthetize 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. The concentration versus averaging time and frequency diagram might
have as its components the weather factors and the source factors. The
analysis of the source factor arrowhead chart 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 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 spectrum. This should give us useful leads to control
strategies.
In the papers cited (mainly those of 1969, 1973 and 1974), LARSEN pro-
vides examples for interrelating air pollutant effects, air quality standards,
air quality monitoring, diffusion calculations, source reduction calculations,
and emission standards.
In the same papers, LARSEN published extensive tables -
1. interrelating the ratio of expected annual maximum pollutant concen-
trations to arithmetic mean concentrations for various averaging times and
standard geometric deviations, and
2. the slope of the annual maximum concentration line for various stand-
ard geometric deviations of the one-hour frequency plot.
With the experimental arrowhead diagram at hand, the expected annual
maximum, or the slope of the line linking it to various averaging times, or
36
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to any other parameter of interest, can be read off at least as easily as
would be their readout from tables or numerical calculation.
37
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SECTION 7
WIND AND CONCENTRATION RELATIONSHIPS
It is evident that pollutant concentration distributions are only the
footprints of the windfield. At the same time, it has been observed that
the logarithmic normal function is a convenient empirical representation of
the wind velocity distribution (BENARIE, 1969). The fact that we are con-
cerned at this point with a rough approximation appropriate to the argument
that follows below -- without pretending to describe general physical pro-
perties of the wind -- was stressed in the Appendix and a subsequent discuss-
ion of a paper by BENARIE (1972).
Using numerical simulation, for area sources represented by n point
sources, BENARIE (1971) obtained fair approximations to the log-normal dis-
tribution, provided that n >_ 10 and that the geometric means and standard
geometric deviations of the component log-normal functions were randomly dis-
tributed. The conditions under which the sum of n lognormal variates is
approximately lognormal for a limited number of variates in the sum, have been
previously formulated by MITCHELL (1968). BENARIE's (1971) paper supports
the empirical observations that pollutant concentration for all cities and
for all averaging times is approximately lognormally distributed (Section 6)
as a consequence of the (approximately) lognormal windfield, but the paper
does not quantitatively link the lognormally distributed windspeeds to urban
pollutant concentrations.
This link was accomplished in an elegant way by KNOX and LANGE (1974),
who noted that the basic box model Eq. 1 suggests that frequency distribution
of the wind speed determines the frequency distribution of the normalized
concentration x/^A where x is the surface air concentration of the pollutant
and Q. is the unit area source strength provided that c (the proportionality
constant) is nearly independent of frequency. In principle, for the cases of
good frequency correlation between x and U~ at a given sampling station, the
38
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constant c1 = cQ. can be found through graphic superposition of the observed
and predicted distributions. In this case, no direct knowledge of the
source strength Q. is required.
The normalization constant c1 for the 50 percentile point, is obtained
from the superposition of c'/U distributions on the corresponding observed
x distribution curves. For the CO-values observed at the building of the
San Francisco, California Bay Area Air Pollution Control District during the
year 1966, c1 was found to equal to 7.5 ppm m s" and with 1970 data, 7.4
ppm m s~ . The average value c1 = 7.45 was used as an experimental normali-
zation factor in Fig. 3.
Instead of using observed x values, c1 may also be estimated by the
values calculated on basis of the means of some model. For this purpose,
KNOX and LANGE used McCRACKEN et al's (1971) multi-box model. Since charac-
teristic times in this model are of the order of one hour (box dimension/
wind speed), the concentration values can be interpreted as hourly averaged
values.
This model was used to predict the CO concentration for a 48-hour period,
July 10-11, 1968. Fig. 4 shows the observed wind speed frequency distribu-
tion for this period as obtained by the U.S. Weather Bureau on top of the
11-story San Francisco Federal Office Building. This frequency distribution
is quite closely lognormal. Fig. 5 shows the observed and the model pre-
dicted CO concentration frequency distributions. The predicted concentration
distribution XpR has the same slope as the observed distribution XQB, and
a geometric mean 20% above that observed. The normalization factor c1,
as derived from this model with the data from Figs. 4 and 5 is c1 = xpR
(50%)(i(50%) = 1.6 x 5.7 = 9.1 ppm m/sec. Fig. 6 shows how the distribution
curves shift when we use this Bay Area model derived normalization factor
c1 = 9.1 on the date of Fig. 3.
It is of interest to note, that an experimental value of c1 could also
be computed from the observed wind speeds and the observed concentrations
XQD used as a basis for the 48-hour period in the Lawrence Livermore Labora-
tory air pollution model study. This factor obtained from Figs. 4 and 5 is
c1 = XgB(50%)U(50%) = 1,3 x 5.7 = 7.4 ppm m/sec, which agrees well with the
39
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experimental c1 = 7.45 discussed previously for the 1966, 1970 annual distri-
butions. The fact that the mean annual normalization constant can be deter-
mined so well by considering only a two-day period indicates that the 48-hour
period may be sufficiently long to give a good average of the CO source varia-
tion in the city. This is not surprising, if one remembers that the main
source of CO is the daily automobile traffic. In other words, to find a
regional normalizing factor c' for an annual mean concentration frequency
distribution, a model need only cover the longest basic time period of any
time-dependent sources or sinks involved, just so long as this period is
typical.
40
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SECTION 8
VALIDATION - OR THE WAYS TO DELUDE ONESELF
It is the proper function of the statistician (and I am not one) to pro-
nounce on the merits of chi square, skill score, correlation, RMS and abso-
lute error, and a host of other measures of goodness-of-fit. I am sure that
everybody knows all about the computation of these indices and so, in prin-
ciple, nobody needs my advice about the fact that any one goodness-of-fit
index may be misleading. Nevertheless, I cannot resist the temptation to
illustrate this point by just one example.
Table 14, in its second column, shows the results of a model calculation,
(LAMB, 1968, based on the concept of mass transport balance taking into con-
sideration chemical reactions) although the nature of the model and the
method of calculation does not concern us here. This model was taken as an
example, since it is rather often quoted as a reference. Along with the
calculated values, a "random" estimate (Column 4) and a "constant" (average)
estimate (Column 5), are presented in Table 14. To obtain the random esti-
mate, monotonically increasing values from 0 to 17 ppm were assigned, in
alphabetical order to each station. As for the last column, values of 14 and
13 (to avoid fractional values as the true mean is 13.5 ppm) were assigned
alternately. Incidentally, 13.5 ppm is not only the average of the first
column but also a very likely average figure for many urban areas with auto-
mobile traffic anywhere in the world.
The entries that give the root mean square error (RMSE) are a caution
against validation by just one statistical criterion. The model shows a
higher RMSE than the (almost) random or the constant value guesses. The
correlation coefficient entry rectifies this situation. The constant esti-
mate -- a parallel line to the abscissa axis — shows as expected, no corre-
lation with the observed values. The model's correlation attains the 5%
significance level for 11 degrees of freedom. However, even the random
41
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guess presents a correlation which could not be entirely rejected. It
should be noted that this "guess" is not completely at random, but rather
an educated guess, since the lowest and highest values are linked to some
knowledge about the concentrations which might actually be observed.
This simple and somewhat superficial example can be generalized and pro-
vides a warning against some of the pitfalls. The lack of representativeness
for any single goodness-of-fit index has already been mentioned. A second
point is that pure chance can frequently produce a fit which is not too bad,
provided that the series to be fitted is short and the span of the estimation
limited. A third point, also linked to a limited span of possible values, is
that judged by the RMS error, the mean is often a very good bet -- better
than most calculations. Finally, no validation should be presented without
a comparison with the random estimate (the skill score does just this).
42
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SECTION 9
CONCLUSION
The guiding idea in the present paper is to recommend the use of models
which correspond with the utmost parsimony to the end result which has to
to attained. Thus, high resolution, sophisticated models should only be used
when high resolution output information is really needed. For long-term,
low-resolution purposes, we frequently have fully adequate, low-cost models.
It is not a safe procedure to obtain long-term, low-resolution informa-
tion by integration from short-term, high-resolution estimates. As the chain
of reasoning lengthens, unavoidable noise is being introduced at each step.
The end result often is that the long-term estimate obtained in this fashion
is less reliable than one obtained by some "computer-less" shortcut. Also,
it has been shown that, for forecasting purposes, models that involve a very
large number of modeling steps must perform less well than those involving
simpler chains.
Finally, brief warning was given against validations based on a restric-
ted number of narrow-span values and the use of a single goodness-of-fit
index.
43
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46
-------
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47
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48
-------
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49
-------
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50
-------
I
-------
52
-------
100
E
Q_
O_
C
o
X
o 1965
D 1966
x 1967
1970
Observed annual hourly CO concentration X
v iy/u ;
I Experimentally predicted annual hourly
CO concentration ———
i ppm - m
C - 7.45
sec
12 5 10 20 30 40 50 60 70 80 90 95 97
Percentage of time ^ or C /U is exceeded
Figure 3. Observed and experimentally predicted annual hourly CO
concentration distribution for San Francisco.
-------
T 1 T
IT)
CN
C -
CD
0) —
C
o
.
4—
c
CL»
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4.0
1.0
E
Q_
Q_
0.1
Bay Area Model
, predicted concentration
, observed concentration
1
10
20 30 40 50 60 70 80
90
Percentage of time X was exceeded
Figure 5. Observed and predicted hourly CO concentration distribu
tions for San Francisco, July 10-11,1968.
55
-------
100
E
o_
o_
o 1965
D 1966
x 1967
v 1970
Observed annual hourly CO concentration \
I
Predicted annual hourly CO
concentration
C -9.1
C1
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- m
sec
\x\
-U
-o
C
0
X
106- \< ^
1
10 20 30 40 50 60 70 80 90 95 97
Percentage of time x or C /U is exceeded
Figure 6. Observed and model-predicted annual hourly CO concentra-
tion distribution for San Francisco.
56
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-------
Table 4
Contingency table of the ozone prediction
results on the training set by RUFF (1974)
Predicted 03 Total
Measured 0~ l.p.p.m 1 p.p.m
I p.p.m 25 4 29
1 p.p.m 1 10 11
Total 26 14 40
Skill score with the training set,
N02 deleted : 0.75
60
-------
Table 5
Breakdown of the episode forecasts for 540
forecadts (3 winters) for Rouen, France, after
BENARIE (1971) and BENARIE and MENARD (1972)
Winter Number of Out of these forecasts An episode was
episode forecast, but did
days Correct Incorrect not materialize
due to in- due to
correct incorrect
meteorolo- meteorolo-
gical gical
forecast forecast
68/69
69/70
70/71
Total
8
11
19
38
6
7
12
25
2
1
0
3
0
3
7
1O
1
3
7
11
3
3
1
7
61
-------
Table 6
Contingency table of the forecast results obtained
by BENARIE (1971) and BENARIE and MENARD (1972) with
apparent meteorological forecast error removed :
523 cases out of the total of 540.
N° episode
P r e d
N° Episode Obser- 484
ved
Episode 3
Total 487
Episode
i c t e d
11
25
36
Total
495
28
523
Per cent
correct
97.5
- 90
Skill score : 0,76
62
-------
Table 7
Contingency table of the forecast results obtained
by BENARIE (1971) and BENARIE and MENARD (1972),
overall results for 540 cases
N° episode Episode Total Per cent
Predicted correct
N° episode Obser- 484 18 502 94.5
ved
Episode 13 25 38 67
Total 497 43 540
Skill score : 0.60
63
-------
Table 8
Multiplying factors to be applied to the 30-day running
average to obtain winter episode concentration in ROUEN
France.
Condition Factor
Mean surface wind
_ it _
_ H _
_ it _
_ it _
Mean temperature below -
Wind blowing from 00° to
Factor for
Factor for
3ms for 24 hours
1ms"1 - " -
0.5m s'1 - " -
-1
0.5m s second 24 hour
0.5m s~ third 24 hour
3°C
80° direction
downtown
"Petit Couronne" station
1.5
2.0
2.5
3
3.5
1.5
1.3
0.7
Wind blowing from 260° - 280° direction,
at 4-7 m s~~ , only for the 2.0
"Petit Couronne" station.
64
-------
Table
Comparison of observed (first of each group of three lines)
data, calculated from the virtually occuring meteorological
data (second lines) and forecast, using forecast meteorological
data (third lines) for seven sampling stations in ROUEN, France
winter 1968/69
Factors for
Wind Temp. Direc-
speed tion
Mean 9Nov-8Dec.
9Dec.
IQDec
UDec
12Dec
Observed
Calc.a posteriori 1.5 0.5
Forecast
Observed
Calc.a posteriori 1.5 0.5
Forecast
Observed
Calc.a posteriori 1.5
Forecast
Observed
Calc.a posteriori 2 1.5 0.7
Forecast
Mean 3ONbv-29Dec.
30Dec
31Dec
Uan.
Observed
Calc.a posteriori 2.5 0.7
Forecast
Observed
Calc.a posteriori 2 1.5
Forecast
Observed
Calc.a posteriori 2
Forecast
Mean 24Dec-22Jan.
23Jan
24Jan
Observed
Calc.a posteriori 2
Forecast
Observed
Calc.a posteriori 2
Forecast
Mean 5jan-3Fev.
(Observed
4 FebfCalc.a posteriori 2
[Forecast
(Observed
5 FebfCalc.a posteriori 2
(Forecast
Mean 18jan-16feb
(Observed
17feb[Calc.a posteriori 2
(Forecast
SS
8
102
103
76
102
119
76
2O4
212
153
204
261
214
204
100
169
175
200
367
300
200
346
200
200
117
211
234
234
145
234
234
97
207
194
194
171
194
194
130
198
260
260
SS
15
102
137
76
102
137
76
204
242
153
204
274
214
2O4
99
143
173
198
352
297
198
358
198
198
110
202
220
220
148
220
220
88
226
176
176
208
176
176
126
180
252
252
Pref.
52
56
39
52
42
39
1O4
193
78
1O4
126
1O9
1O4
46
102
81
92
271
138
92
296
92
92
67
1O4
134
134
42
134
134
54
192
1O8
108
149
108
1O8
78
109
166
166
Sott.
101
133
76
101
111
76
202
377
151
202
218
212
202
121
157
212
242
(360)
362
242
(360)
242
242
131
225
262
262
1O1
262
262
102
306
2O4
204
261
204
2O4
145
(298)
290
290
Fac.
86
106
65
86
52
65
172
127
128
172
286
180
172
75
205
131
150
(214)
235
150
(214)
150
150
30
150
160
160
65
160
160
73
110
146
146
112
156
146
82
(108)
164
164
Mar.
82
131
62
82
80
62
164
136
123
164
323
172
164
92
175
161
184
(236)
276
184
(236)
184
184
103
94
206
206
66
206
206
84
190
168
168
130
168
168 '
95
(115)
170
170
Pt-
Cour.
66
97
50
66
82
50
132
255
99
132
148
138
132
96
86
167
192
256
288
192
188
192
192
105
128
210
210
284
210
210
161
214
322
322
170
322
322
186
226
372
372
Note. The bracketed observed values correspond to 3 days' sampling and were
not taken into consideration for the computation of the RMS error.
65
-------
0
rH
0)
rH
Q
C -
O CTl •
o VD e
CTl •
1 rH fd
O CTI in
U CN
m M -P
O 0) -H
• 3»
Q) 01 T3
3 -P 0)
rH Q, N
(tt 0) -H
rd
>i C -H
rH O -P
D - C
O C -H
A -H
01 0)
VH 18 r<
O 03 10
01 01 01
d 0) c
O rH O
iH 01 -H
•P &> -P
O C O
iH rfj iH
Tj *O
r-oo^O'Hcgro
<~H rH rH rH
F— 1 CNJ OO rH ^D LO ^34
^* o^ ro o^ ^* ^o .
o
00 CN i-H
co CM in
? ? ?
CTl
VO
rH rH 00 rH 00 Q
in VD VD oo o
CTl
i-H
co in co in in r~ X
CN CN u
CTl
in in in in in T Q
j
T rH T IT) TJ- rH °°.
rH I-H l-H Q
T
CO rH CO OO T CO •
1-1 O
co
co
CTi CO VD CO VO CO Q
00
co co CM ro VD co o
• d • d • d
W rH W rH W rH
S3 S3 S3 gt-
•H 3
-P -H
(d U
T in VD "m ijll
• ^j _. W J*~*
S
O U
66
-------
Table
11
Validation of the simple box model,
according to HANNA (1971) and GIFFORD
(1972, 1973).
City
CHICAGO
CHICAGO
LOS
ANGELES
SAN
FRANCISCO
LONDON
Concentra- Period
tion value
modelled
Point 24 hours
(for 18
days)
Point 6 hours
(for 4
days)
Point 1 hour
(for 17
hours
Point 1 hour
(for 48
hours)
Area 24 hours
average average
Pollutant Correlation
coefficient
S02 .67
S02 .66
CO .89
CO .74
S00 .76
67
-------
TABLE 12.DATA RELATED TO PARTICLE AND SO* POLLUTION FOR U.S tints*
City (1) (2) (3) (4) (5) (6) (7) (8)
Washington
New York
Chicago
Philadelphia
Denver
Los Angeles
St. Louis
Boston
Cincinnati
San Francisco
Cleveland
Pittsburg
Buffalo
Kansas City
Detroit
Baltimore
Hartford
Indianapolis
Minneapolis-St. Paul
Milwaukee
Providence
Seattle-Tacoma
Louisville
Dayton
Houston
Dallas-Ft. Worth
San Antonio
Birmingham
Steubenville
247
1795
1780
1168
29
187
662
428
349
174
818
934
410
125
786
255
337
164
215
242
118
225
303
186
144
16
2
33
638
35
243
586
231
29
101
176
74
73
102
304
387
140
60
240
104
56
78
46
100
23
33
128
174
158
52
129
205
155
7.5
8.2
7.3
7.8
6.3
5.1
6.5
8.0
6.2
5.4
7.4
7.1
7.6
7.3
7.3
7.5
8.1
6.8
7.5
7.5
8.3
5.5
6.6
7.0
6.6
7.0
6.5
5.9
6.1
775
2330
2590
4400
260
1035
595
775
905
1035
650
4815
620
390
1035
200
465
415
775
775
155
260
620
1035
620
570
630
520
520
72
98
139
124
117
114
161
83
122
73
106
140
116
97
143
133
81
146
88
95
113
79
121
116
67
96
68
128
173
412
265
154
634
227
205
122
240
323
138
57
426
135
158
155
67
188
182
384
191
218
117
133
166
60
253
75
66
121
90
346
221
217
18
—
132
—
44
—
78
93
25
12
16
107
62
54
44
28
125
35
—
49
—
—
—
—
—
58
128
81
218
35
—
27
—
24
—
16
117
10
10
5
22
24
32
41
23
47
7
—
66
—
—
—
—
—
Average 441 146 7.0 1027 111 202 90 50
* Column legends:
(1) QTOT, SO,, 103 tons yr"1, FENSTERSTOCK et al (1969); 103 tons yr"1 = 28-73 g s-1;
(2) QTOT, particles, 103 tons yr"1, FENSTERSTOCK et al. (1969);
(3) u, m s-1, FENSTERSTOCK et al. (1969);
(4) Approximate area, km2, enclosed by 0.1 tons day1 mi'2 urban particulate source, estimated
from Reports on Consultation, U.S. DHEW (1968-1969);
(5) Observed average concentration, X, of particles, /*g m~3, FENSTERSTOCK et al. (1969);
(6) c (dimensionless) for particles, using equation (2) and cols. (2, 3, 4 and 5);
(7) Observed average concentration, X, of SO,, /*g m~3, from U.S. DHEW (1968);
(8) c (dimensionless) for SO,, using equation (2) and cols. (1, 3, 4 and 7).
68
-------
fc
o
NH
-H HH 4.
u H e
Q 2 .0
g H «
t^ J2J +3
«B g
55 C
O ®
CQ ?r w
ofirH
rH rH
O O O>
OO -4->O»
§O w*
** t—
O O O)
0
V
09
O
C
.2
3
a
o
PL,
c^
CM
rH
T~
j
^
CO
A
00
00
^H
C^
fi
^c
"i
CO
T—
t> Ci O O CC
rM o oo la
»-H rH Tj*
10
0
t"" OO O) CO rH ^>1* ^*
rH Oi O> t- «O Tj<
1 TH CO CO 1
1 i
l 1
1 1
rH CM rH CM rH
rH CO »O rH CO CM
rH CM rH
' «O t- CM O U5 CM
1 r-i rH rH
l
1
CM "3 T* «D CM O» rH
CM rH rH rH
i ^J< O 00 CM Cft U5
1 CO CM rH rH rH
l
1
i-H t- O -^ OO C-
CM CM rH
CO ^^ ^f^ t* tf^
^^
fi 0 0 0
.2 o o o o o o
ZS 0 O 0 0 0 0
Booo°.°.°.
S 0 0 0 0 10 O
T* i T T i i \/
t- O O O U5 O v
• O O >O CM r- 1
O ••* rH
I— I
o
t-
00
<£>
rH
_.J
r^
CO
CM
us
a>
t-
00
o
rH
t-
t-
C^
CM
••4
1"^
C
cd
XI
J2
73
"o
o
o
^
gf
o
c
o
•r"N
-4->
rt
3
^»
o
u,
rS
"§e
09
C3
£
CU
" W
•4-1
O
H*
0
• •— «
c
s
cd
T5
V
ts
O
8
t-H
69
-------
Table 14
Computed CO-concentrations (17 hour day-averages, ppm)
compared with the observed values for Sept. 23, 1966, of
the Los Angeles Basin.
1 2
Stations Observed
concentra-
tion
Downtown LA.
Azusa
Pasadena
Burbank
East IA
West IA
Long Beach
Hollywood
Pomona
Lennox
Anaheim
La Habra
BMSE
Correlation
Coefficient
a
b
16
13
17
16
12
16
14
17
13
13
9
6
3
Computed
(LAMB, 1968)
22
3
15
7
5
13
8
7
3
11
7
3
6.8
0.55
0.32
10.7
4
Random
9
7
15
8
10
17
14
11
16
13
6
12
4.7
0.25
0.23
1O.8
5
Mean 13.5
14
13
14
13
14
13
14
13
14
13
14
13
3
0
0
13
.2
.00
.00
.5
a and b refer to the coefficients of the regression equation
Computed cone. = a (Observed cone.) + b
70
-------
ADDENDUM
P 25 After Lettau reference add:
Instead of the integration of the Gaussian infinite line source,
GOUMANS and CLARENBURG (1975) considered a large number of randomly
distributed point sources over the area and a Sutton-like plume
formula. Their computational formula is equivalent to that proposed
in 2. above (GIFFORD and HANNA 1976)
P 29 After line 19 add:
Calculation of seasonal means by GOUMANS and CLARENBURG (1975) for
The Hague and Amsterdam (Netherlands) show a very good fit with
the observed values
P 46 Add to References:
Goumans, H.H.J.M. and L. A. Clarenburg, 1975: A simple model to
calculate the SCL-concentrations in urban regions. Atmos. Env. 9_,
pp 1071-1077 ^
Gifford, F. A. and S. R. Hanna, 1976: Discussion to the paper of
Goumans and Clarenburg, Atmos. Env. 10, p 564
7 1
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/4-76-055
3. RECIPIENT'S ACCESSION'NO.
4. TITLE AND SUBTITLE
5. REPORT DATE
November 1976
URBAN AIR POLLUTION MODELING WITHOUT COMPUTERS
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
Michael M. Benarie
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
10. PROGRAM ELEMENT NO.
1AA009
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
13. TYPE OF REPORT AND PERIOD COVERED
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
Inhouse
14. SPONSORING AGENCY CODE
EPA-ORD
15. SUPPLEMENTARY NOTES
Prepared by Visiting Scientist
16. ABSTRACT
This report was the basis for a series of three lectures by the author
on urban air pollution modeling, and represents a condensed version of selected
topics from a recent monograph by him. The emphasis is on simple but efficient
models that often can be used without resorting to high-speed computers. It is
indicated that there will be many circumstances under which such simple models
will be preferable to more complex ones. Some specific topics included in the
discussion are the limits set by atmospheric predictability, forecasting pollu-
tion concentrations in real time as for pollution episodes, the simple box model
for pollution concentrations, the frequency distribution of concentration values
including the log-normal distribution and averaging-time analysis, the relation-
ships between wind speed and concentration, and lastly the critical question of
model validation and the need to consider several indices of goodness-of-fit if
pitfalls are to be avoided.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COS AT I Field/Group
* Air pollution
* Meteorological data
* Mathematical modeling
* Model tests
13B
04B
12A
14B
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThisReport)
UNCLASSIFIED
21. NO. OF PAGES
82
20. SECUR
22. PRICE
EPA form 2220-1 (9-73)
72
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