A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENTT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
August, 1966
A MIULTIVARIABLE ATMOSPHERIC
DISPERSION MODEL
By
JOHN BERNARD KOOGLER
Copyright by
John Bernard Koogler
1966
ACKNOWLEDGMENTS
The author would like to express his appreciation
to the persons who assisted with this project and to those
who helped further his education while at the University
of Florida. These include his committee members, Dr. E. R.
Hendrickson, Dr. R. S. Sholtes, Admiral A. L. Danis, Dr.
C. I. Harding, and Dr. A. P. Black. Special gratitude is
due Admriral Danis for his advice and his interpretation of
the meteorological data. The author appreciates the sug
gestions and assistance of Dr. Sholtes and Dr. Harding in
gathering information and data for the preparations and test
ing of the dispersion model and is appreciative of the
personal assistance from Dr. Sholtes during the final stages
of this work. The cooperation of the resident staff of the
Duval Air Improvement Authority is also greatly appreciated.
Acknowledgment is made to Mrs. Eileen Brand for
typing and editing this manuscript, to Dr. F. Barnett of
the Statistics Department for assistance in the statistical
aspects of the dispersion model, and to pDersonnel at the
University of Florida Computing Center for programming sug
gestions.
iii
The author would also like to express his gratitude
to the Division of Air Pollution, Bureau of State Services,
United States Public Health Service, for sponsoring his
studies at the University of Florida.
TABLE OF CONTENTS
Paage
ACKNOWLEDGMENTS ..........
LIST OF TABLES. ..........
LIST OF FIGURES ..........
ABSTRACT. ....... ....
. . . i
. .. .. . .yti
.. .. .. x
. ... .. .. xiii
CHAPTER
I. INTRODUCTION. .........
The Air Pollution Problem ..
Review of the Literature. ..
Historical. ........
General dispersion. ....
Dispersion over rough terrai
urban areas .......
The effect of sampling time
dispersion parameters ..
Plume rise equations. ...
Dispersion models.....
Summary........ .
. 1
.1
.3
.3
S8
n and
on
. .
. . 12
II. PURPOSE A9ND SCOPE. .......
III. THE MODEL ......
. . .
General Description .
Time scale. ......
Spatial scale .....
Meteorological factors.
Sources ........
Mathematical Equations. .
. . .
. . .
. . .
. .
. .
Pagre
CHAPTER
Programming Logic .. .. .. .. .. 56
Effect of an areal source ........ 57
Effect of an internal point source. .. 61
Effect of external areal and
point sources .. .. .. .. .. .. 63
Effect of a drifting plume. . . . 66
Output of the model . .. .. .. 72
IV. EMISSION INVENTORY. .. .. . .. .. 74
Emissions from Industrial, Commercial,
and Institutional Sources ./ 74
Emissions from Dwellings and Small Sources. 78
Emission Data ... ... .. .. .. 81
V. RESULTS AND DISCUSSION. .. .. .. . .. 82
. .82
. .84
. .99
. .106
. .10)7
Sampling Network. ..........
Comparison of Observed and Computed
Sulfur Dioxide Concentrations ...
The chi square test ........
Skill score .... .. .. ....
Number of computed concentrations
within + 0.5 pphm and + 1 pphm of
the observed concentration. ...
Frequency of occurrence of computed
and observed events .......
Discussion. ............
Applications of the Model ......
Contaminant decomposition rate. ..
Relative effect of areal and point
sources . . . . . . .
Effect of reducing point source
emission rates. .........
Effect of an additional source. ..
111
111
114
114
. .
. .115
. .118
Reduction of emission rates of electric
power generating stations ......
Evaluation of the monthly sulfation
pattern . . . . . . . .
Ground level concentration from a
drifting plume. ...........
121
123
131
CHAPTER Page
VI. SUMMARY.................. 135
APPENDIX 1. .. .. .. .. .. .. .. .. .. .. 140
APPENDIX 2... . .. 171
APPENDIX 3....,................ 175
APPENDIX 4. .. .. .. ... .. .. . ... . 188
LIST OF REFERENCES. .. ... .. .,. ... .. .. 197
BIOGRAPHICAL SKETCH..........,....... 205
vii
LIST OF TABLES
TABLE Page
1. Effect of Terrain Roughness on Atmospheric
Dispersion Parameters ... . .. ... 15
2. Maximum Mixing Depth in the Atmosphere over
Northeastern Florida. .. .. . . .. 25
3. Input Parameters for the Dispersion Model .. 36
4. Criteria for Atmospheric Stability Classifi
cation. . .. . .. .. .. .. .. 44
5. The Ground Level Concentration at the Center
of an Areal Source in Micrograms/Cubic
Meter for a Unit Emission Rate from the
Source. .. ... .. .. .. ... .. 59
6. Factors for the Dispersion of Ground Level
Material during Periods of Calm ...... 70
7. Hourly Electric Power Demand as a Percentage
of the Daily Demand for the Winter Season
in Jacksonville, Florida. .. .. .. 77
8. Observed and Computed Sulfur Dioxide Con
centrations (pphm). . .. .. .. .. .. 85
9. Contingency Table  Observed and Computed
Sulfur Dioxide Concentrations Rounded to
Nearest Half PPHM ... . .. . .. 101
10. No Relation Contingency Table  Observed
and Computed Sulfur Dioxide Concentrations
Rounded to Nearest Half PPHM. . .. . 102
11. Contingency Table  Observed and Computed
Sulfur Dioxide Concentrations Rounded to
Nearest Whole PPHM. .. .. .. .. ... 103
viii
TABLE Pacy
12. No Relation Contingency Table  Observed
and Computed Sulfur Dioxide Concentrations
Rounded to Nearest Whole PPHM . ... .. 103
13. Adjusted Contingency Table  Observed and
Computed Sulfur Dioxide Concentrations
Rounded to Nearest Half PPHM. .. .. .. 104
14. Adjusted No Relation Contingency Table 
Observed and Computed Sulfur Dioxide
Concentrations Rounded to Nearest Half PPHM 104
15. Adjusted Contingency Table  Observed and
Computed Sulfur Dioxide Concentrations
Rounded to Nearest Whole PPHM . ... .. 105
16. Adjusted No Relation Contingency Table 
Observed and Computed Sulfur Dioxide
Concentrations Rounded to Nearest Whole PPHM 105
17. Number of Computed Concentrations within
Specified Limits of Observed Concentration
with Respect to Day of Sampling .. .. .. 108
18. Number of Computed Concentrations within
Specified Limits of Observed Concentration
with Respect to Sampling Stations .. .. 109
19. Frequency of Occurrence of Observed Events. . 112
20. Frequency of Occurrence of Computed Events. . 112
21. Relative Ground Level Concentration from a
Drifting Plume. . ... . .. ... 132
LIST OF FIGURES
FIGURE Page
1. Horizontal Dispersion Coefficient as a
Function of Distance from the Source. ....13
2. Vertical Dispersion Coefficient as a
Function of Distance from the Source. 14
3. Effect of Sampling Time and Stability on
Observed Concentrations .. . . .. .. 21
4. Computation Grid and Meteorological Network 41
5. Treatment of External Areal Sources .. .. 51
6. Area Affected by Drifting Plume When Wind
Direction Changes . . .. .. . ... 67
7. Sulfur Dioxide Sampling Network for
Jacksonville. . .. .. .. . .. .. 83
8. Observed and Computed SO2 Concentrations
for Dec. 26, 1966 . ... ... ... 86
9. Observed and Computed SO2 Concentrations
for Jan. 4, 1966. . . .. .. .. ... 87
10. Observed and Computed SO2 Concentrations
for Jan. 6, 1966... .... . ... . .. 88
11. Observed and Computed SO2 Concentrations
for Jan. 9, 1966. . . ... . . .. 89
12. Observed and Computed SO2 Cnetain
for Jan. 11, 1966 . . ... .. .. 90
13. Observed and Computed SO2 Concentrations
for Jan. 13, 1966 .. .. .. ... . .. 91
FIGURE
14. Observed and Computed SO2 Concentrations
for Jan. 16, 1966...........
15. Observed and Computed SO2 Concentrations
for Jan. 18, 1966 ...........
16. Observed and Computed SO 2Concentrations
for Jan. 20, 1966 ...........
17. Observed and Computed SO2 Concentrations
for Jan. 25, 1966 ...........
18. Observed and Computed SO2 Concentrations
for Jan. 27, 1966 ...........
19. Observed and Computed SO2 Concentrations
for Jan. 30, 1966 ...........
20. Areal Source Contribution to SO2
Concentration of Jan. 20, 1966. ....
21. Point Source Contribution to SO
Concentration of Jan. 20, 196 .....
22. Effect of a 25% Reduction of Point Source
Emission Rates. ............
23. Effect of a 50% Reduction in Point Source
Emission Rates. ............
24. Effect of the Addition of a New Power
Generating Station. ..........
25. Effect of Reducing Emission Rates of
Power Generating Stations .......
26. Wind Rose for Jan., 1966, and for Days of
Sampling in January ..........
27. Sulfation Pattern and Monthly Average
SO2 Concentration for January, 1966 ..
Page
. I. .
. .
. .
. .
. . 16
...117
. 119
...120
. . 22
...124
. 126
,. .28
FIGURE Pacr
28. Relationship between Sulfation Rate and
SO2 Concentration . 129
29. Ground Level Concentration from a Drifting
Plume . .. . .. .. . .. 134
xii
Abstract of Dissertation Presented to the Graduate Council
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
A MULTIVARIABLE ATMOSPHERIC DISPERSION MODEL
by
John Bernard Koogler
August, 1966
Cochairmen: Dr. E. R. Hendrickson
Dr. R. S. Sholtes
Major Department: Bioenvironmental Engineering
A computersolved atmospheric dispersion model was
developed to assess the effect of gaseous pollutants emitted
from multiple areal and point sources. The model accounts
for the effects of wind speed and direction, atmospheric
stability, and source emission rate. These factors can be
averaged over any integral multiple of an hourly period from
1 to 24 hours. The output parameter is the ground level
contaminant concentration computed for 225 receptors defined
by a 15 by 15mile grid. The time scale of the output
parameter can be any integral multiple of an hourly period.
The ground level concentration was considered to be
the resultant effect of the emissions from areal sources,
the emissions from point sources, and the airborne pollutant
one time period after emission. These effects were determined
xiii
by the Gaussian dispersion equation and modifications
thereof. Other features of the model are: (1) the wind
speed is considered a logarithmic function of height,
(2) the plume rise is considered to be a function of down
wind distance and is limited by discontinuities in the ver
tical stability structure, (3) only the receptors within
the downwind range of a source, as determined by the product
of wind speed and travel time, are affected by emissions
from that source, (4) the dispersion parameters 0', and G}
are estimated by mathematical equations, and (5) pollutant
decomposition is accounted for by an exponential decay
function.
The model was tested using data collected as part
of the Greater Jacksonville Air Pollution Control Program.
The data included hourly averages of wind speed, wind direc
tion, and vertical temperature measurements. The latter
were made at the ground, 100, 200, 300, 450, and 750
foot levels of a television tower. A sulfur dioxide emission
inventory for December, 1965, and January, 1966, was com
piled for the onemile square areas defined by the grid
system and for major point sources. The computed ground
level concentrations were compared with the monthly sulfa
tion pattern and observed 24hour concentrations from 11
sampling stations.
X1V
Of the 111 24hour concentrations compared, repre
senting 12 days, 95 percent were with + 1 pphm, 4 percent
were high by more than 1 pphm, and 1 percent were low by
more than 1 pphm. This accuracy is significant at the 99
percent level when tested by the chi square test. Several
applications of the model are also illustrated.
The model is progreamed in FORTRAN II compatible
with the IBM 709 computer. Depending upon the time scale
selected and the amount of data to be processed, the time
required to make the computations for a 24hour period
varied from 15 to 30 minutes.
The results from this model demonstrated that dis
persion models are practical and effective and that, if
used judiciously, they could be of great value in many
phases of an air pollution program.
CHAPTER I
INTRODUCTION
The Air Pollution Problem
Some of the effects of air pollution have been
realized for quite some time but, until relatively recent
times, they have either not been acute or have been con
sidered the price of an industrialized society.
Records from ancient Rome have told of the Patri
cians grumbling because smoke smudged their togas, and
early Spanish explorers made what is probably the first
report of the Los Angeles area smog problem, which was, at
that time, caused by Indian fires (1). In these early
periods of history, however, the amount of airborne con
taminants generated by the activities of man was relatively
small when compared with the capacity of the atmosphere to
receive and disperse this material. Thus at that time air
pollution was only a nuisance or, at the most, an extremely
localized problem.
As time progressed, so did the activities of man.
Industrialization drew people together  people to serve
industry and people to serve the needs of other people.
The result was urban areas of the magnitude we know today
and an increasingly complex air pollution problem.
As early as the fourteenth century, air pollution,
caused by coal smoke and gases, became enough of a problem
in England to evoke a royal protest (2). From this time
until the middle of the twentieth century, the air pollu
tion problem became more and more acute, but little was
actually done to alleviate the condition.
The hazardous effects of air pollution were drama
tized very tragically in 1948, when twenty persons were
killed and several hundred were made ill in an industrially
caused incident in Donora, Pennsylvania, and again in
December, 1952, when a smog condition in London caused the
death of some four thousand persons. These events, probably
more than anything else, aroused the public's interest in
air pollution and stimulated the study of this malady.
The study could be resolved into two major parts 
a study of the contaminants and a study of the factors re
sulting in their dispersion. A fairly accurate quantitative
determination of several of the contaminants could be
made analytically. However, very little was known about
the factors affecting their transport. The assessment
of these factors demanded a knowledge of atmospheric trans
port and dispersion. Although there were formulas avail
able at this time (3,4) to describe atmospheric dispersion,
they were not well substantiated because of a lack of suf
ficient empirical data (5).
Review of the Literature
Historical
The pioneers of atmospheric dispersion studies
(6,7) directed their attention toward expanding the Fickian
theory of molecular diffusion and then applying it to the
atmosphere. According to the Fickian theory, the flux of
a diffusing substance in a direction x is proportional to
the concentration gradient in that direction, or, in formula
F = D de.
dx
Taylor (6) and Richardson (7) found that atmos
pheric dispersion could be described with this expression
by using values of D of the order of 103 to 105 square
centimeters/second. These values were larger than values
of D for molecular diffusion by a factor of 104 to 106()
It soon became evident to these workers that a universal
value for D did not exist. Sutton (3), in one of the
classic contributions to atmospheric dispersion formulation,
proposed the hypothesis that the Fickian theory was not
valid in atmospheric dispersion because it did not take into
account the variation in turbulent eddy size. His work was
based on a statistical theory developed by Taylor (8).
Sutton assumed that the concentration density of a dispersed
material in the horizontal and vertical crosswind directions
was distributed according to the Gaussian distribution, and
he defined his diffusion parameters in terms of the standard
deviation of that distribution. The standard deviation was
of the form
.ICe2X2n
where
O' = the standard deviation of the distribution,
C = the virtual dispersion coefficient,
X = the downwind distance, and
n = a parameter which is a function of the
vertical wind profile.
Using data available at the time, Sutton defined
only one dispersion coefficient, but speculated that the
diffusion rates in the vertical and horizontal directions
might not be equal. If this were the case, the dispersion
coefficient C would be the product of a coefficient for
vertical dispersion and one for horizontal dispersion; i.e.,
C2 = CzC .
Also, the dependence of Sutton's dispersion param
eter upon the downwind distance instead of upon time, as
the Fickian theory prescribed, overcame another shortcoming
of the earlier theory. This was the failure to recognize
that the turbulent eddies responsible for instantaneous
dispersion of a plume increased in size as the downwind dis
tance increased; the most effective dispersion being caused
by eddies of the same size as the plume crosssection.
The formula Sutton proposed for determining the
groundlevel concentration of a material emitted from a
continuous point source was
TTC CZ ux X2n ex 2n 2 + z
where, in general units of mass, length, and time,
S= the groundlevel concentration, m/13
Q = the source emission rate, m/t,
TT = the constant 3.1415...,
u = the wind speed, 1/t,
x = the downwind distance, 1,
y = the horizontal crosswind distance, 1,
z = the vertical crosswind distance, 1, and
Cz, Cy ,and n are as previously defined.
The units of the variables may be in any consistent set.
Sutton's assumption of the Gaussian distribution of the
contaminant in the crosswind directions has been verified
(9,10,11,12), and his formula is still used.
Bosanquet and Pearson (4) developed a similar for
mula in 1936. Using data that were unavailable to Sutton,
they defined separate coefficients for vertical and hori
zontal dispersion, thus substantiating. Sutton's thought
that the two diffusion rates might not be equal. They
found that the rate of vertical diffusion was generally less
than the rate of horizontal diffusion and hypothesized it
was due to the fact that vertical dispersion near the ground
is suppressed by the earth's surface.
In 1947, Sutton (13,14) published an extension of
his earlier work and the results of diffusion studies con
ducted at Porton, England. These studies were carried out
under adiabatic lapse conditions, and the data consisted
of 3minute average concentrations determined over a travel
distance of 100 meters. From these data, Sutton found
n = 0.25, Cy = 0.21., and Cz = 0.12.
Sutton also described the vertical wind profile by the
relationship
2/(2n)
u = u, (z Z
OZO
where
u = the wind speed at any elevation,z,
uo = the wind speed at a standard elevation, z and
n = a dispersion parameter dependent upon the
vertical wind profile.
Beginning about 1952, several investigators began
studying the many facets of atmospheric dispersion and re
lated subjects, and there was rapid advancement along many
lines.
General dispersion
Friedmran (15) and Holland (16) were among the
investigators of the early 1950's. Their studies involved
the evaluation of Sutton's dispersion parameters for various
conditions of atmospheric stability and also the relation
ship between these parameters and height above the ground.
The results of their studies are summarized by Strom (17).
In 1955 a series of dispersion studies was conducted
at the Round Hill Field Station in South Dartmouth, Massa
chusetts, by a team from the Massachusetts Institute of
Technology (18). Sulfur dioxide was used as a tracer, and
10minute samples were collected to a distance of 200 meters
from the source. The terrain was fairly flat and the area
was devoid of trees and scrub growth. This study led to a
very extensive investigation of atmospheric dispersion
during 1956 (10,19).
The study, Project Prairie Grass, was conducted over
very level terrain at a site near O'Neill, Nebraska. Again,
sulfur dioxide was used as the tracer and 10minute samples
were collected to a distance of 800 meters from the source.
Some facts revealed by this study and the Round Hill study
were (5,10):
1. There is a general correlation between
horizontal concentration profiles at
short travel distances and the frequency
distribution of the azimuth wind direction.
2. Significant deviation from the assumed
normally distributed concentration pro
files does occur, especially in periods
of instability, but the normal distribu
tion is still the most functional distri
bution.
3. The increase in plume width occurs at a
faster rate than an increase in plume
height. This was considered a consequence
of the suppressive effect of the earth's
surface on the vertical movement of air.
4. There is significant correlation between
the vertical and horizontal diffusion and
vertical and horizontal variances in the
wind. This fact has been verified by
others (20,21).
5. The ground level concentration at a down
wind distance x can be expressed by the
simple power law
Xct xb
where b is an exponent with a value between
0.5 and 2.5, depending upon atmospheric
stability.
It was proposed that the variances in the wind and
the parameter b replace the strictly empirical factors of
Sutton (14) in dispersion equations. This resulted in the
expression
n"r uxb G~
a e
for concentrations along the plume center line where
O'= the variance in the azimuth wind direction,
Ge= the variance in the vertical wind direction,
and the other factors are as previously defined.
Cramer (5,22) presented these factors in a form
in which they could be used in equations such as the one
above. The results calculated by the proposed equation
were onethird to onehalf the values predicted by Sutton's
equation (14) but were in good agreement with results of
other studies (20,21).
Another approach, based upon the Round Hill and
Prairie Grass data, was to define a horizontal dispersion
parameter G~ in terms of b and O' and a vertical dispersion
parameter G~ in terms of b and Ge~. This was done by
regression analysis of the data and presented by Cramer (23).
Results obtained by using these parameters were very close
to the results obtained with the original parameters.
In 1958, a major study was conducted by Stewart,
Gale, and Crooks (21) using radioactive argons gas emitted
from the Harwell BEPO reactor in England. This study was
quite significant because the tracer was emitted from a
stack surrounded by buildings 8 to 16 meters high rather
than from a source on open flat terrain. The dispersion
formula used was the one of Sutton (14) and the coeffi
cients were evaluated over a distance of 10,000 meters.
The significant findings of this study were:
1. The dispersion coefficients are
greatly influenced by the mode in
which the plume is discharged and
the effects of local turbulence.
2. Lateral diffusion is greatly increased
by mechanically induced turbulence.
3. Downwind from a builtup area, dis
persion coefficients revert to "open
country" values.
4. The particular values of diffusion
parameters, for describing dispersion
in a builtup area, can apply only
to a very localized area.
The results of several studies (19,20,21,24,25)
were reviewed by Meade and Pasquill (26), and values were
estimated for the plume height H and the angular plume
width 0. Gifford (27) converted these values to values
for CTy and Ez with the equations
Ciy =x tan
2.15 z
and
"= H~
where
x = the downwind distance in meters,
O = the angular plume width in radians, and
H = the plume height in meters.
The value 2.15 is the number of standard deviations from
the plume centerline to the point where the pollutant con
centration is 10 percent of that at the plume centerline.
This is the usual definition of the crosswind 10mit of the
plume. Gifford's curves for 0 and 0 for various stability
y z
classes (27) and downwind distances are presented in
Figure 1 and Figure 2.
The values Gifford determined for (" agreed well
with later values presented by Singer and Smith (29).
Dispersion over rough terrain
and urban areas
The effect of terrain features on atmospheric dis
persion is evident from the wide range of values reported
for dispersion parameters. Limited results of three
studies conducted over widely differing terrain are pre
sented in Table 1 to illustrate the variation in these
parameters. The parameters 0y and G'Z presented by Gifford
01V 00 10
Distance from the source (meters)
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OF DISTANCE FROM THE SOURCE
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Distanceiiii!i frm hesorc ( etrs
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i~i~ iiriiiiiiiii iiii
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1 extremely unstable
2 moderately unstable
3 slightly unstable
4 neutral
5 slig htly stable
Parameter
Investigator Stability
Condition n Cy Cz
Sutton* (14) unstable 0.20 0.21 0.21
neutral 0.25 0.12 0.12
stable 0.33 0.08 0.08
Singer+ (29) unstable 0.19 0.56 0.58
neutral 0.28 0.50 0.46
stable 0.45 0.45 0.32
StewartS (21) unstable 0.25 0.46 0.25
neutral 0.25 0.46 0.20
stable 0.25 . 0.11
*Study conducted over smooth terrain.
+Study conducted over flat terrain with scrub
growth and 810 meter trees.
+Area within 500 meters of the source contained
several buildings 816 meters high.
TABLE 1
EFFECT OF TERRAIN ROUGHNESS ON ATMOSPHERIC
DISPERSION PARAMETERS
(27) agreed quite well with values of 0~ and 0~ that Singer
and Smith (29) reported as being equivalent to their values
of C Cz, and n.
The selection of a set of parameters to describe
dispersion at a particular site is entirely an empirical
problem. The parameters must be selected to give computed
results which agree with observed concentrations. Once
parameters have been selected, however, they can be used
with a reasonable degree of certainty. But, even with the
most ideal set of parameters, Strom (17) and Smith (30)
have both reported that large deviations from computed con
centrations will exist because of local disturbances. This
is especially true if one set of parameters is used over a
large and heterogeneous area. Dispersion around isolated
and areal disturbances has been studied by several investi
gators. Halitsky (31) reported that turbulence near build
ings existed to a height of about twice the building height.
The effect of this turbulent zone upon the dispersion of an
airborne material will depend upon the level at which the
material is emitted. This can be considered in three lev
els (3:2) :
1. Street Level  Diffusion is the
effect of wind channeling between
buildings and is generally upward.
2. Roof Level  Diffusion occurs in all
directions.
3. Elevated Sources  Dispersion from
these sources approaches nonturbulent,
but as the dispersed material diffuses
toward the ground, it is affected by
turbulence in the lower zones.
The result of this turbulent mixing is a fairly
uniform concentration gradient up to twice the height of
the disturbance. Davidson (33) has studied the turbulence
induced by a geographical ridge and has found the turbu
lent zone to exist between onehalf the elevation of the
ridge line and slightly above the ridge line, depending
upon atmospheric stability. The lower turbulent zone cor
responded to an unstable lapse condition and was much more
intense than the turbulence existing under inversion con
ditions.
The wind is the major cause of turbulence near
local interference (34), but in urban areas the vertical
and horizontal temperature gradient is also a factor.
Studies (35,36,37) have shown that cities function as a
heat sink; i.e., they absorb more heat from solar radia
tion during the day than surrounding nonurban areas do.
At night this heat, along with heat generated by normal
activities within the city, is radiated to warm the air
directly over the city. This phenomenon maintains the air
over the city in an unstable state a large part of the time,
thus increasing turbulence. The effect is most pronounced
at night and is slight to nonexistent during the day.
Another effect of the elevated nocturnal urban
temperature is that cool air from the suburbs will flow
radially inward toward the center of the city, forcing the
warm air at the center upward. This also increases turbu
lence.
Panofsky and Townsend (38) have examined the wind
profile on the lee side of an urban area and have found
that it returns to an "Open country" profile in a distance
equivalent to about twenty building heights. This corres
ponds to a slope of the turbulent boundary layer of about
1:10. This phenomenon was also observed in the dispersion
studies at Harwell (21).
The effect of sampling time on
dispersion parameters
Sutton (13,14) first recognized the effect of
sampling time on the values obtained for dispersion param
eters in the Porton study. It was observed that short
term peak concentrations were generally higher than
longerterm averages.
Hilst (39) gave the reason for this very concisely.
When the effluent material is averaged over a period of
time, it is normally distributed about the plume centerline
with a mean j, a horizontal crosswind variance G 2, and a
vertical crosswind variance Gz2. This concentration is
averaged about the moving centerline of the plume, which is
normally distributed about the mean wind direction with a
variance GVn2. Thus, a shortterm sample taken fromn an
instantaneous position within the plume will have a horizon
tal crosswind variance of essentially 0 2 and will indicate
a higher concentration than a longterm sample because the
variance of the latter sample is the sum of 6 2 and G 2
n y
Studies of the peak to mean ratio for various sam
pling times were made on results collected during the Prairie
Grass project (22) and at Harwell (21). These studies
indicated that concentration is inversely proportional to
the fifth root of time. Based on the results of oilfog
dispersion over a distance of 5,000 meters, Singer (40)
arrived at a 1minute p~eak to 100minute mean ratio varying
from 4 to 14, depending upon atmospheric stability.
McCormick and Xintaras (41) related peak to mean concentra
tions for multiple sources and found the ratio smaller than
the ratio for single sources. They reported 3minute peaks
of 1.5 times the hourly average. The average results o
these studies are summ~arized in Figure 3.
Plume rise equations
The rise of plumes into the atmosphere is proja >
one of the most controversial subjects in atmosaberic Eis
persion. Several eruations (42,43,44,45,4o) hav x, r
developed from both a theoretical and an omairical approach,
but no one formula gives entirely satisfactory results.
Strom (17) reviewed nine formulas that were in use in 1 j2
and concluded that Holland's formula (42) Fgave the highest
values of ground level concentration, folilowac'il lyth
Thomas formula (43), th~e Bosancuet, Carey, and I.altrson for
mula (44?), the Priestley formula (45), and Suttor's formi. a
(46).
Stewart, Gale, and Creooks (21) concrac~ plure:. irova
tions calculated by Bosanc~uet's form:1u witn t..ac ohserv o
plume rise ai Hasrwell. and3 foun2 it to 35 rxOrccnt" CW iL
a distance of 1.,000 m tcrs. Cne. reason for t~is is ~?ic
Bosanquet's formula, as well as the others cited thus f:,
limits the maximprum plu.c ri 2.
Schmidt (47) reported values of a cc *r same.. actor
P which were equal to the observed plume rise divided by
ill.
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the computed rise. Based on this factor, Holland's formula
was superior to five others tested. The standard deviation
of P for the Holland formula was 0.40, with P ranging from
2.055 to 0.420. The standard deviation of P for the other
formulas was as high as 1.9.
In the same paper, Schmidt developed a plume rise
equation which took into account the vertical temperature
gradient, a factor not included explicitly in previous
formulas. Neither did Schmidt limit the rise of t~he plume
in an unstable atmosphere. He stated that under such con
ditions a plume would theoretically rise indefinitely.
Briggs (48) extended a formula which was developed
by Scorer (49) to include the vertical temperature gradient
and arrived at an expression comparable to that of Schmidt.
Briggs concluded that during the transitional rise the
plume height is proportional to the twothirds power of the
downwind distance. Unfortunately, neither the formula
developed by Briggs or by Schmidt is well suited for use in
a largescale dispersion model because of their complexity.
The equations just considered have been for the
rise of plumes from fairly large sources and can not be
used to describe the rise of a plume from a single dwelling.
Lucas (50), however, presented a formula based on a modified
version of Sutton's formula (46) to describe the rise of
plumes from a large number of dwellings. The formula is
AH = 5x ( )3
where
aH = the plume rise in feet, and
u = the wind speed in feet/second.
This formula is applicable under all stability conditions,
with the limitation that AH is limited to 50 feet in the
case of a stable atmosphere.
A feature of the atmosphere that has been recog
nized for quite some time but that is rarely considered in
dispersion calculations is the physical limitation on upward
dispersion imposed by a stable layer aloft. Pasquill (51)
mentioned this feature and suggested that it could be ac
counted for by limiting the maximum value of ([ to a value
equal to the height of the inversion base H, i.e.,
Oz(max) = H.
As a result of studies at Brookhaven, Singer and
Smith (29) placed as a limit
CE (max) =1.5H.
They stated that Pasc uill's zssump~tion: imanlied that sorre of
the airborne contaminant pa~notrated the s:1,10 layer  an
unlikely occurrence. Tihey also reportcc dha cl. :? aP4 t of~
placing a l1buit on 0z is apparent only at crea d ist...es
downwind. As an example, thec effect of an inv :cion base
at a height of 500 mreters would just bacc...a no ace~S.1 in
the computed ground level concentration at a down~wind dis
tance of 9,000 meters.
Gifford (27) su._sted that the limit on: 0 
Ez(max) = 0.5R.
This assumption was based on a c fined plume hei<.t of
2.15 CF ,.
Hosler (52) znd Solzworm.: (53' have re:0~rte 0.
f'requen~cy of" inversions and th~e roaxiumu~ .1..L dept.~ thr,l
might be expected over contiguous United States. So:J of
these data are present in Table 2.
Dis a~rsion :30??13
Several dissorsion molein nave econ a ...C
assess the effects of roiulti 10 sourcies of i:1.s on 0:
re ce ptor These moi .1s have differ.. consi :
time scale involved and the variables consid~cd
Month Max. Mix. Depth Month Max, Mix. Depth
(meters) (meters)
Jan. 700 July 1,400
Feb. 900 Aug. 1,400
March 1,100 Sept. 1,300
April 1,300 Oct. 1,100
May 1,400 Nov. 900
June 1,400 Dec. 700
The most general models are those which consider
all the sources within an area to be distributed uniformly
as a line or as a band of finite width. These distribu
tions are usually assumed to have an infinite crosswind
length. Lucas (50) applied such a model to Leicester and
London, England, using the seasonal average value of wind
speed, wind distribution, and sulfur dioxide emission rate.
The basis of the model was a numerically integrable form
of Sutton's equation that Lucas derived. Limited results
presented by Lucas agreed well with observed sulfur dioxide
concentrations averaged over the same period. Some interest
ing facts brought out by Lucas' model were:
TABLE 2
MYAXIMUM MIXING DEPTH IN THE ATMOSPHERE
OVER NORTHEASTERN FLORIDA (53)
1. A maximum in the ground level concen
tration of a contaminant emitted from
an areal source occurs with a wind
speed of about 2 mph. For higher wind
speeds, the contaminant is diluted by
the wind. For lower wind speeds and a
neutral or unstable lapse rate, the
ground level concentration is reduced
because of plume rise. During stable
conditions, the concentration decreases
as the wind speed drops below 2 mph
because of limited plume rise. But, as
the wind speed drops below 0.5 mph, thle
ground level concentration begins to
build up rapidly.
2. A stable layer of limited height based
at ground level results in a smaller
ground level concentration than a stable
layer of infinite height. This is
especially true if the stack height ap
proaches the top of the stable layer.
3. Within a uniformly distributed areal
source, the ground level concentration
builds up continuously from the windward
edge of the source and reaches a maximum
at the downwind edge of the source.
4. The ground level concentration drops off
very rapidly beyond the downwind edge of
an areal source.
Hilst (54) and Gasiorowski (55) have both developed
similar models. Gasiorowski compared the relative effects
of various stack heights and showed that the maximum ground
level concentration from an areal source occurred with the
lowest stack height and appeared slightly beyond the down
wind edge of the area. As the stack height was increased,
the ground level concentration was decreased and the maxi
mum appeared farther downwind.
A more refined model was designed by Mead and Pas
quill (56) to describe the biannual sulfur dioxide! concen
tration at a fixed distance from the center of Staythorpe,
England. Their model related the sulfur dioxide concentra
tion directly to the average monthly sulfur dioxide emission
rate and the fractional distribution of the wind direction,
and inversely to the mean wind speed. The correlation be
tween concentrations computed with this model and observed
concentrations was 0.604 for the winter months and 0.804 for
the summer months.
A model was formulated along similar lines by Lar
son, Stalker, and Claydon (57') to describe the radial dis
tribution of sulfur dioxide around Nashville, Tennessee.
Their model showed a maximum concentration at the center of
the city, with the concentration decreasing away from the
center according to the proportion
SC~exp[(r) 2]
whe re
s = the sulfation rate,
r = the radial distance from the center
of the city, and
a = an empirically determined constant.
Pooler (58), Clarke (59), and Turner (60) developed
models based upon the basic dispersion equation
X Q
Tru QGj (T
where
7 = the horizontal dispersion coefficient in meters,
Eg = the vertical dispersion coefficient in meters,
and the other parameters are as defined previously.
Pooler subdivided the area to be incorporated in his model
into 1milesquare increments and assumed that all of the
contaminants from each increment were emitted from a point
in the center of the increment. He then computed the rela
tive effect of a source upon all other areas and upon the
area containing the source; the latter being done by inte
grating the effect of a uniformly distributed areal source.
To determine the effect on an area not directly on the down~
wind plume centerline, Pooler linearly interpolated between
adjacent wind directions. Using this relative effect grid
and the monthly average value of wind speed, wind distribu
tion, stability, and contaminant emission rate, POOler com
puted the effect of each source on each area. Ninety five
percent of the concentrations computed with this model were
within a factor of two of the observed monthly concentration.
Turner refined this model by considering each mile
square increment as an areal source and by correcting for
the effect on an area not directly downwind of the source
by the factor
1 y2
f = exp[y(a;) ]
where
f = a correction factor,
y = the horizontal crosswind distance from
the plume centerline, and
~y = the vertical dispersion coefficient.
The time scale for input parameters and computed concentra
tions was also reduced to a 2hour period. Twelve 2hour
concentrations were averaged to give a daily average.
Turner reported 58 percent of the calculated concentrations
were within 1 pphm of observed 24hour concentrations.
Of the 2hour concentrations, most of the overcalculations
occurred near sunrise and sunset, and most of the undercal
culations occurred near midday and midnight. Both Pooler's
model and Turner's model were applied to Nashville, Tennessee,
and were computersolved.
Clarke's model was a simplified version of Pooler's
model and was intended for hand calculation of the concen
tration of a contaminant at a single receptor. The total
area included in the model was divided into irregular areas,
each contributing about the same effect to the receptor.
The effect of each area on the receptor was assessed at 2
hour intervals by considering the parameters wind speed,
wind direction, and atmospheric stability.
Summary
The conclusions reached in the studies of atmos
pheric dispersion and related phenomena can be summarized
as follows:
1. The most functional expression for
describing the dispersion of a plume is
2 2
7T u y z 2 Oy 2
where
X= the ground level concentration
Q = the emission rate,
iT = the constant 3.141l...,
u = the wind speed,
S= the horizontal crosswind dispersion
coefficient,
CF = the vertical crosswind dispersion
coefficient,
y = the horizontal displacement from the
plume centerline, and
z = the effective stack height.
The units on these variables may be in
any consistent set. This expression
describes the plume as being normally
distributed about the centerline axis
with the horizontal variance 0 and the
vertical variance 02 2
2. The most comprehensive set of data for
defining Gy and Ciz was compiled by Meade
and Pasquill (26) and presented by Gifford
(27). These data are shown in Figures 1
and 2.
3. In general, dispersion is greater in urban
areas because of mechanical and thermal
turbulence. The increased rate of disper
sion can be accounted for mathematically
by increasing the values of the dispersion
coe fficients Local dispersive effects
cannot be accounted for in a general dis
persion equation.
4. The time scale of all time dependent
parameters in the dispersion equation must
be adjusted to a consistent time base.
These corrections can be made with the aid
of Figure 3.
5. There is no one plume rise formula that
will give entirely satisfactory results.
The best formulas appear to be the Holland
formula (42) and the Thomas formula (43),
the latter being an extension of Holland's
formula. The Thomas formula predicts the
maximum plume rise. This maximum was re
ported to occur at a distance of about one
32
mile from the source. Other studies
(47,48) indicated that the plume rise
is theoretically unlimited and is pro
portional to an exponential function
of the downwind distance. In practice,
however, the plume rise is affected by
discontinuities in the vertical sta
bility structure .
CHAPTER II
PURPOSE AND SCOPE
The problem was to develop an atmospheric disper
sion model, using computer methodology, for use in an
urban area. The proposed model was to compute the ground
level concentration of gases dispersed from multiple sources
under varying meteorological conditions.
Although the model was to be used immediately in
the JacksonvilleDuval County, Florida, area, it was made
as general as possible, within the practical limits of
computer time and number of input variables, so that it
could be used in almost any area of comparable physical
size.
The development of the model was based upon formu
las and relationships that were in general use and had been
fairly well substantiated by field studies.
The variables accounted for in the model were the
emission rate of contaminants from distributed and point
sources, physical parameters describing the sources, the
wind speed and direction, and the atmospheric stability
structure. These factors can be varied hourly on any
integral multiple thereof. The output variable is the
ground level concentration of the contaminant computed for
receptors located at onemile intervals in the northsouth
and eastwest directions.
A sulfur dioxide emission inventory was compiled
for the months of December, 1965, and January, 1966.
These emissions, together with meteorological data for
these months, collected as part of the Greater Jackson
ville Air Pollution Control Program during the period from
October, 1964, to January, 1966, were used as input vari
ables to test the model. The results from the model, the
ground level sulfur dioxide concentrations, were compared
with observed daily and monthly sulfur dioxide concentra
tions collected as part of the Jacksonville program.
CHAPTER III
THE MODEL
General Description
The purpose of an atmospheric dispersion model is
to describe the ground level concentration of an air pollu
tant with a minimal expenditure of time and effort. Depend
ing upon the requirements of the model, the time over which
the concentration is averaged can range from hourly periods
to seasonal periods.
Time scale
For flexibility, the model was designed so that the
period over which the input and output factors were averaged
could be varied over any integral multiple of an hourly
period between 1 and 24 hours. The period of time over
which the output is averaged, however, does not need to be
the same as the period for which the input variables are
averaged.
Basically, the input parameters (Table 3) are
TABLE 3
INPUT PARAMETERS FOR THE DISPERSION MODEL
AREA the effect of the emissions from a unit
areal source upon a receptor at the center
of the source. There are 25 factors 
one for each combination of the 5 stability
classes and wind speeds of 1,2,3,4, and 5
miles per hour.
CSN the cosine function of the 16 wind direc
tion angles.
SN the sine function of the 16 wind direction
angles.
N the number of cards to be read.
R the eastwest displacement of a point source
from the center of areal source I,J. The
displacement is in meters with east positive.
S the northsouth displacement of a point
source from the center of areal source I,J.
The displacement is in meters with north
positive.
ZPHTY the physical stack height of point source
I,J,M in meters.
M the source number within area I,J. The areal
source is M = 1 and the point sources are
M = 2 5.
KEY the number of sources in area I,J. The
range of KEY is 1 5.
KODE the number of hours over which the output
is averaged.
TABLE 3Continued
KONT a switch controlling the title
on the output.
=1 for the contaminant sulfur dioxide
=2 for the contaminant oxides of nitrogen
= 3 for the contaminant fluorides
=4 for the contaminant hydrocarbons
=5 for the contaminant oxidants
MTHAVG a switch controlling whether or not the out
put is averaged over the total number of days
for which data are read.
NUMDAY the number of days for which data are read
into the model.
ITIME the number of hours over which the input
parameters are averaged.
HALIV the decomposition half life of the contam
inant in hours.
KSTAB the hourly stability classification.
= 1 for extremely unstable
=2 for moderately unstable
=3 for slightly unstable
= 4 for neutral
= 5 for slightly stable
TOP the height to the base of inversions aloft
in hundreds of feet. If no inversion is
recorded, the limiting value of TOP is given
in Table 2.
BTM the height to the top of inversions based at
or near the ground in hundreds of feet. If
no such point exists, set BTM = 100.
YR the year for which the data apply.
AMO
the month for which the data apply.
hourly averages and are read into the computer for a 24
hour period. The ground level concentration at each recep
tor is computed for hourly periods and is either printed
out or stored in the computer to be averaged over a longer
period of time. The input parameter KODE determines the
period of time in hours over which the output is to be
averaged. For example, if the output  the ground level
concentration  is to be averaged over a 12hour period,
KODE would be read as 12. The range of KODE is 1 to 24.
TABLE 3Continued
DAY
DIRVEL
IHRA
IHRP
Q(I,J,NS)
the day for which the data apply.
twelve 1hour averages of wind direction,
on a 16point compass, and wind speed, in
miles per hour, on each of two cards.
the hour ending IHRA is the hour through
which the hourly areal source emissions
which follow are constant.
the areal source emission rate for area
I,J in grams/hour.
the hour ending IHRP is the hour through
which the hourly point source emissions
which follow are constant.
the point source emission rate for point
source I,J,NS (NS = M) in grams/hour.
If the concentration is to be averaged over a period greater
than 24 hours, it can be done by setting KODE to 24 and then
averaging multiples of 24hourperiod concentrations. Thus ,
if the concentration is to be averaged for a period of 72
hours, the concentrations from three 24hour periods would
have to be averaged. Averaging for periods of time greater
than 24 hours can be accomplished within the model by setting
the input parameter MTHAVG equal to 2 and the parameter
NUMDAY equal to the number of days for which the average was
required.
To average the meteorological input factors over an
n hour period, where n is an integer greater than 1, the
input parameter ITIME is set equal to n and the averaged
factor is read in as an hourly value every nth hour. For
example, if the meteorological factors are to be averaged
over a 3hour period, the average value for the first three
hours would be read in at the third hour with the first and
second hour being blank. The average of hours 4,5, and 6
would be read in at the sixth hour and so on.
Spatial scale
The storage capacity of the IBM 709 computer limited
the area included in the model to a 15 by 15mile square.
This scale was large enough to include all major sources of
emissions in the JacksonvilleDuval County area. The 15
by 15mile area was subdivided into 1milesquare increments
by a northsouth, eastwest grid system (Figure 4). The
center of each area increment was considered a receptor,
i.e., a point for which the pollutant concentration was cal
culated. The 1mile dimension was selected primarily be
cause of work by Pooler (58) and Turner (60,61), which indi
cated that concentrations for receptors at this spacing
would satisfactorily describe the pollution pattern and
would not result in an excessive number of computations.
Meteorological factors
When the Jacksonville program began, five stations
for recording wind direction and speed were established
within the area (Figure 4). As the study progressed, anal
ysis of the wind data revealed that the results from sta
tions 1 and 5 and stations 3 and 4 were nearly identical.
As a result of this finding, stations 3 and 5 were discon
tinued midway through the survey (62). The stations retained
were located at the U.S. Weather Bureau (station 1.) north
of the city of Jacksonville at an elevation of 17 feet, at
a power generating station (station 4) in the city's major
industrial zone east of the St. Johns River at an elevation
41
Utn
~8~O
 c
WO
1 II
O *
of 50 feet, and on top of City Hall (station 2) in downtown
Jacksonville at an elevation of 250 feet. Both wind speed
and direction were recorded continuously at all stations by
a BendixFriez Aerovane and a strip chart recorder. Hourly
averages of wind speed, in miles/hour, and wind direction,
from 16 points, were reduced from these charts and put on
punch cards. These data were input parameters of the model
and in addition were sorted by the computer program listed
in Appendix 4 for plotting wind roses.
An inspection of the data revealed that there was
no significant difference in the wind speed and direction
recorded at station I and that recorded at station 4. The
wind speed at station 2 was generally higher than the wind
speed recorded at the other stations during most periods,
but the direction was essentially the same. The higher
wind speed could be ascribed to the elevation of station 2.
Since there was no significant spatial variation in wind
direction, and the wind speed at stations 1 and 4 was about
the same, it was decided that the wind data fron one station
could be used to describe the conditions for the entire
area. The wind data from station 4 were selected for this
purpose primarily because it was located in the zone of
heaviest emissions and because the elevation of the station
was close to the height at which most contaminants were
emitted.
The atmospheric stability was determined by direct
measurement of the vertical temperature profile. This was
considered an improvement over the indirect method suggested
by Pasquill (28) and used by Turner (60). The vertical
temperature profile was measured to 750 feet with a system
using thermistors (63). These were placed at the 100, 200,
300, 450, and 750foot levels of a TV tower (station 6,
Figure 4) located in a relatively unrestricted area at the
center of the grid. The system measured the temperature at
ground level and the temperature difference between the ground
and each of the five levels. Radio observations made by the
U.S. Weather Bureau at 0700 and 1900 hours were relied upon
for information about the vertical structure of the atmos
phere above 750 feet. Based upon the measurements of the
vertical temperature and wind speed, hourly classifications
of atmospheric stability were assigned. The criteria used
to define the stability classes are presented in Table 4.
In addition to the stability classification the
base of inversions aloft and the top of ground level inver
sions were recorded if either existed. Inversions aloft
were of interest because of the limit they impose upon the
TABLE 4
CRITERIA FOR ATMOSPHERIC STABILITY CLASSIFICATION
Wind Lapse Rate (oF/1000 ft.)
Speed 11.0 to 9.0 to 5.0 to
(mph) 10 9.0 5.0 +7.0 +.
2 1* 2 2 4 4
2 4 1  2 2 3 4 4 5
4 6 2 2 3 3 3 4 4
6 2 3 3 3 4 4
"1 Extremely unstable.
2 Moderately unstable.
3 Slightly unstable.
4 Neutral.
5 Slightly stable.
vertical mixing depth. The tops of ground level inversions
were recorded since it was assumed that gaseous material
emitted above this level was prevented by the stable layer
from reaching the ground.
Sources
The model was designed to account for both point
sources and areal sources. Within each area increment, the
model can handle five sources; the first source always
being the areal source. The input parameter KEY (I,J)
defines the number of sources in each area increment I,J
where I is the northerly coordinate of the area increment
(increasing north to south) and J is the easterly coordinate
of the area increment (increasing west to east).
The areal sources consisted of emissions from small
individual sources within each 1mile square described by
the grid system. The emissions were combined and were
assumed to be uniformly distributed over the entire area.
The emission height of these sources was assumed to be 8
meters. Exceptions were made when approximately 50 percent
or more of an area was water. In such cases the emissions
from the area were assumed to be emitted from a point source
at the centroid of the land area. The emission height was
again assumed to be 8 meters. The emissions from larger
sources were considered individually as point sources. A
preliminary study with the model indicated that point
sources with an emission rate of less than 10,000 grams/
hour had a negligible effect on all receptors even under
the most adverse meteorological conditions. Therefore only
sources with an emission rate greater than 10,000 grams/hour
were considered as point sources. The point sources were
located within the area increment containing them by an
internal coordinate system. The origin was at the center
of the area with north and east considered as positive. The
displacement from the origin was measured in meters.
The emissions from areal sources and point sources
are read into the computer by separate READ statements.
This was done to make the model more flexible and efficient.
The areal source emission rates are read in first, preceded
by the variable IHRA. IHRA is the hour through which the
areal emission rates are valid. If IHRA is read as 8, this
would indicate that the areal emission rates following were
valid through the hour ending at 0800 hours. The emission
rates of all areal sources are read at one time by this READ
statement.
The point source emission data are read next, pre
ceded by the variable IHRP. IHRP is the hour through which
the point source emission rates are valid. The emission
rate of each point source is read individually preceded by
the source identification, i.e., the I,J coordinate of the
area containing the source and the source number within that
area NS. Once an emission rate Q(I,J,NS) is read for a
particular point source, the value is held until another
value of Q(I,J,NS) or zero is read.
Factors related to the physical definition of
point sources are the northerly displacement S and the
easterly displacement R from the center of the area and the
physical stack height of the source ZPHY. These factors
are read preceded by the same I,J,NS identification that
preceded the point source emission data.
The other factors read into the model are defined
in Table 3 and in the program listing in Appendix 1.
Mathematical Equations
The basic dispersion equation used in the model was
an equation of mass continuity with a crosswind distribution
described by the Gaussian interpolation formula. The equa
tion is
QY 1 +z2 [1]
where
R/ = the ground level concentration in grams/
cubic meter,
O = the point source strength in grams/second,
TT = the constant 3.141...,
u = the mean wind speed in meters/second,
y = the horizontal crosswind displacement
from the plume centerline in meters,
z = the effective source height in meters,
gy = the horizontal crosswind dispersion
coefficient in meters, and
0, = the vertical crosswind dispersion
coefficient in meters.
The righthand side of Equation 1 contains a multi
plicative factor of 2, which is the conventional means of
accounting for the assumed plume reflection by the ground.
This equation was used to calculate the effect of point
sources.
The effect of areal sources was determined by
treating the source as a crosswind line source and using a
receptor oriented plume (64) in conjunction with the cross
wind integrated form of Equation 1. The equation obtained
by integrating Equation 1 with respect to y from + ooto
f Qo z2
cr aygzu exp(20 2)2 12)
The receptor oriented plume concept considers the
plumes originating at the receptor and extending upwind.
The same relationship exists between sources and receptor
as would exist if the plumes were considered to originate
at the actual sources and be carried downwind to the actual
receptor. The advantage of this procedure is that all
computations pertaining to a receptor can be made at one
time.
If the actual source was an infinite line source of
strength Q grams/metersecond/foot, its effect could be
calculated directly with Equation 2 by using the receptor
oriented plume concept. However, since the sources consid
ered in the development of the model were of finite length
a correction had to be applied. Mathematically, the cor
rection is the fraction of the area under the normal distri
bution curve which falls between the end points of the line
source, Pl and P2. The value of the factor varies between
0 and I and is determined by integrating the area under the
normal curve between Pl and P2. The expression for the
integration is
P2 2 Pl
F = [ exp( 11) exp(.PR2) [3]
where
F = correction factor, and
Pl and P2 = the end points of the line source
measured from the plume centerline
and normalized in terms of Ty.
Each integral can be approximated by the equation
(65)
2 2
x x x
K =, exp(2 ) exp( ) x x 2x 4
o 1 3+ 5
By using five terms of the continuous fraction, Equation 4
reduces to
Sexp(5 ) (945+105x +8x )x
K =*4[5]
2 945210x+15x
Equation 5 approximates the normal integral within
94 percent between 0 and 2.15 standard deviations. Beyond
2.15 0" the approximation diverges rapidly from the true value.
The factor of Equation 3 can now be represented as
F = KP2 Kpl
with KS1 and KP2 being determined by Equation 5 with x=
Pl and P2 respectively.
Distributed sources were considered as crosswind line
sources with a length equal to the crosswind dimension of the
distributed source, and their effects were determined by com~
bining Equations 2 and 6
TZ Q F z2[7
c fu~z exp( ) [7
The downwind distance was considered as being from the recep
tor to the center of the distributed source. Figure 5 illus
trates this concept.
Wind direction
Pollutant distributi >
along line source
2.150P1 Line source P2 2.15 7n
I anrxiatnn I
Rece pt or
FIGURE 5 TREATMENT OF EXTERNAL AREAL SOURCES
Equations for the dispersion coefficients, Ey and
~z, were approximated by fitting equations to the curves
presented by Gifford (27) (Figures 1 and 2). The curves
for Gj~y were approximated by an equation of the form
ay = ax
and those for 0, by fitting a quadratic to three logarithmic
values selected from the curves. The equations derived are
Stability Class 1
= 0.35x0.9
Eg~ = exp(10.81 
Stability Class 2
Gy = 0.22x.9
Ci,= exp(3.82 
Stability Class 3
= 0.18x0.
~z = exp(2.28 +
Stability Class 4
=0.13x.9
Ez~ = exp(3.27 +
 Extremely unstable
4.071nx + 0.4951n2x)
 Moderately unstable
1.251nx + 0.2001n2x)
 Slightly unstable
1.001nx 0.0111n2x)
Neutral
1.231nx 0.0381n2x)
[9a)
[10a)
[9b]
[10b]
[100]
[9d]
[10d]
Stability Class 5  Slightly stable
ly= 0.10x0. (9e]
0 = exp(387 + 1.281nx 0.05212x) [10e]
where
x = the distance from the source to the
receptor in meters.
Gifford.'s stability class F  moderately stable 
was not considered because of the mechanical and thermal
turbulence induced by an urban area.
The plume rise equation for describing the elevation
of a plume from a point source is
H=(0.147 Vd + 0.41xl04g 2/ (F) (lla]
u 2000
whe re
OH = the plume rise in meters,
V = the stack exit velocity in meters/second,
d== the stack diameter in meters,
QH= th~e heat efflux in calories/second,
u = the wind speed in meters/second,
x = the downwind distance in meters, and
F = a factor to account for the stability class.
The value of F ranges from 1.25 for an unstable lapse
condition to 0.90 for a stable atmosphere. The equation is
basically that of Thomas (43). The maxtimum plume rise,
reported to occur at about one mile, was assumed to occur
at 2000 meters and was corrected for other distances by the
term (48)
( 00) 2/, llb]
This resulted in a plume rise greater than that predicted
by Thomas for distances beyond 2000 meters. Equation 11a
was evaluated with values for the parameters which were
assumed to be typical of a large source. The value of QH
was determined by the relationship
QH MCp aT [110]
where
QH = the heat emission rate in calories/hour,
QM = the mass emission rate in pounds/hour,
AT = the difference between stack temperature
and a bient
C, = the coefficient of specific heat at
constant pressure.
The value of Cp for the stack gas was assumed to be equal to
Cp for air, i.e., 0.246 calories/gram.
By assuming
d = 10 feet
V, = 2000 feet/minute
hT = 1750C
Equation 11a reduced to
XO.67
bH = 2.4F( ) [1d]
For simplicity 11d was used in the model to describe the
plume rise from point sources.
The equation for describing the plume rise from
dwellings is (50)
DH = 2[12]
u0.33
whe re
H = the plume rise in meters, and
U = the wind speed in miles/hour.
To account for decomposition of a contaminant in
the plume, the exponential decay function was used. This
function is
0.693t,
DK = exp( T ) (13]
whe re
DK = the fraction of the original material
remaining after a time period t,
t = the time after emission and can be
related to the downwind distance by
t = x/u
where
x = the downwind distance, and
u = the wind speed, and
T = the decomposition half life of the
contaminant.
Programming Logic
The ground level concentration computed for each of
the receptors was considered to be the result of four effects:
1. The effect of emissions from an areal
source upon a receptor located at the
center of the area, henceforth referred
to as the effect of an areal source.
2. The effect of emissions from a point
source upon a receptor located in the
same grid area as the source; the effect
of an internal point source.
3. The effect upon a receptor of emissions
from areal and point sources located
outside of the area containing the recep
tor, the effect of external areal and
point sources.
4. The effect of the airborne material one
time period after the period of emission;
the effect of a drifting plume.
These effects are assessed by the model, which is written
in FORTRAN II language compatible with the IBM 709 computer.
The cumulative effect can be either printed out or stored
for future use in the computer.
Effect of an areal source
The emissions from an areal source were defined as
the combined emissions from all small sources within the
area. These emissions were assumed to be uniformly dis
tributed over the entire area.
With the receptor at the center of the area, only
the material emitted in the upwind half of the area has a
chance of reaching the receptor. Regardless of the wind
direction, half of the emissions will occur upw~ind; only
the distribution will change. With the crosswind limits of
the plume considered to be +2.150' the difference in dis
tribution is noticeable only near the upwind edge of the
area. Because of the relatively great distance to this
point the difference was assumed to be insignificant, thus
making the effect of an areal source independent of wind
direction. The effect is dependent upon wind speed, how
ever, both because of the diluting effect of the wind and
because of the effect of wind speed on plume rise. The
latter effect is noticeable only for wind speeds of 4 miles/
hour or less. Above 4 miles/hour there is essentially no
plume rise (50) and the ground level concentration is pro
portional only to the inverse of the wind speed.
The relative areal source effect was determined
for each combination of the five stability classes and wind
speeds of 1, 2, 3, 4, and 5 miles/hour. This was done by
numerically integrating the effect of the upwind emissions
in eight 100meter increments by using Equation 2. The
twentyfive factors so determined are the effect of a unit
areal source emission rate for the given meteorological con
ditions and have the units (grams/cubic meter)/(grams/hour)
or 7,42. The relative effect factors are constant for the
conditions calculated and are part of the input data of the
program. The factors are presented in Table 5.
For wind speeds greater than 5 miles/hour, the
5mile/hour factors are reduced in proportion to the in
verse of the wind speed, by the expression
s s 5
Ui
where
A the relative effect factor for a wind speed
of u. miles/hour and a stability class s,
and
A5 the relative effect factor for a wind speed
of 5. miles/hour and the same stabil ity
class.
O
O
X
rl
O
rl
I
O
\O
O
O
O
r
61
O
,C
43
C,
*0
*4
o
43
tO
*4(
E
*H
*,
OJ
NOOTO
CDQ~rl
ODAHH
C H O
H H H
m O
c) P
N 0 0~
U1
MU
OHe
For a wind speed of 0 miles/hour, a calm, the verti
cal dispersion coefficient was assumed to increase at a rate
equivalent to the rate of increase for a wind speed of 1000
meters/hour. The emissions from all sources, both areal
and point sources, were assumed uniformly distributed over
the entire area with an effective height of 2.1508, unless
limited by meteorological conditions. The resulting expres
sion for determining the relative ground level concentration
for periods of calm is
a NTFf (1609)2 z
2
exp (2Z
z
whe re
the relative ground level concentration
in (grams/cubic meter)/(grams/hour) ,
z = the plume height in meters and is equal
to 2.15Gz~ unless limited by meteorolog
ical conditions,
Gz = the vertical dispersion coefficient in
meters, and
1609 = the number of meters/mrile.
The ground level concentration at each receptor from
the areal sources is computed by multiplying the relative
effect factor by the emission rate from the source.
This effect is assessed by subroutine CREA, which
is called near statement number 21 in the main program.
Subroutine CREA is listed in Appendix 1.
Effect of an internal point source
The ground level concentration contributed. to a
receptor by an internal point source is determined. by Equa
tion 1. To determine the downwind and the crosswind dis
tances for the equation, the northsouth eastwest coordinate
system which located the point source with respect to the
receptor is rotated so that the eastwest, or the R, axis
becomes parallel to the wind direction. The rotation is
accomplished by first rotating the axes through an integral
multiple of 90 degrees so that the wind direction appears
to be in the northerly quadrant. This quadrant includes the
directions NNW, N, NNE, and NE. The axes are then rotated
so that the translated R axis corresponds to the wind direc
tion with the upwind direction being positive. The trans
lated values of R and S correspond to the downwind distance
x and the crosswind distance yzrespectively.
The physical stack height ZPHY of the source is
compared with BTM. BTM is a meteorological factor and is
the height to the top of an inversion based at or near the
ground. It was assumed that when ZPHY was equal to or
greater than 0.8 BTM, the plume rise would carry the plume
up into the turbulent zone above the inversion, and that
the stable air near the ground would prevent any of the
emitted gaseous material from reaching the ground. Thus,
the effect on the ground level concentration would be zero.
When ZPHY is less than 0.8 BTM, the effective stack height
z is determined by adding the plume rise as determined by
Equation 11a to the physical stack height of the source.
The computed effective stack height is then compared with
the meteorological factor TOP, which is the height to the
base of an inversion aloft  the limit of vertical mixing.
If z exceeds TOP, it is set equal to TOP, implying that the
plume will rise only to the base of the inversion.
The value of 0y and Oz is calculated by Equation 9
and 10 respectively. 0z is compared with 0.67 TOP and if it
is greater it is set equal to 0.67 TOP. This limits the
vertical spread of the plume when an inversion exists aloft.
Decomposition of the contaminant is accounted for
by Equation 13 with the contaminant half life read hourly.
The half life was made to vary hourly primarily to account
for the effects of changes in humidity and intensity of
sunlight on the half life of sulfur dioxide (66).
The ground level concentration from internal point
sources is computed by subroutine PTIN, which is called
near statement 76 in the main program. Subroutine PTIN is
listed in Appendix 1.
Effect of external areal
and point sources
These sources were considered together only because
the computation of the sourcereceptor distance for both
sources involves many of the same steps. Considering them
together eliminated a replication of computations. Other
than this the treatment of the source effects differs com
pletely and will be discussed separately.
Effect of external areal sources.This effect is
assessed similarly to the effect of an areal source, the
main exception being that this effect is dependent upon wind
direction.
A relative effect grid is computed which expresses
the relative effect of an external areal source on all re
ceptors except the one within the source. This is done by
determining the downwind and crosswind distance from the
source to each receptor by the procedure described on page
51 and by using Equation 7 to compute the relative effect.
It was assumed that if the crosswind distance to
the center of the source exceeded 2.15 O the effect on
that receptor was negligible. Also, if the downwind dis
tance from source to receptor was greater than the distance
that the wind could have carried the emitted material, no
effect was noted at the receptor.
In the vertical direction, the value of G' was
assumed limited to 0.67 TOP for reasons previously discussed.
The plume rise is computed by Equation 12 and is assumed
not to be affected by TOP or BTM, since the rise is always
relatively small.
In computing the factor for Equation 7 that corrects
for a finite length line source, the length of the line
source was assumed to be 1609 meters long regardless of the
wind direction. Also, the entire areal source was repre
sented by one line source rather than by numerically inte
grating the source effect as was done when determining the
effect of an areal source. A comparison of the effect as
determined by this method and the effect as determined by
considering the source in three increments showed a dis
crepancy of only 4 percent for a sourcereceptor distance
of one mile. At greater distances the difference would
become smaller. Therefore it was considered justifiable
to approximate the source by only one line source.
Since the plume, in this case, can travel quite a
distance before reaching the receptor, the decomposition of
the contaminant is accounted for by Equation 13. This is
the equation of the exponential decay function.
The effect of all areal sources upon each receptor
is determined by locating the relative effect grid, at each
source and multiplying that source strength by the relative
effect on each receptor. The resultant effect at each
receptor is the cumulative effect from all areal sources.
Effect of external point sources.The downwind
distance from a point source in area I,J to a receptor is
equal to the downwind distance of areal source I,J to the
receptor plus the downwind distance from the point source
to the center of area I,J as determined in the effect of
an internal point source. The crosswind distance from the
point source to the receptor is equal to the sum of the
corresponding crosswind distances.
If the crosswind distance is greater than 2.15 Cj ,
the effect on the receptor is considered negligible. No
effect is computed where the downwind distance exceeds the
distance the plume could have been carried by the wind.
The effect of an external point source is computed
by Equation 1 with a correction added to account for decompo
sition of the contaminant.
The effect of external areal and point sources is
assessed in subroutine OARPT, listed in AppDendix 1. Sub
routine OARPT is called at statement 76 in the main program.
Effect of a drifting plume
The effect of an airborne material, one period after
emission, was considered with respect to the wind conditions
of the current and preceding time periods.
Drifting plume with a change in wind direction.
The plume, as it appeared at the end of the preceding time
period, was assumed to be a line coinciding with the plume
center line with a concentration distribution described by
crosswind integrated concentrations at the ground level.
The line was assumed to be carried in the new direction of
the wind and to affect the receptors it was blown over
(Figure 6).
The effect at a receptor is determined by computing
the crosswind integrated concentration of the plume at the
point on the original plume centerline which passed over
the receptor. This concentration is reduced to account for
contaminant decomposition (Equation 13) and vertical dis
Wind direction
period T+1
Wind direction
period T
SOUICO
FIGURE 6 AREA AFFECTED BY DRIFTING PLUME WHEN WIND DIRECTION CHANGES
person; the latter being accounted for by the relationship
(az) R
where
S= the ground level concentration at
the receptor,
g~) = the vertical dispersion coefficient
z c on the downwind axis of the original
plume, and
( z R =the vertical dispersion coefficient
determined for travel distance in
the current and preceding wind
direction.
The area affected by the drifting plume is described
by a parallelogram with one corner at the source and two
sides parallel to and in the direction of the wind of the
previous time period and equal in lengthsto the product of
that wind speed and the time period. The other two sides
are parallel to and in the direction of the wind of the cur
rent time period and equal in length to the product of that
wind speed and the time period.
Drifting plume with a calm during the current time
period.When a calm persisted during the time period of
computation or if the wind speed and direction were such
that the plume did not drift over a receptor, the drifting
plume effect was assumed to be the ground level concentra
tion of the previous hour decreased by decomposition
(Equation 13) and turbulent dispersion. The dispersion
factor for turbulent dispersion was assumed to be a constant
for each stability class and was calculated by the empirical
expression
E=(Ey z) 3000
(Uyr C)4000
where
E = a reduction factor,
(Ti E ) =00 the product of the dispersion
coefficients for an equivalent
distance of 3000 meters, and
(7 ) =the product of the dispersion
y z 4000
coefficients for an equivalent
distance of 4000 meters.
This expression was empirically selected because it gave
results that agreed with observed data.
The factor E for each stability class is presented
in Table 6.
TABLE 6
FACTORS FOR THE DISPERSION OF GROUND LEVEL
MATERIAL DURING PERIODS OF CALM
Stability Class
Dispersion Factor, E
0.25
0.43
0.62
0.66
0.67
Drifting plume with a calm during the previous
time period.In this situation, the ground level concentra
tion of the previous period was assumed to be the "source."
This is reduced at downwind receptors by the factor
( z)1000 DK
(Tz)x+1000
where
F = a reduction factor,
(Ez~)1000 = the vertical dispersion coeffi
cient at an equivalent distance
of 1000 meters,
(Gj)x+1000 = the vertical dispersion coeffi
cient at a downwind distance
x+1000 meters from the receptor,
and
DK = the exponential decomposition function
with the decomposition time taken as
the interval between the time of
emission and the time of arrival at
the receptor.
Horizontal dispersion was not considered explicitly
but was accounted for by assuming that as much material
diffused into an incremental volume from each side as dif
fused out  an equilibrium condition. This assumption
would not be valid if a large concentration gradient existed
between "sources" or for receptors at the edges of the grid
system parallel to the wind direction. Since the occurrence
of large concentration gradients is relatively infrequent
and the effect near the edge of the grid is small to begin
with, the error introduced by this assumption was ignored.
Drifting plume with no change in wind direction.
The effect of a drifting plume, when there is no change in
wind direction, is determined by exactly the same methods
as are used to determine the effects of external areal and
point sources. The receptors affected are those within the
downwind range to which the plume would have been carried
during the second time period. This range was defined as
u(KT) TIME C_ X & u(IT) TIME
where
u(ET) = the wind speed of the previous hour,
u(IT) = the wind speed of the current hour,
ITIME = the length of the time period, and
X = the downwind distance.
Output of the model
The output parameter of the model is the ground
level concentration of a gaseous pollutant computed for each
element of the 15 by 15mile grid. The concentrations are
printed in terms of both micrograms per cubic meter and
parts per hundred million. The former is printed in the
format listed in Appendix 3. The contaminant printed in
this title is controlled by the variable KONT. The value
of KONT corresponding to a particular contaminant is pre
sented in Table 3.
The concentration in parts per: hundred million is
printed in square 15 by 15 array with the scale 1/2 inch
equal 1 mile. This can be used for plotting concentration
isopleths.
The control of the time scale of the output is
described in the section entitled Time scale. The time
scale of the output is corrected to a time base consistent
with the other factors in the model at statement 521 in the
73
main program. The base time period is one hour and correc
tions to other output time periods are made with the expres
s ion (41)
()0 .14
where
S= the ground level concentration averaged
over some time period T hours.
CHAPTER IV
EMISSION INVENTORY
A sulfur dioxide emission inventory was compiled
for the months of December, 1965, and January, 1966. This
inventory and the meteorological data for this period were
used to test the dispersion model.
The emissions were considered in two categories 
those from dwellings and small sources and those from large
individual sources. The emission rate from the latter
sources was generally greater than 10,000 grams SO2/hour,
although this criterion was not strictly adhered t~o.
Emissions from Industrial, Commercial,
and Institutional Sources
A list of the major industries and commercial estab
lishments was compiled from a list of business firms pub
lished by the Jacksonville, Florida, Chamber of Co~mmerce.
A questionnaire was sent to each firm which was considered
a possible source of pollution and also to large institutions
in the area requesting info ...a~on partaining to activities
on the premises that might result in the emissions, of air
borre contami.n~ants (63. is included the typ~e, q~uantity,
and sullfur content of fuels and any specific activity that
wou~ld result in th:e emission of sulfur dioxide. Whien addi
tional information was necessary fromn a particular source,
a teleph~one survey followed the questionnaire.
Several of the major sources wrere sampled as part
of the overall air pollution stLudy (63). In such cases
the samp~ling and survey data were used to reinforce each
otner.
As a result of this phase of the emission inventory
itwa fun tha~t thre only significant, source of sulfur
dioxide in Duval County was from the corbustion of fuel
oils conang vious a=6unts of sulfulr. Th ajor POr
tion of the process heat requ~ired by industry and commTercial
firmns wa~s produced by the combiustion of No. 5 and No. 6 fuel
oil. The remaindere was from~ natural gas and No. 2 fuel oil.
ccout half oftec=ercial spa~ce heating req~uiremrentls were
satisfied by oilfired heaters and half by natural gas.
A preliminary study with' thne model, using simulated
Etia, revealed that point sorcs it an eission rate or
Ses, than 10,000 g~rams S0323TO2/heSour ou not greatly a~ffec any
receptor even under the most unfavorable circumstances.
Thus, only sources with emission rates of 10,000 grams/hour
or greater were considered individually as point s~ources.
Sources with an emission rate less than this were consid
ered to contribute to the areal source emissions.
There were eighteen sources in the area encompassed
by the model that were classified as point sources. These
included powergenerating stations, various industrial and
commercial sources, and institutions. In addition to these
sources, twentyseven areal sources were treated as point
sources because more than 50 percent of the land area was
water. The point sources representing these areal sources
were located at the centroid of the land area they represented.
The emission rate from these sources is discussed in the next
section.
For several of the large users of fuel oil the daily
fuel oil consumption was obtained. From these data the
average hourly emission rate of sulfur dioxide was determined.
For the electric power generating stations it was possible
to estimate hourly oil consumption based upon projected
hourly power demands for winter months. The hourly power
demand as a percentage of the daily demand for a typical
winter day is shown in Table 7.
TABLE 7
HOURLY ELECTRIC POWER DEMAND AS A PERCENTAGE OF
THE DAILY DEMAND FOR THE WINTER SEASON
IN JACKSONVILLE, FLORIDA
Percentage of Daily Demand
Hour
Week Day S atur day Sunday
3.1
2.7
2.2
2.7
3.2
3.8
4.2
4.6
4.7
4.8
4.9
4.7
4.6
4.5
4.4
4.6
4.8
5.1
5.3
5.0
4.6
4.2
3.8
3.5
3.4
3.0
2.7
2.9
3.1
3.4
3.6
3.9
4.5
5.0
4.9
4.8
4.6
4.5
4.3
4.6
4.9
5.1
5.3
5.0
4.6
4.3
4.0
3.6
3.1
2.9
2.8
3.1
3.4
3.7
4.0
4.3
4.6
4.7
4.7
4.8
4.,9
4.6
4.3
4.0
4.4
4.8
5.2
5.0
4.8
4.6
4.0
3.4
TOTAL 100.0
100.0
100.0
The sulfur dioxide emissions were determined by
assuming that 98 percent of the sulfur in the fuel oil was
converted to sulfur dioxide during combustion (67). This
results in the conversion factor 157 lbs. SO2/1000 gallons
fuel oil for an oil with al1 percent sulfur conten~t. Thus
the combustion of 2000 gallons of fuel oil with a 3 percent
sulfur content would result in the emission
Q = 57 x2000x3=94ls.S.
10002
The emission rate from point sources ranged from
about 10,000 to over 3,000,000 grams SO2/hour. The emission
schedule of each point source was assumed to coincide with
the work schedule at that place unless more accurate informa
tion was available.
Emissions from Dwellings
and Small Sources
In Duval County 80 percent of the dwellings are
heated by oil heat (68); either No. 2 fuel oil or kerosene.
The sulfur content of these fuels averaged about 0.11 per
cent sulfur by weight (69). The consumption of these fuels
and hence the sulfur dioxide emission was based upon the
degreeday concept using 65 F as the base. It has been
suggested that the oil consumption for a fiveroom dwelling
is 0.18 gallon/household/degree day (67). This figure was
checked using the actual fuel oil consumption for Duval
County for December, 1965, and January, 1966 (69), and the
corresponding climatological data. The unit consumption
were found to be 0.21 gallon/household/degree day for
December and 0.17 gallon/household/degree day for January.
The latter values were used when computing the emission
rates for the two months.
The quantity of fuel oil and the sulfur content of
the oil consumed by small commercial establishments were
determined by the survey described in the preceding section.
The sulfur dioxide emission rates for these sources was
determined by the same procedure as was used for the large
sources.
The sulfur dioxide emissions from 80 percent of the
dwellings and all small commercial sources within each area
increment (Figure 4) were combined and were assumed to be
uniformly distributed over the area. Only 80 percent of
the dwellings were used, since that was the fraction heat
ing with oil. The expression used to compute the areal
source emission rates is
Q = (r(5.0) N D] (0.157 p) + q
where
Q = the SO2 emission rate in pounds/8 brs.,
r = the oil consumption factor for dwellings
in gallons/5room dwelling/degree day,
n = the average number of rooms per dwelling
in each area increment (70),
N = the number of dwellings in each area
increment (70),
D = the number of degree days/8br. period,
p = the sulfur content of the fuel oil as
percentage by weight, and
q = the SO2 emission rate from small sources
excluding dwellings within each area
increment in pounds/8 hrs.
The hourly emission rate for each areal source was computed
for three 8hour periods during the day in order to account
for the diurnal temperature pattern. The periods were 00800
hours, 09001600 hours, and 17002400 hours. The emission
rates ranged from 0 to about 12,000 grams SO2/hour and were
assumed constant throughout each period.
Emission Data
The emission rates for the areal sources and point
sources were expressed in the units grams SO2/hour and were
read into the program near statement 1006 and statement 1011
respectively.
The emissions from the areal sources and two of the
major point sources were computed and punched on cards by
the computer program listed in Appendix 2.
CHAPTER V
RESULTS AND DISCUSSION
Sampling Network
The sulfur dioxide sampling network established as
part of the Greater Jacksonville Air Pollution Control
Program and used for testing the model included 44 lead
dioxide candle stations, 11 stations employing the West
Gacke sampling method, and 2 stations equipped with electro
conductivity sampling instruments. The lead dioxide
candles were analyzed monthly with the results reported as
the sulfation rate in micrograms SO /square centimeter/day.
The WestGacke samplers were operated for 24hour periods
three times a week. The results of these samples were
expressed as parts per million (ppm) sulfur dioxide. The
electroconductivity instruments recorded every five minutes
on a continuous schedule. These results were also expressed
as ppm sulfur dioxide. Figure 7 shows the location of the
sampling stations.
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Comparison of Observed and Comouted
Sulfur Dioxide Concentrations
The sulfur dioxide concentrations observed by the
WestGaeke method were used to test the 24hour average
computed concentrations. The concentrations given by the
electroconductivity method were not used for testing the
model because there was a discrepancy between these values
and those determined by the WestGaeke method.
A recent study (71) showed the reproducibility of
the WestGaeke method to be + 0.006 ppm at the 50 percent
confidence interval and + 0.018 ppm at the 95 percent con
fidence interval in the concentration range 0.01 0.25 ppm.
As a result of this study the observed and computed concen
trations were compared after rounding to the nearest half
part per hundred million (pphm) and to the nearest whole
part pphm. The comparison was made to the nearest half
pphm because the range of observed concentrations wras only
0 3 pphm.
The sulfur dioxide concentration was observed at the
11 stations for one day in December, 1965, and 11 days in
January, 1966. The observed concentrations and the corres
ponding computed concentrations are presented in Table 8
and Figures 819. The computer listing of these data is
