Group Title: multivariable atmospheric dispersion model
Title: A Multivariable atmospheric dispersion model
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 Material Information
Title: A Multivariable atmospheric dispersion model
Physical Description: xv, 205 leaves : illus. ; 28 cm.
Language: English
Creator: Koogler, John Bernard, 1937-
Publication Date: 1966
Copyright Date: 1966
Subject: Air -- Pollution -- Research   ( lcsh )
Environmental Engineering Sciences thesis Ph. D
Dissertations, Academic -- Environmental Engineering Sciences -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis - University of Florida.
Bibliography: Bibliography: 197-204.
Additional Physical Form: Also available on World Wide Web
General Note: Manuscript copy.
General Note: Vita.
 Record Information
Bibliographic ID: UF00097862
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000559128
oclc - 13439762
notis - ACY4574


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August, 1966





Copyright by
John Bernard Koogler


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-



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.




LIST OF TABLES. ..........

LIST OF FIGURES ..........

ABSTRACT. ....... ....

. . . i

. .. .. . .yti

.. .. .. x

. ... .. .. xiii


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


n and


. .

. . 12



. . .

General Description .
Time scale. ......

Spatial scale .....
Meteorological factors.
Sources ........
Mathematical Equations. .

. . .
. . .
. . .

. .
. .



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. ..


. .

. .115

. .118

Reduction of emission rates of electric
power generating stations ......
Evaluation of the monthly sulfation
pattern . . . . . . . .
Ground level concentration from a
drifting plume. ...........





VI. SUMMARY.................. 135

APPENDIX 1. .. .. .. .. .. .. .. .. .. .. 140

APPENDIX 2... . .. 171

APPENDIX 3....,................ 175

APPENDIX 4. .. .. .. ... .. .. . ... . 188

LIST OF REFERENCES. .. ... .. .,. ... .. .. 197

BIOGRAPHICAL SKETCH..........,....... 205




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



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



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


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 ..


. I. .

. .

. .

. .

. . 16


. 119


. . 22


. 126

,. .28


28. Relationship between Sulfation Rate and
SO2 Concentration . 129

29. Ground Level Concentration from a Drifting
Plume . .. . .. .. . .. 134


Abstract of Dissertation Presented to the Graduate Council
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy



John Bernard Koogler

August, 1966

Co-chairmen: Dr. E. R. Hendrickson
Dr. R. S. Sholtes

Major Department: Bioenvironmental Engineering

A computer-solved 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 15-mile 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


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


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 one-mile 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 24-hour concentrations from 11

sampling stations.


Of the 111 24-hour 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 24-hour 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.



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


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.

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



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 cross-section.

The formula Sutton proposed for determining the

ground-level concentration of a material emitted from a

continuous point source was

TTC CZ ux X2-n ex 2n 2 + z

where, in general units of mass, length, and time,

S= the ground-level 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 3-minute 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


u = u, (z Z

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


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

10-minute 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 10-minute 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-

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 x-b

where b is an exponent with a value between
0.5 and 2.5, depending upon atmospheric

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


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 one-third to one-half 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 built-up area, dis-
persion coefficients revert to "open-
country" values.

4. The particular values of diffusion
parameters, for describing dispersion
in a built-up 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


"= H~


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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i~i~ iiriiiiiiiii iiii

/:il'"'"'' '''''" il;:lll
i ,,,', I ii; f :
i.i 1 ifll:

II( 1
1 1111 i I

I-------'--.- -r.._

i I- -.-

'i i i i i I:i "' ' I "'i" i ~''1 I :i...i~ i:
,.... -
_ii._ i
i-iiii 1r--i i


''"' '"'
)(!illll~J I j!lii i ijill~i:
'''!''~ ''';

1[1 '''''
i ) i~i~~r

~i~iiiiiiiiii iiil:ii:il~liii!!;l:-Ilii:i~

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~ i-ii I i i i;
i I

1- extremely unstable
2- moderately unstable
3- slightly unstable
4- neutral
5- slig htly stable

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 8-10 meter trees.

+Area within 500 meters of the source contained
several buildings 8-16 meters high.



(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

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 one-half 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-


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-


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

longer-term 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 short-term 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 long-term 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 oil-fog

dispersion over a distance of 5,000 meters, Singer (40)

arrived at a 1-minute p~eak to 100-minute 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 3-minute 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 (4-2,43,44,45,4o) 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'i-l lyth

Thomas formula (43), th~e Bosancuet, Carey, and I.altrson for-

mula (44?), the Priestley formula (45), and Suttor's fo-rmi. a


Stewart, Gale, and Creooks (21) concrac~ plure:. i-rova-

tions calculated by Bosanc~uet's form:1u witn 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


I: ' i ' I

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1.i i~i


M co

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 two-thirds power of the

downwind distance. Unfortunately, neither the formula

developed by Briggs or by Schmidt is well suited for use in

a large-scale 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


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

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 ,.

H-osler (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:



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

Tru QGj (T


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 1-mile-square 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;) ]


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 2-hour period. Twelve 2-hour

concentrations were averaged to give a daily average.

Turner reported 58 percent of the calculated concentrations

were within 1 pphm of observed 24-hour concentrations.

Of the 2-hour 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 computer-solved.

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.


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 O-y 2


X= the ground level concentration

Q = the emission rate,

iT = the constant 3.141l...,

u = the wind speed,

S= the horizontal crosswind dispersion

CF = the vertical crosswind dispersion

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 0-2 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


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 .



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 Jacksonville-Duval 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


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 one-mile intervals in the north-south

and east-west 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.



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


Basically, the input parameters (Table 3) are



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

N -the number of cards to be read.

R -the east-west displacement of a point source
from the center of areal source I,J. The
displacement is in meters with east positive.

S -the north-south displacement of a point
source from the center of areal source I,J.
The displacement is in meters with north

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 3--Continued

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.


-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 12-hour period,

KODE would be read as 12. The range of KODE is 1 to 24.

TABLE 3--Continued






-the day for which the data apply.

-twelve 1-hour averages of wind direction,
on a 16-point 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 24-hour-period concentrations. Thus ,

if the concentration is to be averaged for a period of 72

hours, the concentrations from three 24-hour 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


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 n-th hour. For

example, if the meteorological factors are to be averaged

over a 3-hour 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 15-mile square.

This scale was large enough to include all major sources of

emissions in the Jacksonville-Duval County area. The 15-

by 15-mile area was subdivided into 1-mile-square increments

by a north-south, east-west 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 1-mile 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




- c


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 Bendix-Friez 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


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 750-foot 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



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.


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 1-mile 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


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]


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 right-hand 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


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


If the actual source was an infinite line source of

strength Q grams/meter-second/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]


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


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]
2 945-210x+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


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


Ez~ = exp(-3.27 +

-- Extremely unstable

4.071nx + 0.4951n2x)

-- Moderately unstable

1.251nx + 0.2001n2x)

-- Slightly unstable

1.001nx 0.0111n2x)


1.231nx 0.0381n2x)








Stability Class 5 -- Slightly stable

ly= 0.10x0. (9e]

0 = exp(-387 + 1.281nx 0.05212x) [10e]


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 + 0.41xl0-4g 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]


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
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]
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

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
x = the downwind distance, and
u = the wind speed, and

T = the decomposition half life of the

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 100-meter increments by using Equation 2. The

twenty-five 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

5-mile/hour factors are reduced in proportion to the in-

verse of the wind speed, by the expression

s s 5

A the relative effect factor for a wind speed
of u. miles/hour and a stability class s,

A5 the relative effect factor for a wind speed
of 5. miles/hour and the same stabil ity























m O

c) P

N 0 0~



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

exp (-2Z

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 north-south east-west coordinate

system which located the point source with respect to the

receptor is rotated so that the east-west, 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 source-receptor 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


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 source-receptor 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



person; the latter being accounted for by the relationship

(az) R


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

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


E=(Ey -z) 3000
(Uyr C)4000


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.



Stability Class

Dispersion Factor, E






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


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,

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


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 15-mile grid. The concentrations are

printed in terms of both micro-grams 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


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


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


S= the ground level concentration averaged
over some time period T hours.



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 th-e over-all air pollution stLudy (63). In such cases

the samp~ling and survey data were used to reinforce each


As a result of this phase of the emission invent-ory
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.

c-cout half oftec=ercial spa~ce heating req~uiremrentls were

satisfied by oil-fired heaters and half by natural gas.

A preliminary study with' thne model, using simulated

Etia, revealed that point sorcs it an e-ission rate or

S-es, 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 power-generating stations, various industrial and

commercial sources, and institutions. In addition to these

sources, twenty-seven 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


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.



Percentage of Daily Demand
Week Day S atur day Sunday



















TOTAL 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.

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

degree-day concept using 65 F as the base. It has been

suggested that the oil consumption for a five-room 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


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


Q = the SO2 emission rate in pounds/8 brs.,

r = the oil consumption factor for dwellings
in gallons/5-room 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/8-br. 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 8-hour periods during the day in order to account

for the diurnal temperature pattern. The periods were 0-0800

hours, 0900-1600 hours, and 1700-2400 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


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.



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 micro-grams SO /square centimeter/day.

The West-Gacke samplers were operated for 24-hour 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.




> s



o 3


o a

Comparison of Observed and Comouted
Sulfur Dioxide Concentrations

The sulfur dioxide concentrations observed by the

West-Gaeke method were used to test the 24-hour 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 West-Gaeke method.

A recent study (71) showed the reproducibility of

the West-Gaeke 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 8-19. The computer listing of these data is

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