EPA-R4-73-024
December 1973
Environmental Monitoring Series
•XvXvXv X'X'X'X
illl^lilil^liiSlli!
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, Environmental Protection
Agency, have been grouped into five series. These five broad categories were established
to facilitate further development and application of environmental technology. Elimination
of traditional grouping was consciously planned to foster technology transfer and a maxi-
mum interface in related fields. The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL MONITORING series. This series
describes research conducted to develop new or improved methods and instrumentation
for the identification and quantification of environmental pollutants at the lowest conceiva-
bly significant concentrations. It also includes studies to determine the ambient concentra-
tions of pollutants in the environment and/or the variance of pollutants as a function of time
or meteorological factors.
EPA REVIEW NOTICE
This report has been reviewed by the Office of Research and Development, EPA, and ap-
proved for publication. Approval does not signify that the contents necessarily reflect the
views and policies of the Environmental Protection Agency, nor does mention of trade
names or commercial products constitute endorsement or recommendation for use.
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ERRATA
EPA-R4-73-024
CDM Users: Make the following corrections to the Users Manuals
and check your computer programs for conformance.
User's Guide For The Cljmatological Dispersion Model
A. Page 52 - Insert the following as line 00000010:
DIMENSION DX(4), DY(4), A(4), KPX(18), ICON(2), CCON(2)
B. Page 52 - Modify lines 00000220 and 00000230 to read:
RI = (RX-XGJ/RAT +0.5
RJ = (RY-YG)/RAT +0.5
C. Page 70 - Modify lines 00007530 and 0007540 to read:
PX(IPS) = (X-XG)/RAT+ 0.5
PY(IPS) = (Y-YG)/RAT +0.5
D. Page 16 & 29 - The X-MIN and Y-MIN... etc.
0.750000E 01 should be 0.500000E 01 in all cases
E. Page 66 - Line 5700 change
(9X.6F9.0) to read (7X.6F7.0).
F. Page 15 - Line 1060 change to read same as line 1060 on page 26.
G. Page 12 - starting with "D (diameter of stack in meters)"
change column numbers to read:
44 to 48
49 to 55
56 to 62
63 to 67
H. Page 81, Eqn. 8
Integral upper limit should be TT+$+A
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EPA-R4-73-024
.December 1973
USER'S GUIDE
FOR THE
CLIMATOLOGICAL DISPERSION MODEL
by
Adrian D. Busse
John R. Zimmerman
Both authors on assignment from
National Oceanic and Atmospheric Administration
U.S. Department of Commerce
Program Element No. 1A1009
NATIONAL ENVIRONMENTAL RESEARCH CENTER
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
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PREFACE
This report provides information on and the computer program for the Clima-
tological Dispersion Model (CDM). Although the computer program was formula-
ted and tested with care, it is possible that some forms of valid input data were
not adequately tested.
In case there is a need to correct, revise, or update this model, revisions
will be distributed in the same manner as this report. If your copy was obtained
by purchase or through special order, you may obtain the revisions as they are
issued by completing the mailing form below.
Comments and suggestions regarding this document should be directed to the
Chief, Environmental Applications Branch, using the address indicated on the
mailing form.
Chief, Environmental Applications Branch,
Meteorology Laboratory,
Environmental Protection Agency,
Research Triangle Park, N. C. 27711
I would like to receive future revisions to User1 s
Guide for the Climatological Dispersion
not receive EPA documents through the
lists.
INTamp
Address. ,,
Model.
regular
7.ir>
I do
mailing
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ABSTRACT
The Climatological Dispersion Model (CDM) determines long-term (seasonal or
annual) quasi-stable pollutant concentrations at any ground-level receptor using average
emission rates from point and area sources and a joint frequency distribution of wind
direction, wind speed, and stability for the same period.
This model differs from the Air Quality Display Model (AQDM) primarily in the way
in which concentrations are determined from area sources and in the use in the CDM of
Briggs' plume rise formula and an assumed power law increase in wind speed with height
that depends on stability.
The material presented is directed toward the engineer familiar with computer tech-
niques and will enable him to perform calculations "with the CDM. Technical details of the
computer programming are discussed; complete descriptions of input, output, and a test
case are given. Flow diagrams and a source program listing are included. Companion
papers by Calder (1971) on the technical details of the model and by Turner et al. (1972)
on validation are included.
iv
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CONTENTS
Sectipn Page
PREFACE iii
ABSTRACT iv
LIST OF FIGURES vi
LIST OF TABLES vi
1. INTRODUCTION „ 1
2. CONCENTRATION FORMULAS 3
3. PREPARATION OF INPUT DATA 5
Grid System and Area Emissions 5
Meteorological Parameters 5
Calibration of Computed Concentration 9
Card Input Sequence 10
Interactive Operation 14
4. ALGORITHMS FOR CONTRIBUTIONS BY AREA SOURCES 18
5. COMPUTATIONAL OUTPUT (BATCH MODE) 20
REFERENCES 21
GLOSSARY 22
APPENDIX A. TEST EXAMPLE 24
Introduction 24
Card Input :" 24
Printed Output 25
Card Output 25
Isopleths and Histograms 25
APPENDIX B. FLOW DIAGRAMS 45
APPENDIX C. FORTRAN STATEMENTS 51
APPENDIX D. A CLIMATOLOGICAL MODEL FOR MULTIPLE SOURCE URBAN AIR
POLLUTION 73
APPENDIX E. AN EVALUATION OF SOME CLIMATOLOGICAL DISPERSION MODELS . 107
BIBLIOGRAPHIC DATA SHEET 133
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LIST OF FIGURES
Figure . Page
1. Illustration of Sector Integration . 18
A-l. Emission Grid for Test Problem 24
A-2. Isopleth for Test Example 42
A-3. Histograms for Test Example 43
B-l. Abbreviated Flow Chart of Climatological Dispersion Model 46
B-2. BLOCK DATA 48
B-3. Subroutine CLINT 48
B-4. Subroutine AREA 49
B-5. Subroutine POINT 50
LIST OF TABLES
Table Page
1 . Pasquill-Gifford and Climatological Dispersion Model Stability Classes .... 6
2. Central Wind Speeds ............ .......... -...:. 6
3 . Exponents for Wind Profile • •' ..................... • 7
4. Mixing Height .................... .... ...... 7
5. Parametric Values for a (p )••'••> ................ • • • 8
z
6. Card Input Sequence ........................... 10
7. Data Listed on First Three Cards of an Interactive Data Set- ......... 14
8. Listing of the Example TSO Data Set, TESTSET ......... • ..... 15
9. Interactive Operation of Climatological Dispersion Model, TESTSET Listing • • 1&
10. Increments of Integration ••._••• ................ ...... 19
A-l. Card Input for the Test Example • • •. .............. ..... 26
A-2. Output for Test Example, Input Parameters Used ......... ..... 29
A-3. Output for Test Example, Computed Concentrations • • • .......... 34
A-4. Format of Card Output • • • ...... ..... •. ........... 39
A-5. Listing of Card Output for Test Example ..... ........... • • 41
C-l. FORTPJUtt Statements ..................... ; . . . .v. 52
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USER'S GUIDE
FOR THE
CLIMATOLOGICAL DISPERSION MODEL
.1. INTRODUCTION
This report describes the computer program for the Climatological Dispersion Model
(CDM) and its use in estimating long-term concentrations of nonreactive pollutants due to
emissions from area and point sources in an urban area. Two pollutants may be considered
simultaneously, the most frequent application being for sulfur dioxide and particulate mat-
ter. The program is written in FORTRAN IV language (level G) for the IBM 360/370 com-
puters .
This model differs from the Air Quality Display Model (AQDM) primarily in the way in
which concentrations are determined from area sources and in the use in the CDM of Briggs1
plume rise formula and an assumed power law increase in wind speed with height that de-
pends on the stability.
The material presented is directed toward the engineer familiar with computer tech-
niques and will enable him to perform calculations with the CDM. Technical details of
the computer programming are discussed; complete descriptions of input, output, and a
test case are given; and a test example, flow diagrams, FORTRAN statements, and com-
panion papers are presented as appendixes.
The relevant formulas for -average concentrations resulting from emissions from area
and point sources are presented in Section 2. (For a complete account of the theory.
Appendix D should be consulted.) Section 3 contains information on the grid system, the
emission inventory, and meteorological parameters. In addition, the sequence of cards
for input data is given. The most tedious part of the computations arose from the area
source calculations. Thus, it was considered important that the algorithms used in the
computational program for area sources be described in some detail. These are given in
Section 4. Finally, Section 5 contains a discussion on the computational output that can
be obtained by using the program.
1
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A test example, flow diagrams, and FORTRAN statements are presented in Appendixes
A, B, and C, respectively. Companion papers by Calder (1971) and Turner et. al. (1972)
have been reprinted as Appendixes D and E.
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2. CONCENTRATION FORMULAS
The average concentration C. due to area sources at a particular receptor is given
^ - 16 f [ 16 6 6 1
CA = T- \ \ I q,(P) 2 2 0.8L. New terms in Equations 3 and 4 are defined as follows:
Z
a (p) = vertical dispersion function, i.e., the standard deviation
z of the pollution concentration in the vertical plane
-------
h = effective stack height of source distribution, i.e., the
average height of area source emissions in the k**1 wind
direction sector at radial distance p from the receptor
L = the afternoon mixing height
T, = assumed half life of pollutant, hours
The possibility of pollutant removal by physical or chemical processes is included in
the program by the decay expression exp (-0.692p /UfcT.) .
The total concentration for the averaging period is the sum of concentrations of the
point and area sources for that averaging period.
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3. PREPARATION OF INPUT DATA
GRID SYSTEM AND AREA EMISSIONS
A rectangular grid array of uniform-sized squares is used to overlay the region of
interest. The main purpose of this grid is to catalogue the emission inventories by area
sources. There is some flexibility in the size of the grid squares in that the computer
program will accept information on emissions from squares whose sides have lengths
which are integer multiples of the length of the side of the basic square. Thus, if the
basic square has a length s, emission information for a larger square whose side has a
length, say 4s, will be accepted by the computer and be distributed uniformly into 16
basic squares in the correct manner.
The origin of the overlay grid is located in the lower left-hand corner of the array
with the X-axis pointing toward the east and the Y-axis pointing toward the north. With
respect to the map coordinates of the region, the origin of the grid array is to be located
at some suitably chosen point in the lower left-hand section of the region under considera-
tion. The length of a side of a square is expressed in meters. However, the map coordi-
nates can be expressed in any suitable units, say, thousands of feet or kilometers. The
magnitude of the length of a square will depend on how many squares are needed in the
emission inventory of a region. The computer program is dimensioned to accept 2500 area
sources and 200 point sources. Computations can be performed for any number of receptor
points.
METEOROLOGICAL PARAMETERS
Joint Frequency Function
It is necessary to have information on the joint frequency function ^(k.fc.m) a's input
for the model. This function gives the joint frequency of occurrence of a wind direction
sector k, a wind speed class I, and a stability category index m. There are 576 entries
in the table for the joint frequency function. This number of values results from the 16
different wind vectors, 6 wind speed classes, and 6 stability classes used in determining
the frequency function.
Weather observations are taken hourly by meteorologists of the National Weather
Service at airports serving major urban areas. In most circumstances, these weather data
will be representative of the meteorological conditions of adjacent urban areas. 'This
weather information for localities throughout the United States can be obtained from the
National Climatic Center (NCC) located in Asheville, North Carolina. The Day-Night
version of the NCC program called STAR gives the proper form of the joint frequency
function, which may be used directly as input into the Climatological Dispersion Model.
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The stability classification of the Day-Night STAR program differs from the original
STAR program in that the Pasquill-Gifford stability class 4 has been separated into two
classes, 4 and 5, representing neutral (P-G stability class 4) daytime conditions and
neutral (P-G stability class 4) nighttime conditions, respectively. In addition, in the
revised program the remaining nighttime Pasquill-Gifford stability classes (5 and 6) are
lumped into class 6. The Delation between the Pasquill-Gifford stability classes and those
used in the Climatological Dispersion Model is shown in Table 1.
Table 1. PASQUILL-GIFFORD AND CLIMATOLOGICAL
DISPERSION MODEL STABILITY CLASSES
Pasquill-Gifford
1
2
3
4 daytime
4 nighttime
The wind speed U for the various weather bureau classes (Table 2) is taken as the
central wind speed of the class. It should be noted that the central wind speed of the
lowest wind speed class was arbitrarily taken as 1.5 meters per second. This means
that light winds reported in the first wind speed class were rounded up to this value,
since most operational wind instruments do not sense low wind speeds accurately.
Operational wind instruments are designed for durability and also to withstand exposure
to strong , gusty airflow. For these reasons, most wind sensors have a high starting
speed, which can lead to the erroneous reporting of light winds as calms (Truppi, 1968).
Table 2. CENTRAL WIND SPEEDS
Wind speed
class
1
2
3
4
5
6
Speed interval, knots
0 to 3
4 to 6
7 to 10
11 to 16
17 to 21
> 21
Class wind speed, m/sec
1.50
2.46
4.47
6.93
9.61
12.52
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Wind Profile
To account for an increase of wind with height above a height of 10 meters (anemom-
eter height) to the level of emission, a power law relation of the form'
U(z) = Uj^z/zo)1? (5)
is used in the computational program. The exponent p, as determined by DeMarrais
(1959), depends on the stability class and is given in Table 3.
Table 3. EXPONENTS FOR WIND PROFILE'
Stability class
1
2
3
4
5
6
Exponent (p)
0.1
0.15
0.20
0.25
0.25
0.-30
Mixing Height
The magnitude of the mixing height undergoes considerable diurnal, seasonal, and
annual variation. It is impractical to account for all such variations in detail. Neverthe-
less, some recognition is given to changes in the magnitude of the mixing height by
assigning values to different stabilities according to Table 4.
Table 4. MIXING HEIGHT
Stability class
1
2
3
4 day
4 night
5
6
Mixing height, meters
1.5 x HT
HT
HT
HT
(HT -f HMIN)/2
HHIN
HMN
In Table 4, HT if the cliaatological »e«n value of the mixing height ac tabulated by
Holsworth (1972) and HMIN ic the nocturnal muting height.
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Stability Classes
The lower layer of the urban atmosphere is generally more unstable than is the cor-
responding adjacent rural atmosphere. To account for this, modifications have been made
to the stability class applied in the calculation of concentration from area sources. This
modification consists of decreasing the stability class by one class with the exception of
PI, which is unaltered. This correction is not applied to point sources.
During the night with a surface inversion condition and a rural class stability of PC,
the neutral stability class P^ is assumed for both point and area sources. Otherwise,
there is no modification of the stability classes applied to point source calculations.
Dispersion Functions
An analytical approximation to the curves of Pasquill (1961) and Gifford (1961) for
the vertical dispersion function
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3.5X* (9)
X*= 14 F5/8 ifF < 55
X* = 34F2/5 ifF >55.
where Ah = plume rise, meters
g = acceleration due to gravity, m/sec
Vs = average exit velocity of gases of plume , m/sec
Rs = inner radius of stack , meters
Ts = average temperature of gases in plume, °K
Ta = ambient air temperature, °K
U = wind speed at stack height, m/sec
P = distance from source to receptor , meters
As suggested by Briggs, p/X* was not allowed to exceed the limiting value of 3.5.
For the other option on plume rise, the value of the product of the average wind speed
and the height of plume rise may be used . This option permits no variation of this product
with distance from the stack and the magnitude of the plume rise is at the discretion of the
user.
CALIBRATION OF THE COMPUTED CONCENTRATION
If calibration constants of the linear expression
C'=A+BC (10)
where C1 = calibrated concentration
A, B = calibration constants
C = computed concentration
are known, they may be entered into the program and used to obtain a calibrated concen-
tration . The calibration constants are determined from regression analysis of observed
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pollution data and the computed concentrations produced by the model. Thus, at least one
initial run of the model must be made without use of the calibration feature. Once the
model has been run to obtain computed concentrations, a regression analysis may be made
of computed and observed concentration data. After finding the calibration constants,
calibrated concentrations can be obtained on subsequent operations of the model.
In order to have both measured and observed data on computer cards for input to a
regression analysis, it is possible to enter the observed concentrations on the receptor
input cards. This value will then be punched on the output cards containing the calcu-
lated pollution concentrations.
If it is not desired to use the calibration feature, the value of the calibration constants
A and B should be specified as 0 and 1 respectively. This will result in the output of a
"calibrated" concentration value identical to the computed value.
CARD INPUT SEQUENCE
The arrangement of input data on the cards that follow the program deck is given in
Table 6. Certain data that are permanent features of the model, such as the wind speed
of classes and wind direction of classes, are a part of the program and not read in as
•
separate entities. Interactive operation, discussed in the next section, requires an input
data set somewhat different from that given in Table 6.
Table 6. CARD INPUT SEQUENCE
Card No.
1
Column
1 to 8
9 to 16 -
17 to 21
22 to 26
27 to 31
32 to 36
37 to 41
42 to 59
Format
2A4
2A4
15
15
15
15
15
2F9.0
Contents
AROS(1)-AROS(2) (Identification for
punched output of the computed area
source concentrations of the two
pollutants. See sample punched output.)
PROS(1)-PROS(2) (Identification for
punched output of the computed point
source concentrations of the two
pollutants)
IRUN (Computer run identification
number)
NLIST (Index which indicates whether
input data should belisted. If
NLIST <_ 0, input data is printed.)
IRD (Card input file number)
IWR (Output print file number)
IPU (Output punch file number)
CA(1)-CA(2) (Constants of the linear
equation Y= CA + CB x X, used to
calibrate the calculated concentrations
of the two pollutants considered in the
model )
10
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Table 6 (continued). CARD INPUT SEQUENCE
Card No..
2
3
.Col umn
60 to 77
1 to 6
7 to 12
13 to 18
19 to 24
25 to 30
31 to 36
37 to 42
43 to 48
49 to 54
55 to 60
61 to 66
67 to 72
1 to 6
7 to 12
Format
2F9.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
Contents
CB(1)-CB(2) (Slope of the linear
equation, Y = CA + CB x X, used to
calibrate the calculated concentrations
of the two pollutants considered in
the model)
DELR (Initial integration increment of
radial distance from receptor, meters)
RAT (Ratio of length of a basic emission grid
square and the length of a map grid square)
CV (Conversion factor which upon multi-
plication by RAT expresses the -distance
of the side of an emission grid square
in meters. For example, if the map\
units are in kilometers, CV=1000.)
HT (Average afternoon mixing height
in meters)
HMIN (Average nocturnal mixing height
in meters)
XG (X map coordinate of the southwest
corner of the emission grid array)
YG (Y map coordinate of the southwest
corner of the emission grid array)
XGG (X map coordinate of the southwest
corner of the plotting grid)
YGG (Y map coordinate of the southwest
corner of the plotting grid)
RATG (Ratio of the length of the grid
square used for plotting and the length
of a map grid square)
TOA (Mean atmospheric temperature in
degrees centigrade)
TXX (Width of basic emission square .in
meters)
DINT (Number of intervals used to in-
tegrate over a 22.5° sector. Maximum
value is 20, typical value is 4.)
YD (Ratio of average daytime emission
rate to the 24-hour emission rate
average)
11
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Table 6 (.continued). CARD INPUT SEQUENCE
Card No.
4-99
[Source
cards
follow]
100a
Column
13 to 18
19 to 54
55 to 66
1 to 63
1 to 6
7 to 13
14 to 20
21 to 36
37 to 43
44 to 49fc
50 to 56b
57 to 63b
64 to 68b
Format
F6.0
6F6.0
2F6.0
[9X,6(1X,
F8.6)]
F6.0
F7.0
F7.0
2F8.0
F7.0
F5.0
F7.0
F7.0
F5.0
/
Contents
YN (Ratio of the average nighttime
emission rate to the 24-hour emission
rate average)
SZA(1)-SZA(6) (Initial oz in meters
for each stability class. Six different
values can be used, but normally only
one value is used.)
GB(1)-GB(2) (Decay half life in hours
for the two pollutants)
F(i,j,k) (Joint frequency function,
identical to (k,s,,m); i = index
for stability class, j = index for wind
speed, k = index for wind direction.
See input data of sample problem for
proper ordering of this parameter by
stability class, wind direction, and
wind speed.)
X(X map coordinate of the southwest
corner of the area emission grid, or
if appropriate, the X map coordinate
of a point source)
Y (Y map coordinate of the southwest
corner of the area emission grid, or
if appropriate, the Y map coordinate
of a point source)
TX (Width of an area grid square in
meters. It is important that no entry
be made in the case of a point source.)
S1-S2 (Source emission rate in grams
per second for the two pollutants)
SH (Stack height in meters)
D (Diameter of stack in meters)
VS (Exit speed of pollutants from
stack in meters per second)
T (Gas temperature of stack gases in
degrees centigrade)
SA (If this field is blank, Briggs1
formula is used to compute stack height.
Otherwise, the product of plume rise
and wind speed is entered in square
meters per second.)
12
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Table 6 (continued). CARD INPUT SEQUENCE
Card No.
1000
[Receptor
cards
follow]
1001°
Col umn
--
1 to 8
9 to 16
31 to 34
38 to 41
42 to 46
Format
--
F8.2
F8.2
14
14
15
Contents
This is a blank card which follows
information on the emission sources.
It is used to test the end of sources
and must not be left out.
RX (X map coordinate of the receptor)
RY (Y map coordinate of the receptor)
KPX(9) (Observed concentration at the
receptor of the first pollutant)
KPX(IO) (Observed concentration at the
receptor of the second pollutant)
NROSE (A control that, if greater than
zero, will print out histogram concen-
tration data. If left blank, no
histogram data will be printed.)
There will be as many cards of this type as there are area and point
sources. The next card type will arbitrarily be numbered 1000.
Needed for point sources only. Leave blank on area source cards.
0 There will be as many cards of this type as there are receptors.
Listing of card input for the test case (Table A. 1) should be helpful. However, several
parameters may need additional explanation.
The parameter DELR has usually been set at 250 meters. Assume that an emission
inventory exists with the smallest emission square 5000 feet on a side. Also assume that
all coordinates are given in feet. In this case the basic emission grid square would be
5000 feet on a side and RAT would be 5000, CV would be 0.3048, TXX would be 1524, and
XG, YG, XGG, and YGG would all be in feet. Also, all source and receptor coordinates
would be expressed in feet (map coordinates) .
Now assume that it is desirable to plot the resulting concentrations on a grid system
with 1-kilometer spacing. The lower left corner of this grid is specified by the map
coordinates (in feet) as XGG,YGG; and RATG would be i:524. In this example, TX on
the source cards would be 1524 or some multiple of this number for the area sources.
13
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INTERACTIVE OPERATION
The Climatological Dispersion Model is now accessible to qualified users on remote
computer terminals by means of telephone hookup to the Environmental Protection Agency
computer facilities in the Research Triangle Park, North Carolina. The interactive
version of the model requires an-input data set that is almost the same as has been des-
cribed in the previous section. For interactive processing of the model, a catalogued
data set, whose name is passed on to the model as a parameter, must be created under
standard TSO or TSO/BATCH procedures.
An example TSO data set, which has been given the name TESTSET, is listed in
Tables 7 and 8. This interactive input data set is different from that described in the.
previous section in two respects. The first is that there are fewer parameters required-
on the first three input cards and the second is that receptor locations are submitted
interactively from the computer terminal. Data for the first three cards are entered consecu-
tively, starting in column one for each card and separating the items by commas, as illus-
trated in Table 7.
Card
Table 7. DATA LISTED ON FIRST THREE CARDS.OF AN
INTERACTIVE DATA SET
List
Example
IRUN, IRD, IWR, CA, CE
DELR, RAT, CV, HT, HMIN, XG,
YG, TOA, TXX
DINT, YD, YN, SZA, W
r Col 1
V99999,5,6,0,0,l,l
250,5,1000,800,150,5,5,
1.25,5000
4,1,1,30,30,30,30,30,30
3,999999
The self-explanatory listing in Table 9 illustrates the operation of the Climatological
Dispersion Model with an interactive computer terminal. The user submits computer com-
mands in lower-case letters, and the computer responds in upper-case letters.
14
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Table 8. LISTING OF THE EXAMPLE TSO DATA SET, TESTSET
list testset.data
TESTSET.DATA
00010 99999,5,6,O.,0.,!.,.!.
00020 250.,5.,1000.,800.,150.,5.,5.,1.25,5000.
00030 i)., !.,!., 30., 30., 30., 30. ,30., 30., 3., 999999.
0001)0
00050
44 blank cards
00500
00510
00520
00530
005UO
00550
00560
00570
00580
00590
00600
00610
00620
00630
0061)0
00650
00660
00670
00680
00690
00700-
0.0625
0.0625
0.0625
0.0625
0.0625
0.0625
0.0625
0-.OG25
0.0625
0.0625
0.0625
0.0625
0.0625
0.0625
0.0625
0.0625
t
I
24 blank cards
00950
00960
00970
00930
00990
01000
01010
01020
01030
0101)0
01050
01060
READY
5.
5.
10.
15.
15.
15.
12.
0
0
0
0
0
0
5
5.
15.
15.
15.
10.
5.
12.
0
0
0
0
0
0
5
10000.
5000.
5000.
5000.
5000.
5000.
0.
1)000.
iono.
1000.
1001.
1000.
1000.
1000.
0
0
0
o
n
0
0
'lOOO.
1000.
non.
1000.
1000.
1000.
1000.
n
n
0
0
0
n
n
20.
20.
20.
20.
20.
20.
20.
0
0
0
0
n
0
n
20.n 5.0 i.n o.O
15
-------
Table 9. INTERACTIVE OPERATION OF CLIMATOLOGICAL DISPERSION MODEL, TESTSET LISTING
"logan user id p (unamap) non
.XXXXX LOGON IN PROGRESS AT 10:31:55 ON FEBRUARY 13, 1973
NO BROADCAST MESSAGES
LOGON PROCEEDING
READY
cdm testset
UTILITY DATA SET MOT FREED, IS NOT ALLOCATED
DO YOU WANT A PARTIAL LISTING OF MODEL PARAMETERS? ENTER YES OR NO.
yes
CDHI VERSION 7301*3, RUN 99999
THE CENTRAL WIND SPEEDS OF THE SIX WIND SPEED CLASSES (U):
O.lSOOOOc+01 0.2U5872E+01 O.I»U70I»OE + 01 0.692912E+01 0.961136E+01 0.125171E+02
THE EXPONENTIAL OF THE VERTICAL WIND PROFILE BY STABILITY CLASS (UE):
0.10nOQOE+00 0.150000E+00 0.200000E+00 . 0.250000E+00 0.250000E+00 0.300000E+00
THE INITIAL SIGMA Z FOR AREA SOURCES !?Y STABILITY CLASS (SZA):
0.300000E+02 0.300000E+02 0.300000E+02 0.300000E+02 0.300000E+02 0.300000E+02
THE CLIMATOLOGICAL MEAN NOCTURNAL AND AFTERNOON MIXING HEIGHTS (HMIN,HT):
0.150000C+03 O.RnOOOOE+03
THE DAY AMD NIGHT EMISSION WEIGHT FACTORS (YD,YN):
0.100000C+01 0.100000E+01
THE X-I1IN AMD Y-l-'.l N OF THE AREA tlHISSIljtl INVENTORY GRID (XG,YG):
o.75oooo;:+oi o.75nooon+qi
THE WIDTH OF A 3A3IC AREA SOURCE SQUARE (TXX):
0.5000002+01* !
THE KUMCIiR OF SU3-SECTORS CONSIDERED IN A 22.5 DEGREE SECTOR, AND ANGULAR WIDTH OF A SUB-SECTOR (DlMl,THETA):
O.itOOOOOil + Ol 0.562500E+01
THE INITIAL RADIAL INCREMENT (DELR):
THE RADIAL INCREMENT FACTORS (INC):
1 -2 l»
THE RATIO OF EMISSION GRID TO MAP GRID (RAT):
0. 5000(10a + 01
THE GRID CONVERSION FACTOR (CV) :
o. ioooooi-:+Qi*
THE AMBIENT AIR TEliPERATURE (TOA):
0.27W10E + 33
THE DECAY RATE HALF LIFE FOR P 1 AND P 2 (GB):
0.300000E+01 0.999999E+06
6 AREA SOURCE(S). 1 POINT SOURCE(S).
WHEN ? APPEARS, ENTER RECEPTOR COORDINATES (X,Y) OR ENTER /*. TO TERMINATE.
12.5,12.5
-------
Table 9 (continued). INTERACTIVE OPERATION OF CLIMATOLOGICAL DISPERSION MODEL, TESTSET LISTING
CDMI VERSION 730d3, RUN 99999
(MICROGRAMS PER CUBIC METER)
AREA POINT
COORDINATES
12.50
AREA ROSES
PI d9
P 2 53
POINT ROSES
PI 0
P 2 0
7
5,5
5.00
AREA ROSES
PI 70
r 1 j U
P 2 d5
POINT ROSES
PI 0
P 2 0
20,20
20.00
AREA ROSES
PI d
P 2 d
POINT ROSES
PI 0
P 2 0
-5,12.5
-5.00
AREA ROSES
PI 0
P 2 0
POINT ROSES
PI 0
P 2 0
/*
UTILITY DATA
READY
logoff
XXXXX LOGGED
12.
50
55
0
0
5.
fil
D.1
71
0
0
20.
d
d
0
0
12.
0
0
0
0
SET
OFF
50
S3
58
0
0
00
76
31
d5
00
d
d
0
0
50
0
0
0
0
HOT
TSO
P
810
50
55
0
0
30d
fil
D J.
71
0
0
30d
d
d
0
0
32
9
16
0
0
FREED,
1
It9
53
0
0
dS
0
0
,
d
d
0
0
,
Id
27
11
21
P 2
886.
50 53
55 ' 58
0 0
0 0
3 d9.
d U
0 0
0 0
3d9.
d d
d d
0 0
0 0
59.
9 0
16 0.
0 0
0 0
P 1
0.
50
55
0
0
31.
d
0
0
31.
1)
d
0
0 .
11.
0
0
0
0
d9
53
0
0
d
0
0
39
d5
0
0
0
0
0
0
P 2
0.
50
55
0
0.
d5.
d
0
0
d5.
61
71
0
0
21.
0
0
0
0
53
58
0
0
d
0
0
6d
76
31
itS
0
0
0
0
TOTAL
P 1
810.
50
55
0
0
33d.
d
0
0
33d.
61
71
0
0
ltd.
0
0
0
0
d9
53
0
0
d
0
0
39
dS
0
0
0
0
0
0
P 2
886,
50. .
. 55
0
0
39d,
1,
• *?
d
0
0
39d,
It
d
0
0
81
0
0
0
0
k
53
58
.0
0
•
1,
4
d
0
0
t
d
" d
0
0
0
0
0
0
CALIBRATED
P J P 2
810 886.
50
55
0
0
33d. 39lt.
it
0
0
33d. 39d.
d
d
0
0
dd. 81.
0
0
0
0 •
IS NOT ALLOCATED
AT 10:d5:03
ON FEBRUARY
13,
1973 +
-------
4. ALGORITHMS FOR CONTRIBUTIONS BY AREA SOURCES
Although in principle there is no difficulty in computing the contribution to the
average concentration by the multitude of area sources, it is rather tedious. Since various
computational procedures can be used to determine these contributions, it is relevant to de-
tail the procedures used in this program.
Let us suppose that the receptor, R, is located within the grid array as shown in
Figure 1. The first step in the program is to determine the distance from the receptor to
the furthest corner of the grid array. This distance is taken as the upper limit PM of the
integral q, (p) in Equation 1. Figure 1 also shows one of the sectors for which integra-
tions are to be carried out.
Figure 1. Illustration of sector integration.
An angular integration using the trapezoidal rule is carried out numerically. This
integration determines qj^Cp) at various increments of p, as indicated in Table 10. The
integration to determine concentration (Equation 1) is accomplished next using the
trapezoidal rule. As shown in Figure 1, the integration over p extends beyond the
boundary of the grid system. No additional contribution to the concentration will occur,
however, because the source density is zero beyond the grid boundary.
18
-------
Table 10. INCREMENTS OF INTEGRATION
Range
0 ip
2500 <. p
5000 <. p
, meters
i 2500
< 5000
I'M
Increment,
250a
500
1000
meters
The user can specify any value that is felt to be
appropriate by specifying the value for DELR in
the input. If a value different than 250 is
specified for DELR, the increments in the table
would change proportionately.
The program is also designed to handle the case where the receptor lies outside of
the emission grid array. For this case, the nearest distance Pm to the grid boundary as
well as the maximum distance pj^ is found. The lower limit to the integral in Equation 1
is P m and the upper limit is p M . Evaluating the integral in Equation 1 from a lower limit,
pm , instead of from zero results in a savings in computer time.
19
-------
5. COMPUTATIONAL OUTPUT (BATCH MODE)
In Appendix A, output is displayed for the test example. Table A-2 contains informa-
tion on input data, which may prove useful to the interpretation of the calculated concen-
trations. Printing of these input data (which will be voluminous if there are many sources)
can be suppressed by punching a positive number for the variable NLIST (first input
card).
Table A-3 displays the calculated contribution, due to area and point sources in micro-
grams per cubic meter to the nearest whole number. As discussed in Section 3, "cali-
brated" concentration values are also printed out. To employ the calibration feature,
however, it is necessary to have made a preliminary regression analysis and to have
inserted the proper parameters in the first card of the input sequence. Thus, for the
test example, "calibrated" values are identical to computed values.
An unfolding of the computed concentrations according to sectors of the wind direction
can also be given at each receptor point if desired. This is controlled by the input vari-
able NROSE. The concentrations are displayed clockwise in the sequence, N, NNE, . . .,
NNW.
The calculated concentration is also punched on cards so that an isopleth plot of the
concentrations may be obtained, if desired. At the option of the user, the output of the
contributions to the concentrations by each wind sector may also be punched on cards and
used to make a histogram plot.
20
-------
REFERENCES
Briggs.G.A., 1971. Some Recent Analyses of Plume Rise Observation. In: Proceedings
of the Second International Clean Air Congress, Englund, H.M. and W.T. Baery
(ed.). New York, Academic Press, 1971.
Calder, K.L., 1971. A Climatological Model for Multiple Source Urban Air Pollution. In:
Proceedings of the Second Meeting of the Expert Panel on Air Pollution Modeling.
NATO, Committee on the Challenges of Modern Society (CCMS) . Paris, France.
July 26-27, 1971.
DeMarrais, G.A., 1959. Wind Speed Profiles at Brookhaven National Laboratory.
J. Appl. Meteorol. 16: 181-189, 1959.
Gifford, F.A. , 1961. Uses of Routine Meteorological Observation for Estimating Atmos-
pheric Dispersion. Nuclear Safety. 2_ (4): 47-51, 1961.
Holzworth, G.C., 1972. Mixing Heights, Wind Speeds, and Potential for Urban Air Pollu-
tion throughout the Contiguous United States. Office of Air Programs, Environmental
Protection Agency, Research Triangle Park, N.C. Publication No. AP-101. January
1972.
McElroy, J.L. andF. Pooler, Jr., 1968. St. Louis Dispersion Studies; Vol. II - Analysis.
National Air Pollution Control Administration. Arlington, Va. Publication No.
AP-53. December 1968.
Pasquill, F. , 1961. The Estimation of the Dispersion of Windborne Material. Meteorol.
Magazine. 90(1063): 33-49,1961.
Truppi, L.E., 1968. Bias Introduced by Anemometer Starting Speeds in Climatological
Wind Rose Summaries. Monthly Weather Review. 96_ (5): 325-327, May 1968:
Turner, D.B., J.R. Zimmerman, andA.D. Busse, 1972. An Evaluation of Some Clima-
tological Dispersion Models. In: Proceedings of the Third Meeting of the Expert
Panel on Air Pollution Modeling. NATO, Committee on the Challenges of Modern
Society (CCMS). Paris, France. October 2-4, 1972.
21
-------
GLOSSARY
A, B = calibration constants
CA = average concentration due to area sources, ng/m
Cp = average concentration due to point sources, /ng/m
F = gV R 2 ["(T - T )/T I
B s s Lv s a sJ 2
g = acceleration due to gravity, m/sec
Gn = emission rate of n point source
h = effective stack height, meters
H = stack height, meters
HMIN » nocturnal mixing height, meters
HT = climatological mean value of mixing height, meters
k = index identifying wind direction sector
kn = wind sector appropriate to n point source
i. = index identifying wind speed class
L = afternoon mixing height
m = index identifying class of Pasquill stability category
n = number of point .sources
p = wind profile exponent
Pm = stability class
Q( f't 0) = emission rate of an area source per unit area and unit
time
qk(p) =
Rs = inner radius of stack , meters
S(p .zjUj ,Pm) = dispersion function
Ti = pollutant half life, hours
Ta = ambient air temperature , "K
Ts = average temperature of gases in plume, °K
U = wind speed at stack height, m/sec
U^ = representative wind speed, m/sec
Vs = average exit velocity of gases of plume, m/sec
X, Y = axes of the grid system; the X axis points east, the Y
axis north
z = height of receptor above ground level, meters
Ah = plume rise, meters
6 = angle relative to polar coordinates centered on receptor
P = distance from receptor to source, meters
Pn = distance from receptor to n point source, meters
22
-------
(p) = dispersion function, i.e., standard deviation of pollution
concentration in vertical plane
,m) = joint frequency function
23
-------
APPENDIX A. TEST EXAMPLE
INTRODUCTION
To illustrate various features described earlier and to provide a test that the program
is operating properly, a hypothetical problem has been constructed for the convenience
of the user. It is supposed that a source inventory of an area has been made. The source
inventory grid is depicted in Figure A-l.
(5,15)0
(5,5)6
(10,15)
(15,
15)
(12.5,12.5)
(15:
10)
(15,5)
T
5000 METERS
i
Figure A.1. Emission grid for test problem.
The southwest corner of each grid square is shown and its location given in kilometers
in map coordinate units. The length of the side of a basic square is 5000 meters. It should
be noted that length of the side of the larger square is larger than that of the basic square
by an integral multiple. The program will automatically divide this large square into four
basic squares and assign the correct emission rates. It is assumed that each basic square
emits pollutant at the rate of 1000 grams per second. The larger square emits pollutant
at the rate of 4000 grams per second. The emission height of all the area sources is 20
meters. The circle on the sketch located at (12.5, 12.5) represents a point source. It is
assumed to be emitting pollutant at the rate of 1000 grams per second from a stack which
is 20 meters high.
CARD INPUT
Card input for the test example is listed in Table A-l.
24
-------
PRINTED OUTPUT
Printed output for the test example is given in Tables A-2 and A-3. Table A-2 is a
list of the input parameters used. A list of this type can be obtained if desired, or sup-
pressed by entering a positive number for the variable NLIST on the first input ca.rd.
CARD OUTPUT
Cards containing the calculated concentrations at each receptor will be punched for
use in computer programs that analyze the information produced by the Climatological
Dispersion Model. As discussed in Section 3, a regression program must be applied to
obtain calibration constants. Additionally, the punched output can be used to obtain
isopleth plots of concentration contours, i.e., CALCOMP General Purpose Contouring
Programs.
Besides the cards containing the total concentration from area and point sources,
additional punched output may be produced if the NROSE option is used. If NROSE is
specified as greater than zero, four additional cards will be punched; one card each for
area and point source contributions to the concentration (a value is given for each wind
sector) for the two pollutants. The format of the punched output is given in Table A-4,
and Table A-5 is a listing of punched output for the sample problem. These punched
cards are not output with the interactive version of the model.
ISOPLETHS AND HISTOGRAMS
The plotted isopleth and histograms (Figures A-2 and A-3) in this section were pro-
duced from the punched output of'the test example. Unique plotting programs must be
applied for different computer systems. Thus plotting programs have been omitted from
this paper, and must be supplied by the user to obtain a comparable plotted output
display.
25
-------
Table A-l. CARD INPUT FOR THE TEST EXAMPLE
A P1A P2P PIP P299999 -1567 0.0 0.0 1.0 1.0 00000010
250. 5. 1000. HOO. 150. 5.0 5.0 7.5 7.5 5. 1.25 SOOO. 00000020
4. 1. 1. 30. 30. 30. 30. 30. 30. 3.0999999 00000030
48 BLANK CARDS
COL 10-18
0.0625
0.0625
0.0625
0.0625
0.0625
0.062S
0.0625
0.0625
32 BLANK CARDS
S.O 5.0 10000. '
S.O 15.0 5000.
10.0 15.0 5000.
15.0 15.0 5000.
15.0 10.0 5000.
15.0 5.0 5000.
12.5 12.5 0.
COL 1-8 £QL 9-16
5.0 5.0
5.0 6.25
5.0 7.5
5.0 8.75
5.0 10.0
5.0 11.25
5.0 12.5
5.0 13.75
5.0 15.0
5.0 16.25
5.0 17.5
COL 73-80
00000510
00000520
00000530
00000540
00000550
00000560
00000570
00000580
COL 10-18 .
0.062S
0.062S
0.0625
0.0625
0.0625
0.062S
0.0625
0.062S
4-000.0 4QOO.O ?0.0
1000.0 1000.0 20.0
1000.0 1000.0 20.0
1000.0 1000.0 20.0
1000.0 1000.0 20.0
1000.0 1000.0 ?0.0
1000.0 1000.0 20.0 1.0 5.0 20.0 0.0
COL 46 COL 73-80
1 00001080
00001090
00001100
00001110
00001120
00001130
00001140
00001150
00001160
00001170
0000 llbO
COL 1-8 COL 9-16
5.0 18.75
5.0 20.0
6.25 5. ft
6.25 6.25
6.25 7.5
6.?.5 8.75
6.25 10.0
6.25 11.25
6.25 12.5
6.25 13.75
6.25 15.0
COL 73-80
00000590
00000600
00000610
00000620
00000630
0000064Q
00000650
00000660
00000670
00001000
00001010
00001020
00001030
00001040
00001050
00001060
00001070
COL 46 COL 73-80
00001190
1 00001200
00001210
00001220
00001230
00001240
00001250
00001260
00001270
00001280
00001290
-------
Table A-l (continued). CARD INPUT FOR THE TEST EXAMPLE
CQL 1-8
6.25
6.25
6.25
6.25
7.5
7.5
7.5
7.5
7.5
7.5
7.5
7.5
7.5
7.5
7.5
7.5
7.5
8.75
8.75
8.75
8.75
8.75
8.75
8.75
8.75
8.75
8.75
8.75
8.75
8.75
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
COL 9-16.
16.25
17.5
18.75
20.0
5.0
6.25
7.5
8.75
10.0
11.25
12.5
13.75
15.0
16.25
17.5
18.75
20.0
5.0
6.25
7.5
8.75
10.0
11.25
12.5
13.75
15.0
16.25
17.5
18.75
20.0
5.0
6.25
7.S
8.75
10.0
11.25
12.5
13.75
.CQL 46 CQL 73-80
00001300
00001310
00001320
00001330
00001340
00001350
00001360
00001370
00001380
00001390
00001400
00001410
00001420
00001430
00001440
00001450
00001460
00001470
00001480
00001490
00001500
00001510
00001520
00001530
00001540
00001550
00001560
00001570
00001580
00001590
00001600
00001610
00001620
00001630
00001640
00001650
00001660
00001670
COL 1-8
10.0
10.0
10.0
10.0
10.0
11.25
l.?5
l.?5
1.25
1.25
l.?5
l.?5
1.25
1.25
1.25
1.25
11.25
11.25
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
13.75
3.75
13.75
13.75
13.75
13.75
13.75
COL 9-16, COL 46
15.0
16.25
17.5
18.75
20.0
5.0
6.25
7.5
8.75
10.0
11.25
12.5
13.75
15.0
16.25
17.5
18.75
20.0
5.0
6.25
7.5
8.75
10.0
11.25
12.5
13.75
15.0
16.25
17.5
18.75
20.0
5.0
6.25
7.b
8.75
1.0.0
11.25
12.5
COL 73-80
Od0016£jfl"
00001690
00001700
00001710
00001720
00001730
00001740
00001750
00001760
00001770
00001780
00001790
00001800
00001810
00001820
00001830
00001840
00001850
00001860
00001870
00001880
00001890
00001900
00001910
00001920
00001930
00001940
00001950
00001960
00001970
00001980
00001990
00002000
00002010
00002020
00002030
0000204Q
00002050
-------
Table A-l (continued). CARD INPUT FOR THE TEST EXAMPLE
to
CO
COL 1-8
13.75
13.75
13.75
13.75
13.75
13.75
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
1ft. ?5
16.25
16.25
16.25
16.25
16. ?5
16.25
16.25
16.25
16.25
16.25
16.25
16.25
17.5
17.5
17.5
17.5
COL 9-16 COL 46
13.75
15. 0
16.25
17.5
18.75.
20.0
5.0
6.?5
7.5
8.75
10.0
11.25
12.5
13.75
15.0
16.2?
17.5
18.75
20.0
5.0
6.25
7.5
8.75
10.0
11.25
12.5
13.75
15.0
16.25
17.5
18.75
20.0
5.0
6.25
7.5
8.75
COL 73-80
00002060 '
00002070
00002080
00002090
00002100
00002110
00002120
00002130
00002140
00002150
00002160
00002170
00002180
00002190
00002200
00002210
00002220
00002230
00002240
00002250
00002260
00002270
00002280
00002290
00002300
00002310
00002320
00002330
00002340
00002.350
00002360
00002370
00002380
00002390
00002400
00002410
COL 1-8
-7775-
17.5
17.5
17.5
17.5
17.5
17.5
17.5
17.5
18.75
18.75
18.75
18.75
18.75
18.75
18.75
18.75
18.75
18.75
18.75
18.75
18.75
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
COL 9-16 COL 46
10.. 0
11.25
12.5
13.75
15.0
16.25
17.5
18.75
20.0
5.0
6.25
7.5
8.75
10.0
11.25
12.5
13.75
15.0
16.25
17.5
18.75
20.0
5.0 1
6.25
7.5
fl.75
10.0
11.25
12.5
13.75
15.0
16.25
17.5
18.75
20.0 1
COL 73-80
00002420
00002430
00002440
00002450
00002460
00002470
00002480
00002490
00002500
00002510
00002520
00002530
00002540
00002550
00002560
00002570
00002580
00002590
00002600
00002610
00002620
00002630
00002640
000026-50
00002660
00002670
00002680
00002690
00002700
00002710
00002720
00002730
00002740
00002750
00002760
-------
Table A-2. OUTPUT FOR TEST EXAMPLE, INPUT PARAMETERS USED
CUM VERSION 7?313. RUN 99999
THE
THt
THE
CfliTRAL nINH SPEEDS Or THE SIX WIND SPEED CLASSES :
0? 0.300000E 0? 0.300000F 02 0.300000E 02
0.961136F. 01 0.12S171E 0?
0.?50000E 00 0.300000E 00
0.300000E U2 0.300000fc 02
THE CLIMATOLOGICAL MEAN NOCTURNAL ANO AFTtWNOON MlAlNG HEIGHTS (HMIN.HT):
0.1SOOOOF. 03 O.HOOOOOe 03
THE UAY AND NIGHT EMISSION ^FIGHT FACTORS 'YU.Y.N):
0.100000E 01 0.100000F. 01
THE x-MIN' ANb Y-MjN OF THE AREA EMISSION iNVtNTOKY GPIO ' (XG, Yii) :
0.7SOOOOE 01 0.750000t 01
THt i^lOTH OF A BASIC AkEA SOUWCF SOUAriE ITX.X):
0.500000E Oi .
THE NUMHEH OF SUB-SfcCTOKS CONSIDERED IN .« ??.S DEGkEf SECTOR, AND ANGOLAV wlDTH OF A SUrf-SECTOK (UlNT .THETA) :
o.-ooooot: 01 o.sispspo? 01
THE INITIAL RADIAL INCrtEMEK'T :
C.?HOOOOr 03
THE RADIAL INCREMENT FACTORS d'-IC):
1 ? u <4
THE RATIO OF EMISSION GRIO TO MAP GRID
o.sooonot 01
THE GRID CONVERSION FACTOR ICV) :
0.100000E 0"
THE AMcilFNT AIR TtMPEKATUKE ITOA) :
03
THE DECAY KATE HALF LIFE FOP P 1 AND P ? (Gi-(:
0.300000F. 01 0.499999E 0<-
-------
Table A-2 (continued). OUTPUT FOR TEST EXAMPLE, INPUT PARAMETERS USED
THE
SIGMA L COEFFICIENT TA3LF 01 0.493ft,OOE-01
0.115400E 00 0.101400F. 00
0.73t,800E OC O.P59100E 00
0.1?9ft90E 01 O.Z52700E 00
0
0
0
0
0
.383000E-01
.139300? 00
.HPOOOE 00
.S5ftOOOE-01 '
.eieoooE-oi
0
0
0
0
0
.?OH860t
.111370t
.410900E
,564?OOF
.442100F
01
01
00
00
00
0
0
0
0
0
.?OH860!r
.111370h
.9?6000t
.ftRft900F
.A.34100I:
01
01
00
00
00
0
0
0
0
0
• 12«!l?OE 01
,94f-700t 00
.910000E 00
.eftSOOOE 00
.Bi55ooe oo
SECTOR
u?
COM VERSION 72313.
U3
RUN
lift
1
?
3
14
5
ft
7
H
9
10
11
12
13
14
15
1ft
1
2
3
u
5
ft
7
fa
9
10
11
12
13
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0..0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o.o
0.0
0.0
0.0
0.0
0.0
0.0
0.0
THF JOINT FREQUENCY
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
THt JOINT FREQUENCY
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0.
0.0
0.0
FUNCTION FOR STABILITY CLASS
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
n.o
0.0
0.0
u.o
0.0
0.0
0.0
FUNCTION FOK STABILITY CLASS
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
n.o
1
n.o
o.o
(i.O
o.o
0.0
0.0
u.o
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o.n
0.0
?
o.o
n.o
o.o
n.o
o.o
o.o
o.n
r.o
o.o
o.o
u.o
o.o
o.o
o.o
o.o
o.n
o.n
o.o
o.o
O.n
O.n
o.n
0.0
0.0
0.0
0.0
o.n
o.n
o.o
o.n
o.n
o.o
o.n
O.n
o.o
o.n
o.n
o.n
o.n
o.n
o.o
0."
-------
Table A-2 (continued). OUTPUT FOR TEST EXAMPLE, INPUT PARAMETERS USED
111
SECTOR
!<•
IS
16
0
0
0
.0
.0
.0
UZ
0.0
0.0
0.0
COM VERSION 7?313t RUN y9
0
0
0
0
0
p
u
n
0
0
0
r
n
0
0
II
fl
II
0
0
a
u
0
.0
.0
.0
.0
.0
.0
.u
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.n
.0
.0
.0
.0
.0
.0
.0
Ufc
0
0
0
0
0
0
0
0
0
0
0
0
0
n
0
0
0
0
0
n
0
0
n
0
0
0
0
0
0
0
n
0
0
0
n
.1
.0
.0
.0
.0
.0
.n
.n
.0
.0
.0
.n
.0
.0
.0
.0
.0
.fl
.n
.It
.1
.0
• o
.0
.n
.0
.0
. !>
.11
.0
.11
.0
.0
.11
.0
-------
Table A-2 (continued). OUTPUT FOR TEST EXAMPLE, INPUT PARAMETERS USED
SECTOR
Ul
1
?
3
u
5
6
7
8
9
10
11
12
13
14
15
1*
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
U2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
COM VERSION 72313,
U3
RUN 99999
U4
U5
THE JOINT FWEQUENCY FUNCTION FOR STABILITY CLASS S
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0 -
U.O
0.0
0.0
0.0
0.0
0.0
U.O
0.0
0.0
0.0
0.0
0.0
0.0
n.o
0.0
0.0
0.0
U.O
U.O
0.0
0.0
n.o
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
I'.O
0.0
0.0
0.0
0.0
0.0
THE JOINT FREQUENCY FUNCTION FOR STABILITY CLASS
U6
0.0
0.0
0.0
0.0
O.P
O.n
0.0
O.'1
0.0
0.0
0.0
n.u
0.0
0.0
0.0
o.n
1
2
3
£»
5
h
7
fi
9
10
11
1?
13
14
IS
lf>
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
U.O
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o.n
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
n.o
0.0
0.0
0.0
n.o
0.0
0.0
0.0
n.o
0.0
o.o
0.0
n.o
0.0
0.0
o.o
O.n
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o.o
0.0
0.1
O.n
0.0
n.o
-------
Table A-2 (continued). OUTPUT FOR TEST EXAMPLE,INPUT PARAMETERS USED
COM VERSION 7P313. RUN S999<3
SOURCE INPUT
X
0.50000E
0.50000E
0.10000E
0.15000E
0.15000E
0.15000E
01
01
02
0?
0?
0?
Y
0. 500006.
0.15000E
0.15000E
O.lSOOOt
0.10000E
0.50000E
01
0?
0?
0?
0?
01
TX
0.10000E
0.50000F
0.50000E
0.50000F
0.50000E
0.50000E
05
04
04
04
04
04
bl
0.40000E
0.10000E
0.10000E
O.lOOOOt
0.10000E
0.10000E
04
04
04
04
04
04
S2
0.40000E
0.10000F
o.ioonoE
0.10000F
0.10000F
0.10000E
04
04
04
04
04
04
SH
0.?OOOOF.
0.20000E
O.?0000f-
0.?OOOOE
0.?OOOOE
0.?OOOOE
02 0.0
0? 0.0'
0? 0.0
02 0.0
02 0.0
0? 0.0
0
0
0
0
0
0
0
vs
.0
.0
.0
.p
.0
.0
T
0.0
0.0
0.0
0.0
0.0
0.0
SA
0.0
0.0
0.0
0.0
0.0
0.0
0.1?SOOE 0? 0.12500E 0? 0.0
6 AHE4 SOURCES.
0.10000E 04 0.10000F 04 0.20000E 02 O.lOOOOfc 01 0.50000E 01 0.20000E 02 0.0
1 POINT SOURCES.
-------
Table A-3. OUTPUT OF TEST EXAMPLE, COMPUTED CONCENTRATIONS
COM VERSION 72313. RUN 99999
(MICROGRAMS PER CUBIC METEH)
ArtEA POINT TOTAL
COORDINATES
5.00
AREA ROSES
AD 1
^ 1
AD "3
r ?.
POINT ROSES
C PI
P P2
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
AREA ROSES
AD 1
^ 1
Ar, 3
r f
POINT ROSES
P PI
P P2
6.25
6.25
6.25
6.25
6.25
6.25
6.25
6.25
6.25
6.25
6.25
6.25
6.25
7.50
7.50
7.50
7.50
5.00
"3O <. 1
39 61
/ C 71
45 7 1
0 0
0 0
6.25
7.50
8.75
10.00
11.25
12.50
13.75
15.00
16.25
17.50
18.75
20.00
A 4
A A
0 0
0 0
5.00
6.25
7.50
8.75
10.00
11.25
12.50
13.75
15.00
16.25
17.50
18.75
20.00
5.00
6.25
7.50
8.75
P 1
304.
64 61
1 L "71
76 71
31 0
45 0
406.
443.
460.
474.
477.
478.
477.
474.
460.
443.
406.
304.
A A
A A
0 0
0 0
406.
585.
636.
656.
674.
678.
679.
678.
674.
656.
636.
585.
406.
443.
636.
696.
721.
P 2
J49.
39 4
45 4
0 0
0 0
454.
495.
512.
529.
532.
533.
532.
529.
512.
495.
454.
349.
TO f, 1
.I** O I
/ c -71
Ao f I
0 0
0 0
454.
637.
693.
715.
735.
739.
741.
739.
735.
715.
693.
637.
454.
495.
693.
758.
785.
P 1
31.
A A
A A
0 0
0 0
36.
43.
48.
53.
58.
58.
58.
53.
48.
43.
36.
31.
ft At ft 1
o*» o 1
-f f. 7|
fa f I
31 0
45 0
36.
43.
52.
62.
70.~
79.
79.
79.
70.
62.
52.
43.
36.
43.
52.
64.
80.
P 2
45.
A A
A' A
0 0
0 0
52.
59.
64.
70.
76.
76.
76.
70.
64.
59.
52.
45.
"1G A.
3V» A
A5 A
0 0
0 0
52.
59.
69.
80.
89.
99.
99.
99.
89.
80.
69.
59.
5?.
59.
69.
83.
100.
P 1
334.
A A
A A
0 0
0 0
443.
4H7.
507.
527.
535.
536.
535.
527.
507.
487.
443.
334.
A A
A A
0 0
0 0
443.
628.
688.
718.
743.
756.
758.
756.
743.
718.
688.
628.
443.
487.
688.
760.
801.
P 2
394.
A A -
A A
0 0
0 0
506.
554.
577.
599.
608.
609.
608.
599.
577.
554.
506.
394.
A A
4 A
0 0
0 0
506.
697.
762.
795.
824.
838.
840.
838.
824.
795.
762.
697.
506.
554.
762.
841.
8H5.
CALIBRATED
P 1
334.
A A
A A
0 0
0 0
443.
487.
507.
527.
535.
536.
535.
527.
507.
487.
443.
. 33A*
A A
** **
4 A
0 0
0 0
443.
628.
688.
718.
743.
756.
758.
756.
743.
718.
688.
628.
443.
487.
688.
760.
. 801.
P 2
394.
CA A en A
bUU 3UU
500 500
500 500
500 500
506.
554.
577.
599.
608.
609.
608.
599.
577.
554.
506.
394.
C A A Qfi A ft
:3UU rUUU
c n ft onnn
OU U r UUU
500 2000
500 2000
506.
697.
762.
795.
824.
838.
840.
838.
824.
795.
762.
. 697.
506.
554.
762.
841.
885.
OBSERVED
P 1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
P 2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-------
Table A-3 (continued). OUTPUT OF TEST EXAMPLE, COMPUTED CONCENTRATIONS
COM VERSION 72313. PUN 99999
IMICrfOGPAMS PfK CUblC METtW)
flHHA POINT TOT^L
COOKOINATES
7.50
7.5u
7.50
7.50
7.50
7.50
7.5U
7.50
7.50
3.75
8.75
8.7S
8.75
8.75
W.75
8.75
8. 75
fi.75
8.75
H.75
8.7S
ft. 75
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10. OU
10.00
10.00
10.00
11. 2S
11. 25
11.25
11.25
11.25
11.25
11.25
10.00
11.25
12. 5u
13.75
15.00
16. ?5
17.50
18.75
20.00
5.00
ft. 25
7. SO
H.75
10.00
11.25
12.50
1.1.75
15.00
16.25
17.50
18. 7S
20.00
5.00
6.25
7.50
8.75
10.00
11.25
12.50
13.75
15.00
16.25
17.50
18.75
20.00
5.00
IS. 25
7.50
8.75
10.00
11.25
12.50
P 1
741.
745.
747.
745.
741.
721.
69ft.
636.
44?.
461).
656.
721.
7<,9.
770.
775.
777.
775.
770.
749.
721.
656.
460.
474.
674.
741.
770.
792.
798.
801.
798.
79?.
77(1.
741.
674.
474.
477.
67P.
745.
775.
798.
804.
807.
P 2
809.
"13.
814.
813.
809.
785.
758.
693.
495.
512.
715.
785.
Rib.
841.
846.
84fl.
846.
841.
816.
785.
715.
S12.
5?9.
735.
809.
841.
867.
873.
876.
873.
867.
841.
809.
735.
529.
532.
739.
813.
846.
873.
879.
883.
P 1
95.
111).
114.
lln.
95.
80.
64.
52.
43.
4fa.
62.
80.
103.
13h.
165.
179.
165.
13H.
103.
80.
62.
48.
53.
70.
95.
138.
197.
286.
337.
286.
197.
138.
95.
70.
53.
58.
79.
110.
165.
286.
555. "
884.
P 2
116.
132.
136.
132.
116.
100.
83.
69.
59.
64.
HO.
100.
125.
162.
191.
20S.
191.
162.
125.
100.
80.
6".
70.
89.
116.
162.
224.
316.
368.
316.
224.
162.
116.
89.
7J).
76.
99.
132.
191.
316.
591.
924.
P 1
836.
855.
H60.
855.
836.
801.
760.
6H8.
4fa7.
507.
MB.
801.
852.
908.
941.
956.
941.
908.
852.
801.
718.
507.
527.
743.
836.
908.
990.
1084.
1137.
1084.
990.
906.
836.
743.
527.
535.
756.
855.
941.
1084.
1359.
1691.
P 2
925.
945.
951.
945.
9?S.
885.
841.
762.
554.
577.
795.
885.
941.
1003.
1037.
1053.
1037.
1003.
941.
8HS.
795.
577.
599.
824.
9?5.
1003.
1091.
1188.
1244.
1188.
1091.
1003.
925.
8?4.
599.
608.
838.
945.
1037.
1188.
1470.
1807.
CALIHPATFU
P 1
836.
H55.
860.
855.
836.
HOI.
760.
688.
487.
507.
718.
HOI.
H52.
90ri.
941.
956.
941.
908.
d52.
801.
718.
507.
527.
743.
836.
908.
990.
1084.
1137.
1084.
990.
908.
836.
741.
527.
535.
756.
855.
941.
1084.
1359.
1691.
P 2
925.
945.
951.
945.
925.
8B5.
841.
762.
554.
577.
795.
8ri5.
941.
1003.
1037.
1053.
1037.
1003.
941.
MH5.
795.
S77.
599.
824.
925.
1003.
1091.
1188.
1244.
1188.
1091.
1003.
925.
P24.
599.
608.
83H.
945.
1037.
1188.
1470.
1807.
OBSERVED
P 1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
P '
-------
Table A-3 (continued). OUTPUT OF TEST EXAMPLE, COMPUTED CONCENTRATIONS
CUM VEWSION 72313. RUN 99999
(MICROGPAMS PEH CUbIC METtrK)
AHEA POINT TOTAL
COORDINATES
11.75
11.25
11.25
11.75
11.75
11.75
17.50
12. 5P
12.50
12.50
17.50
12.50
12. SO
12.50
12.50
12.50
12.50
12.50
12.50
13.75
13.75
13.75
13.75
13. 75
13.75
13.75
13.75
13.75
13.75
13.75
13.75
13.75
15.00
15.00
15.00
15.00
15.00
15.00
15.00
15.00
15.00
15.00
13.75
IS. 00
16.25
17.50
18.75
20.00
5.00
6.25
7.50
8.75
10.00
11.25
12.50
13.75
IS. 00
16.25
17.50
18.75
20.00
5.00
6.25
7.50
8.75
10.00
11.25
17.50
13.75
15.00
16.25
17.50
18.75
70-00
S.OO
6.25
7.50
8.75
10.00
11.25
12.50
13.75
IS. 00
16.25
P 1
806.
79fi.
775.
765.
678.
677.
67R.
679.
767.
777.
801.
8C7.
P10.
MO 7.
POl.
777.
767.
679.
678.
677.
678.
765.
775.
798.
806.
P07.
P06.
798.
77S.
765.
678.
677.
676.
676.
761.
77P.
797.
79P.
POl.
79fi.
797.
770.
P 2
879.
873.
866.
813.
739.
532.
533.
761.
816.
868.
876.
P83.
886.
883.
876.
868.
816.
761.
533.
532.
739.
813.
866.
873.
879.
883.
879.
873.
866.
813.
739.
532.
529.
735.
809.
861.
867.
873.
876.
873.
867.
861.
P 1
555.
786.
165.
110.
79.
58.
58.
79.
116.
179.
337.
886.
0.
886.
337.
179.
116.
79.
58.
58.
79.
110.
165.
286.
555.
886.
555.
286.
165.
110.
79.
58.
53.
7u.
95.
138.
197.
286.
337.
286.
197.
138.
P 2
591.
316.
191.
13?.
99.
76.
76.
99.
136.
205.
368.
926.
0.
976.
368.
705.
136.
99.
76.
76.
99.
137.
191.
316.
591.
9?6.
591.
316.
191.
137.
99.
76.
70.
89.
116.
167.
??6.
316.
368.
316.
726.
162.
P 1
1359.
1086.
961.
855.
756.
535.
SJ6.
758.
860.
956.
1137.
1691.
810.
1691.
1137.
956.
86P.
758.
536.
535.
756.
855.
961.
1086.
1359.
1691.
1359.
1086.
961.
855.
7S6.
5J5.
527.
763.
836.
908.
990.
1086.
1137.
1PS6.
990.
908.
P ?
1670.
1188.
1037.
965.
838. -.
608.
609.
860.
951.
1053.
1766.
18Q7.
. 88h.
1807.
1266.
1P53.
951.
860.
609.
608.
838.
965.
1037.
HHd.
1670.
1807.
1670.
1188.
1037.
965.
838.
608.
S99.
826.
925.
10Q3.
1091.
1188.
1266.
1188.
1091.
1003.
CALItlrtATED
P 1
1359.
1086.
961.
855.
756.
535.
536.
758.
860.
956.
1137.
1691.
810.
1691.
1137.
S56.
860.
758.
536.
535.
756.
855.
961.
1U86.
1359.
1691.
1359.
1086.
961.
855.
756.
535.
527.
763.
836.
90P.
990.
1086.
1137.
1086.
990.
90P.
P ?
1670.
1188.
1037.
965.
838.
608.
609.
860.
951.
1053.
1266.
1P(|7.
886.
1P07.
1266.
1053.
951.
8<*0.
6o9.
608.
838.
9<.5.
1037.
118H.
1670.
1807.
1670.
1188.
1037.
9*5.
838.
608.
599.'
82*.
975.
1003.
1091.
1188.
1?64.
1188.
10^1 .
1003.
OBSERVED
P 1
0
0
0
U
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
U
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
P
-------
Table A-3 (continued). OUTPUT OF TEST EXAMPLE, COMPUTED CONCENTRATIONS
COM VERSION 72313. RUN 99999
(MICROGRAMS PER CUtJIC «ETER>
AREA POINT TOTAL CALIBRATED
COORDINATES
15.00
15.00
15.00
16.25
16. ?5
16.25
16.25
16.25
16.25
16.25
16.25
16.25
16.25
16.75
16.25
16.75
17.50
17.50
17.50
17.50
17.50
17.50
17.50
17.50
17.50
17.50
17.50
17.50
17.50
18.75
18.75
1H.75
18.75
lfl.75
18.75
18.75
18.75
18.75
18.75
18.75
18.7 =
18. 7t"
20.00
17.50
18.75
20.00
5.00
6.25
7.50
8.75
10.00
11.25
12.50
13.75
15.00
16. ?b
17.50
18.75
20.00
5.00
6.25
7.50
8.75
10.00
11.25
12.50
13.75
15.00
16.25
17.50
18.75
20.00
5.00
6.25
7.50
8.75
10.00
11.25
12.50
13.75
15.00
16.25
17.50
18.75
70.00
5.00
P 1
741.
674.
474.
460.
656.
721.
749.
770.
775.
777.
775.
770.
749.
721.
656.
460.
44.1.
636.
696.
721.
741.
745.
747.
745.
741.
721.
696.
636.
443.
406.
5H5.
636.
656.
674.
678.
, 679.
678.
674.
656.
636.
585.
406.
304.
P 2
809..
735.
529.
512.
715.
785.
816.
841.
846.
848.
846.
841.
816.
7rt5.
715.
512.
495.
693.
758.
785.
809.
813.
814.
813.
809.
785.
758.
693.
495.
454.
637.
693.
715.
735.
739.
741.
739.
735.
715.
693.
637.
454.
349.
P 1
95.
70.
53.
48.
62.
80.
103.
138.
165.
179.
165.
138.
103.
8u.
62.
48.
43.
52.
64.
80.
95.
110.
114.
110.
95.
80.
64.
52.
43.
36.
43.
52.
62.
70.
79.
79.
79.
70.
62.
52.
43.
36.
31.
P 2
116.
89.
70.
64.
80.
100.
1?5.
167.
191.
205.
191 .
162.
125.
100.
80.
64.
59.
69.
83.
100.
116.
13?.
136.
13?»
116.
100.
83.
69.
59.
57.
59.
69.
80.
89.
99.
99.
99.
89.
80.
69.
59.'
57.
. 45. ,
P 1
836.
743.
527.
507.
718.
801.
852.
908.
941.
956.
941.
908.
H52.
801.
718.
507.
487.
688.
760.
801.
836.
855.
«60.
855.
836.
801.
760.
688.
487.
443.
628.
688.
718.
743.
756.
758.
7^)6.
743.
718.
688.
628.
443.
334.
P 2
.925.
824.
599.
577.
795.
885.
941.
1003.
1037.
1053.
1037.
1003.
941.
885.
795.
577.
554.
76?.
841.
8«5.
975.
945.
951.
945.
975.
885.
841.
76?.
554.
506.
697.
762.
795.
874.
838.
840.
838.
824.
79b.
762.
697.
S06.
394.
P 1
836.
743.
527.
507.
718.
801.
852.
908.
941.
956.
941.
908.
852.
801.
718.
507.
487.
68P.
760.
801.
836.
855.
860.
855.
836.
801.
760.
688.
487.
443.
628.
688.
71P.
743.
756.
/5S.
7S6.
743.
718.
088.
62H.
443.
334.
P ?
975.
874.
599.
577.
795.
885.
941.
1003.
1037.
1053.
1037.
1003.
941.
885.
795.
577.
554.
767.
8«1.
885.
975.
945.
951.
945.
975.
8h5.
841.
767.
554.
506.
697.
767.
79^.
874.
838.
841).
838.
874.
795.
76?.
697.
Su6.
394.
OBSERVED
P 1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(1
0
0
0
0
0
0
0
0
. 0
P 2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(.'
0
0
0
0
0
0
c
0
0
0
0
0
0
0
0
0
y
0
0
0
0
0
P
0
0
0
fl
-------
Table A-3 (continued). OUTPUT OF TEST EXAMPLE, COMPUTED CONCENTRATIONS
UJ
00
COM VERSION 72313, RUN 99999
(MICROGRAHS PER CUBIC METER)
COORDIN
AREa POSES
A PI
ft P?
POINT *OSES
P PI
P P?
PO.OO
PO.OO
PO.OO
PO.OO
PO.OO
PO.OO
PO.OO
?0.00
?0.00
PO.OO
PO.OO
PO.OO
AWEfl POSF.S
A =1
A Pp
P PI
£ P?
ATES
0 0
0 0
6.25
7.50
fl.75
10.00
11.25
IP. 50
13.75
15.00
16.25
17.50
IB. 75
PO.OO
0 0
0 0
AREA
PI P 2
0 0
0 0
406.
443.
460.
474.
477.
478.
477.
474.
460.
443.
406.
304.
0 0
0 0
0 0
0 0
454.
495.
51?.
5?9.
53?.
533.
53?.
5?9.
51?.
495.
454.
349.
0 0
0 0
POINT
PI P 2
0 0
0 0
36.
43.
48.
53.
58.
58.
5H.
53.
48.
43.
36.
31.
0 0
0 0
0 0
0 0
5?.
59.
64.
70.
76.
76.
76.
70.
64.
59.
5?.
45.
39 61
0 0
0 0
TOT
P 1
0 0
0 0
443.
487.
5u7.
5P7.
535.
536.
535.
5P7.
507.
487.
443.
334,
64 61
76 71
31 0
45 0
AL
P 2
39 61
45 71
0 0
0 P
SU6.
554.
577.
599.
608.
6H9.
6C. fl.
599.
577.
554.
506.
344.
0 0
0 0
CALIBRATED
PI P 2
64 61 POOO 500
7ft 71 POOO 500
31 0
45 0
443.
4t)7.
507.
5?7.
535.
536.
535.
5P7.
507.
4H7.
443.
334.
4 4
0 0
0 0
POOO 500
POOO 500
506.
554.
577.
599.
608.
609.
60 e.
599.
577.
554.
506.
3^4.
POOO ?000
POOO POOO
POOO POOO
POOO POOO
OBSERVED
PI P 2
-------
Table A-4. FORMAT OF CARD OUTPUT
Card
1
2a
Col umn
1 to 8
9 to 14
15 to 18
19 to 22
23 to 26
27 to 30
31 to 34
35 to 38
39 to 42
43 to 46
47 to 50
51 to 54
56 to 64
65 to 74
75 to 79
80
1 to 4
5 to 68
69 to 74
75 to 80
Format
F8.2
F6.2
14
14
14
14
14
14
14
14
14
14
F10. 2
F10.2
15
A4
1614
16
16
Contents
PUX (X coordinate of receptor in
plotting grid units)
PUY (Y coordinate of receptor in
plotting grid units)
KPX(l) (Area concentration for
first pollutant)
(2) (Area concentration for
second pollutant)
(3)(Point concentration for
first pollutant)
(4) (Point concentration for
second pollutant)
(5) (Total concentration for
first pollutant)
(6) (Total concentration for
second pollutant)
(7) (Calibrated total concentra-
tion for first pollutant)
(8) (Calibrated total concentrar.
tion for second pollutant)
(9) (Observed concentration of
first pollutant)
(10) (Observed concentration of
second pollutant)
RX (X map coordinate of receptor)
RY (Y map coordinate of receptor)
IRUN (Computer run identification
number)
1 (Card identifier)
AROS(l) (Card identifier)
KPX(1)-KPX(16) (Area concentration
by wind direction)
RX (X map coordinate of receptor
multiplied by 100 to remove decimals
RY (Y map coordinate of receptor
multiplied by 100 to remove decimals)
39
-------
Table A-4 (continued). FORMAT OF CARD OUTPUT
Card
33
43
5^
Col umn
--
1 to 4
5 to 68
69 to 74
75 to 80
--
Format
--
A4
1614
16
16
— —
Contents
(Same as Card 2 for second pollutant)
PROS(l) (Card identifier)
KPX(1)-KPX(16) (Point concentration
by wind direction)
RX (X map coordinate of receptor
multiplied by 100 to remove decimals)
RY (Y map coordinate of receptor
multiplied by 100 to remove decimals)
(Same as Card 4 for second pollutant)
a Cards only punched if NROSE greater than zero.
40
-------
Table A-5. LISTING OF CARD OUTPUT FOR TEST EXAMPLE
0.50
AP 1 TQ
"I J"
Ap o /. c
" r ** D
H Pi 0
HP? 0
O.SO
0.50
0.50
0.50
0.50
O.SO
O.bO
0.50
0.50
0.50
0.50
0.50
A*) 1 A
K J **
AP 'J A
• r. **
P PI 0
H P? 0
0.75
0.75
0.75
C.75
0.75
1.75
0.75
0.75
0.75
0.75
0.7b
0.75
0.75
1.00
1.00
1.00
1.00
1.00
1.00
1.UO
1.00
l.DO
1.00
1.00
1.00
1.00
1.25
.25
.25
.25
.25
.25
.25
.25
.25
.25
.25
.25
.25
.50
.50
1.50
1.50
O.SO
f. 1
O 1
0
0
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3. SO
A
4
£
0
0
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
O.SO
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
?.50
2.75
3.00
3.25
3.bO
0.50
0.75
1.00
1.25
304 349
fa4 (3 j-
7/_ 7 |
f O f 1
31 0
45 0
406 454
443 495
460 512
474 529
477 532
478 533
477 532
474 529
460 512
443 495
406 4S4
304 349
. /,
«* ** -
/. A
** H
0 0
0 0
406 454
585 637
636 693
656 715
674 735
67d 7J9
679 741
67o 739
674 735
656 715
636 t>93
SbS 637
406 454
443 493
636 693
696 758
721 7aS
741 809
745 813
747 b!4
745 813
74l b09
721 785
696 758
636 693
443 495
460 512
656 715
721 7bS
749 b!6
770 841
775 046
777 848
775 846
770 b4i
749 616
721 7bS
6b6 715
-60 512
474 529
674 73b
741 *JU9
770 841
31 45
0 0
0 0
36 52
43 59
48 64
53 70
58 76
5<2 76
58 76
S3 70
48 64
43 59
36 . 52
31 45
•1 ^\ £ 1
J9 61
/.c 7 I
43 f i
0 0
0 0
36 52
43 59
52 69
62 80
70 H9
79 99
79 99
79 99
70 89
62 60
52 69
43 59
36 52
43 59
52 69
64 83
bO 100
95 116
110 132
114 136
110 132
95 116
60 100
64 63
52 69
43 59
48 64
62 80
oO 100
103 125
13« 16?
165 191
179 205
165 191
U8 162
103 125
80 100
62 80
4fi t)4
53 70
70 b9
95 116
13H 162
334 394
0 0
0 0
443 506
487 554
507 577
527 599
535 608
536 609
535 60b
527 599
507 577
487 554
443 506
334 394
t . r J
64 o 1
~1 1* 71
1 0 f I
31 0
45 0
443 506
628 697
68b 762
718 795
743 624
7b6 '838
758 840
7b6 bJrt
743 824
718 795
6ti8 7ts2
628 697
443 506
4H7 S54
6«8 762
760 8-*!
801 8b5
ft36 925
855 945
860 951
855 945
836 925
bOl SbS
760 641
fcbo 762
487 554
507 577
718 795
801 fcb5
652 941
9ob 1003
941 1037
956 10b3
941 1UJ7
908 1003
852 941
froi *as
713 795
507 577
527 5v9
743 r(24
b36 925
9Ub 1.0 U 3
334
0
0
443
487
507
527
535
536
535
527
507
437
443
334
"lij
J1*
*. C
*»3
0
0
443
628
688
718
743
756
758
756
743
718
688
C28
443
407
688
760
801
836
855
860
855
836
801
760
668
487
507
718
801
t52
908
941
956
941
908
852
bC 1
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507
527
743
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394
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577
599
608
609
608
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697
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885
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7.50
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7.50
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7. SO
7.30
7. So
7.5U
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d. 75
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8.75
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3.7b
M. 1-3
10. UO
10.00
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lo.uo
5.00
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7 . 50
b.75
10.00
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lb.7S
20.00
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13.75
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17. 50
lb.75
20.00
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6.2b
7.50
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12. bo
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13.00
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18. /b
20.00
b . 0 0
to.2b
7.b(i
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tirt t\
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999991
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41
-------
Figure A-2. Isopleth for test example.
42
-------
con TEST
RECEPTOR
EXRHPLE (PI I UNIT = HICROORRH PER CUBIC METER
COORDINATES 5-00 S.OO TOTAL = 333
100
90
60
70
60
SO
40
30
20
10
100
80
80
70
60
50
40
30
20
10
0
NNE NE ENE E ESE SE SSE S SSH SU USN H NNU NH NNN
100
90
60
70
60
BO
40
30
20
10
COH TEST EXRnPLE (PI I
RECEPTOR COORDINBTES
UNIT = niCRODRRn PER CUBIC nETER
5.00 20.00 TOTAL = 339
RREB POINT
100
90
80
70
60
50
40
30
20
10
0
NNE NE ENE
ESE SE SSE
SSH SN MSN
HNN NN NNN
Figure A-3. Histograms for test example.
43
-------
COM TEST EXRHPLE (PI) UNIT = MICROORfitl PER CUBIC HETER
RECEPTOR COOROINHTE8 20.00 S.OO TOTRL = 339
OREO POINT
100
90
80
70
80
SO
40
30
20
10
0 '
100
90
80
70
BO
SO
40
30
20
10
0
N NNE HE ENE E E8E
8SE S 'SSN 8M H8N H NKH NU NNH
CON TEST EXRHPLE (PI) UNIT = MICROGRPH PER CUBIC NETER
RECEPTOR COORD1NHTE8 20.00 ZO.OO TOTRL s 339
80
80
70
60
EO
40
30
20
10
0
N NNE NE ENE E ESE 8E 8SE 8 SSN SM MSN N HNM NN
Figure A-3 (continued). Histograms for test example.
go
eo
70
eo
so
40
30
20
10
0
44
-------
APPENDIX B. FLOW DIAGRAMS
45
-------
c
BEGIN
BLOCK
DATA
c
START MAIN PROGRAM
CALL
CLINT
Figure B-1. Abbreviated flow chart of Climatological Dispersion Model.
46
-------
) READ RECEPTOR COORDINATES
RECEPTOR
WITHIN AREA
SOURCE
GRID
DETERMINE MINIMUM DISTANCE OF RECEPTOR TO GRID BOUNDARY
DETERMINE MAXIM DISTANCE OF RECEPTOR TO A VERTEX OF THE
GRID FOR UPPER INTEGRATION LIMIT
Figure B-1 (continued). Abbreviated flow chart of Climatological Dispersion Model.
47
-------
BEGIN
DEFINES CONST ANTS USED
IN THE PROGRAM
END
Figure B-2. BLOCK DATA
ENTER
READS IN PROGRAM PARAMETERS (3 CARDS)
READS IN RELATIVE FREQUENCY ARRAY (96 CARDS)
DEFINES VARIOUS CONSTANTS BASED ON INPUT PARAMETERS
PRINTS OUT INPUT DATA, IF OPTION SELECTED
READS INFORMATION ON SOURCES OF EMISSION
•'NO—
AREA SOURCES PUT IN ARRAY
ENTER POINT SOURCES
YES—RETURN
Figure B-3. Subroutine CLINT.
48
-------
CENTER"")
CALCULATE MIXING HEIGHT ACCORDING TO STABILITY
<'ffz>0.8 (NIIXING\_Y
-YES-
HEIGHT)
NO
—{COMPUTE CONCENTRATION BY GAUSSIAN FORMULA
COMPUTE CONCENTRATION BY BOX MODEL
STORE ACCORDING TO WIND DIRECTION SECTORS
(^RETURN
Figure B-4. Subroutine AREA.
49
-------
ENTER
CALCULATE MIXING HEIGHT ACCORDING TO STABILITY
COMPUTE PLUME RISE BY BRIGGS' FORMULA
PLUME RISE =WU
«>0.8 (MIXING >__ YES
HEIGHT)
COMPUTE CONCENTRATION BY GAUSSIAN FORMULA
COMPUTE CONCENTRATION BY BOX MODEL
STORE ACCORDING TO WIND DIRECTION SECTORS
Figure B-5. Subroutine POINT.
50
-------
APPENDIX C FORTRAN STATEMENTS
51
-------
Table C-l. FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
MAIN
COMMON /Cl/ K,MX,MN»HT.F(6.6«16)»G<6«5) ?U<6) »RI»RJ»INC<4) ,DELR
COMMON /C2/ UE(6).YO,YN»TMN.HMIN,DINT»YCON,TA<4),IPG.XG.YG.IRD
COMMON /C3/ RATG,IRUN,CA<2) »C8 <2> .TK < 16) » AROS < 2) .PROS < 2) .TANG
COMMON /C4/ DECAY(2)»ICA<6) .ICP(6) »H(6).HX(6) .GB(2) .MO.IVER.IWR
COMMON /C5/ Q(100.4).GA »PS<200,4) »PX<200> »PY<200) .FB»200) .
»XX(200).DHF(?00) ,WAd6> »WBd6> .PROSE (16.2) ,CV, IPS.RAT.TOA.PBAR (?)
C CLEAR AND INITIALIZE
CALL CLINT
C
C READ RECEPTOR COORDINATES
401 READ(IRD.402»ENO=403)RX.RYtKPX(9)..XPX«10).NROSE
C RX: COORDINATE OF RECEPTOR
C RY: COORDINATE OF RECEPTOR
C KPX(9)t OBSERVED P 1 CONCENTRATION AT THIS RECEPTOR IF KNOWN
C KPXdO): OBSERVED P 2 CONCENTRATION AT THIS RECEPTOR IF KNOWN
402 FORMAT<2F8.2»14X,I4.3X.I4,15)
C CONVERT COORDINATES TO EMISSION GRID UNITS
RI=(RX-XG)/RAT»1.
RJ=(RY-YG)/RAT»1.
IF(NROSE.aE.l) IPG=IPG+6
IPG=IPG+1
C START NEW PAGE IF LINE COUNT GE 50
IFdPG.LT.50) GOT0499
IPG=0
WRITE (I WR. 4^*4) IVER.IRUN
444 FORMAT* •!• »AOX, «CDM VERSION* , 16. •» RUN", 16)
WRITEdWR.445)
445 FORMAT (• « .40X.MMICROGRAMS PER CUBIC METER)')
WRITEdWR.MO)
410 FORMAT (• • »30X,« AREA «,15X,« POINT «,15X. 'TOTAL1 » 1 3X, t CALIBRATED •»
»11X.«OBSERVED»)
WRITE(IWR,409)
4r,9 FORMATC «, 5X, "COORDINATES • »3X.5< 7X. »P 1«,6X,« P ?•))
499 K=l
C K: PROGRESSES 1 THRU 16 CONTROLLING SECTOR (DIRECTION)
005001=1,?
00000020
00000030
00000040
00000050
00000060
00000070
00000080
00000090
00000100
00000110
00000120
00000130
00000140
00000150
00000160
00000170
00000180
00000190
00000200
00000210
00000220
00000230
00000240
00000250
00000260
00000270
00000280
00000290
00000300
00000310
00000320
00000330
00000340
00000350
00000360
00000370
00000380
00000390
00000400
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
ABAR
-------
Table C-1 (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
6
10
12
7
13
14
15
16
17
70
96
TA(I)=ATAMDY (1
GOT016
TA(I)=180.
GOT016
IF(DY=90.
GOT016
IF(OYd)) 13» 14,15
TAd)=ATAN=360.
GOT016
TAd) =ATAMDY ( D/DX'I) )»RAD
IF(TA,d) .GT.TXI) TXI=TA(I)
IF(TAd) .LT.TNI) TNI=TAd)
CONTINUE
TDIF=TXI-TNI
?7
?8
.10
Ad)=TA(I)
TX=TXI
TN=TNI
IF(TOIF.GT.180.) GOTO?9
TM=90.-TK(K)
IF(TM.LT.O.) TM=TM*360.
IF,(TM.GE.TN-11.?5) GOT028
IF(TM.GE.11.25> GOT0666
TM=TM*360.
IF(TM-JTX+11.25))40*40,666
TM=180.-TK(K)
IF(TM.LT.O.> TM=TM»360.
TX=0.
TN=400.
00361=1,4
Ad)=Ad)+90.
IF (Ad) .GE.360.) Ad)=Ad)-360.
IF(Ad) .GT.TX) TX=A«I)
OOOOOR10
00000820
00000830
00000840
00000850
00000860
00000870
OOOOOH80
00000890
00000^00
00000910
00000920
00000930
00000940
00000950
00000960
00000970
000009HO
00000990
00001000
00001010
00001020
00001030
00001040
00001050
00001060
00001070
00001080
00001090
00001100
00001110
00001120
00001130
00001140
00001150
00001160
00001170
00001180
00001190
00001200
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL 6
un
ui
IF(Ad) .LT.TN) TN = A«I) 00001210
36 CONTINUE 00001220
IF(TX-TN.LE.180.) GOTO?? 00001230
TM=270.-TK(K) 00001240
IF(TM.LT.O.) TM=TM+360. 00001250
GOT030 000012*0
40 DIF=(TX-TN)/<2.*RAD) 00001270
MN=TMN«COS8 IF(K.GE.16) GOT0452 00001410
«=««•! 00001*20
C K LOOPS THRU 16 SECTORS 00001430
005031=1.? 00001440
AROSF.(K,I)=0. 00001450
503 PROSE(K,I)=0. 00001460
C IF NO AREA SOURCES. CHECK POINT SOURCES 00001470
IF(IAS.LT.l) GOT0666 00001480
C BRANCH TO 61 OR 70 DEPENDS ON WHETHER RECEPTOR IS INSIDE AREA G00001490
GOTO<61«70>.18 00001500
C PRINT AND PUNCH OUTPUT 00001510
452 005051=1.? 00001520
TCON(I)=PBAR(I)»ABARU) 00001530
5f5 CCON(I)=CA«I)»CB(I)«TCON(I) 00001540
C TCON: TOTAL CONCENTRATION 00001550
C CCON: CALIBRATED CONCENTRATION 00001560
WRITE
-------
Table C-l (continued).. FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
Ol
a-
PUX=(RX-XGG> /RATG+1.
C PUX: X COORDINATE OF PLOTTING GRID
PUY=(RY-YGG) /RATG+1.
C PUY: Y COORDINATE OF PLOTTING GRID
C KPX: CARD OUTPUT VECTOR
KPX(1)=ABAR< D+0.5
KPX (?) =ABAR <2) + 0.5
KPX(3)=PBAR<1>+0.5
KPX(4)=P8AR <2>+0.5
KPX<5)=TCON(l)+0.5
KPX(6)=TCON(?)+0.5
KPX(7)=CCONU)+0.5
KPX(8)=CCON<2)+0.5
WRITE (IPU, 405) PUX.PUY, (KPX (L) ,L = 1,10) »RX,RY,lRuN
405 FORMAT(F8.2»F6. 2,1014, 2F10. 2,15, •!•)
IF(NROSE.LT.l) GOT0401
KPXU7)=RX»100.
KPX (18>=RY»100.
WRITE(1WR,461)
461 FORMAT (• AREA ROSES')
D0463J=1,?
D046?I=1,16
4fr? KPX(I)=AROSE(I,J>+0.5
WRITE(lWR,467) AROS(J) ,KPX
467FORMATC • , 6X , A4, 1815)
463 WRITt ( IPU.464) AROS< J) ,KPX
WRITE(IWR,468)
4f,6 FORMATC POINT ROSES')
D0466L=1»?
D046SK=1. 16
465 KPX(K)=PROSE(K»L) +0.5
WRITE(IWR,467)PROS(L),KPX
466 WRITE(1PU,464)PROS(L),KPX
464 FORMATIA4, 1614,216)
GOT0401
403 CALL EXIT
END
CALO
SUBROUTINE CALO
DIMENSION C(3)
COMMON /Cl/ K,MX,MN,HT,F (6,6,16) ,G(6,5),U(6) ,RI,RJ,INC(4) ,DELR
00001610
0000 16?0
00001630
00001640
00001650
00001660
00001670
OOOOKS80
00001690
oooo I7on
00001710
00001720
00001730
00001740
00001750
00001760
00001770
00001780
000017
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
C
c
C
c
c
COMMON /C?/ UE(6), YD,YN,TMN,HMIN»OINT,YCON»TA<4>»IPG»XG»YGfIRQ
COMMON /C3/ RATG,IRUN,CA<2),CB<2),TK<16)»AROS<2),PROS<2),TANG
COMMON /C4/ OECAY(2> »ICA(6)»ICP(6),H<6),HX<6),GB(?),NU,IVER»IWR
COMMON /C5/ a<100»4),GAI2>»IAD<4»5) »XGG»YGG,IAS»TDA»TDb»TDC,IPU
COMMON /OCOM/ N,UR»IX»IY»TT<16»21>»KTC»IXX» IYY»RAD»Z<50»50»3)»TD
CALCULATE SECTOR AREA SOURCE VECTOR Q
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
79 IA=1
JA = 5
GOT0101
80 IA = 2
JA=3
GOTO 101
fill IA=?
. JA=4
GOT0101
P? D=TJ-J
IF(A8S
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
D0801L=1.2
801 C(L)=C(L)+Z(IV,JV,L)
IF=C<3)*Z(IV»JV,3>
80? CONTINUE
cu>=c/4.
C<2)=C<2>/4.
IFJCN.GT.0.5) GOT0803
C(3)=l.
GOT0804
803 C(3)=C(3)/CN
804 IF(R.GT.O.) GOT0103
D0201LA=1,3
201 Q(NQ,LA)=C«LA)
GOTO 102
103 IF(LL.NE.l.AND.LL.NE.KTC) GOT0104
C TRAPEZOIDAL INTEGRATION APPLIED
D0203LB=1«2
203 C(LB)=C(LB)»0.5
104 D0204|_C = 1»2
2C4 Q=1.
GOT0102
105 Q(NO»3)=Q(NO,3)/MN
102 N=N»INC
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
o-
o
COMMON /Cl/ K,MXtMN»HT«F(6,6«ie>) ,G<6»5) ,U<6) »*I ,RJ, INC <4) ,DELR
COMMON /C?/ UE«b) ,YD»YN,TMN,nMlN,UINT»YCON,TA<4) , 1PG,XG, YG» IRU
COMMON /C3/ kATG»IRUN,CA<2> »CB<2) iTM 16) »AROS<2) »PROS<2> »TANG
COMMON /C4/ OECAY(?),ICA<6) . ICP <6) »H <6) ,HX «6) «G8 < ?) /NO,IVER»lW«
COMMON /C5/ 0< 100»4) ,GA(?) »IAD<4,5) »XGG» YGGt I AS»TDA» Ti)ri»TOC, 1PU
COMMON /ACOM/ PI,SZA(6) .ABARC2) , AROSE < Iht ?) » AS ' 6)
Y=YD
C CALCULATE SECTOR CONCENTRATION FROM AREA SOURCE VECTOR Y=YN
IC=ICA(IS)
C0338IU=l,b
C IU: CONTOLS WIND SPEED CLASS
C IF FREQUENCY IS ZERO* SKIP
IF(F(IS»Ili»K) .LE.O.) GOT0338
C<1)=0.
C(?)=0.
IR = 1
OVLR1=Q(?,^)-Q(I»4)
7^1 R=0«IR»4)
OVLR=OVLRI
OVLRI=Q(IR*1»^)-R
WZ=(Q(IR»3)«0.1>»*UE(IS)
WS=U(IU)»WZ
D0801JA=1,?
DF=WS*GA(JA)
80 1 .DECAY ( JA ) =EXP ( R/OF >
RXS=R*XSdS)
IF(RXS-5000.) 311.313,310
•^10 12 = 1
GOT03P7
111 IF(RXS.GE.500.) GOT0313
IZ=3
GOT03?7
313 IZ=?
3?7 SZ=G(IZ»IC)»HXS»«G(IZ+3,1C)
IF(SZ.LF.O-) GOT03A6
IF(SZ.GE.HXdS)) GOT0317
STK?=Q(IR,3)*Q
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
C
c
c
c
c
c
c
317
70?
8^2
465
3?0
465
366
319
462
323
4?3
346
367
SB=-0.5«STK2/(SZ*SZ)
S=PI*EXP(SB)/'SZ»WS)
GOT0319
S=1./«WS*H(IS> )
LID HAS BEEN REACHED
IRI=IR
R=0(IRI,6)
DVLR=DVLRI
DVLRI=Q(IRI»1»4)-P
•i!2= (U ( IRI « 3) *0 • 1) **UE" (IS)
WS=U(IU)*WZ
DOfl02JB=l,2
DF=WS*GA( JB)
DECAY(J8)=EXP
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
POINT
447 ABAR»CB(2>,TK(16)»AROS(2)tPROS<2)»TANG
COMMON /C4/ OF.CAY(2),ICA<6),ICP(6) »H(6)»HX<6>,GB<2) ,NQ,IVFR,IWR
COMMON /C5/ Q<100»4),GA(2),IAD(4,5> ,XGG,YGG,IAS»TDA»TDB,TOC,IPU
COMMON XPCOM/ PH<200) »PR (200) »PS
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
XS=(SZI/G<2»IC))*
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
WW=WS»XP*SZ
S(1)=PS(IP,1)/WW
S(2)=PSUP.2)/WW
WV -EXP(B)
s
D0715JE! = 1.2
X=S tTK<16) ,AROS . ICA (6) » ICP (6) »H (6) ,HX <6) »GB (?) »NQ»IVER,IWR
COMMON /C5/ 0<100*4)*GA(?.)fIAD(A«5) »XGG» YGG« I AS»TDA»TDB.TDC, IPU
COMMON /QCOM/ N,DR, IX , IY,TT ( 16. ?1) »KTC, IXX , IYY.RAD.Z (50»50» 3) »TD
COMMON /ACOM/ PltSZA(fi) »ABAR<2) ,A«OSE'16»?) ,XS«6)
COMMON /PCOM/ PH(?00) , PR (POO) »PS(?OO.A) »PX(200) »PY(?00) «FB
-------
Table C-1 (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
005*41=2,16 . 00005210
544 TK oooossao
C N = STABILITY CLASS 00005590
C GB(N): DECAY RATE HALF LIFE 00005600
-------
Table C-l (continued). FORTRAN STATEMENTS. FORTRAN IV. LEVEL G
c
c
c
c
c
c
c
M=l: PI, M = ?: P ?
INPUT RELATIVE. FREQUENCY TABLE OF ST AB IL I TY , WIND SPEED.
005131=1. 6
OC513K=1.16
513 READIIR0.514) D
WB(I)=SIN(ci)
WA(I) =COS«B)
OCB1^J=1.KTC
X = TANG-TK (I) * < J-l)*THtfTA
IFIX.LT.O.) X=X*360.
^>1<3 TT ( I. J) =X/rtAU
DEFINE HALF" LIFE F0» P 1 AND P ?
GA( 1) =GB< D*3ftOO./0.'tc3^
GA (?) =r,rt
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
S=(SA/G<2»JB))*«<1./G<5»JB»
IF(S.GE.500.) GOT0114
S=(SA/G<3«JB»*
WRITE(IWR,802)UE
WRITEdWR,804)
80,4 FORMATCOTHE INITIAL SIGMA Z FOR AREA SOURCES BY STABILITY CLASS
«SZA) :•)
WRITEdWR,802)SZA
WRITE(IWR,805)
8;>5 FORMATCOTHE CLIMATOLOGICAL MEAN NOCTURNAL AND AFTERNOON MIXING
*IGHTS (HMIN.HT):•>
WRITEdWR.SO^JHMlN.hT
WRITE(IWR.806)
806 FORMATCOTHE DAY AND NIGHT EMISSION HEIGHT FACTORS :»>
WRITE (IWR.80?) XG»YG
WRITF.dWR.808)
FORMATCOTHE WIDTH OF
WRITfc"dWR,80?)TXX
WRITE( IWR.809)
FORMATCOTHE NUMBER OF SUB-SECTORS CONSIDERED IN A ?2.5 DEGREE
»TOP» AND ANGULAR WIDTH OF A SUB-SECTOR
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
WRITE(1WR,802)DELR
WRITE
811 FORMAT COTHE RATIO OF EMISSION GRID TO MAP GRID «RAT>:«)
WRITE
816 FORMATCOTHE OEiCAY RATE HALF LIFE FOR P 1 AND P 2 (OB):')
WRITE UWR, 802) GB
v*RITE«6)
8?3 FORMATC • » 12X , «U • » 1 1»5 < 18X, »U« » 1 1 ) )
WRITEUWR.824)
8?4 FORMATC SECTOR1)
IB=L*3
IA=IB-2
00819I=IA»IB
WRITE(IWR,8IB) I
818 FOHMATCO«»*OX,«THE JOINT FREQUENCY FUNCTION FOR STABILITY
«I3»/)
D0819K=1,I6
819 MRITE(IMR*825)K*(F(I«J«K)«J=1*6)
8?5 FORMATC t,l2,6C?0.6)
C INPUT SOURCE DATA
501 READ (IRD, 502 ) X, Y,TX«S1»S2»SH»0» VS»T»SA
C X: COORDINATE
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV LEVEL G
C Si: SOURCE EMISSION RATE IP 1 IN GRAMS/SECOND) 00006810
C S?: SOURCE EMISSION) RATE < P ? IN GRAMS/SECOND) 00006820
C SA: FOR POINT SOURCES, IF BLANK, BRIGGS FORMULA USED, IF NOT 00006830
C BLAN'K, SH»HIND SPEED IS USED. 00006840
C TX: WIDTH OF THIS CELL 00006960
8?6 FORMAT<• SOURCE INPUT') 00006970
WRITE(IWR,822) 00006980
8?? FORMAT*' ',9X,«X',1?X,'Y'.HX,•TX',1IX,'SI•, 1IX,•S?«, 1IX,»SH«, 00006990
*1?X,'D',11X,'VS',1?X,«T',11X, 'SA') 00007000
899 IPG=IPG*I 00007010
WRITE(IWR,820)X,Y,TX,S1,S?,SH,D,VS,T,SA 00007020
8?0 FORMATC «,10fl3.5) 00007030
C EFFECTIVE STACK HEIGHT MUST BE GE 1. 00007040
8ftP IF(SH.LT.L) SH=1. 00007050
C SEPARATE AREA AND POINT SOURCE DATA 00007060
IF(TX.LE.O.) GOT0510 00007070
C STORE AREA SOURCE DATA 00007080
C MOVE COORDINATE TO CENTER OF GRID CELL 00007090
D=TX«0.5/CV 00007100
X=X+D 00007110
Y=Y+D 00007120
W=TX/TXX 00007130
S=TX»TX 00007140
B=S1/S 00007150
D=S2/S 00007160
C BECAUSE OF THE METHOD OF INTEGRATION, AREA SOURCES ARE 00007170
C DIVIDED BY TWO AT THIS POINT FOR MORE EFFICIENT EXECUTION 00007180
C OF SUBROUTINE AREA. 00007190
B=B«0.5 00007200
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
539
fl?l
510
0=0*0.5
X=(X-XG)/PAT*1.
Y=-0.45
N=(L*W)-0.45
0053?I=K,M
0053?J=L,N
Z(I«J»l)=h
Z(ItJ»2)=0
Z(I«J»3)=SH
IF(M.GT.IXX)
IF(N.GT.IYY)
IAS=IAS*1
GOT0501
IPG=70
TDA=0.b-TD
TDH=IXX»0.5»TO
TOC=IYY+0.5»TD
IF(NLIST.LE.O) WRITE ( IWR, 8?1 ) I AS» IPS
FORMAT<«0«»I10»' AREA SOURCES. «. 1 10 ••
RETURN
STORE POINT SOUWCE OATA
IPS=IPS+1
PX(IPS)=(X-XG) /RAT+1.
PY(IPS)=(Y-YG)/RAT+1.
PS(IPS»1)=S1*?.03
IYY=N
POINT SOUHCES.M
PS(IPS»3)=S1»?.55
PS(IPS»4)=S2*?.55
PH(IPS) =SH
PR(IP5)=SA
00007210
00007??0
00007?30
00007?40
00007250
00007260
00007270
00007280
00007290
00007300
00007310
00007320
00007330
00007340
00007350
00007360
00007370
00007380
OOC07390
OOC07400
00007410
00007420
00007430
00007440
00007450
00007460
00007470
00007480
00007490
00007500
00007510
00007520
00007530
00007540
00007550
00007560
00007570
00007580
00007590
OOC076QQ
-------
Table C-l (continued). FORTRAN STATEMENTS, FORTRAN IV, LEVEL G
IF(SA.GT.O.) GOT0501
0=D»0.5
T=T+?73.]6
S=(T-TOA)/T*9.8»VS*0*0
IF(S.GT.55.) GOT0606
XX (IPS) =14.«S**0.6?5
GOT0605
606 XX (IPS) =34.»S»*0.4
60S frB(IPS)=1.6»S»«0. 333.1
DHF (IPS) =FB ( IPS) « ( 3.5*XX (IPS) ) «*0 .6667
GOT0501
END
BLOCK DATA
BLOCK DATA
COMMON /Cl/ K,MX,MN,HT,F (6,6, 16) »G(6.5> »U(6) .RI.RJ, INC<4) .DELR
COMMON /C?/ UE (6) ,YO,YN,TMN,HM1N,OINT.YCON,TA(4) .IPG.XG.YG. IKD
COMMON /C3X RATG,I«UN,CA(?) ,CB(?) ,TK 1 16) » AROS (2) .PROS ( 2) » TANG
COMMON /C4/ DECAY (2) . IC.A ' 6) . ICP (6) .H (6) ,HX ( 6) .fifl ( ?) ,NQ,IVER.IWH
COMMON Xf.5/ Q(100»4),GA(2)*IAO(4«.5) *X(iG*YGG» 1 AS. TOA.TDb.TDC. IPU
COMMON /QCOM/ N,Dn(.IX,IY,TT(16»?l) *KTC. I XX . IYY.RAD, Z (50 .50 . 3) . TO
COMMON /ACOM/ P I . SZ A (fc ) , AB AH ( ?) « AKOSE ( 16. ?) « XS ( 6)
COMMON /PCOM/ PH(?00) *PR(?00) .PS(?00.^> »PX (?00)»PY(?00) *FH(?00) .
»XX (?00) .DHF(?00) .VKAM6) »WB(16) » PROSE* 16.?) . CV, IPS. RAT .TOA.P8AR (?)
DATA G/?« ?. 539E-4,. 0 383. 2»?. 0 886. 1.281 2. ?». 04936.. 1393»?« 1.1 137.
^.9467,.1154,.101^..11?..9109,.9?6».91..736e«.2591,.0856..56A2,
».6fl69. .«65« 1.P969, .?S?7..0818..^A?1..63A1, .8155/
DATA T ANG.U/78. 75,1. 5. ?.4587?,4. 4704, 6.9291?. 9.61 136.1?. 51 7 12/
DATA YCON.UF/0.1E7, 0.1, 0.15, 0.2,0. 25,0. 25, 0 . 3/
DATA INC,IPG,IPS,IX,IY/1,2.4,4,70,0.1»1/
DATA IXX.IYY. IAS/1,1,0/, TO/0.1E-3/
DATA «AD»PI/57.?958,0.797885/
DATA IAO/0,0. 1»1,0,1,0,1,4»0,4«1,0.1.1.0/
DATA 1C A, ICP/1. 1.2.3.4, 4, 1,2, 3, 3*4/
DATA IVEW/72313/
END
00007610
00007620
00007630
00007640
00007650
00007660
00007670
00007680
00007690
00007700
00007710
00007720
00007730
00007740
00007750
00007760
00007770
00007780
00007790
00007800
00007810
00007820
00007830
00007840
00007850
00007860
00007870
00007880
00007890
00007900
00007910
00007920
00007930
00007940
-------
APPENDIX D:
A CLIMATOLOGICAL MODEL FOR MULTIPLE
SOURCE URBAN AIR POLLUTION
by
K.L. Calder
On assignment from
National Oceanic and Atmospheric Administration
U.S. Department of Commerce
Division of Meteorology
National Environmental Research Center
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
Paper presented at
First Meeting of the NATO/CCMS Panel on Modeling
73
-------
Acknowledgements
The Fortran computer program required for application of the model
described in this paper was developed by Messrs. John R. Zimmerman and
Adrian D. Busse, both of the Division of Meteorology, Environmental
Protection Agency. Thanks are also due these gentlemen for the rather
extensive numerical calculations that are described; especially to Mr.
Zimmerman for helpful discussions of many other details.
Abstract
The paper describes a revised form of an urban air pollution model,
originally proposed in 1968 by D.O. Martin and J.A. Tikvart, for estimating
long-term average concentration of gaseous pollutant in terms of appropriate
point- and area-source emission inventories for. the urban area, together with
climatological frequency data relating to wind speed, wind direction, atmospher-
ic stability, and mixing depth. The model is also applied to the estimation
of three-month average S02 concentrations in St. Louis, Missouri, during the
winter of 1964-65. Some shortcomings of the present model are identified and
discussed.
74
-------
A CLIMATOLOGICAL MODEL FOR MULTIPLE SOURCE
URBAN AIR POLLUTION
(A Revised Form of a Model First Proposed
by D. 0. Martin and J. A. Tikvart)
by K. L. Calder
I. INTRODUCTION
A paper by Martin and Tikvart was presented at the annual meeting of the
Air Pollution Control Association in June 1968. The paper described a
computerized climatological model for urban air pollution from multiple
sources. This source-oriented atmospheric diffusion model permits calculation
of the long-period seasonal or annual-average pollutant concentration patterns
resulting from multiple point or area-distributed stationary sources. The
model input comprises a detailed specification of the magnitude and distribu-
tion of pollutant emissions and of the frequency of occurrence of various
meteorological conditions during the time-period of concern. The output
provides a quantitative estimate of the spatial distribution of urban air
quality averaged over the time period considered.
The fundamental physical basis for the model is the assumption that the
steady-state spatial concentration distribution from an elevated, continuously
emitting point source is given by the Gaussian plume formula. However,
following Meade and Pasquill (1958), this formula was first modified to give
the long-term average concentration produced by a given source at any receptor
for specified frequencies of occurrence of the various possible wind directions.
Martin and Tikvart utilized this result in conjunction with a specified joint
frequency function for the occurence of various possible combinations of wind
direction, wind speed, and atmospheric stability to obtain the long-term
average concentration for all the possible combinations of the meteorological
conditions for a multiple source distribution.
The model clearly represents a natural development in the hierarchy of
urban air pollution models that stem directly from the Gaussian plume hypothesis,
The present paper provides a detailed account of the model which has not been
75
-------
previously available. Revisions have been incorporated to clarify some
features of the original analysis. A major revision relates to the
mathematical method for computing the concentration contributions from
area-source distributions.
II. THE GAUSSIAN PLUME
A recent discussion of the structure and assumptions that underlie
urban air pollution models based on the Gaussian plume has been given
elsewhere (Calder, 1969). The common starting point is the assumption that
meteorological conditions over short periods of time of the order of an
hour can be regarded as steady-state. It is also assumed that these
conditions may be adequately approximated with a unique horizontal mean
wind direction for the entire urban area together with a constant and
spatially uniform wind speed.
Let the origin of a rectangular coordinate system be taken at ground
level, with the x-axis in the direction of the mean wind, y-axis crosswind
and the z-axis vertical. Then for a constant, continuously emitting, elevated
point-source of strength G located at x=0, y=0, z=h, the Gaussian plume
formula gives the concentration x(x, y» z) of material at position (x, y, z)
as
S (x, z)
(1)
where
S(x, z) =
exp {-
7-hU
} + exp {-
(2)
76
-------
and o (x), o (x) are horizontal and vertical diffusion functions that give
respectively, the horizontal and vertical standard deviations of the
Gaussian concentration distribution at downwind distance x. The above
formula relates to the atmospheric transport and diffusion of a chemically
stable gas or a cloud of particles sufficiently small that gravitational
settling can be neglected. It is also assumed that no material is lost
from the cloud to the ground surface. The method of images is invoked to
satisfy this condition and the function S(x, z) is the sum of two terms
representing (in the absence of the ground surface) the concentration
contribution from the real source at z = h and that from its image in the
plane z = 0, i.e., at z = -h. It is readily verified that equation (1)
satisfies the equation for the conservation of matter, namely
UX (x, y, z) dydz = G (3)
Equation (1) is assumed to be valid irrespective of the horizontal location
of the source and of the horizontal mean wind direction that defines the
orientation of the coordinate system.
The standard deviation functions a (x) and a (x) are dependent on
meteorological conditions and are assumed to be parameterized in terms of
an atmospheric stability category P first introduced in discussions of
atmospheric diffusion by Pasquill (1961). Actually, a completely objective
scheme for determing the appropriate stability category in terms of
meteorological observations that are routinely taken at airports was
suggested by Turner (1964) and used in the application of the model. This
scheme admits five different Pasquill-type stability categories P (m = 1, 2,
3, ..5) for an urban environment, P-, being a very unstable category and Pr
a slightly stable one. For given stability category P the standard
deviation functions a (x; P ) and a (x; P ) are obtained as functions of
the downwind distance x from some graphical plots of Gifford (1961). The
77
-------
latter are simple transforms of some rather crude empirically established
dispersion curves first given by Pasquill (1961, 1962). For the final
computerized model, it is convenient to represent the Gifford plots by
simple formulae of the type
oz(x; PJ = axb + c .
where for each stability category a, b, c, are constants within given ranges
of x.
The above values of a (x; P ) refer to conditions where there are no
restrictions to diffusion in the vertical direction so that a (x; P )
increases continually with x. However, when a stable atmospheric layer
exists above an unstable near-surface layer, the vertical diffusion will
be limited to a mixing layer of finite depth L, within which pollutants
will be trapped. If this occurs, a uniform vertical distribution of con-
centration would be expected throughout the depth of the mixing layer for
sufficiently large values of x and some modification of the Gaussian formula
will be necessary. Providing that the emission height h is small compared
with L, a crude but simple method of allowing for this effect has been
suggested by Pasquill (1962) and Turner (1969). By assigning h = 0 in
the equation (2), it is readily verified that, when z = 2.15 oz, the
concentration is one-tenth its value at the ground surface. When this value
is occurring at the level of the top of the mixing layer, it is assumed
that the "lid" begins to influence appreciably the vertical distribution of
concentration. Turner suggests the following rough method to allow for
the situation. Use equations (1) and (2) for downwind distances such that
a (x) <^ L/2.15 or 0 (x) <_ 0.47 L corresponding to downwind distances, say
x,. Assume that for x >^ 2x, the concentration has become uniform through the
depth of the mixing layer, so that S(x, z) of equation (2) is replaced by
S(x, z) = jj- (x >.2xL) (4)
For x, <_ x <_ 2x. , Turner suggests linear interpolation between the concentration
values for these two distances. This procedure was adopted in the Martin-Tikvart
air pollution model.
78
-------
A more refined method of correcting for the finite depth of the mixing
layer is to utilize the "method of images" in the same manner that this
technique is used to allow for the "reflecting" ground surface in establishing
the function S of equation (2). For a point source situated between two
parallel "reflecting" surfaces at distance L apart, i.e., the ground and
the lid of the mixing layer, it is evident that an infinite series of image
sources arises and the concentration distribution is thus expressed as an
infinite series [Bierly and Hewson (1962), Fortak (1969)]. In this case
it is readily shown
x(x, y, z) =
2LU
A {
z - h
2L
2 \ x A / z + h
TT> + A { Tr-
where the function A is defined by
A(v;w) = -L- r1
/™ ^
(5)
(6)
n = -o
When L -*- °°, only the term corresponding to n = 0 remains in each of the two
infinite series that are involved, and in this case (5) reduces to (1) with
S given by (2). In the general case the infinite series converge rapidly,
and it is only necessary to consider a few terms.
Before leaving this discussion of the Gaussian plume, it should be
noted that the emission height h for large point sources can rarely be taken
as the actual physical height of a pollutant emitting stack since there is
normally considerable plume rise associated with the upward momentum of dis-
charge and thermal buoyancy effects. Frequently a crude attempt to allow for
these effects is made by simply adding an estimate of the plume rise to the
stack height and using this sum as the quantity h in the diffusion formulae.
Consideration of plume rise is a complicated and somewhat controversial topic,
although it is generally regarded as an important element in realistic urban
79
-------
air pollution models. A comprehensive and hopefully definitive critical
review of the subject has been recently prepared by Briggs (1969).
III. AVERAGE CONCENTRATION WITH VARIABLE WIND DIRECTION FROM A SINGLE SOURCE
For fixed locations of both source and receptor, the maximum concen-
tration will occur at the receptor when the v/ind blows directly from the
source towards the receptor. The concentration varies with wind direction.
Therefore, the average value when the wind direction is a random variable
governed by a probability or frequency distribution is considered first.
Relative to a rectangular coordinate system with x-axis along the
wind direction, the point source concentration distribution will be given
by equation (1), where
I.
6S(x, z) = x(x, y, z) dy
(7)
In the diagram below, let the source be at the origin of a polar
coordinate system, with (p,e) the polar coordinates of the receptor, and
6 the angular direction measured clockwise from north from which the wind
blows.
North
Receptor (p,$)
South
80
-------
Then if f(0)de is the probability that the wind direction is in the
angular range e, e + de, the average concentration at the receptor
corresponding to all possible wind directions will be approximated by
ITT-6+A
x(pcos e-B-ir, psin e-e-ir, z) f (e)de
ir+B-A
(8)
where, since the plume from a point source is normally narrow, A is a
small angle. If the total range of integration were made larger than
2A, this would have negligible effect on the value of the integral.
With i|/ = e - B - IT, equation (8) becomes
A
x(pcos\|>, psinijj, z) f (y + e + -fr)di|;
-A
or since \i> is small and hence costy ^ 1, we have, using equation (1),
rA
' -p2sin2i|j
-A
=
+ 6 + ir)dijj
The integral in (9) could be evaluated numerically if the frequency function
were specified. However, with small ty, we have approximately
rA
-= GS(Pt z)
(10)
-A
We now assume that, because of the small ness of the angular range -A <_ $ <_ A,
the variations of the wind direction frequency function in the integral of
(10) can be disregarded and the function replaced by its central value f(3 +TT)
81
-------
so that
f(g
-A
PA
-pA
_
2
e dw
(11)
The integral is recognized as that of the Gaussian probability function whose
value tends to unity when both limits of the integration tend to infinity.
However, the value of x" is not affected by increasing the value of A
as it appears in the limits of integration, which can only be so if the
integral differs inapreciably from its asymptopic value of unity. With
this .approximation, we have
(12)
It may be noted that:
1) although both equations (9) and (10) for x" involve the
crosswind standard deviation function a (p), this is not so
for the final approximate relation (12) which is independent
of o (p).
2) equation (12) expresses "x as the product of an "isotropic"
meteorological.-diffusion function GS(p, z)/p and the directionally
dependent wind frequency function.
3) although x" is the average concentration at the receptor
corresponding to all possible wind directions, the narrow plume
assumption renders it possible to relate this average value to the
frequency function for a particular wind direction, viz. the source-
receptor direction.
With a 16-point compass if all wind directions within any given 22 1/2°
sector are equally probable, then if the source-receptor direction [here
defined by the angle (B + ir)] is in the k-th sector (k = 1, 2, ... 16) and
82
-------
F(k) is the total frequency of wind directions™ the k-th sector, we have
f(B + ir) x^f= F(k)
so that from (12)
7-16 Fm GS(P> z)
x-27F(k) p - (13)
With an 8-point compass the corresponding formula would be identical with
one used by Meade and Pasquill (1958) in examining „ the average distribution
of sulfur pollution around a power station in the U.K.
In the analysis leading to equation (13), only wind direction is
considered to be a random variable. However, it is straightforward to
generalize where several meteorological variables are regarded as random with
values specified through a joint frequency function. Thus assume that the
wind direction (defined by sectors k = 1, 2, . . 16), the urban wind speed*
Uj (I = 1, 2, . . . 6), and the Pasquill -type stability category Pm(m =1,2,
... 5) are such random variables having a joint frequency function 4>(k, t, m)
that expresses the relative frequency with which the wind is in the k-th
sector with representative speed IL and stability category P . Such a three-
variable joint frequency function was first used in the context of the present
problem by Leavitt (1960) and subsequently by Szepsi (1964, 1967). Evidently
in equation (13) the diffusion function S(p, z) = S(p, z; U, , P ) where, from
equation (2), S involves P through the standard deviation function
a (p) = a (p; P ). It immediately follows from equation (13) that the
average concentration x corresponding to all possible combinations of wind
direction, wind speed, and stability will be given by
- 16 V^ V~^ .' p, z; U.P)
*Here wind speed is assumed to be specified in terms of one of the
standard Weather Bureau classes (i.e., with wind estimated to an integral
number of knots in the classes 0-3, 4-6, 7-10, 11-16, 17-21, and > 21 knots)
and each class is represented by its central wind speed (i.e., 0.67, 2.46,
4.47, 6.93, 9.61, 12.52 meters per sec).
83
-------
where as before the source-receptor direction is assumed to lie in the k-th
wind section (N.B. the summation in equation (14) does not involve k). A
virtuallly identical solution was first proposed by Szepsi (1964). In
principle the Martin-Tikvart model simply sums equation (14) for a given
receptor location over the multiplicity of contributing sources.
It is important to note that the summand in equation (14) cannot
legitimately be used, as is attempted by Szepsi (1967), as a basis for
analysis of the frequency occurrence of various levels of concentration.
This is because it was obtained through averaging over all possible wind
directions. It is this averaging process that eliminates the crosswind
variance function a (p) that appears in the original point-source concen-
tration distribution function of equation (1).
IV. THE MULTIPLE SOURCE POLLUTION MODEL
It is customary in estimating community air pollution emissions
from fixed sources [e.g. Ozolins and Smith(1966)] and in modeling urban
air pollution to distinguish between two main categories of pollutant
sources. Very large sources with emissions in excess of 100 tons per year
are readilyidentified and located individually as single (elevated) point-
sources. However, when there are a large number of small sources too
numerous to identify individually such as domestic heating units, then it is
normal to combine these sources in any small area and to specify them
through the total pollutant emission associated with the area. The size and
number of the sub-areas are chosen in relation to the spatial uniformity
of the source distribution. Thus a complete urban pollution emissions
inventory for stationary sources will normally comprise the strenths and
locations of all major point sources together with area-source strengths
corresponding to a large number of area elements into which the total urban
area has been sub-divided. In most emission inventories, it is difficult
or impossible to specify with accuracy much detail concerning the temporal
variations of the emissions, although an estimate of variation from season
84
-------
to season is frequently attempted. In the theoretical analysis of
the previous section, it was assumed that the source strength G was
constant. When the source is variable, it will only be legitimate to
use the same formulae providing that the source strength and each of
the meteorological variables are completely uncorrelated, and, in this
case, G is given its arithmetic average value corresponding to the total
time period considered (i.e., season or year). This assumption, however,
may be questionable in some circumstances. For example, in winter very
cold conditions with increased air pollution due to increased fuel consump-
tion may occur most frequently with certain wind directions. If the source
strength and meteorological conditions are not uncorrelated, a more
sophisticated development is required that is outside the scope of the
present analysis. Although this may be straightforward mathematically,
the serious practical questions of specifying short-term temporal variations
of source strength have yet to be resolved.
Considering equation (14) it is evident that if k (k =1,2,. . .16)
is the wind sector appropriate to the n-th point source (of strength G and
distance p from receptor) and there are N point sources, then the average
total concentration at the receptor, C~ , due to all the point sources will
be given by
r 16 \ V^ V^ n.> nV' E' m (15)
cp - 2, 2_j l_s L* ^
n = 1 I m
Obviously the contribution to the total from just those sources located in
the k-th sector will be obtained by restricting the summation to these
sources (i.e., those for which k = k).
To obtain the concentration contribution,, say (T., at the receptor due
to the area-soruce distribution we use a polar coordinate system with origin
at the receptor and with angle e measured clockwise from north as in
specifying the wind direction.
85
-------
Wind
*Receptor
An element of area surrounding the point (p,e) will have magnitude
pdedp. Let Q(p,e) denote the magnitude (emission rate per unit area and
unit time) of the area source strength at (p,e), so that Q(p,e) pdedp
is the total emission rate from the element of area surrounding (p,e).
Then by considering the area source contributions from the different
22 1/2° wind sectors, it immediately follows from (15) that the total
average concentration due to the area-source distribution will be*
16
r - _L".
"A 2n
*(k, £, m)
k=l £
m
S(P, z; Ur Pm)
P
0
Q(p,e)Pde
k sector
(16)
Here the upper limit of integration for p can be taken as infinite since
Q(p,e) becomes zero outside the domain of the area-source distribution.
Equation (16) can be rewritten as
*In equation (16), it is assumed that the effective height of.the area
source distribution can be regarded as a constant for the entire area. This
is an assumption made in the original Martin-Tikvart Model. If the height is
variable, then the function S becomes a function of e and cannot be taken
outside the sector integral sign in equation (16). This, of course, raises
no fundamental problem but complicates the numerical integration.
86
-------
r - 16
CA " 27
qk(p)
*(ki £, m) S(p, z; lh,
(17)
where
qk(p) =
Q(p,e)de
k sector
so that T,— qk(p) is the average value of Q in the k-th sector at a radial
distance p. Evidently, if the integral in (17) is replaced by just a single
term of its sum we obtain the average concentration from area sources lying
within the corresponding wind sector.
The total average concentration U at the receptor due to both point and
area sources is given by C" = C". + Cp.
M r
In applying equation (17), we have to determine for each receptor
location the source functions Q (p,e) and qk(p). The air pollution emission
inventory for a stationary area source distribution is, of course, specified
once and for all fop areas of fixed locations on a map of the urban area. A
typical inventory as used in the St. Louis Study referred to in a later
section may divide the entire urban area into 5000 ft. squares with a seasonal
emission rate assigned for each square. However, from such an inventory, it
is simple to determine, for any given values of the polar coordinates relative
to a selected receptor location, the appropriate numerical values of the
source function Q(p,e).- The sector function qi,(p) may then be determined by
numerical integration of the values of 0 (p,e) along the appropriate circular
arc. For this purpose the trapezoid rule of numerical integration was applied
on each arc to Q -values spaced 2 1/4° apart, i.e., the 22 1/2" arc was
subdivided into ten intervals. The second integration with respect to the
radial distance p as required in equation (17) was also performed numerically
by the trapezoid rule with an interval length in p of 100 meters.
87
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V. MODEL INPUT DATA AND PARAMETERS
A basic feature of the present model is the assumption that for short
time periods (of the order of one hour) meteorological conditions can be
regarded as steady and uniform over the entire urban area and may be specified
through some single representative value for wind direction, wind speed,
stability category, and mixing depth. Since detailed urban meteorological
observations are not normally available, it may be necessary in practice to
utilize information collected at some nearby airport weather station with
the assumption that this is roughly representative of the urban area. Thus,
in using the Martin-Tikvart model to estimate seasonal or annual urban air
quality, the standard hourly Weather Bureau data from the local airport station
is normally used. The climatological joint frequency function 4>(k, £, m) of
the model can be readily obtained from the hourly airport observations using
a computer program specially developed for this purpose by J. Tikvart.
The objective method proposed by Turner (1961, 1964) is used to estimate
the hourly atmospheric stability category P at the airport. This method
requires no vertical sounding data but is based on ground-level meteorological
observations only (surface wind speed, cloud amount and height) supplemented
by solar elevation data (latitude, time of day, and time of year).
The values of the standard deviation function o (x; P ) used in the
application of the model are those of Pasquill (1961) and Gifford (1961) and
represented for the computation in the form
oz(x; Pm) = axb + c
where a, b, c are constants for each stability category, as shown in the
following table..
Stability Category Distance
x(M.eters)
>1000
100-1000
<100
1
.001
.001
.174
2
.048
.048
.143
3
.119
.119
.23
4
2.610
.187
.080
5
52.600
.135
.060
88
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Stability Category
Distance
1.890
1.890
.936
1.110
1.110
.922
.915
.915
.905
.450
.755
.881
.150
.745
.845
9
9
.600
.600
.000
2.
2.
•
000
000
000
.000
.000
.000
-25
-1
.500
.400
.000
-126.
-1.
•
000
100
000
x(Meters)
>1000
100-1000
<100
>1000
100-1000
<100
The values of a (x; P ) described above were originally established
from diffusion experiments conducted over flat and relatively smooth rural
terrain. To make some crude allowance for the thermal and mechanical influences
of the urban area, two types of correction have been suggested and are used
with the model. The first is intended to reflect the fact that the lowest part
of the typical urban atmosphere is less stable than its rural counterpart. To
take this into account during the daytime a stability category one step more
unstable than for the "rural" airport situation is used, i.e.., m is decreased
by unity except for the case m = 1, for all the area source calculations.
Nhen the rural stability category is Pg, corresponding to a nighttime surface-
inversion, the neutral stability category P. is assumed to apply for both the
area and point source calculations in the urban situation (so that for urtfan
applications the values of the constants a, b, c above are not needed for Pr).
The second modification of the values of a (x; P ) attempts to incorporate
an experimental finding of Pooler (1966) that for low level releases of tracer
material in an urban area the data are best represented by assigning
an initial value a at x = 0. [Note in the above table of o-values
a + 0 as x -»• 0.] This initial value is added to the Pasquill-Gifford
values obtained from the table above. In the urban air pollution model,
an initial value of 30 meters is assumed for low level sources ( an
effective source height of 20 meters or less). Arbitrarily this
89
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initial value is decreased linearly to zero as the effective source
height increases to 50 meters and is then taken as zero when the source
height exceeds 50 meters. In all cases it is convenient to incorporate the
effect of the initial 0 by use of the virtual source concept, i.e., by
regarding the a -values as the result of diffusion from an imaginary source
located upwind of the real source and then adding the virtual source distance
to the actual physical distance.
The mixing depth L that occurs in the formulation of the model varies
greatly diurnally, seasonally, and annually. Since it is impractical to
account for all these variations, a procedure reflecting only major changes
is used. The procedure determines an effective mixing depth by modifying the
average maximum (afternoon) mixing depths, as tabulated by Holzworth (1964),
depending on the stability category being considered. Stability categories
Pl' ^2' P3' are afternoon conditions, with P, corresponding to very unstable
conditions. With P,, the value of L is assumed to be 50% greater than the
climatological value tabulated by Holzworth; with P2 or P, the climatological
value is adopted. According to the objective criteria of Turner, the stability
category Pr can only occur at night under conditions when ground-based inver-
sions would occur over open level country. Since - shallow layer of neutral
or weak lapse conditions has been found to occur over urban areas, even with
\
strong nocturnal surface inversions in the surrounding rural areas, a mixing
.depth t = 100 meters is adopted for stability category Pr, when the latter is
indicated by the objective criteria. The 100-meter value is suggested by some
-observations of Clarke (1969). Stability category P^ is a neutral stability
condition that may occur either during the day or at night. In the present
version of the model, it was divided into day and night sub-classes. The
Holzworth climatological mean value was associated with a daytime case, and the
arithmetic average of the daytime value and the 100-meter value above associated
with a nighttime case.
To apply the Martin-Tikvart model, it is necessary to estimate the
effective heights of pollutant emission for both the area and point sources.
For the low level area sources (predominately residential.and commercial
90
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heating), an average height emission may be estimated roughly from consideration
of building heights. It is not usual to apply any correction-for plume rise
to these small sources. In the application to St. Louis, Missouri,
considered in the next section, a constant effective height of 20 meters was
assumed for all the area sources. As previously indicated, if this height
is not considered constant for the entire urban area, it is necessary to modify
the procedure for numerical evaluation of the area source concentration integral
of equation (17). For the large point sources considered through equation (15),
the effective source height h is determined from the physical stack height h*
and the estimated plume rise Ah, i.e., h = h* + Ah. The plume rise equation
used in the original Martin-Tikvart model (and in the calculations of the
next section) is from Holland (1953) and is given by
V T<; Ta
Ah = -4- [1.5 + 2.68 x 1Q-3P( V )d]
where V = stack gas exit velocity (meters/sec)
d = stack exit diameter (meters)
U = mean wind speed (meters/sec)
P = atmospheric pressure (mb)
T = stack gas exit temperature (°K)
T = ambient air temperature (°K)
a
Since this equation is appropriate for the neutral stability condition, it
must be modified for application over a range of stability conditions. The
following modification has been used to allow for a range from 1.3 Ah for very
unstable conditions to o.9Ah f°r the most stable.
h = h* + Ah(1.4 - 0.1 m) (m = 1, 2, 3, 4, 5)
and is a crude attempt to account for the increase of plume rise with de-
creasing stability. However, it is recommended that for future applications
the old plume rise formula of Holland should be replaced with the more recent
ones suggested by Briggs (1969).
Finally, note that for some point sources (e.g. power plants with
tall stacks), the effective emission height (h* + Ah) may be greater
91
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than the mixing depth when the latter is small. On the assumption that
the plume will not diffuse downward through the stable layer, these cases
are identified and eliminated from consideration in the Martin-Tikvart model.
VI. AN APPLICATION WITH DISCUSSION
The model was originally applied in 1968 to the calculation of average
sulfur dioxide concentrations during the winter months (1 Dec. 1964 to
28 Feb. 1965) for St. Louis, Missouri, since comprehensive data was
available from a special air pollution study (Farmer and Williams, 1966).
However, the data on emissions inventory, air quality, and meteorological
conditions that are used in the present calculations were specially compiled
by Turner and Edmisten (1968). The area-source emissions inventory was
provided for 1200 squares (30 x 40); each square was 5000 ft. on a side.
This area completely surrounded a central region of 17 x 19 squares within
which an air quality network of 40 sampling stations with 24-hour S0? bubblers
was located for the 3-month period. In addition, 62 major point sources were
considered individually in the emissions inventory. The meteorological joint
frequency distribution required for use with the model was determined from
hourly observations covering the 3-month period at the Lambert Field Weather
Bureau. As the topography is relatively flat and umcomplicated, the observations
are assumed to be representative of the entire St. Louis area. In effect, the
joint frequency function pre-digests the meteorological data into a discrete
number of possible cases. Since wind speed is classified into 6 categories,
wind direction into 16 categories, and stability into 6 categories (here
with differentiation between nighttime and daytime category 4), the distribution
covers 6 x 16 x 6 = 576 cases. Finally, the average climatological mixing
depth was estimated from rawinsonde observations made at neighboring Columbia,
Missouri, and Peon a, Illinois. The mean depth for the three winter months
i
in question was 800 meters.
Calculations of average air quality were made using an IBM 360-50
computer, and the running time was 1.6 minutes per receptor location. An
IBM 1130 was then used to calculate regression lines of observed versus
92
-------
calculated concentrations, and, by coupling with a CALCOMP plotter*, also to
generate the isopleths of average pollution concentrations that follow. The
results of several different calculations are given in Figures 2 through 7.
Figure 1 is a computer generated map of the isopleths of 3-month
average observed S02 concentrations (in ug/m3) for the central area of 17 x 19
squares in which the air quality network was located. Figure 2 is the isopleth
map for the average concentrations as calculated by straightforward application
of the model, and Figure 3 is a corresponding regression of the observed versus
calculated values for the 40 sampling stations of the network. If y and x
denote observed and calculated values, respectively, then
y = 0.26x + 19.98
with a correlation coefficient r - 0.775. Therefore, in this case, the model
overcalculates the average concentrations by an appreciable factor. In an
attempt to improve agreement with observations, calculations were also made
employing some simple modifications of the basic model. The latter only uses
a single representative wind speed for a given time and thus disregards the
known increase of wind speed with height above the ground. However, a wind
speed more prepresentative of the transport and diffusion of pollutant from
large, elevated point sources would probably be that estimated to occur at the
appropriate effective height for each point source. A crude estimate of this
speed may be made by extrapolating the surface speed (actually the 10-meter
airport wind) using a simple power law of the form
u(z) _
where, following DeMarrais (1959), the exponent p is taken to be a function
of the stability category. For the present calculations, the following values
were assumed
*CALCOMP is the manufacturer's name for an X-Y plotter that is used xo generate
the isopleths. The program for this operation is an IBM routine entitled
"Numerical Surface Techniques and Contour Map Plotting" (113-CX-11X).
93
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17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
_ \
50
10 11 12 13 14 15 16 17 18 19
Figure 1. Isopleths of observed average S02 concentration (pg/m3) for period December 1, 1964,
through February 28,1965.
94
-------
1
3
7
9
10 11 12
13
14 15 16
17
18 19
Figure 2. Isopleths of computed average SO2 concentration (pg/m3) for the period December 1, 1964, through
February 28, 1965. For this calculation. Wind speed was assumed constant with height and SO2
decay rate~was assumed to be zero.
95
-------
300
I I I
INTERCEPT = 19.98
SLOPE =0.26
— CORRELATION COEFFICIENT =0.7746
.E
o>
Z
o
200
o
o
O
LLJ
i
100
100
200
300
400
500
600
700
CALCULATED CONCENTRATION, pg/m
Figure 3. Regression line of observed versus calculated average S02 concentration (jjg/m^) for period December 1, 1964, through
February 28, 1965. For this calculation, wind speed was assumed constant with height and SC>2 decay rate was assumed
to be zero.
-------
Stability category
P 0.1 0.15 0.2 0.25 0.3
The results of calculations made on this basis are shown in Figure 4 and 5.
Figure 4 shows the calculated concentration isopleths, while Figure 5 shows
the regression of the observed on calculated values. In this case,
y = 0.32x + 20.26
with a correlation coefficient r = 0.772. Again, the model overcalculates
although to a slightly smaller degree. The final set of calculations, represented
in Figures 6 and 7, were made to provide some indication of the effect of assuming
that SOp pollutant is subject to some removal process in the atmosphere
which might considerably reduce the ground-level concentrations. A recent
paper (Weber, 1970) indicates that, depending on the meteorological conditions,
a loss of almost 50% may occur in a period of 20 minutes to 1 hour. Calculations
were, therefore, made assuming an exponential decay of SOp with travel time
using a half-life value T-, ,2 = 3^ minutes (also a single representative wind
speed was assumed for these calculations). Figure 6 shows the isopleths
based on the calculated values, and Figure 7 shows the regression line of
observed on calculated values. In this case
y = 0.39x + 52.05
with a correlation coefficient r = 0.786. Thus, in spite of the high decay
rate, the model still systematically overcalculates the average concentration
values.
Unambiguous reasons for this feature are not clear, although a number
of possibilities are under study at the present time. Some of the probable
shortcomings of the model are identified in the discussion that follows.
Although the model is conceptually quite simple, the superposition of the
effects produced by a complex distribution of pollution emissions and under a
complex sequence of meteorological conditions quickly obscure the simpler
quantitative properties of Hie model in the massive details of particular
97
-------
i i i r
\
10 11 12 13 14 15 16 17 18
19
Figure 4. Isopleth of computed average S02 concentration (|ug/m3) period December 1, 1964, through February 28,
1965. For this calculation, a power-law wind profile was introduced and S09 decay rate was assumed to
be zero.
98
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300
INTERCEPT =20.26
SLOPE = 0.32
— CORRELATION COEFFICIENT =0.7719
o>
200
vD
vO
o
UJ
100
1
100
200 300
CALCULATED CONCENTRATION, pg/m
400
3
500
600
Figure 5. Regression line of observed versus calculated average S02 concentration ((jg/m3) for period December 1,
1964, through February 28, 1965. For this calculation, a power-law wind profile was introduced and SO2
decay rate was assumed to be zero.
-------
o
o
1
7
10
11 12 13 14 15 16 '17 18
19
Figure 6. Isopleths of computed average S02 concentration (ug/m3) for period December 1, 1964, through February 28,
1965. For this calculation, wind speed was assumed constant with height and S02 half-life was assumed
to be 30 minutes.
-------
300
E
o>
| 200
i
s
g 100
I
INTERCEPT =52.05
SLOPE =0.39
— CORRELATION COEFFICIENT = 0.7864
1
100 200
CALCULATED CONCENTRATION, /jg/m
300
3
400
Figure 7. Regression line of observed versus calculated average S02 concentra-
tion (ug/m3) for the period December 1, 1964, through February 28,
1965. 'For this calculation, wind speed was assumed constant with
height and SC>2 half-life was assumed to be 30 minutes.
101
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applications. Under these circumstances, the numerical properties, i.e.,
the relationship between model output and its numerous inputs, are only
poorly understood. To improve understanding, the model is currently being
subjected to an input-output sensitivity analysis.
The urgent practical need to apply the Martin-Tikvart model immediately
and prior to further development and analysis has given rise, as an interim
measure, to the concept of "calibrating" the model with observed air quality
data (TRW Systems Group, 1969). As in the particular examples considered
above for St. Louis, this involves determination of the least-squares
regression line of observed concentration values on the values calculated
by use of the model. If the scatter of points about the regression line is
small enough for thelatter to be regarded as a statistically significant
description of the relationship between the observed and calculated values,
then, in other applications of the model to the same urban area and over the
same climatological period, e.g., to estimate air quality with a different
hypothetical source inventory, the model output would be adjusted at each
receptor location according to the regression line equation. To determine
whether the regression line is adequate, the coefficient of correlation, a
measure of the data scatter about the regression line, is calculated and
interpreted by standard statistical procedure.
Finally, some more obvious sources of error and shortcomings of the
model should be noted. In the absence of a sensitivity analysis of the type
mentioned, any attempt to provide a complete listing could amount to self-
deception, and we therefore mention only the following:
(a) It is evident that emissions inventory estimates are inherently
crude and subject to uncertainties. One shortcoming of the model in
its present form is that it uses a constant average emissions inventory
although significant variations must occur throughout the day, day-to-
day and seasonally. The fact that the assumption of a diurnally constant
emission rate may lead to overcalculation of concentrations has been
previously noted by Clarke (1964) and Turner (1964), who indicated the
need for a lower emission rate at night. That this is a source of
102
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over-calculation in the Martin-Tikvart model was demonstrated by some
ad hoc calculations, although difficulty of developing a generally
applicable objective scheme for specifying diurnal variability of
emissions is apparent.
(b) The climatological data used in the model calculations must,
in practice, frequently be obtained from a nearby airport weather
stations and is a poor indication of urban meteorological conditions.
Particular caution should be exercised in applying the model to any
locales where the topography is at all complicated.
(c) The method proposed for estimating the mixing depth for use in
the model calculations is very crude. Better modeling should result
when data based on actual atmospheric soundings can be utilized. It
is particularly desirable to refine the estimates of nighttime
mixing depth as it may be shown, when the concentration calculations
are separated by stability category, that the contribution from the
nighttime stability category PC (when a 100 meter mixing depth is
assumed) is frequently much greater than from all other stabilities
even though PS only represents about 25% of the total observations.
103
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REFERENCES
Bierly, E. W., and Hewson, E.W., 1962: Some restrictive meteorological
conditions to be considered in the design of stacks. J. Appl.
Meteorol., 1_, 3, 383-390.
Briggs, G. A., 1969: Plume Rise. A.E. C. Critical Review Series, U.S.
Atomic Energy Commission, Division of Technical Information
Calder, K. L., 1969: Some miscellaneous aspects of current urban pollution
models. Symposium on multiple source urban diffusion models,
Univ. of North Carolina, Chapel Hill (To be published)
Clarke, J.F., 1964: A simple diffusion model for calculating point con-
centrations from multiple sources. APCA Jdurnal, 14, 9, 347-352.
Clarke, O.F., 1969: Nocturnal urban boundary layer over Cincinnati, Ohio
Monthly Heather Review, 97_, 8, 582-589.
DeMarrais, G. A., 1959: Wind speed profiles at Brookhaven National Laboratory
0. Appl. Meteorol.. 16^, 181-189.
Farmer, J.R., and Williams, J.D., 1966: Interstate Air Pollution Study, Phase
II Project Report, III Air Quality Measurements, USDHEW, NAPCA,
Cincinnati, Ohio.
Fortak, H., 1969: Numerical simulation of the temporal and spatial distri-
butions of urban air pollution concentrations. Symposium on
multiple source urban diffusion models. Univ. of North Carolina,
Chapel Hill (To be published).
Gifford, F. A., 1961: Use of routine meteorological observations for
estimating atmospheric dispersion. Nuclear Safety, 2, 4, 47-51.
Holland, J. Z., 1953: A meteorological survey of the Oak Ridge area. U.S.
AEC Report PRO. 99, Tech.Inf. Serv., Oak Ridge, Tennessee.
Holzworth, G. C., 1967: Mixing depths, wind speeds, and air pollution
potential for selected locations in the United States. J. Appl.
Meteorol.. 6, 6, 1039-1044.
Leavitt, J. A., 1960: Meteorological considerations in air quality planning.
J. Air Poll. Contr. Assoc.. lp_, 3, 246-250.
Ozolins, G., and Smith, R., 1966: A^Rapid Survey Technique for Estimating
Community Air Pollution Emissions.U.S. Dept. of Health, Education,
and Welfare, Public Health Service, National Air Pollution Control
Administration, Raleigh, North Carolina, PHS Pub. No. 999-AP-29.
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Pasquill, F., and Meade, P.O., 1958: A study of the average distribution of
pollution around Staythorpe. Int. J. Air Poll., 1, 60-70.
Pasquill, F., 1961: The estimation of the dispersion of windborne material
Meteorol. Mag.. 90, 1063, 33-49.
Pasquill, F., 1962: Atmospheric Diffusion. Van Nostrand Co., New York.
Pooler, F., 1966: A tracer study of dispersion over a city. J. Air Poll.
Contr. Assoc., 16, ~\2, 677-681.
Szepsi, D.J., 1967: A model for the long-term distribution of pollutants
around a single source. IDOJARAS (Budapest), 68, 257-69.
Szepsi, D.J., 1967: Meteorological Conditions of the Turbulent Diffusion
Of Atmospheric Pollutants in Hungary!Official Publications of
the National Meteorological Institute, Vol. 32, Budapest.
TRW Systems Group, 1969: Air Quality Display Model. Contract No. PH 22-68-60
USDHEW, Public Health Service, National Air Pollution Control
Administration, Washington, D.C.
Turner, D.B., 1961: Relationship between 24-hr, mean air quality measurements
and meteorological factors in Nashville, Tennessee. J. Air Poll.
Contr. Assoc., ]_]_, 483-489.
Turner, D.B., 1964: A diffusion model for an urban area. J. Appl. Meteorol.,
3^ 83-91.
Turner, D.B., nnd Edaristen, N.G., 1968: St. Louis S02 dispersion model
study - Description of basic data (Unpublished report, Division
of Meteorology, NAPCA).
Turner, D.B., 1969: Workbook of Atmospheric Dispersion Estimates. USDHEW
PHS, National Air Pollution Control Administration, Cincinnati, Ohio,
PHS Pub. No. 999-AP-26.
Weber, E., 1970: Contribution to the residence time of sulfur dioxide in
a polluted atmosphere. J. Geophys. Res., 75, 15, 2909-2914.
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APPENDIX E:
AN EVALUATION OF SOME
CLIMATOLOGICAL DISPERSION MODELS
by
D.B. Turner, J.R. Zimmerman, and A.D. Busse
On assignment from
National Oceanic and Atmospheric Administration
U.S. Department of Commerce
Division of Meteorology
National Environmental Research Center
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
Paper presented at
Third Meeting of the NATO/CCMS Panel on Modeling
107
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AN EVALUATION OF SOME CLIMATOLOGICAL DISPERSION MODELS
by
D. Bruce Turner*, John R. Zimmerman*, and Adrian D. Busse*
ABSTRACT
Six different dispersion models were used in a climatological
mode of application with point source and area emission data to
calculate annual (1969) sulfur dioxide and total suspended particulate
matter for the New York Air Quality Control Region. Two of the models,
the Air Quality Display Model and the Climatological Dispersion Model,
use joint frequency distributions of wind direction, wind speed, and
stability class as meteorological data. The Climatological Dispersion
Model (single stability) requires only a wind direction frequency and
i
harmonic mean speed for each direction. The other three models: Gifford
'72, Modified Hanna, and Modified Hanna Including Source Height; require
only mean annual wind speeds for climatological application.
Simple models are as highly correlated with measurements as are
the more complex models, explaining 70% of the sulfur dioxide variance
and 40% of the particulate variance. For S02» root mean square errors
for the best complex model are 52; those for the simple models are 56
to 59. The standard deviation of the measurements is 72. For particulates,
root mean square errors for the complex model are 16; those for the
simple models are 19 to 40. The standard deviation of the measurements
is 23.
It is difficult to achieve results surpassing those of the simple
models. Of the two more complex models, the AQDM and the COM, the COM
yields smaller errors with means and maxima nearer those of the measurements.
Evaluation of models should include comparison of results with those
from simple models applied to the same data.
*0n Assignment from the National Oceanic and Atmospheric Administration,
Department of Commerce
108
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INTRODUCTION
Six different dispersion models were used to calculate annual
(1969) sulfur dioxide and total suspended particulate matter for the
New York Air Quality Control Region. Two of the models, the Air Quality
Display Model and the Climatological Dispersion Model, use joint frequency
distributions of wind direction, wind speed, and stability, as
meteorological data. The Climatological Dispersion Model applied for
a single stability requires only a wind direction frequency and harmonic
mean speed for each direction. The other three models based upon ideas
of Gifford and Hanna (1971, 1972) require only mean annual wind speeds
for Climatological application. These are referred to as: Gifford '72,
Modified Hanna, and Modified Hanna Including Source Height.
The emission inventory, measured air quality data, meteorological
data, and Climatological estimates of pollution concentration using the
Air Quality Display Model were obtained from EPA's Air Quality Manage-
ment Branch. Emission estimates for 1969 for both pollutants for 854
2 2
area sources varying in size from 1 km to mo km , and for 674 point
sources were included. Estimates of stack height, stack diameter,
stack gas exit velocity, and stack gas temperature were also included
for the point sources. A stability wind rose (joint frequency distribution
of wind direction, wind speed, and stability class) was available for
La Guardia Airport based on the 3-hourly observations during 1969. These
observations are routinely available in computer compatible form (punch
cards or magnetic tape).
109
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Each of the models was used to calculate mean annual concentrations
of sulfur dioxide at 75 locations and total suspended particulate matter
at 113 locations. These estimates were compared with mean annual
concentrations based upon measurements.
DESCRIPTION OF MODELS
1. Air Quality Display Model (AQDM)
The AQDM, a climatological model based on ideas of Martin and Tikvart
(TRW Systems Group, 1969; Martin and Tikvart, 1968; and Martin, 1971),
considers the joint frequency distribution of wind direction to 16
points, wind speed in 6 classes, and stability categories in 5 classes.
Computations for a receptor point are made by considering the contribution
of each point and area source to this receptor. Separate calculations
are made for each speed class - stability class combination for the
wind direction sector about the receptor that contains the source.
For area sources a modification of the virtual point source method is
used. Estimation of area source heights are assumed to be effective
height of the area source. The effective height can be different for
each area source. Holland's plume rise equation (Holland, 1953) is
used to estimate the effective height of point sources. A feature
of the AQDM is that a source contribution file consisting of the
partial concentration of each receptor due to each point and area
source is retained at the end of the computation. This is primarily
used as input to control strategy studies.
no
-------
2. Climatological Dispersion Model (COM)
The COM described in detail by K. L. Calder (1971) has been applied
to air quality estimates for Ankara, Turkey, and St. Louis (Zimmerman,
1971, 1972) for the Committee on Challenges of Modern Society. Although
similar in many respects to the AQDM, the COM contains several distinct
features. In the COM, area sources are calculated using the narrow
plume hypothesis (Gifford and Hanna, 1971) applied for winds within a
sector (Calder, 1971) which involves an upwind integration over the
area sources. Emission rates at various upwind distances, using an
expanding scale, are averaged over an arc within the sector. A power
law for the vertical wind profile which is a function of stability is
used to extrapolate surface winds to the source height. Estimation
of effective height of point sources is by Briggs plume rise (Briggs,
1969). The total concentration at each receptor is the sum of 32
concentrations. These concentrations are those from point and from
area sources for each of the 16 wind directions. These values are
retained and are useful in plotting direction contribution pollution
roses. The running time of the COM is about 73% of that required by
the AQDM.
3. Climatological Dispersion Model (Single Stability)
Whereas both the AQDM and the COM are applied for 5 different
stabilities and 6 wind speed classes within each stability class,
th_is model performs the calculations for a single stability and further
ill
-------
reduces the computations by using a single wind speed for each of
the 16 wind direction sectors. The single wind speed is a harmonic
mean of the average speed for each wind speed class weighted for its
frequency. The running time of this single stability version of the
COM is about 30% of that required by the COM.
4. Gifford '72
Drs. Frank Gifford and Steve Hanna of NOAA's Atmospheric Turbulence
and Diffusion Laboratory in Oak Ridge, Tennessee, have been active
in developing simple dispersion models for estimating concentrations
(Gifford and Hanna, 1971; Hanna, 1971). In a recent manuscript
(Gifford and Hanna, 1972), they have suggested use of
_3
where x/\ is the concentration in pgm of the pollutant of interest
due to all area sources for a particular averaging time, C is a
- _ -? -l
dimensionless constant, q is an average area emission rate in ygm sec
in the vicinity of the receptor, and u is the mean wind speed in m sec" .
Both q and u are for the same averaging time as the concentration, x^
They suggest that the values of C are 50 for sulfur dioxide and 225
for particulate matter. Concentrations at this receptor from point
sources for the same averaging time should be added to the concentrations
112
-------
from area sources. These can be determined from an appropriate point
source model. Without firm direction from the manuscript of Gifford
and Hanna as to what area about the receptor should be used to obtain
average area emissions, the authors selected an area after an investi-
gation which will be described later.
5. and 6. Modified Hanna
Since emissions close to a receptor at about the same height as
the receptor have a greater influence than emissions at greater distances,
it was felt that an improvement to the above Gifford '72 model could
be made which would eliminate the use of the rather arbitrary constant
C, and would also eliminate the difficulty of not knowing just which
area should be considered in determination of the average area emission
rate. The model can be expressed as:
XA
where i is an index referring to a range of distances from the receptor,
q. is the average area emission rate for this range of distance about
the receptor, u is mean wind speed as before, b is background concentration
of the pollutant considered beyond the last distance considered in the
summation, and the coefficient, k, is determined from:
113
-------
dx (3)
exp
2
where x, and x are the lower and upper limits of distance of the i
range, a is a dispersion parameter dependent upon distance and
representative of mean stability conditions for the period of interest,
H is a single effective height of emission for the pollutant considered
for area sources in the region under consideration. In general, the
value of b will be the concentration of the particular pollutant at
the boundaries of the region considered, i.e., the boundary of the
.emission inventory. Note that the k's are dependent only upon the
mean meteorological conditions and the height of emission and, therefore
will be constant for a given distance range, and independent of receptor
location. On the other hand, the q. 's are determined for different
distance ranges about each receptor and, therefore, are dependent
upon receptor loration.
Model 5, referred to as the Modified Hanna, is applied with H=0.
This is the same in concept as that of Steve Hanna (1971). The only
difference is that in this model sources are considered for ranges of
distance without regard to direction variations. For this model the
values of k can be determined analytically.
114
-------
Model 6, referred to as the Modified Hanna Including Source Height,
uses a mean value of effective height of emission for each pollutant.
For this case the values of k are determined by numerical integration.
\
Both Models 5 and 6 can be considered as further simplifications
to the COM and COM (single stability) models since another liberty
has been taken, that of calculating emissions for various distance
ranges instead of in each wind direction sector.
APPLICATION OF THE MODELS TO THE NEW YORK REGION
With each of the models, calculations of ground level concentrations
of both sulfur dioxide and total suspended particulate matter were made.
Measurements of sulfur dioxide were available at 75 locations and of
particulate matter at 113 locations.
As indicated, the AQDM was applied to the data for this area by
the Air Quality Management Branch. A background of 35 ygm" was added
to each calculated value of particulate concentration before comparing
with measurements. A background of 35 was also added to each calculated
value of particulate matter by the COM before comparing with the
measurements. \
For applying the COM for a single stability, Table 1 lists the
frequencies and the harmonic mean wind speeds for each direction. The
model was applied for three different single stabilities. The values
used for the a parameter most closely approximate those corresponding
115
-------
TABLE 1
Frequencies and Harmonic Mean Wind Speeds for Each Direction
SECTOR
NNE
NE
ENE
E
ESE
SE
SSE
S
SSW
SW
WSW
VI
WNW
NW
NNW
N
f(e)
0.088
0.054
0.076
0.084
0.036
0.010
0.014
0.025
0.117
0.044
0.062
0.075
0.071
0.086
0.082
0.075
u (9)
(m sec"! )
3.65
2.98
3.27
3.53
2.82
2.04
2.78
3.54
4.00
2.93
3.27
3.72
4.73
4.43
3.90
4.12
TABLE 2
Dispersion Parameter Coefficients and Exponents
Range of x
(meters)
<500
500-5000
>5000
0
z = a x'
C Stability
a b
0.
0.
0.
1120
1014
1154
0.
0.
0.
9100
9260
9109
)
C/D Stabil
a
0.
0.
0.
1078
1725
3546
0.
0.
0.
ity
b
87645
80072
71611
D Stability
a b
0.
0.
0.
0856
2591
7368
0.8650
0.6869
0.5642
116
-------
to Pasqulll's C, D, and something between C and D (Pasqulll, 1962;
Turner, 1967) so the notation: C, D, C/D is used to designate these.
The coefficients and exponents for various downwind distances from
the source, x, for these three stabilities used to determine a from:
az = axb (4)
are given in Table 2.
For application of the Gifford '72 model, the mean wind speed for
La Guardia Airport for the year 1969 as given by the Local Climatological
Data (Environmental Science Service Administration, 1969) of 11.6 miles
per hour (5.1852 m sec" ) was used. As indicated, Gifford (1972) is
not clear as to the size of the area that should be considered for
averaging area emission rates. Therefore, three distances were
selected: 3, 5, and 10 km. Using the emission rates for the area
sources on the 1 km basis previously prepared as part of the COM run,
a computer calculation was made to determine average emissions for
both SOp and particulate within circles centered on each receptor for
radii corresponding to the three above-mentioned distances. If the
center of a 1 km source square was within the circle, it was included
in the averaging; if the center was outside, it was not included.
After determining the average emission rate for the three different
radius circles, the linear correlation coefficient of measurements of
concentration as a function of average emission rate was determined
117
-------
for both pollutants. This appears on the left side of Table 3. From
these results, the average emission rates for circles with a radius of
10 km were selected for use in applying the Gifford '72 model. At a
later time the average emissions for larger circles and the corresponding
correlation coefficients were determined. These appear in the right
hand portion of Table 3.
Since Gifford indicates that the values of the factor C of 50 for
sulfur dioxide and 225 for particulate matter were determined without
consideration of any background values, no background was added to the
estimates from this model before comparing with measurements. Comparisons
of this model were made with measurements for both: estimates from
area sources only, and estimates from the area sources using this model
with estimates of concentration due to point sources as determined
from the COM model added to the area estimates. (After noting the
results achieved with this model, a background of 35 was added for
particulate matter estimates for an additional comparison.)
In applying the Modified Hanna Model to this region, six ranges
of distances were used as shown in Table 4. From intermediate results
punched on cards during the determination of the average emission rates
for various sized circles, it was simple to determine the average
emission rates for the 5 annular areas. For application of the Modified
Hanna Including Source Height (Model 6), the average emission heights
118
-------
TABLE 3
Linear Correlation Coefficients of Measured Air Quality Data
with Average Emission Rate of Circles of
Given Radius about Each Receptor
Pollutant
Sulfur dioxide
Particulate matter
Number of
Receptors
75
113
Radius of
0.
0.
3
73
61
0.
0.
5
79
64
Emission Area (km)
1
0.
0.
r>
81
63
20
0.
0.
85
63
30
0.78
0.63
40,
0.70
0.60
TABLE 4
Limits of Integration and Corresponding
Values of k from Equation (3)
km
1 0
2 3
3 5
4 10
5 20
6 30
km
3
5
10
20
30
40
Model 5
H = 0
163.468
12.264
19.344
23.551
16.085
12.589
H = 10
Particulate
50.331
12.133
19.183
23.053
15.580
12.120
Model 6
H = 30
S02
30.715
11.844
18.993
22.97:
15.555
12.110
119
-------
of 30 meters for sulfur dioxi'de and 10 meters for particulate matter
were chosen as representative of effective heights of emission for
the New York region. (One could apply this model using different
effective heights of emission for various receptor locations, but
only one height for each pollutant was used here.) Using values of
the dispersion parameter, a , corresponding to C/D stability the
k.'§ were determined by integrating analytically over appropriate
distance ranges for use in Model 5 and using the a 's for C/D stability
and the above ems si on heights, numerical integrations were performed
to determine the values of the factors, k. for use with Model 6.
These are also shown in Table 4. Values of background concentration,
b, of 0 and 35 were used for sulfur dioxide and particulate matter
respectively in equation (2).
STATISTICS USED FOR EVALUATION
To evaluate the various models, 12 different statistics were used.
One of these was the mean concentration for all stations. Considering
the error for each location to be defined as the calculated concentration
from the model minus the measured concentration, the root mean square
error and the mean absolute error were determined. As an indication
of the range of errors at the individual measurement locations, the
largest negative error (underestimate), the largest positive error
(overestimate), and the range of errors (the largest positive error
120
-------
minus the largest negative error) were tabulated. Linear correlation
coefficients, the variance of the correlation (the square of the
correlation coefficient) and the slope and intercept of the least
squares line of regression between model estimates and the measured
values were also calculated.
Because of its importance to the meeting of air quality standards,
the error at the location with the highest measured concentration is
of interest as well as the maximum estimated concentration at any of
the measuring station locations.
RESULTS
The results of the comparison of model estimates with measurements
are given in Table 5 for sulfur dioxide and in Table 6 for particulates.
In addition to comparing the calculated AQDM estimates with measurements,
the Air Quality Management Branch had used the measured air quality
data to calibrate the AQDM. Considering the calculations without
background as the independent variable, the measurements as the dependent
variable, least square lines that are forced to have an intercept of 0
for sulfur dioxide and 35 for particulate matter were determined. The
slope and intercepts for these lines are given in Table 7. Using the
equations of these lines, "calibrated" concentration estimates were
determined from the calculated concentrations. This was done similarly
for all other models. The comparisons of these estimates with the
121
-------
TABLE 5. NEW YORK - SULFUR DIOXIDE
MAX HEAS * 350
MEAN NUM RMSE MEAN LARGEST LARGEST ERROR LINEAR VAKI- INTER- ERROR AT MAXIMUM
(MEAS BERISTD ABSOLUTE NEGATIVE POSITIVE RANGE CORREL. ANCE SLOPE CEPT POINT OF ESTIMATED
1 AIR QUALITY DISPLAY MODEL IAODH)
2 CLIMATOLOGICAL DISPERSION MODEL (COM) 138
3 COM (SINGLE STABILITY!
3A COM (D STABILITY)
3B COM (C STABILITY)
3C COM (C/0 STABILITY)
4 f.IFFORO «7?
4A AREA ONLY
WITH COM POINT ESTIMATES
5 MODIFIED HANNA
SA AREA ONLY
SB WITH COM POINT ESTIMATES
6 MODIFIED HANNA INCL. SOURCE HEIGHT
6A AREA ONLY
*a WITH COM POINT ESTIMATES
«135>
211
(116) (
138
(1151 (
206
(112) (
94
(101) (
139
(107) (
54
( 91) (
79
(107) (
279
( 77) (
305
( 81) (
102
( 96) (
(105) (
75
75)
75
75)
75
75)
75
75)
75
75)
75
75)
75
75)
75
75)
75
75)
75
75)
75
75)
OEV
OF
MEAS
121
( 37)
52
( 44)
1?4
( 45)
56
( 55)
64
( 49)
82
( 63)
59
( 48)
330
( 77)
348
( 73)
58
( 57)
56
( 48)
ERROR
92
( 28)
37
I 32)
69
( 33)
46
( 45)
45
( 39)
72
( 54)
50
( 38)
178
< 65)
193
( 61)
45
( 46)
38
( 37)
ERROR
-87
(-117)
-118
(-143)
-112
(-153)
-128
(-'22)
-115
(-125)
-175
(-151)
-137
(-118)
-145
(-152)
-120
(-145)
-151
(-151)
-126
(-131)
ERROR
310
( 74)
166
(121)
332
(114)
96
(118)
188
(109)
29
(125)
49
(115)
1232
(188)
1270
(189)
190
(170)
225
(157)
397
(191)
284
(264)
444 .
(267)
224
(240)
303
(234)
204
(276)
186
(233)
1377
(340)
1390
(334)
341
(321)
351
(288)
WITH
MEAS.
0.89
(0.89)
0.84
(0.84)
0.84
(0.84)
0.82
(0.82)
0.84
10.84)
0.81
(0.81)
0.85
(0.85)
0.77
(0.77)
0.78
(0.78)
0.84
(0.84)
0.86
(0.86)
0.79 0
(0.79) (0
0.70 0
(0.70) (0
0.71 0
(0.71) (0
0.67 0
(0.67) (0
0.70 P
(0.71) (0
0.66 1
(0.66) (0
0.72 0
(0.72) (0
0.60 0
(0.60) (0
0.62 0
(0.62) (0
0.71 0
(0.71) (0
.45 31
.82) (31)
.66 35
.79) (35)
.41 40
.76) (40)
.73 56
.68) (56)
.55 49
.72) (48)
.07 67
.63) (67)
.97 48
.72X48)
.16 80
.58) (80)
.16 76
.60) (76)
.62 62
.66) (62)
0.74 0.59 SO
(0.74X0.71) (SO)
MAXIMUM
MEAS.
112
( -97)
-101
(-143)
13
(-153)
-119
(-101)
-56
(-125)
-175
1 -54)
-137
( -64)
1153
( 63)
1191
( 62)
49
( 26)
87
( 11)
CONC. AT
A MEAS.
POINT
566
( 310)
368
( 307)
577
( 313)
307
( 329)
423
( 3241
180
( 304)
219
( 294)
1503
( 413)
1541
( 412)
399
( 376)
437
( 361)
-------
TABLE 6. NEW YORK - PARTICULATE MATTER
MAX HEAS = 169
MEAN NUM RMSE
(MEAS 8ERISTO
* 82) OEV
OF
MFAS
= 23)
I AIR QUALITY DISPLAY MODEL (AOOM)
2 CLlMATOLOGICAL DISPERSION MODEL (COM)
3 COM (SINGLE STABILITY)
3A COM (D STABILITY)
38 COM
2H
22)
31
28)
75
25)
53
30)
331
47
27)
361
41
31)
45
28)
31
78)
25
24)
MEAN
ABSOLUTE
C.RROR
28
( 15)
16
( 15)
21
( 17)
26
( 21)
19
( 19)
47
( 24)
1 271
40
( 21)
1 281
30
( 2S>
32
( 22)
26
( 22)
19
( 18)
LARGEST
NEGATIVE
EKROH
-51
( -60)
-63
( -62)
-hO
( -67)
-78
I -74)
-73
( -72)
-117
I -H3)
1 -821
-111
( -79)
1 -761
-77
I -81)
-71
1 -78)
-BO
( -77)
-71
( -69)
LARGEST
POSITIVE
ERROR
115
( 54)
68
( 74)
98
( 65)
59
(104)
75
( 82)
46
( 42)
1 811
59
( 38)
1 941
177
I 80)
190
« 74)
25
( 68)
37
( 55)
ERROR
RANGE
166
(114)
131
(136)
158
(132)
137
(173)
148
(154)
163
(125)
11631
170
(117)
11701
254
(161)
261
(152)
105
(145)
108
(124)
LINEAR VARI- INTER-
COHPEL. ANCE SLOPE CEPT
WITH
MEAS.
0.62
(0.63)
0.61
(0.61)
0.64
(0.64)
0.57
(0.57)
0.61
(0.61)
0.63
(0.63)
10.631
0.63
(0.63)
10.631
0.64
(0.64)
0.64
(0.64)
0.66
(0.66)
0.62
(0.62)
0.39 0
(0.39) (0
0.37 0
(0.37) (0
0.41 0
(0.40) (0
0.32 0
(0.32) (0
0.37 0
(0.37) (0
0.40 0
(0.40) (0
10.401 10
0.40 0
10.40) (0
10.401 10
0.40 0
(0.40) (0
0.40 0
(0.40) (0
0.43 0
(0.43) (0
0.39 0
(0.39) (0
.38 43
.62) (34)
.63 35
.59) (37)
.42 45
.57) (40)
.69 42
.16) (50)
.54 45
.50) (46)
.35 68
.47) (51)
.351 1561
.32 65
.49) (48)
.3211541
.28 59
.47) (53)
.27 57
.48) (50)
.72 41
.49X49)
.63 39
.54) (42)
ERROR AT
POINT OF
MAXIMUM
MEAS.
5
( -48)
-48
( -43)
-6
( -39)
-71
( -404
-43
( -37)
-56
( -50)
1 -211
-44
< -5?)
1 -91
61
( -16)
73
< -20)
-58
( -23)
-53
( -39)
MAXIMUM
ESTIMATED
CONC. AT
A MEAS.
POINT
199
( 136)
135
( 141)
165
( 132)
126
( 171)
142
( 149)
151
( 147)
1 1861
164
( 143)
1 1991
281
( 184)
294
( 178)
129
( 172)
141
< 159)
-------
TABLE 7
Equations of Least Squares Lines (y=a+bx)
Used to Determine Calibrated Concentrations
Model
1.
2.
3a.
3b.
3c.
4.
5.
6.
AQDM
COM
COM (D
COM (C
Stabi
li
Stabi li
COM (C/D Stabi
Gifford
A. Area
B. With
Modified
A. Area
B. With
Modified
A. Area
B. With
'72
only
COM
Sulfur
Dioxide
b a
0.
0.
ty) 0.
ty)
1.
lity) 0.
1.
point estimates
Hanna
only
COM
point estimates
Hanna
only
COM
1.
0.
0.
Including Source Height
point estimates
0.
0.
5478
8330
5429
0790
7653
6909
3435
2746
2676
9435
8265
0
0
0
0
Parti cul ate
Matter
b a
0
1
0
1
0 1
i
0
0
0
0
0
0
0
0
0
0
1
1
.6162
.0630
.7452
.4956
.0637
.7430
.6557
.6063
.5512
.4594
.1717
35
35
35
35
35
35
35
35
35
35
35
124
-------
measured concentrations are reported in Tables 5 and 6 in parentheses
with each model. Note that the "calibrated" estimates are compared
with the same measurements used for determining the calibration equations,
not with independent data. Although the development of the coefficients
for the Gifford '72 should not require the addition of a background
f"
concentration, the estimated values from this model were also tested
_3
after adding a background of 35 ygm to the particulate values. These
results are reported in brackets in Table 6.
Models 1 and 2 (both AQDM and COM) each require joint frequency
distributions of wind direction, wind speed, and stability. For the
COM (single stability) only the frequency and mean speed for each
direction (Table 1) are required. For the last three models only the
mean annual wind speed is used although the effects of the point sources,
that are added in, have used the joint frequency distribution information.
Considering first the results for sulfur dioxide, for the mean
concentration for the 75 locations, Model 2 with 138, Model 3c with
139, and Model 6 b. with 127 are all close to the mean of measurements
_3
of 135 ygm . Note that calibration causes all models to underestimate
the mean. For the root mean square error, Model 2 with 52, Models 3b
and 6b with 56 are examples. Six of the 11 models have a RMSE
_3
less than the standard deviation of the measured values, 72
125
-------
As expected, calibration reduces the root mean square error but in
some cases only slightly. The smallest mean absolute errors are from
Model 2 with 37 and Model 6 b with 38. Calibration reduces the mean
absolute error. The range of errors is lowest, 186 (-131 to 49), for
Model 4 b. Note that all correlations are quite close, ranging from
0.77 to 0.89. The error at the point of the maximum measurement varies
from an underestimate of 175 ygnf to an overestimate of 112 ygnf ,
ignoring the huge overestimates of Model 5. Model 3 a. with an over-
_3
estimate of 13 ygm. has -the least error. Calibration causes Model 6
_3
b's overestimate of 11 ygm to be smallest. The maximum estimated
-3 -3
concentration at a measurement point ranges from 180 ygm to 577 pgm
(again ignoring Model 5) with Model 2's estimate of 368 closest to the
_3
measured maximum of 350 ygm . Calibration improves some estimates
of the max, notably Model 6 b. with 361.
In the results for the particulate matter (Table 6) for the mean
concentration, the 80 ygnf from Model 5 a is closest to the mean of
all measurements of 82. Models 3a, 2, and 5b also are close. Calibration
improves the means from most of the models. For the root mean square
error, only Model 2 with 21 is less than the standard deviation of
_3
measures ^articulate values of 23 ygm . With calibration, Models 1,
2, and 3a have RSME less than 23. For the mean absolute error, Model
2 with 16 ygm" is the smallest. With regard to the largest errors,
126
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the models are not greatly different if Model 5 is excluded. Model
2 has the smallest error range, 131. Generally calibration doesn't
have too much effect on the range of errors. The correlations are
not greatly different for the various models ranging from 0.57 to
0.66 although they are poorer than those for S0?. The variance is
about half those for SO^: 0.32 to 0.43 for particulate, 0.60 to 0.79
for SOp. This may be due, in part, to the difficulty in obtaining a
reliable emission inventory for particulate matter and in obtaining
representative measurements. The error at the point of maximum
-3
concentration is a slight overestimate of 5 ygm for Model 1 and a
_3
slight underestimate of 6 pgm for Model 3a. For the maximum
concentration at any measurement point, Model 3a with 165 and Model
4b. with 164 are near the maximum measured at any sampling station
of 169. Generally, calibration does not greatly improve the estimate
of the maximum. An exception is Model 3b. whose calibrated maximum
is 171.
CONCLUSIONS
There is no one model that is superior in all statistics. The
AQDM (Model 1) overestimates concentrations. Although we feel that
the use of the Holland plume rise equation contributes to this over-
estimation, it is not the only cause. Many measurements of air quality
are needed in order to calibrate the AQDM. This results in a low
127
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error but also, in this case, results in underestimated concentrations
for both the mean and the maximum.
The COM (Model 2) gives a good estimate of the mean and maximum
for SOp in this test, but somewhat underestimates the particulate
concentrations, particularly the maximum. It should be noted that
this is without a calibration, therefore no extensive measurement
network was required to obtain the result.
The COM (single stability) with the dispersion parameters given'
by the C - D stability class (model 3c) gives a better estimate of
the mean of all stations than of the other statistics. The errors
are somewhat larger than the full model. Like the COM Model, the
COM (C/D stability) overestimates the SCL maximum concentration but
underestimates the particulate concentration.
The Gifford '72 Model underestimates both the mean concentrations
and also the maximum S0? but produces a good estimate of the particulate
maximum for this test region. Although the errors are somewhat larger
than with the other models, they are not greatly different considering
the degree of simplicity of this model over the preceding ones. The
_3
addition of a background of 35 ugm for the particulate estimates
improves the results of this model in most statistics with the exception
of the maximum concentration at any measurement point.
128
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The Modified Hanna Including Source Height seems to be an improvement
over the Gifford '72 Model with regard to means and errors but does not
perform as well on the maxima, overestimating SOp and underestimating
particulate. Note that there is a relatively close correspondence
between the COM (C/D stability) and Model 6b in nearly all statistics
and for both pollutants.
Simple models using only mean annual wind speeds and emissions do
quite well compared to the more complex models. The input and the
calculations are simple. They do have limitations when trying to
use the results to apply control strategies. For the simple models
at each receptor there are two concentration estimates available:
that due to point sources and that due to area sources. Of the
more complex models (1 and 2), these data indicate a preference for
the COM over the AQDM.
ACKNOWLEDGEMENTS
The authors are indebted to Herschel H. Slater, William M. Cox,
Russell F. Lee, and others of the Air Quality Management Branch for
the emission inventory and air quality data for the New York Region
and the results of the computations by the AQDM. They are also indebted
to Frank Gifford and Steve Hanna for their unpublished manuscript
indicating their recent studies of simple modeling, and to Lea Prince
and Dot Avent for their valuable assistance.
129
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REFERENCES
Briggs, G. A., 1969: Plume Rise. AEC Critical Review Series. Oak
Rdige, Tenn., USA, Atomic Energy Commission, Division of Technical
Information, 81 p. (Available from NTIS as TID-25075)
Calder, Kenneth L., 1970: Some miscellaneous aspects of current urban
pollution models. Proc. of Symposium on Multiple-Source Urban
Diffusion Models, 13 p. US Envir. Prot. Agency Air Pollution Control
Office Pub. No. AP-86.
Calder, Kenneth L., 1971: A climatological model for multiple source
urban air pollution. Proc. 2nd Meeting of the Expert Panel on
Air Pollution Modeling, NATO Committee on the Challenges of Modern
Society, Paris, France, July 1971, 33 p.
Environmental Science Services Administration, 1969: Local climatological
data, New York, N. Y., La Guardia Airport.
Gifford, F. A., Jr., and Hanna, Steven R., 1971: Urban air pollution
modeling. Proc. 2nd International Clean Air Congress. Edited by
H. M. Englund and W. T. Berry, Academic Press, New York and London,
1146-1151.
Gifford, F. A., Jr., and Hanna, S. R., 1972: Modeling urban air pollution.
Atmos. Environ, in press.
Hanna, Steven R., 1971: A simple method of calculating dispersion from
urban area sources. J. Air. Poll. Contr. Assoc., 21, 12, 774-777.
Holland, J. Z., 1953: A meteorological survey of the Oak Ridge area.
554-559, Atomic Energy Comm., Report ORO-99, Washington, D. C.,
584 p.
Martin, Delance 0., 1971: An urban diffusion model for estimating
long term average values of air quality. J. Air Poll. Contr.
Assoc., 21, 1, 16-19.
Martin, Delance 0., and Tikvart, Joseph A., 1968: A general atmospheric
diffusion model for estimating the effects of air quality of one
or more sources. APCA Paper 68-148, Presented at 61st annual APCA
meeting, St. Paul Minn., June 1968.
Pasquill, F., 1962: Atmospheric Diffusion. London, D. Van Norstrand,
297 p.
130
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TRW Systems Group, 1969: Air quality display model. Prepared for
Department of Health, Education, and Welfare, Public Health
Service, Consumer Protection and Environmental Health Service,
National Air Pollution Control Administration, Washington, D. C.,
Contract No. Ph-22-68-60. (Available from NTIS, Springfield, Va.,
22151 as PB-189-194)
Turner, D. B., 1967: Workbook on atmospheric dispersion estimates.
National Air Pollution Control Administration, Cincinnati, Ohio,
PHS Pub. No. 999-AP-26, 84 p.
Zimmerman, John R., 1971: Some preliminary results of modeling from
the air pollution study of Ankara, Turkey. Proc. 2nd Meeting of
the Expert Panel on Air Pollution Modeling, NATO Committee on the
Challenges of Modern Society, Paris, France, July 1971, 28 p.
Zimmerman, John R.,1972: The NATO/CCMS air pollution study of St.
Louis, Missouri. To be presented at 3rd Meeting of the Expert
Panel on Air Pollution Modeling, NATO Committee on the Challenges
of Modern Society, Paris, France, October 1972.
131
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BIBLIOGRAPHIC DATA
SHEET
1. Report No.
EPA-R4-73-024
3. Recipient's Accession No.
4. Title and Subtme
5* Report Date
December 1973
User's Guide for the Climatological Dispersion Model
6.
7. Author(s)
A.D. Busse and J.R. Zimmerman*
8. Performing Organization Kept.
No.
9. Performing Organization Name and Address
National Environmental Research Center
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
10. Project/Task/Work Unit No.
11. Contract/Grant No.
12. Sponsoring Organization Name and Address
13. Type of Report & Period
Covered
14.
IS. Supplementary Notes
*Both authors on assignment from National Oceanic and Atmospheric Administration,
U.S. Department of Commerce.
16. Abstracts
The Climatological Dispersion Model (CDM) -^determines long-term (seasonal or annual)
quasi-stable pollutant concentrations at any ground-level receptor using average emis-
sion rates from point and area sources and a joint frequency distribution of wind di-
rection, wind speed, and stability for the same period. This model differs from the
Air Quality Display Model (AQDM) primarily in the way in which concentrations are de-
termined from area sources, the use of Briggs' plume rise formula, and the use of an
assumed power law increase in wind speed with height that depends on the stability.
The material presented is directed toward the engineer familiar with computer tech->
niques and will enable him to perform calculations with the CDM. Technical details of
the computer programming are discussed; complete descriptions of input, output, and a
test case are .given. Flow diagrams and a source program listing are included.
Companion papers on the technical details of the model and on validation are included
as appendices. '
17. Key Words and Document Analysis. 17o. llcscriptors
Air pollution
Climatological Dispersion Model
Air Quality Display Model
Computer modeling
Computer programs
*Point sources
*Area sources
17b. Identifiers/Open-Ended Terms
*Air pollution
17e. COSATI Field/Group
18. Availability Statement
Release unlimited
19. Security Class (This
Report)
UNCLASSIFIED
20. Security Class (This
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21. No. of Pages
144 -
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FORM NTIS*39 (REV. 3'72)
USCOMM-OC 140S2-P72
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