015
/
PROPERTY OF
DIVISION
OF
METEOROLOGY
ADDENDUM
TO USER'S GUIDE
R CLIMATOLOGICAL
DISPERSION MODEL
NOT TO BE
HENTAL PROTECTION AGENCY
Air and Waste Management
Quality Planning and Standards
ngle Park, North Carolina 27711
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EPA-450/3-77-015
ADDENDUM
TO USER'S GUIDE
FOR CLIMATOLOGICAL
DISPERSION MODEL
by
Kenneth L. Brubaker, Polly Brown, and Richard R. Cirillo
Argonne National Laboratory
9700 South Cass Avenue
Argonne, Illinois 60439
Contract No. EPA-IAG-D6-F101
Program Element No. 2AC129
EPA Lead Project Officer: Joseph A. Tikvart
Office of Air Quality Planning and Standards
EPA Co-Project Officer: John S. Irwin
Environmental Sciences Research Laboratory
Prepared for
ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
May 1977
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This report is issued by the Environmental Protection Agency to report
technical data of interest to a limited number of readers. Copies are
available free of charge to Federal employees, current contractors and
grantees, and nonprofit organizations - in limited quantities - from the
Library Services Office (MD-35), Research Triangle Park, North Carolina
27711; or, for a fee, from the National Technical Information Service,
5285 Port Royal Road, Springfield, Virginia 22161.
This report was furnished to the Environmental Protection Agency by the
Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois
60439, in fulfillment of Contract No. EPA-IAG-D6-F101. The contents of
this report are reproduced herein as received from the Argonne National
Laboratory. The opinions, findings, and conclusions expressed are those
of the author and not necessarily those of the Environmental Protection
Agency. Mention of company or product names is not to be considered
as an endorsement by the Environmental Protection Agency.
Publication No. EPA-450/3-77-015
11
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iii.
Preface
The Climatological Dispersion Model (COM) has been widely used in
the development of air pollution control programs. However, users have
been hampered in some instances by the lack of several peripheral routines
and printouts. These include (1) a source contribution table, (2) inter-
nal calibration, and (3) statistical conversion of averaging times.
The addition of these routines and printouts is straightforward,
except for the area source contribution table. Due to the mathematical
treatment of area sources in COM, it is computationally difficult to
create such a table. However, based on work performed by John Irwin of
the Meteorology and Assessment Division (EPA), a satisfactory method was
recently developed. It then became desirable to implement at one time
all the peripheral routines and printouts noted above. These additions
to COM are documented in this report as an addendum to the COM user's
guide. This report, however, cannot stand alone; it only supplements
the original user's guide.*
The computer program which contains the peripheral routines and
printouts is designated CDMQC. This computer code provides pollutant
concentration estimates which are essentially the same as those given by
the original COM code. However, major revisions and additions to the
original code have been necessary so as to incorporate the new routines
and printouts.
CDMQC is one of the atmospheric dispersion models on the User's
Network for Applied Modeling of Air Pollution (UNAMAP) system. The
UNAMAP system may be purchased on magnetic tape from NTIS for use on
the user's computer system, or may be accessed through phone lines and
time-share computer terminals. For information on accessing UNAMAP
contact: Chief, Data Management Section, Meteorology and Assessment
Division, U.S. Environmental Protection Agency, Research Triangle Park,
NC 27711.
Although attempts are made to thoroughly check out computer pro-
grams with a wide variety of input data, errors are occasionally found.
In case there is a need to correct, revise or update this model, revi-
sions will be distributed to those who complete and return the mailing
*Busse, A. D. and J. R. Zimmerman. "User's Guide for the Climato-
logical Dispersion Model." Publication No. EPA-RA-73-024 (NTIS PB
227346/AS), Environmental Protection Agency, Research Triangle Park,
North Carolina 27711, December, 1973.
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IV.
form on page v. A user can be assured that the latest version of the
CDMQC Model is on the UNAMAP system.
Comments and suggestions regarding this publication should be
directed to: Chief, Environmental Applications Branch, Meteorology
and Assessment Division, U.S. Environmental Protection Agency, Research
Triangle Park, NC 27711.
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V.
Chief, Environmental Applications Branch
Meteorology and Assessment Division (MD-80)
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
I would like to receive future revisions to the kdde.nd.um
to tkn UACA'A Gtu.de. J$OA the. CtundtoiaQ-icjaJL Vi&peMA-ion Modet.
Name
Address •«
ZIP
Telephone (Optional)_
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vii.
TABLE OF CONTENTS
Section
Preface
Table of Contents vii
List of Figures ; ix
List of Tables ix
1. Introduction 1
2. Description of New Features 3
2.1 Calibration Procedure 3
2.2 Source Contribution List 8
2.3 Averaging Time Transformation Procedure 14
3. Description of Input 21
3.1 General Description 21
3.2 Detailed Card Input Sequence 22
4. Description of Output 31
4.1 Printed Output 31
4.2 Diagnostic Messages 33
4.3 Punched Output 35
References 38
Appendix A. Description of the Area Source Contribution
Algorithm 39
Appendix B. Statistical Information from the Calibration
Procedure 57
Appendix C. Test Example 63
C.I General Description 63
C.2 Detailed Input and Output Listing 63
Appendix D. General Flow Diagram 91
Appendix E. Computer Program Listings 95
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ix.
LIST OF FIGURES
Figure Page
2.1 Model Calibration by Linear Regression 4
2.2 The Lognormal Distribution 15
A.I Angular and Radial Skipover 44
A.2 Percent Error in Individual Emission Grid Square
Contributions 49
C.I TEST CITY Base Map 64
C.2 TEST CITY Input Data Set 65
C.3 TEST CITY Printed Output 67
C.4 TEST CITY Punched Output 90
D.I CDMQC Flow Diagram 92
E.I CDMQC FORTRAN Listing 96
•
LIST OF TABLES
Table Page
2.1 Model Calibration Options 6
2.2 Source Contribution List Options 11
2.3 Maximum Range of Area Source Integration as a Function of DELR . . 12
2.4 Ratio of (CPU Time for the Indicated No. of Arcs and
Value of DINT) to (CPU Time for 60 Arcs, DINT=4) 14
2.5 Larsen Transformation Options 18
3.1 Differences in Card Input Sequence Between CDM and CDMQC 23
3.2 Card Input to CDMQC 24
4.1 Format of Punched Output 36
A.I Number of Layers of Emission Grid Squares Before the Onset
of Skipover 45
A.2 Dependence of Effective Range and Example Percent of Total
Contribution on DELR Value 46
A.3 Comparison of Test City Area Source Contribution Results 55
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-1-
1. INTRODUCTION
This report describes the additions made to the computer
program of the Climatological Dispersion Model (COM) and provides the
necessary information to make use of these new features in the model.
The basic algorithms used to calculate pollutant concentrations have
not been modified, and results obtained using the previous version of
the program may be reproduced using the new version. The applicability
of COM has in no way been altered, although substantial additional informa-
tion may now be obtained from a single computer run.
Three new features have been added:
a calibration package which allows the user to calibrate the
model and obtain statistical information relating model
estimates to observations;
a capability for producing an individual source contribution
list at any desired location;
an averaging time transformation package based on the Larsen
procedure, which allows the user to obtain estimated maximum
short-term concentrations in addition to long-term values.
This report takes the form of an addendum to the COM User's Guide
(Busse and Zimmerman, 1973), and supplements that report. It is assumed
that a copy of the original User's Guide is available to the user. No
attempt has been made to include in this addendum any information in the
User's Guide which is not directly relevant to the changes which have been
made. The expanded computer program which includes the three new features
is referred to as CDMQC throughout this addendum.
Detailed descriptions of the algorithms, input and output options
and guidelines for use for each of the new features are given in Sec. 2.
The total input required by the program is described in Sec. 3 and the out-
put from the program in Sec. 4. The appendices contain a description of
the area source contribution algorithm, a discussion of the statistical
output produced by the calibration package, a detailed description of
a test example, a new general flow diagram showing the overall logic of
the program, and a complete set of computer listings.
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2. DESCRIPTION OF NEW FEATURES
This section describes the procedures used in the implementation
of the model calibration, individual source contribution list, and
averaging time transformation features. Also presented are the various
options available to the user, the specific input requirements, the
specific output for each feature, and guidelines for usage.
2.1 CALIBRATION PROCEDURE
Model calibration is a technique for improving the predictive
capability of a general air quality simulation model within some region of
interest, based upon the comparison of model predictions with actual air
quality measurements. The term model calibration refers specifically to
the determination of the coefficients of a linear equation relating
observed to predicted concentration values. The determination is done
by standard linear least-squares regression methods. Two slightly different
calibration procedures were used in the Air Quality Implementation Planning
Program (IPP), TRW (1970) and the Air Quality Display Model (AQDM),
TRW (1969). The algorithm incorporated in CDMQC is the same as that used
in IPP.
Algorithm. In order to provide a direct comparison of model estimates
with observations, the "observed" concentration value at each receptor is
taken to be the measured value at that receptor minus the background value.
Thus for each pollutant
Ot _ o _ Y
Ai Aim Abg
in which
X". = measured (input) concentration at the i-th receptor
X, = background concentration (also input; assumed the
same for all receptors)
X'. = "observed" concentration at receptor i, assumed to
represent the contribution from those sources given
in the emission inventory.
This distinction between observed and measured concentration values has
been maintained in this addendum and in the captions labeling the output
of CDMQC.
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-4-
For each pollutant, a linear least-squares regression of observed
concentration values against calculated values is carried out using standard
methods; see for example, Draper and Smith (1966) or Mood and Graybill (1963)
This procedure results in the straight line (the regression line) which best
fits, in a least-squares sense, the plot of observed versus calculated con-
centrations, as illustrated in Fig. 2.1.
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-5-
A = intercept of the regression line on the vertical
(observed concentration) axis,
B = slope of the regression line.
If the regression line is statistically significant for the set of
receptors at which air quality data is available, then the regression
equation is assumed to be valid over the entire region of interest.
Thus, the concentration value x calculated by the basic CDMQC
algorithm at any receptor location is adjusted according to Eqn. (3):
X = Xbg + A + BX (3)
in which x is the calibrated total concentration of the pollutant estimated
at the receptor under consideration and all other quantities are as previously
defined.
The statistical adequacy of the regression line, Eqn. (2), is tested
by comparing the value of the correlation coefficient, a measure of the
scatter about the line, against the theoretical maximum correlation coefficient.
The theoretical maximum is the maximum correlation coefficient
expected to occur by chance when the true value is zero, for the specific
•
number of receptors being used. The maximum value used in the test is the
theoretical 5% confidence level value, defined such that there are fewer
than five chances out of 100 that a value greater than this would arise
solely due to random sampling variation. If the correlation coefficient
determined from the regression is greater than this theoretical maximum,
it is considered statistically significant at this level of confidence
and the regression line is used to adjust the calculated values. If the
calculated correlation coefficient is less than the theoretical value, the
regression line is not used.
User Options. Four options relating to the model calibration procedure
are available to the user. They are specified by the value of the input
parameter IOCAL, as indicated in Table 2.1. The first option (IOCAL = 0)
was the only option available in the earlier version of CDM.
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Table 2.1. Model Calibration Options
IOCAL Value Option
Regression coefficients input by the user and not determined
during the current run.
Regression coefficients calculated by the program. Program
proceeds using the calculated values if confidence level test
is satisfied, and stops if it is not.
Regression coefficients calculated by the program. Program
proceeds using the calculated values if confidence level test
is satisfied, and proceeds using values of 1 for slope and
0 for intercept as defaults if it is not.
Regression coefficients calculated by the program. The results
are printed, and processing stops.
In any given run either one or two pollutants may be treated. If
two pollutants are being treated simultaneously, the calibration option
selected by the user refers to both pollutants. In the second and third
options the statistical test must be satisfied by both correlation coefficients
before either set of calculated regression coefficients will be used by the
program. ,
Inpu t. To use the calibration procedure, the user must specify the
following information:
• the value of IOCAL appropriate to the desired option,
• the calibration coefficients to be used if IOCAL = 0,
• a background concentration for each pollutant being treated,
• the total number (NCALR) of distinct receptor sites which
are to be used in the calibration, and
. a measured arithmetic mean concentration for one or both
pollutants at each receptor location.
The total number of sites, NCALR, which are to be used in model cal-
ibration must be at least three and no more than fifty. Air quality
data from any specific site to be used may consist of measurements for
only one or for both pollutants. The actual number of sites used in
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-7-
calibration for a given pollutant is the number for which data is available; -
this number is determined by the program from an examination of the first
NCALR receptors specified by the user in the input data set. For example,
if data is available for both pollutants from two sites, for pollutant 1
from a third, and for pollutant 2 from two others, the total number of
sites to be used is five and NCALR should be so specified. The actual number
of receptors used for pollutants 1 and 2 would be three and four, respectively
If only one pollutant is to be treated in a given run, that pollutant
must be number one. NCALR still represents the number of receptors that
the program will examine in its search, except that only those of the first
NCALR receptors which have measured concentrations for pollutant 1 will be
used. In the simplest case, NCALR represents the number of receptors to
be used, all of which are placed at the beginning of the set of receptor
cards.
Output. If the user specifies option 0 and inputs the values of the
regression coefficients, a message to that effect is printed along with the
values of the input coefficients and the background pollutant level(s).
If the user attempts to calibrate the model by selecting any one of options
1, 2, or 3, the following results from the regression analysis for each
pollutant are printed out:
regression coefficient values (slope and intercept of the
regression line) and the corresponding user-input background
value,
estimated standard deviations of the regression coefficients,
the calculated correlation coefficient and the theoretical
5% confidence level value,
an analysis of variance table.
The definition of these quantities and their significance are given in
Appendix B. In addition, for each receptor used in the calibration, both
calibrated and uncalibrated concentration estimates are printed along with
the observed value to allow direct comparison by the user. The
calibrated estimates are always obtained using the coefficients determined
by the regression analysis.
Guidelines. The importance of providing physically realistic back-
ground values should be emphasized. The value obtained for the intercept A
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-8-
depends on the assumed background. Ideally, A should be near zero and B
should be near one. Tests can be made to determine if the values actually
obtained are significantly different from zero and one at any desired
confidence level. The required information is part of the statisitcal
output; see Appendix B for a description.
Realistic input background values are particularly important if
individual source contribution lists are desired. Any adjustment in the
value of the intercept due to unrealistic background values will affect
the calibration factor used' for determining individual source contributions.
See the following discussion regarding the source contribution list feature.
Each background value (X, ) should at least satisfy the following conditions:
• X, must be greater than or equal to zero, and
• X, should not exceed in value the lowest measured (input)
value for the given pollutant.
2.2 SOURCE CONTRIBUTION LIST
For a variety of reasons, it is desirable to know what part of the
total predicted pollutant concentration at a given receptor is due to each
of the individual sources in the emission inventory. A new feature in
CDMQC allows the user to obtain an individual source contribution list
for any or all receptors, including those used for model calibration.
Algorithm. At each receptor, the sum of all the individual source con-
tributions plus the background should equal the total calibrated concentration
•
value; however, the basic CDM algorithm determines uncalibrated individual
contributions. Eqn. 4 shows the breakdown of the total predicted, uncalibrated
concentration (X.) at the i-th receptor into a sum of N source contributions
1 S
(X. ), including both point and area sources:
is *
X. = ^ X... (4)
The connection between individual contributions and the final calibrated
concentration at the i-th receptor is given by Eqn. 5:
N
Xbg + A + B X±s (5)
+ A + B y
5=1
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Using Eqn. 4, this may be rewritten in the following form:
N
s=l
(6)
Thus the calibrated contribution from source s at the i-th receptor is taken
to be
"as
X-,-
and the total calibrated value )(. is thereby represented as a sum of individual
calibrated contributions plus the background. The factor within parentheses
in Eqn. 7 is simply the ratio of the total calibrated and uncalibrated contributions
from known sources, and the assumption is that calibration affects all sources
by the same factor. This procedure is identical to that used in the Air
Quality Implementation Planning Program (TRW, 1970).
In principle, the sums over s in the above equations run over all
sources, both point and area. The manner in which the point source contribu-
tions are evaluated by the basic algorithm is simply the straightforward appli-
cation of the formulas presented in the CDM User's Guide. The contribution
from each point source at each receptor position is calculated by the program
and is calibrated using Eqn. 7.
The determination'of the individual area source contributions is less
straightforward due to the procedure used to evaluate the total area source
value. A detailed description of that procedure is presented in Appendix A,
along with a discussion of the manner in which individual area source contri-
butions are evaluated.
Briefly, the total area source contribution is evaluated by numerical
integration, in which the emission rate per unit area is determined at
sampling points located on a polar grid centered on the receptor of interest.
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The limitations of the numerical approach, are due to the finite resolution
obtainable using a finite set of sampling points. At great enough distances
from the receptor, the angular spacing between sampling points on an arc
may correspond to a distance larger than the size of an emission grid
square. In such situations, the contribution from a grid square which has
been skipped over is not included in the calculations. Even at closer
distances, the density of points at which emission rates are sampled is low
enough to cause significant error in the evaluation of the average emission
rate within a strip unless the variation in emission rate from one grid
square to the next is small. The approach used by COM and CDMQC involves
the implicit assumption that area source emissions are relatively uniform
and do not vary substantially from one grid square to the next.
The procedure for the determination of individual area source
contributions that was adopted in this version of CDM is the following:
1. Evaluate the contribution made by each emission grid square to
the total for each arc, and
2. Sum all contributions from each user-specified area source during
the process of summing over all arcs in all sectors, to obtain
the total contribution from each area source.
The sum of all the individual area source contributions equals the calculated
total area source contribution. The procedure for calculating area source
contributions is discussed in more detail in Appendix A.
Specifically, the following quantities are saved for each arc which
contributes in a given sector:
1. The total contribution from the arc to the receptor in question,
2. The value of q, for that arc (see Appendix A for the definition
of qk),
3. The value of each of the individual terms in the sum defining q,
(Eqn. 6, Appendix A), and
4. Labels identifying the specific area source(s) associated with
each individual term in the sum.
The contribution from each grid square to the total for a given arc is simply
proportional to its contribution to the average emission rate, and may be
easily evaluated from the quantities just listed. A given grid square may
contribute to more than one arc and to more than one sector. The cumulative
total for each area source is calibrated using Eqn. 7.
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User options. The user has the option of requesting or not requesting
a source contribution list for either or both pollutants, at any or all
receptors including those used in calibration. For any given receptor,
the desired option is specified by the value of the input parameter NCULP
as indicated in Table 2.2.
Table 2.2 Source Contribution List Options
a
NCULP Value Option
0 No list is printed for the given receptor.
1 A source contribution list is printed for
pollutant 1 but not for pollutant 2.
2 A source contribution list is printed for
pollutant 2 but not for pollutant 1.
3 Source contribution lists are printed for
both pollutants.
•a
If only one pollutant is treated in a given run, that pollutant is always
number one, and NCULP should be zero or one.
Input. The only input required of the user in addition to the value
of NCULP is the value of the parameter CTOF, which regulates the amount of
output from the source contribution algorithm as described below. .
Output. Both the calculated calibrated contribution in micrograms/cubic
meter and the percent of the total that this value represents are printed for
each source explicitly given in the list. As mentioned in the previous
paragraph, the user may exercise some control over the amount of output
obtained when asking for a source contribution list. Normally, those sources
which make the largest contributions at a given receptor are the ones of greatest
interest to the user. If an entire source contribution list is obtained,
the volume of the output may be inconveniently large, depending on the size
of the emission inventory. To bring the amount of output down to more
manageable levels, particularly when the principal interest is in the largest
contributions, the user may make use of the parameter CTOF. The printing of
each individual calibrated point or area source contribution which is less
than CTOF percent of the total including background is suppressed. The
accumulated total of all these small contributions is printed at the end of
the list along with the background and the overall total. By leaving the
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space corresponding to the input CTOF value blank, or by explicitly
specifying a value of zero, the entire source contribution list can be
obtained.
Guidelines. No guidelines are required for the use of CDMQC to obtain
individual point source contributions since the calculations involved are
straightforward. A different situation exists in regard to the area source
contribution calculations. The user is cautioned that in order to assure
reasonable accuracy, care must be exercised in the specification of the
values of the parameters DELR and DINT. Care must also be exercised regarding
the interpretation of the individual source contribution list for area sources.
In order to have a basis for the formulation of guidelines, the
algorithm for determining individual area source contributions was subjected
to a variety of tests. The test procedures and their results are discussed
in Appendix A.
Based upon the test results, the following general guidelines for
the use and interpretation of the individual area source contribution list
seem reasonable:
1. Use the largest emission grid spacing consistent with the desired
resolution in the emission pattern;
2. Use the value of DELR which corresponds to the desired maximum
range of integration (the maximum distance to which the area
source integration will be taken); Table 2.3 gives the maximum
range obtainable with various DELR values;
3. Use a value of DINT of at least 10, and preferably higher if area
source contributions beyond about seven emission grid squares
from the receptor are of interest.
Table 2.3. Maximum Range of Area Source Integration as a Function of DELR
DELR
(meters)
10
25
50
75
100
125
150
175
200
250
MAXIMUM RANGE
(kilometers)
0.990
2.475
9.800
19.500
29.500
39 . 500
49.050
58.975
69.000
89.000
DELR
(meters)
300
350
400
450
500
600
700
800
900
1000
MAXIMUM RANGE
(kilometers)
108.3
127.4
147.6
167.4
187.5
226.2
266.0
304.0
344.7
385.0
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-13-
The first two guidelines in effect promote the use of the smallest
feasible value of the quantity DELR/GRID SPACING. The third is based upon
the test results presented in Fig. A.I. The user is urged to consider the
specific application of interest, particularly with regard to what level of
accuracy is acceptable and over what distance in emission grid square lengths
this level of accuracy is desired. Once these factors are considered,
the appropriate value of DINT may be approximately determined for the given
value of DELR/GRID SPACING by examining Fig. A.I.
In the test example presented in Appendix C, the area source grid
has x and y dimensions of 25 km and 20 km, respectively, and all receptors
of interest lie within the grid. The diagonal distance across the grid
is approximately 32 km, and this represents the maximum range required to
include all area sources in the calculation for each receptor without
regard to the precise receptor locations. A range of 32 km corresponds to
a value of DELR slightly greater than 100 m as indicated in Table 2.3,
but the actual positions of the receptors in the test example are such that
a value of 100 m may be used and still cover the entire area source emission
grid. Consequently, a value of DELR = 100 m was chosen for the example.
In accord with the third guideline, a value of DINT = 10 is used in the
example. A comparison of the individual area source contributions obtained
in the test example using DELR = 100 m and DINT = 10 with those obtained
using DELR = 250 m and DINT = 4 (the values recommended in the COM User's
Guide) is presented in Appendix A.
In general, the results from area sources more than a few emission
grid lengths from the receptor should not be considered to be as accurate
as those from nearby sources. However, the effective grid length is the size
of the area source input by the user, not the size of the basic emission
square. Since the user may define area sources which are multiples of the
basic emission grid square, some additional control is obtained over the
accuracy with which the contributions from relatively distant sources may be
evaluated. Ideally, to maintain a comparable level of accuracy, the area
sources should increase in size as one gets farther away from the receptor of
interest.
It is important to re-emphasize that if the area emissions are reasonably
uniform, the determination of the total area source contribution may be done
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-14-
with larger radial and angular increments than are required for the
determination of individual area source contributions.
Going to smaller radial and/or smaller angular increments will in-
crease the computer time required to a calculation. The radial integral is
evaluated using up to 100 strips. Increasing the radial increment (DELR) will
not decrease the computer time unless the increment is increased to such an
extent that the distance to the edge of the emission grid can be covered in
less than 100 steps, in which case the computer time will decrease. The user
has direct control over the number of points per arc at which calculations
are done, that number being simply DINT + 1. Table 2.4 gives the computer
processing unit (CPU) times for a test case involving one sector, for two
different values of DELR and three different values of DINT. Each time in
Table 2.4 is normalized by the time for 60 arcs and DINT = 4. Sixty arcs
corresponds to a range of approximately 50 km with DELR = 250 meters.
Table 2.4. Ratio of (CPU Time for the Indicated No. of Arcs and
Value of DINT) to (CPU Time for 60 Arcs, DINT=4)
Number
of Arcs
60
100
DINT
1.
1.
= 4
00
13
DINT
1.
1.
= 10
13
38
DINT =
1
1
.25
.63
20
The results shown in Table 2.4 indicate that a significant increase
in computer time may be expected if small radial and/or small angular
increments are selected in order to obtain more accurate individual area
source contributions.
2.3 AVERAGING TIME TRANSFORMATION PROCEDURE
COM is designed to calculate arithmetic average concentrations over
relatively long averaging times, typically a month, season or year, 'it
is desirable, however, to be able to estimate the maximum concentration
for averaging times of a few hours to a day that is likely to occur over
a one-year period, in addition to the annual average. Knowledge of the
frequency distribution for the pollutant of interest for a variety of
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-15-
averaging times would enable this calculation to be made. Larsen (1971,1974)
has shown that in urban areas, the frequency distribution of air pollutants
may be approximated to a reasonable level of accuracy by a lognormal distri-
bution for all averaging times. In addition, the median concentrations are
approximately proportional to averaging time,raised to an exponent, and the
maximum concentrations are approximately inversely proportional to averaging
time raised to an exponent. Based upon these observations, Larsen developed
a procedure by which the maximum concentration, for an arbitrary averaging time,
which is expected to occur over a one-year period may be estimated given the
annual arithmetic average and the standard geometric deviation for some other
known averaging time. The Larsen procedure has been used in both IPP and AQDM,
and is the procedure adopted for use in CDMQC
Algorithm. The basic assumption of the Larsen procedure employed in
CDMQC is that the actual frequency distribution of pollutant concentration
values is approximately lognormal. These Larsen procedures are inappropriate
for any pollutant having a concentration frequency distribution that is not
lognormal. (Larsen, 1977, has developed a three parameter averaging time model
which may be applicable in such situations.) The lognormal distribution is
simply the usual "normal" or Gaussian distribution applied to the logarithm of
the variable instead of the variable itself. Such a distribution is shown in
Fig. 2.2.
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UJ
cc
50-PERCENTILE
\
\ /HIG
N f 16-
HIGHEST
PERCENTILE
\
/mv
3-
HIGHEST
PERCENTIL
log(Mg/Sg) log(Mg)
LOG OF CONCENTRATION
log(MgS§)
Fig. 2.2 The Lognormal Distribution
-------
-16-
Just as the normal distribution is specified completely once the arithmetic
mean and standard deviation are known, the lognormal distribution is
specified completely once the mean value and standard deviation of the
logarithm of the concentration are known. The antilogarithm of this mean
is in fact the geometric mean (M ), and the antilogarithm of the corre-
5
spending standard deviation is called the standard geometric deviation (S ).
o
Given that the concentration is lognormally distributed, with
known geometric mean and standard geometric deviation, the probability P of
observing a concentration higher than C is given by Eqn. 8:
-oo
C2TT)
exp
x
2
dx,
(8)
with
ln(C) - ln(M
z =
(9)
The symbol ln(C) denotes the natural logarithm (i.e., the logarithm
to the base e, where e — 2.718) of the quantity C. The concentration
corresponding to any specified probability, p, or percentile may be determined,
since Eqn. 8 implicitly allows the determination of z for a given P.
Once the corresponding z is known, C may be obtained from Eqn. 9 or its
equivalent
C = M S
g g
(10)
Since a specified averaging time corresponds to a certain number of samples
in a year, the highest sample corresponds to a well-defined percentile or
probability. An approximate expression for the probability P for the
highest sample of T-hours averaging time in a year is
0.6
C8760/T) '
Thus, Eqn. 11 provides the probability corresponding to the highest
expected T-hour concentration, and when combined with Eqns. 8 and 10
allows the estimation of that value.
(11)
-------
-17-
Both the geometric mean and the standard geometric deviation for
a set of samples are functions of the averaging time, and in order to make
the final calculation determining C from z using Eqn. 10, both M and S
O O
must be known for the appropriate averaging time. The standard geometric
deviation for an arbitrary averaging time may be obtained from the value
for a known averaging time. Assuming for example that the standard geometric
deviation for 24-hour samples is known, the standard geometric deviation
for T-hour samples may be obtained from Eqn. 12:
S (T hours) = (S (24 hours))k (12)
g g
with
' ln(8760/T)
k
_
ln(8760/24)
(13)
Once S is known for the desired averaging time, M may be determined
o o
using Eqn. 14:
M - XS -^V ,(14)
g g
in which x represents the arithmetic mean for the same set of samples,
precisely the quantity which is calculated i»,y CDMQC.
Thus, given the calibrated annual average concentration as calculated by
CDMQC, and the 24-hour standard geometric deviation (assumed knowns-, the maximum
concentration value expected to occur in one year may be estimated for any
specified averaging time using Eqns. 8-14. Larsen (1974) has further dis-
cussed the effect of procedures such as this on design concentrations for
determining allowable emissions.
User Options. The user may obtain at-any or all receptors, for
either or both pollutants, the estimated maximum concentrations for up to
three averaging times per pollutant. The averaging times to be used for
each pollutant must be specified by the user and are used at each receptor
at which the Larsen procedure is applied. For each receptor, the user may
request the Larsen statistical output for neither, one, or both pollutants by
appropriate specification of the parameter NLARS, on the receptor card, as
indicated in Table 2.5.
-------
-18-
o
Table 2.5. Larsen Transformation Options
NLARS Value Option
No averaging time transformation done for
either pollutant.
Averaging time transformation output for
pdllutant 1 only.
Averaging time transformation output for
pollutant 2 only.
Averaging time transformation output for
both* pollutants.
If only one pollutant is treated in a given run, that pollutant is always
number one, and NLARS should be zero or one.
Input. If the use of the Larsen procedure is desired at any receptor,
the user must supply at least one and up to three averaging times for the
pollutant(s) for which the procedure is to be used. The averaging times
should be in hours, and are supplied as the input variables PAV(I,J),
I =» 1 to 3,and J = 1, 2. If only one averaging time is to be used for
pollutant J, PAVO-.J) should be specified as this value, with PAV(2,J)
.and PAV('3,J) left blank. Similarly, if two are to be used, they should
be given in the first two positions and PAV(3,J) left blank. The sets
of averaging times may be different for the two pollutants, but the same
sets are used at every receptor.
In addition to the averaging times, the user must select and specify
the appropriate value of NLARS at each receptor, and must also provide
observed standard geometric deviation values of the 24-ho,ur samples
at each receptor and for each pollutant for which the transformation
is to be used. The user must also provide appropriate climatological input
data so that annual average concentration estimates are calculated, rather
than seasonal or monthly averages.
Output. The following information is printed out for each pollutant
and each receptor for which averaging time transformation output is requested:
1. The expected geometric mean concentration for each specified
averaging time,
-------
-19-
2. The expected maximum concentration for each specified
averaging time,
3. The standard geometric deviation for each specified averaging
time, and
4. The annual arithmetic mean concentration.
Guidelines. The Larsen procedure employed in CDMQC is an approximate
method based on certain assumptions, particularly that of lognormal concentra-
tion distributions. If it is definitely known that the pollutant distribution
in a particular application is not lognormal, a three parameter model may be
used through separate calculations, as discussed by Larsen (1977).
-------
-21-
3. DESCRIPTION OF INPUT
This section provides a description of the input required by CDMQC,
including a detailed card input sequence listing. The input may be logically
divided into four blocks:
• miscellaneous operation data
' meteorological joint frequency function
. source emission inventory
• receptor data.
Of these four parts, only the meteorological joint frequency function
input is identical to that for COM. The changes in the other inputs
are not large, however, and relatively little modification of existing
data sets will be required to make them usable with the new version.
The discussion will be in terms of cards as the sole input to the
program, but in fact only the first two records or card images must be input
on logical unit number 5 (by convention, a card reader). All subsequent
data must be input on the unit specified by the parameter IRD on the second
card. This unit may be the card reader (IRD=5) or any other device set up
to supply the required data in the appropriate format.
3.1 GENERAL DESCRIPTION
The first b,lock of data contains miscellaneous operational data
including a title card, input and output option specifications, miscellaneous
meteorological data, area source emission grid specifications and integration
parameters and pollutant background values. This block corresponds generally
to cards 1-3 in the basic COM, although two entirely new cards have been
added and a minor change has been made in a third.
The second block consists of the meteorological joint frequency
function. No changes have been made from the basic CDM.
The third block consists of the source emission inventory data.
For convenience, the poj.^ -ind area inventories are now read in separately,
the point source data first, followed by the area source data. The format
of the individual cards is such that existing inventory data can be used
unchanged except for the separation of point and area sources and the
insertion of a blank card between the two parts.
-------
-22-
The fourth block consists of the set of receptor cards, and substantial
additions have been made to each receptor card compared to the basic CDM
requirements. Due to program changes, a limit of 200 now exists on the total
number of receptors which CDMQC can treat in a given run. As explained in
Sec. 2.1, if calibration is to be done in a given run of the program, the
cards for the NCALR receptors involved must be placied at the beginning of
the set of receptor cards. Additional receptor cards may follow. Each receptor
card contains receptor coordinates, measured pollutant concentrations, pollutant
standard geometric deviations, four output control parameters, and an optional
four-character receptor identification name. The measured concentrations of
either or both pollutants are required if that receptor is to be used for model
calibration, but are optional if the receptor is not used for calibration.
The standard geometric deviations of either or both pollutants are required
if Larsen statistical output is desired for the specified pollutants at that
receptor, but are optional otherwise. The coordinates are the only parameters
which should never be blank; any or all of the other quantities may be
omitted under various circumstances.
Either one or two pollutants may be treated in a single run of the
computer program. If only one pollutant is treated, that pollutant must be
pollutant 1. A test is made on the name of pollutant 2, LPNAM(2) on card num-
ber 3; if this space is left blank, it is assumed that only one pollutant will be
treated. If LPNAM(2) is not blank, it is assumed that two pollutants are to be
treated. No test is made on the name of pollutant 1. In general, a name
should be supplied for each pollutant treated since it is used for identification
in the output.
Table 3.1 gives a summary of the differences in input requirements and
format between CDM and CDMQC.
3.2 DETAILED CARD INPUT' SEQUENCE
Table 3.2 provides the detailed card input sequence for the CDMQC. The
parameters are defined in the table for the benefit of the user, but the User's
Guide or other sections of this addendum should be consulted if questions arise
regarding the significance of any input variable.
-------
-23-
Table 3.1. Differences in Card Input Sequence Between
CDM and CDMQC
Card
CDMQC
1
2
3
4
5
6-101
102-299
300
301-999
1000
1001
number
CDM
—
1
—
2
3
4-99
100-999
—
100-999
1000
1001
Modification or
Comparison
Entirely new card
NLIST replaced by new parameters NLIST1
and NLIST2
Entirely new card
No difference
No difference
No difference
Point source inventory separated
Addition of blank card
Area source inventory separated
No difference
Measured concentrations renamed, new format used;
Addition of standard geometric deviations;
Redefinition of NROSE output control parameter;
Addition of output control parameters IPNCH,
NCULP and NLARS;
Addition of receptor identifier NRAM.
-------
-24-
Table 3.2. Card Input to CDMQC
a,b
CARD NO.
COLUMN
FORMAT
CONTENTS
1-80
1-8
20A4
2A4
9-16
2A4
17-21
23-24
25-26
27-31
32-36
37-41
42-59
60-77
1-6
15
12
12
15
15
15
2F9.0
2F9.0
16
*ITIT (1) - ITIT (20)
(Title of run to be printed at
top of every page of output)
AROS (1) - AROS (2) (Identifica-
tion for punched output of the
computed area source concentrations
of the two pollutants )
PROS (1) - PROS (2) (Identification
for punched output of the computed
point source concentrations of the
two pollutants )
IRUN (Computer run identification
number )
*NLIST1 (Index governing printout
of wind rose input data: If
NLISTl
-------
-25-
Card Input to CDMQC (continued)
CARD NO.
COLUMN
FORMAT
CONTENTS
3 (cont'd)
8-11
14
13-22
23-32
34-37
39-42
44-55
57-68
70-74
F10.0
F10.0
A4
A4
3F4.0
3F4.0
F5.0
1-6
F6.0
*IOCAL (Indicates calibration
option desired.
If IOCAL=0, regression constants
are input and not computed.
If IOCAL=1, constants will be
computed and processing will stop
if confidence level not satisfactory.
Otherwise, constants will be used to
calibrate.
If IOCAL=2, constants will be
computed and default values (slope=l,
intercept=0) will be used to calibrate
if confidence level not satisfactory.
Otherwise, calculated constants will
be used to calibrate.
If IOCAL=3, constants will be
computed, the results printed and
processing will stop.)
*BKGR(1) (Arithmetic mean background
concentration of pollutant 1,
in micrograms/cubic meter)
*BKGR(2) (Arithmetic mean background
concentration of pollutant 2,
in micrograms/cubic meter)
*LPNAM(1) (Name of pollutant 1)
*LPNAM(2) (Name of pollutant 2)
*PAV(1,1) - PAV(3,1) (Up to three
desired averaging times (hours) for
statistical output for pollutant 1 )
*PAV(1,2) - PAV(3,2) (Up to three
desired averaging times (hours) for
statistical output for pollutant 2 )
*CTOF (Percentage: sources contri-
buting less than this percent to
total calibrated concentration will
not be individually listed in any
culpability lists.)
DELR (Initial integration increment
of radial distance from receptor,
meters)
-------
-26-
Card Input to CDMQC (continued)
CARD NO.
COLUMN
FORMAT
CONTENTS
4 (cont'd) 7-12
13-18
19-24
25-30
31-36
37-42
43-48
49-54
55-60
61-66
67-72
1-6
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
F6.0
7-12
F6.0
RAT (Ratio of length of a basic
emission grid square and the length
of a map grid square)
CV (Conversion factor which upon
multiplication 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 south-
west corner of the emission grid
array)
YG (Y map coordinate of the south-
west corner of the emission grid
array)
XGG (X map coordinate of the
southwest corner of the plotting
grid)
YGG (Y map coordinate of the south-
west 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
integrate over a 22.5° sector.
Maximum value is 20, typical value
is 4.)
fD (Ratio of average daytime emission
rate to the 24-hour emission rate
average.)
-------
-27-
Card Input to CDMQC (continued)
CARD NO.
COLUMN
FORMAT
CONTENTS
5 (cont'd) 13-18
19-54
6-101
[Point Source cards
follow]
102C
55-66
1-49
1-6
7-13
F6.0
6F6.0
2F6.0
[7X, 6F7.0]
F6.0
F7.0
YN (Ratio of the average nighttime
emission rate to the 24-hour emission
rate average)
SZA (1) - SZA (6) (Initial az 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
-------
-28-
Card Input to CDMQC (continued)
CARD NO.
COLUMN
FORMAT
CONTENTS
300
[Area source cards
follow]
301d
1-6
7-13
14-20
21-36
37-43
1000
jReceptor cards
follow]
iooie
1-8
9-16
30-35
36-41
F6.0
F7.0
F7.0
2 F8.0
F7.0
F8.0
F8.0
F6.0
F6.0
*This is a blank card which
follows information on the
emission point sources. It
is used to test the end of
the point sources and must not
be left out.
X (X map coordinate of the south-
west corner of an area emission
grid square)
Y (Y map coordinate of the south-
west corner of an area emission
grid square)
TX (Width of an area grid square
in meters)
S1-S2 (Source emission rate in
grams per second for the two
pollutants)
SH (Stack height in meters)
This is a blank card which follows
information on the area 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)
*COBS(l)XMeasured concentration of the
first pollutant at the receptor in micro-
grams/cubic meter. Leave blank if not
known.)
*COBS( 2 ^Measured concentration of the
second pollutant at the receptor in micro-
grams/cubic meter. Leave blank if not
known.)
-------
-29-
Card Input to CDMQC (continued)
CARD NO.
COLUMN
FORMAT
CONTENTS
1001 '(cont'd) 43-47
F5.0
48-52
54-55
F5.0
12
56-57
12
58-59
12
60-61
12
77-80
A4
*SGD(1) (Standard Geometric
Deviation (24-hour) of pollutant 1
to be used for output at other
averaging times)
*SGD(2f (Same as SGD(l), but for
pollutant 2)
*IPNCH (A control parameter which,
if greater than zero will cause
standard concentration output to be
punched.)
*NROSE (A control parameter for
concentration rose output:
If NROSE = 0 (blank), no
concentration rose data will
be printed or punched;
If NROSE = 1, concentration
roses will be printed but not
punched;
If NROSE = 2, concentration
roses will be printed and
punched.)
*NCULP (A control parameter which
specifies source contribution list
option (print only):
If NCULP = 0, no list is printed;
If NCULP = 1, list for pollutant 1;
2, list for pollutant 2;
3, list for both pollu-
If NCULP
If NCULP
tants.)
*NLARS (A control parameter which
specifies Larsen statistical output
option (print only):
If NLARS = 0 (blank), no statis-
tical output;
If NLARS = 1, for pollutant 1 only;
If NLARS = 2, for pollutant 2 only;
If NLARS = 3, for both pollutants.)
*NRAM (Optional receptor identi-
fication name)
-------
--3U-
Card Input to CDMQC (continued)
o
Asterisks denote additions to or changes in card input sequence given in
Table 6 of the CDM User's Guide.
The data listed on "cards" 1 and 2 must in fact be input on cards. All
data on subsequent "cards" must be input from logical unit number 1RD,
provided on card number 2. This unit may be the card reader or any other
input device which can supply the data in card image format.
Q
There will be as many cards of this type as there are point sources. The
maximum number of point sources which can be handled is 200. The next
card type will arbitrarily be numbered 300.
There will be as many cards of this type as there are area sources. The
maximum number of area sources which can be handled is 2500. The next
card type will arbitrarily be numbered 1000.
Q.
There will be as many cards of this type as there are receptors. The maximum
number of receptors which may be handled is 200.
Required only if this receptor is to be used in calibration for pollutant 1.
o
&Required only if this receptor is to be used in calibration for pollutant 2.
Required only if Larsen statistical output is desired for pollutant 1 at
this receptor.
Required only if Larsen statistical output is desired for pollutant 2 at
this receptor.
-------
-31-
4. DESCRIPTION OF OUTPUT
This section provides a description of the output which may be obtained
in a given run of the CDMQC computer program. The user must specify the
logical unit numbers for the output; this is done by means of the parameters
IWR and IPU on input data card number two. It is intended that IWR refer
to a line printer and that IPU refer to a punched card output unit, but
they may refer to any other devices compatible with the output format.
The discussion will be in terms of printed and punched output. Samples
of both types of output for a test example may be found in Appendix C.
4.1 PRINTED OUTPUT
The user has considerable flexibility in specifying what quantities
will or will not be printed out. For job identification purposes, a three-
line heading is supplied at the top of each page of printed output. This
heading consists of the phrase CLIMA.TOLOGICAL DISPERSION MODEL, below which
the user-supplied job title (ITIT(l) - ITIT(20)) is printed, below which
the user-supplied run identification number (IRUN) is printed. The heading
allows the output to be separated without losing track of what job the output
resulted from.
The following information is always printed on the first two pages
of output:
« pollutant list (user-supplied pollutant names)
• area source grid specification and integration parameters
• miscellaneous meteorological data including morning and afternoon
mixing heights, mean ambient temperature and pollutant halflives
• day and night emission rate factors
• background pollutant concentrations
• the cut-off for source contribution lists
• the calibration option in effect and related input parameters
• averaging times to be used for each pollutant in applying the
Larsen procedure.
-------
-32-
Following this section of output, the user may have the meteorological
joint frequency function printed or not as desired. The joint frequency data
will be printed if the parameter NLIST1 is less than or equal to zero (or
left blank). The printing is suppressed if NLIST1 is greater than zero.
Similarly, the source emission inventory will be printed next if
the parameter NLIST2 is less than or equal to zero (or blank) and will not
be printed if NLIST3 is greater than zero.
Calibration results are then printed if calibration is attempted
on the given run (i.e., if IOCAL is greater than zero). See Sec. 2.1 and
Appendix B for a description of the output from the calibration procedure.
An explicit statement of the results of the statistical test on the cal-
culated correlation coeffielentCs) is printed along with a statement of
the action taken by the program as described in Table 2.1.
The last major section of output contains the calculated concentrations.
For each receptor, including those used for calibration, the calibrated
calculated point and area contributions for each pollutant treated, the
background values, and the total predicted concentration of each pollutant
at the given receptor along with the receptor identifier (NRAM) and receptor
coordinates are always printed. These results are printed in tabular form.
In addition, the user may request the following additional output
at any or all receptors:
Point and area concentration roses for each pollutant being
treated; concentration roses are printed if the parameter NROSE
is greater than zero, and not printed if NROSE is less than or
equal to zero (or blank).
Individual source contribution lists for either or both
pollutants, according to the value of the parameter NCULP;
see Sec. 2.2.
Results from the application of the Larsen statistical
transformation for either or both pollutants, according to
the value of the parameter NLARS; see Sec. 2.3.
The order in which the results are printed depends upon the nature
of any additional output beyond the basic point, area and total concentration(s)
at each receptor. Receptors are processed by the program one at a time in
the order in which they are specified by the user. If pollution roses and/or
an individual source contribution list are requested for a given receptor,
-------
-33-
these results are printed out immediately following the calculations
and are not saved through the entire run. Consequently, these results are
the first to appear, and are arranged by receptor in the order in which
the receptors are processed.
Following any pollution roses or source contribution lists requested
by the user, the table of point, area and total concentration estimates
previously described is printed.
Finally, if Larsen statistical transformation results are requested
for either or both pollutants at any or all receptors, these results are
printed out in tabular form following the table of annual average con-
centration estimates. A separate table is printed for each combination
of pollutant and averaging time, containing results for only those receptors
at which statistical output was requested for the given pollutant.
Examples of each type of output are given in Appendix C as part of
the output from the test example.
4.2 DIAGNOSTIC MESSAGES
Three new tests have been added to the program to detect common
user input errors and to call the user's attention to their existence
when they occur. A brief description of each together with the diagnostic
message that is printed follows.
Inconsistent Specification of Area Source Locations. The area source
emission grid may be not larger than 50 grid squares in either the x or the y
direction, this limit being determined by the dimensions of various arrays
defined within the computer program. This limit, together with the user-
specified size of a basic grid square (TXX), imposes a limit to the total
size of the emission grid. A test is made to see that each area source
falls within the boundaries of the grid. If any area source lies partially
or wholly outside these boundaries, the following message is printed:
• NOTE: AREA SOURCE NNNNN, WITH X COORD XXXXXXX.XX AND Y COORD
YYYYYYY.YY, VIOLATES AREA SOURCE ARRAY LIMITS. AREA SOURCES
MUST LIE ENTIRELY WITHIN A MMMMMMMM.MM METER SQUARE WITH
SOUTHWEST CORNER AT THE USER-DEFINED ORIGIN (XG, YG).
AREA SOURCE NNNNN WILL NOT BE INCLUDED IN THIS CALCULATION.
In this message, the actual values of all quantities indicated will be
printed. The quantities printed are:
-------
-34-
NNNNN Area source ID
XXXXXXX.XX X coordinate of southwest corner of area source
which violates limits.
YYYYYYY.YY Y coordinate of southwest corner of area
source which violates limits
MMMMMMMM.MM Total possible size of emission grid, equal to
(50)(TXX) meters
As indicated in the message, the calculation will proceed but the area
source in violation will be omitted from the inventory,
Inconsistent Specification of RAT, CV, and TXX. The user-supplied
quantities CV, RAT, and TXX are not all independent, but are related by the
equation
RAT = TXX/CV. (1)
A test is made to insure that this relationship is satisfied, and if it is
not the following message is printed:
INPUT ERROR: RAT*CV MUST EQUAL TXX. CALCULATION TERMINATED.
As the message indicates, the run is stopped after the message is printed.
The user must correct the input and resubmit the job.
Insufficient Range in Area Source Calculations. As discussed in
Section 2.2 and in Appendix A, the area source algorithm evaluates the
average emission rate on a series of arcs centered on the receptor of
interest. No more than 100 arcs, are used, this limit again being determined
by internally fixed array dimensions. This limit, together with the user-
supplied radial integration step DELR, imposes an upper limit to the distance
to which the area source calculations will be taken. If there are area
sources beyond this range, they will not be included in the calculations.
A test is made for each receptor to determine if this situation exists,
and if it does the following message will be printed:
WARNING: MORE THAN 100 ARCS ARE REQUIRED FOR CALCULATION
OF AREA CONTRIBUTION. AREA SOURCES BEYOND 100TH
ARC ARE NOT INCLUDED IN CALCULATION.
The limit need be violated for only one sector at a given receptor in
order for the message to be printed. As indicated, the program does not
-------
-35-
terminate the job, but ignores the contribution from area sources beyond
the range. Table A.2 gives the range of the area source integration as
a function of DELR.
4.3 PUNCHED OUTPUT
Two types of punched card output for each receptor are available to the
user. The first type, called the standard concentration output, consists of one
card containing the receptor coordinates in both plotting grid units and in map
units, calibrated point and area concentrations, background concentrations,
total predicted concentrations, measured concentrations of each pollutant,
and the computer run identification number. All concentrations are reported
in micrograms/ cubic meter. To obtain the first type of punched card output
for a given receptor, the value of the parameter IPNCH on the corresponding
receptor card must be greater than zero.
The second type of punched output consists of the point and area
concentration roses for each designated receptor. Two or four cards are
punched, depending on the number of pollutants treated. Each concentration
rose card contains a user-supplied card identifier (PROS(I) or AROS(I),
1=1 or 2), sixteen calibrated concentration values corresponding to the
sixteen wind directions used, and receptor map coordinates. To obtain
this output for a given receptor, the parameter NROSE on the receptor
card must be assigned the value 2.
These two types of output are independent of each other; either or
both may be obtained at a given receptor. The punching of the standard
concentration output is controlled entirely by the parameter IPNCH and the
punching of the pollution roses is controlled entirely by the parameter NROSE.
Table 4.1 gives the detailed format of the punched card output
available from CDMQC.
-------
-36-
Table 4.1. Format of Punched Output
CARD COLUMN
Ia 1-8
9-14
15-18
19-22
23-26
27-30
31-34
35-38
39-42
43-46
FORMAT
F8.2
F6.2
14
14
14
14
14
14
14
14
CONTENTS
PUX (X coordinate of receptor
in plotting grid units)
PUY (Y coordinate of receptor
in plotting grid units)
KPX(l) (Calibrated area con-
centration for first pollutant)
(2) (Calibrated area con-
centration for second pollutant)
(3) (Calibrated point con-
centration first pollutant)
(4) (Calibrated point con-
centration for second pollutant)
(5) (Input background con-
centration for first pollutant)
(6) (Input background con-
centration for second pollutant)
(7) (Calibrated total con-
centration for first pollutant)
(8) (Calibrated total con-
47-50
51-54
55-64
65-74
75-79
80
1-4
5-68
14
14
F10.2
F10.2
15
A4
1614
centration for second pollutant)
COBS(l)(Measured concentration
of first pollutant)
COBS(2) (Measured concentration
of second pollutant)
RX (X map coordinate of receptor)
RY (Y map coordinate of receptor)
IRUN (Computer run identification
number)
I (Card identifier, a literal 'I')
PROS(l) (Card identifier)
KPX(1)-KPX(16) (Point concen-
tration by wind direction)
-------
-37-
Format of Punched Output (continued)
CARD
COLUMN
FORMAT
CONTENTS
2° (cont'd)
5b
69-74
75-80
1-4
5-68
69-74
75-80
16
16
A4
1614
16
16
RX (X map coordinate of
receptor multiplied by 1QO to
remove decimals)
RY (Y map coordinate of
receptor multiplied by 100 to
remove decimals)
(Same as Card 2 for.second
pollutant)
AROS(l) (Card identifier)
KPX(1)-KPX(16) (Area concen-
tration 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)
Card punched only if IPNCH greater than zero.
Card punched only if NROSE equals two.
-------
-38-
REFERENCES
Busse, A.D. and J. R. Zimmerman. "User's Guide for the Climatological
Dispersion Model," Publication No. EPA-RA-73-024 (NTIS PB 227346/AS),
Environmental Protection Agency, Research Triangle Park, North Carolina
27711 (December 1973).
Draper, N.R. and H. Smith, "Applied Regression Analysis," John Wiley and
Sons, Inc., New York (1966).
Larsen, R. I. "A Mathematical Model for Relating Air Quality Measurements
to Air Quality Standards." Office of Air Programs Publication No. AP-89
(NTIS PB 205277), Office of Technical Information and Publications, Environ-
mental Protection Agency, Research Triangle Park, North Carolina 27711
(November 1971).
Larsen, R. I., "An Air Quality Data Analysis System for Interrelating Effects,
Standards, and Needed Source Reductions—Part 2," J. Air Poll. Control Assoc.
24: 5511-558 (June 1974).
Larsen, R. I., "An Air Quality Data Analysis System for Interrelating Effects,
Standards, and Needed, Source Reductions: Part 4. A Three-Parameter Averaging-
Time Model," J. Air Poll. Control Assoc. 27: 454-459 (May 1977).
Mood, A. M. and F. A. Graybill, "Introduction to the Theory of Statistics,"
2nd Edition, McGraw-Hill Book Co., New York (1963).
TRW Systems Group, "Air Quality Display Model." Prepared for National Air
Pollution Control Administration under Contract No. PH-22-68-60 (NTIS PB 189194),
DHEW, U.S. Public Health Service, Washington, D.C. (November 1969).
TRW Systems Group, "Air Quality Implementation Planning Program." Prepared
for Environmental Protection Agency under Contract No. PH 22-68-60 (Vol. I,
NTIS PB 198299 and Vol. II, NTIS PB 198300), U.S. Environmental Protection
Agency, Research Triangle Park, North Carolina 27711 (November 1970).
-------
-39-
APPENDIX A. DESCRIPTION OF THE AREA SOURCE CONTRIBUTION ALGORITHM
The purpose of this appendix is to describe the algorithm used to
estimate both total and individual area source contributions and to present
the results of tests carried out to determine the accuracy of the individual
area source contribution estimates.
The total area source contribution is given by Eqn. 1 on page 3 of
the CDM User's Guide, which is reproduced here with very slightly altered
notation:
16
2lT
(-16
Lk=l
\J *-/
LI
=1 m=l
dr
CD
with
q (r) = I Q(r,6) d0 (over sector k). (2)
K.
If we define f, 00 by
K.
6 6
Vr)
m=l
(3)
then the total area source contribution may be written as follows:
16
16
XA " 2TT
k-1
fk(r)
Both radial and angular integrations are done numerically using the
trapezoidal rule. Operationally, the radial integral in Eqn. 4 and the
angular integral defining q(r) are replaced by
fk(r)qk(r)dr - Ar
(5)
-------
-40-
and
qk(r) ~ A8
Q(r,92)
(6)
The quantity Q(r,6) represents the pollutant emission rate per unit area at the
location specified by (r,0). The quantity q (r) is proportional to the
K.
average emission rate along an arc at a distance r from the receptor. The
radial di3tances r , 1=1 to M, in Equation 5 are determined from
r - (i-1) Ar (7)
with
Ar = DELR until r _> 2500 meters,
then
Ar = 2DELR until r >_ 5000 meters,
then
Ar = 4DELR thereafter.
The special case of i=l corresponds to a single point rather than an arc,
the point being located at the receptor position. The value of q for this "arc"
fcC
is obtained from the emission rate per unit area of the grid square in which
the receptor is located, If the receptor is located outside the emission
grid, the first distance at which calculations are done corresponds to the
first arc which intersects the grid.
The parameter DELR is specified by the user,and a value of 250 meters
is suggested in the CDM User's Guide. The radial integral is
handled in the code in a manner equivalent to dividing the integral into
three parts, corresponding to the three distance ranges given above, and
applying the trapezoidal rule separately to each part. The upper index, M,
is determined by the distance from the receptor to the farthest point of
the area emissioa grid or the maximum allowed number of arcs (100 in the
current version), whichever gives the smaller distance.
-------
-41-
The angles 6., j=l to N, in Eqn. 6 are determined from the compass
direction which defines the sector under consideration, and represent the
angular coordinates of the points on each arc at which the emission rate
Q(r,6) is evaluated. The number of intervals into which each arc is divided
is given by the user-supplied parameter DINT, and the number of points used
on each arc is given by N=DINT + 1. The angular increment A6 is given by
radlans-
A value of 4 is suggested in the User's Guide as being a typical value of DINT.
The maximum allowed value is 20.
The determination of the quantities Q(r,0) in Eqn. 6 requires some
discussion. In the simplest case, the emission grid square in which each
point falls is identified and the appropriate emission rate per unit area
-4
used. If, however, the sampling point falls within 1 x 10 emission grid
units of the boundary between two adjacent squares, the average emission
rate per unit area for those two squares is used at that point. If the
-4
sampling point falls within 1 x 10 emission grid units of both a horizontal
and a vertical boundary, i.e., very close to the intersection of four grid
squares, the average emission rate for the four squares involved is used at
that point .
Thus, conceptually the COM algorithm consists of the following steps:
' 1. Evaluate the average area source emission rate per unit area
within concentric annular strips of width Ar centered on radial
distances given by Eqn. 7. The average is approximated by the
average along the central arc of each strip.
2. Multiply the average emission rate per unit area for each strip
by the area of the strip and by a distance-dependent meteorological
factor which accourtts for transport and dispersion. Each such
product gives the contribution from that strip to the pollutant
concentration at the receptor.
3. Sum over all strips to obtain the total area source contribution
from that sector.
4. Sum over all sectors.
-------
-42-
As described briefly in Sec. 2.2, the procedure by which individual area source
contributions are estimated consists of 1) an evaluation of the contribution
made by each emission grid 'square to the total for each arc and 2) the
summation for each user-defined area source of all such contributions.
Two types of error arising from the area source algorithm may
be present in the individual area source contributions given in the list.
The first is due to inaccuracy in the value of the average emission rate
used to calculate the contribution from a given strip. Errors in this
quantity arise from a combination of significant variability in emission
rate from one grid square to the next and too low a density of sampling
points. If all area sources in the grid emit pollutant at the same rate
per unit area, the algorithm will always obtain the correct average
emission rate for any strip which lies wholly within the grid. In this
case, che first type of error does not occur. If the application in which
CDMQC is being used is consistent with the implicit assumption of relatively
uniform area emissions, this type of error will be of minimal importance.
The second type of error in the individual area source contributions
exists even if the average emission rate for each strip has been correctly
evaluated, and arises from the way in which the relative weight of each
grid square is determined. If all grid squares have the same emission
rate, the relative weighting of their contributions does not affect the
numerical value of the average. However, the individual contributions do
»
depend on the weights and may be in error if the weights are inaccurate.
In cases involving non-uniform emissions, the error made in calculating the
average may in fact be thought of as arising from inaccuracies in the
relative weights.
An admittedly extreme example may clarify the situation. Suppose
a value of 1 is used for DINT. In this case, the average emission rate for
each strip is obtained as an average of the two values corresponding to
the grid square(s) in which the two end points of the central arc happen
to fall. Suppose the orientation of the emission grid is such that one
axis is perpendicular to the wind direction and the other is parallel.
In this case, if the distance from the receptor to the arc is greater than
about 1.31 grid lengths, the separation between the two end points is
sufficiently large that it is possible to completely miss a grid square
-------
.-43-
located directly upwind of the receptor. If the emission rate is the same
for all grid squares, the average emission rate and the total contribution
for each strip will be numerically correct, but beyond 1.31 grid lengths
the total contribution will be equally divided between the two squares
detected by the program. The middle square will be reported as having
made no contribution at all. Figure A.I illustrates the possibilities
of angular and radial skipover, and part (a) of that figure illustrates
the example just described.
A relatively accurate determination of individual area source
contributions requires a relatively accurate determination of the weight
with which each square contributes to each strip. The accuracy of this
determination is directly related to the density of sampling points, which
is in turn related to the values of DELR (or more precisely, the ratio of
DELR to the grid spacing) and DINT, as well as to the distance of the strip
in question from the receptor. More accurate results can be expected for
those area sources near the receptor, but it may be very difficult to get
accurate results for sources farther away.
Three types of phenomena attributable to the distribution of sampling
points have been observed in test cases. The most obvious problem is
that of skipover, the failure to detect a grid square at all. Table A.I
shows in three cases the number of layers of grid squares that are
encountered before reaching a layer in which at least one square is
skipped entirely, for various values of DINT and the ratio DELR/TXX (TXX
is the user-input parameter giving the width of a basic emission grid
square in meters).
These test cases correspond to the following combinations of receptor
location and wind direction:
Case 1: Northerly wind (sector 1); receptor located on the southern
edge of the emission grid, and on the boundary between two
of the bottom-layer grid squares.
Case 2: Northerly wind (sector 1); receptor located in the center
of one of the bottom (southern ) - layer grid squares.
Case 3: Northeast wind (sector 3); receptor located at the southwest
corner of the emission grid.
-------
-44-
SAMPLING POINTS
DINT = I
a) ANGULAR SKIPOVER
b) RADIAL SKIPOVER
RECEPTOR
SAMPLING POINTS
DINT = 4
22,5'
RECEPTOR
Fig. A.I. Angular and Radial Skipover
-------
-45-
Table A.I. Number of Layers of Emission Grid Squares
Before the Onset of Skipover
DINT
3
4
5
7
10
15
20
Case 1
DELR/TXX
0.0625 0.125
10
15a 15
15
21
15a 30
39a
15a 39a
Case 2 Case 3
0.250
10
15
15
20
30
41
>49b
DELR/TXX DELR/TXX
0.0625 0.125 0.250 0.125 0.250
_ — — — — — 5
14 13 13 8
10
15
15 28 28 20
27a
16a 40S 47 27a
4
7
5
9
16
14
21
At the limit Imposed by the finite range of radial integration.
At the limit imposed by the finite size of the test emission grid.
In each case, the emission grid consisted of a 49 x 49 array of 1000 meter
squares all having the same emission rate. A single stability class (no. 4)
and wind speed class (no. 3) were used.
The general conclusion to be drawn from the table is that to avoid
the skipover problem altogether, one must generally go to smaller radial and
angular increments. However, as indicated elsewhere, the use of smaller
radial increments may result in the' termination of the radial integration
due to computer storage restrictions before the far edge of the emission
grid is reached, with the corresponding omission of a significant part of the
total area source contribution. Table A. 2 gives the effective maximum range
of the radial integral obtainable with three values of DELR, corresponding to
the restriction that the total number of arcs that can currently be handled
is 100, and the corresponding percent of the total area source contribution
obtained in test case number one.
-------
-46-
Table A.2. Dependence of Effective Range and Example Percent
of Total Contribution on DELR Value
DELR (meters)
250.0
125.0
62.5
Range (km)
89.0
39.5
14.8
Percent of Total Contribution
Test Case 1
100.0
86.2
52.5
A second phenomenon observed in the tests that were run is that the
calculated contributions from adjacent grid squares having the same emission
rates were often in the ratio of small whole numbers, and not nearly
identical as one might expect. The ratio of contributions from adjacent
grid squares reflects the relative number of times that the two grid squares
were sampled. Examples of this type of situation in which the ratio is
nearly that of small whole numbers are quite easy to produce. The problem
can be alleviated near the receptor by using smaller radial and angular
increments, but the problem always appears again farther away.
The third phenomenon is associated with the first and is in a sense
complementary to it. As pointed out earlier, it is possible to obtain the
correct average emission rate for a given strip without having even
detected many of the grid squares which in reality do contribute. The entire
calculated contribution from that strip is allocated among only those
squares which are actually detected. As a result, the squares which are
missed are assigned no contribution and those which are found are assigned
a larger contribution than they deserve. At large enough distances, for a
conservative pollutant, the contribution from those squares which are found
levels off to a constant value rather" than decreasing with distance as
would be the case if the allocation were correct.
In order to have a basis for providing guidelines for use, CDMQC area
source contribution values were compared against values calculated using
exactly the same algorithm as CDMQC except that the relative weight of each
grid square to each strip was accurately evaluated. This comparison was
made only for test cases 1 and 2 described previously, and the results are
-------
-47-
shown in Fig. A.2(a)-(f) in the form of percent error of individual
contributions, defined by
. (CDMQC value) - (more accurate value) , __ ,..,.
percent error = - *—-. - —r — x 100. (9)
(more accurate value)
Results are presented for all combinations of DELR/GRID SPACING values
of 0.0625, 0.125, and 0.250 and DINT values of 4, 10 and 20. These results
should be considered as illustrative only, but should be useful to the user
in providing guidance for the selection of DELR and DINT values for a given
application.
Each box in the figures represents one emission grid square, and
only the first ten rows of squares upwind of the receptor are shown. In
addition, due to the'position of the receptors, only part of each of the first
ten rows need be considered, the omitted results being identical to those
which are given, by reason of symmetry. In parts (a), (b) and (c) for
example, only the top half of the results are shown, the bottom half being
a mirror image of the top.. In parts (d), (e), and (f) the top two rows of
boxes should be reflected below the bottom row, making five rows in all.
The three numbers appearing in each box correspond to the three values
of DINT which were considered: the top number corresponds to DINT = 20,
the middle to DINT = 10, and the bottom to DINT = 4. The six parts of the
figure correspond to three values of DELR/GRID SPACING at each of two
receptor positions, as indicated on the figures.
In addition, a somewhat similar comparison was made using results
based upon the test example presented in Appendix C. Ten receptors and
seventeen area sources were considered. Initially, values of DELR=250m
and DINT=4 were used, although values of DELR=100m and DINT=10 are used in
Appendix C in accordance with the guidelines presented in Section 2.2.
Table A.3 presents the results of a comparison between the two sets of
individual area source SO contributions. The table entries represent
the approximate percent change that occurred in individual contributions
to the estimated SO concentration upon changing the DELR and DINT values
from 250m and 4 to 100m and 10. It should be pointed out that the largest
percentage changes in Table A.3 are usually associated with very small
-------
-48-
contributions. For example, the 50% changes observed for receptor no. 5
with area source 4A and for receptor no. 7 with area source ISA represent
increases from 0.02 to 0.03 micrograms/cubic meter. An entry of 0 (zero)
in Table A.3 indicates that the difference in the two indicated values was
less than 0.01 micrograms/cubic meter. A comparison of the two values of
the total area source contribution to the estimated SO- concentration is
also presented on the last line of Table A.3, again in terms of percent
change.
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-57-
APPENDIX B. STATISTICAL INFORMATION FROM THE CALIBRATION PROCEDURE
The process of model calibration involves doing a linear least-
squares regression analysis of observed against calculated concentration
values for a given set of receptors. The purpose of this appendix is
to present the formulas used in the CDM calibration routine and to define
briefly the various quantities which are printed by the program upon
completion of the calibration calculations.
Equations are presented for the general case in which the regression
line between a set of values y (i = 1,2....N) and a different set x
(1*1, 2 .... N) is to be determined. For calibration purposes,
the set y. represents the set of observed concentration values for a given
pollutant at N different receptor locations, and the set xj represents
the corresponding set of calculated values. Linear regression of the set
y against the set x involves the determination of the regression
coefficients A and B, which are defined such that the regression line
y - A + Bx (1)
represents the straight line which best fits, in a least-squares sense,
the plot of the y. values against the x values. In Eq. 1, y represents
the value of y which is predicted for a given value of x on the basis of
the regression line, and is not necessarily equal to the observed value
for that same x because of both measurement errors and model approximations,
It can be shown (see for example Draper and Smith (1966) or Mood and
Graybill (1963)) that the regression coefficients determined from specific
sets of observed and calculated values are given by Eqns. 2 and 3:
N
and
A = 7 - B3£ (3)
with N
x. (4)
-------
-58-
and
* -1
1=1
To simplify the notation used in writing further equations, we will
henceforth omit the summation limits; the summation limits implicit in
all subsequent equations are 1 and N, exactly as in Eqns. 2, 4 and 5.
In evaluating B, it is convenient for computational reasons to use
the equivalent formula
Zx y - NX y
B -
The sample correlation coefficient is defined by:
Z(x - x) (y, - y)
R = -= - - - ~ - i- (7)
Z(y.-T)2 ]
although it is again more convenient computationally to use a different
but equivalent formula:
Zx y - NX- J
R = -= - ^-i - TT75- (8)
[(Ex.2 -Nx2) (Zy^ -Ny2)]1/2
The correlation coefficient is a measure of the degree to which the
quantities x and y are linearly related, and is rather closely related
to the slope of the regression line as can be seen by a comparison
of Eqns . 2 and 7 (or 6 and 8). Furthermore, the square of the correlation
coefficient is a measure of the extent to which the variation in the
observed values about the mean is explained by the variation in the cal-
culated values about their mean. The square of the correlation coefficient
is printed under the heading "R-SQUARED."
An estimate can be made of the uncertainty in the specific slope
and intercept values obtained in any given analysis. The sample variances
of the slope and intercept are given by:
-------
-59-
Variance of _ s2
E(x.-x)2
s2 Ex 2
Variance of _ _ ± ,.. ,
Intercept ~ ^. _. ,
* N E(x± - x)
The quantity s2 is defined below. A convenient measure of the uncertainty
in the slope and intercept estimates is the standard deviation for each,
the standard deviations being simply the square roots of the corresponding
variances. The standard deviations are printed next to the estimated
values in the regression analysis output.
The total sum of squares of observed values about the mean,
Total Sum , __ 2
of Squares = Z (yi ~ *>
may be written as the sum of two terms: 1) the sum of squares due to
regression;
Regression Sum 2
of Squares L Vyi j)
with
y\ = A + BXi, (13)
and 2) the sum of squares due to deviations of observed values about the
regression line:
Deviations „., ^ \z /i/\
Sum of Squares = E (yi ' yi} (14)
The ratio of the deviations sum of squares to the total sum of squares
can be shown to be equal to the square of the correlation coefficient,
and the significance of this ratio was mentioned earlier. All three of
these quantities together with their respective numbers of degrees of
freedom are printed in the analysis of variance table in the output from
-------
-60-
the CDMQC regression routine. The number of degrees of freedom are 1, N-2,
and N-l for regression, deviations and total sum of squares, respectively.
Two other quantities are of interest: the mean square due to regression,
equal to the regression sum of squares divided by its degrees of freedom
and the mean square due to deviations about regression, equal to the deviations
sum of squares divided by its degrees of freedom. The latter quantity is
denoted by s2
2 _ Deviations Sum of Squares
N-2
s- = = ^ • ' (15)
n
s is an unbiased estimate of the variance of the deviations of the y. about
the regression line only when the true relationship between the y. and the
i
x is linear and when the random deviations are distributed normally
•*• >
with zero mean. Both mean square values are printed in the regression
output.
The observed mean concentration (y) and the calculated mean concentration
(x"),given by Eqns. 5 and 4 respectively, are also printed.
From the statistical output just described, the user may perform
additional calculations relating to the regression analysis if he so desires.
For example, he may
1) determine confidence intervals for the estimated slope
and intercept values,
2) perform an F-test to test the significance of the
regression, and
3) determine confidence intervals about specific y values.
In order to do the latter calculation, the user needs the value of the
*
quantity £ (x. - x)2; this quantity is not. explicitly printed out, but
is equal to the ratio of the mean square due to deviations about regression
and the variance of the slope:
s2
E (x - x)2 (16)
(Standard deviation of slope)2
The procedures for doing the calculations just listed are given in
Draper and Smith (1966) or Mood and Graybill (1963).
-------
-61-
REFERENCES: APPENDIX B
Draper, N.R. and Smith, H,, Applied Regression Analysis, John Wiley & Sons,
Inc., New York (1966).
Mood, A.M. and Graybill, F.A., Introduction to the Theory of Statistics,
2nd Edition, McGraw-Hill Book Co., New York C1963).
-62-
-56-
20
-------
-------
-63-
APPENDIX C. TEST EXAMPLE
In this appendix, the use of CDMQC in a hypothetical test situation
is described in sufficient detail so as to illustrate the format for the
input data and the various types of output that the user may obtain.
C.I. GENERAL DESCRIPTION
The test situation that is used in this appendix was adapted from
the AQDM "TEST CITY" example described in the AQDM user's manual. This
example, although hypothetical and not as complex as is usually encountered
in practice, nevertheless provides a more realistic and interesting test
of CDMQC's capabilities than does the test case which appears in the COM
User's Guide. Fig. C.I shows the map of TEST CITY and the locations of
all sampling stations, point and area sources used in this adaptation.
C.2 DETAILED INPUT AND OUTPUT LISTINGS
Fig. C.2 shows the complete input data set in card image format
for the TEST CITY example. It should be pointed out that all input was
provided on punched cards (1RD=5).
Fig. C.3 shows the entire printed output obtained from the given
input data set, and Fig. C.4 shows the punched output in card image form
obtained from the same run.
-------
-64-
a:
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A ~ POINT SOURCES
® ~ SAMPLING STATION, SULFUR DIOXIDE
X ~ SAMPLING STATION, PARTICULATES
ZONES I-I7~ AREA SOURCES
1—
-^ 47?n
—
1 1 1 1 1
540 550 560 570 580 - 590
UTM HORIZONTAL TICK MARKS, KILOMETERS EAST
Fig. C.I. TEST CITY Base Map
-------
-65-
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-91-
APPENDIX D. GENERAL FLOW DIAGRAM
Fig. D.I shows the overall flow for CDMQC, indicating in what order
each general set of calculations are done.
-------
-92-
BEGIN
Read and print* operations
and meteorological data
Read and print*
Source inventory data
Calibration constants
to be determined?
>
NO
REGRESSION
>
YES
ANALYSIS
r
Read receptor 'and observed
concentration data
I
Calculate concentrations at
indicated receptors
Perform regression analysis:
Determine calibration constants
and other statistical data
I
Print results of
regression analysis
L_
I
Recalculate and print* desired
results for the set of receptors
used for calibration.
1
I
*Asterisks denote output subject to user option*
Figure D.I, CDMQC Flow Diagram
-------
-93-
Read next receptor location
and output options
r
STANDARD ^CALCULATIONS
"1
Calculate concentrations (and other information*)
at indicated location for future use
Calibrate computed mean concentration
values using either values obtained
in calibration in same run or values
input by user
i
Store standard receptor output
Punch standard receptor output*
J I
/'Area and point concentration ^ NO
V roses desired? y
1
YES
t
Calibrate area and point
roses
i
Print calibrated area, point roses
1
Punch calibrated area, point roses*
Figure D.I. CDMQC Flow Diagram, continued,
-------
-94-
NO
1 Source contribution list desired? 1 **"
1 YES
1 ' 1
• SOURCE CONTRIBUTION CALCULATIONS |
1 * 1
1
1 Calibrate point and area source contributions. 1
1
!
1 '
1 Print results - significant point, area sources |
!
•
I
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| plus calibration intercept value '
|__
~ S
(Have all desii
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I
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L
r
red rprftptnr A NO ^/Ov
sen input J _>/ >• — '
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t
(Concentration est
other averaj
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1 !
NO I " "1
*-| STOP |
YES
:AL CALCULATIONS
f !
' Calculate geometric means ,
'
I i
\ "- ' • — - • - - •• • i
j Calculate and print concentration i
1 estimates for desired averaging times '
| — -i
( 1
1 STOP J
Figure D.I. CDMQC Plow Diagram, continued,
-------
-95-
APPENDIX E. COMPUTER PROGRAM LISTINGS
Fig. E.I gives the detailed FORTRAN listing of the entire CDMQC computer
program, separated for convenience into parts corresponding to each separate
routine in the program.
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* U.S. GOVERNMENT PRINTING OFFICE: 1977—740-110/323 Region No. 4
-------
TECHNICAL REPORT DATA
(Please read laslructions on the reverse before completing)
1 REPORT NO
EPA-450/3-77-015
4 TITLE AND SUBTITLE
Addendum to User's Guide for Climatological
Dispersion Model
3 RECIPIENT'S ACCESSION NO.
5. REPORT DATE
May, 1Q77
6. PERFORMING ORGANIZATION CODE
7 AUTHOR(S)
Kenneth L. Brubaker, Polly Brown, Richard R. Cirillo
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Argonne National Laboratory
9700 South Cass Avenue
Argonne, Illinois 60439
10. PROGRAM ELEMENT NO.
2AC129
11. CONTRACT/GRANT NO.
EPA-IAG-D6-F101
12. SPONSORING AGENCY NAME AND ADDRESS
ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
Supplements A. D. Busse and J. R. Zimmerman, User's Guide for the Climatological
Dispersion Model. U.S. EPA Report No. EPA-R4-73-024, 1973.
16. ABSTRACT
Three significant new features have been added to the computer
program of the Climatological Dispersion Model: 1) a calibration package,
2) the capability of providing individual source contribution lists for
arbitrary receptors, and 3) a Larsen averaging time transformation package.
This report provides documentation for the use of the new features,
descriptions of the corresponding algorithms and guidelines for use.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
Air Pollution
Climatological Dispersion Model
Computer modeling
Computer programs
*Point sources
*Area sources
b.IDENTIFIERS/OPEN ENDED TERMS
*Air Pollution
c. COSATI Field/Group
13. DISTRIBUTION STATEMENT
Release Unlimited
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
134
20. SECURITY CLASS (This page)
Unclassified
22. PRTCE
EPA Form 2220-1 (9-73)
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