EPA-520/1-74-004
AIREM PROGRAM MANUAL
A COMPUTER CODE FOR CALCULATING DOSES,
POPULATION DOSES, AND GROUND DEPOSITIONS
DUE TO ATMOSPHERIC EMISSIONS
OF RADIONUCLIDES
U.S. ENVIRONMENTAL PROTECTION AGENCY
liice of Radiation Programs
ill
m*
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A COMPUTER CODE FOR CALCULATING DOSES,
POPULATION DOSES, AND GROUND DEPOSITIONS
DUE TO ATMOSPHERIC EMISSIONS
OF RADIONUCLIDES
J. A. Martin, Jr.
C.B. Nelson
P. A.Cuny
May 1974
LioAL PROTECTKT
013-17
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Radiation Programs
Field Operations Division
Washington, D.C. 20460
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FOREWORD
The Office of Radiation Programs carries out a national program
designed to evaluate the exposure of man to ionizing and nonionizing
radiation, and to promote the development of controls necessary to pro-
tect the public health and safety and assure environmental quality.
Office of Radiation Programs technical reports allow comprehensive
and rapid publishing of the results of intramural and contract projects.
The reports are distributed to State and local radiological health
offices, Office of Radiation Programs technical and advisory committees,
universities, laboratories, schools, the press, and other interested
groups and individuals. These reports are also included in the collec-
tions of the Library of Congress and the National Technical Information
Service.
I encourage readers of these reports to inform the Office of
Radiation Programs of any omissions or errors. Your additional comments
or requests for further information are also solicited.
W. D. Rowe, Ph.D.
Deputy Assistant Administrator
for Radiation Programs
iii
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PREFACE
As part of the Office of Radiation Programs' responsibilities to
evaluate the radiation exposure of man and his environs, the Field
Operations Division is developing a Comprehensive Dose Computational
System (CDCS) that will provide an up-to-date measure of population
dose related to sources. To achieve this goal, a large amount of data
will be organized, collated, and summarized using automated data
processing techniques.
Discharges of radioactivity to the environment from facilities in
the nuclear fuel cycle contribute to the radiation dose received by the
general population. Atmospheric diffusion is a primary pathway for the
transportation of radionuclide emissions through the troposphere to man.
Members of the general population may be exposed to radiation from
radionuclides deposited from the atmosphere onto crops and animal forage,
as well as from the airborne radionuclides directly. In some cases air-
borne emissions of radionuclides can be detected worldwide; more often
this is not the case and the consequences of a given airborne release
cannot be detected using even highly sophisticated and sensitive nuclear
instrumentation. In these latter instances, radionuclide concentrations
in the environment must be calculated in lieu of measurements.
As a first step toward the automated CDCS, this AIREM computer code
has been developed and is presently being used as a working tool to
analyze atmospheric radionuclide emissions from the nuclear fuel cycle.
The results of studies performed using this code will normally be pub-
lished in this Division's monthly publication, Radiation Data and
Reports.
Charles L. Weaver
Director
Field Operations Division
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ACKNOWLEDGEMENT
The authors wish to express their gratitude to Dorothy Mitchell
for her assistance in preparing this manuscript, to Mary Martin for
typing early drafts, and to Harold Peterson and Charles Weaver for their
support of our efforts.
vi
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CONTENTS
Page
FOREWORD iii
PREFACE v
ACKNOWLEDGEMENT vi
ABSTRACT ix
1. INTRODUCTION 1
2. DIFFUSION GEOMETRY - GENERAL 2
2.1 Diffusion Equation 5
2.2 Dry Deposition 6
2.3 Wet Deposition 6
3. DOSE CALCULATIONS - GENERAL 7
4. CALCULATIONS 8
4.1 Vertical Dispersion Coefficients 8
4.2 In-plant Holdup and Decontamination 8
4. 3 Diffusion Equation 8
4.4 Wet Deposition and Cloud Depletion 10
4.5 Organ Dose Calculations 12
4.6 Population-Dose Calculations. 14
4.7 Problem Summary 14
5. INPUT REQUIREMENTS AND DATA FORMAT 14
5.1 First Card 17
5.2 Second Card 17
5.3 Wind Rose Data 17
5.4 Population Data and Radii Limits 17
5.5 Deposition Velocities 18
5.6 Radionuclide Cards 18
5.7 User Options 19
5.8 Radionuclide Inventory and Pre-Release Filtering 19
5.9 Dose Integrals 19
6. BACKGROUND INFORMATION AND AIDS TO THE USER 20
6.1 Plume Rise - Determination of Effective Release Height... 20
6.2 Annual Average Mixing Layer Heights 20
6.3 Finite Cloud vs. Semi-Infinite Cloud Dose Calculations... 23
6.4 Sector-Averaged vs. Single Plume Dose Calculations 23
vii
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Page
6.5 Wind Speed Dependences , 23
6.6 Doses Due to Deposited Radionuclides 26
6.7 Sample Problem Description 26
6.8 Accident Problems 28
REFERENCES 30
APPENDIXES
A. AIREM Glossary, Sample Problem, and Program Listing 31
B. Dose Integral Calculations, Input Variables, Input Data De-
scription, Modified EGAD Listing, and Dose Integral Tables.... 87
TABLES
1. Classification of atmospheric stability 2
2. AIREM input card sequence and data format 15
3. Dose rate conversion factors for exposure while standing on
contaminated ground 27
4. Short sample problem description 28
FIGURES
1. Geometry of AIREM - plan view 3
2. Vertical dispersion coefficient as function of downwind dis-
tance from the source 4
3. Simplified AIREM flow diagram 9
4. Simplified illustration of deposition and depletion routine
used in AIREM 11
5. Source-depletion fraction from source heights from 10 to 100 m
above the ground and for various stability categories 13
6. Isopleths (m x 102) of mean annual morning mixing heights 21
7. Isopleths (m x 102) of mean annual afternoon mixing heights... 22
8. Comparison of external gamma whole body dose calculated using
finite and semi-infinite cloud dose models 24
9. Comparison of cloud gamma dose rate calculated using single
plume (ACRA) and sector-averaged (AIREM/EGAD) diffusion models 25
Bl. Geometry of EGAD 90
B2. Illustration of EGAD normalized dose integrals as a function
of stack height for az = 1, 10, and 100 m, and Ey = 0.08 and
0.5 MeV 91
viii
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ABSTRACT
A computer code useful for the calculation of doses to the general
population due to atmospheric emissions of radionuclides is presented
and discussed. The code is written in Fortran IV, requires 188k stor-
age, and runs in about 20 seconds on an IBM 370 system. A standard
sector-averaged gaussian-diffusion equation is solved repeatedly for
each radionuclide, wind sector, stability class and downwind distance.
Radionuclide contributions to doses to up to four critical organs are
summed and printed by sector and downwind distance. Population doses
(person-rem) are also calculated.
The code accounts for the following physical processes: cloud
diffusion, ground and inversion-lid reflections, radionuclide decay by
time of flight, first daughter-product buildup, ground deposition of
particulates and halogens (independently), cloud depletion, in—plant
holdup and decontamination factors, and sector-to-sector contributions
to external gamma dose.
The code is dose model independent in the sense that dose conver-
sion factors, provided as input data, are used for calculations of dose
that are proportional to radionuclide concentrations in the cloud, and
dose conversion tables obtained from a model that considers the finite
extent of the overhead cloud, also required as input data, are used for
calculations of whole body dose due to external gamma emitters in the
cloud. A set of dose tables obtained using one finite cloud model
(EGAD) are provided in this manual.
The code is extensively annotated and simply written, hopefully
facilitating its use. All significant parameters are fully dimensioned
and stored during a problem run. Thus, it is normally a simple matter
for the user to write out various combinations and collations of data
as desired.
ix
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A COMPUTER CODE FOR CALCULATING DOSES,
POPULATION DOSES, AND GROUND DEPOSITIONS
DUE TO ATMOSPHERIC EMISSIONS OF RADIONUCLIDES
1. INTRODUCTION
The Office of Radiation Programs is developing a Comprehensive
Dose Computational System (CDCS) for the analysis of emissions and
effluents from the nuclear fuel cycle. The AIREM code described in
this program manual represents an initial, interim version of a code
being used to calculate doses to populations due to the emission of
radionuclides to the air. The code uses a sector-averaged gaussian-
diffusion equation (1»_2) to determine radionuclide concentrations from
which doses1 (rem) and population doses (person-rem) are calculated for
up to 16 wind sectors and 12 downwind distances (192 sector-segments).
Ground deposition, cloud depletion, and first daughter product ingrowth
are considered in the calculations. In-plant holdup time and in-plant
radionuclide decontamination factors may be provided as input data if
desired. Radionuclide dose contributions are calculated for up to four
critical organs.
The code is dose model independent. It requires dose conversion
factors for each radionuclide, organ, and population group as input
data. Suggestions for deriving these factors are given in the annota-
tions to the code in appendix A. AIREM is also independent of a finite
cloud dose model; however, dose conversion tables obtained from one
finite cloud model, (EGAD), are included in appendix B. Any other
finite cloud model with a compatible output format can be used at the
users' discretion.
As presently written the printout of the program includes: the
input data, ground deposition in picocuries per square meter (if a
deposition calculation is requested by the user), organ doses and popu-
lation doses in sector-segments, and total man-rem by radionuclide. A
typical problem involving 20 radionuclides, 16 wind sectors, 12 down-
wind distances, and 6 atmospheric stability classes runs about 20
seconds on an IBM 370/155 and about 90 seconds on an IBM 360/50.
The code is composed of two basic parts: a diffusion calculation
and a dose calculation. These will be discussed generally, then
specifically.
Corresponding to common practice, dose = dose equivalent herein.
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2. DIFFUSION GEOMETRY - GENERAL
The geometry of the code is similar to a cartwheel. The geometry
is illustrated in figure 1, The release height can be either elevated
or at ground level. Winds blow the emissions down pie-shaped sectors
from the apex. The concentration of radionuclides in the sectors is
assumed to have a gaussian distribution in the vertical direction,
centered always at the effective release height (stack of vent height
plus plume rise less ground elevation), and a uniform distribution in
the horizontal direction across each sector. The standard deviation
(az) of the vertical distribution of the concentration increases mo-
notonically with downwind distance (figure 2) until az is set equal to
a fraction of the inversion layer height (3) at which point no further
diffusion of the cloud in the vertical direction is allowed. As illus-
trated in figure 2, the extent of vertical diffusion is defined by the
stability classes; the stability classes are defined by the meteorology
data in table 1. The portion of the cloud that would have existed
below the air-ground interface (if the interface were absent) is mirror
reflected and added to the concentration above the ground which doubles
the unreflected ground level concentration.
The geometry introduces a discontinuity at the edges of the sectors
since wind frequencies and stability classes may be significantly dif-
ferent in adjacent sectors. These discontinuities can be reduced by
using a large number of wind sectors in the calculations. In AIREM, up
to 16 sectors may be used. With 16 sectors large discontinuities are
rare.
Table 1. Classification of atmospheric stability
Stability
classification
Extremely unstable
Moderately unstable
Slightly unstable
Neutral
Slightly stable
Moderately stable
Pasquill
categories
A
B
C
D
E
F
oea
(degrees)
25.0
20.0
15.0
10.0
5.0
2.5
Temperature change
with height
(°C/100 m)
<-1.9
-1.9 to -1.7
-1.7 to -1.5
-1.5 to -0.5
-0.5 to 1.5
1.5 to >4.0
a
Standard deviation of horizontal wind direction fluctuation over
a period of 15 minutes to 1 hour. The values shown are averages for
each stability classification.
Reference: AEG Safety Guide 23.
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N
NNE
ME
ENE
UP TO 12
ANNULAR RINGS
J
UP TO 16 SECTORS
UP TO 6
STABILITY
CLASSES
PER SECTOR
SEGMENT
Figure 1. Geometry of AIREM - plan view
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roooh
A/
_
0)
S 100
N
b
10 H
B/" ,
••" r .••'
cx
0.1
1 10
Distance Downwind (km)
Figure 2. Vertical dispersion coefficient as function
of downwind distance from the source Q_)
100
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2.1 Diffusion Equation
The basic diffusion equation used in AIREM is a standard sector-
averaged equation (1_,.2_) modified to include radionuclide decay By time
of flight:
, \ f expr r exp(-xt)
X _ * _ /2V1 \ z
- _
u a 2ir-
z n
where:
X = ground level airborne concentration in Ci/m ,
¥ =* time integrated ground level concentration-exposure
in Ci-sec/m3,
Q1 = source release rate in Ci/s,
Q = time integrated release in Ci (i.e., total release),
f = fractional wind frequency in a sector,
r = distance from the stack in meters,
h = effective stack height in meters,
n = number of sectors,
= sector width at distance r in meters,
a = standard deviation of the vertical distribution of an
assumed gaussian cloud, in meters,
u = average wind speed in the sector in m/s,
X = decay constant of radionuclide in sec , and
t = transit time from the stack to distance r, in seconds
(« - &
AIREM calculates and prints the oz's for each downwind distance
and stability class. Equation 1 is solved for each radionuclide, each
stability class within each sector, and each downwind distance. Un-
decayed (x/Q')'s summed over stability classes are printed out. De-
cayed (x/Q')'s are not printed out because of the fact that there could
be as many as 19,200 in a problem.
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2.2 Dry Deposition
Ground dry depositions are calculated using the relation (2_) ;
Q • v • (l-e~XP)/AP (2)
where:
to = Ci/m2 deposited on the ground at end of P,
A = decay constant in inverse seconds,
v, = deposition velocity in m/sec, and
P = period of release (or one year if release period is not
specified) .
Deposition velocities for each stability class are derived by the code
using the relation:
,
+ a\ u + &2 u2 + 33 u3 (3)
where the a's are user-supplied deposition velocity coefficients. Con-
stant, linear, quadratic, and/or cubic polynomial fits to experimental
deposition velocity data are easily accommodated.
2.3 Wet Deposition
Ground deposition and cloud depletion by below cloud washout is
included as an option to the user. This option is exercised by pro-
viding the fraction of the time it rains (RAINF) and a washout factor
(WASHCO) in inverse seconds as input data. If either of these param-
eters is zero, washout will not be calculated.
Ground level activity density is calculated using the relationship:
/•- ff AQ
w(r) = A / x(z)d(z) = -^— (4)
J0
where fr = rainfall frequency (fraction) A is the washout factor and z
is the vertical coordinate. Upwind depletion of the cloud is calculated
using:
Q(r) = Qo exp(-A J) . (5)
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The AIREM output lists total activity deposited within radii and
deposition density at the end of the release period (or one year if the
release period is not specified). The latter is calculated by multi-
plying deposited activity by the relation (1 - exp(-XP)/XP) where P is
the release period.
This formulation includes washout from the cloud from the time of
release throughout its travel. It does not include washout from an
already established cloud.
3. DOSE CALCULATIONS - GENERAL
Two general classes of dose calculations are treated explicitly by
the code. These are: doses that are directly proportional to the
ground level air concentration of radionuclides, and whole body doses
due to gamma rays emitted by nuclides in the overhead cloud (cloud gamma
doses).
Doses from inhalation, external beta, and transpiration dose modes
are directly proportional to ground level radionuclide concentrations.
For these dose modes AIREM uses "dose conversion factors" (DCF's) that
relate dose rate to concentrations. The units for the DCF's used as
input must be millirem per second per curie per cubic meter. DCF's may
be derived from any appropriate model. Two simple models are discussed
in the annotations to the code in appendix A.
Cloud gamma doses are calculated using dose tables obtained from a
model that considers the finite extent of the cloud in the vertical
direction. The calculation requires two data sets: the energies and
abundances of the gamma rays emitted by the radionuclide, and a set of
dose tables which are functions of gamma energies, az's, lid height,
and stack height. The annotations to the code listing provide refer-
ences for the gamma ray groups.
Doses to up to four organs can be calculated in a single AIREM run.
The total dose to a single organ from all contributing radionuclides is
calculated and printed out. If a given radionuclide contributes to
doses for two organs, it is entered twice in the input data using dif-
ferent DCF's and is counted twice in the isotope card queue. A maximum
of 20 radionuclides can be processed in a single problem. One of the
input cards is a count of radionuclides contributing to the dose to a
single organ. The total of these counts cannot exceed 20.
For a parent-daughter radionuclide combination, it is possible to
obtain both the cloud gamma and inhalation doses in a single problem
run. Daughter nuclides must follow their parents in the nuclide queue.
To obtain all combinations of dose modes by radionuclide, two or more
problem runs must be made.
In general, contributions to dose are first summed over stability
class, then radionuclide, before printout commences.
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4. CALCULATIONS
The general flow of the calculations is illustrated in figure 3.
Detailed discussions of the calculations follow.
4.1 Vertical Dispersion Coefficients (CTZ'S)
The CTZ'S are calculated using the FUNCTION SIGZ.2 The equations
for six stability classes, 1 through 6, corresponding to Pasquill Cl_,_2)
stability classes A through F, respectively, are solved for each crz.
The functions are polynomial fits to the crz curves in figure 2. The
az's are written out by downwind distance and stability class. The oz's
are also limited to a maximum value of 10,000 meters in the FUNCTION
SIGZ subprogram unless limited to a lower value by the user by assign-
ment of a value to SIGMAX2 in the input data U ,J3). Details of calcu-
lating SIGMAX values are covered in section 6.1.
4.2 In-plant Holdup and Decontamination
If the input datum HOLDUP2 is greater than zero, all parent
nuclides are decayed in-plant before release from the stack, and user-
supplied decontamination factors are applied to each radionuclide before
release. Daughter products are grown-in during holdup. Input holdup
time and input decay constants are in days and seconds respectively.
All parent inventories are decayed by the equation:
Qp(HOLDUP) = Qp(0) • exp - (Xp • HOLDUP • 8.64 • 101*) (6)
First daughter products Qd are grown-in using the standard equa-
tion:2
Ad
-Xpt -Xdt
where t = HOLDUP • 8.64 • 101* and DECON2 is an isotope-dependent in-
plant decontamination factor greater than 1. If the resultant (Q)'s
are less than one microcurie they are set equal to zero.
4.3 Diffusion Equation
Diffusion is calculated using the sector-averaged gaussian dif-
fusion equation (reference^, eq. 3.144). The assumption is made that
within a stability class in a sector there is equal probability of the
cloud being found at any cross-wind (horizontal) location in the sector.
Except for the gaussian cloud expansion, no cross-wind components of
2See Glossary in appendix A for definition of terms.
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READ/WRITE
INPUT DATA
CALCULATE crz s
PRINT
APPLY IN-PLANT DECAY,
GROW-IN DAUGHTERS,
AND FILTER INVENTORY
BEFORE RELEASE
CALCULATE DECAYED
X/Q''s
GROW DAUGHTERS
PRINT DEPOSITION
DENSITIES
IF NDEP (LL) >0 CALCULATE
DEPOSTION & DEPLETE x/Q1's
CALCULATE ALL DOSES
PROPORTIONAL TO X
IF NWB>0 AND IF
NGAMMA (LL)>0,
CALCULATE CLOUD
GAMMA DOSES USING
THE DOSE INTEGRALS
SUM DOSES OVER
STABILITY CLASS
SUM RADIONUCLIDE
CONTRIBUTION TO
ORGAN DOSES, CAL-
CULATE POPULATION
DOSES
PRINT RESULTS
Figure 3. Simplified AIREM flow diagram
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the velocity vector, either horizontally or vertically, are allowed by
this model. This is a typical working assumption used in state-of-the-
art deterministic models used in the air pollution field.
The ratio of the ground level volume concentration x (Ci/m3) of
pollutant per curie per second release rate (Q1) in a cloud at a down-
wind range MM, for radionuclide LL, for a release height H, for sta-
bility class JJ, in sector II, is calculated by the code. The format
of the printout is normally for a 16-sector problem, but reformatting
for fewer sectors can be done for an AIREM run. However, the code
assumes that the sectors span 360 degrees.
The formulation of the x/Q* calculations include decay during time
of flight from the emission point and only in this regard does it differ
from common practice. (The user can insert a Fortran write statement
before the dose calculation program steps to obtain a listing of the
individual (x/Q')'s. However, a large amount of printout will result.)
Undecayed (x/Q')'s summed over stability class are printed out.
4.4 Dry Deposition and Cloud Depletion
Deposition velocities for each stability class are calculated using
equation 3. The areas of each sector-segment are calculated before the
deposition and cloud depletion routine is entered. Daughter products
are grown-in during time of flight and added to the decayed initial
daughter product inventory. At any distance, if the activity deposited
on the ground within a given stability class is less than 10~12 curie
it is set equal to zero.
Cloud deposition and depletion are treated using a physical model.
Deposition starts at the first (inner) radius for the first stability
class (figure 4) . The total activity deposited on the ground in the
first sec tor- segment is calculated as well as the fraction of the total
release deposited on the ground in that sector-segment. x/Q' at tne
second radius is depleted by one minus the fraction on the ground at
the first radius. This process of deposition and depletion continues
outward to the last radius in the sector. (The routine is essentially
the same as that indicated by equations 5.44 through 5.46 in refer-
ence 2^. ) For each stability class in a sector, ground deposition and
cloud depletion are calculated using the following set of recursion
formulas :
F(l) = l.
M
C - 2. - Y] F(MM)
(8)
QG(MM) = -|r(MM) • C • Q • vd • A(MM)
F(MM + 1) = QG(MM)/(Q • f) .
10
-------
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-------
Where QG(MM) is the activity deposited on the ground in the sector-
segment at distance MM, f is the wind frequency, A is the area and
indexes II, JJ, and LL have been suppressed for legibility. The calcu-
lations are performed for a single nuclide (LL), for a single stability
class (JJ), and in a single sector (II) at a time. At each downwind
distance (MM), C is tested before the deposition calculation; if C is
less than or equal to zero, x/Q' at that MM and at further downwind
distances is set to zero. If QG(MM) is less than or equal to 10~12
curie, QG(MM) is set equal to zero.
Advantage is taken of the fact that previously calculated (x/Q')'s
include depletion by time of flight decay. The recursion equations are
solved repeatedly for each stability class in each sector. The second
recursion relation assures that the total activity deposited on the
ground does not exceed that originally blown into the sector within the
stability class. (If the area of the outer sector segments are very
large and the wind speed is small the code may calculate more deposited
material than released. In this case, the user must adjust the geome-
try of the problem to avoid this type of error.)
Activity deposited within areas is then summed over sectors and
stability classes. Activity density at the end of the release period
is printed out by the code for each sector-segment. This activity is
calculated by applying the factor (1 - exp(-AP)/XP), where P is the
period of release and X is the decay constant of the radionuclide.
The accuracy of the deposition calculations is affected by the size
of the problem grid. The smaller the intervals between downwind ranges,
the more accurate will be the calculation. In test problems, excellent
results have been observed for 1 m/s wind speeds and 1 cm/s deposition
velocities, using range intervals as large as 15 kilometers. (See
figure 5 and reference 2_.)
Cloud depletion becomes less significant at higher wind speeds.
At normal wind speeds averaging 5 m/s, and for a normal mix of stability
classes, most of the emissions are blown outside a 50-mile radius, even
at release heights as low as 20 meters.
4.5 Organ Dose Calculations
Radionuclide contributions to up to any four organs are summarized
in the output. Should one of the organ doses be the whole body dose
calculated using finite cloud model dose integrals, (i.e., the cloud
gamma dose), the contributing radionuclides must be presented first in
the isotope card queue, and NGAMMA2 for all such isotopes must be
greater than zero. In such cases, the cloud gamma doses will be calcu-
lated using the listed dose integrals. If NGAMMA is zero, or if the
organ is not the first, the dose will be calculated using the semi-
infinite cloud assumption (4^,5) that dose rate is directly proportional
to ground level concentration:
12
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Q'(x)
Q'(0)
0 1
Pasquill Type C
101 10 , . 10 104
10'
i i i in ii i in inn i i i mi I 1—LJJ
10'
Q'(xl
Q'(o!
0 1
0.01
0 001
50
100m
- Pasquill Type F
i _j i i iii ill
101 102
10
104 105
Q'(x)
Q'(0)
1.0
01
0 01
0 001
- Mtleoroloiy I Atomic
X AIREM, 50 m
. Pasquill Type E
10
' 102 , , 103 10* 105
x[m]
Figure 5. Source-depletion fraction for source heights from 10 to 100 m
above the ground and for various stability categories
13
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Dose • 7- • Q • (DCF) (9)
where the units of the dose conversion factor (DCF) are mrem/s per
Ci/m3, Q is in curies, x/Q' is in s/m3, and the dose is in millirems.
Methods for obtaining the DCF's are suggested in the AIREM program
listing in appendix A. The sample problem in appendix A presents DCF's
for several radionuclides, for several organs.
Doses are calculated for each radionuclide, each sector, each sta-
bility class, and each downwind distance. These doses are available in
storage for printout, but, as presently constituted, AIREM does not
print them all. Rather, in each sector-segment the doses are first
summed over all stability classes, then over the radionuclides contribu-
ting dose to the same organ. The resulting total doses in each sector-
segment are printed by AIREM. (Even though some or all of the cloud
gamma doses may be calculated using the finite cloud dose integrals, the
DCF's are all printed out in the summary tables of radionuclides con-
tributing to the organ dose.)
4.6 Population-Dose Calculations
For population-dose calculations use is made of the doses already
summed over stability classes and contributing radionuclides in each
sector-segment. The contribution to the total population dose from each
sector-segment is merely the product of the dose and the population in
the sector-segment. Population doses are added within each annular ring
and the accumulated (running total) population dose vs. distance is cal-
culated. Both sector-segment and running total population dose are
printed by the code. This procedure is repeated for each of the remain-
ing organs if more than one organ dose is calculated.
Finally, a table of radionuclide contributions to the population
dose is generated and printed out.
4.7 Problem Summary
At the end of the last tabular dose listing, a few key parameters
identifying the problem run are printed out. These, plus the listing of
the radionuclides contributing to the doses should highlight any gross
errors in the input data. The input data is also listed to identify the
total problem being run. The authors believe the latter to be highly
desirable because of the large amount of data required to run the pro-
gram. For the same reason, the technique of writing out input data
immediately after reading it in (not normally done) has proved useful
in debugging input data.
5. INPUT REQUIREMENTS AND DATA FORMAT
Some 200 lines of input data are required to run AIREM. Through
coding, a variety of options are available to the user. Because of
14
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Table 2. AIKEM input card sequence and data format
Card sequence Columns
1 card 2-20
21-25
27-30
31-35
37-40
41-45
46-55
1 card 2- 5
6-10
11-15
16-20
21-30
31-40
41-50
51-60
61-70
Title
Facility name
No. months of data
Beginning month
Beginning year
Ending month
Ending year
Thermal energy generated (MWD)
No. sectors (I) (16 max.)
No. classes (J) (6 always)
No. radii (M) (12 max.)
No. isotopes (L) (20 max.)
Stack height (m)
SIGMAX3 (m)
In-plant holdup time (d)
Rainfall frequency (fraction)
Washout factor (1/s)
Format
5A4
F5.0
IX, A4
15
1X.A4
15
F10
15
15
15
15
F10
F10
E10
E10
E10
I cards 1-60
I cards 1-60
M cards (I<8) 1-80
2M cards (I>8)
M cards 1-30
4 cards 1-60
4 cards 1-60
1 card 1-20
Wind frequencies by stability 6F10
class (%), 10 columns each
Wind speeds by stability class 6F10
(m/s), 10 columns each
Annular ring population, 8 sec- 8F10
tors to a card, 10 columns
each
Midpoint, lower and upper radii 3F10
(m), 10 columns each
"Particulate" deposition ve- 6E10
locity coefficients, 10
columns each
"Halogen" deposition velocity 6E10
coefficients, 10 columns each
Number of sets of isotopes per 415
organ (up to 4 organs and 20
nuclides), 5 columns each
See footnote at end of table.
15
-------
Table 2. AIKEM input card sequence and data format—continued
Card sequence Columns Title Format
L sets of isotope cards (two to four cards per nuclide):
1st card 2- 5 Isotope symbol IX,A4
7-10 Atomic weight 1X,A4
11-15 Critical organ 1X,A4
16-25 Dose conversion factor FlO
(mrem/s per Ci/m3)
26-35 Decay constant (s"1) E10
36-40 Deposition call code 15
0 for gases
1 for particulates
>2 for halogens
41-45 Finite cloud call code: 0 for 15
semi-infinite cloud approxi-
mation; <10 for finite cloud
calculation using the dose
integrals; used only when
NWB>0.
46-50 Daughter call code: 0 for 15
parent; 1 if parent is pre-
ceding set of isotope cards.
2nd card or 1-72 If NGAMMAa >0, NGAMMA pairs of 12F6
2nd & 3rd cards lines (MeV) and abundances,
up to 10 pairs, 6 columns per
item
2nd, 3rd, or 1-10 Curies of isotope LL in inven- FlO
4th card(s) tory
11-20 In-plant decontamination factor E10
(greater than or equal to 1);
a blank defaults to 1.
aSee Glossary in appendix A for definition of terms.
Note: After the full queue (up to 20 sets of isotope cards), add
dose integrals title card and dose integrals to rear of data deck if
finite cloud gamma doses are to be calculated, otherwise add 8 blank
cards.
16
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these factors a detailed discussion of the input data deck is presented
here. However, the information given in table 2 and the input data
format illustrated in the sample problem printout in appendix A should
suffice for most applications.
5.1 First Card
The thermal-energy-generated datum is obviously meant for nuclear
power plant applications. No calculations are made using this number;
it is merely printed out in the problem summary (it may be left blank).
5.2 Second Card
No. classes refers to the number of stability classes; this should
always be 6. Stability classes are defined by the az's used in the
diffusion calculation; these are displayed in figure 2. Stability
classes A through F are numbered 1 to 6, respectively. No. radii refers
to the number of downwind distances for which calculations are desired.
This cannot be greater than 12. SIGMAX should be 0.8 times the height
of the inversion layer (3). Section 6.2 includes a further discussion
of this parameter.
5.3 Wind Rose Data
Wind frequencies (%) and wind speeds (m/s) are entered in a clock-
wise direction beginning with the north sector. For a 16-sector prob-
lem, 16 frequency and 16 speed cards are required. Note that most
meteorological summaries list wind roses as directions from which the
wind blows while the direction 'blown to is required here. Each card in
the frequency and speed queues may contain up to six numbers—one for
each of up to six stability classes, for each sector. Any of these
data may be left blank by the user.
Calculations derived from data on the first cards in these queues
will be printed under the north headings. Since the printout formats
presume a 16-sector problem, some shifting of data with respect to
column headings will occur if fewer sectors are run. (Since AIREM
assumes 360 degree geometry, sectors will be 22.5 degrees for 16 sec-
tors, 45 degrees for 8 sectors, etc.)
5.4 Population Data and Radii Limits
Population data are entered clockwise starting in the north sector
and within the inner ring. For a 16-sector, 10-radii problem, 32 cards
are required.
The definition of the midpoint, lower and upper bounds of the
sector-segments establish the radial grid for the problem (see figure 1).
For a 10-radii problem, 10 cards are required. The minimum midpoint
radius that can be used is 100 meters.
17
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5.5 Deposition Velocities
Deposition velocity coefficients are entered as 24 numbers for
each of two types of deposition (particulate and halogen).
Deposition velocity coefficients, vd, are assumed to be of the
form:
KOF
where ui,j is the (average) wind speed in stability class j in sector i;
an,j's are KOF expansion coefficients for stability class j; and vd,j
is the deposition velocity (m/s) for stability class j. In AIEEM nmax =
KOF = 4.
The input data format is simple. All constant terms appear on the
first card, linear terms on the second card, quadratic on the third,
and cubic on the fourth. Eight cards are required. The first four are
for particulate expansion coefficients and the second four for halogen
expansion coefficients. Thus, if only the constant value 0.01 m/s is
applied for all cases, 0.01 appears six times on the first and fifth of
eight cards. The other six cards are blank in this case. The program
listing in appendix A contains a further description of how v
-------
No calculations are performed on the isotope symbol, atomic weight,
and critical organ descriptions. Since only four spaces are provided
to describe the critical organ, either numbers or cryptic symbols must
be used. For example, the dose to an adult thyroid due to inhalation
could be cryptically described by IATY, or a number, at the user's
choice. XBS could cryptically describe the skin dose due to external
beta particles in a cloud. The dose conversion factor (DCF) must per-
tain to the desired organ dose and sample population. The units of the
dose conversion factor are mrem/s per Ci/m3.
Two to four cards per radionuclide are required. Only two cards
are required if the semi-infinite cloud approximation is appropriate
for the dose calculation. For finite cloud whole body dose calculations
three or four cards are required. The second or second and third
card(s) contain NGAMMA energy and abundance pairs. Two gamma energy
and abundance cards are required if NGAMMA exceeds 6. NGAMMA cannot
exceed 10.
5.7 User Options
The numbers in columns 36-40, 41-45, and 46-50 on the first card
af a radionuclide card set must be right-adjusted. Columns 36-40 may
be left blank if deposition is not requested. If a 1 appears in
column 40, the "particulate" deposition velocity coefficients will be
used to calculate dry depositions; if the number is greater than 1, the
"halogen" deposition velocity coefficients will be used. If columns
41-45 are blank or zero, the dose conversion factor in columns 16-25
will be used for the dose calculation. If the isotope card belongs to
the first organ set in the queue, and if a number NGAMMA between 1 and
10 appears in columns 41-45 on an isotope card, doses will be calculated
using the finite cloud dose integrals. NGAMMA is the number of gamma
lines to be used in the finite cloud gamma dose calculation for this
particular radionuclide. If NGAMMA is not zero, the gamma lines (MeV)
and their abundances (gammas per disintegration) are read in pairs on
the next, or next two cards (two cards are required if NGAMMA is greater
than 6).
5.8 Radionuclide Inventory and Pre-Release Filtering
The last card in each of the sets of two to four isotope cards
contains the total activity (curies) in inventory and an in-plant decon-
tamination factor. The decontamination factor is a number equal to or
greater than 1. If DECON is zero or blank, DECON will automatically
default to 1.
5.9 Dose Integrals
Following the isotope card queue is the set of finite cloud dose
integral cards, beginning with a title card. If only semi-infinite
cloud calculations are performed, these may be skipped and eight blank
19
-------
cards substituted. The format for the dose integral cards is explained
in appendix B.
Last are the job control cards /* and //, announcing the end of
the data deck.
6. BACKGROUND INFORMATION AND AIDS TO THE USER
As an aid to the user, several examples and suggestions regarding
the use of the AIREM code are presented in this section.
6.1 Plume Rise - Determination of Effective Release Height
Of a variety of plume rise equations to be found in the'literature,
those of Briggs (6^) are the most extensive and exhaustive. Briggs1
formulation accounts for plume rise as a function of downwind distance,
stability class, and height of inversion layers. Estimates of plume
rise based upon Briggs' equations, for operating boiling water nuclear
power reactors, are presented in reference J3. Dose integrals are in-
cluded in appendix B for Heff's of 0, 10, 50, 75, 100, 120, 150, and
200 m. Alternatively a new set of dose integrals can be generated by
the user using the modified version of EGAD listed in appendix B.
6.2 Annual Average Mixing Layer Heights
An estimate of the annual average height of the mixing layer
at a given locale may be obtained using figures 6 and 7 taken from
reference _3. SIGMAX in AIREM should be set at approximately 0.8
consistent with the available dose integral sets.
An estimate of H-! „. A can be obtained from:
2. II . U
"am "-pm
= H + H_ '
am pm
where Ham and Hpm are the mean annual morning and afternoon mixing
heights obtained from figures 6 and 7.
The value used for SIGMAX based on a daytime lid will normally ex-
ceed 500 meters. Since classes D through F have crz's which are less
than 500 meters at distances up to 100 kilometers, only stability
classes A through C are normally affected by a lid. At night an in-
version extends down to the ground for E and F stabilities. Under these
conditions there is no lid, but since SIGMAX will be greater than any
crz calculated for these stabilities it is not necessary to treat them
separately. In short, the daytime lid provides a reasonable bound for
the conditions which are affected by a lid and does not disturb those
which are not. For a mixture of stability classes the dose calculations
are not very sensitive to the presence or absence of a lid.
20
CLD
-------
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-------
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en
•4->
.c
O>
cu
CD
X
o
o
c
cu
re
re
(O
cu
CVl
o
X
J=
I/)
.c
+->
O)
O-
o
in
r--.
£
3
CD
22
-------
6.3 Finite Cloud vs. Semi-Infinite Cloud Dose Calculations
The assumption of a semi-infinite cloud (2,.4_,_5) has been used to
calculate cloud gamma doses. For comparison, the difference between
doses calculated using EGAD finite cloud dose model and doses calculated
using the semi-infinite cloud assumption is displayed in figure 8. As
expected, the difference is small at large distances from the release
point since by then the cloud has expanded considerably. At intermedi-
ate ranges, the semi-infinite cloud assumption overestimates the dose
since it assumes that the concentration everywhere is identical to the
ground level concentration, whereas the concentration actually dimin-
ishes with height. At close distances the semi-infinite cloud assump-
tion results in a very low ground level concentration and gross under-
estimates of doses since it ignores gamma rays emanating aloft.
6.4 Sector-Averaged vs. Single Plume Dose Calculations
Since AIREM utilizes a sector-average diffusion equation, it can-
not be used to obtain accurate results for a single plume. The differ-
ences between results calculated using sector-averaged and single plume
models are illustrated in figure 9. At large ranges, the sector-
averaged diffusion equation (assuming a 22.5 degree sector) leads to
calculated doses that are lower than for the single plume. This is
because the sector-averaged diffusion equation spreads the activity
(pollutant) fully and equally across the sector at all heights. Con-
versely, the single plume model restricts the crosswind horizontal
spread of the plume. Thus, the single plume model results in higher
centerline doses.
At close distances, the EGAD assumption that concentration varies
only in the z direction results in a higher calculated dose.
6.5 Wind Speed Dependences
As with many codes, AIREM uses an average wind speed in the dif-
fusion equation. This poses a difficulty since the diffusion equation,
which includes radionuclide decay by time of flight, is a transcendental
function with five variables: (1) radionuclide (half-life), (2) down-
wind distance, (3) sector, (4) stability class, and (5) wind speed group
within a stability class (e.g., 0-1, 1-3, 3-5, etc., m/s intervals).
Since the full equation is not linear in u or 1/u, it is not possible
to compute an average wind speed which provides the exact decay correc-
tion. In practice, the average wind speed for stability class j in
sector i is obtained using the equation:
where k is the index for the wind speed groups.
23
-------
10
0.1
.01
STACK HEIGHT • 120 M
STABILITY CLASS • D
BWR RADIOISOTOPE MIX
WIND FREQUENCY - 2.76%
WIND SPEED • 6.76 m/s
-FINITE CLOUD
SEMI-INFINITE CLOUD—i
100
1,000 10,000
DISTANCE FROM STACK
(IN METERS)
100,000
Figure 8. Comparison of external gamma whole body dose calculated
using finite and semi-infinite cloud dose models
24
-------
10
D
iren
1.0
Class D Stability
u = 5 m/s
Heff = 10° m
f « 1007.
88,
100 uCi/sec release of 8BKr
Single Plume (ACRA)
Sector-
Averaged
(AIREM/EGAD)
0.1
88
Rb (AIREM/EGAD)
0.1
1.0
Downwind Distance (km)
Figure 9. Comparison of cloud gamma dose rate calculated
using single plume (ACRA) and sector-averaged (AIREM/EGAD)
diffusion models
25
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The sample problem in appendix A illustrates the sensitivity of
calculated doses to wind speed. The dependence is almost hyperbolic
for a normal BWR radionuclide mix for normal wind speed variations (4
to 8 m/s), at short ranges. This is an artifact of the sample problem,
because the lower wind speeds, although providing less ventilation,
provide more time for short half-lived radionuclides to decay and vice
versa. For the long half-lived radionuclides the diffusion equation
is not transcendental and the average as defined above is mathematically
correct.
6.6 Doses Due to Deposited Radionuclides
Doses due to radionuclides deposited on the ground may be of par-
ticular interest to users of this code. AIREM prints out the activity
density (pCi/m2) on the ground at the end of the release period. This
can be the starting point for dose calculations for the milk, food crop,
and direct radiation pathways. The treatment of these pathways is
beyond the scope of this manual. As an aid to the user, table 3 (£)
lists some dose conversion factors for skin and whole body doses due to
standing in a radionuclide-contaminated field. Reference 9_ also in-
cludes a detailed discussion of food pathways.
6.7 Sample Problem Description
The sample problem was devised to illustrate the effects of sta-
bility class and wind speed variations on doses, population doses, and
ground depositions. A 100-meter effective stack height was assumed.
Populations were assumed to be distributed in direct proportion to the
areas of the sector-segments. A wind frequency of one percent for all
sectors, with only one stability class in each sector, was used. An
illustrative set of radionuclides was chosen and released in equal
quantities without holdup inplant. Two daughter products were grown-in
during time of flight. Cloud gamma and skin doses were calculated to
illustrate the finite cloud and semi-infinite cloud dose model assump-
tions. Table 4 illustrates the major parameters used. Included in
appendix A is a coded input data form.
Certain table captions and footnotes require some explanation. The
activity density on the ground is the activity density at the end of the
release period or one year if the release period is not specified. For
dry deposition, the total activity dispersed is the activity presented
as input times the sum of the wind frequencies. For wet deposition, the
total activity dispersed is the input activity times the sum of the wind
frequencies, times the rainfall frequency. In the dose printout tables
the DCF's are printed out even if the dose integrals are used. In these
tables, the activities listed are input activities modified by in-plant
decay or growth during holdup and in-plant filter decontamination fac-
tors. Recognition of these factors can be a debugging aid.
26
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Table 3. Dose rate conversion factors for exposure
while standing on contaminated ground (9)
(mrem/h per pCi/m3)
Nuclide
3H
^C
22Na
2»Na
51Cr
5V
55Fe
59Fe
58Co
6°Co
63Ni
<*Cu
65Zn
88Rb
89Sr
90Sr
95Zr
95Nb
Skin
0
0
1.8 E-8
2.9 E-8
2.6 E-10
6.8 E-9
0
9.4 E-9
8.2 E-9
2.0 E-8
0
1.7 E-9
4.6 E-9
4.0 E-9
6.5 E-13
0
6.2 E-9
6.8 E-9
Total body
0
0
1.6 E-8
2.5 E-8
2.2 E-10
5.8 E-9
0
8.0 E-9
7.0 E-9
1.7 E-8
0
1.5 E-9
4.0 E-9
3.5 E-9
5.6 E-13
0
5.9 E-9
5.8 E-9
Nuclide Skin
103Rua 4.2 E-9
106Rua 1.8 E-9
132Te 2.0 E-9
129I 9.6 E-12
131la 3.4 E-9
132I 2.0 E-8
133I 4.5 E-9
135I 1.4 E-8
138Cs 2.4 E-8
13I*Cs 1.4 E-8
137Cs 4.9 E-9
lf+0Ba 2.4 E-9
1HQT „ 1 -7 IT Q
La _L . / t— o
llflCe 6.2 E-10
i^Ce 1.4 E-10
(l^Pr) (2.3 E-10)
(llfl*Ce + (3.7 E-10)
Total body
3.6 E-9
1.5 E-9
1.7 E-9
7.0 E-12
2.8 E-9
1.7 E-8
3.7 E-9
1.2 E-8
2.1 E-8
1.2 E-8
4.1 E-9
2.1 E-9
1.5 E-8
5.5 E-10
1.2 E-10
(2.0 E-10)
(3.2 E-10)
Includes daughter radiations.
Use these factors for llfltCe unless lltl+Pr daughter concentration is
given separately.
27
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Table 4. Short sample problem description
Sector
number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Notes: 1.
2.
3.
4.
5.
Accident Problems
Sector Stability
class
N A 2
NNE B 2
NE C 2
ENE D 2
E E 2
ESE F 2
SE B 5
SSE C 5
S D 5
SSW E 5
SW F 5
WSW B 10
W C 10
WNW D 10
NW E 10
NNW F 10
Class A = 1, B = 2, etc. Class A
is most highly diffused.
Sector is direction wind blows to
All frequencies are 1 percent.
Deposition velocities = 0.5 and 2
(for comparative illustration) .
Rainfall frequency = 5 percent;
washout factor = 2 x 10-Vs.
6.8
AIREM can be used to study the approximate effects of an acci-
dental release of radioactivity. Releases can be propagated down a
single 22.5 degree sector, for example. Since AIREM always assumes a
360 degree problem, the number of sectors (L) must be 16 in such, a case.
Given a single release inventory, several sets of meteorological con-
ditions and populations may be analyzed in different sectors in one run,
28
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making certain parametric studies rather simple to do. For a short
term or puff release, calculated doses will be low relative to doses
calculated using a single plume model that restricts the cross-wind
horizontal spread of the cloud. This is because the diffusion equation
in AIREM spreads the activity uniformly across a sector. However, if
an accidental release occurs over a long time period (e.g., over several
hours), AIREM calculations may be more realistic since the wind would
probably meander during the release period. A single plume model would
calculate doses that would be too high in this case. For the case of a
strong wind shift during the release period, wind direction invarient
codes (such as AIREM) are inapplicable.
Since the printout format was devised for routine releases, which
are orders of magnitude less than for accident cases, the accident
radionuclide inventories may cause overflows in the printout. Accident
problems should be scaled down if AIREM is used for such analyses.
29
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REFERENCES
(1) TURNER, D. BRUCE. Workbook of atmospheric dispersion estimates,
Publication No. AP-26. U.S. Environmental Protection Agency, Office
of Air Programs, Research Triangle Park, N.C. 27711 (July 1971).
(2) SLADE, D. H., Editor. Meteorology and atomic energy, 1968, TID-
24190. National Technical Information Service, Springfield, >Va.
22151 (July 1968).
(3) HOLZWORTH, G. C. Mixing heights, wind speeds and potential for
urban air pollution throughout the contiguous United States, Publi-
cation No. AP-101. U.S. Environmental Protection Agency, Office of
Air Programs, Research Triangle Park, N.C. 27711.
(4) U.S. ATOMIC ENERGY COMMISSION. Safety guide 3, Assumptions used
for evaluating the potential radiological consequences of a loss of
coolant accident for boiling water reactors, November 2, 1970. (Re-
issued as Regulatory Guide 1.3, June 27, 1973.)
(5) INTERNATIONAL COMMISSION ON RADIOLOGICAL PROTECTION. Report of ICRP
Committee II on permissible dose for internal radiation, ICRP Publi-
cation No. 2. Pergamon Press, New York, N.Y. (1959), (cf. Publi-
cation No. 6. also).
(6) BRIGGS, G. A. Plume rise, TID-25075. U.S. Atomic Energy Commission
Critical Review Series. National Technical Information Service,
Springfield, Va. 22151 (November 1969).
(7) BRIGGS, G. A. Some recent analyses of plume rise observations.
NOAA Research Laboratories, Oak Ridge, Tenn. (December 1970).
(8) MARTIN, J. A. and C. B. NELSON. Calculations of doses and popula-
tion dose in the general environment due to boiling water nuclear
power reactor radionuclide emissions in the United States in 1971.
To be published in Radiation Data and Reports.
(9) FLETCHER, J. F. and W. L. DOTSON. Hermes—a digital computer code
for estimating regional radiological effects from the nuclear power
industry, HEDL-TME-71-168, UC-80. Hanford Engineering Development
Laboratory, Richland, Wash. (December 1971).
30
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APPENDIX A
AIREM Glossary, Sample Problem, and Program Listing
-------
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GLOSSARY
Term
ABUN(LL,NL)
AGAM(LL.NL)
AREA (MM)
BONDOS(MM,II)a
CHIOQ(MM,II,JJ,LL)
CRTORG(LL)
DCF(LL)
DECON(LL)
DI
DISUM
DMIJL(MM,II,JJ,LL)
DMIL
DOSEI
DPBON(MM,II)
DPBONM(MM)
DPL(LL)
Definition
Absolute abundance of line NL for nuclide LL
Gamma energy in MeV of line NL for nuclide LL
Area of sector-segment MM in square meters
Bone dose at radius MM, in sector II, summed
over all contributing nuclides and stability
classes
Ratio of concentration to release rate
Critical organ
Dose or dose commitment conversion factor
Inplant filter decontamination factor. If
DECON = 0 it is set to unity (DECON >!.).
Interpolated dose integral
DI • ABUN(LL,NL)
Dose at radius MM in sector II and stability
class JJ, due to radionuclide LL
DMIJL summed over stability classes
Dose integral (rad m2 • Ci"1 • s"1)
Bone man-rem at radius MM, in sector II
Sum of bone man-rem within radius MM
Population dose due to radionuclide LL
See footnote at end of Glossary.
33
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Term
DPSKN(MM,II)
DPSKNM(MM)
DPTHY(MM,II)
DPWB(MM,II)
DPWBM(MM)
ETHEKM
F(MM)
FACIL-FACIL5
FREQ(II,JJ)
GAMEN(NG)
H
HDEPV(II,JJ)
HOLDUP
HV(JJ,KOF)
I
II
ISO(LL)
J
JJ
Description
Skin man-rem at radius MM in sector II
Sum of skin man-rem within radius MM
Thyroid man-rem at radius MM in sector II
Whole body man-rem at radius MM in sector II
Whole body man-rem within radius MM
Thermal energy generated
Fraction of curies deposited on the ground in
a sector-segment within one stability class.
(Only the last set calculated will be in
storage at the end of the run.)
Facility description (name, etc.)
Frequency that the wind blows in sector II in
stability class JJ (not direction from)
Gamma energy in MeV corresponding to DOSEI(NG,
NS)
Height of release in meters
"Halogen" deposition velocity in m/s
Holdup time in days
Halogen deposition velocity expansion co-
efficient
Indicator of number of wind sectors
Sector index (1 = N, 2 = NNE, etc.)
Isotope symbol
Indicator of number of stability classes used
(must be 6)
Index for stability class (1 - A, 2 = B, etc.)
See footnote at end of Glossary.
34
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Term
Description
KKOF
KOF
L
LATWT(LL)
LL
M
MM
MONTHS
MONTH1
MONTH2
NBON
NDEP(LL)
NDTR(LL)
NG
NGAM
NGAMMA(LL)
PDEPV(II,JJ)
Number of terms (=4) in the polynomial expan-
sion of deposition velocities as a function
of windspeed and stability class
Index for KKOF
Indicator of number of radionuclides con-
sidered (20 max.)
Atomic weight
Index used for radionuclide
Indicator of radial distances considered
(12 max.)
Index for M
Number of months of operation
Beginning month of operation
Ending month of operation
Number of cards in the isotope card queue for
which doses will be summed for bone
Deposition code for gases, particulates and
halogens (0, 1, 2, respectively)
Equals 0 if nuclide is a parent and equals 1
if nuclide is a daughter of the preceding
nuclide
Index for GAMEN
Maximum value of NG
Number of gamma lines considered for each
nuclide in a finite cloud gamma dose calcula-
tion. If NGAMMA = 0 the DCF will be used
(NGAMMA <10.).
"Particulate" deposition velocity in m/s
See footnote at end of Glossary.
35
-------
Term
POP(MM,II)
PV(JJ,KOF)
QG(MM,JJ)
QGAIML(II,MM,LL)
QL(LL)
SIGMAX
SIGMZ(JJ.MM)
SIGZ
SKNDOS(MM,II)a
THYDOS(MM,II)a
TOTFREQ
TOTPOP
TQG
TQM (MM)
UBAR(II,JJ)
WBDOS(MM,II)a
X(MM)
Description
Population in a given wind sector and distance
Particulate deposition velocity expansion
coefficient
Curies deposited on the ground in a sector-
segment for a given stability class
Picocuries per square meter of nuclide LL
deposited on the ground at radius MM
Curies of radionuclide LL in inventory before
HOLDUP and DECON(LL) are applied
Maximum value of SIGMZ for x/Q' calculation
Vertical dispersion parameters (meters)
FUNCTION subprogram that calculates the SIGMZ
(JJ,MM)'s
Skin doses summed at radius MM in sector II
Thyroid dose at radius MM in sector II summed
over all contributing nuclides and stability
classes
Total of wind frequencies
Total population
Total curies on the ground within upper radius
Total curies per square meter deposited on the
ground within XUP(MM)
Average wind speed in sector II for stability
class JJ (m/s)
Whole body dose at radius MM in sector II,
summed over all contributing nuclides and
stability classes
Radial distance from the release point to the
midpoint of an annulus (meters)
See footnote at end of Glossary.
36
-------
Term Description
XLMDA(LL) Decay constant for parent and daughters in
s~l. XLMDA for parent and daughter must not
be equal.
XLOW(MM) Lower limit to radial bin MM
XUP(MM) Upper limit to radial bin MM
aThe prefixes BON, SKN, THY, and WB are cryptic only; they may
represent any four critical organs, all alike if desired.
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-------
APPENDIX B
Dose Integral Calculations, Input Variables,
Input Data Description, Modified EGAD Listing,
and Dose Integral Tables
-------
-------
DOSE INTEGRAL CALCULATIONS
For the calculation of whole body doses due to gamma rays emanating
from radionuclides in the overhead airborne cloud (cloud gamma doses),
AIREM can utilize dose integrals obtained from a model that considers
the finite extent of the cloud. A set of dose integrals obtained from
one such model is included in this Appendix, as well as a short discus-
sion and listing of the code used to generate the dose integrals.
Gamma doses are calculated using a sector-average diffusion model
based on a crosswind integrated gaussian plume constrained between the
ground and an inversion lid. A slightly modified and corrected version
of Cooper's EGAD code (Bl) may be used to produce a table of dose inte-
grals appropriate to the effective stack height and lid height (HI^)
for the facility. The table of dose integrals is interpolated by AIREM
for specific gamma energies and vertical dispersion coefficients. The
energy and dispersion values used in generating the table are approxi-
mately logrithmic in sequence.
Cooper's original program has been modified so that vertical dis-
persion parameter az values are input data rather than program generated
values. Cooper assumes a concentration which is uniform in the hori-
zontal plane and gaussian with reflections from the ground and lid in
the vertical direction. The geometry of EGAD is illustrated in fig-
ure Bl. Buildup factors are calculated using a third order polynomial
fitted to experimental data. The three-dimensional integration is re-
duced to two dimensions by an explicit integration in one direction in
terms of modified Bessel functions. The remaining integrations are
performed by gaussian quadrature.
The assumption that the horizontal concentration is uniform means
that the dose contribution from an adjacent sector will be accounted
for as if it had the same concentration distribution as the sector of
interest. Contributions from adjacent sectors are seldom a considera-
tion at distances greater than 1000 meters. If one is dealing with a
uniform wind rose, calculations based on dose integrals (DI's) are valid
for distances greater than 200 meters from a 100-meter stack. Varia-
tions in the parameter DI/E (where E is the gamma energy in MeV) with
stack height and az's are illustrated in figure B2. Dose integral
tables for typical effective release heights are presented in this
Appendix.
In AIREM, cloud gamma doses are calculated using the dose integral
tables if NWB>0, and if NGAMMA is greater than zero on a radionuclide
card; otherwise, the dose conversion factor on the card will be used
for the calculations.
Note that cloud depletion by deposition is not considered in EGAD.
For normal wind speeds (~5 m/s), deposition velocities less than 1 cm/s
and a mixture of stability classes, this does not represent a major
source of error.
89
-------
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-------
10
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CM
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2
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10'
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0.08
I
0.08
I
100 200
STACK HEIGHT (M)
-------
INPUT VARIABLES
Definition
Card type 1. Eighty characters are read into TITLE and become a
heading for the printed output and the first card
for the punched output.
Card type 2. NGAM is the number of gamma energies which will be
used to generate the dose integral table 1
-------
REFERENCES
(Bl) COOPER, R. E. EGAD - A computer program to compute dose integrals
from external gamma emitters, DP-1304 (TID-4500, UC-32). E. I.
DuPont de Nemours & Company, Savannah River Laboratory, Aiken, S.C.
29801 (September 1972).
(B2) U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE. Radiological
health handbook, revised edition. U.S. Department of Health.,
Education, and Welfare, Rockville, Md. 20852 (January 1970).
(B3_) U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE. Radiological
health handbook, revised edition. U.S. Department of Health,
Education, and Welfare, Rockville, Md. 20852 (January 1970) p. 140.
93
-------
EGAD INPUT DATA DESCRIPTION
Card type 1. List: TITLE
Format: 20A4
Columns 1-80, TITLE = heading for output
Number of cards: 1
Card type 2. List: NGAM, NSIG, NFLG
Format: 2014
Columns 1- 4, NGSM = number of gamma energies in the
gamma data table
Columns 5- 8, NSIG = number of oz's
'0 - print but do not punch
dose integral table
Columns 9-12, NFLG
|l - print and punch dose
integral table
Number of cards: 1
Card type 3. List: GAMEN(I), GMU(I), GNU(I), [COF(J,I), J-1,3]
Format: 8E10.4
Columns 1-10, GAMEN(I) = gamma energy in MeV
Columns 11-20, GMU(I) = mass attenuation coeffi-
cient v/P for air in cm2/g
Columns 21-30, GNU(I) = mass energy absorption co-
efficient yetl/P for muscle
in cm2/g
Columns 31-40, COF(1,I)) . . , ... . fc
/n -, /i en /WP^O T\ ( polynomial coeffxcients
Columns 41-50, COF(2,I) > = * J' .,, _ ^
n i ci c.t\ nm?f-> -r\ I f°r buxldup factor
Columns 51-60, COF(3,I);
Number of cards: NGAM (1 for each energy in table)
Card type 4. List: [SIGMZ(I), 1=1, NSIG]
Format: 8E10.4
SIGMZ(I) = vertical dispersion, az, in meters
Number of cards: NSIG
94
-------
Card type 5.
List: HS, HL, SGMX,
Format: 8E10.4
Columns 1-10, HS
Columns 11-20, HL
Columns 21-30, SGMX =
Columns 31-40, RHO
Number of cards: 1
RHO
= effective stack height in
meters
1 mixing lid height in meters
: critical value for az in
meters. If az >SGMX, a uni-
form concentration between the
ground and the lid is used to
calculate the corresponding
dose integrals. Typically,
SGMX =2. • HL.
: density of air in g/m^
95
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§*•• a ••• a ••• a •••
-------
THE ABSTRACT CARDS accompanying this report
are designed to facilitate information retrieval.
They provide suggested key words, bibliographic
information, and an abstract. The key word con-
cept of reference material filing is readily
adaptable to a variety of filing systems ranging
from manual-visual to electronic data processing.
The cards are furnished in triplicate to allow
for flexibility in their use.
-------
A COMPUTER CODE FOR CALCULATING DOSES, POPULATION DOSES,
AND GROUND DEPOSITIONS DUE TO ATMOSPHERIC EMISSIONS OF
RADIONUCLIDES, EPA-520/1-74-004, May 1974. J. A.
Martin, Jr., C. B. Nelson, and P. A. Cuny.
ABSTRACT: A computer code useful for the calculation
of doses to the general population due to atmospheric
emissions of radionuclides is presented and discussed.
The code is written in Fortran IV, requires 188k stor-
age, and runs in about 20 seconds on an IBM 370 system.
A standard sector-averaged gaussian-diffusion equation
is solved repeatedly for each radionuclide, wind sec-
tor, stability class and downwind distance. Radio-
nuclide contributions to doses to up to four critical
organs are summed and printed by sector and downwind
(over)
A COMPUTER CODE FOR CALCULATING DOSES, POPULATION DOSES,
AND GROUND DEPOSITIONS DUE TO ATMOSPHERIC EMISSIONS OF
RADIONUCLIDES, EPA-520/1-74-Q04, May 1974. J. A.
Martin, Jr., C. B. Nelson, and P. A. Cuny.
ABSTRACT: A computer code useful for the calculation
of doses to the general population due to atmospheric
emissions of radionuclides is presented and discussed.
The code is written in Fortran IV, requires 188k stor-
age, and runs in about 20 seconds on an IBM 370 system.
A standard sector-averaged gaussian-diffusion equation
is solved repeatedly for each radionuclide, wind sec-
tor, stability class and downwind distance. Radio-
nuclide contributions to doses to up to four critical
organs are summed and printed by sector and downwind
(over)
A COMPUTER CODE FOR CALCULATING DOSES, POPULATION DOSES,
AND GROUND DEPOSITIONS DUE TO ATMOSPHERIC EMISSIONS OF
RADIONUCLIDES, EPA-520/1-74-004, May 1974. J. A.
Martin, Jr., C. B. Nelson, and P. A. Cuny.
ABSTRACT: A computer code useful for the calculation
of doses to the general population due to atmospheric
emissions of radionuclides is presented and discussed.
The code is written in Fortran IV, requires 188k stor-
age, and runs in about 20 seconds on an IBM 370 system.
A standard sector-averaged gaussian-diffusion equation
is solved repeatedly for each, radionuclide, wind sec-
tor, stability class and downwind distance. Radio-
nuclide contributions to doses to up to four critical
organs are summed and printed by sector and downwind
(over)
-------
distance. Population doses (man-rem) are also calcu-
lated.
KEY WORDS: Atmospheric diffusion; computer code; com-
puter program; dose; dry deposition; population dose;
radionuclide; rainout.
distance. Population doses (man-rem) are also calcu-
lated.
KEY WORDS: Atmospheric diffusion; computer code; com-
puter program; dose; dry deposition; population dose;
radionuclide; rainout.
distance. Population doses (man-rem) are also calcu-
lated.
KEY WORDS: Atmospheric diffusion; computer code; com-
puter program; dose; dry deposition; population dose;
radionuclide; rainout.
-------
-------
------- |