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ED02 – Whole Body External Dose Assessment 

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Date: April 30, 2021 

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DEFENSE THREAT REDUCTION AGENCY

NUCLEAR TEST PERSONNEL REVIEW PROGRAM

RADIATION DOSE ASSESSMENT

STANDARD METHOD

ED02 – Whole Body External Dose Assessment

Revision 2.0 

Cleared for Release 

Key to SOP ID Codes 

RA (Radiation Assessment - SOP) 

ED (External Dose - Standard Methods) 

ID (Internal Dose - Standard Methods) 

UA (Uncertainty Analysis - Standard Methods)
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Revision Control

Revision Revision Description Revision 

Date

Authorization 

Official

1.0 Original 10/31/2007 Paul K. Blake

1.1 − Attachments 1 and 2 are removed. All references to these 

attachments now refer to Appendices B–C. 

03/31/2008 Paul K. Blake

1.2 − Included discussion of intensity calculator function and methods to 

interpolate early time intensity data.

− Minor editorial changes.

10/31/2008 Paul K. Blake

1.3 − Expanded dose model equations to include used in probabilistic 

approach. 

− Expanded formulation of protection and shielding factors.

− Expanded section of time dependence of intensity.

− Expanded section on dose from neutron activation products.

− Added default input parameter table as Attachment 1.

− Added references.

− Minor editorial changes.

01/31/2010 Paul K. Blake

2.0 − Edited and expanded Section 5.2.1 and split it into five subsections 

to improve readability, augment the discussion of GSMF, and 

clarify the use of measured intensity data points in establishing the 

intensity calculator function.

− Added a table of GSMF values as new Attachment 2. 

− Revised and moved content as needed to improve flow.

− Updated References with new references and current versions, such 

as revised NTPR Technical Memorandums/Technical Notes.

− Editorial changes and corrections throughout as needed.

04/30/2021 James D. Franks
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Table of Contents

Table of Contents............................................................................................................................ 3

List of Figures................................................................................................................................. 4

List of Tables .................................................................................................................................. 4

1. Purpose/Summary..................................................................................................................... 5

2. Scope......................................................................................................................................... 5

3. Responsibilities......................................................................................................................... 5

4. Definitions................................................................................................................................. 5

5. Method Description .................................................................................................................. 6

5.1 Initial Radiation ............................................................................................................ 6

5.1.1 Initial Neutron Radiation Dose ................................................................... 7

5.1.2 Initial Gamma Radiation Dose.................................................................... 8

5.2 Residual Gamma Radiation Dose ................................................................................. 9

5.2.1 Surface-Deposited Fallout .......................................................................... 9

5.2.1.1 Intensity Function ......................................................................... 11

5.2.1.2 Film Badge Conversion Factor..................................................... 11

5.2.1.3 Use of the Gamma Source Modification Factor (GSMF)............. 11

5.2.1.4 External Dose Multiplier (EDM).................................................. 12

5.2.1.5 Intensity Calculator Function and Estimation of External Dose .. 14

5.2.2 Activated Sources..................................................................................... 17

5.2.3 Contaminants Adhering to the Hulls of Naval Vessels ............................ 19

5.2.4 Swimming in Contaminated Water........................................................... 20

5.2.4.1 Fallout-Contaminated Seawater.................................................... 20

5.2.4.2 Neutron-Activated Seawater......................................................... 20

5.2.5 Aircraft-Related Exposures....................................................................... 21

6. Data and Input......................................................................................................................... 22

7. Referenced SOPs and Standard Methods from this Manual................................................... 22

8. References............................................................................................................................... 22
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Attachment 1. Distributions and Deterministic Values for Model Parameters for External Dose 

Assessments.......................................................................................................... 24

Attachment 2. Gamma Source Modification Factor (GSMF) for Various Ship Types................ 29

List of Figures

Figure 1. ICF(t) and early time radiation intensity plot............................................................... 17

List of Tables

Table 1. Example of early time radiation time-intensity pairs..................................................... 15

Table 2. Example using multiple decay exponents...................................................................... 15

Table A1-1. Distributions and deterministic values for model parameters for external dose 

assessments................................................................................................................. 25

Table A2-1. Average gamma source modification factors (GSMF) for various ship types........ 30
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Standard Method

ED02 – Whole Body External Dose Assessment

1. Purpose/Summary

This Standard Method (SM) provides methods and techniques for assessing the whole 

body external doses to nuclear test participants for the Nuclear Test Personnel Review 

(NTPR) Program according to the procedures specified in standard operating procedure 

(SOP) RA01. Whole body external doses include those resulting from exposures to initial 

neutron and gamma radiation following detonation and to residual gamma radiation from 

radioactive materials external to the body.

2. Scope

This SM provides technical guidance for reconstructing the whole body doses that 

resulted from external neutron and gamma radiation sources encountered by nuclear test 

participants. The doses are reconstructed in accordance with the requirements of Title 32, 

Part 218, Code of Federal Regulations, “Guidance for the Determination and Reporting 

of Nuclear Radiation Dose for DoD Participants in the Atmospheric Nuclear Test 

Program” (DoD, 2020). The SM is intended primarily for use by dose reconstruction 

analysts working in the NTPR Program. It also provides formal documentation of these 

methods and techniques for internal and external reviewers of the Program. Additional 

operation-specific data and information for whole body external dose reconstruction is 

provided in Appendices A–C of this NTPR SOP Manual and references therein. The 

uncertainties associated with the reconstructed whole body external doses are discussed 

in SM UA01.

3. Responsibilities

It is the responsibility of dose reconstruction analysts to understand and correctly apply 

the methods and techniques presented below. If situations arise where these methods and 

techniques are inadequate to address a specific exposure scenario, it is the responsibility 

of the analyst encountering this deficiency to bring it to the attention of the SOP Task 

Manager so that the methodology can be extended as required to provide adequate 

estimates of whole body external doses. It is the responsibility of the staff member 

executing and implementing this extension to document such in a revision to this 

standard method.

4. Definitions

Intensity: a legacy term of the NTPR Program which is the same as the free-field 

radiation exposure rate expressed in units of roentgen per unit of time. 
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Film Badge Dosimeter (Film Badge): a device containing a packet of photographic film 

contained within a holder/filter combination used to measure external radiation exposure 

for the purpose of personnel monitoring.

Initial Nuclear Radiation: neutrons and gamma radiation emitted from the fireball and the 

cloud column during the first minute after a nuclear explosion.

Neutron Activation: radioactivity produced in certain materials as a result of nuclear 

reactions induced in those materials by neutrons, resulting in the formation of unstable 

isotopes.

Residual Nuclear Radiation: nuclear radiation emitted from fission products and other 

debris at times, including fallout (see Section 5.2), greater than 1 minute after a nuclear 

detonation.

5. Method Description

Whole body external dose results from exposure to radiation sources outside the body 

whose emissions are sufficiently penetrating so as to deposit energy throughout the body. 

The specific emissions of concern here are neutrons and gamma rays. Whole body 

external dose is distinct from skin or eye dose, which is the dose delivered to the skin or 

lens of the eye of an individual by both penetrating and non-penetrating (primarily beta) 

radiations (addressed by SMs ED03, ED04, and ED05), and from internal dose, which is 

dose delivered by radiation sources inside the body (SM ID01). The gamma component 

of whole body external dose was frequently measured by an individual film badge affixed 

to the external clothing of a participant; film badge dosimetry for nuclear test participants 

is discussed in SM ED01. In the absence of film badge data, or if the validity of such data

is suspect due to damage to the film medium, it is necessary to reconstruct the dose based 

on knowledge of the radiation environment and the participant’s interaction with that 

environment. Almost all neutron doses must be reconstructed because film badges were 

insensitive to neutrons. This standard method addresses the methods and techniques used 

to reconstruct whole body external doses for nuclear test participants. The values of the 

input parameters for the deterministic models and parameter value distributions used in 

the probabilistically based analyses are given in Attachment 1.

5.1 Initial Radiation

As indicated above, the neutrons and gamma radiation emitted during the first minute 

after a nuclear detonation constitute the initial radiation. Doses from initial radiation 

emitted from even the largest U.S. detonations were not measurable at distances greater 

than about 11 kilometers (or approximately 7 miles) for personnel at or near ground or 

sea level because of absorption of the radiation by the atmosphere and geometric 

dispersal with distance from the source (r−2effect) (Glasstone and Dolan, 1977). For most 

nuclear tests, the distances at which the dose from initial radiation becomes negligible are 

much smaller. Care must be taken, however, when assessing initial doses to personnel 

who are airborne at the time of detonation, as the reduced density of the air with altitude 
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allows these radiations to propagate farther than through air at ground or sea level. A 

listing of previously determined initial doses was compiled by Weitz and Egbert (2010). 

5.1.1 Initial Neutron Radiation Dose

More than 99 percent of the neutrons produced in a nuclear detonation are emitted in the 

first microsecond (10−6s) after detonation. The propagation of these “prompt” neutrons 

outward from the point of origin is a complicated physical process. Thus, the reliable 

reconstruction of the neutron doses to personnel in the vicinity of a nuclear detonation 

generally requires the use of radiation transport techniques coupled with knowledge of 

the neutron output spectrum for the nuclear device and of the surrounding physical 

environment. Such a calculation effort is not warranted for the vast majority of nuclear 

test participants, however, because they were located at distances sufficiently far from the 

detonation point that their neutron doses were immeasurably small. A study was 

performed in 1984-85 to screen the various units that participated in nuclear tests to 

identify those personnel who may have received neutron doses of 0.001 rem or greater

(Goetz et al., 1985). It is concluded from this study that the following personnel received 

neutron doses less than 0.001 rem:

 Continental United States (CONUS): (1) all participants of Project (Operation) 

TRINITY, and (2) all personnel who, at the times of the detonations at the Nevada 

Test Site (NTS), were located at News Nob, the nearby Control Point, Yucca Flat 

Airstrip, Camp Mercury, Camp Desert Rock, and Indian Springs Air Force Base

 OCEANIC: all personnel located on land or aboard ship at the times of detonations.

Conversely, the study identified 160 units or projects as possibly having received neutron 

doses exceeding 0.001 rem. Of these, approximately 75 percent are aircrews and the 

remainder ground-based units. These units or projects (minus those that have 

subsequently been shown to have had neutron doses less than 0.001 rem) are provided in 

the operation-specific sections of Appendices B and C of this SOP manual and in Weitz 

and Egbert (2010). Neutron doses that have been calculated for those exposures or, in the 

case of Operation HARDTACK I, that are indicated by sulfur packet measurements made 

aboard aircraft, are included in these tabulations. Doses listed for personnel who were in 

trenches at the time of detonation were derived by modeling this geometry in the 

radiation transport calculation. (Note: all neutron doses taken from Goetz et al. (1985) or 

later assessments have been multiplied by a factor of 2 for inclusion in SOP 

Appendices B and C, in accordance with the recommendation made in Kocher (2007). 

This adjustment accounts for the difference between the radiation weighting factor of 20 

now recommended by ICRP for neutrons (ICRP, 1991) and the mean quality factor of 10 

used in the original calculations.)

For participants in units/projects for which neutron doses are not provided, scenariospecific calculations are required to reconstruct these doses. In most scenarios of interest, 

almost the entire neutron dose is delivered within a fraction of a second after the 
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detonation. The recipient of that dose can be considered stationary during its deposition, 

thereby simplifying the calculation. Version 6 of the Air Transport of Radiation code 

(ATR6) code (Kaul et al., 1992) may be used with device- and scenario-specific input 

data to provide estimates of free-field neutron doses. For scenarios involving other than 

free-field exposures (e.g., troops in a trench), more sophisticated radiation transport 

codes, such as MCNP (Briesmeister, 2000), are required.

5.1.2 Initial Gamma Radiation Dose

The initial gamma radiation emitted by a nuclear device detonation consists of three 

components:

 Prompt gamma-gamma rays produced directly by the fission process and emitted 

within 10−7s of the detonation

 Secondary gamma-gamma rays produced by the inelastic scattering and capture of 

neutrons by the nuclei of atoms in the air and ground, emitted from 10−7s to 10−1s 

after detonation

 Fission product or debris gamma-gamma rays from the radioactive decay of fission 

products and other debris from the device, emitted up to 1 minute after the detonation

to include gamma rays from short lived isotopes that would have decayed within that 

first minute. 

The reconstruction of doses from the prompt and secondary gamma radiation components 

are amenable to standard radiation transport techniques using appropriate neutron and 

gamma weapon output spectra (available in various references, some of which are 

classified). However, calculation of the dose from fission product or debris gamma 

radiation is complicated by three factors:

 The movement of the radiation source (fireball) as it rises in the atmosphere

 Hydrodynamic enhancement (a dose enhancement caused by a decrease in the 

attenuation of fission product gamma rays emitted after the passage of the positive 

phase of the shock wave as the radiation propagates through low density air)

 Possible movement of personnel (e.g., those flying in an aircraft) during the time

interval that debris gamma radiation is being emitted.

In most cases, the doses from initial gamma radiation can be adequately calculated with 

the ATR6 code mentioned above. This code addresses each of the three initial gamma 

components separately, and the algorithm used for the fission product gamma component 

accounts for the movement of the fireball and hydrodynamic enhancement effects. The 

code calculates doses for stationary targets and can be used to reconstruct the fission 

product gamma dose to personnel in an aircraft flying in the vicinity of the rising fireball. 
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However, more elaborate transport techniques must be applied to reconstruct doses to 

personnel whose shielding configuration changes significantly shortly after the 

detonation. These include, for example, volunteer observers who emerged from a trench 

after the shock wave had passed their position.

Due in large part to the complications outlined above with respect to determining the 

fission product gamma dose, it is more difficult to define bounding distances beyond 

which the initial gamma dose can be considered negligible. Consequently, no 

comprehensive screening has been performed for initial gamma doses as was done for 

initial neutron doses. However, based on data provided in Glasstone and Dolan (1977)

and the known distances of personnel from the shots, it can be stated with confidence that

the participants in the oceanic test series who were present on land or aboard ship at the 

times of detonation received initial gamma doses of less than 0.001 rem. For the CONUS 

test series, an extensive number of calculations have been performed and documented on 

the initial gamma doses to participating units (Goetz et al., 1980 and 1981; Frank et al., 

1981). Available initial gamma doses are provided in the operation-specific sections of 

SOP Appendices B and C. For cases where initial gamma dose reconstructions are not 

available, specific ATR6 or other calculations may be required to obtain them. 

5.2 Residual Gamma Radiation Dose

Residual gamma radiation is that gamma radiation emitted in the radioactive decay of 

fission products, neutron-activated products, and other nuclear device debris 1 minute or 

more after the detonation. Very few neutrons are emitted in this timeframe. The most 

commonly encountered source of residual gamma radiation is fallout, but test participants 

were also exposed to gamma radiation emitted from activation products in the soil or on 

target ships, contaminants in water, or contaminants encountered by aircraft flying near 

or through radioactive clouds. Reconstructions of doses from these sources are addressed 

in the following sections.

5.2.1 Surface-Deposited Fallout

Fallout was the prevalent source of exposure for most nuclear test participants. The 

geographical pattern of the fallout field was influenced primarily by the direction and 

magnitude of the prevailing winds above the test site. At NTS, test participants operated 

in both freshly deposited and aged fallout at the site, and occasionally resided in camps 

that received light fallout. Personnel who participated in the oceanic tests encountered 

both fresh and aged fallout on residential and recreational land areas and on ships 

supporting the operation. The fallout fields are characterized by radiation intensity 

measurements taken at specific times and locations after the detonation. The intensities at 

later times can be readily estimated because fallout decays in a predictable manner.

For CONUS tests, monitors conducted radiological surveys shortly after virtually all of 

the shots, documenting intensities at specified times and locations (Hawthorne, 1979). 

Thus, the radiation intensities in the vicinities of these shots are relatively well known
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from several post-detonation surveys and can be estimated for later times using time 

decay functions as indicated above. 

A test participant walking through or operating in a residual radiation fallout field 

experienced radiation intensities that varied in time due to the movement through the 

non-uniform field and radiological decay in time. The whole body gamma dose from 

moving and operating in a fallout field is given by:





end

start

t

t

D FB I(t,r(t )) dt 



(1)

where 

Dγ = Whole body external gamma dose (rem)

I(t,r(t)) 

= Free-field intensity at a participant’s time-varying location 

r(t)



at 

time t (R h−1)

FB = Film badge conversion factor (rem R−1)

tstart = Start time of exposure to external radiation (h)

tend = End time of exposure to external radiation (h)

If the intensity function can be expressed as a function of time only, as I(t), for a 

particular shot and known exposure movement, then the external gamma dose can be 

calculated as shown in Equation 2:

D = FB EDM ∫ I(t) dt tend

tstart

(2)

where

I(t) = Intensity as a function of time; see Section 5.2.1.3 for cases where 

intensity measurement is taken from a nearby location other than 

the location where a dose estimate is sought (R h

−1

)

EDM = External dose multiplier (dimensionless)

Equation 2 is used for a participant who was exposed to ground-deposited fallout from 

tstart to tend. The EDM parameter is used to account for any shielding or protection that the 

veteran may have had due to being indoors on land or below deck on a ship. If more than 

one shot contributed to the fallout, the dose from each contributing shot must be 
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calculated and the increments added to get the total whole body dose unless an intensity 

measurement is available that simultaneously captures the total exposure rate from all 

contributing shots. The parameter EDM is discussed in Section 5.2.1.4. 

5.2.1.1 Intensity Function

The integration in Equation 1 must often be performed numerically since 

I(t,r(t)



generally cannot be integrated in analytical form. In many scenarios of interest, a test 

participant remained in a fallout field with little spatial variation of intensity for 

significant periods of time. This occurred for NTS and oceanic participants whose 

residential or recreational areas were contaminated by fallout, and for oceanic 

participants who resided on ships that received topside fallout. In these cases, a spatial 

average intensity was recorded and the intensity function in Equation 1 takes the 

simplified form I(t), indicating that it does not depend on the participant’s movement 

within the field. 

For assessments where a participant’s movement and timing are well-documented and the 

movement occurred in an intensity varying field, it is possible to convert the space and 

time relationship of the intensity function to a simple function of time. In this case, 

Equation 2 above can be used. Also, the integration can be approximated with a 

summation of doses for each segment of the participant movement using an average 

intensity for each segment or the highest value for each segment. 

5.2.1.2 Film Badge Conversion Factor

The film badge conversion factor (FB) is the ratio of dose recorded on a properly worn 

film badge to free-in-air integrated intensity. This factor, which accounts for body 

shielding of the film badge to gamma radiation, has been assigned the deterministic 

values of 0.7 for the standing position in a planar fallout field and 1.0 for one facing the 

source of radiation, e.g., a contaminated aircraft during an inspection.

5.2.1.3 Use of the Gamma Source Modification Factor (GSMF)

To calculate doses at a location where no exposure rate measurements are available, 

surrogate data from a nearby location can be used. Use of surrogate data from a nearby 

location is justified by the assumption of similarity in surface activity density at the 

location of the measurement and the location where a dose needs to be assessed. The 

Gamma Source Modification Factor (GSMF) corrects for situations where surfaces

contaminated by fallout were not infinite in spatial extent. For land-based applications,

the area of fallout deposition was generally large enough that the correction is 

insignificant. Thus, for exposures to fallout on land, GSMF is 1. However, for shipboard 

exposures, the deposited fallout was limited to the finite area of the weather deck of the 

ship and GSMF values are greater than 1. (Weitz, 2010)
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For external dose calculations that use exposure rate measurements from a nearby 

location, the measured rates should be multiplied by the ratio of GSMF for the 

measurement location to the GSMF for the assessment location. The exposure rate 

correction is expressed as follows:

( ) I (t)

GSMF

GSMF I t m

m



(3)

where

I(t) = Intensity at location where dose estimate is sought (R h

-1

) 

Im(t) = Intensity at location where measurement was made (R h

-1

) 

GSMF = GSMF for the location of dose assessment

GSMFm = GSMF for the location of intensity measurement

If the ratio 

GSMF

GSMFm

in Equation 3 is lower than 1, a ratio of 1 may be used as a highsided value. An example of a GSMF ratio of less than 1 is when exposure rate 

measurements were made on an island or on a large ship and then used as surrogate data 

for a small ship or a ship with a large superstructure that provides shielding. 

An example of a GSMF ratio greater than 1 is when exposure rate measurements on a 

nearby ship are used as surrogate data for an island, or measurements from a small ship 

are used for a larger ship or with less superstructure. 

A nominal value of 2 has been typically used for GSMF in internal dose estimation for 

shipboard personnel assessments. However, results from an improved method developed 

for probabilistic assessments of shipboard exposures should be used that take into 

consideration the ship dimensions and the shielding afforded by its superstructure. Except 

for aircraft carriers, the more explicitly calculated GSMF values are higher than 2. The 

mean values of GSMF for the deterministic models and distributions parameters used in 

the probabilistically based analyses are given in Attachment 2. (Weitz, 2010)

5.2.1.4 External Dose Multiplier (EDM)

The external dose multiplier EDM is used to account for any shielding or protection that 

the veteran may have had due to being indoors on land or below deck on a ship. If more 

than one shot contributed to the fallout, the dose from each contributing shot must be 

calculated and the increments added to get the total whole body dose. EDM for 

deterministic models is given by the following equations:
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EDMland = Fos +

(1− Fos)

PF

 for land-based participants

EDMship = Fts + SF (1 − Fts) for ship-based participants

(4)

where

Fos = Average fraction of time the participant spent outside 

Fts = Average fraction of time the participant spent topside

PF = Protection factor for land-based structures

SF = Shielding factor for ships 

The use of an EDM assumes that no specific knowledge exists of where the veteran was 

at any particular time, and is therefore based on distributions around average central 

values for times spent inside and outside. If the exact location of the veteran is known 

specific to an occurrence of descending fallout or any other operation that could lead to 

higher radiation exposures, the EDM would need to be reconsidered and perhaps

modified.

For dose assessments using probabilistic methods, shielding afforded the participant by a 

land-based structure is accounted for with an EDM given by the following equation 

(Weitz et al., 2009):

EDMland = Fos ∙ I1 + (1 − Fos) ∙ [

Ft

PFt

∙ I2 +

(1 − Ft)

PFb

∙ I3] (5)

where

Fos = Fraction of time the participant spent outside

Ft = Fraction of time the participant spent inside a tent

PFt = Protection factor for a tent

PFb = Protection factor for a building

I1, I2, I3 = Intensities drawn from a distribution that characterizes the 

variation in outside intensities

The values of the input parameters for the deterministic models and parameter 

distributions used in the probabilistically based analyses are given in Attachment 1.
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For dose assessments using probabilistic methods, shielding afforded the participant by 

the decks of a ship are accounted for with an EDM given by the following equation 

(Weitz et al., 2009):

EDMship = Fts ∙ I1 + (

1 − Fts

2

) ∙ [SFw ∙ I2 + SFb ∙ I3

] (6)

where

Fts = Fraction of time the participant spent topside

SFw = Shielding factor for the veteran’s work location

SFb = Shielding factor for the veteran’s billeting location

I1, I2, I3 = Intensities drawn from a distribution that characterizes the 

variation in topside intensity

The formulation of Equation 6 assumes that the participant split his below-deck time 

evenly between his work and billet locations. The values of the input parameters for the 

deterministic models and parameter distributions used in the probabilistically based 

analyses are given in Attachment 1.

5.2.1.5 Intensity Calculator Function and Estimation of External Dose

The functional dependence of fallout intensity on time can be specified in various ways. 

For the time interval during which fallout was descending, time-intensity data pairs are 

often available. These early time intensity data are modeled by applying a curve fitting 

algorithm to produce an “early time intensity function” denoted by Iearly(t) in this 

application. The Mathcad software, the principal computational platform used for NTPR 

dose reconstruction, offers a number of options for functional fitting of data sets. Linear 

interpolation in logarithmic space is often used for the early time intensity function. In 

Mathcad syntax, this takes the form:

linterp[ log ]

10 T, (EarlyI), tI (t ) early 

(7)

The right side of Equation 7 is simply 10 raised to the power of the base-10 logarithm of 

the intensity at time t, as linearly interpolated (“linterp”) from time-intensity data pairs. A 

generic example of the time-intensity pair structure is shown in Table 1. The parameter T

in Equation 7 is the time array (t0, t1, t2, ...) and EarlyI is the intensity array (I0, I1, I2, ...)
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of the measured time-intensity pairs. To establish Iearly(t), all time-intensity pairs listed in 

the operation-specific SOP appendix for each operation and shot should be used, when 

available, even if some of the pairs represent measurements made after the time of peak 

intensity. This ensures consistency in the data used in the dose reconstructions for all

operations. 

Table 1. Example of early time radiation time-intensity pairs

Time after Detonation

(t, in h)

Measured Intensity (EarlyI, in R h

−1)

t < t0 0

t0 I0

t1 I1

t2 I2

t3 I3

t4 I4

Following the time of the last measured intensity, the time variation of the radiation 

intensity of the fallout can be approximated as t

−λ

, where t is the time after detonation in 

hours and the decay exponent λ is constant over a specified period of time (Glasstone and 

Dolan, 1977). The most frequently used values of λ are 1.2 for the first 6 months (4380 h) 

after detonation and 2.2 thereafter. However, the decay of fallout material from specific 

shots is sometimes better characterized by other values of λ as described in SOP 

Appendices A–C. The lack of information on removal mechanisms such as weathering, 

decontamination, or remediation requires approximations of λ to neglect these factors. 

The non-consideration of removal mechanisms causes the intensity to diminish at a 

slower rate than if leaching, dispersal, or removal of the contaminants were considered. 

As a result, the use of these parameters generally results in high-sided dose estimates.

Occasionally, multiple values of λ, each applicable for a specified period of time, are 

used to better quantify the time variation of the post-deposition fallout intensity for 

specific shots. An example is given in Table 2 to demonstrate the use of multiple

λ values.

Table 2. Example using multiple decay exponents

Time Interval (h) Decay Exponent λi

t0 ≤ t < t4 n/a*

t4 to t5 λ1 = 1.1

t5 to 4380 λ2 = 1.2

t > 4380 λ3 = 2.2

* In this example, measured intensities are used for this time interval.
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In this example (Table 1 and Table 2), the first measurement (I0) was taken at time t0, 

descending fallout continued until the peak measurement at time t3, and t4 corresponds to 

the time of the last early time intensity measurement. Time t5, found in Table 2, 

corresponds to the end of the operational period. Time t5 is assumed to be less than 

4380 h post-detonation and is often used to define a period for use of a unique decay 

constant (λ2), so determined such that when used, legacy tabulations of intensity 

measurements can be matched.

The intensity parameterizations can be combined into a piecewise single intensity 

calculator function, ICF(t), which is applicable for all times. The intensity calculator 

function for using the generic parameters in Table 1 and Table 2 can be expressed as:

ICF(t) =

{

 

 

 

 

0

Iearly(t)

I4(t4/t)

1.1

I4(t4/t5)

1.1

(t5/t)

1.2

I4(t4/t5)

1.1

(t5/4380)

1.2

(4380/t)

2.2

if t < t0

if t0 ≤ t < t4

if t4 ≤ t < t5

if t5 ≤ t < 4380

if t ≥ 4380 }

 

 

 

 

(8)

A plot of ICF(t) (solid black curve) overlaid on early time measured intensity data 

(squares) is shown in Figure 1 for the following time-intensity pairs, which specify the 

intensities on Parry Island, Enewetak Atoll, caused by fallout from Operation 

GREENHOUSE Shot EASY:

t0 = 17 h I0 = 0.0001 R h

−1

t1 = 20 h I1 = 0.00035 R h

−1

t2 = 22 h I2 = 0.00065 R h

−1

t3 = 24 h I3 = 0.001 R h

−1

t4 = 30 h I4 = 0.00085 R h

−1

The function ICF(t) in Figure 1 was constructed decayed using λ1 = 1.1 for the interval

from t4 to t5 (t5 = 978 h), λ2 = 1.2 for the interval t5 to 4380, and λ = 2.2 thereafter (see 

Table 2). 

Once an intensity calculator function, ICF(t), is established for a particular shot and 

location or scenario of exposure, the external gamma dose can be calculated using 

Equation 2 where I(t) is replaced with ICF(t) as follows:





end

start

t

t

D FB EDM ICF(t ) dt 

(9)
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Figure 1. ICF(t) and early time radiation intensity plot

5.2.2 Activated Sources

For shots at NTS that were detonated at altitudes such that the neutrons reached the 

surface but the fireball did not, the residual radiation field was mapped with nearly 

circular iso-intensity contour lines around ground zero. These indicate neutron activation 

of the soil with peak intensity at ground zero with a strong gradient as one moves away 

from ground zero in any direction. These contours were measured by radiation monitors 

shortly after the detonations and are documented in Hawthorne (1979). Doses to 

personnel who traversed the activated area can be determined by evaluating Equation 1

above, but the decay function given by Equation 8 above no longer applies. An accurate 

determination of the intensity of an activation field as a function of time requires

knowledge of the elemental constituents of the soil in the vicinity of the burst, the neutron 

absorption cross sections of these constituents, the decay properties of the activation 

products, and the attenuation of the emitted radiation by the soil. This analysis can be 

performed in a spreadsheet, supplemented by a limited number of radiation transport 

calculations. In this manner, it is found that sodium-24 (Na-24, half-life = 15 h) was the 

dominant radioisotope in the first two days after a detonation over typical NTS soil. 

Other activation products relevant for NTS exposures include manganese-56 (Mn-56, 

half-life =2.6 h) and potassium-42 (K-42, half-life = 12.4 h).

To determine the intensity due to exposure from Na-24, Mn-56, and K-42 in the first 

hours after detonation, it is required to determine the intensity at time-zero t0 (H+0)

intensity based on normalized radiation intensity. Using a measured intensity at a known 

time T, the zero time intensity is then calculated by: 
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T T T

T

Na Mn K . e . e . e

I

I( )

  

    



0 668 0 274 0 058

0

(10)

where

I(0) = Normalized zero-time gamma radiation intensity due to the 

principal soil activation products (R h

−1

)

IT = Gamma radiation intensity (R h

−1

) observed at measurement time T

(hours after the detonation that produced the activated field)

T = Time after the detonation when IT was measured (h). 

Na = Decay constant for Na-24 [l 0.0462 h

−1

]

Mn = Decay constant for Mn-56 [0.265 h

−1

]

K = Decay constant for K-42 [l0.056 h

−1

]

Having normalized the activation product gamma radiation intensity, the intensity at any 

elapsed time t is given by:













     

 t  t  t Na Mn K I(t ) I( ) e e e  

0 0.668 0.274 0.058

(11)

where

I(t) = Time-dependent intensity from the principal neutron activation 

products (R h

−1

)

See SOP Appendix C-7, Attachment C-7-1 for a more complete explanation of estimating 

the radiation intensity from soil activation products. Equation 11 should not be used for 

times less than one hour after detonation (H+1) due to the omission of short-lived neutron 

activation products such as aluminum-28 (Al-28).

The activation of naval vessels is assessed in Weitz et al. (1982) with regard to exposures 

to neutron-activated target ships following Shot ABLE of Operation CROSSROADS. It 

was found that the dominant radioisotope formed on these ships was copper-64 

(Cu-64, half-life = 12.8 h). Decay functions for representative ship types are available in 

SOP Appendix B-1.
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The activation of seawater in the Bikini lagoon at Shot ABLE of Operation 

CROSSROADS is assessed in Weitz et al. (1982). The dominant radioisotope formed 

was Na-24. Individuals aboard ships located in the lagoon following the ABLE 

detonation were exposed to this residual radiation. 

5.2.3 Contaminants Adhering to the Hulls of Naval Vessels

It was observed during Operation CROSSROADS and subsequent oceanic operations 

that ships operating in fallout-contaminated water accumulated radioactive materials on 

their underwater hulls and in salt water piping and evaporators. The physical processes 

responsible for this radioactive accumulation appear to include assimilation of 

radionuclides by aquatic organisms (e.g., algae and barnacles) that were or became 

attached to the ship, and ion-exchange absorption of the polyvalent fission products by 

inert material (e.g., paint or rust) on the ship’s hull and in the piping. A detailed analysis 

of this contamination source is presented in Weitz et al. (1982) along with an algorithm 

for estimating doses to personnel resident on contaminated ships. Based on this model, 

the intensity of the contaminated hull quickly approached a saturation value given by:

1.3

hull I (t ) S t





(12)

where

Ihull(t) = Time dependent saturation intensity on the hull of a ship (R day−1)

S = Constant on the order of 1.6 R day0.3 that depends somewhat on 

ship type (Weitz et al., 1982)

t = Time after detonation (day)

The average intensity in the spaces of the ship below deck is related to the ship’s hull 

intensity by an apportionment factor Fa that depends on the ship’s dimensions:

I (t ) F I (t ) belowdeck 

a hull

(13)

where

Ibelowdeck(t) = Time dependent intensity below deck from hull contamination 

(R day−1) 

Fa = Apportionment factor (Weitz et al., 1982)
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As examples, Fa equals 0.39 for a destroyer, 0.05 for a cruiser and 0.10 for a light aircraft 

carrier. The engine room is estimated to have had an intensity 1.5 times the hull intensity, 

so personnel with engineering ratings received larger doses than those with nonengineering ratings. The dose from hull contamination would then be calculated using 

Equation 1. 

5.2.4 Swimming in Contaminated Water

It is occasionally necessary to reconstruct the external gamma dose for a nuclear test 

participant who swam in fallout-contaminated or neutron-activated seawater. 

5.2.4.1 Fallout-Contaminated Seawater

The external dose due to swimming is related to the exposure measurements above the 

water. From measurements taken in fallout-contaminated water during Operation 

CROSSROADS (Weitz et al., 1982), the activity in water and the relationship to the 

intensity above the water was determined (Weitz, 2012). The dose to a swimmer as 

related to the intensity above the water is approximated by: 

Dγ = 1.4 Iff Δt (14)

where

Dγ = External gamma dose accrued by a swimmer during the short 

duration of swimming Δt (rem)

Iff = Free-field gamma intensity above the water surface from fallout, 

assumed to be constant over the short duration of swimming Δt

(R h

−1

)

Δt = Duration of swimming (h)

The factor 1.4 in Equation 14 incorporates a film badge conversion factor of 0.7 to result 

in a dose that is equivalent to a film badge dose; it is also based on a tissue density of

1 g cm−3. (Weitz, 2012)

5.2.4.2 Neutron-Activated Seawater

As indicated earlier, Na-24 is the dominant radioisotope produced in seawater by a lowaltitude nuclear detonation (Weitz et al., 1982). The gamma dose accrued by a swimmer 

from the Na-24 activity while swimming in neutron-activated seawater (Weitz, 2012) is

approximated by:
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Dγ = 1.4 Iff Δt (15)

The parameter Iff in Equation 15 represents the above-water intensity due to neutronactivated seawater. The factor 1.4 in Equation 15 incorporates a film badge conversion

factor of 0.7 to result in a dose that is equivalent to a film badge dose; it is also based on a 

tissue density of 1 g cm−3. (Weitz, 2012)

5.2.5 Aircraft-Related Exposures

Personnel who flew in cloud sampling, cloud tracking, weather monitoring, or other 

support aircraft may have been exposed to radiation from the radioactive cloud from 

contaminants that adhered to or entered the aircraft while flying through or under the 

cloud, or from fallout or activation products on the ground while flying at low altitude. 

Fortunately most pilots and other crew members of aircraft susceptible to radiation 

exposure were provided with film badges to record their doses. In cases where film badge 

data are unavailable, the methods used in dose reconstruction are strongly scenariodependent, making it difficult to present generalized approaches.

A more frequently encountered scenario involving lack of film badge coverage relates to 

ground personnel who were tasked to decontaminate or perform maintenance on aircraft 

that had flown through airborne contamination and thereby became contaminated. Often 

the radiation intensities of the surfaces and engines of these aircraft were measured after 

landing at several time intervals. If such intensity information is available or can be 

estimated from measurements made under similar circumstances on similar aircraft, the 

reconstruction of the participant’s dose is straightforward. If an intensity I(tm,rm) was 

measured at time tm from a distance rm from the contaminated surface, and if the 

participant was exposed for a period Δt at time te and at a distance re, his reconstructed 

dose is given by:

D f (r ,r ) I(t ,r )(t / tm ) t 

m e m m e 





(16)

In this expression, the function f(rm,re) relates the magnitude of the intensity at distance re

to that at distance rm. If the dimensions of the contaminated area are large compared to rm

and re, then f ~ 1; this approximates an infinite plane of contaminated material. If the 

dimensions of the contaminated area are small compared to rm and re, then f ~ (rm/re)

−2

;

this approximates a point source. Most cases fall somewhere between these two extremes 

and the appropriate function should be derived by radiation transport techniques for 

specific cases. Note that the film badge conversion factor of 0.7 is omitted in this case 

because most of the participant’s exposure would have occurred while he was facing the 

source of radiation.
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6. Data and Input

The values of the input parameters for the deterministic models and parameter 

distributions used in the probabilistically based analyses are given in Attachment 1. 

Information and data specific to each test series to be used for the reconstruction of whole 

body external doses are contained in SOP Appendices A–C.

7. Referenced SOPs and Standard Methods from this Manual

(1) SOP RA01 - Radiation Dose Assessment for Cases Requiring Detailed Analysis

(2) SM ED01 - Film Badge Dose Assessment

(3) SM ED03 - Skin Dose from External Sources

(4) SM ED04 - Skin Dose from Dermal Contamination

(5) SM ED05 - Lens of the Eye Dose

(6) SM ID01 - Doses to Organs from Intake of Radioactive Materials

(7) SM UA01 - Dose Uncertainty and Upper-Bound Dose Determination

8. References

Briesmeister, J.F. (ed.), 2000. MCNP–A General Monte Carlo N-Particle Transport Code–

Version 4B. LA-13709-M, Los Alamos National Laboratory, Los Alamos, NM.

DoD (Department of Defense), 2020. “Guidance for the Determination and Reporting of Nuclear 

Radiation Dose for DoD Participants in the Atmospheric Nuclear Test Program (1945-

1962).” Title 32, Code of Federal Regulations, Part 218. Washington, DC. July 1.

Frank, G., Goetz, J., Klemm, J., Thomas, C., and Weitz, R., 1981. Analysis of Radiation 

Exposure, 4th Marine Corps Provisional Atomic Exercise Brigade, Exercise Desert Rock 

VII, Operation PLUMBBOB. DNA 5774F, Defense Nuclear Agency, Washington, DC.

June 15. 

Glasstone, S., and Dolan, P.J., 1977. Effects of Nuclear Weapons. U.S. Department of Defense 

and U.S. Department of Energy (3rd Edition).

Goetz, J., Kaul, D., Klemm, J., McGahan, J., and Weitz, R., 1980. Analysis of Radiation 

Exposure for Troop Observers, Exercise Desert Rock VI, Operation TEAPOT. DNA 

5354F, Defense Nuclear Agency, Washington, DC. July 15. 

Goetz, J., Kaul, D., Klemm, J., McGahan, J., and Weitz, R., 1981. Analysis of Radiation 

Exposure for Troop Observers, Exercise Desert Rock V, Operation UPSHOTKNOTHOLE. DNA 5742F, Defense Nuclear Agency, Washington, DC. April 28. 
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Goetz, J., Klemm, J., Thomas, C., and Weitz, R., 1985. Neutron Exposure for DoD Nuclear Test 

Personnel. DNA-TR-84-405, Defense Nuclear Agency, Washington, DC. August 15. 

Hawthorne, H.A. (ed.), 1979. Compilation of Local Fallout Data from Test Detonations 1945-

1962 Extracted from DASA 1251, Volume I—Continental U.S. Tests. DNA 1251-1-EX,

Defense Nuclear Agency, Washington, DC. May 1. 

ICRP (International Commission on Radiation Protection), 1991. 1990 Recommendations of the 

International Commission on Radiological Protection. ICRP Publication 60, Ann. ICRP 

21(1–3), Pergamon Press, New York, NY.

Kaul, D.C., McGuffin, S., and Dolatshahi, F., 1992. User’s Manual, Personal Computer (PC) 

Edition, Version 6 of ATR (ATR6). DNA-TR-91-163, Defense Nuclear Agency, 

Washington, DC.

Kocher, D.C., 2007. Considerations on Estimating Upper Bounds of Neutron Doses to Military 

Participants at Atmospheric Nuclear Tests. DTRA-TR-07-3, Defense Threat Reduction 

Agency, Fort Belvoir, VA. April. 

Weitz, R., Stuart, J., Muller, E., Thomas, C., Knowles, M., Landay, A., Klemm, J., and Goetz, J.,

1982. Analysis of Radiation Exposure for Naval Units of Operation CROSSROADS, 

Volume I—Basic Report. DNA-TR- 82-05-V1, Defense Nuclear Agency, Washington, 

DC. March 3. 

Weitz, R., Case, D., Chehata, M., Egbert, S., Mason, C., Singer, H., Martinez, D., McKenzieCarter, M., and Stiver, J. 2009. Probabilistic Approach to Uncertainty Analysis in NTPR 

Radiation Dose Assessments. DTRA-TR-09-13, Defense Threat Reduction Agency, Fort 

Belvoir, VA. November 1. 

Weitz, R.L., 2010. Formulation of the Gamma Source Modification Factor for Ship-based 

Applications, Revision 1. NTPR-TM-09-04(R1), Defense Threat Reduction Agency, Fort 

Belvoir, VA. November 30.

Weitz, R. and Egbert, S., 2010. Compilation of Initial Radiation Doses to Atmospheric Test 

Participants, Revision 1. NTPR-TM-09-01(R1), Defense Threat Reduction Agency, Fort 

Belvoir, VA. November 30. 

Weitz, R.L., 2012. External Gamma and Skin Doses from Immersion in Contaminated Water. 

NTPR-TM-11-04, Defense Threat Reduction Agency, Fort Belvoir, VA. June 18. 
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Attachment 1.

Distributions and Deterministic Values for Model Parameters for External 

Dose Assessments

The values of input parameters to the external dose models (presented in this SM) provided in 

Table A1-1 of this attachment are default numbers that are applicable in most cases. They should

be adjusted or replaced for cases where veteran-specific data are available. These default 

parameter values were estimated or derived in Weitz et al. (2009) and other technical basis 

documents listed in the references section of that document.

The column labeled “Nominal Value for Central Estimation” contains model input values that 

can be used to calculate the central (best) estimate of a dose. These values are usually based on 

documented observed data or best estimates, and were used in building the statistical 

distributions for each parameter. For numerically generated distributions, such as GSMF, PFt,

PFb, SFb, SFw, etc., nominal values are the central estimates of those distributions, which are 

based on physical and mathematical models that characterize input parameters and their 

uncertainty and variability. Calculations of nominal doses provide point estimates using a dose 

reconstruction model with nominal values for all of its input parameters. In addition, nominal 

values are used as input parameters for model sensitivity analyses (Weitz et al., 2009).
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Table A1-1. Distributions and deterministic values for model parameters for 

external dose assessments

Parameter Definition

Distribution for 

Probabilistic Analysis *

Nominal Value 

for Central 

Estimation Deterministic†

SCENARIO PARAMETERS

Dates and Times of Arrival and Departure at Assigned Location

DateArrived Start date[time]

Triangular 

Example

min = Jun 19 [0000]

mode = Jun 19 [1200]

max = Jun 19 [2400]

Jun 19 [1200] Jun 19 [0800]

DateDeparted End date[time]

Triangular

Example

min = Jul 5 [0000]

mode = Jul 5 [1200]

max = Jul 5 [2400]

Jul 5 [1200] Jul 5 [2400]

FB

Film Badge Conversion 

Factor n/a

0.7 for planar 

source, 1.0 for 

facing a source

0.7 for planar 

source, 1.0 for 

facing a source

PARAMETERS FOR MANEUVER UNITS AT NTS

ST Start time of maneuver after 

detonation

Normal

Parameters are case specific Case specific Case specific

Rate Walk rate during maneuver Triangular 

Parameters are case specific Case specific Case specific 

LT Linger time at Rad-Safe 

limit location

Triangular

Parameters are case specific Case specific Case specific

SHOT MIXTURE FRACTION for OPERATION HARDTACK I SHOTS FIR AND KOA

Fallout 

Composition

Fallout proportion from 

each shot (applies to 

FIR/KOA only)

Triangular

min = 0

mode = 0.4

max = 1

for FIR fraction

Intensity based on 

0.4/0.6 mixture of 

FIIDOS-derived 

FIR/KOA decay 

functions

Intensity data based 

on time-dependent 

decay exponents for 

FIR/KOA mixture
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Parameter Definition

Distribution for 

Probabilistic Analysis *

Nominal Value 

for Central 

Estimation Deterministic†

EXTERNAL DOSE MULTIPLIER (EDM) FOR LAND-BASED PERSONNEL

Fos

Fraction of time spent 

outside

Triangular 

NTS Example

min = 5/24

mode = 12/24

max = 18/24

0.5

(or 12/24)

0.6 

(or 14.4/24)

PPG Example

min = 2/24

mode = 8/24

max = 16/24

0.34

(or 8/24)

0.6

(or 14.4/24)

Ft

Fraction of inside time 

spent in tent (the remainder 

of the time spent indoors is 

assumed to take place in 

barracks with walls made of 

metal or wood.)

Triangular

min = 0

mode = 0.5

max = 1

0.5 0

I1, I2, I3

Modifier of local gamma 

radiation intensity relative 

to the average outdoor 

intensity when veteran is 

outdoors (I1), inside a tent 

(I2) and inside a barrack (I3)

Lognormal

GM = 1.0

GSD = 1.5

1.0 1.0

PFb

Protection factor for 

building

Numerical model 

(see Weitz et al. [2009])

Mean = 2.1

95%tile = 3.9

2.0

(median of 

distribution)

2.0

PFt Protection factor for a tent

Numerical model

(see Weitz et al. [2009])

Mean = 1.4

95%tile = 1.9

1.4

(median of 

distribution)

1.5

INTENSITY MEASUREMENTS FOR LAND-BASED PERSONNEL

Im

Measured intensities (with 

errors due to instrument 

precision, calibration and 

operator manipulation)

Normal

Mean = Im

95%tile/Mean = (1.5–2.0)

Im Im

Contour 

intensities 

I(t)

Intensities obtained from 

iso-intensity plots See Weitz et al. (2009) I(t) I(t)
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Parameter Definition

Distribution for 

Probabilistic Analysis *

Nominal Value 

for Central 

Estimation Deterministic†

a

Exponent of multiplicative 

error factor (t/t0)

±a

applied 

to FIIDOS-generated 

intensity functions

Normal

μ = 0

σ = 0.15

0 0

EXTERNAL DOSE MULTIPLIER (EDM) FOR SHIP-BASED PERSONNEL

Fts

Fraction of time spent 

topside

Triangular

min = 4/24

mode = 9.6/24

max = 18/24

0.4

(or 9.6/24)

0.4

(or 9.6/24)

I1, I2, I3

Modifier of local gamma 

radiation intensity relative 

to the average topside 

intensity when veteran is 

topside (I1), below deck at a 

work location (I2) and 

below deck at in a billet 

area (I3)

Post-decontamination 

numerical model for 

elliptical ships typical of 

USS ESTES

(see Weitz et al. [2009])

μ = 1.0

σ = 0.70

0.88

(median of 

distribution)

1.0

Im

Measured intensities (with 

errors due to instrument 

precision, calibration and 

operator manipulation)

Normal

Mean = Im; 

95%tile/Mean = (1.5–2.0)

Im Im

SFb

Shielding factor at belowdeck billet location 

(assumed on 3rd deck below 

topside)

Elliptical ship model 

(see Weitz et al. [2009])

GM = 0.016

0.016 0.1

Shielding factor at belowdeck billet location 

(assumed equally likely on 

3

rd or 4th decks below flight 

deck)

Rectangular ship model 

(see Weitz et al. [2009])

GM = 0.021

0.021 0.1

SFw

Shielding factor at belowdeck worksite (assumed 

equally likely on 1st or 2nd

decks below topside)

Elliptical ship model

(see Weitz et al. [2009])

GM = 0.079

0.079 0.1

Rectangular ship model

(see Weitz et al. [2009])

GM = 0.11

0.11 0.1

INTENSITY MEASUREMENTS FOR SHIP-BASED PERSONNEL

a

Exponent of multiplicative 

error factor (t/t0)

±a

applied 

to FIIDOS-generated 

intensity functions

Normal

μ = 0

σ = 0.15

0 0
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Parameter Definition

Distribution for 

Probabilistic Analysis *

Nominal Value 

for Central 

Estimation Deterministic†

Im

Measured topside 

intensities (with errors due 

to instrument precision, 

calibration and operator 

manipulation)

Normal

Mean = Im; 

95%tile/Mean = (1.5–2.0)

Im Im

Isc

Measured ship 

contamination intensity 

(with errors due to 

instrument precision, 

calibration and operator 

manipulation)

Lognormal multiplier 

GM = 1

95%tile = 3.2

Isc Isc

Iws

Measured water shine 

intensity (with errors due to 

instrument precision, 

calibration and operator 

manipulation)

Lognormal multiplier

GM = 1

95%tile = 2.4

Iws Iws

* μ = arithmetic mean; σ = standard deviation; GM = geometric mean; GSD = geometric standard deviation; 

95%tile = value of the distribution at the 95th percentile.

† For deterministic dose models, high-sided (conservative) parameter values are selected to obtain upper-bound doses 

at least equal to the 95th percentile of a probability distribution.
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Attachment 2.

Gamma Source Modification Factor (GSMF)

for Various Ship Types

Table A2-1 of this attachment lists various types of ships and example ship names along with the 

estimated superstructure ratios and corresponding GSMF. The methods used to estimate GSMF 

and the key parameters shown in Table A2-1 are described in Weitz (2010). 
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Table A2-1. Average gamma source modification factors (GSMF) for various ship types

Ship Type Designation Example L

*

(m)

W*

(m)

Snom

*

(fraction)

<GSMF>

w/o SS†

<GSMF> w/SS‡

Average 95th percentile

Aircraft Carrier, ASW CVS USS BOXER 271 45 0

§ 1.51 1.56 1.60

Aircraft Carrier, Escort CVE USS BAIROKO 203 32 0

§ 1.65 1.70 1.74

Amphibious Force 

Flagship

AGC USS ESTES 140 19 0.40 1.99 2.95 3.85

Attack Transport APA USS GENEVA 139 19 0.50 2.01 3.14 4.31

Battleship BB USS NEW YORK 175 29 0.50 1.77 2.58 3.39

Cruiser CA USS PENSACOLA 179 20 0.50 1.95 3.07 4.14

Destroyer DD USS MANSFIELD 115 12 0.50 2.37 4.06 5.79

Destroyer Escort DE USS SILVERSTEIN 93 11 0.50 2.43 4.31 6.25

Dock Landing Ship LSD USS BELLE GROVE 140 22 0.40 1.92 2.75 3.56

Fleet Oiler AO USS CACAPON 169 23 0.30 1.87 2.57 3.22

Fleet Tug ATF USS TAKELMA 62 12 0.35 2.42 3.79 5.09

Infantry Landing Craft LCI LCI-327 48 7 0.30 3.03 5.04 7.17

Salvage Ship ARS USS BOLSTER 65 12 0.50 2.42 4.20 6.00

Store Ship AF USS MERAPI 103 15 0.30 2.18 3.16 4.18

Submarine Rescue Ship ASR USS CHANTICLEER 77 13 0.60 2.36 4.40 6.79

Tank Landing Craft LCT LCT-1013 36 10 0

** 2.60 2.80 2.96

Tank Landing Ship LST USS LAWRENCE CO. 100 15 0.30 2.19 3.17 4.16

* Ship characteristics: L = Length; W = Beam; Snom = Nominal superstructure fraction; SS = superstructure (Weitz, 2010).

† This column contains the mean of the distribution of average GSMF values obtained without allowance for superstructure for each ship type. 

‡ These columns contain the average and 95th percentile values of the distribution of average GSMF values calculated for various values of S for each ship type.

§ As a first approximation, the superstructure of an aircraft carrier was neglected in this assessment because it is located on the extreme starboard side of the 

flight deck and therefore provides little shielding to those crewmembers who worked on the flight deck.

** LCT has a nearly rectangular deck with a modest superstructure at the far aft end.