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UA01 – Dose Uncertainty and Upper-Bound Dose Determinations 

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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

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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 - Section 5.3.1: Added reference to a case as an example for the 

treatment of uncertainties for mission film badges. 

- Minor editorial changes

03/31/2008 Paul K. Blake

1.3  There was no Revision 1.2.

 Expanded to include probabilistic uncertainty analysis

 Expanded equations on combining errors and examples in 

Attachment 1.

 Other editorial changes

01/31/2010 Paul K. Blake

1.3a Removed references to attachments in other SMs 03/31/2010 Paul K. Blake

2.0 - Section 5.1.1.1: clarified how the uncertainty factors for 

neutron dose are applied.

- Section 5.1.1.2: clarified that the uncertainty factor of 3 

should be applied as a default value for reconstructed external 

gamma doses.

- Section 5.1.2.1: clarified that an uncertainty factor of 1 should 

be used for doses from incidental ingestion of soil and dust, and

doses from inhalation of blast-driven resuspended fallout.

- Revised Attachment 1 to improve readability and make 

corrections.

- Updated References, and made editorial changes throughout.

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

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

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

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

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

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

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

5. Method Descriptions........................................................................................................... 5

5.1 Deterministic Method ............................................................................................. 6

5.1.1 Uncertainties and Upper Bounds in External Dose .................................... 6

5.1.2 Uncertainties and Upper Bounds in Internal Dose ................................... 12

5.1.3 Uncertainties and Upper Bounds in Skin Dose......................................... 14

5.2 Probabilistic Method............................................................................................. 17

5.2.1 Uncertainties in External Dose ................................................................. 18

5.2.2 Uncertainties in Internal Dose Models ..................................................... 24

5.2.3 Treatment of Correlations......................................................................... 28

6. Data and Input................................................................................................................... 28

7. Referenced SOPs from this Manual.................................................................................. 28

8. References......................................................................................................................... 29

Attachment 1 Sample Uncertainty Calculations.................................................................... 31

Attachment 2 Implementation of Probability Density Functions in Mathcad....................... 34
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List of Tables

Table 1. Sample Output from FBDOSE Program ........................................................................ 10

Table 2. Proposed Ranges of Uncertainty Factors for Estimating Point Values Using Measured 

Intensities and Iso-Intensity Contour Maps................................................................ 22
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Standard Method

UA01 – Dose Uncertainty and Upper-Bound Dose Determinations

1. Purpose/Summary

This Standard Method (SM) provides the technical and computational methods for 

assessing the upper-bound doses for external (gamma and neutron), internal, and skin 

doses for individuals in the Nuclear Test Personnel Review (NTPR) Program according 

to the procedures specified in SOP RA01. The upper-bound dose represents the estimated

dose that was received by less than five percent of the population of participants who 

were exposed under similar conditions. That is, 95 percent of all the veterans exposed 

under similar conditions received a dose smaller than the upper-bound dose. As such, the 

upper-bound dose is the 95th percentile of the dose distribution.

2. Scope

This Standard Method provides technical guidance for calculating the upper-bound

external, internal, and skin doses for personnel resulting from exposure to a nuclear 

detonation and to the resulting radioactive material, including both fallout and activated 

sources. This Standard Method is used in conjunction with other Standard Methods for 

assessing radiation exposures in accordance with the requirements of Title 32, Code of 

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

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

2020). 

3. Responsibilities 

Qualified radiation dose analysis staff members use these methods and associated tools 

for assessing the upper-bound radiation doses for exposed individuals.

4. Definitions

Uncertainty factor The ratio of the upper-bound dose to the best estimate dose.

Upper-bound dose A reconstructed dose that has a 95 percent probability of being 

higher than the actual dose. This is equivalent to the 95th percentile 

of a probabilistically determined dose distribution.

5. Method Descriptions

The NTPR Program uses two methods—deterministic and probabilistic—for estimating 

dose uncertainties with the objective of producing an upper-bound dose that represents at 

least the 95th percentile of the dose to the exposed population. That is, that the estimated

dose in either method will be greater than the dose received by 95 percent of the veterans 
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in similar conditions. The deterministic method is based on high-sided estimates of key 

parameters and fixed uncertainty factors that are believed to produce a credible upper 

bound and are considered “veteran friendly” in the absence of full consideration of 

uncertainties. The probabilistic method uses Monte Carlo simulations to provide a full 

analysis of uncertainties. The Monte Carlo simulations consist of randomly sampling 

values of the input parameters from their credible assigned probability distributions; 

those values are input to the dose models to build an output distribution of dose, whose 

summary statistics are calculated. Such distributions account for both inaccuracy, and 

spatial and temporal variability of input parameters to dose models. Procedures are 

available (SOP RA01) to select the method that produces a credible upper-bound dose 

with the best use of time and resources. The following two sections discuss the 

deterministic and the probabilistic methods.

5.1 Deterministic Method

This section describes the methods used to calculate the upper-bound doses of 

deterministically reconstructed mean doses and film badge doses. The following 

subsections discuss the uncertainties and upper-bound doses associated with neutron 

dose, reconstructed external gamma dose, doses from film badges, reconstructed internal 

doses, and skin doses.

5.1.1 Uncertainties and Upper Bounds in External Dose

The external doses are treated as if they are normally distributed when combining 

uncertainties (even if they are more appropriately characterized by a different 

distribution), and are combined using statistical methods appropriate for normally 

distributed data. External gamma and neutron doses, if they are accrued from different 

locations or different sources, are assumed to be statistically independent. Doses from 

multiple detonations accrued while aboard a given ship or on a particular residence island 

during a single operation, or during multiple operations where the participant’s duties 

have not appreciably changed, are treated as being correlated, because the major source 

of uncertainty is from the assumed exposure scenario, e.g., time spent indoors versus 

outdoors or topside versus below deck. Because neutron doses are reported separately 

from external gamma doses, the statistical combination of those two doses is 

unnecessary.

5.1.1.1 Neutron Dose

There are few instances where participants were exposed to neutron radiation from a 

nuclear detonation. In those cases, rigorous assessments have been performed to 

determine estimates of the neutron environments created by the respective detonations. 

As a consequence of adoption of certain recommendations about neutron dose of a 

committee of the National Research Council of the National Academy of Science (NRC, 

2003), earlier best-estimate neutron equivalent doses were increased by approximately a 
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factor of 2. This increase was mostly due to an increase from 10 to 20 of the radiation 

weighting factor (previously referred to as “quality factor”). Uncertainties in the original 

neutron doses were assessed based on estimates of the uncertainties in the underlying 

parameters (e.g., source spectrum and intensity, flux asymmetry) and combined to 

generate a total uncertainty in the prompt neutron doses. These methods for estimating

uncertainties were reevaluated after NRC’s 2003 recommendations and are appropriate 

for current neutron dose assessments. Thus, to determine upper-bound neutron doses the 

revised best estimates of neutron doses (Weitz and Egbert, 2010) were multiplied by the 

neutron dose uncertainty factors derived in the analysis of radiation exposure reports 

prepared for specific groups and ships for certain operations and shots (commonly called 

the “White Books,” e.g., Goetz et al., 1981). For neutron doses for which uncertainty 

factors were not previously calculated or are otherwise inadequate, a UF of 3 is

recommended by Weitz and Egbert (2010). Reconstructed neutron doses and 

corresponding upper bounds thus calculated are reported in Weitz and Egbert (2010). 

Specific information on neutron equivalent doses and their uncertainties is provided for 

specific operations in SOP Appendices A–C.

5.1.1.2 Reconstructed External Gamma Dose

Upper Bound for Initial Gamma Dose

Whole body external gamma doses from initial gamma radiation are assigned uncertainty 

factors based on the uncertainties as determined by gamma transport modeling or 

measurement for participants who were not wearing film badges. The estimates of mean 

initial gamma dose and the uncertainty factors can be found in the analysis of radiation 

exposure reports prepared for specific groups and ships for certain operations and shot 

(“White Books”). Some of the initial gamma doses were found to be underestimated and 

have been revised (Weitz and Egbert, 2010). To obtain upper-bound initial gamma doses, 

the available initial gamma uncertainty factors should be multiplied by the revised best 

estimates for initial gamma doses contained in Weitz and Egbert (2010). For initial 

gamma doses where an uncertainty factor has not been determined, use the high-sided 

default uncertainty factor of 3 (Weitz and Egbert, 2010). Specific information on initial 

gamma doses and their uncertainties is provided for specific operations in SOP 

Appendices A–C.

Upper Bound for Reconstructed Gamma Dose

Whole body external gamma doses from residual radiation exposure, e.g., fallout, and 

neutron-activated soil, are assigned a nominal uncertainty factor of 3. Higher factors 

should be used if demonstrably justified by a greater uncertainty in one or more aspects

of the scenario (Schaeffer, 2015).

For a reconstructed deterministic whole body gamma dose, the upper bound is given by:

UBUFext D

(1)
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where 

UB = The upper-bound dose (rem)

D = Whole body external gamma dose (rem)

UFext = Uncertainty factor associated with reconstructed whole body 

external gamma dose

The upper-bound uncertainty factor for whole body external gamma dose is set to 3 in 

deterministic models as recommended in Schaeffer (2015).

Total Dose, Uncertainty, and Upper Bound for Reconstructed Whole Body External 

Gamma Dose

For n reconstructed deterministic whole body external gamma dose components that are 

uncorrelated, the total whole body external gamma dose, dose component uncertainty, 

and the upper-bound dose are given by:







n

i

D D i

1

  ,

(2)

( 1) u ,i  D ,i UFext  (3)





 

n

i

UB D u i

1

2

   ,

(4)

where 

D = Whole body external gamma dose (rem)

D,i = The i

th component of the total gamma dose D (rem)

u,i = The uncertainty associated with the i

th component of the total 

reconstructed gamma dose D (rem)

UB = The total upper-bound whole body external gamma dose (rem)

5.1.1.3 Dose from Film Badges

Uncertainties associated with film badge readings are treated differently than the 

uncertainties for reconstructed whole body gamma doses (SM ED01). The uncertainty for 

film badge readings has many sources and is handled differently for individually issued,

permanent or mission, dosimeters than for cohort film badges. Dose uncertainty related to 

doses from cohort film badges or other dosimeters are addressed at the end of this 

subsection. 
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Uncertainties in film badge dosimetry are treated using the guidance contained in the 

report entitled Film Badge Dosimetry in Atmospheric Nuclear Tests (NRC, 1989). With 

all dose uncertainty calculations associated with film badges, the total reported mean 

dose is the officially recorded film badge reading while the upper-bound assessment uses 

the bias-corrected mean dose, which is derived from recommendations in NRC (1989). 

The exceptions to this general approach are for Operations BUSTER-JANGLE and 

TUMBLER-SNAPPER, where the bias correction is greater than the overall uncertainty 

and the calculated upper-bound dose is less than the reported dose for a given badge. For 

those operations, the NTPR program considers the recorded film badge reading and the 

upper bound to be one and the same.

Sources of Uncertainty in Film Badge Readings

The NTPR program implements three of the four principal types of bias and uncertainty

that affect film badge dosimetry results for atmospheric nuclear test participants

discussed in NRC (1989). These types of bias and uncertainty are radiological, 

laboratory, and environmental factors. The fourth source of bias and uncertainty

discussed in NRC (1989) is the conversion of film badge (FB) exposure in milliroentgens 

(mR) to Deep-dose Equivalent (DDE) (USNRC, 2020) in millirem (mrem), which is the 

dose equivalent from penetrating radiation to soft tissue located at a depth of 10 

millimeters in the body and is due to variations in geometries and size and shape of 

individual badge wearers. NTPR does not consider the bias caused by the FB to DDE 

conversion but does consider the uncertainty (SAIC, 2006).

In addition to the types of uncertainties associated with bias in film badge results, there 

are several sources of uncertainty due to film badge handling, administration, and 

documentation. These non-statistical categories of uncertainty include film badge 

readings incapable of being properly analyzed during processing for the exposure 

scenario, or due to film badge damage. The handling of these types of uncertainties is

discussed in SM ED01.

In addition to the uncertainties associated with individual film badges, the use of cohort 

film badges creates additional uncertainty. The additional uncertainty is due to variations 

in activities and locations that would cause variation in the doses between the badge

wearing member of the cohort and others in the cohort (NRC, 2003).

Uncertainty and Upper Bound for Film Badge Readings

NTPR uses the FBDOSE program (SAIC, 2006) to estimate the component of external 

gamma dose, uncertainty, and upper-bound dose from film badge readings. The FBDOSE 

manual has a detailed discussion of how to run the program, enter data, and use the 

output. An example of an FBDOSE output (FBDOSE.OUT) is given in Table 1. 

Although specific to Operation BUSTER-JANGLE, the format in the example in Table 1

is completely generic.
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Table 1. Sample Output from FBDOSE Program

 FILM BADGE DOSE EQUIV

FILM BADGE INTERVAL MR MRADJ LOWER MEAN UPPER UPP90 EXPL CODE

10 28 51 TO 10 28 51 380 380 221 332 498 466 

10 28 51 TO 10 28 51 0 0 0 0 0 0 3

10 30 51 TO 10 31 51 240 240 139 209 314 294 

11 5 51 TO 11 5 51 0 20 0 17 57 47 5

11 19 51 TO 11 19 51 100 100 52 87 145 134 

11 29 51 TO 11 29 51 140 140 77 122 192 178 

11 30 51 TO 12 2 51 320 320 186 279 419 393 

12 3 51 TO 12 3 51 190 190 109 166 252 235 

 ----- ----- ----- ----- ----- -----

TOTALS FOR FB, FBDE: 1370 1390 903 1215 1633 ( 1557 @ 90 PCT)

EXPLANATION CODES: 1 = UNIT DOSIMETRY READS ZERO

 2 = RECONSTRUCTED ZERO DOSE

3 = NO EXPOSURE POTENTIAL

4 = HELD AS ZERO PENDING RESEARCH TO DEFINE EXPOSURE

5 = CONVERTED TO HALF OF MDL

6 = TOTAL OF MULTIPLE FILM BADGE READINGS

The FBDOSE variable names in the output above are defined as follows:

FILM BADGE INTERVAL – Dates of coverage for each badge as input by the 

user in MM DD YY format.

MR – Film badge reading (mrem) for each badge and their total sum.

MRADJ –Film badge reading (mrem) adjusted to account for sub-MDL doses and 

their total sum. In Table 1, the first zero badge was treated as a “definite” zero and 

the second as a “soft” zero resulting in a dose of 20 mrem, which is half of the 

minimum detection limit (MDL) of 40 mrem.

LOWER – Lower limit of the 95-percent confidence interval associated with each 

individual mean dose equivalent and total dose equivalent (mrem). LOWER 

includes 2.5 percentile of the dose distribution. 

MEAN – Central estimate of dose equivalent (mrem) for each exposure and for 

the total dose equivalent (bias removed).

UPPER – Upper limit of the 95-percent confidence interval associated with each 

individual mean dose equivalent and total dose equivalent (mrem). UPPER 

includes 97.5 percentile of the dose distribution.

UPP90 – Upper limit of the 90-percent confidence interval, which brackets the 5th

to 95th percentile, associated with each individual mean dose equivalent and total 

dose equivalent (mrem). This value is used for reporting the 95th percentile upperbound dose.
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In uncertainty calculations, the analyst uses the total in the MRADJ column shown in 

Table 1 as the total external gamma dose and the total of the UPP90 column as the upperbound 95th percentile dose. For external dose involving only film badge readings, upperbound dose and the uncertainty of the film badge dose are given by:

D FB

(5)

UBFB FBUB

(6)

uFB FBUB  FBMEAN

(7)

where

FBγ = The total dose from all film badge dosimetry taken from the total 

of the MR column of the FBDOSE output (rem)

UBFBγ = The upper-bound whole body external gamma dose based only on 

film badges (rem)

FBUB = The upper bound for all film badge dosimetry taken from the 

UPP90 column of the FBDOSE output (rem)

uFBγ = The uncertainty of the film badge gamma dose (rem)

FBMEAN = The total mean film badge dose adjusted for bias taken from the 

MEAN column of the FBDOSE output (rem)

The uncertainty associated with the total film badge dose, uFBγ, is used to estimate upperbound doses involving a combination of film badge readings and reconstructed whole 

body external doses.

Uncertainty and Upper Bound in Cohort Film Badge Readings

Because cohort badges have a greater degree of uncertainty than individually issued

permanent or mission film badges, the FBDOSE-based method of uncertainty analysis 

should not be used (Kocher, 2004). When using cohort film badges, the mean dose 

should be calculated using the FBDOSE program the same as above. However, when an 

external gamma dose is estimated based on the results from one or more film badges 

worn by other members of a participant’s exposure cohort, the external uncertainty factor 

UFext of 3 for reconstructed doses should be applied instead of UPP90. The uncertainty of 

the estimated dose should be calculated using Equation 3. 
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5.1.1.4 Combined Reconstructed and Film Badge External Gamma Doses

The total gamma doses and their associated uncertainties from each of the two categories 

(reconstructed whole body external gamma and film badge-based) are combined 

assuming the dose distributions are normal (even though it is likely both tend towards 

being lognormal or something different entirely). This assumption simplifies the 

calculations required to generate an upper-bound dose and does not appreciably affect the 

overall result. As was stated above, what is important to remember is that, if film badges 

are part of the uncertainty calculation, the reported film badge dose is used for the 

reported mean total external gamma dose, while the bias-corrected mean dose is used 

with its associated uncertainty for the upper-bound external gamma dose.

Estimate and Upper Bound for Reconstructed Gamma Dose and Film Badge Dose

For n reconstructed gamma dose components and film badge results, the total whole body 

external gamma dose and the upper-bound dose are given by: 

D D FB

n

i

  i 

1

,

(8)

2

1

2

,

1

  ,  FB

n

i

MEAN i

n

i

UB D i  FB  u  u

 

(9)

Note: the uncertainty for the reconstructed doses is given by Equation 3 and the

uncertainty for film badge results is given in Equation 6.

5.1.2 Uncertainties and Upper Bounds in Internal Dose 

Prior to NRC’s 2003 recommendations, internal doses were reported using a single point 

estimate that, based on the high-sided value used for the resuspension factor and other 

factors, was considered to be equivalent to or greater than the 95th percentile. However, 

the uncertainty in the dose coefficients used to calculate those internal doses was not 

taken into account. Therefore, it was estimated that all previously reported (upper-bound) 

internal doses could be low by a factor of 10 or perhaps more. To take these facts into 

account, an uncertainty factor UFint of 10 was selected (Schaeffer, 2015). Because the 

previously reported “best estimate” doses were still high-sided, it should be understood 

that those doses are not true means and that the uncertainty factor of 10 is in addition to 

the already included high-sided parameters underlying that previously reported best 

estimate dose. An uncertainty factor of 1 is used for incidental ingestion doses since that

internal dose calculation represents an upper-bound estimate (SM ID01). 
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Internal doses, having uncertainties that are not necessarily related to the source or 

location of the exposure, may be combined assuming all internal component doses are 

fully correlated. Though it is possible that there is some degree of independence among 

the component doses, NTPR assumes the component doses are fully correlated, which 

high-sides the resultant upper-bound doses. An exception is made when combining 

internal doses based on mission film badges that have different issue and return dates. 

This exception is discussed below. 

5.1.2.1 Reconstructed Internal Dose

The total and upper-bound doses from intakes by inhalation or ingestion of the combined 

radionuclides in a mixture produced by alpha particles, or by beta particles plus gamma 

rays are given by:







n

i

D Di

1

(10)







n

i

UB UFint i Di

1

,

( )

(11)

where 

D = The total internal dose to a specific organ from all sources of

intake (rem)

Di = The i

th component of internal dose to a specific organ (rem)

UFint,i = The uncertainty factor for internal doses to a specific organ is

assumed to be 10 in deterministic models, except for incidental 

ingestion, and inhalation from blast-resuspended fallout, for which 

the uncertainty factor is assumed to be 1 because the estimated 

doses are estimates of upper-bound doses (see SM ID01)

UB = The upper-bound total internal dose to a specific organ (rem) 

5.1.2.2 Additional Uncertainty in Internal Dose from Mission Film Badges with Periods of 

Coverage Exceeding One Day

When film badge readings from mission film badges are used to determine internal doses, 

the estimated total dose is determined in accordance with SM ID01. In addition to the 

internal dose uncertainty described above, an additional uncertainty is added to the 

overall uncertainty. The additional mission film badge uncertainty is determined using 

the difference between the internal dose calculated assuming that the entire dose was 

received on the film badge issue date and the internal dose assuming the entire dose was 

received on the film badge return date. The mission film badge uncertainty is combined 

in quadrature such as in Equation 14 with other independent sources of internal dose. The 
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uncertainty of the internal dose determined from mission film badge results, the 

uncertainty of internal doses based upon reconstructed gamma doses, and the upperbound dose for combined internal doses are given by: 

uFB  D1  D2

(12)

( 1) ui  Di UFint,i  (13)





  

n

i

UB D uFB ui

1

2 2

(14)

where

uFB = The additional uncertainty for an internal dose calculated using 

mission film badges that have different issue and return dates (rem)

D1 = The internal dose calculated using mission film badge readings 

assuming all of the dose was received in an 8-hour period on the 

date of film badge issue (rem)

D2 = The internal dose calculated using mission film badge readings 

assuming all of the dose was received in an 8-hour period on the 

date of film badge return (rem)

ui = The uncertainty for an internal dose from the i

th intake (rem)

UB = The upper-bound internal dose of combined internal doses and 

uncertainties (rem)

5.1.3 Uncertainties and Upper Bounds in Skin Dose

5.1.3.1 Skin Doses from External Sources (Gamma and Beta Shine)

The uncertainties in skin doses from external gamma and beta shine sources not in 

contact with the skin are generally assumed to be no greater than the uncertainty in the 

associated external gamma dose from such an external source. This is due, in part, to the 

fact that the beta-to-gamma ratios used to relate external gamma dose to beta dose were 

intended to be high-sided estimates. Thus, most beta shine skin doses are assigned the 

same uncertainty factor (UFext) as their associated gamma skin dose (Schaeffer, 2015), 

unless otherwise indicated (Barss and Weitz, 2006). Beta shine doses and their 

accompanying external gamma skin doses are assumed to be fully correlated, as are most 

doses from a single source exposure location (e.g., multiple disparate periods aboard the 

same ship are treated as if all of those individual doses are fully correlated). Skin doses

may be calculated from reconstructed external gamma doses or film badges readings. 
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Total Dose, Uncertainty and Upper Bound for Reconstructed Gamma and Beta Shine

Skin Dose

The skin dose for n reconstructed external gamma doses is based on the reconstructed 

gamma doses (Dγ,i). The estimated beta shine skin dose, total skin dose, the uncertainty of 

the total skin dose, and the upper bound of the total skin dose are given by:

D,i  D ,i R

(15)

( ) DSkin,i  D ,i  D,i

(16)







n

i

DSkin DSkini

1

,

(17)

( 1) u ,i  DSkin,i UFext  (18)





 

n

i

UBSkin DSkin u i

1

2

 ,

(19)

where

D,i = The i

th component of the gamma skin dose (rem)

D,i = The i

th correlated corresponding component mean beta skin 

dose (rem)

R = The beta-gamma ratio used to convert reconstructed whole body 

external gamma doses to beta shine skin doses

DSkin,i = The i

th component of combined beta and gamma skin dose (rem)

DSkin = The total skin dose (rem)

u,i = The uncertainty associated with the i

th component of the beta plus 

gamma reconstructed skin doses (rem)

UBSkin = The total upper-bound skin dose (rem)

Note that it is possible to accrue a gamma skin dose without an accompanying beta shine 

dose, in which case the corresponding beta terms for that particular gamma dose are all 

zero.

5.1.3.2 Skin Doses Based on Film Badge Readings

Film badges were often worn in areas affected by fallout or neutron activation and 

measured the external gamma doses that resulted from exposures to these sources. The 

beta shine skin dose from accompanying beta radiation, while not directly recorded by 
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the film badge, can be correlated with the measured gamma dose by means of beta-togamma ratios. In such cases, the upper-bound skin dose is calculated based on the upper 

bound of the film badge dose. The upper bound of a total beta dose that is based on 

multiple film badge readings can be calculated by multiplying the ratio of the total mean 

and total upper-bound film badge doses by the total mean beta dose.

Reconstructed Gamma and Beta Skin Dose Combined with Film Badge-Derived Skin 

Dose 

If a skin dose is estimated by reconstructed external gamma doses and film badge doses, 

the total skin dose and the upper bound of the skin dose are given by:

( ) (1 )

1

D D , FB R

n

i

Skin   Skini  



(20)

( )(1 ) uFB FBUB  FBMEAN  R

(21)

2

1

2

,

1

,

(1 )

 



FB

n

i

i

MEAN

n

i

Skin Skini

u u

UB D FB R



   









(22)

where 

uFBβγ = The uncertainty of the skin dose determined from film badge 

doses (rem)

The same formula can be used for the combined beta and gamma skin dose that is based

only on film badge results by setting the other variables to zero.

5.1.3.3 Skin Contamination Dose

Skin contamination doses were not routinely reported prior to the NRC recommendations 

of 2003. Thus, a methodology (and accompanying uncertainty analysis) has been

developed to address that need (SM ED04). The uncertainties in the doses associated with 

skin contamination range from a factor of 4 up to a maximum of slightly less than 18

(Schaeffer, 2015), depending on the location of the skin cancer site (Apostoaei and 

Kocher, 2010). All skin contamination doses can be assumed to be fully correlated. 

Though it is possible that there is some degree of independence among the component 

doses, NTPR assumes the component doses are fully correlated.
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The total skin contamination dose is simply the sum of all the component skin 

contamination doses and the total upper-bound skin contamination dose is the sum of all 

the component upper-bound skin contamination doses. Each component of the skin 

contamination dose (descending and resuspended) has its own uncertainty. For n sources 

of skin contamination, the total skin contamination dose and the upper-bound skin 

contamination dose are given by:







n

i

DSC DSC i

1

,

(23)







n

i

UBSC UFSC i DSC i

1

, ,

( )

(24)

where

DSC = Total skin contamination dose from all sources of contamination 

(rem)

DSC,i = The i

th component skin contamination dose (rem)

UFSC,i = Uncertainty factor associated with the i

th skin contamination dose 

UBSC = Upper-bound total skin contamination dose (rem) 

5.1.3.4 Combined Skin Dose

The total skin dose is the sum of the component skin doses. As with the external gamma 

doses, the dose distribution associated with each category of uncertainty is assumed to be 

normal. The uncertainties would be combined in quadrature and the upper bound would 

be the sum of the mean doses and the combined uncertainties.

5.2 Probabilistic Method

The alternative approach for treating uncertainties is the probabilistic or Monte Carlo

method. In a Monte Carlo simulation, each input parameter is considered as a random 

variable whose value is determined by randomly sampling from its assigned probability

distribution. These distributions reflect the variability and uncertainties in the values of 

the associated input parameters. The collection of sampled values, one per input 

parameter, defines a “scenario.” An output quantity, such as an external or internal dose, 

is then computed for each scenario using an algorithm that models the relevant physical 

and biological processes; this calculation constitutes one “history.” By repeating this 

procedure for many histories, a distribution of output values is accumulated. Analysis of

the output distribution yields statistical parameters such as its mean, standard deviation, 

and percentiles, all of which increasingly represent their corresponding “true” population 

values as the number of histories increases. Monte Carlo methods can become 
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computationally intensive if the algorithm is complex and the number of histories is 

large.

As indicated, the probabilistic method requires that the uncertainties of input parameters 

be represented as probability distributions. However, not all input parameters require 

such formal representations. It is obviously unnecessary to develop uncertainty 

distributions for input parameters that have virtually no uncertainty – an arrival or 

departure date confirmed by ship’s logs, travel orders, flight manifests, morning reports

and/or muster logs can be considered to have little or no uncertainty unless there are 

conflicts in such documentation. (The formal probability distributions in such cases are 

sharply peaked delta functions). Other input parameters, while uncertain, may have 

negligible impact on dose and likewise do not require the development of distributions. 

For example, a participant’s arrival date at a test site may be uncertain, but this 

uncertainty is not important if it is known that he arrived before the first fallout event at a 

previously uncontaminated location. Thus, the first task in the application of the 

probabilistic method to dose reconstruction is to screen all input parameters to identify 

those which warrant the formal development of uncertainty distributions.

The next task is to develop or acquire the requisite parameter uncertainty distributions. 

Much of the remainder of this section and Attachment 2 are devoted to this topic. Once

accomplished, the parameter distributions are input to a computer program which 

contains the Monte Carlo sampling logic. The program selects values of a parameter from 

its assigned distribution as it executes the iterative Monte Carlo algorithm to generate the 

output distributions of external and internal doses. A typical probabilistic dose 

reconstruction is based on 10,000 histories, each involving the random sampling of 

multiple input parameter distributions. The 95th percentiles of the output dose 

distributions, representing the doses accrued by at least 95 percent of the exposed 

population—personnel involved in similar activities—are taken as the respective upper 

bounds. 

The following two subsections focus on uncertainty modeling of parameters associated 

with external and internal doses, respectively. The probabilistic methodology has not yet 

been extended to neutron doses and beta skin/eye doses.

5.2.1 Uncertainties in External Dose

Input parameters for external dose models may be categorized as operational parameters 

that define a participant’s location, movement, and habitat, and environmental parameters 

that characterize the radiation environment in his vicinity. The modeling of uncertainties 

for parameters of both types is discussed below.

5.2.1.1 Operational Parameters

Site Arrival/Departure Dates/Times

Dates of arrival and departure from test sites are generally well known. If an uncertainty 

exists in one of these dates that may impact the reconstructed doses, each of the candidate
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dates may be assigned a probability that reflects the likelihood it is the correct date. For 

arrival date, in light of the remarks made above, this will be required for only if the 

participant arrived at a previously contaminated location and/or after the first fallout 

event. As examples, if it is known that a participant arrived at a test site no earlier than 

May 5 and no later than May 25, in the absence of any other information a uniform 

distribution covering the inclusive period May 5–25 can be used. If a morning report 

indicates that he departed on July 25 but travel orders list a departure date of July 28, and 

the documentation is considered equally authoritative, each of those dates could be 

assigned a probability of 0.5 and his departure date treated stochastically. 

Arrival and departure times are usually less well known than the dates, but they generally 

have a proportionally smaller impact on reconstructed dose. Time may be important if a 

radiologically significant event, such as an abrupt, intense period of fallout, occurred on 

the day of arrival or departure, for which the participant may or may not have been 

present depending on the timing of his arrival or departure. In cases where the 

arrival/departure time may be important, that parameter can be modeled as uniform over 

some interval if all times within that interval are considered equally likely, or with a nonuniform distribution if some times are thought to be more likely than others.

Film Badge Issue/Return Dates/Times

There are frequently inconsistencies in film badge issue and/or return dates entered in the 

dosimetric record. As a common example, the dosimetry record of a participant issued a 

sequence of badges states that he turned in his first badge a number of days after 

receiving his second. If taken literally, this implies that he had two badges in the interim, 

whereas documented radiation safety procedures indicate that badge turn-in and receipt 

occurred concurrently. Apparent discrepancies of this type are usually resolved in 

deterministic assessments by assuming the actual turn-in date of the first badge coincides 

with the issue date of the second. While this may be a likely scenario, it is still possible 

that the dates in the dosimetry record are correct. In a probabilistic assessment, the turn-in 

date can be treated as a random variable to be selected on the basis of probabilities 

assigned to the two dates.

The time of a film badge exchange is usually unknown. In the unlikely event that this 

time impacts a dose reconstruction, it can be treated as a random variable in a manner 

similar to that discussed above regarding arrival and departure times.

Maneuver Characteristics

Maneuvers frequently were conducted at the Nevada Test Site (NTS) in conjunction with 

nuclear detonations. These events are characterized by parameters such as start times, 

march rates, distances of closest approach to radioactive objects or sites, and linger times 

at critical locations. The uncertainties of these and similar continuous parameters can be 

modeled using probability distribution functions (pdfs) of the forms discussed in Weitz et 

al. (2009). For example, the uncertainty in rate of march toward an objective can be 
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represented by a triangular distribution whose defining characteristics (minimum, most 

likely, and maximum march speeds) are assigned in consideration of the distance, known 

duration times, weather, and type of terrain traversed. Discrete probability distributions 

may also be relevant. If it is known that, of 1000 Marines who took part in a maneuver,

700 followed path A to an objective and 300 followed path B, the reasonable pdf for 

cases where this parameter is unknown would have two discrete outcomes: path A with 

probability 0.7 and path B with probability 0.3.

Fraction of Time Spent Outside

The fraction of time a participant spent outside versus inside while in a fallout field 

impacted his external dose because buildings and other structures provide partial 

shielding to the outside environment. Lacking specific statistical data on this parameter 

for an individual or a cohort, a triangular distribution is recommended. Factors such as 

the participant’s job, the weather, the availability of outdoor recreational facilities, and 

veteran-provided information, are considered in assigning the distribution’s defining 

values of minimum, most likely, and maximum fraction of time outdoors. Standard 

Method ED02 lists default values of the input parameters used in external dose 

estimations.

Structural Occupancy 

The types of structures a participant occupied while not outside impacted his dose 

because structures of different types provide varying degrees of protection from radiation 

(see discuss of structural shielding below). It was common for personnel stationed on one 

of the residence islands in the Pacific Proving Ground (PPG) to work in wood-framed 

buildings and billet in tents. If, while indoors, a participant spent the majority of his time 

in one or the other of these two structures, a relevant input parameter is the fraction of his 

indoor time he spent in a tent (versus in a building). If specific statistical information on 

this parameter for an individual or cohort is not available, a triangular distribution is 

recommended. Factors such as job responsibilities, shift hours, and building type are 

considered in assigning the distribution’s defining values of minimum, most likely, and 

maximum fraction of time inside a tent. ED02 lists default values of the input parameters 

used in external dose estimations.

5.2.1.2 Environmental Parameters

Film Badge Results

The uncertainty in undamaged film badge exposure readings is modeled by a lognormal 

distribution (NRC, 1989), which defined two quantities—the measurement bias B and the 

95th percentile uncertainty factor K. As the name implies, B is the estimated systematic 

error or bias introduced into the measurement process by, for example, an error in film 

calibration, pre-issue exposure to radiation of the film, or fogging of the film due to heat 
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and/or humidity. The parameter K is a measure of the random error characterized by a 

lognormal distribution, and is related to the geometric standard deviation (GSD) as 

follows:

1.645 K  GSD

(25)

The usefulness of this parameterization lies in the fact that there is only a 5-percent 

probability that the true exposure associated with a film badge-measured exposure 

E—the film badge reading—is greater than K∙E/B. Estimates of B and K, by nuclear test 

series, are provided in NRC (1989). From these, the geometric mean GM = E/B and 

GSD = K

1/1.645 are determined and the lognormal distribution representing the uncertainty 

in a film badge reading is thereby defined. The resulting distributions can be combined 

with the distributions for other dose components to produce an overall dose distribution 

and associated parameters (mean and upper bound). If a film badge dose is assessed as 

being from a damaged film badge, then the corresponding dose and uncertainty 

distribution should be estimated by reconstruction using the methodology provided in 

Section 5.2.1.1 above (also see SM ED01).

Radiation Intensity Reading Data

The uncertainty in intensity reading data represents the overall error in intensity readings 

collected using survey meters or similar instruments, then processed and recorded in data 

logs and other documentation. These errors resulted mainly from inherent instrument 

precision, calibration error, instrument drift, operator bias, data processing tools, and data 

recording errors. Based on previous modeling efforts, it is recommended that the 

uncertainty in intensity reading data be modeled as a normal distribution with an 

uncertainty factor of 1.5 to 2, as indicated in Table 2. This uncertainty factor, defined as 

the ratio of the 95th percentile to the mean of the normally distributed intensity reading 

data, is a dimensionless quantity to be used as a multiplier on the estimated central value 

of the intensity reading data. 

Use of Iso-Intensity Contour Maps

When using measurements or iso-intensity maps to estimate point values in time and 

space (location), the related uncertainty comprises two components. The first component 

is the uncertainty from errors in the intensity reading data (see source of uncertainty from 

radiation intensity reading data discussed above) and uncertainty introduced when maps 

are created from a discrete and often sparse set of point observation measurement data. 

The second component is the additional uncertainty that arises when an estimate is made 

at any point on a map by interpolation (or in some cases by extrapolation) from an 

iso-intensity contour map. In addition, when assessing the radiation environment for 

atmospheric nuclear test participants, information on the reliability of data collection and 

processing is often lacking and adds to the overall uncertainty from modeling the 

radiation environment. 
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Table 2. Proposed Ranges of Uncertainty Factors for Estimating Point Values Using 

Measured Intensities and Iso-Intensity Contour Maps

Source of Uncertainty Uncertainty Factor * Distribution Note

Instrument precision, 

calibration and operator 

error (this is applicable 

when no interpolation is 

carried out, i.e., where a 

measurement was 

recorded at the location of 

interest) 

1.5–2 Normal Location and time 

known 

With additional 

uncertainty due to 

contouring scatter point 

data

2–3

† Lognormal/

triangular

Lognormal most 

adequate for intensity 

distributions around 

and not far away from 

GZ

With additional 

uncertainty due to using 

contour maps to determine 

point estimates by 

interpolation (factor is 

higher when location and 

time of measurements are

unknown or inaccurate)

3–5

† Lognormal/

triangular

Lognormal most 

adequate for intensity 

distributions around 

and not far away from 

GZ

Additional uncertainty due 

to using contour maps to 

determine point estimates 

by extrapolation

5–10 † Lognormal/

triangular

Lognormal most 

adequate for intensity 

distributions around 

and not far away from 

GZ

Extrapolation with high 

uncertainty from all other 

sources and surrogate data 

are used

10–15 ‡ Lognormal/

triangular

Lognormal most 

adequate for intensity 

distributions around 

and not far away from 

GZ

* The 95-percent uncertainty factor (UF) is the ratio of the 95th percentile to the central estimate of the 

distribution, which in most cases is the median, mean, or geometric mean (e.g., lognormal distributions).

† Combined uncertainty factors, which include instrument and operator error and all antecedent uncertainty 

sources. 

‡ When surrogate data are used, estimates are presumed to be made by extrapolation, e.g., as when using 

processed intensity data from a neighboring ship or island. 
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The guidelines in Table 2 provide ranges of uncertainty factors and types of distributions 

that are based on the various sources of uncertainties and their cumulative effects 

(Chehata, 2009). The uncertainty factor, defined as the ratio of the 95th percentile to the 

central estimate of the variable distribution, is a dimensionless quantity to be used as a 

multiplier on the estimated central value of the radiation intensity. The selection of an 

uncertainty factor within the suggested ranges should be based on knowledge of the 

reliability of the documentation and the methods used to produce the supporting 

iso-intensity map. 

Non-Uniformity of Intensity

A model of the time-dependent, area-averaged outdoor intensity on each of the residence 

islands at PPG is well established for each fallout event. The outdoor intensity as a 

function of location on the island undoubtedly varied about this average, and at the 

locations occupied by a participant (e.g., at his work site, in his billet area, at a 

recreational area) may have been greater or less than the average. This uncertainty in the 

site-to-site variation in intensity on the residence islands is characterized with a 

lognormal distribution having a geometric mean of 1.0 and a geometric standard 

deviation of 1.5 as provided in SM ED02 and in Weitz et al. (2009).

For ships that received fallout from a nuclear test, the area-averaged topside intensity was 

frequently documented in deck logs, in operational reports, or an average intensity can 

reasonably be inferred from intensity readings reported on nearby ships or land masses. 

The variability of intensity with topside location contributes to the uncertainty in the 

external dose of an individual crewman who may have manned a topside workstation 

where the intensity differed significantly from the average. When calculating doses 

probabilistically the algorithm available in Weitz (2009a) is recommended for estimating 

the distributions of gamma intensities on the weather decks of fallout-contaminated ships

with appropriate user-supplied values of the input parameters to generate ship-specific 

distributions of topside intensity.

Intensity Decay Rate

The radiation intensity in a fallout contaminated area will decrease with time due to 

radiological decay and weathering. As discussed in SM ID01 shot-specific, timedependent radiological decay functions can be obtained directly from the FIIDOS 

software (Raine et al., 2007). The primary uncertainty in the FIIDOS-derived decay 

functions is the degree to which radiochemistry data based on cloud samples are 

representative of the radionuclide mix that was deposited and remained on the ground at 

any given location. That is, how much fractionation took place during the deposition 

process and thereafter due to weathering. Inherent in the FIIDOS database is the 

assumption that no fractionation, other than removal of noble gases, occurred during and 

after deposition. A rigorous study of fractionation has not yet been performed. 
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Lacking that, an empirical model of the uncertainty in decay rate was developed and is 

recommended for NTPR assessments. In that model, the FIIDOS decay functions are 

multiplied by a time-dependent error factor (t/to)

a

, where exponent a is drawn from an 

appropriate normal distribution. Justification and details of this model are provided in 

Weitz et al. (2009). Parameters of the distribution for a are provided in SM ED02. 

Structural Shielding

The protection factor PF of a land-based structure, such as a building or tent, is defined 

as the quotient of the free-field radiation intensity outside the structure and the free-field 

radiation intensity inside the structure. Thus, it is a measure of the radiological protection 

provided by that structure. When performing probabilistic dose reconstructions for landbased personnel, the uncertainty in PF is characterized using both the physical properties 

of that structure (e.g., its width, length, type of construction material) and on the random 

location within the structure where an individual can be positioned. The algorithm for 

developing structure-specific PF uncertainty distributions is provided in Weitz (2014) 

and is recommended as general procedure. 

The shielding factor SF for ships is defined as the ratio of intensity at some below-deck

location to the average topside intensity above the head of the exposed individual. The 

shielding factor depends on the characteristics of the ship, i.e., maximum width (beam), 

length, number of decks, deck height, and decking thickness, and on one’s position 

within the ship (which deck and location on that deck). Uncertainties or variability in all 

these parameters are reflected collectively in the uncertainty distribution of SF. The 

algorithm described in Weitz (2009b) is recommended to calculate ship- and deckspecific shielding factor distributions from contaminants deposited on weather deck 

surfaces.

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 examination). However, the 

uncertainty in this parameter is expected to be relatively small and to contribute 

negligibly to the overall uncertainty in dose. For this reason, uncertainty distributions for 

FB have not yet been developed.

5.2.2 Uncertainties in Internal Dose Models

Internal doses from inhalation and ingestion intakes of fallout and of neutron-activated 

soil and dust are evaluated in probabilistic assessments with the equations given in 

SM ID01. The input parameters for these internal dose models may be categorized as 
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environmental parameters that characterize the contaminant environment and biokinetic 

parameters that relate the contaminant environment to human intake and organ dose. 

Techniques for quantifying the uncertainties for parameters of both types are discussed 

below.

5.2.2.1 Contaminant Environment

Activity Fractions of Descending Fallout Particles

Internal dose from inhalation of descending fallout depends on the amount of activity 

fallout particles contain and the concentration in air of particles that can be inhaled. 

Particle size and activity are correlated, and as described in Weitz (2009c) these 

correlations are expressed as activity fractions. An activity fraction is defined as the 

fraction of total activity that is carried by particles with sizes within a specific range. 

For probabilistic dose assessments, the activity fractions AF1, AF2, and AF3 are calculated 

for the particle aerodynamic diameter in three size classes—1, 2, and 3. These activity 

fractions are calculated as described in SM ID01 using the parameters AF100, f1 and f2, 

where AF100 is the fraction of total activity carried by all particles with diameters less 

than 100 μm, and f1 and f2 are the fractions of AF100 that are attributable to particles in 

size Class 1 and Class 2, respectively.

For a given fallout event, values of the parameters AF100, f1, and f2 are randomly sampled 

from their assigned triangular distributions. A distribution for the fraction of AF100 that is 

attributable to particles in size Class 3 is generated using the quantity (1 - f1 - f2). The 

distribution for AF100 is shot-specific, and those for f1 and f2 are generic. The minimum, 

most likely, and maximum values for these uncertainty distributions are provided in 

Weitz (2009c) and are summarized in SM ID01.

Deposition Velocity

Internal dose from inhalation of descending fallout is inversely related to the velocities at 

which fallout particles descend to the ground (deposition velocities), as seen in SM ID01. 

Three such velocities, V1, V2, and V3, one for each of the size classes specified above, 

have been modeled for use in probabilistic analyses. The uncertainty distributions 

assigned to these deposition velocities are log-triangular with the parameters given in 

Weitz (2009c) and in SM ID01.

Gamma Source Modification Factor

Ratios of surface activity density to intensity (Ci m−2per R h

−1

), generated with the 

FIIDOS code for infinite plane sources, are used in internal dose calculations to estimate 

airborne activity concentrations based on intensity measurements. The Gamma Source 

Modification Factor (GSMF) corrects for the fact that the contaminated surface was not 

infinite in spatial extent, as assumed in the FIIDOS calculations. For land-based 
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applications, the area of fallout deposition was generally large enough that the correction 

is insignificant. Thus, for exposures to fallout on land, GSMF is set equal to 1. 

However, for shipboard exposure scenarios, the contaminated area was limited to the 

weather deck of the ship and the correction is necessary. Weitz (2010) discusses the 

formulation of GSMF for probabilistic assessments of shipboard exposures and provides 

Mathcad-based programs for generating ship-specific distributions for aircraft carriers, 

ships with elliptical shapes and superstructure. 

Activity Density-to-Intensity (FIIDOS) Ratios

The discussion above on GSMF focuses on how to adjust the value of the FIIDOSgenerated surface activity density-to-intensity ratios to account for finite source size. 

There is an underlying uncertainty in the FIIDOS ratios themselves, independent of 

source size. A major contributor to this uncertainty is fractionation, which has not yet 

been taken into account. Quantification of this uncertainty is a subject for future study.

Resuspension Factor

The resuspension factor K (m−1), defined as the ratio of air activity concentration in 

Ci m−3to surface activity density in Ci m−2, is an important input parameter in the 

calculations of internal dose from resuspended fallout (SM ID01). For a probabilistic 

analysis, the time-dependent expression given in SM ID01 is used for resuspension due to 

typical land-based activities. It is recommended that the uncertainty associated with this 

parameter be estimated for each history by multiplying each calculated value of K by a 

factor randomly selected from a lognormal distribution with a geometric mean of 1.0 and 

a geometric standard deviation of 4.05. This distribution, discussed in Weitz et al. (2009) 

is based on the results of a study reported in Anspaugh et al. (2002).

For blast-driven resuspension of fallout, different resuspension factors are based upon a 

non-time dependent value of K with a log-normal distribution that depend on proximity 

to the blast and the size of the blast. The blast-driven resuspension of fallout resuspension 

factors for the blast-wave region and the thermal-pulse (formerly precursor) region can be 

found in SM ID01. 

5.2.2.2 Biokinetic Parameters

Breathing Rate

Physiological parameters related to ventilation influence the volume and rate of air 

inhaled and the proportions entering through the nose and mouth, thus affecting the 

amount of radioactive particles and gases inhaled, their penetration into the respiratory 

tract, and the quantities deposited. 

Breathing characteristics and respiratory parameters vary among individuals because they 

are largely a function of age and body size, level of physical activity, state of health of 
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the respiratory tract, and if the individual is a smoker. The distribution of breathing rates 

appropriate for nuclear test participants developed in Weitz et al. (2009), is recommended 

for performing probabilistic analyses of internal dose. This distribution is triangular with 

the defining values of minimum, most likely, and maximum breathing rates given in 

SM ID01.

Respiratory Tract Deposition Fractions

Respiratory tract deposition fractions are defined as the fractions of inhaled particles in a 

given size class that deposit in a defined portion of the human respiratory tract. For use in 

the NTPR probabilistic methodology, deposition fractions for two regions are defined, 

the posterior extra-thoracic (ET2) region and thoracic (TH) airway (bronchial, 

bronchiolar, and alveolar-interstitial regions). Particles are described by the same 

classes—1, 2, and 3—as those for activity fractions. Characterizations of deposition 

fractions of particle size classes for use as modifying factors are described in SM ID01 

and are designated in Mathcad implementations as R1, R2, and R3 for particles that deposit 

in the thoracic region, and as NR1, NR2, and NR3 for particles that deposit in ET2. These 

characterizations are derived in McKenzie-Carter and Stiver (2009). The values and 

distributions of these modifying factors, are provided in SM ID01. These multiplicative 

parameters are used only in descending fallout scenarios (SM ID01).

Dose Conversion Factors

Dose conversion factors (DCFs) are used in NTPR dose reconstructions for the 

assessment of doses accrued from internally deposited radionuclides by the inhalation 

and ingestion pathways. Specific applications to the reconstruction of internal doses 

resulting from the inhalation of resuspended and descending fallout are given in 

SM ID01. 

The uncertainties in inhalation and ingestion DCFs are incorporated into the NTPR 

modeling by multiplying the unbiased DCFs—discussed in SM ID01—by lognormal 

distributions. For these lognormal distributions, the geometric means are set equal to 1.0

and the geometric standard deviations are assigned such that the ratios of the 95th

percentiles to their geometric means are 30 (equivalent to GSD = 7.91) for alpha DCFs 

and 10 (GSD = 4.05) for beta-plus-gamma DCFs (Weitz et al.; 2009; Kocher et al., 

2009). These parameters are also provided in SM ID01.

Incidental Ingestion

A pathway considered in the case studies of land-based units is incidental ingestion, a 

chronic type of exposure that involves the daily intake of relatively small quantities of 

contaminated soil and dust. The sources of the ingested contamination include direct 

contact with airborne soil and dust due to walking, vehicular traffic, and wind-driven 

lofting of contaminated particles in areas where military personnel were temporarily 
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stationed. Routine daily activities by test participants may also have involved the 

inadvertent ingestion of small quantities of soil and dust particles that adhered to food, 

beverages, cigarettes, or their hands.

SM ID01 contains the equation describing the basis for probabilistic assessments of 

internal dose from incidental ingestion. Uncertainty models for most of the parameters 

appearing in that equation (e.g., intensity, DCFing) have been addressed in Weitz et al. 

(2009). There are two parameters specific to this pathway, however, whose uncertainties 

are additionally modeled. These parameters are qing, the soil ingestion rate, and ρsoil, the 

bulk density of the soil. It is recommended that the uncertainties of both these quantities 

be modeled with triangular distributions, the characteristics of which are developed in 

Chehata and Stiver (2009) and tabulated in SM ID01.

5.2.3 Treatment of Correlations

Potential correlations among uncertainties of key parameters must be considered in 

formulating the Monte Carlo sampling of parameter values from their assigned pdfs. The 

degree of correlation between two parameters can range continuously from none (their 

values are completely independent) to full (the value of one is entirely predictable based 

on the value of the other). Nevertheless, correlations between parameters in NTPR 

probabilistic assessments have been assumed to be either non-existent or full; methods of 

modeling partial correlations have not yet been integrated into the probabilistic 

formalism. Correlations are addressed much more fully in Appendix G of 

Weitz et al. (2009).

In performing probabilistic analyses of internal dose accrual, it is recommended that 

uncertainty distributions that are uncorrelated be sampled independently by drawing 

separate random numbers during each history. It is further recommended that fully

correlated distributions be sampled using the same random number.

6. Data and Input

Operation and shot-specific data are compiled in SOP Appendices A–C. Attachment 1 to 

this standard method provides sample uncertainty calculations. Attachment 2 provides 

guidance on the implementation of the pdfs described in Weitz et al. (2009) used in 

probabilistic dose calculations.

7. Referenced SOPs from this Manual

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

(2) SM ED01 - Film Badge Dose Assessment

(3) SM ED02 - Whole Body External Dose Assessment

(4) SM ID01 - Doses to Organs from Intake of Radioactive Materials
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8. References

Anspaugh, L.R., Simon, S.L., Gordeev, K.I., Likhtarev, I.A., Maxwell, R.M., and Shinkarev, 

S.M., 2002. “Movement of Radionuclides in Terrestrial Ecosystems by Physical 

Processes.” Health Physics 82:669–679.

Apostoaei, A.I. and Kocher, D.C., 2010. Radiation Doses to Skin from Dermal Contamination.

DTRA-TR-09-16, Defense Threat Reduction Agency, Defense Threat Reduction Agency. 

October 28.

Barss, N.M. and Weitz, R.L., 2006. “Reconstruction of External Dose from Beta Radiation 

Sources of Nuclear Weapon Origin.” Health Physics 91:379–389.

Chehata, M., 2009. Uncertainty in Estimating Radiation Intensity from Intensity Measurements 

and Iso-Intensity Maps. NTPR-TM-09-13, Defense Threat Reduction Agency, Fort 

Belvoir, VA. December 31.

Chehata, M., and Stiver, J., 2009. Evaluation of Internal Doses from the Incidental Ingestion of 

Contaminated Soil and Dust for NTPR Participants. NTPR-TM-09-03, Defense Threat 

Reduction Agency, Fort Belvoir, VA. December 31.

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.

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, Science Applications, Inc., McLean, VA. April 28.

Kocher, D., 2004. “Policy Statements To Implement Interim Guidance”, Defense Threat 

Reduction Agency, Fort Belvoir, VA. May 14.

Kocher, D.C., Trabalka, J.R., and Apostoaei, A.I., 2009. Derivation of Effective Resuspension 

Factors in Scenarios for Inhalation Exposure Involving Resuspension of Previously

Deposited Fallout by Nuclear Detonations at Nevada Test Site. DTRA-TR-09-15,

Defense Threat Reduction Agency, Fort Belvoir, VA. November 30.

McKenzie-Carter, M. and Stiver, J., 2009. Deposition Fraction Modifications for Inhalation of 

Descending Fallout. NTPR-TM-09-09, Defense Threat Reduction Agency, Fort Belvoir, 

VA. December 31.

NRC (National Research Council), 1989. Film Badge Dosimetry in Atmospheric Nuclear Tests.

National Academy Press, Washington, DC.

NRC (National Research Council), 2003. A Review of the Dose Reconstruction Program of the 

Defense Threat Reduction Agency. National Academies Press, Washington, DC.

Raine, D.A. III, Egbert, S.D., Stiver, J.H., and Case, D.R., 2007. FIIDOS—A Computer Code for 

the Computation of Fallout Inhalation and Ingestion Dose to Organs, Computer User’s 

Guide (Revision 4). DTRA-TR-07-11, Defense Threat Reduction Agency, Fort Belvoir, 

VA. May.
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SAIC (Science Applications International Corporation), 2006. FBDOSE User’s Guide. Science 

Applications International Corporation, McLean, VA. June 26.

Schaeffer, D.M., 2015. Development of Upper-Bound Uncertainty Factors for Dose 

Reconstruction in the NTPR Program. NTPR-TM-15-02, Defense Threat Reduction 

Agency, Fort Belvoir, VA. April 15.

USNRC (U.S. Nuclear Regulatory Commission), 2020. “Standards for Protection Against 

Radiation,” Title 10, Code of Federal Regulations, Part 20. January 1.

Weitz, R.L., 2009a. Model of Topside Intensity Distributions from Fallout on Ship Weather 

Decks. NTPR-TM-09-05, Defense Threat Reduction Agency, Fort Belvoir, VA.

December 31.

Weitz, R.L., 2009b. Modeling of Shielding Factors for Ships. NTPR-TM-09-11, Defense Threat 

Reduction Agency, Fort Belvoir, VA. December 31. 

Weitz, R.L., 2009c. Characterization of Descending Fallout. NTPR-TM-09-06, Defense Threat 

Reduction Agency, Fort Belvoir, VA. December 31. 

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.L., 2014. Modeling of Protection Factor Distributions for Land-Based Structures. 

NTPR-TM-09-10 (R1),. Defense Threat Reduction Agency, Fort Belvoir, VA.

December 31.

Weitz, R.L., Case, D.R., Chehata, M., Egbert, S.D., Mason, C.L., Singer, H.A., Martinez, D.G.,

McKenzie-Carter, M. A., and Stiver, J.S., 2009. A 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., and Egbert, S.D., 2010. Compilation of Initial Radiation Doses to Atmospheric Test 

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

VA, November 30. 
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Attachment 1 Sample Uncertainty Calculations

The following sections contain calculations and clarifying explanations detailing how to 

calculate the total upper-bound doses in various situations. All equations cited are 

described in Section 5.1. 

A1-1 Sample Calculations for External Gamma Doses

a. Independent Reconstructed Gamma Doses

This example is for two reconstructed external gamma doses: a reconstructed dose Dγ,1 of 

1.0 rem and a reconstructed dose Dγ,2 of 0.1 rem. Using Equation 2, the total 

reconstructed external gamma dose is: 

Dγ = Dγ,1 + Dγ,2 = (1.0 rem + 0.1 rem) = 1.1 rem.

Using Equation 3 above, the uncertainty for Dγ,1 is:

uγ,1 = Dγ,1 × (UFext − 1) = 1.0 rem × (3 − 1) = 2 rem

and the uncertainty for Dγ,2 is:

uγ,2 = Dγ,2 × (UFext − 1) = 0.1 rem × (3 − 1) = 0.2 rem.

Using Equation 4, the upper bound for the total estimated gamma dose is then:

UBγ = Dγ + (uγ,1

2 + uγ,22

)

1/2 = (1.1 rem) + (2.01 rem) = 3.11.

b. A Reconstructed Gamma Dose and a Film Badge Dose

This example is for a reconstructed external gamma dose (Dγ,1) of 1.0 rem and a film 

badge dose (FBγ) using the data from the FBDOSE output in Table 1 (Section 5.1.1.3). 

Using Equation 8, the total estimated whole body external gamma dose (Dγ) is:

Dγ = Dγ,1 + FBγ = (1.0 rem + 1.370 rem) = 2.370 rem

where FBγ is the total from the MR column in the FBDOSE output.

The uncertainty for Dγ,1 (uγ,1) is:

uγ,1 = Dγ,1 × (UFext − 1) = 1.0 rem × (3 − 1) = 2.0 rem.

Using Equation 7, the uncertainty of the film badge dose FBγ (uFBγ) is: 

uFBγ = FBUB – FBMEAN = (1.557 rem − 1.215 rem) = 0.342 rem.

This quantity is the total of the UPP90 column from the FBDOSE output minus the total 

of the MEAN column of the FBDOSE output. 

Using Equation 9, the upper bound for the total reported gamma dose is: 

Dγ,1 + FBMEAN + (uγ,1

2 + uFBγ2

)

1/2 = 1.0 rem + 1.215 rem + [(2.0 rem)2 + (0.342 rem)2

]

1/2

= (2.215 rem + 2.029 rem) = 4.24 rem.
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A1-2 Sample Calculation for Total Internal Dose

This example is for two internal doses to the same organ: a reconstructed beta-gamma 

dose from inhalation of resuspended fallout (D1) of 1.0 rem and an incidental ingestion 

dose D2 of 0.1 rem. Note that the method does not change with additional internal doses, 

there are just more terms. 

Using Equation 10, the total internal dose (D) is: 

D = D1 + D2 = (1.0 rem + 0.1 rem) = 1.1 rem.

Using Equation 11, the upper bound for the internal dose for a single organ is:

UB = (UFint,1 × D1 + UFint,2 × D2) = (10 × 1 rem + 1 × 0.1 rem) = 10.1 rem.

A1-3 Sample Calculation for Total Skin Contamination Dose

This example is for two independent skin contamination doses: a dose DSC,1 of 2.0 rem 

and a dose DSC,2 of 0.2 rem. The uncertainty factors UFSC,1 and UFSC,2 are assumed to be 

the same for both doses and are 11 for this example. The uncertainty factors are 

determined as part of the original skin contamination dose. The value of 11 represents the 

midpoint of the range of 4–18 for the uncertainty factor applied to dermal contamination 

(Schaeffer, 2015).

Using Equation 22, the total skin contamination dose (Dsc) is:

Dsc = DSC,1 + DSC,2 = (2.0 rem + 0.2 rem) = 2.2 rem.

Using Equation 23, the upper-bound dose (UBSC) is: 

UBSC = (DSC,1 × UFSC,1) + (DSC,2 × UFSC,2) = (2.0 rem × 11) + (0.2 rem × 11) = 24.2 rem.

A1-4 Sample Calculation for Total Skin Dose from External Sources

a. Independent Reconstructed Gamma and Beta Shine Doses

This example is for two reconstructed external gamma skin doses and two beta skin doses

that are correlated with the external gamma skin doses. One reconstructed gamma skin 

dose (Dγ,1) is 0.3 rem and the second reconstructed gamma dose (Dγ,2) is 0.1 rem. 

Assuming a beta-gamma ratio (Rβγ) of 7.3 (ED03), the correlated beta skin doses are: 

Dβ,1 = Dγ,1 × Rβγ = (0.3 rem × 7.3) = 2.2 rem

Dβ,2 = Dγ,2 × Rβγ = (0.1 rem × 7.3) = 0.73 rem

Using Equation 16, the total gamma and beta shine skin dose is: 

Dskin = Dγ,1 + Dβ,1 + Dγ,2 + Dβ,2 = (0.3 rem + 2.2 rem + 0.1 rem + 0.73 rem) = 3.33 rem.

Using Equation 18, the uncertainty for DSkin,1 (uβγ,1) is:

uβγ,1 = (Dγ,1 + Dβ,1) × (UFext − 1) = (0.3 rem + 2.2 rem) × (3 − 1) = 5.0 rem.
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and the uncertainty for DSkin,2 (uβγ,2) is: 

uβγ,2 = (Dγ,2 + Dβ,2) × (UFext − 1) = (0.1 rem + 0.73 rem) × (3 −1) = 1.66 rem

and using Equation 19, the upper-bound dose is:

UBskin = Dskin + [(uβγ,1)

2 + (uβγ,2)2

]

1/2 = 3.33 rem + [(5.0 rem)2 + (1.66 rem)2

]

1/2

= (3.33 rem + 5.27 rem) = 8.6 rem

b. A Reconstructed Gamma and Beta Dose and a Film Badge Dosimeter with a 

Corresponding Beta Dose

This example is for a simplified total skin dose using a reconstructed whole body external 

gamma dose (Dγ,1) of 0.3 rem and the sample FBDOSE output in Table 1. Assuming a 

beta-gamma ratio (Rβγ) of 7.3, the correlated beta skin dose (Dβ,1) is: 

Dβ,1 = Dγ,1 × Rβγ = (0.3 rem × 7.3) = 2.2 rem

The total skin dose from the reconstructed skin dose is: 

Dskin,1 = Dγ,1 + Dβ,1 = (0.3 rem + 2.2 rem) = 2.5 rem 

The uncertainty of the total reconstructed skin dose Dskin,1 (uβγ,1) is: 

uβγ,1 = (Dγ,1 + Dβ,1) × (UFext − 1) = (2.5 rem) × (3 − 1) = 5.0 rem

For the film badge dose, from Table 1 (Section 5.1.1.3):

FBγ is 1.370 rem (the total of the MR column of the FBDOSE output)

FBMEAN is 1.215 rem (the total of the MEAN column of the FBDOSE output)

FBUBγ is 1.557 rem (the total of the UPP90 column of the FBDOSE output). 

Using Equation 20, the total reported skin dose from gamma and beta dose from both the 

reconstructed external gamma dose and the film badge dose is: 

Dskin,1 + FBγ × (1 + Rβγ) = 2.5 rem + [1.370 rem × (1 + 7.3)] = 13.9 rem 

Using Equation 21, the uncertainty of the total skin dose determined from film badge 

doses uFBβγ is:

uFBβγ = (FBUBγ − FBMEAN) × (1 + Rβγ) = (1.557 rem − 1.215 rem) × (1 + 7.3) = 2.85 rem

Using Equation 22, the upper bound for the total skin dose is:

UBskin = Dskin,1 + FBMEAN × (1 + Rβγ) + [(uβγ,1)

2 + (uFBβγ)2

]

1/2

 = 2.5 rem + 1.215 rem × (1 + 7.3) + 5.75 rem = 18.4 rem
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Attachment 2 Implementation of Probability Density Functions

in Mathcad

Mathcad is the software platform most likely to be used for probabilistic dose 

reconstructions in the NTPR Program. For that reason, the implementation in Mathcad of 

specific and arbitrary probability density functions is outlined in this attachment. 

Mathcad has a rather large array of pdfs in its internal library, including uniform, 

Gaussian, and lognormal. Hence, sampling from these pdfs can be readily implemented 

using the following standard Mathcad commands. 

 Ri = runif(n,a,b)i – produces n values of a random variable R uniformly distributed 

between a and b.

 Ri = rnorm(n,μ,σ)i – produces n values of a random variable R normally distributed 

with mean μ and standard deviation σ.

 Ri = rlnorm(n,ln(GM),ln(GSD))i – produces n values of a random variable R

lognormally distributed with geometric mean GM and geometric standard deviation 

GSD.

There is a straightforward way of sampling from a pdf that is not in the Mathcad library, 

such as the triangular distribution. Let x be the variable of interest (e.g., a time duration, 

intensity reading, shielding factor) and P(x) the pdf that characterizes the uncertainty in x. 

The cumulative probability function C(x) is defined as:







 

x

C(x) P(x )dx

(A2-1)

The following algorithm allows one to sample x from an arbitrary pdf P(x):

1. Perform the integration indicated in Equation A2-1, either in closed form or 

numerically, and set the resulting expression equal to a constant R, i.e., C(x) = R.

2. Solve this expression for x as a function of R, giving x = f(R).

3. Sample R from a uniform random distribution between 0 and 1. This sampling can be 

accomplished using the Mathcad command for uniform distribution given above.

4. The resulting xi = f(Ri) will be distributed according to P(x).

As an example of the use of this algorithm when P(x) is expressed in a functional form 

that allows closed-form integration of Equation A2-1, consider a triangular distribution 

defined by P(a) = 0, P(m) = Pk (peak value), and P(b) = 0, where a ≤ m ≤ b. The 

constraint that C(∞) = 1 requires that Pk = 2/(b-a). (Alternatively, this can be derived 
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without formally integrating C(x) by noting that the total area under P(x) is 1⁄2·Pk·(b-a).

P(x) can then be written in functional form as:















 

 



 

 





for m x b

b m b a

b x

for a x m

m a b a

x a

P x

( )( )

2( )

( )( )

2( )

( )

(A2-2)

Substituting Equation A2-2 into Equation A2-1 and integrating gives:















   

 









 

 





b m x for m x b

b m b a

x m

b a

m a

for a x m

m a b a

x a

C x

(2 )

( )( )

( )

( )( )

2

( )

( )

(A2-3)

Setting each of the two components of C(x) in Equation A2-3 equal to R and solving the 

quadratic equations for x yields the desired result:









       

      



(1 )( )( ) ( ) ( ) 1

( )( ) 0 ( ) ( )

b R b m b a for m a b a R

a R m a b a for R m a b a

x

(A2-4)