Defense Threat Reduction Agency 

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DTRA-TR-09-13 

A Probabilistic Approach to Uncertainty 

Analysis in NTPR Radiation Dose Assessments 

Approved for public release; distribution is unlimited 

November 2009 

HDTRA1-07-C-0015 

Subcontract No. 06-792-SA 

Weitz, Ronald L. et al. 

 Prepared by: 

Science Applications International Corporation 

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TECHNICAL REPORT

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1. REPORT DATE (DD-MM-YYYY)

11-01-2009 

2. REPORT TYPE

Technical report 

3. DATES COVERED (From - To)

5a. CONTRACT NUMBER

HDTRA1-07-C-0015 

5b. GRANT NUMBER

 

4. TITLE AND SUBTITLE

A Probabilistic Approach to Uncertainty Analysis in NTPR Radiation 

Dose Assessments 

5c. PROGRAM ELEMENT NUMBER

139D 

5d. PROJECT NUMBER

CS 

5e. TASK NUMBER

AH 

6. AUTHOR(S)

Weitz, Ronald L; Case, David R; Chehata, Mondher; Egbert, 

Stephen D; Mason, Carol L; Singer, Harvey A; Martinez, Daniel G; 

McKenzie-Carter, Michael A; Shaw, Robert S; and Stiver, John S. 

5f. WORK UNIT NUMBER

 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

Science Applications International Corporation 

8301 Greensboro Drive, Suite 500, M/S E-5-5 

McLean, VA 22102 

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REPORT NUMBER

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DTRA RD-NTSN 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

Nuclear Technology Directorate 

Defense Threat Reduction Agency 

8725 John J. Kingman Road Stop 6201 , 

Fort Belvoir, VA 22060-6201

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AGENCY REPORT NUMBER

12. DISTRIBUTION AVAILABILITY STATEMENT

Approved for public release; distribution is unlimited. 

13. SUPPLEMENTARY NOTES

 

14. ABSTRACT

This report discusses the approach, technical basis, and special studies investigated in the process of developing 

probabilistically-based methods for performing radiation dose assessments for atmospheric nuclear weapons test 

participants of the Nuclear Test Personnel Review Program. Developed methods were applied to six case studies of 

exposed groups at three island locations in the Pacific Proving Ground (PPG), two ships in the PPG, and one US 

Marine Corps brigade at the Nevada Test site. Results of the case studies indicate that the methodologies 

successfully produced reliable estimates of doses from external sources and internally-deposited materials. Sample 

sensitivity analyses identified the relative contributions to uncertainty for input parameters and may serve as the basis 

for screening out less significant parameters for a given scenario of exposure. 

15. SUBJECT TERMS

Nuclear Test Personnel Review, Veterans, Atmospheric Nuclear Weapons Test, Dose Reconstruction, Uncertainty, 

Probabilistic Methods, External Dose, Internal Dose 

16. SECURITY CLASSIFICATION OF: 19a. NAME OF RESPONSIBLE PERSON 

Dr. Paul K. Blake

a. EPORT R

U

b. BSTRACT A

U

c. THIS 

P E AG

U

17. IMITATION 

OF BSTRACT 

 L

 A

UU

18. NUMBER 

OF PAGES 

268 19b. TELEPONE NUMBER (Include area code ): 

703 767-3384 

Table of Contents 

Table of Contents............................................................................................................................ 1 

List of Figures................................................................................................................................. 5 

List of Tables .................................................................................................................................. 9 

Acknowledgments......................................................................................................................... 13 

EXECUTIVE SUMMARY .......................................................................................................... 14 

1 INTRODUCTION ............................................................................................................ 23 

2 BACKGROUND .............................................................................................................. 25 

3 RADIATION DOSE ESTIMATION AND UNCERTAINTY MODELING.................. 26 

3.1 Definitions of Types of Parameters and Doses..................................................... 26 

3.1.1 Nominal Doses.......................................................................................... 26 

3.1.2 Probabilistic Doses.................................................................................... 26 

3.1.3 Deterministic “NTPR” Doses ................................................................... 27 

3.2 Whole Body External Dose .................................................................................. 27 

3.2.1 External Dose from Exposure to Fallout .................................................. 27 

3.2.2 External Dose from Exposure to Activated Soil....................................... 33 

3.2.3 Film Badge Dosimetry.............................................................................. 33 

3.3 Internal Dose......................................................................................................... 34 

3.3.1 Inhalation Intakes...................................................................................... 34 

3.3.2 Ingestion Intakes ....................................................................................... 40 

3.4 Uncertainty Modeling ........................................................................................... 41 

3.4.1 Overview of Probability Distributions...................................................... 41 

3.4.2 Propagation of Uncertainties..................................................................... 50 

3.4.3 Monte Carlo Method................................................................................. 51 

3.4.4 Quantifying Uncertainty ........................................................................... 53 

3.4.5 Reporting of Representative Doses........................................................... 55 

4 TECHNICAL APPROACH AND METHODOLOGY.................................................... 56 

4.1 Pilot Study............................................................................................................. 56 

4.1.1 Software Selection .................................................................................... 57 

4.1.2 Generation of Parameter Distributions ..................................................... 58 

4.2 Special Studies: Model Parameters, Uncertainties, and Distributions.................. 58 

1 
4.2.1 Intensity Distribution from Fallout on Ship Weather Decks .................... 59 

4.2.2 Protection Factors for Land-Based Structures .......................................... 66 

4.2.3 Shielding Factors for Ships....................................................................... 70 

4.2.4 Shot-Specific Radiological Decay Functions ........................................... 75 

4.2.5 Gamma Source Modification Factor......................................................... 77 

4.2.6 Resuspension Factors................................................................................ 86 

4.2.7 Breathing Rate .......................................................................................... 89 

4.2.8 Internal Dose Conversion Factors............................................................. 95 

4.2.9 Characterization of Descending Fallout.................................................. 100 

4.2.10 Internal Deposition Fraction Adjustment................................................ 104 

4.2.11 Sources of Uncertainty When Estimating Radiation Intensity from 

Measured Intensities and Iso-Intensity Maps ......................................... 106 

4.2.12 Incidental Ingestion of Contaminated Soil and Dust .............................. 111 

4.3 Dependencies and Correlations between Model Input Parameters..................... 111 

5 CASE STUDY RESULTS.............................................................................................. 114 

5.1 Case Study #1: Operation REDWING (1956), 7126th Army Unit 

Headquarters (HQ) Detachment, Enewetak Atoll .............................................. 115 

5.1.1 Case Description and Cohort Participation Scenario.............................. 115 

5.1.2 Available Dosimetry ............................................................................... 115 

5.1.3 External Dose.......................................................................................... 116 

5.1.4 Internal Dose........................................................................................... 118 

5.2 Case Study #2: Operation HARDTACK I (1958), Army Unit 

Administrative and Operations Detachments, Enewetak Atoll .......................... 122 

5.2.1 Case Description and Cohort Participation Scenario.............................. 122 

5.2.2 Available Dosimetry ............................................................................... 122 

5.2.3 External Dose.......................................................................................... 122 

5.2.4 Internal Dose........................................................................................... 124 

5.3 Case Study #3: Operation PLUMBBOB (1957), 4th Marine Corps 

Provisional Atomic Exercise Brigade (MCPAEB) Maneuver at Shot 

HOOD................................................................................................................. 127 

5.3.1 Case Description and Cohort Participation Scenario.............................. 127 

5.3.2 Available Dosimetry ............................................................................... 128 

5.3.3 External Dose.......................................................................................... 128 

5.3.4 Internal Dose........................................................................................... 130 

2 
5.4 Case Study #4: Operation REDWING (1956), USS ESTES (AGC 12)............ 133 

5.4.1 Case Description and Cohort Participation Scenario.............................. 133 

5.4.2 Available Dosimetry ............................................................................... 133 

5.4.3 External Dose.......................................................................................... 133 

5.4.4 Internal Dose........................................................................................... 135 

5.5 Case Study #5: Operation HARDTACK I (1958), USS BOXER (CVS 21)..... 136 

5.5.1 Case Description and Cohort Participation Scenario.............................. 136 

5.5.2 Available Dosimetry ............................................................................... 137 

5.5.3 External Dose.......................................................................................... 137 

5.5.4 Internal Dose........................................................................................... 138 

5.6 Case Study #6: Operation CASTLE (1954), Army Personnel, Enewetak 

Island................................................................................................................... 140 

5.6.1 Case Description and Cohort Participation Scenario.............................. 140 

5.6.2 Available Dosimetry ............................................................................... 141 

5.6.3 External Dose.......................................................................................... 141 

5.6.4 Internal Dose........................................................................................... 142 

5.7 Summary of Results and Comparison of Upper Bound Doses........................... 144 

6 SENSITIVITY ANALYSIS FOR THE DOSE MODELS OF CASTLE 

ENEWETAK CASE STUDY......................................................................................... 147 

6.1 Technical Approach............................................................................................ 147 

6.2 External Dose Model Sensitivity Analysis ......................................................... 148 

6.3 Internal Dose Model Sensitivity Analysis .......................................................... 150 

7 CONCLUSIONS AND RECOMMENDATIONS ......................................................... 154 

8 REFERENCES ............................................................................................................... 158 

APPENDIX A Monte Carlo Analysis of Dose to Army Units Stationed on Enewetak 

Island During Operation REDWING............................................................ 165 

APPENDIX B Monte Carlo Analysis of Dose to Army Units Stationed on Enewetak 

Island During Operation HARDTACK I...................................................... 179 

APPENDIX C Monte Carlo Analysis of Dose for Company E of the 4th Marine Corps 

Provisional Atomic Exercise Brigade (MCPAEB) Maneuver at Shot 

HOOD During Operation PLUMBBOB (1957)........................................... 196 

APPENDIX D Monte Carlo Analysis of Dose to Personnel Aboard USS ESTES 

During Operation REDWING ...................................................................... 213 

APPENDIX E Monte Carlo Analysis of Dose to Personnel Aboard USS BOXER 

During Operation HARDTACK I................................................................. 226 

3 
APPENDIX F Monte Carlo Analysis of Dose for Personnel Stationed on Enewetak 

Island During Operation CASTLE ............................................................... 238 

APPENDIX G Model Variables Dependencies and Correlations......................................... 250 

Distribution List.......................................................................................................................... 263 

4 
List of Figures 

Figure 1. Graph of ICF(t) and Early Time Intensity Data ........................................................... 31 

Figure 2. FIIDOS-Derived Intensity Functions for Selected Shots ............................................. 32 

Figure 3. Probability Density Function of a Uniform Distribution ............................................ 42 

Figure 4. Probability Density Function of a Gaussian Distribution............................................. 44 

Figure 5. Probability Density Functions of the Lognormal Distribution for Various 

Values of σ .............................................................................................................. 46 

Figure 6. Probability Density Functions of a Triangular Distribution (1) Skewed Right, 

(2) Skewed Left, and (3) Symmetric....................................................................... 47 

Figure 7. Symmetric Triangular Approximation to the Gaussian Distribution ........................... 49 

Figure 8. A Right-Skewed Log-Triangular Distribution ............................................................. 49 

Figure 9. Distribution of Intensities for Fallout Deposited Uniformly on Weather Deck of 

YAG (normalized to a mean of 1 R hr−1

)................................................................ 61 

Figure 10. Topside Intensity Distributions on YAG Prior to Decontamination 

(normalized to a mean of 1 R hr−1).......................................................................... 62 

Figure 11. Topside Intensity Distribution on YAG after Partial Decontamination 

(normalized to a mean of 1 R hr−1).......................................................................... 63 

Figure 12. Best Fit to YAG Pre-Decon Intensity Distribution .................................................... 63 

Figure 13. Best Fit to YAG Post-Decon Intensity Distribution................................................... 64 

Figure 14. Pre- and Post-Decon Topside Intensity Distributions for USS ESTES 

(normalized to a mean of 1 R hr−1).......................................................................... 65 

Figure 15. Pre- and Post-Decon Topside Intensity Distributions for USS BOXER 

(normalized to a mean of 1 R hr−1

).......................................................................... 65 

Figure 16. Calculated Protection Factor Distribution for 48-man Barracks................................ 68 

Figure 17. Calculated Protection Factor Distribution for 8-man Tent......................................... 68 

Figure 18. Estimated EDM Distribution for Land-based Personnel............................................ 70 

Figure 19. Distribution of Below-Deck Shielding Factors for USS BOXER.............................. 73 

Figure 20. Distribution of Below-Deck Shielding Factors for USS ESTES ............................... 73 

Figure 21. EDM Distribution for Personnel on USS BOXER..................................................... 74 

Figure 22. EDM Distribution for Personnel on USS ESTES ...................................................... 75 

Figure 23. Uncertainty Model Comparison for Operation GREENHOUSE Shot EASY ........... 77 

Figure 24. Uncertainty Model Comparison for Operation CASTLE Shot BRAVO ................... 78 

Figure 25. Uncertainty Model Comparison for Operation PLUMBBOB Shot SHASTA........... 78 

Figure 26. GSMF Probability Distribution for USS BOXER...................................................... 80 

5 
Figure 27. Probability Distribution of Average GSMF for USS BOXER................................... 81 

Figure 28. Superstructure Model ................................................................................................. 83 

Figure 29. GSMF Probability Distribution for USS ESTES........................................................ 84 

Figure 30. Dependency of Average GSMF on Areal Fraction S for USS ESTES....................... 85 

Figure 31. Probability Distribution of Average GSMF for USS ESTES..................................... 85 

Figure 32. Sample Breathing Rate Distribution for Atmospheric Nuclear Test 

Participants .............................................................................................................. 94 

Figure 33. Comparison of the Dose Distribution from Probabilistic Analysis with 

Unbiased Film Badge Readings for the 7126th AU at Enewetak Atoll during 

Operation REDWING ........................................................................................... 117 

Figure 34. Distribution of Estimated LLI Wall Doses from Alpha Radiation for the 

7126th Army Unit Stationed at Enewetak Atoll during Operation 

REDWING ............................................................................................................ 120 

Figure 35. Probability Plot of Estimated LLI Wall Doses from Alpha Radiation for the 

7126th Army Unit Stationed at Enewetak Atoll during Operation 

REDWING ............................................................................................................ 120 

Figure 36. Distribution of Estimated LLI Wall Doses from Beta plus Gamma Radiation 

for the 7126th Army Unit Stationed at Enewetak Atoll during Operation 

REDWING ............................................................................................................ 121 

Figure 37. Probability Plot of Estimated LLI Wall Doses from Beta plus Gamma 

Radiation for the 7126th Army Unit Stationed at Enewetak Atoll during 

Operation REDWING ........................................................................................... 121 

Figure 38. Comparison of Film Badge, Monte Carlo, and Deterministic Results for the 

Administrative Detachment (a) and the Operations Detachment (b) at 

Operation HARDTACK I ..................................................................................... 125 

Figure 39. Sensitivity Scores for Input Parameters to Total External Dose Model for the 

CASTLE Enewetak Case Study............................................................................ 149 

Figure 40. Sensitivity Scores for Input Parameters to Total Internal (α) Dose Model 

(Lung) for the CASTLE Enewetak Case Study .................................................... 151 

Figure 41. Sensitivity Scores for Input Parameters to Total Internal (β + γ) Dose Model 

(Lung) for the CASTLE Enewetak Case Study .................................................... 152 

Figure A-1. Distribution of Unbiased Film Badge Results for HQ Detachment Personnel...... 169 

Figure A-2. Comparison of Distribution of Estimated External Gamma Doses from 

Monte Carlo Analysis with Distribution of Unbiased Film Badge Results 

for the 7126th Army Unit Stationed at Enewetak Island during Operation 

REDWING ............................................................................................................ 172 

Figure A-3. Probability Plot of Estimated External Gamma Doses for 7126th Army Unit 

Stationed at Enewetak Island during Operation REDWING ................................ 173 

6 
Figure A-4. Distribution of Estimated LLI Wall Dose from Alpha Radiation for 7126th

Army Unit Stationed at Enewetak Island during Operation REDWING.............. 176 

Figure A-5. Probability Plot of Estimated LLI Wall Dose from Alpha Radiation for 

7126th Army Unit Stationed at Enewetak Island during Operation 

REDWING ............................................................................................................ 177 

Figure A-6. Distribution of Estimated LLI Wall Dose from Beta plus Gamma Radiation 

for 7126th Army Unit Stationed at Enewetak Atoll during Operation 

REDWING ............................................................................................................ 177 

Figure A-7. Probability Plot of Estimated LLI Wall Doses from Beta plus Gamma 

Radiation for 7126th Army Unit Stationed at Enewetak Atoll during 

Operation REDWING ........................................................................................... 178 

Figure B-1. Comparison of Parry Island Intensity Model with PHS Measurements................. 183 

Figure B-2. Comparison of Enewetak Island Intensity Model with PHS Measurements ......... 183 

Figure B-3. Distribution of Estimated External Gamma Doses for Army Personnel at 

Enewetak Island during Operation HARDTACK I (Turn-in Date: June 12) ....... 187 

Figure B-4. Probability Plot Estimated External Gamma Doses for Army Personnel at 

Enewetak Island during Operation HARDTACK I (Turn-in Date: June 12) ....... 188 

Figure B-5. Distribution of Estimated LLI Wall Doses from Alpha Radiation for Army 

Personnel at Enewetak Island during Operation HARDTACK I.......................... 192 

Figure B-6. Probability Plot of Estimated LLI Wall Doses from Alpha Radiation for 

Army Personnel at Enewetak Island during Operation HARDTACK I ............... 192 

Figure B-7. Distribution of Estimated LLI Wall Doses from Beta plus Gamma Radiation 

for Army Personnel at Enewetak Island during Operation HARDTACK I.......... 193 

Figure B-8. Probability Plot of Estimated LLI Wall Doses from Beta plus Gamma 

Radiation for Army Personnel at Enewetak Island during Operation 

HARDTACK I ...................................................................................................... 193 

Figure C-1. Shot HOOD Residual Radiation (mrem hr−1

 at H+1) and MCPAEB 

Movements (Frank et al., 1981) ............................................................................ 199 

Figure C-2. Distribution of Estimated External Gamma Dose for Company E Personnel 

at the NTS during Operation PLUMBBOB .......................................................... 204 

Figure C-3. Probability Plot of Estimated External Gamma Dose for Company E 

Personnel at the NTS during Operation PLUMBBOB ......................................... 204 

Figure C-4. Distribution of Estimated Dose for LLI Wall from Alpha Radiation for 

Company E Personnel during Operation PLUMBBOB........................................ 207 

Figure C-5. Probability Plot of Distribution of Estimated LLI Wall Dose from Alpha 

Radiation for Company E Personnel during Operation PLUMBBOB ................. 208 

Figure C-6. Distribution of Estimated LLI Wall Dose from Beta plus Gamma Radiation 

for Company E Personnel during Operation PLUMBBOB .................................. 209 

7 
Figure C-7. Probability Plot of Estimated LLI Wall Dose from Beta plus Gamma 

Radiation for Company E Personnel during Operation PLUMBBOB ................. 209 

Figure D-1. Distribution of Estimated External Gamma Doses from Monte Carlo 

Analysis for Crew of USS ESTES during Operation REDWING........................ 219 

Figure D-2. Probability Plot of Estimated External Gamma Doses from Monte Carlo 

Analyses for Crew of USS ESTES during Operation REDWING ....................... 219 

Figure D-3. Distribution of Estimated LLI Wall Dose from Alpha Radiation for Crew of 

USS ESTES during Operation REDWING .......................................................... 223 

Figure D-4. Probability Plot of Estimated LLI Wall Dose from Alpha Radiation for Crew 

of USS ESTES during Operation REDWING ...................................................... 223 

Figure D-5. Distribution of Estimated LLI Wall Dose from Beta plus Gamma Radiation 

for Crew of USS ESTES during Operation REDWING....................................... 224 

Figure D-6. Probability Plot of Estimated LLI Wall Dose from Beta plus Gamma 

Radiation for Crew of USS ESTES during Operation REDWING ...................... 224 

Figure E-1. Distribution of Estimated External Gamma Doses for Crew of USS BOXER 

during Operation HARDTACK I.......................................................................... 231 

Figure E-2. Probability Plot of Estimated External Gamma Doses for Crew of USS 

BOXER during Operation HARDTACK I ........................................................... 231 

Figure E-3. Distribution of Estimated LLI Wall Dose from Alpha Radiation for Crew of 

USS BOXER during Operation HARDTACK I ................................................... 235 

Figure E-4. Probability Plot of Estimated LLI Wall Dose from Alpha Radiation for Crew 

of USS BOXER during Operation HARDTACK I............................................... 235 

Figure E-5. Distribution of Estimated LLI Wall Dose from Beta plus Gamma Radiation 

for Crew of USS BOXER during Operation HARDTACK I ............................... 236 

Figure E-6. Probability Plot of Estimated LLI Wall Dose from Beta plus Gamma 

Radiation for Crew of USS BOXER during Operation HARDTACK I............... 236 

Figure F-1. Distribution of Estimated External Gamma Dose from Uncertainty Analysis 

for Personnel Stationed at Enewetak Island during Operation CASTLE ............. 243 

Figure F-2. Probability Plot of Estimated External Gamma Dose from Uncertainty 

Analysis for Personnel Stationed at Enewetak Island during Operation 

CASTLE................................................................................................................ 243 

Figure F-3. Distribution of Estimated LLI Wall Doses from Alpha Radiation for 

Personnel Stationed at Enewetak Island during Operation CASTLE ................... 246 

Figure F-4. Probability Plot of Estimated LLI Wall Doses from Alpha Radiation for 

Personnel Stationed at Enewetak Island during Operation CASTLE ................... 247 

Figure F-5. Distribution of Estimated LLI Wall Doses from Beta plus Gamma Radiation 

for Personnel Stationed at Enewetak Island during Operation CASTLE ............. 247 

Figure F-6. Probability Plot of LLI Wall Doses from Beta plus Gamma Radiation for 

Personnel Stationed at Enewetak Island during Operation CASTLE ................... 248 

8 
List of Tables 

Table ES-1. Ratios of Deterministic Upper Bound over 95th Percentile Probabilistic 

Doses ....................................................................................................................... 20 

Table 1. Generic Example of Early Time Intensity Data............................................................. 29 

Table 2. Generic Example of Multiple Decay Exponents ........................................................... 30 

Table 3. Distribution Specifics for Fos and Ft for Land-Based Personnel on Enewetak 

during Operation HARDTACK I............................................................................ 70 

Table 4. Average GSMF for Various Ship Types........................................................................ 86 

Table 5. Resuspension Factors (m-1) for Fallout Resuspended by Nuclear Detonations at 

the NTS ................................................................................................................... 89 

Table 6. ICRP Reference Breathing Rates for Workers .............................................................. 90 

Table 7. ICRP Daily Time Apportionment for Workers ............................................................. 91 

Table 8. NCRP Reference Breathing Rates for Workers............................................................. 91 

Table 9. USEPA Reference Breathing Rates for Adults and Outdoor Workers for 

Short-term Exposures.............................................................................................. 92 

Table 10. USEPA Summary of Breathing Rates for Adult Males............................................... 92 

Table 11. Breathing Rate Distributions by Activity Level–NTPR Test Participants .................. 93 

Table 12. Breathing Rate Distribution Parameters: 10,000 Monte Carlo Histories .................... 94 

Table 13. FIIDOS Target Organs................................................................................................. 96 

Table 14. Organ-Specific Bias Adjustment Factors .................................................................. 100 

Table 15. Model Parameters for Dose Conversion Factor Distributions................................... 101 

Table 16. Triangular Distributions of Total Activity Fraction for PPG Case Study Units........ 103 

Table 17. Model Parameters for Activity Fraction and Settling Velocity ................................. 104 

Table 18. Model Parameters for Internal Deposition Fractions................................................. 106 

Table 19. Proposed Ranges of Uncertainty Factors for Estimating Point Values Using 

Measured Intensities and Iso-intensity Contour Maps.......................................... 110 

Table 20. Summary of External Dose for the 7126th Army Unit Stationed at Enewetak 

Atoll during Operation REDWING ...................................................................... 117 

Table 21. Summary of Estimated Internal Doses for the 7126th Army Unit Stationed at 

Enewetak Atoll during Operation REDWING...................................................... 119 

Table 22. Summary of External Dose for Army Units Stationed at Enewetak Island 

during Operation HARDTACK I.......................................................................... 124 

9 
Table 23. Internal Dose Summary for Army Units Stationed at Enewetak Island during 

Operation HARDTACK I ..................................................................................... 127 

Table 24. Summary of External Dose for Company E Personnel of the 4th MCPAEB 

during Operation PLUMBBOB ............................................................................ 130 

Table 25. Summary of Internal Dose for Company E of the 4th MCPAEB at the NTS 

during Operation PLUMBBOB ............................................................................ 132 

Table 26. Summary of External Dose for the Crew of USS ESTES during Operation 

REDWING ............................................................................................................ 134 

Table 27. Summary of Internal Dose for the USS ESTES Crew during Operation 

REDWING ............................................................................................................ 136 

Table 28. Summary of External Dose for the Crew of USS BOXER during Operation 

HARDTACK I ...................................................................................................... 138 

Table 29. Summary of Internal Dose for the Crew of USS BOXER during Operation 

HARDTACK I ...................................................................................................... 140 

Table 30. Summary of External Dose for Personnel Stationed at Enewetak Island during 

Operation CASTLE............................................................................................... 142 

Table 31. Summary of Internal Dose for Personnel Stationed at Enewetak Island during 

Operation CASTLE............................................................................................... 144 

Table 32. Ratios of Deterministic Upper Bounds to 95th Percentile Probabilistic Doses.......... 145 

Table 33. Sensitivity Scores for Input Parameters to the External Dose Model........................ 149 

Table 34. Sensitivity Scores for Input Parameters to the Internal (α) Dose Model (Lung)....... 151 

Table 35. Sensitivity Scores for Input Parameters to the Internal (β+γ) Dose Model 

(Lung).................................................................................................................... 152 

Table A-1. Peak Radiation Intensities on Enewetak Island during Operation REDWING...... 167 

Table A-2. Early Time Intensity Function on Enewetak Island following Shot ZUNI............ 167 

Table A-3. Early Time Intensity Function on Enewetak Island following Shot APACHE ..... 167 

Table A-4. Early Time Intensity Function on Enewetak Island following Shot TEWA.......... 168 

Table A-5. Input Parameter Specification for External Gamma Dose Reconstruction, 

Case Study #1........................................................................................................ 170 

Table A-6. Summary of Estimated External Dose for Army Units stationed at Enewetak 

Island during Operation REDWING..................................................................... 171 

Table A-7. Input Parameter Specification for Internal Dose Reconstruction, Case 

Study #1................................................................................................................. 174 

Table A-8. Summary of Estimated Internal Doses for 7126th Army Unit Stationed at 

Enewetak Island during Operation REDWING .................................................... 176 

Table B-1. Film Badge Data for HARDTACK I Army Subunits.............................................. 185 

10 
Table B-2. Input Parameter Specification for External Gamma Dose Reconstruction, 

Case Study #2........................................................................................................ 186 

Table B-3. Summary of External Doses for Army Subunits Stationed at Enewetak Island 

during HARDTACK I........................................................................................... 189 

Table B-4. Input Parameter Specification for Internal Dose Reconstruction, Case 

Study #2................................................................................................................. 190 

Table B-5. Summary of Internal Dose for Army Personnel at Enewetak Island during 

Operation HARDTACK I ..................................................................................... 194 

Table C-1. Data On Selected Operation PLUMBBOB Shots.................................................... 197 

Table C-2. Deterministic Intensities (R hr−1

) and Times (hr) Associated with Traversal of 

Shot HOOD Test Area by Company E ................................................................. 201 

Table C-3. Fallout Intensities for Company E in Forward Test Areas and at CDR .................. 201 

Table C-4. Input Parameters for External Gamma Dose Reconstruction,Case Study #3.......... 203 

Table C-5. Summary of Estimated External Dose for Company E Personnel of the 4th

MCPAEB during Operation PLUMBBOB ........................................................... 205 

Table C-6. Input Parameter Specification for Internal Dose Reconstruction, Case 

Study #3................................................................................................................. 206 

Table C-7. Summary of Estimated Internal Dose for Company E Personnel during 

Operation PLUMBBOB........................................................................................ 210 

Table D-1. Peak Radiation Intensities on USS ESTES during Operation REDWING............. 215 

Table D-2. Early Time-Intensity Data for USS ESTES After Shot ZUNI ................................ 215 

Table D-3. Early Time-Intensity Data on USS ESTES After Shot FLATHEAD ..................... 216 

Table D-4. Early Time-Intensity Data on USS ESTES After Shot NAVAJO .......................... 216 

Table D-5. Early Time-Intensity Data on USS ESTES After Shot TEWA.............................. 216 

Table D-6. Input Parameter Specification for External Gamma Dose Reconstruction, 

Case Study # 4....................................................................................................... 218 

Table D-7. Summary of Estimated External Dose for Crew of USS ESTES during 

Operation REDWING ........................................................................................... 220 

Table D-8. Input Parameter Specification for Internal Dose Reconstruction, Case 

Study #4................................................................................................................. 220 

Table D-9. Summary of Estimated Internal Doses for Crew of USS ESTES during 

Operation REDWING ........................................................................................... 222 

Table E-1. Input Parameter Specification for External Gamma Dose Reconstruction, 

Case Study #5........................................................................................................ 230 

Table E-2. Summary of Estimated External Dose for Crew of USS BOXER during 

Operation HARDTACK I ..................................................................................... 232 

11 
12 

Table E-3. Input Parameter Specifications for Internal Dose 

Reconstruction,Case Study #5............................................................................... 232 

Table E-4. Summary of Estimated Internal Doses for Crew of USS BOXER during 

Operation HARDTACK I ..................................................................................... 234 

Table F-1. Operation CASTLE Detonations ............................................................................. 239 

Table F-2. Input Parameter Specification for External Gamma Dose Reconstruction, 

Case Study #6........................................................................................................ 242 

Table F-3. Summary of External Dose for Personnel Stationed at Enewetak Island during 

Operation CASTLE............................................................................................... 244 

Table F-4. Input Parameter Specification for Internal Dose Reconstruction, Case 

Study #6................................................................................................................. 244 

Table F-5. Internal Dose Summary for Personnel Stationed at Enewetak Island during 

Operation CASTLE............................................................................................... 248 

Table G-1. Case Study Model Variables – Dependencies and Correlations ............................. 252 
Acknowledgments 

The authors thank Mr. Harold L. Beck, Mr. Paul G. Voillequé and Dr. Gary H. Zeman, members 

of the Subcommittee on Dose Reconstruction of the Veterans’ Advisory Board on Dose 

Reconstruction (VBDR) for their critical review of this report and their valuable suggestions to 

improve its content. The authors also extend their gratitude and appreciation to Drs. David C. 

Kocher and F. Owen Hoffman of SENES Oak Ridge, Inc., who provided valuable discussions 

and advice in the early stages of the studies described in this report as well as a thorough review 

of the first draft of the report, which allowed substantial improvements in the project and final 

report. 

13 
EXECUTIVE SUMMARY 

Summaries of the individual sections of this report are provided in this executive summary. Each 

heading within this summary is labeled with the section number of the narrative report for easy 

reference to additional details and discussion. 

Introduction (1) and Background (2) 

In October 2007, the Veterans’ Advisory Board on Dose Reconstruction (VBDR) recommended 

that the Nuclear Test Personnel Review (NTPR) Program develop procedures to perform 

probabilistic uncertainty analyses for Radiation Dose Assessments (RDAs) (VBDR, 2007). 

Specifically, the NTPR standard operating procedures should specify whether uncertainty 

estimates from individual sources are independent or correlated and when and how uncertainties 

should be propagated. The Defense Threat Reduction Agency (DTRA) tasked Science 

Applications International Corporation (SAIC) to investigate methods that could be used for 

conducting analyses for NTPR RDAs (DTRA, 2007b). In response, SAIC identified the effort’s 

main goal to develop and demonstrate a methodology and its enabling computational tools to 

perform probabilistic radiation dose assessments for NTPR atomic veterans. The objectives 

identified for the study are addressed in Section 1. 

The NTPR Program’s reconstructed radiation doses for atomic veterans have traditionally 

employed methods using high-sided estimates for parameters that are difficult to characterize, 

but were considered to overestimate actual doses and therefore provided reliable upper bounds. 

In a 2003 review of DTRA’s dose reconstruction program, a committee of the National Research 

Council of the National Academy of Sciences (NAS/NRC) concluded that although central 

estimates of reconstructed doses for external gamma exposures were valid in most cases, upper 

bounds could not always be shown to be at least as great as a 95 percent upper confidence limit 

(NRC, 2003). Therefore, the Committee recommended “... a comprehensive re-evaluation of 

the methods being used to estimate doses and their uncertainties to establish more credible 

upper-bound doses to atomic veterans.” DTRA and the Department of Veterans Affairs (DVA) 

acknowledged these findings and committed to plans to improve models for dose reconstructions 

(DOD/DVA, 2004). 

In addition, DOD and DVA jointly established the VBDR to oversee the dose reconstruction 

process. VBDR, Subcommittee 1 on dose reconstruction audited radiation dose assessments, 

reviewed methodologies, and developed conclusions and recommendations. In October 2007, 

the VBDR recommended to DTRA that it stop using default upper bound factors and develop 

procedures that make use of probabilistic uncertainty analyses in dose reconstructions (VBDR, 

2007). DTRA endorsed efforts to pursue that VBDR recommendation, which forms the basis for 

the investigations documented in this report (DTRA, 2007c). 

Radiation Dose Estimation and Uncertainty Modeling (3)

Types of Doses (3.1) 

This report involves the calculation of “nominal,” “probabilistic” and “deterministic” doses, 

which are described further in the following discussions. Nominal doses are based on observed 

data or best estimates; probabilistic doses are based on distributions of parameters using Monte 

14 
Carlo analyses; and deterministic doses are based on certain high-sided parameter estimates 

according to DTRA guidance. Doses fall into two main classes—whole body external dose, and 

internal dose. 

Whole body external dose (3.2) results from exposure to radiation sources outside the body and 

involves initial nuclear radiation, and residual nuclear radiation. The most commonly 

encountered source of residual radiation is gamma rays emitted from fallout particles, but some 

test participants were also exposed to gamma rays emitted from neutron activation products in 

the soil. 

Methods for estimating whole body external dose address external dose from exposure to 

fallout (3.2.1), and external dose from exposure to activated soil (3.2.2). Methods for external 

dose from fallout involve the modeling of fallout intensity decay (3.2.1.1), and addressing the 

effects of shielding (3.2.1.2). Doses from neutron-activated soil components arise from 

exposures to radionuclides produced in the soil by a detonation whose neutrons reached the 

surface, but whose fireball did not. 

In addition to methods for calculating doses from intensity measurements, film badge dosimetry 

(3.2.3) provides an alternate method subject to biases and uncertainties that can be corrected. 

Internal dose (3.3) involves dose in internal organs from exposures to radioactive sources inside 

the body. Participants in nuclear weapons tests could have accrued internal doses as a result of 

intakes of radionuclides by inhalation, ingestion, or absorption through the skin or open wounds. 

Intakes by inhalation are the most common pathway for the majority of participants; most 

exposure scenarios involve inhalation of descending fallout and/or fallout that had been 

deposited previously on the ground or other surfaces and subsequently resuspended into the air. 

Calculation of internal organ doses requires the use of factors that convert intakes of radioactive 

material to the dose each organ would receive from that intake. The NTPR program develops 

composite dose conversion factors (DCFs) that apply to mixtures of radionuclides based on 

ICRP-recommended dose coefficients. 

Internal doses derive from inhalation intakes (3.3.1), and ingestion intakes (3.3.2). Inhalation 

intakes address inhalation of fallout resuspended from surfaces (3.3.1.1), inhalation of 

descending fallout (3.3.1.2), and inhalation of suspended soil activation products (3.3.1.3). 

All of these intakes require knowledge of the airborne radioactivity concentration and other 

factors—breathing rate, time of exposure as duration and clock time, and the DCFs. 

Ingestion Intakes (3.3.2) arise from a chronic type of exposure that involves the daily intake of 

relatively small quantities of contaminated soil and dust containing a mixture of radionuclides 

that changes with time. Guidance (USEPA, 1996, 1997 and 2002; USACHPPM, 2003) provides 

soil/dust ingestion rates for use in calculations. 

Uncertainty modeling (3.4) reviews the statistical probability distributions (3.4.1) available 

for use in describing the nature of assumed characteristics for the range and frequency 

distribution of parameters, data, and results. Five distributions considered in the study are 

Uniform Distribution (Section 3.4.1.1), Gaussian Distribution (Section 3.4.1.2), Lognormal 

Distribution (Section 3.4.1.3), Triangular Distribution (Section 3.4.1.4), and Log-Triangular 

Distribution (Section 3.4.1.5). In addition, discussions address approaches to the propagation 

of uncertainties (3.4.2), the Monte Carlo Method (3.4.3), quantifying uncertainty (3.4.4), 

and the reporting of representative doses (3.4.5). 

15 
Technical Approach and Methodology (4)

This effort to investigate the use of probabilistic methods for dose reconstruction involved five 

major phases of the probabilistic uncertainty analysis studies for NTPR radiation dose 

reconstruction, which are: 

 A pilot study and proof of concept designed to experiment and test the implementation of 

probabilistic methods using existing deterministic dose reconstruction and assessment 

models currently used in NTPR radiation dose assessments. 

 Special studies to develop statistical models and uncertainty distributions of key input 

parameters used in whole body external gamma dose assessment. 

 Application of prototype methods to three generic cohorts and comparison with dosimetry 

records. These allowed testing and verification that the selected computational tools and 

techniques were capable of producing the types of model results sought. 

 Expansion of the methodology to include application to internal dose estimation where 

deterministic models were enhanced to incorporate improved estimation of input parameter 

central values and uncertainty distributions. 

 Evaluation of the feasibility of the methods developed through six case studies that consisted 

of the three original and three additional cohorts. The selection of case study cohorts was 

based on criteria developed during the pilot study. 

The pilot study (4.1) was carried out to select software tools, study groups, and develop and test 

the basic models using a probabilities approach to NTPR dose reconstructions and uncertainty 

analysis. Software Selection (4.1.1) resulted in choosing Mathcad® as the primary tool for 

Monte Carlo calculations and was supplemented with the Crystal Ball® adjunct to Microsoft 

Excel®, and Mathematica®. Generation of parameter distributions (4.1.2) discusses 

approaches to distributions that model variability and uncertainty of model parameters generated 

in Mathcad. 

The special studies of model parameters, uncertainties, and distributions (4.2) describes 

detailed analyses to support the development of uncertainty models and input values for certain 

parameters, which include: 

For External Dose Models: 

 Intensity distribution from fallout on ship weather decks (4.2.1). 

 Protection factors for land-based structures (4.2.2). 

 Shielding factors for ships (4.2.3). 

 Shot-specific radiological decay functions (4.2.4). 

 Sources of uncertainty when estimating radiation intensity from measured intensities and isointensity maps (4.2.11). 

For Internal Dose Models 

 Gamma source modification factor (4.2.5). 

 Resuspension factors (4.2.6). 

16 
 Breathing rate (4.2.7). 

 Internal dose conversion factors (4.2.8). 

 Characterization of descending fallout (4.2.9) 

 Internal deposition fraction adjustment (4.2.10) 

 Incidental ingestion of contaminated soil and dust (4.2.12). 

Intensity distribution from fallout on ship weather decks (4.2.1) addresses the variability of 

intensity with topside location and its contribution to the uncertainty in the dose of an individual 

crewman and requires modeling this variability in topside intensity when calculating doses 

probabilistically. This study addressed variations in topside configuration, radiation transport 

through air, distributions pre- and post-decontamination, and application to various ship types. 

Models were benchmarked against available measurements for two ships involved in Operation 

CASTLE. 

Protection factors for land-based structures (4.2.2) addresses the protection factor (PF) of a 

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

radiation intensity inside the structure. It is a measure of the radiation shielding provided by that 

structure. This study used building configurations on Enewetak Island contained in contractor 

reports to model PFs and test them for a 48-man barracks building and an 8-man tent. Mathcad 

software was used to calculate a distribution of PFs for locations inside a rectangular shelter with 

known length, width, height, and wall/roof thickness situated in a field of uniformly deposited 

fallout that extends infinitely in all directions. It was further assumed that the interior of the 

shelter was free of fallout, and walls of wood, aluminum, and iron were considered for buildings; 

wall thickness was set to 0 for tents. Fallout initially deposited on a pitched roof would run off 

and redeposit on the adjacent ground with a fraction of the fallout on the roof forming line 

sources alongside the structure. 

Shielding factors for ships (4.2.3) addresses shielding factors (SFs), which are the ratio of 

intensity at some below-deck location to the average topside intensity. The shielding factor is 

dependent on the characteristics of the ship (e.g., beam or maximum width, length, number of 

decks, deck height, and decking thickness) and on one’s position within the ship (deck and 

location on that deck). An approach similar to that for developing protection factors accounted 

for attenuation of radiation emitted by fallout deposited on the weather deck of a ship to various 

levels of interior spaces (decks). 

Shot-specific radiological decay functions (4.2.4) obtained directly from the FIIDOS code 

were compiled in a database that provides relative intensities from 3 seconds to 5 years postdetonation for most shots and most operations. An empirical model of the uncertainty in the 

FIIDOS decay functions was developed for use in the case studies. The model presumed that the 

modeling error will generally increase with time from zero at the time of a known measurement 

to a later time with the amount of error drawn from a Gaussian distribution for each sample in 

the Monte Carlo analysis. 

Gamma source modification factor (4.2.5) (GSMF) corrects for the fact that the contaminated 

surface was not infinite in spatial extent, as assumed in the FIIDOS calculations. A Monte Carlo 

approach is used in a Mathcad program to generate a distribution of GSMF values for a ship. 

The values in the distribution are averaged over all deck locations to produce an average 

17 
GSMF—designated <GSMF>. The uncertainty in <GSMF> is determined by considering 

factors that contribute to it for an aircraft carrier that include (1) shielding provided by aircraft 

that may have been located on the flight deck, (2) the impact of the superstructure, and (3) the 

deviations of the flight deck from the idealized rectangular configuration. Account is taken for 

these factors for aircraft carriers, and extended to other ship types considering similar factors to 

produce a collection of <GSMF> values for the common ship types involved in nuclear test 

operations. 

Resuspension factors (4.2.6) relate air concentrations of radioactivity to ground contamination 

levels. Time-dependent models for deterministic and nominal point estimates for resuspension 

of fallout as used in the case studies for typical activities are given in that section. For the 

probabilistic analysis, the uncertainty associated with the nominal resuspension factor values 

(land and ship) is assumed to have a lognormal distribution with the median equal to the nominal 

value, and a 90-percent confidence interval between 0.1 and 10 times the median. Supplemental 

uncertainty models were developed to address special resuspension characteristics associated 

with the precursor and blast-wave regions that accompany nuclear detonations near the 

detonation point. 

Breathing rate (4.2.7) is an important parameter for calculating intakes by inhalation and 

depends on the level of physical activity and other physiological parameters related to 

ventilation. It influences the volume and rate of air inhaled and the proportions entering through 

the nose and mouth, their penetration into the respiratory tract, and the quantities deposited. 

Summary data and guidance provided by the International Commission of Radiological 

Protection (ICRP, 1994), the National Council on Radiation Protection (NCRP, 1997) and the 

United States Environmental Protection Agency (USEPA, 1997) are used to construct probability 

distribution functions of breathing rates for various types of activity and to apportion time among 

such activities for atmospheric nuclear test participants. 

Internal dose conversion factors (DCFs) (4.2.8) used in NTPR dose reconstructions are derived 

from published ICRP dose coefficients (ICRP, 1996; ICRP, 2002) and involve biases and 

uncertainties that must be addressed to perform best-estimate probabilistic analyses. Studies to 

address these included estimation of inhalation dose conversion factors using FIIDOS (4.2.8.1), 

uncertainty in inhalation and ingestion dose conversion factors (4.2.8.2), and maximum dose bias 

in inhalation DCFs (4.2.8.3). 

Characterization of descending fallout (4.2.9)—Special studies were conducted (1) to 

calculate the fraction of the activity in descending fallout (“activity fraction”) (4.2.9.1) that was 

carried by particles in each of three size classes and (2) to estimate the deposition velocities 

(4.2.9.2) in the breathing zone for particles in each size class. 

Internal deposition fraction adjustments (4.2.10) are defined as the fractions of inhaled 

particles in a given size class that are respirable and non-respirable. The deterministic inhalation 

dose models assume that all of the fallout inhaled is in the size range between 1–10 μm. 

However, the use of this assumption for all scenarios is undoubtedly high-sided, especially for 

descending fallout. Probabilistic analyses require more realistic descriptions of the activity 

deposited by particles of various sizes. This section discusses an approach that characterizes the 

deposition in the respiratory tract of particles in the three inhalable size classes 1 (1–10 μm), 

2 (10–20 μm) and 3 (20–100 μm). 

18 
Sources of uncertainty when estimating radiation intensity from measured intensities and 

iso-intensity maps (4.2.11) has a related uncertainty comprised of two components—the 

uncertainty due to errors introduced during the actual intensity measurement and when maps are 

created from a discrete and often sparse set of point observation measurements; and 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. 

Incidental ingestion of contaminated soil and dust (4.2.12) containing radioactivity is another 

route of entry for participants in atmospheric nuclear testing. As in analysis of exposure to 

internally-deposited materials, this depends on the intake amount of activity, which in turn 

depends on the ingestion rate of soil and soil density. A literature review identified guidelines 

compiled in USEPA (1997, 2001 and 2002) and the USACHPPM (2003), which served as the 

basis for preparing a skewed triangular distribution of soil ingestion rates. Soil density data for 

NTS and PPG locations were identified and used to develop a triangular distribution for input to 

Monte Carlo analyses. 

Dependencies and correlations between model input parameters (4.3) for the distributions 

and sensitivity to model parameters of the reconstructed doses for the six case studies were 

estimated using probabilistically-based Monte Carlo simulation techniques. Model parameter 

values were randomly selected from each of their distributions. There are 54 explicit input 

parameters used in the six case studies, which have associated uncertainty distributions. Two 

types of correlations were considered: correlations among different parameters and those from 

shot to shot for the same parameter. The discussion focuses on the various aspect of parameter 

dependencies and correlations, and the basis for each correlation decision is presented in 

Table G-1 of Appendix G. 

Case Study Results (5) 

The methods and tools developed in this investigation were applied in six case studies to 

demonstrate their feasibility, and to check their validity through comparison to existing methods 

and to film badge data where available. Case studies were performed for the following cohorts: 

 7126th Army Unit (AU) Headquarters (HQ) Detachment, Enewetak Atoll, Operation 

REDWING (1956) 

 Army Unit Administrative and Operations Detachments, Enewetak Atoll, Operation 

HARDTACK I (1958) 

 4th Marine Corps Provisional Atomic Exercise Brigade (MCPAEB) Maneuver at Shot 

HOOD, Operation PLUMBBOB (1957) 

 USS ESTES (AGC 12), Operation REDWING (1956) 

 USS BOXER (CVS 21), Operation HARDTACK I (1958) 

 Army Personnel, Enewetak Atoll, Operation CASTLE (1954) 

Sections 5.1 through 5.6 provide summaries of the scenarios, relevant film badge and other 

radiation data for the case, and detailed discussions of the results. Additional details about each 

unit’s activities, assumptions about scenario parameters, and uncertainty distributions used in the 

probabilistic analysis are provided in Appendices A–F. 

19 
 A summary of study results and discussions (Section 5.7) provide the ratios of deterministic 

(current NTPR high-sided) upper bound doses to the 95th percentile probabilistic doses—called 

upper bound dose ratios— for the six case studies investigated in this report, and shown in Table 

ES-1. These ratios illustrate the difference in upper bound doses estimated using deterministic 

and probabilistic methods at the current stage of development. The upper bound dose ratios for 

external doses exceed 1.0 in all cases considered, indicating that the upper bounds of the 

deterministic external doses are greater than the 95th percentiles of the corresponding 

probabilistically-calculated doses. The upper bound dose ratios for internal doses equal or 

exceed 1.0 for all case studies except for the scenario for the 4th MCPAEB maneuver at Shot 

HOOD, Operation PLUMBBOB (Case Study #3). Although these results support the 

reasonableness of DTRA’s default uncertainty factors, general conclusions about these 

comparisons should not be made from these limited test cases. 

Table ES-1. Ratios of Deterministic Upper Bound over 95th Percentile Probabilistic Doses 

Upper Bound Dose Ratio

Internal α

Upper Bound Dose Ratio 

Internal β+γ

Case 

Study Study Group 

Upper Bound 

Dose Ratio 

External All Organs Evaluated Thyroid Lung 

LLI 

wall 

1 RW/Enewetak 1.6 1.4 1.5 3.7 1.3 

2 HTI/Enewetak 1.5–1.6 2.5–2.6 1.8 4.6 1.8 

3 PB 1.7 0.58-0.68 0.43 0.87 0.42 

4 RW/USS ESTES 1.1 1.5 1.1 3.2 1.0 

5 HTI/USS BOXER 1.3 4.0–4.2 2.0 6.2 2.0 

6 CASTLE/Enewetak 1.5 2.5–2.6 2.2 5.6 2.2 

Discussions of factors contributing to the results observed for internal doses are provided. 

Sensitivity Analysis for the Dose Models of CASTLE Enewetak Case Study (6) 

Sensitivity analyses were performed for the external and internal dose models applied to the 

Army personnel at Enewetak Atoll at Operation CASTLE (1954) (Case Study # 6) for a sample 

organ. These analyses were performed to evaluate to which input parameters the models are 

most sensitive, and to develop an approach on how to implement and use sensitivity analyses in 

NTPR dose reconstructions. It is not the intent of this analysis to develop generalized 

conclusions to be applied across many scenarios with a broad range of exposures and types of 

intakes, or across all target organs considered in NTPR dose assessments. Indeed, it is 

recognized that the parameters to which models are most sensitive would likely be different for 

different target organs. 

20 
Discussions of the technical approach (6.1), external dose model sensitivity analysis (6.2), 

and internal dose model sensitivity analysis (6.3) provide details of the sensitivity analyses. 

Results of sensitivity analyses for the sample scenario and target organ evaluated using 1000 

Monte Carlo runs varying one parameter at a time indicate the following: 

 The external dose model is most significantly sensitive to the variability and uncertainty in 

intensity measurement and data errors, fallout distribution and decay constants. 

 The internal alpha and beta-plus-gamma dose models are most significantly sensitive to the 

uncertainties in the DCF for inhalation and the resuspension factor. 

Conclusions and Recommendations (7) 

The main goal of this study was to investigate and demonstrate a methodology and the enabling 

computational tools to perform probabilistic radiation dose assessments for NTPR atomic 

veterans. This goal was achieved through the use of Monte Carlo simulation techniques and 

available data and information. Probabilistic models for both external and internal dose 

calculations that account for uncertainty and variability of input parameters were developed, 

tested, and applied in six case studies. Extensive research of the relationship of fallout 

deposition times to particle size distributions constituted one of the most difficult aspects of 

model parameter characterization due to the limited availability of applicable data. Fallout 

deposition were developed and compared with the limited available data to provide reasonable 

estimates of the activity fractions in respirable and non-respirable particle-size classes. Despite 

this progress to date, further efforts are needed to enhance the characterization of particle size 

distributions in fallout that can be applied to a broader range of exposure situations. 

A comparison of reconstructed external doses and film badge readings was carried out for units 

where reliable dosimetry data were available. For four groups, reconstructed probabilistic 

external doses matched well with the film badge doses, and the 95th percentile of the 

probabilistic dose distribution exceeded the 95th percentile of the film badge dose distribution. In 

addition, NTPR deterministic upper bound doses, determined by multiplying the external doses 

by a factor of 3 were higher than the probabilistic 95th percentile external doses in all case 

studies. 

For internally-deposited radioactive materials, the NTPR deterministic method resulted in 

internal upper bound doses, determined by multiplying the internal doses by a factor of 10, were 

higher than the probabilistic 95th percentile internal doses, except in the case of the Marine unit 

at PLUMBBOB discussed in Section 5.7. 

The case studies included in this investigation varied in type (land and two very different types 

of ships), number and time of occurrence of fallout events, radiation intensities and fallout 

deposition, time veterans spent at the PPG, etc. Therefore, implementation of the probabilistic 

methodologies can proceed but with the expectation that further refinements should take place 

and any adjustments will require revision of the standard methods as applicable. 

A sensitivity analysis was performed to identify the possibility of screening out sources of 

uncertainty with small or limited impact on dose. A simple method that varied model parameters 

one-at-a-time was applied for both external and internal doses using the Army personnel at 

Enewetak during CASTLE and for one organ as an example. Successful application of this 

21 
methodology for sensitivity analysis provides a basis for use in future refinements of existing 

methods and extension to new exposure situations. 

The results of this investigation are valid for the six case studies only and cannot be generalized 

to all exposure scenarios. Only the methodologies developed and presented in this report can be 

applied and expanded to other scenarios of exposure. The analyses conducted provide 

reasonable estimates of dose and associated uncertainties for the types of exposure scenarios 

studied and support implementation of the probabilistic approach to radiation dose assessments 

in the NTPR Program. The following recommendations are offered to achieve implementation 

of the approach: 

 Conduct testing of probabilistic methods applied to other exposure scenarios, test series, and 

participant units to develop experience with preparing reasonable distributions of parameters 

to support implementation of these methods. 

 Incorporate probabilistic approaches developed in this report to NTPR RDA procedures and 

methodologies. 

 Implement the probabilistic analyses described herein when performing future radiation dose 

reconstructions and adapt model parameter distributions when case-specific scenarios are 

well documented. 

22 
1 INTRODUCTION 

In October 2007, the Veterans’ Advisory Board on Dose Reconstruction (VBDR) recommended 

that the Nuclear Test Personnel Review (NTPR) Program develop procedures to perform 

probabilistic uncertainty analyses for Radiation Dose Assessments (RDAs) (VBDR, 2007). 

Specifically, the NTPR standard operating procedures should specify whether uncertainty 

estimates from individual sources are independent or correlated and when and how uncertainties 

should be propagated. The Defense Threat Reduction Agency (DTRA) tasked Science 

Applications International Corporation (SAIC) to investigate methods that could be used for 

conducting analyses for NTPR RDAs (DTRA, 2007b). In response, SAIC identified the effort’s 

main goal to develop and demonstrate a methodology and its enabling computational tools to 

perform probabilistic radiation dose assessments for NTPR atomic veterans. The specific 

objectives of this investigation are: 

 Conduct technical studies and develop approaches for estimating uncertainties associated 

with model input parameters in the dose reconstruction process. 

 Create a methodology for incorporating probabilistic uncertainty analysis into dose 

reconstructions related to exposures to external gamma rays and internally-deposited 

radioactive materials. 

 Adapt dose models and create computational tools with improved capabilities in assessing 

uncertainty in reconstructed doses using accepted probabilistic methods for external gamma 

rays and internally-deposited radioactive materials. 

 Demonstrate the feasibility of the developed methodologies and tools through application to 

case studies that are representative of large groups of participants. 

 Compare the results of probabilistic dose reconstructions for the case studies with current 

methods that use high-sided estimates and upper bound factors mandated in interim policy. 

The steps necessary to achieve the aforementioned objectives include the following: 

 Identify key model parameter measurement- and activity-based uncertainty and variability 

and characterize corresponding probabilistic distributions. 

 Select and develop appropriate software tools capable of performing Monte Carlo (MC) 

simulations for the purpose of estimating dose distributions for specific cohorts and exposure 

scenarios. 

 Perform tests of the simulation models and assess the success of the methods for supplying 

reasonable dose estimates and associated uncertainties through application in the sample 

cohort case studies. 

This report is organized into seven sections, a reference listing and seven appendices. Section 2 

provides the background about the need for the study; Section 3 describes relevant dose 

calculation and statistical methods for radiation dose estimation and uncertainty modeling. 

Section 4 presents the technical approach and methodologies and concentrates on 11 parameters 

and dose reconstruction factors and associated uncertainty distributions. Section 5 reports the 

results of six case studies, Section 6 discusses the methods and results of a sensitivity analysis, 

and Section 7 discusses conclusions and provides recommendations. Appendices A through F 

provide detailed descriptions of the case studies for the selected participant units including 

23 
scenario of radiation exposures and environment, model input data, and results. Finally, 

Appendix G provides information and rationale used on the dependencies and correlations of 

model parameters. 

24 
2 BACKGROUND 

The NTPR Program reconstructs radiation doses for atomic veterans when personnel dosimetry 

(film badge) results are not available according to the requirements specified in governing 

regulations (Title 32 Code of Federal Regulations Part 218) (DoD, 2009). The reconstructions 

combine information about personal activities, the radiation environment, and scientific and 

technical principles to estimate radiation doses and their uncertainties. Traditionally, the 

methods have used high-sided estimates for parameters and uncertainties that are difficult to 

characterize. These high-sided estimates were considered to overestimate actual doses and 

therefore provided reliable upper bounds. 

In a 2003 review of DTRA’s dose reconstruction program, a committee of the National Research 

Council of the National Academy of Sciences (NAS/NRC) concluded that although central 

estimates of reconstructed doses for external gamma exposures were valid in most cases, upper 

bounds could not always be shown to be at least as great as a 95 percent upper confidence limit 

(NRC, 2003). As a result, the Committee recommended “... a comprehensive re-evaluation of 

the methods being used to estimate doses and their uncertainties to establish more credible 

upper-bound doses to atomic veterans.” In a 2004 report to Congress, DTRA and the 

Department of Veterans Affairs (DVA) acknowledged these findings and committed to plans to 

improve models for calculating the upper bound in the total reconstructed external gamma dose, 

and for estimating the inhalation dose to participants in Nevada tests (DOD/DVA, 2004). 

In response to other NAS recommendations, DOD and DVA jointly established the VBDR with 

a memorandum prepared by the Undersecretary of Defense (USD, 2004) to oversee the dose 

reconstruction process. The VBDR established subcommittees to perform the majority of its 

work. Specifically, Subcommittee 1 on Dose Reconstruction audited radiation dose assessments, 

reviewed methodologies, and developed conclusions and recommendations. In October 2007, 

the VBDR recommended to DTRA to develop procedures that use probabilistic analyses in dose 

reconstructions, and to discontinue using default upper bound factors that were mandated in 

interim policy (VBDR, 2007). DTRA endorsed efforts to pursue thiss recommendation, which 

forms the basis for the investigations documented in this report (DTRA, 2007c). 

In addition to the aforementioned activities toward implementation of the VBDR’s 

recommendations, DTRA also tasked SENES Oak Ridge to investigate whether the DTRA 

policy of applying an upper bound factor of three to external reconstructed doses was adequate 

for providing an upper bound with at least 95 percent credibility. SENES approached the 

investigation by performing a review to verify whether upper bounds determined by applying the 

factor of three to doses supplied in previous unit dose reconstruction reports was adequate to 

contain at least 95 percent of the reported film badge readings for the same unit. 

At about the same time, a committee of the National Council on Radiation Protection (NCRP) 

published a report that addressed uncertainties in external dose reconstruction (NCRP, 2007). 

This report provides important information for the approach and methods employed in this study. 

A complementary study addressing uncertainties in internal radiation dose reconstruction is 

underway by another committee of the NCRP and will be reviewed for relevance to this study 

after it is published. 

25 
3 RADIATION DOSE ESTIMATION AND UNCERTAINTY MODELING 

This Section contains general discussions of the dose reconstruction methodologies and 

uncertainty distributions relevant to the case studies of this report. Section 3.1 defines the three 

types of doses that are calculated. Methodologies used for external dose reconstruction are 

described in Section 3.2, and those for internal dose reconstruction in Section 3.3. The 

fundamentals of uncertainty modeling are discussed in Section 3.4. 

3.1 Definitions of Types of Parameters and Doses 

This report involves the calculation of “nominal,” “probabilistic” and “deterministic” doses, 

which are described further in the following discussions. 

3.1.1 Nominal Doses 

To build model input parameter distributions for the probabilistic analyses conducted in this 

study, realistic central estimates (or best estimates) are useful, many of which were recorded 

from measurements and documented in operational and technical reports. In other cases where 

data are not available or not well documented, surrogate data are used. Analysts with extensive 

knowledge of NTPR-related historical information used their collective and subjective judgments 

within a collaborative process to make best estimates of input parameters and related uncertainty 

distributions. The best estimates for central values of model parameters are termed “nominal 

values.” 

As nominal values are usually based on documented observed data or best estimates, they are 

used in building the statistical distributions of each uncertain parameter. Other nominal values 

are extracted from numerically generated distributions which are based on physical and 

mathematical models that characterize input parameters and their uncertainty and variability. 

Nominal dose calculations 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. In this 

case, model parameters or groups of related parameters are varied one at a time. While one 

single input parameter is allowed to vary within its range of values based on its own distribution, 

all other parameters in the model are held to their nominal values. The outcome of such analyses 

allows evaluating the sensitivity of a dose model to its input parameters, thus showing which 

parameter uncertainties would have the most influential effect on the dose distribution. 

3.1.2 Probabilistic Doses 

The probabilistic models use nominal values as central estimates to define the probability 

distributions for each input parameter. Depending on the type of distribution employed, the 

central estimate can be the arithmetic mean (hereafter called mean), geometric mean, median or 

mode (peak). A full probabilistic analysis, where all uncertain input parameters are assigned 

distributions, results in a dose distribution that reflects both uncertainty and variability of the 

reconstructed dose. The upper bound dose for a probabilistic analysis is defined for the purpose 

of this report as the 95th percentile value of the dose distribution. The uncertainty factor is 

26 
defined as the ratio of the 95th percentile value to the central value of the dose distribution. Note 

that “uncertainty analysis” is sometimes used in this report in place of “probabilistic analysis.” 

3.1.3 Deterministic “NTPR” Doses 

The NTPR program has historically relied on dose reconstruction models that utilize 

conservative “high-sided” input parameters and processes to generate what are termed in this 

report “deterministic” doses. Such doses are not the same as nominal doses and should, in 

principle, be equal to or higher than nominal doses. 

The “deterministic upper bound” dose is defined as the deterministic dose multiplied by a fixed 

factor. The fixed factors are currently equal to three (×3) for external reconstructed doses and 

10 (×10) for internal reconstructed doses, as defined by an interim action referenced in the NTPR 

Policy and Guidance Manual (DTRA, 2007a). These factors are believed to result in upper 

bound doses equal to or greater than the 95th percentile of a probabilistically-based distribution 

prepared using credible distributions of the important parameters that contribute to uncertainty. 

The deterministic upper bound dose is expected to equal or to be higher than the 95th percentile 

value of the dose distribution resulting from a credible probabilistic analysis. 

3.2 Whole Body External Dose 

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 radiation 

sources relevant to NTPR include: 

 Initial nuclear radiation: Neutrons and gamma rays emitted from the fireball and the cloud 

column during the first minute after a nuclear explosion. 

 Residual nuclear radiation: Nuclear radiation emitted from fission products, soil activation 

products, and other radioactive debris at times greater than 1 minute after a nuclear 

detonation. 

In the case studies described in this report, none of the participants were exposed to initial 

nuclear radiation. The most commonly encountered source of residual radiation is gamma rays 

emitted from fallout particles, but some test participants were also exposed to gamma rays 

emitted from neutron activation products in the soil. Methodologies useful in reconstructing 

doses from exposures to these two source types are discussed in Sections 3.2.1 and 3.2.2, 

respectively. The whole body external doses from gamma radiation were frequently measured 

by individual film badges affixed to the external clothing of the participants; film badge 

dosimetry for nuclear test participants is addressed briefly in Section 3.2.3. 

3.2.1 External Dose from Exposure to Fallout 

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

pattern of the fallout field was determined primarily by the direction and magnitude of the 

prevailing winds above the test site. At the Nevada Test Site (NTS), test participants operated in 

the vicinity of both freshly deposited fallout and fallout that had been deposited days or weeks 

prior to exposure while in the test area, and occasionally resided in camps that received light 

fallout. Personnel who participated in the oceanic tests also were exposed to both freshly 

27 
deposited and older 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 from these data because fallout intensity decays in a reasonably predictable manner. 

For NTS tests, monitors conducted radiological surveys shortly after virtually all of the shots, 

documenting exposure rates (typically referred to in this report as “intensities”) at specified times 

and locations (Hawthorne, 1979). Thus, the radiation intensities in the vicinities of these shots 

are relatively well known and can be estimated for later times using time scaling techniques 

discussed below. A test participant marching through or operating in such a fallout field 

experienced radiation intensities that varied in time due to (1) his movement through the nonuniform field and (2) radiological decay. Let trtI ))(,(  denote the free field intensity at a 

participant’s time-varying location tr )(  at time t. tI ,( tr ))( is often expressed in units of 

roentgen per hour (R hr−1

). The dose D (rem) from operating in that fallout field is then given 

by: 

 (3-1)   2

1

70

t

t

dt))t(r,t(I.D 

where the interval t1→t2 encompasses the time he spent in the fallout field. The coefficient 0.7, 

often called the “film badge conversion factor,” converts from roentgen (as measured by a 

survey instrument) to rem (as would be assigned from a film badge reading) by taking into 

account the shielding of the film badge to gamma radiation by the human body for a person 

standing upright in a large planar fallout field. It is acknowledged that the film badge conversion 

factor has associated uncertainties; however quantification of the uncertainties is deferred for 

future studies. The integration in Equation 3-1 must often be performed numerically, since 

trtI ))(,(  generally cannot be reduced to a tractable functional form. 

In many scenarios of interest, a test participant remained for significant periods of time in an 

essentially uniform fallout field or in a possibly non-uniform field for which only an average 

intensity is known. This occurred for NTS and oceanic participants whose residential, working 

or recreational areas were contaminated by fallout, and for oceanic participants who resided on 

ships that received topside fallout, or were exposed to shine or contaminated surfaces. In these 

cases, the intensity takes the simplified functional form I(t), indicating that a participant’s dose 

(Equation 3-1) does not depend on the details of his movement within the field. In the latter 

scenario involving a non-uniform field, I(t) is interpreted as the intensity averaged over a 

confined area of contamination such as an island or ship’s weather deck. 

The following section discusses various representations of the time dependence of intensity. 

3.2.1.1 Modeling of Fallout Intensity Decay 

The change in fallout intensity with time is dependent on radiological decay as well as 

environmental processes such as weathering and human influences such as decontamination. In 

general, only radiological decay is explicitly accounted for in NTPR analyses, except when 

specific actions such as decontamination are known to have occurred. However, in cases where 

a decay function is based on measured intensities, all processes that affect the intensities are 

28 
implicit in the measured values, and hence the intensity function, over the period of time the 

measurements were taken. 

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. 

A generic example of such data is shown in Table 1. 

These early-time intensity data are modeled by applying a curve fitting algorithm to produce an 

“early time intensity function,” named Iearly(t) in this example. Mathcad®, 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 

 (3-2) T,linterp[ t]),log(EarlyI early )t(I  10

The right side of this equation is simply 10 raised to the power of the base-10 logarithm of the 

intensity at time t, as linearly interpolated (“linterp”) from the time-intensity data of Table 1, 

where T is the time vector (t0, t1, t2) and EarlyI is the intensity vector (I0, I1, I2). Linear 

interpolation in linear space and cubic spline fitting (“cspline”) have also been used for this 

purpose. 

Table 1. Generic Example of Early Time Intensity Data 

Time after Detonation 

(t, in hours) 

Measured Intensity 

(EarlyI, in R hr−1) 

t < t0 0 

t0 I0

t1 I1

t2 I2

t3 I3

t4 I4

It is well documented (e.g., Glasstone and Dolan, 1977, p. 451) that, following the end of 

deposition, the time variation of the radiation intensity of the fallout can be approximated as t

−λ, 

where t is the time after detonation and λ is constant over specified periods of time. The most 

frequently used values of λ are 1.2 for the first 6 months (4380 hours) after detonation and 2.2 

thereafter. However, the decay of fallout material from specific shots is sometimes better 

characterized by other values of λ. Decay rate uncertainties have been addressed in the 

probabilistic analysis, as discussed in Section 4.2.4. As an example of shot-specific decay, the 

contaminants produced by Shot BAKER of Operation CROSSROADS were observed to decay 

as t

−1.3, so a value of λ = 1.3 is generally used in that case (Weitz et al., 1982). 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. A generic example is 

given in Table 2. In this example, time t3, found in Table 1 and Table 2, corresponds to the time 

of peak intensity, and t4, found in Table 1, corresponds to the last early time intensity. Time t5, 

found in Table 2, corresponds to the end of the operational period; this time is often used to 

29 
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. 

Table 2. Generic Example of Multiple Decay Exponents 

Time Interval (hours) Decay exponents λi

t3 to t5 λ1

t5 to 4380 λ2

t > 4380 2.2 

The pre- and post-deposition intensity parameterizations can be integrated into a single “intensity 

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

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

ICF(t) = 0 if t < t0

ICF(t) = Iearly(t) if t0 ≤ t < t3

ICF(t) = I3 (t3/t)

λ1

if t3 ≤ t < t5 (3-3)

ICF(t) = I3 (t3/t5)

λ1

(t5/t)

λ2 if t5 ≤ t < 4380

ICF(t) = I3 (t3/t5)

λ1

(t5/4380)

λ2

(4380/t)

2.2

if t ≥ 4380

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 intensity on Parry 

Island, Enewetak Atoll, caused by fallout from Operation GREENHOUSE Shot EASY: 

 t0 = 17 hr, I0 = 0.0001 R hr−1

 t1 = 20 hr, I1 = 0.00035 R hr−1

 t2 = 22 hr, I2 = 0.00065 R hr−1

 t3 = 24 hr, I3 = 0.001 R hr−1

 t4 = 30 hr, I4 = 0.00085 R hr−1

The ICF(t) curve in Figure 1 was decayed using λ1 = 1.1 for the interval t3 to t5 (=978 hrs), λ2 = 

1.2 for the interval t5 to 4380, and λ = 2.2 thereafter. Note that in this example, the last early 

time/pair (t4, I4) is not used to define ICF(t) because it occurs after the peak time (t3, I3) and falls 

on the decay curve. 

The computer code FIIDOS (Fallout Inhalation and Ingestion Dose to Organs, Version 4) was 

developed in the NTPR Program as a primary tool for internal dose reconstruction (Raine et al., 

2007). Starting with a shot-specific initial inventory of radionuclides (taken, for example, from 

Hicks, 1984), the code calculates the subsequent production and decay of fission products, 

activation products, and actinides. (It is generally assumed in these calculations that no 

30 
Time after Detonation (hr)

Instensity (R hr-1)

101 102 103 104

10-7

10-6

10-5

10-4

10-3

10-2

ICF(t)

Measurements

End of Operation

Figure 1. Graph of ICF(t) and Early Time Intensity Data 

fractionation occurred except for the removal of noble gases. However, additional fractionation 

and other processes such as weathering may be included in the future as refinements to the 

FIIDOS inventories.) The code tallies (among other things) the collective gamma emissions and 

intensities at 42 times ranging from 3 seconds to 5 years after the detonation. This output can be 

utilized directly to define I(t) for virtually any shot of interest. Intensities as functions of time for 

selected shots, normalized to I = 1 R hr−1

 at t = 1 hour, are plotted in Figure 2. 

In the above (FIIDOS) representations of fallout intensity decay, weathering has been neglected. 

Weathering generally causes the intensity to diminish at a faster rate due to runoff, leaching and 

migration of the contaminants into the soil. As a result, the use of these formulations may result 

in somewhat high-sided dose estimates for exposures that took place a few weeks or more after 

deposition. 

3.2.1.2 Effects of Shielding 

The radiation intensity inside a structure surrounded by fallout was less than that which existed 

outside the structure due to (1) attenuation of the radiation by the walls, roof, and other 

intervening materials and (2) the displacement of the radiation source from interior locations. 

The shielding afforded participants while inside structures for land-based scenarios is quantified 

in terms of a “protection factor,” defined as the average free-field intensity outside the structure 

31 
Time after Detonation (hr)

Intensity (R hr-1)

100 101 102 103 104 105 106

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

CASTLE BRAVO

HARDTACK I FIR

PLUMBBOB WILSON

Figure 2. FIIDOS-Derived Intensity Functions for Selected Shots 

divided by the free-field intensity inside the structure. Thus, the dose accrued during a given 

time interval spent inside a structure with protection factor PF is equal to the dose that would 

have been accrued during the same time interval outside the structure divided by PF. Specific 

values of PF that have frequently been used in deterministic dose reconstructions are 2.0 for 

permanent and semi-permanent structures such as barracks, office buildings, and Quonset huts, 

and 1.5 for tents (Goetz et al., 1987). Because the intensity inside a structure varies with 

location, PF can be expressed as a probability distribution, as described in Section 4.2.2. 

In an analogous manner, the shielding afforded crewmen while below deck on a ship that had 

received topside fallout is frequently expressed as a shielding factor, defined as the free-field 

intensity below deck divided by the free-field intensity topside. (Note that this is the reciprocal 

of the protection factor.) Thus, the dose accrued during a given time interval spent below deck, 

where the shielding factor was SF, equals the dose that would have been accrued during the same 

time interval topside multiplied by SF. A value of SF = 0.1 is frequently used for below deck 

areas (Rinnert, 1957) in deterministic dose reconstructions. As with the protection factor, the 

shielding factor can be represented by a probability distribution, reflecting the range and 

frequency of values of SF at the various below deck locations. It is recognized that during early 

times post detonation the specific times of shielding, as opposed to the fraction of time shielded, 

are important because of the rapidly decaying exposure rate. Additional consideration of this 

effect is a matter for future refinements. 

32 
3.2.2 External Dose from Exposure to Activated Soil 

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

the fireball did not, the residual radiation intensity near ground zero (GZ) was dominated by 

neutron-activated radionuclides in the soil. In these cases, nearly circular radiation intensity 

contours were formed around GZ due to the neutron activation of the soil. 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 reconstructed by evaluating 

Equation 3-1, but the temporal dependencies discussed above for fallout no longer apply. 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 the constituents, the decay properties of the reaction products, and 

the attenuation of the emitted radiation by the intervening 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 (24Na, half-life = 15 hours) was the dominant radioisotope the 

first two days after a detonation over typical NTS soil. Other activation products relevant for 

NTS exposures include manganese-56 (56Mn, half-life = 2.6 hours) and potassium-42 (42K, halflife = 12.4 hours). Although the uncertainties in this analysis are not currently included here, 

future refinements could include uncertainties in variables such as concentrations of elemental 

constituents in the soil, and attenuation by soil. 

3.2.3 Film Badge Dosimetry 

During the period of U.S. atmospheric nuclear weapon testing, the exposure of military and 

civilian personnel to external radiation was monitored primarily with film badge dosimeters. 

Specific details regarding film badge dosimetry practices employed for the atmospheric nuclear 

testing operations are found in NRC (1989). That detailed information can be summarized as 

follows: prior to Operation CASTLE in 1954, film badges were typically issued only to 

individuals involved in activities with anticipated potential for radiation exposure (e.g., cloud 

samplers and associated ground crews, sample recovery teams, decontamination crews, radiation 

safety personnel). At CASTLE, cohort badging was introduced as a means of monitoring the 

radiation exposures of all individuals, regardless of their anticipated potential for exposure. At 

Operation REDWING in 1956, film badge dosimetry practices were further expanded. 

Permanent film badges, which were to be worn at all times, were issued to all individuals who 

entered the test area. In addition, individuals involved in activities with potential for radiation 

exposure were issued mission badges for those activities. Mission badges were to be worn with 

the individual’s permanent film badges. For test series subsequent to Operation REDWING, 

most individuals were issued one or more film badges for the duration of their participation. 

NRC (1989) identifies three principal types of error that affected film badge dosimetry results for 

atmospheric nuclear test participants: radiological, laboratory, and environmental. Based on an 

evaluation of the impact of these errors on the film badges used at each test series, this reference 

provides, by series, an overall “exposure” bias factor B and an uncertainty factor K. The 

interpretation of B and K and their application to quantifying the uncertainty in a film badge 

reading are addressed in Section 3.4.1.3. It is noted here that, for the purpose of comparing film 

badge readings with reconstructed doses, the bias should first be removed from those readings by 

dividing them by B (or incorporated into the reconstructed doses by multiplying them by B). The 

33 
overall topic of cohort badges is to be the subject of a separate report and is thus outside the 

scope of this report. 

3.3 Internal Dose 

Internal organ doses result from exposures to radioactive sources inside the body. Participants in 

nuclear weapons tests could have accrued internal doses as a result of intakes of radionuclides by 

inhalation, ingestion, or absorption through the skin or open wounds. Intakes by inhalation are 

the most common pathway for the majority of participants; most exposure scenarios involve 

inhalation of descending fallout and/or fallout that had been deposited previously on the ground 

or other surfaces and subsequently resuspended into the air. Additional pathways of internal 

exposure involve the consumption of food and/or water that has been contaminated by fallout 

and the incidental ingestion of contaminated soil. Absorption of radionuclides through the skin 

or an open wound is uncommon in exposures of atomic veterans and is not considered in the case 

studies. 

Internal dose cannot be measured directly but must be estimated based on other available data. 

Because no relevant air monitoring data and very little bioassay data are available for 

atmospheric nuclear test participants, indirect methods must be used. The methods are based on 

available data, such as gamma intensity measurements, used in conjunction with models and 

various assumptions. (Barrett et al., 1986) 

Calculation of internal organ doses requires the use of factors that convert intakes of radioactive 

material to the dose each organ would receive from that intake. Organ doses resulting from 

intake of a single radionuclide, such as a soil activation product, are calculated using ICRPrecommended dose coefficients. These dose coefficients relate organ-specific equivalent doses 

to intake of a single radionuclide, and are generally tabulated in units of sievert per becquerel 

(Sv Bq−1

). Because most internal exposure scenarios associated with nuclear testing involve 

intakes of mixtures of radionuclides, the dose to an organ or tissue of concern is the sum of the 

doses from intakes of all of the radionuclides. Thus, composite dose conversion factors (DCFs) 

that apply to mixtures of radionuclides have been calculated with the FIIDOS code using ICRP 

dose coefficients and are used in most assessments. As used in this report, the term dose 

coefficient recommended by the ICRP pertains to the equivalent dose from a unit intake of a 

single radionuclide, and the term dose conversion factor pertains to a similar dose quantity for 

mixtures of radionuclides, such as in fallout, and is reported in units of rem per curie (rem Ci−1

). 

The radionuclide composition of any mixture is based on shot-specific radiochemistry data. The 

concentration and composition of radionuclides on the ground and in air, and the associated 

composite DCFs, are time-dependent due to radioactive decay and in-growth. 

3.3.1 Inhalation Intakes 

Any estimate of inhalation dose is based on the following simplified equation: 

    DFTBRAAD (3-4) 

where: 

ΔD = 50-year committed equivalent dose (CED) (rem) to the organ or tissue of 

interest over an incremental time period 

34 
AA = airborne activity concentration (Ci m−3

) of radioactive material 

BR = breathing rate (m3

 hr−1) 

ΔT = incremental time period of exposure (hr), with established start and stop times 

DF = CED inhalation dose factor for the organ or tissue of interest (rem Ci−1

) (DF

can be an inhalation dose coefficient or an inhalation dose conversion factor) 

There are four basic pathways for the inhalation of radioactive material by nuclear test 

participants: (1) inhalation of fallout particles deposited on the ground or other surfaces and 

resuspended by mechanical or natural disturbances, or, in limited cases, by thermal effects of a 

shot; (2) inhalation of radioactive material contained in descending fallout; (3) inhalation of 

neutron-induced radioactivity in the soil (or other material) lofted into the air by mechanical or 

natural disturbances; and (4) inhalation of radioactive material in an atmospheric cloud. (Barrett 

et al., 1986) 

The following sections describe methods that have been used to estimate inhalation doses to 

atomic veterans for the first three pathways identified above. Inhalation of radioactive material 

in an atmospheric cloud is not a common exposure pathway, is not relevant to the case studies 

addressed in this report and is thus excluded from this report. 

3.3.1.1 Inhalation of Fallout Resuspended From Surfaces 

Because measured air concentrations of radionuclides are not generally available for 

contaminated areas occupied or visited by nuclear test participants, air concentrations resulting 

from resuspension of radioactive material from surfaces must be estimated. For this pathway, 

the inhalation intake is assumed to occur concurrently with the accrual of external dose from the 

deposited material. An airborne concentration of radioactive material is estimated through the 

use of a factor that relates the surface activity (SA) in curies per square meter (Ci m−2

) to the 

corresponding gamma radiation intensity, I (R hr−1

), measured at a given distance (nominally 

1 meter) above the surface. Time-dependent surface activity-to-intensity factors (SA/I(t) denoted 

FR(t)) for each shot have been calculated for specific times post-detonation using the FIIDOS 

code. Thus, by using the measured radiation intensity and a pre-calculated surface activity-tointensity factor, a time-dependent surface activity is effectively estimated. By multiplying by a 

resuspension factor K (m−1

), which is the ratio of air activity concentration in Ci m−3 to surface 

activity density in Ci m−2

, an air concentration is estimated. (Barrett et al., 1986, p. 5) 

A generalized expression for the calculation of organ doses as 50-year CEDs from the inhalation 

of resuspended fallout is 

  GSMFtD   dt)t(DCFBR'tK)t(FR)t(I (3-5) inh

T

T

inh

End

Start

   

where: 

Dinh(t) = 50-year CED to the organ (rem) 

GSMF = gamma source modification factor 

35 
TStart = start of exposure, generally when fallout was deposited (hr) 

TEnd = end of exposure, generally when individual left the contaminated area (hr) 

I(t) = gamma radiation intensity (R hr−1

) 

FR(t) = time-dependent and shot-specific ratio of surface activity density to 

radiation intensity (Ci m−2

 per R hr−1) 

K(t') = resuspension factor (Ci m−3

 per Ci m−2, or m−1) 

BR = breathing rate (m3

 hr−1) 

DCFinh(t) = time-dependent and shot-specific inhalation dose conversion factors 

(rem CED per curie of intake) for a specific organ 

t = time after detonation of exposure (hr) 

t' = time after deposition of fallout (hr) 

In this formulation, GSMF adjusts the activity density for finite sources relative to infinite plane 

sources to achieve a given intensity measurement. This is necessary because the FR(t) ratios 

were calculated with FIIDOS assuming an infinite plane source. This applies primarily to 

shipboard exposures, where a typical value of GSMF is 2. 

The resuspension factor K(t') adopted for use in deterministic land-based calculations as 

discussed in Section 3.1.3 is given by the time-dependent expression: 

24 9 010 5 10 10

    

t .

e)t(K (3-6) 

where t' is in hours after deposition and K(t') is in m−1

. This formulation, reported in Till and 

Meyer (1983), is similar to functions proposed by other studies. 

The resuspension factor K(t') adopted for use in nominal land-based calculations is given by the 

time-dependent expression: 

24 9 003024 9 070 5 10 106 10

       

t . t .

e)t(K e (3-7) 

where t' is in hours after deposition and K(t') is in m−1

. This formulation, reported in Anspaugh 

et al. (2002), is based on an extensive review of all resuspension measurement data. Because the 

formulation is intended to describe the observed results over the entire span of an expanded 

dataset, it is currently used for both NTS and PPG scenarios. For shipboard applications, a 

resuspension factor of 10−5

 m−1 for the first 4 days after deposition and zero thereafter is utilized. 

The use of a value of zero after 4 days is based on the fact that naval ships were routinely washed 

or scrubbed regardless of the presence of any contamination. Therefore, any fallout remaining 

on a ship after several days would be strongly bound to the surface and would not be susceptible 

to resuspension. 

Inhalation of fallout that was resuspended by the thermal pulse or blast (shock) wave produced 

by a detonation is also a potential source of exposure at the NTS. This pathway is limited in its 

36 
applicability, and NTPR addresses it using an evaluation of potential inhalation doses resulting 

from this resuspension conducted by Kocher et al. (2006)1

. That report provides central 

estimates and associated uncertainty for “effective” resuspension factors as well as other 

resuspension factors that are useful for the nominal and probabilistic resuspension analyses in 

this report. Kocher et al. use the term “effective” to indicate that these resuspension factors do 

not necessarily correspond to actual values that may have applied to radionuclides that could 

have been inhaled at the time of exposure, but rather they are to be used to ensure that credible 

upper bounds of inhalation doses are obtained in deterministic NTPR dose analyses for scenarios 

involving resuspension by detonations. Resuspension factors for two regions around ground 

zero are available: the precursor region, where resuspension was caused by the initial thermal 

pulse from a detonation, and the more distant blast-wave region, where resuspension was caused 

by blast effects (high winds). The other relevant resuspension factors available in Kocher et al. 

(2006) that were used in the nominal and probabilistic analyses described in this report are those 

that account for respirable and for inhalable but non-respirable forms of resuspended fallout. 

The factors considered in developing these resuspension factors are discussed in detail in Kocher 

et al. (2006), and the values from that report that are used in the PLUMBBOB case study are 

given in Section 4.2.6. 

A deterministic breathing rate of 1.2 m3

 hr−1 has generally been used in the NTPR Program. 

This breathing rate applies to an adult male during light activity, comparable to walking at a rate 

of 3 miles per hour on a flat firm surface (Barrett et al., 1986, p. 13; NCRP, 1997, p. 31). For 

more or less strenuous activity, different breathing rates can be applied as appropriate. 

Additional breathing rates and probability distribution functions for breathing rate for different 

levels of activity for NTPR participants are discussed in detail in Section 4.2.7. 

3.3.1.2 Inhalation of Descending Fallout 

The inhalation of descending fallout (Barrett et al., 1986, p. 24–26) can be considered the 

ground-based analog of the inhalation of cloud debris. Except for the onset of fallout or for very 

fine particles, the radiation intensity at the breathing zone (nominally the 1.6 meter of air 

immediately above the Earth’s surface) is dominated by fallout already deposited. This follows 

from the deposition velocities of fallout particles, the range of gamma radiation, and the duration 

of fallout deposition at a given position. 

A generalized expression for the calculation of organ dose from inhalation of descending fallout 

is given in Weitz (2009a) as 

 

1

 This draft report was recently published with several changes in terminology, resuspension values, and values for 

uncertainty factors for several parameters. See Kocher, D. C., Trabalka, J.R., and Apostoaei, A.J., 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, SENES, Oak Ridge, Inc., Oak 

Ridge, TN and Defense Threat Reduction Agency, Fort Belvior, VA. 

37 
































 



















 







  



























)t(DCF)t(FR R

R

NRNR

V

AF

BR

)t(FDC R

R

V

AF

BR

BR HFBCF

D )t(IGSMF

p ping

n

i

i

i

i

i

pinh

i

n

i i

i

inh p

1 1

1

1 1 0

0

(3-8) 

where: 

Dinh = 50-year CED to the organ (rem) from inhalation 

GSMF = gamma source modification factor 

FBCF = film badge conversion factor (0.7 rem R−1

 from Raine et al. (2007)) 

H0 = nominal height of stabilized cloud, 104

 m 

BR = breathing rate (m3

 hr−1) 

BR0 = deterministic breathing rate of 1.2 m3

 hr−1

i = index of particle-size class bins 

n = number of particle size bins employed (typically 3) 

AFi = activity fraction—the fraction of all activity deposited in a fallout event by 

particles in the i

th particle size class 

Ri = fraction of i

th size class particles deposited in the thoracic airways of the 

respiratory tract (bronchial, bronchiolar, and alveolar-interstitial regions) 

R1 = fraction of particles in the 1-10 μm (i = 1) size class deposited in the 

thoracic airways of the respiratory tract 

NRi = fraction of i

th size class particles initially deposited in the posterior extrathoracic (ET2) region of the respiratory tract and subsequently cleared to 

the gastro-intestinal (GI) tract 

NR1 = fraction of particles in the 1-10 μm (i = 1) size class initially deposited in 

the ET2 region and subsequently cleared to the GI tract 

Vi = deposition velocity (m hr−1

), or average velocity of descent for i

th sized 

particles 

tp = time after detonation (hr) of maximum radiation intensity from fallout 

deposited on the ground or other surface, such as the weather deck of a 

ship 

I(tp) = gamma radiation intensity (R hr−1

) at tp

FR(tp) = FIIDOS-generated time- and shot-dependent ratio of surface activity 

density to intensity (Ci m−2

 per R hr−1) referred to as the “FIIDOS ratio” 

DCF'inh(tp) = shot-specific inhalation dose conversion factors at tp with unit 

rem CED rem−1

; i.e. CED in rem to organ per dose to the whole body 

(rem) from a film badge reading 

38 
DCFing(tp) = shot-specific dose conversion factors at time tp for CED from ingestion 

(rem Ci−1

) for the organ of interest (applies to those particles initially 

deposited in the ET2 region and subsequently cleared to the GI tract) 

In this formulation, GSMF and BR are as discussed for inhalation of resuspended fallout. The 

film badge conversion factor (FBCF) adjusts free-in-air exposure above a fallout field to 

exposures in the same fallout field reported for a film badge placed on a human body, which is 

generally at chest height. The factors related to particle size class including activity fractions AFi, 

fractions of particles depositing in the thoracic airways Ri and the posterior extra-thoracic (ET2) 

region NRi, , and settling velocity Vi are discussed in detail in Weitz (2009a). Particle size 

classes designated Class 1, Class 2 and Class 3 are associated with particles with aerodynamic 

diameters of 1–10 m, 10–20 m, and 20–100 m, respectively (Weitz, 2009a). 

This formulation assumes the duration of fallout deposition at the site of interest was much 

smaller than the time after detonation at which it occurred (Weitz, 2009a). Two additional 

assumptions reduce Equation 3-8 to the more approximate form of the dose equation used in 

deterministic assessments. 

 All fallout particles have aerodynamic diameters in the range of 1–10 μm, corresponding to 

the i = 1 size bin. This implies that AF1 = 1, and AFi = 0 for i > 1. 

 Deposition velocity V1 = H0/tp, the nominal height of the stabilized cloud divided by the time 

(after detonation) of the peak intensity at the site of interest. 

The resulting deterministic form (Weitz 2009a) is 

)t(FDC)t(It BR

BR D GSMF FBCF pp pinh

o

inh   . (3-9) 

For the internal dose evaluation from descending fallout to be valid, the measured intensities 

must correspond to the deposited fallout and personnel exposure must correspond to the full 

period of deposition. 

3.3.1.3 Inhalation of Suspended Soil Activation Products 

The method for estimating airborne concentrations of radionuclides due to suspension of 

radioactive material produced by neutron activation in soil is similar to the method used in 

Section 3.3.1.1 involving resuspension of deposited fallout. 

Relative activities of neutron-induced radioisotopes in soil are estimated on the basis of field 

intensity measurements, known elemental compositions of soil, neutron transport in air and soil, 

neutron capture in nuclei of stable elements in soil, and known decay characteristics of the 

product radioisotopes. Activities of radionuclides per unit volume of surface soil (Ci m−3

) are 

then determined by scaling the estimated relative activities to a calculated photon exposure in air 

above ground or exposure rate at a particular time that matches available measurements with film 

badges or field instruments, taking radioactive decay into account. Radionuclide activities per 

unit volume of surface soil are converted to equivalent surface concentrations (Ci m−2

) by 

assuming the top 1 cm of soil can be suspended in the air. Finally, an appropriate resuspension 

factor is applied to the calculated concentrations of radionuclides in surface soil to obtain an 

39 
estimate of the concentrations in air. As with resuspension of deposited fallout, an important 

condition in using this method is that the film badge or instrument readings must be due 

primarily to activation products in soil (Barrett et al., 1986, pp. 20–22; NRC, 2003, p. 97). 

3.3.2 Ingestion Intakes 

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

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

contaminated soil and dust containing a mixture of radionuclides that changes with time. 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 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. Technical guidance on incidental 

ingestion rates is available in publications from the U.S. Environmental Protection Agency 

(USEPA) and the U.S. Army Center for Health Promotion and Preventive Medicine 

(USACHPPM) (USEPA, 1996, 1997 and 2002; USACHPPM, 2003). 

For this incidental intake of soil and dust scenario, the ingestion dose is calculated as follows: 

      End

Start

T

T ing

soilsoil

ing

ing dt)t(DCF Thick

q )t( I

SA D )t(I



 (3-10) 

Ding = 50-year committed equivalent dose (rem, CED) to an organ due to 

ingestion of contaminated material with either alpha or beta-plus-gamma 

emitting radioactive materials 

ρsoil = bulk density of soil (g m−3) 

qing = average incidental ingestion rate (g hr−1) 

DCFing(t) = time-dependent and shot-specific ingestion dose conversion factors 

(rem CED per curie of intake) for a specific organ 

Thicksoil = thickness of soil layer available for intake, generally assumed to be 

1 centimeter (0.01 meter) 

After due consideration of the cited references, a soil/dust ingestion rate of 500 mg day−1

 was 

selected for the deterministic soil ingestion model in all case studies as an upper bound value for 

the entire period of residence for military personnel who were stationed at NTS facilities, where 

dusty conditions were prevalent. This ingestion model is also applicable to personnel located on 

shore at the Pacific Proving Ground (PPG); the incidental ingestion rate for shipboard personnel 

is assumed to have been zero because ship decks were routinely washed or scrubbed. Because 

500 mg day−1

 rate is consistent with the highest value recommended in USEPA screening level 

guidance and USACHPPM exposure guidance for deployed military personnel, the resultant 

doses are credible estimates of upper bound doses. Parameter distributions for the probabilistic 

and nominal soil ingestion model are discussed in Section 4. 

In addition, an upper-bound pathway considered in deterministic dose reconstructions is the 

ingestion of fallout material deposited on food. For each episode of descending fallout that could 

40 
reasonably have occurred during mealtimes, the test participant is assumed to have ingested an 

amount of fallout equivalent to a 15-minute deposition on a 9-inch diameter plate at the average 

rate of deposition. The ingestion dose conversion factors cited in Equation 3-10 are also 

employed in evaluating this internal dose component. 

3.4 Uncertainty Modeling 

3.4.1 Overview of Probability Distributions 

Generally, probability distributions are mathematical expressions for calculating probability. 

The probability distributions used in this uncertainty analysis study are briefly described in this 

section. They include the uniform, Gaussian, lognormal, triangular, and log-triangular 

distributions. These are all continuous probability distributions, because the random variable of 

interest can take any real value within a defined continuous range (domain). When a distribution 

is normalized so that it sums (or integrates) to unity, it is referred to as a probability density 

function (pdf). 

In a graph of a pdf, the vertical scale does not represent the actual probability of the 

corresponding x-axis value; the probability of a single x value is zero. Instead, it represents the 

probability (per x-axis unit) of generating a value within a very small range around the x-axis 

value. Specifically, the probability of finding a continuous random variable X between two 

values x1 and x2 is equal to the area under the pdf curve from x1 to x2. The probability that X will 

take a value not exceeding x1 is the area under the pdf curve from its lower bound to x1; this is 

often referred to as a cumulative probability function (cpf). The area under the entire pdf and the 

upper limit of the cpf are both one. 

The references for Section 3.4.1 in its entirety are Bulmer (1979), Doane and Seward (2009), 

Hahn and Shapiro (1967), Kirchner (2008), NCRP (2007), NIST (2009), and Vose (2008). 

3.4.1.1 Uniform Distribution 

The uniform (or rectangular) distribution applies if all values of random variable X between a 

minimum value a and a maximum value b have an equal probability of being sampled. More 

precisely, X has the uniform distribution if the probability that X can take values within any 

segment of a fixed width in the range from a to b is the same for all segments of the same width. 

Alternatively, a random variable is uniformly distributed whenever the probability is inversely 

proportional to the interval’s length. The uniform distribution is shown in Figure 3. 

The uniform distribution is a cumulative distribution in the sense that probabilities for specified 

ranges of X are associated with areas under the bounding rectangle for the distribution. For any 

value x*, a  x*  b (a < b), the probability that X will be at most x* (cpf) is 

  ab

ax xXProb 

 

*

* (3-11) 

41 
 = (a+b)/2

a b

x

f(x)

1/(a+b)

 = (a+b)/2

a b

x

f(x)

1/(a+b)

Figure 3. Probability Density Function of a 

Uniform Distribution 

The probability that X will take any value between c and d, a  c  d  b (a < b), is 

  ab

dc dxcProb 

  (3-12) 

The mean and standard deviation of an uniform distribution are, respectively, 

2

 ba

 12

 ab

 (3-13) 

The median (the 50th percentile) of the uniform distribution is . However, the uniform 

distribution has no mode (that is, all values are equally probable). 

The uniform distribution is used as a very approximate model when there is little or no available 

data. It is often used to assess whether it is appropriate to assign uncertainty to a parameter. In 

this use, a parameter is assigned a uniform distribution with reasonably wide bounds and a 

sensitivity analysis is performed to determine whether or not the parameter produces any 

influence on the output uncertainty; if it does not, it may as well be left as a single-valued 

parameter. Rarely, a parameter may truly be uniformly distributed, as the angular resting 

position of a camshaft after spinning. 

3.4.1.2 Gaussian Distribution 

Also known as the normal distribution, the Gaussian distribution is defined by two parameters, 

the mean  and the standard deviation . The Gaussian distribution has the following properties: 

 The curve of the Gaussian distribution (referred to hereafter as the Gaussian curve) is “bellshaped” with one central peak. 

 The width of the bell is measured by the standard deviation . 

 The peak occurs at the mean . 

 The Gaussian curve is symmetrical about its mean . 

42 
- The mean divides the curve (and the range of the random variable) in half. 

 All measures of central tendency are equal to each other. 

- The mean, median (the 50th percentile), and mode (the most probable value) are equal. 

 The random variable X has an infinite range: - < X < . 

 The Gaussian curve asymptotes to (i.e., approaches but never touches) the horizontal axis. 

 There is an infinite family of normal curves, each defined by its own unique pair of  and . 

Although the Gaussian has an infinite range, as a practical matter the interval  – 3 < X <  + 

3 contains almost all (99.73 percent) of the possible values of X. 

The Gaussian distribution is a cumulative distribution in the sense that probabilities for specified 

ranges of X are associated with areas under the Gaussian curve. The pdf of the Gaussian 

distribution has the equation 

     2 2 2

2

1 



/x xf e   (3-14) 

The probability that X will take any value less than some given specific value x* is 

  

    e dx

dxxf*xXProb

*x

/x

*x















2 2 2

2

1 



 (3-15) 

Note that the entire Gaussian curve encloses unit area. The Gaussian distribution is shown in 

Figure 4. 

The probability that X may take any value in the range between the values c and d (c < d) is the 

area under the normal curve between the range limits c and d, that is, 

  

    e dx

dxxfdXc

d

c

/x

d

c





 



2 2 2

2

1

Prob





 (3-16) 

43 
x

 x*

 

      2 2 2/

2

1 

  x exf

      Prob xX e dx

x

x











*

2/ 2 2

2

1 *

x

 x*

 

      2 2 2/

2

1 

  x exf

      Prob xX e dx

x

x











*

2/ 2 2

2

1 *

Figure 4. Probability Density Function of a Gaussian Distribution 

Every normally distributed random variable X has its own unique pair of  and  and therefore 

its own unique Gaussian distribution. Because there are an infinite number of possible X’s, this 

will entail an infinite number of Gaussian distributions. For this reason, the original random 

variable X is transformed by subtracting the mean  and dividing the result by the standard 

deviation  to obtain the standardized variable Z. If X is Gaussian, then Z has the standard 

Gaussian distribution with mean 0, standard deviation 1, and density 

 







    x ezf z

/z where

2

1 2 2

 (3-17) 

The standard Gaussian has been tabulated. The important point is that there is only one standard 

Gaussian distribution, which has been tabulated. In practice, the task is to make any Gaussian 

look like the standard Gaussian, so that the single standard Gaussian can be applied in all cases. 

There are many reasons for the prominence of the Gaussian distribution. For one, the Gaussian 

describes the distributions observed in many natural processes and phenomena (e.g., most 

biometrical data). It is also the basis for population modeling (population proportions and 

tolerance intervals), statistical inference (sampling distributions, confidence intervals, and 

hypothesis testing) and linear regression (for the distribution of errors). Moreover, the Gaussian 

is used to approximate both the binomial and Poisson distributions, which model nuclear decay 

processes. Perhaps most importantly, it is a good approximation for the distribution of an 

estimated parameter. This follows from the central limit theorem, which states that the sum of a 

number of independent random variables, all of which have the same distribution, will 

asymptotically approach a Gaussian, regardless of distribution of the individual variables. 

Caution should be used when applying a Gaussian distribution to model the uncertainty of a 

random variable that inherently has zero or positive values (e.g., dose), because the lower tail of 

the distribution may produce values that are less than zero, which are not possible. A truncation 

rule that eliminates negative values or the use of a properly chosen lognormal or triangular 

44 
distribution that adequately replicates the Gaussian distribution in the region of positive values 

will avoid this problem. 

3.4.1.3 Lognormal Distribution 

If the distribution of the logarithms of the random variable is Gaussian, then the random variable 

itself is lognormally distributed. That is, the random variable X is lognormally distributed if 

Y = ln(X) is normally distributed. Also, if Y is a random variable with a normal distribution, then 

X = eY has a lognormal distribution. (The base of the logarithmic function does not matter: if 

loga(Y) is normally distributed, then so is logb(Y), for any two positive numbers a, b ≠ 1.) 

The rationale of the lognormal distribution lies in the central limit theorem, which states that the 

sum of a many independent random variables will be nearly Gaussian regardless of their 

individual distributions. The theorem only applies if the variables are independent and additive. 

If the variables are multiplicative, so that the effect produced at any stage is proportional to its 

current magnitude, then their logarithms will be additive. The resulting distribution of the sum 

of the logarithms of the independent variables is normally distributed. 

The density function of the lognormal is: 

       2 2 2

2

1 



/xln e

x

xf   (3-18) 

for x > 0, where μ and σ are the mean and standard deviation of the variable's natural logarithm, 

that is, of X = ln(Y) (and X is normally distributed). The lognormal is right (positively) skewed. 

If X is lognormally distributed, then its mean or expected value E(X), variance Var, standard 

deviation SD, mode (the most probable value), geometric mean GM or median (the 50th

percentile), and geometric standard deviation GSD are given by the following equations. 

  2 2 / eXE       2 2 2 1    eeXVar   1 2 2 2     eeXSD /

  2   eXmode     eGMXmedian     eXGSD

 (3-19) 

Lognormal pdf’s for six values of , where are presented in Figure 5. 

As already noted, the lognormal is used to describe the distribution of the product of random 

variables. Lognormal distributions often provide a good representation for a physical quantity 

that is positive definite, that is, it extends indefinitely over only the positive values. 

Lognormal distributions are important in human and ecological risk assessment because many 

physical, chemical, biological, toxicological, and statistical processes tend to create random 

variables that follow lognormal distributions. For example, the physical dilution of one material 

(say, a miscible or soluble contaminant) into another material (say, surface water in a bay) tends 

to create non-equilibrium concentrations which are lognormal in character. 

45 
Figure 5. Probability Density Functions of the Lognormal Distribution 

for Various Values of σ

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

(NRC, 1989, pp. 61–74). It is useful to define two quantities when assessing film badge 

uncertainty: 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 of the film to radiation, or fogging of 

the film due to heat and/or humidity. K is a measure of the random error characterized by the 

lognormal distribution, and is related to the geometric standard deviation by 

 (3-20) .6451  GSDK

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 is greater than K·E/B. 

Estimates of B and K, by nuclear test series, are provided in NRC (1989). 

46 
3.4.1.4 Triangular Distribution 

The triangular distribution is a simple distribution whose continuous random variable X can take 

on any value in the finite, fixed range from a to c such that a < X < c) with mode (or peak value) 

at b (a ≤ b ≤ c). Triangular distributions are shown in Figure 6. 

f(x)

x a c b

(2)

f(x)

x a c b

(2)

f(x)

x a c b

(1)

f(x)

x a c b

(1)

f(x)

x a c b

(3)

f(x)

x a c b

(3)

Figure 6. Probability Density Functions of a Triangular Distribution 

(1) Skewed Right, (2) Skewed Left, and (3) Symmetric 

The pdf of the triangular distribution is given by: 

 

 

  

 

   











 



 





cxb for bcac

xc

bxa for acab

ax

xf 2

2

 (3-21) 

47 
The triangular distribution is a cumulative distribution in the sense that probabilities for specified 

ranges of X are associated with areas under its pdf curve. The probability that X will take any 

value less than some given specific value x* is: 

 

 

  

 

   













 



 





c*xb for bcac

*xc

b*xa for acab

a*x

*xXProb

2

2

 (3-22) 

It is important to note that a is the absolute minimum below which values of X are prohibited; the 

minimum a has zero probability of occurrence. Likewise, c is the absolute maximum above 

which values of X are prohibited; the probability of occurrence of the maximum c is zero. 

The mean  and standard deviation  of X are: 

 (3-23) 

An interesting special case is a symmetric triangular distribution centered at 0, with range 

-d ≤ X ≤ d (i.e., whose lower limit is identical to its upper limit except for sign). This distribution 

has mean 0 and standard deviation d/6. The median (the 50th percentile) and mode (the most 

probable value) are both 0. Setting d = 2.45, the symmetric triangular distribution closely 

resembles a standard normal distribution, as shown in Figure 7. Random samples from this 

symmetric triangular distribution are very similar to samples drawn from the standard normal 

distribution. 

The triangular distribution is the sum of two random variables that each have uniform 

distributions. In particular, a symmetric triangular is the sum of two identically distributed 

uniform variates. 

Although it has no theoretical basis, the appeal of the triangular is its great flexibility. The 

triangular distribution is most often used when the true distribution is unknown but the extremes 

and the mean or mode of the distribution can be estimated. That is, if the range (a and c) and 

most likely value (b) can be estimated, then probabilities can be calculated from a fitted 

triangular. Unlike the Gaussian, the triangular can be symmetric or skewed in either direction. 

If symmetric, the triangular has a single central peak, like the Gaussian. On a practical level, the 

finite range of the triangular is often preferred over the infinite range of the Gaussian; this is 

especially so when the random variable of interest is inherently positive. 

18

222  bcacabcba

  3

 cba



48 
f(x)

z

0 -2.45 2.45

f(x)

z

0 -2.45 2.45

Figure 7. Symmetric Triangular Approximation to the Gaussian Distribution 

3.4.1.5 Log-Triangular Distribution 

The log-triangular distribution is obtained when the distribution of the logarithms of the random 

variable is triangular. Like the triangular distribution, the log-triangular distribution is not easily 

associated with natural phenomena. On the other hand, a triangular distribution of the values in 

log space may reflect that underlying exponential processes are driving the random variable. 

Also like the triangular distribution, it can be used to model a process in the absence or scarcity 

of data to represent uncertainty. The log-triangular distribution is most useful when the range of 

the possible values covers several orders of magnitude (a property shared with the lognormal 

distribution) and when uncertainties are large. A severely right-skewed log-triangular 

distribution is shown in Figure 8, in which values extend over nine orders of magnitude. 

x

f(x)

100 101 102 103 104 105 106 107 108 109

Figure 8. A Right-Skewed Log-Triangular Distribution 

49 
There is no theoretical basis for the log-triangular model. The appeal of the log-triangular 

distribution is its great flexibility. It is typically used to represent subjective uncertainties when 

the range of possible values extends over several orders of magnitude. It is often used as a rough 

model in the absence of data when the random variable is known to be asymmetric and bounded, 

that is, when the values toward the middle of a range of possible values in log space are more 

likely to occur than values near either extreme. 

3.4.2 Propagation of Uncertainties 

The methods to propagate through a model the uncertainties in the parameters used may be 

classical analytical or numerical uncertainty propagation methods (Hoffman and Gardner, 1983; 

Morgan and Henrion, 1990; NCRP, 1996). The analytical methods are outlined below. 

Let X and Y be two random variables with means μx and μy and standard deviations σx and σy, 

respectively. The standard deviations are taken as representations of the uncertainties in the 

random variables. If W is defined as the random variable X + Y, then the mean of W is 

μw = μx + μy. If X and Y are independent, the selection of a value x from the distribution of X

does not influence the selection of a value y from the distribution of Y, and vice versa. In such 

cases, the uncertainties in X and Y are uncorrelated and the uncertainty in W can be expressed as: 

22   yxw (3-24) 

The term “uncorrelated” is used in the sense that there is no association or relationship between 

X and Y. When the uncertainties propagate in this manner, they are said to be combined in 

quadrature. Conversely, if X and Y are strongly dependent such that the value of x has a large 

influence on the value of y, then the uncertainties in X and Y are highly correlated and propagate 

as: 

    yxw (3-25) 

The degree of correlation between two random variables is given by the correlation coefficient , 

which measures the strength of the linear association between the variables on a scale from -1 to 

+1; the stronger the relationship, the closer the absolute value of  is to 1. In general, the 

uncertainty in W can be expressed as: 

2 2  2  yyxxw (3-26) 

If X and Y are totally uncorrelated so that  = 0, then Equation 3-24 is obtained. If X and Y are 

perfectly correlated so that || = 1, then Equation 3-25 is obtained. 

As an example, consider X and Y to be two reconstructed doses. If these are doses received years 

apart by a test participant at different test series where different film badge types and/or radiation 

measurement equipment were used, they can reasonably be considered independent and 

Equation 3-24 expresses the uncertainty in his total dose. If, however, doses X and Y were 

received on successive days at the same location in the same fallout field, it is likely their errors 

are correlated since any error in characterizing the local radiation environment would affect both 

50 
doses in a similar way (i.e., both reconstructed doses are likely to be high or both low). In this 

case, Equation 3-25 applies. Often X and Y are partially correlated (-1 <  < 1, where ). If 

 is known, the error can be calculated from Equation 3-26. If  is not known, judgment is 

required in the selection of the most appropriate method of uncertainty propagation. 

This discussion of uncertainty propagation has used the simple function W = X + Y as an 

illustrative example. Other simple functions such as W = X × Y, W = X ÷ Y, as well as other 

functions such as exponential functions, are used in this uncertainty analysis. However, the 

simple function W = X + Y was included only as an illustration, and a more thorough discussion 

of propagation of uncertainties, including additional functional types, is beyond the scope of this 

report. The reader is referred to other more in-depth discussions such as those included in NCRP 

Report No. 158 (NCRP, 2007). However, the aforementioned approaches are tedious and 

difficult to implement. For that reason, an alternative approach is to conduct the Monte Carlo 

simulation that is discussed in the next section. 

3.4.3 Monte Carlo Method 

The Monte Carlo method was developed at Los Alamos by scientists working on the Manhattan 

Project and later on thermonuclear weapon design. Their approach to solving complex physics 

problems was to consider all key parameters to be random variables with associated probability 

density functions. By running many trials (commonly called “histories”), and on each history 

selecting random values from each of the pdf’s, they were able to conduct “numerical 

experiments” and derive critical data efficiently and accurately. These methods and attributes 

are applicable to a wide range of problems, including probabilistic dose reconstruction of the 

type addressed in this report. 

3.4.3.1 Method Overview 

In a Monte Carlo simulation, a random sample of scenarios is selected to represent all possible 

scenarios. Each scenario is generated by randomly selecting a value for an input parameter, 

regarded as a random variable, according to its assigned probability distribution. In so doing, a 

distribution is built for the output variable, which is representative of all possible output values. 

(Morgan and Henrion, 1990; Hahn and Shapiro, 1967; Vose, 2008) 

Operationally, for a model described by k stochastic parameters, each parameter is sampled at 

random from its respective distribution. Altogether, this set of k random parameter values 

defines a scenario, also referred to as a history, and is used as input to the model; a scenario is a 

complete model run. A new set of randomly sampled k parameter values is used as input for 

each and every one of the m scenarios performed, resulting in m sets of calculated values. These 

m output values are arranged into a probability distribution, which is characterized by standard 

statistical methods. (Morgan and Henrion, 1990; Hahn and Shapiro, 1967; Vose, 2008) 

The resulting distribution for the output using this approach is an approximation to the exact 

distribution. The accuracy of a Monte Carlo scheme, that is, to the degree to which the output 

distribution approximates the exact distribution, can be increased simply by increasing the 

sample size of scenarios. As a result, very large numbers of Monte Carlo runs are performed; 

typically, m may be of the order of up to tens of thousands, with the result that execution time 

may become a significant issue. Moreover, the accuracy can be estimated with standard 

51 
statistical techniques. An important point is that, for a given output distribution, its accuracy 

depends on the number m of scenarios and not on the number k of inputs. 

For large, complex models, Monte Carlo methods are computationally intensive—both k and m

contribute to the computational burden and long execution times of the Monte Carlo dose 

simulations performed in the case studies. The effort to run the model for each scenario is 

generally proportional to k. Even so, the amount of effort expended in a Monte Carlo simulation 

is less than other methods, particularly full enumeration of all possible scenarios. (Morgan and 

Henrion, 1990; Hahn and Shapiro, 1967; Vose, 2008) 

There are a variety of measures of uncertainty propagation through a Monte Carlo simulation. 

One approach is to attribute output uncertainty to the individual inputs. This is the approach 

adopted for the sensitivity analysis in Section 6. An overall measure of uncertainty propagation 

through a Monte Carlo simulation is taken to be the variance of the output distribution. This is 

the measure adopted throughout this uncertainty analysis (Morgan and Henrion, 1990) 

In the present analyses of nuclear test-related exposures, a multitude of key parameters such as 

radiation intensities, stay times, and structure protection factors are considered random variables. 

The uncertainties of these random variables are expressed as distributions of the type discussed 

in Section 3.4.1 or derived via the Monte Carlo technique from the uncertainties of more 

fundamental parameters. A typical dose reconstruction production run for each of the case 

studies presented in this report consists of 10,000 histories, each involving the random sampling 

of up to 40 distributions. The specific k parameters used, their assigned distributions, and their 

nominal values are listed in the parameter tables for external and internal doses in the individual 

case studies. The results of this effort are distributions of external and internal doses. These 

distributions well characterize the uncertainties of these doses in terms of their means, standard 

deviations, percentile uncertainty factors, etc. 

As alluded to in the previous section, potential correlations among uncertainties of key 

parameters must be considered in formulating the Monte Carlo sampling. Two uncertainty 

distributions that are uncorrelated are each sampled independently by drawing separate random 

numbers during each history, while two highly correlated distributions are jointly sampled with 

the same random number. Assumptions regarding correlations of uncertainties are addressed 

elsewhere in Appendix G. 

3.4.3.2 Characterizing Resulting Distributions 

A random variable that follows a lognormal distribution will appear as a straight line on a logprobability plot, in which the logarithm of the random variable is graphed on the vertical axis 

and cumulative probability is graphed on the horizontal axis. This appears to be generally true 

for the external gamma, internal alpha, and internal beta-plus-gamma dose distributions derived 

in the case studies. The linearity of the internal dose log-probability plots (for all example 

organs considered) is particularly strong. The downturn of the lines at lower doses is a result of 

the assignment of zeros to negative values that occasionally occur when the uncertainties of 

positive-definite parameters are modeled with Gaussian distributions. 

It is reasonable that the case study doses are distributed lognormally. As discussed in Section 

3.4.1.3 the lognormal distribution arises naturally from the product of all the contributing 

52 
independent random variables, regardless of their individual distributions. The important issue is 

the independence of the contributing variables, not their individual pdf’s. 

The probabilistic doses reported herein are calculated as the product of their contributing 

parameters. Many of these parameters are independent (uncorrelated) of each other; others are 

mutually dependent upon each other. For the latter, the correlations may be weak or strong. 

Even so, most of the plotted points fall close to a straight line. This implies that any departures 

from strict independence only lead to slight departures from a straight line. Even weak to 

moderate dependencies do not cause severe departures from linearity in log-probability plots. 

As a result, and without presupposing any distribution for dose (only for its constituent 

parameters), a lognormal distribution is obtained in all case studies. On this basis, it may be 

concluded that the lognormal distribution is the logical and appropriate choice to model the 

probabilistic doses derived in the case studies. 

3.4.4 Quantifying Uncertainty 

As used herein, uncertainty is the lack of sureness or confidence in predictions of models or 

results of measurements. Uncertainty may be due either to random variation (e.g., gambling) or 

to a lack of knowledge (level of ignorance) resulting from an incomplete specification, 

understanding, or measurement of the quantity of interest (e.g., chance of rain in numerical 

weather prediction). This is as opposed to variability, which is the natural heterogeneity, 

diversity, or range of variation that is inherent in a measured value or parameter (e.g., differences 

in height and weight in a population) or in a response (e.g., differences in sensitivity to a 

hazardous agent in a population). Further study cannot reduce variability but may reduce 

uncertainty by providing greater confidence in quantitative characterizations of variability. Note 

that there is a cause-effect relationship: variability may lead to or cause uncertainty. 

(NCRP, 2007) 

A parameter will in general be variable from one history to another. As a result, the parameter is 

regarded as a random variable; the chance that the parameter will take any specific value for a 

particular history is described by a probability distribution with its mean as the expected value. 

The uncertainty in the parameter is often quantified by the variance or standard deviation or 

some other measure of variation of the parameter about the mean. The approach taken herein to 

quantify the uncertainty of a parameter is to select a probability distribution that best models the 

parameter behavior and then select best values for the mean and standard deviation of that 

parameter. That distribution and its chosen parameterization are held fixed for the Monte Carlo 

simulation described in Section 3.4.3, with the result that the same parameter distribution is 

repeatedly sampled for each and every one of the Monte Carlo histories. 

3.4.4.1 Quantification Methods 

There are various numerical methods for quantifying uncertainty. Alternatively, the 

quantification of uncertainty may simply reflect the state of knowledge or the quality of the data. 

Usually, quantification of uncertainties requires analysis and interpretation of incomplete data 

and other complementary information; it may also use professional judgment, which is 

inherently subjective in nature. Thus, different analysts may produce different statements 

quantifying the uncertainty in a parameter. 

53 
Often, quantifying the uncertainty of a parameter is based on expert opinion and judgment. The 

quantification itself is expressed using mathematical probability (Morgan and Henrion, 1990). 

The assignment of probability distribution functions to model parameters can rely on analysis of 

data (i.e., fitting probability distribution curves through existing data). More often, it relies on 

expert judgment about how available data may be used to represent the uncertainty in that model 

parameter. This often comes down to applying common sense rules. 

Consider the probability distributions summarized in Section 3.4.1. If a parameter can be 

thought to vary with equal probability between a minimum and maximum value, then a uniform 

probability distribution may be assigned to describe the parameter. If one value of the parameter 

is more probable than others, and the possible values range between known (or presumed) 

minimum and the maximum values, then a triangular distribution may be assumed for the 

parameter. When minimum and/or maximum values cannot be set, unbounded distributions 

(e.g., Gaussian or normal, lognormal) are used to ensure that a small probability is assigned to 

any outlying parameter value. On the other hand, bounded or truncated distributions must be 

used when the parameter has physical limits (e.g., a parameter representing a proportion is 

always greater than zero and is expected to be less than one). If parameter values are expected to 

vary over more than one order of magnitude, giving rise to a highly right skewed distribution 

modeled by a lognormal, then the selected distribution should be logarithmic, e.g., log-uniform 

or lognormal (see Sections 3.4.1.3 and 3.4.5 for the latter). Some of these distributions may be 

used in combination over portions of the parameter range, for example, using piecewise uniform 

distributions in different possible ranges as suggested by expert opinion. 

The selection of a probability function is often based on the degree of belief that the possible 

values of the parameter are within a certain range (with some subjectively assigned probability), 

rather than describing the statistical frequency of measured values. Additional information about 

the mechanics of assigning probability distributions to model parameters can be found in Morgan 

and Henrion (1990) and NCRP (1996). 

3.4.4.2 Stating Parameter Uncertainties 

Uncertainties in parameters are stated in terms appropriate to the probability distribution used to 

describe that parameter. For example, if a Gaussian distribution is assigned to a parameter, then 

its uncertainty is quantified by its standard deviation about its mean; if a lognormal distribution 

is assigned, then the uncertainty is quantified by its geometric standard deviation about the 

geometric mean. In general, the uncertainty in a parameter is expressed by at least two numbers 

(e.g., a lower and an upper bound of an uncertainty range, or a mean and a standard deviation), 

complemented by a probability for the confidence that the actual value is contained within the 

reported range. 

There are several ways to state the uncertainty in a parameter. One way is to specify an interval 

which should contain some representative value of the parameter (e.g., its mean, median, etc.) 

with some degree of confidence (e.g., the actual dose is expected to be between 0.05 and 

0.5 rem, with 90 percent confidence). These intervals are called “confidence intervals” in 

classical statistics and “credibility intervals” in Bayesian statistics; sometimes the more generic 

term “uncertainty ranges” is used. 

Another way to state the uncertainty in a parameter is as a “factor of x”, where x represents the 

ratio of the upper and lower bounds of the parameter or of the upper bound and the central value 

54 
of the parameter (e.g., the actual dose is expected to be within a factor of 3 above or below 

0.05 rem, with 90 % confidence). Finally, uncertainties can be expressed as a “± x”, where x

may be one standard deviation (e.g., the actual dose is expected to be 0.05 ± 0.01 rem) or a 

margin of error, with a confidence probability (e.g., the actual dose is expected to be 

0.05 ± 0.01 rem at 90% confidence). 

There are methods to propagate through a model the uncertainties in the parameters used. The 

methods may be classical analytical or numerical uncertainty propagation methods (Hoffman and 

Gardner, 1983; Morgan and Henrion, 1990; NCRP, 1996). The result is a statement quantifying 

the uncertainty about the output parameter. Suppose a Monte Carlo (MC) simulation is built 

through which parameter uncertainties are propagated; the MC simulation is exercised to 

produce m realizations. The resulting m-sized output can be used to obtain a complete 

description of the uncertainty in the parameter in terms of its mean or median value, standard 

deviation, and desired confidence intervals. Moreover, parameter uncertainties can be combined 

(or aggregated) into a summary statement of uncertainty. See Section 3.4.2 for combining 

uncertainties. 

3.4.5 Reporting of Representative Doses 

The (arithmetic) mean , is the appropriate measure of central tendency and the best point 

representation for randomly sampled data that is at most only slightly or moderately skewed and 

for random variables that follow many probability distribution functions, particularly the 

Gaussian (Section 3.4.1.2). The objective and rational measure of variability about  is the 

standard deviation . However, the arithmetic mean is strongly affected by extreme values, in 

which case it may be misrepresentative and misleading. This is a particularly severe problem for 

random variables whose range of variability may extend over several orders of magnitude, as 

occurs for many of the parameters in radiation dose reconstruction. In this case, the geometric 

mean is more appropriate. (Doane and Seward, 2009; Hahn and Shapiro, 1967; Vose, 2008; 

NCRP, 2007) 

The geometric mean GM of a set of n positive numbers is the multiplicative average calculated 

as the n

th root of their product. GM is the antilogarithm of the mean of the logarithms of all the 

values. In this way, GM mitigates the influence of high extremes which will strongly skew the 

arithmetic mean. GM is the appropriate measure of central tendency for highly skewed data that 

is all positive valued and for random variables that follow the lognormal distribution (see Section 

3.4.1.3). The appropriate measure of the variability about the GM is the geometric standard 

deviation GSD, which is the antilogarithm of the standard deviation of the logarithms of all the 

values. (Doane and Seward, 2009; Hahn and Shapiro, 1967; Vose, 2008; NCRP, 2007)

The normal distribution, characterized by  and , is appropriate to model events that are 

randomly affected by very many random variables that all contribute additively; see Section 

3.4.1.2. In particular, the size or magnitude of a quantity that follows the normal distribution is a 

function of the sum of all contributing random variables. The lognormal distribution, 

characterized by GM and GSD, is best to model events which are randomly affected by very 

many random variables that all contribute multiplicatively; see Section 3.4.1.3. In particular, the 

size or magnitude of a quantity that follows the lognormal distribution is a function of the 

product of all the contributing random variables. (Doane and Seward, 2009; Hahn and Shapiro, 

1967; Vose, 2008; NCRP, 2007) 

55 
4 TECHNICAL APPROACH AND METHODOLOGY 

The probabilistic uncertainty analysis studies for NTPR radiation dose reconstruction were 

carried out in five major phases consisting of the following: 

 A pilot study and proof of concept designed to experiment and test the implementation of 

probabilistic methods using existing deterministic dose reconstruction and assessment 

models currently used in NTPR radiation dose assessments. 

 Special studies to develop statistical models and uncertainty distributions of key input 

parameters used in whole body external gamma dose assessment. 

 Application of prototype methods to three generic cohorts and comparison with dosimetry 

records. These allowed testing and verification that the selected computational tools and 

techniques were capable of producing the types of model results sought. 

 Expansion of the methodology to include application to internal dose estimation where 

deterministic models were enhanced to incorporate improved estimation of input parameter 

central values and uncertainty distributions. 

 Testing and implementation of the methods developed through six case studies that consisted 

of the three original and three additional cohorts. The selection of case study cohorts was 

based on criteria developed during the pilot study. 

The five phases were designed and implemented with the primary objective that the investigation 

of probabilistic uncertainty would ultimately help improve current NTPR radiation dose 

assessment procedures and methods and develop better ways to estimate realistic uncertainties. 

Work under the various phases was performed to develop a standard dose reconstruction 

uncertainty model framework. From simple computational tools to sophisticated science-based 

physical models, the best available information relevant to NTPR case studies was accessed, 

reviewed and used in the development of the methods and techniques provided in this report. 

The steps listed above were implemented in the first stages of the investigation. Additional 

consultation with experts and multiple meetings provided the technical bases for making 

adjustments to early selections and further refinements of both the approach and methodology. 

This section first describes the pilot study proof of concept that demonstrated the feasibility of 

the probabilistic approach and the application of Monte Carlo techniques for NTPR dose 

reconstruction. It then presents key model input parameters, their formulation and the submodels used to develop their central estimates and probability distribution functions. This 

section describes the first four phases of the investigation, whereas the case study results are 

summarized in Section 5 and details of the analyses are provided in Appendices A–F. 

4.1 Pilot Study 

A pilot study was carried out to select software tools, study groups, and develop and test the 

basic models using a probabilities approach to NTPR dose reconstructions and uncertainty 

analysis. This proof-of-concept approach was employed to investigate best methods of 

incorporating probabilistic techniques in NTPR dose assessment procedures. The specific 

objectives of the pilot study were to develop an uncertainty model applicable to three 

representative cohorts of atmospheric nuclear test participants, generate distributions of 

56 
reconstructed external gamma doses for those cohorts, and compare the results to deterministic 

reconstructed doses and dose distributions from film badge dosimetry records. Once the 

uncertainty model was verified and tested, it was to be applied to three more groups of nuclear 

test participants and further expanded for the analysis of uncertainties in internal doses. 

The pilot study involved the following steps: 

 Investigate and select appropriate software tools based on study requirements to include 

statistical analysis and Monte Carlo simulation capabilities. 

 Select representative study groups based on the following criteria: 

- Reliable individual film badge dosimetry. 

- Adequate number of participants within the group for statistical analysis of dosimetry 

records and comparison to corresponding probabilistic analysis of reconstructed doses. 

- Cohesive participants’ activities performed in the radiation environment within each 

group. 

- Well-characterized radiation environment with adequately-documented data or surrogate 

information that can be used to make best estimates of input parameters to the dose 

models. 

 Characterize the pdf of input parameters that are significant in the dose reconstruction of the 

selected study groups through review of the literature and the expert judgment of experienced 

radiation analysts. These pdfs were updated and improved through an iterative review 

process and only the distributions used in the case studies described in Section 5 are 

presented later in this Section and in Appendices A–F. 

 Construct a working model for whole body external gamma dose estimation that incorporates 

Monte Carlo simulation capabilities and estimate dose distributions. 

 Compare external gamma dose distributions resulting from the probabilistic uncertainty 

analysis to those from film badge dosimetry. 

4.1.1 Software Selection 

Three commercially available software packages were considered for Monte Carlo model 

development, all of which have the required functionalities. The three packages were Mathcad, 

the Crystal Ball® adjunct to Microsoft Excel®, and Mathematica®. Mathcad was the favored 

platform for model development because it is the primary calculation tool for NTPR dose 

assessments, and template worksheets have already been prepared for most units and test series. 

Preliminary investigation revealed that modifying existing Mathcad deterministic dose 

calculation worksheets to include Monte Carlo simulations is fairly straightforward. Thus, 

Mathcad was selected as the principal software tool for this project. Because Crystal Ball is 

widely accepted in the scientific community and has been extensively validated and verified, it 

was selected to generate some distribution types for comparison to those generated in Mathcad. 

Mathematica was also used for one study group during the pilot and initial implementations as a 

supplemental tool to probabilistically model the spatial movement of a participant within a 

radiation environment. 

57 
4.1.2 Generation of Parameter Distributions 

Monte Carlo simulation capability was added to existing dose reconstruction models coded in 

Mathcad calculation worksheets during the pilot study and subsequently to case studies involving 

six atmospheric test groups. Dose reconstruction simulations using distributions that model 

variability and uncertainty of model parameters generated in Mathcad from simple random 

sampling were compared to simulations using distributions generated in Crystal Ball with Latin 

hypercube (McKay et al., 1979) random sampling. No discernible difference was seen when the 

number of simulations exceeded 500. Because the six case study analyses were to employ 

10,000 simulations and the NTPR reports 95th percentile upper bounds, potentially underrepresented sampling from quantiles greater than two standard deviations above the mean did not 

present an issue. 

4.2 Special Studies: Model Parameters, Uncertainties, and Distributions

Some of the dose reconstruction model input parameters and their associated variability and 

uncertainty are sufficiently complex to warrant special studies with detailed analyses. 

Distributions of several such parameters were estimated in separate auxiliary models and input 

numerically as cumulative distribution functions to the case study models. 

The dose reconstruction models were continually refined and improved based on the results of 

ongoing analyses and feedback from several analysts and subject matter experts. Specific input 

parameters were analyzed and refined through special studies or thorough review of existing 

investigations and guidelines. The dose input parameters listed below were addressed in special 

studies. 

For External Dose Models:

 Intensity distribution from fallout on ship weather decks. 

 Protection factors for land-based structures. 

 Shielding factors for ships. 

 Shot-specific radiological decay functions. 

 Sources of uncertainty when estimating radiation intensity from measured intensities and isointensity maps. 

For Internal Dose Models

 Gamma source modification factor. 

 Resuspension factors. 

 Breathing rate. 

 Internal dose conversion factors. 

 Characterization of descending fallout 

 Internal deposition fraction adjustment. 

 Incidental ingestion of contaminated soil and dust. 

58 
Details of the resulting methodologies are presented in the following sections along with the 

mathematical and physical models on which they are based. Discussions of the results and 

decisions on model input parameter distributions are also included. 

Conversely, a few parameters were assigned fixed values in this study although some uncertainty 

or variability may exist regarding those values. A brief listing of parameters falling into this 

category follows. 

 Fallout event times – times associated with specific intensity readings during a fallout event. 

 Film badge conversion factor (FBCF) – 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, was assigned the deterministic value of 0.7 in this study. 

 Bias factors (Biasα and Biasβγ) – parameters to remove high-sided bias in inhalation dose 

conversion factors (discussed in Section 4.2.8). These factors are aggregated for three organ 

groups (Table 14) and are assumed to be constant in time. 

 Surface activity density-to-Intensity (SA/I) ratios – parameters used to infer activity densities 

from concurrent intensity readings. 

 Distribution of exertion levels (BRfrac) – fraction of time at rest, or in light, moderate, or 

heavy activity, assumed constant in the present breathing rate formulation (Section 4.2.7). 

 Indoor/outdoor scenario during fallout event – treated in a time-averaged manner in present 

study instead of randomly selecting specific indoor/outdoor scenarios for periods of 

potentially significant exposure. 

Parameters such as fallout event times and FBCF have well-established central values and small 

uncertainties, and therefore were treated as constants in this analysis. The SA/I ratios utilized in 

the study were derived with FIIDOS assuming no fractionation. Because of the complexity of 

the fractionation process, formal treatment of the uncertainty of I/SA, along with an assessment 

of its impact on other fractionation-sensitive parameters such as internal dose conversion factors, 

have been deferred until time and resources are available to thoroughly research this subject. 

The significance of uncertainty in the bias factors, the exertion level distribution, and the 

indoor/outdoor scenario for descending fallout remain to be evaluated. 

4.2.1 Intensity Distribution from Fallout on Ship Weather Decks 

For ships that received fallout from a nuclear test, the average topside intensity was frequently 

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

inferred from intensity readings reported on nearby ships or land masses. While this areaaveraged intensity is useful for calculating a deterministic “best estimate” dose for generic 

crewmen, the variability of intensity with topside location contributes to the uncertainty in the 

dose of an individual crewman, who may have manned a topside workstation where the intensity 

differed significantly from the average. It is therefore necessary to model this variability in 

topside intensity when calculating doses probabilistically. This special study investigates the 

distribution of gamma intensities on the weather decks of fallout-contaminated ships. 

59 
4.2.1.1 Technical Approach and Methodology 

In the idealized scenario of uniform fallout deposition on a flat weather deck of a ship, a 

theoretical distribution of topside intensities can be constructed using a point-kernel method 

(Stevens and Trubey, 1972, pp. 46–53) to calculate relative intensity for random topside 

locations. The point kernel used here is given by 

2 22

2 22

)(

)(Prop

H)Yy(Xx

H)Yy(Xx

)Y,X,y,x(PK







 



 

 (4-1) 

where x and y are the Cartesian coordinates of a point source, X and Y the coordinates of an 

observer’s topside location, and H the height above the deck (taken as 1 meter). The propagation 

function Prop(R) used in this assessment was derived from two-dimensional transport results 

obtained with the ITS CYLTRAN code (Halbleib et al., 1992) for propagation of gamma rays 

through air over an iron substrate. Fission gamma spectra given in Finn et al. (1979) were used 

in these CYLTRAN calculations to characterize the source radiation. A fit to these data resulted 

in the Mathcad functional expression shown below, where the independent variable R is the slant 

distance from the source in meters. 

69710 0047870 316.2 R if 

590601020161 316.2 R31.65 if 

10185 109662

54040 31.65 R 17.35 if 

45470 50 17.35 R if 

4

38 25

33440

57960

  

 



  

  







R).(-exp.

 . ) .R -

.R.(exp R

R) .(exp

R.exp()R(opPr ).

-

.-

.

 (4-2) 

The intensity at a particular topside location (Xi,Yi) is obtained by integrating the point kernel 

over that part of the topside area A that is within the field of view of an observer at (Xi,Yi). 

Designating the latter area Ai, the intensity can then be expressed as 

 

Ai

ii ii dydx)Y,X,y,x(PK)Y,X(I (4-3) 

It is assumed in performing this integration that (1) the weather deck on an aircraft carrier is 

rectangular with no obstructions (so Ai = length × width), and (2) the weather decks for all other 

ships are elliptical with centrally located superstructures that are opaque to radiation (so Ai < A). 

The dimensions of the rectangle/ellipse and superstructure are selected to best characterize the 

ship of interest. Details of this integration for the various ship types are provided in 

Weitz (2009b). The observation point (Xi,Yi) is sampled randomly (i = 1,...,n for a sample size 

of n) over the area Ai to generate a distribution of intensities. An example of a distribution thus 

derived with n = 10,000 for a Liberty ship (YAG) is shown in Figure 9. This distribution has 

been normalized to a mean of 1 R hr−1

. The highest intensities pertain to locations in the 

relatively open areas in front and back of the superstructure, where shielding is minimal. As 

60 
0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.25 0.50 0.75 1.00 1.25

Intensity (R hr-1)

Relative Frequency

Figure 9. Distribution of Intensities for Fallout Deposited Uniformly on Weather Deck of 

YAG (normalized to a mean of 1 R hr−1) 

there are many such locations, the probability of randomly occupying one of them is substantial. 

The modal peak is associated with the numerous locations available alongside the superstructure, 

while the low intensity tail results from locations very near the superstructure where shielding is 

maximized. 

It is shown in Molumphy and Bigger (1957), however, that the fallout deposition on ships is not

uniform. These deposition data, graphically represented as beta surface activity contours, were 

collected aboard the test ships YAG-39 and YAG-40 after both had been intentionally subjected 

to fallout during Operation CASTLE (1954). The significant non-uniformity of deposition 

indicated in those contour plots introduces an element of uncertainty in the intensity I(Xi,Yi) of 

Equation 4-3. This uncertainty is modeled by multiplying each value of I(Xi,Yi) by a number 

gi(μ, σ) drawn randomly from a Gaussian distribution with mean μ = 1 and standard deviation σ. 

This Gaussian “spreading function” further spreads the intensity distribution in Figure 9. 

A companion set of gamma intensity data for the YAG test ships, also provided in Molumphy 

and Bigger (1957), was utilized to determine σ, the standard deviation of the spreading function. 

This database includes three contour plots constructed from measurements taken on YAG-40 

after that ship had received fresh fallout following Shots ROMEO, UNION, and YANKEE, but 

before any decontamination was attempted (the “pre-decon” data set). In addition, it contains 

two contour plots based on measurements made after partial decontamination of YAG-40 

following ROMEO and on YAG-39 following YANKEE (the “post-decon” data set). Because 

YAG-39 employed an automatic wash down system during periods of fallout deposition, there 

are no pre-decon data for that ship. 

61 
The first step in establishing reasonable values for σ (one each for the pre- and post-decon 

environments) was to convert the contour plots into intensity probability distributions. To 

accomplish this, the contours for a given ship and fallout event were digitized and the enclosed 

areas integrated using the DIGITIZE-PRO (Danon, 2008) and DPLOT (HydeSoft Computing, 

2008) software packages. It is straightforward to then recast these areal distributions into the 

intensity probability distributions (i.e., the relative frequency plots) in Figure 10 and Figure 11

for the pre- and post-decon environments, respectively. Both the individual ship/fallout event 

distributions and the composite (averaged) distributions are displayed in these figures. In all 

cases, the distributions have been normalized such that the average intensity is 1 R hr−1

. The 

pre-decon plots in Figure 10 are fairly symmetrical, aside from secondary peaks in the very low 

intensity region, while Figure 11 indicates that partial decontamination results in a skewed 

distribution. This is not unexpected because wash down will remove the more loosely bound 

contaminant fraction, but some areas of high concentration are more resistant to removal due to 

difficulty of access (e.g., scuppers) or the presence of grease or porous surfaces (e.g., wood 

decking). 

0.00

0.05

0.10

0.15

0.20

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Intensity (R hr-1)

Relative Frequency

YAG-40/ROMEO

YAG-40/UNION

YAG-40/YANKEE

Composite

Figure 10. Topside Intensity Distributions on YAG Prior to Decontamination (normalized 

to a mean of 1 R hr−1) 

The next step was to generate distributions of gi(μ, σ)·I(Xi,Yi) to determine the value of σ that 

gives the best fit to the composite YAG pre-decon distribution (black curve in Figure 10). For 

convenience, the secondary peak near zero intensity that appears in Figure 9 was neglected in 

this fitting. The best fit to the pre-decon distribution, shown in Figure 12, occurs for σ = 0.23. A 

similar procedure was applied to the YAG post-decon distribution by using the black curve in 

Figure 11 as the standard to be matched by varying σ. This produced the best fit with σ = 0.50, 

as shown in Figure 13. 

62 
0.00

0.02

0.04

0.06

0.08

0.10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Intensity (R hr-1)

Relative Frequency

YAG 40/ROMEO

YAG 39/YANKEE

Composite

Figure 11. Topside Intensity Distribution on YAG after Partial Decontamination 

(normalized to a mean of 1 R hr−1) 

0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.0 0.5 1.0 1.5 2.0 2.5

Intensity (R hr-1)

Relative Frequency

Model

Measured: YAG40 Composite

Figure 12. Best Fit to YAG Pre-Decon Intensity Distribution 

(normalized to a mean of 1 R hr−1

) 

63 
0.00

0.02

0.04

0.06

0.08

0.10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Intensity (R hr-1)

Relative Frequency

Model

Measured: YAG-40

Composite

Figure 13. Best Fit to YAG Post-Decon Intensity Distribution 

(normalized to a mean of 1 R hr−1

) 

These pre- and post-decon values for σ were derived on the basis of intensity data taken on a 

single ship type, the YAG. An additional uncertainty is therefore encountered when applying 

them to ships that are not YAGs. Based on subjective judgment, these values of σ were each 

doubled, to 0.46 and 1.0 respectively, when used for other ship types. This was done so that the 

uncertainty associated with the application of this model to ship types other than that on which 

the data were taken is adequately reflected in the analysis, thereby ensuring that a 95th-percentile 

upper bounds of doses calculated on the basis of this model are not underrepresented. 

4.2.1.2 Results and Discussion 

The model described above was applied to the amphibious force flagship USS ESTES and the 

aircraft carrier USS BOXER. The resulting intensity distributions (probability density functions) 

for these ships are shown in Figure 14 and Figure 15, respectively. The pre- and post-decon 

distributions derived by this algorithm are ship-specific because they are obtained by “spreading” 

a ship-specific uniform-deposition distribution in a prescribed manner. 

These results, recast in the form of cumulative probability distributions, were utilized in the USS 

ESTES and USS BOXER case studies to model the distribution of topside intensities in the EDM

(external dose multiplier) parameter (defined in Section 4.2.3). The arithmetic mean of the 

intensity distributions displayed in Figure 14 and Figure 15 is 1 R hr−1

 so they will not introduce 

a bias in probabilistic dose reconstructions. However, they will cause significant dispersion of 

the topside-accrued doses. The 95th percentile upper bounds of the pre- and post-decon 

distributions for USS ESTES are 2.0 and 2.3 R hr−1

, respectively; those for BOXER are 1.8 and 

64 
0.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Intensity (R hr-1)

Relative Frequency

Pre-Decon

Post-Decon

Figure 14. Pre- and Post-Decon Topside Intensity Distributions for USS ESTES 

(normalized to a mean of 1 R hr−1) 

0.00

0.02

0.04

0.06

0.08

0.10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Intensity (R hr-1)

Relative Frequency

Pre-Decon

Post-Decon

Figure 15. Pre- and Post-Decon Topside Intensity Distributions for USS BOXER 

(normalized to a mean of 1 R hr−1

) 

65 
2.2 R hr−1

, respectively. (Because both distributions in Figure 14 and Figure 15 are normalized 

to 1 R hr−1

, the fact that the post-decon upper bound values are greater than the pre-decon upper 

bounds merely indicates that the post-decon distribution is broader than the pre-decon 

distribution.) 

4.2.2 Protection Factors for Land-Based Structures 

The protection factor (PF) of a structure, defined as the quotient of the free-field radiation 

intensity outside and the free-field radiation intensity inside the structure, is a measure of the 

radiation shielding provided by that structure. In deterministic dose reconstructions, point-value 

protection factors of 2 for buildings and 1.5 for tents have generally been used. When 

performing probabilistic dose reconstructions for land-based personnel, however, the uncertainty 

in PF must also be characterized. The PF in a structure depends both on the physical properties 

of the structure (e.g., width, length, type of construction material) and on the location within the 

structure. The modeling of PF uncertainty is addressed in this section. 

4.2.2.1 Technical Approach and Methodology 

The Operation REDWING contractor completion report (Holmes & Narver, 1956) provides 

illustrations of the types and numbers of tents and buildings occupied by Army personnel at 

Enewetak during nuclear testing. Based on this report, the dimensions of the various structures 

can be estimated with confidence. It is assumed that the basic building configuration from 

REDWING adequately describes those properties for Operations CASTLE and HARDTACK I. 

Mathcad software was used to calculate a distribution of PFs for locations inside a rectangular 

shelter of length L, width W, height V, and wall/roof thickness twall situated in a field of 

uniformly deposited fallout that extends infinitely in all directions. It was assumed that the 

interior of the shelter was free of fallout. For buildings, walls of wood, aluminum, and iron are 

considered. The wall thickness twall was set to 0 for tents. Because the roofs of these buildings 

were generally pitched, fallout initially deposited on a roof would, over time, run off and 

redeposit on the adjacent ground. This was also modeled, allowing a fraction f of the fallout on 

the roof to form line sources alongside the structure. Because f is unknown, its value was 

selected from a uniform distribution between 0 and 1. 

The point-kernel method (Stevens and Trubey, 1972, pp. 46–53) was utilized in this analysis. 

The propagation of gamma radiation over a distance R through air was modeled by a point kernel 

Prop(R)/R2

, where Prop(R) accounts for all the propagation effects (e.g., absorption, scattering, 

build-up, air-ground interface) except for 1/ R2

 dispersion. The function Prop(R) was derived 

with the two-dimensional transport code CYLTRAN (Halbleib et al., 1992) for propagation of 

gamma radiation through air over soil. Spectra provided in Finn et al. (1979) were used to 

characterize the gamma radiation emitted by the fallout field. The resultant data were then fit 

piecewise in Excel to obtain the Mathcad equation shown below, where R is in meters. 

66 
80880 00472130 R316.2 if 

1037632 463680 316.2R31.65 if 

104234 1072412

57620 31.65 R3517 

03560 17.35 R if 

4

38 25

30630

09320

  

 

 

  

 







.(-exp. R) 

 . ).R 

.(exp .R R

 R).(exp .if

 R).(exp)R(opPr

-

.-

.

 (4-4) 

The attenuation of gamma radiation through wall materials was modeled in Mathcad by means of 

similar functional fits to results obtained with the one-dimensional transport code CEPXS 

(Lorence et al., 1989). 

The distribution of PFs for a specific structure was calculated by randomly sampling horizontal 

locations in that structure and, for each location, integrating the point kernel over the external 

gamma source to obtain the intensity at a height of 1 meter above the floor. At each step in the 

integration, the gamma radiation was attenuated through the proper slant thickness of the 

designated wall material. This algorithm was tested by comparing predicted values of PF with 

those derived from intensity measurements taken on Enewetak Island of Rongerik Atoll 

following fallout deposition from Operation CASTLE Shot BRAVO and reported in 

Scoville (1954). It was found that the PFs deduced from Scoville’s measurements could be 

reproduced only by accounting for the additional shielding effects of incidental materials in the 

structures, such as wall studs, wall coverings, desks, bedding, footlockers, and filing cabinets. 

Because of the unknown and unpredictable positioning of many such objects, this incidental 

material is not localized in the model, but instead is treated as a heavy dust suspended in the air. 

The Scoville data allows an estimation of the range of densities for incidental dust. Assuming 

the incidental materials had the shielding characteristics of wood, a triangular distribution of the 

incidental dust density thus derived has a minimum of 0.01 gram per cubic centimeter (g cm−3

), 

mode of 0.033 g cm−3

, and maximum of 0.06 g cm−3. An incidental dust density randomly 

drawn from this distribution was applied in calculating the attenuation of radiation coming 

through the sides of the structure. It was not applied to the radiation emitted from fallout 

deposited on the roof since most of the incidental material (and conceptually the dust) would 

have been located in the lower portion of the structure. A more detailed discussion of the PF

uncertainty algorithm is available in Weitz (2009c). 

4.2.2.2 Results and Discussion 

Examples of distributions derived with this algorithm are presented as histograms in Figure 16

and Figure 17 for two structures representative of the types used at PPG: 

 A 48-man barracks building (L = 38.6 m, W = 8.6 m, V = 4 m, twall = 1.27 cm (1⁄2") wood) 

 An 8-man tent (L = 8.6 m, W = 4.3 m, V = 3.5 m, twall = 0) 

67 
0

0.05

0.1

0.15

0.2

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Protection Factor

Relative Frequency

Figure 16. Calculated Protection Factor Distribution for 48-man Barracks 

0

0.05

0.1

0.15

0.2

0.25

1.0 1.5 2.0 2.5

Protection Factor

Relative Frequency

Figure 17. Calculated Protection Factor Distribution for 8-man Tent 

It was assumed that the values of L, W, and V are known without error, based on the quality of 

the information provided in the Holmes & Narver completion report and on the insensitivity of 

the computed values of PF to small changes in these parameters. The uncertainties in twall and 

68 
wall material composition are subsumed in the uncertainty model of the incidental material. The 

mean PF and 95th percentile upper bound for the barracks building are 2.2 and 3.6, respectively. 

Corresponding values for the tent are 1.4 and 1.8. 

It is generally straightforward to calculate the film-badge equivalent dose D* a hypothetical 

participant would have received by remaining outside and thereby continuously exposed to the 

average outdoor intensity. The dose D for a real participant who spent only part of his time 

outside will vary from D* because (1) he spent the remaining part of his time inside one or more 

structures where the intensity was reduced by a factor 1/PF due to displacement and shielding, 

and (2) his time outside was spent at a location that had an intensity different from the average. 

An external dose multiplier (EDM), defined as the ratio D/D*, can be calculated to facilitate the 

determination of D. 

The distribution of EDM is computed based on the following assumptions regarding the 

locations of a participant and relevant radiation intensities: 

 A participant was outside a fraction Fos of his time at a location where the relative outside 

intensity was I1. Relative outside intensity is defined as the ratio of the local outside intensity 

to the average outside intensity. 

 He spent a fraction Ft of his indoor time billeted or working in a tent with a protection factor 

PFt where the relative outside intensity was I2. 

 He spent the remainder of his time in a building with protection factor PFb and relative 

outside intensity I3. 

The equation for EDM for this scenario is given by: 





 



   1 2  3

1 1 I

PF

)F( I

PF

F )F(IFEDM

b

t

t

t

os os (4-5) 

The relative outside intensities I1, I2, and I3 are drawn from a distribution that characterizes the 

variation in outside intensity. In the present study, the values of the relative outside intensities, 

assumed to be uncorrelated, were drawn separately from a lognormal distribution with a 

geometric standard deviation of 1.5. If a person remained at essentially the same location most 

of the time, the relative outside intensities could be considered equal (I1 = I2 = I3) or proportional 

(I1 α I2 α I3). In these special cases, the intensities at the three locations are fully correlated and a 

single draw from the distribution would suffice. This would produce a slightly broader 

distribution for EDM. (Note that I1, I2, and I3 do not include measurement error since this error 

is treated as a fully-correlated multiplicative bias in this study and cancels when forming the 

local-to-average intensity ratios.) The protection factors PFb and PFt are sampled from the 

distributions shown in Figure 16 and Figure 17. An example of a distribution of EDM values 

derived for personnel at Enewetak during Operation HARDTACK I is presented in Figure 18; 

the distributions of Fos and Ft are specified in Table 3. 

69 
0

0.05

0.1

0.15

0.2

0.0 0.5 1.0 1.5 2.0 2.5 3.0

EDM

Relative Frequency

Figure 18. Estimated EDM Distribution for Land-based Personnel 

Table 3. Distribution Specifics for Fos and Ft for Land-Based Personnel on Enewetak 

during Operation HARDTACK I 

Parameter Definition 

Distribution for 

Probabilistic 

Analysis (*)

Nominal Value 

for Central 

Estimation 

Deterministic(*) 

Fos

Fraction of time spent 

outside 

Triangular 

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 

Triangular 

min = 0 

mode = 0.5 

max = 1 

0.5 0 

(*) High-sided per guidance in NTPR Policy and Guidance Manual (DTRA, 2007). 

4.2.3 Shielding Factors for Ships 

A shielding factor (SF) is defined as the ratio of intensity at some below-deck location to the 

average topside intensity. An investigation of shielding factors in interior spaces of ships from 

contaminants deposited on weather deck surfaces is conducted in this special study. The 

70 
shielding factor is dependent on the characteristics of the ship (e.g., beam or maximum width, 

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

ship (deck and location on that deck). A Mathcad program was developed to calculate ship- and 

deck-specific distributions of SF, assuming uniform topside deposition of fallout. 

4.2.3.1 Technical Approach and Methodology 

A methodology analogous to that employed in the calculation of protection factors was used 

here: the propagation of gamma radiation over a distance R through air was modeled with a point 

kernel AirAttn(R)/R2

, where AirAttn(R) accounts for all propagation effects (e.g., absorption, 

scattering, build-up, air-ground interface) except 1/R2

 dispersion. The function AirAttn(R) was 

derived with the two-dimensional transport code CYLTRAN for propagation of Finn-spectra 

gamma radiation through air over iron. The resultant data were then fit piecewise in Excel to 

obtain the equation shown below, where R is in meters. 

 69710 0047870 316.2 R if 

590601020161 316.2 R31.65 if 

 10185 109662

 54040 31.65 R 17.35 if 

45470 50 17.35 R if 

4

38 25

33440

57960

  

 



  

  







R).(-exp.

 . ) .R -

.R.(exp R

R) .(exp

R.exp()R(AirAttn ).

-

.-

.

 (4-6) 

The attenuation of gamma rays passing through deck materials was modeled by first using the 

CEPXS transport code to calculate ratios of doses for normally-incident Finn-spectra gamma 

radiation before and after passing through various thicknesses of shielding materials. The results 

were then fit in Excel to obtain the equations displayed below for steel and wood. The deck 

thickness t is in centimeters in these expressions. 

 otherwise 9044041790

167370 10 t if 

0003070 0066080 051350 4 3 2

).t.(-exp

)t.

t.t.t.exp()t(SteelAttn

 

 



(4-7) 

otherwise 1541208470 

 00170240 167370 100 t if 

10302121006951

2

47 35

).t.(-exp

)t.t.

.exp()t(WoodAttn .t t

 

  

 

In this Mathcad algorithm, the weather deck surface is assumed to be either rectangular (for 

aircraft carriers) or elliptical (for all other ships). The distribution of SF for a given deck on a 

specific ship was calculated by randomly sampling horizontal locations on that deck. Then, for 

71 
each location, the point kernel AirAttn(R)/R2 was integrated over the gamma source, which is 

assumed to have been uniformly distributed over the weather deck of the ship, to obtain the 

intensity at a height of 1 meter above the decking. At each step in the integration, the gamma 

radiation was attenuated via SteelAttn(t) for steel decks or WoodAttn(t) for wooden decks. In 

these expressions, “t” is the line-of-sight thickness of all decking material between the source 

point and the location of interest, multiplied by a factor fw (“Waldorf factor”) to account for 

miscellaneous materials such as pipes, bulkheads, etc. Measurements made in the late 1950s on 

the test ship USS COWPENS (a light aircraft carrier originally designated CVL 25, but relegated 

to the reserve fleet and re-designated AVT 1 by the time of the experiment) and reported in 

Waldorf (1959) indicate that the best estimate of fw is 2.35 ± 0.27. In the present formulation, the 

distribution of fw is assumed to be Gaussian with a mean of 2.35 and a standard deviation of 0.27 

for all ship types. This estimate should be fairly representative for aircraft carriers, but its 

applicability to other ship types is less certain. The question of applicability manifests itself as 

an increase in uncertainty which could be incorporated by increasing the standard deviation of 

the distribution. 

A more detailed discussion of the SF uncertainty algorithm is available in Weitz (2009d). 

4.2.3.2 Results and Discussion 

Distributions of below-deck shielding factors for various ship types were generated using the 

algorithm discussed above. Examples of these distributions are presented in Figure 19 for five 

decks of the aircraft carrier USS BOXER and in Figure 20 for the three decks of USS ESTES. In 

this analysis, the uncertainty in deck height was modeled as a triangular distribution with 

minimum of 2.2 m, mode of 2.44 m, and maximum of 3 m. The uncertainty in decking thickness 

was modeled as triangular distribution with deck-specific minima, peaks, and maxima derived 

from thicknesses reported for USS COWPENS (Tomoeda et al., 1959). The mean SFs for the 

five decks of USS BOXER, in descending order below the flight deck, are 0.16, 0.074, 0.038, 

0.013, and 0.005, and for the three decks of USS ESTES are 0.20, 0.035, and 0.017. 

An approach utilizing the EDM concept, similar to that discussed in the preceding section for 

land-based personnel, was also applied here. It is straightforward to calculate the film-badge 

equivalent dose D* that a hypothetical crewman would have received by remaining topside and 

being continuously exposed to the average topside intensity. The dose D for a real crewman who 

spent only part of his time topside will vary from D* because (1) he spent the remaining portion 

of his time below deck where the intensity is reduced by a factor SF due to displacement and 

shielding, and (2) his time topside was most likely spent at a location that had an intensity 

different from the average. As before, EDM is defined as the ratio D/D* and is used to 

determine D. 

In this case, EDM is calculated based on the following assumptions regarding the locations of a 

generic crewman and relevant radiation intensities: 

 A crewman was topside a fraction Fts of his time at a location where the relative topside 

intensity was I1. Relative topside intensity is defined here as the ratio of the local topside 

intensity to the average topside intensity. 

72 
0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.0001 0.001 0.01 0.1 1

Ship Shielding Factor

Relative Frequency

Deck 1

Deck 2

Deck 3

Deck 4

Deck 5

Figure 19. Distribution of Below-Deck Shielding Factors for USS BOXER 

0.00

0.05

0.10

0.15

0.20

0.25

0.0001 0.001 0.01 0.1 1

Ship Shielding Factor

Relative Frequency

Deck 1

Deck 2

Deck 3

Figure 20. Distribution of Below-Deck Shielding Factors for USS ESTES 

73 
 He split his below-deck time evenly between his worksite, where the shielding factor was 

SFw and the relative topside intensity was I2, and his billet location characterized by 

analogous parameters SFb and I3. (The distribution of time between worksite and billet 

location could appropriately be treated as a random variable and drawn from yet another 

distribution). For a below-deck location, the relative topside intensity is the intensity at the 

topside location vertically above the below-deck location divided by the average topside 

intensity. 

EDM for this scenario is then given by: 

 1 2 3 2

1 ISFISF F IFEDM w b

ts

ts   

 



    (4-8) 

The relative topside intensities I1, I2, and I3 may be drawn from a distribution that characterizes 

the variation in topside intensity, such as those shown in Figure 14 and Figure 15. Similarly, SFw

and SFb, which are treated as fully correlated test to test, can be sampled from distributions such 

as those shown in Figure 19 and Figure 20. Examples of EDM distributions thus derived are 

displayed in Figure 21 for personnel on the aircraft carrier USS BOXER and in Figure 22 for 

personnel on the USS ESTES. 

0

0.05

0.1

0.15

0.0 0.5 1.0 1.5 2.0 2.5 3.0

EDM

Relative Frequency

Figure 21. EDM Distribution for Personnel on USS BOXER 

74 
0

0.04

0.08

0.12

0.16

0.0 0.5 1.0 1.5 2.0 2.5 3.0

EDM

Relative Frequency

Figure 22. EDM Distribution for Personnel on USS ESTES 

A value of 0.1 for the shielding factor of below-deck spaces has been used in deterministic dose 

reconstructions. Because the shielding factors developed in this study depend on deck level, the 

appropriate average shielding factor for a particular case depends on the fraction of time the 

subject spent on each deck. For example, if the worksite of a representative crewman aboard 

BOXER is equally likely to have been on either of the first two decks below the flight deck, and 

his billet area equally likely to have been on either of the two decks below that, as assumed in 

Case Study 5, his composite average shielding factor is 0.072. 

4.2.4 Shot-Specific Radiological Decay Functions 

As discussed in Section 3.2, shot-specific, time-dependent decay functions can be obtained 

directly from the FIIDOS code. A database compiled from FIIDOS output provides relative 

intensities from 3 seconds to 5 years post-detonation for most shots and most operations. This 

database was utilized in the present case studies to characterize the time dependence of fallout 

intensity. 

The key uncertainty in the FIIDOS-derived decay functions is most likely 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 is beyond the scope of the present 

effort, but constitutes an area for future research and model refinement. In the meantime, an 

empirical model of the uncertainty in the FIIDOS decay functions was developed for use in the 

case studies. 

75 
4.2.4.1 Technical Approach and Methodology 

Most fallout events are characterized by a set of early-time intensity-time pairs (as illustrated in 

Table 1 of Section 3), the last pair of which is typically used as the baseline or starting point for 

extrapolating the intensity forward in time. In the case studies, the extrapolation in time for any 

Shot X was accomplished with the FIIDOS-generated, shot-specific decay function IX(t). Let Ib

be the baseline intensity for Shot X and tb be the time (after detonation) at which Ib occurred, 

such that IX(tb) = Ib. The model intensity IX(t) and the actual intensity I'X(t) agree at tb but will 

generally deviate thereafter. The difference between IX(t) and I'X(t) is the modeling error at 

time t. The premise is that the modeling error will generally increase with time from zero at tb. 

(Any uncertainty in Ib is attributable to measurement (and/or possibly other) error, but not to the 

decay model.) The following equation represents a family of possible decay paths that satisfy 

this premise. 

)t(I

t

t )t(I X

a

b

Xi

i

 













  ' (4-9) 

In a Monte Carlo simulation, a different decay path is followed each time the exponent ai is 

drawn. In this implementation, ai is drawn for each history from a Gaussian distribution with 

mean μa = 0 and standard deviation σa = 0.15; the basis for this value of σa is discussed below. 

4.2.4.2 Results and Discussion 

The criterion for determining σa is that about two-thirds of the population of real intensity decay 

functions fall within the bounds IX(t)·K and IX(t)/K, where 

a

bt

t K

















  (4-10) 

Shot-specific decay data extending to 6 months or more after the detonation are sparse. Decay 

functions for the following three shots were deduced from experimental measurements and are 

used here to quantify σa. 

 Operation GREENHOUSE Shot EASY, using decay data from the example following 

Table 2 in Section 3.2. 

 Operation CASTLE Shot BRAVO, a power law decay function t

−λ with six values of λ for 

specific time intervals (Thomas et al., 1984). 

 Operation PLUMBBOB Shot SHASTA, with a power law decay function defined on page 94 

of Goetz et al. (1979). 

For the decay function uncertainty model described above to be judged adequate on the basis of 

this admittedly small data set, two of these measurement-based decay functions should fall 

essentially between the bounds established by Equation 4-10, and the third should spend 

significant time outside these bounds. Results for the aforementioned three shots are displayed 

76 
in Figure 23–Figure 25. In each of these figures, the dashed line is the FIIDOS-derived decay 

function IX(t), the two dotted lines are the bounds about IX(t) given by Equation 4-10 for σa = 

0.15, and the solid line is the measured decay function. It is seen that, for the most part, the 

measurement-based decay functions are appropriately bounded by the uncertainty model. 

Therefore, the model passes the two-thirds criterion, although the sample of measurement-based 

decay functions is quite small. 

4.2.5 Gamma Source Modification Factor 

Ratios of surface activity density to intensity [Ci m−2 per R hr−1], generated with the FIIDOS 

code (Raine et al., 2007) 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 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. A deterministic value of 2 has typically been used for GSMF in internal dose 

assessments of shipboard personnel performed in the NTPR Program. This section discusses the 

formulation of GSMF for probabilistic assessments of shipboard exposures. 

Time after Detonation (hr)

Instensity (R hr-1)

101 102 103 104

10-7

10-6

10-5

10-4

10-3

FIIDOS Baseline

IX(t0)

Standard Model

Bound

Figure 23. Uncertainty Model Comparison for Operation GREENHOUSE Shot EASY 

77 
Time after Detonation (hr)

Intensity (R hr-1)

101 102 103 104

10-6

10-5

10-4

10-3

10-2

FIIDOS Baseline

IX(t0)

Standard Model

Bound

Figure 24. Uncertainty Model Comparison for Operation CASTLE Shot BRAVO 

Tim e afte r Detonation (hr)

Instensity (R hr-1)

1 01 102 10 3 1 04

10 -6

10 -5

10 -4

10 -3

10 -2

FIIDOS Baseline

IX (t 0 )

Standard Model

Bound

Figure 25. Uncertainty Model Comparison for Operation PLUMBBOB Shot SHASTA 

78 
4.2.5.1 Technical Approach and Methodology 

In the present formulation, it is assumed that homogeneous fallout material was deposited 

uniformly over the weather deck of a ship. The dose rate at a height of 1 meter above the deck 

from an increment of gamma-emitting fallout on the deck at a horizontal distance R is modeled 

by a point-kernel function Prop(R)/R2

, as in the analysis of intensity distribution from fallout on 

ships discussed in Section 4.2.1. The function Prop(R) is given by Equation 4-2. 

GSMF Distribution for Aircraft Carrier

An aircraft carrier presents the simplest case for calculating GSMF: its flight deck is nearly 

rectangular, and the superstructure is isolated on the starboard side of the ship so that, as a first 

approximation, it can be ignored. The value of GSMF for a topside location specified by the 

Cartesian coordinates (X,Y) on an aircraft carrier whose flight deck has width W and length L is 

calculated by the following Mathcad expression: 

(4-11) 

GSMF X Y ( )  



x





y

Prop x2

y

2

 H2   

x

2

y

2

 H2











d











d

L

2 

L

2

y

W

2 

W

2

x Prop x X ( )  2 ( ) y Y 2

 H2 

 

( ) x X 2 ( ) y Y 2 H2













d













d



In this equation, H is the height above the topside surface, taken as 1 meter in this analysis. 

A Monte Carlo approach is used in a Mathcad program to generate a distribution of GSMF

values for this ship. Specifically, n sets of coordinates (Xi,Yi), each representing a possible 

observer location, are selected randomly such that {-1⁄2W ≤ Xi ≤ 1⁄2W} and {-1⁄2L ≤ Yi ≤ 1⁄2L} for 

i = 1,...,n. These coordinates are than used in Equation 4-11 to generate values of GSMF

corresponding to the random topside locations. One such distribution, generated for the aircraft 

carrier USS BOXER (L = 271 m, W = 45 m) with a sample size of n = 10,000, is shown in 

Figure 26. The probability, expressed as relative frequency, is strongly peaked at the lower 

values of GSMF because much of the topside area of a uniformly contaminated aircraft carrier 

has a relatively uniform intensity profile. Near the boundaries of the topside area (i.e., near the 

edges of the flight deck), the intensity decreases because the radiation, on average, must travel 

farther to reach these locations and, hence, is subject to increased dispersion and attenuation. 

This causes the denominator of Equation 4-11 to decrease and GSMF to increase, resulting in the 

“tail” of higher GSMF values evident in Figure 26. 

The details of this distribution are not particularly relevant here—the important feature is its 

value when averaged over all topside locations, designated <GSMF>. Based on the dynamics of 

fallout deposition, it is likely that the airborne activity concentration, Ca(t), at any time t during a 

79 
0

0.1

0.2

0.3

0.4

0.5

1.0 1.5 2.0 2.5

GSMF

Relative Frequency

3.0

Figure 26. GSMF Probability Distribution for USS BOXER 

fallout event was nearly uniform over the extent of a ship. Therefore, it can be assumed that all 

personnel who were topside during such an event were exposed to the same Ca(t), regardless of 

their specific locations. The general approach employed in the NTPR Program to quantify Ca(t) 

is to use the aforementioned FIIDOS surface activity density-to-intensity ratios in conjunction 

with average topside intensities that were recorded in deck logs and/or in operational reports, or 

that were reconstructed on the basis of average intensity data reported on nearby ships or islands. 

Thus, it is appropriate to also use the topside-averaged value of GSMF when correcting Ca(t) for 

the finite extent of the source. 

The task now is to estimate the uncertainty in <GSMF>. Factors that contribute to this 

uncertainty for an aircraft carrier include (1) shielding provided by aircraft that may have been 

located on the flight deck, (2) the impact of the superstructure, and (3) the deviations of the flight 

deck from the idealized rectangular configuration. 

Photographs of carriers, including USS BOXER, taken during operations circa 1950’s (available 

http://www.navsource.org/archives/) indicate that aircraft were frequently parked in tight 

formation on the aft of the ship, typically spanning the width W of the flight deck and occupying 

an area of roughly W×W to 2W×W. To the extent that these parked aircraft attenuated the gamma 

radiation emitted by fallout deposited around and behind them, the length L of the flight deck 

was effectively reduced by an increment δ. In the limit of total attenuation, δ ranges from 0 

(when no aircraft were parked on the flight deck) to 2W (when parked aircraft occupied an area 

of 2W×W), with the most likely reduction perhaps being W. While the parked aircraft could not 

have provided such effective shielding, use of this seemingly high-sided assumption allows for 

80 
the shielding effects of various other aircraft and equipment that may have been located in other 

areas of the flight deck. On this basis, δ is treated here as a random variable drawn from a 

triangular distribution with minimum = 0, mode = W, and maximum = 2W. The “effective” 

length of the flight deck is then Leff = L − δ. 

In an analogous manner, deviations from the idealized rectangular configuration of the fallout 

field due to the presence of the superstructure and variations in the topside width can be crudely 

modeled as a reduction in the overall width of the flight deck. Photographs of various carriers 

indicate that the superstructure and associated “clutter” occupy roughly 5–10 percent of the 

topside area. Another 5–10 percent of the idealized rectangular fallout field is “lost” due to a 

narrowing of the flight deck in the forward section of the carrier. This relatively minor 

perturbation would most affect those working in that area. To incorporate these features into the 

uncertainty model, the nominal width W of the flight deck is reduced by a fraction f to determine 

an “effective” width Weff = (1−f)×W. The random variable f is assigned a triangular probability 

distribution with minimum = 0, mode = 0.1, and maximum = 0.2. 

The distribution of <GSMF> for fallout deposition on an aircraft carrier is derived by a Monte 

Carlo algorithm employing two loops: an outer loop in which randomly selected values of δ and f

are used to define Leff and Weff, and an inner loop where, given these dimensions, the locations 

(X,Y) on the flight deck are randomly sampled and GSMF computed for each. Each inner loop 

provides a GSMF distribution similar to that shown in Figure 26, and from that, one value of 

<GSMF>. The probability distribution of <GSMF> shown in Figure 27 was thus obtained with 

a composite sample size of 90,000 (300 outer loops x 300 inner loops) for USS BOXER. The 

average value of <GSMF> in this example is 1.56. It is seen that the distribution of <GSMF> is 

narrow, indicating that this uncertainty does not have significant impact. 

0

0.05

0.1

0.15

0.2

1.40 1.45 1.50 1.55 1.60 1.65 1.70

<GSMF>

Relative Frequency

Figure 27. Probability Distribution of Average GSMF for USS BOXER 

81 
GSMF Distributions for Other Ship Types

All ship types other than aircraft carriers are modeled as having an elliptical topside 

configuration with major axis equal to the length L of the ship and minor axis equal to the ship’s 

maximum width (beam) W. If the ship did not have a superstructure, GSMF could be calculated 

by simply integrating over the elliptical surface, as indicated in the denominator of 

Equation 4-12. 

GSMF X Y ( )  



x





y

Prop x2

y

2

 H2   

x

2

y

2

 H2











d











d

L

2 

L

2

y

 W

1

4

y

L













2















1

2



W

1

4

y

L













2















1

2



2

x Prop x X ( )  2 ( ) y Y 2

 H2 

 

( ) x X 2 ( ) y Y 2 H2

















d

















d



 (4-12) 

On most ship types, however, the superstructure significantly impacts the topside topology. The 

configuration of the superstructure is generally quite complex and difficult to treat analytically. 

To simplify the analysis, the superstructure is modeled as an ellipse with a reduced length 

 LS and a reduced width WS (with 0 < S < 1), concentric and co-oriented with the 

ellipse that defines the ship’s topside boundary. The parameter S is the fraction of the ship's total 

topside area that is occupied by the superstructure. The values of S are chosen to best 

characterize the superstructure’s “footprint” for each type of ship. For example, S is 

approximately 0.25 for a liberty ship (YAG), 0.3 for a tank landing ship (LST), and 0.5 for an 

attack transport (APA), amphibious cargo ship (AKA), and destroyer (DD). For given values of 

W, L, and S, the outer and inner ellipses are defined in Cartesian (x,y) coordinates by 

Equations 4-13 and 4-14, respectively. 

1

1⁄21⁄2

2 2

  

 



    





L

y

W

x (4-13) 

S

L

y

W

x   

 



    





1⁄21⁄2

2 2

 (4-14) 

This ellipse-in-ellipse configuration is shown in Figure 28. 

82 
Figure 28. Superstructure Model 

The superstructure is assumed to be opaque to radiation, and therefore provides complete 

shielding to a topside observer from radiation emitted by fallout that is not within his direct field 

of view. Thus, in the denominator of Equation 4-12, the limits of integration must be adjusted so 

that only the topside area within the field of view of the observer is included. For an observer at 

the topside location indicated by the red dot in Figure 28, his field of view of the fallout field is 

bounded by the two red lines drawn through his location to the points of tangency on the inner 

ellipse (superstructure). The area of integration is the shaded region indicated in the figure. The 

geometric formulae that are relevant to establishing the limits of integration are provided in 

Weitz (2009e). 

The top of the superstructure of a ship consists primarily of horizontal surfaces 8 feet or more 

above the main deck. Most of the contaminants deposited on the exterior of these surfaces were 

therefore not in the field of view of an observer standing on the main (topside) deck, and 

radiation emitted by these contaminants is strongly attenuated by the superstructure material 

before reaching that person. For this reason, radiation from contaminants deposited directly on 

the superstructure is neglected as a first approximation. 

Monte Carlo sampling is used in the Mathcad program to calculate the distribution of GMSF

over the topside surface of an elliptically-shaped ship. Sets of coordinates (Xi,Yi), each 

representing a possible observer location, are selected randomly such that {-1⁄2W ≤ Xi ≤ 1⁄2W} and 

{-1⁄2L ≤ Yi ≤ 1⁄2L}. The coordinate pair (Xi,Yi) is accepted only if 1

2

1⁄2L

2

1⁄2W   

 



   

 



  Xi Yi S , thus 

ensuring that the observer is on or within the boundary defined by Equation 4-13 and on or 

outside the boundary defined by Equation 4-14 (i.e., between the two ellipses shown in 

Figure 28). A value of GSMF is then calculated for each acceptable set of coordinates with an 

83 
expression similar to Equation 4-12, but with the integration in the denominator limited to the 

line-of-sight regions of the topside area, exclusive of the superstructure. The probability density 

function of GSMF obtained in this manner for USS ESTES, an amphibious force flagship with 

parameters L = 140 m, W = 19 m, and S = 0.40, is displayed in Figure 29. 

0

0.02

0.04

0.06

0.08

0.1

0.12

1.00 1.75 2.50 3.25 4.00 4.75 5.50

GSMF

Relative Frequency

Figure 29. GSMF Probability Distribution for USS ESTES 

As with the aircraft carrier, the details of the distribution in Figure 29 are not particularly 

important for the present purpose, where only the mean value <GSMF> is needed. The mean of 

this distribution (2.95), along with those obtained by varying S, are plotted in Figure 30 as a 

function of S. 

To estimate the uncertainty in average GSMF (<GSMF>), S is treated as a random variable with 

a triangular distribution having a minimum value of 0 (no superstructure effect, conceivably 

because the “shine” from fallout that adhered to the superstructure exactly compensated the 

shielding it provided); a mode of Snom, the nominal value of S for the ship of interest 

(corresponding to a “black” superstructure—one that totally absorbs incident radiation and has 

no shine); and a maximum given by Snom + 1⁄2(1− Snom) (black superstructure plus shielding from 

topside “clutter” taken as equivalent to expanding the superstructure to encompass half of the 

area outside the superstructure footprint). The distribution of <GSMF> for USS ESTES is 

shown in Figure 31; it has a mean of 2.95. 

84 
0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Areal Fraction S

Average Gamma Source 

Modification Factor

Figure 30. Dependency of Average GSMF on Areal Fraction S for USS ESTES 

0

0.02

0.04

0.06

0.08

0.1

12345

GSMF

Relative Frequency

Figure 31. Probability Distribution of Average GSMF for USS ESTES 

85 
4.2.5.2 Results and Discussion 

The average values of GMSF for various ship types, obtained with Mathcad implementations of 

the models described in this Section, are provided in the rightmost column of Table 4, together 

with the characteristic values of length L, width W, and nominal superstructure areal fraction Snom

used in these analyses. These results are based on Monte Carlo runs of 10,000 histories each. 

The average values of GSMF obtained for similar vessels without allowance for superstructure 

are included for comparison (“Average GSMF w/o SS” column). It is apparent from Table 4 that 

the presence of the superstructure can significantly impact the value of the GSMF for ship types 

other than an aircraft carrier. While the deterministic value of 2 is representative of the average 

GSMF obtained when the superstructure is neglected, it significantly under-represents the 

average value of <GSMF> obtained for ships (other than aircraft carriers) when accounting for 

the superstructure. 

The distributions of <GSMF> used in the case studies of USS BOXER and USS ESTES are 

shown in Figure 27 and Figure 31. 

Table 4. Average GSMF for Various Ship Types 

Ship Type Designation

L 

(m) 

W 

(m) 

Snom

(fraction) 

Average 

GSMF

w/o SS 

Average 

GSMF 

w/SS 

Aircraft Carrier CVS 271 45 0* 1.56 1.56 

Amphibious Force Flagship AGC 140 19 0.40 1.99 2.95 

Attack Transport APA 139 19 0.50 1.99 3.33 

Destroyer DD 115 12 0.50 2.35 4.32 

Dock Landing Ship LSD 140 22 0.40 1.90 2.78 

Fleet Tug ATF 62 12 0.35 2.42 3.66 

Salvage Ship ARS 65 12 0.50 2.42 4.47 

Store Ship AF 103 15 0.30 2.17 3.02 

Tank Landing Ship LST 100 15 0.30 2.18 3.03 

* 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. 

4.2.6 Resuspension Factors 

Resuspension factors are defined in Section 3, and time-dependent models for deterministic and 

nominal point estimates for resuspension of fallout as used in the case studies for typical 

86 
activities are given in that section. For the probabilistic analysis, the uncertainty associated with 

the nominal resuspension factor values (land and ship) is assumed to have a lognormal 

distribution with the median equal to the nominal value, and a 90-percent confidence interval 

between 0.1 and 10 times the median. This is based on the results of a study reported in 

conjunction with the basic formulation of the nominal resuspension factor 

(Anspaugh et al., 2002). 

The remainder of this section discusses resuspension factors used for the special case of 

resuspension of fallout in the vicinity of detonations at NTS. 

4.2.6.1 Technical Approach and Methodology 

The characterization of the resuspension factors for resuspended fallout in the vicinity of 

detonations at the NTS is based on a study conducted by Kocher et al. (2006). Of the case 

studies documented in this report, this type of resuspension is applicable only to the Marine unit 

at Operation PLUMBBOB. Two general regions of enhanced resuspension in the vicinity of a 

detonation have been identified. The area closest to ground zero (GZ) is referred to as the 

precursor region1

, where the peak overpressure associated with a blast wave was 6 pounds per 

square inch (psi) or greater and resuspension was due to the thermal pulse produced by the 

detonation. The second region is referred to as the blast-wave region, where the peak 

overpressure associated with the blast wave was between 6 and 2 psi and resuspension was due 

to high winds associated with the blast wave of the detonation. The extent of each of these 

regions is shot-specific, and each is a function of yield and height of burst of the detonation 

(Glasstone and Dolan, 1977). In the study (Kocher et al., 2006) the contributions of several 

factors to the overall uncertainty of inhalation doses due to resuspension of previously-deposited 

fallout in both regions were studied. Those several factors include the following: 

 ground surface concentrations of radionuclides 

 effects of the detonation on resuspension of deposited fallout 

 inhalability and respirability of the resuspended radionuclides 

 breathing rates 

 inhalation dose coefficients 

One conclusion of that report forms the basis for the deterministic model resuspension factors 

(see Section 3.3.1.1) that were used in the PLUMBBOB case study, i.e., estimation of “effective” 

resuspension factors for each region that should ensure that deterministic inhalation doses for 

these scenarios result in credible upper bound doses when used with point estimates of all other 

parameters normally used in NTPR dose reconstructions. In addition to deterministic values, 

probability distributions of resuspension factors were available that were used for the 

 

1

 The term “precursor” was changed to “thermal pulse” in a revision to Kocher et al. (2006) recently published as 

Kocher, D. C., Trabalka, J.R., and Apostoaei, A.J., 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, SENES, Oak Ridge, Inc., Oak Ridge, TN and Defense Threat Reduction Agency, Fort 

Belvior, VA. However, the definition of the region did not change, and the term “precursor region” is retained in 

this report. 

87 
probabilistic analysis. Several of the key factors listed above, the uncertainties of which are 

lumped in the Kocher et al. (2006) analysis into the effective resuspension factor used in the 

deterministic model, are included separately from the resuspension factor in the inhalation dose 

probabilistic analysis of the PLUMBBOB case study. In particular, the factors explicitly 

addressed include uncertainties in breathing rates and inhalation dose coefficients. Therefore, 

the resuspension factors from the Kocher et al. (2006) report judged to be appropriate for use in 

the current probabilistic analysis of the PLUMBBOB case are those that account only for 

uncertainties in the resuspension factors and in the respirable and non-respirable portions of 

resuspended fallout. 

4.2.6.2 Results and Discussion 

Values obtained from Kocher et al. (2006) and used in the PLUMBBOB case study are shown in 

Table 5 for respirable and for inhalable but non-respirable forms of fallout resuspended by 

nuclear detonations. Based on descriptions in the Kocher et al. (2006) report, and specifically for 

the purposes of estimating the doses from this pathway, “respirable” is taken to mean particles 

with activity median aerodynamic diameters (AMAD) less than 10 μm, and “non-respirable” 

means particles with AMAD between 10 μm and 100 μm (see Section 4.2.10 for an alternate 

definition of these terms for use in the descending fallout analysis). Accordingly, and consistent 

with the modeling of descending fallout in this probabilistic study, unbiased inhalation DCFs 

were applied to the respirable portion of this resuspended fallout, and ingestion DCFs were 

applied to the non-respirable portion. ET2 deposition (i.e., ingestion) of the non-respirable 

portion of this pathway is currently taken to be 1.0, but this will be the subject of a future 

modification. Unbiased inhalation DCFs are discussed later in this section. 

The deterministic resuspension factors shown in Table 5 are significantly larger than the median 

values used in the probabilistic analysis, also shown in Table 5. This large difference is 

explained by considering the basis of each of the values. The deterministic values are not 

intended to represent central estimates, but are instead intended to result in credible upper bound 

doses by this pathway. In addition, the deterministic values are applied to all particles, not just 

inhalable or respirable. So, for example in the precursor region, the two 95th percentile 

probabilistic values (for respirable and non-respirable) can be combined as approximately 

2.5  10−4

 m−1, and this value would be applicable to an upper bound value for particles with an 

AMAD of less than 100 μm. This value can then be compared to the deterministic value of 

1  10−3

 (also applicable to an upper bound dose), yielding a ratio of 2.5 rather than the ratios of 

greater than 100 when comparing the deterministic value for each region to the medians for that 

region. 

88 
Table 5. Resuspension Factors (m−1

) for Fallout Resuspended by Nuclear Detonations at 

the NTS 

Median or 

point 

estimate(*) 5th percentile 95th percentile 

Precursor region

Deterministic – for all resuspended 

radionuclides 1  10−3 n/a n/a 

Probabilistic – Respirable form(†) 1  10−6 

(GSD = 10.8) 4  10−8 5  10−5

Probabilistic – Non-respirable form(†) 8  10−6

(GSD = 7.08) 3  10−7 2  10−4

Blast-wave region

Deterministic – for all resuspended 

radionuclides 1  10−4 n/a n/a 

Probabilistic – Respirable form(†, ‡) 1  10−7

(GSD = 10.8) 4  10−9 5  10−6

Probabilistic – Non-respirable form(†, ‡) 8  10−7

(GSD = 7.08) 3  10−8 2  10−5

(*) Median values (and GSDs) are given for probabilistic analysis values and point estimates for the 

deterministic analysis values. 

(†) Modeled distributions for these resuspension factors are lognormal, with distributions characterized 

by the listed median, 5th and 95th percentile values for each category. 

(‡) The distributions for the blast-wave region resuspension factors were recently revised in an update 

to Kocher et al. (2006)3

 that was published after the analyses described in this report were 

conducted. The revised distributions are characterized by median (and GSD) values of 1 × 10−8

(GSD ≈ 26) for respirable particles, and 8 × 10−8

 (GSD ≈ 22) for non-respirable particles. 

4.2.7 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. Such parameters directly impact radiation doses to tissues of the respiratory tract, but 

also influence doses to other organs and tissues of the body from the inhalation pathway. 

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 the 

respiratory tract, and if the individual is a smoker. The population of atmospheric nuclear test 

participants was more homogeneous than the population at large with regard to breathing 

characteristics, having been comprised mainly of Caucasian males in their late teens to early 30s. 

 

3

 Kocher, D. C., Trabalka, J.R., and Apostoaei, A.J., 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, SENES, Oak Ridge, Inc., Oak Ridge, TN and Defense Threat Reduction 

Agency, Fort Belvior, VA. 

89 
Variability and uncertainties in breathing rates of test participants result principally from 

differences in duties and activity levels and to a lesser extent, individual physiological variation. 

A large amount of data is available on the variability of breathing rates in human populations 

based on age, gender, race, health conditions, smoking status, and other factors. For this report, 

summary data and guidance provided in ICRP (1994), NCRP (1997) and USEPA (1997) are 

used to construct probability distribution functions (pdf) of breathing rates for various types of 

activity and to apportion time among such activities for atmospheric nuclear test participants. 

Each of these source documents contains extensive descriptions of data that form the basis for 

the parameter values used in the analyses described in this report. 

4.2.7.1 ICRP 66, Human Respiratory Tract Model (HRTM) for Radiological Protection 

The ICRP Committee obtained respiratory physiological data for representative ethnic groups of 

both sexes, different ages, and for different levels of activity. From these data, reference values 

representing working Caucasian males and females (17 years and older) were selected for use in 

the dosimetric respiratory tract model for workers. A second set of values, representing nonworking Caucasian males and females of all ages was selected for use in the dosimetric model 

for the general population. 

Because the physiological attributes and activity levels of Caucasian workers are most 

representative for nuclear test participants, only the reference values for adult males are utilized 

in the analyses performed for this report. These data are provided in Table 6

(ICRP, 1994, Annex B). 

Table 6. ICRP Reference Breathing Rates for Workers 

Activity Level Percent of Maximum 

Workload a Breathing Rate (m3

 hr−1) 

Sleep 8 0.45 

Rest, sitting 12 0.54 

Light exercise 32 1.5 

Heavy exercise 64 3.0 

a

 Maximum workload = 250 Watts (ICRP, 1994, Annex B) 

The recommended daily time fractions associated with each activity are provided in Table 7

(ICRP, 1994). 

90 
Table 7. ICRP Daily Time Apportionment for Workers 

Activity Duration (hr day−1) 

Sleep 8 

Occupational 

 (5.5 hr light exercise and 2.5 hr rest, sitting) 8 

 (7 hr light exercise and 1 hr heavy exercise) 8 

Non-occupational 

 (4 hr rest or sitting, 3 hr light exercise and 1 hr 

 heavy exercise) 8 

4.2.7.2 NCRP Report 125: Deposition, Retention and Dosimetry of Inhaled Radioactive 

Substances 

NCRP (1997) cites the reference breathing rates shown in Table 8 for adults (18 years old). The 

reported values are adapted from Phalen et al. (1985). While an in-depth review of the bases for 

these values is not provided in the source document, they are similar to the ICRP values. 

4.2.7.3 USEPA Exposure Factors Handbook, Volume 1, General Factors 

USEPA (1997) provides a comprehensive discussion of respiratory parameters for human 

populations categorized by age, gender, and activity. Values relevant to nuclear test participants 

are those for adults from 19 to over 65 years old and outdoor workers for short-term exposures. 

Breathing rates and corresponding activity patterns are provided in Table 9. 

Table 8. NCRP Reference Breathing Rates for Workers 

Activity Level Breathing Rate (m3 hr−1) 

 Rest a 0.6 

 Light Exertion b 1.2 

 Heavy Exertion c 3.6 a

 About 30 percent above basal with respect to minute volume 

b

 Matched to minute volume of a reference man (ICRP, 1977) 

c

 About 50 percent of maximum level that can be sustained for a few 

minutes)

91 
Table 9. USEPA Reference Breathing Rates for Adults and Outdoor Workers for 

Short-Term Exposures 

Adults Outdoor Worker 

Activity Level Breathing Rate 

(m3

 hr−1) Activity Level Breathing Rate (m3 hr−1) 

Rest 0.4 N/A 

Sedentary activities 0.5 N/A 

Light activities 1.0 Slow activities 1.1 

Moderate activities 1.6 Moderate activities 1.5 

Heavy activities 3.2 Heavy activities 2.5 

Activity levels for the average adult male are defined by USEPA as: 

 Rest: lying down. 

 Sedentary: sitting and standing. 

 Light: walking on a level firm surface at 3 miles per hour (mph). 

 Moderate: fast walking or slow running (3.3 to 4 mph), climbing stairs, digging with a spade. 

 Heavy: fast running (4.5 to 6 mph), cross-country skiing. 

The outdoor worker cohort consisted of 15 men and 5 women between the ages of 15 and 50, 

who worked outdoors at least 10 hours per week. Activity (exertion) levels, self-reported by the 

test subjects as slow, moderate, and fast, are nominally equivalent to normal walking, moderate 

walking, and running, respectively. Table 10 presents summary data for adult males that list 

breathing rate ranges by age and activity level (USEPA, 1997, Table 5A-7). 

Table 10. USEPA Summary of Breathing Rates for Adult Males 

Breathing Rate (m3 hr−1) 

Activity Level Sample Size 

(n) Low Mean High 

 Rest 454 0.14 0.73 1.13 

 Light 102 0.14 0.83 1.66 

 Moderate 102 0.86 2.45 4.68 

 Heavy 267 2.08 4.8 11.00 

92 
The low and high values in Table 10 above are from reported ranges in Table 5A-7 in 

USEPA (1997) and therefore represent the minima and maxima of the data sets. 

4.2.7.4 Results and Discussion 

A comparison of the USEPA summary data in Table 10 with values reported in ICRP (1994) and 

NCRP (1997) (Table 6 and Table 8, respectively) reveals a disparity for light and heavy exercise 

levels. The USEPA mean value of 0.83 m3

 hr−1 for light exercise is only about 62 percent of the 

average of the ICRP and NCRP values (1.35 m3

 hr−1) and that the USEPA mean value of 

4.8 m3

 hr−1 for heavy exercise is about 1.46 times the average of the ICRP and NCRP values 

(3.3 m3

 hr−1). 

Deterministic NTPR dose assessments for the inhalation of airborne contaminants have 

traditionally been based on a breathing rate of 1.2 m3

 hr−1, which is the NCRP value that 

corresponds to light physical exertion. For this analysis we selected mean breathing rates of 1.35 

and 3.3 m3

 hr−1 for light and heavy exercise, respectively, which correspond to the average of the 

ICRP and NCRP mean values. Reference breathing rates for rest and moderate exercise are 

taken directly from the USEPA data having values of 0.73 and 2.45 m3

 hr−1, respectively. 

The breathing rate is correlated with the exertion level, as discussed above. Consistent with 

standard NTPR assumptions, it is assumed that the inhalation of contaminants only occurred 

while participants were outside. It is further assumed that, while outside, a participant spent 

25 percent of his time sitting/resting, 60 percent in light activity, 8 percent in moderate activity, 

and 7 percent in heavy activity. Although some variability in these values is likely, they are 

taken as constants in this report in order to simplify the analysis. The triangular pdf was selected 

to characterize the variability of breathing rates for each activity level. This choice was based on 

several factors, including the somewhat subjective definition of exertion levels, that the 

underlying data distributions are not well defined, and uncertainty as to the degree that the data is 

representative of breathing rates of nuclear test participants. The breathing rates at the various 

activity levels are assumed to be fully correlated; that is, someone who has an above-average 

breathing rate while at rest will have above-average breathing rates during light, moderate, and 

heavy activities as well. Given these assumptions, the mean and lower and upper limits of the 

breathing rate distributions by activity level are presented in Table 11. 

Table 11. Breathing Rate Distributions by Activity Level–NTPR Test Participants 

Activity Level Low Mean High 

 Rest 0.1 0.7 1.1 

 Light 0.2 1.4 2.7 

 Moderate 0.9 2.5 4.7 

 Heavy 1.4 3.3 7.6 

93 
For the probabilistic modeling, triangular distributions were defined for breathing rates for each 

activity level, with low, mean, and high values used as minimum, mode, and maximum values, 

respectively, of each distribution. Samples from the distributions were then multiplied by the 

activity fractions defined above; e.g., 0.25  (sample from triangular distribution for “Rest”). 

The products were then summed for each simulation. Table 12 provides sample statistics from a 

run of 10,000 Monte Carlo simulations of the breathing rate formulation based on the forgoing 

parameters, with results also shown in Figure 32. Note that these results are sample statistics, 

and because the distribution is generated for each dose calculation, actual statistics in any 

particular dose calculation may be slightly different. All breathing rates are in units of m3

 hr−1. 

Table 12. Breathing Rate Distribution Parameters: 10,000 Monte Carlo Histories 

Parameter Breathing Rate (m3

 hr−1) 

 Mean (peak) 1.53 

 Minimum 0.33 

 Maximum 2.79 

 95th percentile 2.40 

 Standard deviation 0.51 

 95th percentile/mean ratio 1.57 

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.

Breathing Rate (m3 hr-1)

Relative Frequency

5

Figure 32. Sample Breathing Rate Distribution for Atmospheric Nuclear Test Participants 

94 
4.2.8 Internal Dose Conversion Factors 

This section discusses biases and uncertainties in the internal dose conversion factors (DCF), 

which are derived from published ICRP dose coefficients (ICRP, 1996; ICRP, 2002). DCFs are 

used in NTPR dose reconstructions for the assessment of doses accrued from internallydeposited radionuclides by the inhalation and ingestion routes of entry. 

4.2.8.1 Estimation of Inhalation Dose Conversion Factors Using FIIDOS 

NTPR uses the computer program FIIDOS to calculate the 50-year committed equivalent doses 

(CEDs) to various body organs and tissues that would result from the ingestion or inhalation of 

radioactive material produced by a nuclear detonation. These organ dose calculations are based 

on the amount of radioactive material ingested or inhaled, the radionuclide composition of the 

material, and organ DCFs for each radionuclide. A library of published ICRP dose coefficients 

(listed in units of rem μCi−1

) is used in FIIDOS, which are tabulated for individual organs and 

effective dose for up to 148 fission products, 17 activation products, and 18 actinides. These 

dose coefficients have been used with shot-specific radiochemistry data to produce lookup tables 

of shot-specific, time-dependent composite DCFs for the assessment of tissue or organ dose 

commitments from the ingestion and inhalation routes of entry. Composite DCFs are reported 

either in units of rem CED Ci−1

 intake or rem CED per rem film badge equivalent (FBE) dose for 

the calculation of internal doses based on a radiation intensity or external dose measurement. 

All routine inhalation dose calculations (i.e., inhalation of descending or resuspended fallout), 

are typically evaluated using composite DCFs in the unit rem CED per rem FBE. Equations for 

evaluating ingestion doses are normally formulated using composite ingestion DCFs in the unit 

rem CED Ci−1

. 

As described in the FIIDOS manual (Raine et al., 2007), dose reconstructions performed before 

2006 used radionuclide-specific DCFs as input to FIIDOS that were based in large part on 

internal dosimetry models recommended in ICRP Publication 30 (ICRP, 1979). Current NTPR 

dose reconstructions use DCFs that are based on radionuclide-specific dose coefficients from 

current ICRP recommendations for adult members of the public (ICRP, 1996; ICRP, 2002). 

Table 13 lists the 23 organs and tissues, and the quantity—effective dose—for which ICRP-72 

dose coefficients were available as input to FIIDOS. 

For NTPR, a subset of ICRP-72 inhalation dose coefficients was selected and assembled for 

input to FIIDOS, to address concerns about particle size distribution. Developed for use in the 

deterministic dose calculations, this set uses the dose coefficient for the particle size distribution 

that produces the highest dose to the organ of interest from among 1-, 3-, 5-, and 10-micrometer 

(μm) activity median aerodynamic diameter (AMAD) particle size distributions for the 

absorption type applicable to the oxide form of each constituent radionuclide. This set of 

“maximum dose” inhalation dose coefficients supplants all previous sets for NTPR internal dose 

assessments. The composite DCFs derived from these dose coefficients are inherently biased 

(high-sided), and their use with the entire inventory of descending or resuspended fallout results 

in high-sided doses for many inhalation scenarios. This is especially the case for scenarios 

involving descending fallout, for which the particle size distributions may include particles much 

larger than respirable sizes. To obtain the deterministic upper bound internal doses, an 

uncertainty factor of 10 is then applied to the deterministic internal dose estimates 

(DTRA, 2003). The uncertainty factor is thus the ratio of the upper bound dose to the 

95 
Table 13. FIIDOS Target Organs 

Organ Name Organ Name 

Adrenals Muscle 

Bone Surfaces Ovaries 

Brain Pancreas 

Breast Red Marrow 

Stomach Wall Skin 

Small Intestine Wall Spleen 

Upper Large Intestine Wall Testes 

Lower Large Intestine Wall Thymus 

Kidneys Thyroid 

Liver Uterus 

Extra-Thoracic Region Urinary Bladder Wall 

Lung Effective Dose 

deterministic point estimate. Use of the uncertainty factor of 10 with the deterministic point 

estimate is believed to result in an upper bound dose that is not an underestimate of the true 

95th percentile dose. 

The regulation governing the NTPR RDA process (32 CFR 218 [DoD, 2009]), specifies that only 

published conversion factors are to be used to estimate internal doses. Furthermore, The NTPR 

Policy and Guidance Manual (DTRA, 2007a) requires the use of dose coefficients currently 

recommended by the ICRP. Because some diseases and conditions for which claims are filed do 

not have well-defined sites of origin or published DCFs, “surrogate” organs and their DCFs are 

sometimes used. Surrogate organs are assigned based on target organs and tissues that are 

judged to be most similar to the organ or tissue of concern with regard to biokinetic modeling. It 

is recognized that these DCFs are inherently more uncertain with regard to dosimetry and 

biokinetics when applied to other organs or tissues. However, addressing this source of 

uncertainty is beyond the scope of the current study. 

While the high-sided approach currently used for NTPR deterministic analyses is in the spirit of 

providing test participants with the maximum benefit of the doubt, as articulated by DTRA, use 

of high-sided DCFs as central estimates is not appropriate in an uncertainty analysis. 

Accordingly, a credible application of inhalation DCFs for uncertainty analysis, particularly with 

regard to inhalation of descending fallout scenarios, requires use of nominal DCFs and explicit 

treatment of uncertainties. The following sections discuss sources of bias and uncertainty in the 

deterministic DCFs, and how these were addressed in the uncertainty analysis. The adjustments 

in the following sections addressing uncertainty in dose conversion factors and maximum dose 

bias were applied to all special study cases; the adjustments addressing deposition fraction and 

activity fraction in the two subsequent sections were used with the PPG special study cases 

because only those cases involved inhalation of descending fallout. 

96 
4.2.8.2 Uncertainty in Inhalation and Ingestion Dose Conversion Factors 

The primary sources of uncertainty in dose conversion factors used by NTPR stem from 

uncertainties in the dosimetric and biokinetic models used by the ICRP to estimate dose 

coefficients that form the basis for NTPR DCFs. These uncertainties vary depending on factors 

such as target organ, radionuclide, type of radiation, and chemical form of the radionuclide. In 

addition to inherent model uncertainties, a complicating factor is that biokinetic models used by 

ICRP may be based on studies of chemical and physical forms of radionuclides that differ 

substantially from chemical and physical forms in fallout. A comprehensive review of published 

studies on uncertainties in dose coefficients was undertaken by SENES Oak Ridge, Inc., in 

support of a study on inhalation doses from high resuspension scenarios for NTPR program 

participants (Kocher et al., 2006)4

. The SENES analysis, in conjunction with subsequent 

discussions with the primary author, provides the basis for the selection of uncertainty factors 

and probability distribution function (pdf) parameters used in this report. 

Because of the impracticality of developing and implementing estimates of DCF uncertainties for 

all combinations of organs and radionuclides, a rigorous analysis of uncertainty in dose 

coefficients for inhalation or ingestion of radionuclides in fallout was not attempted in this study. 

Such an undertaking would have required consideration of uncertainties in dose coefficients for 

essentially all organs or tissues, including organs or tissues that are not major sites of deposition 

but often are of concern in dose reconstructions, and for hundreds of radionuclides. 

Furthermore, uncertainties appear to be well characterized for only a few combinations of 

radionuclide and organ or tissue, and those organs or tissues usually are not of concern in NTPR 

dose reconstructions because they are considered presumptive for the purposes of adjudicating 

claims for service-connected disability for atomic veterans. (DVA, 2002; Kocher et al., 2006). 

In Kocher et al. (2006), uncertainties in dose coefficients for inhalation of fission and activation 

products were evaluated separately from uncertainties in dose coefficients for plutonium. This 

separation was based on the potential for greater uncertainties in dosimetric models for alphaemitting radionuclides than for beta/gamma emitters. The SENES report also notes that, unless 

there are strong correlations among dose coefficients for important radionuclides, the uncertainty 

in a dose coefficient for mixtures of radionuclides should be no larger than the largest 

uncertainty that applies to any radionuclide in a mixture when exposures generally should 

involve some radionuclides for which the uncertainty is relatively small. On the other hand, some 

correlation among dose coefficients for different radionuclides is likely and, therefore, adding 

doses from different radionuclides may increase the overall uncertainty more than would 

otherwise be expected. The impact of correlations among dose coefficients of different 

radionuclides requires further study. For this current study, to maximize the uncertainties in 

composite DCFs, the dose coefficients for all alpha emitters are assumed to be fully correlated 

with each other, and those for the beta-gamma emitters are also assumed to be fully correlated 

with each other.

 

4

 The studies on uncertainties in dose coefficients were updated in Kocher, D. C., Trabalka, J.R., and Apostoaei, 

A.J., 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, 

SENES, Oak Ridge, Inc., Oak Ridge, TN and Defense Threat Reduction Agency, Fort Belvior, VA. and will be 

considered during further testing and refinement of internal dose methods. 

97 
The NTPR approach to accounting for uncertainty in DCFs for inhalation and ingestion is to 

develop estimates of such uncertainty that are applicable to all exposure situations of concern. 

This approach should result in uncertainty estimates that do not underestimate the upper bound 

doses for any combination of radionuclides and organ or tissue of concern. Under current 

procedures, a single uncertainty factor of 10 is applied to the deterministic internal doses to most 

organs and tissues from the inhalation or ingestion of any mixture of fission products, activation 

products, and actinide elements (DTRA, 2003). 

For this probabilistic study, NTPR has incorporated DCF uncertainty distributions defined by 

distinct uncertainty factors associated with alpha DCFs and beta-plus-gamma DCFs. An 

uncertainty factor of 10 is used for beta-plus-gamma DCFs for all organs and tissues, which is 

recommended by SENES as the upper bound factor that produces a reasonable estimate of 

uncertainty in the dose coefficients for mixtures of fission and activation products currently 

published by ICRP (Kocher et al., 2006; ICRP, 2002). An uncertainty factor of 15 is used for 

alpha DCFs, based on discussions and recommendations in the 2006 SENES report5

. In 

particular, uncertainties in DCFs for inhalation or ingestion of plutonium, due to uncertainties in 

dosimetric and biokinetic models, should be substantially larger than uncertainties in dose 

coefficients for mixtures of beta/gamma-emitting fission and activation products. This 

conclusion is based mainly on two considerations: (1) the greater importance of uncertainties in 

dosimetric models for alpha-emitting radionuclides in some organs or tissues (e.g., the skeleton 

and gastro-intestinal (GI) tract) compared with beta-gamma emitters and (2) the larger 

uncertainty in absorption of plutonium in the GI tract compared with uncertainties in GI-tract 

absorption for many other fission and activation products (Eckerman et al., 1999; Harrison et al., 

2001). Kocher et al. (2006) also note that estimated uncertainties in dose or risk coefficients for 

plutonium are among the highest for any radionuclide. Finally, two additional considerations 

from the SENES report support an uncertainty factor of 15 for alpha DCFs: (1) an estimated 

uncertainty factor greater than 10 in the risk coefficient for plutonium ingestion in USEPA’s 

Federal Guidance (USEPA, 1997), and (2) an assumption that uncertainties in deposition of 

plutonium at minor sites should be significant, given the low concentrations of plutonium in soft 

tissues other than the liver and the apparent variability in those concentrations among different 

soft tissues (Kocher et al., 2006). 

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

multiplying the unbiased DCFs (see below for a discussion of bias adjustments) by values 

randomly drawn from lognormal distributions with geometric means equal to 1, and geometric 

standard deviations such that the ratios of 95th percentile to the geometric means are 15 for alpha 

DCFs and 10 for beta-plus-gamma DCFs. As noted earlier, the recommended alpha DCF

uncertainty factor was changed from 15 to 30 after completion of the case study analyses 

described in this report. If NTPR adopts the revised uncertainty factor, the probabilistic internal 

organ alpha doses and uncertainties will be impacted. The impacts will vary somewhat 

depending on organ, scenario, and correlations between doses, but some generalizations about 

these impacts can be predicted as described below. 

 

5

 The alpha DCF uncertainty factor was changed from 15 to 30 in an update to Kocher et al. (2006) that was 

published after the completion of the analyses described in this report as Kocher, D. C., Trabalka, J.R., and 

Apostoaei, A.J., 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, 

SENES, Oak Ridge, Inc., Oak Ridge, TN and Defense Threat Reduction Agency, Fort Belvior, VA. 

98 
 The geometric means of the individual exposure pathways and the total alpha doses will not 

change. 

 The arithmetic means and the 95th percentiles of the individual exposure pathways and total 

alpha doses will increase by factors of roughly 2×; increases in total alpha doses will be 

driven by the dominant exposure pathway. 

 Because of the increase in 95th percentile doses, the spreads of the distributions of doses will 

increase by roughly two times. As a measure of the spread, the uncertainty factors (ratios of 

95th percentiles to geometric means) will increase accordingly with increases in 95th

percentiles. 

 Because of the increase in 95th percentile doses, the ratios of deterministic upper bound to the 

95th percentile doses will decrease accordingly with increases in 95th percentiles. 

Specific details about these impacts and their implications for implementing a probabilistic 

approach to NTPR radiation dose assessments will need to be assessed in future technical efforts. 

4.2.8.3 Maximum Dose Bias in Inhalation DCFs 

As discussed in Section 4.2.8.1, a “maximum dose” strategy was employed in developing 

inhalation DCFs for use in NTPR deterministic internal dose calculations. This strategy was 

implemented through the selection of the DCF, for the absorption type applicable to the oxide 

form of each radionuclide, from among those for 1, 3, 5, and 10- μm AMAD particle size 

distributions that provide the highest dose to the organ of interest. The composite DCFs derived 

in this manner are inherently high-sided. In order to produce inhalation DCFs for use in the 

uncertainty analysis, the bias introduced by this procedure must be removed. The amount of bias 

and method of removal were investigated (McKenzie-Carter, 2009). This research focused on 

two representative shots: BADGER, a 23-kiloton shot detonated atop a 300-foot tower at 

Operation UPSHOT-KNOTHOLE (1953) at the Nevada Test Site (NTS), and TEWA, a 

5-megaton shot detonated on a barge at Bikini Atoll during Operation REDWING (1956). For 

each shot and organ, the differences between the maximum dose DCF (DCFmax) and the average 

of the DCFs for the four particle size classes (DCFavg) were computed separately for alpha and 

beta-plus-gamma radiations for all times post-detonation and were used to construct bias factors 

BF, defined as 

avg

Max

DCF

DCF

BF  . (4-15) 

Similar patterns of bias for both alpha and beta-plus-gamma DCFs are observed for Shots 

BADGER and TEWA. For all organs except the ET region, alpha bias factors were closely 

grouped at values between 1.25 to 1.30. For the ET region, the alpha bias factors were slightly 

lower, with consistent values at about 1.15 for all post-detonation times. For beta-plus-gamma 

DCFs, bias factors for lung, breast, thymus, adrenals, spleen, liver, and pancreas peak at about 

1.35 to 1.45 at about 4 months post-detonation, while bias factors for all other organs were 

clustered around 1.20 at all times. 

99 
Based on the results described above, bias adjustment factors shown in Table 14 were selected 

for use in removing bias from the DCF values (McKenzie-Carter, 2009). 

Table 14. Organ-Specific Bias Adjustment Factors 

Organ(s) Alpha Radiation 

Beta-PlusGamma 

Radiation 

lung, breast, thymus, adrenals, spleen, liver, 

and pancreas 1.30 1.35 

extra-thoracic region 1.15 1.20 

all FIIDOS organs not listed elsewhere in 

table 1.30 1.20 

Incorporation of these bias factors into the stochastic dose modeling was accomplished according 

to the following equation: 

BF

DCF DCFadj  (4-16) 

where DCFadj is the adjusted (unbiased) shot-specific, time-dependent inhalation DCF

(rem CED rem−1

 film badge dose) 

The adjusted shot-specific, time-dependent inhalation DCFs produced by removal of the 

“maximum dose” bias effect are effectively inhalation DCFs that are the average values over the 

1-, 3-, 5-, and 10-μm sizes. 

4.2.8.4 Summary of Results 

The parameters and uncertainty distributions relevant to the stochastic modeling of DCFs are 

summarized in Table 15. Also indicated are the values used in nominal and deterministic 

analyses. 

4.2.9 Characterization of Descending Fallout 

Special studies were conducted (1) to calculate the fraction of the activity in descending fallout 

(“activity fraction”) that was carried by particles in each of three size classes and (2) to estimate 

the settling velocities in the breathing zone for particles in each size class. These parameters are 

inputs to Equation 3-8 in the calculation of internal dose from inhalation of descending fallout. 

The results of these studies are summarized in this section; details of the analyses leading to 

these results are contained in Weitz (2009f). 

100 
 Table 15. Model Parameters for Dose Conversion Factor Distributions 

Parameter Definition Distribution for 

Uncertainty Analysis 

Nominal Value for 

Central Estimation 

Deterministic 

Analysis 

DCFInhα

DCFIngα

Inhalation and ingestion 

dose conversion factors for 

fallout α radiation 

DCFs calculated with 

FIIDOS multiplied by 

Lognormal 

(GM=1.0, GSD=5.19) 

DCFs calculated with 

FIIDOS 

DCFs calculated 

with FIIDOS 

DCFInhβγ

DCFIngβγ

Inhalation and ingestion 

dose conversion factors for 

fallout β+γ radiation 

DCFs calculated with 

FIIDOS multiplied by 

Lognormal 

(GM=1.0, GSD=4.05) 

DCFs calculated with 

FIIDOS 

DCFs calculated 

with FIIDOS 

Biasα

Biasβγ

Bias factors to adjust highsided inhalation DCF values 

Assumed to be Constant 

(see Table 14) See Table 14 

1.0 

1.0 

4.2.9.1 Activity Fractions 

As discussed above, the inhalation DCFs have been applied previously to all of the activity 

(intensity) associated with descending or resuspended fallout, under the high-sided assumption 

that all radioactive particles have aerodynamic diameters in the range 1–10 μm. (“Aerodynamic 

diameter” is the diameter of a sphere of density 1 g cm−3

 that exhibits the same settling velocity 

as the particle in question.) However, descending fallout generally included particles of nonrespirable and even non-inhalable sizes that may have contained a significant fraction of the total 

fallout radioactivity. A compounding factor is that the activity was distributed non-uniformly 

with particle size (Glasstone and Dolan, 1977; Kellogg et al., 1957). The objectives of this 

special study were (1) to develop a method to estimate activity fractions for specific descending 

fallout exposure scenarios, and (2) to formulate uncertainty distributions for these fractions. The 

particle size classes utilized in this study are defined by the following ranges of aerodynamic 

diameters: 1–10 μm (designated Class 1), 10–20 μm (Class 2), and 20–100 μm (Class 3). 

Particles with aerodynamic diameters larger than 100 μm are generally non-inhalable and thus 

contribute little to internal dose through the inhalation route of entry. The class-specific activity 

fractions, AFi, i = 1, 2, and 3, that appear in the internal dose Equation 3-8 are related to the total 

activity fraction AF100 for sub-100 μm particles by: 

AF100 = AF1 + AF2 + AF3. (4-17) 

A paucity of data exists on particle size distributions and activity fractions for most fallout 

deposition times relevant to the PPG case studies. Although extensive fallout measurements 

were made at Operation REDWING (Triffet and LaRiviere, 1982), collection stations were 

usually located within 10 to 20 nautical miles from surface zero so that most particle size and 

activity distribution data were collected during the first few hours post-detonation. In contrast, 

almost all fallout events relevant to the case studies took place more than 10 hours after 

detonation. It was therefore decided to develop a physics-based, probabilistic fallout deposition 

model that could be benchmarked with the available particle size-activity data at early times and 

then used to characterize the fallout at the later times of interest. The deposition model provides 

estimates of activity fractions for fallout that descended on specific locations (i.e., on residence 

islands and on certain ships) during defined periods of time. Since the locations are fixed, only 

101 
the vertical motion of the fallout particulates is of interest and a one-dimensional equation of 

motion suffices. The formulation of the algorithm, its implementation in Mathcad, sample 

results, and comparison with REDWING measurements are discussed in Weitz (2009f). 

4.2.9.2 Deposition Velocity of Fallout Particles 

“Deposition velocity” is defined here to be the velocity at which fallout particles descend to the 

ground in the breathing zone, which nominally extends from the surface to 1.6 meters above the 

surface. An average deposition velocity is calculated by dividing the initial debris height H by 

the time T it takes a particle to reach the ground. This average is a valid estimate for the larger 

particles whose descent is governed predominantly by gravity and atmospheric drag. However, 

some of the smaller particles become entrained in vertical air currents and carried downward at 

rates determined by the vertical wind velocities, which may be much different than the average 

descent rate of H/T. The vertical component of the air current must vanish near the ground 

because the Earth serves as a boundary in that direction. Therefore, the velocity of small 

particles entrained in the air can slow significantly as they approach and enter the breathing zone. 

A formulation based on the Stokes equation was utilized to estimate these small-particle 

deposition velocities, as discussed in Weitz (2009f). 

4.2.9.3 Results and Discussion 

In the present approach, the activity fractions AFi in particle size classes 1, 2, and 3 are derived 

as follows. First, the total activity fraction AF100 for the combined class consisting of all 

particles with aerodynamic diameters less than 100 μm is determined by randomly drawing from 

the relevant event-specific triangular distribution defined Table 16 in terms of its minimum, 

mode, and maximum values. Derivation of this table is discussed in Weitz (2009f). Second, the 

fractions of AF100 attributable to the three size classes, denoted as frac1, frac2, and frac3, are 

determined by drawing frac1 and frac2 from the respective triangular distributions defined in 

Table 17 and then using the relation 

 frac3 = 1 – frac1 – frac2 (4-18) 

Finally, the activity fraction for the i

th size class is calculated from 

AFi = fraci ·AF100 (4-19) 

(Within the Mathcad program, the activity fractions are referred to as "activity adjustment 

factors" and denoted by RNA.) 

102 
Table 16. Triangular Distributions of Total Activity Fraction (AF100) for PPG Case Study 

Units 

Operation 

Unit Event 

Deposition Interval

(H+hr) Tp (H+hr) Minimum Peak Maximum

CASTLE

BRAVO H+9–H+16 16 0.071 0.391 0.770 

ROMEO 1 H+10.5–H+14.5 14.5 0.132 0.462 0.812 

ROMEO2 H+39–H+77.5 77.5 1.000 1.000 1.000 

Enewetak Island 

NECTAR H+12–H+14.7 14.7 0.543 0.781 0.971 

REDWING

ZUNI H+8–H+18 11 0.094 0.280 0.565 

MOHAWK H+2–H+3 3 0.013 0.070 0.140 

APACHE H+18–H+22 21 0.939 0.973 1.000 

Enewetak Island 

TEWA H+10–H+26 25 0.403 0.572 0.732 

ZUNI H+27–H+40 37 1.000 1.000 1.000 

FLATHEAD H+30–H+44 44 1.000 1.000 1.000 

NAVAJO H+18–H+22 22 1.000 1.000 1.000 

USS ESTES 

TEWA H+18 18 0.396 0.587 0.801 

HARDTACK I

FIR/KOA H+45–H+58 58 1.000 1.000 1.000 

REDWOOD H+10.5–H+13.5 12 0.609 0.787 0.971 

Enewetak Island 

OAK H+14 14 0.469 0.732 0.975 

FIR/KOA H+45–H+58 58 1.000 1.000 1.000 

REDWOOD H+10.5–H+16.5 16.5 0.624 0.816 0.986 

USS BOXER 

OAK H+12.25–H+14 14 0.469 0.732 0.975 

The following class-specific average settling velocities were obtained using the methodology 

described in Weitz (2009f): 13 cm s−1

 (V3) for Class 3 particles (20-100 μm), 0.83 cm s−1 (V2) for 

Class 2 particles (10-20 μm), and 0.22 cm s−1

 (V1) for Class 1 particles (1-10 μm). The 

uncertainty of the settling velocity for each size class is modeled with a log-triangular 

distribution, that is, a distribution in which the natural logarithm of velocity is assumed to obey a 

triangular distribution. The parameters defining these distributions are provided in Table 17, 

which summarizes the uncertainty distributions relevant to the probabilistic characterization of 

descending fallout. Also indicated are the values used in nominal and deterministic analyses. 

103 
Table 17. Model Parameters for Activity Fraction and Settling Velocity 

Parameter Definition Distribution for 

Uncertainty Analysis 

Nominal Value for 

Central Estimation 

Deterministic 

Analysis 

AF100

Fraction of all activity 

carried to surface on 

particles with aerodynamic 

diameter <100 μm 

Triangular 

min, mode, max 

(see Table 16) 

Mode of distributions 

(see Table 16) 

1.0 

frac1 

frac2

Fraction of AF100 carried 

by Class 1 particles 

by Class 2 particles 

Triangular 

min, mode, max 

0, 0.00136, 0.01 

0, 0.025, 0.1 

Mode of distributions 

0.00136† 

0.025†

1.0 

0.0 

V1

V2 

V3

Particle settling velocities 

Class 1 particles 

Class 2 particles 

Class 3 particles 

Log-triangular 

min, mode, max (cm s−1) 

0.22/2, 0.22, 27.8 

0.83/2, 0.83, 27.8 

13.0/2, 13.0, 27.8 

Mode of distributions 

0.22 cm s−1

0.83 cm s−1 

13.0 cm s−1

106

(cm) / T(sec) 

†

For Shots FLATHEAD and NAVAJO at Operation REDWING on the USS ESTES frac1 and frac2 are 

set to 0.0. 

4.2.10 Internal Deposition Fraction Adjustment 

Calculation of internal dose is based on the patterns of internal deposition fractions—designated 

Ri in Equation 3-8. These are defined as the fractions of inhaled particles in a given size class 

that deposit in the thoracic airway and in the posterior extra-thoracic airway. An inherent 

assumption of the NTPR deterministic inhalation dose models is that all of the fallout is in the 

size range 1–10 μm. However, the use of this assumption for all scenarios is undoubtedly highsided, especially for descending fallout, which likely contains larger particles that are less likely 

to deposit in the thoracic airway. All activity associated with particles of size 1–10 μm is 

considered to apply for inhalation dose conversion factors. However, adjustments to the 

descending inhalation dose conversion factors were developed to provide a more credible 

accounting of deposition in the respiratory tract for larger particles in the size classes 2 

(10–20 μm) and 3 (20–100 μm). 

4.2.10.1 Estimation of Internal Deposition Fractions 

Based on the ICRP 66 human respiratory tract model (HRTM) (ICRP, 1994), for particles 20 μm 

or larger, about half of the available inhaled activity is deposited in the ET region and about half 

of that is subsequently ingested. Thus, one approach to adjusting internal dose calculations for 

large particle exposures would be to use ingestion DCFs and adjust them by a factor of about 

0.25. However, such an approach would produce averaged results with their own associated 

104 
uncertainty and would involve reworking all of the NTPR internal dose calculations to be based 

on activity intake instead of being based on film badge equivalent dose. Because of resource 

constraints, that approach was judged to be impractical. 

The approach used for the NTPR uncertainty study is based on data from Bolch et al. (2001), 

which describes a systematic review of the deposition component within the ICRP 66 HRTM in 

which probability density functions were assigned to all input parameters. These distributions 

were subsequently incorporated within a computer code LUDUC (LUng Dose Uncertainty Code) 

in which Latin hypercube sampling techniques were used to generate multiple trials for all of the 

model parameters needed to assess particle deposition within the ET (anterior and posterior), 

bronchial, bronchiolar, and alveolar-interstitial regions of the ICRP 66 HRTM. Particle 

deposition values for the various trial simulations were shown to be well described by lognormal 

probability distributions. 

Using the data in Table 7 of Bolch et al. (2001), a Mathcad model was constructed to generate 

deposition fraction distributions for each of the lung regions based on those data. The 

distributions were then combined to estimate total respiratory tract deposition for a given particle 

size class. Effective filtration in each region is included (inhalation and exhalation are not 

modeled separately) and the model limits total deposition to unity. Region ET1 is considered for 

filtration but not for total deposition because material deposited in that region is cleared quickly 

externally (e.g., nose blowing). A second Mathcad model was used to calculate geometric mean 

deposition fractions and associated geometric standard deviation for selected ranges of particle 

size classes in respirable and non-respirable regions of the respiratory tract. For the purposes of 

this uncertainty study, particle size classes of 10–20 μm and 20–100 μm were explicitly 

considered, in addition to the 1–10 μm size class. Using results reported in Bolch, the 

“respirable” fraction, defined as the fraction of each size class depositing in the thoracic airways 

(bronchial (BB), bronchiolar (bb), and the alveolar-interstitial (AI) regions, and the “nonrespirable” fraction, defined as the fraction of each size class depositing in the posterior extrathoracic region (ET2), were determined. The non-respirable (ET2) fraction is essentially cleared 

entirely to the digestive tract in a short time (the mean retention time in ET2 prior to swallowing 

is about 15 minutes) (ICRP, 1994; McKenzie-Carter and Stiver, 2009). Because the 

nonrespirable fraction is defined here as the fraction depositing in ET2, ingestion DCFs can be 

applied to the entire non-respirable fraction, as numerically defined in the following section. 

4.2.10.2 Results and Discussion 

Lognormal distributions of respirable and non-respirable internal deposition fractions, derived on 

the basis of the Bolch et al. (2001) results in McKenzie-Carter and Stiver (2009), are listed in 

Table 18. These distributions corresponding to the terms Ri and NRi of Equation 3-8 are 

designated by their Mathcad representations RNDRes1, RNDRes2 and RNDRes3 for the respirable 

portions of size classes 1, 2 and 3, and by RNDNonRes1, RNDNonRes2 and RNDNonRes3 for the 

respective non-respirable portions. These multiplicative parameters are used only in descending 

fallout scenarios of probabilistic and nominal value assessments; they are not used in 

deterministic analyses because of the assumption that all radioactive particles have aerodynamic 

diameters in the range of 1–10 μm. 

RNDRes1 and RNDNonRes1 depend on the age of the individual, level of activity, whether breathing 

from the nose, the mouth, or both, and ventilation rate (Bolch et al. 2001). Assuming RNDRes1 is 

105 
set to 1.0 and RNDNonRes1 is set equal to 0.0 simplifies Equation 3-8 to the form used in the six 

case studies discussed in Section 5. Limited tests with both RNDRes1 set to 1.0 and RNDNonRes1

set to 0.0 show that these assumed values estimate total internal doses that are less than 4 percent 

smaller than the doses for the organs (LLI wall, lungs, and thyroid) assessed in Case Study #6 for 

the unit at Enewetak Atoll during Operation CASTLE discussed in Section 5. Because values 

for RNDRes1 and RNDNonRes1 were not evaluated for this study, the simplified formulation was 

used in all case studies discussed in Section 5. However, better estimates for these parameters 

should be developed for future case studies or radiation dose assessments. 

Table 18. Model Parameters for Internal Deposition Fractions 

Parameter Definition Distribution for 

Uncertainty Analysis 

Nominal Value for 

Central Estimation 

Deterministic 

Analysis 

RNDRes1

RNDRes2

RNDRes3

Respirable deposition 

fractions 

Class 1 particles 

Class 2 particles 

Class 3 particles 

Lognormal 

GM, GSD 

1.0 (assumed constant) 

0.0056, 1.744 

0.001, 1.65 

Geometric Mean 

1.0 (assumed constant) 

0.0056 

0.001 

n/a 

RNDNonRes1

RNDNonRes2

RNDNonRes3

Non-Respirable deposition 

fractions 

Class 1 particles 

Class 2 particles 

Class 3 particles 

Lognormal 

GM, GSD 

0.0 (assumed constant) 

0.363, 1.106 

0.285, 1.185 

Geometric Mean 

0.0 (assumed constant) 

0.363 

0.285 

n/a 

4.2.11 Sources of Uncertainty When Estimating Radiation Intensity from Measured 

Intensities and Iso-Intensity Maps 

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

(location), the related uncertainty is comprised of two components. The first component is the 

uncertainty due to errors introduced during the actual intensity measurement and when maps are 

created from a discrete and often sparse set of point observation measurements. 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. 

4.2.11.1 Uncertainty in Recorded Intensity Data 

In the case of iso-intensity maps used in dose assessment for atmospheric nuclear test 

participants, some uncertainties are hard to quantify because the original survey measurements 

and even processed data are unavailable. When assessing uncertainty, an analyst uses all 

available information to estimate and bound its distribution. In doing so, it is important to 

consider essential factors that have the potential to affect the reliability and confidence in the 

recorded or estimated data. These factors include: 

 Documentation of data collection plans and procedures. 

 Conditions of data collection. 

106 
 Accuracy and calibration of measuring instruments. 

 Experience and training of field monitors. 

 Availability of raw measurements versus processed or graphed data. 

 Processing of raw measurements. 

 Methods used to process and transform raw measurements. 

 Quality assurance and control in the collection, recording and reporting of raw and processed 

data. 

In many cases, uncertainties have to be estimated through subjective judgment based on an 

analyst’s confidence in the documentation, understanding of the impact of the sources of errors 

listed above, and the levels of related uncertainties. 

4.2.11.2 Uncertainties Due to Creating Iso-Intensity Maps from Survey Data 

The main sources of error that affect the accuracy of iso-intensity maps, which are due to data 

collection and plotting of such maps, mainly involve (Stearns, 1968): 1) measurements and data 

processing, 2) simultaneity of measurements, and 3) data interpolation. Interpolation here refers 

to the determination and positioning of iso-intensity values to create iso-intensity contour lines 

based on the measured values at the observation points. Point value interpolation is discussed in 

the following subsection. 

Measurement and Data Processing

Iso-intensity maps are produced from the measurement of three types of variables: 

 Quantity being observed (i.e., radiation intensity). 

 Time of the observation. 

 Position of the observation, which involves the measurement of one or more geographic 

coordinates. 

Measurement of each of the above types of variables is impacted by one or more of the following 

sources of errors: 

 Instrument precision and calibration. 

 Operator manipulation during observation and data recording, including verbal and radiotransmitted communication of data in some cases. 

 Reduction, correction, scaling and other pre-processing of data before being documented in 

data logs or reports. 

Simultaneity of Measurements

The lack of simultaneity of observations of a quantity that varies in time results in uncertainties 

that impact iso-intensity maps. These uncertainties may be reduced through accurate estimation 

107 
of the time dependency of the measured variable and processing the observed data to a reference 

time map. In the case of radiation intensity maps used in NTPR, knowledge of the time decay 

functions was generally used to create iso-intensity maps for the reference time of one hour after 

a detonation (H+1). Simultaneity uncertainties are also called synopticity uncertainties. 

Interpolation (when producing Contour Lines from Observation Data)

Many interpolation schemes have been used to create iso-line maps from scattered data points. 

These can range in sophistication from manual linear interpolation between pairs of observation 

points to geostatistical techniques that allow estimation of interpolation uncertainties under 

certain assumptions about the quantity being mapped (Chilès and Delfiner, 1999). Although 

automated mapping techniques have been developed and used widely, human judgment remains 

critical in specifying such assumptions and making decisions concerning the types and 

parameters of the interpolating functions employed, as well as the determination of 

discontinuities and boundary conditions. The interpolation scheme that NTPR used to create isointensity contour maps for most NTS shots is described in (Goetz et al., 1980). Many of the 

initial and follow-up survey maps appear to have been drawn by hand. 

Most mapping interpolations rely on sets of data points with an irregular layout also termed 

scatter points. In such instances, most automated contour mapping is conducted in three steps. 

First, pre-processed observation data is used to interpolate values at closely-spaced points (or 

cells) on a regular grid. This step is appropriately called gridding. Second, the discrete location 

of iso-values is estimated along the grid lines using the regularly-spaced interpolation points and 

their corresponding interpolated values. Last, smooth contouring functions are used to connect 

iso-values. 

Each of the aforementioned three steps requires input parameters that an operator supplies to 

guide the automated mapping. The discrete point data (either original or gridded) do not in and 

of themselves lead to a unique set of mapped contours (Chilès and Delfiner, 1999). A trial and 

error iterative process is usually followed to create the “best estimate” of a contour map through 

knowledge of the physical characteristics of the mapped variable, the distribution of collected 

data, and other related conditions. 

4.2.11.3 Uncertainties from Estimating Point Values of a Variable Using an 

Iso-intensity Map 

Estimating point values from a digital map can be rendered highly precise, given the 

sophistication of modern computer-aided interpolation. This is not the case when using 

hardcopy iso-intensity contour maps. Manually estimating discrete point values from a hardcopy 

iso-intensity contour map introduces several types of potential errors in the estimated value at 

any particular location. Additional uncertainty in the final point estimate may result from one or 

more of the following sources of error: 

 Scale of map and distance between contour lines. 

 Thickness of contour iso-lines. 

 Point positioning and measurement of distance on a map. 

108 
 Distortion from duplication and printing. 

 Interpolation method (linear, logarithmic, other) and relevance to underlying variable 

gradients. 

 Eye-balling estimates versus calculated interpolation. 

 Extrapolation outside of contours, especially where high gradients are observed. 

Each of these sources of uncertainty is in addition to those inherent in making the map and adds 

to the uncertainty in the final estimate at the location of interest. Some uncertainties, such as 

those from positioning or measuring distances on the map, can be minimized through use of 

proper procedures. Others, such as those due to distortion and thickness of contour lines, are 

inherent to the map used and cannot be reduced. 

4.2.11.4 Guidelines for Selecting Uncertainty Factors for Point Estimates Derived from 

Iso-Intensity Data and Contour Maps 

Each source of error related to the use of iso-intensity data and maps in determining point 

estimates in space and time discussed above contributes to the overall uncertainty of the final 

mapped contour lines or iso-lines and in the subsequent estimation of point values. The relative 

importance of each source of uncertainty should be assessed and accounted for in creating a basis 

for the overall uncertainty distributions of the mapped variable and point estimates. 

The guidelines in Table 19 provide ranges of uncertainty factors that are based on the various 

sources of uncertainties and their cumulative effects (Chehata, 2009). The ranges were 

developed based on the collective experience and expertise of radiation analysts who regularly 

used NTPR iso-intensity maps, NCRP Report 158 (NCRP, 2007), and experience using 

geostatistics in other fields of science (Chehata et al., 2007). 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. As discussed 

elsewhere in this report, the uncertainty factor is defined as the ratio of the 95th percentile to the 

central estimate of the variable distribution, generally the mean, the geometric mean, the median 

or the mode. As defined, the uncertainty factor is a dimensionless quantity to be used as a 

multiplier on the estimated central value of radiation intensity. 

109 
Table 19. 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. 

110 
4.2.12 Incidental Ingestion of Contaminated Soil and Dust 

4.2.12.1 Soil Ingestion Rate 

A literature review was conducted to determine rates of incidental ingestion of potentially 

contaminated soil and dust that can be used in internal dose assessment for atmospheric nuclear 

test participants. The review examined guidelines mainly from the USEPA and the USACHPPM, 

which are agencies with major roles in environmental health protection programs for the general 

public and the military. 

Information compiled in USEPA (1997, 2001 and 2002) and the USACHPPM (2003), and 

studies cited therein, provide the basis for estimating rates of incidental ingestion of soil and dust 

for atmospheric nuclear test participants. The estimated maximum incidental ingestion rate is 

500 mg day−1

 (Chehata and Stiver, 2009). Mean ingestion rates for long-term exposures are in 

the range of 50 to 100 mg day−1

. Proposed rates for children are not applicable for NTPR 

personnel, as children ingest higher quantities of soil when mouthing objects and hands while 

playing outside and eating dirt. 

Based on this investigation, the rate of incidental soil ingestion for NTPR personnel assumed to 

have been outdoors part of the day and inside tents or temporary buildings the rest of the day, 

varies between 10 and 500 mg day−1

, with a central estimate of about 50 to 100 mg day−1. In the 

current study, a nominal value of 100 mg day−1

 was selected. For uncertainty analyses, the 

distribution of incidental ingestion rates is assumed to be best described by a skewed triangular 

distribution with a peak value of 100 mg day−1

 and bounds of 10 and 500 mg day−1. A more 

precise distribution is not warranted due to a lack of data. Given the low doses obtained when the 

highest rates were used in actual internal dose estimates (Chehata and Stiver, 2009), it became 

clear that the dose contribution to internal organs and tissues from the incidental ingestion 

pathway are expected to be relatively small. 

4.2.12.2 Soil Density 

The estimation of internal doses using measurements of activity on the ground requires 

knowledge of the bulk density of soil. At NTS, surface soils are characterized by being 

moderately to poorly sorted sand to silty loam. These soils have a bulk density that ranges from 

1.3 to 1.6 g cm−3

 with an average of 1.45 g cm−3 (Hillel, 1980). Soil density at the PPG 

residence islands would be slightly higher but within a similar range. A symmetrical triangular 

or a uniform probability distribution can be used unless site-specific data supports another type 

of distribution. In this study, a symmetric triangular distribution was used in all land-based 

scenario case studies. 

4.3 Dependencies and Correlations between Model Input Parameters 

The distributions and sensitivity to model parameters of the reconstructed doses for the six case 

studies were estimated using probabilistically-based Monte Carlo simulation techniques. Model 

parameter values were randomly selected from each of their distributions. There are 54 explicit 

input parameters used in the six case studies, which have associated uncertainty distributions. To 

better understand and interpret the results of the uncertainty analyses, known or potential 

111 
correlations among input parameters were qualitatively examined and are summarized in this 

section. Two types of correlations were considered: correlations among different parameters and 

those from shot to shot for the same parameter. 

Five of the explicit input parameters were not varied for any case study group because they were 

known to a high enough degree of certainty not to have an impact on the overall uncertainty of 

the calculated total doses. The remaining 49 input parameters are impacted by both uncertainty 

and variability, and were assigned uncertainty distributions based on experimental, theoretical, or 

reasoned estimates. A thorough discussion among radiation analysts and peers led to choosing 

these 49, which with three exceptions, were only weakly or not correlated to each other. 

Therefore, it was assumed that parameter-to-parameter correlations were zero for the 46 model 

parameters. The three exceptions are the fallout intensity distribution pairs for both island and 

ship case studies. These are fully correlated because the same fallout intensity is used for both 

the external and internal dose models in a single Monte Carlo history. The other exception is the 

breathing rate, which combines weighted distributions from two sub-input parameters, the 

activity level and metabolic rate as described earlier in this section. 

Of the 46 independent parameters, not all were used in each case study. For example, for the 

case study groups that participated on Enewetak Island, typically 9 and 17 independent input 

parameters were varied to estimate external and internal doses, respectively. For case study units 

that were aboard a ship, typically 10 and 16 independent parameters were varied for the 

calculation of external and internal doses, respectively. 

External dose inputs for land-based personnel are the fraction of time outside, fraction of inside 

time in a tent, protection factors for tent and building, intensity distribution outside, near a tent 

and near a building, decay rate, and errors resulting from measured intensity data. Ship-based 

external dose inputs are the fraction of time topside, protection factors for work and sleeping 

areas, intensity distribution of fallout, which affects topside, work and sleeping areas, decay rate, 

and errors resulting from measured intensity data. 

Internal dose input parameters are dose conversion factors for α and β + γ radiation, breathing 

rate, a number of respirable and non-respirable deposition fractions, multiple activity adjustment 

factors and particle settling velocity. Additionally, land-based dose models include the timedependent resuspension factor and ship-based models comprise the gamma source modification 

factor and ship resuspension factors, which are treated differently from those for land. 

For some case studies, additional parameters were varied to simulate an uncertainty on arrival 

and departure time, end of film badge exposure dates, and proportion of debris cloud mixing. 

For the NTS-based case study additional sources of variation and uncertainty include the use of 

iso-intensity contour map for point estimate of exposure rates, troop maneuver start time, march 

rate, linger time when not maneuvering, and adjusted resuspension factors in the precursor6

 and 

blast-wave regions. 

 

6

 The term “precursor” was changed to “thermal pulse” in a revision to Kocher et al. recently published as Kocher, 

D. C., Trabalka, J.R., and Apostoaei, A.J., 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, SENES, Oak Ridge, Inc., Oak Ridge, TN and Defense Threat Reduction Agency, Fort 

Belvior, VA., however it is retained in this report. 

112 
Most case study exposures extended over a long period, some the entire length of an operation. 

For these, fallout was deposited from several shots or from several deposition events from a 

single shot. So the question was for a single Monte Carlo history, does an input parameter value 

remain the same for exposure to all fallout throughout the period of presence or does it randomly 

vary within its distribution for each day or each shot? After a thorough evaluation, a matrix was 

compiled to examine each input parameter and to state why it might change or stay the same for 

each Monte Carlo history. While dose input parameters have varying degrees of autocorrelation 

from shot-to-shot, it was decided to assume either full correlation or weak to no correlation. 

A complete matrix showing model input parameters, correlation state, and basis for each 

correlation decision is presented in Table G-1 of Appendix G. The parameter in each row is 

uncorrelated to the parameter in any other row, but for the three exceptions mentioned earlier. 

Parameters shown together in the same row, such as DCFinh and DCFing, are selected from a 

single random number draw and are fully correlated to each other. Their absolute distributions 

differ, but the values picked for a given history are at the same cumulative probability. For each 

case study, model input parameters and distributions with their nominal and NTPR high-sided 

deterministic values are given in the respective appendices. 

When different components of dose depend on a common input parameter, they will be 

correlated to some extent with each other. An example would be the breathing rate, which is an 

input parameter for both descending and resuspended internal dose, and deviates from the 

nominal breathing rate the same for the entire operation for a given Monte Carlo history. A 

lower than nominal breathing rate would tend to result in a lower internal dose for all shots for 

all inhalation pathways. However, because each internal pathway and shot depends on other 

input parameters, which may be independent from each other, there is only partial correlation 

between inhalation dose components. 

The list of parameters in Appendix G does not include dependent variables, such as the fraction 

of time inside shielding, which is one minus the fraction of time outside. Because this parameter 

is derived within the Monte Carlo simulation, it does have a negative correlation to the time 

outside. These derived parameter distributions and their correlations are not listed in the tables. 

An example is provided here to illustrate the evaluation of shot-to-shot correlation for a single 

parameter. Consider the parameter Fos defining the fraction of time each day that an individual 

spent outdoors on an island, i.e., not in a tent or a building. The uncertainty distribution for Fos is 

such that a given participant could have spent a minimum of 2, a maximum of 16, with most 

likely 8 hours outdoors each day. A triangular distribution was employed to describe this 

parameter mathematically. Because most personnel on islands participated in essentially the 

same activities from day-to-day and from shot-to-shot, it is reasoned that the value of Fos for a 

particular participant is likely the same throughout the operation for a single Monte Carlo 

history. Therefore, an individual’s daily time outside after one shot is fully correlated with his 

daily time outside after another shot. For each Monte Carlo history, the amount of time outdoors 

is drawn once and utilized for all days following all events from all shots. For each succeeding 

history a new fraction of time outdoors is randomly selected. 

113 
5 CASE STUDY RESULTS 

Six case studies to test methods discussed in Sections 3 and 4 were conducted successfully and 

provide relevant results that identify limitations of the methods, identify areas of further study 

and confirm important approaches to conducting radiation dose assessments that include full 

uncertainty analyses. The studies were conducted for representative units selected on the basis of 

their ability to satisfy some or all of the following criteria that were identified in a pilot study. 

 Adequate number of participants within the group for statistical analysis of dosimetry and 

comparison to corresponding probabilistic analysis of reconstructed doses. 

 Cohesive group participants’ activities that were performed in the radiation environment. 

 Well-characterized radiation environment with adequately documented data or surrogate 

information that can be used to make best estimates of input parameters to the dose models. 

 Reliable individual film badge dosimetry. 

The six units comprise five from the PPG and one from the NTS and are: 

 7126th Army Unit (AU) Headquarters (HQ) Detachment, Enewetak Atoll, Operation 

REDWING (1956) 

 Army Unit Administrative and Operations Detachments, Enewetak Atoll, Operation 

HARDTACK I (1958) 

 4th Marine Corps Provisional Atomic Exercise Brigade (MCPAEB) Maneuver at Shot 

HOOD, Operation PLUMBBOB (1957) 

 USS ESTES (AGC 12), Operation REDWING (1956) 

 USS BOXER (CVS 21), Operation HARDTACK I (1958) 

 Army Personnel, Enewetak Atoll, Operation CASTLE (1954) 

Based on input from external review boards and DTRA, probabilistic uncertainty analysis 

methods include internal dose assessments in addition to the external dose methods developed 

during in the initial pilot phase, which were further refined in this study. Probability distribution 

functions were generated for the uncertainty parameters as discussed in Section 4. These were 

incorporated into Monte Carlo simulation models for each of the six study groups. Mean and 

upper bound internal doses were calculated for thyroid, lung, and lower large intestine to provide 

example analyses for several organs. 

Sections 5.1 through 5.6 provide summaries of the scenarios, relevant film badge and other 

radiation data for each case, and detailed discussions of the results. Additional details about each 

unit’s activities, assumptions about scenario parameters, and uncertainty distributions used in the 

probabilistic analysis are provided in Appendices A–F. 

For each study unit, a summary of external dose is provided as follows: 

 Film badge doses (if available): unbiased mean and 95th percentile of the distribution of 

readings. 

 Monte Carlo doses: arithmetic mean, standard deviation, and the 95th percentile dose. 

114 
 Deterministic doses: dose and upper bound based on the upper bound multiplier of 3. 

 The ratio of the deterministic upper bound dose to the 95th percentile dose. 

The CEDs from internally-deposited radionuclides are reported separately for alpha and betaplus-gamma emitters. For CEDs from Monte Carlo simulations, all of which were lognormally 

distributed, geometric mean, geometric standard deviation and 95th percentile dose are reported 

for each of the three organs mentioned above. Finally, the geometric mean and 95th percentile 

CEDs from Monte Carlo simulations are compared to the deterministic CEDs and upper bounds, 

respectively. 

5.1 Case Study #1: Operation REDWING (1956), 7126th Army Unit Headquarters (HQ) 

Detachment, Enewetak Atoll 

5.1.1 Case Description and Cohort Participation Scenario 

The 7126th AU provided most of the personnel for the Army Task Group (TG), designated 

TG 7.2. It was the permanent garrison force at Enewetak Island between Operations CASTLE 

and REDWING. Except for its military police detachment and several mail clerks on Eneu and 

Parry Islands, the 7126th AU was stationed on Enewetak Island. TG 7.2 was, in effect, a 

housekeeping unit, providing garrison and support elements for the joint task force in the PPG 

(Bruce-Henderson et al., 1982). To accommodate the buildup to Operation REDWING's 

operational phase, the 7126th AU was reorganized into the following four detachments: 

Headquarters (HQ), Service, Transportation, and Military Police. The HQ Detachment, 

consisting of 39 officers and 348 enlisted personnel, was stationed on Enewetak Island during 

Operation REDWING. (Bruce-Henderson et al., 1982). 

Assigned personnel arrived at Enewetak Island prior to the first nuclear detonation of the series. 

By the nature of their duties, it is likely that most HQ Detachment personnel remained on the 

island continuously, or nearly so, throughout the operation. Further details of this analysis are 

included in Appendix A. 

5.1.2 Available Dosimetry 

Complete records of film badge results are available for the HQ Detachment. Most personnel in 

the unit were issued three consecutive permanent film badge dosimeters during their stay in the 

test area, which covered a total period extending from mid-April to early August 1956. 

However, most film badges issued for periods of 4 weeks or more at Operation REDWING were 

damaged by the high heat and humidity in the test area (NRC, 1989), which resulted in 

overstated readings. Thus, most of the badges for the unit were not suitable as a benchmark for 

comparison with reconstructed doses. It was, therefore, necessary to identify a set of badges 

worn for a shorter period and for which previous analysis had demonstrated the integrity of the 

readings. Based on previous experience in identifying damaged dosimeter films and a review of 

the Operation REDWING dosimetry database, a group of film badge doses for this unit was 

analyzed for a period extending from July 11 to August 3, 1956. As a result, a set of 323 badges 

was selected. Bias was removed from the film badge readings based on guidance on film badge 

dosimetry (NRC, 1989). The average unbiased film badge reading for the distribution is 2.9 rem, 

115 
with a standard deviation of 0.61 rem. Figure A-1 of Appendix A displays the distribution of 

film badge readings (adjusted for bias) for the HQ Detachment. 

5.1.3 External Dose 

External gamma dose reconstruction for personnel stationed on Enewetak Island during 

Operation REDWING was accomplished by incorporating uncertainty distributions for various 

parameters into the model discussed in Section 3. This model incorporates the fallout-induced 

radiation environments discussed in detail in Appendix A, and the fallout intensity decay model 

and effects of shielding as discussed in Section 3. 

5.1.3.1 Exposure Pathways 

The only sources of potential external radiation exposure for personnel stationed at Enewetak 

Atoll during Operation REDWING were residual gamma radiation from fallout due to Shots 

ZUNI, MOHAWK, APACHE, and TEWA. See Appendix A for additional details. 

5.1.3.2 Assumptions and Parameter Uncertainty 

The following specific uncertainty distributions, discussed in Section 4, were used in the 

uncertainty analysis for external gamma dose calculations: 

 Amount of time spent outdoors each day. 

 Fraction of time spent indoors that was spent in a tent-type structure or in a building. 

 Protection factors for tents and buildings. 

 Distributions of fallout intensity at locations on the island where a veteran most likely spent 

time, i.e., during time spent outdoors, location of the tent for the time spent indoors in a tent, 

and location of a building for the time spent indoors in a building. 

 Measurement error associated with intensity measurements on the island. 

 Uncertainty in shot-specific radiological decay functions. 

The types of distributions, means, and confidence intervals for each of these distributions are 

shown in Table A-4 of Appendix A. The values used in the deterministic analysis that generated 

the deterministic doses reported for the film badge period of July 11 to August 3, 1956, are also 

summarized in Table A-4 of Appendix A. 

5.1.3.3 Results and Discussion 

The results of the external gamma dose deterministic analysis and the probabilistic analysis are 

shown in Table 20. These results indicate that the probabilistic analysis yields mean doses that 

are similar to the deterministic dose, and that the 95th percentile dose from the probabilistic 

analysis is lower than the upper-bound deterministic dose. In addition, the probabilistic mean 

dose is approximately 25 percent higher than the mean film badge dose, just inside the standard 

deviation of the film badge doses for this study group. Figure 33 provides a comparison of the 

probabilistic dose distribution with the distribution of film badge readings. Note the much 

116 
broader distribution for the probabilistic analysis, which is likely attributed to the many uncertain 

parameters involved with the calculation of reconstructed doses. 

Table 20. Summary of External Dose for the 7126th Army Unit Stationed at Enewetak 

Atoll during Operation REDWING 

Mean Dose (rem) Upper Bound Dose (rem) 

Film 

Badge Probabilistic* Deterministic (NTPR) 

Film 

Badge 

(95th

Percentile) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic/

Probabilistic) 

2.9 3.4 

(1.5) 3.4 4.0 6.2 10 1.6 

* The arithmetic mean (and standard deviation) are shown. The geometric mean external dose is 3.1 rem. 

 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0 2 4 6 8 10

Dose (rem)

Relative Frequency

Monte Carlo Simulation

Film Badge

Figure 33. Comparison of the Dose Distribution from Probabilistic Analysis with Unbiased 

Film Badge Readings for the 7126th AU at Enewetak Atoll during Operation REDWING 

117 
5.1.4 Internal Dose 

Internal dose reconstruction for army units stationed on Enewetak Island during Operation 

REDWING was accomplished by incorporating uncertainty distributions for various parameters 

into the models discussed in Section 3. These models incorporate the fallout-induced radiation 

environments discussed in detail in Appendix A, and the fallout intensity decay model and 

various other parameters discussed in Sections 3 and 4. 

5.1.4.1 Exposure Pathways 

Internal dose pathways included in the probabilistic analysis are inhalation of descending fallout, 

inhalation of resuspended fallout, and incidental ingestion of soil and dust based on the models 

discussed in Section 3. 

5.1.4.2 Assumptions and Parameter Uncertainty 

The following specific uncertainty distributions, discussed in Section 4, were used in the 

uncertainty analysis for internal dose calculations: 

 Amount of time spent outdoors each day. 

 Time-dependent resuspension factor K(t). 

 Breathing rate distribution correlated with activity levels. 

 Time-dependent shot-specific dose conversion factors (DCFs). 

 Bias factors for inhalation DCF. 

 Deposition fractions for particle size classes deposited in the thoracic airways of the 

respiratory tract. 

 Deposition fractions for particle size classes deposited in ET2 and cleared to digestive tract. 

 Activity fractions for inhalation of descending fallout for three particle size classes; activity 

fractions vary for Shots ZUNI, MOHAWK, APACHE, and TEWA. 

 Ingestion rate and soil bulk density for incidental ingestion of soil and dust. 

The types of distributions, means, and confidence intervals for each of these distributions are 

shown in Table A-6 of Appendix A. The values used in the deterministic analysis that generated 

the doses for the film badge period of July 11 to August 3, 1956 are also summarized in 

Table A-6. 

5.1.4.3 Results and Discussion 

Fifty-year committed equivalent dose (CED) distributions to three organs, thyroid, lung, and 

lower large intestine (LLI) wall, were derived using the probabilistic model for a sample size of 

10,000 (i.e., 10,000 Monte Carlo histories). The geometric mean and 95th percentile CEDs of the 

distribution for each organ are given in Table 21. The ratio of the deterministic upper bound 

CED to the probabilistic 95th percentile CED, provided in the rightmost column, is a factor of 1.3 

or greater for alpha doses and for beta-plus-gamma doses. These results indicate that the 

probabilistic analysis yields lower central doses than the doses calculated using deterministic 

118 
models based on methodologies discussed in Section 3 with nominal or mean values of various 

parameters as shown in Table A-6 of Appendix A. This result is primarily due to the partitioning 

of the descending inhalation dose based on estimates of the fraction deposited in the respiratory 

tract and inhaled versus the fraction deposited in ET2 and ingested. It is also concluded that the 

probabilistic analysis 95th percentile doses are lower than the upper-bound deterministic internal 

doses, indicating that the upper bound factor of 10 used in the deterministic analysis results in a 

conservative estimate of the upper-bound internal dose for this specific set of exposures. 

Table 21. Summary of Estimated Internal Doses for the 7126th Army Unit Stationed at 

Enewetak Atoll during Operation REDWING 

Mean Dose (rem) Upper Bound Dose (rem) 

Organ 

Probabilistic* Deterministic 

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic 

 Probabilistic) 

Alpha Dose 

Thyroid 0.000024 

(8.6) 0.00011 0.00083 0.0011 1.4 

Lung 0.00029 

(8.7) 0.0014 0.010 0.014 1.4 

LLI wall 0.000024 

(8.5) 0.00011 0.00085 0.0011 1.4 

Beta plus Gamma Dose 

Thyroid 0.72 

(4.8) 1.5 9.7 14 1.5 

Lung 0.16 

(6.6) 1.4 3.8 14 3.7 

LLI wall 0.54 

(4.8) 1.0 7.2 9.6 1.3 

* Geometric means and (geometric standard deviations) from the probabilistic analysis are shown. 

The relative frequency distribution and the probability plot of estimated doses to the LLI Wall 

from alpha radiation are shown in Figure 34 and Figure 35, respectively, and for the doses from 

beta plus gamma radiation are shown in Figure 36 and Figure 37, respectively. These figures 

demonstrate that the distributions are well represented by lognormal distributions, and are 

formally similar to the plots of the same results for the other two organs studied. 

119 
0

0.025

0.05

0.075

0.1

6.8E-09 1.6E-07 3.9E-06 9.2E-05 2.2E-03 5.2E-02

Dose (rem, CED)

Relative Frequency of log 10(dose)

 

Figure 34. Distribution of Estimated LLI Wall Doses from Alpha Radiation for the 7126th

Army Unit Stationed at Enewetak Atoll during Operation REDWING 

Cumulative Probability

Dose (rem, CED)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Dose

Fitted Curve

Figure 35. Probability Plot of Estimated LLI Wall Doses from Alpha Radiation for the 

7126th Army Unit Stationed at Enewetak Atoll during Operation REDWING 

120 
0

0.025

0.05

0.075

0.1

2.5E-04 3.6E-03 5.1E-02 7.1E-01 1.0E+01 1.4E+02

Dose (rem, CED)

Relative Frequency of log 10(dose)

 

Figure 36. Distribution of Estimated LLI Wall Doses from Beta plus Gamma Radiation for 

the 7126th Army Unit Stationed at Enewetak Atoll during Operation REDWING 

Cumulative Probability

Dose (rem, CED)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

10-4

10-3

10-2

10-1

100

101

102

103

Dose

Fitted Curve

Figure 37. Probability Plot of Estimated LLI Wall Doses from Beta plus Gamma Radiation 

for the 7126th Army Unit Stationed at Enewetak Atoll during Operation REDWING 

121 
5.2 Case Study #2: Operation HARDTACK I (1958), Army Unit Administrative and 

Operations Detachments, Enewetak Atoll 

5.2.1 Case Description and Cohort Participation Scenario 

Permanent base camps were established on three islands to support the operations at Enewetak 

Atoll during Operation HARDTACK 1. The largest of the three, Enewetak Island (or Site Fred), 

was manned continuously during the operation with a maximum population of approximately 

3200 people. Among the units assigned to Enewetak Island were two Army detachments, the 

Army Administrative Detachment and the Army Operations Detachment. The compositions and 

duties of these detachments are as follows (Gladeck et al., 1982): 

 Administrative Detachment (AD): Personnel of this detachment supported the Chaplain, the 

Provost Marshal, and the Finance, Information, and Postal Sections. Its scheduled strength 

was 50 officers and 482 enlisted men during the operational period. 

 Operations Detachment (OD): Duties of this detachment were administrative and logistic 

support for assigned personnel, including laundry, medical, dental, commissary, engineering, 

depot, gear loft, truck motor pool, and maintenance support. Its scheduled strength was 

25 officers and 379 enlisted men. 

A complete record of film badge data was obtained for these units. By the nature of their duties, 

it is likely that most personnel remained on the island continuously, or nearly so, throughout the 

operation. Further details of this analysis are included in Appendix B. 

5.2.2 Available Dosimetry 

About 18,000 test participants received film badge dosimetry during Operation HARDTACK I 

to measure exposure to external gamma radiation, and approximately 62,000 individual film 

badges were issued and processed. Most participants had such dosimetry throughout their period 

of service at Enewetak Proving Ground (EPG). A study of the HARDTACK I film badge design 

and the calibration, issue, exchange, and processing procedures utilized during the operation 

concluded that the dosimetry, while generally reliable, over-reported exposures by about 

20 percent due to environmental effects in the hot, humid Pacific test area. (NRC, 1989) 

Complete files of film badge data were obtained for these units. The databases were then 

processed to (1) correct for apparent inconsistencies in the recorded return dates of some badges 

and (2) distill the records to a subset of readings that most likely represent the exposure 

conditions of those personnel continuously resident on Enewetak Island throughout the 

operation. The statistics derived for these film badges are summarized in Table B-1 of 

Appendix B. 

5.2.3 External Dose 

External gamma dose reconstruction for army units stationed on Enewetak Island during 

Operation HARDTACK I was accomplished by incorporating uncertainty distributions for 

various parameters into the model discussed in Section 3. This model incorporates the fallout122 
induced radiation environments discussed in detail in Appendix B, the fallout intensity decay 

model and effects of shielding as discussed in Section 3. 

5.2.3.1 Exposure Pathways 

The only sources of potential external radiation exposure for army units stationed at Enewetak 

Atoll during Operation HARDTACK I were residual gamma radiation from fallout due to Shots 

FIR/KOA, REDWOOD, and OAK. See Appendix B for additional details. 

5.2.3.2 Assumptions and Parameter Uncertainty 

The following specific uncertainty distributions, discussed in Section 4, were used in the 

uncertainty analysis for external gamma dose calculations: 

 Amount of time spent outdoors each day. 

 Fraction of time spent indoors that was spent in a tent-type structure or in a building. 

 Protection factors for tents and buildings. 

 Distributions of fallout intensity at locations on the island where a veteran most likely spent 

time, i.e., during time spent outdoors, location of the tent for the time spent indoors in a tent, 

and location of a building for the time spent indoors in a building. 

 Measurement error associated with intensity measurements on the island. 

 Uncertainty in fallout proportion from combined debris clouds for Shots FIR and KOA. 

 Uncertainty in shot-specific radiological decay functions. 

The types of distributions, means, and confidence intervals for each of these distributions are 

shown in Table B-2 of Appendix B. The values used in the deterministic analysis that generated 

the deterministic doses reported in Table 22 for the various film badge periods are also 

summarized in Table B-2. 

5.2.3.3 Results and Discussion 

The Monte Carlo-derived (arithmetic) mean and 95th percentile doses for each subunit are listed 

in Table 22. Also provided for comparison are similar statistics based on the distribution of film 

badge doses and on deterministic doses with the “times 3” upper bound convention. The last 

column displays the ratio of the deterministic upper bound dose to the probabilistic 

95th percentile dose. It is seen that both the probabilistic and deterministic approaches compute 

mean doses that are generally consistent with the average film badge doses of the various 

subunits. The deterministic upper bound doses exceed the probabilistic 95th percentile doses by a 

nearly constant factor of 1.5–1.6; the latter doses exceed the 95th percentile film badge doses for 

all subunits. Figure 38 illustrates the relative comparisons of these quantities for the 

Administrative Detachment and the Operations Detachment. 

123 
Table 22. Summary of External Dose for Army Units Stationed at Enewetak Island 

during Operation HARDTACK I 

Dose (rem) Upper Bound (NTPR) or 

95th Percentile Doses (rem) Parent 

Unit 

FB Turnin 

Date 

(1958) Mean FB Mean MC NTPR Det. FB MC NTPR UB 

Ratio 

NTPR UB/ 

MC 

AD May 31 0.54 0.889 0.85 0.74 1.65 2.6 1.6 

OD May 31 0.57 0.889 0.85 0.76 1.65 2.6 1.6 

OD Jun 4 0.89 0.939 0.90 1.15 1.75 2.7 1.5 

AD Jun 5 0.76 0.950 0.91 1.04 1.77 2.7 1.5 

OD Jun 5 0.89 0.950 0.91 1.26 1.77 2.7 1.5 

AD Jun 7 1.09 0.970 0.93 1.38 1.82 2.8 1.5 

AD Jun 10 0.98 0.997 0.95 1.18 1.87 2.9 1.5 

OD Jun 10 1.06 0.997 0.95 1.38 1.87 2.9 1.5 

OD Jun 11 1.39 1.01 0.96 1.85 1.88 2.9 1.5 

OD Jun 12 0.72 1.01 0.97 0.97 1.90 2.9 1.5 

OD Jun 13 1.31 1.02 0.98 1.84 1.91 2.9 1.5 

AD Jun 17 1.11 1.05 1.00 1.28 1.97 3.0 1.5 

AD Jun 27 1.00 1.10 1.05 1.28 2.09 3.1 1.5 

AD Jun 28 1.09 1.11 1.05 1.40 2.10 3.2 1.5 

AD Jun 29 1.00 1.12 1.06 1.25 2.11 3.2 1.5 

AD Jul 7 1.01 1.17 1.10 1.49 2.20 3.3 1.5 

FB: film badge dose 

MC: dose from the probabilistic model (Monte Carlo simulation) 

Det.: dose from the deterministic model (NTPR)

5.2.4 Internal Dose 

Internal dose reconstruction for army units stationed on Enewetak Island during Operation 

HARDTACK I was accomplished by incorporating uncertainty distributions for various 

parameters into the models discussed in Section 3. These models incorporate the fallout-induced 

radiation environments discussed in detail in Appendix B, and the fallout intensity decay model 

and various other parameters discussed in Sections 3 and 4. 

5.2.4.1 Exposure Pathways 

Internal dose pathways included in the probabilistic analysis are inhalation of descending fallout, 

inhalation of resuspended fallout, and incidental ingestion of soil and dust based on the models 

discussed in Section 3. 

124 
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

31-May 5-Jun 7-Jun 10-Jun 17-Jun 27-Jun 28-Jun 29-Jun 7-Jul

AD AD AD AD AD AD AD AD AD

Turn-In Date (in 1958) for AD - Administrative Detachment

External Whole Body Dose (rem)

Film Badge (mean) Monte Carlo (mean) Deterministic (mean)

Film Badge (95%) Monte Carlo (95%) Deterministic UB

a

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

31-May 4-Jun 5-Jun 10-Jun 11-Jun 12-Jun 13-Jun

OD OD OD OD OD OD OD

Turn-In Date (in 1958) for OD - Operations Detachment

External Whole Body Dose (rem)

Film Badge (mean) Monte Carlo (mean) Deterministic (mean)

Film Badge (95%) Monte Carlo (95%) Deterministic UB

b

Figure 38. Comparison of Film Badge, Monte Carlo, and Deterministic Results for the 

Administrative Detachment (a) and the Operations Detachment (b) at 

Operation HARDTACK I 

125 
5.2.4.2 Assumptions and Parameter Uncertainty 

The following specific uncertainty distributions, discussed in Section 4, were used in the 

uncertainty analysis for internal dose calculations: 

 Amount of time spent outdoors each day. 

 Time-dependent resuspension factor K(t). 

 Breathing rate distribution correlated with activity levels. 

 Time-dependent shot-specific dose conversion factors (DCFs). 

 Bias factors for inhalation DCFs. 

 Deposition fractions for particle size classes deposited in the thoracic airways of the 

respiratory tract. 

 Deposition fractions for particle size classes deposited in ET2 tract and cleared to digestive 

tract. 

 Activity fractions for inhalation of descending fallout for three particle size classes; activity 

fractions vary for Shots FIR/KOA, REDWOOD, and OAK. 

 Ingestion rate and soil bulk density for incidental ingestion of soil and dust. 

The types of distributions, means, and confidence intervals for each of these distributions are 

shown in Table B-4 of Appendix B. The values used in the deterministic analysis that generated 

the doses for the film badge period of April 12 to July 7, 1958 are also summarized in Table B-4

of Appendix B. 

5.2.4.3 Results and Discussion 

Fifty-year committed equivalent dose (CED) distributions for three organs, thyroid, lung, and 

lower large intestine (LLI) wall, were derived using the refined uncertainty model for a sample 

size of 10,000 (i.e., 10,000 Monte Carlo histories). Examples of these results are shown in 

Appendix B, where the relative frequency distribution and the probability plot of estimated doses 

to the LLI wall from alpha radiation are shown in Figure B-5 and Figure B-6, respectively, and 

from beta plus gamma radiation in Figure B-7 and Figure B-8, respectively. The CED 

distributions are lognormally-distributed, as indicated by their Gaussian (bell) shapes when 

plotted on a logarithmic axis. These figures for LLI wall are formally similar to those obtained 

for the other two trial organs. 

The results of the internal dose deterministic analysis and the probabilistic analysis are shown in 

Table 23. These results indicate that the probabilistic analysis yields lower central doses than the 

doses calculated using deterministic models based on methodologies discussed in Section 3 with 

nominal or mean values of various parameters as shown in Table B-4 of Appendix B. This result 

is primarily due to the partitioning of the descending inhalation dose based on estimates of the 

fraction deposited in the respiratory tract and inhaled versus the fraction deposited in the ET tract 

and ingested. It is also concluded that the probabilistic 95th percentile doses are lower than the 

upper-bound deterministic internal doses, indicating that the upper bound factor of 10 used in the 

deterministic analysis results in a conservative estimate of the upper-bound internal dose for this 

126 
Table 23. Internal Dose Summary for Army Units Stationed at Enewetak Island during 

Operation HARDTACK I 

Mean Dose (rem) Upper Bound Dose (rem) 

Organ 

Probabilistica

Deterministic 

(NTPR Upper 

Bound) 

Ratio 

(Deterministic/

Probabilistic) 

Deterministic

(NTPR) 

Probabilistic 

(95th Percentile) 

Alpha Dose 

Thyroid 0.000040 

(8.5) 0.00036 0.0014 0.0036 2.6 

Lung 0.00054 

(8.6) 0.0049 0.019 0.049 2.6 

LLI wall 0.000042 

(8.3) 0.00036 0.0014 0.0036 2.5 

Beta plus Gamma Dose 

Thyroid 0.24 

(4.7) 0.57 3.0 5.5 1.8 

Lung 0.030 

(6.5) 0.31 0.67 3.1 4.6 

LLI wall 0.17 

(4.7) 0.40 2.1 3.9 1.8 

a

 Geometric means (and geometric standard deviations) from the probabilistic analysis are shown 

specific set of exposures. Illustrations of the lognormal nature of the internal dose distributions 

are shown in Figure B-5 and Figure B-7 of Appendix B for the dose to the LLI wall from alpha 

particles and the dose from beta plus gamma radiation, respectively. 

5.3 Case Study #3: Operation PLUMBBOB (1957), 4th Marine Corps Provisional Atomic 

Exercise Brigade (MCPAEB) Maneuver at Shot HOOD 

5.3.1 Case Description and Cohort Participation Scenario 

The 4th Marine Corps Provisional Atomic Exercise Brigade (MCPAEB), commonly called the 

“Brigade” conducted an exercise at the NTS during Operation PLUMBBOB in 1957. The 

Brigade was organized as a standard air-ground task force totaling approximately 2,000 

personnel. One of the units comprising the Brigade is the subject of this case study: Company E 

of the 2nd Battalion, 5th Marine Regiment, 1st Marine Division. 

All of the Brigade troops arrived at Camp Desert Rock (CDR) by June 20, 1957, where they 

began preparing for a maneuver that was to be held in conjunction with Shot DIABLO. A full 

rehearsal in the NTS forward area was conducted on June 20 and 21. On the morning of 

127 
June 28, with the entire Brigade in place, DIABLO misfired and all Brigade personnel returned 

to CDR. The maneuver was reassigned to Shot HOOD, and on the morning of July 5, with the 

Brigade in its trenches 5,360 yards southwest of ground zero (GZ), Shot HOOD was detonated. 

About 15 minutes later Company E, preceded and flanked by radiation safety personnel, began 

its march from the trenches in the direction of the HOOD GZ. Having approached to within 

1,100 to 1,400 yards of the HOOD GZ, at which time they reached the Rad-Safe limit of 5 R hr−1

in that shot’s neutron-activated radiation field, the company reversed its direction of march 

enroute back to the trenches. By 0700 the company had returned to the trench area, then 

marched to a nearby helicopter landing zone where it enplaned and was transported to a location 

about 7,000 yards to the west of the trenches. From there, the company participated in a mock 

assault on a nearby objective. By 1430 they had marched to a nearby road from where they were 

transported by motor vehicle convoy back to CDR. Company E did not tour the HOOD display 

area on HOOD shot day. Most Brigade personnel had departed from CDR by July 6, 1957. 

(Frank et al., 1981; USMC, 1957) 

5.3.2 Available Dosimetry 

Brigade personnel were issued individual film badges for the duration of their stay at CDR. Film 

badge dosimetry records for the 2nd Battalion, 5th Marines is available only for senior personnel, 

and very few low-ranking enlisted men are represented in the dosimetry records. A total of 12 

film badge readings are available for Company E personnel for the period prior to and including 

Shot HOOD. The 12 readings, in mrem, are: 1200, 980, 760, 560, 560, 520, 520, 520, 500, 500, 

500 and 480. Although the three highest readings are thought to be outliers, there is not 

sufficient documentation to definitively conclude that the high readings are not representative of 

the actual film badge dose received by the majority of Company E personnel. One explanation 

for the higher readings might be the additional activities known to have been conducted by some 

of the senior personnel for whom the readings are available. Based on the 12 readings, the mean 

film badge reading for Company E is 633 mrem and the 95th percentile is 1079 mrem. No 

environmental bias is associated with PLUMBBOB film badges, so no bias adjustments are 

necessary. (Frank et al., 1981; NRC, 1989). 

5.3.3 External Dose 

External gamma dose reconstruction for Company E personnel during Operation PLUMBBOB 

was accomplished by incorporating uncertainty distributions for various parameters into the 

model discussed in Section 3. This model incorporates the radiation environments and variables 

discussed in Appendix C, and the fallout intensity decay model as discussed in Section 3. 

5.3.3.1 Exposure Pathways 

Company E personnel were potentially exposed to residual radiation at CDR and in forward test 

areas of the NTS. The sources of potential external radiation exposure for Company E personnel 

during Operation PLUMBBOB are listed below, grouped by each primary activity in which 

Company E engaged (Frank et al., 1981): 

128 
 During the rehearsal and the misfire, residual radiation from Shot BOLTZMANN and Shot 

WILSON fallout in the DIABLO test area. 

 During the maneuver, residual radiation from Shot BOLTZMANN and Shot WILSON 

fallout in the HOOD test area. 

 During the maneuver, residual radiation from neutron-induced soil radioactivity in the 

HOOD test area. 

 While at CDR, residual radiation from Shot WILSON fallout. 

5.3.3.2 Assumptions and Parameter Uncertainty 

Probability distributions for the following model parameters were used in the probabilistic 

analysis for external gamma dose calculations, and are discussed in Section 4 and Appendix C: 

 Protection factors for tent-type structures. 

 Distributions of fallout intensity at locations at CDR where a veteran most likely spent time, 

i.e., during time spent outdoors, and location within a tent for the time spent indoors. 

 Measurement error associated with intensity measurements and data collection and reporting. 

 Interpolation and extrapolation errors associated with creating and using iso-intensity contour 

maps. 

 Uncertainty in shot-specific radiological decay functions. 

In addition, probability distributions were used for CDR arrival and departure times, the amount 

of time spent outdoors at CDR, and several maneuver parameters. The types of distributions, 

central values and confidence intervals for each of these distributions are shown in Table C-4 of 

Appendix C. The values used in the deterministic analysis are also summarized in Table C-4. 

5.3.3.3 Results and Discussion 

The results of the deterministic and probabilistic external gamma dose analyses are shown in 

Table 24. The pathway that contributes most significantly to the external dose is the external 

exposure to neutron-induced radionuclides in the soil traversed during the maneuver. This 

source contributes approximately 96 percent of both the deterministic (NTPR) and mean 

(probabilistic analysis) doses. The amount of time Company E spent at the radiological safety 

limit is likely the dominant source of the external dose. Although the deterministic dose is 

typically considered to be a high-sided dose, it is slightly lower than both the mean film badge 

dose and the mean dose of the probability distribution. This reflects the use of film badge 

records that are thought to reflect activities that are not typical for Company E, as well as the use 

of large upper bound parameter values for certain parameters such as interpolated intensities and 

linger time at the Rad-Safe limit. 

A comparison of the upper-bound doses shows that the deterministic (NTPR) upper bound dose 

is about 70 percent higher than the 95th percentile dose from the probabilistic analysis. This 

indicates that the upper bound factor of 3 used in the deterministic external dose analysis results 

in an adequate estimate of the upper bound external gamma dose for Company E personnel at 

PLUMBBOB. 

129 
Table 24. Summary of External Dose for Company E Personnel of the 4th MCPAEB 

during Operation PLUMBBOB 

Mean Dose (rem) Upper Bound Dose (rem) 

Film 

Badge Probabilistic(*) Deterministic (NTPR) 

Film 

Badge 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic/ 

Probabilistic) 

0.63 0.62 

(0.23) 0.58 1.1 1.0 1.8 1.7 

(*) The arithmetic mean (and standard deviation) is shown. The geometric mean external dose is 

0.57 rem. 

5.3.4 Internal Dose 

Internal dose reconstruction for Company E personnel at the NTS during Operation 

PLUMBBOB was accomplished by incorporating probability distributions for input parameters 

of the models discussed in Section 3. These models incorporate the radiation environments and 

input parameters discussed in Appendix C. 

5.3.4.1 Exposure Pathways 

The sources of potential internal radiation exposure for Company E personnel during Operation 

PLUMBBOB are listed below, grouped by each primary activity in which Company E engaged 

(Frank et al., 1981): 

 During the rehearsal and the misfire, inhalation of resuspended fallout from shots 

BOLTZMANN and WILSON fallout in the DIABLO test area. 

 During the maneuver, inhalation of resuspended fallout from shots BOLTZMANN and 

WILSON in the HOOD test area. 

 During the maneuver, inhalation of highly-resuspended fallout from shots BOLTZMANN 

and WILSON in the HOOD test area. 

 During the maneuver, inhalation of suspended neutron-induced soil contaminants in the 

HOOD test area. 

 While at CDR, inhalation of resuspended fallout from Shot WILSON. 

 While at CDR and during all activities in the forward test area, incidental ingestion of 

contaminated soil and dust. 

5.3.4.2 Assumptions and Parameter Uncertainty 

Probability distributions for the following model parameters were used in the probabilistic 

analysis for internal dose calculations, and are discussed in Section 4 and Appendix C: 

 Time-dependent resuspension factors for routine activities. 

130 
 Resuspension factors for detonation-related and helicopter downwash resuspension. 

 Breathing rate distribution correlated with activity levels. 

 Time-dependent shot-specific inhalation and ingestion DCFs. 

 Bias factors for inhalation DCFs. 

 Soil ingestion rate and soil bulk density. 

In addition, probability distributions were used for CDR arrival and departure times, the amount 

of time spent outdoors at CDR, and several maneuver parameters. The types of distributions, 

confidence intervals, and central estimates for each of these distributions are shown in Table C-6

of Appendix C. The values used in the deterministic analysis are also summarized in Table C-6. 

5.3.4.3 Results and Discussion 

Distributions of fifty-year committed equivalent doses (CED) for three organs, thyroid, lung, and 

lower large intestine (LLI) wall, were derived using the uncertainty model for a sample size of 

10,000 (i.e., 10,000 Monte Carlo histories). Examples of these results are shown in Appendix C, 

where the relative frequency distribution and the probability plot of estimated doses to the 

LLI wall from alpha radiation are shown in Figure C-4 and Figure C-5, respectively, and from 

beta plus gamma radiation in Figure C-6 and Figure C-7, respectively. 

The results of the deterministic and probabilistic internal dose analyses are shown in Table 25. 

These results show that each deterministic organ dose is higher than the geometric mean dose 

from the corresponding probabilistic organ dose distribution. This result is expected, and it 

reflects the use of high-sided deterministic parameter values, including resuspension factors that 

result in upper bound internal doses from inhalation of detonation-induced resuspended fallout. 

Inhalation of detonation-induced resuspended fallout accounts for roughly 90 percent of the 

alpha organ doses, and between 70 and 90 percent of the total deterministic beta plus gamma 

organ doses. The deterministic doses due to detonation-induced resuspension are based on 

resuspension factors that were estimated to result in upper bound inhalation doses from this 

pathway, so they are not multiplied by 10 in the determination of upper bound deterministic 

doses. Therefore, the upper-bound deterministic doses are not simple 10× multiples of the 

deterministic doses. 

For this case study, all deterministic upper bound organ doses are lower than the corresponding 

95th percentile organ doses. The upper bound ratios in the last column of Table 25 show that the 

deterministic upper bound alpha organ doses are roughly 60 to 70 percent of the corresponding 

95th percentile organ doses, and the deterministic upper bound beta plus gamma organ doses are 

between approximately 40 and 85 percent of the corresponding 95th percentile organ doses. This 

outcome was initially attributed to the effects of correlations between very large lognormally 

distributed parameter uncertainties resulting in large 95th percentiles. However, evaluations 

accomplished to date that have examined the effects of removing many of the inherent 

correlations have shown this not to be the cause. 

Of the pathways that contribute to internal organ doses, inhalation of resuspended fallout is the 

primary cause of the observed deterministic upper bound to 95th percentile ratios. This finding is 

not unique to this NTS case, as an examination of the pathway doses for other case studies 

included in this report also shows that most of the 95th percentile resuspended fallout doses for 

131 
Table 25. Summary of Internal Dose for Company E of the 4th MCPAEB at the NTS 

during Operation PLUMBBOB 

Mean Dose (rem) Upper Bound Dose (rem) 

Organ 

Probabilistic* Deterministic 

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic/ 

Probabilistic) 

Alpha Dose 

Thyroid 0.0000046 

(7.3) 0.000051 0.00013 0.000087 0.68 

Lung 0.00013 

(7.4) 0.0011 0.0036 0.0022 0.58 

LLI Wall 0.0000050 

(6.9) 0.000051 0.00013 0.000087 0.66 

Beta plus Gamma Dose 

Thyroid 0.0042 

(5.0) 0.0096 0.062 0.028 0.43 

Lung 0.0016 

(6.3) 0.016 0.034 0.030 0.87 

LLI Wall 0.0016 

(5.0) 0.0045 0.025 0.010 0.42 

* Geometric means (and geometric standard deviations) from the probabilistic analysis are shown 

the three example organs are greater than the deterministic upper bound resuspended fallout 

doses. Looking more closely at the PLUMBBOB case study, inhalation of resuspended 

WILSON fallout during the rehearsal and maneuver appears to be the primary cause of the 

observed ratios of deterministic upper bound organ doses to corresponding 95th percentile organ 

doses. Additional evaluations of the calculations that lead to such ratios must be undertaken to 

further explain the outcome. 

Factors that will have to be specifically examined include the use of different time-dependent 

resuspension factors, the detonation-induced resuspension factors, the inclusion of upper-bound 

pathways (e.g., detonation-induced resuspension) in the deterministic dose calculations, and the 

very large uncertainties associated with several consequential variables. The time-dependent 

resuspension factor used in the probabilistic analysis may be a complication when assessing 

inhalation of fallout that has decayed more than about 200 hours (such as BOLTZMANN fallout 

in this case), after which the resuspension factor starts to drop appreciably. The large differences 

(2 or 3 orders of magnitude) between deterministic and probabilistic resuspension factors for 

detonation-induced resuspension also must be examined further. In addition, the inclusion of 

upper-bound pathways (most importantly the inhalation of detonation-induced resuspension) in 

the deterministic dose calculations presents a complication, because for these pathways a single 

dose is treated as both the deterministic dose and the upper-bound dose. Finally, large 

uncertainties associated with resuspension factors, inhalation dose conversion factors and the 

132 
intensities obtained from iso-intensity contour plots must be examined in more detail. These 

uncertainty distributions are large (geometric standard deviations between 2 and 5.2), and 

additional evaluations must be undertaken to verify that they are reasonable. 

5.4 Case Study #4: Operation REDWING (1956), USS ESTES (AGC 12) 

5.4.1 Case Description and Cohort Participation Scenario 

USS ESTES was an amphibious force flagship that served during REDWING as the Flagship 

Element (Task Element 7.3.0.1) of the Flagship Unit (Task Group 7.3). The ship arrived in the 

PPG on March 31, 1956, and departed from Enewetak for Bikini on May 3, two days before the 

first shot of the series. It returned to Enewetak twice: once for Shot SEMINOLE on June 6 and 

again during the last four days of June when no shots were detonated. USS ESTES was, 

therefore, present at Enewetak for only one of the eleven shots fired at that atoll. The ship 

participated in all of the six Bikini shots, providing communications, air control, and facilities for 

Program 2 (Nuclear Radiation) and radiation safety activities. For each shot at Bikini, the ship 

was out of the lagoon and on station at sea, departing the lagoon prior to each detonation and not 

returning until several hours after the detonations. At all other times at Bikini, the ship was 

moored to buoy Nan-9 at the Eneu Island anchorage. USS ESTES departed from the PPG on 

July 25, 1956, proceeded to Pearl Harbor, Hawaii, and then to San Diego, California. It arrived 

at San Diego on August 7, 1956. (Bruce-Henderson et al., 1982). 

5.4.2 Available Dosimetry 

The entire crew was issued film badges for the duration of the ship’s participation in the 

operation. Two series of badges were issued; the first was from April 25 to June 25 and the 

second from June 25 to July 25. As was the case with the 7126th Army Unit REDWING study 

group, most film badges issued to USS ESTES personnel for periods of 4 weeks or more at 

Operation REDWING were damaged by the high heat and humidity in the test area (BruceHenderson et al., 1982; NRC, 1989), and are therefore not suitable for comparison with Monte 

Carlo dose distributions. 

5.4.3 External Dose 

External gamma dose reconstruction for the crew of USS ESTES during Operation REDWING 

was accomplished by incorporating uncertainty distributions for various parameters into the 

model discussed in Section 3. This model incorporates the fallout-induced radiation 

environments discussed in detail in Appendix D, and the fallout intensity decay model and 

effects of shielding as discussed in Section 3. 

5.4.3.1 Exposure Pathways 

Sources of potential external radiation exposure for the crew of USS ESTES during Operation 

REDWING include residual gamma radiation from fallout due to Shots ZUNI, FLATHEAD, 

133 
NAVAJO, and TEWA, external ship contamination, and shine from lagoon waters. See 

Appendix D for additional details. 

5.4.3.2 Assumptions and Parameter Uncertainty 

The following specific uncertainty distributions, discussed in Section 4, were used in the 

uncertainty analysis for external gamma dose calculations: 

 Amount of time spent topside each day. 

 Ship shielding factors while present at worksites and billet areas below deck. 

 Distributions of fallout intensity at locations on the ship where a veteran most likely spent 

time, i.e., during time spent topside, worksite location, and billet location. 

 Measurement error associated with intensity measurements on the ship. 

 Error associated with ship contamination and shine data. 

 Uncertainty in shot-specific radiological decay functions. 

The types of distributions, means, and confidence intervals for each of these distributions are 

shown in Table D-6 of Appendix D. The values used in the deterministic analysis that generated 

the deterministic doses reported for the operational period of May 28 to August 6, 1956, are also 

summarized in Table D-6. 

5.4.3.3 Results and Discussion 

The results of the external gamma dose deterministic analysis and the probabilistic analysis are 

shown in Table 26. These results indicate that the probabilistic analysis yields a slightly higher 

mean dose than the deterministic analysis, but that the probabilistic 95th percentile dose is lower 

than the upper-bound deterministic dose. 

Table 26. Summary of External Dose for the Crew of USS ESTES during Operation 

REDWING 

Mean Dose (rem) Upper Bound Dose (rem) 

Probabilistic* Deterministic 

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic/ 

Probabilistic) 

0.50 

(0.28) 0.43 1.0 1.2 1.1 

* The arithmetic mean (and standard deviation) is shown. The geometric mean external 

dose is 0.44 rem. 

134 
5.4.4 Internal Dose 

Internal dose reconstruction for the crew of USS ESTES during Operation REDWING was 

accomplished by incorporating uncertainty distributions for various parameters into the models 

discussed in Section 3. These models incorporate the fallout-induced radiation environments 

discussed in detail in Appendix D, and the fallout intensity decay model and various other 

parameters discussed in Sections 3 and 4. 

5.4.4.1 Exposure Pathways 

Internal dose pathways included in the probabilistic analysis are inhalation of descending fallout 

and inhalation of resuspended fallout based on the models discussed in Section 3. 

5.4.4.2 Assumptions and Parameter Uncertainty 

The following specific uncertainty distributions, discussed in Section 4, were used in the 

uncertainty analysis for internal dose calculations: 

 Amount of time spent topside each day. 

 Resuspension factor K (assumed to be constant with time). 

 Breathing rate distribution correlated with activity levels. 

 Time-dependent shot-specific dose conversion factors (DCFs). 

 Bias factors for inhalation DCFs. 

 Deposition fractions for particle size classes deposited in the thoracic airways of the 

respiratory tract. 

 Deposition fractions for particle size classes deposited in ET2 and cleared to digestive tract. 

 Activity fractions for inhalation of descending fallout for three particle size classes; activity 

fractions vary for Shots ZUNI, FLATHEAD, NAVAJO, and TEWA. 

The types of distributions, means, and confidence intervals for each of these distributions are 

shown in Table D-8 of Appendix D. 

5.4.4.3 Results and Discussion 

Distributions of fifty-year committed equivalent doses (CED) to three organs, thyroid, lung, and 

lower large intestine (LLI) wall, were derived using the refined uncertainty model for a sample 

size of 10,000 (i.e., 10,000 Monte Carlo histories). Examples of these results are shown in 

Appendix D, where the relative frequency distribution and the probability plot of estimated doses 

to the LLI wall from alpha radiation are shown in Figure D-3 and Figure D-4, respectively, and 

from beta plus gamma radiation in Figure D-5 and Figure D-6, respectively. The CED 

distributions are lognormally-distributed, as indicated by their Gaussian (bell) shapes when 

plotted on a logarithmic axis. 

The results of the internal dose deterministic analysis and the probabilistic analysis are shown in 

Table 27. These results indicate that the probabilistic analysis yields lower central doses than the 

doses calculated using deterministic models based on methodologies discussed in Section 3 with 

135 
nominal or mean values of various parameters shown in Table D-8 of Appendix D. This result is 

primarily due to the partitioning of the descending inhalation dose based on estimates of the 

fraction deposited in the respiratory tract and inhaled versus the fraction deposited in the ET 

region and ingested. These results indicate that the probabilistic 95th percentile doses are lower 

than the upper-bound deterministic internal doses, implying that the upper bound factor of 10 

used in the deterministic analysis results in a conservative estimate of the upper-bound internal 

dose for this set of specific exposures. Note that the probabilistic 95th percentile LLI wall beta 

plus gamma dose is approximately equal to the deterministic upper bound dose. 

Table 27. Summary of Internal Dose for the USS ESTES Crew during Operation 

REDWING 

Mean Dose (rem) Upper Bound Dose (rem) 

Organ 

Probabilistica Deterministic 

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR Upper 

Bound) 

Ratio 

(Deterministic/ 

Probabilistic) 

Alpha Dose 

Thyroid 0.0000072 

(7.8) 0.000032 0.00021 0.00032 1.5 

Lung 0.000088 

(7.8) 0.00040 0.0026 0.0040 1.5 

LLI wall 0.0000076 

(7.6) 0.000033 0.00022 0.00033 1.5 

Beta plus Gamma Dose 

Thyroid 0.56 

(4.6) 0.70 6.6 7.0 1.1 

Lung 0.088 

(6.0) 0.58 1.8 5.8 3.2 

LLI wall 0.36 

(4.6) 0.44 4.2 4.4 1.0 

a

 Geometric means (and geometric standard deviations) from the probabilistic analysis are shown 

5.5 Case Study #5: Operation HARDTACK I (1958), USS BOXER (CVS 21) 

5.5.1 Case Description and Cohort Participation Scenario 

USS BOXER was an antisubmarine aircraft carrier that served during HARDTACK I as 

command ship for Commander Joint Task Force 7, flagship for the Commander Task Group 

(CTG) 7.3 (Navy), headquarters for CTG 7.1 (Scientific) and CTG 7.4 (Air Force), and Air 

Operations Center for Air Force personnel. The ship also hosted Marine Helicopter Transport 

Squadron (Light) 361. USS BOXER transported many of the nuclear devices from CONUS to 

EPG. The ship arrived at Enewetak Atoll on March 3, 1958, with a crew of approximately 1100 

personnel. It made numerous transits between Enewetak and Bikini atolls during May and June 

in support of the test series, finally departing EPG for Pearl Harbor on June 30. The ship 

136 
subsequently was present at Johnston Island in late July and August to support the two 

HARDTACK I shots at that location. During the operation, USS BOXER performed a variety of 

shot-specific tasks; for example, it served as the launch platform for the balloon that carried the 

YUCCA device aloft, the evacuation unit for island-based personnel for several shots, and the 

recovery element for rocket nosecones and other instrumented devices employed at several shots. 

(Gladeck et al., 1982) 

Extensive preparation and planning for radiological safety were performed aboard USS BOXER. 

The ship was equipped with a washdown system to remove fallout, and was staffed with 18 

radiological monitoring teams and two decontamination squads. These teams were used 

extensively on shot days for fallout watch and decontamination, as needed. Radiological surveys 

were made hourly during USS BOXER’s stay in EPG (Gladeck et al., 1982). Unfortunately, 

little of this monitoring data has been located to date. 

5.5.2 Available Dosimetry 

The entire crew was issued film badges prior to the start of testing. The issue date for officers 

and senior non-commissioned officers was April 11; most enlisted personnel received their 

badges on April 14. For the majority of crewmembers, the available dosimetry record provides 

total operational doses but does not include complete information linking the readings to badge 

numbers and to turn-in dates. Therefore, an additional uncertainty was applied to film badge 

turn-in dates. 

The average of the available film badge readings is 0.735 rem. Removing the 20 percent 

environmental bias discussed in the NRC film badge dosimetry report (NRC, 1989) results in an 

unbiased average film badge dose of 0.735/1.2 = 0.612 rem. 

5.5.3 External Dose 

External gamma dose reconstruction for the crew of USS BOXER during Operation 

HARDTACK I was accomplished by incorporating uncertainty distributions for various 

parameters into the model discussed in Section 3. This model incorporates the fallout-induced 

radiation environments discussed in detail in Appendix E, and the fallout intensity decay model 

and effects of shielding as discussed in Section 3. 

5.5.3.1 Exposure Pathways 

Sources of potential external radiation exposure for the crew of USS BOXER during Operation 

HARDTACK I include residual gamma radiation from fallout due to Shots FIR/KOA, 

REDWOOD, and OAK (Gladeck et al., 1982). 

5.5.3.2 Assumptions and Parameter Uncertainty 

The following specific uncertainty distributions were used in the uncertainty analysis for external 

gamma dose calculations: 

 Amount of time spent topside each day. 

137 
 Ship shielding factors while present at worksites and billet areas below deck. 

 Distribution of fallout intensities at locations on the ship where a veteran most likely spent 

time, i.e., during time spent topside, worksite location, and billet location. 

 Error associated with intensity measurements on the ship. 

 Uncertainty in fallout proportion from combined debris clouds for Shots FIR and KOA. 

 Uncertainty in shot-specific radiological decay functions. 

 Film badge turn-in date. 

The types of distributions, means, and confidence intervals for each of these distributions are 

shown in Table E-1 of Appendix E. The values used in the deterministic analysis that generated 

the deterministic doses reported for the period starting with the first shot, May 12, 1958, through 

the turn-in of film badges are also summarized in Table E-1 of Appendix E. 

5.5.3.3 Results and Discussion 

The results of the external gamma dose deterministic analysis and the probabilistic analysis are 

shown in Table 28. These results indicate that the probabilistic analysis yields similar mean 

doses as the deterministic analysis, and that the probabilistic 95th percentile dose is lower than 

the upper-bound deterministic dose. The mean doses derived deterministically and 

probabilistically are also in reasonable agreement with the unbiased mean film badge dose. Of 

the 980 available USS BOXER film badge readings, only one (0.1 percent) exceeds the 

95th percentile upper bound of the probabilistic distribution. 

Table 28. Summary of External Dose for the Crew of USS BOXER during Operation 

HARDTACK I 

Mean Dose (rem) Upper Bound Dose (rem) 

Film 

Badge Probabilistic* Deterministic 

(NTPR) 

Film 

Badge 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic/ 

Probabilistic) 

0.61 0.53 

(0.36) 0.52 0.97 1.2 1.6 1.3 

* The arithmetic mean (and standard deviation) is shown. The geometric mean external dose is 0.42 rem. 

5.5.4 Internal Dose 

Internal dose reconstruction for the crew of USS BOXER during Operation HARDTACK I was 

accomplished by incorporating uncertainty distributions for various parameters into the models 

discussed in Section 3. These models incorporate the fallout-induced radiation environments 

discussed in detail in Appendix E, and the fallout intensity decay model and various other 

parameters discussed in Sections 3 and 4. 

138 
5.5.4.1 Exposure Pathways 

Internal dose pathways included in the probabilistic analysis are inhalation of descending fallout 

and inhalation of resuspended fallout based on the models discussed in Section 3. 

5.5.4.2 Assumptions and Parameter Uncertainty 

The following specific uncertainty distributions, discussed in Section 4, were used in the 

uncertainty analysis for internal dose calculations: 

 Amount of time spent topside each day. 

 Constant resuspension factor K. 

 Breathing rate distribution correlated with activity levels. 

 Time-dependent shot-specific dose conversion factors (DCFs). 

 Bias factors for inhalation DCFs. 

 Deposition fractions for particle size classes deposited in the thoracic airways of the 

respiratory tract. 

 Deposition fractions for particle size classes deposited in ET2 and cleared to digestive tract. 

 Activity fractions for inhalation of descending fallout for three particle size classes; activity 

fractions vary for Shots FIR/KOA, REDWOOD, and OAK. 

The types of distributions, means, and confidence intervals for each of these distributions are 

shown in Table E-3 of Appendix E. 

5.5.4.3 Results and Discussion 

Fifty-year committed equivalent dose (CED) distributions to three organs, thyroid, lung, and 

lower large intestine (LLI) wall, were derived using the refined uncertainty model for a sample 

size of 10,000 (i.e., 10,000 Monte Carlo histories). Examples of these results are shown in 

Appendix E, where the relative frequency distribution and the probability plot of estimated doses 

to the LLI wall from alpha radiation are shown in Figure E-3 and Figure E-4, respectively, and 

from beta plus gamma radiation in Figure E-5 and Figure E-6, respectively. The CED 

distributions are lognormally-distributed, as indicated by their Gaussian (bell) shapes when 

plotted on a logarithmic axis. 

The results of the internal dose deterministic analysis and the probabilistic analysis are shown in 

Table 29. These results indicate that the probabilistic analysis yields lower central doses than the 

doses calculated using deterministic models based on methodologies discussed in Section 3 with 

nominal or mean values of various parameters as shown in Table E-3 of Appendix E. This result 

is primarily due to the partitioning of the descending inhalation dose based on estimates of the 

fraction deposited in the respiratory tract and inhaled versus the fraction deposited in the ET tract 

and ingested. These results also indicate that the probabilistic 95th percentile doses are lower 

than the upper-bound deterministic internal doses, implying that the upper bound factor of 10 

used in the deterministic analysis results in a conservative estimate of the upper-bound internal 

dose for this set of specific exposures. 

139 
Table 29. Summary of Internal Dose for the Crew of USS BOXER during Operation 

HARDTACK I 

Mean Dose (rem) Upper Bound Dose (rem) 

Organ 

Probabilistica Deterministic 

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR Upper 

Bound) 

Ratio 

(Deterministic/ 

Probabilistic) 

Alpha Dose 

Thyroid 0.000019 

(7.9) 0.00026 0.00061 0.0026 4.2 

Lung 0.00025 

(8.0) 0.0035 0.0081 0.035 4.2 

LLI wall 0.000020 

(7.6) 0.00026 0.00063 0.0026 4.0 

Beta plus Gamma Dose 

Thyroid 0.32 

(4.5) 0.76 3.8 7.6 2.0 

Lung 0.032 

(5.9) 0.38 0.60 3.8 6.2 

LLI wall 0.21 

(4.5) 0.49 2.5 4.9 2.0 

a

 Geometric means (and geometric standard deviations) from the probabilistic analysis are shown 

5.6 Case Study #6: Operation CASTLE (1954), Army Personnel, Enewetak Island 

5.6.1 Case Description and Cohort Participation Scenario 

This case study applies to Army personnel stationed at Enewetak Island during Operation 

CASTLE for the period March 1 to May 31, 1954. More than 1,500 Army personnel were at 

Operation CASTLE during the testing period. Most Army personnel in Joint Task Force (JTF) 

7, the civilian-military organization formed to conduct the operation, were assigned to TG 7.2. 

Most of these were assigned to the 7126th Army Unit that provided ground security, 

transportation and logistics support. These personnel were primarily stationed at Enewetak 

Island (Martin and Rowland, 1982). By the nature of their duties and residence, it is likely that 

most of the personnel remained on the island continuously, or nearly so, throughout the operation 

and therefore had continuous exposure to deposited fallout. 

Because calculated film badge external gamma doses were reported for the operational period of 

March 1 to May 31, 1954 (Thomas et al., 1984), a comparison is made between these doses and 

reconstructed external gamma doses calculated using methodologies and uncertainty 

distributions, described in Sections 3 and 4, over the same time period for the four fallout 

episodes that occurred at Enewetak Island during Operation CASTLE. In addition to external 

gamma doses, similar techniques, discussed in Section 3, were used to generate internal dose 

140 
distributions for the lung, lower large intestine, and thyroid. Appendix F contains the details of 

this analysis. 

5.6.2 Available Dosimetry 

Film badge dosimetry during Operation CASTLE included mission badges issued to individuals 

when they were expected to enter areas of radioactive contamination other than those 

encountered during routine activities, and cohort badges that were issued to one individual in a 

group of individuals who performed similar duties in similar locations (Servis, 1981). However, 

sufficient dosimetry data are not available for land-based personnel to allow meaningful 

comparisons between actual film badge data and reconstructed external gamma doses (Thomas et 

al., 1984). Therefore, reconstructed doses due to fallout exposure during Operation CASTLE 

cannot be compared to concurrent film badge data. 

5.6.3 External Dose 

External gamma dose reconstruction for personnel stationed on Enewetak Island during 

Operation CASTLE was accomplished by incorporating uncertainty distributions for various 

parameters into the model discussed in Section 3. This model incorporates the fallout-induced 

radiation environments discussed in detail in Appendix F, and the fallout intensity decay model 

and effects of shielding as discussed in Section 3. 

5.6.3.1 Exposure Pathways 

The only sources of potential external radiation exposure for personnel stationed at Enewetak 

Atoll during Operation CASTLE were residual gamma radiation from fallout due to Shots 

BRAVO, ROMEO, and NECTAR (Thomas et al., 1984). 

5.6.3.2 Assumptions and Parameter Uncertainty 

The following specific uncertainty distributions, discussed in Section 4, were used in the 

uncertainty analysis for external gamma dose calculations: 

 Amount of time spent outdoors each day. 

 Fraction of time spent indoors that was spent in a tent-type structure or in a building. 

 Protection factors for tents and buildings. 

 Distributions of fallout intensity at locations on the island where a veteran most likely spent 

time, i.e., during time spent outdoors, location of the tent for the time spent indoors in a tent, 

and location of a building for the time spent indoors in a building. 

 Error associated with intensity measurements on the island. 

 Uncertainty in shot-specific radiological decay functions. 

The types of distributions, means, and confidence intervals for each of these distributions are 

shown in Table F-2 of Appendix F. The values used in the deterministic analysis that generated 

141 
the deterministic doses reported for the operational period of March 1 to May 31, 1954, (Thomas 

et al., 1984) are also summarized in Table F-2 of Appendix F. 

5.6.3.3 Results and Discussion 

The results of the external gamma dose deterministic analysis and the probabilistic analysis are 

shown in Table 30. These results indicate that the mean dose of the probabilistic analysis is 

approximately equal to the deterministic dose. It is also concluded that the probabilistic 95th

percentile dose is lower than the upper-bound deterministic external gamma dose, indicating that 

the upper bound factor of 3 used in the deterministic analysis results in a conservative estimate of 

the upper bound external gamma dose. 

Table 30. Summary of External Dose for Personnel Stationed at Enewetak Island during 

Operation CASTLE 

Mean Dose (rem) Upper Bound Dose (rem) 

Probabilistic* Deterministic 

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic/ 

Probabilistic) 

1.3 

(0.54) 1.2 2.3 3.5 1.5 

* The arithmetic mean (and standard deviation) is shown. The geometric mean external dose 

is 1.2 rem. 

5.6.4 Internal Dose 

Internal dose reconstruction for personnel stationed on Enewetak Island during Operation 

CASTLE was accomplished by incorporating uncertainty distributions for various parameters 

into the models discussed in Section 3 and 4. These models incorporate the fallout-induced 

radiation environments discussed in detail in Appendix F, and the fallout intensity decay model 

and various other parameters discussed in Sections 3 and 4. 

5.6.4.1 Exposure Pathways 

Internal dose pathways included in the uncertainty analysis are inhalation of descending fallout, 

inhalation of resuspended fallout, and incidental ingestion of soil and dust based on the models 

discussed in Section 3 and Section 4. 

5.6.4.2 Assumptions and Parameter Uncertainty 

The following specific uncertainty distributions, discussed in Section 4, were used in the 

uncertainty analysis for internal dose calculations: 

 Amount of time spent outdoors each day. 

 Time-dependent resuspension factor K(t). 

142 
 Breathing rate distribution correlated with activity levels. 

 Time-dependent shot-specific dose conversion factors (DCFs). 

 Bias factors for inhalation DCFs. 

 Deposition fractions for particle size classes deposited in respiratory tract. 

 Deposition fractions for particle size classes deposited in ET2 and cleared to digestive tract. 

 Activity fractions for inhalation of descending fallout for three particle size classes; activity 

fractions vary for Shots BRAVO, ROMEO, and NECTAR. 

 Ingestion rate and soil bulk density for incidental ingestion of soil and dust. 

The types of distributions, means, and confidence intervals for each of these distributions are 

shown in Table F-4 of Appendix F. The values used in the deterministic analysis that generated 

the deterministic doses for the operational period of March 1 to May 31, 1954, are also 

summarized in Table F-4 of Appendix F. 

5.6.4.3 Results and Discussion 

Distributions of fifty-year committed equivalent doses (CED) to three organs, thyroid, lung, and 

lower large intestine (LLI) wall, were derived using the refined uncertainty model for a sample 

size of 10,000 (i.e., 10,000 Monte Carlo histories). Examples of these results are shown in 

Appendix F, where the relative frequency distribution and the probability plot of estimated doses 

to the LLI wall from alpha radiation are shown in Figure F-3 and Figure F-4, respectively, and 

from beta plus gamma radiation in Figure E-5 and Figure F-6, respectively. The CED 

distributions are lognormally-distributed, as indicated by their Gaussian (bell) shapes of their 

histograms when plotted on a logarithmic axis. 

The results of the internal dose deterministic analysis and the probabilistic analysis are shown in 

Table 31. These results indicate that the probabilistic analysis yields lower central doses than the 

doses calculated using deterministic models based on methodologies discussed in Section 3 with 

nominal or mean values of various parameters as shown in Table F-4 of Appendix F. This result 

is primarily due to the partitioning of the descending inhalation dose based on estimates of the 

fraction deposited in the respiratory tract and inhaled versus the fraction deposited in the ET tract 

and ingested. These results also indicate that the probabilistic 95th percentile doses are lower 

than the upper-bound deterministic internal doses, implying that the upper bound factor of 10 

used in the deterministic analysis results in a conservative estimate of the upper-bound internal 

dose for this set of specific exposures. 

143 
Table 31. Summary of Internal Dose for Personnel Stationed at Enewetak Island during 

Operation CASTLE 

Mean Dose (rem) Upper Bound Dose (rem) 

Organ 

Probabilistica Deterministic 

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic/ 

Probabilistic) 

Alpha Dose 

Thyroid 0.000039 

(8.5) 0.00036 0.0014 0.0036 2.6 

Lung 0.00048 

(8.6) 0.0044 0.017 0.044 2.6 

LLI wall 0.000041 

(8.3) 0.00036 0.0014 0.0036 2.5 

Beta plus Gamma Dose 

Thyroid 0.20 

(4.7) 0.59 2.5 5.7 2.2 

Lung 0.066 

(6.2) 0.80 1.4 8.0 5.6 

LLI wall 0.18 

(4.6) 0.54 2.3 5.3 2.2 

a

 Geometric means (and geometric standard deviations) from the probabilistic analysis are shown 

5.7 Summary of Results and Comparison of Upper Bound Doses 

Application of the mathematical models implemented with Mathcad calculation tools to case 

studies of five military units assigned to nuclear test operations in the PPG and one unit assigned 

to nuclear test operations at the NTS illustrate the feasibility of performing probabilistic 

uncertainty analyses for those six cases. A comparison of the upper bound doses determined 

using Monte Carlo analyses with the upper bound doses estimated using current NTPR 

deterministic techniques provides a basis for assessing whether the deterministic upper bounds 

are reasonable. 

The ratios of deterministic (NTPR) upper bound doses to the 95th percentile probabilistic doses 

for the six case studies investigated in this report—called upper bound dose ratios— are 

compiled in Table 32. The upper bound dose ratios for external doses exceed 1.0 in all cases 

considered, indicating that the upper bounds of the deterministic external doses are greater than 

the 95th percentiles of the corresponding probabilistically-calculated doses. The upper bound 

dose ratios for internal doses equal or exceed 1.0 for case studies involving exposures in the 

PPG, whereas Case Study #3 of a unit exposed at NTS produced upper bound dose ratios that are 

consistently less than 1.0. 

144 
Table 32. Ratios of Deterministic Upper Bounds to 95th Percentile Probabilistic Doses 

Upper Bound Dose Ratio

Internal α

Upper Bound Dose Ratio 

Case Internal β+γ 

Study Study Group 

Upper Bound 

Dose Ratio 

External All Organs Thyroid Lung LLI 

wall 

1 RW/Enewetak 1.6 1.4 1.5 3.7 1.3 

2 HTI/Enewetak 1.5–1.6 2.5–2.6 1.8 4.6 1.8 

3 PB 1.7 0.58–0.68 0.43 0.87 0.42 

4 RW/USS ESTES 1.1 1.5 1.1 3.2 1.0 

5 HTI/USS BOXER 1.3 4.0–4.2 2.0 6.2 2.0 

6 CASTLE/Enewetak 1.5 2.5–2.6 2.2 5.6 2.2 

Consider trends in upper bound ratios of external doses. The consistency of the ratios for the 

four land-based cases stands out: all have values of 1.5–1.7. The reason for this consistency is 

that the models used in these assessments are quite similar. The two ship-based cases have 

somewhat smaller ratios: 1.1 and 1.3. The difference between these two values can be attributed 

to the fact that the vessels had different configurations. The USS ESTES was an amphibious 

force flagship approximately elliptical in topside shape, complex and extensive superstructure, 

and three habitable decks below topside. The USS BOXER was an aircraft/helicopter carrier 

with a much larger, approximately rectangular weather deck, relatively little superstructure, and 

four habitable decks below topside. The ratios for the ship-based cases are smaller than those for 

land-based primarily because of the manner in which the variation in fallout intensity was 

modeled. For land-based, this variation is assigned a lognormal distribution with a geometric 

standard deviation of 1.5. For the ship-based cases, the variability in fallout intensity was 

modeled as described in Section 4.2.1. The latter distributions are broader, having geometric 

standard deviations of approximately 2. These broader distributions push the 95th percentiles to 

larger values and, consequently, suppress the ratios. 

Understanding the variations observed in the upper bound internal dose ratios is more 

challenging. The PPG cases are addressed first, then the NTS case. 

The implementation of a probabilistic formulation of internal dose reconstruction involved the 

integration of new algorithms into a deterministic framework that had been used in past NTPR 

assessments. The new algorithms, discussed in Section 4, resulted from more thorough modeling 

of the physics and biokinetics relevant to the various internal dose pathways, and thus represent 

improvements in the dose reconstruction methodology available to the NTPR Program. The 

upper bound internal dose ratios derived with this more complex model are dependent on a 

variety of input parameters, sometimes in relatively subtle ways. These dependencies can be 

illustrated by varying one input parameter at a time and observing the resulting variations in the 

upper bound ratios. 

Consider, for example, the upper bound ratios for exposures that occurred aboard USS BOXER 

during HARDTACK I. It is seen in Table 32 that the ratios for alpha radiation are 

approximately 4, and those for beta-gamma radiation are 2.0 for thyroid and LLI wall and 6.2 for 

145 
lung. Internal doses aboard BOXER were accrued primarily from exposures to intermingled 

fallout from Shots FIR and KOA. It was assumed in deriving the cited values that all fallout 

came from FIR, so that the time from detonation to peak intensity was about 58 hours. If one 

assumes that the fallout actually came from KOA, which was detonated about one day after FIR, 

the ratios for alpha radiation drop to about 3 and those for thyroid, lung, and LLI wall from beta 

and gamma radiation become 1.2, 5.9, and 1.1, respectively. If, on the other hand, the time of 

peak deposition had occurred 1 day later (i.e., around 82 hours after the detonation), the upper 

bound ratios increase to 4.5 for alpha, and to 2.3 (thyroid and LLI wall) and 10 (lung) for betagamma radiation. This demonstrates that the timing of the deposition has a significant effect on 

the upper bound ratios. 

Another trend evident in this example and seen more generally in Table 32 is that the upper 

bound beta-gamma dose ratios for the lung are substantially larger than those for the thyroid and 

LLI wall. This can be explained as follows. Dose to the lung depends critically on the 

respirability of the descending fallout particles—unlike the thyroid and LLI wall, the lung 

receives little dose from the non-respirable fraction that is inhaled and subsequently ingested (see 

Table 18 in Section 4). Loss of this potential dose component reduces the lung dose from the 

inhalation of descending fallout and, consequently, its 95th percentile upper bound. The 

deterministic dose is not affected by this feature because the fallout particles are assumed to have 

been totally respirable in that formulation. This causes the ratio of deterministic to probabilistic 

upper bounds to increase with respect to those of the thyroid and LLI wall, as observed. 

In contrast to the PPG results, the upper bound internal dose ratios evaluated for the NTS in Case 

Study #3 are all less than 1.0, indicating that the probabilistic 95th percentile dose is larger than 

the deterministic upper bound dose. A possible explanation for this disparity between PPG and 

NTS cases is that that both PPG and NTS case studies include internal dose contributions from 

inhalation of resuspended fallout, while only the PPG cases include contributions from the 

inhalation of descending fallout. The components of dose related to the inhalation of 

resuspended fallout have two large contributors to uncertainty: the DCFs and the resuspension 

factors. Both of these parameters are modeled as lognormal distributions with large GSDs, so 

they significantly drive up the probabilistic upper bound doses. As a result, the 95th percentileto-geometric mean dose ratio for intake of resuspended fallout typically is in the range of 40–50. 

For the inhalation of descending fallout, DCFs are major contributors to uncertainty, with lesser 

contributions from the collective uncertainties in the activity fractions, deposition fractions, and 

settling velocities. The 95th percentile-to-geometric mean dose ratios for these components are 

10 and typically 2 for beta-gamma dose to the thyroid and LLI wall, which combine 

logarithmically in quadrature to give a combined ratio of about 12; the combined ratio for lung is 

about 22. Thus, the resuspension/inhalation internal dose pathway involves a significantly larger 

uncertainty than does the descending/inhalation pathway. This larger uncertainty tends to 

increase the 95th percentile dose and decrease the upper bound dose ratios. This results in upper 

bound internal organ dose ratios of less than 1.0 for Case Study #3, for which inhalation of 

resuspended fallout dominates the internal doses. For the PPG case studies, the presence of a 

sizeable dose component from inhalation of descending fallout with its smaller uncertainty 

moderates the extent of the 95th percentile doses, thereby resulting in upper bound dose ratios 

that are equal to or greater than 1.0. 

146 
6 SENSITIVITY ANALYSIS FOR THE DOSE MODELS OF CASTLE 

ENEWETAK CASE STUDY 

Sensitivity analyses were performed for the external and internal dose models applied to the 

Army personnel at Enewetak Atoll at Operation CASTLE (1954). These analyses were carried 

out to confirm prior inference as to the input parameters to which the models are most sensitive, 

and to develop an approach on how to implement and use sensitivity analyses in NTPR dose 

reconstructions. In this section, the approach and the results are presented and discussed for both 

the external and internal dose models. It is not the intent of this analysis to develop generalized 

conclusions to be applied across many units with a broad range of exposure scenarios. 

6.1 Technical Approach 

Sensitivity analyses are performed to study how the output of a model is affected by variations or 

uncertainties in input parameters, both qualitatively or quantitatively (Saltelli et al., 2008). Case 

study doses were calculated using the Monte Carlo simulation model developed for the Army 

personnel unit that was stationed at Enewetak Atoll at Operation CASTLE and described in 

detail in Appendix F. 

In the sensitivity analyses conducted in this study, input parameters were varied one at a time 

keeping all other parameters at their respective nominal value in separate runs of the Monte 

Carlo simulation. An additional run was performed where all the input parameters were allowed 

to vary to obtain the distribution of the full probabilistic model. For each parameter varied, the 

output dose distribution was compared to the distribution that resulted from varying all the 

parameters at once. One thousand Monte Carlo simulations were performed to generate each 

distribution. A smaller number of simulations (100 trials) was also tried and results were similar 

to those presented here as far as the relative sensitivities are concerned. Generally, a smaller 

number of simulations produces a slightly narrower range in the output distribution. This is 

acceptable for this type of analysis. 

Measures of the sensitivity of the model to its input parameters and how they are evaluated can 

be defined in many ways (Hoffman and Gardner, 1983; Kirchner, 2008; Saltelli et al., 2008). 

For this study, a sensitivity score (SS) that compares ranges of variations in output dose 

distributions can be determined as follows: 

)5 -(95

)5 - (95 SS th

all

th

all

th

i

th

i

i  (6-1) 

where the 5th and 95th represent the 5th and 95th percentiles of the output dose distribution. The 

subscript “i” indicates that only the i

th parameter is randomly varied and the subscript “all” 

indicates that all the parameters are varied simultaneously as in a full Monte Carlo model 

simulation. Use of the 5th and 95th percentiles cuts off values in the tails of model output 

distributions that potentially could incorrectly influence the estimated score. As defined above, 

SS varies theoretically on a scale of 0 to 1. A score close to 0 indicates a low sensitivity of the 

model to the corresponding parameter. The closer SSi approaches 1, the more sensitive the dose 

model is to the i

th parameter. 

147 
For lognormally distributed variables, such as internal doses, a sensitivity score equivalent to that 

in Equation 6-1 can be defined by: 

th

all

th

all

th

i

th

i

i

5/ 95

5 / 95 SS  (6-2) 

or in log scale, an equivalent expression is given by SSlog, such as: 

)log(5 -)log(95

)log(5 - )log(95 SS th

all

th

all

th

i

th

i

i log  (6-3) 

Other types of sensitivity scores and measures can be devised. A few examples are as follows: 

Si = 1 – 5i

th / 95ith (6-4) 

Si = 95i

th / 5ith (6-5) 

Si = 95i

th / (central estimate)i (6-6) 

Si = 95i

th - 5ith (6-7) 

It is important that the analyst have a good understanding of the characteristics of the output and 

the underlying distributions and true range of variations of each input parameter so as to apply an 

appropriate sensitivity score. It is therefore essential to decide a priori over which range and 

scale input parameters are varied. Further discussions on sensitivity analyses and screening 

procedures can be found in Hoffman and Gardner (1983) and Kirchner (2008). 

6.2 External Dose Model Sensitivity Analysis 

The nine input parameters to the external dose model in the CASTLE Enewetak case study were 

varied one at a time. All were assumed independent of each other because they present at most a 

weak correlation. The three normalized intensity variables I1, I2, and I3 reflect the non-uniform 

distribution of fallout. They were sampled simultaneously from the same distribution and a 

combined sensitivity score for a “lumped” sensitivity parameter labeled “fallout distribution” 

was determined. This resulted in calculating a total of seven sensitivity scores. Input parameters 

with weak correlation from shot-to-shot were selected independently for each fallout event (see 

Section 4.3). 

The results of the external dose sensitivity analysis are listed in Table 33. In addition to SS, 

calculated using Equation 6-1, other sensitivity measures, shown in Equations 6-5 and 6-6, are 

included for comparison purposes. Figure 39 shows a comparison of the SS for each input 

parameter. These results show that the external dose model is most significantly sensitive to the 

variability and uncertainty in, by decreasing order of importance, intensity measurement and data 

errors, fallout distribution and decay constants. Each of these three parameters is a direct 

148 
Table 33. Sensitivity Scores for Input Parameters to the External Dose Model 

Input Parameter Varied 

All Fos Ft PFt PFb

Fallout (FO) 

Distribution 

Intensity 

Measurement Decay

5th Percentile 0.58 0.98 1.0 1 0.97 0.87 0.59 0.95 

Geometric Mean 

(GM) 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.2 

95th Percentile 2.3 1.2 1.1 1.2 1.2 1.5 1.7 1.5 

Ratio 95th/5th 4.0 1.2 1.2 1.2 1.2 1.7 2.9 1.6 

Ratio 95th/GM 2.0 1.1 1.1 1.1 1.1 1.3 1.6 1.3 

SS(*) 1.0 0.13 0.089 0.093 0.13 0.36 0.64 0.31 

(*) Sensitivity Scores may differ from the exact results of their calculation due to rounding. 

Fos is fraction of time outside; Ft is time in a tent; PFt is tent protection factor; PFb is building protection 

factor

0.0

0.2

0.4

0.6

0.8

1.0

All

Fos

Ft

PFt

PFb

FO

Distribution

Intensity

Meas.

Decay

Model Parameter

Sensitivity Score (SS)

Figure 39. Sensitivity Scores for Input Parameters to Total External Dose Model 

for the CASTLE Enewetak Case Study 

multiplier in the dose model. While the fallout distribution, which reflects the spatial variability 

of deposited radioactive materials, and decay may have broader intrinsic distributions, the 

intensity measurement and data uncertainty, which combines intensity measurement and data 

processing errors, is the only one fully correlated from shot-to-shot. Hence, deviations are larger 

149 
as values corresponding to each shot are added, and this source of uncertainty propagates more 

influence on the resultant dose distribution. The other model input parameters contribute much 

less to the overall variability of the total external dose. Ranked in decreasing sensitivity score, 

these are Fos, PFb, PFt and Ft. 

The sensitivity analysis of the external dose model for the CASTLE Enewetak cohort shows that 

uncertainties of two parameters, Ft and PFt, each contribute less than 10 percent to the overall 

variability of the external dose based on the 5th to 95th percentile ranges. It also indicates that the 

uncertainty attributed to intensity measurement, arising collectively from instrument precision, 

operator error and data recording and manipulation, constitutes the single largest contributor to 

the overall distribution of the external dose model. This was due to both the distribution 

assigned to this source of uncertainty but also to the assumption that this uncertainty was fully 

correlated from shot-to-shot. It is therefore necessary to perform a more thorough assessment of 

the values and uncertainty related to intensity data, when such a model is used for dose 

reconstruction. 

6.3 Internal Dose Model Sensitivity Analysis 

Model input parameters to the internal dose model in the CASTLE Enewetak case study were 

each varied one at a time. Each input parameter was randomly sampled from its distribution and 

was considered independent from the other parameters. However, several input parameters were 

treated as a group and varied simultaneously while the other parameters and parameter groups 

were fixed. For groups of parameters that were varied together, one sensitivity score was 

determined for the group. The groups of input parameters as well as those parameters that were 

kept single are as follows: 

 Intensity measurement data and decay factors (designated INT). 

 Inhalation dose conversion factors (DCF Inh). 

 Ingestion dose conversion factors (DCF Ing). 

 Settling Velocity (V). 

 All deposition fractions for respirable and non-respirable fallout particle sizes (RND). 

 Activity fraction parameters AF100, frac1, and frac2 (RNA). 

 Breathing rate (BR). 

 Intensity distribution of fallout near outdoor location normalized to the intensity averaged 

over the whole island, Ios, and then multiplied by Fos (OD). 

 Resuspension factor (K). 

 Incidental ingestion of soil and dust parameters: ingestion rate and soil density (“q and ρ”). 

The results of the sensitivity analysis of the internal dose to the lung for the CASTLE at 

Enewetak case study are shown in Table 34 and Table 35. In addition to SSlog, calculated using 

Equation 6-3, other sensitivity measures (depicted by Equations 6-5 and 6-6) are included for 

comparison purposes. Equation 6-3 was used because internal dose distributions tend to exert 

highly skewed lognormal behavior, so sensitivity scores were determined for the logarithm of the 

150 
Table 34. Sensitivity Scores for Input Parameters to the Internal (α) Dose Model (Lung) 

Model Input Parameter Varied (*)

All INT DCF 

Inh 

DCF 

Ing V RND RNA BR OD K q and ρ

5th Percentile 1.7E-05 2.0E-04 3.5E-05 5.4E-04 5.0E-04 5.4E-04 5.3E-04 1.7E-04 2.0E-04 8.0E-05 5.3E-04

Geometric 

Mean (GM) 4.7E-04 3.9E-04 3.4E-04 5.4E-04 5.1E-04 5.4E-04 6.2E-04 3.7E-04 3.9E-04 4.3E-04 5.3E-04

95th Percentile 1.7E-02 7.2E-04 4.4E-03 5.4E-04 5.5E-04 5.4E-04 7.6E-04 6.2E-04 8.1E-04 3.6E-03 5.3E-04

Ratio 95th/GM 37 1.8 13 1.0 1.1 1.0 1.2 1.7 2.0 8.3 1.0 

Ratio 95th/5th 991 3.6 128 1.0 1.1 1.0 1.4 3.6 4.1 45 1.0 

SSlog

(**) 1.0 0.19 0.70 0.001 0.015 0.001 0.052 0.18 0.20 0.55 0.0001 

(*) Input parameters as defined in the bulleted list above.

(**) Sensitivity Scores may differ from the exact results of their calculation due to rounding.

dose distributions. Figure 40 and Figure 41 show a comparison of SSlog, which correspond to 

each input parameter or lumped group of parameter for alpha and for beta-plus-gamma doses, 

respectively. These results show that, for this exposure scenario and organ, the internal alpha 

and beta-plus-gamma dose models are most significantly sensitive to the uncertainty in DCF for 

inhalation and resuspension factor. The models are moderately sensitive to the errors in intensity 

and decay factors, fallout distribution and breathing rate. Finally, the models for this exposure 

0.0

0.2

0.4

0.6

0.8

1.0

All Int DCF

Inh

DCF

Ing

V RND RNA BR OD K q and

r

Model Parameter

Sensitivity Score (SSlog)

ρ

Figure 40. Sensitivity Scores for Input Parameters to Total Internal (α) Dose 

Model (Lung) for the CASTLE Enewetak Case Study 

151 
scenario and organ show no or very little sensitivity to the remaining parameters or groups 

thereof, i.e., RND, RNA, DCF for ingestion and “q and ρ”. 

Table 35. Sensitivity Scores for Input Parameters to the Internal (β+γ) Dose Model (Lung)

Input Parameter Varied (*)

All INT 

DCF 

Inh 

DCF 

Ing 

Vs 

RND RNA BR OD K q and 

ρ

5th Percentile 3.1E-03 2.6E-02 5.8E-03 6.7E-02 5.4E-02 6.7E-02 6.9E-02 2.5E-02 3.4E-02 2.0E-02 6.8E-02

Geometric 

Mean (GM) 7.1E-02 5.1E-02 4.6E-02 6.8E-02 6.0E-02 6.7E-02 9.5E-02 5.2E-02 5.6E-02 6.5E-02 6.8E-02

95th Percentile 1.4E+00 8.5E-02 3.5E-01 7.1E-02 7.1E-02 6.7E-02 1.4E-01 8.7E-02 9.8E-02 4.1E-01 6.8E-02

Ratio 95th/GM 19 1.7 7.6 1.0 1.2 1.0 1.4 1.7 1.7 6.3 1.0 

Ratio 95th/5th 444 3.3 60 1.1 1.3 1.0 2.0 3.5 2.9 20 1.0 

SSlog

(**) 1.0 0.20 0.67 0.0084 0.045 0.0017 0.11 0.21 0.17 0.49 0.0002

(*) Input parameters as defined in the bulleted list above.

(*) Sensitivity Scores may differ from the exact results of their calculation due to rounding.

0.0

0.2

0.4

0.6

0.8

1.0

All Int DCF

Inh

DCF

Ing

V RND RNA BR OD K q & r

Model Parameter

Sensitivity Score (SSlog)

ρ

Figure 41. Sensitivity Scores for Input Parameters to Total Internal (β + γ) 

Dose Model (Lung) for the CASTLE Enewetak Case Study 

152 
The sensitivity analysis of the internal alpha and beta-plus-gamma lung dose models for the 

CASTLE Enewetak cohort shows that the uncertainty and variability RND, DCF Ing and 

“q and ρ”, contribute less than 1 percent each to the overall variability of internal doses based on 

the 5th to 95th percentile range of logarithmic dose. The uncertainty in the internal alpha and 

beta-plus-gamma dose models is each dominated by the dose conversion factors for inhalation 

(DCF Inh) and the resuspension factor. In the intermediate to low range and in descending order, 

the breathing rate, intensity distribution variability and fraction of time spent outdoors, 

uncertainty due to intensity measurement and processing, the activity fraction adjustment factors, 

and settling velocity have a lesser but sizeable influence on internal doses. It is emphasized that 

these observations relate only to lung dose to participants at Enewetak during Operation 

CASTLE. The results of sensitivity studies for other organs and other exposure scenarios may 

vary significantly. 

When models such as these are implemented for dose reconstruction, a thorough assessment of 

the values and uncertainties related to parameters to which the model is most sensitive should be 

conducted. Conversely, less attention should be paid to the parameters for which the models 

exhibit little or no sensitivity. 

153 
7 CONCLUSIONS AND RECOMMENDATIONS 

The main goal of this study was to investigate and demonstrate a methodology and the enabling 

computational tools to perform probabilistic radiation dose assessments for NTPR atomic 

veterans. This goal was achieved through the use of Monte Carlo simulation techniques and 

available data and information. Probabilistic models for both external and internal dose 

calculations that account for uncertainty and variability of input parameters were developed, 

tested, and applied in six case studies. Physics-based models, analysis of available operational 

and test data, and the keen judgment of analysts experienced in NTPR dose reconstruction, 

health physics, and related specialties were employed to develop realistic central values and 

distributions of model input parameters. Experience in coding the various dose components’ 

formulations and reconstruction techniques using Mathcad was essential. 

The six case studies applied probabilistic dose assessment models to five PPG cohorts and one 

NTS unit. Conventional NTPR deterministic doses were also estimated and the upper bounds 

were compared with the probabilistic 95th percentile doses. The PPG case studies comprised 

three scenarios for land-based personnel that were stationed at Enewetak Island during 

Operations CASTLE, REDWING, and HARDTACK I. The two other scenarios were for shipbased units, one that participated at Operation REDWING aboard the amphibious force flagship 

USS ESTES and the second at Operation HARDTACK I aboard the aircraft carrier USS 

BOXER. The NTS unit participated in a rehearsal and a maneuver at Shot HOOD during 

Operation PLUMBBOB. 

A pilot study developed the initial scope of the effort and quantified the uncertainty of most dose 

model parameters. Additional consultations with experts and a more refined assessment of 

available studies and literature provided further insight in parameters with more complex 

uncertainties and biases in existing models. This included improved estimates of the central 

values and uncertainties for dose conversion factors, time-dependent resuspension factors, 

resuspension factors in regions of high resuspension near detonation sites, and gamma source 

modification factors accounting for shielding afforded by ship superstructure, to name a few. 

Extensive research of the relationship of fallout deposition times to particle size distributions 

constituted one of the most difficult aspects of exposure characterization due to the limited 

availability of applicable data. Fallout deposition models to address fallout activity distributions 

based on particle settling velocities and activity fractions were developed and benchmarked with 

the limited available data to provide reasonable estimates of the activity fractions in respirable 

and non-respirable classes. Although it is believed that the methodology developed is acceptable 

for the purpose of this study, additional investigations are warranted to further elucidate other 

important factors that affect airborne concentrations of radioactivity, such as fractionation. 

A comparison between reconstructed model doses and film badge readings was carried out for 

units where reliable dosimetry data were available. These units are the Army personnel at 

Enewetak during REDWING and HARDTACK I, the crew of the USS BOXER during 

HARDTACK I, and the Marine unit at NTS during PLUMBBOB. For these four groups, 

reconstructed probabilistic external doses matched well with the film badge doses. The 

95th percentile of the probabilistic dose distribution exceeded the 95th percentile of the film badge 

dose distribution. 

154 
Results show that in all cases, deterministic (NTPR) upper bound external gamma doses were 

higher than the corresponding probabilistic 95th percentile doses. Deterministic upper bounds 

were 50 to 60 percent higher than the probabilistic 95th percentile doses for the land-based PPG 

and NTS cases. For ship-based groups, the deterministic upper bound external doses were 10 

and 30 percent higher. The case studies are consistent with each other in that upper bound 

external doses calculated using the NTPR deterministic “high-sided” approach and an upper 

bound factor of 3 are higher that the 95th percentile confidence limit determined by a 

comprehensive probabilistic analysis using Monte Carlo simulations. The consistency of these 

results shall be verified in other scenarios of participation for application in future NTPR dose 

assessments. 

For internally-deposited radioactive materials, the NTPR deterministic method resulted in 

internal upper bound doses, determined by multiplying the doses by a factor of 10, higher than 

the probabilistic 95th percentile doses, except in the case of the Marine unit at PLUMBBOB 

discussed below. For all the PPG cases, the deterministic upper bound doses from alpha 

radiation to three sample organs (thyroid, lung, and lower large intestine wall) were 1.4 to 4.2 

times higher than the probabilistic 95th percentile doses. The highest ratios of 4 to 4.2 were those 

for the crew of the USS BOXER at HARDTACK I. For beta-plus-gamma radiation, the 

deterministic upper bound doses ranged from about 1 to 6 times the probabilistic 95th percentile 

doses, with the ratio of 1.0 observed for the dose to the LLI wall of personnel aboard the USS 

ESTES during Operation REDWING. Although it is clear that for all the PPG case studies, the 

deterministic model has captured at least the 95th percentile confidence limit, a broad conclusion 

cannot be made for all types of scenarios. Having said that, the case studies included in this 

investigation varied in type (land and two very different types of ships), number and time of 

occurrence of fallout events, radiation intensities and fallout deposition, time veterans spent at 

the PPG, etc. Therefore, implementation of the probabilistic methodologies can proceed but with 

the expectation that further refinements should take place and any adjustments will require 

revision of the standard methods as applicable. 

In the PLUMBBOB case study, the NTPR deterministic upper bound internal doses were lower 

than the 95th percentile doses calculated using the probabilistic model. The deterministic upper 

bound alpha doses to the three selected organs are about 60 to 70 percent of the corresponding 

95th percentile doses estimated by the probabilistic analysis. For beta-plus-gamma radiation, the 

deterministic upper bound internal doses are 42 to 87 percent of the corresponding probabilistic 

95th percentile doses. It is clear that in this case, either the deterministic model is not high-sided 

enough to capture at least the 95th percentile of the dose distribution, or the probabilistic model 

overestimates the uncertainty and variability of key influential input parameters. For the 

probabilistic model, the multiplicative effect of several input parameter distributions with 95th

percentile factors of 10 or more produces, in the case studied, 95th percentile doses that are 15 to 

30 times their corresponding geometric means. These parameters include dose conversion 

factors, resuspension factors and radiation intensities when extrapolated from iso-intensity maps. 

Although the geometric means are 2 to 11 times lower than the deterministic doses, the 

95th percentiles are higher than the deterministic upper bounds by factors of 1.1 to 2.4. 

It is evident that a broad-based conclusion about the comparison of deterministic and 

probabilistic upper bounds cannot be made based on the study of the PLUMBBOB Marine unit 

given the specific scenario of exposure and activities. Nevertheless, the probabilistic analysis 

methodology and capability for estimating uncertainty for NTS participation has been 

155 
demonstrated and can be applied to other units and individual cases. As for PPG cases, further 

refinements are recommended with emphasis on additional analysis of individual dose 

components that contribute to the total internal dose and their corresponding input parameters 

and distributions. In addition, investigation of the impacts of revised distributions of 

resuspension factors, uncertainty factors for dose coefficients for alpha particles, and estimated 

uncertainties for other internal dose parameters in the recently published update to Kocher et al. 

(2006)7

 may contribute to further understanding of these results. The results and findings 

summarized in the preceding paragraphs were based on the best available information on 

parameter distributions as of the time the models for the case studies were last ran. 

A sensitivity analysis was performed to identify the possibility of screening out sources of 

uncertainty with small or limited impact on dose. A simple method that varied model parameters 

one-at-a-time was applied for both external and internal doses using the Army personnel at 

Enewetak during CASTLE as an example. Each parameter or group of parameters in the dose 

models was varied individually according to its probability distribution while all other 

parameters or groups of parameters were held fixed. In this way, the variation of that single 

parameter or group of parameters was studied for its individual influence on the model output. 

The findings of the sensitivity analysis show that, in the case of external dose to participants who 

served at Enewetak during Operation CASTLE, the most significant source of uncertainty is that 

related to intensity measurements and intensity data recording and processing, with the 

variability resulting from the non-uniform distribution of fallout and uncertainty in fallout decay 

rates showing lower, but significant influence. The least influential parameters for this scenario 

are the tent and building protection factors and fraction of time a person spent outdoors or inside 

a tent versus a building. For internal lung dose, the dominant source of uncertainty is that 

associated with the inhalation dose conversion factors, followed closely by the uncertainty in 

resuspension factors. In the medium range of influence were the uncertainties related to the 

breathing rate and the radiation environment, which included intensity measurement and related 

data collection and processing, and the non-uniform distribution of fallout. The least influential 

parameters were the ingestion dose conversion factors, deposition fraction, and activity fraction. 

The uncertainty on parameters specific to the incidental ingestion of soil (rate of ingestion and 

soil density) had no effect on internal dose. It is useful to note, however, that these model 

sensitivities are specific to the sample organ and scenario used to illustrate how to use sensitivity 

analyses in dose reconstruction. Successful application of this methodology to a broader range 

of organs and exposure scenarios will provide a basis for future refinements of existing dose 

models. 

Therefore, it is concluded from this study that methods for applying probabilistic uncertainty 

analyses in NTPR radiation dose reconstructions are feasible. In particular, these methods, to the 

level of modeling and parameterization described herein, have been shown to perform 

successfully when applied to the estimation of radiation doses received by participants in six 

cases of exposure during atmospheric nuclear testing. In addition, the results of the case studies 

support conclusions that the deterministic upper bound factors of “3” and “10” proscribed in 

DTRA policy provide reasonable upper bounds, except for the internal doses in the PLUMBBOB 

 

7

 Kocher, D. C., Trabalka, J.R., and Apostoaei, A.J., 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, SENES, Oak Ridge, Inc., Oak Ridge, TN and Defense Threat Reduction 

Agency, Fort Belvior, VA. 

156 
scenario of exposure. For this and similar scenarios where the dose component from inhalation 

of resuspended materials dominates the overall internal dose, an uncertainty factor higher than 

“10” is possible, as for the PLUMBBOB case study. Such scenarios of exposure need to be 

assessed using a more detailed uncertainty analysis, such as the one described in this report. 

The results discussed above and in Section 5 are valid for the six case studies only and cannot be 

generalized to all exposure scenarios. Only the methodologies developed and presented in this 

report can be applied and expanded to other scenarios of exposure. The analyses conducted in 

this study provide reasonable estimates of dose and associated uncertainties for the types of 

exposure scenarios investigated and support implementation of the probabilistic approach to 

radiation dose assessments in the NTPR Program. The following recommendations are offered 

to achieve implementation of the approach: 

 Conduct testing of probabilistic methods applied to other exposure scenarios, test series, and 

participant units to develop experience with preparing reasonable distributions of parameters 

to support implementation of these methods. 

 Incorporate probabilistic approaches developed in this report to NTPR RDA procedures and 

methodologies. 

 Implement the probabilistic analyses described herein when performing future radiation dose 

reconstructions and adapt model parameter distributions when case-specific scenarios are 

well documented. 

157 
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 (2002). 

Barrett, M., Goetz, J., Klemm, J., McRaney, W., and Phillips, J., 1986. Low Level Internal Dose 

Screen – CONUS Tests. DNA-TR-85-317 (Defense Nuclear Agency, Washington, D.C.). 

Bolch, Wesley. E., Farfán, E.B., Huh, C., Huston, T.E., and Bolch, W. Emmett, 2001. Influence 

of Parameter Uncertainties within the ICRP 66 Respiratory Tract Model: Particle 

Deposition. Health Physics 81(4):378 –394 (2001). 

Bruce-Henderson, S., Gladeck, F.R., Hallowell, J.H., Martin, E.J., McMullan, F.W., Miller, 

R.H., Rogers, W.E., Rowland, R.H., Shelton, C.F., Sturman, P., Berkhouse, L.H., Davis, 

S., DeSantis, H., Dean, P., Doyle, M.K., and Patterson, D.S. , 1982. Operation 

REDWING: 1956, United States Atmospheric Nuclear Weapons Tests, Nuclear Test 

Personnel Review. DNA 6037F (Defense Nuclear Agency, Washington, D.C.). 

Bulmer, M.G., 1979. Principles of Statistics. Dover, New York. 

Chehata, M., 2009. Guidelines for Estimating Uncertainty from Measured Intensity Data and IsoIntensity Maps. NTPR-TM-09-13 (Science Applications International Corporation. 

McLean, VA.) 

Chehata, M., Jasinski, D., Monteith, M.C., and Samuels, W.B., 2007. Mapping ThreeDimensional Water Quality Data in the Chesapeake Bay Using Geostatistics. Journal of 

the American Water Resources Association (JAWRA), Vol. 43, No. 3, pp. 813–828, June 

2007. 

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 (Science 

Applications International Corporation, McLean, VA). 

Chilès, J.P., and Delfiner, P., 1999. Geostatistics, Modeling Spatial Uncertainty. Wiley Series in 

Probability and Statistics, John Wiley and Sons, New York. 

Danon, Y., 2008. DIGITIZE-PRO, Version 4.1. http://www.rpi.edu/~danony/software.htm

(Accessed February 23, 2010) or http://www.nuceng.com/Digitizepro.htm (Accessed 

February 23, 2010), Rensselaer Polytechnic Institute, Troy, NY. 

Doane, D.P. and Seward, L.E., 2009. Applied Statistics in Business and Economics, 2nd edition. 

McGraw Hill Irwin, Burr Ridge, IL. 

DoD/DVA (Department of Defense/Department of Veterans Affairs), 2004. Radiation Dose 

Reconstruction Program of the Department of Defense (DoD) Report to Congress. 

June 3, 2004. 

DoD (Department of Defense), 2009. 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, Government Printing Office. 

Current version is March 24, 2009. 

158 
Donley, H.E., 2009. The Drag Force on a Sphere, a module available at 

http://www.ma.iup.edu/projects/CalcDEMma/drag/drag.html (Accessed February 23, 

2010). Mathematics Department, Indiana University of Pennsylvania, Indiana, PA. 

DTRA (Defense Threat Reduction Agency), 2003. Letter from C. Benavides (Contracting 

Officer) to Mr. Steve Powell (Titan Corporation), re: DTRA01-01-C-0007, July 16, 2003. 

DTRA (Defense Threat Reduction Agency), 2007a. Policy and Guidance Manual – Nuclear Test 

Personnel Review Program. Revision 7 (Defense Threat Reduction Agency, Fort Belvoir, 

VA), November 26, 2007. 

DTRA (Defense Threat Reduction Agency), 2007b. Director’s Letter to Chairman. VBDR, 

December 10, 2007. 

DVA (U.S. Department of Veterans Affairs), 2002. Title 38, Code of Federal Regulations, Part 

3, Section 309, Disease Subject to Presumptive Service Connection. 

Eckerman, K.F., Leggett, R.W., Nelson, C.B., Puskin, J.S., and Richardson, A.C.B., 1999. 

Cancer Risk Coefficients for Environmental Exposure to Radionuclides. Federal 

Guidance Report No. 13, EPA 402-R-99-001, U.S. Environmental Protection Agency, 

Washington, DC.

Finn, S.P., Simmons, G.L., and Spencer, L.V., 1979. Calculation of Fission Product Gamma 

Ray and Beta Spectra at Selected Times after Fast Fission of U238 and U235 and Thermal 

Fission of U235. SAI Report SAI-78-782-LJ/F, prepared by Science Applications, Inc., for 

National Bureau of Standards. 

Frank, G., Goetz, J., Klemm, J., Thomas, C., 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, D.C.). 

Gladeck, F.R., Gould, K.G., Hallowell, J.H., Martin, E.J., McMullan, F.W., Miller, R.A., 

Osborn, M.J., Shelton, C.F., Berkhouse, L., and Calhoun, F.S., 1982. Operation 

HARDTACK I (1958). DNA 6038F (Defense Nuclear Agency, Washington, D.C.). 

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

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

Goetz, J.L., Kaul, D., Klemm, J., and McGahan, J.T., 1979. Analysis of Radiation Exposure for 

Task Force Warrior – Shot SMOKY – Exercise Desert Rock VII–VIII Operation 

PLUMBBOB. DNA 4747F (Defense Nuclear Agency, Washington, D.C.). 

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, July 15, 1980. 

Goetz, J., Klemm, J., Phillips, J., and Thomas, C., 1987. Analysis of Radiation Exposure—

Service Personnel on Rongerik Atoll, Operation CASTLE—Shot BRAVO. DNA-TR-86-

120 (Defense Nuclear Agency, Washington, D.C.). 

Hahn, G.J and Shapiro, S.S., 1967. Statistical Models in Engineering. John Wiley, New York. 

159 
Halbleib, J.A., Kensek, R.P., Mehlhorn, T.A., Valdez, G.D., Seltzer, S.M., and Berger, M.J., 

1992. ITS Version 3.0: The Integrated TIGER Series of Coupled Electron/Photon Monte 

Carlo Transport Codes. SAND 91-1634 (Sandia National Laboratories, Albuquerque, 

NM). 

Harrison, J.D., Leggett, R.W., Noßke, D., Paquet, F., Phipps, A.W., Taylor, D.M. and Metivier, 

H., 2001. Reliability of the ICRP's Dose Coefficients for Members of the Public, II. 

Uncertainties in the Absorption of Ingested Radionuclides and the Effect on Dose 

Estimates. Radiation Protection Dosimetry, 95:295–308 (2001), Oxford University Press. 

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, D.C.). 

Hicks, H. G., 1984. Results of Calculations of External Gamma Radiation Exposure Rates from 

Local Fallout and the Related Radionuclide Compositions of Selected U.S. Pacific 

Events. UCRL-53505 (Lawrence Livermore National Laboratory, Livermore, CA). 

Hillel, D., 1980. Fundamentals of Soil Physics. Acad. Press, N.Y. 413 p. 

Hoffman, F.O. and Gardner, R.H., 1983. Evaluation of Uncertainties in Radiological Assessment 

Models. Chapter 11 in Radiological Assessment, A Textbook on Environmental Dose 

Analysis, Till, J.E. and Meyer, H.R., Eds., NUREG/CR-3332; ORNL-5968 (Oak Ridge 

National Laboratory, Oak Ridge, Tennessee). 

Holmes & Narver, 1956. Completion Report, Operation REDWING, Pacific Proving 

Ground,1954–1956. Holmes & Narver for U. S. Atomic Energy Commission. 

HydeSoft Computing, 2008. DPLOT, Graph Software for Scientists and Engineers. 

http://www.dplot.com/ (Accessed February 23, 2010), HydeSoft Computing, LLC, 

Vicksburg, MS. 

ICRP (International Commission on Radiological Protection), 1977. Recommendations of the 

International Commission on Radiological Protection. ICRP Publication 26, Annals of 

the ICRP 1(3), Pergamon Press, Oxford, England. 

ICRP (International Commission on Radiological Protection), 1979. Limits for Intakes by 

Workers, A Report of Committee 2 of the International Commission on Radiological 

Protection. ICRP Publication 30, Annals of the ICRP 2(3/4), Pergamon Press, Elmsford, 

NY. 

ICRP (International Commission on Radiological Protection), 1994. Human Respiratory Tract 

Model for Radiological Protection. ICRP Publication 66, Pergamon Press, Elmsford, 

NY. 

ICRP (International Commission on Radiological Protection), 1996. Age-Dependent Doses to 

the Members of the Public from Intake of Radionuclides Part 5, Compilation of Ingestion 

and Inhalation Coefficients. ICRP Publication 72, Ann. ICRP 26/1, Pergamon Press, 

Elmsford, NY. 

ICRP (International Commission on Radiological Protection), 2002. The ICRP Database of Dose 

Coefficients: Workers and Members of the Public. Compact Disc Version 2.01, ICRP, 

Stockholm, Sweden. 

160 
Jacobson, M.Z., 1998. Fundamentals of Atmospheric Modeling. Cambridge University Press, 

New York, NY. 

Kellogg, W.W., Rapp, R.R., and Greenfield, S.M., 1957. Close-in Fallout. Journal of 

Meteorology, 14(1):1–8 (February, 1957). 

Kirchner, T.B., 2008. Estimating and Applying Uncertainty in Assessment Models, in 

Radiological Assessment and Environmental Analysis, Till, J. E. and Grogan, H. A., 

Editors, Oxford University Press, Oxford, New York. 

Kocher, D.C., Trabalka, J.R., Apostoaei, A.I., 2006. Evaluation of Inhalation Doses in Scenarios 

Involving Resuspension by Nuclear Detonations at Nevada Test Site (Revision 2). 

December, 2006. (SENES Oak Ridge, Inc., Center for Risk Analysis, Oak Ridge, TN). 

Lorence, L.J., Morel, J.E., and Valdez, G.D, 1989. Users Guide to CEPXS/ONEDANT: A OneDimensional Coupled Electron-Photon Discrete Ordinates Code Package, Version 1.0. 

SAND 89-1661 (Sandia National Laboratories, Albuquerque, NM). 

Martin, E.J. and Rowland, R.H., 1982. CASTLE Series: 1954, United States Atmospheric 

Nuclear Weapons Tests, Nuclear Test Personnel Review. DNA 6035F (Defense Nuclear 

Agency, Washington, D. C.). 

McKay, M. D. Beckman, R. J. and Conover, W. J., 1979. A Comparison of Three Methods for 

Selecting Values of Input Variables in the Analysis of Output from a Computer Code. 

Technometrics, Vol. 21(2), pp. 239–245, May, 1979. 

McKenzie-Carter, M., 2009. Bias Adjustments for Use with FIIDOS Inhalation Dose Conversion 

Factors. NTPR-TM-09-08 (Science Applications International Corporation. McLean, 

VA). 

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

Descending Fallout. NTPR-TM-09-09 (Science Applications International Corporation. 

McLean, VA). 

Molumphy, G.G., and Bigger, M.M., 1957. Proof Testing of Atomic Weapons Ship 

Countermeasures. WT-927 (U.S. Naval Radiological Defense Laboratory). 

Morgan, M.G. and Henrion , M., 1990. Uncertainty: A Guide to Dealing with Uncertainty in 

Quantitative Risk and Policy Analysis. Cambridge University Press, New York. 

NCRP (National Council on Radiological Protection and Measurements), 1996. A Guide for 

Uncertainty Analysis in Dose and Risk Assessments Related to Environmental 

Contamination. NCRP Commentary No. 14 (National Council on Radiation Protection 

and Measurements, Bethesda, Maryland). 

NCRP (National Council on Radiological Protection and Measurements), 1997. Deposition, 

Retention and Dosimetry of Inhaled Radioactive Substances, NCRP Report No. 125 

(National Council on Radiation Protection and Measurements, Bethesda, Maryland). 

NCRP (National Council on Radiological Protection and Measurements), 2007. Uncertainties in 

the Measurement and Dosimetry of External Radiation. NCRP Report No. 158 (National 

Council on Radiation Protection and Measurements, Bethesda, Maryland). 

161 
NIST (National Institute of Standards and Technology), 2009. NIST/SEMATECH e-Handbook 

of Statistical Methods. http://www.itl.nist.gov/div898/handbook/ (Accessed February 23, 

2010), (National Institute of Standards and Technology, Gaithersburg, Maryland). 

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

(National Research Council, Washington, D.C.). 

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

Defense Threat Reduction Agency. (National Research Council, Washington, D.C.). 

PDAS (Public Domain Aeronautical Software), 2009. Available at 

http://www.pdas.com/m1.htm (Accessed February 23, 2010), Public Domain 

Aeronautical Software, Santa Cruz, CA. 

Phalen, R.F., Oldham, M.J., Beaucage, C.B., Crocker, T.T., and Mortensen, J.D., 1985. PostNatal Enlargement of Human Tracheobronchial Airways and Implications for Particle 

Deposition. The Anatomical Record, 212(4), 368–380 (1985). 

Raabe, O.G., 1972. Instruments and Methods for Characterizing Radioactive Aerosols. IEEE 

Transactions on Nuclear Science, Vol. NS19, No. 1 (February, 1972). 

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 (Science Applications International 

Corporation, McLean, VA and Defense Threat Reduction Agency, Fort Belvoir, VA). 

Rapp, R.R., 1959. Summary Report of RAND Work on the AFSWP Fallout Project. AFSWP 

1134 (The RAND Corporation, Santa Monica, CA). 

Rinnert, H.R., 1957. Project 2.71: Ship Shielding Studies, Operation REDWING. WT-1321 

(U.S. Naval Radiological Defense Laboratory, San Francisco, CA). 

Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D. Saisana, M., and 

Tarantola, S., 2008. Global Sensitivity Analysis, The Primer. John Wiley & Sons. 

Scoville, H., 1954. Radiological Survey of Downwind Atolls Contaminated by BRAVO. TU13-54-375 (memorandum from Technical Director, AFSWP, to Headquarters Task 

Unit 13). 

Servis, J.D., 1981. Operation CASTLE Radiological Safety. WT-942 (EX) (Defense Nuclear 

Agency, Washington D.C.). 

Soule, R.R. and Shirasawa, T.H., 1981. Operation REDWING, Project 2.61, Rocket 

Determination of Activity Distribution Within the Stabilized Cloud. WT-1315 (EX) 

(Defense Nuclear Agency, Washington, D.C.). 

Spellman, F.R., and Whiting, N.E., 2004. Environmental Engineer’s Mathematical Handbook. 

CRC Press, Boca Raton, FL. 

Stearns, F., 1968. A Method for Estimating the Quantitative Reliability of Isoline Maps. Annals 

of the Association of American Geographers, Vol. 58, No. 3, pp. 590–600, September 

1968. 

162 
Stevens, P.N., and Trubey, D.K., 1972. Weapons Radiation Shielding Handbook – Chapter 3: 

Methods for Calculating Neutron and Gamma-Ray Attenuation. DNA-1892-3 (Defense 

Nuclear Agency, Washington, D.C.). 

Thomas, C., Goetz, J., Klemm, J., and Weitz, R., 1984. Analysis of Radiation Exposure for 

Naval Personnel at Operation CASTLE. DNA-TR-84-6 (Defense Nuclear Agency, 

Washington, D.C.). 

Till, J.E. and Meyer, H.E., 1983. Radiological Assessment, A Textbook on Environmental Dose 

Analysis. NUREG/CR-3332, ORNL-5968, September, 1983 (U.S. Nuclear Regulatory 

Commission, Washington, D.C.). 

Tomoeda, S., Kreger, W.E., Hastings, M.B., and Miller, W.G., 1959. Gamma Ray Penetration 

into the Compartments of a Light Aircraft Carrier. USNRDL-TR-343 (U.S. Naval 

Radiological Defense Laboratory, San Francisco, CA). 

Triffet, T. and LaRiviere, P.D., 1982. Operation REDWING, Project 2.63, Characterization of 

Fallout. WT-1317 (EX) (Defense Nuclear Agency, Washington, D.C.). 

USACHPPM (U.S. Army Center for Health Promotion and Preventive Medicine), 2003. 

Reference Document (RD) 230, Exposure Guidelines for Deployed Military, a 

Companion Document to Technical Guide (TG) 230, Chemical Exposure Guidelines for 

Deployed Military Personnel, Version 1.3 (updated May 2003). RD-230. 

USD (Undersecretary of Defense), 2004. Advisory Board on Veterans Dose Reconstruction 

Charter. Memorandum, November 17, 2004. 

USEPA (U.S. Environmental Protection Agency), 1996. Soil Screening Guidance: Technical 

Background Document. EPA/540/R-95/128 (U.S. Environmental Protection Agency, 

Washington, D.C.). 

USEPA (U.S. Environmental Protection Agency), 1997. Exposure Factors Handbook. 

EPA/600/P-95/002Fa, Fb, Fc. (U.S. Environmental Protection Agency, Washington, 

D.C.). 

USEPA (U.S. Environmental Protection Agency), 2001. Risk Assessment Guidance for 

Superfund (RAGS) Volume III – Part A: Process for Conducting Probabilistic Risk 

Assessment. EPA 540-R-02-002, OSWER 9285.7-45, PB2002 963302, December 2001. 

USEPA (U.S. Environmental Protection Agency), 2002. Supplemental Guidance for Developing 

Soil Screening Levels for Superfund Sites. OSWER 9355.4-24 (U.S. Environmental 

Protection Agency, Washington, D.C.). 

USMC (United States Marine Corps), 1957. “USMC Final Report of Exercise Desert Rock 

VII,” circa 1957. 

VBDR (Veteran’s Advisory Board on Dose Reconstruction), 2007. Letter from Chairman of 

VBDR to Director of DTRA. October 16, 2007. 

Vose, D., 2008. Risk Analysis: A Quantitative Guide. John Wiley, Chichester, England 

Waldorf, W.F., 1959. A Correlation Between Theory and Experiment in Ship Shielding Studies. 

USNRDL-TR-373 (U.S. Naval Radiological Defense Laboratory, San Francisco, CA). 

163 
Weitz, R.L., 2009a. Internal Dose from Inhalation of Descending Fallout. NTPR-TM-09-07 

(Science Applications International Corporation, McLean, VA). 

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

Deck. NTPR-TM-09-05 (Science Applications International Corporation, McLean, VA). 

Weitz, R.L., 2009c. Modeling of Protection Factors for Land-Based Structures. NTPR-TM-09-10 

(Science Applications International Corporation, McLean, VA). 

Weitz, R.L., 2009d. Modeling of Shielding Factors for Ships. NTPR_TM-09-11 (Science 

Applications International Corporation, McLean, VA). 

Weitz, R.L., 2009e. Formulation of the Gamma Source Modification Factor (GSMF) for Shipbased Applications. NTPR-TM-09-04 (Science Applications International Corporation, 

McLean, VA). 

Weitz, R.L., 2009f. Characterization of Descending Fallout. NTPR-TM-09-06 (Science 

Applications International Corporation, McLean, VA). 

164 
APPENDIX A Monte Carlo Analysis of Dose to Army Units Stationed on 

Enewetak Island During Operation REDWING 

Carol Mason 

165 
APPENDIX A Monte Carlo Analysis of Dose to Army Units Stationed on Enewetak 

Island During Operation REDWING 

Introduction

Distributions of external and internal doses were generated by Monte Carlo techniques for 

personnel of the Headquarters (HQ) Detachment of the 7126th Army Unit (AU) stationed on 

Enewetak Island of Enewetak Atoll during Operation REDWING (1956). Doses are reported for 

the period extending from the film badge issue date of July 11, 1956, until the film badge return 

date of August 3, 1956. 

Background 

Operation REDWING was a series of 17 atmospheric nuclear tests, conducted from May 5 to 

July 22, 1956, at the Pacific Proving Ground (PPG) in the Marshall Islands. The PPG consisted 

of the land areas of Enewetak and Bikini Atolls, their lagoons, and the waters within 2.6 nautical 

miles (3 statute miles) of their seaward sides. (Bruce-Henderson, 1982) 

The HQ Detachment of the 7126th AU, consisting of 39 officers and 348 enlisted personnel, was 

stationed on Enewetak Island during Operation REDWING. The 7126th AU provided most of 

the personnel for Task Group (TG) 7.2. It was the permanent garrison force at Enewetak Island 

between Operations CASTLE and REDWING. Except for its military police detachment and 

several mail clerks on Eneu and Parry Islands, the 7126th AU was stationed on Enewetak Island. 

To accommodate the buildup to Operations REDWING's operational phase, the 7126th AU was 

reorganized into the following four detachments: Headquarters, Service, Transportation, and 

Military Police. TG 7.2 was, in effect, a housekeeping unit, providing garrison and support 

elements for the joint task force in the PPG. 

Assigned personnel arrived at Enewetak Island prior to the first nuclear detonation of the series. 

By the nature of their duties, it is likely that most of these personnel remained on the island 

continuously, or nearly so, throughout the operation. 

Exposure Scenario 

Enewetak, Parry, and Japtan Islands were the residence islands of Enewetak Atoll, where most 

land-based personnel were stationed. Fallout from four Operation REDWING detonations 

contributed to the radiation environment at the residence islands. Table A-1 identifies these 

shots and the corresponding peak fallout intensities in units of mR hr−1

 at the indicated elapsed 

times after the detonations in hours (H+hours). Additional early-time intensity data for 

Enewetak Island are provided after the table. (Jacks, 1957) 

The early-time intensity function for Enewetak Island following Shot ZUNI is defined by the 

time-intensity pairs shown in Table A-2. 

166 
Table A-1. Peak Radiation Intensities on Enewetak Island during 

Operation REDWING 

Shot Shot Date (1956) (Time) Peak Intensity (mR hr−1) 

 ZUNI May 28 (0556) 0.25 at H+11 hours 

 MOHAWK Jul 3 (0606) 12 at H+3 hours 

 APACHE Jul 9 (0606) 0.84 at H+20.9 hours 

 TEWA Jul 21 (0546) 120 at H+26 hours 

Table A-2. Early Time Intensity Function on 

Enewetak Island following Shot ZUNI 

Time After 

Detonation (hr) Intensity (mR hr−1

) 

8.5 0.01 

11 0.25 

18 0.13 

The early-time intensity data for Shot MOHAWK contains 25 time-intensity data pairs and is not 

included here. The intensity for MOHAWK fallout on Enewetak Island peaked at 12 mR hr−1

3 hours after the detonation and then reached a second, lower peak of about 4 mR hr−1

 at 9 hours 

after the detonation. 

The early-time intensity function for Enewetak Island following Shot APACHE is defined by the 

time-intensity pairs shown in Table A-3. 

Table A-3. Early Time Intensity Function on 

Enewetak Island following Shot APACHE 

Time After 

Detonation (hr) Intensity (mR hr−1

) 

16.9 < 0.01 

17.4 0.01 

17.65 0.69 

17.9 0.74 

20.9 0.84 

21.9 0.74 

25.9 0.60 

167 
Shot TEWA resulted in most of the dose accrued by personnel at the residence islands in late 

July 1956. Fallout radiation intensities from TEWA were measured at two locations on Parry 

Island: HQ JTF 7 and the Radsafe Building. Those measurements form the basis for the Shot 

TEWA early-time intensity model for the residence islands. Decontamination at HQ JTF 7 

began on July 26 (H+114 hours) and was completed on July 31 (H+258 hours). On August 10, 

the entire island was monitored and most readings were 0.003 rep·hr−1

 (beta plus gamma) or less. 

Using the Radsafe Building data decayed to August 10 yields an intensity of about 1.5 mR hr−1

, 

which is consistent with the survey results, assuming a ratio of (beta plus gamma)/gamma of 1.5 

to 2. The modeled early time intensity data for the residence islands are presented in Table A-4. 

Table A-4. Early Time Intensity Function on 

Enewetak Island following Shot TEWA 

Time After Detonation 

(T in hr) 

Intensity 

(EarlyI in mR hr−1

) 

1 0.129

5 0.145

9 0.638

11 4.913

12 21.338

14 53.875

15 84.000

18 100.351

19 94.063

21 108.438

25 115.500

26 112.125

29 87.375

33 71.938

47 39.277

57 33.205

67 28.854

77 23.572

96 17.964

114 15.254

There was no documented decontamination effort on Enewetak Island soon after Shot TEWA, 

suggesting that the intensity levels were lower. As a conservative estimate, the intensities at 

Enewetak Island are taken to be the average of measurements from HQ JTF 7 and the Radsafe 

building at Parry Island to July 26 (prior to decontamination at Parry Island). The last early-time 

intensity data point for Enewetak Island is 15.25 mR hr−1

 at 114 hours after detonation. 

Extrapolation beyond the time of the last time-intensity point for each shot is accomplished by 

assuming t−1.2 decay for deterministic calculations and by utilizing the shot-specific FIIDOS 

decay functions for probabilistic calculations as discussed in Section 3.2. 

168 
External Dose: Approach 

Film Badge Data 

Complete records of film badge results are available for the HQ Detachment. Most personnel in 

the unit were issued three consecutive permanent film badge dosimeters during their stay in the 

test area, which covered a total period extending from mid-April to early August 1956. 

However, most film badges issued for periods of 4 weeks or more at Operation REDWING were 

damaged by the high heat and humidity in the test area (NRC, 1989), which resulted in 

overstated readings. Thus, most of the badges for the unit were not suitable as a benchmark for 

comparison with reconstructed doses. It was, therefore, necessary to identify a set of badges 

worn for a shorter period and for which previous analysis had demonstrated the integrity of the 

readings. Based on previous experience in identifying damaged dosimeter films and a review of 

the Operation REDWING dosimetry database, a group of film badge doses for this unit was 

analyzed for a period extending from July 11 to August 3, 1956. As a result, a set of 323 badges 

was selected. Bias was removed from the film badge readings based on guidance on film badge 

dosimetry (NRC, 1989). Both the distribution of film badge readings and the cumulative 

distribution function (CDF) (Figure A-1) demonstrate that the unbiased film badge readings for 

the HQ Detachment follow a Gaussian distribution, which suggests relative internal cohesion in 

the unit with regard to radiation exposure conditions. The average unbiased film badge reading 

for the distribution is 2.9 rem, with a standard deviation of 0.61 rem. 

0.00

0.05

0.10

0.15

0.20

1.0 2.0 3.0 4.0 5.0

Dose (rem)

Relative Frequency of Dose

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Cumulative Distribution of Dose

Rel. Freq. of dose

Cumulative Distribution

Figure A-1. Distribution of Unbiased Film Badge Results for HQ Detachment Personnel 

169 
Monte Carlo-Based Dose Reconstruction 

Probabilistic external gamma dose reconstruction for personnel stationed on Enewetak Island 

during Operation REDWING was accomplished by incorporating uncertainty distributions for 

various parameters into the model discussed in Section 3. The specific parameters used in both 

the deterministic and uncertainty analyses of external dose are shown in Table A-5. 

Table A-5. Input Parameter Specification for External Gamma Dose Reconstruction, 

Case Study #1 

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 

min = 2/24 

peak = 8/24 

max = 16/24 

0.34 (or 8/24) 0.6 (or 14.4/24) 

Ft Fraction of inside time spent in tent 

Triangular 

min = 0 

peak = 0.5 

max = 1 

0.5 0 

PFt Protection factor for tent 

Numerical model 

(see Section 4.2.2) 

μ = 1.4 

UB95 = 1.9 

1.4 

(median of 

distribution) 

1.5 

PFb Protection factor for building 

Numerical model 

(see Section 4.2.2) 

μ = 2.1 

UB95 = 3.9 

2.0 

(median of 

distribution) 

2.0 

Ii

Intensity of fallout near outdoor 

location (i=1), tent location (i=2), 

and building location (i=3) 

frequented by veteran, normalized 

to the intensity averaged over entire 

island 

Lognormal 

GM = 1.0 

GSD = 1.5 

1.0 1.0 

INTENSITY MEASUREMENTS FOR LAND-BASED PERSONNEL 

Im Measured intensities 

Normal 

μ = Im, σ = 0.3·Im 

(to account for 

measurement error) 

1.0 1.0 

a

Exponent of multiplicative error 

factor (t/t0)

±a

 applied to FIIDOSgenerated intensity functions 

Normal 

μ = 0 

σ = 0.15 

0 0 

170 
Parameter Definition 

Distribution for 

Probabilistic 

Analysis (*)

Nominal Value 

for Central 

Estimation 

Deterministic(**) 

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

deviation; 

UB95 = upper bound at the 95th percentile. 

(**) High-sided per guidance in NTPR Policy and Guidance Manual (DTRA, 2007).

External Dose Results 

The Monte Carlo dose distribution derived for a sample size of 10,000 for the film badge period 

of July 11 to August 3, 1956 is displayed in Figure A-2 and compared with the distribution of 

unbiased film badge results. The probability plot is shown in Figure A-3. The statistics of this 

distribution are compared with those of a deterministic calculation in Table A-6. 

Table A-6. Summary of Estimated External Dose for Army Units stationed at Enewetak 

Island during Operation REDWING 

Mean Dose (rem) Upper Bound Dose (rem) 

Film 

Badge Probabilistic(*) Deterministic 

(NTPR) 

Film 

Badge 

(95th Percentile)

Probabilistic 

(95th Percentile)

Deterministic 

(NTPR) 

Ratio 

(Deterministic/ 

Probabilistic) 

2.9 3.5 

(1.5) 3.4 4.0 6.2 10 1.6 

(*) The arithmetic mean (and standard deviation) are shown. The geometric mean external dose is 3.2 rem. 

171 
0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0 2 4 6 8 10

Dose (rem)

Relative Frequency

Monte Carlo Simulation

Film Badge

Figure A-2. Comparison of Distribution of Estimated External Gamma Doses from Monte 

Carlo Analysis with Distribution of Unbiased Film Badge Results for the 7126th Army Unit 

Stationed at Enewetak Island during Operation REDWING 

172 
Cumulative Probability

Dose (rem)

0.1% 1% 10% 30% 50% 70% 90% 99% 99.9%

10-1

100

101

102

Dose

Fitted Curve

Figure A-3. Probability Plot of Estimated External Gamma Doses for 7126th Army 

Unit Stationed at Enewetak Island during Operation REDWING 

Internal Dose: Approach 

Internal dose reconstruction for Army units stationed on Enewetak Island during Operation 

REDWING was accomplished by incorporating uncertainty distributions for the fallout-induced 

radiation environments discussed above and for various other parameters as discussed in 

Sections 3 and 4. The specific parameters used in both the deterministic and probabilistic 

analyses are shown in Table A-7. 

173 
Table A-7. Input Parameter Specification for Internal Dose Reconstruction, 

Case Study #1 

Parameter Definition Distribution for 

Probabilistic Analysis

Nominal Value for 

Central Estimation Deterministic(*)

INTERNAL DOSE (GENERAL) 

DCFInhα

DCFIngα

Inhalation and ingestion 

dose conversion factors for 

fallout α emitters 

DCFs calculated with 

FIIDOS multiplied by 

Lognormal with 

GM=1.0, GSD=5.19 

DCFs calculated with 

FIIDOS 

(see Section 4.2.8) 

DCFs calculated 

with FIIDOS 

(see Section 

4.2.8) 

DCFInhβγ

DCFIngβγ

Inhalation and ingestion 

dose conversion factors for 

fallout β+γ radiation 

DCFs calculated with 

FIIDOS multiplied by 

Lognormal with 

GM=1.0, GSD=4.05 

DCFs calculated with 

FIIDOS 

(see Section 4.2.8) 

DCFs calculated 

with FIIDOS 

(see Section 

4.2.8) 

Biasα Assigned Constant 

α: 1.3 for each organ α: 1.3 for each organ 1.0 

Biasβγ

Bias factors to adjust highsided inhalation DCF

values βγ: 1.2 for thyroid & 

LLI, 1.35 for lung 

βγ: 1.2 for thyroid & LLI, 

1.35 for lung 1.0 

BR Breathing rate 

Triangular distribution 

derived from USEPA 

(1997) data (see 

Section 4.2.7): 

min = 0.33 m3 hr−1

peak = 1.53 m3 hr−1

max = 2.79 m3 hr−1

Mean of Distribution 

~1.5 m3 hr−1

 1.2 m3 hr−1

DESCENDING INHALATION DOSE (†)

RNDRes1 1.0 (assumed constant) 1.0 (assumed constant) 

RNDRes2

Lognormal: GM, GSD 

0.0056, 1.744 

Geometric Mean 

0.0056 

RNDRes3

Deposition fractions for 

particle sizes deposited in 

Regions BB, bb and AI Lognormal: GM, GSD 

0.001, 1.65 0.001 

n/a 

RNDNonres1 0.0 (assumed constant) 0.0 (assumed constant) 

RNDNonres2 Lognormal: GM, GSD 

0.363, 1.106

Geometric Mean 

0.363 

RNDNonres3

Deposition fractions for 

particle sizes deposited in 

Region ET2 and cleared to 

digestive tract Lognormal: GM, GSD 

0.285, 1.185 0.285 

n/a 

V1

Logtriangular 

min, peak, max (cm 

s

−1

) 

0.22/2, 0.22, 27.8 

0.22 cm s−1

V2 0.83/2, 0.83, 27.8 0.83 cm s−1 

V3

Particle settling velocities 

13.0/2, 13.0, 27.8 13.0 cm s−1

106

(cm)/T(sec) 

174 
Parameter Definition Distribution for 

Probabilistic Analysis

Nominal Value for 

Central Estimation Deterministic(*)

Triangular 

(min, mode ,max) Peak of Distributions 

ZUNI 

(0.094, 0.280, 0.565) 

ZUNI 

0.280 

MOHAWK 

(0.013, 0.070, 0.140) 

MOHAWK 

0.070 

APACHE 

(0.939, 0.973, 1.000) 

APACHE 

0.973 

AF100 Surface activity fraction 

<100 μm particles 

TEWA 

(0.403, 0.572, 0.732) 

TEWA 

0.572 

1.0 

frac1

Triangular 

Min, peak, max 

0, 0.00136, 0.01 

Peak of Distribution 

0.00136 

frac2

Surface fraction of Class 1-

2 from 1-100 μm particles 

0, 0.025, 0.1 0.025 

n/a 

RESUSPENDED INHALATION DOSE 

K(t) Time-dependent 

resuspension factor 

Lognormal multiplier 

of Anspaugh equation 

GM=1, GSD=4.05 

Anspaugh equation Till and Meyer, 

1983 

INCIDENTAL INGESTION DOSE 

qing Soil ingestion rate 

Triangular 

min, peak, max 

(mg d−1

) 

10, 100, 500 

Peak of Distribution 

100 mg day−1 500 mg day−1

ρsoil Soil bulk density 

Triangular 

g cm−3

Min, peak, max 

1.3, 1.45, 1.6 

Peak of Distribution 

1.45 g cm−3 1.3 g cm−3

(*) High-sided per guidance in NTPR Policy and Guidance Manual (DTRA, 2007). 

(†) AMAD particle size classes: 1 = 1–10 μm, 2 = 10–20 μm, 3 = 20–100 μm.

Internal Dose Results 

Fifty-year committed equivalent dose (CED) distributions to three organs, thyroid, lung, and 

lower large intestine (LLI), were derived using the probabilistic model for a sample size of 

10,000. The geometric mean and 95th percentile CEDs of the various distributions are given in 

Table A-8, along with analogous doses derived deterministically. The ratio of the deterministic 

upper bound CED to the probabilistic 95th percentile CED is provided in the rightmost column. 

Examples of these distributions are shown in Figure A-4 through Figure A-7, where the relative 

frequency distribution and probability plot of CED to the LLI wall from alpha radiation and from 

beta plus gamma radiation, respectively, are plotted. 

175 
Table A-8. Summary of Estimated Internal Doses for 7126th Army Unit Stationed at 

Enewetak Island during Operation REDWING 

Mean Dose (rem) Upper Bound Dose (rem) 

Organ 

Probabilistic(*) Deterministic 

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic/ 

Probabilistic) 

Alpha Dose 

Thyroid 0.000024 

(8.6) 0.00011 0.00083 0.0011 1.4 

Lung 0.00029 

(8.7) 0.0014 0.010 0.014 1.4 

LLI Wall 0.000024 

(8.5) 0.00011 0.00085 0.0011 1.4 

Beta plus Gamma Dose 

Thyroid 0.72 

(4.8) 1.5 9.8 14 1.5 

Lung 0.16 

(6.7) 1.4 3.8 14 3.7 

LLI Wall 0.54 

(4.8) 1.0 7.3 9.6 1.3 

(*) Geometric mean and (geometric standard deviation) are shown for the probabilistic analysis results. 

0

0.025

0.05

0.075

0.1

6.8E-09 1.6E-07 3.9E-06 9.2E-05 2.2E-03 5.2E-02

Dose (rem, CED)

Relative Frequency of log 10(dose)

Figure A-4. Distribution of Estimated LLI Wall Dose from Alpha Radiation for 7126th

Army Unit Stationed at Enewetak Island during Operation REDWING 

176 
Cumulative Probability

Dose (rem, CED)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Dose

Fitted Curve

Figure A-5. Probability Plot of Estimated LLI Wall Dose from Alpha Radiation for 7126th

Army Unit Stationed at Enewetak Island during Operation REDWING 

0

0.025

0.05

0.075

0.1

2.5E-04 3.6E-03 5.1E-02 7.1E-01 1.0E+01 1.4E+02

Dose (rem, CED)

Relative Frequency of log 10(dose)

Figure A-6. Distribution of Estimated LLI Wall Dose from Beta plus Gamma Radiation 

for 7126th Army Unit Stationed at Enewetak Atoll during Operation REDWING 

177 
Cumulative Probability

Dose (rem, CED)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

10-4

10-3

10-2

10-1

100

101

102

103

Dose

Fitted Curve

Figure A-7. Probability Plot of Estimated LLI Wall Doses from Beta plus Gamma 

Radiation for 7126th Army Unit Stationed at Enewetak Atoll 

during Operation REDWING 

References 

Bruce-Henderson, S., Gladeck, F.R., Hallowell, J.H., Martin, E.J., McMullan, F.W., Miller, 

R.H., Rogers, W.E., Rowland, R.H., Shelton, C.F., Sturman, P., Berkhouse, L.H., Davis, 

S., DeSantis, H., Dean, P., Doyle, M.K., and Patterson, D.S. , 1982. Operation 

REDWING: 1956, United States Atmospheric Nuclear Weapons Tests, Nuclear Test 

Personnel Review. DNA 6037F (Defense Nuclear Agency, Washington, D.C.). 

DTRA, 2007. Policy and Guidance Manual – Nuclear Test Personnel Review Program. 

Revision 7 (Defense Threat Reduction Agency, Fort Belvoir, VA). 

Jacks, G. L., 1957. Operation REDWING Radiological Safety. WT-1366 (extracted version 

prepared for DNA in 1983; Defense Nuclear Agency, Washington D.C.). 

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

(National Research Council, Washington, D.C.). 

Till, J.E. and Meyer, H.R. (eds), 1983. “Radiological Assessment – A Textbook on 

Environmental Dose Analysis,” NUREG/CR-3332, (United States Nuclear Regulatory 

Commission), September 1983. 

USEPA, 1997. Exposure Factors Handbook. EPA/600/P-95/002Fa-c (Office of Research and 

Development, U.S. Environmental Protection Agency, Washington, D.C.). 

178 
APPENDIX B Monte Carlo Analysis of Dose to Army Units Stationed on 

Enewetak Island During Operation HARDTACK I 

Ron Weitz 

179 
APPENDIX B Monte Carlo Analysis of Dose to Army Units Stationed on Enewetak 

Island During Operation HARDTACK I 

Introduction

Distributions of external and internal reconstructed doses were generated by Monte Carlo 

techniques for two Army units, the Administrative Detachment and the Operations Detachment, 

stationed on Enewetak Island during Operation HARDTACK I (1958). Doses are reported for 

periods of time corresponding to available film badge readings. The deterministic and 

probabilistic external dose results are also compared to the mean and upper bound values of 

available film badge readings for the units. 

Background

Operation HARDTACK I was a series of 35 atmospheric nuclear weapon tests conducted in the 

Pacific Ocean from April 28 to August 18, 1958. All but three of these shots occurred at the 

Enewetak Proving Ground (EPG), which consisted of the land areas of Enewetak and Bikini 

Atolls, their lagoons, and the waters within 2.6 nautical miles (nmi) (3 statute miles) of their 

seaward sides. (Gladeck et al., 1982) 

Permanent base camps were established on three islands to support the operations at Enewetak 

Atoll. The largest of the three, Enewetak Island (or Site Fred), was manned continuously during 

the operation with a maximum population of approximately 3200 people. Among the units 

assigned to Enewetak Island were two Army detachments, the Army Administrative Detachment 

and the Army Operations Detachment. The compositions and duties of these detachments are as 

follows (Gladeck et al., 1982): 

 Administrative Detachment (AD): Personnel of this detachment supported the Chaplain, the 

Provost Marshal, and the Finance, Information, and Postal Sections. Its scheduled strength 

was 50 officers and 482 enlisted men during the operational period. 

 Operations Detachment (OD): Duties of this detachment were administrative and logistic 

support for assigned personnel, including laundry, medical, dental, commissary, engineering, 

depot, gear loft, truck motor pool, and maintenance support. Its scheduled strength was 

25 officers and 379 enlisted men. 

The personnel assigned to these units arrived at Enewetak Island prior to the first nuclear 

detonation of the series. By the nature of their duties, it is likely that most of these personnel 

remained on the island continuously, or nearly so, throughout the operation. 

Exposure Scenario 

All HARDTACK I detonations took place at least 10 nmi from Enewetak Island. In 

consideration of these distances and shot yields, none of the island-based participants was 

exposed to measurable levels of initial gamma and neutron radiation. (Gladeck et al., 1982; 

Glasstone and Dolan, 1977; Goetz et al., 1985) They were, however, exposed to residual gamma 

radiation from fallout on the islands. 

180 
Prior to the first HARDTACK I fallout deposition on May 14, 1958, the only source of residual 

radiation exposure on the residence islands of Enewetak Atoll was fallout from Shot TEWA, 

fired at Bikini on July 21, 1956, as part of Operation REDWING. During the HARDTACK I 

operational period, the intensity of the TEWA fallout at Enewetak Atoll was on the order of 

0.01 milli-Roentgen per hour (mR hr−1

) (Thomas, 1991). Because its intensity was so small, this 

source was not included in the present assessment. 

The first and most significant episode of HARDTACK I fallout on Enewetak Island occurred 

during May 14–15, 1958, and apparently contained contributions from both the FIR and KOA 

shots. Subsequent minor incidences of fallout were recorded on these islands on June 28 (from 

Shot REDWOOD), June 29 (Shot OAK), July 12 (Shot POPLAR), and July 18 (Shot PISONIA). 

However, because the film badges for the Army units considered in this study are evaluated 

through July 7, radiation environments from Shots POPLAR and PISONIA are not included 

herein. A Rad-Safe Center, established on Parry Island (Site Elmer) prior to the operation, 

provided primary radiological survey support; a similar facility did not exist on Enewetak Island 

(Minkkinen et al., 1959). Therefore, the following quantitative descriptions of these fallout 

events are based on intensity measurements made on Parry Island. The adaptation of these data 

for modeling the intensity on Enewetak is discussed subsequently. 

FIR-KOA Fallout (May 14–15) 

The following significant events of the FIR-KOA fallout episode are taken from Minkkinen et al. 

(1959): 

 0550 hours, May 12 – Shot FIR was detonated at Bikini Atoll 

 0630 hours, May 13 – Shot KOA was detonated at Enewetak Atoll 

 0300 hours, May 14 – Background radiation intensity on Parry Island started to rise 

 1600 hours, May 14 – Peak intensity of 25 mR hr−1 reported on Parry Island 

 0730 hours, May 15 – Intensity of 10–15 mR hr−1 reported on Parry Island 

Due to meteorological conditions, it was difficult at the time to determine whether the observed 

fallout came from Shot FIR or Shot KOA. In contemporary reports the fallout was variously 

attributed individually to Shot FIR and to Shot KOA; in retrospect it appears likely that the 

clouds from the two shots intermingled somewhat to produce the observed fallout (Gladeck et 

al., 1982). The most substantial piece of available evidence in determining the origin of the 

fallout is a decay curve (Minkkinen et al., 1959) that was derived from measurements made on a 

fallout sample collected on Parry Island during May 15–17. Using the computer code FIIDOS 

(Raine et al., 2007) with shot-specific radionuclide inventories, the beta activities for both Shot 

FIR and Shot KOA were calculated and compared with the measured beta activity from the 

fallout sample. It was found that neither of the decay rates of the individual shots agrees well 

with the measured rate, but that a mixture of 40 percent Shot FIR and 60 percent Shot KOA 

(based on the fraction of total fission events attributed to each shot) provides a very good fit to 

the data. 

181 
Shot REDWOOD Fallout (June 28) 

Shot REDWOOD was detonated on Bikini Atoll at 0530 hours, June 28. Rainout at Enewetak 

Atoll started at 1600 hours on that day and continued for approximately 3 hours, during which 

the background intensity on Parry Island rose to 0.7 mR hr−1

 (Minkkinen et al., 1959). The time 

of this peak intensity reading was not reported. 

Shot OAK Fallout (June 29) 

Shot OAK was detonated at 0730 hours, June 29, at Enewetak Atoll. At 1945 hours on that date, 

it began to rain on Parry Island and the background intensity began to rise slowly, reaching a 

peak intensity of 2.5 mR hr−1

 at 2130 hours before subsiding. Although this fallout episode has 

been reported as occurring at Eneu Island, Bikini Atoll (Minkkinen et al., 1959), there is 

substantial evidence (Weitz, 2006) that it actually took place on Parry Island. 

A deterministic model was developed on the basis of the radiation intensity data described above 

(Weitz, 1995), which subsequently evolved into the stochastic model utilized for this case study. 

The adequacy of this intensity model is supported by a comparison of model results with an 

extensive set of intensity measurements taken on Parry Island by the Public Health Service 

(PHS, 1958). The daily averages of these measurements are displayed in Figure B-1 along with 

the curve of daily-averaged intensities generated with the model. It is seen that the agreement is 

generally good. The one notable discrepancy is the absence in the measurements of an intensity 

peak corresponding to the Shot PISONIA deposition on July 18. Because that intensity 

excursion lasted only about 2 hours and the PHS readings were not continuous but taken 

periodically throughout the day, it is likely that they simply missed this brief event. The fact that 

the calculated values progressively overestimate the intensity with increasing time between/after 

shots most likely results from the omission of weathering effects in the intensity model. 

The detailed information on the HARDTACK I fallout events (Minkkinen et al., 1959) for Parry 

Island is not available for Enewetak Island. However, PHS (1958) provides daily averages of 

intensity readings on Enewetak Island from May 19 through July 31, 1958, as shown in 

Figure B-2. These data indicate that the intensities on Enewetak Island were somewhat less than 

those on Parry Island. The model described above for Parry Island is adapted for application to 

Enewetak Island exposures as follows. It is assumed that the fallout deposition on Enewetak 

Island from the Bikini-based Shot REDWOOD was the same as that on Parry Island. For the 

combined FIR-KOA event and the Enewetak-based Shot OAK, the time profiles are retained but 

the intensity readings are scaled to achieve best fit to the PHS data. Thus, the FIR/KOA 

intensities are reduced to 75 percent of the values for Parry Island, while the OAK intensities are 

reduced to 30 percent of the Parry Island values. These reductions are not unreasonable, since 

Enewetak Island was farther from the relevant local detonation sites than was Parry Island. The 

resulting model output is compared with the PHS data in Figure B-1. As noted with respect to 

Figure B-2, the overestimation of intensity between and after shots most likely results from 

weathering effects which are not included in the intensity model. 

182 
0.1

1

10

100

0 10 20 30 40 50 60 70 80

Reference Date (Days after FIR)

Daily-Averaged Intensity 

(mR/hr)

Calculated

Measured

Fir/Koa

Redwood

Poplar

Pisonia

Oak

Figure B-1. Comparison of Parry Island Intensity Model with PHS Measurements 

0.1

1

10

0 10 20 30 40 50 60 70 80

Reference Date (Days after FIR)

Daily-Averaged Intensity 

(mR/hr)

Measured

Calculated

Fir/Koa

Redwood

Poplar

Oak

Pisonia

Figure B-2. Comparison of Enewetak Island Intensity Model with PHS Measurements 

183 
External Dose: Approach 

Film Badge Data 

About 18,000 test participants received film badge dosimetry during HARDTACK I to measure 

exposure to external gamma radiation, and approximately 62,000 individual film badges were 

issued and processed. Most participants had such dosimetry throughout their period of service at 

EPG. The film packets used at HARDTACK I were designed to measure exposures up to 

800 roentgen (R) with a minimum detectable exposure of approximately 0.04 R. A study of the 

HARDTACK I film badge design and the calibration, issue, exchange, and processing 

procedures utilized during the operation concluded that the dosimetry, while generally reliable, 

over-reported exposures by about 20 percent due to environmental effects in the hot, humid 

Pacific test area. (NRC, 1989) 

Complete files of film badge data were obtained for the two Army detachments. The databases 

were then processed to (1) correct for apparent inconsistencies in the recorded return dates of 

some badges and (2) distill the records to a subset that most likely represent valid readings of 

those personnel continuously resident on Enewetak Island throughout the operation. In the first 

step, the return dates of badges were revised, when necessary, to correspond to the issue dates of 

subsequently issued badges. (This was done under the assumption that the return of a badge and 

the issue of the next occurred concurrently.) The second step involved screening all badge 

entries and eliminating from further consideration those records that fall into one or more of the 

following categories: 

 Badges without return dates recorded in the database (indicative of lost or damaged badges); 

 Badges with anomalous zero readings (i.e., those issued for periods when island residents are 

known to have been exposed to residual radiation); 

 Complete sets of badges for those personnel with unusual or confusing badge sequences 

(taken as an indicator of an unusual duty assignment); 

 Badges that required excessive adjustments in return date (typically greater than 10 days) to 

accomplish (1) above; 

 Badges with identification numbers lower than those used for the initial general issue (lower 

than #27442 for the Administrative Detachment and lower than #31042 for the Operations 

Detachment; badges falling into this group were apparently issued to personnel with more 

specialized assignments than the general population); 

 Badges for personnel known to have been assigned to duty on Japtan Island (all such 

personnel were previously identified). 

The badges remaining in the database after this screening process were then sorted by issue 

and/or return date and the exposure statistics compiled. The statistics thus derived for badges 

issued on or about April 12, 1958, before the first fallout event of the series (May 14), are 

summarized in Table B-1 for turn-in date groupings that have sample sizes of ten or more, 

identified as “subunits.” 

184 
Table B-1. Film Badge Data for HARDTACK I Army Subunits 

Parent 

Unit(*) 

FB Turn-in 

Date (1958) Subunit Size 

Average FB 

Dose 

(mrem) 

Unbiased 

Average FB 

Dose 

(mrem) 

Unbiased FB 

Standard 

Deviation 

(mrem) 

Relative 

Error 

(%) 

AD May 31 41 642 535 88 17 

OD May 31 24 687 573 122 21 

OD Jun 4 45 1074 895 154 17 

AD Jun 5 16 907 756 173 23 

OD Jun 5 36 1072 893 193 22 

AD Jun 7 28 1303 1086 150 14 

AD Jun 10 33 1174 978 135 14 

OD Jun 10 69 1269 1058 195 18 

OD Jun 11 43 1653 1378 307 22 

OD Jun 12 93 864 720 163 23 

OD Jun 13 16 1573 1311 288 22 

AD Jun 17 18 1328 1107 133 12 

AD Jun 27 121 1202 1002 189 19 

AD Jun 28 108 1303 1086 166 15 

AD Jun 29 22 1201 1001 189 19 

AD Jul 7 22 1207 1006 238 24 

(*) AD: Administrative Detachment OD: Operations Detachment 

Monte Carlo-Based Dose Reconstruction 

External gamma dose reconstruction for Army units stationed on Enewetak Island during 

Operation HARDTACK I was accomplished by incorporating uncertainty distributions for 

various parameters into the model discussed in Section 3. Time-dependent radiological decay 

for the uncertainty analysis was modeled using shot-specific decay functions derived with the 

FIIDOS code (Raine et al., 2007). The specific parameters used in both the deterministic and 

uncertainty analyses of external dose are shown in Table B-2. 

185 
Table B-2. Input Parameter Specification for External Gamma Dose Reconstruction, 

Case Study #2 

Parameter Definition 

Distribution for 

Probabilistic 

Analysis (*)

Nominal Value for 

Central Estimation Deterministic(**) 

SHOT MIXTURE FRACTION 

Fallout 

Composition 

Fallout proportion from each 

shot (applies to FIR/KOA 

only) 

Triangular 

min=0 

peak=0.4 

max=1 

for FIR fraction 

Intensity data based 

on 0.4/0.6 mixture of 

FIIDOS-derived 

FIR/KOA intensity 

functions 

Intensity data based 

on time-dependent 

decay exponents for 

FIR/KOA mixture 

EXTERNAL DOSE MULTIPLIER (EDM) FOR LAND-BASED PERSONNEL 

Fos

Fraction of time spent 

outside 

Triangular 

min = 2/24 

peak = 8/24 

max = 16/24 

0.34 (or 8/24) 0.6 (or 14.4/24) 

Ft

Fraction of inside time spent 

in tent 

Triangular 

min = 0 

peak = 0.5 

max = 1 

0.5 0 

PFt Protection factor for tent 

Numerical model 

(see Section 4.2.2) 

μ = 1.4 

UB95 = 1.9 

1.4 

(median of 

distribution) 

1.5 

PFb Protection factor for building

Numerical model 

(see Section 4.2.2) 

μ = 2.1 

UB95 = 3.9 

2.0 

(median of 

distribution) 

2.0 

Ii

Intensity of fallout near 

outdoor location (i=1), tent 

location (i=2), and building 

location (i=3) frequented by 

veteran, normalized to the 

intensity averaged over entire 

island 

Lognormal 

GM = 1.0 

GSD = 1.5 

1.0 1.0 

INTENSITY MEASUREMENTS FOR LAND-BASED PERSONNEL 

Im Measured intensities 

Normal 

μ = Im, σ = 0.3·Im 

(to account for 

measurement error) 

1.0 1.0 

a

Exponent of multiplicative 

error factor (t/t0)

±a

 applied to 

FIIDOS-generated intensity 

functions 

Normal 

μ = 0 

σ = 0.15 

0 0 

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

deviation; UB95 = upper bound at the 95th percentile. 

(**) High-sided per guidance in NTPR Policy and Guidance Manual (DTRA, 2007).

186 
External Dose Results 

Dose distributions were derived for a sample size of 10,000 for the film badge turn-in dates 

identified in Table B-1. The sample dose distribution shown in Figure B-3 is for personnel who 

returned their badges on June 12. The relative frequency (probability density function) is shown 

in Figure B-3 and the Probability Plot is shown in Figure B-4. The distributions for the other 

badge turn-in dates have very similar lognormal shapes. 

The Monte Carlo-derived (arithmetic) mean and 95th percentile doses for each subunit are listed 

in Table B-3. Also provided for comparison are similar statistics based on the distribution of 

film badge doses, NTPR deterministic doses, and NTPR upper bound doses calculated using the 

3 upper bound convention. The last column displays the ratio of the deterministic upper bound 

dose to the probabilistic 95th percentile dose. It is seen that both the probabilistic and 

deterministic approaches compute mean doses that are generally consistent with the average film 

badge doses of the various subunits. The deterministic upper bound doses exceed the 

probabilistic 95th percentile doses by a nearly constant factor of 1.5; the latter doses exceed the 

95th percentile film badge doses for all subunits except one. 

From a total of 735 film badges issued to all subunits, only 2 (or 0.3%) exceed the 95th percentile 

doses of the respective subunits. Both of these high readings come from the Operations 

Detachment subunit that turned their badges in on June 11. 

0.00

0.05

0.10

0.15

0.20

0.25

0.0 1.0 2.0 3.0 4.0

External Gamma Dose (rem)

Relative Frequency

Figure B-3. Distribution of Estimated External Gamma Doses for Army Personnel at 

Enewetak Island during Operation HARDTACK I (Turn-in Date: June 12) 

187 
Cumulative Probability

Dose (rem)

0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

10-1

100

101

Dose

Fitted Curve

Figure B-4. Probability Plot Estimated External Gamma Doses for Army Personnel at 

Enewetak Island during Operation HARDTACK I (Turn-in Date: June 12) 

188 
Table B-3. Summary of External Doses for Army Subunits Stationed at Enewetak Island 

during HARDTACK I 

Dose (rem) Upper Bound (NTPR) or 

95th Percentile Doses (rem) Parent 

Unit 

FB Turn-in 

Date 

(1958) Mean FB Mean MC NTPR Det. FB MC NTPR UB 

Ratio 

NTPR UB/ 

MC 

AD May 31 0.54 0.889 0.85 0.74 1.65 2.6 1.6 

OD May 31 0.57 0.889 0.85 0.76 1.65 2.6 1.6 

OD Jun 4 0.89 0.939 0.90 1.15 1.75 2.7 1.5 

AD Jun 5 0.76 0.950 0.91 1.04 1.77 2.7 1.5 

OD Jun 5 0.89 0.950 0.91 1.26 1.77 2.7 1.5 

AD Jun 7 1.09 0.970 0.93 1.38 1.82 2.8 1.5 

AD Jun 10 0.98 0.997 0.95 1.18 1.87 2.9 1.5 

OD Jun 10 1.06 0.997 0.95 1.38 1.87 2.9 1.5 

OD Jun 11 1.39 1.01 0.96 1.85 1.88 2.9 1.5 

OD Jun 12 0.72 1.01 0.97 0.97 1.90 2.9 1.5 

OD Jun 13 1.31 1.02 0.98 1.84 1.91 2.9 1.5 

AD Jun 17 1.11 1.05 1.00 1.28 1.97 3.0 1.5 

AD Jun 27 1.00 1.10 1.05 1.28 2.09 3.1 1.5 

AD Jun 28 1.09 1.12 1.05 1.40 2.10 3.2 1.5 

AD Jun 29 1.00 1.12 1.06 1.25 2.11 3.2 1.5 

AD Jul 7 1.01 1.17 1.10 1.49 2.20 3.3 1.5 

FB: film badge dose 

MC: dose from the probabilistic model (Monte Carlo simulation) 

Det.: dose from the deterministic model (NTPR)

Internal Dose: Approach 

Internal dose reconstruction for Army units stationed on Enewetak Island during Operation 

HARDTACK I was accomplished by incorporating uncertainty distributions for various 

parameters into the models discussed in Section 3. These models incorporate the fallout-induced 

radiation environments discussed above, the fallout intensity decay model discussed in Section 3, 

and various other parameters discussed in Sections 3 and 4. The specific parameters used in both 

the deterministic and probabilistic analyses are shown in Table B-4. 

189 
Table B-4. Input Parameter Specification for Internal Dose Reconstruction, Case Study #2 

Parameter Definition Distribution for 

Probabilistic Analysis

Nominal Value for 

Central Estimation Deterministic(*)

INTERNAL DOSE (GENERAL) 

DCFInhα

DCFIngα

Inhalation and ingestion 

dose conversion factors for 

fallout α emitters 

DCFs calculated with 

FIIDOS multiplied by 

Lognormal with 

GM=1.0, GSD=5.19 

DCFs calculated with 

FIIDOS 

(see Section 4.2.8) 

DCFs calculated 

with FIIDOS 

(see Section 

4.2.8) 

DCFInhβγ

DCFIngβγ

Inhalation and ingestion 

dose conversion factors for 

fallout β+γ radiation 

DCFs calculated with 

FIIDOS multiplied by 

Lognormal with 

GM=1.0, GSD=4.05 

DCFs calculated with 

FIIDOS 

(see Section 4.2.8) 

DCFs calculated 

with FIIDOS 

(see Section 

4.2.8) 

Biasα

Assigned Constant 

α: 1.3 for each organ α: 1.3 for each organ 

1.0 

Biasβγ

Bias factors to adjust highsided inhalation DCF values

βγ: 1.2 for thyroid & 

LLI, 1.35 for lung 

βγ: 1.2 for thyroid & LLI, 

1.35 for lung 1.0 

BR Breathing rate 

Triangular distribution 

derived from USEPA 

(1997) data (see 

Section 4.2.7): 

min = 0.33 m3 hr−1

peak = 1.53 m3 hr−1

max = 2.79 m3 hr−1

Mean of Distribution 

~1.5 m3 hr−1

 1.2 m3 hr−1

DESCENDING INHALATION DOSE (†)

RNDRes1 1.0 (assumed constant) 1.0 (assumed constant) 

RNDRes2

Lognormal: GM, GSD 

0.0056, 1.744 

Geometric Mean 

0.0056 

RNDRes3

Deposition fractions for 

particle sizes deposited in 

Regions BB, bb, and AI Lognormal: GM, GSD 

0.001, 1.65 0.001 

n/a 

RNDNonres1 0.0 (assumed constant) 0.0 (assumed constant) 

RNDNonres2 Lognormal: GM, GSD 

0.363, 1.106

Geometric Mean 

0.363 

RNDNonres3

Deposition fractions for 

particle sizes deposited in 

Region ET2 and cleared to 

digestive tract Lognormal: GM, GSD 

0.285, 1.185 0.285 

n/a 

V1

Logtriangular 

min, peak, max (cm 

s

−1

) 

0.22/2, 0.22, 27.8 

0.22 cm s−1

V2 0.83/2, 0.83, 27.8 0.83 cm s−1 

V3

Particle settling velocities 

13.0/2, 13.0, 27.8 13.0 cm s−1

106

(cm)/T(sec) 

190 
Parameter Definition Distribution for 

Probabilistic Analysis

Nominal Value for 

Central Estimation Deterministic(*)

Triangular 

(min,peak,max) Peak of Distributions 

FIR/KOA 

(1.000, 1.000, 1.000) 

FIR/KOA 

1.000 

REDWOOD 

(0.609, 0.787, 0.971) 

REDWOOD 

0.787 

AF100 Surface activity fraction 

<100 μm particles 

OAK 

(0.469, 0.732, 0.975) 

OAK 

0.732 

1.0 

frac1

Triangular 

Min, peak, max 

0, 0.00136, 0.01 

Peak of Distribution 

0.00136 

frac2

Surface fraction of Class 1–

2 from 1–100 μm particles 

0, 0.025, 0.1 0.025 

n/a 

RESUSPENDED INHALATION DOSE 

K(t) Time-dependent 

resuspension factor 

Lognormal multiplier 

of Anspaugh equation 

GM=1, GSD=4.05 

Anspaugh equation Till and Meyer, 

1983 

INCIDENTAL INGESTION DOSE 

qing Soil ingestion rate 

Triangular 

min, peak, max 

(mg d−1

) 

10, 100, 500 

Peak of Distribution 

100 mg day−1 500 mg day−1

ρsoil Soil bulk density 

Triangular 

g cm−3

Min, peak, max 

1.3, 1.45, 1.6 

Peak of Distribution 

1.45 g cm−3 1.3 g cm−3

(*) High-sided per guidance in NTPR Policy and Guidance Manual (DTRA, 2007). 

(†) AMAD particle size classes: 1 = 1–10 μm, 2 = 10–20 μm, 3 = 20–100 μm.

Internal Dose Results 

Distributions of fifty-year committed equivalent doses (CED) for three organs, thyroid, lung, and 

lower large intestine (LLI) wall, were derived using the refined uncertainty model for a sample 

size of 10,000. Examples of these results are shown in Figure B-5 through Figure B-8, where the 

relative frequencies and probability plots of CED to the LLI wall from alpha radiation and from 

beta plus gamma radiation, respectively, are shown. The CED distributions are lognormal, as 

indicated by their Gaussian (bell) shapes when plotted on a logarithmic axis and the straight-line 

nature of their probability plots. 

The geometric mean and 95th percentile CEDs of the various distributions are given in 

Table B-5, along with corresponding doses derived deterministically. The ratio of the 

deterministic upper bound CED to the probabilistic 95th percentile CED, provided in the 

rightmost column, ranges from 1.8 to 4.6 for the organs reported. 

191 
0

0.025

0.05

0.075

0.1

5.5E-08 1.8E-06 5.6E-05 1.8E-03 5.7E-02

Dose (rem, CED)

Relative Frequency of log 10(dose)

Figure B-5. Distribution of Estimated LLI Wall Doses from Alpha Radiation for Army 

Personnel at Enewetak Island during Operation HARDTACK I 

Cumulative Probability

Dose (rem, CED)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Dose

Fitted Curve

Figure B-6. Probability Plot of Estimated LLI Wall Doses from Alpha Radiation for Army 

Personnel at Enewetak Island during Operation HARDTACK I 

192 
0

0.025

0.05

0.075

0.1

6.7E-04 9.1E-03 1.2E-01 1.6E+00 2.2E+01

Dose (rem, CED)

Relative Frequency of log 10(dose)

Figure B-7. Distribution of Estimated LLI Wall Doses from Beta plus Gamma Radiation 

for Army Personnel at Enewetak Island during Operation HARDTACK I 

Cumulative Probability

Dose (rem, CED)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

10-4

10-3

10-2

10-1

100

101

102

Dose

log10(y)=-0.7944+0.6874s(x)

Figure B-8. Probability Plot of Estimated LLI Wall Doses from Beta plus Gamma 

Radiation for Army Personnel at Enewetak Island during Operation HARDTACK I 

193 
Table B-5. Summary of Internal Dose for Army Personnel at Enewetak Island 

during Operation HARDTACK I 

Mean Dose (rem) Upper Bound Dose (rem) 

Organ 

Probabilistic* Deterministic 

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR Upper 

Bound) 

Ratio 

(Deterministic 

 Probabilistic) 

Alpha Dose 

Thyroid 0.000040 

(8.5) 0.00036 0.0014 0.0036 2.6 

Lung 0.00054 

(8.6) 0.0049 0.019 0.049 2.6 

LLI wall 0.000042 

(8.3) 0.00036 0.0014 0.0036 2.5 

Beta plus Gamma Dose 

Thyroid 0.24 

(4.7) 0.57 3.0 5.5 1.8 

Lung 0.030 

(6.5) 0.31 0.67 3.1 4.6 

LLI wall 0.17 

(4.7) 0.40 2.1 3.9 1.8 

*

 Geometric mean and (geometric standard deviation) are shown for probabilistic analysis results. 

194 
References 

DTRA (Defense Threat Reduction Agency), 2007. Policy and Guidance Manual – Nuclear Test 

Personnel Review Program. Revision 7, (Defense Threat Reduction Agency, Fort 

Belvoir, VA), November 26, 2007. 

Gladeck, F.R., Gould, K.G., Hallowell, J.H., Martin, E.J., McMullan, F.W., Miller, R.A., 

Osborn, M.J., Shelton, C.F., Berkhouse, L., and Calhoun, F.S., 1982. Operation 

HARDTACK I (1958). DNA 6038F (Defense Nuclear Agency, Washington, D.C.). 

Glasstone, S., and Dolan, P. J., 1977. Effects of Nuclear Weapons, 3rd Edition (U.S. Department 

of Defense and U.S. Department of Energy). 

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, D.C.). 

Minkkinen, C., Schlacks, H. P., Goeke, R. H., and Weaver, C. L., 1959. Task Group 7.5 

Radiological Safety Support, Operation HARDTACK, Phase I. OTO-58-3 (Holmes & 

Narver, Inc., Los Angeles, CA). 

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

(National Research Council, Washington, D.C.). 

PHS (US Public Health Service), 1958. Report of Public Health Service Off-Site Radiological 

Monitoring Data, Operation Hardtack, Phase I. Report # 410975 (Public Health Service, 

Washington, D.C.). 

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 (Science Applications International 

Corporation, McLean, VA and Defense Threat Reduction Agency, Fort Belvoir, VA). 

Thomas, C., 1991. REDWING Fallout Intensity Model. Internal memorandum (Science 

Applications International Corporation, McLean, VA). 

Weitz, R. L., 1995. Dose Estimates for Residence Islands during Operation HARDTACK I. 

Memorandum to Defense Nuclear Agency (Science Applications International 

Corporation, McLean, VA). 

Weitz, R. L., 2006. Analysis of 29 June 1958 Fallout Event at Operation HARDTACK I. 

Internal memorandum (Science Applications International Corporation, McLean, VA). 

195 
APPENDIX C Monte Carlo Analysis of Dose for Company E of the 4th 

Marine Corps Provisional Atomic Exercise Brigade 

(MCPAEB) Maneuver at Shot HOOD During Operation 

PLUMBBOB (1957) 

Michael A. McKenzie-Carter 

196 
APPENDIX C Monte Carlo Analysis of Dose for Company E of the 4th Marine Corps 

Provisional Atomic Exercise Brigade (MCPAEB) Maneuver at Shot 

HOOD During Operation PLUMBBOB (1957) 

Introduction 

External and internal dose distributions were generated using probabilistic analysis techniques 

for a Nevada Test Site (NTS) participant unit case study and are documented in this Appendix. 

The unit participated in a maneuver during Shot HOOD of Operation PLUMBBOB in 1957. The 

probabilistic and deterministic (NTPR) dose model parameters are described and results of the 

upper bound doses are compared for both external and internal reconstructed doses for members 

of the participating unit. The deterministic and probabilistic external dose results are also 

compared to the mean and upper bound values of available film badge readings for the unit. 

Background 

During Operation PLUMBBOB, 24 nuclear shots were fired and 6 safety experiments were 

conducted at the NTS from May 28 to October 7, 1957 (Harris et al., 1981; DNA, 1996). 

Table C-1 presents information on the nuclear shots that are relevant to this case study. 

Table C-1. Data On Selected Operation PLUMBBOB Shots 

Shot 1957 Date Time Type Yield (kT)* HOB† (ft) 

BOLTZMANN May 28 0455 Tower 12 500 

WILSON June 18 0455 Balloon 10 500 

HOOD July 5 0440 Balloon 74 1,500 *

 kiloton 

†

 height of burst

The 4th Marine Corps Provisional Atomic Exercise Brigade (MCPAEB), or the “Brigade,” 

conducted an exercise during Operation PLUMBBOB. The exercise took place over a period of 

slightly more than 2 weeks, during which the Brigade trained, rehearsed, experienced a misfire, 

and eventually observed and conducted maneuvers at Shot HOOD on July 5, 1957. The Brigade 

was organized as a standard air-ground task force totaling approximately 2,000 personnel. One 

unit of the Brigade is the subject of the special study described in this Appendix: Company E of 

the 2nd Battalion, 5th Marine Regiment, 1st Marine Division. (Frank et al., 1981) 

The 2nd Battalion, 5th Marine Regiment constituted the infantry battalion assault force for the 

exercise, and was composed of 5 companies, each of which conducted somewhat different 

activities during portions of their participation. All of the Brigade troops arrived at Camp Desert 

Rock (CDR) by June 20, 1957, where they began preparing for a maneuver that was to be held in 

conjunction with Shot DIABLO, which was planned for June 27, 1957. A full rehearsal in the 

NTS forward area was conducted on June 20 and 21. On June 26, the Brigade was notified that 

DIABLO had been postponed until June 28. At 0430 on June 28, with the entire Brigade in 

197 
place, DIABLO misfired and all Brigade personnel returned to CDR. Instead of waiting for 

DIABLO, which had been rescheduled for July 12, the Brigade was assigned to conduct its 

maneuver on July 3, 1957, in conjunction with Shot HOOD. On July 2, based on a weather 

forecast, Shot HOOD was postponed until July 5. By 2230 on July 4, the Brigade had departed 

from CDR enroute to the forward area to maneuver in conjunction with HOOD. 

(Frank et al., 1981; USMC, 1957) 

At 0440 on July 5, 1957, with the Brigade in its trenches 5,360 yards (3 miles) southwest of 

ground zero (GZ), Shot HOOD was detonated (Figure C-1). About 15 minutes later Company E, 

preceded and flanked by radiation safety personnel, began its march from the trenches in the 

direction of the HOOD GZ. Having approached to within 1,100 to 1,400 yards of the HOOD 

GZ, at which time they reached the Rad-Safe limit of 5 R/hr in that shot’s neutron-activated 

radiation field, the company reversed its direction of march enroute back to the trenches. By 

0700 the company had returned to the trench area, then marched to a nearby helicopter landing 

zone where it enplaned and was transported to a location about 7,000 yards (4.4 miles) to the 

west of the trenches. From there, the Company participated in a mock assault on a nearby 

objective. By 1430 they had marched to a nearby road from where they were transported by 

motor vehicle convoy back to CDR. Company E did not tour the HOOD display area on HOOD 

shot day. Most Brigade personnel had departed from CDR by July 6, 1957. (Frank et al., 1981; 

USMC, 1957) 

Film Badge Data 

A total of 12 film badge readings are available for Company E personnel for the period prior to 

and including Shot HOOD: 1200, 980, 760, 560, 560, 520, 520, 520, 500, 500, 500 and 480 

(Frank et al., 1981). The mean of these 12 readings is 633 mrem. 

Sources of External Exposure 

Company E personnel were exposed to residual radiation during Operation PLUMBBOB while 

they were housed and trained at CDR, and also while participating in activities in the forward 

area of the NTS. The most significant source of external radiation exposure for members of 

Company E was neutron-activated radionuclides in the ground resulting from the detonation of 

HOOD, which the Marines traversed during the company’s march toward the HOOD GZ. To 

model the intensity gradient from this source, an intensity array was developed that described the 

intensities encountered during traversal of the radiation field. The primary source of intensity 

data was the H+1 iso-intensity lines plotted for the HOOD test area, as depicted in Figure C-1

(Figure 4-3 of Frank et al., 1981). For use in subsequent time-dependent equations, these 

intensities were converted to H+0 intensities, using Equation C-1. 

     hr hr hr

hr

Na Mn K e. e. e.

Int

Int

1 1 1

1

0

24 56 42 6680 2740 0580      

    (C-1)

198 
where: 

Int0 = H+0 intensity (R hr−1) 

Int1hr = H+1 intensity (R hr−1) 

λNa24 = decay constant for Na-24 (0.0462 hr−1) 

λMn56 = decay constant for Mn-56 (0.269 hr−1) 

λK42 = decay constant for K-42 (0.0559 hr−1) 

The values 0.668, 0.274, and 0.058 are the initial fractional contributions to intensity of Na-24, 

Mn-56, and K-42, respectively. Although accurate values for initial fractional contributions 

depend on site-specific conditions, the use of these average values does not significantly affect 

the calculations. 

Figure C-1. Shot HOOD Residual Radiation (mrem hr−1 at H+1) and MCPAEB 

Movements (Frank et al., 1981) 

Using a start time (ST) and march rate (Rate) from Frank et al. (1981), the distances to each isointensity line and the times of arrival at each iso-contour line were calculated. From these times 

and the H+0 intensities, an array was created defining the intensities encountered at the location 

of each iso-intensity line at the time of traversal, using equation C-2. 

199 
(C-2)    iNa   iMn   iK  i

t t t

en i e.IntInt e. e.     24  56  42 6680 2740 0580 0

  

where, in addition to previously-defined variables: 

Inteni = intensity encountered at each iso-intensity line (R hr−1) 

ti = time each iso-intensity line was encountered during approach toward the 

HOOD GZ and return toward the trenches (hr) 

Equation C-1 was also used to calculate the H+0 intensity at the location the Rad-Safe limit was 

reached, using the calculated time this point was reached. A logarithmic fitting function was 

then used with the array calculated with Equation C-2 to create a time-dependent function for the 

intensities encountered by Company E. The H+1 intensities, corresponding H+0 intensities, 

nominal H+ times each iso-contour line was traversed, and encountered intensities are listed in 

Table C-2. 

Fallout from shots BOLTZMANN and WILSON were also sources of external exposure. During 

the rehearsal, DIABLO misfire, and maneuver at HOOD, the Brigade personnel likely operated 

in NTS forward areas where fallout from these shots had deposited. The test areas for shots 

DIABLO and HOOD were relatively close (the DIABLO trenches used for the rehearsal and 

misfire were located about 1,500 yards from the HOOD trenches), and therefore the activities 

conducted during the rehearsal and misfire took place very near the area eventually used during 

Shot HOOD. Fallout from Shot WILSON had also descended at CDR on June 18, prior to the 

arrival of most Brigade personnel. (Frank et al., 1981; Maag et al., 1983) 

Fallout intensities that are relevant to each primary activity of Company E in forward test areas 

and at CDR are characterized in Table C-3. Radiological decay for the deterministic calculations 

was modeled as t−1.2. For the probabilistic model, radiological decay was determined from shotspecific fallout decay functions using the FIIDOS software (Raine et al., 2007). 

200 
Table C-2. Deterministic Intensities (R hr−1

) and Times (hr) Associated with Traversal of 

Shot HOOD Test Area by Company E 

Location 

H+1 Intensity†

at Location 

H+0 Intensities 

at Location 

H+ Time 

Location Was 

Reached 

Intensities 

Encountered at 

Location 

Depart trenches 0.00 0.000 0.25 0.000 

0.01 R hr−1 Iso-intensity line 

(Approach) 

0.01 0.011 0.85 0.010 

0.1 R hr−1 Iso-intensity line 

(Approach) 

0.10 0.111 0.92 0.101 

1 R hr−1 Iso- intensity line 

(Approach) 

1.00 1.11 1.00 1.00 

Rad-Safe Limit (Arrival) 5.03 5.58 1.06 5‡

Rad-Safe Limit (Departure) 5.03 5.58 1.13 4.97 

1 R hr−1 Iso- intensity line (Return) 1.00 1.11 1.19 0.982 

0.1 R hr−1 Iso- intensity line 

(Return) 

0.10 0.111 1.27 0.097 

0.01 R hr−1 Iso- intensity line 

(Return) 

0.01 0.011 1.34 0.010 

Arrive trenches 0.00 0.000 1.94 0.000 

†

 H+1 intensity at each iso-intensity line was obtained from an iso-intensity plot. 

‡

 This intensity is the measured Rad-Safe limit. 

Table C-3. Fallout Intensities for Company E in Forward Test Areas and at CDR 

Activity/Source 

of Fallout Intensity* Reference 

Rehearsal and Misfire (near the DIABLO trenches) 

BOLTZMANN 0.001 R hr−1* at H+1 (deterministic) 

0.0004 R hr−1* at H+1 (probabilistic) 

Figure 168, Hawthorne (1979) 

Figure 168, Hawthorne (1979) 

WILSON 0.01 R hr−1 at H+12 Figure 4-2, Frank et al. (1981) 

HOOD Maneuver (near the HOOD trenches) 

BOLTZMANN 0.01 R hr−1

 at H+1 (near HOOD trenches) 

2 R hr−1

 at H+1 (1000-2000 yd from HOOD GZ) 

Figure 168, Hawthorne (1979) 

Figure 168, Hawthorne (1979) 

WILSON 0.045 R hr−1 at H+12 Figure 4-2, Frank et al. (1981) 

Camp Desert Rock 

WILSON 0.0004 R hr−1 at H+12.9 Placak et al. (1957) 

* Except where indicated, listed intensities were used for both the deterministic and probabilistic models 

201 
Values for other parameters used in both the deterministic and probabilistic external analyses are 

shown in Table C-4. Intensities encountered during the maneuver for the probabilistic analysis 

were calculated using Equation C-2, with arrival times derived probabilistically according to 

variable definitions in Table C-4. Modeled correlations associated with these parameters in the 

probabilistic analysis are identified and discussed in Appendix G. 

Reconstructed External Doses 

A probabilistic dose reconstruction for Company E personnel was accomplished by 

incorporating distributions of uncertainty and variability for model input parameters discussed in 

Section 3 and 4 of this report. The distribution of results for 10,000 probabilistic simulations of 

the dose calculations is shown in Figure C-2, and is supplemented with a probability plot in 

Figure C-3. Key statistics from the distribution are compared with those of the deterministic 

(NTPR) model in Table C-5. These results show that the deterministic dose and the geometric 

mean dose from the probabilistic analysis are identical, and are the same as the external dose 

previously reported in an analysis done for NTPR (Frank et al., 1981). Both are comparable to 

but less than the arithmetic mean of the probabilistic analysis and the mean film badge reading of 

available film badge readings for Company E. The neutron-activated radionuclides in the soil 

resulting from the detonation of Shot HOOD resulted in approximately 96% of the external 

gamma dose to personnel of Company E. Fallout from previous shots at various locations 

resulted in the remaining external dose. The doses in Table C-5 also show that the 95th

percentile dose from the probabilistic analysis is lower than the upper bound deterministic dose, 

indicating that the generic upper bound uncertainty factor of 3 used in the deterministic model 

results in a conservative estimate of the upper bound dose for Company E cohort at Shot HOOD, 

Operation PLUMBBOB. The deterministic upper bound dose is 70 percent higher that the 95th

percentile probabilistic dose. 

202 
Table C-4. Input Parameters for External Gamma Dose Reconstruction,Case Study #3 

Parameter Definition Distribution for 

Probabilistic Analysis 

Nominal Value for 

Central Estimation Deterministic*

DATES AND TIMES 

DateArrived CDR start date[time] 

Triangular 

min=19 Jun[0800] 

peak=19 Jun[1600] 

max=20 Jun[1600] 

19 Jun[1600] 19 Jun[0800] 

DateDeparted CDR end date[time] 

Triangular 

min=5 Jul[1800] 

peak=6 Jul[0800] 

max=6 Jul[2400] 

6 Jul[0800] 6 Jul[2400] 

EXTERNAL DOSE 

Fos

Fraction of time spent 

outside at CDR 

Triangular 

min=5/24 

peak=12/24 

max=18/24 

0.5 (or 12/24) 0.6 

(or 14.4/24) 

PFt Protection factor for a tent Numerical model (see 

Section 4.2.2) 

1.4 

(median of 

distribution) 

1.5 

Ii

Intensity distribution of 

fallout while outdoors 

(i=1) and indoors (i=2) 

normalized to average 

CDR intensity 

Lognormal 

(GM=1.0; GSD=1.5) 

(used with Fos and PFt ) 

1.0 1.0 

INTENSITIES 

Im

Measured intensities 

(CDR and Rad-safe limit) 

Normal 

(mean=Im; SD=0.304 · Im) 

see Table C-2 and 

Table C-3 

see Table C-2 and 

Table C-3 

Contour 

intensities 

Intensities obtained from 

iso-intensity plots 

(all forward test area 

intensities) 

Interpolated values: 

Lognormal 

(GM=1.0; GSD=1.95) 

Extrapolated values: 

Lognormal 

(GM=1.0; GSD=4.05) 

see Table C-2 and 

Table C-3 

see Table C-2 and 

Table C-3 

a 

Exponent of multiplicative 

error factor (t/t0)

±a

 applied 

to FIIDOS-generated 

fallout intensity functions 

Normal 

(mean=0; SD=0.15) 0 0 

MANUEVER PARAMETERS

ST Start time of maneuver Normal 

(mean=15; SD=1.83) H+15 min H+15 min 

Rate Walk rate during maneuver Triangular (min=50, 

peak=70, max=100) 70 yd min−1 88 yd min−1

LT Linger time at Rad-Safe 

limit location 

Triangular (min=1,peak=2, 

max=10) 2 min 4.1 min 

* High-sided per guidance in NTPR Policy and Guidance Manual (DTRA, 2007). 

203 
0.00

0.05

0.10

0.15

0.20

0.0 0.5 1.0 1.5 2.0

External Gamma Dose (rem)

Relative Frequency

Figure C-2. Distribution of Estimated External Gamma Dose for Company E Personnel at 

the NTS during Operation PLUMBBOB 

Cumulative Probability

Dose (rem)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

10-2

10-1

100

101

Dose

Fitted Curve

Figure C-3. Probability Plot of Estimated External Gamma Dose for Company E 

Personnel at the NTS during Operation PLUMBBOB 

204 
Table C-5. Summary of Estimated External Dose for Company E Personnel of the 4th

MCPAEB during Operation PLUMBBOB 

Mean Doses (rem) Upper Bound Doses (rem) 

Film 

Badge Probabilistic* Deterministic(NTPR) 

Film 

Badge 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic



Probabilistic) 

0.63† 0.62 

(0.23) 0.58 1.0‡ 1.1 1.8 1.7 

*

 The arithmetic mean and standard deviation (SD) are shown. The geometric mean external dose is 

0.57 rem. 

†

 Arithmetic mean of 12 available film badge readings. 

‡

 95th percentile value of the 12 available film badges.

Internal Reconstructed Doses 

A probabilistic internal dose reconstruction for Company E personnel who participated during 

Operation PLUMBBOB was accomplished by incorporating uncertainty distributions for various 

input parameters into the models discussed in Section 3 and 4. These models incorporate the 

fallout-induced radiation environments, time-dependent intensities discussed above, and various 

other parameters discussed in Sections 3 and 4. The specific parameters used in both the 

deterministic and uncertainty analyses are shown in Table C-6. Modeled correlations associated 

with these parameters in the probabilistic analysis are identified and discussed in Appendix G. 

205 
Table C-6. Input Parameter Specification for Internal Dose Reconstruction, 

Case Study #3 

Parameter Definition Distribution for Probabilistic 

Analysis 

Nominal Value for 

Central Estimation Deterministic*

DATES AND TIMES 

DateArrived CDR start date[time] Triangular (see Table C-4) 19Jun[1600] 19Jun[0800] 

DateDeparted CDR end date[time] Triangular (see Table C-4) 6Jul[0800] 6Jul[2400] 

INTERNAL DOSE (GENERAL) 

DCFInhα

DCFIngα

Inhalation and ingestion 

dose conversion factors 

for fallout α emitters 

DCFs calculated with FIIDOS 

multiplied by lognormal 

multiplier 

(GM=1; GSD=5.19) 

Unbiased FIIDOS 

DCFs (see Section 

4.2.8) 

FIIDOS DCFs 

(see Section 3.3) 

DCFInhβγ

DCFIngβγ

Inhalation and ingestion 

dose conversion factors 

for fallout α emitters 

DCFs calculated with FIIDOS 

multiplied by lognormal 

multiplier 

(GM=1; GSD=4.05) 

Unbiased DCFs 

calculated with 

FIIDOS (see Section 

4.2.8) 

DCFs calculated 

with FIIDOS (see 

Section 3.3) 

Biasα

Biasβγ

Bias factors to adjust highsided inhalation DCF 

values 

Assigned Constant 

α: 1.3 for each organ 

βγ: 1.2 for thyroid & LLI wall, 

1.35 for lung 

α: 1.3 for each 

organ 

βγ: 1.2 for thyroid & 

LLI wall, 1.35 for 

lung 

1.0 

BR Breathing rate 

Triangular distribution: 

min=0.33 m3

·hr−1

peak=1.53 m3

·hr−1

max=2.79 m3

·hr−1 

(see Section 4.2.7) 

mean of distribution 

(app. 1.5 m3

·hr−1 ) 1.2 m3

 hr−1

RESUSPENDED INHALATION DOSE 

K(t) Time-dependent 

resuspension factor 

Lognormal multiplier 

(GM=1; GSD=4.05) 

See Sections 3.3 and 

4.2 

See Sections 3.3 

and 4.2.6 

Kpc, Kbw

Resuspension factors for 

fallout in thermal pulse or 

blast wave regions due to 

detonation effects 

Lognormal 

(see Section 4.2.6) 

Respirable: 

Kpc = 110−6

 

Kbw = 110−7

NonRespirable: 

Kpc = 810−6

 

Kbw = 810−7

Respirable & 

Nonrespirable: 

Kpc = 110−3

Kbw = 110−4

Fos

Fraction of time spent 

outside at CDR 

Triangular 

min=5/24 

peak=12/24 

max=18/24 

0.5 (or 12/24) 0.6 

(or 14.4/24) 

Ii

Intensity distribution of 

fallout while outdoors 

(i=1) and indoors (i=2) 

normalized to average 

CDR intensity 

Lognormal 

(GM=1.0; GSD=1.5) 

(used with Fos) 

1.0 1.0 

INCIDENTAL INGESTION DOSE 

qing Soil ingestion rate 

Triangular 

min=10 mg day−1

peak=100 mg day−1

Max=500 mg day−1

100 mg day−1 500mg day−1

206 
Parameter Definition Distribution for Probabilistic 

Analysis 

Nominal Value for 

Central Estimation Deterministic*

ρsoil Soil bulk density 

Triangular 

min=1.3 g cm−3

peak=1.45 g cm−3

max=1.6 g cm−3

1.45 g cm−3 1.3 g cm−3

* High-sided per guidance in NTPR Policy and Guidance Manual (DTRA, 2007). 

Internal Dose Results 

Distributions of the fifty-year committed equivalent dose (CED) resulting from 10,000 

probabilistic simulations were calculated according to the details described above. CED 

distributions were calculated for three representative organs: thyroid, lung, and lower large 

intestine (LLI) wall. Examples of relative frequencies and probability distributions of dose to the 

LLI wall from alpha radiation are shown in Figure C-4 and Figure C-5, respectively. The same 

properties for the doses to LLI wall from beta-plus-gamma radiation are displayed in Figure C-6

and Figure C-7, respectively. These figures for LLI wall are similar to those obtained for the 

other two organs included in the analysis. 

0

0.025

0.05

0.075

0.1

9.8E-09 5.4E-08 2.9E-07 1.6E-06 8.9E-06 4.9E-05 2.7E-04 1.5E-03 8.1E-03

Dose (rem, CED)

Relative Frequency of log 10(dose)

Figure C-4. Distribution of Estimated Dose for LLI Wall fromAlpha Radiation 

for Company E Personnel during Operation PLUMBBOB 

207 
Cumulative Probability

Dose (rem, CED)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Dose

Fitted Curve

Figure C-5. Probability Plot of Distribution of Estimated LLI Wall Dose 

fromAlpha Radiation for Company E Personnel during Operation PLUMBBOB 

208 
0

0.025

0.05

0.075

0.1

1.2E-05 1.1E-04 1.1E-03 1.0E-02 9.9E-02 9.4E-01

Dose (rem, CED)

Relative Frequency of log 10(dose)

Figure C-6. Distribution of Estimated LLI Wall Dose from Beta plus Gamma Radiation 

for Company E Personnel during Operation PLUMBBOB 

Cumulative Probability

Dose (rem, CED)

0.01% 0.2% 1% 10% 50% 90% 99% 99.9%

10-6

10-5

10-4

10-3

10-2

10-1

100

101

Dose

Fitted Curve

Figure C-7. Probability Plot of Estimated LLI Wall Dose from Beta plus Gamma 

Radiation for Company E Personnel during Operation PLUMBBOB 

209 
Key statistics from the internal dose distributions are compared with those of the deterministic 

model in Table C-7. Note that geometric means are given as central estimates of the 

probabilistic analysis, because they are judged to be more representative central estimates of 

approximately lognormal distributions whose range is several orders of magnitude. Although 

not displayed, arithmetic mean alpha and beta plus gamma organ doses are approximately 8× 

larger and 4×–5× larger than the geometric mean alpha and beta plus gamma doses listed in 

Table C-7, respectively. These results show that each deterministic organ dose is higher than the 

geometric mean of the corresponding probabilistic organ dose distribution, by factors of between 

about 9× to 11× for alpha doses, and between 2× and 10× for beta plus gamma doses. This result 

Table C-7. Summary of Estimated Internal Dose for Company E Personnel during 

Operation PLUMBBOB 

Mean Dose (rem) Upper Bound Dose (rem) 

Organ 

Probabilistic* Deterministic

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic 

 Probabilistic) 

Alpha Dose 

Thyroid 0.0000046 

(7.3) 0.000051 0.00013 0.000087 0.68 

Lung 0.00013 

(7.4) 0.0011 0.0036 0.0022 0.58 

LLI 

Wall 

0.0000050 

(6.9) 0.000051 0.00013 0.000087 0.66 

Beta plus Gamma Dose 

Thyroid 0.0042 

(5.0) 0.0096 0.063 0.028 0.43 

Lung 0.0016 

(6.3) 0.016 0.034 0.030 0.87 

LLI 

Wall 

0.0016 

(5.0) 0.0045 0.025 0.010 0.42 

* Geometric means and geometric standard deviations (GSD) are shown. 

reflects the contributions to the total deterministic organ doses of the very high-sided internal 

doses from inhalation of highly-resuspended fallout, which accounts for roughly 90 percent of 

the alpha organ doses, and between 70–90 percent of the beta plus gamma organ doses. The 

ratios of upper bound organ doses show the opposite result of the deterministic dose comparison, 

i.e., all deterministic upper bound organ doses are lower than the corresponding 95th percentile 

organ doses. The ratios of upper bound doses in Table C-7 show that the deterministic upper 

bound alpha organ doses are roughly 60–70 percent of the corresponding 95th percentile organ 

doses, and the deterministic upper bound beta plus gamma organ doses are between about 

210 
40–85 percent of the corresponding 95th percentile organ doses. These general comparisons 

reflect the effects of the combined large uncertainties associated with resuspension factors, dose 

conversion factors and intensities, and are expected to be the same for all organs if similar input 

variable uncertainties are used. 

211 
References 

DNA (Defense Nuclear Agency), 1996. For the Record – A History of the Nuclear Test 

Personnel Review Program, 1978–1993. DNA 6041F (Defense Nuclear Agency, 

Washington, D.C.), March 1, 1996. 

DTRA (Defense Threat Reduction Agency), 2007. Policy and Guidance Manual – Nuclear Test 

Personnel Review Program. Revision 7. (Defense Threat Reduction Agency, Fort 

Belvoir, VA), November 26, 2007. 

Frank, G., Goetz, J., Klemm, J., Thomas, C., 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, D.C.), 

June 15, 1981. 

Harris, P. S., Obermiller, S., Lowery, C., Ozeroff, W. J., Nelson, A., Weary, S.E. 1981. 

PLUMBBOB Series, 1957. DNA 6005F (Defense Nuclear Agency, , Washington, D.C.), 

September 15, 1981. 

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, 

May 1, 1979 (General Electric Company-TEMPO, Santa Barbara, CA). 

Maag, C., Wilkinson, M., Striegel, J., Collins, B. 1983. Shot HOOD, A Test of the 

PLUMBBOB Series, DNA 6002F (Defense Nuclear Agency, Washington, D.C.), 

May 13, 1983. 

Placak, O. R., Carter, M.W., Gilmore, R.A., Goeke, R.H., Weaver, C.L. 1957. Operation 

PLUMBBOB, Off-Site Radiological Safety Report, Nevada Test Site, OTO-57-3 

(Reynolds Electrical & Engineering Co., Inc., Las Vegas, NV), 1957. 

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 (Science Applications International 

Corporation, McLean, VA and Defense Threat Reduction Agency, Fort Belvoir, VA). 

USMC (United States Marine Corps), 1957. USMC Final Report of Exercise Desert Rock VII, 

circa 1957. 

212 
APPENDIX D Monte Carlo Analysis of Dose to Personnel Aboard USS 

ESTES During Operation REDWING 

Ron Weitz 

213 
APPENDIX D Monte Carlo Dose Probabilistic Analysis of Dose to Personnel Aboard 

USS ESTES During Operation REDWING 

Introduction

Distributions of external and internal doses were generated by Monte Carlo techniques for 

personnel who served aboard USS ESTES (AGC 12) during Operation REDWING (1956). 

Doses are reported for the period extending from the arrival of USS ESTES in the Pacific 

Proving Grounds (PPG) on March 31, 1956, until the end of Operation REDWING on 

August 6, 1956. 

Background

Operation REDWING was a series of 17 atmospheric nuclear tests, conducted from May 5 to 

July 22, 1956, at the Pacific Proving Ground (PPG) in the Marshall Islands. The PPG consisted 

of the land areas of Enewetak and Bikini Atolls, their lagoons, and the waters within 

2.6 nautical miles (3 statute miles) of their seaward sides (Bruce-Henderson et al., 1982). 

USS ESTES was an amphibious force flagship that served during REDWING as the Flagship 

Element (Task Element 7.3.0.1) of the Flagship Unit (Task Group 7.3). The ship arrived in the 

PPG on March 31, 1956, and departed from Enewetak for Bikini on May 3, two days before the 

first shot of the series. It returned to Enewetak twice: once for Shot SEMINOLE on June 6 and 

again during the last four days of June when no shots were detonated. USS ESTES was, 

therefore, present at Enewetak for only one of the eleven shots fired at that atoll. The ship 

participated in all of the six Bikini shots, providing communications, air control, and facilities for 

Program 2 (Nuclear Radiation) and radiation safety activities. It sortied at Bikini just before, 

during, and following each shot. At all other times at Bikini, the ship was moored to buoy Nan-9 

at the Eneu Island anchorage. USS ESTES departed from the PPG on July 25, 1956, proceeded 

to Pearl Harbor, Hawaii, and then to San Diego, California. It arrived at San Diego on August 7, 

1956 (Bruce-Henderson et al., 1982). 

Exposure Scenario 

Residual Radiation from Topside Fallout Contamination 

Shipboard radiological data for USS ESTES during Operation REDWING is minimal. The 

absence of such data likely results from the ship having received relatively little fallout 

following any of the REDWING detonations. In the absence of ship-specific data, it is 

assumed that, while at anchor in Bikini Lagoon (or operating in close proximity to that atoll) 

during periods of documented fallout on nearby ships and islands, USS ESTES was similarly 

affected. Topside intensities are inferred from recorded intensity data on Eneu Island (ZUNI 

and TEWA) and USNS FRED C. AINSWORTH (Shots FLATHEAD and NAVAJO), as listed 

in Table D-1. Peak intensities are reported in units of mR hr−1

 at the indicated elapsed time from 

the detonation (H+hours). (Bruce-Henderson et al.,1982; Jacks, 1957) 

214 
Table D-1. Peak Radiation Intensities on USS ESTES during Operation REDWING 

Shot Shot Date (1956) (Time) Peak Intensity (mR hr−1) 

 ZUNI * May 28 (0556) 11.6 at H+37.4 hours 

 FLATHEAD** Jun 12 (0626) 1.12 at H+43.6 hours 

 NAVAJO** Jul 11 (0556) 1.49 at H+22 hours 

 TEWA * Jul 21 (0546) 3.68 at H+18.3 hours 

* Inferred from Eneu Island data 

** Inferred from USNS FRED C. AINSWORTH data

The early time-intensity pairs for fallout on USS ESTES from Shot ZUNI, as inferred from 

measurements taken on Eneu Island, are provided in Table D-2. Allowance has been made for 

the effectiveness of washdown as documented in the ship’s deck logs (USS ESTES, 1956). 

Table D-2. Early Time-Intensity 

Data for USS ESTES After Shot ZUNI 

Time After 

Detonation (hr) Intensity (mR hr−1

) 

27 0.1 

28 2.0 

30 6.0 

32 8.0 

34 11 

37.4 11.6 

37.6 5.8 

40 6.63 

42 6.26 

The radiological environment on USS ESTES following FLATHEAD fallout is presumed to 

have been the same as on USNS FRED C. AINSWORTH, as specified in Table D-3. 

The radiological environment on USS ESTES following NAVAJO fallout is presumed to have 

been the same as on USNS FRED C. AINSWORTH is shown in Table D-4. 

215 
Table D-3. Early Time-Intensity Data on USS ESTES 

After Shot FLATHEAD 

Time After 

Detonation (hr) Intensity (mR hr−1

) 

17.6 0.01 

29.6 0.08 

33.6 0.33 

41.6 0.89 

43.6 1.12 

65.6 0.69 

Table D-4. Early Time-Intensity Data on USS ESTES 

After Shot NAVAJO 

Time After 

Detonation (hr) Intensity (mR hr−1

) 

10 0.01 

14 0.02 

18 0.49 

22 1.49 

26 1.19 

30 0.96 

34 0.69 

38 0.60 

The TEWA fallout intensity profile on USS ESTES is presumed to have been the same as on 

Eneu Island, as indicated in Table D-5. 

Table D-5. Early Time-Intensity Data on 

USS ESTES After Shot TEWA 

Time After 

Detonation (hr) Intensity (mR hr−1

) 

15 0.1 

18.25 3.68 

Extrapolation beyond the time of the last time-intensity point for each shot is accomplished by 

assuming t−1.2 decay for deterministic calculations and by utilizing the shot-specific FIIDOS 

decay functions for probabilistic calculations as discussed in Section 3.2. 

216 
Residual Radiation from Ship Operation in Contaminated Water 

USS ESTES also accumulated radioactive materials on its underwater hull and in salt water 

piping and evaporators when the ship operated in contaminated lagoon water at Bikini and 

Enewetak Atolls, a phenomenon termed “ship contamination.” Although partially attenuated by 

the hull and piping structures, the gamma radiation emitted by these contaminants was a source 

of exposure to crewmembers in below-deck spaces. In addition, crewmen who were topside 

when the ship operated in contaminated water were exposed to gamma radiation emitted directly 

from the contaminants in the water (often called “shine”). Daily external gamma dose 

increments from shine and ship contamination have been computed for personnel assigned to 

USS ESTES (Stiver, 2000). (For perspective, the dose reconstructions discussed below indicate 

that approximately 10 percent of the dose to a representative USS ESTES crewman came from 

exposure to ship contamination, and about 1 percent resulted from exposure to water shine.) 

External Dose: Approach 

Film Badge Data 

The entire crew was issued film badges for the duration of the ship’s participation in the 

operation. Two series of badges were issued, the first covering the period April 25 to June 25 

and the second from June 25 to July 25. As was the case with the 7126th Army Unit REDWING 

study group discussed in Appendix A, most film badges issued to USS ESTES personnel for 

periods of 4 weeks or more at Operation REDWING were damaged by the high heat and 

humidity in the test area (Bruce-Henderson et al., 1982; NRC, 1989). Therefore film badge 

dosimetry is not available for comparison with the probabilistic dose distributions of USS 

ESTES.

Monte Carlo-Based Dose Reconstruction 

Probabilistic external gamma dose reconstruction for the crew of USS ESTES during Operation 

REDWING was accomplished by incorporating uncertainty distributions for various parameters 

into the model discussed in Section 3. The specific parameters used in both the deterministic and 

uncertainty analyses of external dose are shown in Table D-6. 

External Dose Results 

The Monte Carlo dose distribution derived for a sample size of 10,000 is displayed in 

Figure D-1. The probability plot is shown in Figure D-2. The statistics of this distribution are 

compared with those of a deterministic calculation in Table D-7. 

217 
Table D-6. Input Parameter Specification for External Gamma Dose Reconstruction, 

Case Study # 4 

Parameter Definition 

Distribution for 

Uncertainty 

Analysis* 

Nominal Value for 

Central Estimation 

Deterministic 

Analysis** 

EXTERNAL DOSE MULTIPLIER (EDM) FOR SHIP-BASED PERSONNEL 

Fts

Fraction of time spent 

topside 

Triangular 

min=4/24 

peak=9.6/24 

max=18/24 

0.4 (or 9.6/24) 0.4 (or 9.6/24) 

SFw

Shielding factor at belowdeck worksite (assumed 

equally likely on 1st or 2nd

decks below topside) 

Elliptical ship model 

(see Section 4.2.3) 

GM = 0.079 

0.079 0.1 

SFb

Shielding factor at belowdeck billet location (assumed 

on 3rd deck below topside) 

Elliptical ship model 

(see Section 4.2.3) 

GM = 0.016 

0.016 0.1 

Ii

Intensity of fallout near 

topside location (i=1), 

topside location above 

below-deck worksite (i=2), 

and topside location above 

below-deck billet area (i=3) 

frequented by veteran, 

normalized to the intensity 

averaged over the entire 

topside deck 

Post-decon model for 

elliptical ships 

(see Section 4.2.1) 

μ = 1.0 

σ = 0.70 

0.88 

(median of 

distribution) 

1.0 

INTENSITY MEASUREMENTS FOR SHIP-BASED PERSONNEL 

Im Measured topside intensities 

Normal 

μ = Im, σ = 0.3·Im 

(to account for 

measurement error) 

1.0 1.0 

a

Exponent of multiplicative 

error factor (t/t0)

±a

 applied to 

FIIDOS-generated intensity 

functions 

Normal 

μ = 0 

σ = 0.15 

0 0 

Isc Ship contamination intensity 

Lognormal multiplier 

GM=1 

UB95=3.2 

1.0 1.0 

Iws Water shine intensity 

Lognormal multiplier 

GM=1 

UB95=2.4 

1.0 1.0 

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

deviation; UB95 = upper bound at the 95th percentile. 

** High-sided per guidance in NTPR Policy and Guidance Manual (DTRA, 2007).

218 
0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.0 0.5 1.0 1.5 2.0

External Gamma Dose (rem)

Relative Frequency

Figure D-1. Distribution of Estimated External Gamma Doses from Monte Carlo Analysis 

for Crew of USS ESTES during Operation REDWING 

Cumulative Probability

Dose (rem)

0.01% 1% 10% 50% 90% 99% 99.9% 99.999%

10-2

10-1

100

101

Dose

Fitted Curve

Figure D-2. Probability Plot of Estimated External Gamma Doses from Monte Carlo 

Analyses for Crew of USS ESTES during Operation REDWING 

219 
Table D-7. Summary of Estimated External Dose for Crew of USS ESTES during 

Operation REDWING 

Mean Doses (rem) Upper Bound Doses (rem) 

Probabilistic(*) Deterministic 

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic/ 

Probabilistic) 

0.50 

(0.28) 0.43 1.0 1.2 1.1 

(*) The arithmetic mean (and standard deviation) are shown. The geometric mean external 

dose is 0.44 rem. 

Internal Dose: Approach 

Internal dose reconstruction for the crew of USS ESTES during Operation REDWING was 

accomplished by incorporating uncertainty distributions for the fallout-induced radiation 

environments discussed above and for various other parameters as discussed in Sections 3 and 4. 

The specific parameters used in both the deterministic and probabilistic analyses are shown in 

Table D-8. 

Table D-8. Input Parameter Specification for Internal Dose Reconstruction, 

Case Study #4 

Parameter Definition Distribution for 

Probabilistic Analysis

Nominal Value for 

Central Estimation Deterministic(*)

INTERNAL DOSE (GENERAL) 

DCFInhα

DCFIngα

Inhalation and ingestion 

dose conversion factors for 

fallout α emitters 

DCFs calculated with 

FIIDOS multiplied by 

Lognormal with 

GM=1.0, GSD=5.19 

DCFs calculated with 

FIIDOS 

(see Section 4.2.8) 

DCFs calculated 

with FIIDOS 

(see Section 

4.2.8) 

DCFInhβγ

DCFIngβγ

Inhalation and ingestion 

dose conversion factors for 

fallout β+γ radiation 

DCFs calculated with 

FIIDOS multiplied by 

Lognormal with 

GM=1.0, GSD=4.05 

DCFs calculated with 

FIIDOS 

(see Section 4.2.8) 

DCFs calculated 

with FIIDOS 

(see Section 

4.2.8) 

Biasα Assigned Constant 

α: 1.3 for each organ α: 1.3 for each organ 1.0 

Biasβγ

Bias factors to adjust highsided inhalation DCF values βγ: 1.2 for thyroid & 

LLI, 1.35 for lung 

βγ: 1.2 for thyroid & LLI, 

1.35 for lung 1.0 

BR Breathing rate 

Triangular distribution 

derived from USEPA 

(1997) data (see 

Section 4.2.7): 

min = 0.33 m3 hr−1

peak = 1.53 m3 hr−1

max = 2.79 m3 hr−1

Mean of Distribution 

~1.5 m3 hr−1

 1.2 m3 hr−1

220 
Parameter Definition Distribution for 

Probabilistic Analysis

Nominal Value for 

Central Estimation Deterministic(*)

DESCENDING INHALATION DOSE (†)

RNDRes1 1.0 (assumed constant) 1.0 (assumed constant) 

RNDRes2

Lognormal: GM, GSD 

0.0056, 1.744 

Geometric Mean 

0.0056 

RNDRes3

Deposition fractions for 

particle sizes deposited in 

Regions BB, bb, and AI Lognormal: GM, GSD 

0.001, 1.65 0.001 

n/a 

RNDNonres1 0.0 (assumed constant) 0.0 (assumed constant) 

RNDNonres2 Lognormal: GM, GSD 

0.363, 1.106

Geometric Mean 

0.363 

RNDNonres3

Deposition fractions for 

particle sizes deposited in 

Region ET2 and cleared to 

digestive tract Lognormal: GM, GSD 

0.285, 1.185 0.285 

n/a 

V1

Logtriangular 

min, peak, max (cm 

s

−1

) 

0.22/2, 0.22, 27.8 

0.22 cm s−1

V2 0.83/2, 0.83, 27.8 0.83 cm s−1 

V3

Particle settling velocities 

13.0/2, 13.0, 27.8 13.0 cm s−1

106

(cm)/T(sec) 

Triangular 

(min,peak,max) Peak of Distributions 

ZUNI 

(0.999,1.000, 1.000) 

ZUNI 

1.000 

FLATHEAD 

(1.000,1.000,1.000) 

FLATHEAD 

1.000 

NAVAJO 

(0.707, 0.869, 0.988) 

NAVAJO 

0.869 

AF100 Surface activity fraction 

<100 μm particles 

TEWA 

(0.396, 0.587, 0.801) 

TEWA 

0.587 

1.0 

frac1

Triangular 

Min, peak, max 

0, 0.00136, 0.01 

Peak of Distribution 

0.00136 

frac2

Surface fraction of Class 1–

2 from 1–100 μm particles 

0, 0.025, 0.1 0.025 

n/a 

RESUSPENDED INHALATION DOSE 

K(t) Time-dependent 

resuspension factor 

Lognormal multiplier 

GM=1, GSD=4.05 

10−5

 m−1 for first 4 days 

post-deposition, 0 

thereafter 

10−5

 m−1 for first 

4 days postdeposition, 0 

thereafter 

(*) High-sided per guidance in NTPR Policy and Guidance Manual (DTRA, 2007). 

(†) AMAD particle size classes: 1 = 1–10 μm, 2 = 10–20 μm, 3 = 20–100 μm.

Internal Dose Results 

Fifty-year committed equivalent dose (CED) distributions to three organs, thyroid, lung, and 

lower large intestine (LLI) wall, were derived using the probabilistic model for a sample size of 

221 
10,000. The geometric mean and 95th percentile CEDs of the various distributions are given in, 

Table D-9 along with analogous doses derived deterministically. The ratio of the deterministic 

upper bound CED to the probabilistic 95th percentile CED is provided in the rightmost column. 

Examples of these distributions are shown in Figure D-3 through Figure D-6, which show the 

relative frequency distributions and probability plots of CED to the LLI wall from alpha 

radiation and from beta plus gamma radiation, respectively. 

Table D-9. Summary of Estimated Internal Doses for Crew of USS ESTES during 

Operation REDWING 

Mean Dose (rem) Upper Bound Dose (rem) 

Organ 

Probabilistic(*) Deterministic 

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR Upper 

Bound) 

Ratio 

(Deterministic/ 

Probabilistic) 

Alpha Dose 

Thyroid 0.0000072 

(7.8) 0.000032 0.00021 0.00032 1.5 

Lung 0.000088 

(7.8) 0.00040 0.0026 0.0040 1.5 

LLI 0.0000076 

(7.6) 0.000033 0.00022 0.00033 1.5 

Beta plus Gamma Dose 

Thyroid 0.56 

(4.6) 0.70 6.6 7.0 1.1 

Lung 0.088 

(6.0) 0.58 1.8 5.8 3.2 

LLI 0.36 

(4.6) 0.44 4.2 4.4 1.0 

(*) Geometric mean and (geometric standard deviation) are shown for the probabilistic analysis results. 

222 
0

0.025

0.05

0.075

0.1

8.1E-09 1.8E-07 3.8E-06 8.4E-05 1.8E-03 3.9E-02

Dose (rem, CED)

Relative Frequency of log 10(dose)

Figure D-3. Distribution of Estimated LLI Wall Dose from Alpha Radiation for Crew of 

USS ESTES during Operation REDWING 

Cumulative Probability

Dose (rem, CED)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Dose

Fitted Curve

Figure D-4. Probability Plot of Estimated LLI Wall Dose from Alpha Radiation for Crew 

of USS ESTES during Operation REDWING 

223 
0

0.025

0.05

0.075

0.1

1.7E-03 1.8E-02 1.9E-01 2.0E+00 2.1E+01

Dose (rem, CED)

Relative Frequency of log 10(dose)

Figure D-5. Distribution of Estimated LLI Wall Dose from Beta plus Gamma Radiation 

for Crew of USS ESTES during Operation REDWING 

Cumulative Probability

Dose (rem, CED)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

10-4

10-3

10-2

10-1

100

101

102

103

Dose

Fitted Curves

Figure D-6. Probability Plot of Estimated LLI Wall Dose from Beta plus Gamma 

Radiation for Crew of USS ESTES during Operation REDWING 

224 
References 

Bruce-Henderson, S., Gladeck, F.R., Hallowell, J.H., Martin, E.J., McMullan, F.W., Miller, 

R.H., Rogers, W.E., Rowland, R.H., Shelton, C.F., Sturman, P., Berkhouse, L.H., Davis, 

S., DeSantis, H., Dean, P., Doyle, M.K., and Patterson, D.S., 1982. Operation 

REDWING: 1956, United States Atmospheric Nuclear Weapons Tests, Nuclear Test 

Personnel Review. DNA 6037F (Defense Nuclear Agency, Washington, D.C.). 

DTRA (Defense Threat Reduction Agency), 2007. Policy and Guidance Manual – Nuclear Test 

Personnel Review Program. Revision 7 (Defense Threat Reduction Agency, Fort Belvoir, 

VA), November 26, 2007. 

Jacks, G. L., 1957. Operation REDWING Radiological Safety. WT-1366 (extracted version 

prepared for DNA in 1983; Defense Nuclear Agency, Washington D.C.). 

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

(National Academy Press, Washington, D.C.). 

Stiver, J.H., 2000, “REDWING fallout intensity model, codified in Excel spreadsheet” Dose 

Tables-Island based-1.xls,” (Science Applications International Corporation), 2000. 

USEPA, 1997. Exposure Factors Handbook. EPA/600/P-95/002Fa, Fb, Fc (Office of Research 

and Development, U.S. Environmental Protection Agency, Washington, D.C.). 

USS ESTES (AGC 12), Deck log excerpts, March–July 1956. 

225 
APPENDIX E Monte Carlo Analysis of Dose to Personnel Aboard USS 

BOXER During Operation HARDTACK I 

Ron Weitz 

226 
APPENDIX E Monte Carlo Analysis of Dose to Personnel Aboard USS BOXER During 

Operation HARDTACK I 

Introduction

Distributions of external and internal doses were generated by Monte Carlo techniques for 

personnel who served aboard USS BOXER (CVS 21) during Operation HARDTACK I (1958). 

Doses are reported for the period extending from May 12, 1958, until the turn-in of film badges 

(date unknown, treated as an uncertainty). 

Background

Operation HARDTACK I was a series of 35 atmospheric nuclear weapon tests conducted in the 

Pacific Ocean from April 28 to August 18, 1958. All but three of these shots occurred at the 

Enewetak Proving Ground (EPG), which consisted of the land areas of Enewetak and Bikini 

Atolls, their lagoons, and the waters within 2.6 nautical miles (nmi) (3 statute miles) of their 

seaward sides. Enewetak Atoll is located about 2400 nmi southwest of Hawaii; Bikini Atoll is 

approximately 190 nmi east of Enewetak Atoll. (Gladeck et al., 1982) 

USS BOXER was an antisubmarine aircraft carrier that served during HARDTACK I as 

command ship for Commander Joint Task Force 7, flagship for the Commander Task Group 

(CTG) 7.3 (Navy), headquarters for CTG 7.1 (Scientific) and CTG 7.4 (Air Force), and Air 

Operations Center for Air Force personnel. The ship also hosted Marine Helicopter Transport 

Squadron (Light) 361. USS BOXER transported many of the nuclear devices from CONUS to 

EPG. The ship arrived at Enewetak Atoll on March 3, 1958, with a crew of approximately 

1100 personnel. It made numerous transits between Enewetak and Bikini atolls during May and 

June in support of the test series, finally departing EPG for Pearl Harbor, Hawaii, on June 30. 

The ship subsequently was present at Johnston Island in late July and August to support the two 

HARDTACK I shots at that location. During the operation, USS BOXER performed a variety of 

shot-specific tasks; for example, it served as the launch platform for the balloon that carried the 

Shot YUCCA device aloft, the evacuation unit for island-based personnel for several shots, and 

the recovery element for rocket nosecones and other instrumented devices employed at several 

shots. (Gladeck et al., 1982, and ship’s deck log) 

Extensive preparation and planning for radiological safety were performed aboard USS BOXER. 

The ship was equipped with a washdown system to remove fallout, and was staffed with 

18 radiological monitoring teams and two decontamination squads. These teams were used 

extensively on shot days for fallout watch and decontamination, as needed. Radiological surveys 

were made hourly during USS BOXER’s stay in EPG (Gladeck et al., 1982). Unfortunately, 

little of this monitoring data has been located to date. 

227 
Exposure Scenario 

There was only one recorded incidence of fallout on USS BOXER, as reported in USS BOXER 

CO (1958): 

Only one instance of contamination by fallout occurred. This was on 14 May 1958 at 

0630 M while at anchor in Eniwetok Atoll after the KOA shot. Intensities topside rose to 

an average of 8 MR/HR (Gamma) with high levels of 20/30 MR/HR. Washdown system 

was not activated immediately due to flight operations, however.....all monitoring stations 

[were] manned. After approximately 1 hour of washdown operation intensity had 

dropped to 4 MR/HR and subsequently decayed to background..... 

It is likely that mixed FIR-KOA fallout began to descend on USS BOXER at approximately 

0300 hours that morning and continued until 1600 hours that afternoon, as indicated by 

measurements taken with a continuous monitor on nearby Parry Island (Appendix B). The ship’s 

deck log for that day states that the washdown system was activated four times on the morning of 

May 14: during the periods 0736 to 0805, 0920 to 1010, 1047 to 1056, and 1130 to 1144. The 

effectiveness of the washdown system is uncertain in view of a second, ostensibly contradictory 

statement in USS BOXER CO (1958) implying that the system only succeeded in leveling off 

the rise in radiation intensity on the flight deck during operation, and that it was 30 percent 

efficient in other areas. In any case, it is apparent from the measurements on Parry Island that 

the fallout continued to descend in the area after USS BOXER’s washdown system was secured 

for the final time at 1144. 

Although USS BOXER CO (1958) identified the mid-May episode as the only fallout event to 

impact USS BOXER, that report is dated June 18, 1958, midway through the operation. It is 

likely that two unreported incidences of fallout occurred in the two days prior to the ship’s 

departure from EPG on June 30: 

 USS BOXER was operating in the vicinity of Enewetak Atoll when light fallout was 

measured on Parry Island during rainfall on the afternoon of June 28, following the 

detonation of Shot REDWOOD at Bikini Atoll that morning (see Appendix B). The deck log 

states that USS BOXER departed Enewetak Atoll late that afternoon and steamed to the 

southeast, in the general direction of increasing REDWOOD fallout (based on the fallout 

pattern shown in Figure 40 of Gladeck et al., 1982). The deck log weather observation sheet 

for that day indicates that the ship could have spent up to 6 hours that evening in rain 

showers. 

 On the evening of June 29, while USS BOXER was anchored in Enewetak Lagoon, fallout 

from Shot OAK descended during rain showers in the vicinity of Enewetak Atoll. 

External Dose: Approach 

Film Badge Data 

The entire crew was issued film badges prior to the start of testing. The issue date for officers 

and senior non-commissioned officers was April 11; most enlisted personnel received their 

badges on April 14. For the majority of crewmembers (979 personnel, comprising 89 percent of 

the crew), the available dosimetry record (referred to as the “fourth quarter report”) provides 

total operational doses but does not include complete information linking the readings to badge 

228 
numbers and to turn-in dates. Because of its impact on dose reconstruction, the question of 

badge turn-in date was examined carefully. According to rad-safe policy, film badges were to be 

turned in upon recall by the Task Group Rad-Safe organization, upon exit from a contaminated 

area, or upon departure from EPG. In keeping with this policy, the badges worn by the USS 

BOXER crew should have been returned on or just prior to June 30, when the ship departed 

Enewetak for Pearl Harbor. However, based on an analysis of all available USS BOXER 

dosimetry records, ship logs and personnel diaries, and interviews with members of the ship’s 

crew, it is concluded that the embarked crew turned their badges in while the ship was underway 

for Pearl Harbor from June 30 to July 6; the turn-in date is treated as an uncertainty in the 

probabilistic assessment. Consequently, these badges were probably processed at Pearl Harbor 

in early July and not at the film badge stations established at Enewetak and Bikini Atolls for that 

purpose. This may explain the lack of completed film badge records of the type available for 

most ships and units supporting HARDTACK I. 

It appears that the remaining 11 percent of the crew, for whom more detailed film badge 

information is recorded, either transferred off USS BOXER prior to its departure from EPG or 

was involved in special activities requiring their absence from the ship during operations at EPG. 

This has been confirmed for individuals reassigned from USS BOXER during the May–June 

period, and for a contingent of USS BOXER-based Marines who were on temporary duty off the 

ship during the badging period. These personnel probably turned their badges in prior to their 

departure from EPG, so that these badges were processed and recorded at the test site. 

The average of these film badge readings is 0.735 rem. Removing the 20 percent environmental 

bias discussed in the NRC film badge dosimetry report (NRC, 1989) results in an unbiased 

average film badge dose of 0.735/1.2 = 0.612 rem. 

Monte Carlo-Based Dose Reconstruction 

Probabilistic external gamma dose reconstruction for the crew of USS BOXER during Operation 

HARDTACK I was accomplished by incorporating uncertainty distributions for various 

parameters into the model discussed in Section 3. The specific parameters used in both the 

deterministic and uncertainty analyses of external dose are shown in Table E-1. 

External Dose Results 

The Monte Carlo dose distribution derived for a sample size of 10,000 is displayed in Figure E-1. 

The probability plot is shown in Figure E-2. The statistics of this distribution are compared with 

those of a deterministic calculation and of the film badge distribution in Table E-2. 

229 
Table E-1. Input Parameter Specification for External Gamma Dose Reconstruction, 

Case Study #5 

Parameter Definition 

Distribution for 

Uncertainty 

Analysis* 

Nominal Value for 

Central Estimation 

Deterministic 

Analysis** 

FILM BADGE DATA 

DateFbend Date of film badge turn-in 

Daily probabilities 

for period Jun 30 to 

Jul 6, 1958: 0.2, 0.3, 

0.1, 0.1, 0.1, 0.1, 0.1.

July 2, 1958 July 2, 1958 

SHOT MIXTURE FRACTION 

Fallout 

Composition 

Fallout proportion from each 

shot (applies to FIR/KOA 

only) 

Triangular 

min = 0 

peak = 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 

EXTERNAL DOSE MULTIPLIER (EDM) FOR SHIP-BASED PERSONNEL 

Fts

Fraction of time spent 

topside 

Triangular 

min=4/24 

peak=9.6/24 

max=18/24 

0.4 (or 9.6/24) 0.4 (or 9.6/24) 

SFw

Shielding factor at belowdeck worksite (assumed 

equally likely on 1st or 2nd

decks below flight deck) 

Rectangular ship 

model 

(see Section 4.2.3) 

GM = 0.11 

0.11 0.1 

SFb

Shielding factor at belowdeck billet location (assumed 

equally likely on 3rd or 4th

decks below flight deck) 

Rectangular ship 

model (see Section 

4.2.3) 

GM = 0.021 

0.021 0.1 

Ii

Intensity of fallout near 

topside location (i=1), 

topside location above 

below-deck worksite (i=2), 

and topside location above 

below-deck billet area (i=3) 

frequented by veteran, 

normalized to the intensity 

averaged over the entire 

topside deck 

Post-decon model for 

rectangular ships 

(see Section 4.2.1) 

μ = 1.0 

σ = 0.63 

0.92 

(median of 

distribution) 

1.0 

INTENSITY MEASUREMENTS FOR SHIP-BASED PERSONNEL 

Im Measured topside intensities 

Normal 

μ = Im, σ = 0.3·Im 

(to account for 

measurement error) 

1.0 1.0 

a

Exponent of multiplicative 

error factor (t/t0)

±a

 applied to 

FIIDOS-generated intensity 

functions 

Normal 

μ = 0 

σ = 0.15 

0 0 

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

deviation; UB95 = upper bound at the 95th percentile. 

** High-sided per guidance in NTPR Policy and Guidance Manual (DTRA, 2007).

230 
0.00

0.10

0.20

0.30

0.40

0.0 1.0 2.0 3.0 4.0

Whole Body Gamma Dose (rem)

Relative Frequency

Figure E-1. Distribution of Estimated External Gamma Doses for Crew of USS BOXER 

during Operation HARDTACK I 

Cumulative Probability

Dose (rem)

1% 10% 30% 50% 70% 90% 99% 99.9% 99.999%

10-1

100

101

Dose

Fitted Curve

Figure E-2. Probability Plot of Estimated External Gamma Doses for Crew of USS 

BOXER during Operation HARDTACK I 

231 
Table E-2. Summary of Estimated External Dose for Crew of USS BOXER during 

Operation HARDTACK I 

Mean Dose (rem) Upper Bound Dose (rem) 

Film 

Badge Probabilistic(*) Deterministic

(NTPR) 

Film 

Badge 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic/ 

Probabilistic) 

0.61 0.53 

(0.36) 0.52 0.97 1.2 1.6 1.3 

(*) The arithmetic mean (and standard deviation) are shown. The geometric mean external dose is 0.42 

rem. 

Internal Dose: Approach 

Internal dose reconstruction for the crew of USS BOXER during Operation HARDTACK I was 

accomplished by incorporating uncertainty distributions for the fallout-induced radiation 

environments discussed above and for various other parameters discussed in Sections 3 and 4. 

The specific parameters used in both the deterministic and probabilistic analyses are shown in 

Table E-3. 

Table E-3. Input Parameter Specifications for Internal Dose Reconstruction,Case Study #5 

Parameter Definition Distribution for 

Probabilistic Analysis

Nominal Value for 

Central Estimation Deterministic(*)

INTERNAL DOSE (GENERAL) 

DCFInhα

DCFIngα

Inhalation and ingestion 

dose conversion factors for 

fallout α emitters 

DCFs calculated with 

FIIDOS multiplied by 

Lognormal with 

GM=1.0, GSD=5.19 

DCFs calculated with 

FIIDOS 

(see Section 4.2.8) 

DCFs calculated 

with FIIDOS 

(see Section 

4.2.8) 

DCFInhβγ

DCFIngβγ

Inhalation and ingestion 

dose conversion factors for 

fallout β+γ radiation 

DCFs calculated with 

FIIDOS multiplied by 

Lognormal with 

GM=1.0, GSD=4.05 

DCFs calculated with 

FIIDOS 

(see Section 4.2.8) 

DCFs calculated 

with FIIDOS 

(see Section 

4.2.8) 

Biasα Assigned Constant 

α: 1.3 for each organ α: 1.3 for each organ 1.0 

Biasβγ

Bias factors to adjust highsided inhalation DCF values βγ: 1.2 for thyroid & 

LLI, 1.35 for lung 

βγ: 1.2 for thyroid & LLI, 

1.35 for lung 1.0 

BR Breathing rate 

Triangular distribution 

derived from USEPA 

(1997) data (see 

Section 4.2.7): 

min = 0.33 m3 hr−1

peak = 1.53 m3 hr−1

max = 2.79 m3 hr−1

Mean of Distribution 

~1.5 m3 hr−1

 1.2 m3 hr−1

232 
Parameter Definition Distribution for 

Probabilistic Analysis

Nominal Value for 

Central Estimation Deterministic(*)

DESCENDING INHALATION DOSE (†)

RNDRes1 1.0 (assumed constant) 1.0 (assumed constant) 

RNDRes2

Lognormal: GM, GSD 

0.0056, 1.744 

Geometric Mean 

0.0056 

RNDRes3

Deposition fractions for 

particle sizes deposited in 

Regions BB, bb, and AI Lognormal: GM, GSD 

0.001, 1.65 0.001 

n/a 

RNDNonres1 0.0 (assumed constant) 0.0 (assumed constant) 

RNDNonres2 Lognormal: GM, GSD 

0.363, 1.106

Geometric Mean 

0.363 

RNDNonres3

Deposition fractions for 

particle sizes deposited in 

Region ET2 and cleared to 

digestive tract Lognormal: GM, GSD 

0.285, 1.185 0.285 

n/a 

V1

Logtriangular 

min, peak, max 

(cm s−1

) 

0.22/2, 0.22, 27.8 

0.22 cm s−1

V2 0.83/2, 0.83, 27.8 0.83 cm s−1 

V3

Particle settling velocities 

13.0/2, 13.0, 27.8 13.0 cm s−1

106

(cm)/T(sec) 

Triangular 

(min,peak,max) Peak of Distributions 

FIR/KOA 

(1.000, 1.000, 1.000) 

FIR/KOA 

1.000 

REDWOOD 

(0.624,0.816, 0.986) 

REDWOOD 

0.816 

AF100 Surface activity fraction 

<100 μm particles 

OAK 

(0.469, 0.732, 0.975) 

OAK 

0.732 

1.0 

frac1

Triangular 

Min, peak, max 

0, 0.00136, 0.01 

Peak of Distribution 

0.00136 

frac2

Surface fraction of Class 1–

2 from 1–100 μm particles 

0, 0.025, 0.1 0.025 

n/a 

RESUSPENDED INHALATION DOSE 

K(t) Time-dependent 

resuspension factor 

Lognormal multiplier 

GM=1, GSD=4.05 

10−5

 m−1 for first 4 days 

post-deposition, 0 

thereafter 

10−5

 m−1 for first 

4 days postdeposition, 0 

thereafter 

(*) High-sided per guidance in NTPR Policy and Guidance Manual (DTRA, 2007). 

(†) AMAD particle size classes: 1 = 1–10 μm, 2 = 10–20 μm, 3 = 20–100 μm.

233 
Internal Dose Results 

Fifty-year committed equivalent dose (CED) distributions to three organs, thyroid, lung, and 

lower large intestine (LLI) wall were derived using the probabilistic model for a sample size of 

10,000. The geometric mean and 95th percentile CEDs of the various distributions are given in 

Table E-4, along with analogous doses derived deterministically. The ratio of the deterministic 

upper bound CED to the probabilistic 95th percentile CED is provided in the rightmost column. 

Examples of these distributions are shown in Figure E-3 through Figure E-6, where the relative 

frequency distribution and probability plot of CED to the LLI wall from alpha radiation and from 

beta plus gamma radiation, respectively, are plotted. 

Table E-4. Summary of Estimated Internal Doses for Crew of USS BOXER 

during Operation HARDTACK I 

Mean Doses (rem) Upper Bound Doses (rem) 

Organ 

Probabilistic(*) Deterministic 

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR Upper 

Bound) 

Ratio 

(Deterministic/ 

Probabilistic) 

Alpha Doses 

Thyroid 0.000019 

(7.9) 0.00026 0.00061 0.0026 4.2 

Lung 0.00025 

(8.0) 0.0035 0.0081 0.035 4.2 

LLI 0.000020 

(7.6) 0.00026 0.00063 0.0026 4.0 

Beta plus Gamma Doses 

Thyroid 0.32 

(4.5) 0.76 3.8 7.6 2.0 

Lung 0.032 

(5.9) 0.38 0.60 3.8 6.2 

LLI 0.21 

(4.5) 0.49 2.5 4.9 2.0 

(*) Geometric mean and (geometric standard deviation) are shown for the probabilistic analysis results. 

234 
0

0.025

0.05

0.075

0.1

2.1E-08 4.7E-07 1.0E-05 2.2E-04 4.9E-03

Dose (rem, CED)

Relative Frequency of log 10(dose)

Figure E-3. Distribution of Estimated LLI Wall Dose from Alpha Radiation for Crew of 

USS BOXER during Operation HARDTACK I 

Cumulative Probability

Dose (rem, CED)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Dose

Fitted Curve

Figure E-4. Probability Plot of Estimated LLI Wall Dose from Alpha Radiation for Crew 

of USS BOXER during Operation HARDTACK I 

235 
0

0.025

0.05

0.075

0.1

4.4E-04 4.8E-03 5.2E-02 5.6E-01 6.1E+00 6.6E+01

Dose (rem, CED)

Relative Frequency of log 10(dose)

Figure E-5. Distribution of Estimated LLI Wall Dose from Beta plus Gamma Radiation 

for Crew of USS BOXER during Operation HARDTACK I 

Cumulative Probability

Dose (rem, CED)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

10-4

10-3

10-2

10-1

100

101

102

103

Dose

Fitted Curve

Figure E-6. Probability Plot of Estimated LLI Wall Dose from Beta plus Gamma 

Radiation for Crew of USS BOXER during Operation HARDTACK I 

236 
References 

DTRA (Defense Threat Reduction Agency), 2007. Policy and Guidance Manual – Nuclear Test 

Personnel Review Program. Revision 7 (Defense Threat Reduction Agency, Fort Belvoir, 

VA), November 26, 2007. 

Gladeck, F.R., Gould, K.G., Hallowell, J.H., Martin, E.J., McMullan, F.W., Miller, R.A., 

Osborn, M.J., Shelton, C.F., Berkhouse, L., and Calhoun, F.S., 1982. Operation 

HARDTACK I (1958). DNA 6038F (Defense Nuclear Agency, Washington, D.C.). 

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

(National Academy Press, Washington, D.C.) 

USEPA, 1997. Exposure Factors Handbook. EPA/600/P-95/002Fa, Fb, Fc (Office of Research 

and Development, U.S. Environmental Protection Agency, Washington, D.C.). 

237 
APPENDIX F Monte Carlo Analysis of Dose for Personnel Stationed on 

Enewetak Island During Operation CASTLE 

Carol Mason 

238 
APPENDIX F Monte Carlo Analysis of Dose for Personnel Stationed on Enewetak 

Island During Operation CASTLE 

Introduction 

Distributions of external and internal doses were generated by Monte Carlo techniques for 

personnel stationed at Enewetak Island, Enewetak Atoll, during Operation CASTLE (1954). 

Doses are reported for the entire operational period from March 1, 1954, through May 31, 1954. 

Background 

Operation CASTLE, the fifth nuclear test series at the Pacific Proving Ground (PPG), consisted 

of the six nuclear weapon tests identified in Table F-1. The operation was conducted by a joint 

military and civilian organization, designated Joint Task Force (JTF) 7, for the Atomic Energy 

Commission (AEC) from March 1 through May 14, 1954. The PPG consisted principally of 

Enewetak and Bikini Atolls in the northwestern Marshall Islands in the central Pacific Ocean. 

Enewetak Atoll, located about 2400 nautical miles (nmi) southwest of Hawaii and approximately 

190 nmi west of Bikini Atoll, served as a base of operations and the location of the last shot in 

the series (NECTAR). The other five tests were conducted at Bikini Atoll. (DNA, 1996; Martin 

and Rowland, 1982) 

Table F-1. Operation CASTLE Detonations 

Shot Date (1954) 

and Time Location 

BRAVO Mar 1 at 0645 Bikini 

ROMEO Mar 27 at 0630 Bikini 

KOON Apr 7 at 0629 Bikini 

UNION Apr 26 at 0605 Bikini 

YANKEE May 5 at 0610 Bikini 

NECTAR May 14 at 0620 Enewetak 

This case study applies to personnel in the 7126th Army Unit (AU) stationed at Enewetak Island 

during the period March 1 to May 31, 1954. The 7126th AU provided ground security, 

transportation and logistics support (Martin and Rowland, 1982). By the nature of their duties 

and residence, it is likely that most of the personnel remained on the island continuously, or 

nearly so, throughout the operation and therefore had continuous exposure to deposited fallout. 

Exposure Scenario 

Extensive radiation intensity readings obtained at Bikini Atoll following Shot BRAVO indicated 

decay rates that varied considerably from the standard t−1.2 rule, where t denotes time after 

239 
detonation. Average values for the decay exponent (λ) for various time intervals were derived 

from measurements made with several gamma ionization time-intensity meters on Bikini Atoll 

(Thomas et al., 1984). These time-dependent decay rates are used in reconstructing the radiation 

environments on the residence islands of Enewetak and Parry Islands. 

Of the six CASTLE shots, only Shots BRAVO, ROMEO, and NECTAR caused measurable 

fallout on the residence islands of Enewetak Atoll. Generally, such fallout was secondary (onset 

was well after the time of detonation) and relatively minor in nature. The time-intensity data for 

measurements collected during each fallout event are fitted by an interpolating function to 

produce the early-time intensity function denoted as Iearly(t) over the interval To ≤ t < Tend, where 

To and Tend are the beginning and end of fallout deposition for the specific shot. The type of 

interpolating function is selected to obtain the best fit of the data pairs. The equations describing 

the free-field gamma radiation intensity (I in R hr−1

) as functions of time t (in hours) on 

Enewetak Island are defined for several periods of time using either the specific decay constants 

derived from the measurements or the standard 1.2 decay constant, as appropriate. These 

equations were used to obtain the deterministic results reported below. 

Shot BRAVO 

The equations describing the free-field gamma radiation intensity of the fallout from Shot 

BRAVO descending on Enewetak Island are as follows: 

I(t) = 0 if t < 9.5

I(t) = Iearly(t) if 9.5 ≤ t < 16

I(t) = 0.010 (16/t) 0.82 if 16 ≤ t < 65.25

I(t) = 0.010 (16/65.25) 0.82 (65.25/t) 1.5 if 65.25 ≤ t < 473.25

I(t) = 0.010 (16/65.25)

 0.82 (65.25/473.25) 1.5 (473.25/t) 1.2 if 473.25 ≤ t < 4380

Shot ROMEO 

Fallout from Shot ROMEO occurred in two waves, referred to as ROMEO1 and ROMEO2. The 

equations describing the free-field gamma radiation intensity of the fallout from Shot ROMEO 

descending on Enewetak Island are as follows: 

For ROMEO1 fallout: 

I(t) = 0 if t < 10.5

I(t) = Iearly(t) if 10.5 ≤ t < 14.5

I(t) = 0.003 (14.5/t) 0.82 if 14.5 ≤ t < 39.5

240 
For ROMEO2 fallout: 

I(t) = 0 if t < 39.5

I(t) = Iearly(t) if 39.5 ≤ t < 77.5

I(t) = 0.009 (77.5/t) 1.5 if 77.5 ≤ t < 473.25

I(t) = 0.009 (77.5/473.25)

 1.5 (473.25/t) 1.2 if 473.25 ≤ t < 4380

Shot NECTAR 

The equations describing the free-field gamma radiation intensity of the fallout from Shot 

NECTAR descending on Enewetak Island are as follows: 

I(t) = 0 if t < 12

I(t) = Iearly(t) if 12 ≤ t < 14.7

I(t) = 0.002 (14.7/t) 0.82 if 14.7 ≤ t < 65.7

I(t) = 0.002 (14.7/65.7)

 0.82 (65.7/t) 1.5 if 65.7 ≤ t < 473.7

I(t) = 0.002 (14.7/65.7)

 0.82 (65.7/473.7) 1.5 (473.7/t) 1.2 if 473.7 ≤ t < 4380

External Dose: Approach 

Film Badge Data 

Film badge dosimetry during Operation CASTLE included two types (Servis, 1981). Mission 

badges were issued to individuals when it was anticipated that they had the potential to enter 

areas of radioactive contamination other than those encountered during routine activities. Cohort 

badges were issued to one individual in a group of individuals who collectively performed 

similar duties in similar locations. Even so, sufficient dosimetry data are not available for landbased personnel to allow meaningful comparisons between actual film badge data and 

reconstructed external gamma doses (Thomas et al., 1984). Therefore, reconstructed doses due 

to fallout exposure during Operation CASTLE cannot be compared to concurrent film badge 

data. 

Monte Carlo-Based Dose Reconstruction 

Probabilistic external gamma dose reconstruction for personnel the 7126th AU stationed on 

Enewetak Island during Operation CASTLE was accomplished by incorporating uncertainty 

distributions for various parameters into the model discussed in Section 3. The specific 

parameters used in both the deterministic and uncertainty analyses are shown in Table F-2. 

241 
Table F-2. Input Parameter Specification for External Gamma Dose Reconstruction, 

Case Study #6 

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 

min = 2/24 

peak = 8/24 

max = 16/24 

0.34 (or 8/24) 0.6 (or 14.4/24) 

Ft

Fraction of inside time spent 

in tent 

Triangular 

min = 0 

peak = 0.5 

max = 1 

0.5 0 

PFt Protection factor for tent 

Numerical model 

(see Section 4.2.2) 

μ = 1.4 

UB95 = 1.9 

1.4 

(median of 

distribution) 

1.5 

PFb Protection factor for building

Numerical model 

(see Section 4.2.2) 

μ = 2.1 

UB95 = 3.9 

2.0 

(median of 

distribution) 

2.0 

Ii

Intensity of fallout near 

outdoor location (i=1), tent 

location (i=2), and building 

location (i=3) frequented by 

veteran, normalized to the 

intensity averaged over entire 

island 

Lognormal 

GM = 1.0 

GSD = 1.5 

1.0 1.0 

INTENSITY MEASUREMENTS FOR LAND-BASED PERSONNEL 

Im Measured intensities 

Normal 

μ = Im, σ = 0.3·Im 

(to account for 

measurement error) 

1.0 1.0 

a

Exponent of multiplicative 

error factor (t/t0)

±a

 applied to 

FIIDOS-generated intensity 

functions 

Normal 

μ = 0 

σ = 0.15 

0 0 

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

deviation; UB95 = upper bound at the 95th percentile. 

(**) High-sided per guidance in NTPR Policy and Guidance Manual (DTRA, 2007).

External Dose Results 

The Monte Carlo dose distribution derived for a sample size of 10,000 is displayed in Figure F-1. 

The cumulative probability distribution is shown in Figure F-2. The statistics of this distribution 

are compared with those of a deterministic calculation in Table F-3. 

242 
0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.0 0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8

Whole Body Gamma Dose (rem)

Relative Frequency

Figure F-1. Distribution of Estimated External Gamma Dose from Uncertainty Analysis 

for Personnel Stationed at Enewetak Island during Operation CASTLE 

Cumulative Probability

Dose (rem)

0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

1x10-1

5x10-1

1x100

5x100

1x101

Dose

Fitted Curve

Figure F-2. Probability Plot of Estimated External Gamma Dose from Uncertainty 

Analysis for Personnel Stationed at Enewetak Island during Operation CASTLE 

243 
Table F-3. Summary of External Dose for Personnel Stationed at Enewetak Island during 

Operation CASTLE 

Mean Dose (rem) Upper Bound Dose (rem) 

Probabilistic(*) Deterministic 

(NTPR) 

Probabilistic 

(95th Percentile) 

Deterministic 

(NTPR) 

Ratio 

(Deterministic 

 Probabilistic) 

1.3 

(0.54) 1.2 2.3 3.5 1.5 

(*) The arithmetic mean and (standard deviation) are shown. The geometric mean external dose 

is 1.2 rem.

Internal Dose: Approach 

Internal dose reconstruction for personnel stationed on Enewetak Island during Operation 

CASTLE was accomplished by incorporating uncertainty distributions for various parameters 

into the models discussed in Section 3. These models incorporate the fallout-induced radiation 

environments discussed above, the fallout intensity decay model discussed in Section 3, and 

various other parameters discussed in Sections 3 and 4. The specific parameters used in both the 

deterministic and uncertainty analyses are shown in Table F-4. 

Table F-4. Input Parameter Specification for Internal Dose Reconstruction, 

Case Study #6 

Parameter Definition Distribution for 

Probabilistic Analysis

Nominal Value for 

Central Estimation Deterministic(*)

INTERNAL DOSE (GENERAL) 

DCFInhα

DCFIngα

Inhalation and ingestion 

dose conversion factors for 

fallout α emitters 

DCFs calculated with 

FIIDOS multiplied by 

Lognormal with 

GM=1.0, GSD=5.19 

DCFs calculated with 

FIIDOS 

(see Section 4.2.8) 

DCFs calculated 

with FIIDOS 

(see Section 

4.2.8) 

DCFInhβγ

DCFIngβγ

Inhalation and ingestion 

dose conversion factors for 

fallout β+γ radiation 

DCFs calculated with 

FIIDOS multiplied by 

Lognormal with 

GM=1.0, GSD=4.05 

DCFs calculated with 

FIIDOS 

(see Section 4.2.8) 

DCFs calculated 

with FIIDOS 

(see Section 

4.2.8) 

Biasα Assigned Constant 

α: 1.3 for each organ α: 1.3 for each organ 1.0 

Biasβγ

Bias factors to adjust highsided inhalation DCF values βγ: 1.2 for thyroid & 

LLI, 1.35 for lung 

βγ: 1.2 for thyroid & LLI, 

1.35 for lung 1.0 

BR Breathing rate 

Triangular distribution 

derived from USEPA 

(1997) data (see 

Section 4.2.7): 

min = 0.33 m3 hr−1

peak = 1.53 m3 hr−1

max = 2.79 m3 hr−1

Mean of Distribution 

~1.5 m3 hr−1

 1.2 m3 hr−1

244 
Parameter Definition Distribution for 

Probabilistic Analysis

Nominal Value for 

Central Estimation Deterministic(*)

DESCENDING INHALATION DOSE (†)

RNDRes1 1.0 (assumed constant) 1.0 (assumed constant) 

RNDRes2

Lognormal: GM, GSD 

0.0056, 1.744 

Geometric Mean 

0.0056 

RNDRes3

Deposition fractions for 

particle sizes deposited in 

Regions BB, bb and AI Lognormal: GM, GSD 

0.001, 1.65 0.001 

n/a 

RNDNonres1 0.0 (assumed constant) 0.0 (assumed constant) 

RNDNonres2 Lognormal: GM, GSD 

0.363, 1.106

Geometric Mean 

0.363 

RNDNonres3

Deposition fractions for 

particle sizes deposited in 

Region ET2 and cleared to 

digestive tract Lognormal: GM, GSD 

0.285, 1.185 0.285 

n/a 

V1

Logtriangular 

min, peak, max (cm 

s

−1

) 

0.22/2, 0.22, 27.8 

0.22 cm s−1

V2 0.83/2, 0.83, 27.8 0.83 cm s−1 

V3

Particle settling velocities 

13.0/2, 13.0, 27.8 13.0 cm s−1

106

(cm)/T(sec) 

Triangular 

(min,peak,max)

BRAVO 

(0.071, 0.391, 0.770) 

Peak of Distributions 

BRAVO 

0.391 

ROMEO1 

(0.132, 0.462, 0.812) 

ROMEO1 

0.462 

ROMEO2 

(1.000, 1.000, 1.000) 

ROMEO2 

1.000 

AF100 Surface activity fraction 

<100 μm particles 

NECTAR (0.543, 

0.781, 0.971) 

NECTAR 

0.781 

1.0 

frac1

Triangular 

Min, peak, max 

0, 0.00136, 0.01 

Peak of Distribution 

0.00136 

frac2

Surface fraction of Class 1–

2 from 1–100 μm particles 

0, 0.025, 0.1 0.025 

n/a 

RESUSPENDED INHALATION DOSE 

K(t) Time-dependent 

resuspension factor 

Lognormal multiplier 

of Anspaugh equation 

GM=1, GSD=4.05 

Anspaugh equation Till and Meyer, 

1983 

245 
Parameter Definition Distribution for 

Probabilistic Analysis

Nominal Value for 

Central Estimation Deterministic(*)

INCIDENTAL INGESTION DOSE 

qing Soil ingestion rate 

Triangular 

min, peak, max 

(mg d−1

) 

10, 100, 500 

Peak of Distribution 

100 mg day−1 500 mg day−1

ρsoil Soil bulk density 

Triangular 

g cm−3

Min, peak, max 

1.3, 1.45, 1.6 

Peak of Distribution 

1.45 g cm−3 1.3 g cm−3

(*) High-sided per guidance in NTPR Policy and Guidance Manual (DTRA, 2007). 

(†) AMAD particle size classes: 1 = 1–10 μm, 2 = 10–20 μm, 3 = 20–100 μm. 

Internal Dose Results 

Distributions of the fifty-year committed equivalent doses (CED) to three organs, thyroid, lung, 

and lower large intestine (LLI) wall, were derived using the refined uncertainty model for a 

sample size of 10,000. Examples of these results are shown in Figure F-3 through Figure F-6, 

where the relative frequency distributions and probability plots of CED to the LLI wall from 

alpha radiation and from beta plus gamma radiation, respectively, are plotted. The geometric 

mean and 95th percentile CEDs of the various distributions are given in Table F-5, along with 

analogous doses derived deterministically. The ratio of the deterministic upper bound CED to 

the probabilistic 95th percentile CED is provided in the rightmost column. 

0

0.025

0.05

0.075

0.1

2.9E-08 2.6E-07 2.3E-06 2.0E-05 1.8E-04 1.6E-03 1.4E-02 1.3E-01

Dose (rem, CED)

Relative Frequency of log 10(dose)

Figure F-3. Distribution of Estimated LLI Wall Doses from Alpha Radiation for 

Personnel Stationed at Enewetak Island during Operation CASTLE 

246 
Cumulative Probability

Dose (rem, CED)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

1x10-9

1x10-8

1x10-7

1x10-6

1x10-5

1x10-4

1x10-3

1x10-2

1x10-1

1x100

Dose

Fitted Curve

Figure F-4. Probability Plot of Estimated LLI Wall Doses from Alpha Radiation 

for Personnel Stationed at Enewetak Island during Operation CASTLE 

0

0.025

0.05

0.075

0.1

4.1E-04 2.5E-03 1.5E-02 9.2E-02 5.6E-01 3.4E+00 2.1E+01

Dose (rem, CED)

Relative Frequency of log 10(dose)

Figure F-5. Distribution of Estimated LLI Wall Doses from Beta plus Gamma Radiation 

for Personnel Stationed at Enewetak Island during Operation CASTLE 

247 
Cumulative Probability

Dose (rem, CED)

0.001% 0.1% 1% 10% 50% 90% 99% 99.9% 99.999%

1x10-4

1x10-3

1x10-2

1x10-1

1x100

1x101

1x102

1x103

Dose

Fitted Curve

Figure F-6. Probability Plot of LLI Wall Doses from Beta plus Gamma Radiation for 

Personnel Stationed at Enewetak Island during Operation CASTLE 

Table F-5. Internal Dose Summary for Personnel Stationed at Enewetak Island during 

Operation CASTLE 

Mean Dose (rem) Upper Bound Dose (rem) 

Organ Probabilistic Deterministic

(NTPR) 

Probabilistic 

(95th Percentile)

Deterministic 

(NTPR)

Ratio 

(Deterministic 

 Probabilistic) 

Alpha Dose 

Thyroid 0.000039 

(8.5) 0.00036 0.0014 0.0036 2.6 

Lung 0.00048 

(8.6) 0.0044 0.017 0.044 2.6 

LLI 0.000041 

(8.3) 0.00036 0.0014 0.0036 2.5 

Beta plus Gamma Dose 

Thyroid 0.20 

(4.7) 0.59 2.5 5.6 2.2 

Lung 0.066 

(6.2) 0.80 1.4 8.0 5.6 

LLI 0.18 

(4.6) 0.55 2.3 5.2 2.2 

* Geometric mean and (geometric standard deviation) are shown for the probabilistic analysis results. 

248 
References 

DNA (Defense Nuclear Agency), 1996. “For the Record—A History of the Nuclear Test 

Personnel Review Program, 1978-1993.” DNA 6041F (Defense Nuclear Agency, 

Washington, D.C.), March 1996. 

DTRA (Defense Threat Reduction Agency), 2007. Policy and Guidance Manual – Nuclear Test 

Personnel Review Program. Revision 7 (Defense Threat Reduction Agency, Fort Belvoir, 

VA), November 26, 2007. 

Martin, E. J. and Rowland, R. H., 1982. “CASTLE Series: 1954, United States Atmospheric 

Nuclear Weapons Tests, Nuclear Test Personnel Review,” DNA 6035F (Defense Nuclear 

Agency, Washington, D.C.), April 1, 1982. 

Servis, J. D., 1981. “Operation CASTLE Radiological Safety,” WT-942, Defense Nuclear 

Agency, Extracted Version, (Defense Nuclear Agency, Washington, D.C.), April 1, 1981. 

Thomas, C., Goetz, J., Klemm, J., and Weitz, R., 1984. “Analysis of Radiation Exposure for 

Naval Personnel at Operation CASTLE,” DNA-TR-84-6 (Defense Nuclear Agency, 

Washington, D.C.), February 28, 1984. 

Till, J.E. and Meyer, H.R. (eds), 1983. “Radiological Assessment – A Textbook on 

Environmental Dose Analysis,” NUREG/CR-3332 (United States Nuclear Regulatory 

Commission), September 1983. 

249 
APPENDIX G Model Variables Dependencies and Correlations 

Stephen D. Egbert, Ph.D. 

250 
251 

APPENDIX G Model Variables Dependencies and Correlations 

Table G-1 lists the input parameters which were used in the Monte Carlo modeling calculations 

for external and internal dose. As discussed in Section 4.3, 49 input parameters were allowed to 

vary within their assigned uncertainty distributions, and five parameters explicitly listed did not 

vary. The table describes each input parameter and explains why each would change or stay the 

same during a single history of the case study. Although all dose input parameters have a partial 

degree of correlation with themselves at other times, they were categorized into either 1) full 

correlation, or 2) no or weak correlation, which is mathematically treated as zero correlation. 
Table G-1. Case Study Model Variables – Dependencies and Correlations 

Parameter Definition Correlation* Basis DATES and TIMES Shot Dates Shot dates and times from appropriate references No distribution No correlation Shot dates and times are well documented. Any differences from these times are likely to have cau

shot-to-shot. 

Fallout Event Times 

Fallout event and intensity measurement times 

No distribution No correlation 

Intensity measurement dates and times are well documeAny differences from these times are likely to have caushot-to-shot or fallout event -to- fallout event. 

DateArrived (skew-tri+)

Start date for study group analysis 

Distribution for PLUMBBOBHOOD only No correlation 

Usually arrival dates and times are well documented. PLUMBBOB-HOOD study group was the only case whuncertainty extended over a significant period. This groother arrival events affecting dose. However, if other arrival events would have taken placethe nominal times are likely to have independent causes

DateDeparted (skew-tri+)

End date for study group analysis 

Distribution for PLUMBBOBHOOD only No correlation 

Usually departure dates and times are well documentedPLUMBBOB-HOOD study group was the only case whuncertainty extended over a significant period. This groother departure events affecting dose. However, if other departure events would have taken plfrom the nominal times are likely to have independent c

252 
Table G-1. Case Study Model Variables – Dependencies and Correlations 

Parameter Definition Correlation* Basis FILM BADGE DATADateFBstart Start date and time for film badge(s) No distribution No correlation 

Usually start date for a film badge is well documented. There was no study group where the start-date uncertainsignificant period. However, if other film badges with uncertain dates woudifferences in their start date have independent causes. 

DateFBend End date and time for film badge(s) 

Distribution for HARDTACK I BOXER only Multiple end dates for HARDTACK I Enewetak No correlation 

Usually end date for a film badge is well documented. HARDTACK I-BOXER study group was the only case uncertainty extended over a significant period. However, if other film badges with uncertain dates woudifferences in their end date have independent causes. 

SHOT MIXTURE FRACTIONComposite Shots (skew-tri+ ) 

Fallout proportion from combined debris clouds 

Distribution for HARDTACK I FIR/KOA Enewetak and BOXER only No correlation of mixture fraction for combined shots’ fallout to any other shots 

FIR and KOA fallout were the only debris clouds which fallout simultaneously. However, if other debris clouds had combined, the fract

253 
Table G-1. Case Study Model Variables – Dependencies and Correlations 

Parameter Definition Correlation* Basis EXTERNAL DOSE MULTIPLIER (EDM) FOR LAND-BASED PERSONNELFos (skew-tri+ ) Fraction of time spent outside Fully correlated with all shots Personnel participated in essentially the same activities 

from shot-to-shot. Therefore, the fraction of time spent location, Fracos, is likely the same for him throughout t

Ft (skew-tri+ )

Fraction of time spent in a tent while not outside 

Fully correlated with all shots 

Personnel participated in essentially the same activities from shot-to-shot. Therefore, the fraction of time spent outside, FIStent, is likely the same for him throughout th

PFt (numeric)

Protection factor for tent Fully correlated with all shots 

Personnel participated in essentially the same activities from shot-to-shot. Thus, location in the tent where he wthe same day-to-day and from shot-to-shot. Therefore, tthe tent, PFt, is likely the same for him throughout the o

PFb (numeric) Protection factor for building Fully correlated with all shots 

Personnel participated in essentially the same activities from shot-to-shot. Thus, location in the building where rested is the same day-to-day and from shot-to-shot. Thfactor for the building, PFb, is likely the same for him th

Ios × (lognormal) Also for OD calc

Intensity distribution of fallout near outside location normalized to the intensity averaged over the whole island 

Weak correlation between separate fallout depositions 

Fallout deposition from each debris cloud had a differenbecause of variations in wind direction, surface adhesioat the outside location is likely to have varied independisland for each deposition event. 

It × (lognormal)

Intensity distribution of fallout near tent location normalized to the intensity averaged over the whole island 

Weak correlation between separate fallout depositions 

Fallout deposition from each debris cloud had a differenbecause of variations in wind direction, surface adhesioat the tent location is likely to have varied independentlfor each deposition event. 

254 
Table G-1. Case Study Model Variables – Dependencies and Correlations 

Parameter Definition Correlation* Basis Ib × (lognormal)

Intensity distribution of fallout near building location normalized to the intensity averaged over the whole island 

Weak correlation between separate fallout depositions 

Fallout deposition from each debris cloud had a differenbecause of variations in wind direction, surface adhesioat the building location is likely to have varied independisland for each deposition event. 

EXTERNAL DOSE MULTIPLIER (EDM) FOR SHIP-BASED PERSONNELFts (skew-tri+ ) Fraction of time spent topside Fully correlated with all shots Personnel participated in essentially the same activities 

from shot-to-shot. Therefore, the fraction of time spent location, Fracts, is likely the same for him throughout th

SFw (numeric) Shielding factor at worksite Fully correlated with all shots 

Personnel participated in essentially the same activities from shot-to-shot. Thus, location in the ship where he wday-to-day and from shot-to-shot. Therefore, the shieldiworksite, SFw, is likely the same for him throughout the 

SFb (numeric)

Shielding factor at billet location 

Fully correlated with all shots 

Personnel participated in essentially the same activities from shot-to-shot. Thus, location in the ship where he bday-to-day and from shot-to-shot. Therefore, the shieldi

location, SFb, is likely the same for him throughout the 

Its (numeric) Also for TS

Intensity distribution of fallout topside, which affects topside activity area, normalized to the intensity averaged over the whole topside deck 

Weak correlation between separate fallout depositions 

Fallout deposition from each debris cloud had a differenbecause of variations in wind direction, surface adhesioat the topside location is likely to have varied independtopside intensity for each deposition event. 

Iw (numeric)

Intensity distribution of fallout topside, which affects workplace area, normalized to the intensity averaged over the whole topside deck 

Weak correlation between separate fallout depositions 

Fallout deposition from each debris cloud had a differenbecause of variations in wind direction, surface adhesioat the topside location above the worksite is likely to hafrom the expected topside intensity for each deposition 

255 
Table G-1. Case Study Model Variables – Dependencies and Correlations 

Parameter Definition Correlation* Basis Ib (numeric)

Intensity distribution of fallout topside, which affects billet area, normalized to the intensity averaged over the whole topside deck 

Weak correlation between separate fallout depositions 

Fallout deposition from each debris cloud had a differenbecause of variations in wind direction, surface adhesioat the topside location above the billet area is likely to hindependently from the expected topside intensity for e

INTENSITY MEASUREMENTS FOR LAND-BASED PERSONNELIm× (normal) Measurement error applied to initial and peak intensity data 

for each shot 

Fully correlated with all shots 

Intensity measurements were made by the same personnsimilar instruments for all shots. Therefore, measureme

from day-to-day and from shot-to-shot throughout the o

a × ((t/tm)normal) 

Decay-rate error applied to FIIDOS-generated decay model 

Weak correlation between shots 

The deviation from the FIIDOS-generated decay model independent according to the three examples shown in Sreasonable that because the sources for deviation (i.e. fretc) vary for each shot, that the decay model error factofor each shot. 

MANUEVERS (NTS ONLY)Contour Intensity × (lognormal) 

Error in intensity obtained from interpolation or extrapolation from isointensity contour maps 

Fully correlated with all shots and contours 

Intensity contours derived from intensity measurements personnel using the same methods for all shots and contcontour interpolation error is likely the same from day-tand from contour-to-contour throughout the operation. extrapolation error is both larger and fully correlated to 

ST × (normal) 

Start time of unit maneuver 

Distribution for PLUMBBOBHOOD Maneuver only No correlation between maneuvers 

The PLUMBBOB-HOOD maneuver was the only one wsignificantly depended on the start time of the maneuveIf other maneuvers had contributed to the total dose, the be uncorrelated to each other. This is because the error nearest 5 minutes. 

256 
Table G-1. Case Study Model Variables – Dependencies and Correlations 

Parameter Definition Correlation* Basis Rate (skew-tri+ ) 

Walk rate during unit maneuver 

Distribution for PLUMBBOBHOOD Maneuver only No correlation between maneuvers 

The PLUMBBOB-HOOD maneuver was the only one wsignificantly depended on the walk rate of the maneuveIf other maneuvers had contributed to the total dose, the be uncorrelated to each other. This is because the error conditions during the maneuver. 

LT (skew-tri+ ) 

Linger time at closest approach to the <5 R/hr location during unit maneuver 

Distribution for PLUMBBOBHOOD Maneuver only No correlation between maneuvers 

The PLUMBBOB-HOOD maneuver was the only one wsignificantly depended on the linger time of the maneuvIf other maneuvers had contributed to the total dose, the be uncorrelated to each other. This is because the error objectives of maneuvers. 

INTENSITY MEASUREMENTS FOR SHIP-BASED PERSONNELIm× (normal) Measurement error applied to initial and peak intensity data 

for each shot 

Weak correlation between shots 

Intensity measurements for ships were made by differendifferent instruments based on the islands or neighborineach shot’s deposition. Therefore, the ship measuremen

from shot-to-shot. 

a × ((t/tm)normal) 

Decay-rate error applied to FIIDOS-generated decay model 

Weak correlation between shots 

The deviation from the FIIDOS-generated decay model independent according to the three examples shown in Sreasonable that because the sources for deviation (i.e. fretc) vary for each shot, that the decay-constant error facfor each shot. 

257 
Table G-1. Case Study Model Variables – Dependencies and Correlations 

Parameter Definition Correlation* Basis Contamination Intensity Isc× (lognormal) 

Measurement error applied to ship contamination data 

Fully correlated with all shots 

The model for calculating ship contamination dose is baof experimental observations and from using a ship (or differs from the particular ship used for this study. Alsoin essentially the same activities on the ship from shot-tlikely to be biased in the same amount and direction whfor the particular ship. Therefore, the measurement errocontamination is likely the same for him throughout the 

Shine Intensity Iws

× (lognormal) Measurement error applied to shine intensity data Fully correlated with all shots 

The model for calculating ship shine dose is based on a experimental observations and from using a ship (or an differs from the particular ship used for this study. Alsoin essentially the same activities on the ship from shot-tlikely to be biased in the same amount and direction whfor the particular ship. Thus, for one ship, this error is th

Therefore, the measurement error applied to shine intenhim throughout the operation. 

INTERNAL DOSE (GENERAL)DCFinhαDCFingα×(lognormal)

Inhalation and ingestion dose conversion factors for α fallout radiation 

Fully correlated for inhalation and ingestion with all shots 

Deposition times are from several hours to several daysresuspension doses are accrued on the following days. Aisotopes are gone. Most of the internal dose comes primisotopes, thus there is likely to be significant correlationThe error is likely the same from day-to-day and shot-to

DCFinhβγDCFingβγ×(lognormal)

Inhalation and ingestion dose conversion factors for β+γfallout radiation 

Fully correlated for inhalation and ingestion with all shots 

Deposition times are from several hours to several daysresuspension doses are accrued on the following days. Tisotopes are gone. Most of the internal dose comes primβγ isotopes, thus there is likely to be some correlation. The error is likely the same from day-to-day and shot-to

BiasαBiasβγ

Bias factors to adjust highsided inhalation DCF values No distribution for each organ Different values for different organs and α, βγ DCFs – n

258 
Table G-1. Case Study Model Variables – Dependencies and Correlations 

Parameter Definition Correlation* Basis BRfrac 

Fraction of time at rest, or in light, moderate, or heavy activity 

No distribution Personnel participated in essentially the same activities 

shot. 

BRdist (skew-tri+ ) Breathing rate distribution 

Fully correlated with all shots and activities 

Health and metabolic rates remained the same for the voperation. Therefore, a veteran’s breathing rates are likedeviation from the average breathing rate for any activi

BR Breathing rate from combined BRfrac and BRdist See BRdist See BRdist DESCENDING INHALATION DOSERNDRes2× (lognormal)

Deposition fraction for 10–20 

μm particles (Class 2) in Regions BB, bb, and AI 

Fully correlated with all shots 

Error is due to ICRP lung model parameters and their inmanipulation – same resulting distribution used for all s

RNDRes3× (lognormal)

Deposition fraction for 20–100 

μm particles (Class 3) in Regions BB, bb, and AI 

Fully correlated with all shots 

Error is due to ICRP lung model parameters and their inmanipulation – same resulting distribution used for all s

RNDNonRes2× (lognormal)

Deposition fraction for 10–20 

μm particles (Class 2) in Region ET2

Fully correlated with all shots 

Error is due to ICRP lung model parameters and their inmanipulation – same resulting distribution used for all s

RNDNonRes3× (lognormal)

Deposition fraction for 20–100 

μm particles (Class 3) in Region ET2

Fully correlated with all shots 

Error is due to ICRP lung model parameters and their inmanipulation – same resulting distribution used for all s

259 
Table G-1. Case Study Model Variables – Dependencies and Correlations 

Parameter Definition Correlation* Basis AF100 × (triangle) 

Fraction of all activity carried to surface on particles with aerodynamic diameter <100 μm 

Weak correlation between shots 

Variation is from distribution obtained from three initiathree activity/size correlation models and two temporal Cloud height measurements were made by the same persimilar methods for all shots in operation – Also debris ought to be from one model for all shots suggesting corActivity/size typically applied at similar conditions, dowtime suggesting correlation possible Temporal models from very early fallout at one shot, Rapplied to all other shots suggesting correlation possiblIn spite of possible shot-to-shot correlations due to thesin weather make overall AF choice from models indepe

frac1× (triangle) 

Fraction of AF carried by Class 1 particles 

Weak correlation between shots Variations in weather cause deposition to be independen

frac2× (triangle) 

Fraction of AF carried by Class 2 particles 

Weak correlation between shots Variations in weather cause deposition to be independen

V1× (log-triangle) 

Particle settling velocities for 1–10 μm particles (Class 1) 

Weak correlation between shots 

Variations in weather cause settling velocity for Class 1 independent from shot-to-shot 

V2× (log-triangle) 

Particle settling velocities for 10–20 μm particles (Class 2) 

Weak correlation between shots 

Variations in weather cause settling velocity for Class 2 independent from shot-to-shot 

V3× (log-triangle) 

Particle settling velocities for 20–100 μm particles (Class 3) 

Weak correlation between shots 

Variations in weather cause settling velocity for Class 3 independent from shot-to-shot 

260 
Table G-1. Case Study Model Variables – Dependencies and Correlations 

Parameter Definition Correlation* Basis RESUSPENDED INHALATION DOSE (LAND-BASED PERSONNEL)K(t)× (lognormal) 

Time-dependent resuspension factor 

Fully correlated with all shots 

Mechanical disturbances, wind and weather conditions same from day-to-day and from shot-to-shot. Personnel essentially the same activities from shot-to-shot. Thereffactor, K, is likely the same for him throughout the oper

Kpc, Kbw × (lognormal)

Resuspension factors for highly-resuspended fallout at NTS (thermal pulse and blastwave regions) 

Fully correlated with all shots 

Mechanisms of resuspension and environment are essenshot-to-shot. Personnel participated in essentially the sato-shot. Therefore, the resuspension factors, Kpc and Kbw

him throughout the operation.

OD 

Intensity distribution of fallout near outside location normalized to the intensity averaged over the whole island 

Same as Ios above Because it is the same modification, it is fully correlated 

above. 

RESUSPENDED INHALATION DOSE (SHIP-BASED PERSONNEL)K × (lognormal) 

Resuspension factor (assumed constant with time) 

Fully correlated with all shots 

Mechanical disturbances, wind and weather conditions same from day-to-day and from shot-to-shot for 4 days participated in essentially the same activities topside froTherefore, the resuspension factor, K, is likely the same 

operation. 

TS 

Intensity distribution of fallout topside, which affects topside activity area, normalized to the intensity averaged over the whole topside deck 

Same as Its above Because it is the same modification, it is fully correlated 

above. 

261 
262 

Table G-1. Case Study Model Variables – Dependencies and Correlations 

Parameter Definition Correlation* Basis <GSMF> (numeric) 

Topside-averaged gamma source modification factor 

Fully correlated with all shots 

<GSMF> depends on uncertainties related to the dimen

topside obstructions (e.g., superstructure). Therefore, thsource modification factor, <GSMF>, is likely the sam

operation. 

INCIDENTAL INGESTION DOSE (LAND-BASED PERSONNEL ONLY)qing (skew-tri+ ) Soil ingestion rate Fully correlated with all shots Personnel activities remain essentially the same from da

to-shot. Therefore, the soil ingestion rate, q, is likely the 

throughout the operation. 

ρsoil (tri) Soil bulk density Fully correlated with all shots Personnel activities and soil density in those locations r

same from day-to-day and from shot-to-shot. Therefore

is likely the same for him throughout the operation. 

* For fallout dose calculations associated with different shots, this column indicates how the parameter uncertainty is corre

modeled exactly the same for each shot (Full), or modeled as independent for each shot (Weak or No Correlation). Except for two pairs (Ios and OD) and (Its and TS), all parameters that are on different rows are at most weakly correlated 

are considered independent and modeled without correlation. 

+ skew-tri means skewed triangular distribution.
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