State-of-the-Art Reactor 

Consequence Analyses 

Project 

Uncertainty Analysis of the 

Unmitigated Long-Term Station 

Blackout of the Peach Bottom 

Atomic Power Station

Office of Nuclear Regulatory Research

NUREG/CR-7155

SAND2012-10702P

State-of-the-Art Reactor 

Consequence Analyses 

Project 

Uncertainty Analysis of the 

Unmitigated Long-Term Station 

Blackout of the Peach Bottom 

Atomic Power Station

Manuscript Completed: September 2015

Date Published: May 2016

Prepared by: 

P. Mattie, R. Gauntt, K. Ross, N. Bixler, D. Osborn,

C. Sallaberry, and J. Jones

Sandia National Laboratories

Severe Accident Analysis Dept. 6232

Albuquerque, NM 87185-0748

T. Ghosh, NRC Technical Lead

NRC Job Code N6306

Office of Nuclear Regulatory Research

NUREG/CR-7155

SAND2012-10702P
Sandia National Laboratories is a multi-program laboratory managed and

operated by Sandia Corporation, a wholly owned subsidiary of Lockheed

Martin Corporation, for the U.S. Department of Energy’s National Nuclear

Security Administration under contact DE-AC04-94AL85000. 
iii

ABSTRACT

This document describes the U.S. Nuclear Regulatory Commission’s (NRC’s) uncertainty 

analysis of the accident progression, radiological releases, and offsite consequences for the 

State-of-the-Art Reactor Consequence Analyses (SOARCA) unmitigated long-term station 

blackout (LTSBO) severe accident scenario at the Peach Bottom Atomic Power Station. The 

objective of the SOARCA Uncertainty Analysis is to evaluate the robustness of the SOARCA 

deterministic results and conclusions documented in NUREG-1935, and to develop insight into 

the overall sensitivity of the SOARCA results to uncertainty in key modeling inputs. As this is a 

first-of-a-kind analysis in its integrated look at uncertainties in the MELCOR accident 

progression and the MELCOR Accident Consequence Code System, Version 2 (MACCS) offsite 

consequence analyses, an additional objective is to demonstrate uncertainty analysis 

methodology that could be used in future source term, consequence, and Level 3 probabilistic 

risk assessment studies. 

This work assessed key MELCOR and MACCS modeling uncertainties in an integrated fashion 

to quantify the relative importance of each uncertain input (included in the analysis) on potential 

accident consequences. A detailed uncertainty analysis was performed for a single-accident 

scenario at the Peach Bottom pilot plant. Not all possible uncertain input parameters were 

included in the analysis. Rather, a set of key parameters was carefully chosen to capture 

important influences on release and consequence results. 21 MELCOR parameters and 

350 MACCS parameters (representing 20 parameter groups) were included in the integrated 

analysis. The uncertainty in these parameters was propagated to consequence results in a 

two-step Monte Carlo simulation with a total of 865 realizations. This quantitative uncertainty 

analysis provides measures of the effects for each of the selected uncertain parameters both 

individually and through interaction with other parameters, through the use of four regression 

methods. Phenomenological insights are also qualitatively described and corroborated through 

the analysis of individual Monte Carlo realizations that show different accident progression, 

release, and consequence behavior.

Sampling the chosen input parameters in this uncertainty analysis revealed three groupings of 

similar accident progression sequences within the Peach Bottom unmitigated LTSBO scenario: 

(1) early stochastic failure of the cycling safety-relief valve (SRV), which was the SOARCA 

estimate scenario in NUREG-1935; (2) thermal failure of the SRV without main steam line 

(MSL) creep rupture; and (3) thermal failure of the SRV with MSL creep rupture. Even with the 

sequences that could lead to higher source terms, the results corroborated the SOARCA results 

and conclusions in NUREG-1935; the projected consequences are still much smaller than 

previous studies (the 1982 Siting Study in particular) calculated, and the projected early fatality 

risk is essentially zero.

For the release magnitude (source term) and timing, the regression methods rank the SRV 

stochastic failure probability, chemical forms of cesium and iodine, station battery duration, SRV 

open area fraction (after thermal failure), and drywell liner melt-through area as the most 

important parameters. For the conditional, mean (average over weather variability), individual 

latent cancer fatality risk, the regression methods rank the MACCS dry deposition velocity, the 

MELCOR SRV stochastic failure probability, and the MACCS residual cancer risk factor as the 

most important input parameters. 

v 

FOREWORD

The U.S. Nuclear Regulatory Commission (NRC) initiated the State-of-the-Art Reactor 

Consequence Analyses (SOARCA) project to develop current realistic evaluations of the offsite 

radiological health consequences for potential severe reactor accidents for two pilot plants—the 

Peach Bottom Atomic Power Station, a boiling-water reactor (BWR) in Pennsylvania, and the 

Surry Power Station, a pressurized-water reactor in Virginia. The SOARCA project evaluated 

plant improvements and changes not reflected in earlier NRC publications from 1975-1990.

This report describes the NRC’s first integrated uncertainty analysis (UA) for the SOARCA 

project that was directed by the NRC and conducted by Sandia National Laboratories. This UA 

evaluates the SOARCA unmitigated long-term station blackout (LTSBO) severe accident 

scenario for Peach Bottom. The analysis used the existing SOARCA models implemented in 

the MELCOR code for accident progression and release analysis, the MACCS code for offsite 

consequence analysis, and a representative set of important uncertain parameters. The UA 

used expert judgment supplemented with limited external peer review to select a set of 

parameters and to define distributions of values representing the state-of-knowledge for each 

parameter. The uncertainty in these parameters was then propagated to release and offsite 

radiological health consequence results (individual latent cancer fatality risk and individual early 

fatality risk) using a two-step Monte Carlo simulation process. The analysis used a variety of 

techniques to examine the results including regression analyses, study of select individual 

Monte Carlo samples, scatter plots, and supplemental separate sensitivity analyses. This UA 

corroborates the conclusions from the SOARCA study that (1) the public health consequences 

from severe nuclear accidents modeled are smaller than previously calculated; (2) delayed 

releases calculated provide more time for emergency response actions such as evacuation and, 

hence, the long-term dominates health effect risks; and (3) negligible early fatality risk is 

projected.

The results and insights from this UA are expected to be useful for ongoing and future work 

such as informing the technical bases for post-Fukushima regulatory activities and the NRC’s 

Site Level 3 Probabilistic Risk Assessment (PRA) project. This study adds to the body of 

knowledge created by earlier uncertainty analyses (such as those conducted in conjunction with 

NUREG-1150, “Severe Accident Risks: An Assessment for Five U.S. Nuclear Power Plants”) as 

well as the SOARCA project through the generation of over 800 variations of how an LTSBO 

scenario may evolve in a BWR such as Peach Bottom. This study has already informed some 

NRC activities such as the projected spread of consequence results in the UA supporting 

SECY-12-0157, “Consideration of Additional Requirements for Containment Venting Systems 

for Boiling Water Reactors with Mark I and Mark II Containments,” and SECY-15-0085, 

“Evaluations of the Containment Protection and Release Reduction for Mark I and Mark II 

Boiling Water Reactor Rulemaking Activities.” Other envisioned uses of this work are to help 

identify key sources of model uncertainty (per NUREG-1855, “Guidance of the Treatment of 

Uncertainties Associated with PRAs in Risk-Informed Decision Making,” guidance on treatment 

of uncertainty) for the Level 2 portion of PRA studies for BWR Mark I plants and the Level 3 

portion of PRA studies for light-water reactors. The results also identify areas where improving 

our state-of-knowledge or our state-of-modeling capabilities could significantly reduce 

uncertainties in the accident scenario studied. 

Examples of these results and insights are improving our knowledge of BWR safety-relief valve 

behavior under severe accident conditions and improving our knowledge and modeling of offsite 

radionuclide deposition velocities. This analysis also confirms the importance of using more 

advanced regression techniques, such as recursive partition analysis, for identifying important 

inputs (and their joint influences on outcomes) in complex uncertain systems.
vi 
vii

TABLE OF CONTENTS

Section Page

ABSTRACT ................................................................................................................... iii

FOREWORD.................................................................................................. v

TABLE OF CONTENTS ................................................................................................vii

LIST OF FIGURES.........................................................................................................xi

LIST OF TABLES ....................................................................................................... xxi

EXECUTIVE SUMMARY ......................................................................................... xxvii

ACKNOWLEDGMENTS ..........................................................................................xxxv

ACRONYMS ..........................................................................................................xxxvii

1. INTRODUCTION ............................................................................................ 1-1

1.1 Background of the SOARCA Project............................................................1-1

1.2 SOARCA Comparison and Contrast with Fukushima Accidents..................1-3

1.3 Objectives of the Uncertainty Analysis .........................................................1-7

1.4 Uncertainty Analysis Report Outline...........................................................1-10

2. UNCERTAINTY ANALYSIS APPROACH...................................................... 2-1

2.1 Accident Scenario Selection.........................................................................2-1

2.2 Selection of Uncertain Parameters...............................................................2-2

2.3 Treatment of Uncertainty..............................................................................2-4

3. DESCRIPTION OF ANALYSES..................................................................... 3-1

3.1 Software Used..............................................................................................3-1

3.1.1 MELCOR ........................................................................................... 3-1

3.1.2 MELMACCS ...................................................................................... 3-1

3.1.3 MACCS ............................................................................................. 3-1

3.2 Code Integration...........................................................................................3-2

3.3 Probabilistic Model Calculation for Uncertainty Analysis..............................3-3

3.3.1 Source Term Uncertainty Calculations .............................................. 3-3

3.3.2 Consequence Analysis Calculations.................................................. 3-4

3.4 Uncertainty and Sensitivity Analysis.............................................................3-4

3.4.1 Uncertainty Analysis: Purpose and Results Generated.................... 3-4

3.4.2 Sensitivity Analysis: Purpose and Results Generated...................... 3-6

4. UNCERTAIN INPUT PARAMETERS AND DISTRIBUTIONS ....................... 4-1

4.1 Source Term Model Uncertainty (MELCOR Inputs) .....................................4-1
viii

4.1.1 Sequence Issues............................................................................... 4-2

4.1.2 In-Vessel Accident Progression Issues ............................................. 4-6

4.1.3 Ex-Vessel Accident Progression Issues .......................................... 4-19

4.1.4 Containment Behavior Issues.......................................................... 4-24

4.1.5 Chemical Forms of Iodine and Cesium............................................ 4-35

4.1.6 Aerosol Deposition .......................................................................... 4-39

4.2 Consequence Model Uncertainty (MACCS Inputs) ....................................4-45

4.2.1 Wet Deposition Model (CWASH1)................................................... 4-46

4.2.2 Dry Deposition Velocities (VEDPOS) .............................................. 4-48

4.2.3 Shielding Factors (CSFACT, GSHFAC, PROTIN)........................... 4-51

4.2.4 Early Health Effects (EFFACA, EFFACB, EFFTHR) ....................... 4-54

4.2.5 Latent Health Effects (GSHFAC, DDREFA, Inhalation 

Dose Coefficients, CFRISK)............................................................ 4-57

4.2.6 Dispersion (CYSIGA, CZSIGA) ....................................................... 4-68

4.2.7 Hot Spot and Normal Relocation (DOSNRM, TIMNRM, 

DOSHOT, TIMHOT) ........................................................................ 4-71

4.2.8 Evacuation Delay (DLTEVA) ........................................................... 4-74

4.2.9 Evacuation Speed (ESPEED) ......................................................... 4-77

4.3 Other Phenomena Considered...................................................................4-79

4.3.1 Source Term Model......................................................................... 4-80

4.3.2 Consequence Model........................................................................ 4-83

5. STATISTICAL CONVERGENCE.................................................................... 5-1

5.1 Source Term Model (MELCOR)...................................................................5-1

5.1.1 Statistical Convergence Testing (Probabilistic Base Case)............... 5-1

5.2 Consequence Model ....................................................................................5-8

5.2.1 Statistical Convergence Testing - Probabilistic Base Case ............... 5-8

6. SOARCA MODEL PARAMETER UNCERTAINTY AND SENSITIVITY 

ANALYSES .................................................................................................... 6-1

6.1 Source Term Parameter Uncertainty Analysis .............................................6-1

6.1.1 Fraction of Iodine Released to the Environment................................ 6-2

6.1.2 Fraction of Cesium Released from the Core Inventory.................... 6-11

6.1.3 Hydrogen Production....................................................................... 6-19

6.1.4 Analysis of Important Phenomena and Single Realizations ............ 6-22

6.2 Offsite Consequence..................................................................................6-55

6.2.1 Latent Cancer Fatality Risk ............................................................. 6-56
ix

6.2.2 Early Fatality Risk............................................................................ 6-64

6.2.3 Regression Analysis........................................................................ 6-70

6.2.4 Analysis of Single Realizations........................................................ 6-86

6.3 Summary of Phenomena Important to Uncertainty in Analysis Results ...6-106

6.3.1 Source Term Analysis ................................................................... 6-106

6.3.2 Consequence Analysis.................................................................. 6-107

6.4 Separate Sensitivity Studies.....................................................................6-109

6.4.1 Manual Control of the Safety Relief Valve (Operator Actions)....... 6-109

6.4.2 Sensitivity of Fission Product Release to Reactor Lower 

Head Penetration Failures............................................................. 6-113

6.4.3 Dose Truncation Uncertainty Sensitivity Analyses......................... 6-116

6.4.4 Habitability Criterion ...................................................................... 6-139

6.4.5 Weather Sampling Effects............................................................. 6-154

7. SUMMARY OF RESULTS AND CONCLUSIONS.......................................... 7-1

7.1 Source Term Analyses.................................................................................7-1

7.2 Consequence Analyses................................................................................7-4

7.2.1 Regression Summary for LCF Risks ................................................. 7-6

7.2.2 Regression Summary for Early-Fatality Risk..................................... 7-7

7.2.3 Regression Summary of LCF Risk using Dose Truncation................ 7-8

7.2.4 Habitability Sensitivity Study Summary ........................................... 7-11

7.2.5 Weather Effects Summary............................................................... 7-11

7.2.6 Single Realization Summary ........................................................... 7-13

7.2.7 Importance Summary ...................................................................... 7-15

7.3 Use of Multiple Regression Techniques.....................................................7-16

7.4 Conclusions................................................................................................7-17

8. REFERENCES ............................................................................................... 8-1

APPENDIX A PROBABILISTIC ANALYSIS METHODOLOGY.............................. A-1

APPENDIX B SOFTWARE USED AND CODE INTEGRATION ............................. B-1

APPENDIX C MODEL VERIFICATION AND CONVERGENCE.............................. C-1

APPENDIX D PEER REVIEW/ACRS COMMENT RESOLUTION REPORT........... D-1

APPENDIX E ADDITIONAL INFORMATION AND ANALYSES IN RESPONSE 

TO ACRS QUESTIONS............................................... ........... E-1 

APPENIDX F GLOSSARY OF UNCERTAINTY ANALYSIS TERMS ...................F-1 
 x 
xi

LIST OF FIGURES 

Figure Page

Figure 1-1 Comparison of Peach Bottom Long Term Station Blackout RPV 

Pressure (left) and Fukushima Unit 3 accident (right, [3]) .................... 1-3

Figure 1-2 Comparison of Peach Bottom Long Term Station Blackout RPV 

Pressure (left) and Fukushima Unit 2 accident (right, [3]) .................... 1-4

Figure 1-3 Comparison of Peach Bottom STSBO Term Station Blackout 

hydrogen distribution (left) and MELCOR-predicted Fukushima 

Unit 1 hydrogen conditions (right, [3]) .................................................. 1-6

Figure 1-4 SOARCA Uncertainty Analysis Information Flow Diagram................... 1-9

Figure 2.3-1 Typical complementary cumulative distribution function (CCDF) of 

consequence........................................................................................ 2-6

Figure 3.2-1 Diagram of the information flow of the SOARCA Uncertainty 

Analysis................................................................................................ 3-3

Figure 3.4-1 Time-dependent results reflecting uncertainty due to lack of 

knowledge (epistemic) ......................................................................... 3-5

Figure 3.4-2 Distribution of results presented as a complementary cumulative 

distribution function for a selected time................................................ 3-6

Figure 4.1-1 Cumulative distribution function of safety relief valve failure to 

close valve cycle (λ = per demand failure probability 

(1/λ = number of SRV demands))......................................................... 4-4

Figure 4.1-2 Cumulative distribution function of duration of direct current power..... 4-5

Figure 4.1-3 Depiction of the fuel rod degradation ................................................... 4-7

Figure 4.1-4 Cumulative distribution function of zircaloy melt breakout 

temperature.......................................................................................... 4-8

Figure 4.1-5 Cumulative distribution function of molten clad drainage rate .............. 4-9

Figure 4.1-6 Cumulative distribution function of criteria for thermal seizure of 

safety relief valve due to heating after onset of core damage............ 4-11

Figure 4.1-7 Cumulative distribution function of safety relief valve open area 

fraction after thermal seizure.............................................................. 4-12

Figure 4.1-8 Cumulative distribution function of main steam line creep rupture 

area.................................................................................................... 4-13

Figure 4.1-9 Probability density function of fuel failure criterion alternatives 

(transformation of intact fuel to particulate debris) ............................. 4-15

Figure 4.1-10 Fuel failure criterion functions ............................................................ 4-15

Figure 4.1-11 Cumulative distribution of radial debris relocation time constants: 

(a) solid debris and (b) liquid debris ................................................... 4-17

Figure 4.1-12 Drywell floor regions........................................................................... 4-20

Figure 4.1-13 Cumulative distribution function debris overflow head as a 

function of debris at specified fixed temperatures: 

(a) T-solidus/no-flow head at 1420 K and (b) T-liquidus at 1670 K .... 4-23

Figure 4.1-14 Cumulative distribution function of flow area resulting from drywell 

liner failure ......................................................................................... 4-25

Figure 4.1-15 Cumulative distribution function of hydrogen ignition criteria 

(where flammable) ............................................................................. 4-26
xii

Figure 4.1-16 Cumulative distribution function of railroad door open fraction due 

to over-pressure failure in reactor building: (a) inner door and 

(b) outer door ..................................................................................... 4-28

Figure 4.1-17 Drywell head flange connection details.............................................. 4-30

Figure 4.1-18 Force balance on drywell head .......................................................... 4-31

Figure 4.1-19 Drywell head flange gap area versus pressure .................................. 4-34

Figure 4.1-20 Probability density function for five alternative combinations for 

MELCOR model radionuclide classes 2, 4, 16, and 17 (I2, CsI, 

CsOH, and Cs2MoO4) ........................................................................ 4-38

Figure 4.1-21 Cumulative distribution function of particle density............................. 4-44

Figure 4.2-1 Cumulative distribution function for the linear coefficient 

(CWASH1) in the MACCS wet deposition model ............................... 4-47

Figure 4.2-2 Cumulative distribution functions of dry deposition velocities for 

MACCS aerosol bins/aerosol mass median diameters ...................... 4-49

Figure 4.2-3 Cumulative distribution for shielding factors....................................... 4-52

Figure 4.2-4 Cumulative distribution functions of three early health effects: 

(a) hematopoietic system, (b) pulmonary system, and 

(c) gastrointestinal system ................................................................. 4-55

Figure 4.2-5 Cumulative distribution functions for the groundshine shielding 

factors, GSHFAC, for the three types of activity................................. 4-58

Figure 4.2-6 The probability density for DDREFA applied in the uncertainty 

analysis for breast and all other cancers [49, Figure 10].................... 4-59

Figure 4.2-7 The cumulative distribution for DDREFA applied in the uncertainty 

analysis for breast and other cancers ................................................ 4-61

Figure 4.2-8 Cumulative distribution functions for latent health effects: mortality 

risk coefficients (CFRISK) for each of the organs included in the 

SOARCA analysis.............................................................................. 4-67

Figure 4.2-9 Cumulative distribution functions of linear (a) crosswind 

dispersion coefficients, a(m) and (b) vertical dispersion 

coefficients, a(m)................................................................................ 4-70

Figure 4.2-10 Cumulative distribution functions of hotspot and normal 

(a) relocation doses and (b) relocation times ..................................... 4-73

Figure 4.2-11 Cumulative distribution functions of evacuation delay........................ 4-76

Figure 4.2-12 Cumulative distribution functions of evacuation speed....................... 4-78

Figure 4.3-1 Creep rupture parameter distribution ................................................. 4-81

Figure 5.1-1 Results of three replicates and q = 0.95 confidence interval (using 

bootstrap resampling) over selected statistics for released fraction 

of Cesium: (a) mean, (b) median, (c) quantile q = 0.05 and (d) 

quantile q = 0.95 .................................................................................. 5-4

Figure 5.1-2 Results of three replicates and q = 0.95 confidence interval (using 

bootstrap resampling) over selected statistics for released fraction 

of Iodine: (a) mean, (b) median, (c) quantile q = 0.05 and (d) 

quantile q = 0.95 .................................................................................. 5-6

Figure 5.2-1 Conditional, mean, individual LCF risk (per event) for all distances 

with the LNT dose model for emergency and long-term phases 

ranked from highest to lowest LCF risk result .................................... 5-10
xiii

Figure 5.2-2 Complementary cumulative distribution function for conditional, 

mean, individual LCF risk (per event) for the MACCS 

Convergence Analysis for specified circular areas............................. 5-11

Figure 5.2-3 Complementary cumulative distribution function for conditional, 

mean, individual early-fatality risk (per event) for the MACCS 

Convergence Analysis for specified circular areas............................. 5-13

Figure 5.2-4 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual LCF risk (per event) within 

a 10-mile radius for the MACCS Convergence Analysis.................... 5-17

Figure 5.2-5 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual LCF risk (per event) within 

a 20-mile radius for the MACCS Convergence Analysis.................... 5-18

Figure 5.2-6 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual LCF risk (per event) within 

a 30-mile radius for the MACCS Convergence Analysis.................... 5-19

Figure 5.2-7 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual LCF risk (per event) within 

a 40-mile radius for the MACCS Convergence Analysis.................... 5-20

Figure 5.2-8 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual LCF risk (per event) within 

a 50-mile radius for the MACCS Convergence Analysis.................... 5-21

Figure 5.2-9 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual early-fatality risk (per 

event) within a 1.3-mile radius for the MACCS Convergence 

Analysis.............................................................................................. 5-25

Figure 5.2-10 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual early-fatality risk (per 

event) within a 2-mile radius for the MACCS Convergence 

Analysis.............................................................................................. 5-26

Figure 5.2-11 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual early-fatality risk (per 

event) within a 2.5-mile radius for the MACCS Convergence 

Analysis.............................................................................................. 5-27

Figure 5.2-12 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual early-fatality risk (per 

event) within a 3-mile radius for the MACCS Convergence 

Analysis.............................................................................................. 5-28

Figure 5.2-13 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual early-fatality risk (per 

event) within a 3.5-mile radius for the MACCS Convergence 

Analysis.............................................................................................. 5-29

Figure 6.1-1 Time-dependent fraction of iodine core inventory released to the 

environment for the first 48 hours for combined (865) results for 

the Peach Bottom Unmitigated LTSBO................................................ 6-2
xiv

Figure 6.1-2 Cumulative distribution function of fraction of iodine core inventory 

released to the environment at 48 hours based on all combined 

(i.e., 865) results, with 95% confidence interval over mean, 

median and quantiles q = 0.05 and q = 0.95 for the Peach Bottom 

Unmitigated LTSBO ............................................................................. 6-3

Figure 6.1-3 Cumulative distribution function of SRVOAFRAC with samples 

where main steam line creep rupture occur indicated for Replicate 

1 for the Peach Bottom Unmitigated LTSBO........................................ 6-5

Figure 6.1-4 Time-dependent fraction of the cesium core inventory released to 

the environment over the first 48 hours for combined (865) results 

for the Peach Bottom Unmitigated LTSBO......................................... 6-12

Figure 6.1-5 Cumulative distribution function of fraction of cesium core 

inventory released to the environment after 48 hours based on all 

combined (i.e., 865) results, with 95% confidence interval over 

mean, median and quantiles q = 0.05 and q = 0.95 for the Peach 

Bottom Unmitigated LTSBO............................................................... 6-13

Figure 6.1-6 Time-dependent fraction (a) and cumulative distribution function 

(b) of in-vessel hydrogen production over 48 hours based on 

combined (i.e., 865) results, with 95% confidence interval over 

mean, median and quantiles q = 0.05 and q = 0.95 for the Peach 

Bottom Unmitigated LTSBO............................................................... 6-20

Figure 6.1-7 Distribution for the fraction of cesium core inventory released to 

the environment for Replicate 1 of the source term uncertainty 

analysis of the SOARCA Peach Bottom unmitigated LTSBO 

scenario ............................................................................................. 6-23

Figure 6.1-8 Single realizations selected for detailed analysis from Replicate 1 

of the Peach Bottom unmitigated LTSBO, fraction of cesium core 

inventory released to the environment for (a) SRV stochastic 

failures, (b) SRV thermal failures, and (c) MSL creep ruptures.......... 6-24

Figure 6.1-9 SRV open area fraction after thermal seizure Peach Bottom 

unmitigated LTSBO Replicate 1: (a) cumulative distribution 

function and (b) fraction of cesium core inventory released to the 

environment. Samples with MSL creep ruptures are identified ......... 6-31

Figure 6.1-10 Reactor and containment pressure and water level for Realization 

62 of the Peach Bottom unmitigated LTSBO Replicate 1, an MSL 

creep rupture...................................................................................... 6-32

Figure 6.1-11 Fraction of cesium core inventory released to the environment for 

Peach Bottom unmitigated LTSBO Replicate 1: (a) SRV 

stochastic failures, (b) SRV thermal failures, and (c) MSL creep 

ruptures. Realizations are identified that have cesium core 

inventory initialized as CsOH ............................................................. 6-33

Figure 6.1-12 Time dependent relocation of core material from the RPV to the 

reactor cavity for Realization 268 of the Peach Bottom 

unmitigated LTSBO Replicate 1, an SRV thermal seizure failure ...... 6-35

Figure 6.1-13 In-vessel hydrogen production for Realization 268 of the Peach 

Bottom unmitigated LTSBO Replicate 1, an SRV thermal seizure 

failure ................................................................................................. 6-36
xv

Figure 6.1-14 Cumulative distribution function for the flow area resulting from 

drywell liner failure for Peach Bottom unmitigated LTSBO 

Replicate 1 with samples identified that have a surge of water 

from the wetwell during depressurization of the drywell..................... 6-37

Figure 6.1-15 Water level in containment for Realization 170 of the Peach 

Bottom unmitigated LTSBO Replicate 1, an SRV Stochastic 

failure ................................................................................................. 6-38

Figure 6.1-16 Fraction of cesium core inventory released to the environment for 

Peach Bottom unmitigated LTSBO Replicate 1: (a) SRV 

stochastic failures, (b) SRV thermal failures, and (c) MSL creep 

ruptures. The realizations are identified that have closed railroad 

doors.................................................................................................. 6-39

Figure 6.1-17 Fraction of cesium core inventory released to the environment for 

the updated deterministic SOARCA Peach Bottom unmitigated 

LTSBO case documented in Section 5.1.1.1 for two scales on the 

ordinate: (a) 0 to 1.0 and (b) 0 to 0.20............................................... 6-41

Figure 6.1-18 Fraction of cesium core inventory released to the environment for 

Realization 18 of Replicate 1 for two scales on the ordinate: 

(a) 0 to 1.0 and (b) 0 to 0.20 .............................................................. 6-44

Figure 6.1-19 Fraction of cesium core inventory released to the environment for 

Realization 51 of Replicate 1 for two scales on the ordinate: 

(a) 0 to 1.0 and (b) 0 to 0.02 .............................................................. 6-45

Figure 6.1-20 Fraction of cesium core inventory released to the environment for 

Realization 52 of Replicate 1 for two scales on the ordinate: 

(a) 0 to 1.0 and (b) 0 to 0.2 ................................................................ 6-46

Figure 6.1-21 Fraction of cesium core inventory released to the environment for 

Realization 62 of Replicate 1 for two scales on the ordinate: 

(a) 0 to 1.0 and (b) 0 to 0.2 ................................................................ 6-47

Figure 6.1-22 Fraction of cesium core inventory released to the environment for 

Realization 63 of Replicate 1 for two scales on the ordinate: 

(a) 0 to 1.0 and (b) 0 to 0.2 ................................................................ 6-48

Figure 6.1-23 Fraction of cesium core inventory released to the environment for 

Realization 86 of Replicate 1 for two scales on the ordinate: 

(a) 0 to 1.0 and (b) 0 to 0.2 ................................................................ 6-49

Figure 6.1-24 Fraction of cesium core inventory released to the environment for 

Realization 90 of Replicate 1 for two scales on the ordinate: 

(a) 0 to 1.0 and (b) 0 to 0.2 ................................................................ 6-50

Figure 6.1-25 Fraction of cesium core inventory released to the environment for 

Realization 122 of Replicate 1 for two scales on the ordinate: 

(a) 0 to 1.0 and (b) 0 to 0.2 ................................................................ 6-51

Figure 6.1-26 Fraction of cesium core inventory released to the environment for 

Realization 134 of Replicate 1 for two scales on the ordinate: 

(a) 0 to 1.0 and (b) 0 to 0.2 ................................................................ 6-52

Figure 6.1-27 Fraction of cesium core inventory released to the environment for 

Realization 170 of Replicate 1 for two scales on the ordinate: 

(a) 0 to 1.0 and (b) 0 to 0.2 ................................................................ 6-53
xvi

Figure 6.1-28 Fraction of cesium core inventory released to the environment for 

Realization 268 of Replicate 1 for two scales on the ordinate: 

(a) 0 to 1.0 and (b) 0 to 0.2 ................................................................ 6-54

Figure 6.2-1 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual LCF risk (per event) within 

a 10-mile radius ................................................................................. 6-58

Figure 6.2-2 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual LCF risk (per event) within 

a 20-mile radius ................................................................................. 6-59

Figure 6.2-3 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual LCF risk (per event) within 

a 30-mile radius ................................................................................. 6-60

Figure 6.2-4 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual LCF risk (per event) within 

a 40-mile radius ................................................................................. 6-61

Figure 6.2-5 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual LCF risk (per event) within 

a 50-mile radius ................................................................................. 6-62

Figure 6.2-6 Complementary cumulative distribution function for conditional, 

mean, individual LCF risk (per event) within a 10-mile and 20-mile 

radius for ‘overall’ and ‘long-term phase’ LCF risk ............................. 6-63

Figure 6.2-7 Complementary cumulative distribution function for conditional, 

mean, individual LCF risk (per event) within a 10-mile and 20-mile 

radius for ‘overall’ and ‘emergency phase’ LCF risk........................... 6-63

Figure 6.2-8 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual early-fatality risk (per 

event) within a 1.3-mile radius ........................................................... 6-67

Figure 6.2-9 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual early-fatality risk (per 

event) within a 2-mile radius .............................................................. 6-68

Figure 6.2-10 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual early-fatality risk (per 

event) within a 2.5-mile radius ........................................................... 6-68

Figure 6.2-11 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual early-fatality risk (per 

event) within a 3-mile radius .............................................................. 6-69

Figure 6.2-12 Complementary cumulative distribution function and statistical 

values for conditional, mean, individual early-fatality risk (per 

event) within a 3.5-mile radius ........................................................... 6-69

Figure 6.2-13 Conditional, mean, individual LCF risk (per event) for MELCOR 

Replicate 1 single realizations for the 10-mile circular area ............... 6-89

Figure 6.2-14 Conditional, mean, individual LCF risk (per event) for MELCOR 

Replicate 1 single realizations for the 20-mile circular area ............... 6-90

Figure 6.2-15 Conditional, mean, individual LCF risk (per event) for MELCOR 

Replicate 1 single realizations for the 30-mile circular area ............... 6-91

Figure 6.2-16 Conditional, mean, individual LCF risk (per event) for MELCOR 

Replicate 1 single realizations for the 40-mile circular area ............... 6-91
xvii

Figure 6.2-17 Conditional, mean, individual LCF risk (per event) for MELCOR 

Replicate 1 single realizations for the 50-mile circular area ............... 6-92

Figure 6.2-18 MELCOR Replicate 2 Realization 291 reactor and containment 

pressure response ............................................................................. 6-96

Figure 6.2-19 MELCOR Replicate 3 Realization 046 reactor and containment 

pressure response ............................................................................. 6-96

Figure 6.2-20 MELCOR Replicate 3 Realization 267 reactor and containment 

pressure response ............................................................................. 6-97

Figure 6.2-21 Conditional, mean, individual LCF risk (per event) MACCS 

Uncertainty Analysis single realizations for the 10-mile circular 

area.................................................................................................... 6-99

Figure 6.2-22 Conditional, mean, individual LCF risk (per event) MACCS 

Uncertainty Analysis single realizations for the 20-mile circular 

area.................................................................................................. 6-100

Figure 6.2-23 Conditional, mean, individual LCF risk (per event) MACCS 

Uncertainty Analysis single realizations for the 30-mile circular 

area.................................................................................................. 6-101

Figure 6.2-24 Conditional, mean, individual LCF risk (per event) MACCS 

Uncertainty Analysis single realizations for the 40-mile circular 

area.................................................................................................. 6-101

Figure 6.2-25 Conditional, mean, individual LCF risk (per event) MACCS 

Uncertainty Analysis single realizations for the 50-mile circular 

area.................................................................................................. 6-102

Figure 6.2-26 Conditional, mean, individual early-fatality risk (per event) 

MACCS Uncertainty Analysis single realizations for specified 

circular areas ................................................................................... 6-103

Figure 6.4-1 Environmental iodine release fraction for UA SOARCA sensitivity 

cases for the manual control of the SRV.......................................... 6-112

Figure 6.4-2 Environmental cesium release fraction for UA SOARCA sensitivity 

cases for the manual control of the SRV.......................................... 6-113

Figure 6.4-3 Cesium distribution in a high-release case of the Lower Head 

Penetration Model Sensitivity Study................................................. 6-116

Figure 6.4-4 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for specified circular areas for the LNT doseresponse model ............................................................................... 6-142

Figure 6.4-5 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 10-mile circular area for the LNT 

dose-response model....................................................................... 6-143

Figure 6.4-6 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 20-mile circular area for the LNT 

dose-response model....................................................................... 6-144

Figure 6.4-7 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 30-mile circular area for the LNT 

dose-response model....................................................................... 6-144

Figure 6.4-8 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 40-mile circular area for the LNT 

dose-response model....................................................................... 6-145
xviii

Figure 6.4-9 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 50-mile circular area for the LNT 

dose-response model....................................................................... 6-145

Figure 6.4-10 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 10-mile circular area for the USBGR 

dose-response model....................................................................... 6-148

Figure 6.4-11 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 20-mile circular area for the USBGR 

dose-response model....................................................................... 6-148

Figure 6.4-12 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 30-mile circular area for the USBGR 

dose-response model....................................................................... 6-149

Figure 6.4-13 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 40-mile circular area for the USBGR 

dose-response model....................................................................... 6-149

Figure 6.4-14 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 50-mile circular area for the USBGR 

dose-response model....................................................................... 6-150

Figure 6.4-15 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 10-mile circular area for the HPS 

dose-response model....................................................................... 6-152

Figure 6.4-16 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 20-mile circular area for the HPS 

dose-response model....................................................................... 6-152

Figure 6.4-17 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 30-mile circular area for the HPS 

dose-response model....................................................................... 6-153

Figure 6.4-18 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 40-mile circular area for the HPS 

dose-response model....................................................................... 6-153

Figure 6.4-19 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for the 50-mile circular area for the HPS 

dose-response model....................................................................... 6-154

Figure 6.4-20 Example wind rose diagram............................................................. 6-156

Figure 6.4-21 Peach Bottom wind rose and atmospheric stability chart, year

2006................................................................................................. 6-158

Figure 6.4-22 Weather sampling comparison of the conditional, mean, individual 

LCF risk (per event) using the LNT dose-response model within 

specified circular areas .................................................................... 6-160

Figure 6.4-23 Weather sampling comparison of the conditional, mean, individual 

LCF risk (per event) using the USBGR dose-response model 

within specified circular areas .......................................................... 6-161

Figure 6.4-24 Weather sampling comparison of the conditional, mean, individual 

LCF risk (per event) using the HPS dose-response model within 

specified circular areas .................................................................... 6-162

Figure 6.4-25 CCDF of conditional, mean, individual LCF risk (per event) within 

the 10-mile circular area for aleatory weather uncertainty and the 

MACCS CAP17 analysis.................................................................. 6-165
xix

Figure 6.4-26 CCDF of conditional, mean, individual LCF risk (per event) within 

the 20-mile circular area for aleatory weather uncertainty and the 

MACCS CAP17 analysis.................................................................. 6-166

Figure 6.4-27 CCDF of conditional, mean, individual LCF risk (per event) within 

the 30-mile circular area for aleatory weather uncertainty and the 

MACCS CAP17 analysis.................................................................. 6-167

Figure 6.4-28 CCDF of conditional, mean, individual LCF risk (per event) within 

the 40-mile circular area for aleatory weather uncertainty and the 

MACCS CAP17 analysis.................................................................. 6-167

Figure 6.4-29 CCDF of conditional, mean, individual LCF risk (per event) within 

the 50-mile circular area for aleatory weather uncertainty and the 

MACCS CAP17 analysis.................................................................. 6-168

Figure 6.4-30 CCDF of conditional, mean, individual LCF risk (per event) within 

the 10-mile circular area for aleatory weather uncertainty for the 

LNT, USBGR, and HPS dose-response models using the 

SOARCA uncertainty analysis base case source term .................... 6-171

Figure 6.4-31 CCDF of conditional, mean, individual LCF risk (per event) within 

the 20-mile circular area for aleatory weather uncertainty for the 

LNT, USBGR, and HPS dose-response models using the 

SOARCA uncertainty analysis base case source term .................... 6-172

Figure 6.4-32 CCDF of conditional, mean, individual LCF risk (per event) within 

the 30-mile circular area for aleatory weather uncertainty for the 

LNT, USBGR, and HPS dose-response models using the 

SOARCA uncertainty analysis base case source term .................... 6-173

Figure 6.4-33 CCDF of conditional, mean, individual LCF risk (per event) within 

the 40-mile circular area for aleatory weather uncertainty for the 

LNT, USBGR, and HPS dose-response models using the 

SOARCA uncertainty analysis base case source term .................... 6-174

Figure 6.4-34 CCDF of conditional, mean, individual LCF risk (per event) within 

the 50-mile circular area for aleatory weather uncertainty for the 

LNT, USBGR, and HPS dose-response models using the 

SOARCA uncertainty analysis base case source term .................... 6-175

Figure 6.4-35 CCDF of conditional, mean, individual LCF risk (per event) within 

the 10-mile circular area for aleatory weather uncertainty using 

the USBGR dose-response model and the MACCS CAP15 

analysis............................................................................................ 6-176

Figure 6.4-36 CCDF of conditional, mean, individual LCF risk (per event) within 

the 20-mile circular area for aleatory weather uncertainty using 

the USBGR dose-response model and the MACCS CAP15 

analysis............................................................................................ 6-177

Figure 6.4-37 CCDF of conditional, mean, individual LCF risk (per event) within 

the 30-mile circular area for aleatory weather uncertainty using 

the USBGR dose-response model and the MACCS CAP15 

analysis............................................................................................ 6-178

Figure 6.4-38 CCDF of conditional, mean, individual LCF risk (per event) within 

the 40-mile circular area for aleatory weather uncertainty using 

the USBGR dose-response model and the MACCS CAP15 

analysis............................................................................................ 6-179
xx

Figure 6.4-39 CCDF of conditional, mean, individual LCF risk (per event) within 

the 50-mile circular area for aleatory weather uncertainty using 

the USBGR dose-response model and the MACCS CAP15 

analysis............................................................................................ 6-180

Figure 6.4-40 CCDF of conditional, mean, individual LCF risk (per event) within 

the 10-mile circular area for aleatory weather uncertainty using 

the HPS dose-response model and the MACCS CAP16 analysis ... 6-182

Figure 6.4-41 CCDF of conditional, mean, individual LCF risk (per event) within 

the 20-mile circular area for aleatory weather uncertainty using 

the HPS dose-response model and the MACCS CAP16 analysis. .. 6-183

Figure 6.4-42 CCDF of conditional, mean, individual LCF risk (per event) within 

the 30-mile circular area for aleatory weather uncertainty using 

the HPS dose-response model and the MACCS CAP16 analysis ... 6-184

Figure 6.4-43 CCDF of conditional, mean, individual LCF risk (per event) within 

the 40-mile circular area for aleatory weather uncertainty using 

the HPS dose-response model and the MACCS CAP16 analysis ... 6-185

Figure 6.4-44 CCDF of conditional, mean, individual LCF risk (per event) within 

the 50-mile circular area for aleatory weather uncertainty using 

the HPS dose-response model and the MACCS CAP16 analysis. .. 6-186
xxi

LIST OF TABLES

Table Page

Table 2.2-1 SOARCA uncertain parameter groups................................................. 2-4

Table 4.1-1 MELCOR uncertain parameters—sequences issues........................... 4-5

Table 4.1-2 Time versus temperature relationship for intact fuel rod collapse ........ 4-8

Table 4.1-3 MELCOR uncertain parameters—In-Vessel accident progression 

issues ................................................................................................. 4-18

Table 4.1-4 Concrete composition ........................................................................ 4-21

Table 4.1-5 MELCOR uncertain parameters—Ex-vessel accident progression 

issues ................................................................................................. 4-24

Table 4.1-6 MELCOR uncertain parameters—containment behavior issues ........ 4-35

Table 4.1-7 MELCOR uncertain parameters for chemical forms of iodine and 

cesium. ............................................................................................... 4-39

Table 4.1-8 Densities of several radionuclide compounds .................................... 4-41

Table 4.1-9 Released radionuclide masses and weighting factors from 

SOARCA Peach Bottom Unmitigated LTSBO Case .......................... 4-42

Table 4.1-10 Totals and density ranges .................................................................. 4-43

Table 4.1-11 MELCOR uncertain parameters—aerosol deposition ........................ 4-44

Table 4.2-1 MACCS uncertain parameters—wet deposition model ...................... 4-47

Table 4.2-2 MACCS uncertain parameters—dry deposition velocities.................. 4-50

Table 4.2-3a MACCS uncertain parameters—cloudshine shielding factors............ 4-52

Table 4.2-3b MACCS uncertain parameters—groundshine shielding factors ......... 4-53

Table 4.2-3c MACCS uncertain parameters—inhalation protection factors ............ 4-53

Table 4.2-4 MACCS uncertain parameters—early health effects.......................... 4-56

Table 4.2-5 MACCS uncertain parameters—multiplier for groundshine dose 

coefficients......................................................................................... 4-57

Table 4.2-6 Piecewise uniform distributions for the combined uncertainty in 

groundshine shielding factors (GSHFAC) including multiplier............ 4-58

Table 4.2-7 Piecewise uniform distributions for DDREFA..................................... 4-62

Table 4.2-8 MACCS uncertain parameters—geometric mean (i.e., median 

values, which were also used in the SOARCA analyses) for 

inhalation dose coefficients (Gy/Bq) [49]............................................ 4-63

Table 4.2-9 MACCS uncertain parameters—geometric standard deviations for 

inhalation dose coefficients (i.e., σ[49]).............................................. 4-65

Table 4.2-10 Crosswalk between reference type from Tables 4.2-8 and 4.2-9 

and WINMACCS organ doses ........................................................... 4-66

Table 4.2-11 Age-averaged cancer mortality risk estimates and uncertainties 

for low-dose, low-LET uniform irradiation of the body [49] ................. 4-68

Table 4.2-12 MACCS uncertain parameters—inputs for log-normal dispersion 

parameters distributions..................................................................... 4-69

Table 4.2-13 MACCS uncertain parameters—dispersion ....................................... 4-71

Table 4.2-14 MACCS uncertain parameters—relocation doses and times ............. 4-74

Table 4.2-15 MACCS uncertain parameters—evacuation delay............................. 4-76

Table 4.2-16 MACCS uncertain parameters—evacuation speed............................ 4-79

Table 4.3-1 A worst-case scenario of SRV-1 set point drift time estimates........... 4-83
xxii

Table 5.1-1 Success rates of MELCOR simulations for STP08, STP09, and 

STP10.................................................................................................. 5-1

Table 5.1-2 MELCOR error summary for STP08, STP09, STP10........................... 5-2

Table 5.2-1 Conditional, mean, individual LCF risk (per event) basic statistics 

for the LNT dose model at specified circular areas .............................. 5-8

Table 5.2-2 Conditional, mean, Individual LCF risk (per event) basic from the 

SOARCA UA base case for the LNT dose model at specified 

circular areas ....................................................................................... 5-9

Table 5.2-3 Conditional, mean, individual early-fatality risk (per event) for the 

Surry ISLOCA Scenario ..................................................................... 5-12

Table 5.2-4 Conditional, mean, individual early-fatality risk (per event) basic 

statistics ............................................................................................. 5-12

Table 5.2-5 Radionuclide specific contribution to overall ‘effective’ inhalation 

dose ................................................................................................... 5-14

Table 5.2-6 Combined conditional, mean, individual LCF risk (per event) 

average statistics for the MACCS statistical convergence test for 

specified circular areas ...................................................................... 5-15

Table 5.2-7 Combined conditional, mean, individual LCF risk (per event) 

standard error statistics for the MACCS statistical convergence 

test for specified circular areas .......................................................... 5-16

Table 5.2-8 Combined conditional, mean, individual LCF risk (per event) lower 

bounding case statistics for the MACCS statistical convergence 

test for specified circular areas .......................................................... 5-16

Table 5.2-9 Combined conditional, mean, individual LCF risk (per event) 

upper bounding cases statistics for the MACCS statistical 

convergence test for specified circular areas..................................... 5-16

Table 5.2-10 Correlation matrix for the MELCOR STP08 Uncertainty Model 

Source Term MACCS Analysis for the conditional, mean, 

individual LCF risk (per event) for specified circular areas................. 5-22

Table 5.2-11 Correlation matrix for the MELCOR STP09 Uncertainty Model 

Source Term MACCS Analysis for the conditional, mean, 

individual LCF risk (per event) for specified circular areas................. 5-22

Table 5.2-12 Correlation matrix for the MELCOR STP10 Uncertainty Model 

Source Term MACCS Analysis for the conditional, mean, 

individual LCF risk (per event) for specified circular areas................. 5-22

Table 5.2-13 Combined conditional, mean, individual early-fatality risk (per 

event) average statistics for the MACCS statistical convergence 

test for specified circular areas .......................................................... 5-23

Table 5.2-14 Combined conditional, mean, individual early-fatality risk (per 

event) standard error statistics for the MACCS statistical 

convergence test for specified circular areas..................................... 5-24

Table 5.2-15 Combined conditional, mean, individual early-fatality risk (per 

event) lower bounding case statistics for the MACCS statistical 

convergence test for specified circular areas..................................... 5-24

Table 5.2-16 Combined conditional, mean, individual early-fatality risk (per 

event) upper bounding cases statistics for the MACCS statistical 

convergence test for specified circular areas..................................... 5-24
xxiii

Table 5.2-17 Correlation matrix for the MELCOR STP08 Uncertainty Model 

Source Term MACCS Analysis for the conditional, mean, 

individual early-fatality risk (per event) for specified circular areas .... 5-30

Table 5.2-18 Correlation matrix for the MELCOR STP09 Uncertainty Model 

Source Term MACCS Analysis for the conditional, mean, 

individual early-fatality risk (per event) for specified circular areas .... 5-30

Table 5.2-19 Correlation matrix for the MELCOR STP10 Uncertainty Model 

Source Term MACCS Analysis for the conditional, mean, 

individual early-fatality risk (per event) for specified circular areas .... 5-30

Table 6.1-1 Regression analysis of fraction of iodine released after 48 Hours........ 6-6

Table 6.1-2 Regression analyses of fraction of iodine released after 48 hours 

for realizations leading to SRV stochastic failures................................ 6-7

Table 6.1-3 Regression analyses of fraction of iodine released after 48 hours 

for realizations leading to SRV thermal failures without MSL creep 

rupture.................................................................................................. 6-8

Table 6.1-4 Regression analyses of fraction of iodine released after 48 hours 

for realization leading to SRV thermal failure and MSL creep 

rupture.................................................................................................. 6-9

Table 6.1-5 Regression analyses over time when the fraction reaches 0.001 of 

the iodine inventory released over the first 48 Hours ......................... 6-11

Table 6.1-6 Regression analyses of fraction of cesium released over 48 hours ... 6-15

Table 6.1-7 Regression analyses of fraction of cesium released over 48 hours 

for realizations leading to SRV stochastic failure ............................... 6-16

Table 6.1-8 Regression analyses of fraction of cesium released over 48 hours 

for realizations leading to SRV thermal failure without MSL creep 

rupture................................................................................................ 6-18

Table 6.1-9 Regression analyses of fraction of cesium released over 48 hours 

for realizations leading to SRV thermal failure and MSL creep 

rupture................................................................................................ 6-19

Table 6.1-10 Regression analysis of hydrogen production. .................................... 6-22

Table 6.1-11 Sampled parameter values for Replicate 1 (STP08) for selected 

individual realizations......................................................................... 6-25

Table 6.1-12 Timing of events, key occurrences/attributes, and environmental 

releases for selected individual realizations of the Peach Bottom 

unmitigated LTSBO Replicate 1 (STP08)........................................... 6-27

Table 6.2-1 MACCS probabilistic analyses ........................................................... 6-56

Table 6.2-2 Conditional, mean, individual LCF risk (per event) average 

statistics for the MACCS Uncertainty Analysis for five circular 

areas (using all three source term replicates) .................................... 6-56

Table 6.2-3 Correlation matrix of the conditional, mean, individual LCF risk 

(per event) for the MACCS Uncertainty Analysis for specified 

circular areas (using all three source term replicates)........................ 6-64

Table 6.2-4 Conditional, mean, individual early-fatality risk (per event) for the 

Surry ISLOCA Scenario ..................................................................... 6-65

Table 6.2-5 Conditional, mean, individual early-fatality risk (per event) 

average statistics for the composite MACCS Uncertainty Analysis 

for specified circular areas (using all three source term replicates) ... 6-66
xxiv

Table 6.2-6 Correlation matrix for the MACCS Uncertainty Analysis for the 

conditional, mean, individual early-fatality risk (per event) for 

specified circular areas (using all three source term replicates)......... 6-70

Table 6.2-7 Conditional, mean, individual LCF risk (per event) regression of 

the MACCS Uncertainty Analysis for the 10-mile circular area .......... 6-72

Table 6.2-8 Conditional, mean, individual LCF risk (per event) regression of 

the MACCS Uncertainty Analysis for the 20-mile circular area .......... 6-73

Table 6.2-9 Conditional, mean, individual LCF risk (per event) regression of 

the MACCS Uncertainty Analysis for the 30-mile circular area .......... 6-74

Table 6.2-10 Conditional, mean, individual LCF risk (per event) regression of 

the MACCS Uncertainty Analysis for the 40-mile circular area .......... 6-75

Table 6.2-11 Conditional, mean, individual LCF risk (per event) regression of 

the MACCS Uncertainty Analysis for the 50-mile circular area .......... 6-76

Table 6.2-12 Conditional, mean, individual early-fatality risk (per event) 

regression of the MACCS Uncertainty Analysis for the 1.3-mile 

circular area ....................................................................................... 6-80

Table 6.2-13 Conditional, mean, individual early-fatality risk (per event) 

regression of the MACCS Uncertainty Analysis for the 2-mile 

circular area ....................................................................................... 6-81

Table 6.2-14 Conditional, mean, individual early-fatality risk (per event) 

regression of the MACCS Uncertainty Analysis for the 2.5-mile 

circular area ....................................................................................... 6-83

Table 6.2-15 Conditional, mean, individual early-fatality risk (per event) 

regression of the MACCS Uncertainty Analysis for the 3-mile 

circular area ....................................................................................... 6-84

Table 6.2-16 Conditional, mean, individual early-fatality risk (per event) 

regression of the MACCS Uncertainty Analysis for the 3.5-mile 

circular area ....................................................................................... 6-85

Table 6.2-17 Brief source term description for the single realizations selected 

from Replicate 1 (STP08) MELCOR Analyses................................... 6-87

Table 6.2-18 Conditional, mean, individual early-fatality risk (per event) for the 

MELCOR Replicate 1 single realization nonzero realizations for 

specified circular areas ...................................................................... 6-93

Table 6.2-19 Timing of key events for MELCOR source terms selected from the 

three replicates for the MACCS single realization analysis................ 6-95

Table 6.2-20 Brief source term description for the MELCOR source terms 

selected from the three replicates for the CAP17 MACCS 

Uncertainty Analysis of single realizations ......................................... 6-97

Table 6.2-21 Conditional, mean, individual LCF risk (per event) for the MACCS 

Uncertainty Analysis single realizations for specified circular 

areas for MELCOR source terms selected from the three 

replicates............................................................................................ 6-98

Table 6.2-22 Conditional, mean, individual early-fatality risk (per event) for the 

MACCS single realizations for specified circular areas.................... 6-102

Table 6.2-23 Conditional, mean, individual early-fatality risk (per event) for the 

MACCS single realizations for specified circular areas beyond 

10 miles............................................................................................ 6-104
xxv

Table 6.4-1 Timing of key events for Peach Bottom Unmitigated LTSBO, 

manual SRV operation action at 0.5 hr, 1.0 hr, 2.0 hr and 3.0 hr..... 6-110

Table 6.4-2 Conditional, mean, individual LCF risk (per event) average 

statistics for the Dose Truncation Sensitivity Analysis at specified 

Radial Distances ............................................................................ 6-117 

Table 6.4-3 Conditional, mean, individual LCF risk (per event) regression of 

MACCS sensitivity LNT model at the 10-mile circular area.............. 6-119

Table 6.4-4 Conditional, mean, individual LCF risk (per event) regression of 

MACCS sensitivity LNT model at the 20-mile circular area.............. 6-120

Table 6.4-5 Conditional, mean, individual LCF risk (per event) regression of 

MACCS sensitivity LNT model at the 30-mile circular area.............. 6-121

Table 6.4-6 Conditional, mean, individual LCF risk (per event) regression of 

MACCS sensitivity LNT model at the 40-mile circular area.............. 6-122

Table 6.4-7 Conditional, mean, individual LCF Risk (per event) regression of 

MACCS sensitivity LNT model at the 50-mile circular area.............. 6-123

Table 6.4-8 Conditional, mean, individual LCF Risk (per event) regression of 

MACCS sensitivity USBGR model at the 10-mile circular area........ 6-126

Table 6.4-9 Conditional, mean, individual LCF risk (per event) regression of 

MACCS sensitivity USBGR model at the 20-mile circular area........ 6-127

Table 6.4-10 Conditional, mean, individual LCF risk (per event) regression of 

MACCS sensitivity USBGR model at the 30-mile circular area........ 6-128

Table 6.4-11 Conditional, mean, individual LCF risk (per event) regression of 

MACCS sensitivity USBGR model at the 40-mile circular area........ 6-129

Table 6.4-12 Conditional, mean, individual LCF risk (per event) regression of 

MACCS sensitivity USBGR model at the 50-mile circular area........ 6-130

Table 6.4-13 Conditional, mean, individual LCF risk (per event) regression of 

MACCS sensitivity HPS model at the 10-mile circular area ............. 6-134

Table 6.4-14 Conditional, mean, individual LCF risk (per event) regression of 

MACCS sensitivity HPS model at the 20-mile circular area ............. 6-135

Table 6.4-15 Conditional, mean, individual LCF risk (per event) regression of 

MACCS sensitivity HPS model at the 30-mile circular area ............. 6-136

Table 6.4-16 Conditional, mean, individual LCF risk (per event) regression of 

MACCS sensitivity HPS model at the 40-mile circular area ............. 6-137

Table 6.4-17 Conditional, mean, individual LCF risk (per event) regression of 

MACCS sensitivity HPS model at the 50-mile circular area ............. 6-138

Table 6.4-18 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for LNT dose-response model ......................... 6-142

Table 6.4-19 Percentage change in conditional, mean, individual LCF risk (per 

event) for the LNT dose-response model from variations in 

habitability criterion (reduction/increase (-/+)).................................. 6-143

Table 6.4-20 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for USBGR dose-response model ................... 6-147

Table 6.4-21 Percentage change in conditional, mean, individual LCF risk (per 

event) for the USBGR dose-response model from variations in 

habitability criterion (reduction/increase (-/+)).................................. 6-147

Table 6.4-22 Habitability criterion comparison of conditional, mean, individual 

LCF risk (per event) for HPS dose-response model......................... 6-151
xxvi

Table 6.4-23 Percentage change in conditional, mean, individual LCF risk (per 

event) for the HPS dose-response model from variations in 

habitability criterion (reduction/increase (-/+)).................................. 6-151

Table 6.4-24 Weather sampling inputs for Peach Bottom..................................... 6-157

Table 6.4-25 Statistical summary of raw meteorological data ............................... 6-158

Table 6.4-26 Weather sampling comparison of the conditional, mean, individual 

LCF risk (per event) using the LNT dose-response mode................ 6-159

Table 6.4-27 Weather sampling comparison of the conditional, mean, individual 

LCF risk (per event) using the USBGR dose-response model......... 6-160

Table 6.4-28 Weather sampling comparison of the conditional, mean, individual 

LCF risk (per event) using the HPS dose-response model .............. 6-161

Table 6.4-29 Brief source term description for the single realizations selected 

from Replicate 1 (STP08) MELCOR Analyses for the aleatory

weather uncertainty analyses........................................................... 6-163

Table 6.4-30 MACCS aleatory uncertainty analyses conditional mean, 

individual LCF risk (per event) comparison of source terms to the 

conditional, mean, individual LCF risk (per event) CCDF of the 

MACCS CAP17 analysis for specified circular areas ....................... 6-164

Table 6.4-31 The MACCS CAP17 analysis conditional, mean, individual LCF 

risk (per event) of the source terms for specified circular areas....... 6-164

Table 6.4-32 Conditional, mean, individual LCF risk (per event) ratio for the 

MACCS aleatory uncertainty analyses and the MACCS CAP17 

analysis for specified circular areas ................................................. 6-168

Table 6.4-33 MACCS aleatory uncertainty analyses median LCF risk per event 

comparison of source terms to the CCDF of the MACCS CAP14 

analysis (LNT) for specified circular areas ....................................... 6-169

Table 6.4-34 MACCS aleatory uncertainty analyses median LCF risk per event 

comparison of source terms to the CCDF of the MACCS CAP15 

analysis (USBGR) for specified circular areas ................................. 6-170

Table 6.4-35 MACCS aleatory uncertainty analyses median LCF risk per event 

comparison of source terms to the CCDF of the MACCS CAP16 

analysis (HPS) for specified circular areas....................................... 6-170

Table 6.4-36 MACCS aleatory uncertainty analyses percent contribution of the 

emergency phase for the conditional, mean, individual LCF risk 

(per event) using the LNT dose-response model for specified 

circular areas ................................................................................... 6-170

Table 6.4-37 Conditional, mean, individual LCF risk (per event) ratio for the 

MACCS aleatory uncertainty analyses using the USBGR doseresponse model and the MACCS CAP15 analysis for specified 

circular areas ................................................................................... 6-181

Table 6.4-38 Conditional, mean, Individual LCF risk (per event) ratio for the 

MACCS aleatory uncertainty analyses using the HPS doseresponse model and the MACCS CAP16 analysis for specified 

circular areas ................................................................................... 6-187
xxvii

EXECUTIVE SUMMARY

The U.S. Nuclear Regulatory Commission (NRC), the nuclear power industry, and the

international nuclear energy research community have devoted considerable research over the 

last several decades to examining severe reactor accident phenomena and offsite 

consequences. The NRC initiated the State-of-the-Art Reactor Consequence Analyses 

(SOARCA) project to leverage this research and develop current estimates of the offsite 

radiological health consequences for potential severe reactor accidents for two pilot plants: the 

Peach Bottom Atomic Power Station, a boiling-water reactor (BWR) in Pennsylvania and the 

Surry Power Station, a pressurized-water reactor in Virginia. By applying modern analysis tools 

and techniques, the SOARCA project developed a body of knowledge regarding the realistic 

outcomes of select severe nuclear reactor accidents. To accomplish this objective, the 

SOARCA project’s integrated modeling of accident progression and offsite consequences used 

both state-of-the-art computational analysis tools (the MELCOR code and the MELCOR 

Accident Consequence Code System [MACCS]) and best modeling practices drawn from the 

collective wisdom of the severe accident analysis community. The SOARCA project is 

documented in NUREG-1935, “State-of-the-Art Reactor Consequence Analyses (SOARCA) 

Report” (2012), NUREG/CR-7110, “State-of-the-Art Reactor Consequence Analyses (SOARCA) 

Project Volume 1: Peach Bottom Integrated Analysis” and “State-of-the-Art Reactor 

Consequence Analyses (SOARCA) Project Volume 2: Surry Integrated Analysis” (2013).

This document describes the NRC’s uncertainty analysis of the SOARCA unmitigated long-term 

station blackout (LTSBO) severe accident scenario for the Peach Bottom Atomic Power Station. 

The objective of this uncertainty analysis is to evaluate the robustness of the SOARCA project’s 

deterministic results and conclusions, and to develop insight into the overall sensitivity of the 

SOARCA results to uncertainty in key modeling input parameters. As this is a first-of-a-kind 

analysis in its integrated look at uncertainties in MELCOR severe accident progression and 

MACCS offsite consequence analyses, an additional objective is to demonstrate an uncertainty 

analysis methodology that could be used in future combined Level 1/2/3 consequence and 

probabilistic risk assessment (PRA) studies.

Approach

The SOARCA offsite consequence results presented in NUREG-1935 incorporated only the

aleatory uncertainty associated with weather conditions at the time of the accident. The 

reported offsite consequence values represent the average (mean) value obtained from a large 

number of random (aleatory) weather trials. The weather uncertainty is handled the same way 

in this uncertainty analysis. In addition, the impact of state-of-knowledge (epistemic) uncertainty 

in the input parameters is explored in detail by randomly sampling distributions for model 

parameters that are considered to be potentially important. Assessing key MELCOR and 

MACCS parameter uncertainties in an integrated fashion helps form an understanding of the 

relative importance of each uncertain input on the potential consequences. 

This analysis uses the existing SOARCA models and software. In other words, the uncertainty 

stemming from the choice of conceptual models and model implementation is not explicitly 

explored, nor is completeness uncertainty. In addition, not all possible uncertain input 

parameters were included in the analysis. Rather, a set of key parameters was carefully chosen 

by NRC staff and severe accident experts at Sandia National Laboratories to capture important 

influences on the potential release of radioactive material to the environment and on offsite 

health consequences. 
xxviii

A detailed uncertainty analysis was performed for a single accident scenario rather than for all 

seven of the SOARCA scenarios documented in NUREG-1935. The SOARCA Peach Bottom 

BWR unmitigated LTSBO scenario was analyzed. While a single scenario cannot provide a 

complete exploration for all possible effects of uncertainties in analyses for the two SOARCA 

pilot plants, it can be used to provide initial insights into the overall sensitivity of SOARCA 

results and conclusions to input uncertainty. In addition, since station blackouts are an 

important class of events for BWRs in general, the phenomenological insights gained on severe 

accident progression and radionuclide releases may prove useful for BWRs in general.

Through expert judgment and iteration after interim reviews by the independent SOARCA peer 

review panel1 and the NRC’s Advisory Committee on Reactor Safeguards, 21 key MELCOR 

parameters and 20 key MACCS parameter groups were identified for inclusion in the uncertainty 

analysis, and distributions were defined for each parameter. The 20 MACCS parameter groups 

were comprised of 350 individual parameters, many of which were fully correlated to form a 

parameter group. For example, there were many individual organ-specific and radionuclidespecific dose conversion factors, which were considered one group of parameters.

The MELCOR uncertain parameters were selected to capture:

• accident sequence issues,

• accident progression issues within the reactor vessel,

• accident progression issues outside the reactor vessel,

• containment behavior issues, and

• fission product release, transport, and deposition upon plant structures.

These broad areas span the severe accident progression over time, ranging from minor 

sequence variations as affected by safety relief valve (SRV) behavior and battery duration, to 

uncertainties in the core damage and melt progressions. Other parameters more specific to 

fission product transport include deposition and settling processes, and chemical speciation of 

cesium and iodine which affects both release and transport within plant structures. 

The parameters selected from the MACCS consequence model were those that affect individual 

latent cancer fatality (LCF) risk and individual early fatality risk, due to:

• cloudshine during radiological plume passage,

• groundshine from deposited radionuclides, and

• inhalation during plume passage and following plume passage from resuspension of 

deposited radionuclides. 

Parameters related to emergency response were also varied. Although there is high confidence 

in emergency response actions, an emergency is a dynamic event with uncertainties in 

elements of the response. The following three emergency planning parameter sets were 

selected:

• hotspot and normal relocation criteria,

• evacuation delay, and 

 

1 The peer review panel did not review the final distributions.
xxix

• evacuation speed.

Several of the distributions for non-site-specific MACCS parameters selected for this analysis 

were based on past expert elicitation data. The United States and the Commission of European 

Communities conducted a series of expert elicitations in the 1990’s to obtain distributions for 

uncertain variables used in health consequence analyses related to accidental releases of 

nuclear material. The distributions reflect degrees of belief for non-site specific parameters that 

are uncertain and are likely to have a significant or moderate influence on the results.

This uncertainty analysis uses a two-step Monte Carlo simulation. Simple random sampling 

was chosen for MELCOR calculations as some of the results do not converge. 865 of the 9002

MELCOR realizations ran to completion. From these complete MELCOR realizations, a family 

of source term results were produced. Latin hypercube sampling was chosen for MACCS, with 

a sample size of 865 to match the number of source terms. The MACCS results are presented 

as individual LCF risk and individual early fatality risk, averaged over the aleatory uncertainty 

stemming from weather.

Four regression techniques were used in this analysis to estimate the importance of the input 

parameters with respect to the uncertainty in source terms and consequences: linear rank 

regression, quadratic regression, recursive partitioning, and multivariate adaptive regression 

splines (MARS). This analysis provides measures of the effects of the selected uncertain 

parameters both individually and in interaction with other parameters, and helps:

• Identify which of these uncertain important parameters and phenomena are driving the 

variability in model results. 

• Verify and validate the SOARCA model through exploration of unexpected or non-physical 

phenomena in the distributions of results.

• Provide an assessment of linear and non-linear regression techniques and the overall 

uncertainty analysis approach. 

• Provide a technical basis for future work.

Results

Performing the source term calculations of the Peach Bottom unmitigated LTSBO uncertainty 

analysis revealed three groupings of similar accident progression sequences within the Peach 

Bottom unmitigated LTSBO scenario: (1) early stochastic failure of the cycling SRV, which was 

the deterministic SOARCA scenario in NUREG-1935; (2) thermal failure of the SRV without 

main steam line (MSL) creep rupture; and (3) thermal failure of the SRV with MSL creep 

rupture. The three sequence groups exhibited differences in release magnitude, with MSL 

failure generally leading to the largest environmental releases. The majority of samples in this 

uncertainty analysis resulted in larger iodine and cesium releases than the SOARCA project 

calculated because early stochastic failure of the cycling SRV generally leads to smaller 

releases. The accident progression path depended on the values sampled for a couple of key 

 

2 The other 35 samples that did not run to completion were due to numerical convergence challenges, and not 

because of any problems with extending the MELCOR model into a larger parameter value domain.
xxx

uncertain variables: the SRV stochastic failure rate (the rate at which the SRV fails to close on 

demand, thereby remaining fully open), and the SRV open area fraction if the SRV fails 

thermally. The data supporting the input distributions of these two variables is sparse. 

Similarly, there was considerable uncertainty in the selection of appropriate distributions for 

other important variables, such as the size of the opening that results from core melt contacting 

and failing the drywell liner. This uncertainty analysis was most useful in uncovering important 

influences, and defining the plausible range in accident progression and consequences given 

uncertainty in the input parameters studied. The relative likelihood of different results within the 

range, on the other hand, still retains considerable uncertainty given the scarcity of relevant data 

to support the definition of some key input distributions.

Several influences were found to strongly affect the magnitude and timing of fission product 

releases to the environment, as summarized below. Most notably, with respect to the magnitude 

of the source term (the magnitude of cesium and/or iodine releases), the following were found to 

be influential:

• whether the SRV sticks open before or after the onset of core damage, with higher 

releases if after core damage, and the SRV open area if the SRV fails thermally rather 

than stochastically,

• whether MSL creep rupture occurs (largely determined by the two SRV factors above), 

with higher releases if MSL failure occurs due to fission products being vented straight to 

the drywell and thus bypassing wetwell scrubbing,

• the amount of cesium chemisorbed (if any) from cesium hydroxide (CsOH) into the 

stainless steel of reactor pressure vessel (RPV) internals; more chemisorption results in 

less cesium release to the environment for high-temperature scenarios such as MSL 

creep rupture,

• whether core debris relocates from the RPV to the reactor cavity all at once or over an 

extended period of time with relocation all at once leading to lower releases to the 

environment,

• the degree of oxidation, primarily fuel-cladding oxidation, occurring within the vessel with 

greater oxidation resulting in larger releases, and

• whether a surge of water from the wetwell up onto the drywell floor occurs at drywell liner 

melt-through (which depends on the sampled value of the drywell liner open area), with 

the development of a wetwell water surge leading to larger releases.

With respect to release timing, the strongest influences identified were:

• when the reactor core isolation cooling (RCIC) system fails (determined solely by the time 

taken to exhaust the station batteries),

• when the SRV fails to reseat, and

• what the open fraction of the SRV is when it fails to reseat if it fails thermally.

Figure ES-1 shows the fraction of the iodine core inventory released to the environment over 

time, for the 865 samples. For contrast, note the SST1 source term from the 1982 Siting Study 

(NUREG/CR-2239, “Technical Guidance for Siting Criteria Development”) assumed an 

environmental iodine release starting at 1.5 hours, and steadily rising to a final value of 0.45 by 
 xxxi

3 hours (as noted in NUREG-1935 for the SOARCA project). The earliest releases in this 

uncertainty analysis began after 10 hours, with average (mean) and 95th percentile iodine 

releases a factor of 10 and 4 smaller, respectively.

Figure ES-2 shows the fraction of cesium core inventory released to the environment over time, 

for the 865 samples. For contrast, the SST1 source term from the 1982 Siting Study assumed a 

cesium release starting at 1.5 hours and steadily rising to a final value of 0.67 by 3 hours. The 

earliest releases in this uncertainty analysis began after 10 hours, with average (mean) and 

95th percentile cesium releases a factor of 30 and 7 smaller, respectively.

Table ES-1 shows the distribution of results for the conditional, mean, individual LCF risk using 

the linear-no-threshold dose-response model. For contrast, the 10-mile LCF risk recalculated 

for the SST1 source term in NUREG-1935 was more than an order of magnitude higher than the 

95th percentile from this uncertainty analysis. 

For the conditional, mean, individual LCF risk, within different circular areas (within 10- to 

50-mile radii around the plant), the different regression techniques explain 40-85% of the 

variance in the results, with the recursive partitioning analysis consistently capturing the most 

variance. 

Figure ES-1 Time-dependent fraction of iodine core inventory released to the 

environment for the first 48 hours for combined (865) results for the Peach 

Bottom Unmitigated LTSBO
xxxii

Figure ES-2 Time-dependent fraction of cesium core inventory released to the 

environment for the first 48 hours for combined (865) results for the Peach 

Bottom Unmitigated LTSBO

Table ES-1 Conditional3

, mean4, individual LCF risk (per event) averaged statistics of 

the MACCS uncertainty analysis for circular areas around the plant,

considering all 865 MELCOR/MACCS samples with the linear-no-threshold 

dose-response model.

 0-10 miles 0-50 miles

5th percentile 3 x 10-5 2 x 10-5

Median 1 x 10-4 7 x 10-5

Mean 2 x 10-4 1 x 10-4

95th percentile 4 x 10-4 3 x 10-4

SOARCA UA Base Case 9 x 10-5 3 x 10-5

 

3 Note that the scenario frequency is ~3 x 10-6 per reactor-year as documented in NUREG-1935.

4 The ‘mean’ within this context is in reference to the expected value over sampled weather conditions representing a 

year of meteorological data and over the entire residential population within a circular region. This is also 

applicable for early-fatality risk results.
xxxiii

All regression methods consistently rank the following parameters as the most important input 

variables for LCF risk:

• The MACCS dry deposition velocity, 

• The MELCOR SRV stochastic failure rate, and 

• The MACCS risk factor for cancer fatality for the ‘residual’ organ5

. 

The following additional variables also consistently showed some level of importance at all 

circular areas in at least one of the regression methods: 

• The MELCOR fuel failure criterion,

• The MELCOR drywell liner melt-through open area,

• The MACCS dose and dose-rate effectiveness factor for the ‘residual’ organ. 

These six variables alone account for 25%-75% of the variance in individual LCF risk results 

using the different regression methods. In other words, of the hundreds of variables included in 

this uncertainty analysis, a handful of variables drove most of the uncertainty in the 

consequence results. The MELCOR variables included those that were responsible for much of 

the variance in the source term (environmental releases). The MACCS dry deposition velocity 

describes how fast radionuclides deposit on the ground, and groundshine is the major 

contributor to long-term doses. While wet deposition (during precipitation events) more rapidly 

deposits radionuclides on the ground, the wet deposition parameters are not as important 

because precipitation occurs only ~7% of the time at the Peach Bottom site. The MACCS risk 

factor for cancer together with the dose and dose-rate effectiveness factor determine the 

potential lethality of a given dose assuming the linear-no-threshold dose response model.

Conclusions

In explaining the variations in possible source terms and consequences, the use of more 

advanced non-linear regression techniques proved to be advantageous because they capture 

interaction effects and non-monotonic effects missed by the linear rank regression technique. 

Interaction effects among variables and non-monotonic effects are common in complex 

systems, such as nuclear power plant systems and environmental factors during and after a 

severe accident. Furthermore, the use of select single-realization analyses (analyzing the 

MELCOR and MACCS results of one Monte Carlo sample) in this uncertainty analysis proved 

useful in validating the results of the statistical regression analyses through phenomenological 

explanations.

The uncertainty analysis documented in this NUREG/CR corroborates the SOARCA project 

(NUREG-1935) conclusions with the following:

• Public health consequences from severe nuclear accident scenarios modeled are smaller 

than those projected in NUREG/CR-2239.

• The delay in releases calculated provide more time for emergency response actions (such 

as evacuating or sheltering).

 

5 The ‘residual’ organ is represented by the pancreas and is used to define all latent cancers not specifically 

accounted for in the MACCS model. The pancreas is chosen to be a representative soft tissue.
xxxiv

• “Essentially zero” absolute early fatality risk is projected:

— The mean absolute early fatality risk is on the order of 10-12 per reactor-year6 within 

one mile of the plant boundary, and even this minute risk is based on less than 13% of 

865 samples having a non-zero calculated risk; 87% had zero (no) risk.

• The long-term phase dominates the overall health effect risk within the 10-mile emergency 

planning zone (EPZ) because the emergency response is expected to be effective prior to 

the onset of environmental release. More than half the time, the long-term phase is the 

larger contributor to overall health effect risk beyond the EPZ. 

• A major determinant of source term magnitude is whether the SRV sticks open before or 

after the onset of core damage. Compounding this effect is whether or not MSL creep 

rupture occurs, which leads to higher environmental releases and consequences.

• Health-effect risks don’t vary as much as the source terms (environmental releases) 

because people are not allowed to return until doses are below the habitability criterion.

• This analysis confirms the known importance of some phenomena (e.g., the dry 

deposition velocity in MACCS), and reveals some new phenomenological insights (e.g., 

the importance of the drywell liner melt-through area in MELCOR).

• The use of multiple regression techniques provides better explanatory power of which 

input parameters are most important to uncertainty in the results.

 

6 Estimated risks below 10-7 per reactor-year should be viewed with caution because of the potential impact of events 

not studied within the analyses, and the inherent uncertainty in very small calculated numbers.
xxxv

ACKNOWLEDGMENTS

The contributions from the following individuals in preparing this document are gratefully 

acknowledged:

Jon Barr U.S. Nuclear Regulatory Commission

Richard Chang U.S. Nuclear Regulatory Commission

Edward Fuller U.S. Nuclear Regulatory Commission

S. Tina Ghosh U.S. Nuclear Regulatory Commission Document Co-lead

Jason Schaperow U.S. Nuclear Regulatory Commission

Nathan E. Bixler Sandia National Laboratories

Jeffrey N. Cardoni Sandia National Laboratories

Randall O. Gauntt Sandia National Laboratories

Andrew S. Goldmann Sandia National Laboratories

Jon C. Helton Sandia National Laboratories

Joseph A. Jones Sandia National Laboratories

Donald A. Kalinich Sandia National Laboratories

Patrick D. Mattie Sandia National Laboratories Document Co-lead

Douglas M. Osborn Sandia National Laboratories

Kyle W. Ross Sandia National Laboratories

Cedric J. Sallaberry Sandia National Laboratories

Mike F. Young Sandia National Laboratories

Mark T. Leonard Dycoda, LLC

Deborah Phipps Nuclear Regulatory Support Services

xxxvii

ACRONYMS

BEIR Biological Effects of Ionizing Radiation

BWR boiling-water reactor

CC correlation coefficient

CCDF complementary cumulative distribution function

CDF cumulative distribution function

DC direct current

DCF dose conversion factor

DDREFA dose and dose rate effectiveness factor

EPDM ethylene propylene diene methylene 

EOP emergency operating procedure

EPA Environmental Protection Agency

EPZ emergency planning zone

ETE evacuation time estimate

FTC failure to close

GUI graphical user interface

HPCI high-pressure coolant injection system

HPS Health Physics Society

ICRP International Commission or Radiological Protection

IPE Individual Plant Examination

ISLOCA Interfacing System Loss-of-Coolant-Accident 

LHS Latin hypercube sampling

LET linear energy transfer

LNT linear no threshold

LOCA loss-of-coolant accident

LTSBO long-term station blackout 

MACCS MELCOR Accident Consequence Code System

MSL main steam line

MCCI molten core-concrete interactions
xxxviii

NA Not Applicable

NCRP National Council on Radiation Protection and Measurements

NPP nuclear power plant

NRC U.S. Nuclear Regulatory Commission

OROs Offsite Response Organizations

PAGs Protective Action Guidelines

PCC partial correlation coefficient

PDF Probability Density Function

PIRT Phenomena Identification and Ranking Table

PRA Probabilistic Risk Assessment

PRCC partial rank correlation coefficient

PWR pressurized-water reactor

RCIC reactor core isolation cooling

RCS reactor coolant system

RPV reactor pressure vessel

SAE Site Area Emergency

SAMG Severe Accident Management Guideline

SBO station blackout

SGTR steam generator tube rupture

SNL Sandia National Laboratories

SOARCA State-of-the-Art Reactor Consequence Analyses

SRC standardized regression coefficient

SRRC standardized rank regression coefficients

SRV safety relief valve

SSE sum of square error

STSBO short-term station blackout 

USBGR U.S. background
1-1 

1. INTRODUCTION 

This document describes the U.S. Nuclear Regulatory Commission’s (NRC’s) uncertainty 

analysis of the accident progression, radiological releases, and offsite consequences for the 

State-of-the-Art Reactor Consequence Analyses (SOARCA) unmitigated long-term station 

blackout (LTSBO) severe accident scenario at the Peach Bottom Atomic Power Station.

The SOARCA project [1] estimated the outcomes of postulated severe accident scenarios which 

could result in release of radioactive material from a nuclear power plant (NPP) into the 

environment. The SOARCA report [1] documents the outcomes of severe reactor accidents 

using an internally-consistent, integrated model of accident progression and offsite 

consequences. The SOARCA model is based on current best practices that are used to 

estimate offsite consequences of important classes of events. SOARCA couples the

deterministic “current-state-of-knowledge estimate” modeling of accident progression (i.e., 

reactor and containment thermal-hydraulic and fission product response), embodied in the 

MELCOR code with modeling of offsite consequences in the MELCOR Accident Consequence 

Code System (MACCS). This uncertainty analysis presents the results of an analysis of 

epistemic uncertainty associated with the accident progression and offsite consequence 

modeling. 

1.1 Background of the SOARCA Project 

The evaluation of accident phenomena and offsite consequences of severe reactor accidents 

has been the subject of considerable research by the NRC, the nuclear power industry, and the 

international nuclear energy research community. Recently, with NRC guidance and as part of 

plant security assessments, updated analyses of severe accident progression and offsite 

consequences were completed [1]. These analyses were detailed in terms of the fidelity of the 

representation of facilities and emergency response, realistic in terms of phenomenological 

models and procedures, and integrated in terms of the coupling between accident progression 

and offsite consequence models.

The results of these previous studies confirmed and quantified what was suspected but not well 

quantified: that some past studies were sufficiently conservative to the point that predictions 

were not useful in characterizing results. The calculation of risk attributable to severe reactor 

accidents should consider realistic estimates of the more likely outcomes and should 

incorporate both the many improvements to NPPs and improved understanding of severe 

accident behavior. Moreover, improvements in plant design and construction, better 

understanding of accidents and their consequences, and realistic modeling should be 

appropriately communicated.

In addition to the improved understanding and calculational capabilities that have resulted from 

these studies, many influential changes have occurred in the training of operating personnel and 

the increased use of plant-specific capabilities. These changes include the following:

• The transition from event-based to symptom-based emergency operating procedures 

(EOPs) for the boiling-water reactor (BWR) and pressurized-water reactor (PWR) designs.

• The performance and maintenance of plant-specific probabilistic risk assessments (PRAs) 

that include a spectrum of accident scenarios.

• The implementation of plant-specific, full-scope control room simulators to train operators.
1-2 

• An industry wide, owners-group-specific guidance, and plant-specific implementation of 

the severe accident management guidelines (SAMGs).

• Additional safety enhancements, described in Title 10, Section 50.54(hh) of the Code of 

Federal Regulations (10CFR50.54(hh)). These enhancements are intended to be used to 

maintain or restore core cooling, containment integrity, and spent fuel pool cooling 

capabilities under the conditions associated with the loss of large areas of the plant due to 

explosions or fire and include strategies for use in the following areas: (i) firefighting; 

(ii) operations to mitigate fuel damage; and (iii) actions to minimize radiological release. 

Successful implementation of this equipment and associated procedures could possibly: 

(i) prevent core damage or (ii) delay or prevent radiological release, which is reflected in 

the SOARCA scenarios. 

• Improved understanding of the underlying phenomena that result in influential processes 

such as the following:

o in-vessel steam explosions

o Mark I containment drywell shell attack

o dominant chemical forms for fission products

o direct containment heating

o hot-leg creep rupture

o reactor pressure vessel (RPV) failure and molten core-concrete interactions (MCCI). 

Additional changes in plant operation have occurred over time, including the following:

• power uprates

• higher core burnups. 

The SOARCA project, conducted by the NRC and Sandia National Laboratories (SNL), was a 

research effort to realistically estimate the outcomes of postulated severe accident scenarios 

that might cause a NPP to release radioactive material into the environment. 

SOARCA [1] conducted an in-depth analysis of two operating NPPs: Peach Bottom, a BWR, 

and Surry, a PWR. SOARCA used computer modeling techniques to understand how a reactor 

might behave under severe accident conditions, and how a release of radioactive material from 

the plant might impact the public. Specifically, SOARCA used MELCOR (i.e., an integral severe 

accident analysis code) to model the severe accident scenarios within the plant, and MACCS

(i.e., a radiological consequence assessment code) to model the offsite health consequences 

for atmospheric releases of radioactive material. 

In determining realistic consequences of postulated severe accidents, SOARCA relied on many 

years of previous national and international reactor safety research. The NRC, the U.S. 

Department of Energy, the nuclear power industry, and international nuclear safety 

organizations have extensively researched plant responses to hypothetical scenarios that could 

damage the reactor core or the containment. This research has significantly improved the 

NRC’s ability to analyze and predict how nuclear plant systems are likely to respond to severe 

accidents, and how accidents progress. In addition, NPP owners have continually improved 

safety by enhancing their plant designs, emergency procedures, inspection programs, and 

operator training. Plant owners and local governments have also refined and improved 

emergency preparedness to further protect the public in the highly unlikely event of a severe 

accident. Finally, the NRC has incorporated insights from health physics organizations and 

employed both the linear-no-threshold model and alternate linear-with-threshold (dose 

truncation) dose-response models for analyzing health effects.
1-3 

SOARCA incorporated the accumulated research and plant operations and design 

enhancements to integrated computer models. These models consider onsite and offsite 

actions, including the implementation of mitigation measures and protective actions for the 

public such as evacuation and sheltering that may prevent or mitigate accident consequences. 

These SOARCA calculations, results, and conclusions are documented in NUREG-1935, 

"State-of-the-Art Reactor Consequence Analyses (SOARCA) Report" [1], and 

NUREG/CR-7110, Volume 1, "State-of-the-Art Reactor Consequence Analyses Project 

Volume 1: Peach Bottom Integrated Analysis" for the Peach Bottom pilot plant [2]. 

1.2 SOARCA Comparison and Contrast with Fukushima Accidents

The SOARCA analyses [2] of station blackout accidents in Peach Bottom were performed 

several years before the accidents at Fukushima occurred and as such, were anticipatory of the 

real-world events that occurred in the three accidents at Fukushima as evident from 

comparisons highlighted in the following. The Fukushima accidents were all variants of either 

the long-term or short-term station blackout scenarios identified in the SOARCA Peach Bottom 

study. The SOARCA study summary report (NUREG-1935) includes an appendix comparing a 

few key aspects of the Fukushima accidents to the SOARCA scenarios. The following are 

some informative contrasts and comparisons between the Peach Bottom station blackout 

analyses and observations from the Fukushima accidents and MELCOR analyses of these 

accidents performed more recently [3]. Shown below on Figure 1-1 is the RPV pressure 

predicted by MELCOR for the Peach Bottom LTSBO (left) compared with the observed and 

predicted pressure response for the Fukushima Unit 3 accident (right). Both sequences are 

considered “long-term” owing to the availability of direct current (DC) power at the start of the 

accident. At a glance, both pressure signatures show similar overall characteristics starting with 

RPV at the safety relief valve (SRV) setpoint with reactor core isolation cooling (RCIC) 

operating, a period of RPV depressurization before loss of turbine-driven injection to the RPV, a 

period where the RPV returns to the SRV setpoint and a final stage where RPV 

depressurization takes place as core damage ensues.

Figure 1-1 Comparison of Peach Bottom Long Term Station Blackout RPV Pressure 

(left) and Fukushima Unit 3 accident (right, [3]) 

The overall signatures of the accidents are strikingly similar, where differences are due to 

differences in the accident management actions taken in the simulated SOARCA analyses and 

the real-world event. Firstly, in the SOARCA LTSBO after approximately one hour the operators 

are assumed to open an SRV to drop the RPV pressure as RCIC maintains water level in the 

core using the available DC power to power the SRV and regulate water level, following EOPs. 
1-4 

In contrast, in Fukushima Unit 3, the RPV remains at the SRV setpoint for more than 20 hours 

as the RCIC system operates, and it is not until the operators engage the high-pressure coolant 

injection system (HPCI) following RCIC shutdown that the RPV pressure is reduced. In the 

SOARCA LTSBO, battery depletion leads to SRV closure and a return to the SRV setpoint 

along with an assumed loss of RCIC function, similar to when the HPCI system in Fukushima 

Unit 3 shuts down and terminates the steam draw from the Unit 3 RPV. In the SOARCA 

LTSBO, after returning to full RPV pressure with SRV’s cycling, one SRV is assumed to seize 

open causing RPV depressurization and concurrent water level loss and core damage. In 

Fukushima Unit 3, the RPV also depressurizes after cycling for a while as water level loss and 

core damage is likely occurring due to HPCI shut down. This depressurization in Fukushima 

Unit 3 has been assumed due to operator actions taken to allow low pressure water injection, an 

action not modeled in the SOARCA LTSBO owing to battery depletion and no additional 

assumed operator actions. Both signatures exhibit features of core degradation after this. It is 

notable that only 4 hours of battery life was assumed with no remedial actions taken to restore 

DC power in the SOARCA analysis, whereas in the Fukushima Unit 3 sequence of events, 

operators refresh batteries to allow ongoing emergency operations to continue.

The same SOARCA LTSBO pressure signature is shown below in Figure 1-2 compared with the 

Fukushima Unit 2 accident. Both accidents begin similarly with RPV pressure at the SRV 

setpoint and RCIC running. For the first approximately 40 minutes in the Fukushima Unit 2 

accident, DC power is available to regulate water level, but after the arrival of the tsunami, all 

DC power is lost and RCIC operation proceeds without level information or ability to regulate 

RCIC operation. In the SOARCA model for Peach Bottom, such loss of DC power would result 

in RCIC flooding water into the steam line and an assumed failure of the RCIC pump. However, 

while it is currently believed that steam line flooding did occur in Fukushima Unit 2 due to 

unregulated RCIC operation, it is also apparent that RCIC failure did not follow as a result of this 

flooding. Instead, the two-phase flow of steam and water through the RCIC turbine is thought to 

have produced the RPV depressurization below the SRV setpoint that was observed between 

about 5 hours and through the time of apparent RCIC failure at about 67 hours. As in the Unit 3 

accident, assumed operator depressurization following RCIC failure and water level loss is 

observed followed by emergency procedures for low pressure water injection and some degree 

of core damage. The SOARCA analyses generally and conservatively did not model such 

extended EOPs. 

Figure 1-2 Comparison of Peach Bottom Long Term Station Blackout RPV Pressure 

(left) and Fukushima Unit 2 accident (right, [3]) 
1-5 

These comparisons7 highlight some of the common system responses modeled by the 

MELCOR code for the Peach Bottom station blackout analyses and consistently observed in the 

Fukushima real-world events. The main differences being due to unappreciated extended 

operability of RCIC turbine operation and additional EOP measure for engaging low pressure 

water injection following manual RPV depressurization. Accident details such as those 

observed at Fukushima can of course be modeled by the MELCOR-SOARCA methodology.

Another difference observed between SOARCA Peach Bottom station blackout (SBO) analyses 

and the Fukushima accidents is with respect to containment failure mode and hydrogen 

behavior. The SOARCA analyses of Peach Bottom, a significantly larger reactor compared with 

the Fukushima reactors, consistently predicted drywell liner failure following vessel lower head 

failure and release of core material to the drywell cavity, caused by contact between core 

materials and the steel liner of the containment. This resulted in containment depressurization

and release of hydrogen to the torus room at a low elevation in the reactor building. 

In contrast, at least for Fukushima Unit 1, such liner failure was not predicted by MELCOR 

analyses and instead a long-term pressurization of the drywell/wetwell containment was 

predicted, eventually producing gross leakage at the drywell head flange, releasing hydrogen to 

the refueling bay at the highest elevation of the reactor building. Evidence (i.e., protracted high 

containment pressure and video of the hydrogen explosion) from the Fukushima Unit 1 

observations supports this modeling prediction. Shown below in Figure 1-3 are hydrogen/steam 

concentrations that are predicted by MELCOR for the Peach Bottom short-term station blackout 

(STSBO) (left) and Fukushima Unit 1 (right). Because of the predicted drywell liner failure and 

resulting release of hydrogen in the torus room, a sequence of hydrogen burns are predicted for 

the torus room as flammable conditions are encountered. In contrast, the predicted conditions 

for the refueling bay in Fukushima Unit 1 suggest that inert conditions were maintained due to 

high steam concentrations, in spite of continuous leakage of hydrogen into the refueling bay 

through the leaking drywell head flange between 15 and 24 hours into the accident. Flammable 

conditions are not predicted until after 24 hours when containment venting and cessation of 

water injection leads to a decrease in steam leakage to the refueling bay, whereupon a large 

hydrogen explosion was observed to have taken place at about 25 hours.

 

7 While other phenomena, such as recirculation pump seal leakage and lower head penetration failure, have been 

proposed, they are not modeled in [3.] Gauntt, R.O., et al., SAND2012-6173, "Fukushima Daiichi Accident 

Study (Status as of April 2012)," Sandia National Laboratories, Albuquerque, NM, 2012.. Future modeling efforts 

and eventual information from decommissioning of the Fukushima reactors themselves may shed light on the 

relative importance of these phenomena.
1-6 

Figure 1-3 Comparison of Peach Bottom STSBO Term Station Blackout hydrogen 

distribution (left) and MELCOR-predicted Fukushima Unit 1 hydrogen 

conditions (right, [3]) 

These comparisons illustrate remarkable consistency in accident sequence progression and 

overall system response between MELCOR-SOARCA modeling and real-world observations 

from Fukushima. Differences in the signatures are generally understood and due to differences 

in operator actions as well as better-than-expected durability of the RCIC turbine driven steam 

system in the Fukushima accidents. The modeled and observed differences in hydrogen 

release (i.e., drywell liner failure versus drywell head flange leakage from over-pressurization) 

are apparently due to modeled differences in corium behavior in the cavity, perhaps attributable 

to the comparatively larger Peach Bottom core which may have a higher potential to flow and 

contact the steel liner. The real-world observations from Fukushima are consistent with 

phenomenology and system responses modeled by MELCOR, and give confidence to the 

overall findings in the SOARCA studies. In time, additional evidence from the Fukushima 

reactors will likely shed additional light on other important issues identified in this uncertainty 

study with respect to potential steam line rupture or SRV seizure occurring under high 

temperature severe accident conditions that may further inform and clarify MELCOR modeling 

practices in future severe accident studies.

Recent work [91] has also been conducted in which a comparative assessment of how 

MELCOR and MAAP5 model in-vessel core damage progression, from onset of core damage to 

breach of the RPV lower head. The objective of the comparative assessment was the

identification of the principal modeling assumptions within the two codes leading to identified 

simulation differences. Key differences in the modeling assumptions were:

• MAAP5 does not explicitly consider the radial relocation of particulate or molten material 

during this early phase of core degradation; it is assumed that downward motion of core 

debris is the primary mode of relocation.

• The two codes use different fuel-failure time-at-temperature failure relationships.

• Particulate debris bed geometries are treated in significantly different manners.

• MAAP5 and MELCOR have different models for the slumping of molten material/debris 

slumping into the lower plenum.
1-7 

• The MAAP5 and MELCOR models of lower plenum core debris are conceptually quite 

different.

1.3 Objectives of the Uncertainty Analysis 

The purpose of SOARCA is to evaluate the consequences of postulated severe reactor accident 

scenarios that might cause a NPP to release radioactive material into the environment. Toward 

that end, the objective of the SOARCA Uncertainty Analysis is to evaluate the robustness of the 

SOARCA deterministic results and conclusions, and to develop insight into the overall 

sensitivity of the SOARCA results to uncertainty in key modeling inputs. As this is a first-of-akind analysis in its integrated look at uncertainties in MELCOR accident progression and 

MACCS offsite consequence analyses, an additional objective is to demonstrate uncertainty 

analysis methodology that could be used in future source term, consequence, and Level 3 PRA 

studies. Figure 1-4 provides a general information flow diagram of the uncertainty analysis 

highlighting specific sections that may be of interest to the reader. 

SOARCA included sensitivity studies to examine issues associated with accident progression, 

mitigation, and offsite consequences for the accident scenarios of interest. The objective of 

these sensitivity studies was to examine specific issues and ensure the robustness of the 

conclusions documented in NUREG-1935 [1]. Single sensitivity studies, however, do not form a 

complete picture of the uncertainty associated with accident progression and offsite 

consequence modeling. Such a picture requires a more comprehensive and integrated 

evaluation of modeling uncertainties. 

In general terms, the SOARCA offsite consequence results presented in NUREG-1935 [1] 

incorporated only the uncertainty associated with weather conditions at the time of the accident 

scenario considered. The reported offsite consequence values represent the expected 

(i.e., mean, the arithmetic average) value of the probability distribution obtained from a large 

number of aleatory weather trials. The weather uncertainty is handled the same way in this 

uncertainty analysis. In addition, the impact of epistemic model parameter uncertainty (the 

focus of this analysis) is explored in detail by randomly sampling distributions for key model 

parameters that are considered to have a potentially important impact on the offsite 

consequences. The objective of this uncertainty analysis is to develop insight into the overall 

sensitivity of the SOARCA results and conclusions to the combined integrated uncertainty in 

accident progression (MELCOR) and offsite health effects (MACCS). Assessing key MELCOR 

and MACCS modeling uncertainties in an integrated fashion, yields an understanding of the 

relative importance of each uncertain input on the potential consequences. 

NRC guidance documents (i.e., Regulatory Guide 1.174 and NUREG-1855) discuss three types 

of epistemic uncertainty: parameter, model, and completeness. Neither completeness 

uncertainty nor model uncertainty are not treated in this study. This analysis leverages the 

existing SOARCA models and software, along with a representative set of key parameters. In 

other words, the uncertainty stemming from the choice of conceptual models and model 

implementation is not explicitly explored. The integrated uncertainty analysis is supplemented 

with limited sensitivity analyses which explore some model uncertainties. In addition, not all 

possible uncertain input parameters were included in the analysis. Rather, a set of key 

parameters was carefully chosen to capture important influences on release and consequence 

results. 

A detailed uncertainty analysis was performed for a single-accident scenario rather than all 

seven of the SOARCA scenarios documented in NUREG-1935 [1]. This work does not include 

uncertainty in the scenario frequency. The SOARCA Peach Bottom BWR Pilot Plant 
1-8 

Unmitigated LTSBO scenario [2] is analyzed. While one scenario cannot provide a complete 

exploration of all possible effects of uncertainties in analyses for the two SOARCA pilot plants, it 

can be used to provide initial insights into the overall sensitivity of SOARCA results and 

conclusions to input uncertainty. In addition, since station blackouts (SBOs) are an important 

class of events for BWRs in general, the phenomenological insights gained on accident 

progression and radionuclide releases may prove useful for BWRs in general. (A second 

uncertainty analysis is currently underway for one of the SOARCA Surry PWR pilot plant 

scenarios.) 

Section 2.0 outlines the uncertainty analysis approach used to meet the two primary objectives 

of this analysis: (1) identify the uncertainty in the input parameters used in the SOARCA

deterministic analysis and (2) to develop insight into the overall sensitivity of the SOARCA 

results and conclusions to uncertainty in key modeling inputs by assessing MELCOR and 

MACCS modeling uncertainties in an integrated fashion to quantify the relative importance of 

each uncertain input on the potential consequences. 

. 
1-9 

Figure 1-4 SOARCA Uncertainty Analysis Information Flow Diagram
1-10

1.4 Uncertainty Analysis Report Outline

Section 2 presents a description of the uncertainty analysis approach including the SOARCA 

probabilistic analysis methodology. Section 3 includes a description of the probabilistic analysis 

structure, process and software used. Section 4 describes the uncertainty input parameters for 

MELCOR and MACCS, respective distributions and technical bases. Section 5 documents the 

Peach Bottom unmitigated LTSBO “base case” results used in this analysis. In addition, 

Section 5 includes a demonstration of the convergence of the probabilistic results used in the 

parameter sensitivity and uncertainty analysis. Section 6 presents the results of parameter 

sensitivity and uncertainty analysis for source term releases and offsite consequences. Section 

7 is a summary of the results and conclusions. Section 8 provides a list of references used in 

this report. 

Appendix A includes a detailed mathematical description of the probabilistic analysis 

methodology described in Section 2.0 and the parameter sensitivity uncertainty analysis 

techniques used in Section 6.0. Appendix B includes a detailed description of the software used 

for the source term and consequence analyses and code integration used for the probabilistic 

analyses as described in Sections 2.0 and 3.0. Appendix C contains an analysis documenting 

changes to the SOARCA model and codes necessary for convergence of the probabilistic 

analysis. Appendix D includes and the SOARCA Uncertainty Analysis team’s responses to 

individual and group comments contained in the two PRC memoranda on the uncertainty 

analysis and the ACRS’ final letter on the SOARCA project. Appendix E contains additional 

information and analyses developed in response to questions from the ACRS for this 

uncertainty analysis. Appendix F contains a glossary of uncertainty analysis terms, as they are 

used in this study. 
2-1 

2. UNCERTAINTY ANALYSIS APPROACH

2.1 Accident Scenario Selection

An accident sequence begins with the occurrence of an initiating event (e.g., a loss of offsite 

power, a loss-of-coolant accident (LOCA), or an earthquake) that perturbs the operation of the 

NPP. The initiating event challenges the plant’s control and safety systems, whose failure might

cause damage to the reactor fuel and result in the release of radioactive material. Because a 

NPP has numerous diverse and redundant safety systems, many different accident sequences 

are possible depending on the type of initiating event that occurs, which equipment 

subsequently fails, and the nature of the operator actions involved, as described in the 

SOARCA study [1, 2]. Individual accident sequences can be grouped into accident scenarios 

that represent functionally similar sequences. The SOARCA project analyzed a handful of 

important scenarios in detail. The scenario selection process for the SOARCA project is 

described in NUREG-1935 [1]. Three accident scenarios were chosen for analysis for Peach 

Bottom (the BWR pilot plant) and four accident scenarios were selected for Surry (the PWR pilot 

plant) [1]. 

The process for selecting a SOARCA scenario for this uncertainty analysis considered both the 

magnitude and timing of the offsite radionuclide release, which have major impacts on both 

early and latent cancer fatality risks. The examination of candidate scenarios considered both 

the timing of core damage and the timing of containment failure. 

SBOs are an important class of events for NPPs, especially BWRs, which pointed to both Peach 

Bottom LTSBO and STSBO scenarios as good candidates. Although the uncertainty analysis 

was already under way by March 2011, the events at the Fukushima Daiichi plant re-confirmed 

the interest in SBOs for BWRs. The STSBO has a more prompt radiological release and a 

slightly larger release compared to LTSBO over the same interval of time. Although it was a 

more prompt release (i.e., 8 hours versus 20 hours), the STSBO release was delayed beyond 

the time needed for successful evacuation. In addition, the STSBO frequency is assessed to be

approximately an order of magnitude lower than the LTSBO (i.e., ~3 × 10-7 per reactor-year 

(STSBO) versus ~3 × 10-6 per reactor-year (LTSBO)). The NUREG-1935 [1] analysis indicated

the absolute risk is smaller for the STSBO than for the LTSBO. The same trends apply for the 

Surry scenarios where the lower-frequency scenarios (the Surry interfacing systems loss of 

coolant accident (ISLOCA) or the Surry steam generator tube rupture (SGTR)) may have 

greater conditional risk but absolute risk is assessed to be smaller than or equivalent to other 

higher-frequency scenarios. 

Another factor that influenced the choice of the LTSBO was the ability to explore the impact of 

parameters that are not evaluated in the STSBO. For example, only the LTSBO could assess 

the importance of battery life. Additionally, the performance of the SRV as it impacts the main 

steam line (MSL) failure was an important sensitivity study identified by the peer review 

committee, assessed in the SOARCA project, and found to be important for the LTSBO 

scenario. Similarly, choosing the unmitigated LTSBO scenario allowed the exploration of the 

effect of a wider set of physical phenomena and parameters on releases and consequences, 

since the mitigated LTSBO scenario was assessed to have no core damage in the SOARCA 

project (the unmitigated and mitigated scenarios are defined in the SOARCA project summary 

report, NUREG-1935 [1]). While it would be interesting to explore the effect of modeling 

uncertainties on the mitigated scenario results as well, it is expected that human actions – 

decisions by the Technical Support Center and actions implemented by plant operators – would 

be a dominant contributor to uncertainties. As with the SOARCA project, a formal human 

reliability analysis was outside the scope of this uncertainty analysis, making the choice of the 

mitigated scenario less useful. 
2-2 

As in NUREG/CR-7110 Volume 1, an expected national level response to a severe NPP

accident provides a basis for truncating the release no later than 48 hours after the accident 

begins. Note that past studies, including PRAs such as NUREG-1150, typically truncated 

releases after 24 hours.

Mitigative actions during an accident are intended to:

• prevent the accident from progressing;

• terminate core damage if it begins;

• maintain the integrity of the containment as long as possible; and

• minimize the effects of offsite releases.

A response to a LTSBO would begin with the onsite emergency response organization and 

would expand as needed to include utility corporate resources, State and local resources, and 

resources available from the Federal government, should these be necessary. It is most likely 

that plant personnel would attempt to mitigate the accident before core melt, but if their efforts 

were unsuccessful the national level response would provide resources to support mitigation of 

the source term. 

In summary, the Peach Bottom Unmitigated LTSBO was selected based on the rationale that: 

(1) SBOs are an important class of events for NPPs and BWRs in particular, and the March 

2011 Fukushima Daiichi accident further renewed interest in SBOs and (2) the choice of 

unmitigated LTSBO also allows the exploration of important phenomena and parameters that do 

not have a part in the Peach Bottom STSBO or Peach Bottom mitigated LTSBO.

2.2 Selection of Uncertain Parameters

A core team of senior staff members from SNL and the NRC was formed with special expertise 

in probability and statistics, uncertainty analysis, MELCOR modeling, and MACCS consequence 

analysis. This SOARCA Uncertainty Analysis team collectively has decades of experience with 

different aspects of severe accident phenomena, accident progression, consequence modeling, 

and uncertainty analysis methodology. The team also includes the developers of the SOARCA 

project MELCOR and MACCS models for Peach Bottom (i.e., those who are most familiar with 

how the influence of various phenomena are captured in the specific Peach Bottom Unmitigated 

LTSBO models). Furthermore, the team gained additional preliminary insight into the important 

influences of particular phenomena and parameters through a host of sensitivity studies 

conducted as part of the SOARCA project itself (many of these sensitivity studies are 

documented in NUREG/CR-7110 Vol. 1 [2]). In addition to the core team, selected subject 

matter experts (SMEs) provided support on an as-needed basis and facilitated the reviews of 

data, parameters, distributions, and their technical bases. The approach to parameter selection 

focuses on available data and relies on expert judgment, informally using methods used in a 

more formalized phenomena identification and ranking table (PIRT) process. Expert judgment 

was used to identify the important phenomena and select parameters. The phenomena and 

related parameters were not ranked; rather, a consensus approach was utilized to include as 

many as practicable. An additional difference between the approach used here and a formal 

PIRT process (or expert elicitation) is that the interim discussions and products were not 

rigorously documented in this uncertainty analysis. Rather, this NUREG/CR report alone is 

intended to capture important aspects of the rationale for inclusion of parameters and 

development of distributions. 

The selection of uncertain parameters was a multi-year iterative process. At multiple points in 

the process, the selected phenomena, parameters, and distributions were technically reviewed 
2-3 

internally at the NRC and SNL. The technical reviews focused on: (1) confirming that the 

parameter representations appropriately reflect major sources of uncertainty, and (2) ensuring 

model parameter representations (i.e., probability distributions) are reasonable and have a 

defensible technical basis. After each review, the selection and technical bases were updated.

In addition, the uncertainty analysis benefited from two interim reviews by the SOARCA Peer 

Review Committee (PRC) (in addition to the benefit of having feedback from the peer reviewers 

as part of the overall SOARCA project). Though the uncertainty analysis was outside the 

original scope of the SOARCA Peer Review charter, the SOARCA team presented the overall 

UA methodology and approach, and initial selection of parameters and distributions in two 

separate meetings with the PRC, after each of which the PRC provided feedback via guidance 

memoranda. In addition, the team held a final teleconference with the PRC on the team’s 

resolutions to peer reviewers’ comments on the uncertainty analysis. The peer review is 

documented in Appendix D, which includes the SOARCA Uncertainty Analysis team’s peer 

review comment resolution report for the two PRC memoranda on the uncertainty analysis. 

Examples of improvements to this analysis in response to peer reviewer comments include the 

revision of several parameter distributions, a more careful evaluation of MELCOR parameters 

that should be correlated, the final selection of weather treatment, and enhanced documentation 

in this NUREG/CR report. 

This uncertainty analysis also benefitted from an interim review by the NRC’s Advisory 

Committee on Reactor Safeguards (ACRS). The uncertainty analysis team presented the 

uncertainty analysis methodology and overall approach, parameter selection and distributions, 

and preliminary insights based on MELCOR results, to the ACRS. In its final letter to the 

Commission on the SOARCA project, the ACRS provided some comments on the uncertainty 

analysis. Appendix D includes the uncertainty analysis team’s responses to uncertainty 

analysis comments the ACRS’ final letter on the SOARCA project. In addition to enhancing the 

documentation of the uncertainty analysis (in this NUREG/CR report) and the addition of 

Section 4.3, one notable addition in response to ACRS comments was the inclusion of a 

sensitivity study for an alternate lower head failure location (see section 6.4.3). Appendix F also 

includes additional information and analyses developed in response to ACRS comments of this 

uncertainty analysis, for example on the relative and combined contributions of aleatory 

(weather) and epistemic MELCOR and MACCS parameter uncertainties, and the convergence 

of MACCS results. 

For this uncertainty analysis, a set of 21 epistemic MELCOR parameters, 20 independent 

MACCS epistemic parameters, and one MACCS aleatory parameter were selected. A 

discussion of the importance of and distributions for each selected parameter is provided in 

Sections 4.1 and 4.2 for the MELCOR and MACCS parameters, respectively. Table 2.2-1 lists 

all of the uncertain parameters (or parameter groups) in this analysis. Some of the MACCS

parameters listed in Table 2.2-1 actually represent a parameter group that contains multiple 

individual parameters. The MACCS parameters are further defined in Section 4.2, which details 

the unique epistemic distributions and a set of random aleatory weather trials.

Limitations of the codes and availability of models and or data limited the ability to evaluate 

some potentially important phenomena in this analysis. Some of these potentially important 

phenomena and related parameters were evaluated in separate sensitivity studies instead, or 

discussed qualitatively (see Sections 4.3 and 6.4). 
2-4 

Table 2.2-1 SOARCA uncertain parameter groups 

MELCOR MACCS

Epistemic Uncertainty Epistemic Uncertainty

Sequence Issues Deposition

SRV stochastic failure to reclose (SRVLAM) Wet deposition model (CWASH1)

Battery Duration (BATTDUR) Dry deposition velocities (VEDPOS) 

In-Vessel Accident Progression Parameters Shielding Factors

Zircaloy melt breakout temperature (SC1131(2)) Shielding factors (CSFACT, GSHFAC, PROTIN)

Molten clad drainage rate (SC141(2)) Early Health Effects

SRV thermal seizure criterion (SRVFAILT) Early health effects (EFFACA, EFFACB, EFFTHR)

SRV open area fraction (SRVOAFRAC) Latent health effects

Main Steam line creep rupture area fraction 

(SLCRFRAC)

Dose and dose rate effectiveness factor (DDREFA)

Fuel failure criterion (FFC) Mortality risk coefficient (CFRISK)

Radial debris relocation time constants

(RDMTC, RDSTC)

Inhalation dose coefficients (radionuclide specific)

Ex-Vessel Accident Progression Parameters Dispersion Parameters

Debris lateral relocation – cavity spillover and 

spreading rate (DHEADSOL, DHEADLIQ)

Crosswind dispersion coefficients (CYSIGA)

Containment Behavior Parameters Vertical dispersion coefficients (CZSIGA)

Drywell liner failure flow area (FL904A) Relocation Parameters

Hydrogen ignition criteria (H2IGNC) Hotspot relocation (DOSHOT, TIMHOT)

Railroad door open fraction (RRIDRFAC, 

RRODRFAC)

Normal relocation (DOSNRM, TIMNRM)

Drywell head flange leakage (K, E, δ) Evacuation Parameters

Chemical Forms of Iodine and Cesium Evacuation delay (DLTEVA)

Iodine and Cesium fraction (CHEMFORM) Evacuation speed (ESPEED)

Aerosol Deposition Aleatory Uncertainty

Particle Density (RHONOM) Weather Trials

2.3 Treatment of Uncertainty 

In the design and implementation of analyses for complex systems, it is useful to distinguish 

between two types of uncertainty: aleatory uncertainty and epistemic uncertainty [4, 5, and 6]. 

It is also important to note that some parameters may have both aleatory and epistemic 

attributes, but are treated as epistemic for analytic convenience.
2-5 

Aleatory uncertainty arises from an inherent randomness in the properties or behavior of the 

system under study. For example, the weather conditions at the time of a reactor accident are 

inherently random with respect to our ability to predict the future. Other potential examples 

include the variability in the properties of a population of system components and the variability 

in the possible future environmental conditions to which a system component could be exposed. 

Alternative designations for aleatory uncertainty include variability, stochastic, irreducible and 

type A.

Epistemic uncertainty derives from a lack of knowledge about the appropriate value to use for a 

quantity that is assumed to have a fixed value in the context of a particular analysis. For 

example, the pressure at which a given reactor containment would fail for a specified set of 

pressurization conditions is fixed but not amenable to being unambiguously defined. Other 

possible examples include minimum voltage required for the operation of a system and the 

maximum temperature that a system can withstand before failing. Alternative designations for 

epistemic uncertainty include state of knowledge, subjective, reducible and type B.

The analysis of a complex system typically involves answering the following three questions 

about the system and one additional question about the analysis itself:

1. What can happen?

2. How likely is it to happen?

3. What are the consequences if it happens?

4. How much confidence exists in the answers to the first three questions?

The answers to questions one and two involve the characterization of aleatory uncertainty, and 

the answer to question four involves the characterization and assessment of epistemic 

uncertainty, which is the objective of this analysis. The answer to question three typically 

involves numerical modeling of the system conditional on specific realizations of aleatory and 

epistemic uncertainty. The posing and answering of questions one through three gives rise to 

what is often referred to as the Kaplan/Garrick ordered triplet representation for risk [6]. 

While not arbitrary, the definitions of aleatory and epistemic uncertainty do depend in a 

fundamental way on the system under study. This is the concept relating to the “inner weather 

loop” approach (described below) in evaluating the uncertainty in the SOARCA consequence 

calculations. 

In the modeling system used to generate the SOARCA results [1], weather is treated as an 

aleatory parameter. Each SOARCA calculation represents the mean offsite consequence for a 

given accident sequence calculated from a large number of weather trials. In this way, the 

SOARCA calculation seeks an answer to the question, “What is the expected consequence of a

given accident scenario, like a LTSBO, at the Peach Bottom Atomic Power Station?” 

(i.e., expected outcome over all aleatory sequences– “inner weather loop” approach”) as 

opposed to, “What is the expected consequence of a given accident scenario during a snow 

storm in February at the Peach Bottom Atomic Power Station?” (i.e., results conditional on a 

specific weather trial). While it is certainly feasible to obtain a reasonable estimate of the 

consequences of a LTSBO at Peach Bottom during any given weather scenario (“outer weather 

loop” approach), this would not be a useful result, since it is not known what the weather 

conditions might be during such an event and no amount of additional information and research 

will serve to reduce that uncertainty.
2-6 

The SOARCA consequences, including weather uncertainty, are illustrated on Figure 2.3-1. A 

single source term release, SBE,, dependent upon the estimated input, xi, BE, was used as input 

to a consequence analysis dependent upon the estimated input, yi,BE. The result is a distribution 

of consequences conditional on the estimated values (i.e., Question 3 above), over the weather 

variability (i.e., Question 1 and Question 2 above). The mean value, ||H||, is the mean 

consequence over the weather variability. However, to address question four (i.e., “How much 

confidence exists in the answer to the first three questions?”), a series of analyses must be 

conducted that quantify the effects of epistemic uncertainty in the system over all possible 

weather conditions. These concepts are detailed in a mathematical description of the 

probabilistic analysis in Appendix A. 

Figure 2.3-1 Typical complementary cumulative distribution function (CCDF) of 

consequence
3-1 

3. DESCRIPTION OF ANALYSES 

3.1 Software Used

This section briefly discusses the codes used in the integrated probabilistic analyses, including 

an overview of the integrated analysis and probabilistic calculations used for the parameter 

uncertainty and sensitivity analysis. To better understand the uses of computer codes that are 

listed in this section, a brief overview of the software used to calculate the source term and 

consequence analysis is included in Appendix B. In addition, Appendix B documents the 

detailed process: the inputs and outputs, information flow, and order of operation for each code 

used to conduct the integrated probabilistic analysis. 

3.1.1 MELCOR 

MELCOR is a computer code that models the progression of severe accidents in PWRs and 

BWRs [7]. MELCOR 1.8.6 YV3780 was used to generate the probabilistic source terms used 

for the parameter uncertainty and sensitivity analysis documented in Section 6.0 of this report. 

MELCOR 1.8.6 YR549 was used for the SOARCA Peach Bottom unmitigated LTSBO analysis 

presented in NUREG 1935 [1] and NUREG/CR 7110, Volume 1 [2]. MELCOR 1.8.6 YV3780 

was used for the Surry pilot plant documented in NUREG 1935 [1]. A comparison between the 

two codes for the Peach Bottom unmitigated LTSBO analysis presented in NUREG 1935 [1] 

and NUREG/CR 7110, Volume 1 [2], and this uncertainty analysis, is presented in Appendix C. 

3.1.2 MELMACCS 

MELMACCS compiles MELCOR outputs for transition into a WinMACCS/MACCS (MELCOR 

Accident Consequence Code System) input [8]. The MELMACCS software is a Windows based 

program that creates a MACCS radionuclide file from the MELCOR output plot file. The 

MELCOR plot files contain large amounts of data, only some of which is needed for MACCS

calculations. The MELMACCS software provides an interface between MELCOR and MACCS

to integrate the required data.

When the SOARCA scenarios, including the Peach Bottom LTSBO scenario in 

NUREG/CR-7110 [2], were developed, the MELCOR output was converted to a MACCS

radionuclide input file using MELMACCS Version 1.5.1. To ensure proper source term 

continuity between MELCOR and MACCS, a comparison of MELCOR source terms was 

conducted using MELMACCS Version 1.7.0 and MELMACCS Version 1.5.1 as documented in 

Appendix C.

3.1.3 MACCS 

MACCS [9] can estimate the consequences associated with a release of radioactive material 

into the environment. Detailed descriptions of the capabilities of the software used in this 

analysis can be found in Appendix B and the referenced user’s manuals [7-9]. 

The original Peach Bottom Unmitigated LTSBO WinMACCS/MACCS simulation in Section 5.1 

of NUREG/CR-7110 Volume 1 [2] was conducted in November 2010. Since this study, MACCS

code changes have caused the numerical results for the Peach Bottom LTSBO scenario used in 

this study to change. These changes have resulted in changes to the conditional, mean (over 

weather variability), individual LCF risk.
3-2 

The updates in the MACCS graphic user interface from the version used in NUREG/CR-7110 

Volume 1, WinMACCS Version 3.6.2, to the version used for this work, WinMACCS 

Version 3.6.4, deal with expanding the uncertainty engine. The older version of WinMACCS 

was not capable of handling the number of MACCS uncertainty distributions required for this 

study. Also, Version 3.6.2 did not allow certain dose conversion factors (DCFs) to be treated as 

uncertain. The newest version of WinMACCS, Version 3.6.4, has corrected these problems.

The updates to MACCS from the version used in NUREG/CR-7110 Volume 1, MACCS Version 

2.5.0.0, to the version used for this work, MACCS Version 2.5.0.9 deal with the following:

• Provide file locations on MACCS cyclical files (e.g., MELMACCS source term files) to 

provide enhances traceability between inputs and results, 

• Lower plume density limit (PLMDEN) consistent with the MACCS User Manual [9], 

• Change to a FORTRAN compiler compatible with the Windows 7 operating system, and

• Correction of the NRC Regulatory Guide 1.145 plume meander model [10], which is not

used in the SOARCA scenarios. 

A comparison between the two codes for the Peach Bottom unmitigated LTSBO analysis 

presented in NUREG 1935 [1] and NUREG/CR 7110, Volume 1 [2] is presented in Appendix C. 

3.2 Code Integration

A description of the elements and processes (e.g., codes and files) used to implement the 

integrated probabilistic analysis is provided in this section. Figure 3.2-1 shows the information 

flow of the SOARCA Uncertainty Analysis. A description of each item on Figure 3.2-1 is 

described in Appendix B. 

• Uncertain MELCOR and MACCS parameters are sampled

• MELCOR is run for each set of its sampled values

• MACCS is run for each set of its sampled values in conjunction with the associated 

MELCOR source term outputs
3-3 

Figure 3.2-1 Diagram of the information flow of the SOARCA Uncertainty Analysis

3.3 Probabilistic Model Calculation for Uncertainty Analysis

This section outlines the calculation of the simulated source term releases and offsite 

consequences documented in Section 5.0 and used in the uncertainty analysis presented in 

Section 6.0. Appendix A presents the formal derivations for the calculation.

3.3.1 Source Term Uncertainty Calculations

Probability distributions for the selected uncertainty parameters are documented in Section 4.1 

for the source term model calculations. In concept, the probability distributions of analysis 

outcomes over the uncertainty are defined by integrals over the sample space defined by the 

uncertain analysis inputs. In practice, such integrals are too complex and are approximated 

with sampling-based procedures. Latin hypercube sampling (LHS) is usually preferred over 

simple random sampling (SRS) for its potential of producing more stable results using fewer 

samples. However, SRS was chosen for MELCOR calculations as some of the results do not 

converge (addressed in Section 5.1.2). If LHS were employed, distributions of analysis 

outcomes with non-convergence issues would need to account for an input sample set with

stratification that was incomplete. Using the MELCOR uncertainty engine, three replicate 

sample sets using an initial size of 300 using SRS have been generated for the group of 

21 epistemic parameter distributions, using a different random seed for each replicate set. Each 

sample set was used to produce a unique distribution of analysis outcomes using MELCOR. 

Model calculation progresses as described in Section 3.2. A family of source term results is

produced that forms the basis for analysis of the uncertainty in the system. As SRS has been 

used to generate all three samples, it is valid to assemble results from the three separate runs 

into one sample of larger size.
3-4 

3.3.2 Consequence Analysis Calculations

Probability distributions for selected MACCS parameters are documented in Section 4.2 for the 

offsite consequence model calculations. Using the LHS technique in the WinMACCS GUI, a 

sample of size matching the number of converged results for each of the three source term 

replicates has been generated for the set of 596 epistemically uncertain inputs specific to 

MACCS calculation (i.e., all 865 MELCOR source terms have 596 epistemically uncertain 

inputs). For each of the three considered sets, each sample element was paired with a single 

result of the population generated from the source term (MELCOR) analysis. The stratification 

used within LHS to propagate uncertainty in MACCS calculations does not easily allow 

assembling the results from the three separate replicates into a valid larger sample set as can 

be done with SRS. Consequently, a fourth analysis has been performed with an LHS sample 

set equal to the total number of converged source term results for all three replicates combined. 

For each epistemic sample, aleatory uncertainty about the weather was taken into account by 

generating 984 weather trials. Calculations were performed for each of these weather trials to 

construct a family of CCDFs for the corresponding LHS sample set. Model calculation 

progresses as described in Section 3.2. A family of consequence results is thus produced that 

form the basis for analysis of the uncertainty in the system.

3.4 Uncertainty and Sensitivity Analysis

In the last step of a probabilistic approach, results are statistically analyzed (via uncertainty 

analysis) and influence of input parameter uncertainty over the variance of the output is 

assessed (via sensitivity analysis). Such analyses help to draw insights with respect to the 

results. Many techniques have been developed to perform such analyses (several are 

presented in Helton et. al. [11]). The method specifically used in this analysis is presented in 

detail in Appendix A.2.

3.4.1 Uncertainty Analysis: Purpose and Results Generated

Uncertainty analysis refers to the determination of the uncertainty in analysis results that derives 

from uncertainty in analysis inputs. This corresponds essentially to a statistical analysis of the 

output set. Most of the results presented in Section 6 are based on uncertainty analysis, as 

statistics over a range of possible results will give more insights than results from a single 

realization. 

Source term results from MELCOR provide several estimates at each timestep representing the 

(epistemic) uncertainty due to lack of knowledge in the result of interest. These estimates can 

be displayed as time-dependent results as shown in the example on Figure 3.4-1).
3-5 

Figure 3.4-1 Time-dependent results reflecting uncertainty due to lack of knowledge 

(epistemic)

Often, statistics such as mean and quantiles are included in order to give a better visualization 

of this uncertainty and a graphical summary of the uncertainty. The quantiles selected for this 

analysis are q = 0.05, q = 0.5 (median) and q = 0.95.

While the preceding representation shows the time dependence of the results, it does not show

the shape of a distribution of results. A cumulative distribution function (CDF) or complementary 

cumulative distribution function (CCDF) of the sampled result at a selected timestep can be 

more informative. An example is displayed on Figure 3.4-2. The x-axis represents the 

distribution of possible results and is generated by sorting (from smallest to largest) all the 

results from the sample of size N at the selected time (for time-dependent results). The y-axis 

represents the likelihood of being lower or equal (for CDF) or higher (for CCDF) than the value

read on the x-axis. When SRS or LHS is used, the likelihood of the outcome is estimated a 

weight of 1/N and increasing the y-value from this weight, starting from zero (for CDF) or 

decreasing by this weight starting from one (for CCDF). The mean can be added on the curve 

(as a dot for instance) to the CDF or CCDF. Quantiles can be read directly by finding the 

corresponding y-value to the graph, or displayed (for a selected quantile) as a dot over the 

curve. 

In risk analysis, it is traditional to plot CCDFs rather than CDFs as they answer the question 

“how likely it is to have such value or higher”.
3-6 

Figure 3.4-2 Distribution of results presented as a complementary cumulative 

distribution function for a selected time

MACCS results incorporate both aleatory (via consideration of 984 potential weather histories) 

and epistemic (input parameter) uncertainty. The results presented in Sections 5 and 6 

correspond to probability of latent cancer fatality and early fatality. These probabilities are

averaged over aleatory uncertainty (weather histories) and therefore represent expected (mean) 

values over aleatory uncertainty. As a consequence, only the spread and effect of epistemic 

uncertainty will be displayed, using figures similar to Figure 3.4-1 and 3.4-2. 

When low probabilities are estimated, the accuracy of the estimate and its stability may be 

questionable. The stability of results depends on the selected numerical method (e.g., SRS or

LHS) and the parameters used with the method (e.g., sample size, choice of input parameters). 

Stability of the results used in this analysis is assessed in Section 5 using confidence intervals. 

3.4.2 Sensitivity Analysis: Purpose and Results Generated

Sensitivity analysis refers to the determination of the contributions of individual uncertain 

analysis inputs to the uncertainty in analysis results. Rank regression, quadratic regression, 

recursive partitioning, and multivariate adaptive regression splines (MARS) are the four 

regression techniques used in this analysis to estimate the importance of the input parameters 

in the uncertainty of the output in consideration. A short description of each technique follows. 

A more detailed description of the techniques (with examples) can be found in [12] and [13]. 

Rank regression 

Rank regression technique consists of using a rank transformation over the input and output 

variables in consideration. The smallest value of a variable is given a rank of one, the next a 

rank of two and so on up to the largest value having a rank of nS (i.e. sample size). A stepwise 
3-7 

linear regression is then applied to the rank-transformed data. The model is linear and additive, 

in the following form:

YY = aa0 + aa1XX1 + aa2XX2 + ⋯ + aannXXnn + εε = aa0 +�aaiiXXii + εε

nn

ii=1

The stepwise approach starts with trying to find the best fit with only one parameter (testing all 

possible input parameters), then builds up from this by selecting the best fit with two parameters 

conditional on keeping the first parameter and so on. An alpha value is selected as a criterion

below which to stop adding parameters. Rank regression is effective in capturing monotonic 

(increasing or decreasing) relationships between inputs and outputs. Its non-parametric aspect 

makes it less sensitive to outliers. This technique is limited to additive models (no conjoint 

influences are considered) and may perform poorly on non-monotonic relationships. 

Three metrics are included for each input variable in the section of the table used to display rank 

regression results. R2

inc gives the cumulative coefficient of determination of the regression 

model for the variable including all variables in the table identified before. R2

cont. gives the gain 

in R2 due only to the variable. Finally, standardized rank regression coefficients (SRRC) display 

the result of rank regression coefficients, standardized to take out the unit influence. The rank 

regression coefficient is an indication of the strength of the influence: an absolute value close to 

zero means no influence while an absolute value of one represents a very strong influence. The 

rank regression coefficient also indicates the direction (positive or negative) of the influence of 

this input variable on the considered output. A negative sign represents negative influence: high 

values of the input lead to low values of the output and low values of the input lead to high 

values of the output. A positive sign represents positive influence: high values of input lead to 

high values of the output and low values of the input lead to low value of the output.

This is a traditional method used in many past analyses, such as NUREG-1150.

Quadratic regression

Quadratic regression technique applies the same approach as linear regression, including

individual input variables, the square of these variables and second order multiplicative 

interaction terms. The prediction model is of the form:

YY = aa0 + �aaiiXXii

nn

ii=1

+�bbiiXXii

2

nn

ii=1

+� � cciiXXiiXXjj

nn

jj=ii+1

+

nn

ii=1

εε

Quadratic regression is not completely additive as it can capture second order interactions. It 

can also capture the parabolic influence measured by the square of variables in the regression 

model. However, a complex relationship between variables and the output, like asymptotic 

behavior, may still be hard to capture with this technique and the method remains parametric 

which makes it sensitive to outliers. As quadratic regression can capture non-monotonic 

relationships, additional sets of metrics are displayed in the table of regression results from this 

method. Si represents the first order sensitivity index and informs on how much of the variance 

of the selected output is explained by the input parameter in consideration by itself. This index 

is similar to the R2

cont. presented above for the rank regression technique and it is acceptable 

to compare the two metrics. The second metric, labeled Ti represents the total order sensitivity 

index and indicates how much of the variance of the selected output is explained by the input 

parameter alone and how much by its interaction with the other uncertain parameters. It has no 

equivalent in the rank regression model (as the additive model does not capture conjoint 
3-8 

influences). The difference between Ti and Si gives an estimate of the conjoint influence for this 

input on the output considered. Finally, a p-value is displayed as third metric, representing the 

probability that the hypothesis Ti = 0 is true, meaning that the parameter has no influence at all. 

A p-value equal or close to zero indicates that the hypothesis is false and therefore, the 

influence is likely to be true in the mathematical sense. It can still be unrealistic physically and 

due to the particularity of the sample. A p-value equal or close to one indicates a relationship

that is not real and is due to a spurious correlation.

Recursive partitioning

Recursive partitioning regression is also known as a regression tree. A regression tree splits

the data into subgroups in each of which the values are relatively homogeneous in. The 

regression function is constructed using the sample mean of each subgroup. This approach, 

results in a piecewise constant function over the input space in consideration. Recursive 

partitioning handles conjoint influences. The predictive model is:

YY = �(ddssIIss(XXii))ii=1,...,nn

nnnn

ss=1

+ εε

The same metrics used for quadratic regression are used for recursive partitioning, that is to say 

the first order sensitivity indices (Si), total order sensitivity indices (Ti) and p-values.

Multivariate Adaptive Regression Splines (MARS)

MARS is a combination of (linear) spline regression, stepwise model fitting and recursive 

partitioning. A regression with a single input starts with a mean only model and adds basis 

functions in a stepwise manner adding the overall linear trend first. A second model using linear 

regression via least squares is fit to the data. This model is then added to the basis functions in 

a way that reduces the sum of square error (SSE) between observation and prediction. A fourth 

basis function is then added to minimize the SSE again. This process is repeated until M basis 

functions have been added.

At this point, the MARS procedure will try to simplify the model using stepwise deletion of basis 

functions, while keeping the y-intercept and linear trend. The M-2 candidate leading to the 

smallest increase of SSE will be selected. This deletion will be applied until regressed to the 

original linear model.

Stepwise addition and deletion leads to the building of two different M-2 different models. The 

“best” model is chosen using a generalized cross validation (GCV) score which corresponds to 

a SSE normalized by the number of basis functions considered. With multiple inputs, the basis 

functions will consider main effects and multiple-way interactions. The options used for this 

analysis consider only two-way interactions to avoid the exponential cost of considering more 

interactions. MARS are presented using the same metrics as quadratic regression and recursive 

partitioning in the summary tables. 
4-1 

4. UNCERTAIN INPUT PARAMETERS AND DISTRIBUTIONS

Sections 4.1 and 4.2 provide the technical basis and justification for parameters included as 

uncertain inputs for the SOARCA Peach Bottom unmitigated LTSBO Uncertainty Analysis. The

uncertain parameters and their distributions were identified/characterized through an informal 

elicitation of subject matter experts. The subject matter experts were asked to define 

distributions for the parameters which they considered most important in describing the 

uncertainty around the SOARCA analysis. In addition, the uncertain parameters and 

distributions were presented to and evaluated by the independent SOARCA peer review panel. 

The SOARCA Peer Review Panel agreed with the basic methods and provided comments on 

the selected parameters and distributions. The parameters and distributions were revised to 

address these concerns. A discussion of the uncertain parameters and distributions are 

contained in Sections 4.1 and 4.2 for the source term model and consequence model 

parameters uncertainty, respectively.

The general approach taken in defining the scope of the SOARCA uncertainty quantification is 

to attain a balanced depth and breadth of coverage so as to obtain contributions from 

uncertainty across the spectrum of phenomena operative in the analyses without excessive 

detail dedicated to any particular regime of phenomenon. Both MELCOR and MACCS permit 

extensive access to parameters that may be uncertain, but for practical reasons, a judiciously 

selected subset of possible uncertain parameters is proposed that covers the range of 

phenomena across the stages of a severe accident.

A variety of distribution shapes are chosen to reflect experts’ degree of belief in different values 

for the uncertain parameters. This uncertainty study began with parameter values anchored to 

the estimates used in the SOARCA study. The team then took a consensus approach to 

constructing distributions around the SOARCA estimates. For those parameters where the 

team assessed that values other than the SOARCA estimate were less likely, a probability 

density function was chosen to reflect a peak at the mode – for example, a triangular or normal 

shape. If the parameters’ range spanned multiple orders of magnitude, a log scale was chosen 

for the distribution. Or if the parameter was thought to be equally likely to be x times the 

SOARCA estimate or 1/x times the SOARCA estimate, a log scale was chosen. In some cases, 

as described in Section 4.2, the distributions are based on a prior expert elicitation, or a 

methodology described in FGR-13 for health effect parameters.

4.1 Source Term Model Uncertainty (MELCOR Inputs)

The MELCOR uncertain parameters are selected to cover the following issues and 

phenomenological areas: 

• sequence issues

• in-vessel accident progression issues

• ex-vessel accident progression issues

• containment behavior issues

• fission product release, transport, and deposition

These broad areas span the temporal domain of the severe accident progression ranging from 

minor sequence variations as affected by SRV behavior, to uncertainties in the core damage 

and melt progressions, especially those affecting rate of core degradation and amount of 

hydrogen generation. Hydrogen production provides an indication of fission product release 

from the fuel, since hydrogen generation is an indicator of cladding oxidation which is an 

indicator that fuel temperatures are rising above 1500 K. This is the temperature range where 

thermally driven release of the volatile fission products, cesium, iodine, and tellurium, occurs. 
4-2 

Source term release behavior in terms of the rate and total amount released in-vessel is 

strongly coupled to in-vessel melt progression behavior owing to the strong temperature 

dependence of fission product release. The onset of volatile fission product release is set by 

the time that fuel is heated to a temperature above about 1500 K (about 1227°C), and this is 

tightly coupled to cladding oxidation rate. Total release of both volatile and less volatile species 

is affected by the time at which fuel remains at elevated temperatures and the state of the fuel 

(rods or debris). Therefore, many of the parameters that affect cladding oxidation and hydrogen 

generation also affect fission product release. Other parameters more specific to fission product 

transport include deposition processes (e.g., chemisorption or hygroscopicity) and settling 

processes (agglomeration shape factors for example). Speciation of cesium and iodine affects 

the volatility of cesium and consequently affects both release and revaporization. The 

parameters selected in the study were considered in terms of both melt progression and fission 

product release and transport. This includes important phenomena taking place following 

vessel lower head melt-through such as melt attack of the drywell liner, containment behavior 

issues, such as uncertainty in onset of drywell head flange leakage, and uncertainties in 

radioactive aerosol transport mechanics. The selection of uncertain parameters ensures a 

commensurate representation of uncertainties in the major phases of the accident evolution. 

Each uncertain parameter, together with the rationale for the range and shape of the uncertainty 

distribution are described in the following sections. All other MELCOR parameters not 

discussed in this section (e.g., eutectic liquefaction temperature for ZrO2/UO2) remain the 

original point estimates used in NUREG/CR-7110, Volume 1.

Additional discussions on certain MELCOR parameters presented are discussed in Appendix E. 

4.1.1 Sequence Issues 

Uncertainty in safety relief valve stochastic failure to reclose (SRVLAM)

One concern regarding the timing of the accident sequence is when the depressurization of the 

reactor coolant system (RCS) occurs. As part of the SOARCA project, the RCS depressurizes 

resulting from the failure of a SRV. The MELCOR model is setup to cause the SRVs to open at 

predetermined pressures and specified flow rates. The SRVs will close when pressure drops 

below 96 percent (%) of their opening pressure. This model sets the SRVs to fail to close based 

on a per-demand failure probability. 

The SOARCA value was cited in the Peach Bottom Individual Plant Examination (IPE) of 

λ = 3.7 × 10-3 per demand [2] or 1/λ = 270 valve cycles. In addition, the Peach Bottom IPE 

considered a failure rate per-demand probability multiplied by a factor of eight to account for the 

fact that the valve was operating under extreme environmental conditions (e.g., λ = 2.96 × 10-2

per demand or approximately 34 valve cycles). 

Recent assessments of component reliability in nuclear systems suggest an SRV failure to 

close (FTC) frequency may be smaller than the SOARCA value cited in the Peach Bottom IPE. 

An NRC analysis of industry-average data for SRV FTC performance was documented in two 

reports: NUREG/CR-6928 [14] and NUREG/CR-7037 [15]. NUREG/CR-6928 computed an 

estimated per demand failure probability e described in Table 5-1 (SRV FTC - SRV failure to 

close) with a mean value of λ = 7.95 × 10-4 per demand (1,258 cycles) with 5th and 

95th percentile values of 3.13 × 10-6 and 3.05 × 10-3 per demand, respectively. NUREG/CR7037 provides updated failure data for BWR SRVs, depending on their operating mode. The 

operating mode of interest for SOARCA is the “pressure mode,” where the SRVs are actuated 

via a pilot sensing port that is internal to the valve (not the air actuator). NUREG/CR-7037 

reports a mean value of λ = 1.39 × 10-2/demand (72 cycles) with 5th and 95th percentile values of 

4.43 × 10-5 and 5.39 × 10-2/demand, respectively [15, Table B-7]. However, when all the data 
4-3 

are considered, the NUREG/CR-7037 approach computed a mean value of 

λ = 7.07 × 10-4/demand (1,414 cycles) with 5th and 95th percentile values of 2.75 × 10-6 and 

2.7× 10-3/demand, respectively [15, Table B-7], very similar to the reported value from 

NUREG/CR-6928. 

Significant reductions in the observed rate of spurious valve opening were achieved by various 

modifications to the Target Rock SRV through a BWR Owner’s Group initiative coordinated 

under Generic Safety issue B-55. The extent to which these modifications would also affect the 

expected failure rates of SRV FTC is not known. However, this might contribute to the 

difference in the current (NRC) estimated failure rates of SRV FTC and the older (circa 1990) 

failure rate reflected in the Peach Bottom IPE. 

It should be noted, however, that the failure rate reflected in the generic data base and the value 

obtained from the Peach Bottom IPE are conceptually different from the situation modeled here. 

In simple terms, the rate at which an SRV fails to reclose is calculated by dividing the number of 

observed valve failures (to reclose) by the number of valve demands. This ratio, therefore, 

reflects the conditional probability that a valve would fail to reclose, given a successful demand 

to open. However, the failure events that represent the numerator of this ratio occurred after 

only a few valve cycles. The precise number is difficult to determine from the raw data 

documented in the NUREG/CRs. However, it is clear that valve failure data after numerous 

cycles are extremely rare (perhaps non-existent) primarily because events involving numerous, 

continuous valve cycling are not observed. It is, therefore, debatable whether the failure rate 

used to calculate the (low) probability of failure to reclose after a few cycles should be 

extrapolated to estimate the (higher) probability of failure after a large number of cycles. Other 

unknown failure mechanisms would likely overwhelm those that lie behind the nominal failure 

rate. This qualitative observation is consistent with the opinion expressed by members of the 

peer review panel that the valve failure rates obtained from the PRA database are too low (e.g., 

predict a high number of cycles before failure). However, it should be noted that comments 

provided by the licensee on the NUREG/CR-7110, Volume 1 indicated the early failure rate 

reported in their IPE was not based on plant-specific performance data, and they have since 

replaced this value with the industry value reported in NUREG/CR-6928. 

A beta distribution, listed in Table 4.1-1, and used for this analysis was fit for the mean value 

from the Peach Bottom IPE (the SOARCA value) using the methodology in NUREG/CR-7037. 

For comparison, Figure 4.1-1 plots the CDF for the Peach Bottom IPE derived beta distributions 

with the NUREG/CR distributions. Qualitatively, the Peach Bottom IPE derived distribution falls 

within the middle of the set of CDFs. Quantitatively, it is clear from the SOARCA results values 

above 5 × 10-2 and below 9 × 10-4 per demand will either fail before the batteries are depleted or 

after SRV will fail from thermal seizure and/or main steam line creep rupture, respectively. The 

Peach Bottom IPE derived beta distribution covers the range of values that are needed to define 

the parametric relationship between the probability that the SRV will fail to close and the severe 

accident. 
4-4 

Figure 4.1-1 Cumulative distribution function of safety relief valve failure to close valve 

cycle (λ = per demand failure probability (1/λ = number of SRV demands)) 

Duration of direct current power (BATTDUR)

DC power is maintained by DC batteries during a SBO. The DC batteries are used to provide 

power to the DC electrical buses for minimum electrical loading to monitor instrumentation in the 

control room. Without DC power, none of the control room instrumentation is available, and 

thus, there is no indication of plant status. Uncertainty in the duration of DC power is influenced 

by the efficiency of operator actions to shed non-essential loads and the age of the batteries. A 

log triangular distribution was selected for BATTDUR with a mode of 4.0 hours, the value used 

in the deterministic SOARCA analysis, and 2.0 and 8.0 hours for the lower and upper bounds, 

respectively (Figure 4.1-2 and Table 4.1-1).

The licensee’s PRA uses a value of two hours, which is the minimum duration required by plant 

technical specifications and represents the worst possible condition. The licensee’s engineering 

judgment is that batteries can last four hours with effective DC load shedding. The upper bound 

of eight hours was selected because the licensee recommended a lower value than what was 

selected in the past studies (i.e., NUREG-1150 [16]) which assumed 10 to 12 hour battery life 

with sufficient load shedding) as there is concern with the ability or requirements necessary to 

demonstrate a capacity for that long.
4-5 

Figure 4.1-2 Cumulative distribution function of duration of direct current power

Table 4.1-1 MELCOR uncertain parameters—sequences issues

Parameter Distribution

SRVLAM: lambda for SRV stochastic failure 

to reclose (per demand)

Beta distribution

Mean = 3.7×10-3

Alpha = 0.494

Beta = 133.2

LB = 0.0

UB = 1.0

SOARCA estimate: 3.7 × 10−3

BATTDUR: Duration of direct current power

(hours)

Log Triangle distribution

LB = 2.0 hr.

Mode = 4.0 hr.

UB = 8.0 hr.

SOARCA estimate: 4.0 hrs.
4-6 

4.1.2 In-Vessel Accident Progression Issues

Zircaloy melt breakout temperature (SC1131(2))

The core melt progression modeling options have been set to be consistent with current 

best-practices guidelines, which are generally default models [17]. As the fuel temperature 

increases, an oxide shell forms on the outer surface of the fuel cladding. Since the oxide shell 

has a higher melting temperature than the unoxidized zircaloy inside the fuel rod, the zircaloy on 

the interior of the cladding will become molten once the temperature rises above the melting 

temperature (Figure 4.1-3). This zircaloy melt breakout temperature represents the uncertain 

properties that determine the conditions at which oxidized clad mechanically fails, releasing 

molten unoxidized zircaloy. This initiates the downward drainage of molten zircaloy on a 

ring-by-ring basis in the MELCOR analysis. Based on prior work on in-vessel melt progression 

[18], this parameter is expected to be among the more important uncertain parameters. As 

described in the previous studies [18], at the "breakout temperature" oxidizing molten zircaloy is 

relocated to cooler regions at a time when the oxidation rate is at its peak value. Fuel 

temperatures are increasing rapidly (~10K/s) at this time, hydrogen generation is locally at a 

maximum, and fission product release rates are large. The relocation of the oxidizing melt has 

the effect of terminating the intense local fuel heating, since the chemical heating source has 

relocated to a cooler region of the vessel. This should affect release rate for volatile fission 

products and total localized releases of low-volatile species. The lower bound value is the 

zircaloy melting temperature of 2100 K. The value of 2100 K also corresponds to fragile outer 

oxide shells that are incapable of retaining molten zircaloy. The upper bound value is based on 

likely rod collapse temperature occurring within 15 minutes. The upper value of 2540 K, was 

selected in the original hydrogen uncertainty study [18] based on qualitative consideration of the 

alpha-Zr(O) phase diagram and observations/analyses of the Phebus experiments [19-23]. The 

mode is the value used in the deterministic SOARCA analysis (Figure 4.1-4 and Table 4.1-3). 

The selection of a triangle distribution suggests that a most probable value for the uncertain 

parameter is recommended (mode), with decreasing likelihood for values away from the most 

probable. This is in contrast to a range-bounded uniform distribution, where it is implied that 

any value lying within a range is equally probable. 
4-7 

Figure 4.1-3 Depiction of the fuel rod degradation

Based on observations from Phebus tests [19-23], MELCOR includes a molten zircaloy 

breakout model of the loss of structural integrity of the oxidized zircaloy. Following the 

relocation of the molten Zircaloy, the oxidation ceases and the fuel rods remain intact based on 

the thermal response of the system which is largely governed by decay heat loss and perhaps 

relocating molten material from above. Subsequently, the fuel rods are only supported by a 

relatively thin oxide structure that can weaken at high temperatures. The calculated failure 

mechanisms include:

• failure due to melting the oxidized shell, or 

• failure of the supporting fuel rods (collapse of the fuel rods will result in fracture of the 

melt-retaining oxide shell), and 

• a time-at-temperature model that calculates the failure of the oxidized zircaloy shell 

holding the fuel rods. 

The time-at-temperature model includes a thermal-mechanical weakening of the oxide shell as 

a function of temperature. As the temperature rises above zircaloy melting temperature 

(i.e., represented as 2098 K in MELCOR) towards 2500 K, a thermal lifetime function linearly 

accrues cladding damage and predicts time to local thermal-mechanical failure (Table 4.1-2). 
4-8 

Table 4.1-2 Time versus temperature relationship for intact fuel rod collapse

Temperature Time to Failure

2000 K 

2090 K 

2100 K 

2500 K 

2600 K 

2700 K 

Infinite

10 days

10 hours

1 hour

5 minutes

30 seconds

Figure 4.1-4 Cumulative distribution function of zircaloy melt breakout temperature

Molten clad drainage rate (SC1141(2))

Time constant for heat transfer to substrate material versus downward molten flow is another 

factor that influences uncertainty in the source term release model. The molten clad drainage 

rate impacts material relocation from the top of active fuel to the bottom of active fuel. This 

parameter (SC11412) represents effective downward flow rate of the molten fuel, balancing 

heat transfer and freezing on substrate against vertical momentum and, therefore, affects the 

overall melt progression behavior. It is one of the few MELCOR melt progression parameters 
4-9 

available for variation. A log triangular distribution is used for the molten clad drainage rate 

(SC1141(2)) with a mode of 0.2 kg/m-s used in the deterministic SOARCA analysis, and 0.1 and 

1.0 kg/m-s respectively for the lower and upper bounds (Figure 4.1-5 and Table 4.1-3). The 

selection of a triangular distribution suggests that a most probable value for the uncertain 

parameter is recommended (mode), with decreasing likelihood for values away from the most 

probable. 

The lower and upper bounds of the distribution represent an order of magnitude of uncertainty. 

This was selected based upon previous studies [18] to ensure the behavior was appropriately 

captured in the uncertainty in this parameter. 

Figure 4.1-5 Cumulative distribution function of molten clad drainage rate 

Criteria for thermal seizure of safety relief valve due to heating after onset of core 

damage [SRVFAILT]

One concern regarding the timing of the accident sequence is the depressurization of the RCS. 

As part of the SOARCA project, the RCS depressurizes resulting from the failure of a SRV to 

close. In the MELCOR SOARCA, model SRVs open at predetermined pressures and specified 

flow rates. The SRVs will close when pressure drops below 96% of their opening pressure. In 

addition, to the stochastic failure to close (SRVLAM), the SRVs fail to close by thermal seizure if 

a specified temperature limit is exceeded [2]. 

For the gas exposure time during open cycles, heat conduction within a valve, and expansion of 

valve components, the MELCOR model estimates the thermal response of a representative 

valve internal component (perhaps the valve stem) as a solid steel cylinder, heated by the gas 
4-10

discharged through the valve when open. The valve is assumed to seize in the open position

(failure to reclose) on the first cycle above a specified component temperature. Model 

uncertainty in valve thermal response, expansion, and seizure is represented by the component 

temperature limit for thermal seizure. For the uncertainty analysis, a beta distribution was 

selected with the mean at 900 K, which is the value used in the deterministic SOARCA 

analysis [2], and 811 K and 1143 K selected for the lower and upper bounds respectively

(Figure 4.1-6 and Table 4.1-3).

An evaluation of thermal seizure of the SRV was included in NUREG/CR-7110, Volume 1, 

Sections 4.4.1 and 4.4.2. An initial criterion for high-temperature valve failure was based on 

manufacturers’ information describing the strength of stainless steel, published by the Stainless 

Steel Information Center (www.ssina.com/composition/temperature.html). Softening or loss of 

strength of stainless steel (300 series) was described to start to occur at “about 1000°F” 

(811 K). This data provides the lower bound for the distribution. The NUREG/CR-7110 

evaluation included differential thermal expansion, effects of temperature gradients, and 

material deformation as the basis for the SOARCA value of 900 K used in the uncertainty 

analysis as the mean of the distribution. A supplemental analysis conducted by the U.S 

NRC [24], independently validated the findings in the NUREG/CR-7110 report for Peach 

Bottom. The letter report evaluated the two analyses presented in NUREG/CR-7110 Volume 1 

that address thermal effects on valve reliability and performance. In the first analysis, thermal 

expansion is calculated due to differences in properties between the valve guide and stem 

materials, and an additional term is added that addresses the fact that the stem experiences a 

greater heat-up than the larger valve body. The result of these calculations presented in the 

NUREG/CR-7110 report gives a total stem to guide gap reduction over time corresponding to a 

MSL temperature of 811 K, which was close to the range of times and MSL temperatures 

calculated independently by Rathbun, 2011 [24]. 

In the second thermal analysis included in NUREG/CR-7110, the effect of strength degradation 

of the valve stem material is analyzed. Based on strength reduction at elevated temperatures, 

an estimate of 900 K is estimated as the temperature at which the stainless steel stem will 

degrade to the point where the valve will fail. The 900 K valve stem temperature corresponds to 

a MSL temperature of approximately 950 K. No direct comparison with the 900 K material 

failure criterion in NUREG/CR-7110 Volume 1 was made in the Rathbun [24] analyses. 

However, the corresponding steam line temperature of 950 K was somewhat higher than the 

highest steam line temperature at failure (900 K) calculated in the Rathbun report [24]. This 

temperature difference has been encompassed within the standard deviation of the distribution 

for thermal seizure temperature used in the uncertainty analysis. 

Sensitivity studies in NUREG/CR-7110 Volume 1 [2], determined that valve stem temperatures 

greater than 1175 K satisfied the conditions necessary for MSL creep rupture. The temperature 

at which material deformation occurs is lower than the value used in the early SOARCA 

calculations (i.e., 1000 K) [2]. This value was selected primarily to reflect the ‘service 

temperature’ for stainless steel components, as reported by the steel industry trade association. 

A review of vendor literature on material properties of 304 stainless steel clearly indicates the 

maximum service temperature of approximately 870°C (~1143 K) is based on the scaling 

properties (or resistance to corrosion) of 300 series stainless steel, rather than its mechanical 

properties. Given that material deformation would be expected at the hot working temperature 

of 304 stainless steel, between 1149-1260°C [25], an upper bound limit for plastic deformation is

based on the vendor recommended service temperature of 1143 K. This upper bound is further 

supported by Rathbun [24] analyses that suggest failure by thermal expansion of moving valve 

components would occur at temperatures below 870°C (~1143 K). 
4-11

Figure 4.1-6 Cumulative distribution function of criteria for thermal seizure of safety 

relief valve due to heating after onset of core damage

Safety relief valve open area fraction after thermal seizure (SRVOAFRAC)

The timing of the accident sequence is dependent upon when the depressurization of the RCS 

occurs. The RCS depressurizes because of failure of a SRV to close. During normal 

operations, the SRVs open at predetermined pressures and specified flow rates. The SRVs will 

close when pressure drops below 96% of their opening pressure unless the SRVs fail to close 

based on high temperature conditions within the SRV as described in the previous section. 

However, thermal expansion of the SRV would occur primarily during periods of gas flow (open 

cycles), although penetration (conduction) of heat transferred to inner surfaces would occur over 

a longer period of time (valve open or closed). This behavior leads to uncertainty in the valve 

position immediately prior to seizure and to the final stem position after seizure and thus the 

open area for releases from the SRV. In addition, sensitivity studies in NUREG/CR-7110 

Volume 1, determined that a valve open fraction of 10% of the nominal flow area satisfied the 

conditions necessary for MSL creep rupture. 

A fraction of 1.0 was used as the value in the deterministic SOARCA analysis [2]. Since there is 

no data available to predict the uncertainty within the SRV position at the time the SRV sticks 

open from thermal seizure, a triangle distribution between 0.1 and 1.0 (fully open) with a mode 

of 1.0 was investigated to measure the potential effects of this event on accident progression 

and source term releases (Figure 4.1-7 and Table 4.1-3). This distribution was selected to skew 

to higher values because the geometry of the SRV is such that it does not have to vertically 

traverse much of its shaft length before reaching an open area close to fully open. 
4-12

Figure 4.1-7 Cumulative distribution function of safety relief valve open area fraction 

after thermal seizure

Main steam line creep rupture area fraction (SLCRFRAC)

Creep rupture is monitored at two locations (i.e., MSL nozzle and MSL piping). This parameter 

represents the size of the opening that would be generated at either location if creep failure 

occurs. The potential for creep failure is calculated using a standard Larson-Miller (L-M)

formulation, identical in structure to the one used in MELCOR PWR calculations of hot leg and 

pressurizer surge line failure. Uncertainties in the L-M model itself are not considered here, in 

part, due to the observation from past calculations that the transition from zero damage to creep 

appears to occur too fast for reasonable variations in the L-M parameter to have a significant 

effect on the time that creep failure occurs. 

Factors that contribute to uncertainty in the size of the opening generated by creep rupture of a 

BWR MSL include: the possibility of pre-existing flaws in weld locations, upper RPV and steam 

line circulation flow patterns, multi-dimensional effects of heat transfer to MSL piping, and the 

impact of pipe restraints on piping mechanical response. 

The MELCOR model preserves the total flow area of the MSL, but partitions this area between 

the intact pipe and the rupture opening. Therefore, a rupture open fraction of 1.0 closes flow 

through the MSL, and replaces it with an opening to the drywell with an equivalent area. A

value of 0.5 partitions the MSL flow equally between the intact pipe flow path and the rupture 

flow path. Therefore, the creep rupture open fraction is the numerical complement of the MSL

open fraction. Sensitivity studies in NUREG/CR-7110 Volume 1, using the SOARCA Peach 
4-13

Bottom case, involving creep rupture of the MSL assumed the structural response of the MSL is 

a fully offset, guillotine break of one MSL (i.e., open fraction of 1.0). This was considered a 

conservative assumption because the large break area maximizes the hydrodynamic load to the 

containment pressure boundary and facilitates fission product transport from the RCS. 

Alternative credible responses, such as a smaller crack or fissure in the MSL were not 

considered in these sensitivity calculations. A piecewise uniform distribution between 0.0 and 

1.0 is used in this analysis to measure the potential effects of this event on accident progression 

and source term releases (Figure 4.1-8 and Table 4.1-3). This distribution was selected based 

upon expert judgment and Peer Review feedback, and based on findings of experimental work 

and analysis for PWR hot leg creep rupture [26]. Some expert judgment was used to adapt the 

PWR hot leg analysis to the BWR MSL and generate the distribution shape, which was the 

numerical way of reflecting the study’s conclusion of a strong bias toward a full-open area. 

Note, the intent of the distribution is to open the MSL to the containment through an area 

equivalent to the full cross-sectional area of the pipe for 85% of the realizations. However, the 

means through which the MSL rupture is accomplished in the MELCOR model (i.e., adjusting 

the flow area of three junctions) leads to an effective break area equal to the full area of the pipe 

for any value of SLCFRAC greater than or equal to 0.5. So, the MSL will actually open fully to 

containment 96% of the time in this analysis, which is slightly more than was intended. 

Figure 4.1-8 Cumulative distribution function of main steam line creep rupture area
4-14

Fuel failure criterion (transformation of intact fuel to particulate debris) (FFC)

MELCOR lacks a deterministic model for evaluating fuel mechanical response to the effects of 

clad oxidation, material interactions (i.e., eutectic formation), zircaloy melting, fuel swelling and 

other processes that occur at very high temperatures. In lieu of detailed models in these areas 

a simple temperature-based criterion is used to define the threshold beyond which normal 

("intact") fuel rod geometry can no longer be maintained, and the core materials at a particular 

location collapse into particulate debris. The temperature-based criterion incorporates 

uncertainties in numerous physico-chemical processes that affect fuel rod integrity. The 

"time-at-temperature" criterion is the time endurance of the upright, cylindrical configuration of 

fuel rod bundles which decreases with increasing temperature. A temperature-based 

'cumulative damage' criterion is used in the MELCOR model to define the remaining lifetime of 

normal fuel rod geometry (Table 4.1-2). The alternative functions represent shifts in 

temperature of +/- 100 K and fuel endurance times of +/- factor of 2.0 (Figure 4.1-9, 

Figure 4.1-10 and Table 4.1-3). The fuel failure criterion distribution is qualitative in nature, but 

based on observations from testing such as Phebus facility tests [19-23], accounting for scale 

effects (small bundles are inherently more stable and less fragile than full length fuel 

assemblies). This approach is considered the best effort at evaluating the importance of this

uncertain parameter. In part the nature of the treatment (time at temperature) is intended to 

avoid non-physical cliff-edge effects that are observed during a calculation when fuel 

temperatures are predicted to hover just below a failure temperature.

Alternative one is derived from the SOARCA estimate by reducing its temperatures by 100 K 

and dividing its time intervals by two. Alternative two is derived from the SOARCA estimate by 

increasing its temperatures by 100 K and multiplying its time intervals by two. The code/model 

then uses the selected table to determine, based on the fuel temperature, the reduction in fuel 

lifetime; and when fuel lifetime is exceeded, the fuel is failed. 
4-15

Figure 4.1-9 Probability density function of fuel failure criterion alternatives

(transformation of intact fuel to particulate debris) 

Figure 4.1-10 Fuel failure criterion functions
4-16

Radial debris relocation time constants (RDMTC, RDSTC) 

The relocation time constant controls the rate of movement of radial molten (RDMTC) and solid 

debris (RDSTC) to the center of the core, and thus the time it takes the debris to move to the 

lower plenum. This specific parameter is used as a surrogate for the broad uncertainty of debris 

relocation rate into water in the lower head. This, in turn, affects the potential for debris 

coolability in the lower head (faster relocation rates decrease coolability; slower rates improve 

coolability). Debris relocation in MELCOR occurs when the lower core plate in a ring yields. 

Molten material and particulate debris from the ring immediately moves towards the center of 

the core and fall into the lower head. The rate at which this debris and debris from adjacent 

rings relocates into the lower head is determined by the radial relocation time constant. Thus, 

adjustments in this parameter affect the overall rate at which debris enters the lower head after 

support plate failure (Figure 4.1-11 (a and b) and Table 4.1-3).

This parameter is only one of a few MELCOR parameters which can be modified to influence 

large scale movement, and thus is a key parameter to core melt progression and ultimately 

source term releases. The distributions are based on expert judgment and are not based on 

any specific data as no data exists for radial debris relocation. Additionally, the radial debris 

relocation time constant influences the axial debris relocation. Like the fuel failure criterion

discussed previously, this parameter is qualitative and is a surrogate for more complex 

relocation processes. Phebus facility tests [19-23] offer no insights here as the scale of the 

testing is too small to provide insights. The parameter ensures that debris does not pile up 

within single radial rings in an unphysical manner. The exact rate of effective relocation is not 

known. The values used are felt to bound possible behavior of leveling of materials that may be 

solid debris, partly molten two phase debris or fully molten.

Exponential time constants for molten debris relocation and solid particulate debris relocation 

control the rate of relocation of core material. For the uncertainty analysis, a log triangular 

distribution was selected for both the molten and solid radial relocation time constants. For solid 

debris, the mode = 360 s, which is the value used in the deterministic SOARCA analysis, and 

180 and 720 s are selected for the lower and upper bounds respectively (Figure 4.1-11a and 

Table 4.1-3). A factor of two variation in the SOARCA value was used to investigate the 

sensitivity of the analysis results to uncertainty in this parameter. For molten debris the 

mode = 60 s, which is the value used in the deterministic SOARCA analysis, and 30 s and 120 s 

are selected for the lower and upper bounds respectively (Figure 4.1-11b and Table 4.1-3). 
4-17

Figure 4.1-11 Cumulative distribution of radial debris relocation time constants: 

(a) solid debris and (b) liquid debris
4-18

Table 4.1-3 MELCOR uncertain parameters—In-Vessel accident progression issues

Parameter Distribution

SC1131(2): Zircaloy melt breakout temperature (k)) 

Triangle distribution

LB = 2098 K

mode = 2400 K

UB = 2550 K

SOARCA estimate = 2400 K 

SC1141(2): Molten clad drainage rate (kg/m-s)

Log Triangle distribution

LB = 0.1 kg/m-s 

mode = 0.2 kg/m-s 

UB = 1.0 kg/m-s 

SOARCA estimate = 0.2 kg/m-s 

SRVFAILT: Criteria for thermal seizure of SRV due to 

heating after onset of core damage (K)

Beta distribution

Mean = 900 K

Alpha = 2.72

Beta = 6.79

LB = 811 K

UB = 1143 K

SOARCA estimate = 900 K 

SRVOAFRAC: SRV open area fraction after thermal 

seizure

Log Uniform distribution

LB = 0.05 

UB = 1.0

SOARCA estimate = 1.0

SLCRFRAC: Main steam line creep rupture area fraction

Piecewise Uniform distribution

weight SLCRFRAC

0.5 5.00 × 10−2

0.5 1.00 × 10−1

1 2.00 × 10−1

1 3.00 × 10−1

1 4.00 × 10−1

1 5.00 × 10−1

1 6.00 × 10−1

1 7.00 × 10−1

3 8.00 × 10−1

5 9.00 × 10−1

85 1.00

SOARCA estimate = 1.0

FFC: Fuel failure criterion (transformation of intact fuel to 

particulate debris)

Discrete distribution

SOARCA model = 0.8

alternate-1 = 0.1

alternate-2 = 0.1
4-19

Table 4.1-3 MELCOR uncertain parameters—In-Vessel accident progression issues

(continued)

Parameters Distribution

FFC: Fuel failure criterion function (SOARCA value) 

Discrete distribution

T [K] Time [s]

2090.0 6.00 × 1031

2100.0 3.60 × 104

2500.0 3.60 × 103

2600.0 3.00 × 102

FFC: Fuel failure criterion function (Alternative one)

Discrete distribution

T [K] Time [s]

1990.0 6.00 × 1031

2000.0 1.80 × 104

2400.0 1.80 × 103

2500.0 1.50 × 102

FFC: Fuel failure criterion function (Alternative two)

Discrete distribution

T [K] Time [s]

2190.0 6.00 × 1031

2200.0 7.20 × 104

2600.0 7.20 × 103

2700.0 6.00 × 102

RDSTC: Radial debris relocation time constant

(Solid debris)

Log Triangle distribution

LB = 180 s

mode = 360 s

UB = 720 s

SOARCA estimate = 360 s

RDMTC: Radial debris relocation time constant

(Molten debris)

Log Triangle distribution

LB = 30 s

mode = 60 s

UB = 120 s

SOARCA estimate = 60 s 

4.1.3 Ex-Vessel Accident Progression Issues

Debris lateral relocation— cavity spillover criteria and spreading rate (DHEADLIQ, 

DHEADSOL)

The dominant mechanism of containment failure in accident sequences involving the drywell

floor, such as the LTSBO, is thermal failure (melting) of the drywell liner following contact with 

molten core debris (i.e., drywell liner melt-through). Containment failure by this mechanism 

occurs after debris is released from the reactor vessel lower head and flows out of the reactor 

pedestal onto the main drywell floor. If a sufficiently large quantity of debris accumulates in the 

pedestal, it can flow out of the pedestal through a large doorway in the concrete pedestal wall. 

If the debris temperatures remain sufficiently high as it spreads across the drywell floor and 

contacts the drywell liner, the liner would melt and fail. The precise conditions under which core 

debris would flow out of the pedestal and across the drywell floor are uncertain. These 

uncertainties are adequately captured by assuming debris mobility and the potential for liner 

failure are represented by two key parameters: debris mass (i.e., static head) necessary for 

lateral flow and debris temperature (which characterizes debris rheological properties and 

internal energy available to challenge the liner).
4-20

The drywell floor is subdivided into three regions for the purposes of modeling 

molten-core/concrete interactions in the MELCOR model. The first region, which receives core 

debris exiting the reactor vessel, corresponds to the reactor pedestal floor and sump areas 

(CAV 0). Debris that accumulates in CAV 0 can flow out through a doorway in the pedestal 

wall 8 to a second region representing a 90-degree sector of the drywell floor (CAV 1). If debris 

accumulates in this region to a sufficient depth, it can spread further around the annular drywell

floor into the third region (CAV2). This discrete representation of debris spreading is illustrated 

on Figure 4.1-12. 

Figure 4.1-12 Drywell floor regions

 

8 Although the drawing provided by the licensee seems to indicate the presence of a swing-door in the personnel 

opening at the base of the reactor pedestal, the analysis described here assumes this door does not actually exist. 

Years of research on the issue of drywell liner melt-through never acknowledged the presence of a door (e.g., 

NUREG/CR-5423 and NUREG/CR-6025). It is noted in the introduction to NUREG/CR-5423 that the geometry of 

the Peach Bottom configuration was used as the template for the analysis. The flow of debris from the pedestal 

onto the outer drywell floor would not be impeded in any way by an obstacle in the concrete ‘doorway’ in the 

pedestal wall. As a result, the current SOARCA analysis applied the same rationale and assumed molten debris 

would freely flow from the pedestal onto the drywell floor. 
4-21

A MELCOR model control function monitors the debris elevation and temperature within each 

drywell floor region, each of which must satisfy user-defined threshold values for debris to move 

from one region to its neighbor. More specifically, when debris in a cavity is at or above the 

liquidus temperature of concrete, all material that exceeds a predefined elevation above the 

floor/debris surface in the adjoining cavity is relocated (i.e., 6 inches for CAV 0 to CAV 1 and 

4 inches for CAV 1 to CAV 2). When debris in a cavity is at or below the solidus temperature of 

concrete, no flow is permitted. Between these two debris temperatures, restricted debris flow is 

permitted by increasing the required elevation difference in debris between the two cavities 

(i.e., more debris head required to flow).

Another MELCOR model control function manages the debris spreading radius across the 

drywell floor within CAVs 1 and 2. Debris entering CAV 1 and CAV 2 is not immediately 

permitted to cover the entire surface area of the cavity floor. The maximum allowable debris 

spreading radius is defined as a function of time. If the debris temperature is at or above the 

concrete’s liquidus temperature, then the maximum transit velocity of the debris front to the 

cavity wall is calculated (e.g., NUREG/CR-7110 Volume 1, Peach Bottom SOARCA results are 

10 minutes to transverse CAV 1 and 30 minutes to transverse CAV 2). When the debris 

temperature is at or below the concrete solidus temperature, the debris front is assumed to be 

frozen, and lateral movement is precluded (i.e., debris velocity is 0 meters per second). A linear 

interpolation is performed to determine the debris front velocity at temperatures between these 

two values.

Full mixing of all debris into a single mixed layer is assumed in each of these debris regions. 

The concrete composition represented in the MELCOR model is listed in Table 4.1-4. The 

drywell floor concrete composition includes 13.5% rebar.

Table 4.1-4 Concrete composition

Species Mass Fraction

Al2O3 0.0091

Fe2O3 0.0063

CaO 0.3383

MgO 0.0044

CO2 0.2060

SiO2 0.3645

H2Oevap 0.0449

H2Ochem 0.0265

The debris lateral relocation criteria determines if and when hot debris contacts the drywell liner. 

There are two principal contributors: (1) Debris (differential) height and temperature required for 

"spill-over" from the pedestal to the quadrant of drywell floor adjacent to the pedestal doorway

(i.e., CAV 0 to CAV 1), and (2) debris velocity as it flows across drywell floor (from the pedestal 

doorway to the liner). This is calculated by control functions discussed above assuming a 

minimum transit time from the pedestal to the drywell liner (i.e., CAV 1) of 10 minutes if 

T(debris) > liquidus temperature. The velocity is zero when T(debris) < solidus temperature. 

The control functions do a linear interpolation between these two temperatures. The assumed 

maximum flow velocity is fixed. It is assumed that lateral debris mobility (i.e., spill-over from the 

pedestal to the drywell floor) is a function of debris temperature and the differential head 
4-22

(i.e., depth) of debris inside relative to the material outside the pedestal doorway. For simplicity, 

it is assumed the temperatures at which debris begins to move and the value at which the 

debris’ lateral velocity is at maximum are fixed. These values are used in the baseline model 

(i.e., the solidus and liquidus, respectively). To represent the uncertainty in debris mobility, 

uncertainty in the heights of debris at those temperatures necessary for lateral movement are 

used (Figure 4.1-13 (a and b) and Table 4.1-5). The two parameters are considered to be 

perfectly correlated in this analysis to avoid non-physical behavior in which the debris height at 

the liquidus temperature is greater than the debris height at the solidus temperature.

The mode of the solidus (0.5 m), the value used in the deterministic SOARCA analysis [2], 

represents the height at which solid particulate debris would ‘tumble’ laterally. The upper and 

lower bounds of the distribution provide an order of magnitude range about the mode.

For the liquidus mode (6-inches), the value used in the deterministic SOARCA analysis [2] for 

CAV 0, was determined from sample distributions documented in NUREG/CR-5423 [27]. Note

that NUREG/CR-5423 only provides sample distributions for cases with water on the drywell

floor, which is not the case for this sequence. However, the upper and lower bounds span a 

distribution for debris depth from the experimental results discussed in NUREG/CR-5423.
4-23

Figure 4.1-13 Cumulative distribution function debris overflow head as a function of 

debris at specified fixed temperatures: (a) T-solidus/no-flow head at 

1420 K and (b) T-liquidus at 1670 K 
4-24

Table 4.1-5 MELCOR uncertain parameters—Ex-vessel accident progression issues

Parameter Distribution

DHEADSOL: Debris overflow head (m) as a function of 

debris at specified fixed temperature (T-solidus/no-flow 

head at 1420 K) 

Triangle distribution

LB = 0.1 m

Mode = 0.5 m 

UB = 1.0 m

Correlation (T-liquidus at 1670 K) = 1 

SOARCA estimate = 0.5 m 

DHEADLIQ: Debris overflow head (m) as a function of 

debris at specified fixed temperature (T-liquidus at 

1670 K) 

Triangle distribution

LB = 0.05 m

Mode = 0.1524 m

UB = 0.25 m

Correlation (T-solidus at 1420 K) = 1 

SOARCA estimate = 0.1524 m 

4.1.4 Containment Behavior Issues

Flow area resulting from drywell liner failure (FL904A)

If debris flows out of the reactor pedestal and spreads across the drywell floor, as described 

above, and contacts the outer wall of the drywell, the steel liner will fail. This failure opens a 

release pathway to the lower reactor building. Heat transfer between the steel liner and molten 

core debris is not explicitly calculated in the MELCOR model, due to limitations of the CAV 

Package, which addresses ex-vessel model debris behavior. The model assumes an opening 

in the drywell liner occurs 15 minutes after debris first contacts the drywell wall. This time delay 

represents an average of estimates for failure time discussed in NUREG/CR-5423 [27] for 

situations in which the drywell floor is not covered with water.

The failure area affects drywell atmosphere discharge rate to the reactor building or post-failure 

'residence time’. The flow area is determined by debris temperature, debris depth against the 

liner, and the possibility of debris plugging part of the opening in the liner. A log-uniform 

distribution was selected for the uncertainty analysis (Figure 4.1-14 and Table 4.1-6).

The lower bound (0.05 m2 ≈ 10-inch diameter hole) of the distribution is a factor of two less than 

the SOARCA estimates for drywell liner failure. The lower bound is also the minimum observed 

critical zone determined for a damage index profile at 1143°

C (2090°F) in NUREG/CR-6025 [21]. 

The upper bound (1.0 m2 ≈ 44-inch diameter hole) is determined as a sufficient flow area to 

provide containment depressurization within the matter of seconds. Additionally, the upper 

bound is 14% greater than the maximum observed critical zone (0.88 m2

) determined for a 

damage index profile at 1260°C (2300°F) in NUREG/CR-6025, and ensures the upper bound 

uncertainty of this parameter is fully captured.
4-25

Figure 4.1-14 Cumulative distribution function of flow area resulting from drywell liner 

failure

Hydrogen ignition criteria (where flammable) (H2IGNC)

An ignition source for hydrogen combustion in the reactor building is unclear during a SBO. 

Since there are no electrically energized components in the reactor building during a SBO, the 

most likely ignition source will be a hot surface. Default ignition parameters were used in the 

SOARCA calculations for NUREG/CR-7110 Volume I. However, the accumulation of hydrogen

due to an absence of an electrical ignition source is credible.

The ignition of hydrogen from a hot surface is caused by local heating of the hydrogen-oxygen 

mixture to a point where there is a sufficiently large volume of the mixture reaching the auto 

ignition. There are other factors which affect the auto ignition temperature such as [28, 29, 

and 30]: 

• mixture concentrations, 

• ambient temperature, 

• size and shape of the hot surface, 

• degree of confinement around the surface, 

• the strength of convection currents across the surface, and 

• the surface material.
4-26

For auto ignition on hot surfaces, a temperature range of 500-1265°C has been observed for 

hydrogen-air and hydrogen-oxygen mixtures [28, 31-33]. Work using very small hot surfaces 

suggests that mixtures as low as 10% to 15% hydrogen are most easily ignited [31, 33]. 

However for hydrogen-oxygen mixtures, research indicates a weak dependence on hydrogen 

concentrations from 20% to 94% [32]. Additionally experiments have shown that for a range of

hydrogen concentrations from 4% to 94%, the minimum ignition temperature for a 

hydrogen-oxygen mixture on a hot surface occurs for a 20% hydrogen concentration [32]. For 

the uncertainty analysis, a triangular distribution was selected for both the hydrogen ignition 

criteria with the mode at 0.1 mole fraction, the value used in the deterministic SOARCA analysis

[2], while 0.05 and 0.20 mole fraction were selected for the lower and upper bounds respectively

(Figure 4.1-15 and Table 4.1-6). 

The lower bound of the distribution is the lower flammability limit for a hydrogen-air mixture. 

The upper bound is based on research into hydrogen auto ignition from hot surfaces for a 

hydrogen-oxygen mixture [32]. 

Figure 4.1-15 Cumulative distribution function of hydrogen ignition criteria (where 

flammable)
4-27

Railroad door open fraction due to over-pressure failure in reactor building (RRIDRAC, 

RRODFRAC)

The mechanical response of the large doors at each end of the equipment tunnel into the 

reactor building affects air infiltration and the establishment of a "chimney effect" through the 

building. This, in turn, greatly reduces the aerosol residence time and the building 

decontamination factor. The MELCOR model calculates aerosol transport and deposition in the 

reactor building, and thus the effective decontamination factor is explicitly calculated as a 

function of time. 

In NUREG/CR-7110 Volume 1, the doors are assumed to fail with a 50% open fraction as an 

estimate if the local internal building pressure is 0.62 psi greater than the environment [34]. 

Smaller open areas are credible and might reduce the airflow and increase residence time. The 

large equipment access doors on the 135-ft level of the reactor building area are assumed to be 

relatively weak when subjected to modest internal pressure loads. 

Past calculations [2] have shown that hydrogen combustion leads to a nearly immediate 

opening of the refueling bay blow-out panels and the railroad doorway at grade level. Blow-out 

panels into the turbine building and personnel access doorways out of the reactor building might 

also open. However, the dominant flow path for fission products to the environment is through 

the refueling bay blowout panels 9

 These past calculations have shown that failure by buckling 

is rather certain during a hydrogen burn. However, the open area that results from this failure is

not known.

The distributions selected for this analysis are based on expert judgment and are not based on 

any specific data (e.g., Fukushima accident) as no data exists for railroad door open area. This 

parameter is only one of a few MELCOR parameters which can be modified to influence the 

dominant flow path for fission products to the environment, and is thus a key parameter for the 

analysis of source term releases. For the uncertainty analysis, uniform distributions were 

selected for both the inner and outer railroad door open area fractions due to overpressure 

failure in the reactor building. For both the railroad inner door and outer door, open area 

fractions 0.05 and 0.75 were selected for the lower and upper bounds respectively

(Figure 4.1-16 (a and b) and Table 4.1-6). 

 

9 A stable flow of air is calculated to enter the building through the open railroad doorway, rise upward through the 

open equipment hatches from grade level to the refueling bay and exit the building to the environment through the 

open blow-out panels.
4-28

Figure 4.1-16 Cumulative distribution function of railroad door open fraction due to 

over-pressure failure in reactor building: (a) inner door and (b) outer door
4-29

Drywell Head Flange Leakage (K, E, and δ)

Peach Bottom has a Mark I containment that consists of a drywell and a toroidal shaped 

wetwell, which is half full of water (i.e., the pressure suppression pool). The drywell has the 

shape of an inverted light bulb. The drywell head is removed during refueling to gain access to 

the reactor vessel. The drywell head flange is connected to the drywell shell with 68 bolts of 

2 1⁄2 inch diameter (Figure 4.1-17). The flanged connection also has two 3⁄4 inch wide and 

1⁄2 inch thick ethylene propylene diene methylene (EPDM) gaskets. The torque on the 2 1⁄2 inch 

diameter bolts range from 817 to 887 foot pounds (ft-lb) [21, 22]. An average bolt torque of 

850 ft. lb. was used in this study. 

The 68 drywell head flange bolts (Figure 4.1-17) are pre-tensioned during reassembly of the 

head. This pre-tension also compresses the EPDM gaskets in the head flange. During an 

accident condition, the containment vessel may be pressurized internally. The internal pressure 

would counteract the pre-stress in the bolts. At a certain internal pressure, all of the 

pre-stressing force from the bolts would be eliminated, and the EPDM gaskets would be 

decompressed. Further increase in the internal pressure would result in leakage at the flanged 

connection.

The EPDM gasket manufacturers recommend a maximum squeeze (compression) of 30% for a 

static seal joint. The gaskets recover about 15% of the total thickness after the compressive 

load is removed from the flange. However, engineering observations are that the gaskets for 

the drywell head flange are squeezed to 50% to have a metal to metal contact to ensure no 

leakage at a design pressure of 56 psig. In addition, the gaskets are exposed to constant 

temperature and radiation, which contribute to early degradation. For this reason, the gaskets 

are replaced during each reassembly of the reactor vessel head. Based on this information and 

actual observations, the Peach Bottom licensee engineers recommended a gasket recovery of 

0.03 inch.
4-30

Figure 4.1-17 Drywell head flange connection details
4-31

Figure 4.1-18 shows the force balance on the drywell head given drywell pressure high enough 

that the head is not resting on the drywell flange.

Figure 4.1-18 Force balance on drywell head

The force balance is given by:

WW + NN ∙ FFbbbbbbbb = PP ∙ AAheeeeee Equation 4.1-1 

where,

W is the weight of the head (130,000 lb.) 

N is the number of bolts (68)

Fbolt is the force attributable to each bolt

P is the pressure in the drywell

Ahead is the projected area of the head

The projected area of the head is given by:

AAheeeeee = ππ ∙ RRheeeeee

2 Equation 4.1-2 

Rhead in Equation 4.1-2 is the internal radius of the drywell at the head flange (194 in). Fbolt has 

two components expressed as: 

FFbbbbbbbb = FFbbbbbbbbpppppp

+ FFbbbbbbbbpppppppppp Equation 4.1-3 

Fbolt,pre is the force associated with the pre-tensioning of the head bolt during assembly and is 

given by [35]: 

FFbbbbbbbbpppppp = TT

KK∙ bbbbbbbb

Equation 4.1-4 
4-32

where,

T is the torque applied to the bolt during assembly (850 ft-lb)

K is the torque coefficient (0.08 SOARCA estimate)

dbolt is the nominal diameter of the bolt (2.5 in)

Fbolt,press is the force associated with the tension developed in the head bolt in response to the 

pressure force developed as drywell pressure increases. This force is given by:

FFbbbbbbbbpppppppppp = EE ∙ ∆LLbbbbbbbb

LLbbbbbbbb

∙ AA Equation 4.1-5 

where,

E is the modulus of elasticity of the bolt (28,000,000 psi SOARCA estimate)

∆Lbolt is the elongation of the bolt

Lbolt is the length of the bolt (37.56 between the head and the nut)

Atensile is the tensile area of the bolt (4.00 in for a bolt of 2.5 in nominal size)

Substituting Equations 2, 3, 4, and 5 into Equation 1 yields:

WW + NN � TT

KK∙

+ EE ∙ ∆LLbbbbbbbb

LLbbbbbbbb

∙ AA � = PP ∙ ππ ∙ RRheeeeee

2 Equation 4.1-6 

Solving for bolt elongation gives:

∆LLbbbbbbbb = LLbbbbbbbb

EE∙AA tt tt

� ∙ππ∙RRh eeee 2 −WW

NN − TT

KK∙ bbbbbbbb

� Equation 4.1-7 

The height of the circumferential gap opened by lifting the drywell head is given by:

LLgg gg = ∆LLbbbbbbbb − δδgg gg Equation 4.1-8 

Where δgasket is the rebound thickness of the gasket (i.e., the increase in thickness that the 

gasket would experience once the compressive force on it was removed; 0.03 is the SOARCA

estimate). The associated area of the gap is:

AAgg gg = LLgg gg ∙ 2 ∙ ππ ∙ RRheeeeee Equation 4.1-9 

Substituting Equation 8 into Equation 9 gives:

AAgg gg = �∆LLbbbbbbbb − δδgg gg �2 ∙ ππ ∙ RRheeeeee Equation 4.1-10

The parameters in the above equations considered uncertain (Table 4.1-6) are the modulus of 

elasticity (E) of the drywell head bolts, the torque coefficient associated with the pre-tensioning 

of the head bolts (K), and the rebound thickness of the drywell head gasket (δgasket). A uniform

distribution between 26,600,000 psi and 29,400,000 psi was investigated to measure the 

potential effects of uncertainty in E. A triangular distribution was selected for K with mode 0.08 

and 0.029 and 0.57 lower and upper bounds, respectively. A uniform distribution between 

0.026 in and 0.034 in was investigated to measure the potential effects of uncertainty in δ.
4-33

The choice of the uniform distribution on E reflects the fact that E for steel varies somewhat with 

temperature and that the temperature of the bolts is not directly determined in the MELCOR 

calculations. The bounds chosen for the distribution on E reflect:

1. The observation that mid-height drywell temperature reaches 227°C in the SOARCA 

estimate calculation. 

2. The assumption that the drywell head flange bolts are carbon steel. 

3. That the modulus of elasticity of carbon steel varies between 29,300,000 psi at 21°C and 

27,300,000 psi at 260°C.

The bounds on E are 5% to either side of the SOARCA estimate which covers the foreseeable 

variation in E due to temperature in the LTSBO scenario.

The mode adopted for K is the SOARCA estimate value identified in work accomplished by 

NRC personnel in their SOARCA-related evaluation of Peach Bottom Nuclear Power Station 

containment strength. The lower and upper bounds imposed on the distribution for K were 

determined from the relation [35]: 

K = � mm

2 � � tan ψψ+μμ sec αα

1−μμ tan ψψ sec αα� + 0.625μμcc Equation 4.1-11

where,

dm is the mean diameter of the bolt

d is the nominal size of the bolt

Ψ is the helix angle of the thread

ψ = tan−1 �

1⁄# oo hrr ii h

Π mm

� Equation 4.1-12

μ is the coefficient of thread friction

α is half the thread angle

μc is the coefficient of collar friction

For a 2.5-inch nominal size bolt assuming American National (Unified) Screw Thread UNC 

Class 2A:

dm = 2.3294 in (nominally)

d = 2.4850 in (nominally)

# of threads per inch = 4

Ψ = 0.03415 rad (= 1.96°) 

α = 0.5236 rad (= 30°)

Friction coefficients μ and μc were taken to fall within the range between 0.029 and 0.57 

applicable to steel (greasy or dry) sliding on steel [36]. 

Substituting values into Equation 4.1-11 yields a lower bound on K of 0.050 for μ = μc = 0.029 

and an upper bound on K of 0.688 for μ = μc = 0.57.

The uniform choice of the distribution on δgasket reflects there not being information about the 

rebound thickness of the gasket other than the value recommended by informed Peach Bottom 

engineers (as described above). The bounds on the distribution are simply 15% to either side of 
4-34

the SOARCA estimate rounded to two significant figures. These bounds are though large 

enough to identify the importance of the uncertainty in the rebound thickness of the drywell head 

flange gasket.

Equation 4.1-9 (i.e., Agap versus P), is plotted on Figure 4.1-19 for three different combinations 

of the uncertain parameters E, K, and δgasket. One of the combinations utilizes the SOARCA 

estimate values of the parameters (E = 28,000,000 psi, K = 0.08, δgasket = 0.03 in), another uses 

the values that would give the smallest gap area (E = 29,400,000 psi, K = 0.050, δgasket = 0.034 

in), and the remaining combination uses the values that would give the largest gap area 

(E = 26,600,000 psi, K = 0.688, δgasket = 0.026 in). 

Figure 4.1-19 Drywell head flange gap area versus pressure

Uncertainty parameters K, E, and δ are introduced to the MELCOR modeling as terms in 

algebraic relationships formed by the following control functions:

0.0

0.0

0.70307140.0 188011 +

+⋅

+⋅ ⋅= time Ktime CF Equation 4.1-13 

0.0

0.0

0.00.188015 4365.588017 +

+⋅

+⋅ ⋅= time ECF CF Equation 4.1-14 

CF ( ⋅⋅= CF 0.00.0880170.10.188019 time δ ) +−⋅++ 0.0 Equation 4.1-15 

where E is in Pascals and δ is in meters.
4-35

Table 4.1-6 MELCOR uncertain parameters—containment behavior issues

Parameter Distribution

FL904A: Flow area resulting from drywell liner failure (m2) 

Log Uniform distribution

LB = 0.05 m2

UB = 1.0 m2

SOARCA estimate = 0.1 m2

H2IGNC: Hydrogen ignition criteria (where flammable)

(H2 mole fraction)

Triangle distribution

LB = 0.04

mode = 0.10

UB = 0.20

SOARCA estimate = 0.10

RRIDFRAC: Railroad inner door open fraction due to overpressure failure in reactor building

Uniform distribution

LB = 0.05

UB = 0.75

SOARCA estimate = 0.5

RRODFRAC: Railroad outer door open fraction due to overpressure failure in reactor building

Uniform distribution

LB = 0.05

UB = 0.75

SOARCA estimate = 0.5

E: Modulus of elasticity of the drywell head bolts (psi)

Uniform distribution

LB = 26.6 × 106

UB = 29.4 × 106

K: Torque coefficient associated with the pre-tensioning of the 

head bolts 

Triangle distribution

Mode=0.08

LB = 0.029

UB = 0.57

δ: Rebound thickness of the drywell head (inches) 

Uniform distribution

LB = 0.026

UB = 0.034

4.1.5 Chemical Forms of Iodine and Cesium

Chemical forms of iodine and cesium (I2, CH3I, CsI, CsOH, and Cs2MoO4) (CHEMFORM)

The predominant speciation of cesium described in NUREG/CR-7110 Volume 1 was based on 

detailed chemical analysis of the deposition and transport of the volatile fission products in the 

Phebus facility tests [19-23]. The chemical analysis revealed molybdenum combined with 

cesium and formed cesium molybdate. Prior to NUREG/CR-7110 Volume 1, the default 

predominant chemical form of cesium was cesium hydroxide. Consistent with past studies, 

NUREG/CR-7110 Volume 1 assumed all released iodine combines with cesium. However, the 

Phebus facility tests show that gaseous iodine is found within containment [19-23]. 
4-36

The presence of gaseous iodine remains an uncertain source term issue, especially with 

respect to long-term radioactive release mitigation issues after the comparatively much larger 

airborne aerosol radioactivity has settled from the atmosphere. Mechanistic modeling of

gaseous iodine behavior is a technology still under development with important international 

research programs to determine the dynamic behavior of iodine chemistry with respect to 

paints, wetted surfaces, buffered and unbuffered water pools undergoing radiolysis, and gas 

phase chemistry. The SOARCA estimate treatment under the best practices recommendation 

was deemed sufficient for the mean effects addressed in NUREG/CR-7110 Volume 1. 

Uncertainty in the gaseous iodine fraction to the total iodine released was identified as a key 

parameter and selected for evaluation of the sensitivity of SOARCA results. 

Partitioning the initial core inventory of cesium and iodine among certain allowable chemical 

forms (for release and transport) is managed within MELCOR input files that define the initial 

spatial mass distribution of each chemical species and its associated decay heat. Changes to 

the mass fractions assumed for a particular chemical group directly affect the mass fractions of 

other chemical groups, and hundreds of individual input records within the MELCOR model for 

Peach Bottom. Due to the complexity of this general modeling uncertainty, five alternative sets 

of MELCOR input files are used to span the range of plausible combinations of chemical forms 

of key radionuclide groups. Fixed partition fractions are used to preserve mass balances. 

The fraction of gaseous iodine for each of the five alternatives was determined using Phebus 

experimental results (see Table 4.1-7). The following provides discussion for the development 

of the five alternative combinations with regards to gaseous iodine release to containment.

(1) Combination 1: From the Phebus FTP0 experiment [19], 3% ± 1.1% of the initial iodine 

inventory was found in containment during 3.75 to 3.81 hours following the first zircaloy 

oxidation phase. After this timeframe, the gaseous iodine concentration in containment 

drops to 0.32% ± 0.16% of the initial iodine inventory. This is due to steam condensation on 

the painted condenser and adsorption process on other containment surfaces, or both. 

Since it is uncertain as to when in the accident progression containment will fail, the 

averaged peak gaseous iodine fraction (3%) is assumed. 

(2) Combination 2: From the Phebus FTP1 experiment [20], 0.2% ± 0.045% of the initial iodine 

inventory was found in containment following the first zircaloy oxidation phase. After the 

second zircaloy oxidation phase, the gaseous iodine concentration in containment drops to 

0.07% ± 0.016% of the initial iodine inventory. This is due to similar reasons described in 

the FTP0 experiment. Since it is uncertain as to when in the accident progression 

containment will fail, the averaged peak gaseous iodine fraction (0.2%) is assumed. 

(3) Combination 3: From the Phebus FTP2 experiment [22], 0.298% of the initial iodine 

inventory was found in containment. However, unlike the two previous experiments, the 

maximum gaseous iodine concentration occurs during the second oxidation phase of 

zircaloy. The minimum gaseous iodine concentration of 0.011% occurs during the main 

zircaloy oxidation phase. Since it is uncertain as to when in the accident progression 

containment will fail, the peak gaseous iodine fraction (0.298%) is assumed. 

(4) Combination 4: From the Phebus FTP3 experiment [23], 7.57% of the initial iodine inventory 

was found in containment. This peak gaseous iodine concentration occurred just after the 

first zircaloy oxidation phase. The minimum gaseous iodine concentration of 0.28% occurs 

prior to the first zircaloy oxidation phase. Since it is uncertain as to when in the accident 

progression containment will fail, the peak gaseous iodine fraction (7.57%) is assumed. 
4-37

(5) Combination 5: From the Phebus experiments [19, 20, 22, and 23], an averaged peak 

gaseous iodine of 2.77% of the initial iodine inventory was assumed.

Each of the five alternative combinations of the four chemical groups has a probability of 

occurrence defined by a discrete distribution (Figure 4.1-20 and Table 4.1-7). Each of the five 

alternatives partitions the radionuclide mass of iodine and cesium between four radionuclide 

classes in the MELCOR model (radionuclide classes: 2 (CsOH), 4 (I2), 16 (CsI), and 

17 (Cs2MoO4), Table 4.1-7). The physical properties of methyl iodide are not currently defined 

for a radionuclide class in the MELCOR model. Therefore, input for a new class and the 

associated mass balance arithmetic in the core inventory would be necessary to model this form 

of iodine. This was considered beyond the scope of this analysis and CH3I is neglected. 

The peak gaseous iodine amounts recorded in the four different Phebus experiments are

fundamental in defining the five speciation combinations of cesium and iodine considered in the

distributions. A combination is devoted to each of the four recorded amounts and a 

5th combination was formed by averaging the four recorded amounts of iodine together. Equal 

weighting in the parameter sampling was given to all but the Combination #5 which was 

weighted four times greater than the other combinations reflecting that it was jointly formed from 

the iodine recorded in the four experiments. 

With gaseous iodine (fraction of initial core inventory) defined for the five combinations, enough 

cesium was defined as CsI to involve all of the iodine not defined as gaseous (i.e., most all of 

the iodine). The remaining cesium was defined in the different combinations to be either in the 

form of all CsOH, all Cs2MoO4, or half CsOH and half Cs2MoO4, to represent uncertainty in 

cesium speciation. In five every eight realizations (Combinations #3 and #5), the remaining 

cesium is all Cs2MoO4. In two of every eight realizations (Combinations #2 and #4), the 

remaining cesium is half CsOH and half Cs2MoO4, representing the possibility of a mixed 

speciation. In one of every eight realizations (Combination #1), the remaining cesium is all 

CsOH, representing the former conventional assumption. Note that in all cases, including the 

SOARCA case, 1% of the initial cesium inventory is defined to be elemental cesium residing in 

the fuel-cladding gap.

With respect to cesium speciation, Combinations #3 and #5 closely match the SOARCA 

calculation. In the sampling of the chemical form of iodine and cesium, Combination #3 results 

once in every eight realizations while Combination #5 results four times in every eight 

realizations. Thus, in five of every eight realizations, the cesium speciation closely resembles 

the cesium speciation in the SOARCA calculation. However, there is no specific speciation 

combination that matches the iodine and cesium speciation of the SOARCA calculation 

identically. Combination #3 comes closest with the smallest fraction of gaseous iodine (~0.3%) 

and 100% Cs2MoO4. Recall, SOARCA did not include any gaseous iodine.
4-38

Figure 4.1-20 Probability density function for five alternative combinations for 

MELCOR model radionuclide classes 2, 4, 16, and 17 (I2, CsI, CsOH, and 

Cs2MoO4) 
4-39

Table 4.1-7 MELCOR uncertain parameters for chemical forms of iodine and cesium. 

Parameter Distribution

CHEMFORM: Five alternative combinations of RN 

classes 2, 4, 16, and 17 (CsOH, I2, CsI, and 

Cs2MoO4) 

Discrete distribution

Combination #1 = 0.125

Combination #2 = 0.125

Combination #3 = 0.125

Combination #4 = 0.125

Combination #5 = 0.500

Five Alternatives Species (MELCOR RN Class)

CsOH (2) I2 (4) CsI (16) Cs2MO4 (17)

Combination #1

fraction iodine -- 0.03 0.97 --

fraction cesiuma 1 -- -- 0 

Combination #2

fraction iodine -- 0.002 0.998

fraction cesium 0.525b -- -- 0.475 

Combination #3

fraction iodine -- 0.00298 0.99702 --

fraction cesium 0 -- -- 1 

Combination #4

fraction iodine -- 0.0757 0.9243 --

fraction cesium 0.525b -- -- 0.475 

Combination #5

fraction iodine -- 0.0277 0.9723 --

fraction cesium 0 -- -- 1 

SOARCA

estimate

Fraction iodine -- 0.0 1.0 -- 

Fraction cesium 0.05b -- -- 0.95

a This represents the distribution of 'residual' cesium which is the mass of cesium remaining after first reacting with the 

amount of iodine assumed to form CsI.

b The MELCOR model used in SOARCA always assumes 5.0% of the cesium is CsOH in the fuel gap. This parameter was 

not varied. 

4.1.6 Aerosol Deposition

Dynamic and Agglomeration Shape Factors 

When two or more aerosol particles collide, they can combine to form a larger particle. This 

process is known as agglomeration or coagulation. MELCOR code includes four agglomeration 

processes: Brownian diffusion, differential gravitational settling, and turbulent agglomeration by 

shear and inertial forces.

Except when they include significant amounts of liquid, aerosol particles are not usually 

assumed to be spherical, and the effective aerosol densities may be significantly less than the 

bulk density of the materials of which the aerosols are composed. In aerosol codes, these 

effects may be taken into account by using the agglomeration shape factor and the dynamic 

shape factor. The shape factors are used to represent the effect of a non-spherical shape upon 

aerosol collision cross sections and aerosol-atmosphere drag forces, respectively. Values of 

the shape factors correspond to dense aerosol of spherical shape (i.e., near 1.0 or unity), while 

porous spherical agglomerates lead, in theory, to values somewhat greater than unity. Highly 

irregular aerosols and agglomerates can have shape factors substantially greater than unity, 

often with the agglomeration and dynamic shape factors being quite unequal.
4-40

Given experimental data for aerosol shapes and densities applicable to light water reactor 

accidents, shape factors could in principle, be derived. Because this is not practical, empirical 

values are obtained by fitting code calculations to the results of aerosol experiments. The 

distributions used for this work can provide sensitivity to aerosol composition and to 

atmospheric conditions, especially to relative humidity. Humid conditions tend to produce more 

nearly spherical aerosols due to condensation of water onto aerosol agglomerates. Only limited 

information is available concerning the dependence of shape factors upon the relevant 

parameters (e.g., particle characteristics and atmospheric conditions [37]), and these 

parameters are themselves quite uncertain under accident conditions. Most experiments used 

in validating aerosol deposition are ideal aerosols comprised of known compositions (e.g., NaCl, 

CsOH, or polystyrene). The experiments are characterized in terms of aerodynamic diameters, 

which is the diameter that the true particle would apparently be if the assumed density was 

unity. Nuclear aerosol particles are difficult to define in terms of true density and diameter, so 

we vary shape factor and density to account for these unknowns.

For this work, it is assumed that hygroscopic effects during the accident sequence will induce 

some condensation of moisture on the aerosol particles causing the particles to tend towards 

being spherical and limit the degree of non-spherical shapes (i.e., 1.0 which is a perfectly 

spherical aerosol particle). 

Particle Density (RHONOM)

Of the natural depletion processes used in MELCOR, gravitational deposition is often the 

dominant mechanism for large control volumes such as those typically used to simulate 

containment. A major uncertainty within gravitational deposition is the particle density. 

Aerosol particles can become wet and when particles agglomerate, the resulting agglomerate is 

not fully dense with respect to the particle’s assumed spherical shape. In its original context, 

"wet" implies "with water" from steam condensation in the containment environment. This can 

be generalized to also reflect that some components of the aerosol are possibly molten. The 

primary aerosol particles are condensation aerosol particles, probably in the sub-micrometer 

size range. Agglomeration of the smaller particles "grows" their size, but they may or may not 

be molten. Hence, the aerosol that escapes the RCS may not be spherical as previously molten 

drops, but rather, chain agglomerates of smaller particles or "puffy" agglomerations that are 

approximately spherical, but not fully dense. The agglomerate particles are clusters of smaller 

particles that have stuck together by collisions. The smaller particles comprising the 

agglomerate are presumed spherical but there are small spaces between the agglomerated 

particles. For this reason the agglomerate particle cannot be fully dense owing to the inherent 

porosity of the agglomerate. The aerosol shape factor and density are individual parameters in 

MELCOR, however, in a review by Brockmann [38] it is stated that the density usually is 

considered as the actual material density, and the shape factor is used to account for the 

porosity of the aerosol particle, thus correcting the aerodynamic diameter used in collision and 

settling terms. The suggested range of packing efficiency α, or ratio of apparent density to 
4-41

material density, is 0.18 to 0.5. The apparent size is derived as follows: given a particle mass 

M, the diameter at the apparent density ρ is related to that at the real density ρ0 by: 

3 3

6 6

DM Doo

π

ρ

π

ρ == Equation 4.1-16 

or 

3/1





 



 == D

Do

ρ o

ρ α

Equation 4.1-17 

Thus the shape factor, defined as the ratio of apparent volumetric diameter to fully dense 

diameter, would vary as ~α-1/3. The suggested range for the shape factor is 1 to 3, although, if 

we use the suggested range for α, we only get a variation of 1 to 1.4. Another factor is whether 

the aerosols are considered to be dry or wet. Wet aerosols are those that absorb water in a 

humid environment, generally when the humidity is >80%. This is a consideration in 

containments, not so much inside a RPV. Wet aerosols would be more spherical and have a 

density closer to that of water (i.e., a value of 1.0). 

The above suggests that density and shape factor are not entirely independent variables, and 

what should actually be varied is the packing efficiency. In particular, for a given density ratio, 

α, the shape factor ratio is α-1/3. Varying the density ratio and shape factor ratio in this manner 

should produce results that are consistent with a relationship between shape factor and density, 

in theory.

Expanding on this, the aerosols of interest in reactor accidents are cesium, iodine, and to some 

extent strontium, because of its biological effects, relatively long half-life, and volatility, meaning 

greater release. In the version of MAEROS (the aerosol package) used in MELCOR, the 

radionuclide density for all radionuclide classes is represented by a single value. Table 4.1-8 

lists some material densities of representative aerosols of interest.

Table 4.1-8 Densities of several radionuclide compounds

Radionuclide aerosol compound Density (kg/m3)

CsOH 3675

Cs2MoO4 4410

Sr(OH)2 3670

SrO 4700

I2 4930

CsI 4150

As can be seen, the material density range of interest is about 3700-4900 kg/m3. Using the 

above suggested range for packing efficiency, this gives a range of apparent density of about 

660-2460 kg/m3

. The default density used in MELCOR and the SOARCA analysis is 

1000 kg/m3

, with a shape factor of 1.0, so this seems to be a reasonable distribution of values, 

with the packing efficiency factor being absorbed in the density value. 
4-42

Aerosol Deposition Uncertainty

For the uncertainty analysis, an average actual material density can be derived in the following 

way. Table 4.1-9 below gives the released mass for the different radionuclide classes in a 

MELCOR run for the SOARCA Peach Bottom Unmitigated LTSBO case (the classes for boron, 

water, and concrete are omitted). Also given are the radionuclide class name, an assumed 

chemical form for the aerosol, and the density. The column labeled “weighting factor” is the 

released class mass divided by the density, or

i

i

i

m

w

ρ =

Equation 4.1-18 

for the ith class. This factor represents the volume of the released radionuclide, and, if we 

assume that the radionuclide was originally released as a vapor and condensed into the 

smallest aerosol size bin, this is proportional to the initial number density of the aerosol for the 

class. These factors are then summed and the inverse multiplied by the total released mass to 

get an average material density for the aerosols, as

∑

=

i

avg w

M

ρ

Equation 4.1-19 

Table 4.1-9 Released radionuclide masses and weighting factors from SOARCA Peach 

Bottom Unmitigated LTSBO Case

RN Class

RN Class 

Name

Chemical 

Form

Released Mass 

(kg)

Density 

(kg/m3

) 

Weighting 

Factor (m3) 

1 Xe Xe 5.32 × 102

2 Cs CsOH 1.71 × 101 3,675 4.64 × 10-3

3 Ba BaO 6.67 × 100 5,720 1.17 × 10-3

4 I I2 5.61 × 10-3 4,930 1.14 × 10-6

5 Te TeO2 5.49 × 101 5,680 9.66 × 10-3

6 Ru RuO2 1.23 × 101 6,970 1.77 × 10-3

7 Mo MoO2 4.38 × 100 6,470 6.77 × 10-4

8 Ce CeO2 3.89 × 100 7,215 5.40 × 10-4

9 La La2O3 1.11 × 10-1 6,510 1.70 × 10-5

10 U UO2 6.04 × 102 10,960 5.51 × 10-2

11 Cd CdO 6.14 × 100 8,150 7.54 × 10-4

12 Ag SnO2 8.31 × 100 6,950 1.20 × 10-3

16 CsI CsI 4.07 × 101 4,510 9.03 × 10-3

17 CsM Cs2MoO4 4.60 × 102 4,410 1.04 × 10-1

18 Sn metal SnO2 6.69 × 102 6,950 9.62 × 10-2

Note: Chemical forms and densities from Wikipedia and MELCOR RN-RM
4-43

Table 4.1-10 gives the totals, not including the noble gas class, with and without the tin metal 

(released from zircaloy cladding) for the weights, average densities, and minimum and 

maximum effective densities using the suggested range for the packing efficiency, 0.18-0.5.

Table 4.1-10 Totals and density ranges

Totals Released 

mass (kg)

Sum of 

weights (m3

) 

Average 

density 

(kg/m3

) 

Minimum 

density 

(kg/m3

) 

Maximum 

density 

(kg/m3

) 

Without class 18 1.22 × 103 1.89 × 10-1 6.45 × 103 1.16 × 103 3.23 × 103

With class 18 1.89 × 103 2.85 × 10-1 6.62 × 103 1.19 × 103 3.31 × 103

The range of densities in Table 4.1-10 can be used for the uncertainty range. It should be noted 

that there is a large variation in the amount of UO2 and tin metal released, depending on 

variations in the accident scenario; the range between minimum and maximum densities should 

be increased to account for this uncertainty. The value of χ should be close to 1.0, since the 

effect of packing efficiency is now absorbed into the apparent density – the maximum noted in 

Hinds [39], for a string of five spheres, is 1.2. Kissane also notes that there is no evidence in 

experiments on reactor accident scenarios for anything but a spherical agglomeration as the 

usual shape of an aerosol particle [37]. 

The average material density of the particulate released to the environment in the SOARCA 

LTSBO MELCOR calculation (6,450 kg/m3

) served as the basis for the sampling of particle 

density in the calculations. Packing factors of 0.18 minus 25% variance (= 0.135) and 0.5 plus 

25% variance (= 0.626) were applied to the average from the SOARCA calculation to define the 

lower and upper bounds of the sampling as 870 kg/m3 and 4,037 kg/m3

, respectively. A 

triangular distribution was invoked with mode equal to the MELCOR default density (and 

SOARCA value) of 1,000 kg/m3 lending somewhat of a bias toward smaller densities in the 

sampling. At first, the aerosol dynamic shape factor was also identified as an uncertain 

parameter for sampling, but there was a worry about simultaneous varying both variables 

potentially leading to the modeling of unphysical conditions. After further deliberation and 

consultation with experts, the team concluded that assuming a shape factor of 1 (perfectly 

spherical) and varying RHONOM should capture the effects of uncertainty stemming from both 

these related parameters.

In this analysis, it is assumed that Chi and Gamma = 1.0, and the particle density has a 

triangular distribution of [870, 1,000, 4,037] kg/m3 for the min, mode, max (Figure 4.1-21 and 

Table 4.1-11). The density distribution is based on the average effective density range 

(1.16 × 103 to 3.23 × 103

) representative of the mass fractions for the various radionuclide

classes released as aerosols as calculated for the SOARCA case, with a 25% variance on the 

min and max to account for variation over the range of uncertainty in the MELCOR in-vessel 

parameters which will yield a range in the amount of the heavier radionuclide classes and tin, 

which are in turn dependent on the amount of core damage and peak temperatures in the RPV. 
4-44

Figure 4.1-21 Cumulative distribution function of particle density 

Table 4.1-11 MELCOR uncertain parameters—aerosol deposition

Parameter Distribution

RHONOM: Particle Density

Triangular distribution

LB = 870 kg/m3

Mode = 1,000 kg/m3

UB = 4,730 kg/m3
4-45

4.2 Consequence Model Uncertainty (MACCS Inputs) 

The MACCS consequence model (Version 2.5.0.0) is used in the SOARCA analysis to calculate 

offsite doses and their effect on members of the public. Epistemic uncertainty was considered 

for the principal phenomena in MACCS, including atmospheric transport using a straight-line 

Gaussian plume model of short-term and long-term dose accumulation through several 

pathways including: cloudshine, groundshine, and inhalation. The ingestion pathway was not 

treated in the SOARCA analyses because uncontaminated food and water supplies are 

abundant within the United States and it is unlikely that the public would eat radioactively 

contaminated food [40]. The parameter uncertainty in the MACCS consequence model will 

impact the following doses included in the SOARCA reported risk metrics:

• cloudshine during plume passage

• groundshine during the emergency and long-term phases from deposited aerosols

• inhalation during plume passage and following plume passage from resuspension of 

deposited aerosols. Resuspension is treated during both the emergency and long-term 

phases.

Development of the emergency planning related uncertainty parameters for MACCS input 

required establishing an emergency response timeline. The timeline includes actions described 

in the onsite and offsite emergency response plans. The emergency response plans are tested 

and exercised often and there is a high confidence in the interactions between onsite and offsite 

agencies. Research of existing evacuations provided information regarding movement of the 

public in response to an emergency and has shown that emergency response actions are 

routinely implemented and successful [41, 42]. Although there is high confidence in response 

actions, an emergency response is a dynamic event with uncertainties in elements of the 

response.

All of the emergency planning parameters used in MACCS were reviewed to determine the 

most appropriate parameters for the uncertainty analysis. The following three10 emergency 

planning parameter sets were selected: 

• Hotspot and normal relocation,

• evacuation delay, and 

• evacuation speed. 

In addition, the SOARCA estimate offsite consequence results presented in the SOARCA study 

include the aleatory uncertainty associated with weather conditions at the time of the accident 

scenario. These SOARCA estimate offsite consequence values represent the expected (mean) 

value of the probability distribution obtained from a large number of weather trials. The 

uncertainty analysis is consistent with the weather-sampling strategy adopted for SOARCA and 

uses the same non-uniform weather-binning approach in MACCS used in the SOARCA

calculation [1]. Weather binning is an approach used in MACCS to categorize similar sets of 

 

10 The habitability criterion is also considered to be an important potentially uncertain parameter, but will not be 

included as part of the integrated uncertainty analysis. A separate discussion is included in Section 4.3 on the 

influence of the habitability criterion.
4-46

weather data based on wind speed, stability class, and the occurrence of precipitation. For the 

non-uniform weather sampling strategy approach for SOARCA, the number of trials selected 

from each bin is the maximum of 12 trials and 10% of the number of trials in the bin. Some bins 

contain fewer than 12 trials. In those cases, all of the trials within the bin are used for sampling. 

This strategy results in roughly 1,000 weather trials for the Peach Bottom accident scenario.

Several of the parameter distributions selected for this analysis are based on expert elicitation 

data captured in the report, Synthesis of Distributions Representing Important Non-Site-Specific 

Parameters in Off-Site Consequence Analysis [43]. The United States and the Commission of 

European Communities conducted a series of expert elicitations to obtain distributions for 

uncertain variables used in health consequence analyses related to accidental release of 

nuclear material [43]. The distributions reflect degrees of belief for non-site specific parameters 

that are uncertain and are likely to have significant or moderate influence on the results. The 

referenced report presents the effort to develop ranges of values and degrees of belief that fairly 

represent the divergent opinions of the experts while maintaining the resulting parameters within 

physical limits, specifically with the MACCS code in mind. The methodology used a resampling 

of the experts’ values and was based on the assumption of equal weights of the experts’ 

opinions. All other MACCS parameters not discussed in this section (e.g., emergency planning 

parameters) remain the original point estimates used in NUREG/CR-7110, Volume 1. 

Additional discussions on certain MACCS parameters presented are discussed in Appendix E. 

4.2.1 Wet Deposition Model (CWASH1)

Wet deposition is an important phenomenon that strongly affects atmospheric transport. Under 

heavy rains, wet deposition is very effective and rapidly depletes the plume. This process can 

produce concentrated deposits on the ground and create what is often referred to as a hot spot 

(i.e., an area of higher radioactivity than the surrounding areas). While rain occurs less than 

10% of the time at Peach Bottom and for most of the U.S., it can significantly affect 

consequence calculations when it does occur. For this reason, uncertainty in the wet deposition 

model is considered in this uncertainty analysis. Table 4.2-1 provides the parameters 

describing the distribution for one of the parameters in the MACCS wet deposition model; the

median value of the distribution was the value used in the deterministic SOARCA analysis [2]. 

The second parameter in the model, CWASH2, is fixed at a value of 0.664. The basis for this 

distribution comes from expert elicitation data [44], as further evaluated in Synthesis of 

Distributions Representing Important Non-Site-Specific Parameters in Off-Site Consequence 

Analysis [43]. The cumulative distribution for the wet deposition model coefficient is shown on 

Figure 4.2-1 and the values are provided in Table 4.2-1.
4-47

Figure 4.2-1 Cumulative distribution function for the linear coefficient (CWASH1) in the 

MACCS wet deposition model 

Table 4.2-1 MACCS uncertain parameters—wet deposition model

CWASH1: Linear coefficient 

in wet deposition model Percentile CWASH1[1/s]

Piecewise log-uniform distribution

0 2.73 × 10−8

1 2.92 × 10−7

5 9.13 × 10−7

10 1.73 × 10−6

25 5.36 × 10−6

50 1.89 × 10−5

75 9.84 × 10−5

90 2.59 × 10−4

95 5.79 × 10−4

99 3.78 × 10−3

100 1.14 × 10−2

SOARCA estimate 1.89 × 10−5
4-48

4.2.2 Dry Deposition Velocities (VDEPOS)

Dry deposition is the only mechanism for deposition onto the ground for more than 90% of the 

hours of the year at Peach Bottom (i.e., the hours during which rainfall does not occur). The 

term dry deposition involves a variety of mechanisms that cause aerosols to deposit, including 

gravitational settling, impaction onto terrain irregularities, including buildings and other 

manmade structures, and Brownian diffusion. Dry deposition is a much slower process than 

wet deposition, but occurs continuously, whereas, wet deposition occurs intermittently. Dry 

deposition is characterized in MACCS with a set of deposition velocities corresponding to a set 

of aerosol size bins. Larger values of dry deposition velocity result in larger long-term doses at 

shorter distances and smaller doses at longer distances; the converse is also true that smaller 

values of dry deposition velocity result in smaller long-term doses at shorter distances and 

larger doses at longer distances. The distributions for dry deposition velocity are based on 

expert elicitation data [44] and the expert data are evaluated in Synthesis of Distributions 

Representing Important Non-Site-Specific Parameters in Off-Site Consequence Analysis [43]. 

The values11 used in this analysis are based on a mean annual wind speed of 2.2 m/s and a

surface roughness length of 10 cm. The cumulative distributions for the dry deposition 

velocities are shown on Figure 4.2-2 and the values are provided in Table 4.2-2.

In revisiting the dry deposition velocities from the expert elicitation, some of the upper ranges of 

the distributions appear too high to be supported by physical understanding. Furthermore, in 

reviewing the original expert elicitation data, in some cases only one outlier expert’s beliefs are 

responsible for the upper 10% of the distribution. However, in this study, surface roughness

was not included as an uncertain parameter (see discussion under Section 4.3.5). Varying the 

dry deposition velocity accounts for the net effects had both VDEPOS and surface roughness 

been varied simultaneously. As noted in the MACCS SOARCA best practices document 

(NUREG/CR-7009 [93]) and the SOARCA detailed analyses documented in NUREG/CR-7110 

Volume 1 [2], surface roughness somewhat greater than 10 cm may be more representative of 

the Peach Bottom site. As such, the higher deposition velocities sampled account for the net 

effect of the potential higher surface roughness.

 

11 Subsequent to completing the UA calculations, the team discovered that there was an incorrect implementation of 

the expert elicitation data resulting in the wrong curves for some particle size bins, most notably bins 9 and 10 (the 

largest particle sizes). However, the effect of this incorrect implementation is judged not to be important, 

especially since there is relatively little mass within these bins.
4-49

Figure 4.2-2 Cumulative distribution functions of dry deposition velocities for MACCS

aerosol bins/aerosol mass median diameters
4-50

Table 4.2-2 MACCS uncertain parameters—dry deposition velocities

Dry Deposition Velocities

VDEPOS (1 to 10) [m/s]

Piecewise Log-Uniform Distribution

Aerosol Bin/Aerosol Mass Median Diameter (micrometers) 

Percentile 1 0.12 2 0.21 3 0.40 4 0.74 5 1.38 6 2.57 7 4.79 8 8.91 9 

0 4.44 × 10−7 1.52 × 10−6 4.71 × 10−6 1.34 × 10−5 3.56 × 10−5 9.11 × 10−5 2.28 × 10−4 5.73 × 10−4 1.47 × 

1 6.25 × 10−6 7.00 × 10−6 1.10 × 10−5 2.27 × 10−5 5.57 × 10−5 1.51 × 10−4 4.18 × 10−4 1.08 × 10−3 2.42 × 

5 5.20 × 10−5 3.99 × 10−5 4.52 × 10−5 7.05 × 10−5 1.42 × 10−4 3.42 × 10−4 9.25 × 10−4 2.62 × 10−3 7.22 × 

10 9.60 × 10−5 7.30 × 10−5 7.99 × 10−5 1.19 × 10−4 2.26 × 10−4 5.19 × 10−4 1.35 × 10−3 3.76 × 10−3 1.05 × 

25 2.51 × 10−4 1.86 × 10−4 2.00 × 10−4 2.92 × 10−4 5.38 × 10−4 1.16 × 10−3 2.75 × 10−3 6.59 × 10−3 1.49 × 

50 8.80 × 10−4 6.63 × 10−4 7.47 × 10−4 1.14 × 10−3 2.10 × 10−3 4.26 × 10−3 8.56 × 10−3 1.53 × 10−2 2.21 × 

75 3.13 × 10−3 2.48 × 10−3 2.69 × 10−3 3.76 × 10−3 6.36 × 10−3 1.22 × 10−2 2.47 × 10−2 4.98 × 10−2 9.39 × 

90 7.35 × 10−3 5.60 × 10−3 6.03 × 10−3 8.67 × 10−3 1.57 × 10−2 3.36 × 10−2 8.03 × 10−2 2.02 × 10−1 5.03 × 

95 1.45 × 10−2 1.11 × 10−2 1.21 × 10−2 1.78 × 10−2 3.32 × 10−2 7.42 × 10−2 1.87 × 10−1 5.00 × 10−1 1.34 × 

99 4.99 × 10−2 3.92 × 10−2 4.25 × 10−2 6.06 × 10−2 1.09 × 10−1 2.33 × 10−1 5.72 × 10−1 1.53 × 100 4.28 × 

100 1.11 × 10−1 8.92 × 10−2 1.00 × 10−1 1.48 × 10−1 2.72 × 10−1 5.83 × 10−1 1.37 × 100 3.35 × 100 7.95 × 

SOARCA

Estimate

5.35 × 10−4 4.91 × 10−4 6.43 × 10−4 1.08 × 10−3 2.12 × 10−3 4.34 × 10−3 8.37 × 10−3 1.37 × 10−2 1.70 × 

Note: VDEPOS is perfectly rank correlated across aerosol sizes. Rank order correlation is the most commonly used method of computing a correlatio

order of the sampled values between two variables, rather than the absolute value sampled from the distribution.
4-51

4.2.3 Shielding Factors (CSFACT, GSHFAC, PROTIN)

In MACCS, shielding and protection factors are specified for each dose pathway and directly 

affect the dose received by individuals at each location. The shielding factors are used as 

multipliers on the dose that a person would receive if there were no shielding or protection. 

Thus, a shielding factor of one represents the limiting case of a person receiving the full dose 

(i.e., standing outdoors and completely unprotected from exposure); a shielding factor of zero 

represents the limiting case of complete shielding from the exposure. The shielding factors 

used in the MACCS calculation are clearly important because the doses received are directly 

proportional to these factors.

The values used in this uncertainty analysis for groundshine and inhalation are derived from 

expert elicitation data [45] by Gregory et al. [46]. Heames et al. [47] further evaluated the expert 

data to also derive distributions for cloudshine. Three types of activity, normal, sheltering, and 

evacuation, are evaluated for each dose pathway, resulting in nine sets of shielding factors, 

which are provided in Tables 4.2-3a, b, and c. Figure 4.2-3 shows a graphical representation of 

the Table 4.2-3 data. In this context, normal activity refers to a combination of activities that are 

averaged over a week and over the population, including being indoors at home, commuting, 

being indoors at work, and being outdoors. These values are used in the uncertainty analysis 

with the further assumption that the distributions for normal activity and sheltering are correlated 

with a rank correlation coefficient (RCC) of 0.75. This correlation should be applied for normal 

and sheltering activities for each of the pathways. There is no correlation between the three 

pathways. Each parameter (CSFACT, GSHFAC, PROTIN) can be specified for each of the six 

cohorts in WinMACCS (see Section 6.1 and 6.3.1 in Reference 1 for further discussions on the 

six cohorts). In the SOARCA analysis, the distributions listed in Tables 4.2-3a, b, and c are

used in the WinMACCS file. In the SOARCA study [1], shielding values for Cohorts 1, 2, 3, 5, 

and 6 are identical. Cohort 4 is special facilities, which has different shielding values in the 

SOARCA study. For this study, a single distribution was sampled and applied to all of the 

cohorts. A rank linear coefficient of 0.75 is associated for normal and sheltering activities for all 

cohorts. 
4-52

Figure 4.2-3 Cumulative distribution for shielding factors 

Table 4.2-3a MACCS uncertain parameters—cloudshine shielding factors

CSFACT

Piecewise Uniform Distribution

Percentile Normal Sheltering Evacuation

0% 0.076 0.015 0.230

1% 0.104 0.016 0.232

5% 0.152 0.022 0.244

15% 0.277 0.073 0.350

25% 0.394 0.124 0.457

50% 0.692 0.251 0.724

75% 0.862 0.624 0.877

85% 0.930 0.773 0.938

95% 0.999 0.922 0.999

99% 0.9999 0.984 0.9999

100% 1.000 1.000 1.000

SOARCA Estimate 0.6 0.5 1.0
4-53

Table 4.2-3b MACCS uncertain parameters—groundshine shielding factors

GSHFAC

Piecewise Uniform Distribution

Percentile Normal Sheltering Evacuation

0% 0.053 0.015 0.083

1% 0.068 0.022 0.128

5% 0.095 0.035 0.182

15% 0.129 0.047 0.243

25% 0.154 0.064 0.280

50% 0.216 0.104 0.396

75% 0.303 0.168 0.552

85% 0.346 0.203 0.641

95% 0.417 0.250 0.755

99% 0.489 0.288 0.870

100% 0.548 0.331 0.935

SOARCA Estimate 0.18 0.1 0.5

Table 4.2-3c MACCS uncertain parameters—inhalation protection factors

PROTIN

Piecewise Uniform Distribution

Percentile Normal Sheltering Evacuation

0% 0.076 0.015 0.230

1% 0.104 0.016 0.232

5% 0.152 0.022 0.244

15% 0.277 0.072 0.350

25% 0.394 0.124 0.457

50% 0.692 0.251 0.724

75% 0.862 0.624 0.877

85% 0.930 0.773 0.938

95% 0.999 0.922 0.999

99% 0.9999 0.984 0.9999

100% 1.000 1.000 1.000

SOARCA

Estimate

0.46 0.33 0.98
4-54

4.2.4 Early Health Effects (EFFACA, EFFACB, EFFTHR)

The uncertain characteristics associated with estimation of four types of early health effects are 

derived from expert elicitation data [48] and evaluated by Bixler et al. [43]. Three of these early 

health effects are potentially fatal: the hematopoietic (acute dose to the red bone marrow), 

gastrointestinal (acute dose to the stomach), and pulmonary (acute dose to the lungs) 

syndromes. The fourth, pneumonitis is generally nonfatal, and was not included in the 

SOARCA calculation. The parameter distributions and SOARCA values associated with these 

three potentially fatal early health effects are shown on Figure 4.2-4 and also in Table 4.2-4. 

Correlations between the coefficients are applied as indicated in the footnote to the table.
4-55

Figure 4.2-4 Cumulative distribution functions of three early health effects:

(a) hematopoietic system, (b) pulmonary system, and (c) gastrointestinal 

system
4-56

Figure 4.2-4 Cumulative distribution functions of three early health effects: 

(a) hematopoietic system, (b) pulmonary system, and (c) gastrointestinal 

system (continued)

Table 4.2-4 MACCS uncertain parameters—early health effects

Early Health Effects

Continuous Linear Distribution

Hematopoietic S. Pulmonary S. Gastrointestinal S.

Percentile

LD-50 

EFFACA 

[Gy] 

Beta 

EFFACB

[-] 

Threshold 

EFFTHR

[Gy] 

LD-50 

EFFACA

[Gy] 

Beta 

EFFACB

[-] 

Threshold 

EFFTHR

[Gy] 

LD-50 

EFFACA

[Gy] 

Beta 

EFFACB

[-] 

Threshold 

EFFTHR

[Gy] 

0 2.00 2.39 0.667 10.0 3.7 5.3 4.80 3.21 2.000

1 2.41 2.54 0.803 12.0 3.8 6.7 6.18 3.25 2.932

5 3.32 2.83 1.113 16.6 4.4 8.6 7.88 3.41 3.773

10 3.69 3.19 1.316 17.8 4.7 9.6 8.51 3.64 4.499

25 4.38 4.15 1.716 19.9 5.6 11.5 10.02 5.99 5.351

50 5.59 6.07 2.319 23.5 9.6 13.6 12.12 9.31 6.516

75 7.24 10.23 3.560 33.6 13.8 18.4 14.94 11.04 7.671

90 8.89 13.22 4.629 42.0 16.9 22.1 17.65 16.01 8.784

95 10.32 14.28 5.256 45.0 18.7 24.0 19.14 18.03 9.522

99 11.84 15.82 6.188 55.7 21.4 32.4 23.35 19.52 12.962

100 16.50 15.99 8.550 76.5 21.7 37.5 30.00 19.94 15.000

SOARCA

Estimate 5.6 6.1 2.32 23.5 9.6 13.6 12.1 9.3 6.5

Note:For each health effect, D-50 or LD-50 is correlated with the Threshold for the same health effect using a 0.99 rank correlation 

coefficient. 
4-57

4.2.5 Latent Health Effects (GSHFAC, DDREFA, Inhalation Dose Coefficients, 

CFRISK) 

The uncertain characteristics associated with the estimation of latent health effects are derived 

from work performed by Keith Eckerman [49]. The two most important exposure pathways are 

groundshine and inhalation. Groundshine is especially important for the long-term phase where 

the only operable exposure pathways correspond to radioactive aerosols that have deposited 

onto the ground. This leads to three potential exposure pathways: groundshine, inhalation of 

resuspended aerosols, and ingestion. Doses from ingestion have not been treated in the 

SOARCA work and are not included in the uncertainty analysis because the supply of clean 

food and water would be more than adequate so that the population in an affected area would 

not need to consume contaminated food and water. 

Groundshine (GSHFAC)

Uncertainty in groundshine doses has two components: uncertainty in the amount of shielding 

between an individual and the source of the groundshine (GSHFAC) and uncertainty in the 

energy deposited within a human organ for a specified incident radiation. Distributions 

representing the uncertainty in the groundshine shielding factors (GSHFAC) are presented in 

Table 4.2-3b. Additional uncertainties of the deposition of radiation in individual organs stem 

from age, height, and weight variations of the population. 

To simplify the implementation of uncertainty in the energy deposited within a human organ for 

a specified incident radiation, Eckerman [49] recommends apply the same uncertainty 

distribution for all radionuclides and for all organs. The distribution is a triangular one with a 

minimum of 0.5, a peak (mode) of 0.8, and a maximum of 1.5. Furthermore, Eckerman 

suggests that the uncertainty in groundshine dose coefficients is highly correlated. As a result, 

it makes sense to combine the uncertainty in the groundshine shielding factor and the 

uncertainty in the dose coefficients into a single uncertainty factor, which can be implemented 

as an overall uncertainty in the groundshine shielding factor (GSHFAC) in WinMACCS. The 

uncertainties in the groundshine shielding factor and in the groundshine dose coefficients 

should be treated as being uncorrelated.

The parameters for the triangular distribution used to represent uncertainty in the dose 

coefficients for groundshine radiation are presented in Table 4.2-5. Piecewise uniform 

distributions for the uncertainty is for the combined scale factor for shielding and resultant dose 

are listed in Table 4.2-6, implemented as an overall uncertainty in the groundshine shielding 

factors (GSHFAC), are presented on Figure 4.2-5. The resulting rank correlation for the 

combined groundshine shielding factors should be implemented using 0.76 for normal and 

sheltering, 0.2 for normal and evacuation, and 0.15 for sheltering and evacuation. 

Table 4.2-5 MACCS uncertain parameters—multiplier for groundshine dose 

coefficients

Multiplier on dose coefficients for groundshine pathway for all 

organs

Triangle distribution

LB = 0.5 

mode = 0.8

UB = 1.5
4-58

Figure 4.2-5 Cumulative distribution functions for the groundshine shielding factors, 

GSHFAC, for the three types of activity

Table 4.2-6 Piecewise uniform distributions for the combined uncertainty in

groundshine shielding factors (GSHFAC) including multiplier

Quantile GSHFAC 

Normal

GSHFAC 

Sheltering

GSHFAC 

Evacuation

0 0.0265 0.0075 0.0415

0.001 0.0394 0.0120 0.0692

0.01 0.0552 0.0179 0.1001

0.05 0.0784 0.0286 0.1491

0.1 0.0967 0.0361 0.1804

0.25 0.1354 0.0563 0.2504

0.5 0.1979 0.0969 0.3635

0.65 0.2433 0.1288 0.4464

0.75 0.2816 0.1549 0.5146

0.83 0.3211 0.1818 0.5843

0.9 0.3719 0.2148 0.6717

0.95 0.4297 0.2533 0.7768

0.99 0.5441 0.3226 0.9665

0.999 0.6660 0.3975 1.1555 (1.0)a

1 0.8220 0.4965 1.4025 (1.0) a

a The piecewise distribution was limited to a maximum value of 1.0, equal to the upper 

bound for GSHFAC in MACCS.
4-59

Dose and Dose Rate Effectiveness Factor (DDREFA) 

An additional parameter that affects the calculation of latent health effects is the dose and dose 

rate effectiveness factor (DDREFA). This factor uses Biological Effects of Ionizing Radiation 

(BEIR) V risk factors for estimating health effects to account for observed differences between 

low and high dose rates. In MACCS, doses received during the emergency phase are divided 

by DDREFA when they are less than 0.2 Gy (20 rad) in the calculation of latent health effects; 

they are not divided by DDREFA when emergency-phase doses exceed 0.2 Gy. Doses 

received during the long-term phase are generally controlled by the habitability criterion to be 

well below 0.2 Gy, so these doses are always divided by DDREFA in the calculation of latent 

health effects. 

Eckerman [49] recommends that the uncertainty in DDREFA be treated with the following 

functional form [49]. For breast cancer, the probability density function is equal to: 

ff(xx) = ee−(xx−1)

, 1 < xx ≤ 3 Equation 4.2-1 

For other types of cancer:

ff(xx) = 0.5 , 1 < xx ≤ 2 and ff(xx) = 0.5 ee−(xx−2)

, 2 < xx ≤ 8 Equation 4.2-2 

Where x is the value of DDREFA and f(x) is the probability associated with a value of DDREFA, 

Figure 4.2-6. Eckerman [49] further recommends that high linear energy transfer (LET) 

radiation be assigned a DDREFA of unity with no uncertainty, but the distinction between low 

and high LET radiation to an organ cannot be accommodated within the MACCS framework so 

the above functions are applied to all types of radiation. The values of DDREFA for the various 

organs are to be treated as uncorrelated.

Figure 4.2-6 The probability density for DDREFA applied in the uncertainty analysis for 

breast and all other cancers [49, Figure 10] 
4-60

To implement the uncertainty in DDREFA, the probability density functions (PDFs) in 

Equation 4.2-1 and Equation 4.2-2 are integrated over the range of DDREFA values. The 

resulting CDF is segmented into equally spaced quantiles to construct the piecewise uniform 

distributions provided in Table 4.2-7. 

As a truncation has been recommended and applied to the original exponential distributions, the 

resulting density functions do not integrate to one over their interval of definition. Therefore, 

they need to be normalized in order to be appropriately defined. 

Normalization of equation 4.2-1: 

FF = � ee−(xx−1)

3

1

dd = ee � ee−xxdd

3

1

= ee[−ee−xx]1

3 = 1 − 1

ee2 = tt1~0.864665

The normalized PDF is then

ff(xx) = 1

tt1 ee−(xx−1)

,wwww h tt1 = 1 − 1

ee2 aaaa 1 < xx ≤ 3

The resulting CDF is 

FF (xx) = 1

1 ∫ ee

xx −(ss−1)

1 dddd = ee

1 ∫ ee−ssdddd xx

1 = ee

1 [−ee−ss]1

ss = 1

1 �1 − 1

ee −1� , 1 < xx ≤ 3 Equation 4.2-3 

Normalization of equation 4.2-2: 

FF1 = � 0.5

2

1

dd = [0.5xx]1

2 = 0.5

FF2 = � ee−(xx−2)

8

2

dd = ee2 � ee−xxdd

8

2

= ee2[−ee−xx]2

8 = �1 − 1

ee6� = tt2~0.997521

The normalized PDF is then

ff(xx) = 0.5, 1 < xx ≤ 2

ff(xx) = 0.5

1

tt2 ee−(xx−2)

, wwww h tt2 = �1 − 1

ee6� aaaa 2 < xx ≤ 8 

The resulting CDF is 

FF (xx) = 0.5(xx − 1), 1 < xx ≤ 2

FF (xx) = 0.5 + 0.5 1

2 ∫ ee xx −(ss−2)

2 dddd = 0.5 + 0.5 ee2

2 ∫ ee−ssdddd xx

2 = 0.5 + 0.5 ee2

2 [−ee−ss]2

ss = 0.5 +

0.5 1

2 �1 − 1ee −2� , 2 < xx ≤ 8 Equation 4.2-4 

Fa(x) (Equation 4.2-3) and Fb(x) (Equation 4.2-4) represent the CDF for the truncated 

distributions. In other words, they allow the estimation of a quantile, given a value of x. In order 

to approximate them with piecewise uniform distribution, it is simpler to work with the inverse 

functions of Fa and Fb, and estimate the values of Fa

-1(q) and Fb-1(q) for a quantile q.
4-61

The inverse function for Fa(x) is:

FF−1(qq) = ll � ee

1− 1 ∙ qq

� , wwww h tt1 = 1 − 1

ee2 aaaa 0 ≤ qq ≤ 1 Equation 4.2-5 

While the inverse of Fb(x) is equal to:

FFbb

−1(qq) = 2qq + 1, wwww h 0 ≤ qq ≤ 0.5

FFbb

−1(qq) = ll � ee2

1−2 2[qq−0.5]

� , wwww h tt2 = 1 − 1

ee6 aaaa 0.5 ≤ qq ≤ 1 Equation 4.2-6 

The resulting CDFs are displayed on Figure 4.2-7 for DDREFA Equation 4.2-3 and 

Equation 4.2-4. The resulting piecewise uniform distributions constructed from the CDFs are 

listed in Table 4.2-7. 

Figure 4.2-7 The cumulative distribution for DDREFA applied in the uncertainty 

analysis for breast and other cancers
4-62

Table 4.2-7 Piecewise uniform distributions for DDREFA

(Equation 4.2-5) (Equation 4.2-6) 

Quantile DDREFA Quantile DDREFA

0.0000 1.000 0.0000 1.0000 

0.1000 1.0904 0.5000 2.0000 

0.2000 1.1899 0.6000 2.2225

0.3000 1.3003 0.7000 2.5092 

0.4000 1.4244 0.8000 2.9126

0.5000 1.5662 0.8500 3.1982

0.6000 1.7315 0.9000 3.5996

0.7000 1.9295 0.9300 3.9510

0.8000 2.1768 0.9500 4.2805

0.8500 2.3279 0.9700 4.7753 

0.9000 2.5060 0.9900 5.7974 

0.9500 2.7228 0.9990 7.4095

1.0000 3.0000 1.0000 8.000

SOARCA

Estimate

1.0 SOARCA

Estimate

2.0

Inhalation Dose Coefficients

For the dose coefficients related to the inhalation pathway, Eckerman [49] recommends that the

coefficients be treated as truncated log normal with the geometric means and standard 

deviations provided in Tables 4.2-8 and 4.2-9, respectively. The geometric means are the same 

as the median values used in the SOARCA analysis. A truncation at ±3 sigma is applied to 

each distribution. The 3 sigma truncation represents a truncation at quantile 0.00135 

(~0.1 percentile) and 0.99865 (~99.9 percentile). In the LHS software used by the WinMACCS 

framework, the truncation is made by normalizing any quantile generated in the probability 

space [0,1] into the truncation space [0.00135; 0.99865].

For an individual radionuclide, the dose coefficients are treated as correlated with a coefficient 

of one for all of the organs except the lung; the lung is to be correlated with a coefficient of 

negative one with all of the other organs. The logic behind this is that the inhaled radionuclides 

may spend more or less time in the lungs, depending on the chemical form of the radionuclide 

and its solubility. After departing from the lung, the radionuclide is carried through the blood 

stream to other systemic tissues. The longer the time spent in the lungs, the greater the dose 

there and the less the dose to the other systemic tissues; the shorter the time spent in the lungs, 

the smaller the dose there and the greater the dose to the other systemic tissues. Table 4.2-10

lists WinMACCS corresponding tissues correlated to the organ dose coefficients from the 

reference report, Eckerman [49]. In addition, the effective dose coefficient (ICRP60ED in 

WinMACCS) is not uncertain in this analysis. 
4-63

Table 4.2-8 MACCS uncertain parameters—geometric mean (i.e., median values, which were also used 

SOARCA analyses) for inhalation dose coefficients (Gy/Bq) [49] 

Nuclide Type Leukemia Bone Breast Lung Thyroid Liver Colon Resid

Co-58 S 7.16 × 10−10 5.26 × 10−10 1.32 × 10−9 1.27 × 10−8 5.18 × 10−10 1.06 × 10−9 8.26 × 10−10 9.27 × 1

Co-60 S 1.24 × 10−8 9.36 × 10−9 2.48 × 10−8 1.83 × 10−7 9.89 × 10−9 1.98 × 10−8 4.50 × 10−9 1.63 × 1

Rb-86 F 1.43 × 10−9 2.82 × 10−9 7.32 × 10−10 7.69 × 10−10 7.46 × 10−10 7.46 × 10−10 1.28 × 10−9 7.52 × 1

Rb-88 F 1.74 × 10−12 1.86 × 10−12 1.65 × 10−12 3.14 × 10−11 1.74 × 10−12 1.66 × 10−12 1.75 × 10−12 1.96 × 1

Sr-89 F 4.33 × 10−9 5.40 × 10−9 1.77 × 10−10 2.03 × 10−10 1.78 × 10−10 1.78 × 10−10 2.26 × 10−9 1.78 × 1

Sr-90 F 1.62 × 10−7 3.69 × 10−7 5.97 × 10−10 6.19 × 10−10 5.97 × 10−10 5.97 × 10−10 3.22 × 10−9 5.97 × 1

Sr-91 F 1.31 × 10−10 1.35 × 10−10 2.07 × 10−11 5.18 × 10−11 2.64 × 10−11 2.54 × 10−11 4.64 × 10−10 2.88 × 1

Sr-92 F 6.10 × 10−11 8.89 × 10−11 1.29 × 10−11 3.70 × 10−11 1.55 × 10−11 1.49 × 10−11 3.13 × 10−10 1.76 × 1

Y-90 S 1.22 × 10−12 1.22 × 10−12 4.23 × 10−14 7.85 × 10−9 4.23 × 10−14 1.20 × 10−12 4.44 × 10−9 4.23 × 1

Y-91 S 6.44 × 10−11 6.42 × 10−11 5.21 × 10−12 6.97 × 10−8 2.83 × 10−12 6.43 × 10−11 4.64 × 10−9 3.93 × 1

Y-91m S 9.41 × 10−13 7.25 × 10−13 8.01 × 10−13 5.00 × 10−11 6.78 × 10−13 8.97 × 10−13 5.26 × 10−12 2.03 × 1

Y-92 S 1.83 × 10−12 1.27 × 10−12 1.43 × 10−12 6.95 × 10−10 1.09 × 10−12 1.75 × 10−12 4.94 × 10−10 2.49 × 1

Y-93 S 1.77 × 10−12 1.29 × 10−12 1.27 × 10−12 1.62 × 10−9 8.99 × 10−13 1.66 × 10−12 1.63 × 10−9 1.75 × 1

Zr-95 M 2.43 × 10−9 1.26 × 10−8 1.21 × 10−9 3.07 × 10−8 6.50 × 10−10 1.05 × 10−9 1.62 × 10−9 1.05 × 1

Zr-97 M 7.77 × 10−11 6.43 × 10−11 3.78 × 10−11 3.43 × 10−9 2.77 × 10−11 4.39 × 10−11 2.81 × 10−9 4.69 × 1

Nb-95 S 3.39 × 10−10 2.49 × 10−10 5.86 × 10−10 1.19 × 10−8 2.35 × 10−10 4.94 × 10−10 7.02 × 10−10 4.23 × 1

Nb-97 S 1.63 × 10−12 1.20 × 10−12 1.39 × 10−12 1.65 × 10−10 1.14 × 10−12 1.56 × 10−12 2.44 × 10−11 3.26 × 1

Mo-99 S 2.07 × 10−11 2.12 × 10−11 2.17 × 10−11 6.02 × 10−9 1.09 × 10−11 2.74 × 10−11 2.00 × 10−9 2.06 × 1

Tc-99m M 1.65 × 10−12 2.32 × 10−12 1.16 × 10−12 7.60 × 10−11 5.45 × 10−12 1.66 × 10−12 1.84 × 10−11 2.30 × 1

Ru-103 S 2.36 × 10−10 1.73 × 10−10 4.06 × 10−10 2.21 × 10−8 1.64 × 10−10 3.32 × 10−10 1.08 × 10−9 3.02 × 1

Ru-105 S 7.95 × 10−12 5.59 × 10−12 6.05 × 10−12 7.99 × 10−10 4.50 × 10−12 7.41 × 10−12 2.96 × 10−10 1.02 × 1

Ru-106 S 6.70 × 10−10 5.44 × 10−10 1.12 × 10−9 5.35 × 10−7 5.43 × 10−10 9.28 × 10−10 1.28 × 10−8 8.44 × 1

Rh-103m S 1.32 × 10−15 3.04 × 10−15 1.64 × 10−15 1.76 × 10−11 7.05 × 10−16 2.70 × 10−15 9.37 × 10−13 5.60 × 1

Rh-105 S 4.64 × 10−12 3.87 × 10−12 4.18 × 10−12 2.31 × 10−9 2.64 × 10−12 4.49 × 10−12 5.62 × 10−10 4.61 × 1

Te-127 M 1.71 × 10−12 1.74 × 10−12 7.84 × 10−13 7.50 × 10−10 2.81 × 10−12 8.01 × 10−13 2.51 × 10−10 8.20 × 1

Te-127m M 2.31 × 10−9 9.03 × 10−9 5.84 × 10−11 5.62 × 10−8 8.62 × 10−10 5.88 × 10−11 1.91 × 10−9 4.89 × 1

Te-129 M 3.51 × 10−13 3.58 × 10−13 3.00 × 10−13 1.48 × 10−10 3.53 × 10−13 3.19 × 10−13 2.06 × 10−11 4.78 × 1

Te-129m M 1.17 × 10−9 2.71 × 10−9 9.12 × 10−11 4.83 × 10−8 1.01 × 10−9 8.69 × 10−11 4.00 × 10−9 8.02 × 1

Te-131 M 5.25 × 10−13 5.36 × 10−13 5.46 × 10−13 9.37 × 10−11 4.79 × 10−11 5.37 × 10−13 5.10 × 10−12 1.06 × 1

Te-131m M 8.85 × 10−11 1.17 × 10−10 7.11 × 10−11 4.65 × 10−9 2.69 × 10−9 7.44 × 10−11 1.46 × 10−9 7.59 × 1

Te-132 M 2.22 × 10−10 2.87 × 10−10 2.30 × 10−10 1.01 × 10−8 4.36 × 10−9 2.21 × 10−10 3.34 × 10−9 2.08 × 1
4-64

Table 4.2-8 MACCS uncertain parameters—geometric mean (i.e., median values, which were also used 

SOARCA analyses) for inhalation dose coefficients (Gy/Bq) [49] (continued)

Nuclide Type Leukemia Bone Breast Lung Thyroid Liver Colon Resid

I-131 F 3.71 × 10−11 4.89 × 10−11 2.12 × 10−11 5.98 × 10−11 1.47 × 10−7 1.67 × 10−11 2.54 × 10−11 1.82 × 1

I-132 F 1.16 × 10−11 1.23 × 10−11 8.59 × 10−12 3.64 × 10−11 1.36 × 10−9 9.91 × 10−12 1.18 × 10−11 1.45 × 1

I-133 F 1.85 × 10−11 2.00 × 10−11 1.37 × 10−11 4.24 × 10−11 2.84 × 10−8 1.38 × 10−11 2.09 × 10−11 1.57 × 1

I-134 F 5.51 × 10−12 5.82 × 10−12 4.40 × 10−12 2.99 × 10−11 2.59 × 10−10 5.00 × 10−12 5.39 × 10−12 8.27 × 1

I-135 F 1.69 × 10−11 1.84 × 10−11 1.26 × 10−11 4.04 × 10−11 5.76 × 10−9 1.35 × 10−11 1.74 × 10−11 1.73 × 1

Cs-134 F 6.37 × 10−9 6.81 × 10−9 4.81 × 10−9 6.02 × 10−9 6.34 × 10−9 6.73 × 10−9 7.20 × 10−9 7.40 × 1

Cs-136 F 9.89 × 10−10 1.12 × 10−9 7.37 × 10−10 9.68 × 10−10 1.01 × 10−9 1.05 × 10−9 1.15 × 10−9 1.17 × 1

Cs-137 F 4.47 × 10−9 4.69 × 10−9 3.82 × 10−9 4.35 × 10−9 4.46 × 10−9 4.62 × 10−9 5.22 × 10−9 4.90 × 1

Ba-139 F 1.17 × 10−11 1.20 × 10−11 1.67 × 10−12 2.91 × 10−11 1.71 × 10−12 1.73 × 10−12 1.12 × 10−10 1.81 × 1

Ba-140 F 1.46 × 10−9 2.07 × 10−9 8.97 × 10−11 1.55 × 10−10 1.21 × 10−10 1.28 × 10−10 5.45 × 10−9 1.66 × 1

La-140 M 1.35 × 10−10 9.67 × 10−11 1.10 × 10−10 3.96 × 10−9 6.60 × 10−11 3.23 × 10−10 2.51 × 10−9 1.23 × 1

La-141 M 3.07 × 10−12 1.21 × 10−11 1.33 × 10−12 6.64 × 10−10 1.13 × 10−12 1.94 × 10−11 3.67 × 10−10 1.56 × 1

La-142 M 7.85 × 10−12 6.06 × 10−12 6.75 × 10−12 2.45 × 10−10 5.81 × 10−12 9.79 × 10−12 8.08 × 10−11 1.34 × 1

Ce-141 S 3.71 × 10−11 1.08 × 10−10 5.97 × 10−11 2.97 × 10−8 2.26 × 10−11 8.18 × 10−11 1.29 × 10−9 4.65 × 1

Ce-143 S 1.45 × 10−11 1.38 × 10−11 1.27 × 10−11 4.98 × 10−9 6.72 × 10−12 1.64 × 10−11 1.73 × 10−9 1.38 × 1

Ce-144 S 1.19 × 10−9 2.06 × 10−9 2.74 × 10−10 4.24 × 10−7 1.44 × 10−10 5.87 × 10−9 1.14 × 10−8 2.16 × 1

Pr-143 S 2.01 × 10−12 2.01 × 10−12 1.29 × 10−14 1.82 × 10−8 1.29 × 10−14 1.60 × 10−11 2.08 × 10−9 1.29 × 1

Pr-144 S 1.58 × 10−14 1.39 × 10−14 1.71 × 10−14 5.66 × 10−11 1.58 × 10−14 1.61 × 10−14 1.28 × 10−12 3.86 × 1

Nd-147 S 3.42 × 10−11 9.92 × 10−11 4.33 × 10−11 1.80 × 10−8 1.65 × 10−11 6.26 × 10−11 1.82 × 10−9 3.35 × 1

Np-239 M 3.46 × 10−11 5.16 × 10−10 1.29 × 10−11 6.35 × 10−9 8.24 × 10−12 3.34 × 10−11 1.18 × 10−9 1.46 × 1

Pu-238 S 4.14 × 10−7 1.62 × 10−4 1.38 × 10−7 9.34 × 10−5 2.77 × 10−7 3.43 × 10−5 2.88 × 10−7 2.77 × 1

Pu-239 S 4.57 × 10−7 1.84 × 10−4 1.59 × 10−7 8.76 × 10−5 3.18 × 10−7 3.91 × 10−5 3.29 × 10−7 3.18 × 1

Pu-240 S 4.58 × 10−7 1.84 × 10−4 1.59 × 10−7 8.78 × 10−5 3.18 × 10−7 3.91 × 10−5 3.29 × 10−7 3.18 × 1

Pu-241 S 9.30 × 10−9 4.08 × 10−6 3.57 × 10−9 4.58 × 10−7 7.11 × 10−9 8.60 × 10−7 7.18 × 10−9 7.12 × 1

Am-241 M 2.94 × 10−6 1.70 × 10−3 1.44 × 10−6 3.72 × 10−5 2.88 × 10−6 1.05 × 10−4 2.89 × 10−6 2.88 × 1

Cm-242 M 9.32 × 10−8 2.73 × 10−5 1.73 × 10−8 3.54 × 10−5 3.47 × 10−8 7.14 × 10−6 4.39 × 10−8 3.47 × 1

Cm-244 M 1.94 × 10−6 9.22 × 10−4 6.42 × 10−7 3.93 × 10−5 1.28 × 10−6 7.53 × 10−5 1.29 × 10−6 1.28 × 1

Notes F = fast dissolution and high level of absorption to blood; M = an intermediate rate of dissolution and level of absorption to blood; and S = s

and low level of absorption to blood. The fractional rate of absorption (d−1) assigned to the default types are: Type F = 100, Type M = 1

exp(-0.005 t), and Type S = 0.1 exp(-100 t)+1.0 x 10-4 exp(-0.0001 t) where t is the time (days) since deposition in the lung.
4-65

Table 4.2-9 MACCS uncertain parameters—geometric standard deviations for 

inhalation dose coefficients (i.e., σ[49]) 

Nuclide Type Lung Leukemia Bone Breast Thyroid Liver Colon Residual

Co-58 S 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Co-60 S 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Rb-86 F 2.51 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Rb-88 F 1.5 1.5 1.5 1.5 1.5 2.56 1.5 1.5

Sr-89 F 5.4 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Sr-90 F 5.15 1.5 1.5 1.5 1.5 2.74 1.5 1.5

Sr-91 F 3.03 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Sr-92 F 2.88 1.56 1.76 1.5 1.5 1.5 1.5 1.5

Y-90 S 1.5 2.05 1.5 1.61 1.61 2.33 1.5 1.61

Y-91 S 1.5 4.51 3.25 1.5 1.65 4.95 1.5 1.5

Y-91m S 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Y-92 S 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Y-93 S 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Zr-95 M 1.5 1.5 1.5 1.5 1.5 1.88 1.5 1.5

Zr-97 M 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Nb-95 S 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Nb-97 S 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Mo-99 S 1.5 1.61 2.05 1.5 1.5 3.05 3 1.5

Tc-99m M 1.5 1.5 1.5 1.5 2.22 1.5 1.5 1.5

Ru-103 S 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Ru-105 S 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Ru-106 S 1.5 2.04 2.49 1.5 1.5 1.88 1.5 1.5

Rh-103m S 1.5 1.5 1.5 1.5 1.5 1.5 3.08 1.5

Rh-105 S 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Te-127 M 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Te-127m M 1.5 3.55 5.72 1.5 3.03 7.38 1.5 1.5

Te-129 M 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Te-129m M 1.5 3.2 4.24 1.5 2.68 4.48 1.5 1.5

Te-131 M 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Te-131m M 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Te-132 M 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

I-131 F 6.54 1.5 1.5 1.5 1.5 1.5 2.74 1.5

I-132 F 1.87 1.5 1.5 1.5 2.64 1.5 1.5 1.5

I-133 F 4.22 1.5 1.5 1.5 1.54 1.5 2.75 1.5

I-134 F 1.5 1.5 1.5 1.5 3.49 1.5 1.5 1.5

I-135 F 2.67 1.5 1.5 1.5 1.97 1.5 1.86 1.5

Cs-134 F 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Cs-136 F 2.04 1.5 1.5 1.5 1.5 1.5 1.5 1.5
4-66

Table 4.2-9 MACCS uncertain parameters—geometric standard deviations for 

inhalation dose coefficients (i.e., σ[49] (continued)) 

Nuclide Type Lung Leukemia Bone Breast Thyroid Liver Colon Residual

Cs-137 F 1.55 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Ba-139 F 1.72 4.25 3.31 2.25 2.47 2.09 1.5 1.85

Ba-140 F 6.28 1.5 1.5 1.5 1.5 3.68 1.5 1.5

La-140 M 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

La-141 M 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

La-142 M 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Ce-141 S 1.5 1.5 1.6 1.5 1.5 1.5 1.5 1.5

Ce-143 S 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Ce-144 S 1.5 4.57 3.39 1.5 1.5 3.32 1.5 1.5

Pr-143 S 1.5 3.88 2.39 5.49 5.49 2.24 1.5 5.49

Pr-144 S 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Nd-147 S 1.5 1.5 1.84 1.5 1.5 1.5 1.5 1.5

Np-239 M 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Pu-238 S 1.5 4.32 2.97 3.15 3.15 3.1 3.17 3.15

Pu-239 S 1.5 4.32 2.95 3.13 3.14 3.08 3.16 3.13

Pu-240 S 1.5 4.32 2.95 3.14 3.14 3.08 3.16 3.14

Pu-241 S 1.84 4.29 2.77 2.96 2.97 2.92 2.99 2.96

Am-241 M 1.5 1.78 1.5 1.5 1.5 1.5 1.5 1.5

Cm-242 M 1.5 1.51 1.5 1.5 1.5 1.5 1.5 1.5

Cm-244 M 1.5 1.71 1.5 1.5 1.5 1.5 1.5 1.5

Notes F = fast dissolution and high level of absorption to blood; M = an intermediate rate of dissolution and level of absorption to 

blood; and S = slow rate of dissolution and low level of absorption to blood. The fractional rate of absorption (d−1) assigned 

to the default types are; Type F = 100, Type M = 10.0 e^(-100 t)+0.005 e^(-0.005 t), and Type S = 0.1 e^(-100 t)+1.0 x 

〖10〗^(-4) e^(-0.0001 t) where t is the time (days) since deposition in the lung.

Table 4.2-10 Crosswalk between reference type from Tables 4.2-8 and 4.2-9 and 

WINMACCS organ doses

Tables 4.2-8 and 4.2-9

(from [49])

WinMACCS Organ List

Leukemia Red Marrow

Bone Bone Surface

Breast Breast

Lung Lung

Thyroid Thyroid

Liver Liver

Effective ICRP60ED 

Residual Bladder Wall (representing the pancreas)

Colon Lower LI

not included Stomacha

a Not used in the calculation of latent cancer fatalities for SOARCA estimate.
4-67

Mortality Risk Coefficient (CFRISK)

Eckerman [49] also provides estimates of the uncertainty in the mortality risk coefficients

(CFRISK) for each of the organs included in the SOARCA analyses for latent health effects. 

The distributions are log normal and are assumed to be uncorrelated. Table 4.2-11 provides the 

geometric mean and geometric standard deviation for each truncated log normal distribution. 

Figure 4.2-8 shows a graphical representation of the data presented in Table 4.2-11. A 

truncation at ±3 sigma is applied to each distribution. The three sigma truncation represents a 

truncation at quantile 0.00135 (~0.1 percentile) and 0.99865 (~99.9 percentile). In the LHS 

software used by the WinMACCS framework, the truncation is made by normalizing any 

quantile generated in the probability space [0, 1] into the truncation space [0.00135; 0.99865].

Figure 4.2-8 Cumulative distribution functions for latent health effects: mortality risk 

coefficients (CFRISK) for each of the organs included in the SOARCA 

analysis
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Table 4.2-11 Age-averaged cancer mortality risk estimates and uncertainties for 

low-dose, low-LET uniform irradiation of the body [49] 

Mortality Risk Coefficient

(CFRISK)

Site Mean(Sv-1)

a Standard 

Deviationb

SOARCA 

Estimate

Leukemia 5.57 × 10-3 Ln(1.23) 1.11 x 10-2

Bone 9.50 x 10-5 Ln(5.70) 1.90 x 10-4

Breast 5.06 x 10-3 Ln(2.21) 5.06 x 10-3

Lung 9.88 x 10-3 Ln(1.87) 1.98 x 10-2

Thyroid 3.24 x 10-4 Ln(4.15) 6.48 x 10-4

Liver 1.50 x 10-3 Ln(4.65) 3.00 x 10-3

Colon 1.04 x 10-2 Ln(2.26) 2.08 x 10-2

Residual 2.46 x 10-2 Ln(2.10) 4.93 x 10-2

Total 5.75 x 10-2

Note: a Geometric mean of the log normal distribution, which is also the median of the 

distribution. b Ln(σ) where σ is the geometric standard deviation of the log normal distribution.

4.2.6 Dispersion (CYSIGA, CZSIGA)

Dispersion directly affects doses to members of the population and resulting health effects. 

Thus, the dispersion parameters used to estimate atmospheric dispersion are important to the 

outcome of the calculation. However, in terms of predicted health effects, these parameters 

tend to have a non-linear effect when using the linear, no-threshold (LNT) dose-response model

for estimating latent health effects because more dispersion simply means lower individual dose 

to a greater population. However, dispersion has a greater effect when using dose truncation 

because a smaller dose to an individual can reduce a finite risk to zero. 

Initially, the authors considered basing the distributions for dispersion on expert data [44] as 

evaluated in Synthesis of Distributions Representing Important Non-Site-Specific Parameters in 

Off-Site Consequence Analysis [43]. However, after a review of the data, it became clear that 

this would not be appropriate. The expert elicitation evaluated the uncertainty in a single 

weather instance over a short period of time. The intended use of the uncertainty analysis, 

though, is to apply the uncertainty to a whole year of weather data. Doing this would imply that 

the uncertainty in the dispersion for a single hour of weather is fully correlated with the 

uncertainty for all hours of the year. This would be an extremely poor assumption; a better 

assumption would be that uncertainty in a single hour of weather data is completely 

uncorrelated with other hours of weather data. Thus, because of the way the uncertainty in 

dispersion is being implemented in this analysis, expert judgment is used to estimate the range 

of uncertainty in dispersion. A previous study compared mean results over a year of weather for 

four different computer codes using different approaches for modeling a plume [50] and found 

that the variation in the results was within a factor of two. Here, we assume that this factor of 

two is the uncertainty in the Gaussian plume model. Because ground-level concentrations in 

the near field are proportional to the product of the horizontal and vertical dispersion 

parameters, the product of the two is assumed to range from 0.5 to 2.0 times the nominal values 

at the 5th and 95th percentiles of a log-normal distribution, respectively. Furthermore, the 
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uncertainty is apportioned evenly between the two parameters, so both σy and σz are assumed 

to be 0.707 and 1.414 times their nominal values at the 5th and 95th percentiles, respectively. 

Because dispersion in the two dimensions are related physically, they are taken to be fully 

correlated. Likewise, the dispersion coefficients for each of the stability classes are fully 

correlated. Tables 4.2-12 and 4.2-13 show log-normal inputs for the CYSIGA and CZSIGA 

parameters. Figure 4.2-9 shows a graphical representation of the data presented in 

Tables 4.2-12 and 4.2-13. 

Table 4.2-12 MACCS uncertain parameters—inputs for log-normal dispersion 

parameters distributions

Linear, Crosswind Dispersion Coefficients 

(CYSIGA) 

Linear, Vertical Dispersion Coefficients

(CZSIGA) 

Stability Class Stability Class

A/B [m] C [m] D [m] E/F [m] A/B [m] C [m] D [m] E/F [m]

Nominal

(50th

quantile 

Ref. 36)

0.7507 0.4063 0.2779 0.2158 0.0361 0.2036 0.2636 0.2463

5th 0.37535 0.20315 0.13895 0.1079 0.01805 0.1018 0.1318 0.12315

95th 1.5014 0.8126 0.5558 0.4316 0.0722 0.4072 0.5272 0.4926

Note: A factor of 2 between 50th and 95th as well as between 5th and 50th quantile is equivalent to a factor of ln(2) in logtransformed data
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Figure 4.2-9 Cumulative distribution functions of linear (a) crosswind dispersion 

coefficients, a(m) and (b) vertical dispersion coefficients, a(m)
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Table 4.2-13 MACCS uncertain parameters—dispersion

Linear, Crosswind 

Dispersion Coefficients, 

a(m) 

(CYSIGA) 

Percentile

Stability Class

A/B [m] C [m] D [m] E/F [m]

Piecewise log-uniform

distribution

0 0.0650 0.0631 0.0341 0.0212

1 0.2817 0.1524 0.1043 0.0810

5 0.3754 0.2032 0.1390 0.1079

10 0.4374 0.2368 0.1619 0.1258

25 0.5650 0.3058 0.2091 0.1624

50 0.7507 0.4063 0.2779 0.2158

75 0.9975 0.5399 0.3693 0.2867

90 1.2883 0.6972 0.4769 0.3703

95 1.5014 0.8126 0.5558 0.4316

99 2.0009 1.0829 0.7407 0.5752

100 4.0698 2.0763 1.7618 1.5307

SOARCA Values 0.7507 0.4063 0.2779 0.2158

Linear, Vertical Dispersion 

Coefficients, a(m) 

(CZSIGA) 

Percentile

Stability Class

A/B [m] C [m] D [m] E/F [m]

Piecewise log-uniform

distribution

0 0.0056 0.0487 0.0421 0.0533

1 0.0135 0.0764 0.0989 0.0924

5 0.0181 0.1018 0.1318 0.1232

10 0.0210 0.1186 0.1536 0.1435

25 0.0272 0.1532 0.1984 0.1854

50 0.0361 0.2036 0.2636 0.2463

75 0.0480 0.2705 0.3503 0.3273

90 0.0620 0.3494 0.4524 0.4227

95 0.0722 0.4072 0.5272 0.4926

99 0.0962 0.5427 0.7026 0.6565

100 0.1951 1.8861 3.6880 4.5386

SOARCA Values 0.0361 0.2036 0.2636 0.2463

Note: CYSIGA and CZSIGA are perfectly rank correlated with each other and across the stability classes.

4.2.7 Hot Spot and Normal Relocation (DOSNRM, TIMNRM, DOSHOT, TIMHOT) 

Protective actions that may be implemented in response to a severe accident and radiological 

release include evacuation and sheltering of individuals who reside in the emergency planning 

zone (EPZ). In addition to these protective actions, there are effective dose thresholds that are 

established to ensure members of the public are relocated from elevated dose areas that 

exceed U.S. Environmental Protection Agency (EPA) protective action guides (PAGs). When 

these thresholds are exceeded, offsite response organizations (OROs) will relocate individuals 

from the affected areas. This application is typically considered for residents beyond the EPZ 

where the effective dose exceeds protective action criteria but also applies to residents who 

refused to follow the initial evacuation orders. It is assumed these individuals will evacuate 

when they understand a release has in fact occurred and they are informed they are located in 
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high dose areas. The OROs determine the affected areas based on dose projections using 

State, utility, and Federal agency computer models together with dose measurements taken in 

the field. The use of multiple dose models combined with field measurements and the need for 

response organizations to mobilize to relocate affected residents provides opportunity for 

variations in dose predictions and response time which makes these parameters good 

candidates for the uncertainty analysis. 

Hot-spot relocation and normal relocation models are included in the MACCS code to reflect this 

relocation activity performed by OROs. Hot-spot and normal relocation models are based on 

effective dose models using the total effective dose commitment projected to be received by an 

individual who remained in place for the entire emergency-phase period while engaging in 

normal activity. The pathways used for calculating the total effective dose commitment are 

cloudshine, groundshine, direct inhalation, and resuspension inhalation. The reference time for 

the relocation dose criterion is plume arrival. Any individuals relocated due to hot spots are 

removed from the problem for the duration of the emergency phase and receive no additional 

dose during this phase [9]. 

Hot-spot and normal dose information would be available shortly before or concurrent with the 

release to the environment which occurs at about 20 hours for the LTSBO. Dose projections 

would be available earlier, however, over a 20 hour period, wind shifts and changing accident 

conditions may not support projections for use in relocation much earlier.

Relocation is a process that requires identification of the affected areas, notification of residents 

within those areas, and movement of the public out of the affected areas. The time values 

represent the average time expected to implement these actions. The baseline for hot-spot 

relocation criteria is 12 hours after plume arrival if the total effective lifetime dose commitment 

for the weeklong emergency phase is projected to exceed 0.05 Sv (5 rem). The 5 rem value is 

the upper limit of the EPA PAGs [51]. A single time value was selected and applied to all of the 

accident scenarios evaluated for the Peach Bottom plant. The relocation time considers that 

response agencies would have competing priorities early in the event. The hot-spot time values 

will be varied from 6 hours to 18 hours in this uncertainty analysis to reflect the possibility that 

relocations could begin early based on dose projections or may be delayed while responders 

address other priorities (Figure 4.2-10b and Table 4.2-14). A lower bound of 1 rem and an 

upper bound of 10 rem will be used for the effective dose (Figure 4.2-10a and Table 4.2-14). 

For normal relocation, individuals are relocated 24 hours after plume arrival if the total effective

lifetime dose commitment for the weeklong emergency phase is projected to exceed 0.005 Sv

(0.5 rem). The relocation time was established because response agencies would evacuate the 

hot-spot areas prior to focusing on the normal relocation areas. Also, there is less urgency in 

relocating these individuals because, similar to hotspot relocation, the 0.5 rem projected value 

represents the effective cumulative dose for the entire early phase and through relocation the

individuals would be moved long before the end of the early phase. Typically, the EPA PAGs of

1 rem is used for normal relocation; however, 0.5 rem was used in the Peach Bottom analysis 

because local officials had expressed this as the value likely to be established for habitability. 

The normal relocation time values will be varied from 12 hours to 36 hours in this uncertainty 

analysis to reflect the possibility that relocations could begin early based on projected dose or 

may be delayed while responders address other priorities (Figure 4.2-10b and Table 4.2-14). A 

lower bound of 0.1 rem and an upper bound of 1 rem will be used for the effective dose

(Figure 4.2-10a and Table 4.2-14). 

The hot-spot and normal relocation values used in NUREG-1150 were 50 rem and 25 rem 

respectively [16]. The values used in SOARCA were established to better align with site 

specific response expectations and EPA PAGs. 
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Figure 4.2-10 Cumulative distribution functions of hotspot and normal (a) relocation 

doses and (b) relocation times
4-74

Table 4.2-14 MACCS uncertain parameters—relocation doses and times

Parameter Triangular Distribution

DOSHOT: Hot-spot relocation – dose

SOARCA estimate: 5 rem 

LB = 1.0 rem

UB = 10.0 rem

Mode = 5.0 rem

TIMHOT: Hot-spot relocation – time

SOARCA estimate: 12 hours 

LB = 6.0 hr.

UB = 18 hr.

Mode = 12 hr.

DOSNRM: Normal relocation – dose

SOARCA estimate: 0.5 rem 

LB = 0.1 rem

UB = 1.0 rem

Mode = 0.5 rem

TIMNRM: Normal relocation – time

SOARCA estimate: 24 hours 

LB = 12.0 hr.

UB = 36.0 hr.

Mode = 24 hr.

Note: Relocation times are perfectly rank correlated. Relocation doses are perfectly rank correlated. 

4.2.8 Evacuation Delay (DLTEVA)

Evacuation delay defines the duration of the sheltering period that occurs before evacuation of 

residents begins [9]. Delay to evacuation might be affected by a delay in response to the 

evacuation order, a need to wait for the return of commuters, a need to wait for public 

transportation, a need to shut down operations prior to leaving work, etc. Research shows that 

delay is not uniform with most of the evacuees experiencing a smaller delay (e.g., 90% of the 

public evacuates in about 60% of the response time) [52, 53]. There is high confidence in the 

alert and notification system to warn the public within the specified time; however, response of 

the public is a function of the time to receive the notification and the time to prepare to evacuate 

[54]. Because people are located throughout the EPZ and have different response timing, this 

variable was considered a good candidate for the uncertainty analysis. 

The DLTEVA parameter is applied at the cohort level and the uncertainty analysis will sample 

on each of the cohorts (Figure 4.2-11 and Table 4.2-15). Cohorts 1 and 2 represent the 0-10

mile public and 10-20 mile shadow respectively, and the baseline DLTEVA value is one hour. 

This value is supported by the ORNL 6615 study, which provided empirical data showing that 

most of the public is mobilized in about an hour [54]. The lower bound is established as 0.0 hr

which would indicate there is no delay after the public becomes aware of the emergency. The 

lower bound was set based on results of a focus group survey of residents of EPZs that indicate 

some people may evacuate immediately upon receipt of an evacuation order [55]. The upper 

bound was selected as four hours to account for the need to gather family members, pack, and 

prepare to evacuate. Cohort 2 is the shadow evacuation which is aligned with the evacuation of 

Cohort 1. 

Cohort 3 represents the schools and the 0-10 mile shadow evacuation. A baseline value of 

45 minutes was used because schools are notified early and are prepared to evacuate when the 

official order is issued. The 0-10 mile shadow has the same response characteristics because 

this cohort has been defined in SOARCA as evacuating when the schools evacuate. The 0-10

mile shadow evacuates spontaneously (prior to receiving an evacuation order) when the 
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emergency is communicated to the residents of the EPZ via the sirens and emergency 

evacuation system messaging for the site area emergency (SAE). Shadow evacuation of the 

public has been observed to occur quickly for industrial accidents [41]. For the uncertainty 

analysis, the lower bound for this cohort was set at 0.25 hr, which is 15 minutes after site 

declares the SAE. The Pennsylvania emergency management plan explains that evacuation 

can be implemented for an SAE or a general emergency. Therefore, there could be conditions 

in which the State might evacuate the schools early, and if the evacuation were to occur in the 

morning at the beginning of school or in the afternoon at the end of school, buses would be 

positioned to begin the evacuation promptly. The early warning for schools provides time for 

buses to mobilize and be at the school if an evacuation were to be ordered. Evacuation drills at 

schools demonstrate the ability to prepare and move students quickly. The upper bound of four 

hours was established to account for potential delay in notification, communication with drivers, 

delay in travel due to weather or other impediments, etc. 

Cohort 4 represents special facilities and was modeled in the baseline as evacuating later in the 

event at 4.25 hours. Special facilities often take longer as a whole than the general public. 

These facilities actually evacuate individually following facility specific evacuation plans and are 

not typically dependent upon one another for support [55]. Therefore, in practice, some facilities 

begin earlier in the event and some begin later. For this uncertainty analysis, the lower bound 

was set at 0.0 hr because facilities may have onsite transportation resources and could prepare

to evacuate promptly. The upper bound was set at six hours to represent a delay in availability 

of transportation resources, communication with drivers, delay in travel due to weather, or other 

impediments. Since the site is located near larger cities such as Lancaster, Pennsylvania, and 

Baltimore, Maryland it is expected there are ample regional resources, should these be needed. 

Six hours is estimated to be a maximum time that it would take to coordinate regional resources. 

Cohort 5 is the evacuation tail, which by definition begins evacuating at the end of the general 

public evacuation. The baseline value of 4.25 hours was based on the site specific evacuation 

time estimate (ETE) study which showed that 90% of the population had completed the 

evacuation in 4.25 hours. The values for the uncertainty analysis are established based on the 

ETE by adding four hours to the Cohort 1 distribution. This equates to Cohort 5 values of four 

hours for the lower bound and eight hours for the upper bound.
4-76

Figure 4.2-11 Cumulative distribution functions of evacuation delay

Table 4.2-15 MACCS uncertain parameters—evacuation delay

DLTEVA

Parameter SOARCA 

Estimate/Mode

Triangular 

Distribution 

Evacuation delay – cohort 1 

(0-10 mile Public) 1.0 LB = 0.0 hr.UB = 4.0 hr.

Evacuation delay – cohort 2 

(10-20 mile Shadow) 1.0 LB = 0.0 hr.UB = 4.0 hr.

Evacuation delay – cohort 3

(Schools/Shadow) 0.75 LB = 0.25 hr.UB = 4.0 hr.

Evacuation delay – cohort 4 

(Special Facilities) 4.25 LB = 0.0 hr.UB = 6.0 hr.

Evacuation delay –cohort 5

(Evacuation Tail) 4.25 LB = 4.0 hr.UB = 8.0 hr.

Note: Evacuation delays are sampled independently for each cohort and for each radial ring.
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4.2.9 Evacuation Speed (ESPEED)

Evacuation speed represents the travel speed of evacuees as they evacuate the EPZ. To 

model evacuation with WinMACCS, evacuees are loaded onto the roadway network at a 

specified time and a single speed is used. However, evacuations typically occur as a 

distribution in which the cumulative percent of the public evacuating the area increases over 

time until all members of the public have evacuated [53]. Evacuations are typically represented 

as a curve of the number of people evacuated that is relatively steep at the beginning and tends 

to decrease over time as the last members of the public exit the area. This distribution curve is 

relatively steep for shorter duration evacuations from areas the size of an EPZ, and the 

distribution curve is less steep for longer duration evacuations typical of those for hurricanes 

which may begin days in advance of landfall. The point at which the curve tends to flatten 

occurs when approximately 90% of the population has evacuated. The last 10% of the 

population is called the evacuation tail [53]. The ESPEED parameter is applied at the cohort 

level and the uncertainty analysis will sample on each of the cohorts (Figure 4.2-12 and

Table 4.2-16). For the uncertainty analysis the distributions are applied to the mid-phase for all 

of the cohorts.

For cohorts 1 and 2 which represent the 0-10 mile public and 10-20 mile shadow respectively, 

the baseline speed was 3 mph. The slow speed is established to account for the model loading 

all members of the public cohort at one time. In reality, the evacuees would load the network 

over a longer period of time and travel a little faster. The 10-20 mile shadow would be expected 

to have a higher speed, but was limited to 3 mph because of the way the general public is 

integrated with this cohort [1]. This speed value was developed using information from the site 

specific ETE. The lower bound is established as 1.0 mph which would indicate there are 

impediments to the evacuation causing travel to be considerably slower. The upper bound was 

selected as 10 mph which would indicate that minimal traffic congestion occurs. 

Cohort 3 represents the schools and the 0-10 mile shadow evacuation. A baseline speed of 

20 mph was used because schools are notified directly and early. The schools contribute the 

first evacuating vehicles on the roadway and their vehicles enter the transportation network 

before congestion from the general public begins. The 0-10 mile shadow has the same 

response characteristics as the schools, leaving almost immediately. A lower bound was set at 

10.0 mph to account for unexpected travel delays due to impediments such as weather. The 

upper bound of 30 mph was established based on the roadway network posted speeds. Most of 

the roadways within the EPZ have posted speeds greater than 30 mph and many roadways 

have 50 or 55 mph speed limits. The average travel speed on a roadway is always less than 

the posted speed because of traffic control requiring stops and starts. 

Cohort 4 (special facilities) was modeled in the baseline as starting evacuation later in the 

event, near the end of the peak traffic congestion. As discussed earlier, in practice some 

facilities move earlier in the event and some move later. The lower bound was set at 1.0 mph to 

represent facilities that have entered the roadway at the peak congestion period when speeds 

are the slowest. The upper bound was set at 30 mph to represent sufficient resources to 

support prompt evacuation of these facilities or for those facilities evacuating very late when 

speeds have increased. 

Cohort 5 (evacuation tail) begins evacuation at the end of the general public evacuation. 

Although their initial speed is the same as the general public, the roadways begin to clear and 

the tail has overall faster exiting speeds. The SOARCA values of 3 mph for the early phase and 

20 mph for the middle phase considers that these are the last vehicles on the roadway entering 

when congestion is at the peak and as congestion clears, the cohorts speed increases. The 
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lower bound and mode of the triangular distribution was set at 3 mph because by definition, the 

tail enters the roadway after 90% of the public has evacuated, therefore they are at the end of 

the peak congestion and the speed at this point could be 1 mph for Cohort 1. The upper bound 

of 30 mph represents roadways that are relatively free of congestion once the majority of 

vehicles have left the area [53]. 

Figure 4.2-12 Cumulative distribution functions of evacuation speed
4-79

Table 4.2-16 MACCS uncertain parameters—evacuation speed

ESPEED

Parameter SOARCA 

Estimate/Mode Distribution 

Evacuation speed – cohort 1

(0-10 mile Public) 3 mph

Triangular

LB = 1.0 

UB = 10.0

Mode = 3.0

Evacuation speed – cohort 2 

(10-20 mile Shadow) 3 mph

Triangular

LB = 1.0 

UB = 10.0

Mode = 3.0

Evacuation speed – cohort 3 

(Schools/Shadow) 20 mph

Triangular

LB = 10.0 

UB = 30.0

Mode = 20

Evacuation speed– cohort 4

(Special Facilities) 20 mph

Triangular

LB = 1.0 

UB = 30.0

Mode = 20

Evacuation speed – cohort 5 

(Evacuation Tail) 20 mph

Triangular

LB = 1.0 

UB = 30.0

Mode = 20

Note: Evacuation speeds are perfectly rank correlated between cohorts. 

4.3 Other Phenomena Considered

In some cases, it is desirable to investigate the influence of phenomena that are considered 

important, but cannot be easily accessed by replacing point estimates with distributions for 

available input parameters. The integrated cases in this study can determine the influence on 

selected results only over the parameters and range of inputs defined in Section 4.1 and 

Section 4.2. Exclusion of specific phenomena from this study does not indicate whether or not 

they are important, rather in some cases it is driven by the lack of knowledge as to how to 

incorporate uncertainty in these phenomena. In other cases, the models and codes used in this 

study have not been parameterized such that uncertainty in these potentially important 

phenomena can be quantified. In some cases, to measure the effects of other potentially 

important phenomena, alternative sensitivity study can be employed using approaches specific 

to the phenomena being investigated. These approaches include one-off analysis, targeted 

modeling scenarios, and sensitivity cases that are tailored to the analysis to help quantify the 

effects. Other cases would require significant code changes to explore the phenomena of 

interest. 

The following section discusses several potentially important phenomena identified during the 

parameter selection and review process, as well as those raised during ACRS and peer 

reviews. While this list is not intended to be all inclusive rather, it is an attempt to qualitatively 

and quantitatively, when possible, assess the potential importance of a few select phenomena 

identified by expert judgment. 
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4.3.1 Source Term Model

4.3.1.1 Early Event Operator Actions

As pointed out during the peer review of the selected parameters and distributions listed in 

Section 4.1 and Section 4.2, as well as by ACRS committee members, there is generally an

uncertainty in the timing of operator actions. It is clear that the operator actions by default, 

through the assumption of in-action, define the unmitigated LTSBO scenario. However, the 

larger uncertainty in operator actions includes either the potential for operators to (i) take 

unexpected actions, (ii) take actions out of order depending upon the severity of the accident,

(iii) experience degradation of specific performance abilities due to stress and other factors, or 

(iv) all of the above. Globally, these issues are beyond the scope of this study and the selected 

unmitigated LTSBO scenario. 

The SOARCA Peach Bottom unmitigated response LTSBO scenario includes some operator 

actions. It is generally accepted that even for an unmitigated response scenario, early in the 

event, some minimal operator actions will be expected to occur. Two operator actions were 

credited in the unmitigated LTSBO calculation12. First, operators are assumed to open one 

SRV to begin a controlled depressurization of the reactor vessel approximately one hour after 

the initiating event. This action is prescribed in station emergency procedures to prevent 

excessive cycles on the SRV. The target reactor vessel pressure is at or above 125 psi, which 

would permit continued operation of RCIC or HPCI, if necessary. Five SRVs associated with 

the automatic depressurization system would be available for this operation. These SRVs are 

provided with accumulators that provide a back-up pneumatic supply for operation of the valves 

upon loss of the Instrument Nitrogen System. Second, operators are assumed to take manual 

control of RCIC approximately two hours after the initiating event. This involves remote (i.e., 

from the control room) manipulation of the position of the steam throttle valve at the inlet to the 

RCIC turbine to reduce and control turbine speed. This action reduces and stabilizes coolant 

flow from the RCIC pump to maintain the reactor vessel level within a prescribed range. In 

addition, there are a general series of actions that shed loads on emergency buses to extend 

the battery lifetime. The effectiveness of those actions is captured in the uncertain distribution 

for battery life included in the uncertainty analysis. 

It is clear that without the expected actions occurring that the RPV would pressurize and the 

RPV would be overfilled by which the RCIC which would then automatically turn off. This would 

accelerate the accident and subsequent releases to the environment. The first operator action, 

opening the SRV to begin a controlled depressurization of the RPV, uses a designated 

MELCOR control function (i.e., CF094) to actuate the SRV. After a predetermined time (e.g., 

one hour after the initiating event) the designated control function actuates SRV-1 to open to 

begin the cool down. However, the second operator action, taking manual control of RCIC 

approximately two hours after the initiating event, does not have designated control functions 

within MELCOR. The MELCOR control functions used when RCIC is initiated are the same as 

those used when manual control is assumed to occur. To create a separate suite of control 

functions specifically for manual control of RCIC would require a significant change to the Peach 

Bottom MELCOR deck. Thus, the second operator action is not analyzed. The uncertain in the 

 

12 The action times used in NUREG/CR-7110 Volume 1 were based on ‘table-top’ exercises among NRC staff and 

licensee personnel, in which the anticipated accident sequence timeline was reviewed to characterize a 

reasonable time at which action would be taken.
4-81

time of the operator action, opening the SRV to begin a controlled depressurization of the RPV, 

in terms of this analysis is considered as scenario uncertainty, and as such, delays in this 

operator action are evaluated in this study in a series of sensitivity analyses presented in 

Section 6.4.1, rather than incorporated into the integrated uncertainty analysis. 

4.3.1.2 Timing of Lower Head Failure

During the peer review and ACRS meetings, the single mode of lower head failure used for 

SOARCA (i.e., gross creep rupture of the lower head) was discussed. To better clarify this 

single mode of lower head failure, the uncertainty analysis took into consideration variations in 

the Larson-Miller creep parameters, and whether small penetration/drain line failures would 

affect the overall timing of lower head failure.

Larson-Miller Creep Parameters

Initial investigations into lower head failure were considered by varying the Larson-Miller creep 

rupture parameter in MELCOR. Current dynamic PRA work [56] indicates that applying a 

distribution to the MELCOR Larson-Miller creep rupture parameter (i.e., LM-Creep (t)) shown on 

Figure 4.3-1, will only result in approximately a 20 minute change in the timing of lower head

failure between the 5th and 95th percentiles. This change in timing will not affect the overall 

accident progression, nor will it noticeably change the environmental source term. Based on 

these analyses, it was determined that Larson-Miller creep rupture parameter uncertainty would 

not be investigated for this work.

Figure 4.3-1 Creep rupture parameter distribution
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Small Penetrations/Drain Line

Detailed analysis of the MELCOR source code and ongoing MELCOR studies associated with 

U.S. Department of Energy and NRC post Fukushima analysis, have determined two issues 

regarding small penetrations and drain line lower head failure modes. The first issue involves a 

computational work-around developed for MELCOR to model corium flow through the lower 

head failure. Due to numerical limitations of computers when MELCOR Version 1.8.6 was 

released, a limit of 10% was applied to the amount of molten corium in the lower RPV prior to 

flow through the lower head failure. The 10% molten material limit was required for corium 

within the RPV to go ex-vessel independent of whether the lower head had failed. This allowed

the MELCOR code to conduct a simulation within a relatively fast time (e.g., weeks instead of 

months for a single MELCOR simulation). Since numerical limitations are no longer an issue 

with current technology, MELCOR Version 2.1 has removed this limitation. However, in order to 

maintain a certain amount of continuity between the analysis done in NUREG/CR-7110 Volume 

1 and this work, MELCOR Version 1.8.6 is used. 

The second issue involves the progression of a small lower head failure into a large failure. A 

sensitivity study for small lower head penetration failures is presented in section 6.4.2. 

4.3.1.3 SRV Set Point Drift

With regard to the sequence issues, specifically the SRV stochastic failure rate, it was noted 

during an ACRS subcommittee review meeting that during as-found testing after outages, the 

SRVs were found to typically fail to activate at the set point pressure by plus three percent of

acceptance criteria. For the Peach Bottom Unmitigated LTSBO MELCOR model, SRV-1 begins 

to open at 1,100 psig, and the valve is full open at 103% of the set point. As the pressure 

decreases, SRV-1 begins to close at 1,100 psig, and the valve is fully closed at 97% of the set 

point. It is assumed the set point drift is due to corrosion bonding of the SRV valve seat and 

disk. The corrosion bonding will cause the SRV lifting set point to increase. For the purpose of 

this discussion, an increase in the SRV set point for set point drift is assumed at 103% (1,133 

psig), 110% (1,210 psig), and 120% (1,320) of the SRV-1 set point. However, it is assumed that 

the corrosion bonding will not raise the reseating set point since the bonding between the valve 

seat and disk will not affect the reseating pressure set point. Thus the reseating pressure value 

is assumed to remain constant (i.e., full closed at 97% of the initial set point of 1,100 psig). 

Based on the Peach Bottom Unmitigated LTSBO MELCOR model, SRV-1 opens approximately 

six seconds into the event. The next SRV-1 cycle opening occurs approximately 30 seconds 

and continues to cycle at approximately 20 second intervals until the cooldown occurs at 

approximately 55 minutes into the scenario. Table 4.3-1 shows the estimated timing of the 

SRV-1 cycles due to set point drift when compared to the SRV-1 original set point. The results 

presented in Table 4.3-1 assume the pressure at which SRV-1 closes remains constant 

(i.e., fully closed at 97% of the original set point of 1,100 psig). It should also be noted that even 

if the SRV-1 set point was to drift upwards, the subsequent SRVs, 10 additional SRVs, could lift 

at their designed pressures which are lower than the 10% and 20% set point drift pressure 

limits. However for this discussion, it is assumed that all SRVs will have the same percentage 

of upward set point drift.
4-83

Table 4.3-1 A worst-case scenario of SRV-1 set point drift time estimates

Original 

Set point

103% Set 

point

110% Set 

point

120% Set 

point

1st SRV-1 cycle 6 seconds 8 seconds 14 seconds 22 seconds

2nd SRV-1 cycle 30 seconds 47 seconds 144 seconds 282 seconds

3rd SRV-1 cycle 48 seconds 71 seconds 222 seconds 440 seconds

SRV-1 failure (270 cycles) 8.2 hours 10 hours 27 hours 52 hours

The simplified analysis of the potential effects on the timing of SRV stochastic FTC assume a 

worst case scenario, one in which all of the SRVs experience set point drift in a positive 

direction (e.g., higher pressure required to open the valve) and this occurs at each demand. 

In this worst case scenario a delay in the SRV stochastic FTC, in the LTSBO scenario will cause 

an increase RPV temperatures (i.e., the RPV is in a water/steam saturated condition during 

SRV cycling) from approximately 295°C to approximately 300 to 310°

C during the SRV cycling 

period. With the increased time for the SRV remaining open during the blowdown, there could 

be potential for uncovering the core. With a longer SRV cycling, SRV-1 will intermittently 

release radionuclides during cycling to the wetwell, and if a sufficient delay occurs, SRV-1 will 

experience a thermal failure due to the high temperature gases exiting the RPV to the wetwell or 

the MSL will creep rupture. Either of these conditions will result in a delay of the overall melt 

sequence of the Peach Bottom Unmitigated LTSBO shown in Table 5-1 of NUREG/CR-7110 

Volume 1. However, the longer the time delay in failure of the SRV will result in a larger 

environmental release. This important phenomenon, the delay in SRV FTC, is the same 

whether due to the potential for set point drift or an increase in the number of demands for SRV 

FTC. This phenomenon is already captured in the uncertainty analysis with the uncertainty in 

the number of SRV demands before FTC (i.e., SRVLAM). Any delays, either by SRV set point 

drift or the increased number of demands before FTC, will increase the likelihood of the SRV 

thermal failure or MSL creep rupture accident sequences.

The as-found testing measurements occur over one or a few lifts, whereas the Peach Bottom 

Unmitigated LTSBO scenario would experience tens to hundreds of demands before a FTC. 

More realistically, the very first few demands would likely break the corrosion bonding and the 

valve would perform as expected. The cumulative delay in timing would be minutes not hours 

before the sampled number of cycles at which SRV FTC occurred.

4.3.2 Consequence Model

An evaluation of the sensitivity to the size of the evacuation zone and evacuation start time, the 

effect of seismic activity on emergency response, surface roughness, and the importance of 

chemical classes was completed in NUREG/CR-7110 Volumes 1 & 2, and is summarized 

below. Two additional sensitivity analyses were performed to support this uncertainty analysis: 

One on the habitability criterion and a second to quantify the uncertainty that results from 

performing a finite set of weather trials. 
4-84

4.3.2.1 Size of the Evacuation Zone and Evacuation Start Time

In NUREG/CR-7110 Volume 1 Section 7.3.3 [2], an analysis provides consequence estimates 

for the unmitigated Peach Bottom STSBO scenario without RCIC blackstart 13. This calculation 

considered evacuation of a 10-mile circular area surrounding the plant. Three additional 

calculations were performed in NUREG/CR-7110 Volume 1 to assess variations in the 

protective actions: 

(1). evacuation of a 16-mile circular area

(2). evacuation of a 20-mile circular area 

(3). delayed Evacuation of a 10-mile circular area

Results show expanding the size of the evacuation zone decreases the latent cancer fatality risk 

beyond the 10-mile radius for the unmitigated STSBO without RCIC blackstart; however, the 

risk within 10 miles increases with this change. This is because evacuating a larger area 

increases the time to evacuate the 10-mile region due to increased traffic congestion. For 

circular areas with greater than a 20-mile radius, the risk reduction associated with increasing 

the size of the evacuation zone is slight. 

4.3.2.2 Evaluation of the Effect of Seismic Activity on Emergency Response

In NUREG/CR-7110 Volume 1 Section 7.3.4 [2], an analysis provides consequence estimates 

that include the effects of the seismic event on public evacuation. These consequence 

estimates were developed for the unmitigated Peach Bottom STSBO without RCIC blackstart

scenario. Even though this has a lower frequency and lower absolute risk than the LTSBO 

scenario, this scenario was chosen because it had the earliest release of the Peach Bottom 

scenarios and was believed to be the most likely to show an increase in risk. Seismic effects on 

emergency response are site-specific and at Peach Bottom, the seismic analysis showed limited 

damage to the roadways and infrastructure. For Peach Bottom, the results demonstrated no 

substantial effect on health consequences at Peach Bottom. Although sirens fail, alternative 

notification is adequate and a larger shadow evacuation is expected as a result of the 

earthquake. The bridges and roadways that fail within the EPZ are not significant for 

evacuation; an adequate road network remains, and evacuation speeds are unchanged. 

4.3.2.3 Surface Roughness

The SOARCA analyses used a surface roughness length that represents a typical value for the 

US, which is 10 cm. This value was used in past studies [16, 57] and has become a de facto 

value for many consequence analyses. However, this value of surface roughness is not 

necessarily the best choice for all regions of the country. In NUREG/CR-7110 Volume 1 

Section 7.3.7 [2], an examination of a more site-specific value of surface roughness as a 

sensitivity study was completed to determine whether this parameter is significant for estimated 

risk. 

The effect of increased surface roughness is twofold: 

• It increases vertical mixing of the plume and 

• It increases deposition velocities for all aerosol sizes. 

 

13 Blackstart of the RCIC system refers to starting RCIC without any ac or dc control power. 
4-85

Both effects were treated in this sensitivity study. A general observation based on this 

sensitivity study is that the specific choice of surface roughness has a modest effect on LNT 

predictions of risk; it has a larger effect, but less than a factor of two for the dose truncation 

models. (See discussion under Section 4.2.2.)

4.3.2.4 Importance of Chemical Classes

Each isotope present in the core of a nuclear reactor contributes to the overall risk from an 

accident; however, the release of some isotopes contributes to risk much more than others. 

There are three reasons some isotopes are more important than others: 

• abundance of an isotope in the inventory in the core at the beginning of an accident,

• release fraction of an isotope into the atmosphere, and

• the dose conversion factors for an isotope, which depends strongly on the type and 

energy of the radiation produced, the half-life of the isotope, and for internal pathways, the 

biokinetics of the isotope.

There are 69 isotopes in the treatment of consequences considered in the MACCS analysis for 

SOARCA. These isotopes are grouped into a set of nine chemical classes in the MELCOR 

analyses that generated the source terms used in the SOARCA analyses. Since release 

fractions are calculated by MELCOR at the level of chemical classes, it is both reasonable and 

useful to examine how these same chemical classes influence the evaluation of risk.

In NUREG/CR-7110 Volume 1 Section 7.3.8 [2], an evaluation of the contribution of a chemical 

class was performed in which MACCS calculations were conducted with all but that one 

chemical class. The effect of that chemical class is then calculated by taking the difference 

between the risk when all chemical classes are included and the risk for all but that one 

chemical class (i.e., setting the release fractions for that chemical class to zero). 

The relative importance of each chemical class was evaluated for all three accident sequences

for Peach Bottom: the unmitigated LTSBO, the STSBO with RCIC blackstart, and the 

unmitigated STSBO without RCIC blackstart. Results were also calculated for each of the three

dose-response models which are the following:

1. LNT dose-response model; 

2. Linear with threshold dose-response model with US average natural background dose 

rate combined with average annual, medical dose as a dose truncation level (USBGR), 

which is 620 mrem/yr; and 

3. Linear with threshold dose-response model using a dose truncation level based on the 

Health Physics Society’s (HPS) position statement that there is a dose below which, due 

to uncertainties, a quantified risk should not be assigned, which is 5 rem/yr with a 

lifetime limit of 10 rem. 

Each accident scenario for each dose-response model at specified circular areas produced 

different results. 
4-86

4.3.2.5 Habitability

Habitability is the consequence model parameter that is used to establish the dose level at 

which residents are allowed to return to their homes. Habitability applies to everyone, not just 

evacuees. Whereas most states adhere to the EPA guidelines for habitability, the state of 

Pennsylvania has its own, stricter, habitability criterion guideline. The Pennsylvania guideline 

was used for the Peach Bottom analysis in the SOARCA project. 

In Section 6.4.4, five habitability sensitivity analyses are presented for the current State of

Pennsylvania guideline, EPA guidelines, the criterion implemented in NUREG-1150, and 

International Commission of Radiological Protection (ICRP) recommendations. 

4.3.2.6 Weather Uncertainty

The atmospheric transport models implemented in MACCS require hourly readings of wind 

speed, wind direction, atmospheric stability, and precipitation as input for each weather 

sequence examined. In addition, four values of daytime and nighttime mixing height (i.e., height 

of the capping inversion layer), one for each season of the year, are also specified.

For SOARCA, a structured Monte-Carlo sampling method was employed for weather sampling. 

This was done by random selection of a user-specified number of weather sequences (i.e., start 

times) from the set of sequences assigned to each user-specified weather category. This 

begins by sorting an annual weather file according to user specified criteria. Each MACCS

analysis uses a user-specified random seed. This random seed was kept constant for all 

MACCS analysis and thus the same weather trials from the same meteorological data file were 

selected for all of the analyses. 

Section 6.4.5 discusses a sensitivity study conducted to determine the overall effect of using all 

8760 hours of weather data (i.e., one year of hourly weather data) for each of the 

dose-response models (LNT, USBGR, and HPS), versus the trials used in SOARCA. In 

SOARCA, the aleatory uncertainties due to weather were characterized in terms of mean 

values. However, a CCDF of aleatory uncertainties can be obtained using a single MACCS

analysis for each source term. A set of sensitivity analyses to evaluate the aleatory weather 

uncertainty using the SOARCA weather sampling technique is also presented in Section 6.4.5 

for the LNT, USBGR, and HPS dose-response models.
 5-1 

5. STATISTICAL CONVERGENCE 

5.1 Source Term Model (MELCOR)

The results presented in this uncertainty analysis (Section 6.0) were generated with an updated 

version of the MELCOR SOARCA Peach Bottom unmitigated LTSBO model that included all of 

the changes discussed in Appendix C. The updated version addresses issues identified during 

the development of the probabilistic analysis that impacted the ability to achieve probabilistic 

model convergence. 

5.1.1 Statistical Convergence Testing (Probabilistic Base Case) 

Statistical convergence testing demonstrates that a sufficient number of stochastic realizations 

have been generated to achieve a numerically converged mean, including: (1) determining 

confidence intervals (based on the successful MELCOR calculations) around the mean and 

percentiles for the combined case and each replicate; and (2) demonstrating numerical 

accuracy of the mean by comparing the results of the three sets of 300 realizations with a 

combined 900 realizations. 

The three replicate sets (STP08, STP09, and STP10) each consist of 300 distinct MELCOR 

simulations. A successful MELCOR calculation is defined by the simulation progressing to 

48 hours after scram, which is the truncation time of each calculation. Each replicate exhibits a 

unique success rate from the MELCOR code, as shown in Table 5.1-1. The success rates from 

MELCOR for STP08, STP09, and STP10 are 94.7%, 96.7%, and 97.0%, respectively. Thus 

about 4% of the total MELCOR simulations do not successfully reach 48 hours. 

Table 5.1-1 Success rates of MELCOR simulations for STP08, STP09, and STP10

Replicate Rep. #

Number of 

successful 

simulations

Number of 

aborted

simulations

Success 

rate 

STP08 1 284 16 94.7%

STP09 2 290 10 96.7%

STP10 3 291 9 97.0%

Total 865 35 96.1%

The 35 simulations that were not run to completion were caused primarily by non-convergence 

issues detected in the MELCOR code, related to the time-step scheme used to progress the 

system transient via the governing equations in MELCOR. Occasional non-convergence issues 

are to be expected when executing hundreds of MELCOR simulations, especially for uncertainty 

analyses in which variations in model input alter the progression of the core and vessel 

degradation, which are the most computationally intensive portions of the simulation. These 

detected non-convergent simulations should not be confused with run-time errors, which occur 

when the code fails due to unexpected reasons; run-time errors do not catch the code fault and 

thus cannot report the nature of the error to the user.

Most of the MELCOR failures are due to thermal-hydraulic convergence issues in the core 

region during core material relocation. Table 5.1-2 provides a summary of the MELCOR errors 

encountered by the 35 failed simulations. MELCOR convergence issues can usually be 

resolved by restarting the simulation before the onset of instabilities that lead to the fatal errors, 
 5-2 

and continuing the transient using smaller time-steps as specified by the refined user input. 

However, manual restarts were not attempted for the 35 failed simulations. The replicates were 

executed on a computer cluster in an automated fashion, and the 865 successful simulations 

were deemed to be a sufficient sample size for the statistical analyses. 

Table 5.1-2 MELCOR error summary for STP08, STP09, STP10

Error description

Number of 

occurrences

Thermal-hydraulic convergence error in core region 24

Core materials eutectics error (component mass less than zero) 3 

Cavity convergence error 3

Radionuclide package: conductivity calculation error for gas mixture 2 

Core geometry error: surface area calculation during core relocation 1 

Core debris temperature convergence error in lower plenum 1

Core temperature convergence error during core relocation 1 

Total 35

A regression analysis has been performed as described in Section 3.4.2 using all 900 input sets 

on an indicator function that was set to one if the realization converged and equal to zero if it did 

not. The resulting regressions show no significant correlation between any input variable and 

the indicator function, giving more confidence that disregarding the non-convergent realizations 

should not affect the parameter uncertainty analyses presented in Section 6.0. The only 

correlation found was with the (unsampled) parameter RRDOOR, which indicates whether 

railroad doors are open (=1) or closed (=0). This correlation is not surprising as most (~88%) of 

the converged realizations lead to open railroad doors. 30 of the 35 non-converged results 

happen in the core calculation before the railroad doors have a chance to open and does not 

affect the railroad doors. Therefore, this correlation between railroad doors and convergence is 

a numerical artifact and does not reflect any bias in the distributions.

Statistical convergence was evaluated by a replicated sampling procedure. Three independent 

Monte Carlo sample sets of epistemic uncertain parameters were generated using 300 samples 

each. As explained in Section 3.4, the simple random sampling (SRS) procedure was preferred 

to LHS as it preserves validity of the sample even in a case of unfinished realizations, as long 

as the failed realizations do not bias the results. Each sample was used to generate three 

estimates of mean fraction of cesium and iodine core inventory released to the environment. 

Other statistics (median, quantiles values q = 0.05 and q = 0.95) were also estimated to test for 

convergence of the output distributions in a more general context. Since all three replicates 

have been generated with SRS, it is appropriate to combine them and estimate confidence 

intervals over the mean and selected quantiles using a bootstrap approach, as described below. 

To estimate convergence of these statistics, a bootstrap resampling technique was used to 

generate 1,000 sample sets, each of size 300, from the pool of 865 results available (the 

non-convergent results were subtracted from the total of 900 runs). From the generated 

distributions of statistics, a mean value and 0.90 confidence interval (using quantiles q = 5% 

and q = 95%) have been estimated. The results are displayed on Figure 5.1-1 (cesium) and 

Figure 5.1-2 (iodine) for mean and median as well as 5th and 95th percentiles. The true value of 

the mean and quantiles displayed will be within the confidence interval with a confidence of 

95%.
 5-3 

Comparison of these estimates, and the associated distributions of uncertainty, showed that the 

three independent sample sets produced statistically similar values, as well as similar 

distributions of uncertainty in the results. The 95th percentile results are more spread out, but 

remain in an appropriate range (within 20% of the bootstrap mean). A sample size of 300 was, 

therefore, considered adequate within the scope of the current analysis.

The results of the analysis are statistically converged. Moreover, the similarity between the 

three replicates demonstrates that performance could be evaluated using any one of the 

replicates. However, considering that greater accuracy will be obtained by using a larger 

sample size, and due to the fact that results will be segregated into three failure modes for 

independent analysis (SRV stochastic, SRV Thermal and MSL Creep rupture), a combined 

sample was used for the uncertainty analysis presented in Section 6 of this report. 
 5-4 

Figure 5.1-1 Results of three replicates and q = 0.95 confidence interval (using 

bootstrap resampling) over selected statistics for released fraction of 

Cesium: (a) mean, (b) median, (c) quantile q = 0.05 and (d) quantile q = 0.95
 5-5 

Figure 5.1-1 Results of three replicates and q = 0.95 confidence interval (using 

bootstrap resampling) over selected statistics for released fraction of 

Cesium: (a) mean, (b) median, (c) quantile q = 0.05 and (d) quantile q = 0.95 

(continued)
 5-6 

Figure 5.1-2 Results of three replicates and q = 0.95 confidence interval (using 

bootstrap resampling) over selected statistics for released fraction of 

Iodine: (a) mean, (b) median, (c) quantile q = 0.05 and (d) quantile q = 0.95
 5-7 

Figure 5.1-2 Results of three replicates and q = 0.95 confidence interval (using 

bootstrap resampling) over selected statistics for released fraction of 

Iodine: (a) mean, (b) median, (c) quantile q = 0.05 and (d) quantile q = 0.95 

(continued)
 5-8 

5.2 Consequence Model

SOARCA uncertainty analysis results presented in Section 6.0 include the updated SOARCA 

source term presented in Section 5.1 and documented in Appendix C combined with the current 

version of WinMACCS/MACCS as discussed in Section 3.1.3 and documented in Appendix C. 

5.2.1 Statistical Convergence Testing - Probabilistic Base Case

This section discusses the LCF risks per event and the early-fatality risks per event using all the 

MACCS uncertainty parameters discussed in Section 4.2 with the 284 MELCOR source terms 

STP08, the first of the three replicates of the uncertainly model. This section also discusses the 

reduction in inhalation dose conversion factors previously discussed in Section 4.2.5. The 

convergence testing of MACCS was determined with a reduced LHS statistical sampling 

technique using all three MELCOR source terms developed from Section 5.1.1 (i.e., MELCOR 

results from the three replicates of the uncertainly model). All results discussed in this section 

use the LNT dose-response model. Uncertainty analyses of the dose truncation models are 

discussed in Section 6.4.3. 

5.2.1.1 Latent Cancer Fatality Risk

To investigate the uncertain parameters discussed in Section 4.2, an initial MACCS analysis 

was conducted using all 598 uncertain input variables. A MACCS cyclical file set was created 

for the 284 MELCOR source terms developed from the work discussed in Section 5.1.1 

(i.e., STP08, the MELCOR results from the first of the three replicates of the uncertainly model). 

In this section, the risk tables represent rounded values obtained from the full data sets. The 

plots were developed from the full data sets and slight differences may be noticed due to this 

rounding. 

Table 5.2-1 displays the basic statistics for the conditional, mean, individual LCF risk (per event) 

for the LNT dose model. The maximum LCF risk results shown in Table 5.2-1 are not the same 

for the 10-mile (i.e., MELCOR source term Realization 133) and the 20-mile (i.e., MELCOR

source term Realization 77) circular areas. None of the circular areas have the same ordered 

sequence from largest to smallest LCF risk per event results. 

Table 5.2-1 Conditional, mean, individual LCF risk (per event) basic statistics for the 

LNT dose model at specified circular areas 

0-10 

miles

0-20 

miles

0-30 

miles

0-40 

miles

0-50 

miles

Mean 1.7x10-4 2.7x10-4 1.9x10-4 1.2x10-4 1.0x10-4

Standard Error 7.7x10-6 1.6x10-5 1.1x10-5 7.1x10-6 5.7x10-6

Median 1.4x10-4 2.1x10-4 1.5x10-4 9.3x10-5 7.7x10-5

Mode 1.2x10-4 1.2x10-4 1.1x10-4 1.2x10-4 1.0x10-4

Standard Deviation 1.3x10-4 2.7x10-4 1.9x10-4 1.2x10-4 9.6x10-5

Sample Variance 1.7x10-8 7.5x10-8 3.7x10-8 1.4x10-8 9.2x10-9

Minimum 1.3x10-5 1.7x10-5 1.2x10-5 7.4x10-6 6.1x10-6

Maximum 8.6x10-4 3.1x10-3 2.2x10-3 1.3x10-3 1.1x10-3

Confidence Level (95.0%) 1.5x10-5 3.2x10-5 2.2x10-5 1.4x10-5 1.1x10-5
 5-9 

Table 5.2-2 shows where the results for the SOARCA uncertainty analysis base case source 

term determined in Appendix C with respect to the results within the distribution of this 

probabilistic case for conditional, mean, individual LCF risk (per event) for the LNT 

dose-response model. From Table 5.2-2, the risk for the 10-mile circular area corresponds to a 

higher percentile compared to the other SOARCA uncertainty analysis base case circular areas 

due to the influence of the uncertain evacuation parameters on the relative timing of evacuation 

compared with the release. 

Figure 5.2-1 shows the results for each of the conditional, mean, individual LCF risk (per event) 

for all 284 MELCOR source terms in STP08 with 598 uncertain MACCS input variables. The 

rank order for each specified circular area on Figure 5.2-1 is ranked from the highest LCF risk

result to the lowest result. None of the specified circular areas have the same ordered 

sequence. The black dots represent the SOARCA uncertainty analysis base case results. The 

overall LCF risk for any circular area is small. The highest absolute LCF risk is 1.0x10-8 pry (i.e., 

recall the Peach Bottom LTSBO core damage frequency is 3x10-6 pry) at 20 miles. 

Table 5.2-2 Conditional, mean, Individual LCF risk (per event) basic from the SOARCA 

UA base case for the LNT dose model at specified circular areas 

SOARCA UA Base Case 

radius of circular area (mi)

Conditional, mean, 

individual LCF risk 

(per event) for the LNT

dose model

Percentile

10 9.0x10-5 30th

20 8.3x10-5 12th

30 5.8x10-5 12th

40 3.7x10-5 11th

50 3.0x10-5 11th
 5-10

Figure 5.2-1 Conditional, mean, individual LCF risk (per event) for all distances with the 

LNT dose model for emergency and long-term phases ranked from highest 

to lowest LCF risk result

Figure 5.2-2 shows the CCDF for the conditional mean, individual LCF risk (per event) 

contribution for both emergency and long-term phases for the specified circular areas. Since 

most people evacuate (99.5%) within the 10-mile EPZ, the LCF risk results from the long-term

exposure are mostly based on the return criteria. For larger circular areas, the majority of the 

LCF risk is contributed from the emergency-phase for approximately 165 MELCOR realizations

(i.e., the emergency-phase LCF risk accounts for ≥50% of the overall LCF risk) but this number 

decreases with circular area (i.e., from 166 MELCOR realizations at 20 miles to 136 MELCOR

realizations at 50 miles have the emergency phase LCF risk account for ≥50% of the overall 

LCF risk). 

On Figure 5.2-2, the x-axis represents the distribution of possible LCF risk per event results 

within the 10-mile circular area and is generated by sorting (from smallest to largest) all the LCF 

risk results from the sample of size ‘N’ (i.e., N=284 samples for Figure 5.2-2). On Figure 5.2-2, 

the y-axis represents the likelihood of being higher or equal than the value read on the x-axis. 

When LHS is used, the likelihood of the outcome is estimated by a weight of 1/N and 

decreasing the y-value by this weight starting from one. The mean can be added on the curve 

(i.e., a dot for Figure 5.2-2) to the CCDF. Quantiles can be read directly by finding the 

corresponding y-value to the graph, or displayed for a selected quantile as a dot over the curve.

In risk analysis, it is traditional to plot CCDFs rather than CDFs as a CCDF answers the 

question, “How likely it is to have such value or higher?”
 5-11

Figure 5.2-2 Complementary cumulative distribution function for conditional, mean, 

individual LCF risk (per event) for the MACCS Convergence Analysis for 

specified circular areas 

5.2.1.2 Early-Fatality Risk

The NRC quantitative health objective (QHO) [58, 59] for prompt fatalities (5x10-7 pry) is 

generally interpreted as the absolute risk within one mile of the exclusion area boundary (EAB), 

so that distance is used as a useful indicator in this study as well. The only SOARCA scenario 

for which the risk of early fatalities is not zero is the Surry ISLOCA (i.e., discussed in 

NUREG/CR-7110 Volume 2, Section 7.3.5). For Surry, the EAB is 0.35 miles from the reactor 

building from which release occurs, so the outer boundary of the one-mile zone is at 1.35 miles. 

The closest MACCS grid boundary to 1.35 miles used in the ISLOCA calculations is at 1.3 

miles. Using the risk at 1.3 miles is considered a reasonable approximation to the risk within

one mile of the EAB. Table 5.2-3 shows the conditional, mean, mean early-fatality risk (per 

event) for the Surry ISLOCA scenario. The core damage frequency for this event is 3x10-8 pry. 

Thus, the absolute early-fatality risk within one mile of the EAB is 4.5x10-14 pry. 
 5-12

Table 5.2-3 Conditional, mean, individual early-fatality risk (per event) for the Surry 

ISLOCA Scenario

Radius of circular area (mi) Early-fatality risk (per event) 

1.3 1.5×10-6

2.0 6.4×10-7

2.5 4.0×10-7

For Peach Bottom, the EAB is 0.5 mile from the reactor building from which release occurs, so 

the outer boundary of this one mile zone is at 1.5 miles. The closest MACCS grid boundary to 

1.5 miles used in this set of calculations is at 1.3 miles. Evaluating the risk within 1.3 miles is 

considered a reasonable, but slightly conservative, approximation to the risk within 1 mile of the 

EAB. In the SOARCA study, the Peach Bottom LTSBO scenario has a conditional, mean, 

individual early-fatality risk (per event) of 0.00 (NUREG/CR-7110 Volume 1, Section 7.3.1). 

Table 5.2-4 displays the basic statistics for the conditional, mean, individual early-fatality risk 

(per event) at specified circular areas for the 284 MELCOR source terms developed from the 

discussion in Section 5.1 (i.e., the MELCOR STP08 uncertainty model). The realization with the 

peak MACCS results shown in Table 5.2-4 is the same for the 1.3-mile to 2.5-mile circular areas 

(i.e., MELCOR STP08 source term Realization 238). The 3-mile to 10-mile circular areas have

the same peak MACCS result (i.e., MELCOR STP08 source term Realization 91). The 10-mile 

distance has only two scenarios where early fatalities occur (i.e., MELCOR STP08 source term 

Realization 91 and 134). In each of these realizations, there is a specific weather trial 

corresponding to the peak dose which produces the early-fatality risk at the 10-mile circular 

area. 

Table 5.2-4 Conditional, mean, individual early-fatality risk (per event) basic statistics

1.3 

miles 2 miles 2.5 miles 3 miles 3.5 miles 5 miles 7 miles 10 miles

Mean 4.6x10-7 1.6x10-7 8.3x10-8 5.8x10-8 2.4x10-8 5.7x10-9 2.4x10-9 1.0x10-9

Standard Error 1.5x10-7 5.0x10-8 3.3x10-8 2.3x10-8 1.1x10-8 3.8x10-9 1.8x10-9 7.9x10-10

Median 0 0 0 0 0 0 0 0

Mode 0 0 0 0 0 0 0 0 

Standard 

Deviation 2.5x10-6 8.4x10-7 5.5x10-7 3.9x10-7 1.8x10-7 6.4x10-8 3.0x10-8 1.3x10-8

Sample 

Variance 6.2x10-12 7.1x10-13 3.0x10-13 1.5x10-13 3.4x10-14 4.1x10-15 9.3x10-16 1.8x10-16

Minimum 0 0 0 0 0 0 0 0 

Maximum 3.2x10-5 9.9x10-6 6.1x10-6 4.3x10-6 2.7x10-6 1.0x10-6 4.7x10-7 2.1x10-7

Confidence 

Level (95%) 2.9x10-7 9.8x10-8 6.4x10-8 4.5x10-8 2.1x10-8 7.5x10-9 3.6x10-9 1.6x10-9

From Table 5.2-4 the grand mean, individual early-fatality per event (i.e., the mean value of the 

conditional, mean, individual early-fatality risk (per event)) for the 1.3-mile circular area is less 

than the SOARCA ISLOCA result. The maximum early-fatality risk per event result for the

1.3-mile circular area is on the same order of magnitude to the SOARCA Uncertainty Analysis

Base Case mean LCF risk per event result (i.e., 9.0x10-5 LCF risk per event – Appendix C) at 

10 miles.
 5-13

Figure 5.2-3 provides the CCDF results for the conditional, mean, individual early-fatality risk 

(per event) for specified circular areas. Figure 5.2-3 shows only those early-fatality risks that 

are nonzero. The 7-mile and 10-mile circular area have only two nonzero early-fatality risk. The 

early-fatality risk for any circular area is small. The highest absolute early-fatality risk is 

9.7x10-11 pry (i.e., recall the Peach Bottom LTSBO core damage frequency is 3x10-6 pry) at 

1.3 miles. There are approximately 265 MACCS realizations less than 1.0x10-6 early-fatality risk 

per event for all circular areas. There are approximately 250 MACCS realizations which have a 

zero early-fatality risk at all distances (i.e., ~88% of all MACCS realizations result in a zero 

early-fatality risk per event at all specified circular areas). There is no early-fatality risk for the 

cohorts that evacuate.

Figure 5.2-3 Complementary cumulative distribution function for conditional, mean, 

individual early-fatality risk (per event) for the MACCS Convergence 

Analysis for specified circular areas

Originally, 58 radionuclides that were treated in this analysis were selected to have uncertainty 

distributions for their long-term inhalation DCFs (see Section 4.2.5). However, it was 

determined that nearly half of the uncertainty resulted from a subset of 27 radionuclides. This

reduces the set of uncertain parameters from 598 input variables to 350 input variables, not 

including the source term input parameters calculated by MELCOR. 

The reduction from 58 to 27 radionuclides was determined by selecting the radionuclides that

collectively contribute at least 99% of the ‘effective’ long-term inhalation dose based on the first 

replicate MELCOR source terms developed from the discussion in Section 5.1 (i.e., the STP08

uncertainty model – Replicate 1) nearest the mean for LCF risk (Replicate 1 Realization 58 and 

Replicate 1 Realization 214), and the MELCOR source term for the SOARCA estimate. Based 
 5-14

on this analysis, it was determined that the MELCOR source term Replicate 1 Realization 58

from the MELCOR STP08 uncertainty model provided the best estimate of the radionuclides 

that contributed to at least 99% of the ‘effective’ inhalation dose. The radionuclides from the 

other source terms (i.e., Replicate 1 Realizations 214 and the SOARCA estimate) which were 

not included accounted for less than 2% of the ‘effective’ long-term inhalation dose for their 

respective source terms. Based on this reduction, the other 31 radionuclides had their 

respective long-term inhalation DCFs converted back to their default values used in 

NUREG/CR-7110 Volume 1. Table 5.2-5 shows the 27 radionuclides used for the probabilistic 

analyses discussed later in this section and in Section 6.0, and their ‘effective’ long-term 

inhalation dose contribution for the Replicate 1 Realization 58 source term. 

Table 5.2-5 Radionuclide specific contribution to overall ‘effective’ inhalation dose

Nuclide ‘Effective’ Inhalation Dose Contribution

I-131 34.600%

I-133 14.475%

I-135 8.782%

Te-132 8.607%

Ce-144 6.099%

Sr-90 3.641%

Ba-140 3.303%

Pu-238 3.005%

Sr-89 1.952%

Pu-241 1.861%

Cs-134 1.571%

Np-239 1.446%

Nb-95 1.326%

Cs-137 1.138%

Te-129m 0.880%

Mo-99 0.808%

Zr-95 0.805%

I-132 0.647%

Ce-141 0.609%

Pu-239 0.605%

Te-131m 0.557%

I-134 0.508%

Pu-240 0.501%

Cm-242 0.425%

Sr-91 0.383%

Te-127m 0.278%

Sr-92 0.252%

Total 99.062%
 5-15

5.2.1.3 MACCS Statistical Convergence – LCF Risk

In order to determine the overall statistical convergence of the MACCS results using the 

reduced set input variables, the three separate MELCOR uncertainty source terms discussed in 

Section 5.1 were used in separate MACCS uncertainty analyses to determine the CCDFs for 

the conditional, mean, individual LCF risk (per event). The three uncertainly MELCOR analyses 

produced 284 (STP08), 290 (STP09), and 291 (STP10) source terms, respectively. Each of 

these MELCOR source term sets were analyzed separately in MACCS using the same LHS 

sampling technique and the same sampled aleatory weather trials. However, since there are a 

different number of source terms for each MELCOR source term group, the LHS sampling is 

independent between the three MACCS analyses even with the same sampled aleatory weather 

trials. The STP08 MELCOR source term was analyzed and resulted in the MACCS CAP14

model. The STP09 MELCOR source term was analyzed and resulted in the MACCS CAP18

model. The STP10 MELCOR source term was analyzed and resulted in the MACCS CAP19

model.

Tables 5.2-6 through 5.2-9 show the conditional, mean, individual LCF risk (per event) average, 

standard error, lower bounding case and upper bounding case statistics for the three MACCS

analyses combined at each specified circular area. Each statistic was determined over the 

epistemic uncertainties samples in the MACCS LHS uncertainty inputs using mean results over 

the weather trials representing aleatory uncertainty. A t-distribution was used to generate 

centered 95% confidence intervals (based on the lower 2.5 and upper 97.5th percentiles). 

Values for mean and selected quantiles have been displayed on the graph along with 

confidence intervals. The small number of replicates (3) used for the t-distribution generate 

large confidence intervals (reflecting the variability in the three replicates), and the position of 

the corresponding statistics provides a more reasonable indicator of stability in results. As a 

comparison, Table 5.2-6 also has the SOARCA Uncertainty Analysis base case conditional, 

mean, individual LCF risk (per event) results from Table C.2-1. 

Table 5.2-6 Combined conditional, mean, individual LCF risk (per event) average 

statistics for the MACCS statistical convergence test for specified circular 

areas 

 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.6x10-4 2.9x10-4 2.0x10-4 1.3x10-4 1.1x10-4

Median 1.3x10-4 1.9x10-4 1.4x10-4 8.8x10-5 7.2x10-5

5th percentile 3.1x10-5 5.1x10-5 3.5x10-5 2.2x10-5 1.8x10-5

95th percentile 4.0x10-4 7.8x10-4 5.6x10-4 3.6x10-4 3.0x10-4

SOARCA UA 

Base Case 9.0x10-5 8.3x10-5 5.8x10-5 3.7x10-5 3.0x10-5
 5-16

Table 5.2-7 Combined conditional, mean, individual LCF risk (per event) standard 

error statistics for the MACCS statistical convergence test for specified

circular areas 

0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 4.4x10-6 1.1x10-5 7.2x10-6 3.7x10-6 2.7x10-6

Median 4.5x10-6 3.0x10-6 2.8x10-6 2.7x10-6 2.6x10-6

5th percentile 4.5x10-6 7.2x10-6 5.5x10-6 3.8x10-6 2.9x10-6

95th percentile 1.5x10-5 5.2x10-5 3.5x10-5 2.5x10-5 3.0x10-5

Table 5.2-8 Combined conditional, mean, individual LCF risk (per event) lower 

bounding case statistics for the MACCS statistical convergence test for 

specified circular areas 

 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.4x10-4 3.4x10-4 2.4x10-4 1.5x10-4 1.2x10-4

Median 1.1x10-4 2.0x10-4 1.5x10-4 9.9x10-5 8.3x10-5

5th percentile 1.2x10-5 8.2x10-5 5.8x10-5 3.9x10-5 3.1x10-5

95th percentile 3.3x10-4 1.0x10-3 7.1x10-4 4.7x10-4 4.3x10-4

Table 5.2-9 Combined conditional, mean, individual LCF risk (per event) upper 

bounding cases statistics for the MACCS statistical convergence test for 

specified circular areas 

 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.8x10-4 3.4x10-4 2.4x10-4 1.5x10-4 1.2x10-4

Median 1.5x10-4 2.0x10-4 1.5x10-4 9.9x10-5 8.3x10-5

5th percentile 5.1x10-5 8.2x10-5 5.8x10-5 3.9x10-5 3.1x10-5

95th percentile 4.6x10-4 1.0x10-3 7.1x10-4 4.7x10-4 4.3x10-4

As shown on Figure 5.2-4, the CCDFs for the three MACCS analyses for the conditional, mean, 

individual LCF risk (per event) are very similar and in good agreement for each analysis for the 

10-mile EPZ. Also, Figure 5.2-4 shows a relatively small uncertainty within the 95th confidence 

interval between each analysis. 
 5-17

Figure 5.2-4 Complementary cumulative distribution function and statistical values for 

conditional, mean, individual LCF risk (per event) within a 10-mile radius 

for the MACCS Convergence Analysis

As shown on Figure 5.2-5, the CCDFs for the three MACCS analyses for conditional, mean, 

individual LCF risk (per event) are very similar and are in good agreement between each 

analysis for the 20-mile circular area. Also, Figure 5.2-5 shows a relatively small uncertainty 

within the 95th confidence interval between each analysis. 

The CCDFs for the three MACCS analyses for the conditional, mean, individual LCF risk (per 

event) for the 30-mile, 40-mile, and 50-mile circular areas are shown on Figure 5.2-6 through 

Figure 5.2-8, respectively. The 30-mile, 40-mile and 50-mile circular areas show similar 

statistical results to those shown on Figure 5.2-5 for the MACCS convergence analysis for the 

20 mile radius statistical data. 
 5-18

Figure 5.2-5 Complementary cumulative distribution function and statistical values for 

conditional, mean, individual LCF risk (per event) within a 20-mile radius 

for the MACCS Convergence Analysis
 5-19

Figure 5.2-6 Complementary cumulative distribution function and statistical values for 

conditional, mean, individual LCF risk (per event) within a 30-mile radius 

for the MACCS Convergence Analysis
 5-20

Figure 5.2-7 Complementary cumulative distribution function and statistical values for 

conditional, mean, individual LCF risk (per event) within a 40-mile radius 

for the MACCS Convergence Analysis
 5-21

Figure 5.2-8 Complementary cumulative distribution function and statistical values for 

conditional, mean, individual LCF risk (per event) within a 50-mile radius 

for the MACCS Convergence Analysis

Tables 5.2-10 through 5.2-12 show the correlation matrix for all three MACCS analyses for the 

conditional, mean, individual LCF risk (per event) at specified circular areas. These tables 

indicate how strongly these MACCS results are correlated amongst each other when the radial 

distances change. The closer the correlation value is to 1.0, the more similar are the results. 

As an example, Table 5.2-10 indicates that while the conditional, mean, individual LCF risk (per 

event) for a radial distance of 10 miles is different than other radials distance (i.e., first row, 

correlation coefficient ranging from 0.31 to 0.42), the other radial distances lead to pretty similar 

results (i.e., coefficients of correlation greater than 0.99). 

The correlation matrix between each of the circular areas outside the EPZ to the EPZ distance 

(i.e., 10 miles) shows that evacuation uncertainty parameters have a noticeable effect on the 

correlation. Additionally, the evacuation parameters affect the correlation in a similar fashion for 

all three MACCS analyses. At circular areas beyond the EPZ (i.e., 10 miles), the results are 

strongly correlated with regards to their respective MACCS input parameters. This is expected 

since there are no MACCS input parameters that would change and affect the correlation of a 

specific circular area beyond the EPZ with another circular area beyond the EPZ.
 5-22

Table 5.2-10 Correlation matrix for the MELCOR STP08 Uncertainty Model Source Term 

MACCS Analysis for the conditional, mean, individual LCF risk (per event) 

for specified circular areas 

0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

0-10 miles 1 0.31 0.34 0.39 0.42

0-20 miles 1 0.998 0.993 0.99

0-30 miles 1 0.998 0.994

0-40 miles 1 0.999

0-50 miles 1

Table 5.2-11 Correlation matrix for the MELCOR STP09 Uncertainty Model Source Term 

MACCS Analysis for the conditional, mean, individual LCF risk (per event) 

for specified circular areas 

0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

0-10 miles 1 0.29 0.30 0.36 0.39

0-20 miles 1 0.998 0.99 0.98

0-30 miles 1 0.997 0.99

0-40 miles 1 0.999

0-50 miles 1

Table 5.2-12 Correlation matrix for the MELCOR STP10 Uncertainty Model Source 

Term MACCS Analysis for the conditional, mean, individual LCF risk (per 

event) for specified circular areas 

0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

0-10 miles 1 0.55 0.57 0.63 0.66

0-20 miles 1 0.998 0.99 0.98

0-30 miles 1 0.995 0.99

0-40 miles 1 0.999

0-50 miles 1

Based on these analyses, the conditional, mean, individual LCF risk (per event) are determined 

to be well converged for this uncertainty analysis. These analyses further verify the overall 

statistical convergence of the MACCS code when applying epistemic (e.g., radionuclide 

inhalation DCFs) and aleatory (e.g., weather trials) uncertainties. 

5.2.1.4 MACCS Statistical Convergence – Early-Fatality Risk

To determine the overall statistical convergence of the MACCS results using the reduced set of

input variables, the three separate sets of MELCOR source terms discussed in Section 5.1 were 

used in separate MACCS uncertainty analyses to determine the CCDFs for the conditional, 

mean, individual early-fatality risk (per event). The three MELCOR analyses produced 284 

(STP08), 290 (STP09), and 291 (STP10) source terms, respectively. Each of these MELCOR 

source term sets were analyzed separately in MACCS using the same LHS sampling technique 
 5-23

and the same sampled aleatory weather trials. However, since there are a different number of 

source terms for each MELCOR source term group, the LHS sampling is independent between 

the three MACCS analyses even with the sampled aleatory weather trials. The STP08 

MELCOR source term was analyzed and resulted in the MACCS CAP14 model. The STP09 

MELCOR source term was analyzed and resulted in the MACCS CAP18 model. The STP10 

MELCOR source term was analyzed and resulted in the MACCS CAP19 model.

Unlike the SOARCA analyses in NUREG/CR-7110 Volume 1 and Volume 2, early-fatality risk 

was observed beyond 2.5 miles (see Table 5.2-3). 0.9% of the 865 scenarios investigated

(i.e., CAP14, CAP18, and CAP19) resulted in nonzero early-fatality risk out to 10 miles. A small 

number of realizations result in a large enough source term release that in combination with 

specific weather trials produce nonzero early-fatality risks out to the boundary of the EPZ. A 

more detailed discussion of the specific combination of inputs that produce early-fatality risks

out to 10 miles is provided in Section 6.2.4. 

Tables 5.2-13 through 5.2-16 show the conditional, mean, individual early-fatality risk (per 

event) mean, median, 75th percentile, and 95th percentile statistics which combined the results 

for all three MACCS analyses for each specified circular area. Each statistic was determined 

from the samples in the MACCS uncertainty inputs. A t-distribution was used to determine the 

75th percentile and 95th confidence intervals. The 75th percentile was selected as a lower 

bounding case in this analysis since all results less than the 75th percentile are zero. At 

2.5 miles and beyond in Table 5.2-13 the mean result is greater than the 95th percentile. This is 

due to the small number of nonzero data points (i.e., less than 5%) available at these distances

and indicates an extremely skewed distribution. It is possible that the smallest nonzero values 

will be lower than the average of all values. In theory, a distribution can be skewed enough so 

that the mean is greater than the 95th percentile. An instance of this is an exponential of a value 

sample from a log-normal distribution. The mean will be higher than the 99th percentile, because 

it will be driven by those very rare but really high values. This is the same thing that happens 

here for early-fatality risk beyond 3.5 miles.

Table 5.2-13 Combined conditional, mean, individual early-fatality risk (per event) 

average statistics for the MACCS statistical convergence test for specified

circular areas 

0-1.3 

miles

0-2 

miles

0-2.5 

miles 0-3 miles 0-3.5 miles

0-5 

miles

0-7 

miles

0-10 

miles

Mean 4.1x10-7 1.5x10-7 9.0x10-8 5.4x10-8 2.7x10-8 8.4x10-9 3.4x10-9 1.4x10-9

Median 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

75th

percentile 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

95th

percentile 3.3x10-6 5.4x10-7 6.3x10-8 9.2x10-9 0.0 0.0 0.0 0.0
 5-24

Table 5.2-14 Combined conditional, mean, individual early-fatality risk (per event) 

standard error statistics for the MACCS statistical convergence test for 

specified circular areas 

0-1.3 

miles

0-2 

miles

0-2.5 

miles 0-3 miles 0-3.5 miles

0-5 

miles

0-7 

miles

0-10 

miles

Mean 1.2x10-7 4.8x10-8 4.3x10-8 3.3x10-8 2.4x10-8 9.0x10-9 3.9x10-9 1.9x10-9

Median 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

75th

percentile 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

95th

percentile 1.2x10-6 4.7x10-8 1.8x10-8 6.2x10-9 0.0 0.0 0.0 0.0

Table 5.2-15 Combined conditional, mean, individual early-fatality risk (per event) lower 

bounding case statistics for the MACCS statistical convergence test for 

specified circular areas 

0-1.3 

miles

0-2 

miles

0-2.5 

miles

0-3 

miles

0-3.5 

miles

0-5 

miles

0-7 

miles

0-10 

miles

Mean 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Median 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

75th

percentile 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

95th

percentile 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Table 5.2-16 Combined conditional, mean, individual early-fatality risk (per event) upper 

bounding cases statistics for the MACCS statistical convergence test for 

specified circular areas 

0-1.3 

miles

0-2 

miles

0-2.5 

miles

0-3 

miles

0-3.5 

miles

0-5 

miles

0-7 

miles

0-10 

miles

Mean 9.4x10-7 3.6x10-7 2.8x10-7 2.0x10-7 1.3x10-7 4.7x10-8 2.0x10-8 9.7x10-9

Median 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

75th

percentile 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

95th

percentile 8.4x10-6 7.4x10-7 1.4x10-7 3.6x10-8 0.0 0.0 0.0 0.0

As shown on Figure 5.2-9, the CCDFs for the three MACCS analysis for the conditional, mean, 

individual early-fatality risk (per event) are very similar and are in good agreement between 

each analysis for the 1.3–mile circular area (i.e., within 1 mile of EAB). Also, Figure 5.2-9 

shows an uncertainty within the 95th confidence interval that is zero to ~8.0x10-6 between each 

analysis. This large confidence level is a result of the limited number of early-fatality risks 

greater than zero. Only 10% to 13% of the results for the three analyses resulted in a nonzero 
 5-25

early-fatality risk at any distance. The highest absolute early-fatality risk is 6.7x10-11 pry (i.e., 

recall the Peach Bottom LTSBO core damage frequency is 3x10-6 pry) at 1.3 miles from the 

CAP19 MACCS model. 

Figure 5.2-9 Complementary cumulative distribution function and statistical values for 

conditional, mean, individual early-fatality risk (per event) within a 1.3-mile 

radius for the MACCS Convergence Analysis

Figures 5.2-10 through 5.2-13 show the CCDFs for the conditional, mean, individual earlyfatality risk (per event) for the 2-mile, 2.5-mile, 3-mile, and 3.5-mile circular areas, respectively. 

The results are similar to those on Figure 5.2-10, however, the number of early-fatality risk

results greater than zero for each subsequent circular area decreases. As a result the data for 

a nonzero early-fatality risk decreases from a maximum of 12% of the total data at 1.3 miles 

(CAP19) to a maximum of 4.5% of the realizations at 3.5 miles (CAP18). Beyond the 3.5-mile 

circular area, the realizations with nonzero early-fatality risk drops below 3% of the total data 

and provides no discernible graphical information.
 5-26

Figure 5.2-10 Complementary cumulative distribution function and statistical values for 

conditional, mean, individual early-fatality risk (per event) within a 2-mile 

radius for the MACCS Convergence Analysis 
 5-27

Figure 5.2-11 Complementary cumulative distribution function and statistical values for 

conditional, mean, individual early-fatality risk (per event) within a 2.5-mile 

radius for the MACCS Convergence Analysis
 5-28

Figure 5.2-12 Complementary cumulative distribution function and statistical values for 

conditional, mean, individual early-fatality risk (per event) within a 3-mile 

radius for the MACCS Convergence Analysis
 5-29

Figure 5.2-13 Complementary cumulative distribution function and statistical values for 

conditional, mean, individual early-fatality risk (per event) within a 3.5-mile 

radius for the MACCS Convergence Analysis

Tables 5.2-17 through 5.2-19 show the correlation matrix for the three MACCS analyses for the 

conditional, mean, individual early-fatality risk (per event) at specified circular areas. The 

correlation data applies to both zero and nonzero early-fatality risk results. The correlation 

between the closer circular areas and the further circular areas is poor due to the small number 

of realizations for which a nonzero early-fatality risk is observed beyond 3 miles. This is most 

noticeable in Table 5.2-17 for the 10-mile correlation. At this location 1% of the total realizations

result in a nonzero early-fatality risk which is about the same percentage as the other two 

uncertainty cases. However in Table 5.2-18, these nonzero early fatality realizations at 10 miles 

account for 40% of the top 3% of the nonzero early fatality realizations at 1.3 miles. Thus the 

correlation at 10 miles is not that dependent on the lower circular areas since it is weighted 

heavily towards the higher end of the early-fatality risks. 
 5-30

Table 5.2-17 Correlation matrix for the MELCOR STP08 Uncertainty Model Source Term 

MACCS Analysis for the conditional, mean, individual early-fatality risk 

(per event) for specified circular areas 

0-1.3 

miles

0-2 

miles

0-2.5 

miles

0-3 

miles

0-3.5 

miles

0-5 

miles

0-7 

miles

0-10 

miles

0-1.3 miles 1 0.84 0.68 0.72 0.37 0.28 0.22 0.22

0-2 miles 1 0.88 0.77 0.51 0.45 0.40 0.40

0-2.5 miles 1 0.90 0.67 0.61 0.56 0.56

0-3 miles 1 0.79 0.74 0.68 0.68

0-3.5 miles 1 0.94 0.88 0.88

0-5 miles 1 0.94 0.94

0-7 miles 1 1

0-10 miles 1

Table 5.2-18 Correlation matrix for the MELCOR STP09 Uncertainty Model Source Term 

MACCS Analysis for the conditional, mean, individual early-fatality risk 

(per event) for specified circular areas 

0-1.3 

miles

0-2 

miles

0-2.5 

miles

0-3 

miles

0-3.5 

miles

0-5 

miles

0-7 

miles

0-10 

miles

0-1.3 miles 1 0.93 0.92 0.85 0.84 0.78 0.57 0.53

0-2 miles 1 0.992 0.95 0.94 0.88 0.63 0.60

0-2.5 miles 1 0.97 0.96 0.91 0.66 0.63

0-3 miles 1 0.994 0.95 0.72 0.68

0-3.5 miles 1 0.98 0.77 0.73

0-5 miles 1 0.87 0.85

0-7 miles 1 0.99

0-10 miles 1

Table 5.2-19 Correlation matrix for the MELCOR STP10 Uncertainty Model Source Term 

MACCS Analysis for the conditional, mean, individual early-fatality risk 

(per event) for specified circular areas 

0-1.3 

miles

0-2 

miles

0-2.5 

miles

0-3 

miles

0-3.5 

miles

0-5 

miles

0-7 

miles

0-10 

miles

0-1.3 miles 1 0.84 0.92 0.75 0.46 0.45 0.39 0.34

0-2 miles 1 0.83 0.80 0.56 0.56 0.48 0.40

0-2.5 miles 1 0.87 0.64 0.64 0.55 0.44

0-3 miles 1 0.76 0.76 0.66 0.51

0-3.5 miles 1 0.991 0.85 0.64

0-5 miles 1 0.86 0.63

0-7 miles 1 0.75

0-10 miles 1
 5-31

Based on these analyses, the conditional, mean, individual early-fatality risk (per event) are 

determined to be well converged for this uncertainty analysis. These analyses further verify the 

overall statistical convergence of the MACCS code when applying epistemic (e.g., radionuclide 

inhalation DCFs) and aleatory (e.g., weather trials) uncertainties.

6-1 

6. SOARCA MODEL PARAMETER UNCERTAINTY AND 

SENSITIVITY ANALYSES

This section presents uncertainty and sensitivity analysis results for the unmitigated LTSBO 

severe accident scenario at the Peach Bottom Atomic Power Station. Uncertainty analyses 

determine the variability in analysis results that derives from uncertainty in analysis inputs. 

Sensitivity analyses determine the contribution to the variability in analysis results that derives 

from individual analysis inputs. This section is divided into four parts. The first two sections 

present the uncertainty and sensitivity analysis results for the probabilistic source term and 

consequence analysis in Sections 6.1 and 6.2, respectively. The procedures used to generate 

these results are described in Appendix A while the independent and dependent variables under 

consideration are listed in Section 4.0. 

In addition, within each section is an analysis of single realizations selected from the 

probabilistic sample set. These detailed analyses provide a unique insight into the coupling of 

various processes and a comprehensive explanation detailing how the key phenomena in the 

various components of the complex system under varying physical-chemical-thermalmechanical conditions provides confidence in the measure of the key uncertainty in the analysis 

results. 

Section 6.3 presents a summary of the key parameters. Section 6.4 presents a series of 

sensitivity cases to target phenomena that could not be directly captured in the parametric study 

and regression analyses. As discussed in Section 4.3, several of the issues and sensitivity 

cases in Section 6.4 lack the technical basis to develop meaningful distributions of the 

uncertainty or the capability of the codes to directly assess the phenomena is absent. 

Collectively the results of the parametric parameter uncertainty analysis, single realizations, and 

selected sensitivity calculations, provide a quantitative measure of the impact of key uncertainty 

within a complex modeling system.

6.1 Source Term Parameter Uncertainty Analysis

For the uncertainty analysis, time-varying fractions of the corresponding radionuclide inventory 

released over the first 48 hours for all results from the three replicates combined were used (as 

discussed in Section 5.1.1), as well as the representative statistics (mean, median and quantiles 

q=0.05 and 0.95). A CDF of the uncertainty at the selected time of 48 hours after the incident is 

also presented, with the inclusion of a 95% confidence interval (CI) over the previously 

mentioned statistics, based on a q-bootstrap estimation, as described below.

All three sample sets for the three replicates were generated using a simple random sampling 

(SRS) technique. Therefore, it is valid to use the combined sample set for this uncertainty 

analysis. Moreover, bootstrap samples (selection of realizations n times from the original 

sample with replacement) of similar size can be generated to estimate mean and selected 

quantiles (median, q=0.05 and q=0.95). Five thousand such samples have been generated to 

construct distributions over the mean and selected quantiles. Quantiles 0.025 and 0.975 in 

each distribution have been selected to represent a 95% CI. 

A sensitivity analysis was also performed at the selected time of 48 hours for both the combined 

population of results and for each of the three individual replicates. Rank regression, quadratic

regression, recursive partitioning, and multivariate adaptive regression splines (MARS) are the 

four regression techniques selected for the regression analysis. While the first regression 

technique gives direct indices of importance of the input parameters, the last three techniques 

are used to construct a surrogate model. Sobol variance decomposition is then applied on the 

surrogate model to estimate the importance of the input parameters in the uncertainty of the 
6-2 

output in consideration. A simplified description of the techniques is presented in Section 3.4.2, 

while a more detailed description can be found in Storlie et al [12, 13]. Each of these methods 

uses an alpha cut off (representing the probability that a value is due to spurious correlation) 

equal to 0.02. Moreover, the maximum number of displayed variables is set to 15 since most of 

the influence will be negligible beyond the first 15 uncertain parameters. 

6.1.1 Fraction of Iodine Released to the Environment

The time-dependent graph of fraction of iodine released over the first 48 hours (Figure 6.1-1) 

shows releases starting after 10 hours and tending to plateau within the following 8 hours for 

some realizations and a second pulse (happening this time for most of the realizations) around 

18 hours after the event. The highest releases correspond to the realizations with thermal SRV 

failure leading to creep rutpure for reasons identified in Section 6.1.4. The distribution of results 

is slightly skewed to the right (positive skew) as to the relative position of the mean compared to 

the median. But considering that a linear scale is used, the skewness is relatively small. The 

expected value and median are around 5% of the fraction of iodine released. The 

95th percentile stands between 10% and 15%, while the maximum (over 865 samples) does not 

go beyond 20%.

A CDF representation at 48 hours is displayed on Figure 6.1-2. 95% confidence intervals over 

all considered statistics show convergence for 5th percentile, median and mean. The 

95th percentile shows more variability (which is expected considering that, for a sample of size 

865, the highest 43 results define its position), but it remains reasonable, within 10% of the 

estimate value, leading to an accuracy of plus or minus 1% of iodine release with 95% 

confidence.

Figure 6.1-1 Time-dependent fraction of iodine core inventory released to the 

environment for the first 48 hours for combined (865) results for the 

Peach Bottom Unmitigated LTSBO
6-3 

Figure 6.1-2 Cumulative distribution function of fraction of iodine core inventory 

released to the environment at 48 hours based on all combined (i.e., 865) 

results, with 95% confidence interval over mean, median and quantiles 

q = 0.05 and q = 0.95 for the Peach Bottom Unmitigated LTSBO

Table 6.1-1 presents the results of four regression analyses applied to the fraction of the iodine 

core inventory released to the environment over 48 hours. The coefficient of determination for 

all four regression models are fairly high, ranging from 0.69 (for rank regression) to 0.93 (for 

recursive partitioning). 

All regression methods rank the uncertainty in lambda in SRV stochastic failure to reclose

(SRVLAM, defined in Section 4.1.1) as the most significant parameter. It explains about half of 

the variability in the fraction of iodine released on average by itself. In conjunction with other 

parameters, the three non-additive techniques (i.e., quadratic regression, recursive partitioning 

and MARS) indicate that SRVLAM may explain up to 70% of the variance. The influences that 

variations in this parameter have on accident progression and releases to the environment are 

discussed at length in Section 6.1.4.

The methods also agree that the second most important parameter is chemical form of iodine 

and cesium (CHEMFORM, defined in Section 4.1.5) which explains an additional 10% of the 

variance. Quadratic and recursive partitioning tend to identify some conjoint influence 

(i.e., carried on by two or more uncertain input parameters in combination) which is not captured 

using MARS. While the conjoint effect is small, it may not have been captured by MARS 

because CHEMFORM has a discrete distribution (integer from 1 to 5 representing 5 different 

chemical states) and the spline regression has difficulties when dealing with discrete variables. 
6-4 

In considering the dependence of iodine release on CHEMFORM, it is important to note that the 

different combinations of chemical form in the uncertainty analysis vary in the amount of 

elemental (gaseous) iodine initialized in the core. Important with respect to gaseous iodine in 

the calculations is that it is scrubbed very effectively when introduced to the wetwell pool, and 

that unless scrubbed in the pool, releases to the environment. Therefore, for gaseous iodine to 

release to the environment, it must bypass the wetwell pool. In the base uncertainty case, all of 

the elemental iodine is released from the core before reactor lower head failure and is swept to 

the wetwell through the stuck-open SRV. The iodine is efficiently scrubbed by the wetwell pool 

such that 99.8% of the original core inventory is retained in the pool. In other calculations, a 

MSL rupture interrupts the sweeping of gaseous iodine to the wetwell introducing it to the 

drywell instead where it is readily available to escape containment through the drywell head 

flange or a drywell liner melt-through. In still other calculations, not all of the iodine releases 

from the core (or core debris) before lower head failure and so too introduces to the drywell 

where it is available to escape through the drywell head flange or a drywell liner melt-through. 

Flow area resulting from drywell liner failure (FL904A, described in Section 4.1.4) and SRV 

open area fraction after thermal seizure (SRVOAFRAC, defined in Section 4.1.2) both explain 

about 5% of the variance. SRVOAFRAC seems, however, to have a greater conjoint influence 

than FL904A. As recursive partitioning associates a higher Ti value than quadratic and MARS, 

it seems that SRVOAFRAC projects its influence in conjunction with one or multiple other 

parameters. The dependence of FL904A reflects the larger fission product releases associated 

with contaminated water surging up from the wetwell given larger values of this parameter as 

described in Section 6.1.4. The conjoint influence noted for SRVOAFRAC reflects the 

importance of this parameter with respect to whether a MSL rupture occurs. MSL ruptures 

consistently resulted in larger releases but SRVOAFRAC alone does not determine whether or 

not a MSL rupture occurs.

Yet, as SRVOAFRAC is considered not as important by rank regression (only 2% of the 

variance explained), it is likely that SRVOAFRAC has a nonlinear/non-monotonic effect. Since 

the significance was determined by quadratic regression, it is likely that the shape of influence is 

parabolic (with one area of the distribution leading to the highest or lowest value set). This 

nonlinear effect is demonstrated on Figure 6.1-3. Samples of SRVOAFRAC for Replicate 1

(without a SRV stochastic failure) indicate that at values below approximately 0.7, main steam 

line rupture and associated higher source term releases will occur. 
6-5 

Figure 6.1-3 Cumulative distribution function of SRVOAFRAC with samples where 

main steam line creep rupture occur indicated for Replicate 1 for the 

Peach Bottom Unmitigated LTSBO

These four input parameters (SRVLAM, CHEMFORM, SRVOAFRAC and FL904A) explain at 

least 70% of the variability in each regression analysis. It is likely, considering the regression 

techniques capture different effects that these parameters actually explain about 80% of the 

variability. The phenomenological effects of these parameters are discussed in Section 6.1.4.

Other parameters were not as important and have a negligible influence. Amongst the 

remaining parameters, the only one worth noting is the criteria for thermal seizure of the SRV 

due to heating after onset of core damage (SRVFAILT, defined in Section 4.1.2), which has a 

small influence (around 2 or 3%) according to all three non-monotonic techniques. 
6-6 

Table 6.1-1 Regression analysis of fraction of iodine released after 48 Hours

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.69 0.76 0.93 0.80

Input name

R2

inc.

R2

cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

SRVLAM 0.49 0.49 -0.72 0.46 0.68 0.00 0.55 0.78 0.00 0.64 0.70 0.00

CHEMFORM 0.58 0.09 0.30 0.10 0.16 0.00 0.07 0.22 0.00 0.09 0.12 0.00

FL904A 0.64 0.06 0.26 0.05 0.06 0.22 0.02 0.12 0.00 0.05 0.08 0.00

RRDOOR 0.67 0.03 0.28 0.01 0.06 0.03 0.04 0.07 0.00 --- --- ---

SRVOAFRAC 0.69 0.02 -0.12 0.06 0.13 0.00 0.05 0.20 0.00 0.06 0.16 0.00

FFC 0.69 0.00 0.06 0.03 0.03 0.17 --- --- --- 0.02 0.00 1.00

RRIDFRAC 0.69 0.00 0.03 --- --- --- --- --- --- 0.00 0.02 0.09

KBOLT 0.69 0.00 -0.04 0.04 0.00 1.00 0.00 0.00 1.00 --- --- ---

BATTDUR --- --- --- 0.00 0.08 0.00 0.00 0.04 0.06 0.00 0.00 1.00

RHONOM --- --- --- 0.00 0.06 0.01 --- --- --- --- --- ---

H2IGNC --- --- --- 0.00 0.04 0.02 0.00 0.00 0.41 0.02 0.01 0.17

DGASKET --- --- --- 0.00 0.02 0.23 0.01 0.00 1.00 --- --- ---

SLCRFRAC --- --- --- 0.02 0.01 0.47 --- --- --- 0.00 0.00 1.00

SRVFAILT --- --- --- 0.03 0.00 1.00 0.03 0.07 0.00 0.00 0.02 0.18

SC1131_2 --- --- --- 0.04 0.00 1.00 0.00 0.06 0.00 0.00 0.02 0.05

DHEADSOL --- --- --- 0.00 0.00 1.00 0.00 0.04 0.00 0.01 0.00 1.00

SC1141_2 --- --- --- --- --- --- 0.00 0.03 0.12 0.01 0.00 1.00

RDSTC --- --- --- --- --- --- 0.00 0.01 0.26 0.00 0.00 1.00

RRODFRAC --- --- --- --- --- --- 0.00 0.00 1.00 0.01 0.01 0.28

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

SRVLAM and SRVOAFRAC combined influences separate the realizations into three groups, 

each representing a distinct mode of venting the RPV during much of the core degradation. 

These groups are: SRV stochastic failure (with about 1⁄2 of the realizations), SRV thermal failure 

without MSL creep rupture (representing ~1/3 of the realizations), and SRV thermal failure with 

MSL creep rupture (for ~1/6 of the realizations). The importance of these parameters is large 

as their values strongly influence the releases of iodine (and other fission products) to the 

environment. To better understand the driving variables for each of these three failure groups, 

separate analyses have been performed for each of them. Table 6.1-2 presents the results of 

regression analysis for environmental iodine release fraction after 48 hours for the realizations 

leading to SRV stochastic failure. Regressions are fairly good with R2 values ranging from 0.7 

to 0.9. 

The most influential parameters are FL904A and SRVLAM. The negative SRRC for SRVLAM

comes from the fact that an earlier stochastic SRV failure results in a decrease in the amount of 

iodine released to the environment. As described at length in Section 6.1.4, earlier SRV failures 

result in less core oxidation and less late revaporization of fission products off reactor vessel 

internals. Since most of the iodine released to the environment in the uncertainty calculations 

can be traced to material revaporized late off of reactor internals, earlier SRV failures result in 

smaller releases to the environment. In the worst case, a long period of SRV valve cycling 
6-7 

promotes a main steam line creep rupture characteristically leading to large releases to the 

environment. These two variables explain together between 50% and 70% of the variance. 

CHEMFORM, the third most influential parameter, explains about 10% of the variance. The 

influence of other parameters is low compared to the influence of these three parameters and 

not necessarily consistent amongst techniques.

Table 6.1-2 Regression analyses of fraction of iodine released after 48 hours for 

realizations leading to SRV stochastic failures

Rank Regression Quadratic 

Recursive 

Partitioning MARS

Final R2 0.69 0.71 0.91 0.80

Input name

R2

inc.

R2

cont. SRRC Si Ti

pval Si Ti p-val Si Ti p-val

FL904A 0.31 0.31 0.53 0.20 0.24 0.00 0.24 0.37 0.00 0.27 0.24 0.00

SRVLAM 0.54 0.23 -0.52 0.30 0.33 0.00 0.36 0.61 0.00 0.56 0.57 0.00

CHEMFORM 0.61 0.07 0.28 0.10 0.12 0.06 0.07 0.21 0.00 0.11 0.06 0.16

RRDOOR 0.63 0.02 0.43 0.06 0.15 0.01 0.00 0.03 0.03 --- --- --- 

BATTDUR 0.65 0.02 0.16 0.01 0.00 1.00 0.01 0.14 0.00 0.03 0.01 0.77

FFC 0.66 0.00 0.10 0.00 0.06 0.15 --- --- --- 0.00 0.00 1.00

RRIDFRAC 0.66 0.01 0.08 --- --- --- --- --- --- 0.02 0.05 0.01

RHONOM 0.67 0.00 -0.07 0.00 0.11 0.00 0.00 0.00 1.00 --- --- --- 

DGASKET 0.67 0.00 0.05 0.00 0.06 0.09 --- --- --- --- --- --- 

H2IGNC 0.67 0.00 0.04 --- --- --- --- --- --- 0.01 0.00 1.00

KBOLT --- --- --- 0.02 0.05 0.07 0.00 0.04 0.09 --- --- --- 

RDSTC --- --- --- 0.03 0.01 0.50 0.00 0.00 1.00 0.00 0.00 1.00

DHEADSOL --- --- --- 0.04 0.01 0.62 0.01 0.07 0.00 0.00 0.10 0.00

SRVFAILT --- --- --- 0.00 0.03 0.72 0.04 0.00 1.00 0.02 0.02 0.20

SC1131_2 --- --- --- 0.03 0.00 1.00 0.01 0.05 0.02 0.00 0.00 1.00

SC1141_2 --- --- --- 0.02 0.00 1.00 0.01 0.04 0.15 0.04 0.03 0.12

SRVOAFRAC --- --- --- 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.06 0.01

EBOLT --- --- --- --- --- --- 0.02 0.03 0.16 --- --- --- 

RRODFRAC --- --- --- --- --- --- 0.02 0.00 1.00 0.03 0.00 0.46

SLCRFRAC --- --- --- --- --- --- --- --- --- 0.00 0.03 0.14

The regression analyses for environmental iodine release fraction for SRV thermal failure 

without MSL creep rupture leads to a high R2 for all techniques (between 0.78 and 0.90), as 

shown in Table 6.1-3. All methods agree that CHEMFORM is the most important parameter in 

explaining between 40% and 50% of the variance. Second, explaining another 20% is the 

condition of the railroad doors, closed or blown open by an overpressure in the reactor building. 

When the railroad doors blow open, a buoyant draft establishes in the reactor building where air 

enters low through the doors and exits high out opened blowout panels or failed roofing in the 

refueling bay. The draft efficiently carries aerosols released from containment out into the 

environment. Note that the RRDOOR is not a sampled parameter. Its status is determined by 

the course of a calculation. RRDOOR assumes the value of one if the doors are blown open 

and the value of zero if they remain closed. The non-detection of RRDOOR effect by MARS is 
6-8 

not surprising as MARS has some difficulties with discrete variables. FL904A comes in third 

with 15% more of the variance explained. The other parameters have negligible influence.

Table 6.1-3 Regression analyses of fraction of iodine released after 48 hours for 

realizations leading to SRV thermal failures without MSL creep rupture

Rank Regression Quadratic

Recursive 

Partitioning MARS

Final R2 0.78 0.89 0.90 0.84

Input name

R2

inc.

R2

cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

CHEMFORM 0.42 0.42 0.68 0.49 0.53 0.00 0.49 0.56 0.00 0.59 0.58 0.00

RRDOOR 0.59 0.18 0.63 0.16 0.22 0.01 0.25 0.24 0.00 --- --- --- 

FL904A 0.74 0.14 0.38 0.15 0.13 0.04 0.17 0.21 0.00 0.14 0.17 0.00

FFC 0.75 0.02 0.17 0.02 0.04 0.11 0.00 0.01 0.30 0.05 0.02 0.37

KBOLT 0.76 0.01 -0.08 0.00 0.00 1.00 0.03 0.03 0.33 --- --- --- 

SC1131_2 0.77 0.01 0.10 0.05 0.07 0.02 0.01 0.00 1.00 0.05 0.02 0.16

DHEADSOL 0.77 0.00 -0.07 0.03 0.02 0.33 0.01 0.00 1.00 0.01 0.02 0.05

RRIDFRAC 0.77 0.00 -0.05 0.00 0.00 1.00 0.03 0.02 0.06 0.00 0.00 1.00

RHONOM 0.78 0.00 -0.05 0.00 0.00 1.00 0.00 0.03 0.06 --- --- --- 

BATTDUR --- --- --- 0.05 0.08 0.03 --- --- --- 0.01 0.03 0.06

SLCRFRAC --- --- --- 0.01 0.06 0.18 --- --- --- 0.00 0.04 0.00

RDSTC --- --- --- 0.00 0.01 0.48 0.01 0.00 1.00 0.00 0.03 0.04

SRVFAILT --- --- --- 0.02 0.00 0.63 0.00 0.01 0.36 0.00 0.01 0.31

DGASKET --- --- --- --- --- --- 0.05 0.05 0.02 --- --- --- 

RRODFRAC --- --- --- --- --- --- 0.00 0.02 0.15 0.00 0.02 0.06

SC1141_2 --- --- --- --- --- --- 0.03 0.00 0.51 0.00 0.00 1.00

H2IGNC --- --- --- --- --- --- --- --- --- 0.00 0.02 0.10

SRVOAFRAC --- --- --- --- --- --- --- --- --- 0.00 0.00 0.55

SRVLAM --- --- --- --- --- --- --- --- --- 0.00 0.00 1.00

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

SRV thermal failure with MSL creep rupture is the last segregated group. Results of the 

analysis on this group for environmental iodine release are presented in Table 6.1-4. R2 values 

are reasonably high for all regression techniques (from 0.7 to 1), suggesting that the important 

parameters are accurately estimated. CHEMFORM is the most important parameter explaining

between 33% and 50% of the variance. Second, is RRDOOR, explaining another 10% (except 

for MARS). At third and found by all techniques, zircaloy melt breakout temperature (SC1131-2, 

defined in Section 4.1.2) explains about 5% of the variance by itself and about 15% in 

conjunction with other parameters. Besides these three parameters, methods seem to disagree 

on what are the next important parameters. 

The importance of CHEMFORM stems from more or less elemental (gaseous) iodine being 

initialized in the core dependent upon the sampled value of this variable. A MSL rupture allows 

some of the iodine to enter the drywell instead of being vented to the wetwell (through the 

stuck-open SRV) where it would be efficiently scrubbed in the wetwell pool. Once in the drywell, 
6-9 

the gaseous iodine is readily available to escape containment through the drywell head flange 

or a drywell liner melt-through.

RRDOOR is important to iodine release in cases of MSL rupture in the same way as described 

earlier in this section.

The importance of zircaloy melt breakout temperature (SC1131-2) is explained by the effect this 

parameter has on oxidation. Larger breakout temperatures lead to greater oxidation. Greater 

oxidation leads to greater heat generation and earlier MSL rupture. Earlier MSL rupture allows 

more gaseous iodine to enter the drywell instead of being vented to the wetwell (through the 

stuck-open SRV) where it would be efficiently scrubbed in the wetwell pool. Once in the drywell, 

the gaseous iodine is readily available to escape containment through the drywell head flange 

or a drywell liner melt-through.

Table 6.1-4 Regression analyses of fraction of iodine released after 48 hours for 

realization leading to SRV thermal failure and MSL creep rupture

Rank Regression Quadratic

Recursive 

Partitioning MARS

Final R2 0.70 0.99 0.82 0.76

Input name

R2

inc.

R2

cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

CHEMFORM 0.33 0.33 0.52 0.12 0.27 0.16 0.48 0.69 0.00 0.41 0.40 0.00

RRDOOR 0.45 0.12 0.39 0.06 0.14 0.01 0.02 0.10 0.11 --- --- --- 

SLCRFRAC 0.50 0.05 0.25 0.01 0.21 0.31 --- --- --- 0.02 0.00 1.00

BATTDUR 0.56 0.06 -0.28 0.02 0.06 0.16 0.02 0.18 0.00 0.18 0.17 0.00

SC1131_2 0.60 0.04 0.16 0.05 0.14 0.05 0.04 0.12 0.02 0.06 0.09 0.00

FL904A 0.62 0.02 0.12 0.04 0.16 0.04 0.00 0.03 0.12 0.02 0.00 0.68

SRVOAFRAC 0.63 0.01 -0.15 0.00 0.16 0.03 0.02 0.10 0.23 0.09 0.08 0.04

SRVFAILT 0.65 0.02 0.13 0.04 0.07 0.15 0.03 0.02 0.36 0.09 0.14 0.01

KBOLT 0.66 0.01 -0.11 0.00 0.14 0.02 --- --- --- --- --- --- 

RHONOM 0.67 0.01 -0.11 0.00 0.04 0.43 --- --- --- --- --- --- 

FFC 0.68 0.02 0.16 0.00 0.00 1.00 --- --- --- 0.02 0.03 0.05

DGASKET 0.69 0.01 -0.09 --- --- --- 0.00 0.03 0.24 --- --- --- 

RRODFRAC 0.70 0.01 -0.08 0.00 0.00 1.00 0.00 0.05 0.13 0.01 0.04 0.01

SC1141_2 --- --- --- 0.02 0.08 0.14 0.05 0.07 0.05 0.00 0.05 0.00

H2IGNC --- --- --- 0.00 0.06 0.20 --- --- --- 0.00 0.07 0.00

RRIDFRAC --- --- --- 0.06 0.00 1.00 0.00 0.04 0.11 0.00 0.00 1.00

EBOLT --- --- --- --- --- --- 0.00 0.05 0.08 --- --- --- 

DHEADSOL --- --- --- --- --- --- 0.00 0.03 0.16 0.00 0.04 0.01

SRVLAM --- --- --- --- --- --- 0.02 0.00 1.00 0.01 0.00 1.00

RDSTC --- --- --- --- --- --- --- --- --- 0.00 0.00 1.00
6-10

6.1.1.1 Timing of Initial Iodine Released to the Environment

In order to better understand what affects the timing of radionuclide release, the time when the 

fraction of iodine released to the environment reaches 0.001(i.e., 0.1% of the iodine inventory)

has been analyzed using the same four techniques. This metric served as an indication of 

when fission product releases to the environment were first nonzero. 

Table 6.1-5 shows the regression analyses over time when the fraction of the iodine inventory 

released to the environment reaches 0.001. Rank regression leads to a relatively small R2

(0.42), while all three other techniques range from 0.67 to 0.87. This difference indicates that 

some conjoint and non-monotonic influences are probably involved in the variance of release 

timing. Battery duration (BATTDUR) is the most influential parameter, explaining 30% of the

variance. The non-additive techniques, with conjoint influence, explain as much as 40%. 

SRVOAFRAC is the second most influential parameter, but once again the difference between 

R2 contribution (purely monotonic) and Si (capturing non-monotonic) indicates that its effect is 

probably non-monotonic. SRVOAFRAC also seems to have conjoint influence as the total 

sensitivity indices (Ti) are between 0.3 and 0.45. And, equally important according to the three 

non-monotonic techniques, but considered as negligible by rank regression, is SRVLAM, with Si

values between 0.1 and 0.2 and Ti values around 0.4. The influence of SRVLAM and 

SRVOAFRAC explains the difference in R2 between rank regression and the three other 

regressions. All the remaining uncertain parameters seem to have negligible influence.

Battery duration (BATTDUR) has an obvious influence on release timing in that RCIC functions 

to keep the reactor cool as long as DC power is available. It isn’t until DC power is lost that the

operators lose control of RCIC and its water delivery increases overfilling the vessel and 

flooding the steam lines. The drive turbine on the RCIC pump is assumed to fail when the steam 

lines flood.

The number of cycles to SRV failure (1/SRVLAM) and the open fraction of an SRV after thermal 

seizure (SRVOFRAC) are important to release timing because they are important to whether or 

not a MSL rupture occurs. When a MSL rupture occurs, containment over pressurizes and leaks 

past the drywell head flange. This results in an early release.
6-11

Table 6.1-5 Regression analyses over time when the fraction reaches 0.001 of the 

iodine inventory released over the first 48 Hours

Rank Regression Quadratic

Recursive 

Partitioning MARS

Final R2 0.42 0.67 0.87 0.68

Input

R2

inc.

R2

cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

BATTDUR 0.32 0.32 0.52 0.32 0.41 0.00 0.30 0.43 0.00 0.39 0.43 0 

SRVOAFRAC 0.40 0.08 0.29 0.13 0.27 0.00 0.20 0.46 0.00 0.22 0.36 0 

FFC 0.41 0.01 0.13 0.00 0.03 0.23 0.01 0.04 0.02 0.00 0.00 0.55

RRDOOR 0.42 0.00 0.13 0.00 0.20 0.00 0.00 0.00 1.00 --- --- --- 

CHEMFORM 0.42 0.00 0.04 0.01 0.00 1.00 --- --- --- 0.00 0.00 1 

SRVFAILT 0.42 0.00 -0.06 0.01 0.00 1.00 0.00 0.00 1.00 0.00 0.03 0.11

FL904A 0.42 0.00 -0.05 0.02 0.05 0.05 0.00 0.00 0.54 0.05 0.02 0.17

SRVLAM 0.42 0.00 0.04 0.12 0.39 0.00 0.21 0.41 0.00 0.18 0.39 0 

SC1141_2 --- --- --- 0.04 0.09 0.00 0.03 0.03 0.07 0.00 0.00 1 

DGASKET --- --- --- 0.01 0.08 0.01 0.00 0.00 1.00 --- --- --- 

H2IGNC --- --- --- 0.02 0.02 0.28 0.00 0.02 0.23 0.00 0.01 0.4

RHONOM --- --- --- 0.00 0.02 0.29 0.00 0.09 0.00 --- --- --- 

SC1131_2 --- --- --- 0.02 0.02 0.35 0.00 0.03 0.05 0.01 0.00 1 

SLCRFRAC --- --- --- 0.00 0.00 1.00 --- --- --- 0.01 0.06 0 

RRIDFRAC --- --- --- 0.00 0.00 1.00 0.00 0.00 1.00 0.01 0.00 1 

RRODFRAC --- --- --- --- --- --- 0.03 0.00 0.61 0.00 0.00 1 

EBOLT --- --- --- --- --- --- 0.04 0.00 1.00 --- --- --- 

DHEADSOL --- --- --- --- --- --- --- --- --- 0.00 0.06 0 

RDSTC --- --- --- --- --- --- --- --- --- 0.01 0.00 0.4

6.1.2 Fraction of Cesium Released from the Core Inventory

The time dependent fraction of the cesium core inventory released to the environment presents 

the same characteristics as seen for iodine releases (Figure 6.1-4). The release fractions are 

smaller than for iodine, ranging from 2% to 3% of the inventory for median and mean 

respectively, and reaching 9% for the 95th percentile. Figure 6.1-5 displays the CDF of the 

results at 48 hours. Confidence intervals confirm that the statistics are fairly converged, with the

95th percentile result having a 95% CI within plus or minus 1% of inventory released.
6-12

Figure 6.1-4 Time-dependent fraction of the cesium core inventory released to the 

environment over the first 48 hours for combined (865) results for the 

Peach Bottom Unmitigated LTSBO
6-13

Figure 6.1-5 Cumulative distribution function of fraction of cesium core inventory 

released to the environment after 48 hours based on all combined 

(i.e., 865) results, with 95% confidence interval over mean, median and 

quantiles q = 0.05 and q = 0.95 for the Peach Bottom Unmitigated LTSBO

Table 6.1-6 presents the results of the four regression analyses applied to the fraction of the 

cesium core inventory released to the environment over 48 hours. R2 are not as good as for 

fraction of iodine released, as three of them range between 0.6 and 0.66 of the variance 

explained and only recursive partitioning seems to find a better match with 0.9 of the variance 

explained. As for fraction of the cesium core inventory released to the environment, the most 

important parameter is SRVLAM, explaining again about half of the variance by itself. All three 

non-additive techniques agree that SRVLAM explain 10% to 20% more of the variance with 

conjoint influence of the other uncertain parameters. The next most important parameter is 

SRVOAFRAC for all three non-monotonic regressions, explaining 7% to 12% of the variance by 

itself and between 19% and 33% with conjoint influence of the other uncertain parameters. The 

regression results also indicate that FL904A, the fuel failure criterion on the transformation of 

intact fuel into particulate debris (FFC, described in Section 4.1.2) and RRDOOR explain 

between 2% and 5% of the uncertainty depending on the techniques. The influence of 

RRDOOR is not captured, as expected, by MARS. 

Finally, three parameters (CHEMFORM, SC1131_2, and RRIDFRAC) seem to explain a very 

small amount of variance in the fraction of cesium released (around 1% each). For 

CHEMFORM, both quadratic and recursive partitioning suggest that it may have an effect in 

conjunction with other variables. This makes sense physically as chemisorption, the 

phenomenon behind the influence of CHEMFORM, is only strong at the relatively higher core
6-14

degradation temperatures consistent with SRV thermal with or without MSL creep rupture (as 

described in Section 6.1.4). The regression analyses confirms that CHEMFORM is the most 

important parameter when only MSL creep rupture cases are considered, explaining between 

30% and 50% of the variance (see Table 6.1-9). This kind of specific influence is better 

captured with tree analysis (which is the basis for recursive partitioning). This explains why only 

recursive partitioning captures fully this influence, leading to a higher R2 value.

The different influences that variations in SRVLAM have on releases to the environment are 

discussed at length in Section 6.1.4. The largest influence with respect to cesium release 

affects the slow revaporization of material off of reactor internals; longer times to SRV failure 

leading to more revaporization. The revaporization comes after reactor lower head failure and 

after drywell liner melt-through. The cesium migrates from the reactor vessel condensing to 

aerosol and exits the drywell through the breach in the liner.

As in the case with iodine, the conjoint influence noted for SRVOAFRAC reflects the importance 

of this parameter with respect to whether a MSL rupture occurs. MSL ruptures consistently 

resulted in larger releases of cesium but SRVOAFRAC alone does not determine whether or not 

a MSL rupture occurs. MSL ruptures result in higher releases because, for a period of time 

before lower head failure, the reactor vents to the drywell rather than to the wetwell. Scrubbing 

by the wetwell is not realized during this time and the cesium introduced to the drywell is 

available to leak to the environment. 

The dependence of FL904A reflects the fission product releases associated with contaminated 

water surging up from the wetwell given larger values of this parameter as described is 

Section 6.1.4. The water pools on the drywell floor, in contact with the core debris relocated 

from the reactor, and eventually boils away, releasing its content of radionuclides including 

cesium. Larger values of FL904A (larger drywell breaches from liner melt-through) support the 

surging of water up from the wetwell. 

FFC is important to cesium release in that it affects how long fuel remains standing. The longer 

fuel remains standing the longer oxidation of fuel cladding persists. Persistent oxidation drives 

continued revaporization of cesium deposits off of reactor internals late (i.e., after reactor lower 

head failure). The revaporized cesium migrates from the reactor to the drywell condensing to 

aerosol and escapes containment through the drywell liner melt-through. Conjoint influence of 

FFC and SC1131_2 (zirconium melt breakout temperature) is suspected as longer standing fuel 

and delayed draining away of zircaloy would combine to give the most persistent oxidation. 

RRDOOR (railroad doors open/closed) is important to cesium release in the same way as it is 

important to iodine release in that open doors promote the development of a buoyant draft in the 

reactor building.

In conclusion, more of the variance is explained by recursive partitioning than by the other 

methods, considering that MARS misses the influence of the discrete variable RRDOOR, while

rank regression misses the non-monotonic influence of SRVOAFRAC, which also seems to be 

underestimated by the quadratic regression. The regression analyses combined indicate that 

eight input parameters (SRVLAM, SRVOAFRAC, FL904A, FFC, RRDOOR, CHEMFORM, 

SC1131_2, and RRIDFRAC) explain between 70% and 75% of the variance, the last three

accounting for a relatively small contribution to the overall variance in the results. The effect of 

CHEMFORM is more important than suspected by regression techniques other than recursive 

partitioning by which the total variance explained is probably closer to 85% to 90%. Once 

again, amongst the remaining parameters, only SRVFAILT seems to have a small influence, but 

at best on the order of 1%.
6-15

Table 6.1-6 Regression analyses of fraction of cesium released over 48 hours

Rank Regression Quadratic

Recursive 

Partitioning MARS

Final R2 0.61 0.64 0.90 0.66

Input name

R2

inc.

R2

cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

SRVLAM 0.50 0.50 -0.72 0.39 0.64 0.00 0.43 0.70 0.00 0.57 0.68 0.00

FL904A 0.53 0.03 0.19 0.01 0.04 0.12 0.06 0.02 0.44 0.00 0.03 0.10

FFC 0.55 0.02 0.19 0.04 0.05 0.31 0.02 0.10 0.00 0.01 0.08 0.00

RRDOOR 0.58 0.03 0.33 0.02 0.10 0.00 0.02 0.03 0.19 --- --- ---

SRVOAFRAC 0.59 0.02 -0.13 0.07 0.19 0.00 0.11 0.33 0.00 0.12 0.27 0.00

CHEMFORM 0.60 0.01 0.09 0.00 0.08 0.38 0.01 0.18 0.00 0.02 0.00 0.87

SC1131_2 0.60 0.01 -0.07 0.02 0.01 0.63 0.00 0.07 0.00 0.00 0.04 0.01

RRIDFRAC 0.61 0.00 0.06 0.05 0.00 1.00 0.00 0.01 0.57 0.01 0.03 0.07

BATTDUR 0.61 0.00 0.04 0.03 0.02 0.49 0.00 0.02 0.47 0.00 0.01 0.53

RRODFRAC --- --- --- 0.01 0.04 0.15 0.00 0.03 0.16 0.00 0.00 1.00

SRVFAILT --- --- --- 0.04 0.03 0.27 0.00 0.04 0.11 0.01 0.00 1.00

DGASKET --- --- --- 0.00 0.03 0.27 0.00 0.06 0.02 --- --- ---

H2IGNC --- --- --- 0.03 0.02 0.34 --- --- --- 0.01 0.00 1.00

SC1141_2 --- --- --- 0.05 0.01 0.52 0.00 0.08 0.00 0.00 0.00 1.00

SLCRFRAC --- --- --- 0.00 0.01 0.66 --- --- --- 0.00 0.02 0.06

EBOLT --- --- --- --- --- --- 0.00 0.03 0.02 --- --- ---

RHONOM --- --- --- --- --- --- 0.03 0.02 0.40 0.00 0.03 0.05

RDSTC --- --- --- --- --- --- --- --- --- 0.00 0.00 1.00

DHEADSOL --- --- --- --- --- --- --- --- --- --- --- --- 

In order to understand the driving factors for cesium release to the environment, the realizations 

have been segregated according to the three different modes of RPV depressurization (SRV 

stochastic, SRV thermal, and MSL creep ruptures) and analyzed through the same techniques. 

Table 6.1-7 presents the results of regression analyses for the environmental cesium release 

fraction over 48 hours for the realizations leading to only an SRV stochastic failure. 

Regressions are not as good as for iodine: R2 values are ranging from 0.4 to 0.5 for three 

regression techniques, with only Recursive partitioning R2 reaching 0.8. 

Similarly to the regression for iodine, FL904A is the most important parameter explaining about 

20% of the variance. CHEMFORM is in the second position, explaining about 10% of the 

variance. The effect of SRVLAM is not as strong here for rank regression and quadratic 

regression (respectively 5% and 10%) but recursive partitioning identifies it as one of the most 

important parameters (while MARS agrees with recursive partitioning, its low R2 value requires 

caution in interpreting results from variance decomposition). Another important parameter is 

FFC: results from quadratic regression, recursive partitioning and MARS attribute this 

parameter and influence varying between 15% and 20% of the variance by itself and up to 50% 

conjointly. Its effect is likely non-monotonic considering it is predicted as unimportant by rank 

regression. As described in Section 4.1.2, FFC is an indicator function whose value varies from 

one to three. The value of one represents the nominal case and the numbers two and three 

represent shifts in temperature of 100 K and in fuel endurance of time with a factor of 1⁄2 and 2 
6-16

respectively (creating optimistic and pessimistic conditions). Such characterization creates by 

default an asymmetry in the influence of the parameter. The influence of the remaining 

parameters is low.

The importance of FL904A is explained by the significant amount of cesium made available for 

release as a consequence of wetwell water surging up onto the drywell floor as described in the 

previous section. The importance of CHEMFORM stems from cesium hydroxide being 

generally more transportable than cesium molybdate due to its higher vapor pressure (i.e., due 

to it being more readily evaporable). Dependent on the CHEMFORM choice, more or less 

cesium is initialized as cesium hydroxide. The fact that SRVLAM is important in the subset of 

cases that experience SRV stochastic failure, given that it is the sole sampled parameter that 

determines whether a case is in the subset, identifies that the timing of the stochastic failure 

(not just whether a stochastic failure happens) is important to cesium release to the 

environment. FFC is important due to its impact on core oxidation as described earlier in this 

section. 

Table 6.1-7 Regression analyses of fraction of cesium released over 48 hours for 

realizations leading to SRV stochastic failure

Rank Regression Quadratic

Recursive 

Partitioning MARS

Final R2 0.47 0.51 0.80 0.39

Input name

R2

inc.

R2

cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

FL904A 0.22 0.22 0.47 0.14 0.21 0.04 0.16 0.40 0.00 0.22 0.19 0.04

CHEMFORM 0.28 0.06 0.24 0.07 0.00 0.95 0.07 0.07 0.81 0.02 0.09 0.02

SRVLAM 0.34 0.05 -0.25 0.10 0.17 0.02 0.19 0.20 0.03 0.38 0.45 0.00

FFC 0.34 0.00 0.07 0.18 0.51 0.00 0.14 0.43 0.00 0.23 0.36 0.00

RRDOOR 0.37 0.03 0.44 0.02 0.16 0.01 0.00 0.00 1.00 --- --- --- 

SC1131_2 0.40 0.03 -0.15 0.02 0.09 0.08 0.04 0.12 0.00 0.02 0.00 1.00

SC1141_2 0.41 0.01 0.10 0.00 0.10 0.02 0.00 0.11 0.01 0.00 0.02 0.30

BATTDUR 0.42 0.01 0.09 0.05 0.02 0.46 0.00 0.03 0.24 0.00 0.15 0.00

RRIDFRAC 0.42 0.01 0.09 --- --- --- --- --- --- 0.00 0.07 0.02

DHEADSOL 0.43 0.01 -0.07 --- --- --- 0.00 0.01 0.65 0.00 0.00 1.00

EBOLT 0.43 0.00 -0.06 0.02 0.10 0.05 0.00 0.08 0.00 --- --- --- 

RRODFRAC --- --- --- 0.00 0.06 0.10 0.02 0.02 0.37 0.01 0.00 1.00

SRVOAFRAC --- --- --- 0.02 0.07 0.20 --- --- --- 0.02 0.02 0.29

RHONOM --- --- --- 0.00 0.00 1.00 0.00 0.07 0.06 --- --- ---

KBOLT --- --- --- --- --- --- 0.00 0.03 0.23 --- --- --- 

RDSTC --- --- --- --- --- --- 0.00 0.00 1.00 0.01 0.00 1.00

DGASKET --- --- --- --- --- --- 0.00 0.00 1.00 --- --- --- 

SRVFAILT --- --- --- --- --- --- --- --- --- 0.00 0.09 0.00

SLCRFRAC --- --- --- --- --- --- --- --- --- 0.00 0.06 0.04

H2IGNC --- --- --- --- --- --- --- --- --- 0.00 0.00 1.00
6-17

Once again the regression analyses for environmental cesium release fraction for SRV thermal 

failures without MSL creep rupture do not lead to an R2 as high as for iodine (between 0.4 and 

0.70), but are better than for SRV stochastic failures as can be shown in Table 6.1-8. 

CHEMFORM, RRDOOR and FFC are the top three parameters explaining about 40% of the 

uncertainty for all regressions techniques. Considering that MARS does not identify RRDOOR 

influences, but may be better estimating other parametric influences, the total variance 

explained by these three parameters is probably closer to 50% to 60%. In fourth position, 

SRVOAFRAC seems to explain an additional 5% to 15% of the uncertainty. It is reasonable to 

consider that, with MARS missing the effect of RRDOOR and Rank regression missing 

non-monotonic and conjoint influences, these four parameters explain about 70% of the 

uncertainty. The influence of the remaining parameters is relatively low and each of them 

should explain no more than 2 to 3% of the variance.

CHEMFORM is important in the subset of cases that experience a thermal SRV failure for a 

different reason than in the subset of cases that experience stochastic SRV failure. The greater 

oxidation taking place during core degradation at the higher pressures and temperatures 

resulting from the SRV cycling successfully for a longer period of time is fundamentally 

important here. The greater oxidation drives reactor temperatures high enough to be supportive 

of the chemisorption of cesium from cesium hydroxide into stainless steel. The chemisorption 

permanently captures cesium in the reactor vessel. RRDOOR and FFC are important as 

described in the previous section and earlier in this section, respectively.
6-18

Table 6.1-8 Regression analyses of fraction of cesium released over 48 hours for 

realizations leading to SRV thermal failure without MSL creep rupture

Rank Regression Quadratic

Recursive 

Partitioning MARS

Final R2 0.51 0.71 0.74 0.38

Input name

R2

inc.

R2

cont. SRRC Si Ti p-val Si Ti p-val Si Ti

pval

RRDOOR 0.20 0.20 0.75 0.12 0.10 0.05 0.20 0.38 0.00 --- --- ---

CHEMFORM 0.31 0.12 0.38 0.09 0.24 0.00 0.06 0.10 0.07 0.20 0.17 0.06

FFC 0.37 0.05 0.40 0.09 0.20 0.01 0.13 0.25 0.00 0.25 0.26 0.00

SRVOAFRAC 0.40 0.03 -0.20 0.09 0.02 0.67 0.08 0.28 0.01 0.15 0.13 0.04

FL904A 0.44 0.04 0.21 --- --- --- 0.02 0.17 0.05 0.00 0.00 1.00

SC1131_2 0.45 0.01 -0.11 0.04 0.10 0.06 0.01 0.09 0.30 0.04 0.04 0.36

RHONOM 0.45 0.01 -0.07 0.01 0.00 1.00 0.00 0.11 0.02 --- --- ---

RRODFRAC 0.46 0.01 -0.09 0.00 0.06 0.16 0.00 0.06 0.24 0.00 0.02 0.13

SC1141_2 0.46 0.00 0.06 0.00 0.04 0.48 0.00 0.00 1.00 0.00 0.00 0.43

SRVLAM --- --- --- 0.00 0.16 0.01 0.02 0.00 1.00 0.00 0.00 1.00

EBOLT --- --- --- 0.00 0.07 0.11 --- --- --- --- --- ---

BATTDUR --- --- --- 0.03 0.06 0.13 0.00 0.13 0.00 0.01 0.05 0.04

DHEADSOL --- --- --- 0.02 0.05 0.15 --- --- --- 0.04 0.00 0.55

RRIDFRAC --- --- --- 0.00 0.04 0.35 --- --- --- 0.00 0.02 0.08

SLCRFRAC --- --- --- 0.00 0.17 0.43 --- --- --- 0.00 0.02 0.15

SRVFAILT --- --- --- 0.00 0.04 0.46 0.02 0.13 0.02 0.04 0.01 0.47

KBOLT --- --- --- --- --- --- 0.00 0.13 0.01 --- --- ---

H2IGNC --- --- --- --- --- --- 0.00 0.04 0.20 0.00 0.03 0.09

DGASKET --- --- --- --- --- --- 0.00 0.01 0.66 --- --- ---

RDSTC --- --- --- --- --- --- --- --- --- 0.02 0.00 1.00

The regression results for the fraction of cesium released to the environment considering only 

realizations exhibiting SRV thermal failure with MSL creep rupture are presented in Table 6.1-9. 

R2 values are high for all regression techniques (from 0.6 to 0.9), as they were for the analysis 

of iodine release. CHEMFORM is the most important parameter explaining between 33%and 

50%of the uncertainty. Second, is RRDOOR explaining another 20% (except for MARS) of the 

uncertainty. SRVOAFRAC and BATTDUR explain between 5% and 10% more of the 

uncertainty. The remaining parameters have a small effect compared to these four.

CHEMFORM is important to the MSL rupture cases in the same way as it is to the SRV thermal 

failure cases; that being through the phenomenon of chemisorption. Chemisorption of cesium is 

most prevalent in the MSL rupture cases because they experience successful SRV cycling for 

the longest period of time. RRDOOR is important as described in the previous section.

That SRVOFRAC explains a significant amount of the uncertainty in the subset of calculations 

that experience a MSL rupture is interesting. As described in Section 6.1.4, the value of this 

variable is the key to whether or not a MSL rupture occurs. That it shows to be important in the 

MSL-rupture subset of calculations means that its influence goes beyond determining whether a 
6-19

rupture occurs. The SRV (that seizes open) is downstream of the MSL rupture. Therefore, it 

seems the further influence of SRVOFRAC on cesium release must come before MSL rupture. 

BATTDUR being important to the magnitude of cesium release is non-intuitive. That this 

variable would affect release timing is intuitive but not that it would affect release magnitude. 

The reason BATTDUR is showing to be important to magnitude is that cesium release in a 

significant number of calculations is not over at 48 hrs. The shift in release history dependent 

upon BATTDUR, and the generally greater release magnitudes in MSL rupture cases, affects 

the reported cumulative release at 48 hrs. 

Table 6.1-9 Regression analyses of fraction of cesium released over 48 hours for 

realizations leading to SRV thermal failure and MSL creep rupture

Rank Regression Quadratic

Recursive 

Partitioning MARS

Final R2 0.67 0.74 0.91 0.64

Input name

R2

inc.

R2

cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

CHEMFORM 0.32 0.32 0.56 0.43 0.48 0.00 0.33 0.57 0.00 0.52 0.51 0.00

RRDOOR 0.50 0.18 0.63 0.24 0.26 0.00 0.18 0.27 0.00 --- --- --- 

SRVOAFRAC 0.56 0.06 -0.27 0.03 0.10 0.06 0.05 0.22 0.00 0.11 0.12 0.00

BATTDUR 0.62 0.05 0.23 0.06 0.03 0.52 0.04 0.18 0.00 0.03 0.06 0.35

SLCRFRAC 0.63 0.01 0.20 0.05 0.08 0.33 0.00 0.03 0.00 0.02 0.00 1.00

RRIDFRAC 0.64 0.01 0.11 --- --- --- 0.00 0.07 0.03 0.01 0.05 0.01

SRVFAILT 0.66 0.02 0.12 0.07 0.04 0.26 0.00 0.03 0.06 0.03 0.00 1.00

FL904A 0.66 0.01 0.09 --- --- --- 0.01 0.01 0.58 0.00 0.03 0.03

SRVLAM 0.67 0.01 -0.09 0.00 0.10 0.04 --- --- --- 0.04 0.04 0.30

RRODFRAC --- --- --- 0.00 0.00 1.00 --- --- --- 0.01 0.00 1.00

DGASKET --- --- --- --- --- --- 0.02 0.09 0.00 --- --- ---

DHEADSOL --- --- --- --- --- --- 0.01 0.05 0.01 0.03 0.05 0.01

SC1131_2 --- --- --- --- --- --- 0.04 0.10 0.04 0.00 0.00 0.49

EBOLT --- --- --- --- --- --- 0.00 0.03 0.13 --- --- --- 

H2IGNC --- --- --- --- --- --- 0.01 0.00 1.00 0.00 0.05 0.02

SC1141_2 --- --- --- --- --- --- 0.02 0.00 1.00 0.00 0.00 1.00

FFC --- --- --- --- --- --- --- --- --- 0.00 0.00 1.00

RDSTC --- --- --- --- --- --- --- --- --- 0.00 0.00 1.00

6.1.3 Hydrogen Production

As described in Section 4.1, in-vessel hydrogen production can be associated with fission 

product release to the environment, and, in its own right, hydrogen production is crucial 

considering the severe damage potential hydrogen poses to a reactor building should it burn. 

The amount of hydrogen generated in-vessel through 48 hours is considered in the following 

analysis. A CDF of the hydrogen production at 48 hours is displayed on Figure 6.1-6. 

Confidence Intervals show that the results are fairly well-converged, even at the 95th percentile. 
6-20

Figure 6.1-6 Time-dependent fraction (a) and cumulative distribution function (b) of 

in-vessel hydrogen production over 48 hours based on combined 

(i.e., 865) results, with 95% confidence interval over mean, median and 

quantiles q = 0.05 and q = 0.95 for the Peach Bottom Unmitigated 

LTSBO
6-21

Table 6.1-10 shows the regression analysis for hydrogen production. SRVLAM is the most 

important parameter explaining between 40% and 66% of the variance, depending on the 

regression technique. All regressions found SRVLAM accounts for at least 50% of the 

uncertainty by itself, with at least 15% more in conjunction with other parameters. SC1131_2 

appears to be the second most influential uncertainty with a contribution between 14% and 25% 

to the variance, followed by SC1141_2 with a contribution between 1% and 5%. All the other 

parameters seem to have negligible influence or questionable results (i.e., are only found in 

some regressions and associated with high p-values). As described in section 6.1.2, FFC and 

SC1131_2 are expected to have a conjoint influence on hydrogen production. While it seems 

that the quadratic regression captures this influence, MARS seems to attribute it mostly to 

SC1131_2 solely, while recursive partitioning recognizes some conjoint influence for SC1131_2 

but fail to attribute it to FFC. This lack of accuracy is not surprising considering that the conjoint 

influence is partly hidden by the strong influence of SRVLAM, and by the particular structure of 

FFC (indicator function) that makes its influence detection more difficult.

Principally important to hydrogen generation is how much core degradation occurs at high 

pressure (i.e., SRV set-point pressure). More core degradation at high pressure relates to more 

hydrogen generation from oxidation. The most important parameter affecting the amount of 

core damage occurring at high pressure is SRVLAM. If the SRV (the lowest set-point SRV) 

sticks open early, e.g., before the onset of core damage, no core degradation takes place at 

high pressure and so relatively little hydrogen is produced. If the SRV sticks open late 

(e.g., 1.25 hours after the onset of core damage,) substantial core degradation takes place at 

high pressure and a relatively large amount of hydrogen is produced.

SC1141_2 is important to hydrogen production, as mentioned in the previous section, in that it 

determines how long un-oxidized molten zirconium is held behind an oxidized cladding shell. 

The longer the zirconium is held the longer oxidation takes place and the more hydrogen 

produced.
6-22

Table 6.1-10 Regression analysis of hydrogen production. 

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.55 0.63 0.88 0.65

Input name

R2

inc.

R2

cont. SRRC Si Ti p-val Si Ti p-val Si Ti

pval

SRVLAM 0.39 0.39 -0.64 0.48 0.65 0.00 0.50 0.70 0.00 0.66 0.75 0.00

SC1131_2 0.53 0.14 0.37 0.19 0.29 0.00 0.17 0.33 0.00 0.25 0.26 0.00

SC1141_2 0.54 0.01 -0.11 0.03 0.08 0.01 0.03 0.14 0.00 0.05 0.05 0.03

RDSTC 0.54 0.01 0.07 0.02 0.00 0.73 0.02 0.04 0.10 0.00 0.02 0.18

CHEMFORM 0.55 0.00 0.04 0.01 0.09 0.00 --- --- --- 0.03 0.01 0.19

BATTDUR 0.55 0.00 0.06 0.00 0.00 1.00 --- --- --- 0.00 0.02 0.04

SRVFAILT 0.55 0.00 0.05 0.03 0.07 0.01 0.02 0.00 1.00 0.00 0.00 1.00

DGASKET 0.55 0.00 0.04 --- --- --- 0.04 0.00 1.00 --- --- --- 

EBOLT 0.55 0.00 0.03 0.01 0.00 1.00 0.01 0.00 1.00 --- --- --- 

RRIDFRAC 0.55 0.00 0.03 --- --- --- 0.00 0.04 0.04 0.01 0.00 1.00

SRVOAFRAC --- --- --- 0.00 0.09 0.00 0.06 0.04 0.02 0.00 0.00 1.00

FFC --- --- --- 0.00 0.05 0.05 --- --- --- 0.02 0.00 0.53

H2IGNC --- --- --- 0.00 0.02 0.46 0.00 0.04 0.02 0.03 0.00 1.00

RRDOOR --- --- --- 0.04 0.02 0.54 --- --- --- --- --- --- 

RHONOM --- --- --- 0.04 0.01 0.66 0.04 0.06 0.00 --- --- --- 

KBOLT --- --- --- 0.00 0.00 1.00 0.00 0.02 0.36 --- --- --- 

RRODFRAC --- --- --- 0.00 0.00 1.00 0.02 0.00 0.62 0.01 0.01 0.32

SLCRFRAC --- --- --- --- --- --- 0.02 0.03 0.00 0.03 0.00 0.40

DHEADSOL --- --- --- --- --- --- 0.04 0.03 0.18 0.00 0.01 0.12

FL904A --- --- --- --- --- --- --- --- --- 0.02 0.00 1.00

6.1.4 Analysis of Important Phenomena and Single Realizations

Analysis of single realizations provides a specific insight into the physical phenomena 

controlling the variability in the source term release results. A comprehensive explanation 

detailing how the release is affected by various components of the complex model of the reactor 

system and associated uncertain parameters for each failure modes (SRV Stochastic, SRV 

thermal, and MSL creep ruptures) under varying physical-chemical-thermal-mechanical 

conditions provides confidence that the various processes are working as expected and insight 

to the phenomena that are driving the results. This in turn defines the phenomenology driven by 

the key uncertain parameters identified in the parameter uncertainty analyses presented in 

earlier sections of this document.

Individual realizations from Replicate 1 were selected for investigation in greater detail to 

identify the phenomena affecting their cesium releases to the environment. The distribution of

the fraction of the cesium inventory released to the environment for Replicate 1 is shown on 
6-23 

Figure 6.1-7, along with selected statistics (median and 5th and 95th percentiles). For 

comparison with Replicate 1 results, Figure 6.1-7, and Figure 6.1-8(a) include the SOARCA 

Peach Bottom unmitigated LTSBO scenario for the case where a stochastic failure of the SRV 

occurs. Figure 6.1-7 also includes the SOARCA Peach Bottom sensitivity case with an MSL 

creep rupture. 

Representative single realizations were selected for each of the three failure modes. These 

realizations, selected for detailed analysis, are representative of the overall distribution of the 

results for all replicate sets. The realizations were also selected to be representative of the 

distribution of results over each group of the three failure scenarios (Stochastic SRV failures, 

Thermal SRV failures, and Thermal SRV failures with MSL creep rupture occurring). 

Figure 6.1-8 shows, on a linear scale, the distribution of results for each of the failure modes as 

well as the realizations selected. The individual analysis includes realizations that represent 

outliers, median and low (5th percentile) and high (95th percentile) behavior. Collectively these 

single realizations describe the phenomena driven by the key uncertainties in the complex 

system. Table 6.1-11 lists the sampled parameter values for the single realizations selected for 

the detailed analysis. Table 6.1-12 presents key event timings, key occurrences/attributes, and

cesium and iodine releases to the environment for the selected realizations. 

Figure 6.1-7 Distribution for the fraction of cesium core inventory released to the 

environment for Replicate 1 of the source term uncertainty analysis of the 

SOARCA Peach Bottom unmitigated LTSBO scenario
6-24

Figure 6.1-8 Single realizations selected for detailed analysis from Replicate 1 of the 

Peach Bottom unmitigated LTSBO, fraction of cesium core inventory 

released to the environment for (a) SRV stochastic failures, (b) SRV 

thermal failures, and (c) MSL creep ruptures
6-25

Table 6.1-11 Sampled parameter values for Replicate 1 (STP08) for selected individual realizations

Parameter SOARCA 18 51 52 62 63 86 90 122 134 

SRV failure to 

reclose 

(SRVLAM) per 

demand

3.70E-03 7.90E-05 4.45E-03 9.42E-04 2.14E-04 2.02E-03 9.90E-04 2.41E-03 2.16E-03 1.78E-

Battery duration 

(BATTDUR) hrs 4.00E+00 4.14E+00 5.11E+00 4.76E+00 3.79E+00 4.66E+00 3.72E+00 2.19E+00 4.26E+00 3.74E+

Zircaloy melt 

breakout 

temperature 

(SC1131(2)) K 

2.40E+03 2.26E+03 2.37E+03 2.41E+03 2.42E+03 2.39E+03 2.16E+03 2.34E+03 2.41E+03 2.48E+

Molten clad 

drainage rate

(SC1141(2)) 

kg/m-s 

2.00E-01 4.56E-01 2.79E-01 2.19E-01 5.70E-01 2.71E-01 3.92E-01 2.20E-01 2.90E-01 1.60E-

SRV thermal 

failure criterion 

(SRVFAILT) K 

9.00E+02 8.38E+02 9.50E+02 9.18E+02 8.72E+02 8.57E+02 8.63E+02 9.29E+02 9.26E+02 8.99E+

SRV open 

fraction 

(SRVOAFRAC) 

unitless

1.00E+00 6.87E-01 5.46E-01 3.23E-01 3.91E-01 7.53E-01 2.46E-01 7.08E-01 5.23E-01 1.64E-

MSL creep 

rupture area 

(SLCRFRAC) 

unitless

0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 4.00E-01 0.00E+00 1.00E-01 0.00E+

Fuel failure 

criterion (FFC)

unitless

0.00E+00 1.00E+00 1.00E+00 1.00E+00 3.00E+00 3.00E+00 1.00E+00 3.00E+00 1.00E+00 1.00E+

Solid debris 

radial relocation 

(RDSTC) s 

3.60E+02 3.10E+02 4.72E+02 2.35E+02 2.82E+02 2.50E+02 2.83E+02 3.04E+02 3.91E+02 4.13E+

Molten debris 

radial relocation 

(RDMTC) s 

6.00E+01 5.31E+01 8.12E+01 4.09E+01 4.73E+01 4.19E+01 4.77E+01 5.21E+01 6.75E+01 7.11E+

Debris height 

for solid coreconcrete 

(DHEADSOL) 

m 

5.00E-01 5.56E-01 6.06E-01 5.95E-01 4.02E-01 7.02E-01 6.41E-01 5.57E-01 5.73E-01 8.73E-
6-26

Table 6.1-11 Sampled parameter values for Replicate 1 (STP08) for selected individual realizations (cont

Parameter SOARCA 18 51 52 62 63 86 90 122 134 

Debris height 

for molten coreconcrete debris 

(DHEADLIQ) m 

1.52E-01 1.47E-01 1.57E-01 1.56E-01 1.16E-01 1.84E-01 1.66E-01 1.47E-01 1.51E-01 2.24E-0

DW liner meltthru area 

(FL904A) m2

1.00E-01 1.49E-01 1.38E-01 5.30E-02 1.88E-01 5.28E-02 1.42E-01 6.83E-01 1.99E-01 7.38E-0

H2 ignition 

criterion 

(H2IGNC) mole 

fraction

1.00E-01 1.41E-01 1.08E-01 5.47E-02 9.45E-02 1.43E-01 5.25E-02 7.16E-02 1.51E-01 1.02E-0

Inner RR door 

open fraction 

(RRIDFRAC) 

unitless

5.00E-01 6.90E-01 1.69E-01 2.69E-01 1.82E-01 4.21E-01 2.32E-01 2.74E-01 4.01E-01 1.44E-0

Outer RR door 

open fraction 

(RRODFRAC) 

unitless

5.00E-01 1.28E-01 1.32E-01 3.17E-01 4.08E-01 2.58E-01 6.74E-01 1.36E-01 5.90E-01 2.60E-0

Chemical form 

of I and Cs

(CHEMFORM)

unitless

5.00E+00 3.00E+00 3.00E+00 1.00E+00 5.00E+00 1.00E+00 4.00E+00 5.00E+00 5.00E+00 5.00E+0

Aerosol particle 

density 

(RHONOM) 

kg/m3

1.00E+03 4.01E+03 1.20E+03 1.62E+03 1.51E+03 2.10E+03 1.74E+03 3.31E+03 3.20E+03 3.48E+0

DW head bolt 

torque coeff. 

(KBOLT) 

unitless

8.00E-02 2.03E-01 3.52E-01 1.59E-01 1.34E-01 2.31E-01 2.42E-01 2.36E-01 3.88E-01 1.16E-0

DW head bolt 

modulus of 

elasticity 

(EBOLT) psi

1.93E+11 2.01E+11 1.86E+11 2.00E+11 2.00E+11 2.01E+11 1.93E+11 1.86E+11 1.91E+11 1.95E+1

DW head 

gasket rebound 

thickness 

(DGASKET) 

inch

7.62E-04 6.80E-04 7.02E-04 8.39E-04 8.48E-04 7.08E-04 7.87E-04 6.66E-04 7.69E-04 7.20E-0
6-27

Table 6.1-12 Timing of events, key occurrences/attributes, and environmental releases for selected in

realizations of the Peach Bottom unmitigated LTSBO Replicate 1 (STP08) 

Event Timing by realization (hr)

SOARCA 18 51 52 62 63 86 90 122 

100 °F/hr cooldown initiated (SRV opened, RCIC 

throttled) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 

SRV closes on battery depletion 4.00 4.10 5.10 4.80 3.80 4.70 3.70 2.20 4.30 

RCIC turbine floods failing RCIC 5.19 5.34 6.36 6.00 4.97 5.89 4.91 2.99 5.46 

SRV fails to close due to excessive cycling 8.19 NA 9.07 NA NA NA NA 8.17 11.6

Downcomer level drops to TAF 8.40 9.23 9.46 10.09 8.76 9.95 8.68 6.84 9.39 

First fuel-cladding gap release 9.12 10.32 10.35 11.24 9.83 11.09 9.75 7.80 10.4

SRV fails to close due the excessive temperature NA 11.51 NA 12.59 10.99 12.34 10.95 NA NA 

MSL creep rupture NA NA NA 14.43 13.59 NA 12.48 NA NA 

First large scale relocation of core debris to lower 

plenum 10.69 13.50 11.92 14.26 13.47 14.09 13.01 9.77 12.4

RPV lower head failure 19.76 19.49 21.54 19.96 18.91 20.60 18.84 16.38 20.0

Drywell head flange leakage begins 19.87 14.87 13.61 14.44 13.61 15.00 12.48 10.54 14.5

Reactor building fails due to overpressure 19.92 16.20 21.60 14.44 13.61 15.90 12.48 16.46 15.7

Wetwell rupture (above waterline) NA NA NA 14.44 NA NA NA NA NA 

Drywell liner melt-through 20.00 19.72 21.78 20.19 19.14 20.83 19.07 16.61 20.2

H2 burns initiate in reactor building grossly damaging 

the building 20.01 19.74 21.68 14.44 18.98 20.85 13.16 16.57 20.2

Key occurrences/attributes Value by realization

SOARCA 18 51 52 62 63 86 90 122 

Elapsed time between SRV sticking open and onset of 

core damage (hr) 0.94 -1.18 1.28 -1.36 -1.16 -1.25 -1.20 -0.37 -1.1

Elapsed time between onset of core damage and MSL 

creep rupture (hr) NA NA NA 3.19 3.76 NA 2.73 NA NA 

In-vessel H2 production (kg) 1,083 1,307 1,203 1,640 1,444 1,343 1,257 1,534 1,36

Surge of water from wetwell up onto drywell floor at 

liner melt-thru (Yes/No) N N N N Y N N Y Y 

Railroad Doors blow open (Yes/No) Y Y N Y Y Y Y Y Y 
6-28

Table 6.1-12 Timing of events, key occurrences/attributes, and environmental releases for selected i

realizations of the Peach Bottom unmitigated LTSBO Replicate 1 (STP08) (continued)

Releases to the environment Value by realization

SOARCA 18 51 52 62 63 86 90 122 

I release to environment > 0.1% (hr) 20.1 19.8 14.3 12.7 14.3 24.0 15.8 21.8 14.7 

Cs release to environment by 48 hr (fraction) 0.005 0.025 0.003 0.021 0.055 0.008 0.042 0.054 0.03

I release to environment by 48 hr (fraction) 0.025 0.070 0.017 0.131 0.160 0.005 0.023 0.045 0.13
6-29

6.1.4.1 Identification of Important Phenomena

Several influences were found to strongly affect the amount of cesium released to the 

environment. The influences were (not necessarily in order of importance): 

(1). Whether the sticking open of the SRV (the lowest setpoint SRV) occurs before or after the 

onset of core damage 

(2). Whether an MSL creep rupture occurs 

(3). The elapsed time between the onset of core damage and MSL creep rupture (if an MSL 

creep rupture occurs) 

(4). The amount of cesium chemisorbed from CsOH into the stainless steel of RPV internals 

(5). Whether core debris relocates from the RPV to the reactor cavity all at once or over an 

extended period of time 

(6). The degree of oxidation, primarily zircaloy oxidation, occurring in-vessel (identified by the 

amount of in-vessel hydrogen production) 

(7). Whether a surge of water from the wetwell up onto the drywell floor occurs at drywell liner 

melt-through 

(8). Whether an overpressure rupture of the wetwell occurs 

(9). Whether the reactor building railroad doors are blown open by a hydrogen deflagration. 

A discussion of each of these influences and their impact on cesium released follows.

SRV Failure Timing

Whether the SRV sticks open before or after core damage relates directly to the amount of 

cesium released from the core that is deposited in the wetwell. When the SRV is open, the RPV 

is vented to the wetwell pool. Fission products carried by the gas flow venting from the RPV are 

largely scrubbed by the pool. The earlier the SRV sticks open in the core degradation process, 

the more fission products are carried to the wetwell rather than deposited in the RPV. If the 

SRV sticks open before the onset of core damage, the venting of released fission products 

directly to the wetwell is maximized.

MSL Rupture

Whether an MSL rupture occurs also relates directly to the amount of cesium released from the 

core that is deposited in the wetwell. If an MSL creep rupture occurs, the path by which fission 

products carry through the stuck-open SRV to the wetwell pool is bypassed as gas venting from 

the RPV flows straight to the drywell. Instead of first being scrubbed by the wetwell pool, the 

fission products are introduced directly to the drywell, and then possibly to the environment via 

leakage through the drywell head flange or a drywell liner melt-through.

The elapsed time between the onset of core damage and MSL rupture similarly relates to the 

amount of cesium deposited in the wetwell. The more time that elapses between the onset of 

core damage and an MSL rupture the more time there is for gas flows venting from the RPV to 

carry fission products through the stuck-open SRV to the wetwell.
6-30

Key to whether an MSL creep rupture occurs is the uncertain parameter of SRV open fraction 

following the sticking open of an overheated SRV. Smaller stuck-open areas relieve steam 

more slowly and so lead to higher pressures. Higher pressures result in elevated stresses in 

the MSL piping which combine with elevated temperatures to accumulate creep damage over 

time that can lead to an MSL rupture. Figure 6.1-9 shows the relationship, for all the 

realizations in Replicate 1 experiencing SRV thermal failure, between (1) SRV open area 

fraction and occurrence of MSL creep rupture, and (2) the fraction of cesium core inventory 

released to the environment with and without MSL rupture, in plots a and b, respectively.
6-31

Figure 6.1-9 SRV open area fraction after thermal seizure Peach Bottom unmitigated 

LTSBO Replicate 1: (a) cumulative distribution function and (b) fraction of 

cesium core inventory released to the environment. Samples with MSL 

creep ruptures are identified
6-32

Figure 6.1-10 shows reactor and containment pressure and water level for Realization 62 of 

Replicate 1, a realization that experienced thermal seizure of the SRV followed by an MSL 

creep rupture. The realization was selected since its plot is near the lower 5th percentile of the 

distribution of MSL creep rupture results. Interesting is that the rupture occurs after the RPV 

has depressurized following the sticking open of the SRV. The re-pressurization resulting from 

a large scale relocation of core debris to the (flooded) RPV lower plenum, and the associated 

energetic steam production, triggers the creep rupture. This is typical of the realizations that 

experienced an MSL creep rupture.

Figure 6.1-10 Reactor and containment pressure and water level for Realization 62 of 

the Peach Bottom unmitigated LTSBO Replicate 1, an MSL creep rupture

Chemisorption

The amount of cesium chemisorbed from CsOH into the stainless steel of reactor internals 

relates to the amount of cesium permanently deposited in the RPV in the MELCOR calculations. 

This influence is only pertinent for the realizations that have all or some of the reactor core 

cesium inventory initialized as CsOH (MELCOR treats the chemisorption of cesium from CsI but 

realizations in the uncertainty analysis did not experience chemisorption from CsI). The 

chemisorption was more robust in the realizations that experienced higher RPV temperatures 

and it very strongly influenced the amount of cesium released to the environment as evidenced 

on Figure 6.1-11. The chemisorption often involved greater than half of the initial core inventory 

of cesium. Important to the chemisorption influence is that CsOH is a more readily evaporable 

form of cesium and so a more transportable form. Without chemisorption of cesium from CsOH, 

cesium being prevalent as CsOH (as opposed to Cs2MoO4) would tend to heighten the release 

of cesium to the environment. 
6-33

Figure 6.1-11 Fraction of cesium core inventory released to the environment for Peach 

Bottom unmitigated LTSBO Replicate 1: (a) SRV stochastic failures, 

(b) SRV thermal failures, and (c) MSL creep ruptures. Realizations are 

identified that have cesium core inventory initialized as CsOH
6-34

Speed of Debris Relocation to the Reactor Cavity and In-Vessel Hydrogen Production

Most all of the cesium that releases to the environment by 48 hours in the realizations of the 

uncertainty analysis does so by the following sequential steps:

(1). Releasing from the dismantling core as CsOH, CsI, or Cs2MoO4 vapor.

(2). Condensing into aerosols.

(3). Gravitational settling onto reactor internals.

(4). Re-vaporizing after RPV lower head failure steadily over approximately the next day.

(5). Re-condensing into aerosols that are carried out a breach in the drywell liner resulting 

from core debris contacting the liner and melting through it.

Key to the re-vaporization of aerosols settled on reactor internals is the temperature of the 

internals; the hotter the temperature the greater the re-vaporization. Whether core debris 

relocates from the RPV to the reactor cavity all at once or over an extended period of time

relates to the strength and duration of energy sources in the RPV after lower head failure. In 

the realizations where not all of the initial core material relocates from the RPV at once, decay 

heat and oxidation persist in the RPV. These persistent energy sources heat the reactor 

internals and drive the re-vaporization. The degree of oxidation occurring in-vessel relates to 

how hot reactor internals can potentially become due to the oxidation of (primarily) fuel canisters 

and cladding; the greater the degree of oxidation the greater the energy deposition in reactor 

internals.

Figure 6.1-12 shows the time history of the relocation of core material from the RPV to the 

reactor cavity for Realization 268 of Replicate 1. This realization was selected in the distribution 

of SRV thermal seizure results that shows outlier behavior (upper 99th percentile). In this 

realization the relocation of core material doesn’t happen all at once, but rather gradually over 

time. For comparison, Figure 6.1-12 includes the time history of the relocation of core material 

from the RPV to the reactor cavity for the updated deterministic SOARCA Peach Bottom 

unmitigated LTSBO case documented in Section 5.1.1.1. The more gradual relocation of 

material in Realization 268 relative to the SOARCA case (UA base case) results in extended 

oxidation and therefore extended and heightened heat generation in the RPV. The extended 

and heightened heat generation efficiently re-vaporizes deposits of cesium from reactor 

internals resulting in a relatively very large release of cesium to the environment.
6-35

Figure 6.1-12 Time dependent relocation of core material from the RPV to the reactor 

cavity for Realization 268 of the Peach Bottom unmitigated LTSBO 

Replicate 1, an SRV thermal seizure failure

Figure 6.1-13 shows the in-vessel hydrogen production associated for Realization 268 of 

Replicate 1 of the Peach Bottom unmitigated LTSBO scenario and for comparison includes the 

time history from the updated deterministic SOARCA Peach Bottom unmitigated LTSBO case 

(UA base case) documented in Section 5.1.1.1.
6-36

Figure 6.1-13 In-vessel hydrogen production for Realization 268 of the Peach Bottom 

unmitigated LTSBO Replicate 1, an SRV thermal seizure failure

Water Surging from the Wetwell

Whether a surge of water from the wetwell up onto the drywell floor occurs relates to amounts of 

cesium that deposit in the wetwell pool but fail to be confined there. In a large number of the 

realizations, a surge of water from the wetwell up onto the drywell floor occurs when the 

containment depressurizes in response to a breach developing in the drywell liner due to core 

debris contacting the liner and melting through it. The wetwell pool is saturated at the time and 

susceptible to flashing given a depressurization. The vacuum breakers between the wetwell 

and the drywell are overwhelmed and contaminated water from the wetwell surges up onto the 

drywell floor. Most of the water moves out the liner breach but some of it pools above the core 

debris on the drywell floor. The pool subsequently evaporates introducing its inventory of fission 

products to the atmosphere and structures of the drywell where they are available for release to 

the environment. (Note that the flow path representing the liner breach in the MELCOR model 

is a 6-cm high horizontal slot with its lowest point 0.41 m off the drywell floor.) 

There is a correlation between the uncertainty in the drywell liner breach size and whether a 

surge of water from the wetwell occurs as evidenced in Figure 6.1-14. Larger sizes cause 

stronger containment depressurizations and hence larger potentials for water to surge from the 

wetwell.
6-37

Figure 6.1-14 Cumulative distribution function for the flow area resulting from drywell 

liner failure for Peach Bottom unmitigated LTSBO Replicate 1 with 

samples identified that have a surge of water from the wetwell during 

depressurization of the drywell

Figure 6.1-15 shows water level in containment for Realization 170 of Replicate 1, a realization 

where a surge of water from the wetwell up onto the drywell floor occurs in response to the 

containment depressurizing when core debris contacts the drywell liner and melts through it. 

This realization was selected from the set of SRV stochastic failure cases whose behavior is 

similar to the upper 95th percentile of the distribution. The small sumps in the reactor cavity and 

outside the reactor pedestal are not accounted for in this figure. Note that most of the water that 

surges up from the wetwell moves out of the drywell and into the reactor building through the 

breach in the drywell liner. The water that pools on the drywell floor is atop core debris and so 

evaporates releasing its content of fission products to the drywell.
6-38

Figure 6.1-15 Water level in containment for Realization 170 of the Peach Bottom

unmitigated LTSBO Replicate 1, an SRV Stochastic failure

Overpressure Rupture of the Wetwell

Whether an overpressure rupture of the wetwell occurs pertains to a containment failure 

whereby a breach occurs in the wetwell above waterline due to overpressure. The breach 

actually has beneficial impact as it results in a venting of containment through the wetwell pool. 

The pool scrubs fission products from the venting gas flows as they make their way to the 

breach.

Compromising of the Railroad Doors

In most of the calculations, the Railroad Doors in the lower reactor building were blown open by 

a hydrogen deflagration. This resulted in a thermal updraft developing in the reactor building 

that adversely impacted fission product settling.

The effect can be seen on Figure 6.1-16 for all three of the failure modes.
6-39

Figure 6.1-16 Fraction of cesium core inventory released to the environment for Peach 

Bottom unmitigated LTSBO Replicate 1: (a) SRV stochastic failures, 

(b) SRV thermal failures, and (c) MSL creep ruptures. The realizations are 

identified that have closed railroad doors
6-40

6.1.4.2 Analysis of Single Realizations

For comparison with the individual single realizations, Figure 6.1-17 includes the time 

dependent distribution of cesium throughout the reactor system from the updated deterministic 

SOARCA Peach Bottom unmitigated LTSBO case documented in Appendix C. The distribution 

of cesium throughout the reactor system for selected individual realizations from Replicate 1 of 

the Peach Bottom unmitigated LTSBO (the realizations of Tables 6.1-11 and 6.1-12), is 

presented in Figures 6.1-18 through 6.1-28. The figures present pairs of plots showing two 

scales for each realization. Noteworthy influences specific to each realization are discussed 

below. In reviewing the figures, the information in Tables 6.1-11 and 6.1-12 should be 

considered realizing that the minimum, median, and maximum values of hydrogen generation in 

Replicate 1 of the Peach Bottom unmitigated LTSBO results were 954.5 kg, 1,305.5 kg, and 

1,850.0 kg, respectively. Similarly, realize that the minimum, median, and maximum values of 

fractional cesium release to the environment were 0.003, 0.021, and 0.124, respectively.
6-41

Figure 6.1-17 Fraction of cesium core inventory released to the environment for the 

updated deterministic SOARCA Peach Bottom unmitigated LTSBO 

case documented in Section 5.1.1.1 for two scales on the ordinate: 

(a) 0 to 1.0 and (b) 0 to 0.20 
6-42

Figure 6.1-18: Realization 18 falls near the median behavior in the distribution of SRV thermal 

seizure results for Replicate 1 exhibiting an approximately median release of cesium to the 

environment relative to the collective results of Replicate 1. Nothing really stands out in the 

progression of this scenario relative to the SOARCA Uncertainty Analysis calculation or the 

Uncertainty Analysis realizations in general. The realization shows median in-vessel hydrogen 

production and did not see a surge of water from the wetwell up onto the drywell floor.

Figure 6.1-19: Realization 51 falls near the 5th percentile behavior in the distribution of SRV 

stochastic failures exhibiting the lowest cesium release of all the Replicate 1 realizations and a 

release lower than the SOARCA Uncertainty Analysis base case calculation. Contributing to the 

low cesium release in this realization is that the SRV fails open before the onset of core 

damage, in-vessel hydrogen production is lower than median, no surge of water from the 

wetwell up onto the drywell floor occurs, and that the Railroad Doors do not blow open.

Figure 6.1-20: Realization 52 falls near the 5th percentile of the distribution of MSL creep 

ruptures exhibiting a median cesium release. Factors in this realization that would tend to 

suppress the release are strong chemisorption, a long elapsed time between the onset of core 

damage and MSL creep rupture, a wetwell rupture, and no surge of water from the wetwell up 

onto the drywell floor. Factors that would tend to heighten the release are high in-vessel 

hydrogen production and a MSL creep rupture.

Figure 6.1-21: Realization 62 falls near the median of the distribution of MSL creep ruptures 

experiencing a high cesium release. There are several factors in this realization that would tend 

to heighten the release, namely: high in-vessel hydrogen production, no cesium in the form of 

CsOH and so no chemisorption, an MSL creep rupture, and a surge of water from the wetwell 

up onto the drywell floor. A factor that would tend to suppress the release is that a relatively 

long period of time elapsed between the onset of core damage and the MSL creep rupture.

Figure 6.1-22: Realization 63 falls near the 5th percentile of the distribution of SRV thermal 

seizure failures exhibiting a low cesium release to the environment. The strong factor identified 

as contributing to the low release in this realization is high chemisorption.

Figure 6.1-23: Realization 86 falls near the median of the distribution of MSL creep ruptures 

exhibiting a high cesium release. Factors here that would tend to suppress the release are

significant chemisorption and no surge of water from the wetwell up onto the drywell floor. 

Factors that would tend to heighten release are MSL creep rupture and a short time between 

the onset of core damage and the MSL creep rupture

Figure 6.1-24: Realization 90 is a very high outlier in the distribution of SRV stochastic failures 

exhibiting a high cesium release to the environment. This realization exhibits high in-vessel 

hydrogen production and a more gradual relocation of core material from the RPV to the reactor 

cavity (over something like a day rather than all at once). Both of these factors, in a related 

fashion, would tend to increase the cesium release. Tending to suppress the release is that no 

surge of water from the wetwell up onto the drywell floor occurred.

Figure 6.1-25: Realization 122 is another high outlier in the distribution of SRV stochastic 

failures showing cesium release to the environment on the high side. There do not seem to be 

any remarkable factors contributing to the release in this realization but in-vessel hydrogen 

production is higher than median and there was a surge of water from the wetwell up onto the 

drywell floor. In this realization, core damage occurs prior to SRV failure.
6-43

Figure 6.1-26: Realization 134 is a high outlier in the distribution of MSL creep ruptures 

showing a high cesium release. Contributors to the release are no CsOH being initialized in the 

core so no chemisorption taking place, a MSL creep rupture occurring, a short elapsed time 

between the onset of core damage and the MSL creep rupture, and core material relocation 

from the RPV over 8 hours (as opposed to all at once). Detractors from the release are low 

in-vessel hydrogen production, a wetwell rupture, and no surge of water from the wetwell up

onto the drywell floor

Figure 6.1-27: Realization 170 falls near the 95th percentile of the distribution of SRV stochastic 

failures relating to an approximately median cesium release. Contributing to the release is that 

all the cesium initialized in the core is in the form of CsOH but that only a modest amount of 

cesium is chemisorbed into the stainless steel of reactor internals. CsOH is a more readily 

evaporable form of cesium, and therefore, a more transportable form. Given little chemisorption 

of cesium from CsOH in this realization, cesium being initialized as CsOH would tend to 

heighten the release of cesium to the environment. Also contributing to the release is that a 

surge of water from the wetwell up onto the drywell floor occurs. Detracting from the cesium 

release in this realization is that the SRV fails open before the onset of core damage and that invessel hydrogen production is on the low side.

Figure 6.1-28: Realization 268 is a high outlier in the distribution of SRV thermal seizure 

failures exhibiting a high release of cesium to the environment. It had the highest cesium 

release of the select realizations. The factor accounting for the high release is the spreading 

over an extended period of time of the relocation of core material from the RPV to the reactor 

cavity (as opposed to a relocation that happens all at once). The extended residence time of 

core material in the RPV, results in continued oxidation (of primarily fuel cladding). The 

continued heat generation associated with the continued oxidation drives off (evaporates) 

cesium deposited on reactor vessel internals earlier in the core degradation process. The 

cesium aerosolizes and transports out of the vessel through the breached lower head and out of 

the drywell to the reactor building through the melt-through in the drywell liner.
6-44

Figure 6.1-18 Fraction of cesium core inventory released to the environment for 

Realization 18 of Replicate 1 for two scales on the ordinate: (a) 0 to 1.0 

and (b) 0 to 0.20 
6-45

Figure 6.1-19 Fraction of cesium core inventory released to the environment for 

Realization 51 of Replicate 1 for two scales on the ordinate: (a) 0 to 1.0 

and (b) 0 to 0.02 
6-46

Figure 6.1-20 Fraction of cesium core inventory released to the environment for 

Realization 52 of Replicate 1 for two scales on the ordinate: (a) 0 to 1.0 

and (b) 0 to 0.2
6-47

Figure 6.1-21 Fraction of cesium core inventory released to the environment for 

Realization 62 of Replicate 1 for two scales on the ordinate: (a) 0 to 1.0 

and (b) 0 to 0.2
6-48

Figure 6.1-22 Fraction of cesium core inventory released to the environment for 

Realization 63 of Replicate 1 for two scales on the ordinate: (a) 0 to 1.0 

and (b) 0 to 0.2
6-49

Figure 6.1-23 Fraction of cesium core inventory released to the environment for 

Realization 86 of Replicate 1 for two scales on the ordinate: (a) 0 to 1.0 

and (b) 0 to 0.2
6-50

Figure 6.1-24 Fraction of cesium core inventory released to the environment for 

Realization 90 of Replicate 1 for two scales on the ordinate: (a) 0 to 1.0 

and (b) 0 to 0.2
6-51

Figure 6.1-25 Fraction of cesium core inventory released to the environment for 

Realization 122 of Replicate 1 for two scales on the ordinate: (a) 0 to 1.0 

and (b) 0 to 0.2
6-52

Figure 6.1-26 Fraction of cesium core inventory released to the environment for 

Realization 134 of Replicate 1 for two scales on the ordinate: (a) 0 to 1.0 

and (b) 0 to 0.2
6-53

Figure 6.1-27 Fraction of cesium core inventory released to the environment for 

Realization 170 of Replicate 1 for two scales on the ordinate: (a) 0 to 1.0 

and (b) 0 to 0.2
6-54

Figure 6.1-28 Fraction of cesium core inventory released to the environment for 

Realization 268 of Replicate 1 for two scales on the ordinate: (a) 0 to 1.0 

and (b) 0 to 0.2
6-55 

6.2 Offsite Consequence

The results of the consequence analyses are presented in terms of risk to the public for each of 

the probabilistic source terms analyzed using the Peach Bottom unmitigated LTSBO MELCOR 

model for the uncertainty analysis presented in Section 6.1. All results are presented as

conditional risk. Absolute risk is discussed in certain instances within the text (see 

NUREG-1935 [1], Section 5.8, for a more full discussion of risk metrics reported). The 

conditional risks assume that the accident occurs and show the risks to individuals as a result of 

the accident (i.e., latent cancer fatality (LCF) risk per event or early-fatality risk per event). The 

absolute risk is the product of the core damage frequency for the accident sequence and the 

conditional risk for that sequence. The absolute risk is the likelihood of incurring a latent fatal 

cancer or early fatality for an average individual living within a specified radius of the plant per

year of plant operation (i.e., LCF risk per reactor year (pry) or early-fatality risk pry).

The reported risk metrics, LCF and early-fatality risks to residents in circular regions 

surrounding the plant, are averaged over the entire residential population within each circular 

region. The risk values represent the predicted number of fatalities divided by the population for 

the selected dose response model. These risk metrics account for the distribution of the 

population within the circular region and for the interplay between the population distribution and 

the wind rose probabilities. 

The three separate replicates representing the uncertainty in the MELCOR source terms, as 

discussed in Section 5.1.1, were combined and used in a single MACCS uncertainty analysis to 

determine the conditional, mean, individual LCF risk (per event) and early-fatality risk per event 

CCDFs. The reported risk is the mean risk over possible variations in weather using the 

weather sampling strategy developed for SOARCA. The three MELCOR replicate analyses 

produced 284 (Replicate 1), 290 (Replicate 2), and 291 (Replicate 3) MELCOR source terms, 

respectively. Each MELCOR source term replicate was analyzed individually with a single 

WinMACCS run using LHS sampling and include the 350 MACCS uncertain input variables. In 

addition, a WinMACCS run created a set of 865 MACCS realizations, each paired with one of 

the MELCOR source terms from all three replicates. Table 6.2-1 identifies the nomenclature for 

the MACCS probabilistic analyses and corresponding MELCOR source terms. 

This section discusses the LCF risks per event and the early-fatality risks per event. All the 

cases use the MACCS uncertainty parameters (i.e., 350 uncertain input parameters) discussed 

in Section 5.2.1. This section also discusses the consequence analyses for the MELCOR single 

realizations discussed in Section 6.1.4, and the three MACCS realizations that resulted in an 

early-fatality risk out to 10 miles. The single realization analysis provides insight into the 

important phenomena driven by the uncertainty in the input parameters and source terms. 
6-56

Table 6.2-1 MACCS probabilistic analyses

MACCS Analysis Description MELCOR Source 

Terms

UAS_CAP14v364_2509 CAP14. MACCS analysis for MELCOR Replicate #1, 

LNT Dose Response model.

UAS_STP08v1.8.6YV3780

UAS_CAP18v364_2509 CAP18. MACCS analysis for MELCOR Replicate #2, 

LNT Dose Response model.

UAS_STP09v1.8.6YV3780

UAS_CAP19v364_2509 CAP19. MACCS analysis for MELCOR Replicate #3, 

LNT Dose Response model.

UAS_STP010v1.8.6YV3780

UAS_CAP17v364_2509 CAP17. MACCS analysis for combined MELCOR 

Replicates #1, #2, & #3, LNT Dose Response model.

UAS_STP08v1.8.6YV3780; 

UAS_STP09v1.8.6YV3780; 

UAS_STP10v1.8.6YV3780

The risk results presented in this section use only the LNT dose-response model. Uncertainty 

analyses using dose truncation models are discussed in Section 6.4.4.

In this section, the risk tables represent rounded values obtained from the full data sets. The 

plots were developed from the full data sets and slight differences may be noticed due to 

rounding of the tabulated values. 

6.2.1 Latent Cancer Fatality Risk

Table 6.2-2 shows statistical results for conditional, mean, individual LCF risk (per event) from

the MACCS uncertainty analysis at each specified circular area for the analysis using all three 

MELCOR source term replicates combined (CAP17). Each statistic was estimated to evaluate

the epistemic uncertainties resulting from the uncertain inputs to MACCS and MELCOR 

(through the source term). A t-distribution was used to determine the 5th and 95th percentiles. 

Table 6.2-2 Conditional, mean, individual LCF risk (per event) average statistics for the 

MACCS Uncertainty Analysis for five circular areas (using all three source 

term replicates)

 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.7x10-4 2.8x10-4 2.0x10-4 1.3x10-4 1.0x10-4

Median 1.3x10-4 1.9x10-4 1.3x10-4 8.7x10-5 7.1x10-5

5th percentile 3.1x10-5 4.9x10-5 3.4x10-5 2.2x10-5 1.9x10-5

95th percentile 4.2x10-4 7.7x10-4 5.3x10-4 3.4x10-4 2.7x10-4

For this work, the emergency phase is defined as the first seven days following the initial 

release to the environment. The long-term phase is defined as the time following the 

emergency phase (i.e., there is no intermediate phase). The long-term phase risk (i.e., the LCF 

risk contribution beyond the emergency phase) dominates the total risks (i.e., 100% of all 

realizations have a long-term risk contribution that is greater than 50% of the total risk) within 

the EPZ for the uncertainty analysis when the LNT dose-response assumption is made. No 

realization resulted in an emergency phase risk contribution greater than 48% of the total risk. 

The emergency phase risk within the EPZ is entirely to the 0.5% of the population who are 

assumed not to evacuate. These results further emphasize the benefits of evacuating the EPZ. 
6-57

The long-term risks are controlled by the habitability (return) criterion, which is the dose rate at 

which residents are allowed to return to their homes following the emergency phase. For Peach 

Bottom, the habitability criterion is an annual dose rate of 500 mrem/yr14. For comparison, only 

55% of all realizations have a long-term risk contribution greater than 50% of the total risk within 

a 20-mile radius (i.e., 45% of the realizations have an emergency phase risk greater than 50% 

of the total risk). Since only hotspot and normal relocation are modeled beyond the EPZ (in 

addition to a 20% shadow evacuation in the 10-20 mile ring), it is possible for residents beyond 

10 miles to incur larger doses during plume passage in the emergency phase before the hotspot 

or normal relocation occurs. It should be noted that earlier ad hoc evacuation would be 

expected to occur in the case of an anticipated large release (see for example, NUREG-2161 

[92], “Consequence Study of a Beyond Design-Basis Earthquake Affecting the Spent Fuel Pool 

for a U.S. Mark I Boiling Water Reactor,” Section 7.1.4) but an ad hoc evacuation model was not 

within the scope of this uncertainty study. 

Figures 6.2-1 to 6.2-5 show the CCDFs for the conditional, mean, individual LCF risk (per event) 

for the composite MACCS uncertainty analysis (CAP17) within five concentric circular areas 

from the plant. Also noted on the figures are the mean, median, 5th and 95th quantiles 

(percentiles) for the conditional LCF risk distributions using each of the three MELCOR replicate 

results (i.e., CAP 14, CAP18, and CAP19 results described in Section 5.2.1.3). The composite 

CCDFs (for CAP17)are very similar and are in good agreement with the three uncertainty 

analyses corresponding to the three sets of MELCOR results (i.e., CAP14, CAP18, and 

CAP19 ). This indicates that incorporation of all 865 MELCOR source terms into a single 

MACCS uncertainty analysis is reasonably well converged compared with smaller samples 

using the MELCOR Replicates 1, 2, and 3 (i.e., compare Table 5.2-6 with Table 6.2-2).

On Figure 6.2-1 to Figure 6.2-5, the x-axis represents the distribution of possible LCF risk per 

event results within the 10-mile circular area and is generated by sorting (from smallest to 

largest) all the LCF risk results from the sample of size ‘N’ (i.e., N=865 samples for 

Figure 6.2-1). On Figure 6.2-1, the y-axis represents the likelihood of being higher than or equal 

to the value read on the x-axis. The likelihood of the outcome is estimated by a weight of 1/N 

and decreasing the y-value by this weight starting from one. The mean (arithmetic average) is 

added to each CCDF curve. Quantiles (q) can be read directly by finding the corresponding yvalue to the graph, and are displayed for the 5th, 50th (median), and 95th quantiles as dots over 

the curve.

In risk analysis, it is traditional to plot CCDFs rather than CDFs as a CCDF answers the 

question, “How likely it is to have such value or higher?”

 

14 In accordance with Pennsylvania State Guidelines.
6-58

Figure 6.2-1 Complementary cumulative distribution function and statistical values 

for conditional, mean, individual LCF risk (per event) within a 10-mile 

radius
6-59

Figure 6.2-2 Complementary cumulative distribution function and statistical values for 

conditional, mean, individual LCF risk (per event) within a 20-mile radius
6-60

Figure 6.2-3 Complementary cumulative distribution function and statistical values for 

conditional, mean, individual LCF risk (per event) within a 30-mile radius
6-61

Figure 6.2-4 Complementary cumulative distribution function and statistical values 

for conditional, mean, individual LCF risk (per event) within a 40-mile 

radius
6-62

Figure 6.2-5 Complementary cumulative distribution function and statistical values 

for conditional, mean, individual LCF risk (per event) within a 50-mile 

radius

When the 10-mile and 20-mile circular area statistics are compared, there is larger influence of 

the emergency phase for the 20-mile region compared to the 10-mile region, for which nearly all 

of the population evacuated. This comparison is shown on Figure 6.2-6 for the contribution to 

LCF risk from the long-term phase, and Figure 6.2-7 for the contribution of the LCF risk from the 

emergency phase. This indicates that variations in doses during the emergency phase are 

greater than variations in dose during the long-term phase. As noted above, ad hoc evacuation 

modeling beyond the 10-mile EPZ was not included in this uncertainty study.
6-63

Figure 6.2-6 Complementary cumulative distribution function for conditional, mean, 

individual LCF risk (per event) within a 10-mile and 20-mile radius for

‘overall’ and ‘long-term phase’ LCF risk

Figure 6.2-7 Complementary cumulative distribution function for conditional, mean, 

individual LCF risk (per event) within a 10-mile and 20-mile radius for 

‘overall’ and ‘emergency phase’ LCF risk
6-64

Table 6.2-3 shows the correlation matrix for the MACCS Uncertainty Analysis for the 

conditional, mean, individual LCF risk (per event) at the specified circular areas. This table 

indicates how strongly the MACCS results are correlated amongst each other when the radial 

distances change. The closer the correlation value is to 1.0, the more similar are the results. 

Table 6.2-3 indicates that while the conditional, mean, individual LCF risk (per event) for a radial 

distance of 10 miles is different than other radials distance (i.e., first row, correlation coefficient 

ranging from 0.41 to 0.55), the other radial distances lead to pretty similar results 

(i.e., coefficients of correlation greater than 0.98). The correlation between all the circular areas 

outside the EPZ to the EPZ distance (i.e., 10 miles) shows that evacuation has a pronounced

effect on the correlation. This is because residents within the EPZ, with the exception of the 

0.5% who are assumed not to evacuate, evacuate ahead of the release and therefore receive 

no dose during the emergency phase. The majority of the residents outside the EPZ do receive 

a dose during the emergency phase. All circular areas beyond the EPZ (i.e., 10 miles) are very 

well correlated with regards to their respective MACCS input parameters. This is expected 

since there are no MACCS input parameters that would significantly affect one region differently 

than another. One minor exception is that 20% of the residents between 10 and 20 miles from 

the site are assumed to be part of the shadow evacuation. Otherwise, all residents outside of 

the EPZ are assumed to behave the same way.

Table 6.2-3 Correlation matrix of the conditional, mean, individual LCF risk (per event) 

for the MACCS Uncertainty Analysis for specified circular areas (using all 

three source term replicates)

 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

0-10 miles 1 0.41 0.44 0.51 0.55

0-20 miles 1 0.998 0.99 0.98

0-30 miles 1 0.996 0.99

0-40 miles 1 0.998

0-50 miles 1

6.2.2 Early Fatality Risk 

The only nonzero early-fatality risk result calculated in the original SOARCA project was for the 

Surry ISLOCA scenario (NUREG/CR-7110 Volume 2, Section 7.3.5). For Surry, the exclusion 

area boundary (EAB) is 0.35 miles from the reactor building from which release occurs, so 

one mile from the EAB is at 1.35 miles. The closest MACCS grid boundary to 1.35 miles used 

in the ISLOCA calculations is at 1.3 miles. Table 6.2-4 shows the conditional, mean, individual 

early-fatality risk (per event) for the Surry ISLOCA scenario. The core damage frequency for 

this event is 3x10-8 pry. Thus the absolute early-fatality risk within one mile of the EAB is 

4.5x10-14 pry.
6-65

Table 6.2-4 Conditional, mean, individual early-fatality risk (per event) for the Surry 

ISLOCA Scenario

Radius of circular area (mi) Early-fatality risk (per event) 

1.3 1.5x10-6

2 6.4x10-7

2.5 4.0x10-7

For Peach Bottom, the EAB is 0.5 mile from the reactor building from which a release occurs, so 

the outer boundary of this one mile zone is at 1.5 miles. The closest MACCS grid boundary to 

1.5 miles used in this set of calculations is at 1.3 miles. The Peach Bottom LTSBO scenario 

has a conditional, mean, individual early-fatality risk (per event) of 0.00 (NUREG/CR-7110 

Volume 1, Section 7.3.1). 

In this uncertainty analysis, the early-fatality risks are zero for 87% of all realizations at all

specified circular areas . This is because the release fractions are too low to produce doses 

large enough to exceed the dose thresholds for early fatalities, even for the 0.5% of the 

population that are modeled as refusing to evacuate. The largest value of the mean, acute 

exposure for the closest resident (i.e., 1.6 to 2.1 kilometers from the plant) for many of these 

replicates is about 0.3 gray (Gy) to the red bone marrow, which is usually the most sensitive 

organ for early fatalities, but the minimum acute exposure that can cause a early fatality is about 

2.3 Gy to the red bone marrow. The calculated exposures for these scenarios are all below this 

threshold.

Unlike the SOARCA analyses in NUREG/CR-7110 Volume 1 and Volume 2, a nonzero earlyfatality risk was calculated beyond 2.5 miles (see Table 6.2-4). 11% of the 865 MACCS 

realizations investigated resulted in a nonzero early-fatality risk per event out to 1.3 miles. 1.3% 

of the realizations result in a early-fatality risk at 2 miles but not at 1.3 miles due to specific 

sampled weather trial conditions, including wind directions, and the nearest location of residents 

in that direction. 0.3% of the 865 realizations that resulted in a nonzero early-fatality risk per 

event out to 10 miles. In other words, a select few realizations (three) result in a large enough 

source term that when combined with specific weather trials in the MACCS calculation result in

early-fatality risks out to the boundary of the EPZ. A more detailed discussion of this is provided 

in Section 6.2.4. 

Table 6.2-5 shows statistical results for conditional, mean, individual early-fatality risk (per 

event) from the MACCS Uncertainty Analysis at the specified circular areas. Each statistic was 

estimated to evaluate the epistemic uncertainties resulting from the uncertain inputs. Since at 

most radial distances there were insufficient results to calculate the 75th and 95th percentiles 

directly, a t-distribution was used to estimate the 75th and 95th percentiles. 

At 2.5 miles and beyond in Table 6.2-5 the mean result is greater than the 95th percentile. This 

is due to the few number of nonzero early-fatality risks (i.e., less than 5% of the realizations) at 

these distances. A distribution can be skewed enough so that the mean is greater than the 95th

percentile. For these cases the mean may be higher than the 99th percentile, because it is

driven by just a few nonzero values within a population comprised overwhelming of zeros. This 

is the case here for early-fatality risk beyond 2.5 miles. 
6-66

Table 6.2-5 Conditional, mean, individual early-fatality risk (per event) average 

statistics for the composite MACCS Uncertainty Analysis for specified 

circular areas (using all three source term replicates)

0-1.3 

miles

0-2 

miles

0-2.5 

miles

0-3 

miles

0-3.5 

miles

0-5 

miles

0-7 

miles

0-10 

miles

Mean 4.5x10-7 1.8x10-7 8.9x10-8 6.4x10-8 3.5x10-8 1.4x10-8 8.3x10-9 4.8x10-9

Median 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

75th

percentile 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

95th

percentile 1.9x10-6 7.4x10-7 3.5x10-8 5.3x10-10 0.0 0.0 0.0 0.0

As shown on Figure 6.2-8, the CCDF for the composite MACCS uncertainty analysis (CAP17) 

for the conditional, mean, individual early-fatality risk (per event) are very similar and are in 

good agreement when compared with the three uncertainty analyses conducted for MACCS

convergence (i.e., CAP14, CAP18, and CAP19 results described in Section 5.2.1) at the 

1.3-mile circular area (i.e., within 1 mile of EAB). Also, Figure 6.2-8 shows a change within the 

95th percentile interval between the MACCS Uncertainty Analysis and the MACCS convergence 

analyses. This is a result of the limited number of early-fatality risks greater than zero. Only 

11% of the total data of the MACCS results for the MACCS Uncertainty Analysis resulted in a 

nonzero early-fatality risk. However, the slight difference between the means indicates that the 

incorporation of all 865 MELCOR source terms into a single MACCS uncertainty analysis does 

not result in any significant change to the overall statistics with respect to the MACCS

uncertainty inputs (i.e., compare Table 5.2-13 with Table 6.2-5). 
6-67

Figure 6.2-8 Complementary cumulative distribution function and statistical values 

for conditional, mean, individual early-fatality risk (per event) within a 

1.3-mile radius

Figures 6.2-9 through 6.2-12 show the CCDFs for the composite MACCS Uncertainty Analysis 

(CAP 17) for the conditional, mean, individual early-fatality risk (per event) for the 2-, 2.5-, 3-, 

and 3.5-mile circular areas, respectively. These figures also show the mean and 95th quantiles 

from the three replicate/convergence analyses (CAP 14, 18, 19) for comparison. The results 

are similar to those discussed on Figure 6.2-8; however, the percent of early-fatality risk results

greater than zero for each subsequent circular area decreases. The nonzero early-fatality risk

results decreases from 11% of the total early-fatality risk results at 1.3 miles to 4% of the total 

early-fatality risk results at 3.5 miles. Beyond the 3.5 mile circular area, the source terms that 

generate nonzero early-fatality risks drop below 2% and the plots convey little useful

information. For distances beyond 2.5 miles, the 95th percentile statistics are not well 

converged (i.e., greater than an order of magnitude difference). Even at a 2-mile radius, the 

95th percentiles differ up to 70%. This is expected, given the small fraction of nonzero results in 

the total population of results.
6-68

Figure 6.2-9 Complementary cumulative distribution function and statistical values for 

conditional, mean, individual early-fatality risk (per event) within a 2-mile 

radius 

Figure 6.2-10 Complementary cumulative distribution function and statistical values 

for conditional, mean, individual early-fatality risk (per event) within a 

2.5-mile radius
6-69

Figure 6.2-11 Complementary cumulative distribution function and statistical values 

for conditional, mean, individual early-fatality risk (per event) within a 3-

mile radius

Figure 6.2-12 Complementary cumulative distribution function and statistical values 

for conditional, mean, individual early-fatality risk (per event) within a 

3.5-mile radius
6-70

Table 6.2-6 shows the correlation matrix for the MACCS uncertainty analysis for the conditional, 

mean, individual early-fatality risk (per event) at specified circular areas. The correlation data 

only applies to nonzero early-fatality risk results. There is poorer correlation between the closer 

circular areas and the further circular areas due to the small number of replicates where a 

nonzero early-fatality risk is observed beyond five miles. Only 1% of the MACCS realizations

result in a nonzero early-fatality risk at the 7-mile circular area. These 7-mile early-fatality risk 

realizations are amongst the top 2% of the realizations (4 realizations total) that result in a 

nonzero early-fatality risk at the 1.3-mile circular area. Thus the risk at seven miles is not 

strongly correlated with the shorter distances since it is heavily weighted towards the higher end 

of the early-fatality risks. Similarly, the realizations at 10 miles that result in a nonzero earlyfatality risk are amongst the top 2% of the realizations that result in a nonzero early-fatality risk 

at 1.3 miles. The 5-mile, 7-mile, and 10-mile circular area early fatality risks are strongly 

correlated with each other. Three of the top four of the realizations that result in a nonzero 

early-fatality risk at the 7-mile circular area also result in a nonzero early-fatality risk at the 

10-mile circular area. These three nonzero early-fatality risk at the 10-mile circular area are 

further discussed in Section 6.2.4. 

Table 6.2-6 Correlation matrix for the MACCS Uncertainty Analysis for the conditional, 

mean, individual early-fatality risk (per event) for specified circular areas 

(using all three source term replicates)

0-1.3 

miles

0-2 

miles

0-2.5 

miles

0-3 

miles

0-3.5 

miles

0-5 

miles

0-7 

miles

0-10 

miles

0-1.3 miles 1 0.93 0.68 0.74 0.54 0.42 0.34 0.26

0-2 miles 1 0.85 0.90 0.77 0.67 0.59 0.50

0-2.5 miles 1 0.93 0.94 0.85 0.77 0.68

0-3 miles 1 0.93 0.87 0.81 0.73

0-3.5 miles 1 0.96 0.91 0.85

0-5 miles 1 0.99 0.95

0-7 miles 1 0.99

0-10 miles 1

6.2.3 Regression Analysis

As part of the statistical analysis of the MACCS Uncertainty Analysis, a series of regression

methods were applied to determine which input parameters most affect LCF risk and earlyfatality risk. The four regression methods used were rank regression, quadratic regression, 

recursive partitioning, and MARS, as described in section 3.4.2. 

6.2.3.1 Regression Analysis from Latent Cancer Fatality Risk

Tables 6.2-7 through 6.2-11 show the results of the regression methods used to correlate the 

conditional, mean, individual LCF risk (per event) results from the MACCS uncertainty analysis 

(CAP17) for the 10-mile, 20-mile, 30-mile, 40-mile, and 50-mile circular areas, respectively. The 

tables are a general indication of input parameter influence on the results. Rank regression

often underestimates the true influence of a parameter since it captures only a monotonic 
6-71

relationship (see discussion in Section 3.4.2). A slightly non-monotonic relationship results in a 

smaller R2 than when the relationship is purely monotonic. 

The tables are ordered by input variables with the highest rank regression results, and then are 

further grouped according to the type of input parameter (i.e., MACCS or MELCOR variables). 

The final R2 determination for all four regression models are fairly high at the five specified

circular areas and range from 0.42 for MARS at 30 miles (Table 6.2-9) to 0.85 for recursive 

partitioning at 10 miles (Table 6.2-7).

All regression methods for the specified circular areas consistently rank the following 

parameters, respectively, as the most important input variables:

• The MACCS dry deposition velocity (VDEPOS), 

• The MELCOR safety relief valve (SRV) stochastic failure probability (SRVLAM), and 

• The MACCS risk factor for cancer fatalities for the residual organ (CFRISK–Residual).

The residual organ is represented by the pancreas and is used to define all latent 

cancers not specifically accounted for in the MACCS model. The pancreas is chosen to 

be a representative soft tissue. 

Additional variables also consistently show some level of importance at all circular areas in at 

least one of the regression methods. These additional input variables include the following: 

• The MELCOR fuel failure criterion,

• The MELCOR drywell liner melt-through open area flow path (FL904A),

• The MACCS dose and dose-rate effectiveness factor for the residual organ 

(DDREFA-Residual). 

These six variables (VDEPOS, SRVLAM, fuel failure criterion, FL904A, CFRISK-residual, and 

DDREFA-residual) account for 26%-75% of the variance for the different circular areas using 

the different regression methods. Other input parameters indicate some importance within 

certain circular areas but not within other circular areas. 

Thus, the most important variable, VDEPOS, appears at the top of the tables followed by the 

consistently important MELCOR variables, (i.e., SRVLAM, fuel failure criterion, and FL904A), 

the LCF risk parameters for residual cancers (i.e., CFRISK-residual and DDREFA-residual), and 

finally other LCF risk parameters, dose conversion factors for inhalation, and MELCOR 

parameters (e.g., rail road doors open or closed – RRDOOR) that appear in only some of the 

tables.

The MACCS dry deposition velocity (VDEPOS) is expected to be important to LCF risk because 

the long-term dose with the LNT model is driven by dry deposition velocity since long-term dose 

results mainly from groundshine. Wet deposition also contributes to groundshine dose, but its 

contribution is smaller on average due to the fact that rain only occurs about 7% of the time at 

Peach Bottom. A larger value of dry deposition velocity results in larger long-term doses at 

shorter distances and smaller doses at longer distances. This explains why the correlation 

coefficient is positive at 10 miles and negative beyond 10 miles for the rank regression analysis. 

As discussed in further detail in Section 4.2.2, dry deposition is characterized in MACCS with a

set of deposition velocities corresponding to a set of aerosol size bins. All of the deposition 

velocities are correlated, so VDEPOS indicates the deposition velocity for each of the aerosol 

bins. Currently, MACCS uses a fixed deposition velocity that is independent of wind speed and 

other conditions (whereas in reality, deposition velocity would vary with wind speed and surface 

roughness). 
6-72

Table 6.2-7 Conditional, mean, individual LCF risk (per event) regression of the 

MACCS Uncertainty Analysis for the 10-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.73 0.76 0.85 0.72

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

VDEPOS 0.31 0.31 0.56 0.15 0.28 0 0.22 0.53 0 0.33 0.37 0 

SRVLAM 0.43 0.12 -0.35 0.07 0.21 0 0.16 0.35 0 0.12 0.12 0.02

Fuel failure 

criterion 0.44 0.01 0.15 0.01 0.03 0.55 --- --- --- 0.07 0.13 0 

FL904A 0.45 0.01 0.12 --- --- --- --- --- --- 0 0 1 

BATTDUR --- --- --- --- --- --- 0 0.01 0.55 0 0 1 

CFRISK

Residual 0.54 0.09 0.31 0.16 0.27 0 0.15 0.48 0 0.18 0.25 0 

DDREFA

Residual 0.57 0.03 -0.18 0.03 0.19 0 0.01 0.05 0.05 0.05 0.16 0 

GSHFAC

Normal 0.63 0.06 0.24 0.05 0.22 0 --- --- --- 0.04 0.09 0.01

CFRISK

Colon 0.66 0.03 0.17 0.03 0.20 0 0 0.04 0.33 0.07 0.08 0.05

DDREFA

Colon 0.67 0.01 -0.08 0.03 0.02 0.4 --- --- --- --- --- ---

CFRISK

Lung 0.70 0.03 0.17 0.03 0 1 0 0.10 0.11 0.05 0.02 0.35

DDREFA

Lung 0.71 0.01 -0.08 --- --- --- 0.01 0.05 0.09 0 0 1 

CFRISK

Breast 0.72 0.01 0.10 0 0.03 0.44 0 0 1 0.04 0.08 0 

CYSIGA 0.73 0.01 0.09 0.01 0.11 0 --- --- --- --- --- ---

CWASH1 0.74 0.01 0.07 --- --- --- 0 0 1 --- --- ---

CFRISK

Liver 0.75 0.01 0.07 0.03 0 1 --- --- --- --- --- ---

GSHFAC

Evacuation --- --- --- 0 0.11 0 0.02 0 1 --- --- ---

Cm-242

Inhalation --- --- --- 0 0.08 0.01 --- --- --- 0 0 1 

Ce-144

Inhalation --- --- --- 0 0 1 --- --- --- --- --- ---

Sr-91

Inhalation --- --- --- --- --- --- 0 0.07 0.03 --- --- ---

RDSTC --- --- --- --- --- --- 0.04 0.05 0.09 --- --- ---

GSHFAC

Sheltering --- --- --- --- --- --- 0.04 0.05 0.11 0.01 0 1 

I-134

Inhalation --- --- --- --- --- --- 0 0 1 --- --- ---

Pu-238

Inhalation --- --- --- --- --- --- --- --- --- 0.03 0 1 

Note: Parameters are grouped by importance and relationship (e.g. MELCOR parameters). Light shading indicates 

parameters with low importance. The dark shading and no shading represent ‘groupings’ of parameters (e.g., source 

term influence from MELCOR inputs or latent cancer risk associated for a specific target organ).
6-73

Table 6.2-8 Conditional, mean, individual LCF risk (per event) regression of the 

MACCS Uncertainty Analysis for the 20-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.50 0.61 0.64 0.44

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

VDEPOS 0.17 0.17 -0.41 0.12 0.26 0 0.12 0.47 0 0.22 0.40 0 

SRVLAM 0.25 0.08 0.28 0.12 0.21 0 0.11 0.24 0.05 0.19 0.31 0 

BATTDUR 0.28 0.03 0.26 --- --- --- --- --- --- 0.05 0.06 0.04

Fuel failure 

criterion 0.30 0.02 0.13 0 0.10 0 --- --- --- 0.02 0 1 

FL904A 0.31 0.01 -0.11 0 0.01 0.67 0.02 0.07 0.15 0.02 0 1 

CFRISK

Residual 0.38 0.07 0.28 0.11 0.07 0.55 0.04 0.16 0.03 0.14 0.12 0.06

DDREFA

Residual 0.40 0.02 0.16 0.01 0 1 0.07 0.08 0.02 0.04 0 1 

Cm-242

Inhalation 0.43 0.03 0.18 0.01 0.07 0.04 0.02 0.04 0.10 0 0.06 0.14

CFRISK

Breast 0.45 0.02 0.13 --- --- --- 0 0.08 0.01 0.02 0.10 0 

CFRISK

Lung 0.47 0.02 -0.14 0.04 0.23 0 0.04 0.34 0 0.07 0.24 0 

DDREFA

Lung 0.48 0.01 -0.09 --- --- --- --- --- --- 0 0 1 

RRDOOR 0.50 0.02 -0.08 0.02 0.06 0.21 --- --- --- --- --- ---

I-134

Inhalation 0.52 0.02 -0.08 0.05 0 1 --- --- --- --- --- ---

CFRISK

Liver 0.53 0.01 0.08 --- --- --- 0 0.01 0.61 --- --- ---

GSHFAC

Evacuation 0.54 0.01 0.08 0.01 0.12 0.01 0.07 0.18 0 --- --- ---

RDSTC --- --- --- 0.01 0.20 0 0.01 0.14 0 --- --- ---

Sr-91

Inhalation --- --- --- 0 0.09 0 0.01 0.04 0.15 --- --- ---

Ba-140

Inhalation --- --- --- 0 0 1 --- --- --- --- --- ---

Sr-90

Inhalation --- --- --- 0 0 1 --- --- --- --- --- ---

DDREFA

Colon --- --- --- --- --- --- 0 0.15 0 --- --- ---

CFRISK

Colon --- --- --- --- --- --- 0 0.06 0.06 0 0 1 

RRIDFRAC --- --- --- --- --- --- 0 0 1 --- --- ---

GSHFAC

Sheltering --- --- --- --- --- --- --- --- --- 0 0.08 0.02

GSHFAC

Normal --- --- --- --- --- --- --- --- --- 0 0 0.48
6-74

Table 6.2-9 Conditional, mean, individual LCF risk (per event) regression of the 

MACCS Uncertainty Analysis for the 30-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.51 0.59 0.64 0.42

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

VDEPOS 0.17 0.17 -0.43 0.13 0.23 0 0.20 0.49 0 0.22 0.29 0 

SRVLAM 0.25 0.08 0.28 0.20 0.26 0 0.05 0.34 0 0.15 0.30 0 

BATTDUR 0.28 0.03 0.26 --- --- --- --- --- --- 0 0.03 0.33

Fuel failure 

criterion 0.31 0.03 0.18 0.02 0.13 0 0.02 0 1 0.01 0.06 0.21

FL904A 0.32 0.01 -0.12 0.01 0.08 0.02 0 0.18 0 0 0 1 

CFRISK

Residual 0.38 0.06 0.27 0.11 0.16 0 0 0.12 0 0.12 0.15 0.02

DDREFA

Residual 0.40 0.02 0.16 0.07 0.11 0 --- --- --- 0.04 0.06 0.12

CFRISK

Colon 0.42 0.02 0.14 0.01 0.06 0.04 0 0.08 0.05 0.01 0.07 0 

CFRISK

Breast 0.44 0.02 0.13 --- --- --- --- --- --- 0 0.05 0.04

Cm-242

Inhalation 0.46 0.02 -0.13 0.06 0.18 0 0.04 0.43 0 0.18 0.22 0 

RRDOOR 0.48 0.02 -0.08 0 0 1 0 0.09 0.09 --- --- ---

DDREFA

Lung 0.50 0.02 -0.09 --- --- --- --- --- --- 0 0 1 

RRIDFRAC 0.51 0.01 0.09 --- --- --- --- --- --- --- --- ---

Ba-140

Inhalation 0.52 0.01 -0.07 0 0 1 --- --- --- --- --- ---

Sr-90

Inhalation 0.53 0.01 0.07 --- --- --- 0 0.01 0.44 --- --- ---

GSHFAC

Evacuation --- --- --- 0.02 0.12 0 --- --- --- --- --- ---

CYSIGA --- --- --- 0.00 0.09 0 --- --- --- --- --- ---

I-134

Inhalation --- --- --- 0.01 0.06 0.03 0.02 0.03 0.20 --- --- ---

CFRISK

Lung --- --- --- 0.03 0.06 0.12 0 0.12 0 0 0.01 0.29

DDREFA

Bone --- --- --- 0 0 1 0 0.11 0 --- --- ---

GSHFAC

Normal --- --- --- --- --- --- 0 0.03 0.40 0.01 0 1 

RDSTC --- --- --- --- --- --- 0.01 0 1 --- --- ---

CFRISK

Liver --- --- --- --- --- --- 0.03 0 1 --- --- ---

GSHFAC

Sheltering --- --- --- --- --- --- --- --- --- 0.03 0.03 0.25

Pu-238

Inhalation --- --- --- --- --- --- --- --- --- 0 0 1 
6-75

Table 6.2-10 Conditional, mean, individual LCF risk (per event) regression of the 

MACCS Uncertainty Analysis for the 40-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.52 0.57 0.67 0.50

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

VDEPOS 0.18 0.18 -0.43 0.10 0.21 0 0.12 0.52 0 0.23 0.24 0 

SRVLAM 0.25 0.07 0.27 0.12 0.28 0 0.16 0.39 0 0.14 0.33 0 

Fuel failure 

criterion 0.28 0.03 0.19 0.01 0.02 0.80 0.05 0.16 0 0.02 0.08 0.06

BATTDUR 0.31 0.03 0.16 --- --- --- 0 0.04 0.24 0.01 0.12 0 

FL904A 0.32 0.01 -0.13 0.03 0.10 0 0.03 0 0.83 0.05 0.06 0.04

CFRISK

Residual 0.37 0.05 0.25 0.04 0.15 0 --- --- --- 0.10 0.14 0.02

DDREFA

Residual 0.40 0.03 0.16 0.08 0 0.94 0 0 1 0.06 0.10 0.03

DDREFA

Lung 0.43 0.03 0.27 0 0 1 --- --- --- 0.05 0 1 

CFRISK

Lung 0.45 0.02 -0.13 0.06 0.25 0 0.04 0.38 0 0.06 0.29 0 

CFRISK

Colon 0.48 0.03 0.16 --- --- --- --- --- --- 0.03 0 1 

RRDOOR 0.50 0.02 -0.07 0 0.06 0.21 --- --- --- --- --- ---

CFRISK

Breast 0.52 0.02 -0.09 0 0 1 0 0 1 0 0 1 

I-134

Inhalation 0.53 0.01 -0.08 --- --- --- 0.01 0 1 --- --- ---

Ce-144

Inhalation 0.54 0.01 0.10 --- --- --- 0.05 0 1 --- --- ---

CYSIGA 0.55 0.01 0.07 --- --- --- --- --- --- --- --- ---

GSHFAC

Normal --- --- --- 0.01 0.11 0 0 0.03 0.37 0 0 1 

GSHFAC

Evacuation --- --- --- 0.07 0.08 0.01 --- --- --- --- --- ---

Ba-140

Inhalation --- --- --- 0 0.07 0.03 0 0 1 --- --- ---

Sr-91

Inhalation --- --- --- 0 0.05 0.06 --- --- --- --- --- ---

Cm-242

Inhalation --- --- --- 0.02 0.04 0.39 0 0.17 0 0.01 0 1 

GSHFAC

Sheltering --- --- --- --- --- --- 0 0.14 0 0.02 0.05 0.02

Pu-238

Inhalation --- --- --- --- --- --- 0.01 0.02 0.38 0.02 0.06 0.01
6-76

Table 6.2-11 Conditional, mean, individual LCF risk (per event) regression of the 

MACCS Uncertainty Analysis for the 50-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.52 0.57 0.71 0.54

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

VDEPOS 0.18 0.18 -0.43 0.09 0.18 0 0.16 0.46 0 0.19 0.39 0 

SRVLAM 0.25 0.07 0.26 0.12 0.31 0 0.05 0.29 0 0.05 0.16 0.06

Fuel failure 

criteria 0.45 0.03 0.16 --- --- --- 0 0.05 0.07 0 0.01 0.38

FL904A 0.48 0.02 -0.14 0.04 0.08 0 0.05 0.28 0 0.02 0 1 

BATTDUR --- --- --- 0.03 0.02 0.46 --- --- --- 0 0.01 0.34

DDREFA

Residual 0.30 0.05 0.24 0.05 0.09 0.07 --- --- --- 0.09 0.09 0.29

CFRISK

Residual --- --- --- 0 0.04 0.33 0 0.12 0 0.02 0.01 0.37

GSHFAC

Normal 0.34 0.04 0.18 --- --- --- 0 0.03 0.45 0.06 0.05 0.14

CFRISK

Lung 0.37 0.03 0.19 0.01 0.12 0.01 0.04 0.22 0 0.03 0.07 0.28

DDREFA

Lung 0.40 0.03 0.26 0 0.13 0 --- --- --- 0.02 0.11 0 

GSHFAC

Evacuation 0.43 0.03 0.16 0.06 0.15 0 0.01 0.23 0 0.04 0.08 0 

Cm-242

Inhalation 0.47 0.02 -0.13 0.09 0.19 0 0.05 0.40 0 0.11 0.22 0 

Ce-144

Inhalation 0.50 0.02 0.10 --- --- --- --- --- --- --- --- ---

CFRISK

Breast 0.51 0.02 -0.09 0.02 0 1 0.03 0 1 0 0.03 0.08

I-134

Inhalation 0.51 0.02 -0.08 0.02 0.06 0.19 --- --- --- --- --- ---

Sr-91

Inhalation 0.52 0.01 0.07 --- --- --- 0.02 0.05 0.09 --- --- ---

RRDOOR 0.52 0.00 0.06 --- --- --- --- --- --- --- --- ---

DDREFA

Bone --- --- --- 0.01 0.06 0.07 --- --- --- --- --- ---

Sr-90

Inhalation --- --- --- 0.03 0 0.6 0.01 0 1 --- --- ---

DDREFA

Colon --- --- --- 0 0 1 --- --- --- --- --- ---

CFRISK

Colon --- --- --- --- --- --- 0 0.09 0.21 0 0.05 0.02

GSHFAC

Sheltering --- --- --- --- --- --- 0 0 1 --- --- ---

Pu-238

Inhalation --- --- --- --- --- --- --- --- --- 0 0.09 0 
6-77

The MELCOR input variables (SRVLAM, fuel failure criterion, and FL904A) account for at least 

7% of the variance with a Ti of 0.16 using the MARS analysis to at most at most 24% of the 

variance using the recursive partitioning analysis at the specified circular areas for all regression 

methods. Based on this uncertainty analysis, these three variables ultimately correlate with 

most of the uncertainty contribution of the source term to LCF risk. As discussed in 

Section 6.1.1 and Section 6.1.2, these MELCOR input variables account for most of the 

variance in iodine and cesium release fractions and hence are expected to be important. The 

MELCOR regression analyses indicate CHEMFORM and SRV open area fraction 

(SRVOAFRAC) to also be important to release magnitude but these two variables, on the other 

hand, do not appear as variables of most importance to LCF risk. 

Within 10 miles, SRVLAM is negatively correlated with LCF risk in the rank regression analysis. 

This is because longer SRV valve cycling (lower failure rate) is more likely to result in a main 

steam line creep rupture, a higher degree of core degradation, and greater releases. The larger 

releases lead to greater LCF risk mainly from long-term doses since the 10-mile area is 

evacuated with the exception of the assumed 0.5% of the population that refuses to evacuate. 

Beyond 10 miles, SRVLAM is positively correlated in the rank regression analysis. Further 

statistical regression and sensitivity studies are required to understand the negative correlation 

beyond 10 miles. A possible explanation is the different dependence on SRVLAM of the 

release fractions for the chemical classes that results in emergency phase dose versus 

long-term phase dose.

The remaining two of the six most important variables in the regression analysis, CFRISKresidual, and DDREFA-residual, account for at most 23% of the variance using the MARS 

analysis at the specified circular areas. The Ti values indicate greater influence in conjunction 

with other variables. As discussed in Section 4.2.5, the mortality risk coefficients (CFRISK) for 

each of the organs included in the SOARCA analyses for latent health effects are assumed to 

be uncorrelated. The dose and dose rate effectiveness factor (DDREFA) is based on BEIR V 

risk factors for estimating health effects to account for observed differences between low and 

high dose rates. Doses received during the emergency phase are divided by DDREFA when 

they are less than 0.2 Gy (20 rad) in the calculation of latent health effects; they are not divided 

by DDREFA when emergency-phase doses exceed 0.2 Gy. Doses received during the 

long-term phase are generally controlled by the habitability criterion to be well below 0.2 Gy, so 

these doses are always divided by DDREFA in the calculation of latent health effects. Since 

DDREFA is in the denominator, it is negatively correlated with LCF risk. 

The MACCS latent cancer parameters CFRISK-residual and DDREFA-residual are used for 

estimating residual cancers not related to the seven organ-specific cancers that were used in

SOARCA: 

• Leukemia,

• bone cancer, 

• breast cancer, 

• lung cancer, 

• thyroid cancer, 

• liver cancer, and

• colon cancer 

It is understandable that the CFRISK and DDREFA factors for the “residual” category would be 

important, because they account for multiple organs, and their respective CFRISK uncertainty 

distributions, that are not modeled separately. 
6-78

In a previous study [60], the amount of shielding between an individual and the source of 

groundshine, the groundshine shielding factor (GSHFAC), was determined to be an important 

variable. However, it is found to be of lesser importance in this study. The long-term GSHFAC 

was directly correlated with the emergency-phase GSHFAC during normal activities for the nonevacuated residents (GSHFAC-Normal). Tables 6.2-7 through 6.2-11 show GSHFAC-Normal 

as an important variable at the 10- and 50-mile circular areas (i.e., 0-11% of the variance for all 

regression methods). The 20-, 30-, and 40-mile circular areas show GSHFAC-Normal as 

variable of much lower importance. The 20-mile, 30-mile, and 40-mile circular areas show a 

larger contribution of the emergency phase (i.e., an average of 44-55% of the overall LCF risk is 

contributed by the emergency phase), than the 10-mile and 50-mile circular areas (i.e., an

average of 5-40% of the overall LCF risk contributed to the emergency phase).

Unlike the previous study, this uncertainty analysis has varied source terms, a more detailed 

evacuation model, and approximately 300 more MACCS uncertainty variables. 

6.2.3.2 Regression Analysis for Early-fatality Risk

Tables 6.2-12 through 6.2-16 show the regression results obtained for conditional, mean, 

individual early-fatality risk (per event) for the MACCS Uncertainty Analysis (i.e., CAP17) for the 

1.3-mile, 2-mile, 2.5-mile, 3-mile, and 3.5-mile circular areas, respectively. Since less than 

2.5% of all the MACCS Uncertainty Analysis realizations resulted in a nonzero early-fatality risk 

for the 5-mile, 7-mile, and 10-mile circular areas, they are not included in the regression 

analysis results due to unreliable statistics regarding variable importance. 

The tables are a general indication of input parameter influence on the results. Rank regression

is often an underestimate the true influence of a parameter since it captures only a monotonic 

relationship. A slightly non-monotonic relationship results in a smaller R2 than when the 

relationship is purely monotonic. The tables are ordered by input variables with the highest rank 

for all regression results, and then are further grouped according to the type of input parameter 

(i.e., MACCS or MELCOR variables). There are two noticeable groupings when the important 

variables are examined. Those within 2 miles, Table 6.2-12 and Table 6.2-13, show the final R2

for the non-rank regression models are fairly high and range from 0.58 for MARS (Table 6.2-13) 

to 0.75 for recursive partitioning (Table 6.2-12). The rank regression shows that monotonic 

relationship for all variables are poor. 

For the circular areas less than 2 miles, the non-rank regression methods consistently rank the 

MACCS wet deposition model (CWASH1), the MELCOR SRV stochastic failure probability 

(SRVLAM), the MELCOR SRV open area fraction (SRVOAFRAC), the MACCS early health 

effects threshold and beta (shape) factor for red bone marrow (EFFTHR-Red Marrow and 

EFFACB-Red Marrow), and the MACCS linear, crosswind dispersion coefficient (CYSIGA), in 

order, as the most important input variables. 

Additional variables also consistently show some level of importance for circular areas less than 

2 miles. These additional input variables include the following:

• The MACCS amount of shielding between an individual and the source of groundshine 

during normal activities for the non-evacuated residents (GSHFRAC-Normal),

• The MACCS evacuation delay for Cohort 5 (DELTVA-Cohort 5), and

• The MELCOR DC station battery duration (BATTDUR) 
6-79

These nine variables (CWASH1, SRVLAM, SRVOAFRAC, EFFTHR-red marrow, EFFACB-red 

marrow, CYSIGA, GSHFRAC-normal, DELTVA-cohort 5, and BATTDUR) account for at least 

24% of the variance for the quadratic regression, at least 46% of the variance for the recursive 

partitioning, and at least 30% of the variance for MARS.

Other input parameters show a low importance at certain circular areas but not for other circular 

areas. Thus, the most important variable, CWASH1, appears at the top of Table 6.2-12 and 

Table 6.2-13 followed by the consistently important MELCOR variables, SRVLAM and 

SRVOAFRAC, and then the other five important variables, and finally a set of parameters not 

consistently seen in all the tables. 

The MACCS wet deposition parameter (CWASH1) accounts for at least 4% of the variance with 

a Ti of 0.78 using the MARS analysis to at most 29% of the variance with a Ti of 0.76 using the 

quadratic regression analysis for circular areas less than 2 miles for all non-ranked regression 

methods and is the most important input variable. Also, CWASH1 consistently has the highest 

rank for interactions with other input variables (Ti). As discussed in detail in Section 4.2.1, the 

wet deposition model shows that under heavy rains, wet deposition is very effective and rapidly 

depletes the plume. This process can produce concentrated deposits on the ground and create 

what is often referred to as a hot spot (i.e., an area of higher radioactivity than the surrounding 

areas). As seen in the non-ranked regression analysis, rain and its interactions with other input 

variables (e.g., see the Ti for recursive partition in Table 6.2-12) can significantly affect 

consequence calculations when it does occur. However, the early-fatality risk is more highly 

correlated with crosswind dispersion (CYSIGA) beyond 2 miles (see Table 6.2-14). The 

crosswind dispersion parameter defines how narrow the plume is while it travels, with a 

narrower plume allowing higher radionuclide concentrations to reach individuals farther from the 

plant. 

The crosswind dispersion coefficient (CYSIGA), early health effects threshold for red bone 

marrow (EFFTHR–Red Marrow), and other important variables also show a large 

non-monotonic interaction with other input variables. While the overall R2 contribution from 

these input variables is low, their interactions with other variables do justify their consideration to 

early-fatality risk. The red bone marrow is usually the most sensitive organ for early fatalities. 

EFFTHR-red marrow and EFFACB-red marrow (discussed below) are important because the 

hematopoietic syndrome has the lowest threshold for an early fatality.
6-80

Table 6.2-12 Conditional, mean, individual early-fatality risk (per event) regression of 

the MACCS Uncertainty Analysis for the 1.3-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.26 0.67 0.75 0.64

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

CWASH1 0.03 0.03 0.10 0.12 0.88 0 0.29 0.77 0 0.11 0.94 0 

SRVLAM 0.07 0.04 -0.10 0 0.03 0.56 0.15 0.60 0 0.01 0.17 0.19

SRVOAFRAC 0.10 0.03 -0.09 0.01 0.20 0.13 0.02 0.15 0.12 0.04 0.23 0.14

BATTDUR --- --- --- --- --- --- 0 0.29 0 --- --- ---

GSHFAC

Normal 0.12 0.02 0.08 0.01 0.60 0 0 0 1 0.01 0.13 0.59

EFFTHR

Red Marrow 0.18 0.06 -0.14 0.01 0 1 0 0 1 0 0.04 0.43

EFFACB

Red Marrow 0.19 0.01 -0.05 --- --- --- --- --- --- 0 0.39 0 

CYSIGA 0.22 0.03 -0.09 0 0 1 0.01 0.39 0 0.02 0.39 0 

DLTEVA

Cohort 5 0.23 0.01 0.01 0.01 0 1 --- --- --- 0 0.13 0.30

ESPEED --- --- --- 0.01 0.52 0 0 0.22 0 0 0 1 

PROTIN

Sheltering --- --- --- 0 0.29 0 0 0.28 0 0 0 1 

EFFTHR

Stomach --- --- --- 0.01 0.32 0 --- --- --- --- --- ---

DLTEVA

Cohort 3 0.25 0.02 -0.10 0.01 0.18 0.07 --- --- --- 0 0.29 0.01

PROTIN

Normal 0.26 0.01 0.06 --- --- --- --- --- --- 0.03 0.12 0.45

RRIDFRAC 0.27 0.01 0.04 --- --- --- --- --- --- --- --- ---

SC1131_2 0.28 0.01 0.03 --- --- --- --- --- --- 0.01 0.27 0.03

DLTEVA

Cohort 4 0.28 0.00 0.03 0 0 1 0.02 0 1 --- --- ---

GSHFAC

Sheltering --- --- --- 0 0.07 0.42 0 0 1 0 0 1 

CZSIGA --- --- --- --- --- --- 0.01 0 1 --- --- ---

DLTEVA

Cohort 2 --- --- --- --- --- --- 0 0 1 --- --- ---
6-81

Table 6.2-13 Conditional, mean, individual early-fatality risk (per event) regression of 

the MACCS Uncertainty Analysis for the 2-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.24 0.62 0.63 0.58

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

CWASH1 0.03 0.03 0.08 0.29 0.76 0 0.15 0.60 0 0.04 0.78 0 

SRVLAM 0.07 0.04 -0.10 0.01 0.41 0 0 0.10 0.35 0.01 0.28 0.07

SRVOAFRAC 0.10 0.03 -0.09 0.01 0 1 0.06 0.53 0 0.06 0 1 

BATTDUR 0.10 0 -0.03 0 0.13 0.09 0 0.05 0.32 --- --- ---

EFFTHR

Red Marrow 0.15 0.05 -0.12 0 0.18 0.13 0.01 0.52 0 0.02 0.47 0 

EFFACB

Red Marrow 0.16 0.01 0.04 --- --- --- --- --- --- 0.01 0 1 

CYSIGA 0.18 0.02 0.07 0 0.40 0 --- --- --- 0.04 0.48 0 

DLTEVA

Cohort 5 0.19 0.01 -0.07 0.02 0 1 0.07 0.15 0.17 0 0 1 

GSHFAC

Normal 0.21 0.02 0.06 --- --- --- --- --- --- 0.01 0.12 0.27

PROTIN

Sheltering 0.22 0.01 0.05 --- --- --- --- --- --- 0 0 1 

PROTIN

Normal 0.23 0.01 -0.04 --- --- --- --- --- --- 0 0 1 

DLTEVA

Cohort 3 0.24 0.01 -0.04 0.02 0.03 0.34 0 0.01 0.58 0 0.39 0 

SC1131_2 0.25 0.01 0.04 0 0.15 0.15 --- --- --- 0 0.06 0.37

DLTEVA

Cohort 4 0.26 0.01 0.03 --- --- --- --- --- --- --- --- ---

RRIDFRAC --- --- --- 0 0.07 0.41 --- --- --- --- --- ---

ESPEED --- --- --- 0 0 1 --- --- --- 0 0 1 

RRDOOR --- --- --- --- --- --- 0 0.15 0.06 --- --- ---

CZSIGA --- --- --- --- --- --- 0.01 0 1 --- --- ---

GSHFAC

Sheltering --- --- --- --- --- --- --- --- --- 0.01 0.07 0.55

For the circular areas greater than two miles but less than five miles (Table 6.2-14 through 

Table 6.2-16), the regression methods consistently rank the following as the most important 

input variables:

• MACCS crosswind dispersion coefficient (CYSIGA), 

• The early health effects threshold risk for red bone marrow (EFFTHR-Red Marrow), 
6-82

• The early health effects beta (shape) factor for red bone marrow (EFFACB-Red 

Marrow), 

• The MELCOR SRV stochastic failure probability (SRVLAM), and 

• The MELCOR SRV open area fraction (SRVOAFRAC). 

However, additional variables also consistently show some level of importance for circular areas 

greater than two miles. These additional input variables include the following: 

• The MACCS inhalation protection factor during sheltering activities for non-evacuated 

residents (PROTIN-Sheltering), 

• The MELCOR DC station battery duration (BATTDUR), and

• The MELCOR railroad inner door open fraction (RRIDFRAC). 

The final R2 for non-rank regression models is reasonable for circular areas between 2.5 to 

3.5 miles. They range from 0.44 for recursive partitioning at 3.5 miles (Table 6.2-16) to 0.82 for 

MARS at 3.5 miles (Table 6.2-16). These eight variables (CYSIGA, EFFTHR-red marrow, 

EFFACB-red marrow, SRVLAM, SRVOAFRAC, PROTIN-sheltering, BATTDUR, and 

RRIDFRAC) account for at least 12% of the variance (Final R2 value) for the quadratic 

regression analysis, at least 96% of the variance for the recursive partitioning analysis, and at 

least 21% of the variance for the MARS analysis. 

Other input parameters show a low importance at certain circular areas but not for other circular 

areas. Thus, the most important variable, CYSIGA, appears at or near the top of Table 6.2-14

through Table 6.2-16 (Table 6.2-14 has PROTIN-sheltering as the most important variable)

followed by EFFTHR-red marrow and EFFACB-red marrow, the consistently important 

MELCOR variables, SRVLAM, SRVOAFRAC, BATTDUR, and RRIDFRAC, and then the other 

important variables, and finally those parameters not consistently seen in all of the tables.

The MACCS crosswind dispersion coefficient (CYSIGA) parameter accounts for at least 0% of 

the variance with a Ti of 0.16 using the quadratic regression analysis to at most 81% of the 

variance with a Ti of 0.25 using the recursive partitioning regression analysis for circular areas 

from 2.5 to 3.5 miles for all non-ranked regression methods and is the most important input 

variable. Also, CYSIGA consistently has one of the highest ranks for interactions with other 

input variables (Ti). As discussed in greater detail in Section 4.2.6, crosswind dispersion directly 

affects peak concentrations, and thus it affects early doses to members of the population and 

resulting early health effects. 
6-83

Table 6.2-14 Conditional, mean, individual early-fatality risk (per event) regression of 

the MACCS Uncertainty Analysis for the 2.5-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.18 0.52 0.50 0.66

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

PROTIN

Sheltering 0.01 0.01 0.04 0.28 0.78 0 0.28 0.41 0 0.10 0.74 0 

CYSIGA 0.02 0.01 -0.04 0.05 0.21 0.03 0.17 0.28 0.01 0 0 1 

SRVLAM 0.05 0.03 -0.06 0 0 1 0.01 0.31 0 0 0.12 0.28

SRVOAFRAC 0.07 0.02 -0.07 0.01 0 1 0.03 0 1 0.03 0.35 0.01

BATTDUR 0.07 0 0.02 --- --- --- --- --- --- --- --- ---

RRIDFRAC 0.08 0.01 0.02 0 0.17 0.11 --- --- --- --- --- ---

EFFTHR

Red Marrow 0.14 0.06 -0.10 0 0 1 0.03 0.42 0 0.01 0.65 0 

EFFACB

Red Marrow 0.14 0 0.02 0 0.41 0 --- --- --- 0 0 1 

CWASH1 0.15 0.01 0.05 0 0.36 0 --- --- --- 0 0 1 

DLTEVA

Cohort 3 0.17 0.02 -0.01 --- --- --- --- --- --- 0.02 0.41 0 

PROTIN

Normal 0.18 0.01 -0.03 0.01 0 1 0 0 1 0 0.48 0 

GSHFAC

Normal 0.18 0 -0.03 0.03 0.01 0.51 --- --- --- 0 0.31 0.01

DLTEVA

Cohort 5 0.19 0.01 0.02 0 0.20 0.08 0 0.02 0.43 0.01 0.15 0.15

SC1131_2 0.19 0 -0.02 --- --- --- --- --- --- 0 0.15 0.22

DLTEVA

Cohort 3 --- --- --- 0 0.35 0 0.01 0 1 --- --- ---

DHEADSOL --- --- --- 0.01 0 1 --- --- --- --- --- ---

DLTEVA

Cohort 4 --- --- --- --- --- --- 0.01 0.50 0 --- --- ---

VDEPOS --- --- --- --- --- --- 0 0.12 0.06 --- --- ---

ESPEED --- --- --- --- --- --- --- --- --- 0 0.18 0.19

GSHFAC

Sheltering --- --- --- --- --- --- --- --- --- 0 0 1 
6-84

Table 6.2-15 Conditional, mean, individual early-fatality risk (per event) regression of 

the MACCS Uncertainty Analysis for the 3-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.16 0.52 0.51 0.59

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

CYSIGA 0.01 0.01 -0.04 0 0.51 0 0.30 0.21 0.24 0 0 1 

EFFTHR

Red Marrow 0.07 0.06 -0.09 0.03 0 1 0.02 0 0.87 0.14 0.82 0 

EFFACB

Red Marrow 0.08 0.01 0.03 0 0.30 0 --- --- --- 0.02 0.35 0 

SRVOAFRAC 0.10 0.02 -0.05 0.01 0.11 0.36 0 0.15 0.06 0 0.50 0 

SRVLAM 0.12 0.02 -0.05 0 0.35 0 0 0.52 0 0 0 1 

BATTDUR --- --- --- 0.02 0.10 0.42 --- --- --- --- --- ---

RRIDFRAC 0.13 0.01 0.03 0 0.71 0 0.17 0.44 0 --- --- ---

DLTEVA

Cohort 3 0.15 0.02 -0.0 0.03 0.46 0 --- --- --- 0.03 0.09 0.28

CWASH1 0.16 0.01 0.04 0.01 0.31 0.01 --- --- --- 0.02 0 1 

DLTEVA

Cohort 5 0.16 0 -0.03 0 0.07 0.38 0.01 0 1 0.01 0 1 

GSHFAC

Normal 0.16 0 -0.03 0 0.21 0.03 --- --- --- 0 0 1 

GSHFAC

Sheltering

0.17 0.01 0.03 --- --- --- --- --- --- 0 0.01 0.59

PROTIN

Normal 0.18 0.01 0.03 --- --- --- --- --- --- 0 0 1 

PROTIN

Sheltering 0.18 0 -0.02 --- --- --- --- --- --- 0 0 1 

SC1131_2 0.18 0 -0.02 --- --- --- --- --- --- 0 0 1 

CZSIGA --- --- --- 0 0.39 0 --- --- --- --- --- ---

EFFTHR

Stomach --- --- --- 0.05 0.06 0.58 --- --- --- --- --- ---

ESPEED --- --- --- 0 0 1 --- --- --- 0 0 1 
6-85

Table 6.2-16 Conditional, mean, individual early-fatality risk (per event) regression of 

the MACCS Uncertainty Analysis for the 3.5-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.16 0.50 0.44 0.82

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

CYSIGA 0.01 0.01 -0.04 0 0.16 0.04 0.81 0.25 0.27 0 0 1 

EFFTHR

Red Marrow

0.07 0.06 -0.08 0.05 0.22 0.06 0.03 0.27 0.10 0.06 0.58 0 

EFFACB

Red Marrow 0.07 0 -0.02 --- --- --- --- --- --- 0 0.13 0.19

SRVLAM 0.09 0.02 -0.05 --- --- --- 0 0.13 0.15 0 0.11 0.34

SRVOAFRAC 0.10 0.01 -0.04 0.02 0 1 0 0.36 0 0 0.55 0 

BATTDUR --- --- --- --- --- --- 0.02 0.16 0.07 --- --- ---

DLTEVA

Cohort 5 0.11 0.01 0.02 0.07 0.38 0 0.05 0.17 0.15 0.01 0 1 

CWASH1 0.12 0.01 0.03 --- --- --- --- --- --- 0 0.37 0 

GSHFAC

Normal 0.13 0.01 -0.03 --- --- --- 0 0.18 0.02 0 0 1 

PROTIN

Normal 0.14 0.01 0.03 0 0.23 0. --- --- --- 0 0 1 

DLTEVA

Cohort 3 0.16 0.02 0.04 0 0.14 0.13 0.04 0.23 0 0.01 0 1 

ESPEED 0.16 0 0.02 --- --- --- --- --- --- 0.01 0.38 0 

SC1131_2 0.16 0 0.02 0 0.25 0 --- --- --- 0.05 0.71 0 

GSHFAC

Sheltering 0.16 0 -0.02 0.01 0.19 0.01 --- --- --- 0.01 0.40 0 

DHEADSOL --- --- --- 0 0.25 0 --- --- --- --- --- ---

CZSIGA --- --- --- 0.02 0.29 0 --- --- --- --- --- ---

VDEPOS --- --- --- 0 0.09 0.20 0.01 0 1 --- --- ---

DLTEVA

Cohort 4 --- --- --- 0.01 0 1 --- --- --- --- --- ---

PROTIN

Sheltering --- --- --- --- --- --- 0 0 1 0 0 1 

The MELCOR input variables (SRVLAM, SRVOAFRAC, BATTDUR, and RRIDFRAC) account 

for at least 0% of the variance with a Ti of 0.5 using the MARS analysis to at most 17% of the 

variance with a Ti of 0.52 using the recursive partitioning regression analysis for circular areas 

greater than 2 miles for all non-ranked regression methods and are the second most important 

group of input variables. As discussed in Section 6.1.1 and Section 6.1.2, these MELCOR input

variables account for the majority of the variance for iodine and cesium release fractions and 

timing. 
6-86

The early health effects threshold risk for red bone marrow (EFFTHR-Red Marrow) and the 

early health effects beta (shape) factor for red bone marrow (EFFACB-Red Marrow) inputs 

account for at least 0% of the variance with a Ti of 0.41 using the quadratic regression analysis 

to at most 16% of the variance with a Ti of 0.82 using the MARS analysis for circular areas of 

2.5 to 3.5 miles for all non-ranked regression methods and are the third most important group of 

input variables. Also, EFFTHR-red marrow and EFFACB-red marrow consistently show 

interactions with other input variables. As discussed in greater detail in Section 4.2.4, 

EFFTHR-red marrow and EFFACB-red marrow are important because the hematopoietic 

syndrome has the lowest threshold for an early fatality. 

The amount of shielding between an individual and the source of groundshine for sheltering 

activities for the non-evacuees (GSHRAC-sheltering), the wet deposition parameter (CWASH1),

and a few other important variables also show a significant non-monotonic interaction with other 

input variables. While the overall R2 contribution from these input variables is low, with the 

exception of PROTIN-sheltering at the 2.5-mile circular area, their interactions with other 

variables do justify their consideration for early-fatality risk. 

In the case of PROTIN-sheltering within the 2.5-mile circular area (i.e. see Table 6.2-14), this 

variable has the largest overall non-monotonic variance (i.e., 15-56% of the variance for the 

regression methods considered) and the highest rank for interactions with other input variables 

(Ti). Since this MACCS input variable does not consistently appear as an important variable at 

other distances, it is considered to be a minor overall variable.

6.2.4 Analysis of Single Realizations

Select individual realizations from the uncertainty analysis were further investigated in greater 

detail to identify the influences affecting the predicted consequences. The cases investigated 

are broken into two groups, the MELCOR single realizations discussed in Section 6.1.4, and the 

MACCS Uncertainty Analysis single realizations that resulted in a nonzero early-fatality risk per 

event at the 10–mile circular area. These analyses were conducted from the results from the 

MACCS Uncertainty Analysis. 

6.2.4.1 MELCOR Single Realizations Consequence Analysis

As discussed in Section 6.1.4, the MELCOR single realizations were selected to illustrate the 

influences affecting the cesium released to the environment. Table 6.2-17 provides a brief 

source term description for each MELCOR single realization and associated release timing. 

The SOARCA estimate and SOARCA uncertainty analysis base case source term descriptions 

are also included to provide a comparison. These individual realizations were selected from the 

MACCS Uncertainty Analysis. Based on these results, a comparison of the consequence

impacts was conducted.
6-87 

Table 6.2-17 Brief source term description for the single realizations selected from 

Replicate 1 (STP08) MELCOR Analyses

Scenario

Integral Release Fractions by Chemical Group

Atmospheric 

Release 

Timing

Xe Cs Ba I Te Ru Mo Ce La Start 

(hr) End (hr)

SOARCA 

Estimate 0.978 0.005 0.006 0.020 0.022 0 0.001 0 0 20 48

SOARCA UA 

Base Case 0.981 0.005 0.010 0.025 0.019 0 0 0 0 19.9 48

RLZ018 0.927 0.024 0.019 0.069 0.042 0 0.003 0 0 16.2 48

RLZ051 0.733 0.003 0.010 0.015 0.013 0 0 0 0 17.4 48

RLZ052 0.955 0.021 0.165 0.082 0.056 0 0 0.023 0.001 14.3 48

RLZ062 0.995 0.055 0.014 0.104 0.089 0 0.012 0 0 13.6 48

RLZ063 0.984 0.008 0.015 0.021 0.013 0 0 0.001 0 15.9 48

RLZ086 0.865 0.041 0.040 0.082 0.093 0.001 0.008 0.002 0 12.5 48

RLZ090 0.875 0.053 0.013 0.064 0.029 0 0.013 0 0 14.8 48

RLZ122 0.906 0.038 0.035 0.086 0.046 0 0.007 0.003 0 15.8 48

RLZ134 0.762 0.064 0.147 0.146 0.119 0 0.014 0.020 0 10.8 48

RLZ170 0.985 0.020 0.022 0.031 0.027 0 0 0.001 0 16.6 48

RLZ268 0.797 0.118 0.015 0.073 0.046 0 0.031 0.001 0 18 48

For this work, the early (emergency) phase is defined as the first seven days following the initial 

release to the environment. The long-term phase is defined as the time following the 

emergency phase (i.e., there is no intermediate phase). Figure 6.2-13 shows the conditional, 

mean, individual LCF risk (per event) for all the selected MELCOR single realizations within the 

EPZ for the emergency phase risk contribution (red) and the long-term phase risk contribution 

(blue). The red dots on Figure 6.2-11 are the fraction of cesium in the core released into the 

environment and the orange dots are the fraction of cerium in the core released to the 

environment. Of the LCF risks presented, Realization 52 of Replicate 1 shows the highest 

contribution to LCF risk from the early phase. This is due to the LCF risk contribution to the red 

bone marrow being appreciably higher than the other single realizations in part due to the

following:

• The mortality risk coefficient (CFRISK) for red bone marrow is 0-40% higher than other 

single realizations analyzed,

• The linear, crosswind dispersion coefficient (CYSIGA) is 25-80% lower than other single 

realizations analyzed, and

• The relatively large release of the barium and cerium groups (i.e., see Table 6.2-17).
6-88

Realization 170 of Replicate 1 shows the highest contribution to LCF risk from the long-term 

phase. This is due to the LCF risk contribution to the lungs being appreciably higher than the 

other single realizations in part due to the following:

• The mortality risk coefficient (CFRISK) for lungs is 0-85% higher than other single

realizations analyzed,

• The crosswind dispersion coefficient (CYSIGA) is 5-70% lower than other single 

realizations analyzed,

• The vertical dispersion coefficient (CZSIGA) is 5-70% lower than other single realizations 

analyzed,

• The Pu-240 inhalation dose conversion factor for the lungs is 0-70% higher than other 

single realizations analyzed,

• The Ce-144 inhalation dose conversion factor for the lungs is 5-60% higher than other 

single realizations analyzed, and 

• The largest contribution to long-term inhalation dose is from the cerium group. Of the 

more important isotopes in the cerium group for long-term inhalation doses are Pu-238, 

which has a 87.7 year half-life; Pu-241, which has a 14.4 year half-life; and Ce-144, which

has a 285-day half-life.

When the fraction of cesium released to the environment is compared for all single realizations 

analyzed, there is no direct relationship to the LCF risk in the long-term phase. However, when 

the cesium and cerium release fractions are both considered, a better relationship to long-term 

risk does appear. This can be seen on Figure 6.2-13. 
6-89

Figure 6.2-13 Conditional, mean, individual LCF risk (per event) for MELCOR Replicate 

1 single realizations for the 10-mile circular area

Figure 6.2-14 shows the conditional, mean, individual LCF risk (per event) for the selected 

realizations from Replicate 1 of the MELCOR analyses within the 20-mile circular area for the 

emergency phase risk contribution (red) and the long-term phase risk contribution (blue). The 

red dots on Figure 6.2-14 are the fraction of cesium in the core released into the environment

and the orange dots are the fraction of cerium in the core released to the environment. The 

LCF risk results show emergency phase LCF risk and long-term phase LCF risk are dependent 

on the same input variables discussed for the Figure 6.2-13 results, and those dominated by the 

emergency phase LCF risk (e.g., Realization 52 and Realization 134) further emphasize the 

advantage of emergency phase evacuation within the EPZ (i.e., compare Figure 6.2-13 with 

Figure 6.2-14). 
6-90

Figure 6.2-14 Conditional, mean, individual LCF risk (per event) for MELCOR Replicate 

1 single realizations for the 20-mile circular area

Figures 6.2-15 through 6.2-17 show the conditional, mean, individual LCF risk (per event) 

results for the selected realizations from Replicate1 of MELCOR analyses for the 30-mile, 

40-mile, and 50-mile circular areas respectively. These figures show similar trends to those 

shown on Figure 6.2-14. 
6-91

Figure 6.2-15 Conditional, mean, individual LCF risk (per event) for MELCOR Replicate 

1 single realizations for the 30-mile circular area

Figure 6.2-16 Conditional, mean, individual LCF risk (per event) for MELCOR Replicate 

1 single realizations for the 40-mile circular area
6-92

Figure 6.2-17 Conditional, mean, individual LCF risk (per event) for MELCOR Replicate 

1 single realizations for the 50-mile circular area

The early-fatality risks are zero for all single realizations at the specified circular areas except 

for two realizations. Both Realizations 52 and 134 have nonzero early-fatality risks. This is 

because the release fractions are too low to produce doses large enough to exceed the dose 

thresholds for early fatalities, even for the 0.5% of the population that are modeled as refusing 

to evacuate. With the exception of Realizations 52 and 134, the largest value of the mean, acute 

exposure for the closest resident (i.e., 1.6 to 2.1 kilometers from the plant) for these realizations 

is about 0.56 Gy to the red bone marrow, which is the most sensitive organ for early fatalities, 

but the minimum acute exposure that can cause a early fatality is about 2.3 Gy to the red bone 

marrow. The calculated exposures for these realizations are nearly an order of magnitude

below this threshold.

Table 6.2-18 shows the conditional, mean, individual early-fatality risk (per event) for only the

MELCOR single realizations selected from Replicate 1 which has a nonzero result for specified

circular areas. Realization 52 has early-fatality risks that are larger than the SOARCA Surry 

ISLOCA results (i.e., see Table 6.2-4) and extend to the 5-mile circular area. The only earlyfatality risks are for the cohort that is assumed not to evacuate. 

For the Realization 52 early-fatality risk at 1.3 miles, only 5% of all weather trials resulted in a 

nonzero early-fatality risk. At two miles this increases to 10% of all weather trials. It peaks at 

2.5 miles, where approximately 15% of all weather trials results in a nonzero early-fatality risk. 

Beyond this distance, the number of weather trials that produce a nonzero early-fatality risk

decreases. These weather trials estimate an early-fatality risk according to their associated 

wind direction, wind speed, and stability class combined with a population located in that 

specific wind direction. 
6-93

Table 6.2-18 Conditional, mean, individual early-fatality risk (per event) for the 

MELCOR Replicate 1 single realization nonzero realizations for specified

circular areas 

1.3 miles 2 miles 2.5 miles 3 miles 3.5 miles 5 miles

RLZ52 4.0x10-6 1.3x10-6 8.5x10-7 5.8x10-7 3.2x10-7 8.7x10-8

RLZ134 1.3x10-6 5.0x10-7 3.1x10-7 0.0 0.0 0.0

When Realization 52 was further examined, it was determined that the crosswind dispersion 

coefficient (CYSIGA) parameter was 25-80% lower than the other single realizations analyzed. 

This results in a higher concentration of radionuclides within the plume (and persisting at further 

distances) and subsequently results in a greater inhalation dose. 

For Realization 52, the early-fatality risk is a result of population exceeding the red bone marrow 

threshold. The threshold dose for red bone marrow (EFFTHR-Red Marrow) is 0-75% lower and 

the beta (shape) factor for red bone marrow (EFFTHR-Red Marrow and EFFACB-Red Marrow) 

is 20-80% higher than the other single realizations analyzed. This reduces the dose to the red 

bone marrow that can cause a early fatality.

When the fraction of cesium in the core released to the environment is compared for all 

realizations, there is no relationship to with the early-fatality risk, as expected. Early fatality risk 

is driven by inhalation and direct exposure during the emergency phase, where iodine (and 

perhaps the cerium group) would be most important. Realization 134 had the highest iodine 

release fraction at 14.6%, and the release began at 10.8 hours.

6.2.4.2 MACCS Single Realization Consequence Analysis

During the MACCS Uncertainty Analysis, it was discovered that three of the 865 realizations

have a conditional, mean, individual early-fatality risk (per event) greater than zero out to the 

10-mile circular area. Since this was not expected, a further investigation into these realizations

was conducted. The three realizations of interest are the following: Replicate 2 Realization 

291, Replicate 3 Realization 46, and Replicate 3 Realization 267. None of these realizations 

were selected for the MELCOR single realization analysis discussed in Section 6.1.4. In order 

to better understand these realizations, a time table of the accident sequence is provided in 

Table 6.2-19. Figures 6.2-18 through 6.2-20 provide the reactor and containment pressure 

responses for Replicate 2 Realization 291 (RLZ291), Replicate 3 Realization 46 (RLZ046), and 

Replicate 3 Realization 267 (RLZ267), respectively. 

As documented in Section 6.1.4, there are five factors found to strongly affect the amount of 

radionuclides released to the environment, namely:

(1). whether the SRV fails open before or after the onset of core damage, 

(2). whether a main steam line creep rupture occurs, 

(3). the elapsed time between the onset of core damage and main steam line creep rupture, 

(4). whether a surge of water from the wetwell goes up onto the drywell floor at drywell liner 

melt through, and

(5). whether an overpressure rupture of the wetwell occurs. 
6-94

The first factor identified relates directly to when the SRV fails open, and the RPV is vented to 

the wetwell pool through the failed SRV. Fission products carried by the gas flow venting from 

the RPV are largely scrubbed by the wetwell pool. The earlier the SRV fails open in the core 

degradation process, the more fission products are carried to the wetwell rather than deposited 

in the RPV. If the SRV fails open before the onset of core damage, the venting of released 

fission products directly to the wetwell is maximized.

The second influence identified is if a main steam line creep rupture occurs. The path through 

the failed open SRV to the wetwell pool is bypassed after main steam line failure and gases and 

aerosols from the RPV flow straight to the drywell. From the drywell, fission products are

released to the environment via leakage/failure through the drywell head flange, containment 

failure due to drywell liner melt through, or containment failure due to wetwell rupture above the 

waterline. All of these release paths avoid fission product scrubbing by the suppression pool. 

The third factor similarly relates to the amount of radionuclides deposited in the wetwell. The 

more time that elapses between the onset of core damage and a main steam line creep rupture 

the more time there is for gases venting from the RPV to carry fission products through the 

failed open SRV to the wetwell.

The fourth factor relates to amount of radionuclides that deposit in the suppression pool but fail 

to be contained there. A surge of water from the wetwell goes up onto the drywell floor when 

the containment depressurizes in response to debris contacting the drywell liner and melting 

through it if the hole in the drywell liner is large enough. The suppression pool is saturated at 

the time and is susceptible to flashing in response to depressurization. The vacuum breakers 

between the wetwell and the drywell are overwhelmed and contaminated water from the wetwell 

surges up onto the drywell floor. The water encounters the core debris on the drywell floor and 

evaporates which introduces fission products into the atmosphere and structures of the drywell 

where they become available for release into the environment.

The last factor is a containment failure due to a wetwell rupture above the waterline. The 

breach actually has beneficial impact as it results in the venting of containment through the 

wetwell. The suppression pool provides some scrubbing of fission products from the venting 

gas flowing just above the suppression pool as the fission products make their way through the 

breach.

None of the single realizations have a stochastic SRV failure. For all cases the accident 

scenario is a SRV thermal failure followed by a main steam line creep rupture and ultimate 

containment failure due to wetwell rupture above the water line and drywell head flange failure.
6-95

Table 6.2-19 Timing of key events for MELCOR source terms selected from the three 

replicates for the MACCS single realization analysis

Event

Single Realization

(time in hours unless noted otherwise)

Replicate 2 

RLZ291

Replicate 3 

RLZ046

Replicate 3 

RLZ267

Station blackout loss of all onsite and offsite AC 

power 0.0 0.0 0.0

Low-level 2 and RCIC actuation signal 10 minutes 10 minutes 10 minutes

Operators manually open SRV to depressurize the 

reactor vessel 1.0 1.0 1.0

RPV pressure first drops below LPI setpoint 

(400 psig) 1.2 1.2 1.2

Battery depletion leads immediate SRV re-closure 3.0 2.3 3.0

RCIC steam line floods with water RCIC flow 

terminates 4.8 3.2 4.2

Downcomer water level reaches top of active fuel 8.5 6.9 7.7

First hydrogen production 8.7 7.2 8.0

First fuel cladding gap release 9.6 8.1 9.0

SRV sticks open because of high temperature 

cycling 10.8 9.1 9.9

SRV sticks open because of excessive cycling - - -

Main steam line creep rupture 11.5 10.8 10.7

Drywell head flange leakage begins 11.5 10.8 10.7

Containment failure due to wetwell rupture above 

the waterline 11.5 10.8 10.7

First hydrogen burns initiated in reactor building 11.5 10.8 10.7

Refueling bay to environment blowout panels open 11.5 10.8 10.7

Equipment Lock Door at 135-ft fails due to 

overpressure 11.5 10.8 10.7

Door to environment through railroad access opens 

because of overpressure 11.5 10.8 10.7

Refueling bay roof fails due to overpressure 11.5 10.8 10.7

Time iodine release to environment exceeds 0.1% 

of initial core inventory 11.5 11.0 10.7

Lower head dries out 12.1 11.2 11.9

Lower head failure 16.7 16.0 16.8

Drywell shell melt-through initiated 17.0 16.2 17.0

Calculation terminated 48.0 48.0 48.0
6-96

Figure 6.2-18 MELCOR Replicate 2 Realization 291 reactor and containment pressure 

response

Figure 6.2-19 MELCOR Replicate 3 Realization 046 reactor and containment pressure 

response
6-97

Figure 6.2-20 MELCOR Replicate 3 Realization 267 reactor and containment pressure 

response

The single realizations were selected to identify the influences affecting the conditional, mean, 

individual early-fatality risk (per event) results. Table 6.2-20 provides a brief source term 

description for each MACCS single realization and subsequent release timing. The SOARCA 

estimate and SOARCA uncertainty analysis base case source term descriptions are also 

included to provide a comparison. The three individual realizations were selected from the 

MACCS Uncertainty Analysis. Based on these results, a comparison of the environmental 

impacts was conducted.

Table 6.2-20 Brief source term description for the MELCOR source terms selected from 

the three replicates for the CAP17 MACCS Uncertainty Analysis of single 

realizations

Scenario

Integral Release Fractions by Chemical Group

Atmospheric 

Release 

Timing

Xe Cs Ba I Te Ru Mo Ce La Start 

(hr)

End 

(hr)

SOARCA 

Estimate 0.978 0.005 0.006 0.020 0.022 0 0.001 0 0 20 48

SOARCA UA 

Base Case 0.981 0.005 0.010 0.025 0.019 0 0 0 0 19.9 48

Replicate 2

RLZ291 0.792 0.085 0.134 0.160 0.132 0 0.019 0.012 0 11.5 48

Replicate 3

RLZ046 0.672 0.099 0.170 0.109 0.097 0 0.025 0.023 0.001 10.8 48

Replicate 3 

RLZ267 0.876 0.102 0.178 0.139 0.125 0 0.024 0.031 0.001 10.7 48
6-98

Table 6.2-21 shows the conditional, mean, individual LCF risk (per event) for the MACCS

Uncertainty Analysis single realizations for the specified circular areas. All LCF risks are above

the 95th percentile of the MACCS Uncertainty Analysis (i.e., see Table 6.2-2) for all replicates

except for the 10-mile, circular area for all replicates, which are about the median. 

Table 6.2-21 Conditional, mean, individual LCF risk (per event) for the MACCS

Uncertainty Analysis single realizations for specified circular areas for 

MELCOR source terms selected from the three replicates

RLZ291 RLZ046 RLZ267

10 miles 1.3x10-4 1.5x10-4 1.2x10-4

20 miles 1.5x10-3 3.3x10-3 1.5x10-3

30 miles 1.2x10-3 2.3x10-3 1.1x10-3

40 miles 7.7x10-4 1.3x10-3 6.6x10-4

50 miles 6.1x10-4 1.0x10-3 5.1x10-4

Figure 6.2-21 shows the conditional, mean, individual LCF risk (per event) for the MACCS

Uncertainty Analysis realizations within the EPZ for the emergency phase risk contribution (red) 

and the long-term phase risk contribution (blue). Of the LCF risks presented, the Replicate 3 

Realization 46 shows the highest contribution to LCF risk from the early phase. This is due to 

the LCF risk contribution to the red bone marrow and lungs and is influenced by the following 

input parameters:

• The mortality risk coefficient (CFRISK) for red bone marrow is 5-20% higher than the 

other realizations analyzed, 

• The vertical dispersion coefficient (CZSIGA)is 35-80% lower than the other realizations 

analyzed, 

• The Ce-141 long-term inhalation dose conversion factor for the lungs is 15-30% higher 

than the other realizations analyzed, 

• The Cs-134 long-term inhalation dose conversion factor for the red bone marrow is 35% 

to 50% higher than the other realizations analyzed, 

• The Pu-238 long-term inhalation dose conversion factor for red bone marrow is 5-95% 

higher than other realizations analyzed,

• The Pu-240 long-term inhalation dose conversion factor for the lungs is 10-75% higher 

than the other realizations analyzed,

• The Pu-241 long-term inhalation dose conversion factor for the lungs is 10-35% higher 

than the other realizations analyzed,

• The Te-129m long-term inhalation dose conversion factor for the lungs is 5-35% higher 

than the other realizations analyzed,

• The Sr-90 long-term inhalation dose conversion factor for the red bone marrow is 5-35%

higher than the other realizations analyzed, and, 
6-99

• The relatively large releases of the cesium, barium, cerium, and iodine groups (i.e., see

Table 6.2-20).

• The relatively earlier start of release (see Table 6.2-20), 10.7-11.5 hours versus ~20 hours 

for the SOARCA estimate and the UA base case.

Replicate 2 Realization 291 has the highest contribution to LCF risk from the long-term phase. 

This is due to the LCF risk contribution to the breast is higher than the other two realizations 

analyzed in part due to the following:

• The mortality risk coefficient (CFRISK) for the breast is 10-65% higher than the other 

realizations analyzed, 

• The crosswind dispersion coefficient (CYSIGA)is 10-85% lower than the other realizations 

analyzed, 

• The long-term groundshine shielding factor (LGSHFRAC) is 45-75% higher (i.e., 1 = No 

shielding protection) than the other realizations analyzed, 

• The Pu-240 long-term inhalation dose conversion factor for the breast is 10-95% higher 

than the other realizations analyzed and, 

• The Pu-241 long-term inhalation dose conversion factor for the breast is 65-80% higher 

than the other realizations analyzed. 

Figure 6.2-21 Conditional, mean, individual LCF risk (per event) MACCS Uncertainty 

Analysis single realizations for the 10-mile circular area
6-100

Figure 6.2-22 shows the conditional, mean, individual LCF risk (per event) for the MACCS

Uncertainty Analysis single realizations within the 20-mile circular area for the emergency phase 

risk contribution (red) and the long-term phase risk contribution (blue). The LCF risk results 

show that the emergency phase LCF risk and long-term phase LCF risk are dependent on the 

same input variables discussed for the Figure 6.2-21 results, and those are dominated by the 

emergency phase risk. 

Figure 6.2-22 Conditional, mean, individual LCF risk (per event) MACCS Uncertainty 

Analysis single realizations for the 20-mile circular area

Figures 6.2-23 through 6.2-25 show the conditional, mean, individual LCF risk (per event) 

MACCS Uncertainty Analysis single realization results for the 30-mile, 40-mile, and 50-mile 

circular areas respectively. These figures show similar trends to those shown on Figure 6.2-23. 
6-101

Figure 6.2-23 Conditional, mean, individual LCF risk (per event) MACCS Uncertainty 

Analysis single realizations for the 30-mile circular area

Figure 6.2-24 Conditional, mean, individual LCF risk (per event) MACCS Uncertainty 

Analysis single realizations for the 40-mile circular area
6-102

Figure 6.2-25 Conditional, mean, individual LCF risk (per event) MACCS Uncertainty 

Analysis single realizations for the 50-mile circular area

Table 6.2-22 and Figure 6.2-26 show the conditional, mean, individual early-fatality risk (per 

event) for the MACCS Uncertainty Analysis single realizations for specified circular areas. All 

early-fatality risks are above the mean and the 95th percentile of the MACCS Uncertainty 

Analysis for specified circular areas (i.e., see Table 6.2-5). 

Table 6.2-22 Conditional, mean, individual early-fatality risk (per event) for the 

MACCS single realizations for specified circular areas 

RLZ291 RLZ046 RLZ267

1.3 miles 1.8x10-5 8.1x10-6 6.9x10-6

2 miles 1.5x10-5 4.7x10-6 4.8x10-6

2.5 miles 1.3x10-5 4.0x10-6 3.9x10-6

3 miles 1.1x10-5 3.1x10-6 3.3x10-6

3.5 miles 8.9x10-6 2.0x10-6 2.2x10-6

5 miles 5.8x10-6 7.8x10-7 1.0x10-6

7 miles 4.8x10-6 4.2x10-7 5.7x10-7

10 miles 3.7x10-6 1.9x10-7 2.9x10-7
6-103

For Replicate 2 Realization 291 early-fatality risk at the 1.3-mile circular area, only 10 of the

all-weather trials resulted in a nonzero early-fatality risk. From the 2-mile to 10–mile circular 

areas this increases to 50% or greater of all-weather trials. This is due to increasing 

populations beyond 1.3 miles and a tighter plume allows a persistent concentration out to further 

distances. For Replicate 3 Realization 46 early-fatality risk at the 1.3-mile circular area, only 5% 

of all weather trials resulted in a nonzero early-fatality risk. From the 2-mile to 10–mile circular 

areas, 10% of all weather trials result in a nonzero early-fatality risk. For Replicate 3 Realization 

267 early-fatality risk at the 1.3-mile to 10-mile circular areas, 10% of all weather trials result in a 

nonzero early-fatality risk. 

Figure 6.2-26 Conditional, mean, individual early-fatality risk (per event) MACCS

Uncertainty Analysis single realizations for specified circular areas 

Of the realizations listed in Table 6.2-22, Replicate 2 Realization 291 produced the highest 

early-fatality risks per event at the specified circular areas. When Replicate 2 Realization 291

was further examined, it determined that the crosswind dispersion coefficient (CYSIGA) is 10% 

to 85% lower than all other realizations analyzed. Also the vertical dispersion coefficients 

(CZSIGA) are 15% to 55% lower than all other realizations analyzed. This results in a higher 

concentration of radionuclides within the plume and in a greater inhalation dose. 

For Replicate 2 Realization 291, the early-fatality risk is a result of population exceeding the red 

bone marrow exposure limit. This is due in part to the early-fatality risk contribution for the red 

bone marrow from following input parameters:
6-104

• The early health effects threshold risk for red bone marrow (EFFTHR-Red Marrow) is 40% 

to 80% lower and the beta (shape) factor for red bone marrow (EFFACB-Red Marrow) is 

5% to 15% higher than the other realizations analyzed. This reduces the dose to the red 

bone marrow that can cause a early fatality.

• The cloudshine shielding factor for sheltering (CSFACT - sheltering) is 75% to 85% higher

(i.e., 1 = No shielding protection) than the other realizations analyzed, 

• The crosswind dispersion coefficient (CYSIGA) is 10% to 90% lower than the other 

realizations analyzed, 

• The vertical dispersion coefficient (CZSIGA) is 10% to 55% lower than the other 

realizations analyzed,

• The peak dose to the red bone marrow within a 10 mile circular area is 60% to 70% higher 

than the other realizations analyzed, and

• The relatively large releases of the iodine and tellurium groups compared to the other 

realizations analyzed (i.e., see Table 6.2-19).

Beyond the 10-mile circular area for Replicate 3 Realization 46 and Replicate 3 Realization 267, 

there is no early-fatality risk for any weather trial (i.e., the conditional, mean, individual earlyfatality risk (per event) = 0.00). For these two realizations, the weather trials produced an earlyfatality risk due to their associated wind direction, wind speed, and stability class combined with 

the proximity of residents in the specified wind. 

For Replicate 2 Realization 291, there is a nonzero early-fatality risk beyond the 10-mile circular 

area and can be seen in Table 6.2-23. The noticeable increase in early-fatality risk beyond the 

10-mile circular area is due to the population beyond 10 mile does not evacuate, except for 

those in the 10-20 mile shadow evacuation for Cohort 2. As a result, the early fatality risk 

beyond 10 miles increases by two orders of magnitude.

From Table 6.2-23, the peak, conditional, mean, individual early-fatality risk is 1.4 x 10-4 per 

event at 13 miles. The core damage frequency for the unmitigated LTSBO event is 

~3 x 10-6 pry. Thus the absolute early-fatality risk within 13 miles of the plant is ~4 x 10-10 pry. 

In this one realization (out of 865), 50% or greater of all-weather trials result in a nonzero early

fatality risk out to 30 miles. 

Table 6.2-23 Conditional, mean, individual early-fatality risk (per event) for the MACCS

single realizations for specified circular areas beyond 10 miles

RLZ291 RLZ046 RLZ267

10 miles 3.7x10-6 1.9x10-7 2.9x10-7 

13 miles 1.4x10-4 0.0 0.0

16 miles 1.3x10-4 0.0 0.0

20 miles 1.1x10-4 0.0 0.0

25 miles 8.4x10-5 0.0 0.0

30 miles 5.4x10-5 0.0 0.0

40 miles 0.0 0.0 0.0
6-105

While the early fatality risk results for Replicate 2 Realization 291 are extreme, further 

investigation into the parameters that affected these results does not indicate the source term 

as a main cause. Instead, the MACCS parameters previously discussed for Replicate 2 

Realization 291, which have a higher early-fatality risk contribution for the red bone marrow, are 

also contributing to the early fatality risk beyond 10 miles. Specifically the following variables 

are at the extreme ends (the end which results in higher early fatality risk) of their respective 

distributions: 

• The EFFTHR for red bone marrow is near the 1st percentile of the distribution,

• The EFFACB for red bone marrow is near the 10th percentile of the distribution,

• The CSFACT for sheltering is near the 80th percentile of the distribution, 

• The CYSIGA is near the 5th percentile of the distribution, 

• The CZSIGA is near the 5th percentile of the distribution and,

• The source term is near the 95th percentile of the distribution. 
6-106

6.3 Summary of Phenomena Important to Uncertainty in Analysis 

Results

6.3.1 Source Term Analysis

Four outputs were selected from the source term results estimated via MELCOR to be analyzed 

using regression techniques. These outputs are the fraction of iodine released to the 

environment, time it took to release 0.1% of the iodine inventory (i.e., a release fraction of 

0.001), environmental fraction of cesium released, and the in-vessel hydrogen production. One 

of the most important parameters, both for amount of radionuclide release and hydrogen 

production is the uncertainty in lambda for the SRV stochastic failure to reclose (SRVLAM – 

described in Section 4.1.1) which sets the expected number of cycles occurring before the 

safety valve fails to reclose. It has a strong negative monotonic influence (indicating that low 

values of lambda leads to higher releases) as indicated by SRRC results. This affects results 

because longer SRV valve cycling will cause a thermal seizure of the SRV and potential main 

steam line creep rupture, in both cases yielding a higher degree of core degradation. This 

ultimately leads to a larger source term release to the environment. Other regressions 

techniques indicate that it also has non-monotonic and conjoint influence. The conjoint 

influence is partly shared with the SRV open area fraction after thermal seizure (SRVOAFRAC –

see section 4.1.2) whose effect appears to be non-monotonic (rank regression captures only a 

small fraction of its influence) for the radionuclide fractional releases. As discussed in 

Section 6.1.4, SRVOAFRAC is an important determinant to whether a MSL creep rupture 

occurs. Smaller stuck-open areas relieve steam more slowly and so lead to protracted higher 

pressures. Higher pressures result in elevated stresses in the MSL piping which combine with 

elevated temperatures to accumulate creep damage over time that can lead to an MSL rupture. 

Combined, these parameters control the type of failure (SRV stochastic, SRV thermal seizure or 

SRV thermal seizure with MLS creep rupture). The importance of failure mode clearly visible on 

Figure 6.1-7 shows the major role of SRVLAM.

The independent regression analyses for each of the failure modes (SRV stochastic, SRV 

thermal seizure or SRV thermal seizure with MLS creep rupture) identified additional important 

parameters and phenomena, as presented in Section 6.1.4. For realizations with only a 

stochastic SRV failure, fractional releases of iodine and cesium are also sensitive to drywell 

liner failure flow area (FL904A). There is a correlation between the uncertainty in the drywell 

liner breach size and whether a surge of water from the wetwell occurs as displayed for the 

cesium releases on Figure 6.1-11. Larger breach sizes cause stronger containment 

depressurizations. The water encounters the core debris on the drywell floor and evaporates 

introducing its inventory of fission products to the atmosphere and structures of the drywell 

where they are available for release to the environment. Due to the larger releases in case of 

thermal seizure of the SRV, with or without an MSL creep rupture, the influence of FL904A is 

negligible for these failure modes. Finally, the chemical form of iodine and cesium, separated 

by the discrete input variable CHEMFORM, can be added to the list of the influential parameters 

for iodine and cesium release fractions for all three failure modes. The influence relates to the 

amount of iodine in iodine gas fraction and the cesium permanently deposited in the RPV via 

chemisorption of cesium from CsOH onto the stainless steel of reactor internals. This influence 

is only pertinent for the realizations that have all or some of the reactor core cesium inventory 

present as CsOH. The chemisorption was more extensive in realizations that experienced 

higher RPV temperatures, which very strongly influenced the amount of cesium released to the 

environment as displayed on Figure 6.1-10. Other important phenomena that that are identified 

to a lesser degree in the analyses includes the occurrence of a thermal updraft that develops in 

the reactor building if the railroad doors are blown open by a hydrogen deflagration 

(RRDOORS).
6-107

The sensitivity analysis for hydrogen production identifies (after SRVLAM) the Zircaloy melt 

breakout temperature (SC1131_2 described in section 4.1.2) and, to a lesser extent Molten clad 

drainage rate (SC1141_2 section 4.1.2) as important parameters. The effect of SC1131_2 on 

the hydrogen production is as expected (as indicated in its description in section 4.1.2). The 

effect of SC1141_2 is also not surprising as it affects the overall melt progression behavior (and 

is one of the few melt progression parameter available for uncertainty analysis).

The duration of battery (BATTDUR) does not seem to affect (or only in a marginal way) the 

amount of radionuclide released or hydrogen production. However, it has a large effect on the 

time the release will start as seen in the regression over the time it takes to release 10-3 of the 

iodine inventory (Table 6.1-5). BATTDUR explains between 30% and 40% of the uncertainty. 

6.3.2 Consequence Analysis

The results generated by MACCS, conditional, mean, individual latent cancer fatality (LCF) risk 

(per event) and conditional, mean, individual early-fatality risk (per event), have been evaluated

using regression techniques. These MACCS analyses are based on the linear no-threshold 

dose-response model. Influential parameters are presented in two groups: (1) the input 

parameters inherited from the source term regression (i.e., MELCOR input parameters), and 

(2) MACCS specific inputs.

The analysis of conditional, mean, individual LCF risk (per event) produces consistent results for

the most influential parameters at all circular areas considered (i.e., 10-mile, 20-mile, 30-mile, 

40-mile and 50- mile). Since the MELCOR source terms are used as inputs for the MACCS

code, it is not surprising that three of the MELCOR parameters (i.e., SRVLAM, fuel failure 

criterion, and FL904A) appear as important in the regression analysis of MACCS LCF risk 

results. 

For MACCS specific parameters, the most important variable is the dry deposition velocity 

(VDEPOS) which accounts for at least 9% of the variance with a Ti of 0.18 using the quadratic 

regression analysis to at most 33% of the variance with a Ti of 0.37 using the MARS analysis for 

LCF risk depending on the technique used and the distance evaluated, and the median value

accounts for around 17% of the variance. Thus VDEPOS is slightly more influential on the 

variance than the MELCOR input group. The VDEPOS uncertainty distribution is described in 

Section 4.2.2. 

Two other consistently important MACCS parameters are the mortality risk coefficient for 

residual cancers (CFRISK-residual) and the dose and dose rate effectiveness factor for residual 

cancer (DDREFA – residual). These two parameters account for at least 0% of the variance 

with a Ti of 0.12 using the recursive partitioning regression analysis to at most 23% of the 

variance with a Ti of 0.25 using the MARS analysis for LCF risk depending on the technique 

used and the distance evaluated, and the median value accounts for around 12% of the 

variance. The CFRISK and DDREFA uncertainty distributions are described in Section 4.2.5.

The regression analysis for conditional, mean, individual early-fatality risk (per event) shows 

some variation in the most important parameters depending on the distance. As with LCF risk, 

MELCOR input parameters (i.e., SRVLAM, SRVOAFRAC, and BATTDUR) are identified as 

important parameters. However, FL904A is not identified as an important input parameter. 

BATTDUR makes sense here since release timing is important for early fatality risk. This group 

accounts for at least 0% of the variance with a Ti of 0.5 using the MARS analysis to at most 

17% of the variance with a Ti of 0.6 using the recursive partitioning regression analysis for earlyfatality risk depending on the technique used and the circular area evaluated. The median

value is around 7% of the variance at shorter distances (i.e., 1.3-mile and 2-mile circular areas) 
6-108

and falls to 3% of the variance when the distance increases (i.e., 2.5-mile, 3-mile, and 3.5-mile 

circular areas).

At short distances (i.e., 1.3-mile and 2-mile circular areas) the most important MACCS input 

parameter is the wet deposition parameter (CWASH1) with mostly non-monotonic and conjoint 

influence and is identified with all three non-additive and non-monotonic regressions techniques. 

This variable explains at least 4% of the variance with a Ti of 0.78 using the MARS analysis to 

at most 29% of the variance with a Ti of 0.76 using the quadratic regression analysis for earlyfatality risk depending on the technique used and the circular area evaluated, and the median 

value is around 12% of the variance at the shorter distances. This influence at short distance is 

expected since wet deposition is very effective and rapidly depletes the plume. The CWASH1 

uncertainty distribution is described in Section 4.2.1. 

At longer distances (i.e., 2.5-mile, 3-mile, and 3.5-mile circular areas), the variation in 

early-fatality risk is more heavily influenced by horizontal dispersion than by the washout

coefficient. For these distances, the crosswind dispersion coefficient (CYSIGA) becomes the 

most important parameter with CWASH1 becoming of marginal importance. This variable 

explains at least 0% of the variance with a Ti of 0.16 using the quadratic regression analysis to 

at most 81% of the variance with a Ti of 0.25 using the recursive partitioning regression analysis

for early-fatality risk depending on the technique used and the circular area evaluated, and the 

median value is around 1% of the variance at the longer distances. The CYSIGA uncertainty 

distribution is described in Section 4.2.6.

Parameters consistently important, but not as important as CWASH1 within 2 miles and not as 

important as CYSIGA beyond 2 miles, are the early fatality threshold for red bone marrow 

(EFFTHR–Red Marrow) and the early health effects beta (shape) factor for red bone marrow 

(EFFACB-Red Marrow). At longer distances (i.e., 2.5-mile, 3-mile, and 3.5-mile circular areas), 

these two variables account for at least 0% of the variance with a Ti of 0.41 using the quadratic 

regression analysis to at most 16% of the variance with a Ti of 0.82 using the MARS analysis for 

early-fatality risk depending on the technique used an the circular area evaluated, and are the 

third most important group of input variables. The median value is around 4% of the variance at 

the longer distances. Also, EFFTHR-red marrow and EFFACB-red marrow consistently show 

interactions with other input variables. The EFFTHR-red marrow and EFFACB-red marrow 

uncertainty distributions are described in Section 4.2.4.
6-109

6.4 Separate Sensitivity Studies 

Some sensitivity studies were conducted as part of the original SOARCA project. These are 

documented in NUREG-1935 [1] and NUREG/CR-7110 Volume 1 [2]. During the course of 

conducting this uncertainty analysis, other sensitivity studies were suggested by UA team 

members, or external reviewers such as the SOARCA peer review panel and the NRC ACRS. 

The separate sensitivity studies conducted in conjunction with this UA are documented in this 

section. 

6.4.1 Manual Control of the Safety Relief Valve (Operator Actions)

A sensitivity study was carried out to determine the effect of manual operation of the SRV. For 

this study, the SOARCA uncertainty analysis unmitigated LTSBO scenario was used. The 

SOARCA uncertainty analysis base case is the current estimate SOARCA case with the 

updates described in Appendix C. The updates include temporal convergence adjustments, 

near equilibrium model turned off, the use of CHEMFORM #5, bottom elevation of separator 

control volume modification, addition of check valve in the vacuum breaker line (FL904A water 

from wetwell relationship) modification, and addition of FL904A open area growth rate. 

MELCOR 1.8.6 Version YV3780 was employed for the subsequent cases.

The study varied the manual opening time of a single SRV. In order to depressurize the reactor 

vessel in a controlled manner, operators can manually open a SRV, as described in the station 

emergency procedures, in order to prevent excessive cycling of the SRVs (NUREG/CR-7110 

Volume I [2]). The base case opened the SRV at 1.0 hours after the initiating event. The three 

variations on the base case open the SRV at 0.5 hours, 2.0 hours, and 3.0 hours. Finally, a 

bounding case is run with no manual SRV opening in order to quantify the effects of excessive 

SRV cycling. 

Table 6.4-1 lists the timing of key events for the base case of manual SRV operation at 

0.5 hours, 1.0 hours, 2.0 hours, and 3.0 hours. The only case that differs significantly from the 

base case (SRV open at 1.0 hour) is the case with SRV opening at 0.5 hours. By opening the 

SRV a half hour earlier than the base case, most key events occur about four hours earlier than 

the base case; i.e. the accident progression is accelerated with earlier SRV opening. However, 

this effect is probably being caused by an unrealistic change in the RCIC operation. Manually 

opening the SRV at 0.5 hours causes the RPV pressure to drop below the RCIC turbine trip 

pressure (75 psig), which terminates the RCIC injection into the feedwater lines three hours 

before the base case. In reality, the operators would not allow the steam line pressure to drop 

so low to trip the RCIC. With manual SRV operation at 2.0 hours, most of the key events are in 

close agreement to the base 1.0 hour case; however, some events occur about 1 hour later 

than the base case. Similarly, with manual SRV operation at 3.0 hours, the timings of most 

important events are close to the 1.0 hour case, and some events in the 3.0 hour case occurring 

slightly later (~1.5 hr).
6-110

Table 6.4-1 Timing of key events for Peach Bottom Unmitigated LTSBO, manual SRV 

operation action at 0.5 hr, 1.0 hr, 2.0 hr and 3.0 hr

Event

LTSBO with 4 hr DC power (time in hours unless noted otherwise)

UA SOARCA 

MELCOR 1.8.6 

Version 

YV3780, SRV 

Manual 

Operation at 

1.0 hr

UA SOARCA 

MELCOR 

1.8.6 Version 

YV3780, SRV 

Manual 

Operation at 

0.5 hr

UA SOARCA 

MELCOR 

1.8.6 Version 

YV3780, SRV 

Manual 

Operation at 

2.0 hr

UA SOARCA 

MELCOR 

1.8.6 Version 

YV3780, SRV 

Manual 

Operation at 

3.0 hr

UA SOARCA 

MELCOR 

1.8.6 Version 

YV3780, No 

SRV Manual 

operation

Station blackout loss of all 

onsite and offsite AC power, 

reactor scram

0.00 0.00 0.00 0.00 0.00

Low-level 2 and RCIC 

actuation signal 0.17 0.17 0.17 0.17 0.17

Operators manually open 

SRV to depressurize the 

reactor vessel

1.0 0.50 2.0 3.0 NA

RPV pressure first drops 

below LPI setpoint 

(400 psig)

1.2 0.77 2.3 3.3 4.9

Battery depletion leads 

immediate SRV re-closure 4.0 4.0 4.0 4.0 4.0

RCIC trip due to low steam 

line pressure (75 psig) -- 2.1 -- -- -- 

RCIC steam line floods with 

water RCIC flow terminates 5.2 -- 5.3 4.8 -- 

SRV sticks open because of 

excessive cycling 8.2 6.4 7.9 7.5 4.6

Downcomer water level 

reaches top of active fuel 8.4 0.71 8.2 8.1 5.0

First hydrogen production 8.6 4.4 8.4 8.4 5.4

First fuel-cladding gap 

release 9.1 5.3 9.0 9.1 6.2

First channel box failure 9.4 5.7 9.4 9.4 6.5

Reactor vessel water level 

reaches bottom of core 

support plate

9.4 6.7 9.3 9.0 6.6

First localized failure of core

support plate 10.7 7.5 10.6 10.8 8.4

First core cell collapse 

because of time at 

temperature

10.0 6.2 9.9 10.0 7.0

Beginning of large-scale 

relocation of core debris to 

lower plenum

10.7 7.5 10.6 10.8 8.4

Lower head dries out 12.1 9.2 12.5 13.4 10.2
6-111

Table 6.4-1 Timing of key events for Peach Bottom Unmitigated LTSBO, manual SRV 

operation action at 0.5 hr, 1.0 hr, 2.0 hr and 3.0 hr (continued)

Event

LTSBO with 4 hr DC power (time in hours unless noted otherwise)

UA SOARCA 

MELCOR 1.8.6 

Version 

YV3780, SRV 

Manual 

Operation at 1.0 

hr

UA SOARCA 

MELCOR 

1.8.6 Version 

YV3780, SRV 

Manual 

Operation at 

0.5 hr

UA SOARCA 

MELCOR 

1.8.6 Version 

YV3780, SRV 

Manual 

Operation at 

2.0 hr

UA SOARCA 

MELCOR 

1.8.6 Version 

YV3780, SRV 

Manual 

Operation at 

3.0 hr

UA SOARCA 

MELCOR 

1.8.6 Version 

YV3780, No 

SRV Manual 

Operation

Ring 5 CRGT column 

collapse 16.1 12.6 16.6 17.6 12.9

Ring 3 CRGT column 

collapse 16.9 13.4 17.2 18.4 12.9

Ring 4 CRGT column 

collapse 17.0 13.5 16.7 18.8 12.9

Ring 1 CRGT column 

collapse 17.4 12.7 17.4 17.4 16.7

Ring 2 CRGT column 

collapse 17.5 12.6 18.6 18.8 12.9

Lower head failure 19.8 15.9 20.9 21.2 17.5

Drywell head flange 

leakage begins 19.9 15.9 20.9 19.7 17.5

Hydrogen burns initiated in 

drywell enclosure region of 

reactor building

19.9 15.9 21.0 20.0

17.5

Refueling bay to 

environment blowout 

panels open

19.9 15.9 21.0 21.3

17.5

Hydrogen burns initiated in 

reactor building refueling 

bay

20.1 16.2 21.2 21.4

17.8

Drywell shell melt-through 

initiated and drywell head 

flange re-closure

20.0 16.1 21.2 21.5

17.8

Hydrogen burns initiated in 

lower reactor building 20.0 16.1 21.2 21.5 17.8

Door to environment 

through railroad access 

opens because of 

overpressure

20.0 16.1 21.2 21.5

17.8

Equipment Lock Door at 

135-ft fails due to 

overpressure

20.0 16.1 21.2 21.5

17.8

Time iodine release to 

environment exceeds 1% 

of initial core inventory

22.8 16.2 21.3 21.6

20.9

Calculation terminated 48.0 48.0 48.0 48.0 48.0
6-112

As a metric for comparison, cesium and iodine release to the environment are used to compare 

the environmental release. For this comparison the only release pathways considered 

(i.e., refueling bay blowout panels and the equipment lock door at 135 feet above ground level) 

are those which would be carried over into the MACCS analysis. 

As shown on Figure 6.4-1, the initial iodine release to the environment is highest (8.7x10-2), and 

occurs about four hours earlier, for the case with manual operation at 0.5 hours compared to the 

base case of 1.0 hour. This can be attributed to the earlier uncovering of the core and ultimately 

earlier lower head and containment failure, due to the early loss of RCIC injection (i.e., turbine 

tripped on low pressure). Similarly, when no manual SRV operation action was taken, RCIC 

operation was negatively impacted due to excessive SRV cycling and ultimately the failure of 

the SRV in the open position. The higher iodine release in this case is due to revaporization 

from hotter internal structures. Manual SRV operation at 2.0 hours and 3.0 hours, along with 

the case with no SRV opening, results exhibit similar release fractions to the base case of 

1.0 hour; the final iodine release fractions for these cases are between 2.5x10-2 and 4.0x10-2. 

The same trends exist for the cesium release fractions to the environment, as shown on 

Figure 6.4-2. Manual opening of the SRV at 0.5 hours results in the greatest release of cesium 

to the environment (4.1x10-2). The other cases have lower release fractions between 6x10-3 to 

9x10-3. 

Figure 6.4-1 Environmental iodine release fraction for UA SOARCA sensitivity cases 

for the manual control of the SRV
6-113

Figure 6.4-2 Environmental cesium release fraction for UA SOARCA sensitivity cases 

for the manual control of the SRV

Based on the results of the sensitivity study, early manual operation (opening at 0.5 hours) of 

the SRVs would lead to larger environmental consequences. The early opening of the SRV 

depressurizes the reactor below 75 psig, which trips the RCIC system since it is a steam driven 

system. This action terminates the RCIC injection into the feedwater lines (suction is from the 

condensate storage tank), leading to less core makeup water being delivered to the reactor.

6.4.2 Sensitivity of Fission Product Release to Reactor Lower Head Penetration 

Failures

In response to a concern raised in an ACRS review letter [94], a sensitivity study was carried 

out late in the uncertainty analysis to investigate the dependence of fission product releases to 

the environment on the mode of RPV lower head failure. The concern was with respect to 

whether the MELCOR release predictions for the LTSBO scenario would change if lower head 

penetration failures were considered as a means of core debris relocating from the RPV to the 

reactor cavity. RPV lower head failure in the SOARCA estimate calculations, and in the subject 

uncertainty calculations, was considered to only occur by gross “creep” failure. The sensitivity 

study was carried out by varying certain input parameters of the available MELCOR penetration 

model, acknowledging that the model is parametric in nature with known limitations. Cesium 

release to the environment was the metric considered.
6-114

The melt ejection model in MELCOR for penetrations is designed to model the failure of a 

penetration and melt ejection through it at high pressure. It includes an ablation model, which is 

a simplified version of one developed from the Hi-Pressure Melt Streaming (HIPS) tests [61]. 

Although the HIPS tests were high pressure ejection tests, the ablation model is based on 

user-specified heat transfer coefficients and an energy balance and so is probably applicable to 

low pressure scenarios (such as the SOARCA LTSBO). Important with respect to the capability 

of the penetration model is that is lacks provisions for calculating molten material flow through 

an instrument guide tube or predicting the plugging of an open penetration by freezing melt.

The penetration model sensitivity study focused primarily on the number of penetrations that 

might fail. The Peach Bottom lower head has penetrations that accommodate control blades 

and instrument tubes. Additionally, the head accommodates a drain line at its lowest point. The 

ACRS concern is most specific to the failure of the penetration accommodating the drain line, 

pointing out that it may be the most vulnerable penetration [62]. Peach Bottom has 55 

instrument tubes. The sensitivity study involved a set of 50 MELCOR calculations in which a 

varying number of penetrations, representative of 1.5-inch diameter instrument tube 

penetrations, was represented. The penetrations were defined in groups of between 1 and 11 

penetrations for each of the 5 radial rings of the active core nodalization. The calculations were 

run to 48 hours. The resulting open area in the lower head in the calculations, given that 

penetrations in some rings failed while penetrations in other rings didn’t, varied between 

0.0024 m2 and 0.0423 m2 averaging 0.01487 m2

. This relates to the area of between 2.2 and 

38.4 instrument tubes averaging the area of 13.5 instrument tubes. The smaller areas of this 

range are thought to account for the drain line vulnerability identified by the ACRS. 

Two other parameters were varied (sampled) in the MELCOR calculations in addition to the 

number of penetrations represented. These parameters were the heat transfer coefficient 

between the penetrations and core debris and the temperature at which a penetration would fail. 

The heat transfer coefficient was varied between half and twice the MELCOR default value of 

1,000 W/m2-K while the failure temperature was varied between 1,500 K and 1,700 K.

Of the 50 MELCOR calculations, seven failed to complete and two progressed to a gross creep 

failure of the lower head. In all but three of the calculations, core debris migrated to and melted 

through the drywell liner. Penetration failures generally occurred 3 hours before the gross lower 

head failure in the base uncertainty calculation. This timing difference was relatively insensitive 

to variations in the sampled input parameters. Relocation of core debris to the reactor cavity 

through penetrations generally began within 6 minutes of the first penetration failure once 

appreciable molten material resided near the penetration. The penetrations did not ablate 

significantly. Fractional releases of cesium to the environment showed the statistics:

• Min: 0.0063

• Mean: 0.0372

• Median: 0.0418

• Max: 0.0701

Comparing these statistics to the fractional cesium release of 0.0052 in the base uncertainty 

calculation, which did not consider the possibility of penetration failures, suggests a marked 

increase in release if penetration failures are considered. Characteristics of the sensitivity 

calculations fundamental to their cesium releases were: 
6-115 

• Calculations experiencing greater and extended degrees of cladding/steel oxidation within 

the reactor vessel, as evidenced by in-vessel hydrogen production, exhibited larger 

releases of cesium to the environment. The releases can be traced to late revaporization 

of material deposited on reactor internals during core degradation as evidenced in 

Figure 6.4-3 for one of the high-release calculations. On this figure, the increasing cesium 

in the environment mirrors the decreasing cesium on “Lower RPV” structures. The 

revaporization is driven by the heat generation associated with the greater and extended 

degrees of oxidation in the high-release calculations15. 

• Calculations experiencing greater degrees of oxidation saw large amounts of core debris 

remaining in the vessel for a protracted period of time.

• Calculations seeing a protracted residence of large amounts of core debris in the vessel 

experienced a middling number of penetration failures, i.e., not a small number of failures 

and not a large number of failures, but a medium number of failures. This dependence is 

intuitive as a small number of failed penetrations would not relieve enough core debris to 

preclude a gross lower head failure and a large number of failed penetrations would allow 

debris to fall readily from the vessel.

The penetration model sensitivity study suggests that it may be important to consider lower 

head penetration failures when modeling severe accidents in a BWR. The influence on relative 

cesium release to the environment is potentially large. In considering the results of the study, 

however, it may be entirely important that the penetration modeling available in MELCOR lacks 

provisions for calculating the plugging of an open penetration by freezing melt. If this 

phenomenon were accounted for, penetration failures might be immaterial in that the associated 

openings readily reclose promoting an eventual gross failure of the lower head. Such plugging 

was observed to have occurred in the Three Mile Island Unit 2 accident where metallic debris 

was found refrozen inside instrument tubes outside of the RPV. 

See Appendix E, section E.10.2, for additional information.

 

15 Since cesium is specified as cesium molybdate here, there is no potential chemisorption of cesium hydroxide.
6-116

Figure 6.4-3 Cesium distribution in a high-release case of the Lower Head Penetration 

Model Sensitivity Study

6.4.3 Dose Truncation Uncertainty Sensitivity Analyses

An uncertainty sensitivity study was conducted on the alternate dose response models used in 

the SOARCA project. Risk results for this sensitivity study are presented for three doseresponse models which are the following:

1. LNT dose response model; 

2. Linear-with-threshold dose response model, using a truncation level of the US average 

natural background dose rate combined with average annual, medical dose as a dose 

truncation level (USBGR), which is 620 mrem/yr; and 

3. Linear-with-threshold model using a dose truncation level based on the HPS position

statement that there is a dose below which, due to uncertainties, a quantified risk should 

not be assigned, which is 5 rem/yr with a lifetime limit of 10 rem. 

The USBGR and HPS dose response models were applied to the MACCS CAP14 uncertainty 

model discussed in Section 5.2.1, which used the LNT dose-response model for the MELCOR 

Replicate 1 source terms. of the same four regression methods, as used in the integrated UA,

were applied to determine which input parameters affect the estimated LCF risk: rank 

regression, quadratic regression, recursive partitioning, and MARS. See Section 3.4.2 for a 

description of these methods.
6-117

Table 6.4-2 provides the basic statistical results related to LCF risk of the MELCOR Replicate 1 

source terms sensitivity analysis (i.e., MACCS uncertainty model CAP14 used the LNT dose 

model, the CAP15 uncertainty model used the USBGR dose model, and the CAP16 uncertainty 

model used the HPS dose model) for the 10-mile and 50-mile radius circular areas. It should be 

noted that the habitability criterion is assumed to be 500 mrem/yr. This dose rate is below the 

USBGR and HPS truncation levels; therefore, most of the doses received during the long-term 

phase are below the dose truncation limit and are not counted toward health effects when using 

this criterion. Thus, most of the risks associated with the USBGR and HPS truncation levels are 

from doses received during the first year. The emergency and long-term phases are not easily 

separated in the first year for purposes of evaluating the annual dose threshold. 

Table 6.4-2 Conditional, mean, individual LCF risk (per event) average statistics for the 

Dose Truncation Sensitivity Analysis at specified Radial Distances

 

LNT

0-10 miles

USBGR

0-10 miles

HPS

0-10 miles

LNT

0-50 miles

USBGR

0-50 miles

HPS

0-50 miles

Mean 1.6x10-4 5.2x10-6 5.4x10-6 1.1x10-4 4.6x10-5 4.2x10-5

Median 1.4x10-4 2.3x10-6 2.3x10-6 7.4x10-5 1.7x10-5 9.1x10-6

5th percentile 3.7x10-5 4.3x10-7 2.3x10-7 2.2x10-5 2.4x10-6 7.4x10-8

95th percentile 4.0x10-4 1.8x10-5 1.9x10-5 3.0x10-4 1.6x10-4 1.6x10-4

 

6.4.3.1 Latent Cancer Fatality Regression Analysis

Tables 6.4-2 through 6.4-16 show the results of regression analyses used to evaluate the 

sensitivity of the conditional, mean, individual LCF risk (per event) results for the MACCS

sensitivity uncertainty analysis for the MELCOR Replicate 1 source terms (i.e., MACCS

uncertainty model CAP14 used the LNT dose model, the CAP15 uncertainty model used the 

USBGR dose model, and the CAP16 uncertainty model used the HPS dose model) for the 

10-mile, 20-mile, 30-mile, 40-mile, and 50-mile radius circular areas, respectively. The tables 

represent input parameter influence on the results of the uncertainty analysis. Rank regression 

is often an underestimate of the true influence of a parameter since it captures only a monotonic 

relationship. A slightly non-monotonic relationship results in a smaller R2 than when the 

relationship is purely monotonic. 

The tables are ordered by input variables with the highest rank regression results, and then are 

further grouped according to the type of input parameter (i.e., MACCS or MELCOR variables). 

The final R2 determination for all four regression models range from good to high confidence for 

all dose models for the five circular areas and range from 0.47 for the rank regression analysis

to 0.92 for the quadratic regression analysis. 

Since the dose truncation models only affect the LCF risk results, early-fatality risk is not 

reported in this sensitivity study.

6.4.3.1.1 Linear No Threshold Dose-Response Model

Tables 6.4-2 through 6.4-6 show the results of the regression analyses used to evaluate the 

sensitivity of the conditional, mean, individual LCF risk (per event) results for the MACCS

sensitivity uncertainty analysis for the MELCOR Replicate 1 source terms using the LNT dose 

model (i.e., MACCS uncertainty model CAP14) for the 10-mile, 20-mile, 30-mile, 40-mile, and 

50-mile circular areas, respectively. For the LNT dose-response model, the regression 
6-118

analyses at the five circular areas consistently rank the MACCS dry deposition velocity 

(VDEPOS) and the MELCOR SRV stochastic failure probability (SRVLAM) as the most 

important input variables. 

Additional variables also consistently show some level of importance at all circular areas. 

These additional input variables include the following: 

• The MELCOR fuel failure criterion, and

• The MELCOR SRV open area fraction (SRVOAFRAC),

• The MELCOR drywell liner melt-through open area flow path (FL904A), and

• The MACCS residual dose and dose-rate effectiveness factor (DDREFA–Residual) 

These four variables (VDEPOS, SRVLAM, SRVOAFRAC, and fuel failure criterion,) account for 

at least 30% of the variance for the five circular areas for the rank regression analysis, at least 

3% of the variance for the five circular areas for the quadratic regression analysis, at least 12% 

of the variance for the five circular areas for the recursive partitioning analysis, and at least 10% 

of the variance for the five circular areas for the MARS analysis. 
6-119

Table 6.4-3 Conditional, mean, individual LCF risk (per event) regression of MACCS

sensitivity LNT model at the 10-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.71 0.89 0.83 0.81

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

VDEPOS 0.25 0.25 0.63 0.10 0.11 0.6 0.15 0.44 0 0.12 0.28 0 

SRVLAM 0.37 0.12 -0.33 0.05 0 1 0.01 0.21 0 0.01 0.34 0 

Fuel failure 

criterion 0.41 0.04 0.21 0.05 0 1 --- --- --- 0 0.01 0.6

SRVOAFRAC 0.43 0.02 -0.08 --- --- --- 0 0.08 0.04 0 0 1 

CHEMFORM --- --- --- 0.03 0.19 0.05 --- --- --- --- --- ---

CFRISK

Residual 0.51 0.08 0.24 0.01 0.27 0 0.14 0.34 0 0.10 0.33 0 

DDREFA

Residual 0.53 0.02 -0.14 0 0.12 0.03 0.03 0.02 0.18 --- --- ---

GSHFAC

Normal 0.60 0.07 0.22 0.02 0 1 0 0.10 0.01 --- --- ---

CFRISK

Colon 0.65 0.05 0.23 0.07 0.25 0 0.05 0.28 0 0.02 0.05 0.56

CFRISK

Lung 0.69 0.04 0.17 0.01 0.06 0.26 0 0.17 0.01 0.02 0.37 0 

ESPEED 0.71 0.02 -0.10 0.05 0.05 0.18 0.03 0.07 0.05 0.02 0 1 

CFRISK

Breast 0.73 0.02 0.11 0.05 0.04 0.47 0 0 1 --- --- ---

DLTEVA

Cohort 5 0.74 0.01 -0.09 0 0.11 0.05 0 0 1 0.03 0.26 0.01

Pu-239

Inhalation 0.75 0.01 0.10 --- --- --- --- --- --- --- --- ---

CZSIGA 0.76 0.01 -0.09 --- --- --- --- --- --- --- --- ---

Te-127m

Inhalation --- --- --- 0.05 0.03 0.55 --- --- --- --- --- ---

CYSIGA --- --- --- 0 0 1 0.01 0.02 0.46 0.01 0.17 0.08

Nb-95

Inhalation --- --- --- --- --- --- 0 0.07 0 0.03 0 1 

Zr-95

Inhalation --- --- --- --- --- --- --- --- --- 0.03 0 1 

I-132

Inhalation --- --- --- --- --- --- --- --- --- 0 0 1 

Note: Parameters are grouped by importance and relationship (e.g. MELCOR parameters). Light shading indicates 

parameters with low importance. The dark shading and no shading represent ‘groupings’ of parameters (e.g., source 

term influence from MELCOR inputs or latent cancer risk associated for a specific target organ).

Other input parameters have a low importance at certain circular areas but not at other circular 

areas. Thus, the most important variable, VDEPOS, appears at the top of the tables followed by 

the consistently important MELCOR variables (i.e., SRVLAM, fuel failure criterion, and

SRVOAFRAC), the LCF risk parameters for residual cancers (CFRISK-residual and 

DDREFA-residual), and finally those LCF risk parameters, dose conversion factors for 

inhalation, and MELCOR parameters (e.g., CHEMFORM) not consistently ranked as important 

variables at the five circular areas. 
6-120

The two most important MELCOR input variables are the same as those in the MACCS

Uncertainty Analysis regression analyses discussed in Section 6.2.3. Since this is a smaller 

subset of the MACCS uncertainty analysis and still ranks very similar important parameters, this 

sensitivity analysis provides additional confidence in the regression analysis for parameters 

considered to be important.

Table 6.4-4 Conditional, mean, individual LCF risk (per event) regression of MACCS

sensitivity LNT model at the 20-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.48 0.92 0.67 0.82

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

VDEPOS 0.22 0.22 0.35* 0.07 0.21 0.76 0.36 0.72 0 0.09 0.66 0 

SRVLAM 0.33 0.11 -0.31 0 0.01 0.37 0.05 0 1 0 0.33 0.01

CHEMFORM 0.34 0.01 0.06 0 0.57 0 --- --- --- --- --- ---

Fuel failure 

criterion --- --- --- 0 0.15 0.04 --- --- --- 0.01 0.73 0 

SRVOAFRAC --- --- --- --- --- --- --- --- --- 0 0.51 0 

CFRISK

Colon 0.37 0.03 0.15 0 0 1 0 0 1 0 0.39 0.02

DLTEVA

Cohort 1 0.40 0.03 -0.13 0 0.01 0.64 0 0.20 0.01 --- --- ---

Nb-95

Inhalation 0.42 0.02 0.15 0 0.10 0.50 0 0.05 0.08 0.01 0.35 0 

CFRISK

Lung 0.44 0.02 -0.11 --- --- --- --- --- --- 0 0.48 0 

Pu-239

Inhalation 0.46 0.02 -0.13 --- --- --- --- --- --- --- --- ---

CYSIGA 0.48 0.02 0.11 0.02 0.08 0.05 0.02 0 1 0 0.58 0 

ESPEED 0.49 0.01 0.12 0.01 0.05 0.37 0 0.02 0.54 0.03 0.66 0 

Zr-95

Inhalation 0.51 0.02 -0.09 --- --- --- 0 0.24 0 0.01 0 1 

Sr-91

Inhalation 0.52 0.01 -0.10 0.01 0.19 0.01 --- --- --- --- --- ---

CFRISK

Breast --- --- --- 0.03 0.11 0.03 --- --- --- --- --- ---

I-132

Inhalation --- --- --- 0 0.08 0.19 --- --- --- 0.03 0.30 0.03

DLTEVA

Cohort 5 --- --- --- 0.02 0.01 0.81 0 0 1 0.07 0.42 0 

Sr-90

Inhalation --- --- --- --- --- --- 0 0.22 0 --- --- ---

Pu-241

Inhalation --- --- --- --- --- --- 0 0.21 0 --- --- ---

CFRISK

Residual --- --- --- --- --- --- 0.04 0 1 0 0.40 0 

* The SRRC for VDEPOS is a sum of positive and negative SRRC values for four VDEPOS particle size bins.
6-121

Table 6.4-5 Conditional, mean, individual LCF risk (per event) regression of MACCS

sensitivity LNT model at the 30-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS 

Final R2 0.49 0.92 0.68 0.64

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

VDEPOS 0.20 0.20 0.37* 0.01 0.40 0 0.22 0.71 0 0.43 0.58 0 

SRVLAM 0.31 0.11 -0.35 0.02 0.18 0.01 0.03 0.03 0.62 0.02 0.01 0.66

CHEMFORM 0.32 0.01 0.07 0.01 0.50 0 0.01 0.02 0.12 --- --- ---

Fuel failure 

criterion --- --- --- 0 0 1 --- --- --- 0 0 1 

SRVOAFRAC --- --- --- --- --- --- --- --- --- 0.01 0.17 0.01

Zr-95

Inhalation 0.38 0.06 0.23 0.02 0 1 0.03 0.09 0.10 0 0 1 

CFRISK

Residual 0.42 0.04 0.14 0 0 1 0 0 1 0.02 0 1 

DDREFA

Residual --- --- --- 0.01 0.07 0.30 --- --- --- --- --- ---

Sr-91

Inhalation 0.44 0.02 0.09 --- --- --- 0 0 1 --- --- ---

CFRISK

Colon 0.46 0.02 0.16 0.07 0.47 0 --- --- --- 0 0 1 

GSHFAC 0.48 0.02 -0.13 --- --- --- 0.05 0.57 0 --- --- ---

ESPEED 0.50 0.02 0.12 0.02 0.30 0 0.01 0 1 0.03 0.31 0.02

CFRISK

Lung 0.53 0.03 -0.10 --- --- --- 0.06 0.09 0.14 0.03 0.41 0 

CYSIGA 0.54 0.01 -0.10 --- --- --- 0 0 1 0 0.12 0.02

DLTEVA

Cohort 1 --- --- --- 0 0.33 0 --- --- --- --- --- ---

I-132

Inhalation --- --- --- 0.04 0.26 0.01 0 0 1 0 0 1 

DLTEVA

Cohort 5 --- --- --- 0.01 0 1 --- --- --- 0.01 0.19 0.05

CFRISK

Breast --- --- --- 0 0 1 --- --- --- --- --- ---

Sr-90

Inhalation --- --- --- 0 0 1 --- --- --- --- --- ---

Te-127m

Inhalation --- --- --- --- --- --- 0 0.07 0.07 --- --- ---

Nb-95

Inhalation --- --- --- --- --- --- --- --- --- 0 0.06 0.26

* The SRRC for VDEPOS is a sum of positive and negative SRRC values for five VDEPOS particle size bins.
6-122

Table 6.4-6 Conditional, mean, individual LCF risk (per event) regression of MACCS

sensitivity LNT model at the 40-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.47 0.88 0.70 0.69

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

VDEPOS 0.14 0.14 -0.04* 0.04 0.13 0.22 0.28 0.64 0 0.28 0.71 0 

SRVLAM 0.26 0.12 -0.34 0 0.14 0.08 0.02 0.15 0.09 0.03 0 1 

SRVOAFRAC 0.30 0.04 0.16 --- --- --- --- --- --- 0.03 0.06 0.27

CHEMFORM --- --- --- --- --- --- 0 0 1 --- --- --- 

Fuel failure 

criterion --- --- --- --- --- --- --- --- --- 0 0 1 

Zr-95

Inhalation 0.36 0.06 0.20 0.02 0.33 0 0 0.09 0.09 0 0 0.63

I-132

Inhalation 0.39 0.03 -0.10 --- --- --- 0 0 1 --- --- --- 

Nb-95

Inhalation 0.42 0.03 0.11 --- --- --- --- --- --- 0.04 0.12 0.09

Pu-239

Inhalation 0.44 0.02 0.09 0 0.59 0 --- --- --- --- --- --- 

Sr-91

Inhalation 0.46 0.02 -0.11 0.02 0.00 1 --- --- --- --- --- --- 

CFRISK

Colon 0.48 0.02 0.15 0.15 0.55 0 0.01 0.18 0 0 0.14 0.04

Sr-92

Inhalation 0.50 0.02 0.07 --- --- --- 0.03 0 1 --- --- --- 

CFRISK

Lung 0.51 0.01 -0.08 --- --- --- 0.01 0.13 0.03 0.04 0.24 0.01

CFRISK

Breast 0.52 0.01 -0.11 --- --- --- --- --- --- --- --- --- 

CYSIGA --- --- --- 0.06 0.49 0 0 0.21 0 0.03 0.19 0.04

ESPEED --- --- --- 0 0.26 0 0 0.04 0.15 0 0.14 0.05

DLTEVA

Cohort 1 --- --- --- 0.04 0.32 0 0.01 0 1 --- --- --- 

DDREFA

Residual --- --- --- 0.02 0.03 0.56 --- --- --- --- --- --- 

CFRISK

Residual --- --- --- --- --- --- --- --- --- 0.01 0.09 0.09

Pu-241

Inhalation --- --- --- 0.01 0 1 --- --- --- --- --- --- 

CZSIGA --- --- --- --- --- --- 0 0.05 0.09 --- --- --- 

GSHFAC --- --- --- --- --- --- 0 0 1 --- --- --- 

I-132

Inhalation --- --- --- --- --- --- --- --- --- 0.06 0.10 0.07

DLTEVA

Cohort 5 --- --- --- --- --- --- --- --- --- 0.01 0.07 0.19

* The SRRC for VDEPOS is a sum of positive and negative SRRC values for four VDEPOS particle size bins.
6-123

Table 6.4-7 Conditional, mean, individual LCF Risk (per event) regression of MACCS

sensitivity LNT model at the 50-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.47 0.92 0.71 0.75

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

VDEPOS 0.17 0.17 0.30* 0 0.21 0.01 0.12 0.45 0 0.07 0.11 0.08

SRVLAM 0.29 0.12 -0.33 --- --- --- 0 0.14 0.08 0.05 0.36 0.03

Fuel failure 

criterion 0.30 0.01 0.08 0 0.21 0.50 --- --- --- 0 0.37 0 

SRVOAFRAC 0.31 0.01 -0.14 0.04 0.21 0.03 0.12 0.58 0 0.14 0.63 0 

ESPEED 0.36 0.05 0.20 0.03 0.25 0 0 0 1 0.04 0 1 

CFRISK

Residual 0.40 0.04 0.11 0.02 0 1 0.06 0.12 0.21 0 0 1 

DDREFA

Residual --- --- --- --- --- --- 0 0.08 0.07 --- --- ---

Sr-91

Inhalation 0.42 0.02 -0.11 0 0.06 0.25 0 0.08 0.08 --- --- ---

CYSIGA 0.44 0.02 -0.01** 0.01 0.03 0.58 0 0 1 0 0 1 

CFRISK

Colon 0.46 0.02 0.15 0 0.42 0 0 0.03 0.23 0 0.02 0.35

DLTEVA

Cohort 5 0.49 0.03 -0.11 --- --- --- 0.05 0 1 0 0.16 0.02

GSHFAC 0.50 0.01 -0.12 --- --- --- --- --- --- --- --- ---

Pu-241

Inhalation 0.51 0.01 0.08 --- --- --- --- --- --- --- --- ---

CZSIGA --- --- --- 0 0.15 0.05 --- --- --- --- --- ---

Sr-90

Inhalation --- --- --- 0.01 0.05 0.22 --- --- --- --- --- ---

DLTEVA

Cohort 1 --- --- --- 0 0 1 --- --- --- --- --- ---

Nb-95

Inhalation --- --- --- 0.04 0 1 --- --- --- 0.02 0 1 

Zr-95

Inhalation --- --- --- --- --- --- 0 0.01 0.46 0 0 1 

I-132

Inhalation --- --- --- --- --- --- 0 0 1 0 0.15 0.03

CFRISK

Lung --- --- --- --- --- --- 0.03 0 1 0.02 0.21 0.15

Sr-92

Inhalation --- --- --- --- --- --- 0 0 1 --- --- ---

* The SRRC for VDEPOS is a sum of positive and negative SRRC values for three VDEPOS particle size bins.

** The SRRC for CYSIGA is a sum of positive and negative SRRC values for two CYSIGA stability classes. 

The MACCS dry deposition velocity (VDEPOS) parameter accounts for at least 0% of the 

variance with a Ti of 0.21 using the quadratic regression analysis to at most 43% of the variance

with a Ti of 0.58 using the MARS analysis at the five circular areas for all regression methods 

and is the most important input variable. As discussed in more detail in Section 4.2.2, dry 

deposition is characterized in MACCS with a set of deposition velocities corresponding to a set 

of aerosol size bins. 
6-124

The MELCOR input variables (SRVLAM, fuel failure criterion, and SRVOAFRAC) accounts for

at least 0% of the variance with a Ti of 0.57 using the quadratic regression analysis to at most 

19% of the variance with a Ti of 0.63 using the MARS analysis at the five circular areas for all 

regression methods. As discussed in Section 6.1.1 and Section 6.1.2, the MELCOR input 

variables SRVLAM and SRVOAFRAC account for the majority of the variance for iodine and 

cesium release. CHEMFORM does appear as a variable of importance but is not consistently 

throughout all distances. The FL904A is not shown to be an important parameter in the 

MELCOR regression analysis discussed in Section 6.1. This discrepancy may be due to the 

smaller sample size used for this sensitivity study. 

6.4.3.1.2 USBGR Dose-Response Model

Tables 6.4-7 through 6.4-11 show the results of the regression analyses used to evaluate the 

sensitivity of the conditional, mean, individual LCF risk (per event) results for the MACCS

sensitivity uncertainty analysis for the MELCOR Replicate 1 source terms using the USBGR 

dose truncation model (i.e., MACCS uncertainty model CAP15) for the 10-mile, 20-mile, 30-mile, 

40-mile, and 50-mile circular areas, respectively. For the USBGR dose-response model, the

regression analyses at the five circular areas consistently rank the MACCS inhalation protection 

factor for normal activity (PROTIN–Normal) and the lung lifetime risk factor for cancer death 

(CFRISK-Lung) as the most important input variables. 

Additional variables also consistently show some level of importance at all circular areas. 

These additional input variables include the following: 

• The MELCOR SRV stochastic failure probability (SRVLAM),

• The MELCOR SRV open area fraction (SRVOAFRAC), and

• The MELCOR DC station battery duration (BATTDUR)

These five variables (PROTIN-Normal, CFRISK-Lung, SRVLAM, SRVOAFRAC, and 

BATTDUR) account for at least 40% of the variance at the five circular areas for the rank 

regression analysis, at least 1% of the variance for the five circular areas for the quadratic 

regression analysis, at least 2% of the variance for the five circular areas for the recursive 

partitioning analysis, and at least 0% of the variance for the five circular areas for the MARS

analysis. 

Other input parameters have a low importance at certain circular areas but not at other circular 

areas. Thus, the most important variables, PROTIN-Normal and CFRISK-Lung, appear at the 

top of the tables followed by the consistently important MELCOR variables (i.e., SRVLAM, 

SRVOAFRAC, and BATTDUR), and finally those LCF risk parameters, dose conversion factors

for inhalation, and MELCOR parameters (e.g., fuel failure criterion) not consistently ranked as 

important variables at the five circular areas. 

The important MELCOR input variables are similar as those in the MACCS Uncertainty Analysis

regression analyses discussed in Section 6.2.3. However, the MACCS input variables are not

the same. The most important MACCS input parameters using the USBGR dose truncation 

model are those associated with doses received in the first year and not ones associated with 

the long-term phase risk beyond the first year. 

For Peach Bottom, the habitability criterion is an annual dose rate of 500 mrem/yr. This dose 

rate is below the USBGR truncation level (620 mrem/yr); therefore, most of the doses received 

during the long-term phase are below the dose truncation limit and are not counted toward 

health effects when using this criterion. Thus, most of the risks associated with the USBGR 

truncation level are from doses received during the first year. The emergency and long-term 
6-125

phases are not easily separated in the first year for purposes of evaluating the annual dose 

threshold. 

To better understand this explanation, it is important to understand the differences between 

exposure periods, commitment periods, and the periods of time when doses are actually 

received. For external dose pathways, the time over which doses are received is concurrent 

with the exposure period. External dose pathways include cloudshine and groundshine. 

The exposure period for internal pathways, inhalation and ingestion, is the period of time when 

the inhalation or ingestion occurs; however, doses continue to be received over a person’s 

entire lifetime following the exposure. A person’s lifetime is obviously variable, depending upon 

the age of the person at the time of exposure, among other things. The period of time over 

which doses are received from an internal pathway is accounted for in the construction of dose 

conversion factors by integrating the doses over a finite period called a dose commitment 

period, which is usually taken to be 50 years when calculating internal-pathway dose conversion 

factors for adults. The implicit assumption is that the average adult lives for an additional 

50 years following the exposure, which is most likely a conservative assumption.
6-126

Table 6.4-8 Conditional, mean, individual LCF Risk (per event) regression of MACCS

sensitivity USBGR model at the 10-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.54 0.90 0.61 0.80

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

CFRISK

Lung 0.14 0.14 0.33 0.04 0.25 0.03 0.03 0.04 0.32 0.15 0.49 0.01

PROTIN

Normal 0.27 0.13 0.38 0.07 0 1 0 0 1 0 0.11 0.15

SRVLAM 0.38 0.11 -0.29 0 0.06 0.34 0.04 0.60 0 0.01 0.23 0.04

BATTDUR 0.42 0.04 -0.16 0 0.01 0.66 0.02 0.09 0.15 0.01 0.05 0.31

SRVOAFRAC 0.44 0.02 -0.17 0.08 0.17 0.17 0.24 0.74 0 0.09 0.56 0 

Fuel Failure 

Criterion 0.44 0 0.06 --- --- --- --- --- --- --- --- ---

Te-127m

Inhalation 0.47 0.03 0.14 0.11 0 1 0 0.16 0 0 0.29 0.08

TIMHOT 0.49 0.02 0.14 0 0.23 0.01 0.04 0.08 0.06 --- --- ---

SC1131_2 0.51 0.02 0.10 0 0 1 --- --- --- 0 0 1 

ESPEED

Cohort 5 0.52 0.01 -0.13 --- --- --- 0.04 0 1 0 0 1 

Cs-137

Inhalation 0.53 0.01 -0.11 --- --- --- 0.02 0 1 0 0 1 

SLCRFRAC 0.54 0.01 -0.13 0.02 0.46 0.07 --- --- --- --- --- ---

Ba-140

Inhalation 0.55 0.01 -0.09 --- --- --- --- --- --- 0 0.19 0.08

I-133

Inhalation 0.56 0.01 0.08 --- --- --- 0.01 0 1 --- --- ---

Sr-90

Inhalation 0.57 0.01 0.08 --- --- --- --- --- --- --- --- ---

DLTEVA

Cohort 4 --- --- --- 0.08 0.27 0 --- --- --- --- --- ---

CFRISK

Thyroid --- --- --- 0.06 0.45 0.01 0.01 0.05 0.52 0.03 0.12 0.12

RHONOM --- --- --- 0 0.04 0.20 --- --- --- --- --- ---

Sr-92

Inhalation --- --- --- 0 0.03 0.44 --- --- --- 0.02 0.09 0.15

Pu-239

Inhalation --- --- --- 0.07 0.05 0.60 0.05 0.24 0.01 --- --- ---

SC1141_2 --- --- --- 0.02 0 1 --- --- --- --- --- ---

Ce-141

Inhalation --- --- --- --- --- --- 0.02 0.05 0.13 --- --- ---

DLTEVA

Cohort 3 --- --- --- --- --- --- 0.05 0.02 0.46 --- --- ---

DLTEVA

Cohort 1 --- --- --- --- --- --- 0 0 1 --- --- ---

SC1141_2 --- --- --- --- --- --- --- --- --- 0 0 1 

CSFACT

Evacuation --- --- --- --- --- --- --- --- --- 0 0 1 
6-127

Table 6.4-9 Conditional, mean, individual LCF risk (per event) regression of MACCS

sensitivity USBGR model at the 20-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.55 0.84 0.64 0.69

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

CFRISK

Lung 0.12 0.12 0.33 0.07 0.34 0 0.01 0 1 0 0.81 0 

PROTIN

Normal 0.23 0.11 0.37 0.01 0 1 0 0 1 0 0.40 0.01

SRVLAM 0.34 0.11 -0.33 --- --- --- 0 0.22 0 0 0 1 

SRVOAFRAC 0.40 0.06 -0.26 0 0 1 0.01 0.06 0.11 0 0.02 0.52

BATTDUR 0.42 0.02 0.13 0 0.21 0 --- --- --- 0 0 1 

DLTEVA

Cohort 4 0.46 0.04 0.17 --- --- --- --- --- --- --- --- ---

Ba-140

Inhalation 0.48 0.02 -0.12 0.03 0.22 0 0.01 0.06 0.10 0.02 0.50 0 

ESPEED 0.50 0.02 -0.12 --- --- --- 0.02 0 1 0 0.50 0.01

SC1131_2 0.51 0.01 -0.13 0.09 0.10 0.55 0.21 0.79 0 0 0.96 0 

CSFACT

Evacuation 0.52 0.01 0.08 0.03 0.21 0 0.03 0.07 0.11 0 0.17 0.11

Zr-95

Inhalation 0.53 0.01 -0.11 0 0.12 0 0 0.47 0 --- --- ---

Te-127m

Inhalation 0.55 0.02 -0.11 0.05 0 1 --- --- --- 0.01 0.30 0.08

SLCRFRAC 0.57 0.02 0.12 0 0.21 0 --- --- --- --- --- ---

Sr-92

Inhalation 0.58 0.01 0.09 0.02 0.04 0.30 0.05 0.06 0.16 0 0.43 0 

Cs-137

Inhalation

0.59 0.01 -0.07 --- --- --- 0 0 1 0 0 1 

Ce-141

Inhalation --- --- --- 0.01 0.21 0 0.01 0 1 --- --- ---

CFRISK

Thyroid --- --- --- 0 0.24 0 --- --- --- 0.01 0 1 

DLTEVA

Cohort 3 --- --- --- 0 0.06 0.05 --- --- --- --- --- ---

Pu-239

Inhalation --- --- --- --- --- --- 0.07 0.23 0 --- --- ---

SC1141_2 --- --- --- --- --- --- --- --- --- 0 0.42 0.01
6-128

Table 6.4-10 Conditional, mean, individual LCF risk (per event) regression of MACCS

sensitivity USBGR model at the 30-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.55 0.87 0.65 0.57

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

CFRISK

Lung 0.11 0.11 0.32 0 0.28 0 0.02 0 1 0.07 0.57 0 

PROTIN

Normal 0.22 0.11 0.37 0.03 0.12 0 0.04 0 1 0 0 1 

SRVLAM 0.33 0.11 -0.33 --- --- --- 0.02 0.23 0.01 0 0 1 

SRVOAFRAC 0.40 0.07 -0.28 0.05 0.05 0.15 0.01 0.29 0 0 0.11 0.12

BATTDUR --- --- --- 0 0.07 0.06 --- --- --- 0 0.08 0.12

I-133

Inhalation 0.44 0.04 0.18 --- --- --- --- --- --- --- --- ---

SC1131_2 0.46 0.02 -0.14 0.04 0.18 0.01 --- --- --- 0.02 0 1 

CSFACT

Evacuation 0.48 0.02 -0.12 --- --- --- 0.04 0 1 0 0.11 0.19

SC1141_2 0.49 0.01 0.12 0.06 0.05 0.38 --- --- --- 0.21 0.20 0.12

ESPEED 0.50 0.01 -0.12 0.05 0.21 0 0.20 0.80 0 0.26 0.83 0 

Te-127m

Inhalation

0.51 0.01 -0.12 --- --- --- --- --- --- 0 0.17 0.07

DLTEVA

Cohort 3 0.52 0.01 -0.11 0.01 0.08 0.07 0.03 0.53 0 --- --- ---

TIMHOT 0.54 0.02 0.11 0 0.10 0 --- --- --- --- --- ---

CFRISK

Thyroid 0.56 0.02 0.08 0.04 0.08 0.28 --- --- --- 0.01 0.21 0.01

Cs-137

Inhalation 0.57 0.01 -0.08 --- --- --- --- --- --- 0 0 1 

Ce-141

Inhalation 0.58 0.01 0.08 0.01 0.17 0 0.02 0 1 --- --- ---

Sr-92

Inhalation --- --- --- 0.06 0.21 0 0.01 0.15 0.03 0.01 0.19 0.01

Ba-140

Inhalation --- --- --- 0.04 0.13 0.01 0.06 0.20 0.01 0.01 0.22 0.01

Pu-239

Inhalation --- --- --- 0 0.04 0.28 --- --- --- --- --- ---

Zr-95

Inhalation --- --- --- --- --- --- 0 0.27 0 --- --- ---

RHONOM --- --- --- --- --- --- 0 0 1 --- --- ---
6-129

Table 6.4-11 Conditional, mean, individual LCF risk (per event) regression of MACCS

sensitivity USBGR model at the 40-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.55 0.86 0.65 0.77

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

PROTIN

Normal 0.11 0.11 0.38 0 0.07 0.07 0.07 0.02 0.67 0.01 0.14 0.23

CFRISK

Lung 0.21 0.10 0.31 0.01 0.32 0 0 0.11 0.11 0 0.55 0 

SRVLAM 0.33 0.12 -0.34 --- --- --- 0 0 1 0 0.27 0 

SRVOAFRAC 0.40 0.07 -0.26 0 0 1 0 0 1 0.01 0 1 

BATTDUR 0.42 0.02 -0.12 --- --- --- 0 0 1 0 0.28 0 

Fuel failure 

criterion --- --- --- 0 0.07 0.12 0.10 0 1 --- --- ---

Ce-141

Inhalation 0.46 0.04 0.18 --- --- --- --- --- --- --- --- ---

SC1131_2 0.48 0.02 -0.14 --- --- --- --- --- --- 0 0 1 

Cs-137

Inhalation 0.50 0.02 -0.01 0.11 0.29 0 0.29 0.78 0 0.10 0.84 0 

CSFACT

Evacuation 0.51 0.01 0.11 0 0.16 0 --- --- --- 0.04 0 1 

Te-127m

Inhalation 0.52 0.01 -0.11 --- --- --- 0.02 0 1 0 0.36 0 

ESPEED 0.54 0.02 -0.08 --- --- --- --- --- --- 0.04 0.02 0.52

SLCRFRAC 0.56 0.02 -0.10 --- --- --- 0.05 0.51 0 --- --- ---

TIMHOT 0.57 0.01 0.11 0 0.04 0.58 --- --- --- --- --- ---

DLTEVA

Cohort 4 0.58 0.01 0.08 0.01 0.21 0 0 0.18 0 --- --- ---

Pu-239

Inhalation --- --- --- 0.05 0.10 0.02 --- --- --- --- --- ---

Sr-92

Inhalation --- --- --- 0.02 0.11 0.08 0 0.17 0.02 0.01 0 1 

DLTEVA

Cohort 1 --- --- --- 0.02 0 0.52 --- --- --- --- --- ---

Ba-140

Inhalation --- --- --- 0.03 0.03 0.66 0 0.02 0.39 0.01 0 1 

CFRISK

Thyroid --- --- --- 0.01 0.03 0.70 --- --- --- 0.02 0 1 

SC1141_2 --- --- --- 0.03 0 0.77 --- --- --- 0 0.15 0.06

Sr-90

Inhalation --- --- --- 0 0 1 0 0 1 --- --- ---

Zr-95

Inhalation --- --- --- --- --- --- 0.02 0.12 0.03 --- --- ---

I-133

Inhalation --- --- --- --- --- --- 0.02 0 0.52 --- --- ---
6-130

Table 6.4-12 Conditional, mean, individual LCF risk (per event) regression of MACCS

sensitivity USBGR model at the 50-mile circular area. 

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.55 0.86 0.64 0.81

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

CFRISK

Lung 0.10 0.10 0.29 0 0.36 0 0.02 0.12 0.09 0.05 0 1 

PROTIN

Normal 0.21 0.11 0.37 0 0.02 0.56 0.04 0 1 0 0.44 0.01

SRVLAM 0.33 0.12 -0.35 0.02 0.03 0.66 0 0 1 0.01 0 1 

SRVOAFRAC 0.40 0.07 -0.25 0 0 1 0.06 0 1 0.02 0 1 

BATTDUR 0.44 0.04 -0.11 --- --- --- 0 0.18 0.01 0.06 0 1 

Fuel failure 

criterion --- --- --- 0.02 0.08 0 0.02 0.08 0.24 --- --- ---

SC1131_2 0.47 0.03 -0.14 --- --- --- --- --- --- 0.02 0.14 0.24

Ce-141

Inhalation 0.48 0.01 0.22 --- --- --- --- --- --- --- --- ---

Ba-140

Inhalation 0.49 0.01 0.12 0.01 0.03 0.62 --- --- --- 0 0 1 

Cs-137

Inhalation 0.50 0.01 -0.12 0.08 0.32 0 0.12 0.72 0 0.32 0.84 0 

ESPEED 0.51 0.01 -0.08 --- --- --- --- --- --- 0.02 0.06 0.42

Te-127m

Inhalation 0.52 0.01 -0.11 --- --- --- 0 0 0.41 0 0.16 0.14

CSFACT

Evacuation 0.54 0.02 0.12 0.02 0.11 0.05 --- --- --- 0 0.26 0.05

SLCRFRAC 0.56 0.02 -0.11 --- --- --- 0.12 0.36 0 --- --- ---

Sr-90

Inhalation 0.57 0.01 -0.08 --- --- --- 0 0 1 --- --- ---

Zr-95

Inhalation 0.58 0.01 0.12 --- --- --- --- --- --- --- --- ---

DLTEVA

Cohort 4 --- --- --- 0 0.22 0 0 0.33 0 --- --- ---

CFRISK

Thyroid --- --- --- 0 0.17 0 --- --- --- 0 0.21 0.07

Sr-92

Inhalation --- --- --- 0.03 0.12 0.03 0 0.01 0.61 0 0.43 0 

DLTEVA

Cohort 1 --- --- --- 0.03 0.07 0.04 0.06 0.16 0.01 --- --- ---

SC1141_2 --- --- --- 0.01 0.09 0.07 --- --- --- 0 0.28 0.01

Pu-239

Inhalation --- --- --- 0 0 1 --- --- --- --- --- ---

I-133

Inhalation --- --- --- --- --- --- 0 0.16 0.02 --- --- ---

TIMHOT --- --- --- --- --- --- 0 0.07 0.09 --- --- ---
6-131

Since ingestion doses are taken to be negligible in SOARCA, inhalation is the only internal 

pathway that is treated. A significant portion of the exposures during the emergency phase are 

from inhalation. As explained above, these exposures are assumed to lead to doses over the 

commitment period, which is the next 50 years following the exposure. However, depending on 

the isotope inhaled, the doses received may diminish rapidly and become negligible for most of 

the dose commitment period.

Most of the exposures during the long-term phase are from groundshine, and a small fraction is 

from inhalation of resuspended aerosols. Since groundshine is an external pathway, doses 

received are concurrent with the exposure period, which is also taken to be 50 years in the 

SOARCA study. On the other hand, exposures from inhalation of resuspended material during 

each year of the long-term phase contribute to doses received over the subsequent 50-year 

commitment period. 

Doses received in the first year thus correspond to: 

• all of the dose from external exposure during the emergency phase,

• most of the dose from internal exposure during the emergency phase,

• all of the dose from external exposure during the first year of the long-term phase, and

• most of the dose from internal exposure during the first year of the long-term phase.

Doses received in the second and subsequent years correspond to:

• a fraction of the dose from internal exposure during all previous years plus most of the 

dose from internal exposure during that year, and

• all of the dose from external exposure during that year. 

Following a single exposure, internal doses decrease more slowly from one year to the next 

when the isotopic half-life is relatively long (i.e., on the order of a year or longer) and the 

solubility of the dominant chemical form of the isotope is low so that the removal rate from the 

human body is low (i.e., the biological half-life is long). A good example is 90Sr, for which the 

second-year effective dose from inhalation is 60% of the first-year dose. The isotopic half-life is 

29 years, so most of the reduction from year one to year two results from the biological half-life. 

The internal doses decrease more rapidly from one year to the next when either the isotopic half 

life is short or when the solubility of the dominant chemical form of the isotope is high so that the 

human body tends to excrete it rapidly. A good example of this is 131I, for which the second-year 

effective dose from inhalation is essentially zero. This isotope has a short isotopic half-life 

(i.e., 8 days) and a short biological half-life because of its high solubility. For comparison, the 

second-year effective dose from inhalation for 137Cs is about 10% of the first-year dose, so it is 

intermediate between the previous examples.

Because the internal doses from inhalation diminish with time, most of the doses in the second 

and subsequent years are from the exposures during that year. But these doses are limited by 

the habitability criterion to be less than 500 mrem in any year. The 500 mrem limit is for all dose 

pathways, except ingestion, in this case groundshine and inhalation from resuspended aerosols. 

The inhalation dose used in this criterion is a committed dose (i.e., it accounts for doses 

received over the next 50 years). Because the annual doses allowed by the habitability criterion 

are less than the USBGR truncation level, nearly all of the risk is from doses received during the 

first year. These doses include most of emergency phase doses and a fraction of the long-term 

phase doses. 
6-132

The MACCS lung lifetime risk factor for cancer death (CFRISK-Lung) input accounts for at least 

0% of the variance with a Ti of 0.11 using the recursive partitioning regression analysis to at 

most 15% of the variance with a Ti of 0.49 using the MARS analysis at the five circular areas for 

all regression methods, and is one of the most important variables. As discussed in 

Section 4.2.5, the mortality risk coefficients (CFRISK) for each of the organs included in the 

SOARCA analyses for latent health effects are assumed to be uncorrelated. 

The MACCS inhalation protection factor for normal activity (PROTIN–Normal) input accounts for 

at least 0% of the variance with a Ti of 0.02 using the quadratic regression analysis to at most 

13% of the variance with a SRRC of 0.38 using the rank regression analysis at the five circular 

areas for all regression methods and is one of the most important input variable. As discussed 

in further detail in Section 4.2.3, protection factors are specified for each dose pathway and 

directly affect the doses received by individuals at each location. The protection factors are 

used as multipliers on the dose that a person would receive if there were no protection. In this 

context, normal activity refers to a combination of activities that are averaged over a week and 

over the population, including being indoors at home, commuting, being indoors at work, and 

being outdoors. These values are used in the uncertainty analysis making the further 

assumption that the distributions for normal activity and sheltering are correlated with a rank 

correlation coefficient of 0.75. 

The MELCOR input variables (SRVLAM, SRVOAFRAC, and BATTDUR) account for at least 0% 

of the variance with a Ti of 0.02 using the MARS analysis to at most 30% of the variance with a 

Ti of 0.74 using the recursive partitioning regression analysis at the five circular areas for all 

regression methods. As discussed in Section 6.1.1 and Section 6.1.2, the MELCOR input 

variables SRVLAM, and SRVOAFRAC, account for the majority of the variance for iodine and 

cesium release. Fuel failure criterion, FL904A, and CHEMFORM do not consistently appear as 

variables of importance. 

6.4.3.1.3 HPS Dose-Response Model

Tables 6.4-12 through 6.4-16 show the results of the regression analyses used to evaluate the 

sensitivity of the conditional, mean, individual LCF risk (per event) results for the MACCS

sensitivity uncertainty analysis for the MELCOR Replicate 1 source terms using the HPS dose 

truncation model (i.e., MACCS uncertainty model CAP16) for the 10-mile, 20-mile, 30-mile, 

40-mile, and 50-mile circular areas, respectively. For the HPS dose-response model, the

regression analyses at the five circular areas consistently rank the MACCS lung lifetime risk 

factor for cancer death (CFRISK-Lung) and the inhalation protection factor for normal activity 

(PROTIN–Normal) and the MELCOR SRV stochastic failure probability (SRVLAM) as the most 

important input variables. 

Additional variables also consistently show some level of importance at all circular areas. 

These additional input variables include the following: 

• The MELCOR SRV open area fraction (SRVOAFRAC),

• The MELCOR DC station battery duration (BATTDUR), and

• The MELCOR fuel failure criterion

These six variables (CFRISK-Lung, PROTIN-Normal, SRVLAM, SRVOAFRAC, BATTDUR, and 

fuel failure criterion) account for at least 39% of the variance at the five circular areas for the 

rank regression analysis, at least 10% of the variance at the five circular areas for the quadratic 

regression analysis, at least 2% of the variance at the five circular areas for the recursive 
6-133

partitioning analysis, and at least 21% of the variance at the five circular areas for the MARS

analysis. 

Other input parameters have a low importance at certain circular areas but not at other circular 

areas. Thus, the most important variables, PROTIN-Normal and CFRISK-Lung, appear at the 

top of the tables followed by the consistently important MELCOR variables (i.e., SRVLAM, 

SRVOAFRAC, BATTDUR, and fuel failure criterion), and finally those LCF risk parameters, 

dose conversion factors for inhalation, and MELCOR parameters (e.g., SC1131_2) not 

consistently ranked as important variables at the five circular areas. 

Overall, the input variables of importance are the same as those for the USBGR dose truncation 

model. The explanations provided for USBGR dose truncation model MACCS also apply to the 

HPS dose truncation model.

The MACCS lung lifetime risk factor for cancer death (CFRISK-Lung) input accounts for at least 

0% of the variance with a Ti of 0.04 using the recursive partitioning regression analysis to at 

most 12% of the variance with a SRRC of 0.34 using the rank regression analysis at the five 

circular areas for all regression methods, and is one of the most important variables. As 

discussed in Section 4.2.5, the mortality risk coefficients (CFRISK) for each of the organs 

included in the SOARCA analyses for latent health effects are assumed to be uncorrelated. 

The MACCS inhalation protection factor for normal activity (PROTIN–Normal) parameter

accounts for 0% of the variance with a Ti of 0.09 using the recursive partitioning regression 

analysis to at most 20% of the variance with a Ti of 0.82 using the MARS analysis at the five 

circular areas for all regression methods and is the most important input variable. As discussed 

in more detail in Section 4.2.3, protection factors are specified for each dose pathway and 

directly affect the doses received by individuals at each location. The protection factors are 

used as multipliers on the dose that a person would receive if there were no protection. In this 

context, normal activity refers to a combination of activities that are averaged over a week and 

over the population, including being indoors at home, commuting, being indoors at work, and 

being outdoors. These values are used in the uncertainty analysis making the further 

assumption that the distributions for normal activity and sheltering are correlated with a rank 

correlation coefficient of 0.75. 

The MELCOR input variables (SRVLAM, SRVOAFRAC, BATTDUR, and fuel failure criterion) 

account for 0% of the variance with a Ti of 0.28 using the MARS analysis to at most 48% of the 

variance with a Ti of 1.0 using the MARS analysis at the five circular areas for all regression 

methods. As discussed in Section 6.1.1 and Section 6.1.2, the MELCOR input variables 

SRVLAM and SRVOAFRAC account for the majority of the variance for iodine and cesium 

release fractions. FL904A and CHEMFORM do not appear as variables of importance. 
6-134

Table 6.4-13 Conditional, mean, individual LCF risk (per event) regression of MACCS

sensitivity HPS model at the 10-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.52 0.92 0.62 0.59

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

CFRISK

Lung 0.12 0.12 0.31 0.04 0.33 0 0 0.09 0.04 0.06 0.32 0.04

PROTIN

Normal 0.25 0.13 0.39 0.03 0.08 0.22 0.02 0 1 0.04 0 1 

SRVLAM 0.37 0.12 -0.30 --- --- --- 0.06 0.53 0 0.02 0.25 0.03

BATTDUR 0.41 0.04 -0.14 --- --- --- 0.01 0 1 0 0.15 0.09

SRVOAFRAC 0.44 0.03 -0.16 0.04 0 1 0.23 0.73 0 0.28 0.73 0 

Fuel failure 

criterion 0.44 0 0.06 0 0 1 --- --- --- --- --- ---

Te-127m

Inhalation 0.47 0.03 0.14 0.02 0.21 0.04 --- --- --- 0.01 0 1 

Ce-141

Inhalation 0.49 0.02 0.11 0.02 0 1 --- --- --- --- --- ---

SC1131_2 0.50 0.01 0.08 --- --- --- --- --- --- 0 0 1 

Sr-92

Inhalation 0.51 0.01 0.08 0.01 0.32 0.01 0.04 0.18 0.02 0.03 0 1 

ESPEED 0.52 0.01 -0.10 --- --- --- --- --- --- 0.01 0 1 

Cs-137

Inhalation 0.53 0.01 -0.10 0.07 0 1 0 0 1 0.04 0 1 

Ba-140

Inhalation 0.54 0.01 -0.09 --- --- --- 0 0.07 0.05 --- --- ---

RHONOM 0.55 0.01 0.08 0 0.05 0.53 --- --- --- --- --- ---

SLCRFRAC 0.56 0.01 -0.12 0 0.34 0.18 --- --- --- --- --- ---

Pw-239

Inhalation --- --- --- 0.01 0.22 0.03 --- --- --- --- --- ---

DLTEVA

Cohort 3 --- --- --- 0.02 0.16 0.03 0.05 0.01 0.67 --- --- ---

CFRISK

Thyroid --- --- --- 0.01 0 1 0 0.26 0.02 0 0.16 0.02

CSFACT

Evacuation --- --- --- 0 0 1 --- --- --- 0 0.25 0.02

VDEPOS --- --- --- --- --- --- 0 0.15 0 0 0 1 

SC1141_2 --- --- --- --- --- --- --- --- --- 0.01 0.19 0.01
6-135

Table 6.4-14 Conditional, mean, individual LCF risk (per event) regression of MACCS

sensitivity HPS model at the 20-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.55 0.80 0.67 0.69

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

PROTIN

Normal 0.08 0.08 0.25 0.07 0.43 0 0.04 0.02 0.56 0.13 0.31 0.04

CFRISK

Lung 0.18 0.10 0.36 0.01 0 1 0.06 0.06 0.19 0 0.27 0 

SRVOAFRAC 0.30 0.12 -0.31 --- --- --- 0.02 0.23 0.04 0.04 0.21 0 

SRVLAM 0.40 0.10 -0.30 0.01 0.01 0.51 --- --- --- 0.02 0 1 

BATTDUR 0.41 0.01 0.10 0.01 0.12 0 0 0.18 0.01 0.04 0 1 

Fuel failure 

criterion 0.41 0 0.07 --- --- --- --- --- --- --- --- ---

Ba-140

Inhalation 0.45 0.04 -0.16 0.04 0.05 0.38 0.02 0.10 0.20 --- --- ---

Sr-92

Inhalation 0.48 0.03 -0.15 0.05 0 1 0 0.21 0 0.02 0.13 0.06

CFRISK

Thyroid 0.50 0.02 0.10 --- --- --- --- --- --- 0 0.14 0.01

RHONOM 0.52 0.02 0.12 0.04 0.07 0.49 --- --- --- --- --- ---

SC1141_2 0.53 0.01 -0.10 0.01 0 1 --- --- --- 0.03 0 1 

SC1131_2 0.54 0.01 -0.12 0.11 0.32 0 0.83 0.78 0 0.32 0.79 0 

VDEPOS 0.56 0.02 0.10 0 0.15 0 0 0 1 0.01 0.12 0.12

Pu-239

Inhalation 0.57 0.01 0.11 0.02 0 1 --- --- --- --- --- ---

Sr-90

Inhalation 0.57 0 -0.06 0.01 0.08 0.07 0.05 0.03 0.45 --- --- ---

ESPEED --- --- --- 0 0.20 0 --- --- --- 0 0 1 

Cs-137

Inhalation --- --- --- 0.01 0.04 0.29 0 0.10 0.07 0.01 0.22 0.01

SLCRFRAC --- --- --- 0 0.05 0.48 --- --- --- --- --- ---

Ce-141

Inhalation --- --- --- --- --- --- 0.04 0 1 --- --- ---

DLTEVA

Cohort 4 --- --- --- --- --- --- 0 0 1 --- --- ---

Te-127m

Inhalation --- --- --- --- --- --- 0.05 0 1 0.02 0 1 

CSFACT

Evacuation --- --- --- --- --- --- --- --- --- 0 0.19 0.02
6-136

Table 6.4-15 Conditional, mean, individual LCF risk (per event) regression of MACCS

sensitivity HPS model at the 30-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.56 0.82 0.70 0.76

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

PROTIN

Normal 0.07 0.07 0.23 0.04 0.21 0 0.02 0.22 0.02 0.20 0.82 0 

CFRISK

Lung 0.19 0.12 0.34 0 0.10 0 0 0.04 0.24 0.01 0.25 0.03

SRVLAM 0.28 0.09 -0.31 0.05 0.11 0.01 --- --- --- 0 0.08 0.47

SRVOAFRAC 0.39 0.11 -0.31 --- --- --- 0.01 0 1 0 0 1 

Fuel failure

criterion 0.40 0.01 0.12 --- --- --- --- --- --- --- --- ---

BATTDUR --- --- --- 0.02 0.01 0.83 --- --- --- 0 0.28 0.01

Ba-140

Inhalation 0.42 0.02 0.11 0.09 0.20 0 0.13 0.16 0.49 --- --- ---

Sr-92

Inhalation 0.43 0.01 -0.12 0.12 0.26 0 0.28 0.64 0 0.05 0.49 0.01

RHONOM 0.47 0.04 -0.15 --- --- --- --- --- --- --- --- ---

SC1131_2 0.50 0.03 -0.17 --- --- --- 0.01 0.01 0.25 0 0 1 

CFRISK

Thyroid 0.52 0.02 0.10 0 0.12 0.02 0 0.04 0.14 0.02 0 1 

SC1141_2 0.53 0.01 -0.09 --- --- --- --- --- --- 0.03 0 1 

ESPEED 0.54 0.01 0.10 --- --- --- 0.02 0.16 0 0.03 0 1 

Ce-141

Inhalation 0.56 0.02 0.10 0.02 0.18 0 0 0 1 --- --- ---

SLCRFRAC 0.56 0 -0.06 0.05 0 1 0.01 0.41 0 --- --- ---

CSFACT

Evacuation --- --- --- 0.01 0.14 0 0 0 1 0 0.16 0.04

Cs-137

Inhalation --- --- --- 0 0.10 0.01 --- --- --- 0.01 0.33 0 

DLTEVA

Cohort 3 --- --- --- 0 0.05 0.48 --- --- --- --- --- ---

Sr-90

Inhalation --- --- --- 0 0 1 --- --- --- --- --- ---

DLTEVA

Cohort 4 --- --- --- --- --- --- 0 0.12 0.01 --- --- ---

VDEPOS --- --- --- --- --- --- 0 0.04 0.65 0 0.31 0 

DLTEVA

Cohort 1 --- --- --- --- --- --- 0 0 1 --- --- ---

Te-127m

Inhalation --- --- --- --- --- --- --- --- --- 0 0 1 
6-137

Table 6.4-16 Conditional, mean, individual LCF risk (per event) regression of MACCS

sensitivity HPS model at the 40-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.56 0.80 0.70 0.85

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

PROTIN

Normal 0.10 0.10 -0.33 0.04 0.05 0.45 --- --- --- 0 0.23 0.11

CFRISK

Lung 0.22 0.12 0.33 0 0 1 0 0.10 0.01 0 0 1 

SRVOAFRAC 0.33 0.11 -0.32 --- --- --- 0.02 0 1 0 0 1 

SRVLAM 0.39 0.06 0.22 0.06 0.27 0 0.01 0.12 0.15 0.21 1 0 

Fuel failure 

criterion --- --- --- 0 0.09 0 --- --- --- --- --- ---

BATTDUR --- --- --- 0.01 0.07 0.17 --- --- --- 0 0.42 0 

Ba-140

Inhalation 0.41 0.02 0.12 0.03 0.22 0 0.20 0.26 0.13 --- --- ---

Sr-92

Inhalation 0.42 0.01 -0.11 0.07 0.18 0 0.28 0.62 0 0 0.39 0.02

Sr-90

Inhalation 0.46 0.04 -0.17 0.01 0 0.67 --- --- --- --- --- ---

SC1131_2 0.49 0.03 -0.19 --- --- --- 0.01 0.02 0.28 0 0 1 

CFRISK

Thyroid 0.51 0.02 0.12 0.01 0.11 0 --- --- --- 0 0.32 0.03

SC1141_2 0.52 0.01 -0.10 --- --- --- --- --- --- 0 0.38 0.03

ESPEED 0.53 0.01 0.10 0.03 0 1 0.03 0.13 0.02 0 0.19 0.18

Ce-141

Inhalation

0.55 0.02 0.10 0 0.22 0 0 0 1 --- --- ---

Pu-239

Inhalation 0.56 0.01 0.11 --- --- --- --- --- --- --- --- ---

Cs-137

Inhalation 0.57 0.01 -0.08 0 0.06 0.19 0 0 1 0 0.54 0 

RHONOM --- --- --- 0.03 0.08 0.13 --- --- --- --- --- ---

SLCRFRAC --- --- --- --- --- --- 0.02 0.47 0 --- --- ---

VDEPOS --- --- --- --- --- --- 0.02 0.17 0.01 0 0 1 

DLTEVA

Cohort 4 --- --- --- --- --- --- 0 0 0.40 --- --- ---

DLTEVA

Cohort 3 --- --- --- --- --- --- 0.03 0 1 --- --- ---

Te-127m

Inhalation --- --- --- --- --- --- --- --- --- 0 0 1 

CSFACT

Evacuation --- --- --- --- --- --- --- --- --- 0.37 0 1 
6-138

Table 6.4-17 Conditional, mean, individual LCF risk (per event) regression of MACCS

sensitivity HPS model at the 50-mile circular area

Rank Regression Quadratic Recursive 

Partitioning MARS

Final R2 0.56 0.82 0.70 0.86

Input R2 inc. R2 cont. SRRC Si Ti p-val Si Ti p-val Si Ti p-val

PROTIN

Normal 0.10 0.10 -0.33 0.05 0 1 --- --- --- 0 0.68 0 

CFRISK

Lung 0.22 0.12 0.33 0 0.08 0.02 --- --- --- 0 0 1 

SRVOAFRAC 0.34 0.12 -0.32 --- --- --- 0.02 0 1 0 0.20 0.13

SRVLAM 0.40 0.06 0.21 0.09 0.33 0 0 0.10 0.07 0.48 1 0 

Fuel failure 

criterion 0.40 0 0.08 0.04 0.07 0.03 --- --- --- --- --- ---

BATTDUR --- --- --- 0 0.13 0.02 --- --- --- 0 0.05 0.46

Sr-90

Inhalation 0.44 0.04 -0.16 --- --- --- 0.03 0.08 0.1 --- --- ---

SC1131_2 0.48 0.04 -0.20 --- --- --- 0 0.01 0.32 0 0 1 

CFRISK

Thyroid 0.50 0.02 0.11 0 0.06 0.13 --- --- --- 0 0.40 0 

Ba-140

Inhalation 0.53 0.03 0.23 0.07 0.23 0 --- --- --- --- --- ---

Te-127m

Inhalation 0.55 0.02 -0.10 --- --- --- 0.02 0.17 0.01 0 0 1 

ESPEED 0.56 0.01 0.10 0 0 1 0 0 1 0 0.27 0.12

Sr-92

Inhalation 0.57 0.01 -0.11 0.06 0.21 0.01 0.05 0.60 0 0.06 0.78 0 

Cs-137

Inhalation 0.59 0.02 -0.09 --- --- --- 0.03 0.15 0 0 0.17 0.27

Pu-239

Inhalation 0.60 0.01 0.12 --- --- --- --- --- --- --- --- ---

RHONOM --- --- --- 0 0.16 0 0.14 0.19 0.31 --- --- ---

SC1141_2 --- --- --- 0 0.15 0 0.03 0 1 0 0 1 

DLTEVA

Cohort 3 --- --- --- 0.02 0.06 0.23 --- --- --- --- --- ---

Ce-141

Inhalation --- --- --- 0 0.06 0.33 0.02 0 1 --- --- ---

DLTEVA

Cohort 1 --- --- --- 0.01 0 1 --- --- --- --- --- ---

SLCRFRAC --- --- --- --- --- --- 0.02 0.40 0 --- --- ---

DLTEVA

Cohort 3 --- --- --- --- --- --- 0 0.12 0.01 --- --- ---

VDEPOS --- --- --- --- --- --- 0 0.12 0.2 0 0.36 0 

DLTEVA

Cohort 4 --- --- --- --- --- --- 0 0 1 --- --- ---

CSFACT

Evacuation --- --- --- --- --- --- --- --- --- 0 0 1 
6-139

6.4.4 Habitability Criterion

Habitability is the consequence model parameter that is used to establish the dose level at 

which residents are allowed to return to their homes. Habitability applies to everyone, not just 

evacuees. During plume passage, hotspot and normal relocation criteria are applied to 

determine whether residents remain in their homes or not. After the emergency phase, the

habitability criterion is applied to determine which residents can return home and which cannot. 

Site specific criterion are used to define the long-term habitability criterion; most states adhere 

to the EPA PAGs, which specify a dose of 2 rem in the first year and 500 mrem per year 

thereafter. This recommendation [63] has traditionally (e.g., NUREG-1150) been implemented 

as a cumulative 4 rem over the first five years (2 rem in the first year + 4 years x 0.5 rem/year) 

of exposure [16]. However, the State of Pennsylvania has a more restricted guideline of 

0.5 rem/yr beginning in the first year. This criterion is expected to influence the consequence 

results because the long-term doses that residents receive typically exceed the emergency 

phase doses, as demonstrated in the SOARCA study. Because the definition of habitability is 

determined by the State of Pennsylvania, it was not considered to be uncertain in the 

uncertainty analysis. 

Evacuees may not return and other residents are potentially relocated according to the hotspot

or normal relocation parameters. The evacuees and relocated residents receive no additional 

emergency phase doses after they are modeled as moving out of the evacuation zone. MACCS

implements user-defined habitability criterion to determine when residents may move back to 

their residence during the long-term phase. Any additional dose to these residents is calculated 

as long-term phase dose.

Habitability decision making in MACCS can result in four possible outcomes:

(1). land is immediately habitable,

(2). land is habitable immediately after decontamination,

(3). land is habitable after decontamination followed by an additional period of interdiction, and

(4). land is condemned and therefore not habitable for the entire calculation.

For the purpose of determining the habitability, dose is the sum of the doses from the 

groundshine and resuspension pathways. The user-specified value of DSCRLT is used to 

determine whether land is considered suitable for habitation during the long-term phase. This 

value is the maximum allowable direct exposure dose commitment to the critical organ during 

the long-term phase action period. If this dose criterion is exceed in any spatial element during 

the long term action period, mitigative actions such as decontamination or decontamination 

followed by temporary interdiction are employed to limit the dose to the critical organ so that the 

allowable dose level is not exceeded in that spatial grid element. Usually, an effective dose is 

used to evaluate habitability. If the property cannot be made habitable within 30 years or if the 

cost of restoring habitability is greater than the cost of condemning it, the property is

condemned and permanently withdrawn from use.

Five habitability sensitivity analyses were performed for each of the three dose-response

models (i.e., LNT, USBGR, and HPS). For the Peach Bottom unmitigated LTSBO scenario, the

conditional, mean, individual LCF risk (per event) (NUREG/CR-7110 Volume 1, Table 7-2) is 

compared for each of the variations considered. All the sensitivity analyses use the SOARCA 

uncertainty analysis base case MELCOR source term described in Appendix C. 
6-140

All results are presented in conditional risk to a member of the public. The conditional risks 

assume that the accident occurs and indicate the risks to individuals as a result of the accident 

(e.g., latent cancer fatality (LCF) risk per event). The risk metrics used in this sensitivity study 

are conditional, mean, individual LCF risk (per event). There were no early-fatality risks 

observed in these analyses.

6.4.4.1 Habitability Sensitivity Inputs

The five habitability sensitivity simulations were based on the current State of Pennsylvania 

public radiation standard, EPA guidelines, NUREG-1150, and ICRP recommendations. The 

discussion below provides background information on the justification of the sensitivity cases 

analyzed. 

SOARCA Estimate for Habitability: 0.5 rem/yr

Most states adhere to the EPA guidelines for habitability which specify a dose of 2 rem in the 

first year and 0.5 rem per year thereafter. However, the State of Pennsylvania guidance is for a 

stricter habitability criterion of 0.5 rem per year beginning in the first year, and this value was 

used in the NUREG/CR-7110 Volume 1 MACCS analyses [2]. 

EPA Habitability Criterion Interoperation: 5 rem over 7 years = 2 rem/yr (1st year) 0.5 

rem/yr (2nd through 7th year)

The habitability criterion currently used by the EPA is 0.05 Sv (5 rem) over a 50 year period. 

For this implementation of the habitability criterion, the EPA recommendation is interpreted as a 

limit of 5 rem over 7 years (i.e., 2 rem in the first year + 6 years at 0.5 rem per year). 

Based on EPA-400-R-92-001 [51] the following determines the EPA guidance habitability 

criterion:

From Section 4.2:

“PAGs for protection from deposited radioactivity during the intermediate phase 

are summarized in Table 4-1. The basis for these values is presented in detail in 

Appendix E. In summary, relocation is warranted when the projected sum of the 

dose equivalent from external gamma radiation and the committed effective dose 

equivalent from inhalation of resuspended radionuclides exceeds 2 rem in the 

first year. Relocation to avoid exposure of the skin to beta radiation is warranted 

at 50 times the numerical value of the relocation PAGs for effective dose 

equivalent.

From Section 4.2.1:

“It is an objective of these PAGs to assure that 1) doses in any single year after 

the first will not exceed 0.5 rem, and 2) the cumulative dose over 50 years 

(including the first and second years) will not exceed 5 rem. For the source 

terms from reactor incidents, the above PAGs of 2 rem projected dose in the 

first year is expected to meet both of these objectives through radioactive decay, 

weathering, and normal part time occupancy in structures.
6-141

NUREG-1150: 4 rem over 5 years = 2 rem/yr (1st year) 0.5 rem/yr (2nd through 5th year)

The habitability criterion used in NUREG-1150 was 0.04 Sv (4 rem) over a 5 year period [16]. 

The NUREG-1150 habitability criterion is the same as the value used for the Surry MACCS

analyses in NUREG/CR-7110 Volume 2. NUREG-1150 was based on a draft EPA document 

[63] and has traditionally been implemented in MACCS16 as a cumulative 4 rem over the first 

5 years (i.e., 2 rem in the first year + 4 years at 0.5 rem per year) of exposure. 

ICRP: 0.1 rem/yr and 2 rem/yr

These two habitability criteria are consistent with ICRP 103 [64] and ICRP 111 [65] guidance. 

These reports serve as a guide for the protection of individuals living in contaminated areas for 

the long term after a nuclear accident or other situations involving dangerous levels of radiation. 

ICRP 103 suggests that appropriate reference levels should preferably be chosen in the 

1-20 mSv (0.1–2 rem) band. As part of this sensitivity study, a lower bound of 0.1 rem per year 

and an upper bound of 2 rem per year were selected. 

6.4.4.2 Habitability Sensitivity Results – LNT Dose-Response Model

A series of sensitivity analyses using the five habitability criteria was conducted for the LNT 

dose-response model. All the sensitivity simulations use the SOARCA uncertainty analysis 

base case source term described in Appendix C. As an additional comparison, the Peach 

Bottom unmitigated LTSBO scenario conditional, mean, individual LCF risk (per event) results 

from the SOARCA study (NUREG/CR-7110 Volume 1, Table 7-2) are also presented. All 

MACCS variables other than the habitability parameters remained fixed. Table 6.4-18 provides 

the results of the conditional, mean, individual LCF risk (per event) for specified circular areas 

and habitability parameters. As shown on Figure 6.4-4 and Table 6.4-18, a lower habitability 

limit results in a lower LCF risk, and a higher habitability limit results in a higher LCF risk. 

Table 6.4-19 shows the percent difference between the habitability sensitivities compared to the 

SOARCA uncertainty analysis base case with 0.5 rem/yr habitability at specified circular areas. 

For this work, the emergency phase is defined as the first seven days following the initial 

release to the environment. The long-term phase is defined as a 50-year period immediately

following the emergency phase (i.e., there is no intermediate phase). Figure 6.4-5 through 

Figure 6.4-9 show the emergency phase (red) and the long-term phase (blue) contributions to 

conditional, mean, individual LCF risk (per event) for each habitability criterion and at each

specified circular area. 

As shown on Figure 6.4-5, the majority of the LCF risk contribution within the EPZ results from 

the long-term phase for all of the habitability choices investigated. Thus the higher the 

habitability dose limit, the higher the LCF risk as a result of long-term dose within the EPZ. 

Figure 6.4-6 shows the majority of the LCF risk within 20 miles for the 0.1 rem/yr habitability 

criterion is from the emergency phase. While the emergency phase LCF risk for the 0.1 rem/yr 

habitability criterion is the same as the risk for all the habitability criteria, the low threshold 

reduces long-term LCF risk. All other habitability criteria have the majority of their respective 

 

16 Note that in the MACCS implementation of 4 rem over 5 years, incurring a dose greater than 2 rem in the first year 

is possible as long as 4 rem is not exceeded in 5 years. Hence as reported in the sensitivity results, a habitability 

criterion of 2 rem/yr is actually more restrictive than 4 rem over 5 years in the MACCS implementation.
6-142

LCF risk from the long-term phase. The 30-mile, 40-mile, and 50-mile circular area results are 

similar in trend to the 20-mile circular area results shown on Figure 6.4-6. 

Table 6.4-18 Habitability criterion comparison of conditional, mean, individual LCF risk 

(per event) for LNT dose-response model

Radius

(mi)

SOARCA 

Estimate*

SOARCA Uncertainty Analysis Base Case Source Term

0.5 rem/yr* 0.1 rem/yr 2 rem/yr 4 rem/

5 yrs

5 rem/

7yrs

10 8.9x10-5 9.0x10-5 3.7x10-5 1.6x10-4 1.7x10-4 1.8x10-4

20 7.6x10-5 8.3x10-5 5.9x10-5 1.1x10-4 1.2x10-4 1.2x10-4

30 5.3x10-5 5.8x10-5 4.2x10-5 7.4x10-5 7.7x10-5 7.8x10-5

40 3.3x10-5 3.7x10-5 2.8x10-5 4.6x10-5 4.7x10-5 4.8x10-5

50 2.7x10-5 3.0x10-5 2.3x10-5 3.7x10-5 3.8x10-5 3.9x10-5

* The differences between the SOARCA estimate and the SOARCA uncertainty analysis base case with a habitability 

criterion of 0.5 rem/yr are discussed in Appendix C

Figure 6.4-4 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for specified circular areas for the LNT dose-response

model 
6-143

Table 6.4-19 Percentage change in conditional, mean, individual LCF risk (per event) 

for the LNT dose-response model from variations in habitability criterion

(reduction/increase (-/+)) 

Radius

(mi)

SOARCA UA 

Base Case 0.5 

rem/yr

0.1 rem/yr 2 rem/yr 4 rem/

5yrs

5 rem/

7yrs

10 0.0% -59% 75% 93% 103%

20 0.0% -30% 34% 41% 43%

30 0.0% -27% 28% 33% 35%

40 0.0% -25% 23% 27% 29%

50 0.0% -25% 21% 25% 28%

Figure 6.4-5 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for the 10-mile circular area for the LNT dose-response

model
6-144

Figure 6.4-6 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for the 20-mile circular area for the LNT dose-response

model

Figure 6.4-7 Habitability criterion comparison of conditional, mean, individual LCF risk 

(per event) for the 30-mile circular area for the LNT dose-response model
6-145

Figure 6.4-8 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for the 40-mile circular area for the LNT dose-response

model

Figure 6.4-9 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for the 50-mile circular area for the LNT dose-response

model
6-146

6.4.4.3 Habitability Sensitivity Results – Additional Dose-Response Models

A series of sensitivity analyses using the five habitability criteria were conducted for the USBGR 

and HPS dose-response models. All the sensitivity simulations use the SOARCA uncertainty 

analysis base case source term described in Appendix C. As an additional comparison, the 

Peach Bottom unmitigated LTSBO scenario, conditional, mean, individual LCF risk (per event) 

results from the SOARCA study (NUREG/CR-7110 Volume 1, Table 7-2) are also presented. 

All other MACCS variables other than the habitability parameters remained fixed. Table 6.4-20

provides the results of the conditional, mean, individual LCF risk (per event) at specified circular 

areas for the USBGR dose-response model and habitability parameters. As shown in 

Table 6.4-20 within the EPZ, when the dose rate for the habitability criterion is below the dose 

truncation level (0.62 rem/yr), LCF risks are two orders of magnitude lower than when the dose 

rate for the habitability criterion is above the dose truncation level. Table 6.4-21 shows the 

percent difference between each of the habitability criteria as compared with the SOARCA 

uncertainty analysis base case, which uses a 0.5 rem/yr habitability criterion. The percent 

differences are similar to those in Table 6.4-19 for the LNT dose-response model for distances 

beyond the EPZ. 

Figures 6.4-10 through 6.4-14 show the LCF risk contribution for each habitability criterion at 

each specified circular area. Since there is no simple way to separate the LCF risks from the 

emergency phase and long-term phase, Figures 6.4-10 through 6.4-14 only show the total risk 

of both phases. 

To better understand this inability to discern the LCF risk between the emergency and long-term 

phases, a discussion on the dose-response models is needed. The long-term phase risk

dominates the total risk for the accident scenario when the LNT dose-response assumption is 

made. These long-term risks are controlled by the habitability (return) criterion, which is the 

dose rate at which residents are allowed to return to their homes following the emergency 

phase. For example, the Peach Bottom habitability criterion is a dose rate of 500 mrem/yr. This 

dose rate is below the truncation levels based on USBGR (620 mrem/yr) and based on the HPS 

position statement (5 rem/yr with 10 rem lifetime); therefore, most of the doses received during 

the long-term phase are below the dose truncation limit and are not counted toward health 

effects when using these criteria. Thus, most of the risks associated with either of the truncation 

levels are from doses received during the first year. The conditional, mean, individual LCF risk 

(per event) for these dose truncation models do not show separate risks for the emergency and 

long-term phases because those phases overlap, especially in the first year, and are not easily 

separated for purposes of evaluating the annual dose threshold. 

Because the internal doses from inhalation diminish with time, most of the doses in the second 

and subsequent years are from the exposures during that year. But these doses are limited by 

the habitability criterion in any year. The habitability criterion limit is for all dose pathways, in 

this case groundshine and inhalation from resuspended aerosols. The inhalation dose used in 

this criterion is a committed dose (i.e., it accounts for doses received over the next 50 years). 

Because the annual doses allowed by the habitability criterion could be less than truncation 

levels based on USBGR and the HPS position statement, nearly all of the risk is from doses 

received during the first year. These doses include most of emergency phase doses and a 

fraction of the long-term phase doses. This explains the risk profiles for these dose-truncation 

criteria. 

Figure 6.4-11 shows that the habitability sensitivities have little effect on the overall LCF risk 

when the USBGR dose-response model is applied beyond the EPZ. The risks are similar to 

those presented in the SOARCA study. The 30-mile, 40-mile, and 50-mile results are similar in 

trend to the 20-mile results shown on Figure 6.4-11. 
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Table 6.4-20 Habitability criterion comparison of conditional, mean, individual LCF risk 

(per event) for USBGR dose-response model

Radius

(mi)

SOARCA 

Estimate*

SOARCA Uncertainty Analysis Base Case Source Term

0.5 rem/yr* 0.1 rem/yr 2 rem/yr 4 rem/

5yrs

5 rem/

7yrs

10 7.4x10-7 8.9x10-7 8.2x10-7 2.5x10-5 3.3x10-5 3.8x10-5

20 1.9x10-5 2.6x10-5 2.0x10-5 3.9x10-5 4.2x10-5 4.3x10-5

30 1.1x10-5 1.6x10-5 1.1x10-5 2.3x10-5 2.5x10-5 2.5x10-5

40 5.0x10-6 7.7x10-6 4.8x10-6 1.2x10-5 1.3x10-5 1.3x10-5

50 3.4x10-6 5.2x10-6 3.2x10-6 8.7x10-6 9.4x10-6 9.7x10-6

* The differences between the SOARCA estimate and the SOARCA uncertainty analysis base case with a habitability 

criterion of 0.5 rem/yr are discussed in Appendix C

Table 6.4-21 Percentage change in conditional, mean, individual LCF risk (per event) 

for the USBGR dose-response model from variations in habitability 

criterion (reduction/increase (-/+)) 

Radius (mi) 0.5 rem/yr 0.1 rem/yr 2 rem/yr 4 rem/5yrs 5 rem/7yrs

10 0.0% -8.6% 2,600% 3,600% 4,100%

20 0.0% -23% 49% 60% 65%

30 0.0% -30% 50% 60% 64%

40 0.0% -37% 57% 67% 72%

50 0.0% -39% 66% 79% 86%
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Figure 6.4-10 Habitability criterion comparison of conditional, mean, individual LCF risk 

(per event) for the 10-mile circular area for the USBGR dose-response

model

Figure 6.4-11 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for the 20-mile circular area for the USBGR 

dose-response model
6-149

Figure 6.4-12 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for the 30-mile circular area for the USBGR 

dose-response model

Figure 6.4-13 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for the 40-mile circular area for the USBGR 

dose-response model
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Figure 6.4-14 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for the 50-mile circular area for the USBGR 

dose-response model

Table 6.4-22 provides the results of the conditional, mean, individual LCF risk (per event) for 

specified circular areas for the HPS dose-response model. As shown in Table 6.4-22, the 

habitability criteria are all below the dose truncation level (5 rem/yr with 10 rem lifetime limit) and 

the results are similar to those for the SOARCA study. Table 6.4-23 shows the percent 

difference between the habitability criteria compared to the SOARCA uncertainty analysis base 

case with 0.5 rem/yr habitability. The percent differences are similar to those shown in 

Table 6.4-19 for the LNT dose-response model for specified circular areas. 

Figures 6.4-15 through 6.4-19 show the conditional, mean, individual LCF risk (per event) 

contribution for each habitability criterion at each specified circular area. Since there is no 

simple way to separate the LCF risks from the emergency phase and long-term phase, 

Figures 6.4-15 through 6.4.4-17 only show the total risk of both phases. The inability to discern 

the emergency and long-term phase LCF risk is the same as that explained for the USBGR 

dose-response model. Figure 6.4-15 shows that the habitability criteria have little effect on the 

overall LCF risk when the HPS dose-response model is applied. The 20-mile, 30-mile, 40-mile, 

and 50-mile circular area results are similar in trend to the 10-mile circular area results shown 

on Figure 6.4-15. 
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Table 6.4-22 Habitability criterion comparison of conditional, mean, individual LCF risk 

(per event) for HPS dose-response model

Radius

(mi)

SOARCA 

Estimate*

SOARCA Uncertainty Analysis Base Case Source Term

0.5 rem/yr* 0.1 rem/yr 2 rem/yr 4 rem/

5 yrs

5 rem/

7 yrs

10 3.7x10-7 5.6x10-7 5.3x10-7 8.2x10-7 8.3x10-7 9.5x10-7

20 2.2x10-6 4.4x10-6 3.8x10-6 6.1x10-6 8.2x10-6 9.1x10-6

30 8.9x10-7 1.7x10-6 1.5x10-6 2.5x10-6 3.5x10-6 3.8x10-6

40 3.7x10-7 7.1x10-7 6.2x10-7 1.0x10-6 1.4x10-6 1.6x10-6

50 2.4x10-7 4.5x10-7 3.9x10-7 6.4x10-7 9.0x10-7 1.0x10-6

* The differences between the SOARCA estimate and the SOARCA uncertainty analysis base case with a habitability 

criterion of 0.5 rem/yr are discussed in Appendix C

Table 6.4-23 Percentage change in conditional, mean, individual LCF risk (per event) 

for the HPS dose-response model from variations in habitability criterion

(reduction/increase (-/+)) 

Radius

(mi)

SOARCA UA 

Base Case 

with 0.5 

rem/yr

0.1 rem/yr 2 rem/yr 4 rem/5yrs 5 rem/7yrs

10 0.0% -5.7% 45% 48% 68%

20 0.0% -12% 40% 89% 110%

30 0.0% -13% 42% 99% 120%

40 0.0% -13% 42% 99% 120%

50 0.0% -13% 42% 98% 120%
6-152

Figure 6.4-15 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for the 10-mile circular area for the HPS dose-response

model

Figure 6.4-16 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for the 20-mile circular area for the HPS dose-response

model
6-153

Figure 6.4-17 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for the 30-mile circular area for the HPS dose-response

model

Figure 6.4-18 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for the 40-mile circular area for the HPS dose-response

model
6-154

Figure 6.4-19 Habitability criterion comparison of conditional, mean, individual LCF 

risk (per event) for the 50-mile circular area for the HPS dose-response

model

6.4.5 Weather Sampling Effects

In the foregoing sections, the uncertainty that has been addressed has been categorized as 

epistemic. In fact, each source of uncertainty has both an epistemic and aleatory component. 

For example, the conditions leading to failure of a SRV are currently poorly quantified. The lack 

of quantification results in epistemic uncertainty. However, if a large set of SRVs were tested to 

failure under accident-like conditions, the epistemic uncertainty would be diminished or even 

eliminated, but some aleatory uncertainty would remain. The source of the remaining aleatory 

uncertainty is sample-to-sample variations and manufacturing flaws. The effect of some of 

these flaws may not be able to be evaluated without testing a specific valve to failure, at which 

point it could no longer be used. Thus, in practice, all uncertainty has some aleatory 

component.

One large source of aleatory uncertainty in a probabilistic risk assessment is from the weather. 

In SOARCA, the aleatory uncertainties due to weather were characterized in terms of mean 

values. Unlike most of the other input parameters used in SOARCA or for any risk analysis, 

weather is inherently unknowable because of the exact time of an accident is unknowable. 

Because weather can have a significant impact on predicted consequences, it must be treated 

in a statistical fashion and the resulting uncertainty is clearly in the category of aleatory 

uncertainty. This section explores the sampling error associated with the aleatory uncertainty 

resulting from weather.
6-155

A set of sensitivity analyses to evaluate the SOARCA weather sampling technique was 

evaluated for the LNT, USBGR, and HPS dose-response models. All of the sensitivity 

simulations use the SOARCA uncertainty analysis base case source term described in 

Appendix C. The SOARCA weather sampling technique was compared to sampling the entire 

weather database used for Peach Bottom. All of the MACCS variables other than the sampled 

weather trials was held fixed. 

For SOARCA, a structured Monte-Carlo sampling method was employed for weather sampling. 

This was done by random selection of a user-specified number of weather sequences (i.e., start 

times) from the set of sequences assigned to each user-specified weather category. This 

begins by sorting an annual weather file according to user specified criteria. Each MACCS

analysis uses a user-specified random seed. This random seed was kept constant for all 

MACCS analysis and thus the same weather trials from the same meteorological data file were 

selected for all of the analyses. 

When evaluating the consequences of a release, MACCS selects a set of weather trials 

(i.e., wind speeds, wind directions, stability classes, precipitation rates, and a diurnal seasonal 

mixing height). Each weather trial is characterized by a starting hour from a meteorological data 

file. Subsequent hours of the release use subsequent hours from the data file. Thus, each hour 

of the release uses weather inputs specific to an hour of weather data from the MACCS

meteorological data file (PB MACCS 2006 Met Data 64WD.inp). However, while the data file 

contains data to perform 8,760 weather trials, only about 1,000 of them were sampled for 

SOARCA. 

Weather binning is an approach used in MACCS to categorize similar sets of weather data 

based on wind speed, stability class, and the intensity of precipitation. The weather sampling 

strategy adopted for SOARCA uses the nonuniform weather-binning approach in MACCS. This 

approach, which allows the user to specify a different number of random samples for each bin, 

has been available since MACCS was first released [9] but was not used in previous studies. 

The weather binning structure defined in SOARCA was used previously in NUREG-1150. This 

structure consists of 16 predefined bins for combinations of stability class and wind speed, and 

20 user-defined bins for rain occurring before the plume travels 32 km (20 miles). The rain bins 

differentiate rain intensity and the distance the plume travels before rain begins. An approach 

called, uniform weather bin sampling was used in NUREG-1150. Four weather sequences were 

sampled per bin, resulting in a nominal 144 weather trials. In conjunction with this sampling 

method, an additional strategy called wind rotation was used. Wind rotation expands the set of 

weather trials by a factor of 16 (i.e., the number of compass sectors used in the analysis) by 

reevaluating the results for each weather trial assuming that the wind had blown in each of the 

other compass directions. The consequences for each wind direction are assigned a probability 

that accounts for the wind rose probability. In effect, this strategy results in 16 x 144 = 2,304 

nominal weather trials. 

A wind rose can be shown graphically using a wind rose diagram. A wind rose diagram 

schematically represents the wind direction and the frequency of occurrence for a particular 

wind direction. It can also differentiate other features of the weather, such as the intensity of the 

wind. Figure 6.4-20 provides an example of a wind rose diagram.
6-156

Figure 6.4-20 Example wind rose diagram

For the nonuniform weather sampling strategy approach adopted in SOARCA, the number of 

trials selected from each bin is the maximum of 12 trials and 10% of the number of trials in the 

bin. Some bins contain fewer than 12 trials. In those cases, all of the trials within the bin are 

used for sampling. This strategy results in 984 weather trials for Peach Bottom. Table 6.4-23 

shows the weather sampling inputs used in SOARCA for Peach Bottom. MACCS does not 

allow wind rotation in conjunction with one of the other models used in SOARCA, network 

evacuation. Thus, expanding the number of weather trials by the number of compass sectors 

was not used in SOARCA, which is one of the main reasons that the number of weather trials 

was significantly increased from the number used in NUREG-1150. 

Meteorological data used in the SOARCA project consisted of one year of hourly meteorological 

data (i.e., 8,760 hourly data points for each meteorological parameter). Stability class data were 

derived from temperature measurements at two elevations on the site meteorological towers. 

The specific year of data chosen was based on data recovery (e.g., greater than 90% being 

desirable) and proximity to the target year for SOARCA, which is 2005. Several trends 

(e.g., wind-rose pattern and hours of precipitation) between the years were evaluated and 

estimated to have a relatively minor (i.e., less than ±10 percent) effect on the final results. 

Data needed for MACCS, as used in the SOARCA project, includes: 10-meter wind speed, 

10-meter wind direction in 64 compass directions, stability class (i.e., Pasquill-Gifford stability 

class using representative values of 1–6 for stability classes A–F/G), hourly precipitation, and 

diurnal (morning and afternoon) seasonal mixing heights. 

Table 6.4-25 presents a summary of the meteorological data and shows that the annual 

average ground-level wind speeds were generally low at Peach Bottom. The atmospheric 

stability frequencies were found to be consistent with expected meteorological conditions. 

Neutral and slightly stable conditions predominated during the year, with stable and neutral 

conditions occurring at night and unstable and neutral conditions occurring during the day.
6-157

Table 6.4-24 Weather sampling inputs for Peach Bottom

MACCS

Variable Description Peach Bottom LTSBO

INWGHT

Number of Samples for Each Bin 

Used for Nonuniform Weather Bin 

Sampling

Bin 1 71

Bin 2 42

Bin 3 12

Bin 4 52

Bin 5 57

Bin 6 74

Bin 7 21

Bin 8 12

Bin 9 49

Bin 10 103

Bin 11 77

Bin 12 35

Bin 13 51

Bin 14 75

Bin 15 14

Bin 16 4

Bin 17 44

Bin 18 12

Bin 19 17

Bin 20 24

Bin 21 24

Bin 22 12

Bin 23 4

Bin 24 8

Bin 25 12

Bin 26 12

Bin 27 12

Bin 28 1

Bin 29 3

Bin 30 5

Bin 31 4

Bin 32 12

Bin 33 1

Bin 34 7

Bin 35 9

Bin 36 12
6-158

Table 6.4-25 Statistical summary of raw meteorological data

Parameter

Peach Bottom

Year 2005 Year 2006

Average Wind Speed (m/s) 2.17 2.12

Yearly Precipitation (hour)

(% of Annual Weather)

588

(6.7%)

593

(6.8%)

Atmospheric Stability (%)

Unstable 21.43 20.56

Neutral 63.97 62.34

Stable 14.60 17.10

Joint Data Recovery (%) 97.53 99.25

Figure 6.4-21 shows the wind direction (i.e., wind rose) that the wind blows towards and 

atmospheric stability conditions (i.e., unstable, neutral, and stable) for two years, including the 

year that was used in the SOARCA consequence analyses for Peach Bottom (i.e., 2006). 

Figure 6.4-21 shows the Pasquill-Gifford stability categories in terms of stable conditions 

(categories A through C), neutral stability (category D), and stable conditions (categories E 

and F) for the weather year used in SOARCA on an hourly basis. The trends shown in the figure 

are expected, which are that unstable conditions occur during daylight hours, peaking around 

mid-day, and stable conditions primarily occur during nighttime hours.

Figure 6.4-21 Peach Bottom wind rose and atmospheric stability chart, year 2006

For the sensitivity case, the SOARCA uncertainty analysis base case described in Appendix C 

was compared with the same MACCS analysis, except instead of using the SOARCA weather

sampling technique; all 8,760 hourly weather data points were selected as the starting time for a 

weather trial. 
6-159

Table 6.4-26 provides the results of the conditional, mean, individual LCF risk (per event) within

specified circular areas for the LNT dose-response model. As shown in Table 6.4-26 the 

SOARCA weather sampling technique consistently produces slightly higher LCF risk results.

Table 6.4-26 Weather sampling comparison of the conditional, mean, individual LCF risk 

(per event) using the LNT dose-response mode

Distance SOARCA UA

Base Case

All Weather 

Trials

Difference

(%)

10 9.0x10-5 8.9x10-5 0.8%

20 8.3x10-5 8.1x10-5 2.4%

30 5.8x10-5 5.7x10-5 1.7%

40 3.7x10-5 3.7x10-5 1.1%

50 3.0x10-5 3.0x10-5 1.3%

Figure 6.4-22 shows the conditional, mean, individual LCF risk (per event) within specified 

circular areas using the LNT dose-response model for the emergency phase risk contribution 

(red or green) and the long-term phase risk contribution (blue or orange). Both the emergency 

and long-term phase LCF risk results are consistently slightly higher for the SOARCA weather 

sampling technique (Base Case) than the sensitivity (All Weather Trials) case. Thus, the 

contribution from the change in the number of weather trials to either the long-term phase or the 

emergency phase does not dominate the overall LCF risk.
6-160

Figure 6.4-22 Weather sampling comparison of the conditional, mean, individual LCF 

risk (per event) using the LNT dose-response model within specified 

circular areas

Table 6.4-27 and Figure 6.4-23 provide the results of the conditional, mean, individual LCF risk 

(per event) within specified circular areas for the USBGR dose-response model. As shown in 

Table 6.4-27 the SOARCA weather sampling technique consistently produces slightly higher 

LCF risk results. 

Beyond the EPZ, the SOARCA weather sampling technique produces larger differential results 

than those for the LNT dose-response model. Clearly, this nonlinear dose-response model is

more sensitive to the specific selection of weather trials than the LNT dose-response model.

Table 6.4-27 Weather sampling comparison of the conditional, mean, individual LCF risk 

(per event) using the USBGR dose-response model

Distance SOARCA UA

Base Case

All Weather 

Trials

Difference

(%)

10 8.9x10-7 8.9x10-7 0.8%

20 2.6x10-5 2.5x10-5 5.0%

30 1.6x10-5 1.5x10-5 5.2%

40 7.7x10-6 7.2x10-6 5.7%

50 5.2x10-6 5.0x10-6 5.5%
6-161

Figure 6.4-23 Weather sampling comparison of the conditional, mean, individual LCF 

risk (per event) using the USBGR dose-response model within specified 

circular areas

Table 6.4-28 and Figure 6.4-23 provide the results of the conditional, mean, individual LCF risk 

(per event) within specified circular areas for the HPS dose-response model. As shown in 

Table 6.4-28 the SOARCA weather sampling technique consistently produces higher LCF risk 

results. 

Beyond the EPZ, the SOARCA weather sampling technique produces larger differential results 

than those for either the LNT or USBGR dose-response models. Clearly, this nonlinear 

dose-response model is more sensitive to the specific selection of weather trials than the LNT 

dose-response model.

Table 6.4-28 Weather sampling comparison of the conditional, mean, individual LCF 

risk (per event) using the HPS dose-response model

Distance SOARCA UA

Base Case

All Weather 

Trials

Difference

(%)

10 5.6x10-7 5.6x10-7 0.9%

20 4.4x10-6 3.9x10-6 11.0%

30 1.7x10-6 1.5x10-6 11.6%

40 7.1x10-7 6.3x10-7 11.6%

50 4.5x10-7 4.0x10-7 11.7%
6-162

Figure 6.4-24 Weather sampling comparison of the conditional, mean, individual LCF 

risk (per event) using the HPS dose-response model within specified 

circular areas

The overall difference between the SOARCA weather sampling technique and sampling all 

8,760 hourly data points is relatively small. However, the increase in computational time is eight 

fold. While this is not prohibitively long for the LNT dose-response model (i.e., ~1 hour to 

~8 hours of run time for a single MACCS realization), the increase in computation time for the 

USBGR and HPS dose-response models would make uncertainty analysis applications less 

feasible (i.e., ~1 day to ~8 days of run time for a single MACCS realization).

6.4.5.1 Aleatory Weather Uncertainty

In SOARCA, the aleatory uncertainties due to weather were characterized in terms of mean 

values. However, a CCDF of aleatory uncertainties can be obtained using a single MACCS

analysis for each source term. A set of sensitivity analyses to evaluate the aleatory weather 

uncertainty using the SOARCA weather sampling technique was evaluated for the LNT, 

USBGR, and HPS dose-response models. 

Three source terms were selected, which provided insights into the overall distribution of LCF 

risk for the sensitivity simulations. The SOARCA uncertainty analysis base case source term 

described in Appendix C was used to represent the lower end of the conditional, mean, 

individual LCF risk distribution. Replicate 1 (STP08) Realization 170 source term described in 

Section 6.1.4 was chosen to represent the median of the conditional, mean, individual LCF risk 

distribution. Replicate 1 Realization 62 source term described in Section 6.1.4 was used to 

represent the upper end of the conditional, mean, individual LCF risk distribution. Table 6.4-29

provides a brief description of the three source terms. The SOARCA weather sampling 
6-163

technique described earlier in this section was used for these analyses. All of the MACCS

variables other than the sampled weather data were held fixed. 

Table 6.4-29 Brief source term description for the single realizations selected from 

Replicate 1 (STP08) MELCOR Analyses for the aleatory weather 

uncertainty analyses

Scenario

Integral Release Fractions by Chemical Group

Atmospheri

c Release 

Timing

Xe Cs Ba I Te Ru Mo Ce La Start 

(hr)

End 

(hr)

SOARCA UA 

Base Case 0.981 0.005 0.010 0.025 0.019 0 0 0 0 19.9 48

RLZ062 0.995 0.055 0.014 0.104 0.089 0 0.012 0 0 13.6 48

RLZ170 0.985 0.020 0.022 0.031 0.027 0 0 0.001 0 16.6 48

Two comparisons are presented to show the effects of aleatory weather uncertainty. The first 

shows the individual LCF risk results of the aleatory weather uncertainty for the three source 

terms using the LNT dose-response model with the conditional, mean, individual LCF risk 

results of the MACCS analysis for the combined MELCOR Replicates 1, 2, and 3 using the LNT 

dose-response model (CAP17) discussed in Section 6.2.1. Recall that the CAP17 MACCS

analysis consists of 865 MELCOR source terms using 21 MELCOR epistemic uncertainty 

variables, and 350 MACCS epistemic uncertainty variables of which 338 variables apply to LCF 

risk. 

The second comparison shows the individual LCF risk results of the aleatory weather 

uncertainty for the three source terms using the LNT, USBGR, and HPS dose-response models 

with the conditional, mean, individual LCF risk results of the MACCS analysis for MLECOR 

Replicate 1 using the LNT, USBGR, and HPS dose-response models (i.e., CAP14, CAP15, and 

CAP16, respectively) discussed in Section 6.4.3. Recall, the CAP14, CAP15, and CAP16 

MACCS analyses consists of 284 MELCOR source terms using 21 MELCOR epistemic 

uncertainty variables, and 350 MACCS epistemic uncertainty variables of which 338 variables 

apply to LCF risk. 

6.4.5.1.1 Aleatory Weather Uncertainty for LNT Dose Response

These analyses used the same 984 MACCS aleatory weather trials used for all other SOARCA 

analyses, except a CCDF of the aleatory weather trials was created for each of the three source 

terms. Table 6.4-30 shows the three source term’s conditional, mean, individual LCF risk (per 

event) result with respect to the percentile of the CCDF for the conditional, mean, individual LCF 

risk (per event) results for the MACCS CAP17 analysis. Table 6.4-31 shows the three source 

term’s conditional, mean, individual LCF risk (per event) results from the MACCS CAP 17 

analysis with respect to the percentile of the CCDF. When Table 6.4-31 is compared with 

Table 6.4-30, the median individual LCF risk results for the three source terms in Table 6.4-30

do provide a good example of the median, lower, and upper bounds of the CAP17 conditional, 

mean, individual LCF risk (per event) CCDF distribution for all specified circular areas.
6-164

Table 6.4-30 MACCS aleatory uncertainty analyses conditional mean, individual LCF 

risk (per event) comparison of source terms to the conditional, mean, 

individual LCF risk (per event) CCDF of the MACCS CAP17 analysis for 

specified circular areas

Radius of Circular 

Area (miles)

SOARCA UA 

Base Case

Replicate 1 

Realization 62

Replicate 1 

Realization 170

10 32nd 94th 77th

20 15th 79th 53rd

30 15th 81st 52nd

40 15th 83rd 52nd

50 15th 83rd 53rd

Table 6.4-31 The MACCS CAP17 analysis conditional, mean, individual LCF risk (per 

event) of the source terms for specified circular areas

Radius of Circular 

Area (miles)

SOARCA UA 

Base Case

Replicate 1 

Realization 62

Replicate 1 

Realization 170

10 32nd 60th 98th

20 15th 54th 84th

30 15th 54th 86th

40 15th 53rd 88th

50 15th 52nd 88th

Figure 6.4-25 shows the CCDF of the aleatory weather uncertainty within the 10-mile circular 

area for the conditional, mean, individual LCF risk (per event) and CCDF of the conditional, 

mean, individual LCF risk (per event) results for the MACCS CAP17 analysis. Unlike the 

MACCS CAP17 analysis, the aleatory uncertainty analyses were bounded at the 99th and 

1st percentiles. As shown in Figure 6.4-25, the conditional, mean, individual LCF risk (per event) 

for aleatory weather uncertainty is bounded for all analyses by the epistemic uncertainty for the

conditional, mean, individual LCF risk (per event) results of the MACCS CAP17 analysis. This 

indicates that the epistemic uncertainties within the MACCS CAP17 analysis have a greater 

effect on the overall uncertainty than the aleatory weather uncertainty.
6-165

Figure 6.4-25 CCDF of conditional, mean, individual LCF risk (per event) within the 

10-mile circular area for aleatory weather uncertainty and the MACCS

CAP17 analysis

Figure 6.4-26 shows the CCDF of the aleatory weather uncertainty within the 20-mile circular 

area for the conditional, mean, individual LCF risk (per event) and CCDF of the conditional, 

mean, individual LCF risk (per event) results for the MACCS CAP17 analysis. Figure 6.4-26 

shows similar results to those in Figure 6.4-25 and also indicates the epistemic uncertainties 

within the MACCS CAP17 analysis have a greater effect on the overall uncertainty than the 

aleatory weather uncertainty.
6-166

Figure 6.4-26 CCDF of conditional, mean, individual LCF risk (per event) within the 

20-mile circular area for aleatory weather uncertainty and the MACCS

CAP17 analysis

Figure 6.4-27 through Figure 6.2-29 show the CCDF of the aleatory weather uncertainty within 

the 30-mile, 40-mile, and 50-mile circular areas, respectively, for the conditional, mean, 

individual LCF risk (per event) and CCDF of the conditional, mean, individual LCF risk (per 

event) results for the MACCS CAP17 analysis. These figures show similar results to those in 

Figure 6.4-25 and also indicate the epistemic uncertainties within the MACCS CAP17 analysis 

have a greater effect on the overall uncertainty than the aleatory weather uncertainty.
6-167

Figure 6.4-27 CCDF of conditional, mean, individual LCF risk (per event) within the 

30-mile circular area for aleatory weather uncertainty and the MACCS

CAP17 analysis

Figure 6.4-28 CCDF of conditional, mean, individual LCF risk (per event) within the 

40-mile circular area for aleatory weather uncertainty and the MACCS

CAP17 analysis
6-168

Figure 6.4-29 CCDF of conditional, mean, individual LCF risk (per event) within the 

50-mile circular area for aleatory weather uncertainty and the MACCS

CAP17 analysis.

Table 6.4-32 shows the ratio between the 5th and 95th percentile for the three source term’s LCF 

risk per event results and the conditional, mean, individual LCF risk (per event) results for the 

MACCS CAP17 analysis. As shown in Table 6.4-32, the aleatory weather uncertainty individual 

LCF risk is narrower for all of the analyses than the epistemic uncertainty for the mean results of 

the MACCS CAP17 analysis within all circular areas. This again shows that the epistemic 

uncertainties within the MACCS CAP17 analysis have a greater effect on the overall uncertainty 

than the aleatory weather uncertainty.

Table 6.4-32 Conditional, mean, individual LCF risk (per event) ratio for the MACCS

aleatory uncertainty analyses and the MACCS CAP17 analysis for 

specified circular areas

Radius of 

Circular Area 

(miles)

SOARCA UA 

Base Case

Replicate 1 

Realization 62

Replicate 1 

Realization 170 CAP17

10 4.9 3.4 4.3 13

20 8.3 5.5 6.5 15

30 11 4.5 6.8 15

40 9.4 5.4 7.4 15

50 9.6 5.8 9.0 14
6-169

6.4.5.1.2 Aleatory Weather Uncertainty for Dose-Truncation

The comparisons shown in this section use the same 984 MACCS aleatory weather trials as all 

other SOARCA analyses, except a CCDF of the aleatory weather trials was created for the 

three source terms using the LNT, USBGR, and HPS dose-response models. Table 6.4-33

through Table 6.4-35 show the three source term’s median LCF risk per event result with 

respect to the percentile of the CCDF conditional, mean, individual LCF risk (per event )results 

for the MACCS CAP14 analysis for LNT, the MACCS CAP15 analysis for USBGR, and the 

MACCS CAP16 analysis for HPS dose-response models, respectively. For Table 6.4-33, the 

median LCF risk results for the three source terms do provide a good example of the median, 

lower, and upper bounds of the CAP14 CCDF distribution for all specified circular areas and are 

similar to those shown in Table 6.4-30 for the MACCS CAP17 analysis. 

However, these three source terms only quantify the median and lower half of the CAP15 and 

CAP16 CCDF distributions of conditional, mean, individual LCF risk (per event) results for all 

specified circular areas. This is due to the dose-truncation models having more of the LCF risk 

contribution from the 1st year and thus a larger contribution from the emergency phase. The 

2nd year and subsequent years have less of a contribution to the individual LCF risk than the 

LNT dose-response model because the majority of the doses in these years are below the 

truncation thresholds. Table 6.4-36 shows the percent contribution from each source term for 

the conditional, mean, individual LCF risk (per event) using the LNT dose-response model. 

Since none of the source terms selected for this sensitivity analyses have a large contribution 

from the emergency phase, the overall conditional, mean, individual LCF risks are at the lower 

end of the range for these dose-response models. Table 6.4-36 shows that the uncertainty 

analysis base case has a larger fractional contribution to the emergency phase than either of 

other realizations. 

Table 6.4-33 MACCS aleatory uncertainty analyses median LCF risk per event 

comparison of source terms to the CCDF of the MACCS CAP14 analysis 

(LNT) for specified circular areas

Radius of 

Circular Area 

(miles)

SOARCA UA 

Base Case

Replicate 1

Realization 62

Replicate 1

Realization 170

10 28th 94th 76th

20 9th 80th 45th

30 9th 81st 46th

40 9th 80th 45th

50 9th 82nd 45th
6-170

Table 6.4-34 MACCS aleatory uncertainty analyses median LCF risk per event 

comparison of source terms to the CCDF of the MACCS CAP15 analysis 

(USBGR) for specified circular areas

Radius of 

Circular Area 

(miles)

SOARCA UA 

Base Case

Replicate 1

Realization 62

Replicate 1

Realization 170

10 13th 62nd 32nd

20 11th 56th 30th

30 11th 59th 30th

40 8th 61st 28th

50 8th 61st 24th

Table 6.4-35 MACCS aleatory uncertainty analyses median LCF risk per event 

comparison of source terms to the CCDF of the MACCS CAP16 analysis 

(HPS) for specified circular areas

Radius of 

Circular Area 

(miles)

SOARCA UA 

Base Case

Replicate 1

Realization 62

Replicate 1

Realization 170

10 7th 58th 25th

20 5th 27th 8th

30 6th 27th 8th

40 6th 29th 8th

50 5th 29th 8th

Table 6.4-36 MACCS aleatory uncertainty analyses percent contribution of the 

emergency phase for the conditional, mean, individual LCF risk (per 

event) using the LNT dose-response model for specified circular areas

Radius of 

Circular Area 

(miles)

SOARCA UA 

Base Case

Replicate 1

Realization 62

Replicate 1

Realization 170

10 1.1% 1.0% 1.3%

20 44% 29% 36%

30 45% 28% 36%

40 44% 25% 34%

50 43% 23% 32%
6-171

Figure 6.4-30 through Figure 6.4-34 show a comparison of the CCDF distribution for conditional,

mean, individual LCF risk (per event) results using the LNT, USBGR, and HPS dose-truncation 

models for aleatory weather uncertainty using the SOARCA uncertainty analysis base case 

source term within the 10-mile, 20-mile, 30-mile, 40-mile, and 50-mile circular areas, 

respectively. Unlike the MACCS CAP17 analysis, the aleatory uncertainty analyses were 

evaluated for the range between the 99th and 1st percentiles. As seen in these figures, the HPS 

dose-response model has the widest CCDF distribution of individual LCF risk per event for each 

of the circular areas and the LNT dose-response models has the narrowest CCDF distribution.

Figure 6.4-30 CCDF of conditional, mean, individual LCF risk (per event) within the 

10-mile circular area for aleatory weather uncertainty for the LNT, 

USBGR, and HPS dose-response models using the SOARCA uncertainty 

analysis base case source term
6-172

Figure 6.4-31 CCDF of conditional, mean, individual LCF risk (per event) within the 20-

mile circular area for aleatory weather uncertainty for the LNT, USBGR, 

and HPS dose-response models using the SOARCA uncertainty analysis 

base case source term
6-173

Figure 6.4-32 CCDF of conditional, mean, individual LCF risk (per event) within the 

30-mile circular area for aleatory weather uncertainty for the LNT, USBGR, 

and HPS dose-response models using the SOARCA uncertainty analysis 

base case source term
6-174

Figure 6.4-33 CCDF of conditional, mean, individual LCF risk (per event) within the 

40-mile circular area for aleatory weather uncertainty for the LNT, USBGR, 

and HPS dose-response models using the SOARCA uncertainty analysis 

base case source term
6-175

Figure 6.4-34 CCDF of conditional, mean, individual LCF risk (per event) within the 

50-mile circular area for aleatory weather uncertainty for the LNT, USBGR, 

and HPS dose-response models using the SOARCA uncertainty analysis 

base case source term

Figure 6.4-35 through Figure 6.4-39 show the CCDF of aleatory weather uncertainty for the 

conditional, mean, individual LCF risk (per event) results using the USBRG dose-response 

model and the CCDF of the conditional, mean, individual LCF risk (per event) results for the 

MACCS CAP15 analysis within the 10-mile, 20-mile, 30-mile, 40-mile, and 50-mile circular 

areas, respectively. As seen in these figures, the aleatory weather uncertainty is bounded for 

the Replicate 1 Realization 62 and Replicate 1 Realization 170 source terms by the epistemic 

uncertainties within the MACCS CAP17 analysis, but not for the SOARCA uncertainty analysis 

base case source term. This indicates that the epistemic uncertainties for the conditional, 

mean, individual LCF risk results of the MACCS CAP15 analysis have a greater effect on the 

overall uncertainty than the aleatory weather uncertainty for the higher source term releases. 

The following trends are observed and are specific to the three source terms analyzed: 

• The dose-truncation model has a larger contribution of the LCF risk from the emergency 

phase and earlier years of the long-term phase.

• The emergency phase risk for the smaller source term release has a larger effect on the 

overall LCF risk (see Table 6.4-36).
6-176

• The three source terms used in these analyses are bounded at the upper end of the 

CCDF individual LCF risk distribution for aleatory weather uncertainty by the epistemic 

uncertainties for the conditional, mean, individual LCF risk results of the MACCS CAP15 

analysis, but are not bounded at the lower end of the distribution for individual LCF risk 

(see Figure 6.4-35 through Figure 6.4-39).

Figure 6.4-35 CCDF of conditional, mean, individual LCF risk (per event) within the 

10-mile circular area for aleatory weather uncertainty using the USBGR 

dose-response model and the MACCS CAP15 analysis
6-177

Figure 6.4-36 CCDF of conditional, mean, individual LCF risk (per event) within the 

20-mile circular area for aleatory weather uncertainty using the USBGR 

dose-response model and the MACCS CAP15 analysis
6-178

Figure 6.4-37 CCDF of conditional, mean, individual LCF risk (per event) within the 

30-mile circular area for aleatory weather uncertainty using the USBGR 

dose-response model and the MACCS CAP15 analysis
6-179

Figure 6.4-38 CCDF of conditional, mean, individual LCF risk (per event) within the 

40-mile circular area for aleatory weather uncertainty using the USBGR 

dose-response model and the MACCS CAP15 analysis
6-180

Figure 6.4-39 CCDF of conditional, mean, individual LCF risk (per event) within the 

50-mile circular area for aleatory weather uncertainty using the USBGR 

dose-response model and the MACCS CAP15 analysis

Table 6.4-37 shows the ratio between the 5th and 95th percentile for the three source term’s 

individual LCF risk per event results using the USBGR dose-response model and the 

conditional, mean, individual LCF risk (per event) results for the MACCS CAP15 analysis. As 

shown in Table 6.4-37, the aleatory weather uncertainty is narrower for all analyses than the 

epistemic uncertainty for the mean results of the MACCS CAP17 analysis within all circular 

areas for Replicate 1 Realization 62 and Replicate 1 Realization 170, but not for the SOARCA 

uncertainty analysis base case. From Figure 6.4-35 through Figure 6.4-39, the SOARCA 

uncertainty analysis base case source term consistently produced much lower individual LCF 

risk results than the conditional, mean, individual LCF risk results for the MACCS CAP15 

analysis. 

A determination of the upper bounding effects of aleatory weather uncertainty cannot be 

determined from these analyses. From Table 6.4-34, the selected source terms do not 

adequately represent the upper end of the range for the MACCS CAP15 analysis.
6-181

Table 6.4-37 Conditional, mean, individual LCF risk (per event) ratio for the MACCS

aleatory uncertainty analyses using the USBGR dose-response model 

and the MACCS CAP15 analysis for specified circular areas

Radius of 

Circular Area 

(miles)

SOARCA UA 

Base Case

Replicate 1 

Realization 62

Replicate 1 

Realization 170 CAP15

10 11 10 12 45

20 190 12 26 58

30 400 11 43 70

40 420 11 53 73

50 480 12 58 72

Figure 6.4-40 through Figure 6.4-44 show the CCDF of aleatory weather uncertainty for the

conditional, mean, individual LCF risk (per event) using the HPS dose-response model and the 

CCDF of the conditional, mean, individual LCF risk (per event) results for the MACCS CAP16 

analysis within the 10-mile, 20-mile, 30-mile, 40-mile, and 50-mile circular areas, respectively. 

As shown in the figures, the aleatory weather uncertainty is bounded for the Replicate 1 

Realization 62 source term by the epistemic uncertainties within the conditional, mean, 

individual LCF risk (per even)t results for the MACCS CAP17 analysis, but not for the SOARCA 

uncertainty analysis base case and Replicate 1 Realization 170 source terms. This indicates 

that the epistemic uncertainties for the conditional, mean, individual LCF risk results of the 

MACCS CAP16 analysis have a greater effect on the overall uncertainty than the aleatory 

weather uncertainty for a larger release, but not for smaller ones. The trend observations are 

similar to those discussed for the USBGR dose-response model. However, these results also 

indicate that a higher dose-truncation threshold is more sensitive to aleatory weather 

uncertainty.
6-182

Figure 6.4-40 CCDF of conditional, mean, individual LCF risk (per event) within the 

10-mile circular area for aleatory weather uncertainty using the HPS 

dose-response model and the MACCS CAP16 analysis
6-183

Figure 6.4-41 CCDF of conditional, mean, individual LCF risk (per event) within the 

20-mile circular area for aleatory weather uncertainty using the HPS 

dose-response model and the MACCS CAP16 analysis.
6-184

Figure 6.4-42 CCDF of conditional, mean, individual LCF risk (per event) within the 

30-mile circular area for aleatory weather uncertainty using the HPS 

dose-response model and the MACCS CAP16 analysis
6-185

Figure 6.4-43 CCDF of conditional, mean, individual LCF risk (per event) within the 

40-mile circular area for aleatory weather uncertainty using the HPS 

dose-response model and the MACCS CAP16 analysis
6-186

Figure 6.4-44 CCDF of conditional, mean, individual LCF risk (per event) within the 

50-mile circular area for aleatory weather uncertainty using the HPS 

dose-response model and the MACCS CAP16 analysis.

Table 6.4-38 shows the ratio between the 5th and 95th percentile for the three source term’s 

conditional, mean, individual LCF risk (per event) results using the HPS dose-response model 

and the MACCS CAP16 analysis. As shown in this table, the aleatory weather uncertainty for 

Replicate 1 Realization 62 is narrower than the epistemic uncertainty for the conditional, mean, 

individual LCF risk (per event) results of the MACCS CAP17 analysis within all circular areas, 

but this is not true for the SOARCA uncertainty analysis base case and Replicate 1 

Realization 170. From Figure 6.4-40 through Figure 6.4-44, the SOARCA uncertainty analysis 

base case and Replicate 1 Realization 170 source terms consistently produced lower individual 

LCF risk results than the conditional, mean, individual LCF risk results for the MACCS CAP16 

analysis. 

A determination of the upper bounding effects of aleatory weather uncertainty cannot be 

determined from these analyses. From Table 6.4-35, the selected source terms do not 

adequately represent the upper end of the range for the MACCS CAP16 analysis.
6-187

Table 6.4-38 Conditional, mean, Individual LCF risk (per event) ratio for the MACCS

aleatory uncertainty analyses using the HPS dose-response model and the 

MACCS CAP16 analysis for specified circular areas

Radius of 

Circular Area 

(miles)

SOARCA UA 

Base Case

Replicate 1

Realization 62

Replicate 1

Realization 170 CAP15

10 110 34 80 80

20 10,000 150 2,800 780

30 11,000 170 3,600 1,400

40 12,000 180 3,900 1,900

50 12,000 190 3,400 2,100

7-1 

7. SUMMARY OF RESULTS AND CONCLUSIONS 

This analysis is an integrated look at uncertainties in MELCOR accident progression and 

MACCS offsite consequence analyses for the SOARCA Peach Bottom unmitigated LTSBO 

scenario and demonstrates uncertainty analysis methodology that can be used in future source 

term, consequence, and Level 3 PRA studies. This work identified key uncertainties in the input 

parameters used in the SOARCA deterministic MELCOR and MACCS models and quantified

the relative importance of each uncertain input on potential accident consequences. This 

quantitative uncertainty analysis provides measures of the effects, both individually and in 

interaction with other parameters, of each of the selected uncertain parameters. The study also

provides phenomenological insights on the effects of important inputs and parameters used in 

the SOARCA calculations [1]. Specifically, this uncertainty analysis helps: 

• Identify which uncertain important parameters and phenomena are driving the variability in 

SOARCA model results. 

• Verify and validate the SOARCA models through exploration of unexpected or nonphysical phenomena in the distributions of results.

• Provide an assessment of the regression techniques and uncertainty analysis approach. 

• Provide a basis for future work. 

This section summarizes the results of the uncertainty analyses including both the quantitative 

and qualitative insights with respect to the key uncertain parameters and phenomena 

influencing the source term and consequence analysis results.

7.1 Source Term Analyses

Performing the source term calculations of the Peach Bottom unmitigated LTSBO uncertainty 

analysis revealed three groups of similar accident progression within the Peach Bottom 

unmitigated LTSBO scenario: (1) early stochastic failure of the cycling SRV, which was the 

SOARCA scenario in NUREG-1935; (2) thermal failure of the SRV without MSL creep rupture; 

and (3) thermal failure of the SRV with MSL creep rupture. Several influences were found to 

strongly affect the magnitude and timing of fission product releases to the environment, as 

summarized below. 

Most notably, with respect to the magnitude of the source term (i.e., the magnitude of cesium 

and/or iodine releases), the following were found to be influential: 

• Whether the sticking open of the SRV (the lowest set-point SRV) occurs before or after 

the onset of core damage, with higher releases if after core damage,

• Whether a MSL creep rupture occurs, with higher releases if MSL rupture occurs due to 

fission products being vented straight to the drywell and bypassing wetwell scrubbing,

• The amount of cesium chemisorbed as CsOH onto the stainless steel of RPV internals; 

more chemisorption relating to less cesium release to the environment in hightemperature scenarios such as MSL rupture, 
7-2 

• Whether core debris relocates from the RPV to the reactor cavity all at once or over an 

extended period of time with relocation all at once leading to lower releases to the 

environment, 

• The degree of oxidation, primarily fuel-cladding oxidation, occurring in-vessel with greater 

oxidation resulting in larger releases, and

• Whether a surge of water from the wetwell up onto the drywell floor occurs at drywell liner 

melt-through with the development of surge water leading to larger releases. 

The sampled parameters shown to strongly or meaningfully influence the magnitude of the 

fission product releases, because they contribute to the important phenomena noted above,

were:

• The expected number of cycles an SRV can undergo before failing to reclose (i.e., remain 

in the fully open position), 

• The chemical form of cesium (i.e., the amount of cesium as CsOH opposed to as 

Cs2MoO4), 

• The size of the breach in the drywell liner resulting from core debris contacting and 

melting through the liner, 

• The fractional open area of an SRV after it has failed to reseat because of overheating, 

• The time-at-temperature criterion specified for loss of “intact” fuel rod geometry, and

• The temperature at which oxidized cladding mechanically fails. 

With respect to release timing, the strongest influences identified were:

• When the RCIC system failed, 

• When the SRV failed to reseat, and

 

• What the open fraction of the SRV was when it failed to reseat given a thermally-induced 

failure.

The sampled parameters shown to strongly or meaningfully influence the timing of releases, by 

affecting the timing influences noted above, were:

• The time taken to exhaust the station batteries (i.e., the sole determinate of when the 

RCIC system fails), 

• The number of cycles an SRV can undergo before failing to reclose (i.e., remain in the 

fully open position), and

• The fractional open area of an SRV after it has failed to reseat because of overheating. 
7-3 

The means by which fission products release to the environment in the MELCOR source term 

calculations are well characterized by what is observed for the release of cesium. Most of the 

cesium released to the environment in the calculations undergoes the following sequential 

processes:

(1). Release from the dismantling core as CsOH, CsI, or Cs2MoO4 vapor. 

(2). Condensation into aerosols. 

(3). Gravitational settling onto reactor internals. 

(4). Re-vaporization after RPV lower head failure over approximately 24 hours. 

(5). Re-condensation into aerosols that are carried out a breach in the drywell liner resulting 

from core debris contacting and melting through the liner.

The most influential sampled parameter identified in the uncertainty analysis affecting the 

re-vaporization of cesium aerosols settled on reactor internals is the number of cycles an SRV 

can undergo before failing to reclose: a smaller number of cycles leading to less re-vaporization 

(and less release to the environment) and a larger number of cycles leading to more 

re-vaporization (and more release to the environment). While the importance of this parameter 

in determining whether or not MSL creep rupture occurs was not previously know, the dramatic 

influence of this parameter was not anticipated going into the uncertainty analysis.

An unexpected influence that arose in the analysis was that specifying the cesium inventory in 

the core in the form of CsOH (as opposed to Cs2MoO4) often led to smaller releases of cesium 

to the environment. This was surprising in that the lower vapor pressure dependence on 

temperature of CsOH than of Cs2MoO4 might intuitively suggest that CsOH would transport 

more readily. What led to a contradiction of intuition was the process of chemisorption where 

cesium bonds with impurities in the stainless steel of reactor internals. This process has a 

strong dependence on temperature, with higher temperatures yielding more chemisorption. In 

calculations where much of the reactor core degradation occurred with the reactor at pressure 

(i.e., where the lowest set-point SRV cycled as designed for a relatively long period before 

failing to reseat), temperatures in the RPV were higher and chemisorption potential was greater. 

In these calculations, if cesium were specified in the core predominantly as CsOH, more than 

half of the initial core inventory deposited on reactor internals through chemisorption. This 

deposition was permanent, making the absorbed cesium unavailable for transport and release 

to the environment. Previously, it was thought that cesium in the form of CsOH would lead to 

larger releases, but in fact for high temperature scenarios, CsOH resulted in smaller releases 

and thus limited the total effect of higher temperatures.

Another surprising influence in the analysis was the surging of water up from the wetwell to the 

drywell floor. This occurred in approximately half of the MELCOR calculations in association 

with large breaches17 (> 0.2 m2

) in the drywell liner caused by core debris contacting the liner 

and melting through it. Large breaches resulted in larger depressurizations of the containment

and a greater pressure differential between the drywell and the wetwell during the 

 

17 Breach size is a user-specified input in the MELCOR model and this was included as an uncertain parameter in 

this study.
7-4 

depressurizations. The suddenly superheated state of the water in the wetwell contributed to 

the pressure differentials in the presence of which some of the water flashed to steam. The 

pressure differentials overwhelmed the vacuum breakers between the wetwell and the drywell 

and contaminated water surged out of the wetwell. Most of the water surging from the wetwell 

flows from the drywell to the reactor building through the breach in the drywell liner.

In the SOARCA Peach Bottom unmitigated LTSBO scenario, two operator actions are credited: 

(1) the operators manually opening an SRV; and (2) the operators taking manual control of 

RCIC. Because there was no formal human reliability analysis for SOARCA, the timing18 of 

these operator actions were not included as uncertain inputs in the uncertainty analysis. 

Instead, the influence of the timing of the opening of an SRV was investigated through a 

separate sensitivity study. The influence on source term for operator action through the

sensitivity calculations identified a significant importance for the only operator action considered; 

the time at which the operators manually opened an SRV. This manual action was assumed to 

occur at one hour in the SOARCA calculation [1]. Sensitivity calculations were carried out as 

part of the uncertainty analysis that varied this time the operator took action and included a 

calculation where the manual action was not taken at all. Substantial increases in iodine and 

cesium releases to the environment occurred in the 0.5-hr calculation. A significant increase in 

iodine release and a noticeable increase in cesium release also occurred for the calculation 

without the operator action to manually open the SRV. In both these cases, RCIC operation 

was negatively impacted early in the accident progression by a loss of sufficient steam to 

operate the RCIC turbine. In the 0.5-hr calculation, the RPV depressurized severely upon 

opening the SRV. In the calculation where the SRV was not opened, over-cycling of the SRV

early in the accident sequence caused it to stick open and depressurize the RPV, which 

interrupted RCIC operation. The impacts to RCIC operation led to more extensive fuel-cladding 

oxidation in the RPV, elevated temperatures of reactor internals, and greater late revaporization 

from the hotter internals of previously accumulated deposits of iodine and cesium. It is worth 

noting that these sensitivity calculations may have led to unrealistic scenarios. For example, 

with respect to the calculation where the operators were assumed to open an SRV at 0.5 hours, 

it is unlikely that the operators would allow reactor pressure to drop sufficiently low to fail RCIC; 

instead, they would operate the valve so that sufficient steam pressure is maintained to drive 

the RCIC turbine. Similarly, given the known importance of manual depressurization in this 

scenario (i.e., identified as an important insight for BWRs in NUREG-1150 more than 20 years 

ago), the case where the SRV was not opened at all is likely to be a very low probability.

7.2 Consequence Analyses

The results of the consequence analyses are presented in terms of risk to the public for each of 

the realizations analyzed using the Peach Bottom unmitigated LTSBO MELCOR and MACCS

models. All results are presented as conditional risk (i.e., assuming that the accident occurs),

and show the conditional risks to individuals as a result of the accident (i.e., latent cancer fatality 

(LCF) risk per event or early-fatality risk per event). 

The risk metrics are LCF risk and early-fatality risks to residents in circular regions surrounding 

the plant. The risks are mean values (i.e., expectation values) over sampled weather conditions

representing a year of meteorological data and over the entire residential population within a 

 

18 In the SOARCA best estimate study (NUREG-1935), the timing of these actions is based on emergency operating 

procedures and interviews with plant personnel.
7-5 

circular region. The risk values represent the projected number of fatalities divided by the 

population, in other words, individual latent cancer fatality risk. LCF risks are calculated for a 

set of dose-response models, which are (1) LNT, (2) a linear with threshold dose-response 

model where the threshold is mean U.S. natural background plus mean medical radiation as a 

dose-truncation level (USBGR), and (3) a linear with threshold dose-response model where the 

threshold is based on an HPS Position Statement. The HPS Position Statement suggests that 

health effects not be quantified below an annual rate of 5 rem/yr provided that the total excess 

dose over a lifetime does not exceed 10 rem. These risk metrics account for the distribution of 

the population within the circular region and for the interplay between the population distribution 

and the wind rose probabilities.

For the LCF risk results, the emergency phase is defined as the first seven days following the 

initial release to the environment. The long-term phase is defined as the time following the 

emergency phase (i.e., there is no intermediate phase in the MACCS modeling). The long-term 

phase risk (i.e., the LCF risk contribution beyond the emergency phase) dominates the total 

risks (i.e., 100% of all realizations have a long-term risk contribution that is greater than 50% of 

the total risk) within the EPZ for the uncertainty analysis when the LNT dose-response

assumption is made. No realization resulted in an emergency phase risk contribution greater 

than 48% of the total risk. The emergency phase risk within the EPZ is entirely to the 0.5% of 

the population who are assumed not to evacuate. These results further emphasize the benefits 

of evacuating the EPZ. The long-term risks are controlled by the habitability (return) criterion, 

which is the dose rate at which residents are allowed to return to their homes following the 

emergency phase. For Peach Bottom, the habitability criterion used is an annual dose rate of 

500 mrem/yr19. For comparison, 55% of all realizations have a long-term risk contribution 

greater than 50% of the total risk within a 20-mile radius (i.e., 45% of the realizations have an 

emergency phase risk which contributes to greater than 50% of the total risk). Additionally, 

53%, 48%, and 46% of all realizations have a long-term phase risk contribution greater than 

50% of the total risk within a 30-mile, 40-mile, and 50-mile radius, respectively.

For the LCF risk results, when the 10-mile and 20-mile circular area statistics are compared, 

there is a larger influence of the emergency phase for the 20-mile region compared to the 

10-mile region, for which nearly all of the population evacuated. This indicates that variations in 

doses during the emergency phase are greater than variations in dose during the long-term 

phase.

Unlike the SOARCA analyses in NUREG/CR-7110 Volume 1 and Volume 2, a non-zero earlyfatality risk was calculated beyond 2.5 miles. 11% of the 865 MACCS realizations investigated 

resulted in a nonzero early-fatality risk per event out to 1.3 miles and 0.3% of the 865 

realizations that resulted in a nonzero early-fatality risk per event out to 10 miles. In other 

words, a select few realizations result in a large enough source term that when combined with 

specific weather trials and LHS sampled uncertainties in the MACCS calculation result in 

calculable early-fatality risks out to the boundary of the EPZ. A more detailed discussion of this 

is provided in Section 6.2.4. 

The early-fatality risks are zero for 87% of all realizations at all specified circular areas. This is 

because in most cases the release fractions are too low to produce doses large enough to 

exceed the dose thresholds for early fatalities, even for the 0.5% of the population that are 

 

19 Per Pennsylvania State guidelines.
7-6 

modeled as refusing to evacuate. The largest value of the mean, acute exposure for the closest 

resident (i.e., 1.6 to 2.1 kilometers from the plant) for many of these replicates is about 0.3 gray 

(Gy) to the red bone marrow, which is usually the most sensitive organ for early fatalities, but 

the minimum acute exposure that can cause a early fatality is about 2.3 Gy to the red bone 

marrow. The calculated exposures for these scenarios are all below this threshold.

At 2.5 miles and beyond the mean result is greater than the 95th percentile. This is due to the 

few number of nonzero early-fatality risks (i.e., less than 6% of the realizations) at these 

distances. In theory, a distribution can be skewed enough so that the mean is greater than the 

95th percentile. An instance of this is an exponential of a value sample from a log-normal 

distribution. For these cases the mean may be higher than the 99th percentile, because it is

driven by few nonzero values. This is the same thing that happens here in practice for earlyfatality risk beyond 2.5 miles. 

The nonzero early-fatality risk results decreases from 11% of the total early-fatality risk results

at 1.3 miles to 4% of the total early-fatality risk results at 3.5 miles. Beyond the 3.5 mile circular 

area, the source terms that generate nonzero early-fatality risks drop below 2%. For distances 

beyond 2.5 miles, the 95th percentile statistics are not well converged (i.e., greater than an order 

of magnitude difference). Even at a 2-mile radius, the 95th percentiles differ up to 70%. 

In the 865 realizations, the highest absolute early-fatality risk calculated is 10-10 pry20 with a 

mean of 1.4x10-12 at 1.3 miles (i.e., recall the Peach Bottom LTSBO core damage frequency is

3x10-6 pry). 

7.2.1 Regression Summary for LCF Risks

The regression techniques used to perform a sensitivity analysis for the consequence results

were conducted with the 865 source terms evaluated with MELCOR using a set of 21 uncertain 

input variables and using 350 MACCS individual uncertain input variables in 20 parameter 

groups. The results of the regression analyses of mean, individual LCF are discussed in 

Section 6.2.3.1. Within the 10-mile circular area, the regression techniques indicate a 

confidence level >72%. Beyond the 10-mile circular area, each of the regression techniques 

indicate a confidence level ≥42% with the recursive partitioning analysis consistently being the 

highest with a confidence level of 71% to 64%. 

Based on this, the statistical regression techniques used to determine the important input 

parameters for LCF risk are considered adequate for this work. While other regression 

techniques (e.g., ACOSSO or Gaussian process) not used in this study may provide additional 

insights, the four selected regression analyses cover a large spectrum of potential interactions 

and influences. Additional regression methods can be employed and may provide more insights 

in the analyses by confirming the influence of some parameters or perhaps capturing other 

kinds of interactions not considered in this work. However, since the monotonic (i.e., rank 

regression) and non-monotonic (i.e., quadratic, recursive partitioning, and MARS) regression 

techniques agree reasonably well, using more advanced methods was considered unnecessary. 

 

20 Estimated risks below 10-7 per reactor year should be viewed with caution because of the potential impact of 

events not studies in the analyses, and the inherent uncertainty in very small calculated numbers.
7-7 

All regression methods at each of the circular areas consistently rank the following, respectively, 

as the most important input parameters:

• MACCS dry deposition velocity (VDEPOS), which involves a variety of mechanisms that 

cause aerosols to deposit, including gravitational settling, impaction onto terrain 

irregularities, including buildings and other manmade structures, and Brownian diffusion, 

• the MELCOR SRV stochastic failure probability (SRVLAM), an important MELCOR 

parameter for source term determination, and 

• the MACCS ‘residual’ cancer risk factor (CFRISK–Residual) which is used for estimating 

residual cancers not related to the seven organ-specific cancers that were used in 

SOARCA.

Some additional parameters also consistently show some level of importance at all circular 

areas. These are the following: 

• The MELCOR fuel failure criterion, which is the time endurance of the upright, cylindrical 

configuration of fuel rod bundles, 

• The MELCOR drywell liner melt-through open area flow path (FL904A), and

• The MACCS ‘residual’ dose and dose-rate effectiveness factor (DDREFA–Residual), 

which is based on BEIR V risk factors for estimating health effects to account for observed 

differences between low and high dose rates. 

The three MELCOR uncertain parameters, SRVLAM, fuel failure criterion FL094A, ultimately 

account for the majority of the uncertainty in the source term inputs (release magnitude) for the 

consequence analysis. 

7.2.2 Regression Summary for Early-Fatality Risk

The conditional, mean, individual early-fatality risk regression analyses are discussed in Section 

6.2.3.2. Because fewer than 3% of all the MACCS uncertainty analysis realizations resulted in 

nonzero early-fatality risk at or beyond 5 miles, these circular areas are not included in the 

results. The regression did not produce any reliable results at these distances. On the other 

hand, the regression analyses produce non-monotonic confidence levels ≥58%) at a distance at 

or within 2 miles. At these distances, approximately 13% of all MACCS realizations have a 

nonzero early-fatality risk, and the top one or two input parameters are correlated to a high 

confidence level. The rank regression analysis consistently produces a poor result, indicating 

that there is a non-linear relationship between the important input variables and early fatality 

risk. 

Beyond 2 miles, at least one of the non-monotonic regression techniques produces poor results. 

Between the 2.5-mile and 3.5-mile circular areas, approximately 7% of all MACCS realizations 

produce nonzero early-fatality risks. This small amount of nonzero data produces a set of 

important input parameters with low confidence. Again, the rank regression analysis 

consistently produces a poor result, indicating that there is a non-linear relationship between the 

important input variables. 
7-8 

Based on these analyses, the statistical regression techniques used to determine the important

input parameters for early-fatality risk are considered adequate for the distances reported in this 

work. 

For the circular areas less than 2 miles, the non-rank regression methods consistently rank the

following as the most important input variables, respectively: 

• The MACCS wet deposition model (CWASH1), which is an important phenomenon that

is very effective at rapidly depleting the plume and can produce concentrated deposits 

on the ground, 

• the MELCOR SRV stochastic failure probability (SRVLAM), which is an important 

MELCOR parameter for source term determination, 

• the MELCOR SRV open area fraction (SRVOAFRAC), which is an important MELCOR 

parameter for source term magnitude and timing, 

• the MACCS early health effects threshold and beta (shape) factor for red bone marrow 

(EFFTHR-Red Marrow and EFFACB-Red Marrow), which is the most sensitive organ for 

the potential of early health effects, and 

• the MACCS linear, crosswind dispersion coefficient (CYSIGA), which defines how 

concentrated the radionuclides are within the plume (i.e., the more concentrated the 

radionuclides are within the plume; the higher the possible dose to an individual within 

the plume). 

Additional variables also consistently show some level of importance for circular areas less than 

2 miles. These additional input variables include the following:

• The MACCS amount of shielding between an individual and the source of groundshine 

during normal activities for the non-evacuated residents (GSHFRAC-Normal),

• The MACCS evacuation delay for Cohort 5 (DELTVA-Cohort 5); Cohort 5 is the 

evacuation tail of the general public evacuation, and

• The MELCOR DC station battery duration (BATTDUR), which is important to release 

timing, which is more important to early fatality risk (than latent cancer fatality risk.) 

For the circular areas between 2.5-miles and 3.5-miles, the regression methods consistently 

rank the MACCS crosswind dispersion coefficient (CYSIGA), the early health effects threshold 

for red bone marrow (EFFTHR-Red Marrow), the MELCOR SRV stochastic failure probability 

(SRVLAM), and the MELCOR SRV open area fraction (SRVOAFRAC), respectively, as the 

most important input parameters. 

7.2.3 Regression Summary of LCF Risk using Dose Truncation

Additional regression analyses were conducted as a sensitivity analysis for the dose-response

models considered in this report (i.e., linear no threshold, linear with a threshold of 0.62 rem/yr, 

and linear with a threshold of 5 rem/yr with 10 rem lifetime limit). The results are discussed in 

Section 6.4.3. The regression techniques were used with Replicate 1 that included 284 source 

terms with the MELCOR uncertain input variables and 350 MACCS uncertain input variables. 

The statistical regression techniques provided adequate results, as described below. 
7-9 

For the linear no-threshold sensitivity analysis, all circular areas for all regression methods 

consistently rank the MACCS dry deposition velocity (VDEPOS) and the MELCOR SRV 

stochastic failure probability (SRVLAM), respectively, as the most important input parameters. 

Some additional variables also consistently show some level of importance at all circular areas, 

including: 

• The MELCOR fuel failure criterion, and

• The MELCOR SRV open area fraction (SRVOAFRAC),

Since this is a smaller subset of the MACCS uncertainty analysis and still ranks the same top 

two parameters as most important, this sensitivity analysis provides additional confidence in the 

regression analyses for parameters considered important.

For the alternative dose-response model (i.e., thresholds of 0.62 rem/yr and 5 rem/yr with a 

10 rem lifetime limit) sensitivity analyses, the five circular areas for all regression methods 

consistently rank the MACCS inhalation protection factor for normal activity (PROTIN–Normal), 

the MACCS lung lifetime risk factor for cancer death (CFRISK-Lung), and the MELCOR SRV 

stochastic failure probability (SRVLAM) as the most important input variables. For the MACCS

variables, the dose threshold models are those associated with doses received in the first year 

and not ones associated with the long-term phase risk beyond the first year. Because the 

internal doses from inhalation diminish with time, most of the doses in the second and 

subsequent years are from the exposures during that year. These doses are limited by the 

habitability criterion to be less than 500 mrem in any year. The inhalation dose used in this 

criterion is a committed dose (i.e., it accounts for doses received over the next 50 years). 

Because the annual doses allowed by the habitability criterion are less than the dose truncation 

levels, nearly all of the risk is from doses received during the first year. Additional variables also 

consistently show some level of importance at all circular areas, including: 

• The MELCOR SRV open area fraction (SRVOAFRAC), and

• The MELCOR DC station battery duration (BATTDUR)

The important MELCOR input parameters are similar to those in the MACCS uncertainty 

regression analyses summarized in Section 7.2.1. However, the MACCS input variables are not 

the same. The use of either the 0.62 rem/yr dose truncation model or the 5 rem/yr with a 

10 rem lifetime limit dose-response model has MACCS input variables associated with doses 

received in the first year and not MACCS input parameters associated with the long-term phase 

risk beyond the first year. Hence they show up as important for the threshold models and not 

for the LNT model where the more of the risk comes from the long-term phase. 

For Peach Bottom, the habitability criterion used is an annual dose rate of 500 mrem/yr. This 

dose rate is below the threshold limit in both dose truncation models; therefore, most of the 

doses received during the long-term phase are below the dose truncation limit and are not 

counted toward health effects when using this criterion. Thus, most of the risks associated with 

either truncation level are from doses received during the first year21. The emergency and 

long-term phases are not easily separated in the first year for purposes of evaluating the annual 

dose threshold. 

 

21 The total risk using the threshold models are substantially lower than the LNT model.
7-10

To better understand this explanation, it is important to understand the differences between 

exposure periods, commitment periods, and the periods of time when doses are actually 

received. For external dose pathways, the time over which doses are received is concurrent 

with the exposure period. External dose pathways include cloudshine and groundshine. 

The exposure period for internal pathways, inhalation and ingestion, is the period of time when 

the inhalation or ingestion occurs; however, doses continue to be received over a person’s 

entire lifetime following the exposure. The period of time over which doses are received from an 

internal pathway is accounted for in the construction of dose conversion factors by integrating 

the doses over a finite period called a dose commitment period, which is usually taken to be 

50 years when calculating internal-pathway dose conversion factors for adults. The implicit 

assumption is that the average adult lives for an additional 50 years following the exposure, 

which is most likely a conservative assumption. 

Since ingestion doses are taken to be negligible in SOARCA, inhalation is the only internal 

pathway that is treated. A significant portion of the exposures during the emergency phase are 

from inhalation. As explained above, these exposures are assumed to lead to doses over the 

commitment period, which is the next 50 years following the exposure. However, depending on 

the isotope inhaled, the doses received may diminish rapidly and become negligible for most of 

the dose commitment period.

Most of the exposures during the long-term phase are from groundshine, and a small fraction is 

from inhalation of resuspended aerosols. Since groundshine is an external pathway, doses 

received are concurrent with the exposure period, which is also taken to be 50 years in the 

SOARCA study. On the other hand, exposures from inhalation of resuspended material during 

each year of the long-term phase contribute to doses received over the subsequent 50-year 

commitment period. 

Doses received in the first year thus correspond to:

• all of the dose from external exposure during the emergency phase,

• most of the dose from internal exposure during the emergency phase,

• all of the dose from external exposure during the first year of the long-term phase, and

• most of the dose from internal exposure during the first year of the long-term phase.

Doses received in the second and subsequent years correspond to:

• a fraction of the dose from internal exposure during all previous years plus most of the 

dose from internal exposure during that year, and

• all of the dose from external exposure during that year. 

Because the internal doses from inhalation diminish with time, most of the doses in the second 

and subsequent years are from the exposures during that year. But these doses are limited by 

the habitability criterion to be less than 500 mrem in any year. The 500 mrem limit is for all dose 

pathways, except ingestion, in this case groundshine and inhalation from resuspended aerosols. 

The inhalation dose used in this criterion is a committed dose (i.e., it accounts for doses 

received over the next 50 years). Because the annual doses allowed by the habitability criterion 

are less than these truncation levels, nearly all of the risk is from doses received during the first 

year. These doses include most of emergency phase doses and a fraction of the long-term 

phase doses.
7-11

7.2.4 Habitability Sensitivity Study Summary

A series of sensitivity studies using five habitability criterions (i.e., 0.1 rem/yr, 0.5 rem/yr, 

2 rem/yr22, 4 rem over 5 years, and 5 rem over 7 years) were conducted for the dose truncation 

models considered in this report (i.e., linear no threshold, threshold of 0.62 rem/yr, and 

threshold of 5 rem/yr with 10 rem lifetime limit). This sensitivity was performed to see how 

values of the habitability criterion might affect the results. The sensitivity results are discussed 

in Section 6.4.4.

Based on the linear no-threshold dose-response model, the majority of the LCF risk contribution 

within the EPZ resulted from the long-term phase for all habitability scenarios. Thus the higher 

the habitability criterion, the higher the LCF risk as a result of long-term dose within the EPZ. 

The majority of the LCF risk for the 0.1 rem/yr habitability criterion results from the emergency 

phase for all circular areas. While the emergency phase LCF risk for the 0.1 rem/yr habitability 

criterion is similar to all other emergency phase LCF risks for other habitability criteria, the low 

value significantly reduces long-term LCF risk, causing the emergency phase risk to exceed the 

long-term phase risk beyond the EPZ. Most of the risk corresponds to the long-term phase for 

all other choices of habitability criterion. 

For the dose-truncation models, most of the doses received during the long-term phase are 

below the dose truncation limit and are not counted toward health effects. Thus, most of the 

risks associated with either of the truncation levels are from doses received during the first year. 

When either of the dose-truncation models is used, the LCF risks within the EPZ are orders of 

magnitude lower when the habitability criterion is below the dose-truncation level, as compared 

with the cases when the habitability criterion is above the dose-truncation level. Beyond the 

EPZ, the habitability criterion has a smaller effect on the overall LCF risk when a 

dose-truncation model is applied, and yield similar results to those presented in the 

NUREG/CR-7110 Volume 1, Section 7, at the specified circular areas.

7.2.5 Weather Effects Summary

A set of sensitivity analyses to evaluate the SOARCA weather sampling technique was 

evaluated for the LNT, USBGR, and HPS dose-response models. All of the sensitivity 

simulations use the SOARCA uncertainty analysis base case source term. The SOARCA 

weather sampling technique was compared to sampling the entire weather database (i.e., 

8,760 hourly weather samples) used for Peach Bottom. All MACCS variables other than the 

sampled weather trials were held fixed. 

For SOARCA, a structured Monte-Carlo sampling method was employed for weather sampling. 

This was done by random selection of a user-specified number of weather sequences (i.e., start 

times) from the set of sequences assigned to each user-specified weather category. This 

begins by sorting an annual weather file according to user specified criteria. Each MACCS

analysis uses a user-specified random seed. This random seed was kept constant for all 

MACCS analysis and thus the same weather trials from the same meteorological data file were 

selected for all of the analyses. 

 

22 The way MACCS implements the habitability criterion, 2 rem/yr, is more restrictive than 4 rem over 5 years.
7-12

The overall difference between the SOARCA weather sampling technique and sampling all 

8,760 hourly data points is relatively small, and the SOARCA weather sampling technique 

consistently produced higher LCF risk results. However, the increase in computational time is 

eight fold. While this is not prohibitively long for the LNT dose-response model (i.e., ~1 hour to 

~8 hours of run time for a single MACCS realization), the increase in computation time for the 

USBGR and HPS dose-response models would make uncertainty analysis applications less 

feasible (i.e., ~1 day to ~8 days of run time for a single MACCS realization). 

In SOARCA, the aleatory uncertainties due to weather were characterized in terms of mean 

values. However, a CCDF of aleatory uncertainties can be obtained using a single MACCS

analysis for each source term. A set of sensitivity analyses to evaluate the aleatory weather 

uncertainty using the SOARCA weather sampling technique was evaluated for the LNT, 

USBGR, and HPS dose-response models. 

Two comparisons are presented to show the effects of aleatory weather uncertainty. The first 

shows the individual LCF risk results of the aleatory weather uncertainty for three chosen 

source terms using the LNT dose-response model with the conditional, mean, individual LCF 

risk results of the MACCS analysis for the combined MELCOR Replicates 1, 2, and 3 using the 

LNT dose-response model (CAP17) discussed in Section 6.2.1. The second comparison shows 

the individual LCF risk results of the aleatory weather uncertainty for the three source terms 

using the LNT, USBGR, and HPS dose-response models with the conditional, mean, individual 

LCF risk results of the MACCS analysis for MLECOR Replicate 1 using the LNT, USBGR, and 

HPS dose-response models (i.e., CAP14, CAP15, and CAP16, respectively) discussed in 

Section 6.4.3. Recall that the CAP17 MACCS analysis consists of 865 MELCOR source terms 

using 21 MELCOR epistemic uncertainty variables, and 350 MACCS epistemic uncertainty 

variables of which 338 variables apply to LCF risk. 

For the first comparison, the median individual LCF risk results for the three source terms 

analyzed do provide a good example of the median, lower, and upper bounds of the CAP17 

conditional, mean, individual LCF risk (per event) CCDF distribution for all specified circular 

areas. For the aleatory weather uncertainty within the 10-mile, 20-mile, 30-mile, 40-mile, and 

50-mile circular areas, the conditional, mean, individual LCF risk (per event) for aleatory 

weather uncertainty is bounded for all analyses by the epistemic uncertainty for the conditional, 

mean, individual LCF risk (per event) results of the MACCS CAP17 analysis. This indicates that 

the epistemic uncertainties within the MACCS CAP17 analysis have a greater effect on the 

overall uncertainty than the aleatory weather uncertainty.

For the second comparison, the median LCF risk results for the three source terms do provide a 

good example of the median, lower and upper bounds of the CAP14 CCDF distribution for all 

specified circular areas and are similar to those for the MACCS CAP17 analysis. However, 

these three source terms only quantify the median and lower half of the CAP15 and CAP16 

CCDF distributions of conditional, mean, individual LCF risk (per event) results for all specified 

circular areas. This is due to the dose-truncation models having more of the LCF risk 

contribution from the 1st year and thus a larger contribution from the emergency phase. The 

2nd year and subsequent years have less of a contribution to the individual LCF risk than the 

LNT dose-response model because the majority of the doses in these years are below the 

truncation thresholds. Since none of the source terms selected for this sensitivity analyses have 

a large contribution from the emergency phase, the overall conditional, mean, individual LCF 

risks are at the lower end of the range for these dose-response models. 

For the conditional, mean, individual LCF risk (per event) results using the USBRG doseresponse model and the CCDF of the conditional, mean, individual LCF risk (per event) results 

for the MACCS CAP15 analysis within the 10-mile, 20-mile, 30-mile, 40-mile, and 50-mile 
7-13

circular areas, the epistemic uncertainties for the conditional, mean, individual LCF risk results 

of the MACCS CAP15 analysis have a greater effect on the overall uncertainty than the aleatory 

weather uncertainty for the higher source term releases. The following trends are observed and

are specific to the three source terms analyzed: 

• The dose-truncation model has a larger contribution of the LCF risk from the emergency 

phase and earlier years of the long-term phase.

• The emergency phase risk for the smaller source term release has a larger effect on the 

overall LCF risk.

• The three source terms used in these analyses are bounded at the upper end of the 

CCDF individual LCF risk distribution for aleatory weather uncertainty by the epistemic 

uncertainties for the conditional, mean, individual LCF risk results of the MACCS CAP15 

analysis, but are not bounded at the lower end of the distribution for individual LCF risk. 

Since the selected source terms do not adequately represent the upper end of the range for the

MACCS CAP15 analysis, a determination of the upper bounding effects of aleatory weather 

uncertainty cannot be determined from these analyses.

For the conditional, mean, individual LCF risk (per event) using the HPS dose-response model 

and the CCDF of the conditional, mean, individual LCF risk (per event) results for the MACCS

CAP16 analysis within the 10-mile, 20-mile, 30-mile, 40-mile, and 50-mile circular areas, the 

trend observations are similar to those discussed for the USBGR dose-response model. 

However, these results also indicate that a higher dose-truncation threshold is more sensitive to 

aleatory weather uncertainty.

Since the selected source terms do not adequately represent the upper end of the range for the 

MACCS CAP16 analysis, a determination of the upper bounding effects of aleatory weather 

uncertainty cannot be determined from these analyses. 

Appendix E contains further analyses on the relative and combined contributions of weather and 

epistemic MELCOR and MACCS parameter uncertainty to uncertainty in consequence results.

7.2.6 Single Realization Summary

Select individual realizations from the uncertainty analysis were further investigated in greater 

detail to identify the influences affecting the predicted consequences. The cases investigated 

are broken into two groups, the MELCOR single realizations discussed in Section 6.1.4, and the 

MACCS Uncertainty Analysis single realizations that resulted in a nonzero early-fatality risk per 

event at the 10–mile circular area. These analyses were conducted from the results in the 

MACCS Uncertainty Analysis. The single realization results are discussed in Section 6.2.4.

For the MELCOR single realizations, when the fraction of cesium released to the environment is 

compared for all the realizations investigated, there is no direct relationship to the LCF risk in 

the long-term phase. However, when the cesium and cerium release fractions are both 

considered, a better relationship to long-term risk does appear. 

For the MELCOR single realizations, the LCF risk results show emergency phase LCF risk and 

long-term phase LCF risk are dependent on the same input variables for all circular areas 

investigated (i.e., 10-, 20-, 30-, 40-, and 50-mile circular areas), and those dominated by the 

emergency phase LCF risk further emphasize the advantage of emergency phase evacuation 

within the EPZ.
7-14

For the MACCS Uncertainty Analysis single realizations, it was discovered that three of 865

realizations have a non-zero calculated conditional, mean, individual early-fatality risk (per 

event) out to the 10-mile circular area. Since this was not expected, a further investigation into 

these realizations was conducted. None of the realizations have a stochastic SRV failure, but 

for all three single realizations the accident progression is a SRV thermal failure followed by a 

main steam line creep rupture and ultimate containment failure due to wetwell rupture above the 

water line and drywell head flange failure. None of these realizations were selected for the 

MELCOR single realization analysis. As documented in Section 6.1.4, there are five factors 

found to strongly affect the amount of radionuclides released to the environment, namely:

(1). Whether the SRV fails open before or after the onset of core damage,

(2). Whether a main steam line creep rupture occurs,

(3). The elapsed time between the onset of core damage and main steam line creep rupture,

(4). Whether a surge of water from the wetwell goes up onto the drywell floor at drywell liner 

melt through, and

(5). Whether an overpressure rupture of the wetwell occurs.

For one of the MACCS Uncertainty Analysis single realizations (i.e., only one of the 865 total 

realizations), there is a nonzero early fatality risk beyond the 10-mile circular area. A noticeable 

increase in early fatality risk beyond the 10-mile circular area was observed and is due to the 

population beyond 10 miles not evacuating, except for those in the 10-20 mile shadow 

evacuation for Cohort 2. As a result, the early fatality risk beyond 10 miles increases by two 

orders of magnitude in this realization. Also, 50% or greater of the weather trials result in a 

nonzero early fatality risk out to the 30-mile circular area in this realization. 

While the early fatality risk results for this MACCS Uncertainty Analysis realization are extreme, 

further investigation into the parameters that affected these results does not indicate the source 

term as the predominant or only cause. Instead, the MELCOR source term and the MACCS

parameters, which have a higher early fatality risk contribution for the red bone marrow, 

contribute to the early fatality risk beyond 10 miles. Specifically the following variables are at 

the upper/lower end (i.e., the worst end for consequence in each input variable) of their 

respective distributions, and hence indicate an extremely unlikely outcome: 

• The early health effects threshold for red bone marrow (EFFTHR-Red Marrow) is near the 

1st percentile of the distribution,

• The beta (shape) factor for red bone marrow (EFFACB-Red Marrow) is near the 

10th percentile of the distribution,

• The crosswind dispersion coefficient (CYSIGA) is near the 5th percentile of the distribution,

• The vertical dispersion coefficient (CZSIGA) is near the 5th percentile of the distribution 

and,

• The MELCOR source term is near the 95th percentile of the distribution.

The first two relate to the most sensitive organ for the early health effects. The third and fourth 

parameters enable higher concentrations to reach individuals further from the plant due to a 

tighter plume.
7-15

For all single realizations analyzed, which have the overall LCF risk dominated by the 

emergency phase LCF risk beyond the 10 mile circular area, those realizations further 

emphasize the advantage of evacuation within the EPZ (i.e., the population of greatest risk) with 

significantly reduced emergency phase LCF risk within the EPZ (i.e., only the 0.5% of the 

population modeled as refusing to evacuate within the EPZ receive an emergency phase dose).

7.2.7 Importance Summary

All of the MACCS input parameters that were identified as being important are ones that were 

expected. A previous internal study at Sandia National Laboratories had identified a very similar 

set of important parameters [60]. In this earlier study, only the LNT dose-response model was 

considered, so the threshold-type dose-response models considered here are new and have no 

analog. 

One parameter was identified for early-fatality risk in the earlier study that did not show up as 

important in this work, which was hotspot relocation time. This parameter clearly could be 

important for early-fatality risk, depending on the timing of the release compared with the timing 

of the relocation. Even when most of the release occurs before relocation, groundshine doses 

would be reduced by earlier relocation. One key difference is that the source term was based 

on one of the NUREG-1150 source terms in the previous study and was much larger than any

of the source terms evaluated in this study. As a result, the number of realizations with nonzero 

early-fatality risk was much greater in the previous study, allowing for better statistics in the 

regression analysis.

Several parameters identified for LCF risk in the earlier study were not identified as important in 

this work. Two of these are protection factors for inhalation and groundshine during normal 

activities. Another key difference between the earlier study and this uncertainty analysis is that 

the earlier study only considered the emergency phase contributions to risk; no calculation was 

done for the long-term phase. This could explain why the inhalation protection factor was 

identified as important in the earlier study, since inhalation is usually the most important dose 

pathway for the emergency phase but is relatively unimportant for the long-term phase. The 

groundshine protection factor, on the other hand, is the dominant dose pathway for the 

long-term phase and is more important for that phase than it is for the emergency phase. This 

implies that the groundshine protection factor should have been identified to be important in the 

current study. In examining why it was not identified to be important, this study has varied 

source terms, a more detailed evacuation model, and approximately 300 more MACCS

uncertainty variables 

The third category of parameters that was found to be important in the earlier study was the 

vertical dispersion coefficients for stable atmospheric conditions. These parameters can affect 

doses at short distances; at longer distances the plume becomes well mixed within the mixing 

layer and additional vertical dispersion has no effect. The connection between dispersion and 

LCF risk tends to be much less than linear because less dispersion results in larger doses to 

fewer people while more dispersion results in smaller doses to more people. For linear nothreshold dose-response, this can result in a minimal dependence of LCF risk on dispersion, 

especially for crosswind dispersion. In practice, the influence of the dispersion parameters is 

somewhat site dependent and the earlier work was for a different site, Surry. Also, for this study 

the dispersion parameters for vertical and crosswind dispersion were correlated with each other 

and across the set of stability classes. This was not done in the earlier study, which most likely 

affected the evaluation of the dispersion parameters differently in the two studies. 
7-16

7.3 Use of Multiple Regression Techniques

The SOARCA project [1] uses two complex codes to estimate the consequences of a severe 

nuclear accident: MELCOR and MACCS. Both of these codes involve complex physics 

phenomena and interactions. Past analyses (e.g., NUREG-1150) relied mostly on linear and 

rank regressions which suppose that the models are mostly additive (i.e., the variance in the 

results is driven by single effects from individual uncertain inputs) and the influences are linear 

or monotonic. Such an approach was valid for some of the MELCOR parameters analyzed, 

however the R2 values (i.e., coefficient of determination) estimated by the regression models 

ranged from 0.42 to 0.69, meaning that between 30% and 60% of the variance was not 

explained. The rank regression analyses performed on selected MACCS results were even 

weaker. Latent cancer fatality analyses had an R2 of 0.73 for a 10 miles radius and about 0.51

for larger radiuses (20, 30, 40, and 50 miles) indicating that most of the time, only half of the 

variance was explained. Rank analyses for early-fatality risk explained at best a quarter of the 

variance.

Such results are a clear indication that one cannot always rely on rank regression to provide a 

good indication of the effects of uncertainty in individual analysis inputs. While there are 

powerful techniques to fully decompose the variance of the selected results, such as Sobol 

decomposition or FAST, they can require such a large sample size that the cost of their 

implementation is prohibitive. 

One of the major problems when trying to capture complex interactions is that so many different 

types of interactions are possible that a single parametric regression is often not effective in 

providing an adequate representation for model results. Some techniques, such as rank 

regression can be too restrictive, while others may be too broad and capture nonphysical 

interactions. This may happen, for instance with quadratic regression that incorporates for all

2nd-order interactions (influence of the type XiXj) as well as recursive partitioning. These 

limitations are increased when the sample size is relatively small compared to the number of 

input variables in consideration. As an example, 100 input variables were considered in the 

analyses for early fatalities, which leads to 10,000 possible regression terms analyzed with 

quadratic regression. LCF analyses considered 300 inputs parameters leading to 90,000 

possible regression terms. In such conditions, it is likely that the regression technique will 

indicate some “important” relationships that are in fact due to spurious correlation, rather than 

actual importance. 

For this reason, four regression techniques have been used for this study. Each has strengths 

and weaknesses. Some effects will be captured only by one or two of these techniques but the 

same techniques can ignore other kinds of interactions. The analysis of the resulting arrays is, 

consequently, not as straightforward. The confidence one has on the influence of a parameter 

is conditional on the number of techniques and the type of techniques capturing this influence. 

This analysis can only be done in conjunction with a careful physical interpretation and checking

of the results. In this sense, the addition of sensitivity cases and study of selected deterministic 

cases provided information that was crucial in the interpretation of the results, as well as the 

subject matter experts’ knowledge: any strange interaction (or non-interaction if one was 

expected) was double-checked in order to understand and explain it (or corrected if mistaken). 

While the four selected regression analyses cover a large spectrum of potential interactions and 

influence, some other regression techniques (such as ACOSSO and Gaussian process for 

instance) have not been used in this study. They could bring more insights on the analysis by 

confirming the influence of some parameters (for which we were not completely confident) or 

capturing other kinds of interactions not considered by the original techniques.
7-17

The increased complexity of interpretation (compared to simple rank regression technique) 

derives from the complexity of the regression models and is necessary to increase the 

understanding with some confidence that the improvement in the R2 is not spurious (and/or

nonphysical) due to the large number of variables considered compared to the sample size. In 

the current analysis, the effort was fruitful as it allowed the achievement of an increase in the R2 

for all analyses such that approximately 80% or more of the variance in MELCOR results was 

captured, and approximately 40% to 85% for LCF and between 45% and 80% for early-fatality

risk results from MACCS. The increase was confirmed by several techniques and via crossvalidation of physical explanation of the results. 

The use of multiple regressions techniques was beneficial in this study. While the R2 associated 

with early-fatality risk results was low, the vast majority of the realizations had an estimated 

early-fatality risk of essentially zero. This tendency was even more pronounced when the 

circular area was increased beyond 1.3 to 2 miles (up to having only a handful of realizations 

from the set of 865 with nonzero values for a 10 miles radius). Statistical analysis of sparse 

data remains a complex domain of study and most methods are inefficient (either not finding 

any relation or over-fitting with spurious relations).

7.4 Conclusions 

This uncertainty analysis corroborates the SOARCA project conclusions with the following:

• Public health consequences from severe nuclear accident scenarios modeled are smaller 

than NUREG/CR-2239, “Technical Guidance for Siting Criteria Development” [57]. 

• The delay in releases calculated provide more time for emergency response actions 

(i.e., evacuating or sheltering).

• The long-term phase dominates the overall health effect risk within the EPZ because the 

emergency response is faster than the onset of environmental release. More than half the 

time, the long-term phase is the larger contributor to overall health effect risk beyond the 

EPZ. Long-term health effect risk is largely controlled by the habitability criterion.

• “Essentially zero” absolute early fatality risk is projected: 

— The mean absolute early fatality risk is 1.4x10-12 per reactor year23 within 1 mile of the 

EAB, and even this minute risk based on less than 13% of the 865 realizations having 

a non-zero risk; 87% had a zero risk. 

— This is orders of magnitude below the NRC quantitative health objective for early

fatalities of 5x10-7 per reactor year

• A major determinant of source term magnitude is whether the sticking open of the SRV 

(i.e., lowest set-point SRV) occurs before or after the onset of core damage. 

Compounding this effect is whether or not main steam line creep rupture occurs

(i.e., leads to higher consequences). 

 

23 Estimated risks below 10-7 per reactor year should be viewed with caution because of the potential impact of 

events not studied in the analyses, and the inherent uncertainty in very small calculated numbers.
7-18

• Health-effect risks vary sublinearly with source term because people are not allowed to 

return home until doses are below the habitability criterion. 

• Analysis confirms known importance of some phenomena (e.g., dry deposition velocity), 

and reveals some new phenomenological insights (e.g., late phase revaporization of 

cesium and other fission products within the RPV).

• The use of multiple regression techniques, most of which include non-linear interactions 

between input variables, to post-process Monte Carlo and Latin Hypercube Sampling 

results provides better explanatory power of which input parameters are most important to 

uncertainty in results. 
 8-1

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APPENDIX A

PROBABILISTIC ANALYSIS METHODOLOGY

A-1

A PROBABILISTIC ANALYSIS METHODOLOGY

A.1 Probabilistic Analysis Methodology

As described in Section 2.3, a consequence analysis for a NPP, or in general any type of 

engineered facility, is an analysis intended to answer three questions about the facility (i.e., Q1, 

Q2 and Q3) and one question about the analysis itself (i.e., Q4). 

In turn, answering the four indicated questions leads to an analysis based on three basic 

mathematical structures or entities: (1) EN1, a probability space characterizing aleatory 

uncertainty; (2) EN2, a function that predicts the physical behavior of the facility under 

consideration; and (3) EN3, a probability space characterizing epistemic uncertainty [66, 67]. 

The probability space corresponding to EN1 characterizes aleatory uncertainty and provides the 

basis for answering Questions Q1 and Q2. In practice, the function corresponding to EN2 is 

one or more very complex numerical models and provides the basis for answering Question Q3. 

The probability space corresponding to EN3 characterizes epistemic uncertainty and provides 

the basis for answering Question Q4. The nature of the basic analysis components EN1, EN2 

and EN3 in the context of the SOARCA Uncertainty Analysis is elaborated on in this section. 

The first entity, EN1, corresponds to a probability space (Α, Α, pA), where Α is the set of 

everything that could occur in the particular universe under consideration (i.e., over some 

specified time period for the facility under analysis). Α is a suitably restricted set of subsets of 

Α for which probability is defined, and pA is the function that defines probability for elements of 

Α (i.e., if Σ is an element of Α, then pA(Σ) is the probability of Σ) (Ref 19). In the usual 

terminology of probability theory, Α is called the sample space or sometimes the universal set; 

elements of Α are called elementary events; elements of Α are called events; pA is called a 

probability measure; and pA(Σ) is the probability of the event Σ. Elements of Α are often called 

futures; elements of Α are often called scenarios or scenario classes; and pA(Σ) is the probability 

of a scenario Σ. 

For NPPs, the probability space (Α, Α, pA) for aleatory uncertainty is usually defined to 

characterize the occurrence of potential future events over some time period of interest (e.g., for 

a time period corresponding to one year plant operation or perhaps the intended operating life of 

the plant) that could affect the behavior/performance of the plant. Specifically, each element a

of the sample space Α is a vector of the form 1 2 [ , , , ], n a = aa a  where the elements of a 

characterize the properties of one potential sequence of occurrences over the time interval

under consideration. The probability space (Α, Α, pA), for aleatory uncertainty is typically 

developed with extensive use of fault and event trees to define the probabilities of all possible 

scenarios, 

For the SOARCA analysis, Α corresponds to the set of all possible five day sequences of 

weather conditions that could potentially occur at the Peach Bottom site. Specifically,

A = = {a vector characterizing 5 day sequence of weather conditons at PB site . } Equation A-1 

In a full consequence analysis for a nuclear power station, the indicated vector of weather 

conditions would be only one of many components of each element of Α (e.g., see summary of 

the NUREG-1150 reactor consequence analyses in [19]). In the SOARCA analyses, weather 

bins (i.e., sets of weather sequences with similar characteristics) correspond to elements of the 
A-2

set Α. Further, the probabilities that are defined by the function pA are approximated on the 

basis on one year of hourly weather data collected at the Peach Bottom site (i.e., if ΩΒ is a 

weather bin, then pA(ΩΒ) is the probability of this weather bin, with this probability being 

approximated on the basis of one year of weather data).

Although the concept of a probability space is important conceptually and convenient 

notationally, calculations involving a probability space (Α, Α, pA) are often described with a 

density function dA(a), where 

( ) ( ) d A A p dS = ∫ a S S

Equation A-2 

for Σ ∈ Α, a ∈ Σ, and dS corresponding to an increment of volume from Σ. Then, the expected 

value, variance, CDF, and CCDF at time τ (yr) associated with a real-valued function y = f(τ|a) 

defined on Α are defined by

( ) ( ) ( ) | | d, Ef f d A A A   τ τ =   ∫ a aa A Equation A-3 

( ) ( ) ( ) { } ( ) 2

| | | d, Vf f Ef d A A A A   τ ττ = −   ∫ a a aa A Equation A-4 

( ) | ( ) ( ) | d, A y A pf y f d A   τ δτ ≤ =   ∫ a a a A Equation A-5 

and

( ) | ( ) ( ) | d, A y A pyf   ≤ = τ δτ f d A   ∫ a aa A Equation A-6 

respectively, where

( ) 1 if | ( ) | 0 otherwise, y

f y δ f

τ

τ

 ≤     = 



a

a ( ) 1 if | ( ) | 0 otherwise, y

f y δ fτ

τ

 >     = 



a

a

and dA represents an increment of volume from Α. 

The equalities in Equations A-5 and A-6 in effect define a CDF and a CCDF, respectively. 

Specifically, if [,] mn mx y y includes the range of possible values for y, then the plots defined by 

the points

{yp f y yp y f , | and , A A     ( ) τ τ a a ≤ } { < ( ) | } Equation A-7 

for mn mx y yy ≤ ≤ correspond to the CDF and CCDF, respectively, for y. A CCDF is defined in 

Equation A-6 because of the typical usage of CCDFs to represent uncertainty in risk 

assessments. In particular, a CCDF answers the question “How likely is it to be this bad or 

worse?” which is usually the question asked with respect to individual consequences in a risk 
A-3

assessment. In particular, CCDFs constitute the standard uncertainty structure used in the 

presentation of offsite consequence results calculated with MACCS. 

The second entity, EN2, corresponds to a model, or more realistically a large system of 

interacting models, that predict the behavior of a NPP under accident conditions and various 

summary measures of this behavior (e.g., radionuclide release rates). Notationally, this model 

can be represented by a function of the form

( ) ( ) | | , | ,, | , 1 2 ( ) ( ) m τ ττ τ =   ff f fa a a a    Equation A-8 

where τ corresponds to time (yr), each element fj(τ|a) of f(τ|a) is a specific calculated result, and 

a is an element of the sample space Α for aleatory uncertainty. In general, the value of f(τ|a), 

and indeed the actual structure of the individual models that are combined to produce f(τ|a), will 

change with changing values for a. In the SOARCA Uncertainty Analysis, the function f(τ|a) 

corresponds to combined calculations performed with models implemented within the MELCOR 

and MACCS programs. Consistent with the notation used in Equation A-8, the indicated models 

produce a large number of time dependent results.

In practice, functions of the form indicated in Equation A-8 are usually too complex for 

quadrature-based evaluations. This is certainly the case for results obtained with MACCS due 

to the complexity of the conditions associated with weather sequences and the extensive 

calculations that underlie the estimation of offsite consequences. As a consequence, results of 

the form indicted in Equations A-3 through A-6 are usually estimated with some form of 

sampling procedure. One possibility is to use simple random sampling from the sample space 

Α for aleatory uncertainty. With this approach, a random sample

1 2 , , , , 1, 2,..., , j j j nj =   a a a j nSE =   a  Equation A-9 

is generated from Α consistent with the defining probabilities for the probability space (Α, Α, pA). 

Then, the results in Equations A-3 through A-6 are approximated on the basis of this sample. 

For example, the approximations to the expected value in Equation A-3 and the exceedance 

probability in Equation A-6 for an element f(τ|a) of the function f(τ|a) in Equation A-8 are:

( ) ( )

1

| |/

nSA

A j

j

E f τ τ f nSA

=

  ≅   a a ∑

Equation A-10

and

( ) ( )

1

| | /,

nSA

A y j

j

p y f τ δτ f nSA

=

  ≤ ≅     ∑   a a

Equation A-11

respectively. 

An alternate procedure is to subdivide Α into a sequence of disjoint subsets Αj, j = 1, 2, ..., nSA, 

and randomly sample a single element aj from each set Αj. Then, the results in Equations A-3 

through A-6 are approximated on the basis of the sets Αj and the sampled elements aj. For 

example, the resultant approximations to the expected value in Equation A-3 and the 
A-4

exceedance probability in Equation A-6 for an element f(τ|a) of the function f(τ|a) in 

Equation A-8 are:

( ) ( ) ( )

1

| |

nSA

A j A j

j

Ef f p τ τ

=

  ≅   a a ∑ A

Equation A-12

and

( ) ( ) ( )

1

| |,

nSA

A y j A j

j

pyf τ δτ f p

=

  ≤ ≅     ∑   a a A

Equation A-13

respectively. This approach corresponds to use of the Kaplan-Garrick ordered triple 

representation for risk.

A variant of the approach indicated in the preceding paragraph is used with MACCS in the 

SOARCA analyses in the estimation of expected values and exceedance probabilities. In this 

variant, the sets Αj, j = 1, 2, ..., nSA, correspond to ΩΒj, j = 1, 2, ..., 36 = nWB, weather bins 

(i.e., subsets of the set Α in Equation A-1), and ajk, k = 1, 2, ..., nWBj, elements are sampled 

from each weather bin ΩΒj. In the SOARCA uncertainty analyses, nWBj is defined by

0 05 ] if 12 0 05 

= 12 if 0 05 12 

 if 12 

j j

j j j

j j

nWBT nWBT

nWB nWBT nWBT

nWBT nWBT







 ≤ 

<

< <

[ . .

.

, Equation A-14

where nWBTj is the number of elements in ΩΒj estimated on the basis of one year of weather 

data and [~] corresponds to the greatest integer function. Then, the results in Equations A-3 

through A-6 are approximated on the basis of the sets ΩΒj and the sampled elements ajk. For 

example, the resultant approximations to the expected value in Equation A-3 and the 

exceedance probability in Equation A-6 for an element f(τ|a) of the function f(τ|a) in 

Equation A-8 are

( ) ( ) ( )

1 1

| | /

nWB nWBj

A jk j A j

j k

E f τ τ f nWB p

= =

    ≅      

a a ∑ ∑ WB

Equation A-15

and

( ) ( ) ( )

1 1

| |/ ,

nWB nWBj

A y jk j A j

j k

p y f τ δτ f nWB p

= =

      ≤ ≅            

a a ∑ ∑ WB

Equation A-16

respectively.

The third entity, EN3, corresponds to a probability space (Ε, Ε, pE) for epistemic uncertainty. 

The conceptual properties associated with probability space (Ε, Ε, pE) are the same as 
A-5

indicated in Equations A-2 through A-6 for the probability space (Α, Α, pA) for aleatory 

uncertainty. In general, the elements of the sample space  are vectors of the form:

[ ]

[ ]

12 , 1 2 ,

1 2

,

, ,, , , ,,

,,, , ,

A M

A A A nEA M M M nEM

nE

ee e e e e

e e e nE nEA nEM

=

=    

= = +

 



e e e

Equation A-17

where 12 , [ , ,, ] A A A A nEA e = ee e  is a vector of epistemically uncertain quantities used in the 

characterization of aleatory uncertainty (not considered in this analysis as no aspect of the 

weather trials are treated as being epistemically uncertain) and 12 , eM M M M nEM = [ , ,, ] ee e 

is a vector of epistemically uncertain quantities used in the evaluation of f(τ|a).

In the SOARCA Uncertainty Analysis, the vector eM of epistemically uncertain model 

parameters has two components: a vector eME of epistemically uncertain parameters used in 

MELCOR calculations and a vector eMA of epistemically uncertain parameters used in MACCS

calculations (Table 2.2-1). Specifically, the form of eM in the SOARCA Uncertainty Analysis is

[ ]

[ ]

,1 ,2 , 1 2 ,

1 2

,

, ,, , , ,,

,,, ,

M ME MA

ME ME ME nME MA MA MA nMA

nE

e e e ee e

e e e nE nME nMA

=

=    

= = +

 



e ee

Equation A-18

with nME = 12 and nMA = 9. 

In practice, the probability space (Ε, Ε, pE) is defined by assigning probability distributions to the 

individual elements of e. In addition, correlations and other restrictions involving the elements of 

e may also be specified. The specified distributions serve as mathematical summaries of all 

available information with respect to where the appropriate values for the elements of e are 

located and are often developed through expert review processes [68, 69, and70]. The 

development of the distributions characterizing epistemic uncertainty in the SOARCA 

Uncertainty Analysis, are discussed in Section 4.1.

With the introduction of the probability space (Ε, Ε, pE) for epistemic uncertainty, the 

representation for the system model in Equation A-8 becomes

( ) ( ) ( ) ( ) 1 2 τ ττ τ |, |, , |, , , |, . M M Mm M =   ff f f ae ae ae    a e Equation A-19

Further, given that there is no uncertainty in the characterization of aleatory uncertainty as is the 

case in the SOARCA analysis, results of the form in Equations A-3, A-5, and A-6 become:

( ) ( ) ( ) | , | , d, E f A M M A   τ τ = f d A   ∫A a e ae a

Equation A-20

( ) | , ( ) ( ) | , d, A M y MA pf y f d A    τ ≤ = δ τ    ∫A a e ae a

Equation A-21
A-6

and

( ) | , ( ) ( ) | , d, A M y MA pyf    τ δτ = f d A    ∫A < a e ae a

Equation A-22

where f(τ|a,eM) corresponds to one of the functions fj(τ|a,eM) contained in f(τ|a,eM). As eM

changes, each of the preceding quantities also changes and has a probability distribution that 

derives from the probability space (Ε, Ε, pE) for epistemic uncertainty.

In concept, probability distributions over epistemic uncertainty for quantities of the form defined 

in Equations A-20 through A-22 are defined by integrals over the sample space Ε for epistemic 

uncertainty. In practice, such integrals are too complex for quadrature approximations and, as a 

consequence, must be approximated with sampling-based procedures. Specifically, a random 

or Latin hypercube sample [71, 72] 

12 , Mi i i i nE =   e e e i nSE , , , , 1, 2,..., , = e    Equation A-23

is generated from Ε in a manner consistent with the probability distributions that characterize 

epistemic uncertainty. Then, analysis results of interest (e.g., results of the form in 

Equations A-20 through A-22) are determined for each element eMi of the indicated sample. For 

example, if random sampling is used to approximate integrals over aleatory uncertainty as in 

Equations A-10 and A-11, the approximations to the results in Equations A-20 and A-22 

become:

( ) ( ) ( )

( )

( )

1

| , |, d

|, /

| ,

A Mi Mi A

nSA

j Mi

j

A Mi

E f f d A

f nSA

E f

τ τ

τ

τ

=

  =  

≅

=    

∫

∑



A a e ae a

a e

a e Equation A-24

and

( ) ( ) ( )

( )

( )

1

| , |, d

|, /

| ,

A Mi y Mi A

nSA

y j Mi

j

A Mi

pyf f d A

f nSA

pyf

τ δτ

δ τ

τ

=

   =   

≅    

=    

∫

∑



A a e ae a

a e

a e

<

< Equation A-25

for each element eMi of the indicated sample. Approximations to distributions summarizing 

epistemic uncertainty can now be obtained from results of the form in Equations A-24 and A-25 

with an equal weight of 1/nSE assigned to the results obtained with each sample element. 

Further, mappings of the form

Mi A , | , , 1, 2,..., , E f ( ) Mi     τ i nSE =      e ae

Equation A-26

and
A-7

, ( ) | , , 1, 2,..., , Mi A Mi   p y f   τ i nSE =     e  < a e

Equation A-27

form the basis for the application of a variety of sensitivity analysis procedures as discussed in

Section 3.2.

In the SOARCA Uncertainty Analysis, a sample of size nSE = 300 is used to generate the 

sample indicated in Equation A-23. Specifically, the component eME of eM will be sampled with 

random sampling and the component eMAof eM will be sampled with Latin hypercube sampling. 

In turn, SOARCA results of the form indicated in Equations A-15 and A-16 will be approximated 

by

( ) ( ) ( )

( )

1 1

| , | , /

| ,

nWB nWBj

A Mi jk Mi j A j

j k

A Mi

E f f nWB p

E f

τ τ

τ

= =

    ≅      

=    

∑ ∑



a e a e WB

a e Equation A-28

and

( ) ( ) ( )

( )

1 1

| , | , /

| ,

nWB nWBj

A Mi y jk Mi j A j

j k

A Mi

p y f f nWB p

pyf

τ δ τ

τ

= =

      ≤ ≅            

= ≤    

∑ ∑



a e a e WB

a e Equation A-29

for each sample element eMi. As discussed in the preceding paragraph, results of the form in 

Equations A-28 and A-29 provided the basis in SOARCA for assessing the effects and 

implications of epistemic uncertainty.

A.2 Parameter Sensitivity and Uncertainty Analysis Methodology

Closely associated with the characterization of epistemic uncertainty provided by the probability 

space corresponding to EN3 and the answering of Question Q4 (described in Section 2.3) are 

the concepts of uncertainty analysis and sensitivity analysis, where uncertainty analysis 

designates the determination of the epistemic uncertainty in analysis results that derives from 

epistemic uncertainty in analysis inputs and sensitivity analysis designates the determination of 

the contribution of the epistemic uncertainty in individual analysis inputs to the epistemic 

uncertainty in analysis results. Specifically, uncertainty analysis involves determining the range 

and distribution of an analysis result of interest that derive from the ranges and distributions of 

uncertain analysis inputs. The goal of uncertainty analysis is to determine the uncertainty in an 

analysis result that derives from the collective uncertainty in analysis inputs. In contrast, the 

goal of sensitivity analysis is to determine the extent to which the uncertainty in individual 

analysis inputs contributes to the uncertainty in an analysis result. Intuitively, sensitivity analysis 

corresponds to decomposing the uncertainty in an analysis result into the fractions of this 

uncertainty contributed by each uncertain analysis input. Commonly used sensitivity analysis 

procedures include scatterplots, correlation coefficients, partial correlation coefficients, stepwise 

regression with raw or rank transformed data, and a number of other techniques. General 

references on uncertainty and sensitivity analysis include [11-13, 71, 73, 74]. Example 

uncertainty and sensitivity analyses include studies of the MAEROS component of MELCOR

model system for reactor accidents [75, 76] and the MACCS model system for offsite 

consequences of reactor accidents [77-80, and 81]. 
A-8

Basically, uncertainty and sensitivity analysis are the means by which EN3 gives rise to the 

answer to Question Q4. As an example, a parameter uncertainty analysis was conducted using 

the methods described below for both source term and radiological consequences to evaluate 

the effects of the uncertainty in key inputs on a selected accident scenario.

Several of the approaches to sensitivity analysis that can be used in conjunction with a 

sampling-based uncertainty analysis are listed and briefly summarized below. In this summary, 

(i) xj is an element of a vector x = [x1, x2, ..., xnX] of epistemically uncertain analysis inputs, (ii) yk

is an element of y(x) = [y1(x), y2(x), ..., ynY(x)], (iii) xi = [xi1, xi2, ..., xi,nX], i = 1, 2, ..., nS, is a 

random or Latin hypercube sample from the possible values for x generated in consistency with 

the joint distribution assigned to the xj

, (iv) yi = y(xi) for i = 1, 2, ..., nS, and (v) xij and yik are 

elements of xi and yi

, respectively. 

Scatterplots

Scatterplots are plots of the points [xij, yik] for i = 1, 2,..., nS and can reveal nonlinear or other 

unexpected relationships (Figure A-1). In many analyses, scatterplots provide all the 

information that is needed to understand the sensitivity of analysis results to the uncertainty in 

analysis inputs. Further, scatterplots constitute a natural starting point in a complex analysis 

that can help in the development of a sensitivity analysis strategy using one or more additional 

techniques [82, 83]. 

Figure A-1 Examples of scatterplots obtained in a sampling-based uncertainty 

/sensitivity analysis ([73], Fig. 8.2)
A-9

Correlation 

A correlation coefficient (CC) provides a measure of the strength of the linear relationship 

between xj and yk. The CC between xj and yk is equal to the standardized regression coefficient 

(SRC) in a linear regression relating yk to xj and is also equal in absolute value to the square 

root of the R2 value associated with the indicated regression. When calculated with raw 

(i.e., untransformed) data, the CC is often referred to as the Pearson CC [47, 82] 

Regression Analysis 

Regression analysis provides an algebraic representation of the relationships between yk and 

one or more xj’s. Regression analysis is usually performed in a stepwise fashion, with initial 

inclusion of most important xj, then two most important xj’s, and so on until no more xj’s that 

significantly affect yk can be identified. Variable importance is indicated by order of selection in 

the stepwise process, changes in R2 values as additional variables are added to the regression 

model, and SRCs for the xj’s in the final regression model (Table A-1). A display of regression 

results in the form shown in Table A-1 is very unwieldy when results at a sequence of times are 

under consideration. In this situation, a more compact display of regression results is provided 

by plotting time-dependent SRCs (Figure A-2) [82, 83]. 

Table A-1 Example of Stepwise Regression Analysis to Identify Uncertain Variables 

Affecting the Uncertainty in Pressure at 10,000 years on Figure 5a ([73], 

Table 8.6)

Stepa Variableb SRCc R2d

1 WMICDFLG 0.718 0.508

2 HALPOR 0.466 0.732

3 WGRCOR 0.246 0.792

4 ANHPRM 0.129 0.809

5 SHRGSSAT 0.070 0.814

6 SALPRES 0.063 0.818

a Steps in stepwise regression analysis.

b Variables listed in the order of selection in regression analysis.

c SRCs for variables in final regression model.

d Cumulative R2 value with entry of each variable into regression model.
A-10

Figure A-2 Time-dependent sensitivity analysis results for uncertain pressure curves in 

Fig. 5a: (a) SRCs as a function of time, and (b) PCCs as a function of time 

([73], Fig. 8.3)

Partial Correlation

A partial correlation coefficient (PCC) provides a measure of the strength of the linear 

relationship between yk and xj after the linear effects of all other elements of x have been 

removed. Similarly to SRCs, PCCs can be determined as a function of time for time-dependent 

analysis results (Figure A-3) [82, 83]. 

Rank Transformations

A rank transformation replaces values for yk and xj with their corresponding ranks. Specifically, 

the smallest value for a variable is assigned a rank of 1; next largest value is assigned a rank 

of 2; tied values are assigned their average rank; and so on up to the largest value, which is 

assigned a rank of nS. Use of the rank transformation converts a nonlinear but monotonic 

relationship between yk and xj to a linear relationship and produces rank (i.e., Spearman) 

correlations, rank regressions, SRRCs and partial rank correlation coefficients (PRCCs). In the 

presence of nonlinear but monotonic relationships between the xj and yk, the use of the rank 

transform can substantially improve the resolution of sensitivity analysis results (Table A-2) 

[and 82, 83, 84]. 
A-11

Table A-2 Comparison of Stepwise Regression Analyses with Raw and 

Rank-Transformed Data for Variable BRAALIC on Figure 4b ([73], Table 8.8)

Raw Data Rank-Transformed Data

Stepa Variableb SRCc R2d Variableb SRRCe R2d

1 ANHPRM 0.562 0.320 WMICDFLG −0.656 0.425

2 WMICDFLG −0.309 0.423 ANHPRM 0.593 0.766

3 WGRCOR −0.164 0.449 HALPOR −0.155 0.802

4 WASTWICK −0.145 0.471 WGRCOR −0.152 0.824

5 ANHBCEXP −0.120 0.486 HALPRM 0.143 0.845

6 HALPOR −0.101 0.496 SALPRES 0.120 0.860

7 WASTWICK −0.010 0.869

a Steps in stepwise regression analysis.

b Variables listed in order of selection in regression analysis.

c SRCs for variables in final regression model.

d Cumulative R2 value with entry of each variable into regression model.

e SRRCs for variables in final regression model.

Figure A-3 Illustration of failure of a sensitivity analysis based on rank-transformed 

data: (a) Pressures as a function of time and (b) PRCCs as a function of 

time ([73], Figure 8.7)

For SOARCA the parameter uncertainty and sensitivity analysis will be based upon a mapping 

between uncertain inputs and analysis results using: (1) Stepwise rank regression analyses, 

and (2) Scatter plots.

Partial rank correlation coefficients provide a measure of the strength of the monotonic 

relationships between an independent variable and a dependent variable after a correction has 

been made to remove the monotonic effects of the other independent variables in the analysis. 

PRCCs involve the analysis of rank transformed data to transform monotonic relationships into 

linear relationships. In a stepwise rank regression, the single independent variable that makes 

the largest contribution to the uncertainty in the dependent variable is selected in the first step. 

This process continues until no additional variables are found that make identifiable 
A-12

(i.e., significant) contributions to the uncertainty in the dependent variable. A significance level 

of 0.01 will be used as the criterion for terminating a stepwise regression analysis. In the 

context of stepwise regression analysis, variable importance is indicated by (1) order of 

selection in the stepwise selection process, (2) incremental changes in cumulative R2 values, 

and (3) the sign and size of the standardized regression coefficients, (i.e., SRRCs, when rank 

regression is being used) in the final regression model. Results will be presented as a set of 

CCDFs. A calculation of the confidence bounds on the mean values for the CCDF and other 

result metrics (e.g., fraction of the cesium released to the environment) will be included. 

Along with rank regression, quadratic, recursive partitioning, and multivariate adaptive 

regression splines (MARS) are the four regression techniques used to estimate the importance 

of the input parameters in the uncertainty of the output in consideration. A short description of 

each technique follows. A more detailed description of the techniques (with examples) can be 

found in [12] and [13]. 

Quadratic regression

Quadratic regression technique applies the same approach as linear regression, including

individual input variables, the square of these variables and second order multiplicative 

interaction terms. The prediction model is of the form:

YY = aa0 + �aaiiXXii

nn

ii=1

+�bbiiXXii

2

nn

ii=1

+� � cciiXXiiXXjj

nn

jj=ii+1

+

nn

ii=1

εε

Quadratic regression is not completely additive as it can capture 2nd order interactions. It can 

also capture the parabolic influence measured by the square of variables in the regression 

model. However, a complex relationship between variables and the output may still be hard to 

capture with this technique (asymptotic behavior for instance), and the method remains 

parametric which makes it sensitive to outliers. As quadratic regression can capture 

non-monotonic relationships, additional sets of metrics are displayed in the table of regression 

results from this method. Si represents the first order sensitivity index and informs on how much 

of the variance of the selected output is explained by the input parameter in consideration by 

itself. This index is therefore very close in concept to the R2

cont. presented above for the rank 

regression technique and it is acceptable to compare the two metrics. The second metric, 

labeled Ti represents the total order sensitivity index and informs on how much of the variance 

of the selected output is explained by the input parameter in consideration by itself and its 

interaction with all of the other uncertain parameters. It has no equivalent in the rank regression 

model (as the additive model does not capture conjoint influences). The difference between Ti

and Si gives an estimate of the conjoint influence for this input on the output of consideration. 

Finally, a p-value is displayed as third metric, informing on how much confidence can be put in 

the results. A p-value equal or close to zero indicates that the influence is likely to be true (in 

the mathematical sense. It can still be unrealistic physically and due to the particularity of the 

sample), while a p-value equal or close to one indicates a relationship that is not real and due to 

spurious correlation.

Recursive partitioning

Recursive partitioning regression is also known as a regression tree. A regression tree splits

the data into subgroups such as the values are more homogeneous in each subgroup. The 

regression function is constructed using the sample mean over each subgroup. This approach 

results in a piecewise constant function over the input space in consideration. Recursive 

partitioning handles conjoint influences. The predictive model is in the form of:
A-13

YY = �(ddssIIss(XXii))ii=1,...,nn

nnnn

ss=1

+ εε

The same metrics used for quadratic regression are used for recursive partitioning, that is to say 

the first order sensitivity indices (Si), total order sensitivity indices (Ti) and p-values.

Multivariate Adaptive Regression Splines (MARS)

MARS is a combination of (linear) spline regression, stepwise model fitting and recursive 

partitioning. A regression with a single input starts with a mean only model and adds basis 

functions in a stepwise manner adding first the overall linear trend. That creates a first model. 

A second model using linear regression via least square is fitted to the data. This model is then 

added to the basis functions in a way that reduce the SSE between observation and prediction. 

A fourth basis function is then added to minimize again the SSE. This process is repeated until 

‘M’ basis functions have been added.

At this point, the MARS procedure will try to simplify the model using stepwise deletion of basis 

function, while keeping the y-intercept and linear trend. Over the ‘M-2’ candidates, the one 

leading to the smallest increase of SSE will be selected. This deletion will be applied until 

regressed to the original linear model.

Stepwise addition and deletion lead to the building of ‘2M-2’ different models. The “best” model 

is chosen using generalized cross validation (GCV) score which corresponds to a SSE 

normalized by the number of basis functions considered. With multiple inputs, the basis 

functions will consists into main effects and multiple-way interactions. The options used for this 

analysis consider only two-way interaction to avoid exponential cost of considering more 

interactions. MARS are presented using the same metrics as quadratic regression and recursive 

partitioning in the summary tables. 

APPENDIX B

SOFTWARE USED AND CODE INTEGRATION

B-1

B.1 SOFTWARE USED

To better understand the uses of computer codes that are discussed in this section, a brief 

overview is in order. MELCOR is a computer code that models the progression of severe 

accidents in PWRs and BWRs [7]. MELMACCS compiles MELCOR outputs for transition into 

part of a MACCS (MELCOR Accident Consequence Code System) input [8]. MACCS [9] can 

calculate the estimated consequences associated with a release of radioactive material into the 

environment. Detailed descriptions of the capabilities of the software used in this analysis can 

be found in the referenced user’s manuals [7-9]. This section documents the process used 

including the inputs and outputs, information flow, and order of operation for each code used to 

conduct the integrated probabilistic analysis.

B.1.1 MELCOR

MELCOR was developed by SNL for the NRC to model the progression of accidents in a light 

water reactor. A broad spectrum of accident phenomena in both PWR and BWR are treated 

within the code. MELCOR can estimate the fission product source term and also apply 

sensitivity and uncertainty analysis for the estimated source term. For this work MELCOR 

Version 1.8.6 YV3780 was used to generate the source terms for the consequence and 

uncertainty analyses, respectively. MELCOR Version 1.8.6 YR549 was used for the Peach 

Bottom unmitigated LTSBO SOARCA estimate case presented in NUREG-1935. A comparison 

of the source term results between the two MELCOR versions is presented in Appendix C. 

However, both versions of MELCOR were used in NUREG-1935 while only MELCOR 1.8.6

YV3780 was used for the Surry ISLOCA scenario [40]. 

MELCOR is divided into 20 different packages and an execution primer. All of these packages 

are coupled within the code to model major reactor plant systems. The codes model response 

to accident conditions which include but are not limited to [7]: 

• Thermal-hydraulic response of the primary reactor coolant system, the reactor cavity, the 

containment, and the confinement buildings;

• Core uncovering, fuel heatup, cladding oxidation, fuel degradation, and core material 

melting and relocation;

• Heatup of reactor vessel lower head from relocated fuel materials and the thermal and 

mechanical loading and failure of the vessel lower head and transfer of core materials to 

the reactor vessel cavity;

• Core-concrete attack and ensuing aerosol generation;

• In-vessel and ex-vessel hydrogen production, transport, and combustion;

• Fission product release, transport, and deposition;

• Behavior of radioactive aerosols in the reactor containment building; and

• Impact of engineered safety features on thermal-hydraulic and radionuclide behavior.
B-2

The MELCOR model uses a ‘control volume’ approach for describing and combining reactor 

plant systems (i.e., see Section 4.1 and 4.2 of Reference 2 for examples of MELCOR ‘control 

volumes’). MELCOR can provide a detailed and unique reactor plant model for any type of 

PWR or BWR and has even been demonstrated to successfully model Russian VVER and 

RMBK-reactor classes [7]. 

The first part of the MELCOR execution is called MELGEN. MELGEN provides a starting point 

for MELCOR. The majority of the initial conditions are specified, processed, and checked for 

execution errors. Upon execution of MELGEN, a restart file for MELCOR is written. The 

MELCOR code is then executed using this restart file and advances the accident scenario 

through predetermined timesteps until a previously end time is achieved. 

As part of the MELCOR/MELGEN output, a plot file (.PTF) is created. The MELCOR output 

variables are written to this plot file at time intervals predetermined by the user. Figure B.1-1 

provides a graphic overview of the MELCOR code and the file relations.

Figure B.1-1 MELCOR code and file relation
B-3

B.1.2 MELMACCS

The MELMACCS software is a Windows based program that is used to create a MELCOR 

Accident Consequence Code System, Version 2 (MACCS) input file from either a MELCOR 

Version 1.8.6 or Version 2.1 plot file (e.g., Case.ptf). The MELCOR plot files contain large 

amounts of data, only some of which is needed for MACCS calculations. The MELMACCS 

software was created to provide an interface utility between MELCOR and MACCS to integrate 

the required data. 

MELMACCS obtains both time-independent and time-dependent data from the MELCOR plot 

files. Time independent data remains constant throughout the MELCOR calculation. Examples 

are radionuclide physical and chemical property classes and MELCOR flow paths to the 

environment. Time dependent data is written to the MELCOR plot file for each plot file timestep 

which has been determined by the user. Examples of this data are fluid temperature, flow rate 

through a MELCOR flow path to the environment, and the mass of each physical and chemical 

property class.

MELMACCS uses a graphical user interface (GUI) to allow the user to convert a MELCOR plot 

file into a radionuclide input file for MACCS. The inputs from the MELCOR plot file correspond 

to the radionuclide file inputs for the ATMOS portion of MACCS. The ATMOS portion of 

MACCS is discussed in Section B.1.3.1. MELMACCS can also be run in DOS to provide the 

user the ability to setup MELMACCS to convert multiple MELCOR plot files using a batch 

process. This batch process was used for this work. Each of the MELCOR plot files used in the 

batch process correspond with one radionuclide input file for MACCS. 

Before converting the MELCOR plot file, the user must specify inputs that are needed for the 

MACCS radionuclide input file, but are not provided by MELCOR. These inputs are:

• Radionuclide classes, 

• high/Medium/Low burnup fuel,

• time of accident initiation, 

• MELCOR height associated with ground level, 

• data for building height, initial plume width and height for wake calculations,

• deposition velocity information,

• mass thresholds fractions for released material, and

• time intervals for plume segments

Figure B.1-2 provides an example of a MELMACCS plume segment. A time-dependent

segmented plume interval is done for each MELCOR release path to the environment. Some 

release paths may not contain all the radionuclides defined in MELCOR (e.g., only noble gases 

are released passed a failed door seal). On Figure B.1-2, the initial black vertical line shows the 

time of radionuclide release into the environment for this specified path, MELCOR Release 

Path 1. For this work, the plume release time intervals are 3,600 seconds (1 hour) as that is the 

minimum time interval which MACCS can incorporate into the analysis.
B-4

Figure B.1-2 MELMACCS plume segment

As shown on Figure B.1-2, not all radionuclide chemical/physical property classes are 

represented for a MELCOR release path (i.e., no uranium, U, class). Table B.1-1 lists the 

classes that are not represented in MELMACCS and are thus not carried over into the MACCS

calculations. The user may also remove any of the 12 classes included in the MELMACCS as 

shown on Figure B.1-2. Class 13 through 16 are not included in the MELMACCS results 

because MACCS only reads the 12 radioactive radionuclide classes defined in MELCOR. 

Class 16 (CsI) is not a group that can be imported into MELMACCS. It is incorporated by 

carrying forward the activities and dose conversion factors for cesium and iodine separately, 

and therefore, is split accordingly into Class 2 (cesium) and Class 4 (halogens) fractions. 

Classes 13, 14, and 15 are nonradioactive. Figure B.1-2 does not show cerium, lanthanum, 

uranium, or ruthenium radionuclide classes as the release fractions of these radionuclides are 

less than 1.0 × 10−5

. MELMACCS does capture fractional releases below 1.0 × 10−5; however, 

for this work, a mass threshold fraction for a release path and a mass threshold fraction for 

plume segments to be used were set to 0.001 for MACCS inputs. These threshold limits are the 

same as those used in SOARCA calculations. The reason the thresholds are used is to keep 

the number of plume segments less than 200, which is the maximum number MACCS can 

analyze.
B-5

Table B.1-1 MELCOR radionuclide classes not included in MELMACCS

Class Name Representative Member Elements

13 Boron B B, Si, P

14 Water H2O H2O 

15 Concrete -- -- 

16 Cesium Iodide CsI CsI

B.1.3 MACCS

MACCS was developed by SNL for the NRC to simulate the release of a radiological plume to 

the atmosphere and estimate the consequences associated with the release. The code uses a 

Gaussian plume dispersion model and incorporates plume depletion, exposure pathway 

assessment, and subsequent dose analysis. MACCS uses include PRA and radiological dose 

assessment for safety analyses and environmental studies such as NUREG-1150 [16]. The 

current version of MACCS 2.5.0.0 has a Windows based GUI called WinMACCS. 

MACCS includes three primary models, ATMOS, EARLY, and CHRONC. Input files for these 

include the following parameter values [8]: 

• ATMOS input: atmospheric transport, dispersion, and deposition parameters;

• EARLY input: parameters pertaining to the emergency phase, up to the first seven days 

after the accident, including mitigative actions such as evacuation, sheltering, and 

dose-dependent relocation; and

• CHRONC input: parameters pertaining to the intermediate and long-term phases.

• Additional auxiliary files are also required to run MACCS. These are a text file containing 

the path and names for the MACCS input files (MACCS.tmp), and an ASCII file containing 

decay-chain information (Indexr.dat). This ASCII file is included as part of the MACCS

installation.

Optional data files may also be required by MACCS [8]: 

• Meteorological file describing weather conditions for one or more years.

• Site files describing population, land use, and economic parameters.

• Dose conversion factor file used to calculate acute or latent health effects from various 

radionuclide exposures for each pathway.

• Comida2 binary file used to define food-chain doses.

• Dose threshold models
B-6

o LNT hypothesis; 

o US average natural background dose rate combined with average annual medical 

exposure as a dose truncation level (USBGR), often cited as 620 mrem/yr [85]; and 

o a dose truncation level based on the HPS that there is a dose below which, due to 

uncertainties, a quantified risk should not be assigned: 5 rem/yr with a lifetime limit of 

10 rem [86]. 

All the optional files listed above were used for this analysis with the exception of the COMIDA2

binary file. The COMIDA2 binary file was not used since the ingestion pathway was not treated 

in SOARCA. An underlying assumption in SOARCA was uncontaminated food and water 

supplies are abundant within the United States, and it is unlikely that the public would eat 

radioactively contaminated food. 

This section only discusses the three major models, ATMOS, EARLY, and CHRONC. For 

further information into the modeling packages described below or the auxiliary and optional 

data files not discussed, refer to NUREG/CR-6613 [9]. 

B.1.3.1 ATMOS Package

The Atmospheric Transport and Deposition (ATMOS) model uses a Gaussian plume model with 

Pasquill-Gifford dispersion parameters to determine the dispersion and deposition of 

radionuclides in the atmosphere as a function of downwind distance. The ATMOS model 

considers the following phenomena [9]: 

• Building wake effects,

• buoyant plume rise,

• plume dispersion during transport,

• wet and dry deposition, and

• radioactive decay and ingrowth.

Figure B.1-3 provides a graphical representation of the Gaussian dispersion model along a 

Cartesian coordinate system. 
B-7

Figure B.1-3 Gaussian dispersion model

For the Gaussian puff dispersion model, isopleths of approximate equal pollutant concentrations 

can be created for downwind areas. Figure B.1-4 provides an example of this.

Figure B.1-4 Isopleths of equal pollutant concentration

For a Gaussian continuous source like that modeled in ATMOS, consider an infinite number of 

puffs, and assume the following:

• Along the x-axis as indicated on Figure B.1-3, the diffusion is negligible compared to 

advection thus, σx = 0.

• Slender plume approximation thus, σσxx

�uu�⃑

xx ≫ 1. 

• The earth’s surface is z=0 and this boundary is ‘totally reflecting’ the plume.
B-8

With the above assumptions, Equation B.1-1 shows a Gaussian continuous source:

Χ�(xx, yy, zz,tt) = 

QQ

2ππσσyyσσzzuu�⃑

∙ ee ee ��− yy2

2σσyy

2� ∙ �ee ee �− (zz−HH)2

2σσzz

2 � + ee ee �− (zz+HH)2

2σσzz

2 ��� Equation B.1-1 

where:

Χ� =mean concentration of the pollutant

t = time

Q = emission strength of pollutant

x = x-direction on a Cartesian coordinate system

y = y-direction on a Cartesian coordinate system

z = z-direction on a Cartesian coordinate system

uu�⃑ = wind velocity

H = effective elevation of source along the z-direction

The dispersion coefficients, σy and σz, depend on atmospheric stability conditions. These 

stability conditions vary from very stratified (Class A) to very unstable (Class B) to stable 

(Class F). The Pasquill-Gifford stability categories (stability classes) reflect the wind, 

turbulence, insolation, and other phenomena that determine dispersion of a pollutant plume in 

the troposphere [9]. Thus, the dispersion coefficients are the following [87]: 

σσyy = 1xx

[1+(xx⁄ 2)]kk3 Equation B.1-2 

σσzz = 4xx

[1+(xx⁄ 2)]kk5 Equation B.1-3 

where:

x = downwind distance in meters from the source

 k1-6 = constants determined as a function of the Pasquill-Gifford Stability Class 

Isopleths (i.e., curves of equal concentration) can be created for downwind areas from a 

Gaussian continuous model. The isopleths shown on Figure B.1-4 can be applied to the 

continuous model. In the ATMOS model at the centerline midpoint of each isopleth, air and 

ground concentrations are determined for each radionuclide. Also, information about the plume 

size, height, and transport timing is determined for each isopleth. Concentrations are calculated 

along the plume centerline. The EARLY and CHRONC models make adjustments for 

off-centerline locations [9]. 

MACCS can include up to 150 radionuclides into the ATMOS model. This was expanded from 

the original MACCS database of 60 radionuclides used for the NUREG-1150 [16]. However, all 

the selected radionuclides must be present in the dose conversion file and the decay-chain 

database. The decay-chain database can include a maximum of six decay generations and 

using branch ratios will allow up to three different daughter products for each decay chain.

The ATMOS model can model up to 200 atmospheric dispersion plumes. Also, there are 

several different options for weather sampling within the ATMOS model. If the user supplies a 

one-year weather file, the ATMOS model can either sample the file using a weather category 

bin sampling method, or by a stratified random sampling method. However, if the user specifies 

a single weather trial, then the ATMOS model can either run the trial with [9]: (1) constant 

weather conditions, (2) fixed start time in the weather file, or (3) user-supplied 120-hr weather 
B-9

sequence. Additionally, the ATMOS model can use multiple wind directions from a weather file. 

This can be graphically shown using a wind rose diagram. A wind rose diagram schematically 

represents the wind direction and the frequency of occurrence for a particular wind direction. 

Figure B.1-5 provides an example of a wind rose diagram.

Figure B.1-5 Percent wind rose

B.1.3.2 EARLY Package

The emergency-phase (EARLY) model is the environmental consequence model for the time 

phase immediately following the radioactive release. This time phase can be up to one week 

following the arrival of the first radioactive plume. For longer time phases, the CHRONC model 

is used. The EARLY model time phase includes evacuation, sheltering, and dose-dependent 

relocation. The EARLY model can also combine up to 20 different emergency response 

scenarios (i.e., evacuation cohorts). 

The EARLY model output is a weighted sum of the emergency-response scenarios. The 

scenarios may be combined using the following ways [9]: 

• Time fractions (fraction of occurrence) or,

• population fractions (fraction of the population engaging in the specific behavior) for each 

scenario or,

• a sum of the results for each emergency-response scenario (when a unique population 

distribution is defined for each emergency-response scenario).
B-10

A CCDF is determined for each emergency-response scenario. The emergency-response 

scenarios are based on population fractions, the CCDFs are a function of the consequence for 

each meteorological trial or wind direction multiplied by the fraction of people assigned for that 

area for each scenario. 

The EARLY model includes five exposure pathways for determining radiation dose. 

Figure B.1-6 provides an example of the five exposure pathways modeled. These five 

pathways are the following [9]: 

1. Direct external exposure to radioactive material in the plume (cloudshine).

2. Exposure from inhalation of radionuclides in the cloud (cloud inhalation).

3. Exposure to radioactive material deposited on the ground (groundshine).

4. Inhalation of resuspended material (resuspension inhalation) and

5. Skin dose from material deposited on the skin.

Figure B.1-6 Exposure pathways

The EARLY model calculates two kinds of doses [9]: 

1. Acute doses used for calculating early fatalities, and

2. lifetime dose commitment used for calculating potential latent cancers resulting from the 

early exposure.

The doses calculated for early exposure are influenced by evacuation, sheltering, relocation 

dose threshold, and early relocation times. The cloudshine and cloud inhalation exposures are 

only determined for the time it takes the plume to pass, while the groundshine and resuspension 

inhalation exposures are calculated throughout the early phase time period (up to one week 

following the arrival of the first radioactive plume). 

The EARLY model determines the dose to evacuees by adding the doses they received before 

evacuation and during evacuation. Once the evacuees are outside the evacuation zone, the 

model assumes no additional EARLY phase dose is received. However, the CHRONC model 

determines additional long-term doses to the evacuees.
B-11

B.1.3.3 CHRONC Package

The intermediate- and long-term phase (CHRONC) model calculates environmental 

consequences for the time phase following the emergency-phase modeled by the EARLY 

model. The intermediate-phase part of the CHRONC model is based on satisfying a dose 

criterion to the resident population. If the population radiation exposure from groundshine and 

the inhalation of resuspended radioactive material for the entire intermediate phase exceeds a 

predetermined threshold (e.g., habitability criterion), the population is assumed to be relocated 

to uncontaminated areas for the entire intermediate phase. The intermediate phase can be as 

short as zero (no intermediate phase, and thus the long-term phase begins immediately 

following the emergency phase) or as long as one year. The intermediate-phase only calculates 

the groundshine and resuspension inhalation exposure pathways to the effected population.

The long-term phase of the CHRONC model is based on two sets of independent actions [9]: 

1. Decisions relating to whether or not land at a specific location and time is suitable for human 

habitation (i.e., habitability criterion), and

2. decisions relating to whether or not land at a specific location and time is suitable for 

agricultural production (i.e., farmability).

The CHRONC model determines doses to the population from direct exposure to groundshine 

and the inhalation of resuspended radioactive material as well as ingestion exposure by 

consumption of contaminated food and water. The ingestion exposure is not limited to the 

population within the contaminated areas. Both groundshine and resuspension inhalation 

exposure pathways can incorporate weathering data in the form of half-lives. The user must 

determine the relationship between the weathering coefficients and weathering half-lives.

In order to estimate doses from ingestion, mitigation of exposure effects are taken into account. 

Values for parameters like agricultural uses of land, whether land is immediately habitable after 

decontamination, or habitable after decontamination and interdiction are user defined. If 

radiation doses do not satisfy the criteria for habitability or for agricultural development after the 

maximum-duration of interdiction, then the land is considered condemned, or permanently 

interdicted. The ingestion pathway was not treated in the analyses reported here because

uncontaminated food and water supplies are abundant within the United States and it is unlikely 

that the public would eat radioactively contaminated food.

B.2 Code Integration

In this section, a description of the elements and processes (e.g., codes and files) used to 

implement the integrated probabilistic analysis is provided. Figure B.2-1 shows the information 

flow of the SOARCA Uncertainty Analysis. A description of each item on Figure B.2-1 is 

described in this section.

• Uncertain MELCOR and MACCS parameters are sampled

• MELCOR is run for each set of its sampled values

• MACCS is run for each set of its sampled values in conjunction with the associated 

MELCOR source term outputs
B-12

Figure B.2-1 Diagram of the information flow of the SOARCA Uncertainty Analysis

MELCOR Uncertain Parameters

The uncertain parameters selected from the MELCOR model for the Peach Bottom unmitigated 

LTSBO scenario are listed by their distribution types and associated parameters (e.g., uniform 

distribution with a lower and upper bound) in Section 4.1. These distributions are incorporated 

into the MELCOR Uncertainty Engine input template file.

MELCOR Input Deck

The input for the MELCOR model of the Peach Bottom unmitigated LTSBO scenario is divided 

into a set of input files. The files listed in Table B.2-1 contain the majority of the information that 

describes the model. The file jelly_MScreep.gen uses the MELCOR R*I*F feature to 

incorporate the individual input files in Table B.2-1 into a single MELGEN file. The file jelly.cor 

contains the MELCOR input information.
B-13

Table B.2-1 SOARCA Peach Bottom unmitigated long-term station blackout MELCOR 

Model input files

10x10-rn-set.gen cont-cvh_mod.gen rb-cvh.gen rn.gen

10x10-rpv-cvh.gen cont-hs.gen rb-fl.gen rpv-hs.gen

10x10-rpv-fl.gen core-sc.gen rb-hs-depos.gen seq-trip.gen

10x10core.gen cvtype.gen rb-hs.gen sloca-rcic.gen

burn.gen dch-midcy.gen rcic2.gen sp-heatcap.gen

cav.gen dw-liner-melt.gen rcs-sys.gen srv-fl3.gen

cf-midcy.gen hpci.gen recirc.gen srv-tailpipe.gen

cf2.gen hpci2.gen rhr2.gen Write_Output.gen

chex-layman-midcy.gen lpcs.gen rn-cor-struc.gen MSLcreep.gen

cont-cvh.gen mp.gen rn-mass-midcy.gen

MELCOR Uncertainty Engine Input Template

The MELGEN/MELCOR uncertainty engine template file consists of three sections. The first 

section contains the uncertain parameter definitions. Also, variables are defined for each 

uncertain parameter. The second section contains the model’s MELGEN input records. These 

are incorporated by using the R*I*F feature to read in the jelly_DAK.gen file. The MELGEN 

records which contain uncertain parameters are also located in this section of the template file. 

The uncertain parameters in each record are replaced by their respective variables and are 

defined in the first section of the template file. The third section contains the model’s MELCOR 

input records. These are incorporated by using the R*I*F feature to read in the jelly_DAK.cor 

file.

MELCOR Uncertainty Engine

Based on the input template, the MELCOR uncertainty engine creates N MELCOR input files

(e.g., N = 300 realizations). Simple Monte Carlo sampling is used to generate N samples of the 

uncertain parameters. In each input file the uncertain parameter variables are replaced with 

their corresponding sampled value. In addition, an output file is created which contains the 

sampled values. 

Sampled MELCOR Uncertain Parameters

The MELCOR Uncertainty Engine generates an Excel.csv file which contains the sampled 

uncertain parameter values. 

RN Parsing Uncertainty Deck Generator

The uncertainty in the partitioning of the initial iodine core inventory between radionuclide 

Class 4 (Halogens - I) and radionuclide Class 16 (Cesium Iodide - CsI) cannot be directly 

implemented as a single sampled parameter value. Rather, that sampled value is an input into 

the core inventory calculation where it influences the distribution of the mass between the 

radionuclide Class 2 (Alkali Metals – Cs), Class 4, Class 7 (Early Transition Elements – Mo), 

Class 16, and Class 17 (Cesium Molybdate – Cs2MoO4) defined in Radionuclide Package 

Reference Manual, Section 2.1 and Table 2.1 [7]. The radionuclide parsing uncertainty deck 
B-14

generator implements the inventory partitioning calculation as an Excel visual basic macro in an 

Excel workbook. The sampled value of the fraction of the initial iodine core inventory in 

radionuclide Class 4 is manually copied and pasted into the Excel workbook. The macro 

performs the partitioning calculation for each sampled value. The results of the calculation are 

incorporated into the appropriate records of the dch-mdcy_mod.gen and 

rn_mass_midcy_mod.gen files. A separate dch-mdcy_mod.gen and rn_mass_midcy_mod.gen 

is created for each sampled value. 

N MELCOR Input File Sets

A MELCOR input file is created for each set of sampled values (i.e., realization). That file 

incorporates the original input deck with its uncertain parameters set equal to their sampled 

values. For uncertainties that cannot be directly implemented as a single parameter value 

(e.g., fraction of initial iodine core inventory partitioned into radionuclide Class 4) additional input 

files are generated, which are incorporated via the R*I*F feature (see Figure B.2-2).

MELGEN/MELCOR

The MELGEN and MELCOR executables are used to run the N MELCOR input files. Each run 

creates its own set of output files.

N MELCOR Output File Sets

Each MELCOR run has its own set of output files (Figure B.2-2). 

Figure B.2-2 MELCOR input files
B-15

MELMACCS Input Template File

The MELMACCS template file contains input needed by MELMACCS to extract the source term 

information from the MELCOR plot file (.ptf file) and generate the source term input files used by 

WinMACCS.

MELMACCS

The plot file from each MELCOR run is processed by MELMACCS to extract the information on 

the source term released to the environment and provide a radionuclide inventory input for a 

MACCS-compatible format.

N MELMACCS Output Files

A MELMACCS output file is created from each MELCOR plot output file.

MACCS Uncertain Parameters

The uncertain parameters in the MACCS model for the Peach Bottom unmitigated LTSBO 

scenario are defined by their distribution types and associated parameters (e.g., uniform 

distribution with a lower and upper bound) (see Section 4.2). These distributions are 

incorporated into MACCS using the WinMACCS GUI. The distributions are sampled using Latin 

Hypercube Sampling (LHS) when WinMACCS is run.

MACCS Input File

The WinMACCS input file contains input used by MACCS (e.g., weather and evacuation 

parameters) to perform consequence calculations. 

MACCS

MACCS is used to calculate consequences for the N source term inputs (from the N

MELMACCS radionuclide files) in conjunction with the uncertainty in the MACCS parameters. 

Weather uncertainty (i.e., weather bin sampling) is evaluated for each source term input and 

associated WinMACCS uncertain parameter sample. 

N MACCS Output Files

A MACCS output file is generated for each source term input.

APPENDIX C

MODEL VERIFICATION AND CONVERGENCE

APPENDIX C – TABLE OF CONTENTS

Section Page

C.1 SOURCE TERM MODEL .............................................................................. C-1

C.1.1 TEMPORAL AND NUMERICAL CONVERGENCE 

(DETERMINISTIC RUNS) ............................................................................. C-2

C.1.1.1 TEMPORAL CONVERGENCE (DTMAX, MELCOR 1.8.6 VERSION 

YR549............................................................................................................ C-3

C.1.1.2 NUMERICAL CONVERGENCE .................................................................... C-7

C.1.2 MODEL UPDATES (DETERMINISTIC RUNS) ............................................C-13

C.1.2.1 UPDATES TO PEACH BOTTOM INPUT DECK..........................................C-13

C.1.2.2 UPDATE TO INCLUDE PHEBUS TEST DATA ...........................................C-16

C.1.3 SOARCA UNCERTAINTY ANALYSIS BASE CASES (DETERMINISTIC) .C-19

C.1.3.1 SOARCA UNCERTAINTY ANALYSIS BASE CASE ESTIMATE................C-19

C.1.3.2 SOARCA MAIN STEAM LINE CREEP SENSITIVITY .................................C-22

C.2 CONSEQUENCE MODEL............................................................................C-25

C.2.1 UPDATE TO MELMACCS PREPROCESSOR ............................................C-26

C.2.2 UPDATE TO MELCOR SOURCE TERM .....................................................C-29

C.2.3 NUMERICAL CONVERGENCE – CODE UPDATES...................................C-35

C.2.4 SOARCA UNCERTAINTY ANALYSIS DETERMINISTIC BASE CASE......C-38

C.3 MODEL ERROR LOG ..................................................................................C-43

C.3.1 ERROR IN SAMPLED VALUES OF DRYWELL HEAD BOLD TORQUE 

COEFFICIENT............................................................................................. C-43 

C.3.2 MISS ORDERING OF SAMPLED VALUES OF FUEL FAILURE 

CRITERION ..................................................................................................C-43
APPENDIX C – TABLE OF FIGURES

Figure Page

Figure C.1-1 Fraction of the core inventory released to the environment 

(a) Iodine and (b) Cesium temporal convergence comparisons for 

the Peach Bottom unmitigated LTSBO scenario................................. C-6

Figure C.1-2 Fraction of the core inventory released to the environment 

(a) Iodine and (b) Cesium numerical convergence comparisons 

for the Peach Bottom unmitigated LTSBO scenario............................ C-9

Figure C.1-3 Fraction of the core inventory released to the environment 

(a) Iodine and (b) Cesium with the revised treatment of the near 

equilibrium model disabled for the Peach Bottom unmitigated 

LTSBO scenario.................................................................................C-12

Figure C.1-4 Fraction of the core inventory released to the environment 

(a) Iodine and (b) Cesium with model updates for the Peach 

Bottom unmitigated LTSBO scenario.................................................C-15

Figure C.1-5 Fraction of the core inventory released to the environment 

(a) Iodine and (b) Cesium with CHEMFORM #5 for the Peach 

Bottom unmitigated LTSBO scenario.................................................C-18

Figure C.1-6 Fraction of the core inventory released to the environment 

(a) Iodine and (b) Cesium for UA SOARCA for the Peach Bottom 

unmitigated LTSBO scenario .............................................................C-21

Figure C.1-7 Fraction of the core inventory released to the environment 

(a) Iodine and (b) Cesium for UA SOARCA MSL creep rupture for 

the Peach Bottom unmitigated LTSBO scenario................................C-24

Figure C.2-1 MELMACCS plume segment .............................................................C-27

Figure C.2-2 Source term comparison of conditional, mean, individual LCF risk (per 

event) with LNT dose truncation for residents within a circular area of 

specified radius from the plant for emergency and long-term 

phases .......................................................................................... C-32

Figure C.2-3 Source term comparison of conditional, mean, individual LCF risk 

(per event) with USBGR dose truncation for residents within a 

circular area of specified radius from the plant for emergency and 

long-term phases ...............................................................................C-33

Figure C.2-4 Source term comparison of conditional, mean, individual LCF risk 

(per event) with HPS dose truncation for residents within a circular 

area of specified radius from the plant for emergency and long-term 

phases ...............................................................................................C-34

Figure C.2-5 SOARCA estimate and SOARCA UA base case comparison of 

conditional, mean, individual LCF risk (per event) with the LNT for 

residents within a circular area of specified radius from the plant 

for emergency and long-term phases.................................................C-40

Figure C.2-6 SOARCA estimate and SOARCA UA base case comparison of 

conditional, mean, individual LCF risk (per event) with USBGR 

dose truncation for residents within a circular area of specified 

radius from the plant for emergency and long-term phases ...............C-41
Figure C.2-7 SOARCA estimate and SOARCA UA base case comparison of 

conditional, mean, individual LCF risk (per event) with HPS dose 

truncation for residents within a circular area of specified radius 

from the plant for emergency and long-term phases..........................C-42
APPENDIX C – TABLE OF TABLES

Table Page

Table C.1-1 Summary of MELCOR model changes to the SOARCA Peach 

Bottom unmitigated LTSBO scenario necessary to achieve UA 

Model convergence............................................................................. C-2

Table C.1-2 Time step definitions used in the probabilistic analysis....................... C-3

Table C.1-3 Timing of key events for Peach Bottom LTSBO temporal 

convergence. ...................................................................................... C-4

Table C.1-4 Timing of key events for Peach Bottom LTSBO numerical 

convergence. ...................................................................................... C-8

Table C.1-5 Timing of key events for Peach Bottom LTSBO numerical 

convergence with near equilibrium model off.....................................C-11

Table C.1-6 Timing of key events for Peach Bottom LTSBO Model updates. .......C-14

Table C.1-7 Timing of key events for Peach Bottom LTSBO with CHEMFORM 

#5.......................................................................................................C-17

Table C.1-8 Timing of key events for Peach Bottom LTSBO UA SOARCA 

Case...................................................................................................C-20

Table C.1-9 Timing of key events for Peach Bottom LTSBO main steam line 

creep rupture......................................................................................C-23

Table C.2-1 Summary of consequence model changes to the Peach Bottom 

unmitigated LTSBO scenario used in the SOARCA Uncertainty 

Analysis. .............................................................................................C-25

Table C.2-2 MELCOR radionuclide classes not included in MELMACCS. ............C-27

Table C.2-3 Radionuclide classes used in SOARCA.............................................C-28

Table C.2-4 Brief source term description for the Peach Bottom unmitigated 

LTSBO. ..............................................................................................C-30

Table C.2-5 Source term comparison of conditional, mean, individual LCF risk 

(per event) for LNT dose truncation. ..................................................C-31

Table C.2-6 Source term comparison of conditional, mean, individual LCF risk 

(per event) for USBGR dose truncation. ............................................C-31

Table C.2-7 Source term comparison of conditional, mean, individual LCF risk 

(per event) for dose truncation based on the HPS position 

statement. ..........................................................................................C-31

Table C.2-8 MACCS version comparison of conditional, mean, individual LCF 

risk (per event) for LNT dose truncation for the SOARCA estimate 

at specified circular areas. .................................................................C-37

Table C.2-9 MACCS version comparison of conditional, mean, individual LCF 

risk (per event) for USBGR dose truncation for the SOARCA 

estimate at specified circular areas....................................................C-37

Table C.2-10 MACCS version comparison of conditional, mean, individual LCF 

risk (per event) for HPS dose truncation for the SOARCA 

estimate at specified circular areas....................................................C-37

Table C.2-11 SOARCA estimate and SOARCA UA base case comparison of 

conditional, mean, individual LCF risk (per event) for LNT dose 

truncation at specified circular areas..................................................C-38
Table C.2-12 SOARCA estimate and SOARCA UA base case comparison of 

conditional, mean, individual LCF risk (per event) for USBGR 

dose truncation at specified circular areas.........................................C-38

Table C.2-13 SOARCA estimate and SOARCA UA base case comparison of 

conditional, mean, individual LCF risk (per event) for HPS dose 

truncation at specified circular areas..................................................C-39

 C-1

C MODEL VERIFICATION AND CONVERGENCE

The intended purpose of the uncertainty analysis is to quantitatively evaluate the effects of 

selected key uncertain parameters on the estimation of the release of radionuclides to the 

environment and downstream consequences. Validation of a computer model for a physical 

system involves a series of activities designed to generate and enhance confidence in the 

model’s conceptualization and results during and after model development. The SOARCA 

Peach Bottom unmitigated LTSBO model presented in NUREG/CR-7110 Volume I represents a 

complex system of the reactor core, pressure vessel, safety systems, environmental conditions, 

and downstream consequences including evacuation planning. In conventional modeling 

practice, model validation is achieved by comparing model results with experimental 

measurements. However, such measurements are impossible to obtain at the temporal and 

spatial scales of interest for a complex integrated level for reactor safety analyses. From a 

strictly computational perspective, a well-designed, correctly implemented numerical model 

should produce results that are explainable and appropriate for its intended purpose. Validation 

of the SOARCA model is a process to establish confidence that the model adequately 

represents with sufficient accuracy the accident scenario and satisfies its intended purpose. 

The SOARCA Peach Bottom LTSBO model presented in NUREG/CR-7110 Volume I included 

verification of the inputs and software and is considered valid for its intended use. Several 

computer software and associated electronic input files were used in the calculation as 

presented in Section 3.0 of this document. The software is verified for its intended use and has 

supporting documentation. 

The results presented in this analysis were generated with an updated version of the SOARCA 

Peach Bottom unmitigated LTSBO model. The updated version primarily addresses issues 

identified during the development of the probabilistic analysis. For the uncertainty analysis, it is 

necessary to demonstrate the convergence of the probabilistic analysis, including both 

temporally and computationally. This section discusses the progression of the model changes 

including updated versions of the MELCOR and MACCS codes from those versions used in 

NUREG/CR-7110 Volume 1. A series of during development model verification and 

convergence activities presented in the following subsections document the MELCOR and 

MACCS model changes including: checking model changes and input verification, temporal 

and computational convergence testing. Model input parameter values and abstraction models, 

including their ranges of applicability, were reviewed and verified for accuracy (Section 4.0). 

Convergence tests were conducted to identify the impacts of timestep size (Section C.1.1.1), 

numerical accuracy (Section C.1.1.2 and C.2.3) and number of realizations (Section 5.1.1 and

Section 5.2.1) to ensure that the model was converged. 

C.1 Source Term Model

Early scoping analysis yielded a high number of failed realizations using MELCOR 1.8.6 code 

version YR549. Since the Peach Bottom unmitigated LTSBO scenario was developed in 

NUREG/CR-7110 Volume 1, developments to the MELCOR 1.8.6 code have improved the code 

convergence. In addition, several configuration inaccuracies in the Peach Bottom unmitigated 

LTSBO MELCOR model have been identified. It was necessary to take advantage of these 

advancements to generate converged probabilistic results for the uncertainty analysis. To 

enhance the convergence of the probabilistic analysis these issues were addressed in the 

updated SOARCA Peach Bottom LTSBO model used for the uncertainty analysis. Table C.1-1 

summarizes the issues addressed. The overall impact of these updates is considered negligible 

on the results of the SOARCA analysis [1] and the SOARCA model [1] is considered adequate 

for the intended purpose.
 C-2

Table C.1-1 Summary of MELCOR model changes to the SOARCA Peach Bottom 

unmitigated LTSBO scenario necessary to achieve UA Model convergence

SOARCA Model 

Issue Issue Description Addressed in Section

Variable timesteps Variable timestep sizes optimized to the accident 

progression for SOARCA. This is done manually by 

stopping the analysis and restarting and over several 

iterations of the model calculation. A constant timestep 

size is needed to run the probabilistic case.

C.1.1.1

Numerical convergence (i) MELCOR Code version 1.8.6 was updated from YR549 

used in SOARA to YV3780. (ii) Disabling an instability in 

the revised near equilibrium model. 

C.1.1.2

Configuration 

inaccuracies

Drywell liner open area rate, elevation of the lower 

separator control volume, check valve in the vacuum 

breaker.

C.1.2.1

Chemical forms of 

iodine and cesium

Include Phebus results including gaseous iodine and 

CsOH that were not used in the SOARCA calculations. 

C.1.2.2

To ensure proper continuity between the SOARCA Peach Bottom unmitigated LTSBO and the 

modified Peach Bottom unmitigated LTSBO scenario used in this UA and for a comparison with 

the parametric uncertainty and sensitivity results, a series of ‘one-off’ MELCOR simulations 

were conducted. Section C.1 contains tables listing the calculated timing of key events that 

follow from key events in accident progression (as presented in NUREG/CR-7110 Volume I) as 

a quantitative comparison between the verification tests cases. In addition, a comparison of the 

fraction of cesium and iodine core inventory released to the environment is used to quantify the 

impact of each change. The only release pathways considered (i.e., refueling bay blowout 

panels and the equipment lock door at 135 feet above ground level) are those that are carried 

over into the MACCS analysis

C.1.1 Temporal and Numerical Convergence (Deterministic Runs)

To quantify the effects of the updates and advancements to the MELCOR 1.8.6 code

implemented in the YV3780 version used in the probabilistic analysis, a series of deterministic 

MELCOR simulations were conducted to quantify the overall effects on the Peach Bottom

unmitigated LTSBO scenario. Furthermore, the original Peach Bottom unmitigated LTSBO 

SOARCA simulation was completed using several restarts for timestep modifications whenever 

a MELCOR convergence error was encountered. Thus the exact same calculation is not 

recreated by simply rerunning the simulation with the optimized timestep input; slight differences 

in start and stop times (caused by MELCOR errors) relative to the user-specified timestep input 

can yield slight differences in the calculated results. The SOARCA Peach Bottom unmitigated 

LTSBO MELCOR simulation in Section 5.1 of NUREG/CR-7110 Volume 1 was conducted in 

September, 2010 and used MELCOR 1.8.6 code version YR549. The following sections outline 

the changes to the code and timesteps and quantify the resulting changes to the timeline of 

events and environmental releases. 
 C-3

C.1.1.1 Temporal Convergence (DTMAX, MELCOR 1.8.6 version YR549

Temporal convergence refers to the use of an appropriate timestep size necessary to achieve a 

converged solution. The numerical solution presented in the SOARA analysis involves 

computations with discrete timesteps, referred to as temporal discretization. The temporal 

discretization may affect the accuracy of the solution to the differential equations, and thus 

affect the outputs. 

The SOARCA Peach Bottom unmitigated LTSBO simulation encountered a few difficulties in 

obtaining a MELCOR solution during the core degradation portion of the calculation. To obtain 

a converged and more accurate solution the SOARCA MELCOR calculation used manual 

changes in the timestep size function during the core melt progression. A solution was obtained 

in an interactive manner–the simulation was restarted using smaller timesteps before the onset 

of code instabilities that lead to the calculation problems. A “hands-on” approach was 

employed, using a manual stopping and restarting of the simulation during run time to get the 

optimal timestep sizes over the defined time intervals. However, with the automated approach 

used in the probabilistic analysis (Section 3.0), it is not possible to interactively (i.e. manually) 

determine the optimal timestep scheme for each individual calculation and exactly replicate the 

changes completed in the SOARCA analysis to customize the timestep function. Rather, the 

final timestep definitions resulting from the SOARCA analyses were used (Table C.1-2).

Table C.1-2 Time step definitions used in the probabilistic analysis

TIME (s) DTMAX DTMIN DTEDT DTPLT DTRST

TIME1 -200 0.1 1.00 × 10-6 600 10 600

TIME2 -135 0.05 1.00 × 10-6 600 10 600

TIME3 0 0.1 1.00 × 10-6 3600 2 600

TIME4 60 0.5 1.00 × 10-6 3600 5 36,000

TIME5 600 1 1.00 × 10-7 3600 10 36,000

TIME6 7,200 1 1.00 × 10-7 3600 60 6,000

TIME7 28,000 1 1.00 × 10-7 7200 60 36,000

TIME8 36,000 0.05 1.00 × 10-7 7200 30 7,200

TIME9 72,000 0.01 1.00 × 10-7 7200 60 7,200

TIME10 86,400 1 1.00 × 10-7 7200 180 7,200

TIME11 172,800 2 1.00 × 10-7 36000 600 36,000

Since the SOARCA analysis was never run from start to finish with the final timestep definitions

defined in Table C.1-2, rather stopped at unequal time intervals, the SOARCA Peach Bottom

unmitigated LTSBO model was re-run with the final SOARCA timestep definitions to assess the 

impact from using the steps defined in Table C.1-2. As shown in Table C.1-3, the timing of the 

core melt progression, lower head failure, and permanent containment failure (shell 

melt-through) have resulted in a slightly earlier releases of radionuclides to the environment. 

Most importantly, vessel breach and containment shell melt-through occur one hour earlier for 

the calculation run continuously with the final SOARCA timestep scheme. The two calculations 

exhibit negligible (<1 hour) variations in event timing for most of the other events listed in 

Table C.1-2.
 C-4

Table C.1-3 Timing of key events for Peach Bottom LTSBO temporal convergence

Event

PB LTSBO w/ 4 hr DC power

(time in hours unless noted)

SOARCA Final Time Steps 

(UAS_STD06)

Station blackout loss of all onsite and offsite AC power 0 0 

Low-level 2 and RCIC actuation signal 10 minutes 10 minutes

Operators manually open SRV to depressurize the reactor vessel 1 1 

RPV pressure first drops below LPI set point (400 psig) 1.2 1.2

Battery depletion leads immediate SRV re-closure 4 4 

RCIC steam line floods with water RCIC flow terminates 5.2 5.2

SRV sticks open because of excessive cycling 8.2 8.2

Downcomer water level reaches top of active fuel 8.4 8.4

First hydrogen production 8.9 8.5

First fuel-cladding gap release 9.1 9.1

First channel box failure 9.3 9.3

Reactor vessel water level reaches bottom of lower core plate 9.3 9.3

First localized failure of lower core plate 10.6 10.6

First core cell collapse because of time at temperature 9.8 10.1

Beginning of large-scale relocation of core debris to lower plenum 10.5 10.6

Lower head dries out 13.3 13

Ring 5 CRGT column collapse (failed at axial level 2) 15.8 16.1

Ring 1 CRGT column collapse (failed at axial level 2) 17.4 18.3

Ring 4 CRGT column collapse (failed at axial level 2) 17.4 17.7

Ring 3 CRGT column collapse (failed at axial level 2) 17.5 17.4

Ring 2 CRGT column collapse (failed at axial level 2) 18.6 18.7

Lower head failure 19.7 18.9

Drywell head flange leakage begins 19.9 19

Hydrogen burns initiated in drywell enclosure region of reactor building 20 19.1

Refueling bay to environment blowout panels open 20 19.1

Hydrogen burns initiated in reactor building refueling bay 20 19.1

Drywell shell melt-through initiated and drywell head flange re-closure 20 19.1

Hydrogen burns initiated in lower reactor building 20.1 19.1

Door to environment through railroad access opens because of 

overpressure

20.1 19.1

Equipment Lock Door at 135-ft fails due to overpressure 20.1 19.1

Refueling bay roof fails due to overpressure 20.2 - 

Time iodine release to environment exceeds 1% of initial core inventory 23.6 23.0

Calculation terminated 48 48

BE_STD01v1.8.6YR549; UAS_STD06v1.8.6YR549
 C-5

Figure C.1-1(a) depicts the fraction of iodine core inventory released to the environment as a 

function of time for the SORACA estimate and the temporal convergence test scenarios. 

Similar information is shown on Figure C.1-1(b) for cesium. As shown on Figure C.1-1(a), the 

overall fraction of the iodine core inventory released to the environmental is approximately 

2×10-2 for both the final timestep case and the SOARCA estimate. As shown on 

Figure C.1-1(b), the overall environmental release fraction of cesium in the core is 

approximately 8×10-4 and 5×10-4 for the results using the final timesteps and the SOARCA 

estimate, respectively. This difference in cesium release is attributed to an increased release of 

cesium molybdate (Cs2MoO4) into the environment. The increased late phase release of 

cesium is caused by reheating of the heat structures in the upper and low reactor vessel, 

causing re-vaporization of radionuclide aerosols that were deposited on these surfaces. 

Overall, despite a slightly earlier release to the environment in the final timestep case, the 

magnitude and trend for the fractions released to the environment are closely represented. The 

timestep sizes can have a notable impact on the solution results for the fraction of the cesium 

core inventory released to the environment. The MELCOR simulation with the final timestep 

definitions (without restarts) calculated a 38% higher release fraction of cesium compared to the 

original SOARCA study; however, given the overall low magnitude of the cesium release 

fraction (~0.01%), this variability is a reasonable response to timestep changes in MELCOR.
 C-6

Figure C.1-1 Fraction of the core inventory released to the environment (a) Iodine and 

(b) Cesium temporal convergence comparisons for the Peach Bottom 

unmitigated LTSBO scenario
 C-7

C.1.1.2 Numerical Convergence

Since the SOARCA Peach Bottom LTSBO scenario was developed, MELCOR code 

advancements have been made that improve the numerical convergence of the physical models 

in MELCOR. The SOARCA estimate for the Peach Bottom unmitigated LTSBO scenario used

MELCOR 1.8.6 Version YR549. For this study, MELCOR 1.8.6 Version YV3780 was used. 

This is the version used to analyze the Surry interfacing loss of coolant accident seen in 

Section 5.5 of NUREG/CR-7110 Volume 2. The improvement in the MELCOR 1.8.6 code

between Versions YR549 and YV3780 resulted in reducing the number of failed UA realizations 

and decreased the individual run times. Typically, for a probabilistic simulation, 30% or more of 

the sample set would fail when using MELCOR 1.8.6 version YR549.

In addition, a revision to the MELCOR 1.8.6 near equilibrium model in a code version prior to 

YR549 resulted in a substantial increase in MELCOR CPU time for ISLOCA analyses of the 

SOARCA Surry model. During MELCOR development and verification testing conducted for 

MELCOR 2.0, this error was discovered and the near equilibrium model is disabled in all 

subsequent versions of MELCOR. Disabling the near equilibrium model increases the model 

convergence, improves the solution accuracy, and decreases run times. Using MECLOR 1.8.6 

Version YV3780 with the near equilibrium model disabled, only two to four percent of the 

sample set failed. 

C.1.1.2.1 MELCOR Code Version YV3780

Table C.1-4 shows a comparison of the results for the SOARCA model using MELCOR 1.8.6 

Version YR549 for the Peach Bottom unmitigated LTSBO scenario versus the most recent 

MELCOR 1.8.6 Version YV3780. The same timestep function is used in both modeling cases 

(as detailed in Section C.1.1.1 and listed Table C.1-2).

The numerical convergence test shows differences in the timing of lower head failure with 

MELCOR 1.8.6 Version YV3780, predicting a time 1 hour 42 minutes later when compared to 

the YR549 version. This is attributed to hotter particulate debris temperature in the YR549 

version due to a higher oxidation power and differences in the hydrogen production between the 

two code versions. The environmental release occurs earlier in the numerical convergence test 

and produces larger overall release of iodine to the environment. As shown on Figure C.1-2(a), 

the initial fraction of the iodine core inventory released to the environment is higher than the 

MELCOR 1.8.6 Version YR549 (SOARCA) cases. 

Figure C.1-2(b) shows the fraction of the cesium core inventory released to the environment for 

the MELCOR 1.8.6 version YV3780 is slightly higher, yet closer, to the SOARCA solution than 

the MELCOR 1.8.6 version YR549 case with the final timesteps. Since the release of CsI is 

higher for the numerical convergence test, the overall difference in cesium release is attributed 

to the greater release of CsI, resulting in an increase in both cesium and iodine when compared 

to the SOARCA estimate. 
 C-8

Table C.1-4 Timing of key events for Peach Bottom LTSBO numerical convergence

Event

PB LTSBO w/4 hr DC power

(time in hours unless noted) 

Version YR549

(UAS_STD06)

Version YV3780

(UAS_STD08)

Station blackout loss of all onsite and offsite AC power 0 0 

Low-level 2 and RCIC actuation signal 10 minutes 10 minutes

Operators manually open SRV to depressurize the reactor vessel 1 1 

RPV pressure first drops below LPI setpoint (400 psig) 1.2 1.2

Battery depletion leads immediate SRV re-closure 4 4 

RCIC steam line floods with water RCIC flow terminates 5.2 5.2

SRV sticks open because of excessive cycling 8.2 8.2

Downcomer water level reaches top of active fuel 8.4 8.4

First hydrogen production 8.5 8.6

First fuel-cladding gap release 9.1 9.1

First channel box failure 9.3 9.4

Reactor vessel water level reaches bottom of lower core plate 9.3 9.4

First localized failure of lower core plate 10.6 10.6

First core cell collapse because of time at temperature 10.1 9.9

Beginning of large-scale relocation of core debris to lower plenum 10.6 10.6

Lower head dries out 13 12.9

Ring 5 CRGT column collapse (failed at axial level 2) 16.1 16.9

Ring 3 CRGT column collapse (failed at axial level 2) 17.4 17.9

Ring 4 CRGT column collapse (failed at axial level 2) 17.7 18.2

Ring 1 CRGT column collapse (failed at axial level 2) 18.3 16.8

Ring 2 CRGT column collapse (failure occurs at different axial 

level) 18.7 18.5

Lower head failure 18.9 20.6

Drywell head flange leakage begins 19 20.7

Hydrogen burns initiated in drywell enclosure region of reactor 

building 19.1 20.7

Refueling bay to environment blowout panels open 19.1 20.7

Hydrogen burns initiated in reactor building refueling bay 19.1 20.9

Drywell shell melt-through initiated and drywell head flange reclosure 19.1 20.8

Hydrogen burns initiated in lower reactor building 19.1 20.9

Door to environment through railroad access opens because of 

overpressure 19.1 20.9

Equipment Lock Door at 135-ft fails due to overpressure 19.1 20.9

Time iodine release to environment exceeds 1% of initial core 

inventory 23.0 21.0

Calculation terminated 48 48

UAS_STD06v1.8.6YR549; UAS_STD08v1.8.6YV3780.
 C-9

Figure C.1-2 Fraction of the core inventory released to the environment (a) Iodine and 

(b) Cesium numerical convergence comparisons for the Peach Bottom 

unmitigated LTSBO scenario
 C-10

C.1.1.2.2 Disable the revised MELCOR Near Equilibrium Model

Table C.1-5 displays the results of the numerical convergence test conducted with

MELCOR 1.8.6 Version YV3780 for the Peach Bottom unmitigated LTSBO scenario and the 

results for the MELCOR 1.8.6 Version YV3780 for the Peach Bottom unmitigated LTSBO 

scenario with the near equilibrium model turned off. The revised treatment of the near 

equilibrium model prevents the collapse of a boiled-up pool in a volume with a very small 

atmosphere and the possible revaporization of a very small pool. The same timestep function 

(Section C.1.1.1, Table C.1-2) is used for both cases.

The disabled near equilibrium model results in an earlier lower head failure (30 minutes) and 

earlier release of iodine to the environment (24 minutes) than when the model is not disabled. 

However, the lower head dryout occurs 36 minutes earlier (36 minutes) when the revised 

treatment of the near equilibrium model is used. The lower head failure is sooner in the 

disabled near equilibrium model because the particulate debris that has relocated is at higher 

temperatures, leading to an earlier failure time. The hotter temperatures are due to a larger 

oxidation power. As shown on Figure C.1-3(a), the iodine release fraction to the environment is 

higher for the case that disabled the revised treatment of the near equilibrium model case when 

compared to the SOARCA estimate. The divergence from the SOARCA values increases if the 

revised equilibrium model is used with MELCOR revision YV3780 (i.e. iodine release fraction is 

greater than the SOARCA values and the YV3780 calculation with the revised model disabled). 

The results with the disabled near equilibrium model are still higher than the SOARCA estimate. 

However, after this initial release, the rate of iodine released to the environment is similar to the 

SOARCA estimate.

Figure C.1-3(b) shows the cesium release fraction to the environment for the case that disabled 

the revised treatment of the near equilibrium is also slightly higher yet is closer to the SOARCA 

estimate than when the model is not disabled. Since the release of CsI for the disabled near 

equilibrium model is still higher than the SOARCA case, the overall difference in cesium release 

is attributed to the greater release of CsI, resulting in an increase in both cesium and iodine 

when compared to the SOARCA estimate.
 C-11

Table C.1-5 Timing of key events for Peach Bottom LTSBO numerical convergence with 

near equilibrium model off

Event

PB LTSBO w/ 4 hr DC power 

(time in hours unless noted)

Version YV3780 

(UAS_STD08)

Revised Near 

Equilibrium 

Model Off/ 

Version YV3780 

(UAS_STD11)

Station blackout loss of all onsite and offsite AC power 0 0 

Low-level 2 and RCIC actuation signal 10 minutes 10 minutes

Operators manually open SRV to depressurize the reactor vessel 1 1 

RPV pressure first drops below LPI setpoint (400 psig) 1.2 1.2

Battery depletion leads immediate SRV re-closure 4 4 

RCIC steam line floods with water RCIC flow terminates 5.2 5.2

SRV sticks open because of excessive cycling 8.2 8.2

Downcomer water level reaches top of active fuel 8.4 8.4

First hydrogen production 8.6 8.6

First fuel-cladding gap release 9.1 9.1

First channel box failure 9.4 9.4

Reactor vessel water level reaches bottom of lower core plate 9.4 9.3

First localized failure of lower core plate 10.6 10.6

First core cell collapse because of time at temperature 9.9 9.9

Beginning of large-scale relocation of core debris to lower plenum 10.6 10.6

Lower head dries out 12.9 12.3

Ring 5 CRGT column collapse 16.9 16.8

Ring 3 CRGT column collapse 17.9 16.8

Ring 4 CRGT column collapse 18.2 16.9

Ring 1 CRGT column collapse 16.8 17.5

Ring 2 CRGT column collapse 18.5 18.0

Lower head failure 20.6 20.1

Drywell head flange leakage begins 20.7 20.2

Hydrogen burns initiated in drywell enclosure region of reactor building 20.7 20.2

Refueling bay to environment blowout panels open 20.7 20.2

Hydrogen burns initiated in reactor building refueling bay 20.9 20.4

Drywell shell melt-through initiated and drywell head flange re-closure 20.8 20.3

Hydrogen burns initiated in lower reactor building 20.9 20.3

Door to environment through railroad access opens because of 

overpressure 20.9 20.3

Equipment Lock Door at 135-ft fails due to overpressure 20.9 20.3

Time iodine release to environment exceeds 1% of initial core inventory 21.0 20.6

Calculation terminated 48 48

UAS_STD08v1.8.6YV3780; UAS_STD11v1.8.6YV3780
 C-12

Figure C.1-3 Fraction of the core inventory released to the environment (a) Iodine and 

(b) Cesium with the revised treatment of the near equilibrium model 

disabled for the Peach Bottom unmitigated LTSBO scenario
 C-13

C.1.2 Model Updates (Deterministic Runs)

C.1.2.1 Updates to Peach Bottom Input Deck

Model updates included defining the vacuum breakers between the drywell and wetwell to allow 

only forward flow, raising the bottom of the separator control volume to remove a nonphysical 

“bucket” for water to collect in, and slowing the drywell liner melt through (extending the time for 

the drywell breach to grow full open).

Table C.1-6 shows the results of the MELCOR 1.8.6 version YV3780 with the near equilibrium 

model disabled for the Peach Bottom unmitigated LTSBO scenario compared with the results 

when then model is updated to address configuration issues mentioned above. The updated 

model uses the same version of MELCOR 1.8.6 version YV3780 with the near equilibrium 

model disabled. The final timestep function (Section C.1.1.1, Table C.1-2) is used in both 

cases. The timing of key events for the updated model case is very similar to the previous test 

case without the updates. Most events occur within 30 minutes or less of each other. As seen 

by the comparison, these configuration errors would not be expected to impact the SOARCA 

results. However, during development of the probabilistic model, these inaccuracies in the 

model configuration contributed to some of the failed and inaccurate solutions. 

As shown on Figure C.1-4(a), the initial fraction of the iodine core inventory released to the 

environment is slightly higher and yet again closer to the SOARCA estimate than the previous 

case using MELCOR 1.8.6 version YV3780 and the near equilibrium model disabled. The 

larger release in the previous case is due to the greater drywell head flange leakage, than in the 

updated model. The model updated to correct configuration inaccuracies results in a smaller 

leakage through the drywell head flange compared to the old model.

Figure C.1-4(b) shows the cesium release to the environment for the updated model is slightly 

higher, yet slightly closer, to the SOARCA estimate than the results previously shown on 

Figure C.1-3(b) without the model updates.

A noteworthy difference between MELCOR Versions YR549 and YV3780 related to cesium 

speciation is the default exchange of Cs2MoO4 between the radionuclide and cavity packages of 

the codes. In Version YR549, Cs2MoO4 was passed from radionuclide to cavity as cesium and 

cesium was passed from cavity to radionuclide as Cs2MoO4. In Version YV3780, Cs2MoO4 is 

passed from radionuclide to cavity as cesium and molybdenum and cesium and molybdenum 

are passed from cavity to radionuclide as cesium and molybdenum. The change from Version 

YR549 to Version YV3780 was made to conserve mass. The inconsistency in the exchange of 

Cs2MoO4 between the radionuclide and cavity packages arises from the shortcoming in the 

cavity package wherein Cs2MoO4 is not a recognized compound. The impact of this difference 

between the code versions is thought to be insignificant given that most all of the Cs2MoO4

initialized in the core is released from the fuel in-vessel in the Peach Bottom LTSBO MELCOR 

calculations.
 C-14

Table C.1-6 Timing of key events for Peach Bottom LTSBO Model updates

Event

PB LTSBO with 4 hr DC power

(time in hours unless noted)

Revised Near 

Equilibrium Model Off/ 

Version YV3780 

(UAS_STD11)

Model Updates 

MELCOR 1.8.6 

Version YV3780

Station blackout loss of all onsite and offsite AC power 0 0 

Low-level 2 and RCIC actuation signal 10 minutes 10 minutes

Operators manually open SRV to depressurize reactor vessel 1 1 

RPV pressure first drops below LPI setpoint (400 psig) 1.2 1.2

Battery depletion leads immediate SRV re-closure 4 4 

RCIC steam line floods with water RCIC flow terminates 5.2 5.2

SRV sticks open because of excessive cycling 8.2 8.2

Downcomer water level reaches top of active fuel 8.4 8.4

First hydrogen production 8.6 8.6

First fuel-cladding gap release 9.1 9.1

First channel box failure 9.4 9.4

Reactor vessel water level reaches bottom of lower core plate 9.3 9.4

First localized failure of lower core plate 10.6 10.7

First core cell collapse because of time at temperature 9.9 10.0

Beginning of large-scale relocation of core debris to lower plenum 10.6 10.7

Lower head dries out 12.3 12.6

Ring 5 CRGT column collapse 16.8 16.8

Ring 3 CRGT column collapse 16.8 16.8

Ring 4 CRGT column collapse 16.9 18.3

Ring 1 CRGT column collapse 17.5 16.5

Ring 2 CRGT column collapse 18.0 18.3

Lower head failure 20.1 20.2

Drywell head flange leakage begins 20.2 20.3

Hydrogen burns initiated in drywell enclosure region of reactor 

building 20.2 20.3

Refueling bay to environment blowout panels open 20.2 20.3

Hydrogen burns initiated in reactor building refueling bay 20.4 20.5

Drywell shell melt-through initiated and drywell head flange reclosure 20.3 20.4

Hydrogen burns initiated in lower reactor building 20.3 20.4

Door to environment through railroad access opens because of 

overpressure

20.3 20.4

Equipment Lock Door at 135-ft fails due to overpressure 20.3 20.4

Time iodine release to environment exceeds 1% of initial core 

inventory 20.6 21.1

Calculation terminated 48 48

UAS_STD11v1.8.6YV3780; UAS_STD12v1.8.6YV3780
 C-15

Figure C.1-4 Fraction of the core inventory released to the environment (a) Iodine and 

(b) Cesium with model updates for the Peach Bottom unmitigated LTSBO 

scenario
 C-16

C.1.2.2 Update to Include Phebus Test Data

As discussed in Section 4.1.5, the predominant speciation of cesium described in 

NUREG/CR-7110 Volume 1 was based on detailed chemical analysis of the deposition and 

transport of the volatile fission products in the Phebus facility tests [19-23]. The chemical 

analysis revealed molybdenum combined with cesium and formed cesium molybdate. Prior to 

NUREG/CR-7110 Volume 1, the default assumed predominant chemical form of cesium was 

cesium hydroxide. Consistent with past studies, NUREG/CR-7110 Volume 1 assumed all 

released iodine combines with cesium. However, the Phebus facility tests show that gaseous 

iodine is found within containment [19-23]. Five alternative combinations of the four chemical 

groups are defined and each alternative has a probability of occurrence defined by a discrete 

distribution (Figure 4.1-20 and Table 4.1-7). Each of the five alternatives partitions the 

radionuclide mass of iodine and cesium between four radionuclide classes in the MELCOR 

model (radionuclide classes: 2 (CsOH), 4 (I2), 16 (CsI), and 17 (Cs2MoO4), Table 4.1-7). The 

SOARCA values are not exactly represented in the uncertainty analysis due to the presence of 

gaseous iodine. To quantify this effect, the most likely combination was selected from the 

Phebus experiments [19, 20, 22, and 23] CHEMFORM #5, with an averaged peak gaseous 

iodine of 2.77% of the initial iodine inventory was assumed and like the SOARCA case the 

cesium is partitioned between CsI and Cs2MO4. 

Table C.1-7 shows the results with the MELCOR 1.8.6 version YV3780 with the revised near 

equilibrium model disabled for the Peach Bottom unmitigated LTSBO scenario compared with

the results when Phebus results are incorporated into the analysis. The same final timestep 

function (Section C.1.1.1, Table C.1-2) is used in both cases. 

The timing of key events for the model using CHEMFORM #5 is very similar to the results with 

the MELCOR 1.8.6 Version YV3780 with the near equilibrium model disabled until lower head 

failure. Lower head failure, and the events that occur after, occur roughly two hours earlier in 

the CHEMFORM #5 model. 

As shown on Figure C.1-5(a), the initial iodine released to the environment is higher than the 

SOARCA estimate. This can be attributed to the presence of iodine gas for the CHEMFORM #5 

case. 2.77% of the iodine core inventory is partitioned into iodine gas. However after this initial 

release, the rate of iodine released to the environment is similar to the SOARCA estimate.

Figure C.1-5(b) shows the cesium released to the environment for the CHEMFORM #5 case is 

higher than the SOARCA estimate. Since the release of CsI is higher for the CHEMFORM #5 

case, the overall difference in cesium release is attributed to this when compared to the 

SOARCA estimate.
 C-17

Table C.1-7 Timing of key events for Peach Bottom LTSBO with CHEMFORM #5

Event

PB LTSBO with 4 hr DC power

(time in hours unless noted) 

Revised Near 

Equilibrium Model Off/ 

Version YV3780 

(UAS_STD11)

ChemForm #5 

Version 

YV3780 

(UAS_STD09)

Station blackout loss of all onsite and offsite AC power 0 0 

Low-level 2 and RCIC actuation signal 10 minutes 10 minutes

Operators manually open SRV to depressurize reactor vessel 1 1 

RPV pressure first drops below LPI setpoint (400 psig) 1.2 1.2

Battery depletion leads immediate SRV re-closure 4 4 

RCIC steam line floods with water RCIC flow terminates 5.2 5.2

SRV sticks open because of excessive cycling 8.2 8.2

Downcomer water level reaches top of active fuel 8.4 8.4

First hydrogen production 8.6 8.5

First fuel-cladding gap release 9.1 9.1

First channel box failure 9.4 9.4

Reactor vessel water level reaches bottom of lower core plate 9.3 9.3

First localized failure of lower core plate 10.6 10.6

First core cell collapse because of time at temperature 9.9 9.9

Beginning of large-scale relocation of core debris to lower plenum 10.6 10.6

Lower head dries out 12.3 12.9

Ring 5 CRGT column collapse 16.8 17.3

Ring 3 CRGT column collapse 16.8 16.8

Ring 4 CRGT column collapse 16.9 18.2

Ring 1 CRGT column collapse 17.5 17.8

Ring 2 CRGT column collapse 18.0 18.4

Lower head failure 20.1 18.9

Drywell head flange leakage begins 20.2 19.0

Hydrogen burns initiated in drywell enclosure region of reactor 

building 20.2 19.0

Refueling bay to environment blowout panels open 20.2 19.0

Hydrogen burns initiated in reactor building refueling bay 20.4 --

Drywell shell melt-through initiated and drywell head flange reclosure 20.3 19.1

Hydrogen burns initiated in lower reactor building 20.3 19.1

Door to environment through railroad access opens because of 

overpressure

20.3 19.1

Equipment Lock Door at 135-ft fails due to overpressure 20.3 19.1

Time iodine release to environment exceeds 1% of initial core 

inventory 20.6 21.1

Calculation terminated 48 48

UAS_STD11v1.8.6YV3780; UAS_STD09v1.8.6YV3780
 C-18

Figure C.1-5 Fraction of the core inventory released to the environment (a) Iodine and 

(b) Cesium with CHEMFORM #5 for the Peach Bottom unmitigated LTSBO 

scenario
 C-19

C.1.3 SOARCA Uncertainty Analysis Base Cases (Deterministic)

The following two subsections present the results from the uncertainty analysis deterministic 

base case model for the SOARCA Peach Bottom unmitigated LTSBO scenario and an updated 

version of the MSL creep failure sensitivity case presented in NUREG/CR-7110 Volume 1. Both 

cases are used in the uncertainty analysis presented in Section 6.0.

C.1.3.1 SOARCA Uncertainty Analysis Base Case Estimate

Table C.1-8 shows the results with the MELCOR 1.8.6 Version YV3780 with the near 

equilibrium model disabled for the Peach Bottom unmitigated LTSBO scenario compared with

the results of the UA SOARCA version of the same scenario using MELCOR 1.8.6 Version

YV3780 including all of the updates and code changes summarized in Table C.1-1. 

The timing of key events for the model using SOARCA Uncertainty Analysis model is very 

similar to the numerical convergence test up until lower head failure. Lower head failure, and 

the events that occur after, occur roughly one hour earlier in the SOARCA Uncertainty Analysis

model. As shown on Figure C.1-6(a), the initial fraction of iodine core inventory released to the 

environment is higher than the SOARCA estimate due the presence of 2.77% of the iodine core 

inventory is partitioned into iodine gas as a result of incorporation of the Phebus test data 

(Section C.1.2.2). However after this initial release, the rate of iodine released to the 

environment is similar to the SOARCA estimate. Figure C.1-6(b) shows the fraction of cesium 

core inventory released to the environment for the SOARCA Uncertainty Analysis case is 

slightly higher than the SOARCA estimate. 
 C-20

Table C.1-8 Timing of key events for Peach Bottom LTSBO UA SOARCA Case

Event

PB LTSBO with 4 hr DC power

(time in hours unless noted) 

Revised Near 

Equilibrium Model 

Off/ Version YV3780 

(UAS_STD11)

UA SOARCA 

MELCOR 1.8.6 

Version YV3780 

(UAS_STD13)

Station blackout loss of all onsite and offsite AC power 0 0 

Low-level 2 and RCIC actuation signal 10 minutes 10 minutes

Operators manually open SRV to depressurize reactor vessel 1 1 

RPV pressure first drops below LPI setpoint (400 psig) 1.2 1.2

Battery depletion leads immediate SRV re-closure 4 4 

RCIC steam line floods with water RCIC flow terminates 5.2 5.2

SRV sticks open because of excessive cycling 8.2 8.2

Downcomer water level reaches top of active fuel 8.4 8.4

First hydrogen production 8.6 8.6

First fuel-cladding gap release 9.1 9.1

First channel box failure 9.4 9.4

Reactor vessel water level reaches bottom of lower core plate 9.3 9.4

First localized failure of lower core plate 10.6 10.7

First core cell collapse because of time at temperature 9.9 10.0

Beginning of large-scale relocation of core debris to lower plenum 10.6 10.7

Lower head dries out 12.3 12.1

Ring 5 CRGT column collapse 16.8 16.1

Ring 3 CRGT column collapse 16.8 16.9

Ring 4 CRGT column collapse 16.9 17.0

Ring 1 CRGT column collapse 17.5 17.4

Ring 2 CRGT column collapse 18.0 17.5

Lower head failure 20.1 19.8

Drywell head flange leakage begins 20.2 19.9

Hydrogen burns initiated in drywell enclosure region of reactor 

building 20.2 19.9

Refueling bay to environment blowout panels open 20.2 19.9

Hydrogen burns initiated in reactor building refueling bay 20.4 20.1

Drywell shell melt-through initiated and drywell head flange reclosure 20.3 20.0

Hydrogen burns initiated in lower reactor building 20.3 20.0

Door to environment through railroad access opens because of 

overpressure

20.3 20.0

Equipment Lock Door at 135-ft fails due to overpressure 20.3 20.0

Time iodine release to environment exceeds 1% of initial core 

inventory 20.6 22.8

Calculation terminated 48 48

UAS_STD11v1.8.6YV3780; UAS_STD13v1.8.6YV3780
 C-21

Figure C.1-6 Fraction of the core inventory released to the environment (a) Iodine and 

(b) Cesium for UA SOARCA for the Peach Bottom unmitigated LTSBO 

scenario
 C-22

C.1.3.2 SOARCA Main Steam Line Creep Sensitivity

Table C.1-9 shows the results of the SOARCA Estimate SOARCA MSL Creep Rupture case 

using MELCOR 1.8.6 Version YR549 and the UA version of the same scenario using MELCOR 

1.8.6 Version YV3780. The UA version of the MSL creep rupture case incorporates all of the 

changes documented in Table C.1-1, including the use of CHEMFORM #5 that contains a 

fraction of iodine as iodine gas (I2). 

The timing of key events for the model using UA MSL Creep Rupture model is very similar to 

the SOARCA MSL Creep Rupture model until lower core support plate failure and main steam 

line rupture. After this, the timing difference ranges from minutes to hours. 

As shown on Figure C.1-7(a), the fraction of iodine core inventory released to the environment 

is higher than the SOARCA MSL Creep Rupture sensitivity analysis. The larger release in the 

UA SOARCA MSL Creep Rupture case is due to the drywell head flange leakage and the 

presence of 2.77% of the iodine core inventory is partitioned into iodine gas. This case includes 

the model updates (from Section C.1.2) and results in a much larger leakage through the 

drywell head flange compared to the old model. The fraction of iodine released in excess of the 

SOARCA MSL creep rupture sensitivity case is on the same order of magnitude as shown in the 

SOARCA base case comparison (Figure C.1-6). Figure C.1-7(b) shows the fraction of cesium 

core inventory released to the environment for the UA MSL Creep Rupture case is much higher 

than the SOARCA estimate. 
 C-23

Table C.1-9 Timing of key events for Peach Bottom LTSBO main steam line creep 

rupture

Event

PB LTSBO with 4 hr DC power

(time in hours unless note) 

SOARCA MSL 

Creep MELCOR 

1.8.6 Version 

YR549

UA MSL Creep 

MELCOR 1.8.6 

Version YV3780

Station blackout loss of all onsite and offsite AC power 0 0 

Low-level 2 and RCIC actuation signal 10 minutes 10 minutes

Operators manually open SRV to depressurize the reactor vessel 1 1 

RPV pressure first drops below LPI setpoint (400 psig) 1.2 1.2

Battery depletion leads immediate SRV re-closure 4 4 

RCIC steam line floods with water RCIC flow terminates 5.2 5.2

SRV sticks open because of excessive cycling 11.8 --

Downcomer water level reaches top of active fuel 9.0 9.0

First hydrogen production 9.2 9.3

First fuel-cladding gap release 10.1 10.1

First channel box failure 10.6 10.7

Reactor vessel water level reaches bottom of lower core plate 11.6 11.7

First localized failure of lower core plate 12.5 13.1

First core cell collapse because of time at temperature 11.2 11.2

Main Steam Line Creep Rupture 11.9 11.9

Beginning of large-scale relocation of core debris to lower plenum 12.5 13.1

Lower head dries out 13.7 13.4

Ring 5 CRGT column collapse 17.8 14.8

Ring 3 CRGT column collapse 17.9 14.3

Ring 4 CRGT column collapse 18.4 14.6

Ring 1 CRGT column collapse 17.3 13.3

Ring 2 CRGT column collapse 16.3 13.3

Lower head failure 19.0 17.6

Drywell head flange leakage begins 11.9 11.9

Hydrogen burns initiated in drywell enclosure region of reactor building -- --

Refueling bay to environment blowout panels open 11.9 11.9

Hydrogen burns initiated in reactor building refueling bay 19.1 11.9

Drywell shell melt-through initiated and drywell head flange re-closure 19.2 17.8

Hydrogen burns initiated in lower reactor building 19.2 11.9

Door to environment through railroad access opens because of 

overpressure 

19.4 11.9

Equipment Lock Door at 135-ft fails due to overpressure -- 11.9

Time iodine release to environment exceeds 1% of initial core inventory 12.9 11.9

Calculation terminated 48 48
 C-24

Figure C.1-7 Fraction of the core inventory released to the environment (a) Iodine and 

(b) Cesium for UA SOARCA MSL creep rupture for the Peach Bottom 

unmitigated LTSBO scenario
 C-25

C.2 Consequence Model

Since the LTSBO scenario was developed in NUREG/CR-7110 Volume 1, improvements to the 

MACCS Version 2.5.0 code and updates to the WinMACCS Version 3.6 Peach Bottom LTSBO

model have been made. Table C.2-1 summarizes the issues addressed. In order to take

advantage of these improvements, but ensure proper continuity between the original LTSBO in 

SOARCA, and the LTSBO scenario used for a comparison with the parametric uncertainty and 

sensitivity results, a series of ‘one-off’ WinMACCS/MACCS simulations were conducted. The 

overall impact of these updates is considered negligible on the results of the SOARCA analysis, 

and the SOARCA model is considered adequate for the intended purpose.

Table C.2-1 Summary of consequence model changes to the Peach Bottom unmitigated 

LTSBO scenario used in the SOARCA Uncertainty Analysis

SOARCA Model 

Change Issue Description Addressed in Section

Updated MELMACCS 

Code

The MELMACCS pre-processor was updated to automate 

the processing of the probabilistic set of source terms 

generated by MELCOR for the uncertainty analysis

C.2.1

Updated MELCOR 

SOARCA source term

MELCOR code version and model updates as identified in 

Section C.1 resulted in an updated SOARCA source term

C.2.2

Numerical Convergence

(WinMACCS) 

WinMACCS Code version 3.6.2 was updated to version 

3.6.4 to accommodate the large number of uncertain 

inputs evaluated in the uncertainty analysis.

C.2.3

Numerical Convergence

(MACCS) 

MACCS Code version 2.5.0.0 was updated to version 

2.5.0.9 to increase convergence and numerical accuracy.

C.2.3

In addition to the items identified in Table C.2-1, to enhance the resolution of the statistical

regression analysis used in the parameter uncertainty analysis, the initial set of uncertain 

parameters used in the MACCS uncertainty analysis base case analysis outlined in Section 4.2 

was reduced. Section 5.2.1 documents the reduction in the number of uncertainty inputs for 

radionuclide inhalation DCFs. Originally, 69 radionuclides were selected to have uncertainty 

distributions applied to their respective DCFs (see Section 4.2.5) and have been reduced to 27 

radionuclides. 

As in presented in NUREG/CR-7110, Volume 1; the results of the consequence analyses are 

presented in terms of risk to the public for the Peach Bottom LTSBO scenario. For this work, 

conditional risk is tabulated. Conditional risk assumes that the accident occurred and shows the 

risk to individuals as a result of the accident (e.g., LCF risk per event). This is the same risk 

metric reported in NUREG/CR-7110 Volume 1.

Risk results are presented for three dose-response assumptions which are the following:

(1). LNT hypothesis; 

(2). US average natural background dose rate combined with average annual medical 

exposure as a dose truncation level (USBGR), which is 620 mrem/yr; and 

(3). A dose truncation level based on the Health Physics Society’s (HPS) position statement 

that there is a dose below which, due to uncertainties, a quantified risk should not be 

assigned, which is 5 rem/yr with a lifetime limit of 10 rem [86]. 
 C-26

The results of the consequence analyses are presented in terms of risk to the public for each of 

the accident scenarios analyzed using the Peach Bottom LTSBO MELCOR model. All results 

are presented in terms of conditional, mean, individual risk (per event) (i.e., assuming that the 

accident occurs) and risk per year of reactor operation (i.e., accounting for the frequency of the 

accident) is discussed in certain instances within the text. The risks per event are conditional 

risks and show the risks to individuals as a result of the accident (i.e., latent cancer fatality 

(LCF) risk per event or early-fatality risk per event). The risks per year of reactor operation are 

absolute risks and are the product of the core damage frequency and the conditional risks. 

Absolute risk is the likelihood of receiving a latent fatal cancer or early fatality for an average 

individual living within a specified radius of the plant per year of plant operation (i.e., LCF risk 

per reactor year (pry) or early-fatality risk pry). 

The risk metrics are LCF and early-fatality risks to residents in circular regions surrounding the 

plant. They are averaged over the entire residential population within the circular region. The 

LCF risk values represent the predicted number of fatalities divided by the population for three 

choices of dose truncation level. These risk metrics incorporate the distribution of the 

population within the circular region and the interplay between population distribution and the 

wind rose probabilities.

C.2.1 Update to MELMACCS preprocessor

The MELMACCS software is a Windows based program developed by to create a MACCS

radionuclide file form the MELCOR output plot file. The MELCOR plot files contain large 

amounts of data, only some of which is needed for MACCS calculations. The MELMACCS 

software was created to provide an interface utility between MELCOR and MACCS to integrate 

the required data.

MELMACCS obtains two classes of data from the MELCOR plot files. The first is time 

independent data, which is data that remains constant throughout the MELCOR calculation. 

Examples of this would be radionuclide chemical/physical property classes and the flow paths to 

the environment. The second class is time dependent data, which is data that is written to the 

MELCOR plot file for each plot file timestep. The plot file timestep is determined by the user. 

Examples of this data would be fluid temperature and flow rate for a flow path to the 

environment and the mass of each chemical/physical property class.

MELMACCS uses a GUI to allow the user to convert one MELCOR plot file into radionuclide 

input file (.INP) for MACCS. The inputs from the MELCOR plot file correspond to the 

radionuclide file inputs for the ATMOS portion of MACCS. 

Prior to MELMACCS converting the MELCOR plot file, the user must first specify specific inputs 

that are needed for the MACCS file, but are not provided by MELCOR. These inputs are:

• Radionuclide Classes,

• high/Medium/Low Burnup fuel,

• time of accident initiation,

• MELCOR height associated with ground level,

• data for building height, initial plume width and height for wake calculations,

• deposition velocity information,

• mass thresholds fractions for released material, and

• time intervals for plume segments
 C-27

Figure C.2-1 provides an example of a MELMACCS plume segment. The plume segment time 

intervals are obtained for each MELCOR release path. Some release paths may not contain all 

the chemical/physical property classes defined in MELCOR. On Figure C.2-1, the initial black 

vertical line shows the time of radionuclide release into the environment for the specified path, 

MELCOR Release Path 1. For this work, the plume release time intervals are 3,600 seconds 

(1 hour) as that is the minimum time interval which MACCS can incorporate into the analysis.

Figure C.2-1 MELMACCS plume segment

As shown on Figure C.2-1, not all radionuclide chemical/physical property classes are 

represented for a MELCOR release path. Table C.2-2 provides the classes which are not 

represented in MELMACCS and are thus not carried over into the MACCS model.

Table C.2-2 MELCOR radionuclide classes not included in MELMACCS

Class Name Representative Member Elements

13 Boron B B, Si, P

14 Water H2O H2O 

15 Concrete -- --

16 Cesium Iodide CsI CsI

17 Cesium Molybdate Cs2MoO4 Cs2MoO4
 C-28

Class 13 through 16 are not included in the MELMACCS results because MACCS only reads 

the 12 radioactive radionuclide classes defined in MELCOR. Class 16 (CsI) is not a group that 

can be imported into MELMACCS. It is incorporated by carrying forward the activities and dose 

conversion factors for cesium and iodine separately, and therefore, is split accordingly into 

Class 2 (cesium) and Class 4 (halogens) fractions. Classes 13, 14, and 15 are nonradioactive. 

Figure C.2-1 does not show cerium, lanthanum, uranium, or ruthenium radionuclide classes as 

the release fractions of these radionuclides are less than 1.0×10−5

. MELMACCS does capture 

fractional releases below 1.0×10−5

; however, for this work, a mass threshold fraction for a 

release path and a mass threshold fraction for plume segments to be used were set to 0.001 for 

MACCS inputs. These threshold limits are the same as those used in SOARCA calculations. 

The reason the thresholds are used is to keep the number of plume segments less than 200, 

which is the maximum number MACCS can analyze.

When the SOARCA scenarios were developed, the MELCOR output was converted to a 

MACCS radionuclide input file using MELMACCS Version 1.5.1. For the SOARCA scenarios 

only the radionuclide classes listed in Table C.2-3 were considered for environmental impacts. 

Class 10, uranium (U), Class 11, more volatile main group (Cd), and Class 12, less volatile main 

group (Sn), were not considered in the environmental impacts. For additional information 

regarding these radionuclide classes, see Table A-1 in NUREG/CR-7110 Volume 1.

Table C.2-3 Radionuclide classes used in SOARCA

Class Name Representative Member Elements

1 Noble Gas Xe He, Ne, Ar, Kr, Xe, Rn, H, N

2 Alkali Metals Cs Li, Na, K, Rb, Cs, Fr, Cu

3 Alkali Earths Ba Be, Mg, Ca, Sr, Ba, Ra, Es, Fm

4 Halogens I F, Cl, Br, I, At

5 Chalcogens Te O, S, Se, Te, Po

6 Platinoids Ru Ru, Rh, Pd, Re, Os, Ir, Pt, Au, Ni

7 Early Transition 

Elements Mo V, Cr, Fe, Co, Mn, Nb, Mo, Tc, Ta, W

8 Tetravalent Ce Ti, Zr, Hf, Ce, Th, Pa, Np, Pu, C

9 Trivalents La Al, Sc, Y, La, Ac, Pr, Nd, Pm, Sm, Eu, Gd, 

Tb, Dy, Ho,, Er, Tm, Yb, Lu, Am, Cm, Bk, Cf

The most current version of MELMACCS is Version 1.7.0. When Peach Bottom LTSBO 

scenario was developed in NUREG/CR-7110, the MELCOR output was converted to a MACCS

radionuclide input file using MELMACCS 1.5.1. To ensure proper source term continuity 

between MELCOR and MACCS, a comparison of MELCOR source terms was conducted using 

MELMACCS Version 1.7.0 and MELMACCS Version 1.5.1. The upgrades to MELMACCS are 

attributed to the following:

• Allow the user incorporation of ORIGEN calculations into the MELMACCS initialization 

file. The Peach Bottom LTSBO ORIGEN calculation did not change (i.e., medium burnup, 

49 MW-days/kg peak fuel rod at mid cycle Peach Bottom Unit 2),

• Provide a record of the user inputs and MELCOR plot file location in the MELMACCS 

output file, 
 C-29

• Implement batch processing, and

• Automation of the mass thresholds based on release path and plume segments.

The updated MELMACCS preprocessor includes an additional option that was applied as a 

mass-fraction threshold for release paths and plume segments. A value of 0.001 was given as 

the mass-fraction threshold for a given release path. This threshold is applied to the mass 

released from a radionuclide class for a given release path to the total mass released for that 

same class summed over all the release paths. If any radionuclide class released in a release 

path is equal to or exceeds this fraction, MELMACCS includes this release path in its evaluation 

of release fractions. If a release path falls below this threshold for every radionuclide class, 

MELMACCS does not include that release path in its evaluation of release fractions. 

A value of 0.001 was also selected as the mass-fraction threshold for a plume segment. This 

threshold value is applied to the mass released from a radionuclide class for a given plume 

segment to the total mass released for that same class summed over all the release paths. If 

any radionuclide class in the plume segment exceeds this fraction, MELMACCS includes that 

plume segment in the results. If the plume segments fall below this threshold for every 

radionuclide class, then MELMACCS does not include that plume segment in the results. 

These two mass thresholds were applied to limit the number of 1-hour plume segments. A 

MACCS analysis is limited to a maximum of 200 plume segments. 

A set of MELCOR plot files were converted to MACCS radionuclide input files using both 

versions of MELMACCS. A line by line comparison of the MELMACCS output files was 

conducted and no differences in the numerical values in the MACCS radionuclide input files 

were identified.

C.2.2 Update to MELCOR Source Term

To re-baseline the SOARCA uncertainty analysis base case and quantify any differences in the 

environmental impact from the changes to the updated MELCOR model for the Peach Bottom 

unmitigated LTSBO scenario discussed in Section C.1, a comparison of the two MELCOR 

source terms was conducted with WinMACCS Version 3.6.2 / MACCS Version 2.5.0.0 for the 

SOARCA estimate and SOARCA uncertainty analysis base case (see Section C.1.3.1). These 

versions of WinMACCS/MACCS were the same versions used for SOARCA to generate the 

results documented in Section 7 of NUREG/CR-7110 Volume 1.

A brief description of the Peach Bottom unmitigated LTSBO scenario for the two source terms 

are provided in Table C.2-4. The changes important to note are the 40% increase in the barium 

class and the 20% increase in the iodine class. These increases are expected to increase the

early phase (i.e., primarily from iodine-131 and iodine-133) and long-term (i.e., primarily from 

barium-140 and strontium-89) risk. The other radionuclide classes that differ represent a small 

contribution to risk. Also, the change in initial release timing does not affect the contribution to 

early phase risk because evacuation is complete before the release begins.
 C-30

Table C.2-4 Brief source term description for the Peach Bottom unmitigated LTSBO

Scenario

Core 

Damage 

Frequency

(Events/yr)

Integral Release Fractions by Chemical Group

Atmospheric 

Release 

Timing

Xe Cs Ba I Te Ru Mo Ce La Start 

(hr)

End 

(hr)

SOARCA 

Estimate 3x10-6 0.978 0.005 0.006 0.020 0.022 0.0 0.001 0.0 0.0 20.0 48.0

SOARCA 

UA Base 

Case

3x10-6 0.981 0.005 0.010 0.025 0.019 0.0 0.000 0.0 0.0 19.9 48.0

Percent 

Increase N/A 0.3% 0.0% 40% 20% -16% 0% -176% 0% 0% -0.5% 0.0%

As part of the source term comparison, the same methodology was applied to MELMACCS as 

that used to determine the NUREG/CR-7110 Volume 1 source terms. This means that only the 

radionuclide classes listed in Table C.2-3 are considered for environmental impacts. The 

uranium (U), more volatile main group (Cd), and less volatile main group (Sn) were not 

considered in the environmental impacts. For additional information regarding these classes, 

see Table A-1 in NUREG/CR-7110 Volume 1. 

In this section, the risk tables represent rounded values obtained from the full data sets. The 

plots were developed from the full data sets and slight differences may be noticed due to 

rounding. 

Tables C.2-5 through C.2-7 display the conditional, mean, individual LCF risk (per event) to 

residents within a set of concentric circular areas centered at the Peach Bottom site for the 

unmitigated LTSBO scenario presented in NUREG/CR-7110, Volume 1, and the SOARCA 

uncertainty analysis base case. Three values of dose truncation level are shown in the tables: 

LNT, USBGR, and HPS. 

Dose-truncation based on the HPS position is more complex than the USBGR truncation 

because it involves both annual and lifetime limits. According to the recommendation, annual 

doses below the 5-rem truncation level do not need to be counted toward health effects; 

however, if the lifetime dose exceeds 10 rem, all annual doses, no matter how small, count 

toward health effects. Because of the 10 rem lifetime limit, risks predicted with the criterion 

based on the HPS position statement can sometimes exceed those using the USBGR 

truncation.
 C-31

Table C.2-5 Source term comparison of conditional, mean, individual LCF risk (per 

event) for LNT dose truncation

Radius (mi) SOARCA Estimate SOARCA UA Base Case

10 8.9x10-5 8.8x10-5

20 7.6x10-5 8.0x10-5

30 5.3x10-5 5.6x10-5

40 3.3x10-5 3.6x10-5

50 2.7x10-5 2.9x10-5

Table C.2-6 Source term comparison of conditional, mean, individual LCF risk (per 

event) for USBGR dose truncation

Radius (mi) SOARCA Estimate SOARCA UA Base Case

10 7.4x10-7 8.8x10-7

20 1.9x10-5 2.5x10-5

30 1.1x10-5 1.5x10-5

40 5.0x10-6 7.4x10-6

50 3.4x10-6 5.1x10-6

Table C.2-7 Source term comparison of conditional, mean, individual LCF risk (per 

event) for dose truncation based on the HPS position statement

Radius (mi) SOARCA Estimate SOARCA UA Base Case

10 3.7x10-7 5.6x10-7

20 2.2x10-6 3.7x10-6

30 8.9x10-7 1.5x10-6

40 3.7x10-7 6.1x10-7

50 2.4x10-7 3.9x10-7d

Figure C.2-2 shows the conditional, mean, individual LCF risk (per event) using the LNT for the 

source term comparison. The figure shows the emergency and long-term phases. The 

emergency phase is defined as the first seven days following the initial release to the 

environment. The long-term phase is defined as the time following the emergency phase (i.e., 

there is no intermediate phase). The entire height of each column shows the combined (total) 

LCF risk for the two phases. The emergency response is very effective within the evacuation 

zone (10 miles) during the early phase, so those risks are very small and entirely represent the 

0.5% of the population that are modeled as refusing to evacuate. The peak emergency-phase 

risk is at 20 miles, which is the first location in the plot outside of the evacuation zone. 

Comparing the two source terms, the differences in the long-term phase risk are trivial; the 

differences in the emergency-phase risks are small but meaningful and result from the 

differences in release fractions described.
 C-32

Figure C.2-2 Source term comparison of conditional, mean, individual LCF risk (per 

event) with LNT dose truncation for residents within a circular area of 

specified radius from the plant for emergency and long-term phases

The long-term phase risks dominate the total risks for the accident scenario when the LNT 

dose-response assumption is made. These long-term risks are controlled by the habitability 

(return) criterion, which is the dose rate at which residents are allowed to return to their homes 

following the emergency phase. For Peach Bottom, the habitability criterion is a dose rate of 

500 mrem/yr. This dose rate is below the truncation levels of the USBGR (620 mrem/yr) and 

based on the HPS position statement; therefore, most of the doses received during the 

long-term phase are below the dose truncation limit and are not counted toward health effects 

when using these criteria. Most of the risks associated with either of the truncation levels are 

from doses received during the first year. The conditional, mean, individual LCF risk (per event) 

for these dose truncation models can be seen on Figure C.2-3 for the USBGR dose truncation 

model and Figure C.2-4 for the HPS dose truncation model. 

Figure C.2-3 and Figure C.2-4 do not show separate risks for the emergency and long-term 

phases because those phases overlap, especially in the first year, and are not easily separated 

for purposes of evaluating the annual dose threshold. To better understand this explanation, it 

is important to understand the differences between exposure periods, commitment periods, and 

the periods of time when doses are actually received. For external dose pathways, the time 

over which doses are received is concurrent with the exposure period. External dose pathways 

include cloudshine and groundshine.
 C-33

Figure C.2-3 Source term comparison of conditional, mean, individual LCF risk (per 

event) with USBGR dose truncation for residents within a circular area of 

specified radius from the plant for emergency and long-term phases

The exposure period for internal pathways, inhalation and ingestion, is the period of time when 

the inhalation or ingestion occurs; however, doses continue to be received over a person’s 

entire lifetime following the exposure. A person’s lifetime is variable, depending upon the age of 

the person at the time of exposure, among other things. The period of time over which doses 

are received from an internal pathway is accounted for in the construction of dose conversion 

factors by integrating the doses over a finite period called a dose commitment period, which is 

usually taken to be 50 years when calculating internal-pathway dose conversion factors for 

adults. An implicit assumption is that everyone in the analyses lives for an additional 50 years 

following the exposure, which is most likely a conservative assumption. 

Most of the exposures during the long-term phase are from groundshine; a small fraction is from 

inhalation of resuspended aerosols. Since groundshine is an external pathway, doses received 

are concurrent with the exposure period, which is also taken to be 50 years in the SOARCA. 

On the other hand, exposures from inhalation of resuspended material during each year of the 

long-term phase contribute to doses received over the subsequent 50-year commitment period. 
 C-34

Figure C.2-4 Source term comparison of conditional, mean, individual LCF risk (per 

event) with HPS dose truncation for residents within a circular area of 

specified radius from the plant for emergency and long-term phases

Doses received in the first year thus correspond to:

• all of the dose from external exposure during the emergency phase,

• most of the dose from internal exposure during the emergency phase,

• all of the dose from external exposure during the first year of the long-term phase, and

• most of the dose from internal exposure during the first year of the long-term phase.

Doses received in the second and subsequent years correspond to:

• a fraction of the dose from internal exposure during all previous years plus most of the 

dose from internal exposure during that year, and

• all of the dose from external exposure during that year. 

After a single exposure, internal doses decrease more slowly from one year to the next when 

the isotopic half-life is relatively long (i.e., on the order of a year or longer) and the solubility of 

the dominant chemical form of the isotope is low so that the removal rate from the human body 

is low (i.e., the biological half-life is long). A good example is 90Sr, for which the second-year 

effective dose from inhalation is 60% of the first-year dose. The isotopic half-life is 29 years, so 

most of the reduction from year one to year two results from the biological half-life. The internal 

doses decrease more rapidly from one year to the next when either the isotopic half life is short 

or when the solubility of the dominant chemical form of the isotope is high so that the human 
 C-35

body tends to excrete it rapidly. A good example of this is 131I, for which the second-year 

effective dose from inhalation is essentially zero. This isotope has a short isotopic half-life 

(i.e., 8 days) and a short biological half-life because of its high solubility. For comparison, the 

second-year effective dose from inhalation for 137Cs is about 10% of the first-year dose, so it is 

intermediate between the previous examples.

The ingestion pathway was not treated in these SOARCA analyses because uncontaminated 

food and water supplies are abundant within the United States, and it is unlikely that the public 

would eat radioactively contaminated food. Since ingestion doses are taken to be negligible in 

SOARCA, inhalation is the only internal pathway that is treated. A significant portion of the 

exposures during the emergency phase are from inhalation. As explained above, these 

exposures are assumed to lead to doses over the commitment period, which is the 50 years 

following the exposure. However, depending on the isotope inhaled, the doses received may 

diminish rapidly and become negligible for most of the dose commitment period. Because the 

internal doses from inhalation diminish with time, most of the doses in the second and 

subsequent years are from the exposures during that year. But these doses are limited by the 

habitability criterion to be less than 500 mrem in any year. The 500 mrem limit is for all dose 

pathways except ingestion, in this case groundshine and inhalation from resuspended aerosols. 

The inhalation dose used in this criterion is a committed dose (i.e., it accounts for doses 

received over the next 50 years). Because the annual doses allowed by the habitability criterion 

are less than the truncation levels based on US background and the HPS position statement, 

nearly all of the risk is from doses received during the first year. These doses include most of 

emergency-phase doses and a fraction of the long-term phase doses. This explains the risk 

profiles for these dose-truncation criteria on Figure C.2-3 and Figure C.2-4. 

The early-fatality risks are zero for both source terms. This is because the release fractions 

shown in Table C.2-4 are too low to produce doses large enough to exceed the dose thresholds 

for early fatalities, even for the 0.5% of the population that are modeled as refusing to evacuate. 

The largest value of the mean, acute dose for the closest resident (i.e., 0.5 to 1.2 kilometers 

from the plant) for this scenario is about 0.1 gray (Gy) to the red bone marrow, which is usually 

the most sensitive organ for early fatalities, but the minimum acute dose that can cause an early 

fatality is about 2.3 Gy to the red bone marrow. Clearly, the calculated doses are all well below 

this threshold.

In this comparison, the peak absolute risk is 2.7x10-10 per reactor year for the SOARCA 

estimate at the 10-mile circular area (i.e., see Table C.2-5, 10 mile circular area, and see 

Table C.2-4 for the LTSBO core damage frequency). Estimated LCF risks below 1×10-7 per 

reactor year should be viewed with caution because of the potential impact of events not studied 

in the analyses and the inherent uncertainty in very small calculated numbers.

C.2.3 Numerical Convergence – Code Updates

To reflect updates and advancements to the WinMACCS/MACCS code, a series of WinMACCS 

and MACCS simulations were conducted to see the overall effect on Peach Bottom LTSBO 

scenario. The original Peach Bottom LTSBO Unmitigated Response WinMACCS/MACCS

simulation in Section 5.1 of NUREG/CR-7110 Volume1 was conducted in November, 2010. In 

the past year and half, MACCS code changes have caused the numerical results for the Peach 

Bottom LTSBO scenario used in this study to change. These changes have resulted in changes 

to the conditional, mean, individual LCF risk. 
 C-36

WinMACCS

The updates in the MACCS graphic user interface, WinMACCS, from the version used in 

NUREG/CR-7110 Volume 1, WinMACCS Version 3.6.2, to the version used for this work, 

WinMACCS Version 3.6.4, deal with expanding the uncertainty engine. The older version of 

WinMACCS was not capable of handling the number of MACCS uncertainty distributions

required for this study. Also, Version 3.6.2 did not allow certain DCF factors to be treated as 

uncertain. The newest version of WinMACCS, Version 3.6.4, has corrected these problems. 

These changes should not affect a deterministic calculation. To verify this, a series of 

WinMACCS/MACCS runs were conducted using the SOARCA estimate and SOARCA 

uncertainty analysis base case source terms (i.e., see Table C.2-4). The results yielded the 

same results shown in Tables C.2-8 through C.2-10 for the SOARCA estimate. 

MACCS

The updates to MACCS from the version used in NUREG/CR-7110 Volume 1, MACCS Version 

2.5.0.0, to the version used for this work, MACCS Version 2.5.0.9 deal with the following:

• Provide file locations on MACCS cyclical files (e.g., MELMACCS source term files) to 

provide enhances traceability between inputs and results, 

• Lower plume density limit (PLMDEN) consistent with the MACCS User Manual [9], 

• Change to a FORTRAN compiler compatible with the Windows 7 operating system, and

• Correction of the NRC Regulatory Guide 1.1.45 plume meander model [10], which is not 

used in the SOARCA scenarios.

The new compiler affects the way rounding is performed. The ‘round off’ changes the random 

values that are calculated, particularly the set of weather trials that are selected. These 

differences result from conversion of real numbers to integers, where the real numbers can be 

slightly greater than or less than the associated integer. This difference is considered 

acceptable and not an error because there is no reason to think that one set of random choices 

is better than another.

NUREG/CR-7110 Volume 1 and this work use 984 randomly selected weather trials selected 

from 36 bins used for nonuniform weather bin sampling. The random seed used to generate 

these weather trials is kept constant throughout the deterministic work in this study and is the 

same used in NUREG/CR-7110 Volume 1. This results in the same weather trials being 

sampled for all MACCS deterministic analysis using the same MACCS code version.

Since MACCS version 2.5.0.9 changes the weather trials sampled using the same random 

seed, the two MACCS versions were compared and the results are shown below. The change 

in weather trials results in about a 2-9% higher conditional, mean, individual LCF risk. Tables 

C.2-8 through C.2-10 show the differences in the SOARCA estimate LCF risk per event for the 

LNT, USBGR, and HPS dose truncation levels, respectively.
 C-37

Table C.2-8 MACCS version comparison of conditional, mean, individual LCF risk (per 

event) for LNT dose truncation for the SOARCA estimate at specified 

circular areas 

Radius (mi) Version 2.5.0.0 Version 2.5.0.9

10 8.9x10-5 9.2x10-5

20 7.6x10-5 7.9x10-5

30 5.3x10-5 5.4x10-5

40 3.3x10-5 3.4x10-5

50 2.7x10-5 2.8x10-5

Table C.2-9 MACCS version comparison of conditional, mean, individual LCF risk (per 

event) for USBGR dose truncation for the SOARCA estimate at specified 

circular areas 

Radius (mi) Version 2.5.0.0 Version 2.5.0.9

10 7.4x10-7 7.5x10-7

20 1.9x10-5 2.0x10-5

30 1.1x10-5 1.1x10-5

40 5.0x10-6 5.1x10-6

50 3.4x10-6 3.4x10-6

Table C.2-10 MACCS version comparison of conditional, mean, individual LCF risk (per 

event) for HPS dose truncation for the SOARCA estimate at specified 

circular areas 

Radius (mi) Version 2.5.0.0 Version 2.5.0.9

10 3.7x10-7 3.8x10-7 

20 2.2x10-6 2.4x10-6 

30 8.9x10-7 9.6x10-7 

40 3.7x10-7 3.9x10-7 

50 2.4x10-7 2.5x10-7 

The overall average difference between versions in terms of conditional, mean, individual LCF 

risk is less than 9%. The largest difference is noticed at the 20-mile radius in Table C.2-10 but 

is still less than 10%. A difference of less than 10% induced by weather sampling is considered 

small. The SORCA UA base case was also compared between versions and yielded similar 

results. 
 C-38

The WinMACCS/MACCS code behavior has been documented with a series of regression tests 

and expansion testing as new updates and models are added to the codes. Many 

WinMACCS/MACCS validation and verification analyses have been conducted. References [8, 

9, 50, 88-90] provide the most current documentation for WinMACCS/MACCS. 

C.2.4 SOARCA Uncertainty Analysis Deterministic Base Case

In this section, the risk tables represent rounded values obtained from the full data sets. The 

plots were developed from the full data sets and slight differences may be noticed due to this 

rounding. 

Tables C.2-11 through Table C.2-13 display the conditional, mean, individual LCF risk (per 

event) to residents within a set of concentric circular areas centered at the Peach Bottom site for 

the unmitigated LTSBO scenario presented in NUREG/CR-7110, Volume 1, and the SOARCA 

uncertainty analysis base case source term using WinMACCS Version 3.6.4 and MACCS

Version 2.5.0.9. Three values of dose truncation level are shown in the tables: LNT, USBGR, 

and HPS. 

Table C.2-11 SOARCA estimate and SOARCA UA base case comparison of conditional, 

mean, individual LCF risk (per event) for LNT dose truncation at specified 

circular areas 

Radius (mi) SOARCA Estimate

Version 2.5.0.9 SOARCA UA Base Case

10 9.2x10-5 9.0x10-5

20 7.9x10-5 8.3x10-5

30 5.4x10-5 5.8x10-5

40 3.4x10-5 3.7x10-5

50 2.8x10-5 3.0x10-5

Table C.2-12 SOARCA estimate and SOARCA UA base case comparison of conditional, 

mean, individual LCF risk (per event) for USBGR dose truncation at 

specified circular areas 

Radius (mi) SOARCA Estimate

Version 2.5.0.9 SOARCA UA Base Case

10 7.5x10-7 8.9x10-7

20 2.0x10-5 2.6x10-5

30 1.1x10-5 1.6x10-5

40 5.1x10-6 7.7x10-6

50 3.4x10-6 5.2x10-6
 C-39

Table C.2-13 SOARCA estimate and SOARCA UA base case comparison of conditional, 

mean, individual LCF risk (per event) for HPS dose truncation at specified 

circular areas 

Radius (mi) SOARCA Estimate

Version 2.5.0.9 SOARCA UA Base Case

10 3.8x10-7 5.6x10-7

20 2.4x10-6 4.4x10-6

30 9.6x10-7 1.7x10-6

40 3.9x10-7 7.1x10-7

50 2.5x10-7 4.5x10-7

Figure C.2-5 shows the conditional, mean, individual LCF risk (per event) with the LNT for the 

SOARCA estimate and SOARCA uncertainty analysis base case comparison for the emergency 

and long term phases. The entire height of each column shows the combined (total) risk for the 

two phases. The emergency response is very effective within the evacuation zone (10 miles) 

during the early phase, so those risks are very small and entirely represent the 0.5% of the 

population that are modeled as refusing to evacuate. The peak emergency phase risk is at 

20 miles, which is the first location in the plot outside of the evacuation zone. The differences in 

the long-term phases are trivial. 

The SOARCA uncertainty analysis base case conditional, mean, individual LCF risks are 

greater for both phases for all circular areas. These higher results are attributed to the 

differences in the source term discussed in Section C.2.2 and the code changes discussed in 

Section C.2.3. 
 C-40

Figure C.2-5 SOARCA estimate and SOARCA UA base case comparison of conditional, 

mean, individual LCF risk (per event) with the LNT for residents within a 

circular area of specified radius from the plant for emergency and longterm phases

The long-term phase risk dominates the total risk for the accident scenario when the LNT 

dose-response assumption is made. These long-term risks are controlled by the habitability 

(return) criterion, which is the dose rate at which residents are allowed to return to their homes 

following the emergency phase. For Peach Bottom, the habitability criterion is a dose rate of 

500 mrem/yr. This dose rate is below the truncation levels based on US background and based 

on the HPS position statement; therefore, most of the doses received during the long-term 

phase are below the dose truncation limit and are not counted toward health effects when using 

these criteria. Thus, most of the risks associated with either of the truncation levels are from 

doses received during the first year. The conditional, mean, individual LCF risk (per event) for 

these dose truncation models can be seen on Figure C.2-6 for the USBGR dose truncation 

model, and Figure C.2-7 for the HPS dose truncation model. Figure C.2-6 and Figure C.2-7 do 

not show separate risks for the emergency and long-term phases because those phases 

overlap, especially in the first year, and are not easily separated for purposes of evaluating the 

annual dose threshold. 
 C-41

Figure C.2-6 SOARCA estimate and SOARCA UA base case comparison of conditional, 

mean, individual LCF risk (per event) with USBGR dose truncation for 

residents within a circular area of specified radius from the plant for 

emergency and long-term phases

Because the internal doses from inhalation diminish with time, most of the doses in the second 

and subsequent years are from the exposures during that year. But these doses are limited by 

the habitability criterion to be less than 500 mrem in any year. The 500 mrem limit is for all dose 

pathways, in this case groundshine and inhalation from resuspended aerosols. The inhalation 

dose used in this criterion is a committed dose (i.e., it accounts for doses received over the next 

50 years). Because the annual doses allowed by the habitability criterion are less than 

truncation levels based on US background and the HPS position statement, nearly all of the risk 

is from doses received during the first year. These doses include most of emergency phase 

doses and a fraction of the long-term phase doses. This explains the risk profiles for these 

dose-truncation criteria on Figure C.2-6 and Figure C.2-7. 
 C-42

Figure C.2-7 SOARCA estimate and SOARCA UA base case comparison of conditional, 

mean, individual LCF risk (per event) with HPS dose truncation for 

residents within a circular area of specified radius from the plant for 

emergency and long-term phases

The early-fatality risks are zero for both source terms. This is because the release fractions 

shown in Table C.2-4 are too low to produce doses large enough to exceed the dose thresholds 

for early fatalities, even for the 0.5% of the population that are modeled as refusing to evacuate. 

The largest value of the mean, acute dose for the closest resident (i.e., 0.5 to 1.2 kilometers 

from the plant) for this scenario is about 0.1 gray (Gy) to the red bone marrow, which is usually 

the most sensitive organ for early fatalities, but the minimum acute dose that can cause an early 

fatality is about 2.3 Gy to the red bone marrow. Clearly, the calculated doses are all well below 

this threshold. 

Estimated risks below 1×10-7 per reactor year should be viewed with caution because of the 

potential impact of events not studied in the analyses and the inherent uncertainty in very small 

calculated numbers. In this comparison, the peak absolute risk is 2.8x10-10 per reactor year for 

the SOARCA Estimate at the 10-mile circular area (i.e., see Table 5.2-1, 10 mile circular area, 

and see Table C.2-4 for the LTSBO core damage frequency).
 C-43

C.3 Model Error Log

The post-model development activities following the completion of the SOARCA Peach Bottom 

unmitigated LTSBO uncertainty analysis identified several issues related to errors in 

implementation, identification of undocumented conservatisms, and/or updates to parameter 

values. These issues are addressed in this Appendix which includes an evaluation of the 

sensitivity of the error. Not all identified issues that are evaluated fall in the category of errors, 

as some of the issues are presented to only evaluate the degree of conservatism from the 

modeling choices made during the model development phase.

C.3.1 Error in Sampled Values of Drywell Head Bolt Torque Coefficient

Issue

The lower and upper bounds on the uncertainty distribution of torque coefficient K, used to 

determine the tensile force developed in the drywell head bolts during assembly, were specified 

incorrectly as 0.029 and 0.57 rather than as 0.050 and 0.00. 

Description

This error effectively shifted the sampled variation in head flange leakage area with pressure 

such that pressures greater than SOARCA estimate were always necessary to initiate leakage. 

While it was desired to initiate leakage at between 46.87 psid and 109.26 psid (sampled around 

the SOARCA estimate of 81.88 psid), the error caused leakage to be initiated between 84.63 

psid and 143.24 psid.

Impact

It is believed that what was most important to accomplish with respect to the sampling of torque 

coefficient was accomplished. The sampling allowed the effect of lifting the head flange earlier 

or later to be investigated. That the flange never lifted as early as desired and that it didn’t lift in 

some calculations until later than desired seems less important than that the effect due to the 

flange lifting relatively early or relatively late was investigated.

C.3.2 Miss Ordering of Sampled Values of Fuel Failure Criterion

Issue

The three discrete sampling possibilities of fuel failure criterion were not defined to the statistics 

analysis in monotonic order.

Description

The sampled parameter of fuel failure criterion (FFC) had three possible outcomes. One of the 

outcomes (Outcome 1) was the SOARCA estimate time-at-temperature relationship for the 

collapse of fully oxidized fuel rods. Another of the outcomes (Outcome 2) was the SOARCA 

estimate relationship altered to cause earlier collapse. The remaining outcome (Outcome 3) 

was the SOARCA estimate altered to cause later collapse. To best analyze FFC for monotonic 

influences, the outcomes should have been defined to the statistics analysis in the order 

Outcome 2, Outcome 1, and Outcome 3. They were instead defined in the order Outcome 1, 

Outcome 2, and Outcome 3.
 C-44

Impact

The significance of the miss ordering of FFC outcomes was investigated by righting the order 

and seeing if the statistical importance of FFC changed significantly with respect to the amount 

of cesium released to the environment in the Replicate 1 set of calculations. It did not suggest 

that the miss ordering was not important to the statistical analysis as a whole. 

An additional analysis into the significance of FFC ordering on the LCF risk parameters for the 

10-mile and 20-mile circular areas using the LNT dose-response model was conducted for all 

three replicates (CAP17). This analysis showed only a slight increase in the FFC contribution. 

The overall order of LCF risk parametric significance did not change.
APPENDIX D

PEER REVIEW/ACRS COMMENT RESOLUTION REPORT

D-1

Peer Review Comment Resolution Report

Uncertainty Analysis Plan

The purpose of this report is to provide the Peer Review Committee with the State-of-the-Art 

Reactor Consequence Analysis (SOARCA) team’s resolution of each written peer review 

comment related to the uncertainty analysis (UA) plan in the December 22, 2010 and April 9, 

2010 memoranda. This report is organized first by individual peer reviewers for comments in 

the December 22, 2010 memorandum, and then concludes with the joint comments in the 

April 9, 2010 Peer Review Guidance Memorandum (see the Contents below). Comments are 

extracted directly from the source documents with no changes. The report sections that are 

identified in the resolutions refer to the revised UA plan, as it is captured in Sections 1-4 of the 

draft NUREG/CR report that will document the UA. 

Contents

Bernard Clément..................................................................................................................... D-2 

Jeff Gabor.............................................................................................................................. .D-6 

Robert Henry .......................................................................................................................... D-9 

David Leaver......................................................................................................................... D-10

Kevin O’Kula ......................................................................................................................... D-17

John Stevenson .................................................................................................................... D-23

Karen Vierow ........................................................................................................................ D-25

Jacquelyn Yanch................................................................................................................... D-28

Peer Review Guidance Memo dated April 9, 2010 ................................................................ D-30 

Advisory Committee on Reactor Safeguards......................................................................... D-32 

Note: Mr. Ken Canavan, Mr. Roger Kowieski, and Mr. Bruce Mrowca, did not provide individual 

written comments on the Uncertainty Analysis in the December 22, 2010 memorandum.
D-2

BERNARD CLÉMENT

December 22, 2010 SOARCA Peer Review Memorandum, “Guidance on the SOARCA 

Uncertainty Analysis Plan”

1. Page 2

Comment: 

General: As explained, the effort is limited due to time and resource constraints. This is 

understandable but will induce limitations in the conclusions that will be drawn from the 

exercise. It can be expected that the applicability of the methodology is, if not fully 

demonstrated, at least illustrated on the specific example that is treated. Concerning the specific 

sequence that will be treated it is expected that the exercise will show the effect of the most 

influential parameters. It will however not be possible to extrapolate in general the conclusions 

to other accidental sequences and other reactors.

The exercise is mainly based on a statistical treatment of the propagation of uncertainties of 

models parameters. This is probably the best way to proceed when using complex simulation 

tools such as MELCOR and MACCS. It should however be recognized that some epistemic 

uncertainties are not taken into account with this method, especially when some physical 

phenomena of potential importance are not modeled. When this is known, it should be clearly 

stated. An example is given in page 43 for CH3I.

Resolution:

The October 2010 draft UA plan did not fully document the technical basis for all chosen 

parameters. The documentation has been improved and Section 4 of the draft UA NUREG/CR 

report has been expanded to include the technical basis and justification of the parameters and 

distributions selected for this SOARCA UA study. The final SOARCA UA NUREG/CR report will 

contain a thorough discussion of the quantification of the uncertainty in the consequence results 

as driven by the uncertainty in the selected input parameters.

The scope of this uncertainty analysis indeed does not include all uncertainties. The effort is 

focused on capturing the effects of uncertainties in MELCOR and MACCS input parameters. 

Though some model uncertainties may be partially captured through surrogate input 

parameters, in general, the epistemic model uncertainties are not treated.

2. Page 2

Comment: 

The Zr melt breakout temperature is certainly an important uncertain parameter. Its influence 

will be evaluated for the chosen scenario but it should be kept in mind that the relative influence 

of this parameter should largely differ for other scenarios.
D-3

Resolution: 

Based on prior work on in-vessel melt progression, this parameter is expected to be among the 

more important uncertain parameters. The lower bound value is the zircaloy melting 

temperature, while the upper bound value is based on likely rod collapse temperature occurring 

within 15 minutes. The mode is the value used in the SOARCA deterministic analysis. The final 

SOARCA UA NUREG/CR report will contain a thorough discussion of the quantification of the 

uncertainty in the consequence results as driven by the uncertainty in the selected input 

parameters. See also response 4 below.

3. Page 2

Comment: 

Molten clad drainage rate: worthwhile to study, but probably less important than Zr melt 

breakout temperature.

Resolution: 

The molten clad drainage rate has an impact on blockage on Top of Active Fuel melt to Bottom 

of Active fuel affecting material relocation. The Zr melt breakout can provide a surrogate for this 

parameter. Both have been included in the SOARCA uncertainty study; the Zr melt breakout 

temperature was added. See section 4.1.2 of the draft NUREG/CR. 

4. Page 2

Comment: 

Fuel failure criterion is also an important parameter. There is certainly some correlation between 

its influence and the influence of Zr melt breakout temperature. The importance of fuel-cladding 

interactions will depend on the latter and in turn affect the temperature and time at which there 

will be transition from rod-like geometry to debris. A kind of correlation between the probability 

density functions of these parameters could in principle be established by looking at the results 

of MELCOR analyses of some experiments such as for instance Phebus FP. If this has not 

already been done, it should however be recognized that it would require quite a lot of work 

probably not manageable by the Project.

Resolution: 

Fuel failure criterion represents complex phenomena and work has not been done in 

determining uncertainties within this parameter. Insights from the hydrogen uncertainty analysis 

completed in 2010 provide the principle basis for selecting Zr breakout temperature and clad 

drain rate as the two “surrogate” parameters for most in-vessel damage progression 

parameters. 

The following discussion was added in the draft UA NUREG/CR report: “MELCOR lacks a 

deterministic model for evaluating fuel mechanical response to the effects of clad oxidation, 

material interactions (i.e., eutectic formation), zircaloy melting, fuel swelling and other processes 

that occur at very high temperatures. In lieu of detailed models in this area, a simple 

temperature-based criterion is used to define the threshold beyond which normal ("intact") fuel 
D-4

rod geometry can no longer be maintained, and the core materials at a particular location 

collapse into particulate debris. The temperature-based criterion rolls up uncertainties in 

numerous physico-chemical processes that affect fuel rod integrity. The "time-at-temperature" 

criterion is the time endurance of the upright, cylindrical configuration of fuel rod bundles which 

decreases with increasing temperature. A temperature-based 'cumulative damage' criterion is 

used in the MELCOR model to define the remaining lifetime of normal fuel rod geometry 

(Table 4.1-2). The alternative functions represent shifts in temperature of +/- 100 K and fuel 

endurance times of +/- factor of 2.0 (Figure 4.1-9, Figure 4.1-10 and Table 4.1-3).

5. Page 2 

Comment: 

The wording about hydrogen ignition criteria is unclear as it is said both “no consideration 

currently given to possibility of the absence of an ignition source” and “accumulation of H2 due 

to the absence of ignition source is credible”.

Resolution: 

Section 4.1.4 of the draft UA NUREG/CR report was updated with an initial attempt to clarify 

these points and to include a detailed discussion of most likely ignition sources with justification 

for the uncertain distribution. This section will likely be updated further to provide additional 

clarification.

6. Page 2 

Comment:

Concerning chemical forms of iodine and cesium, the relative probability of the five different 

combinations is not justified. Concerning the fraction of gaseous iodine (that can be considered 

as I2 as proposed) the value recommended by NUREG-1465, that is supposed to be bestestimate is 0.05. Unless there are good arguments, there should be the central value and not 

the upper bound. Concerning cesium, the partition between CsOH, CsI and Cs2MoO4 might 

have an impact on releases of both cesium and iodine. It is recommended to wait for the first 

results of the study to decide if other partitions (increased number of combinations) would be 

useful.

Resolution: 

The SOARCA team reviewed NUREG-14651 recommendations; however, NUREG-1465 is not 

considered the current 'best estimate' source for iodine and cesium chemical forms. PHEBUS 

experimental results have been reviewed and incorporated instead. The gaseous iodine 

fractions in Section 4.1.5 of the draft UA NUREG/CR report have been updated to reflect 

PHEBUS experimental results and provide justification for each fraction. These are 

summarized in Table 4.1-7 (formerly Table 4.1-5 in the October 2010 plan).

 

1 NUREG-1465 (1995) is under review and a proposal for revision is being considered.
D-5

7. Page 3 

Comment: 

Concerning the dynamic and agglomeration shape factors, not only the hygroscopic effects will 

cause the particles to tend towards being spherical but also the agglomeration processes (see 

e.g. M.P. Kissane: On the nature of aerosols produced during a severe accident of a watercooled nuclear reactor, Nuclear Engineering and Design 238 (2008) 2792-2800).

Resolution: 

The SOARCA team has updated the technical basis to include this reference and ensure the 

distribution is skewed towards spherical. The following text was added Section 4.1.6 of the draft 

UA NUREG/CR report: "For this work, it is assumed that hygroscopic effects during the accident 

sequence will induce some condensation of moisture on the aerosol particles causing the 

particles to tend towards being spherical and limit the degree of non-spherical shapes (i.e., 

1.0 which is a perfectly spherical aerosol particle). Thus a beta distribution which produces a 

distribution that is biased towards 1.0 was selected. This specification expresses the belief that 

the shape factors lie closer to the range of 1.0 to 3.0 which diminishes the likelihood of having 

values approaching 5.0 (See Figure 4.1-18 and Table 4.1-8). The lower bound of 1.0 represents 

an aerosol particle having a perfectly spherical shape. The upper bound of 5.0 represents 

chains of particles which appear to be atypical during severe accident conditions (Ref. 77).
D-6

JEFF GABOR

December 22, 2010 SOARCA Peer Review Memorandum

8. Page 4 

Comment:

Technical justification needs to be documented for the selection of each uncertainty parameter. 

Included should be a discussion of the best estimate value along with the basis for the range of 

uncertainty and the appropriate distribution. Technical references should be included for each 

parameter.

Resolution: 

The October 2010 draft UA plan did not fully document the technical basis for all chosen 

parameters. The documentation has been improved and Section 4 of the draft UA NUREG/CR 

report has been expanded to include the technical basis and justification of the parameters and 

distributions selected for this SOARCA UA study, including identification of the SOARCA 

estimate values and technical references.

9. Page 4

Comment: 

Many of the MELCOR uncertain parameters depend on one another. Correlations between 

various parameters should be developed to represent these dependencies.

Resolution: 

As suggested by peer reviewers during the October 2010 meeting, the SOARCA team carefully 

deliberated on which MELCOR parameters should be correlated (MACCS parameter 

correlations were already included in the October 2010 draft UA plan). In addition, since the 

October 2010 meeting, the SOARCA team developed the capability to correlate input 

parameters in MELCOR. Appropriate correlations were identified and are now included for 

MELCOR parameters. Section 4 of the draft NUREG/CR has been updated to identify the 

correlated parameters.

10. Page 4 

Comment:

(1) In-core failures of instrument tubes have been raised by Dr. Henry and need to be 

addressed in the SOARCA documentation.

(2) If uncertainties exist as to the potential for enhanced radionuclide release, these should be 

included in the uncertainty analysis.
D-7

Resolution: 

The MELCOR model does not currently have the capability to consider the in-core failures of 

instrument tubes raised by Dr. Henry. However, the SOARCA team is currently further 

investigating these topics raised by Dr. Henry and the results will be documented in the Peach 

Bottom integrated analyses volume of the SOARCA reports (NUREG/CR-7110, Volume 1). In 

addition, a preview of insights from analyses to date was shared with peer reviewers at the 

December 2011 meeting, including the insight that the potential bypass pathway is not expected 

to be a concern based on the extremely low frequency of the vulnerability being present 

(i.e., low percentage of time that a bypass pathway is possible). We do not plan to further study 

this issue through inclusion of parameters in this UA, though the topic merits further 

consideration in future studies. 

11. Page 4 

Comment: 

The potential for Main Steam Line creep failure is not being considered as an uncertain 

parameter. The MSL rupture area for such a failure would likely be large and probably does not 

need to be evaluated as an uncertain parameter. I recommend that this uncertain parameter be 

replaced with a parameter that more directly relates to MSL creep failure.

Resolution: 

The SOARCA team re-evaluated this phenomenon in regards to this comment. Our rationale is 

that the uncertainty in the parameters affecting the calculated potential for creep can be 

neglected in this assessment because prior experience (through sensitivity analyses) suggests 

the Larson-Miller (L-M) damage index transitions from zero to values well above unity within a 

very short time. The L-M parameter is not likely to be very sensitive because once the MSL 

enters creep conditions, the progression is very fast from 0 to 1. 

On the other hand, we consider the area of the rupture as an important uncertain parameter 

because it relates to the more important factor of how we model flow to and through the MSL, 

and associated heat transfer to wall piping. And after the October 2010 and December 2011 

peer review meetings and feedback, we have re-assessed the distribution for the MSL rupture 

area. It is now skewed heavily to large open areas, with only a small residual probability (0.01) 

of an open area less than 10%.

12. Page 4

Comment: 

Failure of both sets of railroad doors is included in the uncertainty, however, failure of the 

blowout panels at the top of the refueling floor are not included. Given the complexity of how the 

reactor building will respond to a containment failure, it is recommend that the RR door failure 

parameter be replaced with a more simplified parameter representing the potential 

decontamination factor for the entire reactor building.
D-8

Resolution: 

In the MELCOR code the decontamination factor is a calculated result and not a parameter 

which can be given an uncertain value. However, as part of the overall integrated model, 

MELCOR calculates aerosol transport and retention in the reactor building using mechanistic 

models that account for the effects of changes in flow rates, flow paths and changing properties 

of deposition surfaces. Major uncertainties tend to lie in boundary conditions --- such as the 

criteria used to determine whether doors open and create new transport pathways.

Past calculations (NUREG/CR-7110, Vol. 1) have shown that hydrogen combustion leads to a 

nearly immediate opening of the refueling bay blow out panels and the railroad doorway at 

grade level. Blow-out panels into the turbine building and personnel access doorways out of the 

reactor building might also open. However, the dominant flow path for fission products to the 

environment is through the refueling bay blowout panels. A stable flow of air is calculated to 

enter the building through the open railroad doorway, rise upward through the open equipment 

hatches from grade level to the refueling bay and exit the building to the environment through 

the open blow-out panels. Failing the railroad doors will cause a ‘chimney effect’ and reduce 

the residence time for radionuclides within the reactor building. A smaller railroad door open 

area is credible and might reduce the airflow and increase residence time. 

13. Page 4 

Comment: 

The success and timing of operator actions should also be considered in the uncertainty 

analysis. These actions include opening of the SRVs earlier in the BWR event along with initial 

level control using RCIC.

Resolution: 

As mentioned in the SOARCA documentation, a comprehensive human reliability assessment 

(HRA) was not conducted for operator actions. In the absence of an HRA, it is difficult to assign 

distributions to the timing of these two operator actions. Rather than include a distribution of 

times for these two operator actions in the integrated uncertainty analysis, we plan to explore 

the sensitivity of results to the timing of these two actions in a separate sensitivity study, 

planned to be documented in the UA NUREG/CR report. See also resolution 17 below.
D-9

ROBERT HENRY

December 22, 2010 SOARCA Peer Review Memorandum

14. Page 5 

Comment: 

My comments on the uncertainty study closely parallel my comments related to the information 

that we have yet to receive to quality the code. 

(1) The uncertainty study only has substance when the variations in the mechanistic models are 

based on the uncertainty variations that have been derived by comparing the mechanistic 

models with various experiments. Without this, there is there is no technical basis for the 

variations that are used in the evaluations.

(2) In the framework of the uncertainty study that was sent to us, there were a number of 

parameters that were used to represent variations in the accident progression, but to date, no 

technical basis has been provided for any of these. Out of frustration, I Googled and found a 

presentation entitled "MELCOR Code Development Status, Code Assessment and QA". Under 

the heading of MELCOR 2.1 Assessment Matrix they discuss the TMI-2 accident as well as the 

following experiments: LOFT-FP2, PHEBUS, IIST, BACCHUS, LHF, OLHF, VERCORS, CVTR, 

HDR, NUPEC, Marviken, CSTF, PANDA, ABCOVE, SUPRA, and DEMONA. We have 

requested information relating to how the model parameters are varied as a function of these, or 

other benchmarks, if at all. More to the point, we have asked for these so that we can 

understand how the uncertainty variations are being quantified. The MELCOR best practices 

document that was given to the committee identifies MELCOR 1.8.6 as the code used to assess 

radiological releases to the environment. The assessment matrix that lists the experiments 

given above identifies MELCOR 2.1. Is this the difference that we are confronting? Have these 

benchmarks not been performed with 1.8.6 but are available for version 2.1? The committee 

somehow must be able to develop an appreciation of the extent of benchmarks that exist for the 

code that the NRC is using in this evaluation. Without the identification of the technical basis, 

neither the "best estimate" calculations nor the "uncertainty analysis" have any basis. 

Resolution:

The October 2010 draft UA plan did not fully document the technical basis for all chosen 

parameters. The documentation has been improved and Section 4 of the draft UA NUREG/CR 

report has been expanded to include the technical basis and justification of the parameters and 

distributions selected for this SOARCA UA study. In addition:

(1) Some of the uncertainty variations are based directly on experimental results, for example, 

the PHEBUS Iodine distribution results. Other uncertainty distributions are based on expert 

judgment that is informed by knowledge of the relevant experiments and how they relate to 

MELCOR modeling. Section 4.0, introductory material has been added to the Draft NUREG/CR 

to clarify this.

(2) Many of the experiments listed and TMI-2 have been compared with MELCOR. The 

resolutions to comments 34, 35, 38, and 47 in the Peer Review Comment Resolution Report 

(available at NRC ADAMS number ML11118A0620) for the SOARCA estimate analysis include 

relevant discussions. In addition, the SOARCA team made a detailed presentation at the 

December 2011 peer review meeting on MELCOR validation and benchmarking activities to 

date.
D-10

DAVID LEAVER

December 22, 2010 SOARCA Peer Review Memorandum

15. Page 8 

Comment: 

Section 4 of the first report (UA Plan) notes that for some uncertain parameters there is a limited 

or in some cases no technical basis documented. This must be addressed in the final 

uncertainty report, even if the technical basis is qualitative and subjective. Some examples are

discussed below. The basis should address the upper and lower bounds and the nature of the 

distribution.

Resolution: 

The October 2010 draft UA plan did not fully document the technical basis for all chosen 

parameters. The documentation has been improved and Section 4 of the draft UA NUREG/CR 

report has been expanded to include the technical basis and justification of the parameters and 

distributions selected for this SOARCA UA study.

16. Page 8 

Comment: 

The uncertainty analysis methodology is attempting to address uncertainty in an integrated 

manner within the context of the core damage progression model and the consequence 

analysis. This is a worthwhile approach and it is innovative, but has the problem that 

dependencies among uncertain parameters may be hard to discern in some cases. The 

approach differs from traditional PRA‐based approaches to uncertainty analysis which apply the 

Level 1 and Level 2 logic models, split fractions, and the like to identify these dependencies. In 

light of this, it is suggested that the SOARCA project consider use of traditional sensitivity 

studies as a supplement and sanity check for the integrated uncertainty analysis and as a way 

to provide insight on potential dependencies.

Resolution: 

As suggested by peer reviewers during the October 2010 meeting, the SOARCA team carefully 

deliberated on which MELCOR parameters are dependent and should be correlated (MACCS

parameter correlations were already included in the October 2010 draft UA plan). In addition, 

since the October 2010 meeting, the SOARCA team developed the capability to correlate input 

parameters in MELCOR. Appropriate correlations were identified and are now included for 

MELCOR parameters. Section 4.0 of the draft NUREG/CR has been updated to identify the 

correlated parameters. As part of the SOARCA study, numerous sensitivity studies were 

already completed. These sensitivity studies have informed the selection of important 

parameters and definition of their distributions for this UA study. Additional selected separate 

sensitivity studies will be considered and used as necessary to provide insight. For example, 

sensitivity of results to the timing of key operator actions is one study that is planned separate 

from the integrated analysis (see response 18). 
D-11

17. Page 8

Comment: 

Pg. 41 of Appendix A, “Peach Bottom Integrated Analysis,” indicates that station blackout leads 

to loss of room cooling for the RCIC and HPCI corner rooms, and that the operators are directed 

to block open doors to these rooms to facilitate cross ventilation so as to slow the rate of room 

heat up. These actions were assumed to successfully prevent system isolation from high 

temperature for the maximum period of 4 hours of system operation. Thus there are two 

uncertain aspects to loss of room cooling: (1) the likelihood of successful operator action to 

block open the room doors; and (2) the likelihood that these actions prevent system isolation 

due to high temperature (note that apparently no modeling has been performed on the room 

heat up). Based on this, loss of room cooling should be considered as an uncertain parameter 

for the LTSBO uncertainty analysis.

Resolution: 

The operator action to block open doors is directed by the relevant procedure for the LTSBO 

conditions, so it is expected that the operators would perform this action. From Section 5.1 of 

NUREG/CR-7110 Volume 1: "One consequence of station blackout is the loss of cooling to the 

RCIC and HPCI corner rooms. Heat losses from system piping and equipment to the room 

atmosphere would cause these areas to overheat. In such an event, step H 5 of Special Event 

Procedure SE 11 is applicable. It directs operators to block open doors to these rooms and 

facilitate cross ventilation, which would slow the rate of room heat up. These actions are 

assumed to successfully prevent system isolation from high room temperature for the entire

period of system operation2

. Step H-6 of the procedure directs operators to defeat high torus 

temperature isolation signals for HPCI and RCIC (if operating). MELCOR calculations presented 

in Section 5.1.1 indicate these signals would not be received before the station batteries 

exhaust; therefore, these actions are not important for the LTSBO scenario.” 

While the loss of room cooling is not explicitly modeled or captured as a parameter in this UA 

study, battery duration, which is included as an uncertain parameter, is a good surrogate to 

capture the potential effect.

18. Page 9

Comment: 

For the unmitigated LTSBO sequence, operator actions credited are opening one SRV (1 hour) 

and taking manual control of RCIC (2 hours) and as described on page 43 of Appendix A 

maintaining water level at 5 in to 35 in (i.e., 16 ft above TAF). These actions are uncertain (or 

rather, the time at which these actions are taken is uncertain) and thus should be included on 

the list of uncertain parameters.

 

2 Heat loss from RCIC (or HPCI) systems to their enclosure corner rooms is not explicitly represented in the 

MELCOR model.
D-12

Resolution: 

As mentioned in the SOARCA documentation, a comprehensive human reliability assessment 

(HRA) was not conducted for operator actions. In the absence of an HRA, it is difficult to assign 

distributions to the timing of these two operator actions. Rather than include a distribution of 

times for these two operator actions in the integrated uncertainty analysis, we plan to explore 

the sensitivity of results to the timing of these two actions in a separate sensitivity study, 

planned to be documented in the UA NUREG/CR report.

19. Page 9

Comment: 

In the paragraph on Main steam line creep rupture area, should the uncertainty in main steam 

line temperature be considered?

Resolution: 

The main steam line structure temperature is calculated by the model and hence is not an 

uncertain input parameter. We consider the area of the rupture as an important uncertainty 

parameter. The rupture area is important because it affects containment response to MSL 

failure. Large areas generate relatively large pressure loads on the containment, and offer an 

opportunity for advancing the time of containment failure. The proposed SOARCA UA study 

considers the area of the rupture as an important uncertainty parameter because it relates to the 

more important factor of how we model flow to and through the MSL, and associated heat 

transfer to wall piping. After the October 2010 and December 2011 peer review meetings and 

feedback, we have re-assessed the distribution for the MSL rupture area. It is now skewed 

heavily to large open areas, with only a small residual probability (0.01) of an open area less 

than 10%.

In addition, uncertainty in the parameters affecting the calculated potential for creep is neglected 

in this assessment because prior experience (through sensitivity analyses) suggests the L-M 

damage index transitions from zero to values well above unity within a very short time. The L-M 

parameter is not likely to be very sensitive because once the MSL enters creep conditions, the 

progression is very fast from 0 to 1.

20. Page 9

Comment: 

Fuel failure criterion is an example of a parameter where there is lack of a basis for the 

characterization of the uncertainty (see general comment 1). The uncertainty proposed is not 

unreasonable, but some kind of basis is required, even if it is simply a qualitative discussion of 

how time at temperature can affect the various phenomena that impact fuel mechanical 

response as the fuel heats up.

Resolution: 

A technical basis has been added to Section 4.1.2 of the draft NUREG/CR report. See also 

response 4 above.
D-13

21. Page 9

Comment: 

Radial debris relocation time constants is another example of a parameter where there is no 

basis for the characterization of uncertainty. Also, there are two incomplete sentences at the 

bottom of this paragraph.

Resolution:

A technical basis has been added to Section 4.1.2 of the draft NUREG/CR report for this 

parameter and the editorial changes have been made.

The relocation time constant is meant to capture the rate of radial debris movement to the 

center and thus determine the time the debris moves to the lower plenum. This movement to the 

lower plenum then determines the time at which the lower plenum will fail. The distributions are 

based on expert judgment but are not based on TMI data since no data from TMI exists for 

radial debris relocation distribution. It is one of the few parameters to which a user has access 

to influence large scale movement and influences axial debris relocation as well. The time scale 

is a surrogate for the uncertainty in large scale movement. The range covers molten to solidus 

of core melt.

22. Page 9

Comment: 

Why is Zr oxidation fraction and amount of H2 generation not an uncertain parameter?

Resolution: 

Zr oxidation fraction is a calculated result of in-vessel core damage progression and is not an 

input parameter; it is principally a result of the Zr melt breakout temperature.

H2 generation is directly related to ZrO2 production and thus is also result and not an input 

parameter. Both results are saved in the UA analysis and will be available for investigation and 

potential inclusion in the final NUREG/CR discussion of the results.

23. Page 9

Comment: 

There should be a basis for the fraction of I2. There is a lot of R&D going on regarding iodine 

chemistry that could be consulted.
D-14

Resolution: 

The SOARCA team reviewed NUREG-14653 recommendations; however, NUREG-1465 is not 

considered the current 'best estimate' source for iodine and cesium chemical forms. PHEBUS 

experimental results have been reviewed and incorporated instead. The gaseous iodine 

fractions in Section 4.1.5 of the draft UA NUREG/CR report have been updated to reflect 

PHEBUS experimental results and provide justification for each fraction. These are 

summarized in Table 4.1-7 (formerly Table 4.1-5 in the October 2010 plan).

24. Page 9

Comment: 

Indication of the MACCS values would be useful for comparison with Tables 4.2‐3 and 4.2‐4.

Resolution: 

Tables 4.2-3 and 4.2-4 list the distributions selected for the MACCS shielding and inhalation and 

Early Health Effects parameters for this SOARCA UA study, respectively. 

25. Page 9

Comment: 

What uncertainty is Figure 4.2‐10 reflecting?

Table 4.2-10: dose threshold for what?

Resolution:

Figure 4.2-10 (in the October 2010 draft plan) is the uncertainty in the dose threshold parameter 

used in the MACCS model calculations for latent cancer fatality (LCF) risk. The dose threshold 

represents the threshold for a linear-threshold model (versus a LNT model), so that the LCF risk 

would be calculated only for those members of the population whose total dose exceeded the 

dose threshold. Note that this parameter has been removed in the updated uncertainty analysis 

plan and will no longer be sampled. Instead, the uncertainty analysis will use the same three 

dose models as the SOARCA study: LNT, “US background average threshold,” and “Health 

Physics Society” models. The exploration of this model uncertainty will not be integrated with 

the other UA parameters, i.e., these three models will not be sampled along with the MACCS

parameters. Rather, the three model results will be reported in parallel.

 

3 NUREG-1465 (1995) is under review and a proposal for revision is being considered.
D-15

26. Page 9 

Comment: 

The SOARCA report has 6 cohorts whereas Table 4.2‐8 has 5. Perhaps Cohort 6 (non‐

evacuating public) was left off, but is there not some likelihood that they will actually evacuate 

with some delay?

Resolution:

Cohort 6 (non-evacuating public) is ultimately relocated, but by definition does not evacuate. 

Therefore we do not sample this cohort for evacuation. 

27. Pages 8-9 

Editorial Comments: 

(1) There are significant editorial errors in the first report (UA Plan).

(2) Figure 4.1‐7 has the wrong title.

(3) The abscissa of Figure 4.1‐15 should be labeled (H2 mole fraction?).

Resolution:

(1).The plan has been updated and incorporated within the draft NUREG/CR report that will 

document this SOARCA UA study and results. This initial draft has undergone a single 

round of technical editing with formal technical editing and review planned prior to the final 

release.

(2).The Figure 4.1-7 caption is, "Cumulative distribution function of safety relief valve open area 

fraction after thermal seizure.” It has been corrected and is included in the latest draft 

NUREG/CR report of this SOARCA UA Study.

(3).Yes. The abscissa is hydrogen mole fraction for ignition. The caption is updated in the draft 

NUREG/CR report.
D-16

28. Pages 9-10 

Comments on the Draft NUREG/CR Report, “Evaluation of Distributions Representing 

Important Non-Site-Specific Parameters in Off-Site Consequences”: 

(1) The spread of dispersion estimates in Figures 2.47 through 2.54 are generally 1.5 to 2 

orders of magnitude, and X/Q generally goes as 1/σyσz. This spread is based on the 1995 – 

1998 expert data cited in the report (references 1 to 6). This spread seems too high based on 

what was learned from the more recent comparisons of MACCS predicted X/Q with the LLNL 

detailed model (maybe a factor of 2 – 3 different). Why not adjust the older, subjective expert 

data to reflect the more rigorous and recent LLNL comparison?

(2) To provide a comparison and sanity check on the correlations between dry deposition and 

wet deposition data, the deterministic particle velocity vs. particle size from the MACCS model 

should be displayed.

(3) There should be some discussion and possibly adjustment regarding the fact that ICRP 

indicates ~5x10‐4 fatality risk vs. ~1x10‐3 for the 0.5 quantile in Table 5.1.

(4) On page 89, what is the exposure time associated with the 100 Gy/hr?

(5) Figure 6.1 is puzzling. Expert A has 0.0 – 0.05 quantile threshold dose of about 80 rem and 

Expert I has ~300 rem (seems more like it to me). How can these two “experts” not be at least 

somewhat close on the 0.0 – 0.05 quantile for threshold dose if the problem was well‐posed and 

they are addressing the same problem? And how is it possible for ~0.8 Sv (80 rem) to cause an 

early fatality? Would this be for a non‐healthy person?"

Resolution:

It should be noted that these comments, while relevant to the SOARCA UA study, are not 

specific to the October 2010 draft plan reviewed by the peer review team. Responses to these 

comments on the Draft NUREG/CR Report, “Evaluation of Distributions Representing Important 

Non-Site-Specific Parameters in Off-Site Consequences” are included herein for completeness.

(1). The dispersion distributions have been updated, as documented in Section 4.2.6. 

(2). Through discussion with the peer reviewer, this comment was clarified to mean that the 

SOARCA estimate values should be displayed on the graphs showing the distribution. 

The graphs in Section 4.2.1 and Section 4.2.2 show the SOARCA estimate values.

(3). The ~5x10-4 latent cancer fatality risk is per rem, which corresponds to ~5x10-2 per Sievert. 

The mode of the expert distributions is ~7x10-2 and the mean is ~1x10-1, which are a better 

match to the ~5x10-2 per Sievert.

(4). The specified radiation rate is 100 Gy/hr. Table 6.1 provides a set of doses for thresholds, 

LD50s, etc. The dose divided by the dose rate would provide the exposure period for each 

of the doses in the table. The following errata in Table 6.1 will be fixed: the units were 

listed as Sv when they should have been Gy.

(5). There is indeed a large difference of opinion between Expert A and Expert I for this 

parameter. We are unsure of the basis for this difference. For the purposes of this 

SOARCA UA, the early health effects parameters are not expected to be exercised. In all 

of the demonstration and test cases run to date for the PB LTSBO, early health effects 

have not been observed. We will revisit this issue if early health effects appear in the 

SOARCA UA.
D-17

KEVIN O’KULA

December 22, 2010 SOARCA Peer Review Memorandum

29. Page 11

Comment: 

The set of consequence (MACCS analysis) uncertain parameters is appropriate considering 

their respective importance to the overall outcome. Of the set of eleven parameters to be 

included, i.e., dispersion parameters (σy and σz), washout model linear coefficient, deposition 

velocity, shielding parameters, early health effects, normal and hotspot relocation, evacuation 

delay and speed, ground shine, habitability, the three italicized parameters (deposition velocity, 

ground shine, and habitability) are expected to have large impacts (at least to this reviewer).

Resolution: 

The updated UA plan continues to include 10 of the 11 parameters identified in the October 

2010 draft plan. The habitability criterion is no longer included in the updated list of parameters. 

However, insights on the influence of the habitability criterion have been obtained through the 

UA demonstration and test cases that have been run, most recently with a sizable sample size 

of 263. We plan to include a discussion of the influence of the habitability criterion in an 

appendix to the UA NUREG/CR report, with a summary in the results section. The reason for 

removing it from the list of parameters is that the habitability criterion is a policy decision made 

by individual states, and hence may not be fully appropriate to make assumptions about what 

that decision may be as part of our study. This issue was discussed at the December 2012 

peer review meeting.

30. Page 11

Comment: 

Selection of Peach Bottom Unmitigated Long-Term Station Blackout (PB LTSBO) – This 

scenario is a reasonable choice to exercise appropriate parts of the source term – consequence 

methodology.

Resolution: 

The updated UA plan continues to use the PB unmitigated LTSBO as the chosen scenario.

31. Page 11

Comment: 

Bypassing a PIRT Process - Presentations and discussions made in March, and again in the 

October meetings noted that a PIRT process was not in the scope of work and subsequently, “a 

limited set of key parameters and their distributions was compiled that relies heavily on the best 

available data and expert judgment.” Given that the SOARCA uncertainty analysis will extend 

into the first half of CY2011, it is recommended that this position be revisited. In the long run, a 

targeted PIRT process would be a useful exercise to preclude inadvertent omission of 

parameters from the uncertainty analysis that later are deemed to be important. The PIRT 

process could be done in a short-term, expedited manner for both the source term phase and 

the consequence analysis phase, and documented as appendices to the final report.
D-18

Resolution:

The SOARCA project’s subject matter experts have invested additional thought since the draft 

October 2010 UA plan and peer review meeting. While a formal PIRT process was not used, the 

SOARCA models and results are supported by years of extensive study. The detailed SOARCA 

Peach Bottom model was the basis of the expert judgment from informed subject matter experts 

who identified the key parameters and distributions for this UA study. In addition, the SOARCA 

team was fortunate to have the independent review and advice of the SOARCA peer review 

committee through the meetings and memoranda in 2010, and limited review by non-SOARCA 

staff at SNL and NRC who have specialized expertise in particular subject areas. Thus, the 

SOARCA team believes the UA approach is sound, without an exhaustive PIRT, given this UA 

study's focus on the uncertainty in the SOARCA estimate calculation. Additional rationale has 

been added to the introductory material of section 4.0 of the draft NUREG/CR report outlining 

our approach and identification of the parameters for study in the SOARCA UA, within the scope 

of the study to investigate the key parameters that most influence the uncertainty within the 

SOARCA estimate results.

32. Page 12 

Comment: 

Model Uncertainty – The uncertainty analysis as described by the SNL-NRC SOARCA project 

team is a parameter uncertainty analysis. It would be very informative to explore the uncertainty 

of several model options, or whether refinements in a base model helped reduce uncertainty in 

the overall analysis. NUREG-1855, Volume 1, and Regulatory Guide 1.174 are useful 

approaches to guide these types of analysis. The two categories that are of particular interest 

are:

Refinement of Polar Grid in ATMOS –The previous polar coordinate grid model in MACCS

(Version 1.13.1) allowed 16 sectors. The new model in WinMACCS (V3.5.0 beta) uses 64, 

based on a suggestion made during the first round of SOARCA meetings in Albuquerque 

several years ago. It would be a valuable insight to understand if this helped reduce (1) the 

mean result; and (2) reduced uncertainty about the 50th percentile.

Latent health effect models – Four approaches have been applied in the SOARCA analysis 

for calculation of latent cancer fatality risk, LNT, ICRP 104 (truncation of 10 mrem/y), U.S. 

Background Average (truncation of 620 mrem/y), and the HPS (explanations provided in the 

SNL-NRC reports). It would be a significant milestone if a limited model uncertainty could be 

explored for LCF risk for both plants.

Resolution: 

Model sensitivity analyses or 'one-off' calculations of the type you propose can be very 

informative and will be explored as part of the SOARCA UA, though the scope is not defined 

yet. 

We currently do not have plans to further explore refinement of the polar grid in ATMOS, as 

comparisons completed as part of the SOARCA study showed that the refinement to 64 sectors 

did not make much difference to the mean result for latent health effects. This insight will be 

noted in the UA report.
D-19

As discussed with the peer review committee at the December 2011 meeting, the team’s 

updated UA approach includes reporting the results for the three dose models that are used in 

the SOARCA study: LNT, “US background average threshold,” and “Health Physics Society” 

models. The exploration of this model uncertainty will not be integrated with the other UA 

parameters, i.e., these three models will not be sampled along with the MACCS parameters. 

Rather, the three model results will be reported in parallel. This approach replaces the sampling 

of a dose threshold, which was a proposed parameter in the October 2010 draft UA plan. 

33. Page 12

Comment: 

Clarity of Discussion in Aleatory and Epistemic Uncertainty Results – This discussion is 

very good and needs to be repeated in summary at the end of the uncertainty analysis results. 

In addition, it is imperative that the study note an improvement in uncertainty with respect to 

results over earlier work, such as the Sandia Siting Study, and that is presented clearly without 

being hidden. If a comparison of overall uncertainty is not feasible, perhaps several important 

uncertain parameters can be compared in to what they were previously, then it would be key 

that these same parameters be compared.

Related Comment: 

With the work that has been presented to the Peer Review Group since 2009, and progress in 

research and analytical methods since the Sandia Siting Study, the improvement in uncertainty 

in severe accident consequences should be as important as the reduction in the quantitative 

mean values obtained for specific risk metrics. The clarity of this message is important and must 

be made apparent in the final uncertainty analysis report.

Resolution: 

The discussion of the UA results will summarize the concepts of aleatory and epistemic 

uncertainty with illustrations directly from the SOARCA UA results. A direct comparison to the 

Sandia Siting Study results would not be a feasible comparison because the same kind of 

aleatory and epistemic uncertainties were not included; although weather uncertainty was 

included. Discussion has been added in this draft NUREG/CR report comparing results to an 

earlier MACCS uncertainty analysis that was more similar to the scope of the current analysis.

34. Page 7

Comment: 

Definition of Uncertainty Analysis and Sensitivity Analysis – Section 3.2 of the Uncertainty 

Analysis plan contains two definitions, i.e., that of uncertainty analysis and sensitivity analysis, 

that ought to be rewritten in simpler English for the final report. Although this content was in the 

draft uncertainty analysis plan, there is still too much importance of this section to leave as it 

stands. The sentence reads: “Closely associated with the characterization of epistemic 

uncertainty provided by the probability space corresponding to EN3 and the answering of 

Question Q4 are the concepts of uncertainty analysis and sensitivity analysis, where uncertainty 

analysis designates the determination of the epistemic uncertainty in analysis results that 

derives from epistemic uncertainty in analysis inputs and sensitivity analysis designates the 

determination of the contribution of the epistemic uncertainty in individual analysis inputs to the 

epistemic uncertainty in analysis results.”
D-20

Resolution: 

The following clarification text has been added to Section 3.4: “The goal of uncertainty analysis 

is to determine the uncertainty in an analysis result that derives from the collective uncertainty in 

analysis inputs. In contrast, the goal of sensitivity analysis is to determine the extent to which 

the uncertainty in individual analysis inputs contributes to the uncertainty in an analysis result. 

Intuitively, sensitivity analysis corresponds to decomposing the uncertainty in a result into the 

fractional contributions of each uncertain input. Commonly used sensitivity analysis procedures 

include scatterplots, correlation coefficients, partial correlation coefficients, stepwise regression 

with raw or rank transformed data, and a number of other techniques. General references on 

uncertainty and sensitivity analysis include [1-6]. Example past uncertainty and sensitivity 

analyses include studies of the MAEROS component of MELCOR model system for reactor 

accidents [7; 8] and the MACCS model system for off-site consequences of reactor accidents 

[9-13].” This draft discussion is likely to be clarified further into simpler English during technical 

editing prior to publication. Because it is at the same time important to maintain the technical 

clarity and rigor supporting the mathematical approach, the detailed discussion in Section 3.0 

may be moved to an appendix.

35. Page 12

Comment: 

Section 2.4 Description of the Probabilistic Analysis Methodology for SOARCA - This 

information, while useful, should be published as an appendix in the final report.

Resolution: 

The draft NUREG/CR document for the SOARCA UA has been reorganized. The material in 

question has been partitioned between two new sections, Sections 3.3 and 3.4. Additionally, a 

summary version is planned to replace the detailed discussion and the detailed discussion will 

be moved to an appendix.

36. Page 12

Comment: 

Percentile Bounds on Work – The briefing in October from Patrick Mattie noted that 25th/75th

percentile bounds would be used on the CCDFs using the bootstrap method. There may have 

been a simple explanation for this set of bracketing bounds given during the discussion, such as 

a requirement on the number of simulations, or other limiting factor, but I don’t recall it and the 

more common set of bounds are 5th and 95th. 

Resolution: 

A confidence interval will be estimated using bootstrap methods. The validity and quality of the 

confidence interval depends on the original sample size. If the sample size in consideration is 

relatively small (as it was in the spring 2010 UA demonstration case) then it could be misleading 

to estimate a 90% confidence interval. For example, for a sample of size 50, quantiles q=0.05 

and q=0.95 would be estimated by the bottom and top 2 values respectively. If the distribution is 

skewed and covers a large range, this estimate may not be accurate. Therefore, the confidence 

interval quantile values that can be supported are based on the sample size and the 

consideration that a Monte Carlo sample has an accuracy of 1/sqrt(n) where n represents the 

sample size. The proposed sample size of n=300 for this UA, would be sufficient for the 5th and 

95th percentile bounds.
D-21

37. Page 12-13 

Comment:

Table and Figure Discussion – The importance of weather trials in the MACCS sampling 

methodology is known but inclusion of this term as an uncertainty parameter in Table 2.2-1 is 

not explained although several comments are made throughout Section 2.2. Please clarify in the 

final report. Examples of scatterplots, SRCs/PCCs as a function of time, and illustration of 

failure of a sensitivity analysis are illustrated in Figures 3.2.1, 3.2.2, and 3.2.2, respectively, are 

provided with little if any explanation. While these are meant to be illustrative in the plan, if they 

are used in the final report, please include sufficient discussion as to what is being shown in the 

figure of interest.

Resolution: 

We acknowledge these deficiencies in the October 2010 draft, and will be adding explanatory 

text using the results of this study in the next version of the draft UA NUREG/CR report . These 

theoretical points will be easier to discuss in the presentation and discussion of UA analysis 

results, once they are available, in the UA NUREG/CR report.

38. Page 13 

Comment:

Version of codes being applied – Mattie’s presentation indicated the versions of MELCOR, 

MELGEN, and MACCS/WinMACCS being applied, but this is not documented consistently in 

the reports received to date. It is recommended that the final uncertainty analysis reports state 

directly the codes and versions being applied to support the final uncertainty study.

Resolution: 

The final version of the UA NUREG/CR report, Section 3.1, will include the specific codes and 

versions used in the study, consistent with the codes used in the SOARCA estimate 

calculations.
D-22

39. Page 13 

Comment:

General Comment on “Evaluation of Distributions Representing Important Non-Site Specific 

Parameters in Off-Site Consequence Analyses” and Implementation in SOARCA – The manner 

in which deposition velocities are input for the nine physicochemical groups used in the MACCS

Peach Bottom or Surry plant analysis is still unclear. Specifically, the manner in which each of 

the nine radionuclides groups is associated with a RDPSDIST00X bin and how the median 

diameter bins would be distributed for a given radionuclide group (example shown in Figure 1). 

While a brief discussion on this topic was given in the March briefing, this topic remains an issue 

because this SOARCA study apparently uses information from an updated expert elicitation, 

“Evaluation of Distributions Representing Important Non-Site-Specific Parameters in Off-Site 

Consequence Analysis”. Granted larger particle size deposition velocity will be site-independent 

and behavior should follow Stokes Law, the deposition velocity for smaller aerosol particle size 

groups (say for dp ≲ 1 μm) is site-dependent. This is because smaller particles will interact with 

regional ground cover such as the tree canopy and other vegetation. Consequently, field testing 

over forested sites typically shows higher deposition velocities compared to those with relatively 

little surface cover. Admittedly, this issue is perhaps a minor one for the SOARCA study as both 

sites are in the Eastern U.S. Nonetheless, a discussion on the specifics for implementation of 

final values of the deposition velocity by radionuclide bin should be provided in the final study as 

well as in the uncertainty analysis.

Resolution: 

The NUREG/CR report discussed, "Evaluation of Distributions Representing Important Non-Site 

Specific Parameters in Off-Site Consequence Analyses" will be referenced in the UA report as 

the technical basis for those parameters whose distributions are based on that report. The 

effect of the surface roughness parameter has been analyzed and presented in 

NUREG/CR-7110, Volume 1 of the SOARCA report. This analysis addresses effects of regional 

ground cover and deposition velocities. Furthermore, the uncertainties in deposition velocity 

and dispersion, which are included in this uncertainty analysis, should capture the overall 

influence of surface roughness on the results.
D-23

JOHN STEVENSON

December 22, 2010 SOARCA Peer Review Memorandum

40. Page 14

Comment:

I would like to comment on the text of Section 2.1 of the “Uncertainty Analysis Plan 

Recommended by SANDIA Technical Staff,” Draft dated 10/19/2010 which provides justification 

of the use of a seismic induced Station Beach Out, SBO as the scenario to be evaluated in the 

SOARCA as it relates to other NPP sites in the U.S. 

With respect to seismic being the greatest natural hazard, there are a few NPP sites in Florida 

and along the Gulf of Mexico coast where the potential for a LOCA associated with a Category 5 

hurricane and associated storm surge flooding may exceed the risk from an earthquake at the 

10‐6 to 10‐7/yr probability of exceedence level. Less than 10 percent of all NPP sites in the U.S. 

may be in this category leaving more than 90 percent of NPP sites being dominated by an 

earthquake.

With respect to those NPP sites dominated by earthquakes, perhaps 70 percent seismic 

induced SBO would dominate the risk of an unmitigated LOCA . The other 30 percent might be 

expected to be dominated by early containment failure as a result of seismic induced building 

foundation failure (i.e. liquification or consolidation) of the containment or adjacent structure 

foundation due to an earthquake at the 10‐6 or 10‐7/yr probability of exceedence level.

Resolution: 

The SOARCA analysis was completed for two pilot plants, Peach Bottom and Surry. Hence the 

analyses are specific to those two plants and sites. This UA study is also site-specific, plantspecific, and scenario-specific since it analyzes uncertainty in the model parameters in the longterm station blackout scenario for the Peach Bottom plant. As previously discussed, the 

appropriateness of applying individual SOARCA insights to other plants and sites should be 

evaluated on a case-by-case basis. 
D-24

41. Page 14

Comment: 

I am also providing comments relative to the one and half day meeting held at NRC offices 26 

and 27 October 2010. Again, the selected scenario for the limiting event discussed at the 

meeting was an extremely low probability of exceedence seismic event (i.e. less than 10‐6 or 

10-7/yr probability of exceedence earthquake) causing a Station Blackout. This event would be 

applicable to most of the 70 plus NPP sites in the U.S., but as discussed in response to the 

SANDIA Uncertainty proposal, there are several sites where the wind and storm surge coming 

from a Level 5 hurricane would be at least as likely to cause an SBO as an earthquake 0.4 to 

0.5g peak ground acceleration, pga for these sites at the 10‐6 or 10‐7/yr probability of 

exceedence level. In a significant number of other NPP sites I believe such as is the case of the 

Surry NPP a 0.8 to 1.0g pga earthquake typical of a 10‐6 to 10‐7/yr probability of exceedence 

level would more likely lead to an immediate gross loss of the containment leak tight integrity at 

penetrations resulting from differential settlement caused by foundation soil liquification or 

consolidation between the containment and adjacent safety related structures than would be 

caused by a longer term SBO.

Resolution:

The potential soil liquefaction issue was further evaluated for the Surry SOARCA report, and 

additional discussion is being added to the SOARCA report. This SOARCA UA study is specific 

to the Peach Bottom plant. Please see resolution to comment 40 above. 
D-25

KAREN VIEROW

December 22, 2010 SOARCA Peer Review Memorandum

42. Page 15

Comment: 

Similar to the SOARCA project, which was initially intended to evaluate a larger number of 

reactors than turned out to be feasible with the given time and resource restraints, the SOARCA 

Uncertainty Analysis effort must be justified as reasonable within the given programmatic 

restraints. Further, the sufficiency, or completeness, of the effort must be demonstrated.

A full level III PRA for each SOARCA scenario would require time and resources far beyond 

those which are available. The current effort will include one scenario for one reactor as a 

reasonable substitution approach. This approach has the merits of including establishment of 

the methodology for future Uncertainty Analyses and of allowing for depth of evaluation of the 

selected scenario. The definitions and detailed description of the methodologies in Section 2.4 

are very helpful.

The case for completeness of the Peach Bottom Long Term Station Blackout Scenario must be 

made. That is, even though some low probability or low consequence aspects may be omitted, 

the high risk outcomes must be included.

Resolution: 

The final NUREG/CR report for the UA study will include a more detailed justification of the 

scenario selection in Section 2.1, as well as more clarity in the intended objectives of the 

analysis. The SOARCA analysis evaluated the consequences of the most likely and important 

event sequences and current estimate inputs for the Peach Bottom and Surry sites. Thus the 

fundamental objective of this SOARCA uncertainty study is to quantify how uncertainty in the 

variation of the input parameters (e.g., in the selected SOARCA estimate values) affects the 

calculated consequences (e.g., source term releases and latent cancer fatality risk). 

This systematic look at the uncertainty in the system, as detailed in Section 2.3, provides for the 

quantification of the confidence in the SOARCA result for one scenario in detail, as well as 

some useful insights for the SOARCA results in general. In addition, the uncertainty in the 

response can be quantified as a function of the uncertainty in the inputs. Section 3.0 of the Draft 

NUREG/CR outlines this in greater detail. Consideration of the low and high consequence 

results (e.g., variance) will be included with the discussion of the results of the UA study in the 

final UA NUREG/CR report. Through the integrated inclusion of uncertainty in important 

MELCOR and MACCS parameters, we expect to capture any potential high-risk outcomes 

(conditional on the scenario) that may be supported by the underlying distributions of uncertain 

parameters. This theoretical point will be easier to discuss in the presentation and discussion of 

UA analysis results, once they are available, in the UA NUREG/CR report. 
D-26

43. Page 15

Comment: 

The approach to not consider cross-correlation between uncertainty parameters needs to be 

justified or modified.

Resolution: 

As suggested by peer reviewers during the October 2010 meeting, the SOARCA team carefully 

deliberated on which MELCOR parameters should be correlated (MACCS parameter 

correlations were already included in the October 2010 draft UA plan). In addition, since the 

October 2010 meeting, the SOARCA team developed the capability to correlate input 

parameters in MELCOR. Appropriate correlations were identified and are now included for 

MELCOR parameters. Section 4.0 of the draft NUREG/CR has been updated to identify the 

correlated parameters.

44. Page 15

Comment: 

Several sections of the report describe the aspects of the Uncertainty Analysis effort but do not 

close the loop by relating these to the SOARCA Uncertainty Analysis objectives. Examples: - 

Section 2.3: the type of uncertainties targeted (aleatory and/or epistemic) should be stated up 

front.

- Section 2.3: How this approach enables one to validate the Best Estimate SOARCA 

calculations should be explained.

Resolution: 

Section 2.2 has been updated to identify up front the uncertainty classification (epistemic or 

aleatory) selected for the study. In addition, the updated Section 2.3 contains some additional 

rationale for, and clarification of, the objectives of this study.

45. Page 15

Comment: 

Section 2.1, item 5: consider rewording the “fewer failed MELCOR simulations” as this implied 

doubt about the robustness of the MELCOR code.

Resolution: 

We are in the process of rewriting Section 2.1 of the draft NUREG/CR report to provide more 

thorough justification and background discussion for the selection of the PB LTSBO scenario for 

this study. The note on “fewer failed MELCOR simulations” has been deleted. That is no longer 

an issue, as the mechanics of the uncertainty engine execution have improved since October 

2010. In addition, the robustness of the uncertainty calculation will be discussed in the results 

portion of the document.
D-27

46. Page 15

Comment: 

Section 3.2, 1st sentence: This sentence seems essential to the report, however, this review is 

confused over the meaning. Please reword.

Resolution: 

The draft NUREG/CR report has been reorganized to enhance the clarity of this discussion. 

While minor changes to the 1st sentence were made (now in Section 3.4), moving the discussion 

from Section 2.4 "Probabilistic Analysis Methodology" of the October UA draft Plan document to 

Section 3.3 of the draft NUREG/CR immediately preceding Section 3.4 (which is the section in 

question), should have a substantial benefit in adding clarity to the discussion.

47. Page 15

Comment: 

Many sections of the report need better documentation of their justification, such as the 

selection of uncertainty parameters and/or their distributions. Under recommendation 2, the 

solicitation of these data from “senior SNL and NRC technical staff...” is needed to clarify that 

the effort is less than exhaustive due to programmatic constraints. However, also needed is an 

explanation that the value of the current effort is not compromised.

Resolution: 

Section 4.0 of the draft NUREG/CR report has been expanded to include the technical basis 

and justification of the key parameters and distributions selected for the SOARCA UA study. 

While a formal PIRT process was not used, the SOARCA models and results are supported by 

years of extensive study. The detailed SOARCA Peach Bottom model was the basis of the 

expert judgment from informed subject matter experts who identified the key parameters and 

distributions for this UA study. In addition, the SOARCA team was fortunate to have the 

independent review and advice of the SOARCA peer review committee through the meetings 

and memoranda in 2010, and limited review by non-SOARCA staff at SNL and NRC who have 

specialized expertise in particular subject areas. Thus, the SOARCA team believes the UA 

approach is sound given this UA study's focus on the uncertainty in the SOARCA estimate 

calculation. In addition, the introductory material to Section 4.0 has been updated to document 

the approach used.
D-28

JACQUELYN YANCH

December 22, 2010 SOARCA Peer Review Memorandum

48. Page 16

Comment: 

The main health impact of the severe reactor accident is predicted to be latent cancer fatalities. 

The main source of uncertainty associated with estimating the number of latent cancer fatalities 

arises from taking risk estimates originally generated for a situation involving rapid radiation 

exposure of people (total dose delivered in ≤ 1 minute) and applying these risk estimates to the 

post‐reactor accident scenario where the total dose is delivered over a period of years to 

decades.

The SOARCA team plans to generate distributions to represent uncertainty in risk estimates in 

collaboration with Dr. Keith Eckerman. Their second (fallback) option [N. Bixler presentation, 

October 2010] is to use the spread of risk estimates generated via expert solicitation 

[NUREG/CR-6555, 1997] to represent uncertainty. Since the experts in this solicitation were 

asked to supply estimates of risk of a large dose (1 Gy) delivered rapidly (1 min), a dose rate 

effectiveness factor (DREF) must be used in order to make the risk estimates applicable to the 

prolonged exposure situation. The SOARCA team uses a value of 2 for the DREF and plans to 

sample this value, for determination of uncertainty, from a distribution provided by the EPA 

[EPA 402‐R‐99‐003, 1999]. In my opinion the distribution function provided by the EPA is not 

applicable to the situation involving very prolonged exposures and a broader range of DREF 

values should be included in the uncertainty estimation.

In reviewing available data, the National Council on Radiation Protection and Measurements 

(NCRP) reports that the DREF depends very significantly on the duration of the radiation 

exposure [NCRP 64, 1980]. Short‐term exposures, such as those representative of typical 

occupational radiation scenarios, require a smaller value of DREF than long term exposures 

such as those lasting years or decades. Since the radiation exposure represented by returning 

home to elevated radiation levels following a severe reactor accident involves years or decades 

of exposure, a DREF appropriate to this scenario should be used. This value, according to 

NCRP 64, ranges from 6.6 to 12.8 with a best estimate of 10. However, the distribution function 

of DREF values provided by the EPA peaks at a value of 2 and the probability of sampling a 

value of 10, the most likely applicable value for the post‐accident scenario, is vanishingly small. 

Thus, while the EPA distribution may be relevant to the rapid exposure scenario (e.g., 

occupational radiation protection) it is not very relevant to the situation discussed here. This is 

echoed in BEIR V where it is stated that higher values of DREF reflect situations involving 

continuous irradiation until death. Therefore, in discussions with Dr. Eckerman, it is important 

that the more realistic DREF values be included in the estimate of uncertainty associated with

latent cancer fatalities.

Resolution: 

Since the October 2010 draft UA plan and peer review committee meeting, Dr. Keith Eckerman 

has provided recommendations to the SOARCA team on health effects parameters and 

distributions to include in the SOARCA UA. Dr. Eckerman’s recommendations have been 

incorporated into section 4.2.5 of the draft UA NUREG/CR report. The variables that have been 

added to the updated plan include: (1) DDREFA, (2) uncertainty in the energy deposited within 

a human organ for a specified incident radiation using a multiplicative factor for GSHFAC ,and 
D-29

(3) uncertainty in the risk coefficients for each of the organs included in the SOARCA analyses 

for latent health effects.

For the DDREFA distribution, Dr. Eckerman’s recommendations are based on Federal 

Guidance 13 (FGR 13), which the SOARCA team accepted. The NCRP 64 DREF values cited 

in the comment are based on animal studies. the final chapter of NCRP 64, Chapter 12 entitled 

"Summarizing Arguments; DREF Values", on page 174 states: "It follows from the indicated 

range of DDREFA values that if the linear hypothesis is applied to data on radiation effects 

observed in human beings obtained at high dose and dose rates, the resultant risk coefficient 

would be expected to overestimate the most realistic or correction value, for either single 

exposure to low doses or exposure to high doses delivered at low-dose rates, by a factor of 

between 2 and 10."

NCRP Report 64 was issued in April 1980 and in 1997 NCRP issued Report 126. Chapter 6 of 

that report entitled "Extrapolation to Low Dose or Dose Rate" reviews application of DREF and 

notes the NCRP position taken in Report 116 issued in 1993. On page 64 it states "The choice 

of DREF is somewhat arbitrary and the NCRP considered that it could reasonably range 

between two and three." The report then speaks to the uncertainty in the application of the 

DDREFA and suggest use of a piecewise linear distribution, peaked at 2.0 and spanning the 

interval from 1 to 5. 

The current NCRP position on DDREFA seems to be reasonable consistent across Reports 64, 

116 and 126 however the uncertainty domain has decreased over the last 30 years. The 

DDREFA assumed in FGR 13 and used in the SOARCA Project and its uncertainty distribution 

are consistent with current positions of NCRP, ICRP, and National Academy of Science BEIR 

reports.

49. Page 16

Comment: 

Uncertainty in the shape of the risk/dose model also exists. This uncertainty is accounted for in 

the current SOARCA approach of incorporating different threshold values below which no 

cancer fatalities would be observed.

Resolution: 

As discussed with the peer review committee at the December 2012 meeting, the team’s 

updated UA plan includes reporting the results for the three dose models that are used in the 

SOARCA study, in short-hand: LNT, “US background average threshold”, and “Health Physics 

Society” models. The exploration of this model uncertainty will not be integrated with the other 

UA parameters, i.e., these three models will not be sampled along with the MACCS parameters. 

Rather, the three model results will be reported in parallel. This approach replaces the sampling 

of a dose threshold, which was a proposed parameter in the October 2010 draft UA plan.
D-30

April 9, 2010 SOARCA Peer Review Memorandum, “Guidance on the SOARCA 

Uncertainty Quantification and Sensitivity Analysis”

50. Page 1

Comment: 

Of the two methods presented for quantifying uncertainty, the “Inner” Weather Loop method is 

the appropriate method for evaluating the SOARCA results and for comparing with the previous 

NRC studies. A few sequence results should be explored through the “Outer” Weather Loop 

method to illustrate the influence of uncertainty in weather conditions at the time of the release. 

The inner loop method preserves the perspective that the SOARCA source term is smaller and 

later in release to the environment than source terms used in previous risk work. In this manner, 

the modeling advancements and new insights from experimental testing of the past twenty 

years are reflected. The outer loop method provides results that are more influenced by the 

effects of site-specific weather. While the impact of site weather is important, it will statistically 

change little from year to year, and is not changeable through any SOARCA-based 

understanding or insights. Therefore, the inner loop method should better suit the objectives of 

the SOARCA project in discerning improved understanding of the risk from Nuclear Power Plant 

operation. The outer loop, however, provides a mechanism for looking at more limiting weather 

conditions. By performing a limited number of sensitivity analyses with the outer loop method in 

addition to analyses by the inner loop method, the SOARCA project can provide some insights 

when considering the uncertainty of both the source term and the weather.

Resolution: 

The inner loop approach was selected as the appropriate approach for the SOARCA UA as 

documented in the Draft UA Plan (October 2010) presented to the peer review committee on 

10/26/2010.

51. Page 2

Comment: 

The Uncertainty Quantification and Sensitivity Analysis study is essential to the credibility of the 

SOARCA project and should be documented as part of the SOARCA NUREG report, or as a 

stand-alone supporting reference.

Resolution: 

The SOARCA UA will be documented in a separate NUREG/CR report. At a minimum, a draft 

of the UA report is expected to be published at the same that the final SOARCA reports 

(Summary and Peach Bottom and Surry detailed analyses) are published. 
D-31

52. Page 2

Comment: 

The Uncertainty Quantification study is in its early stages of planning and was not available for 

Committee review. Nonetheless, the uncertainty analysis is an integral part of the SOARCA 

project, and the analysis could be regarded as incomplete if there is not an attempt to address 

uncertainty. The members of the Peer Review Committee concurring with this memo request 

the opportunity to review the uncertainty quantification effort. Parameter selection and 

parameter distributions require particular care. Updates as well as the final set to be used in the 

Uncertainty Quantification study are requested.

Resolution: 

The SOARCA Draft UA Plan (October 2010) was presented to the peer review committee in 

October 2010. Comments were received from the committee in December 2010. A short 

update was presented to the committee on 12/7/11. A teleconference is scheduled in 

January 2012 to discuss resolution of peer review comments and the final parameters and 

distributions used in the study. The UA plan (which is now documented in the draft UA 

NUREG/CR report) has been and continues to be updated in response to peer reviewers’ 

comments.
D-32

Advisory Committee on Reactor Safeguards Comment Resolution 

Uncertainty Analysis Plan

The purpose of this section is to document the SOARCA team’s resolution of each written 

comment related to the uncertainty analysis (UA) plan in the May 15, 2012 letter report of the 

NRC’s Advisory Committee on Reactor Safeguards [D1, D2]. Comments are extracted directly 

from the letter report with no changes.

Comment: 

The selection of parameters, their uncertainty distributions, and their correlations―as well as 

sensitivity studies to assess the impact of uncertainties that are difficult to quantify―are critical 

to the Peach Bottom and Surry uncertainty analyses. The uncertainty reports should describe 

the approaches used to identify the parameters, distributions, and sensitivity studies and justify 

the bases for omission of parameters or effects of interest not addressed in the uncertainty 

analyses. (p. 1)

The selection of parameters, their uncertainty distributions, and their correlations, as well as 

sensitivity studies to assess the impact of uncertainties that are difficult to quantify, are critical to 

the uncertainty analysis. The approach used to identify these parameters is not clear. In Section 

2.2 of the draft NUREG/CR report on uncertainty analysis, it is stated that “the approach is 

based on a formalized PIRT (phenomena identification, and ranking table) process,” while in 

Section 4 it is stated that the “uncertain parameters and their distributions were 

identified/characterized through an informal elicitation of subject matter experts.” The report 

should be consistent and accurate in its description of the approach used to identify the 

parameters and distributions and the selection of sensitivity studies. (p.5)

Resolution: 

The staff enhanced the documentation in Sections 2 and 4 of this NUREG/CR report to better 

describe the approaches for identifying parameters and distributions and parameters and effects 

not treated in the integrated UA. In addition, the UA team added section 4.3 to discuss some 

phenomena of interest that were not addressed in the uncertainty analysis.
D-33

Comment: 

There are a number of physical processes involved during in-vessel and ex-vessel accident 

progression where uncertainties are large. Not all of these uncertainties can be represented by 

parameter distributions. One way to address such phenomenological uncertainties is sensitivity 

analyses for alternative models. For example, one area of uncertainty identified by the Peer 

Review Committee that the staff may have not explored sufficiently is lower head failure. 

MELCOR focuses on creep rupture as the dominant mechanism for lower head failure. The staff 

argues that this approach is supported by experimental results in NUREG/CR-5582, which were 

performed on one-fifth scale models representing PWR heads. They also argue that the timing 

differences between gross lower head failure and penetration failure with the available 

penetration model are not significant to the overall accident progression. The staff also notes 

that the penetration model is a simple lumped parameter model for bulk heat transfer and is not 

adequate to calculate molten material drainage into a BWR reactor pressure vessel drain line. 

More detailed analyses in NUREG/CR-5642 suggest that in certain scenarios failure of this 

penetration is more important than failure of other lower head penetrations or the vessel. 

Sensitivity studies could help to evaluate whether earlier failure of the drain line would have a 

significant impact on outcomes. (p. 6)

Resolution: 

Staff added a sensitivity study of an alternate lower head failure mode in the MELCOR model, 

documented in Section 6.4.2.

References

[D1.] U.S. Nuclear Regulatory Commission, Advisory Committee on Reactor Safeguards, 

“State-of-the-Art Reactor Consequence Analyses (SOARCA) Project May 15, 2012 letter 

report,” ML12135A385, Washington D.C., 2012.

[D2.] U.S. Nuclear Regulatory Commission, “Staff Response to the Advisory Committee on 

Reactor Safeguards (ACRS) May 15, 2012, memorandum, SUBJECT: State-of-the-Art 

Reactor Consequence Analyses (SOARCA) Project,” ML12158A178, Washington D.C., 

2012.

APPENDIX E

ADDITIONAL INFORMATION AND ANALYSES IN RESPONSE TO ACRS 

QUESTIONS

E-1 

APPENDIX E – TABLE OF CONTENTS

Section Page

E.1 Motivation................................................................................................ E-8 

E.2 Discussion of MACCS Results................................................................. E-11

E.3 Selection of the Three Representative MELCOR Realizations........................ E-15

E.3.1 INTRODUCTION................................................................................. E-15

E.3.2 METHODOLOGY................................................................................ E-15 

E.3.3 SELECTION OF THE WEIGHT............................................................... E-16

E.3.4 CHECKING OF RESULTS.................................................................... E-16 

E.3.5 USE OF THE EXCEL WORKBOOK........................................................ E-17 

E.3.6 Results............................................................................................. E-20

E.4 Weather Uncertainty & MACCS Convergence............................................ E-21 

E.5 Conditional Mean, Individual LCF Risk and Prompt Fatality Risk Results 

& Model Convergence.............................................................................. E-29

E.6 SOARCA Uncertainty Analysis Results for Conditional Individual LCF Risk.... E-45 

E.7 Stability Analysis Using Bootstrap Approach............................................. E-47 

E.7.1 Low, Medium, & High Source Term Combined Analysis.............................. E-56 

E.7.2 Bootstrap Comparison......................................................................... E-58

E.8 MELCOR Parameters............................................................................... E-65 

E.8.1 Question 5.a.I – SRVLAM..................................................................... E-65 

E.8.2 Question 5.a.II – CHEMFORM............................................................... E-66 

E.8.3 Question 5.a.III – FL904A..................................................................... E-68 

E.8.4 Question 5.a.IV – BATTDUR................................................................. E-69

E.8.5 Question 5.a.V – SRVOAFRAC............................................................. E-69

E.8.6 Question 5.a.VI – SLCRFRAC............................................................... E-70 

E.8.7 Question 5.a.VII – RDMTC and RDSTC................................................... E-71 

E.8.8 Question 5.a.VIII – RRIDRFRAC and RODRFRAC.................................... E-72 

E.8.9 Question 5.a.X – RHONOM.................................................................. E-72 

E.8.10 Question 5.a.XI – FFC......................................................................... E-72 

E.8.11 Question 5.a.XII – SC1141(2)................................................................ E-73 

E.9 MACCS Parameters................................................................................ E-73 

E.9.1 Question 5.b.I and 5.b.II – DOSNRM, TIMNRM, DOSHOT, and TIMHOT....... E-73 

E.9.2 Question 5.b.III – ESPEED................................................................... E-74 

E.9.3 Question 5.b.IV – GSHFAC................................................................... E-76 

E.10 Other Issues........................................................................................... E-77

E.10.1 Question 6.a – Surrogate Parameters.................................................... E-77

E.10.2 Question 6.b – Lower Head Penetration Failures...................................... E-77

E.10.3 Question 6.c – Drywell Liner Failure...................................................... E-78

E.10.4 Question 6.d – Operator Actions........................................................... E-79

E.11 References............................................................................................. E-80 
E-2 

APPENDIX E – LIST OF FIGURES

 Figure Page

Figure E-1 Run 1 Conditional Mean, Individual LCF Risk (per Event) CCDF for all 

Radial Distances Considered......................................................... E-13

Figure E-2 Run 2 Conditional Mean, Individual LCF Risk (per Event) CCDF for all 

Radial Distances Considered......................................................... E-14

Figure E-3 Example of CDFs Comparison in Linear Scale (left) and Semi-log Scale 

(right)........................................................................................ E-17

Figure E-4 Example of Cobweb Plot Result..................................................... E-18

Figure E-5 Screenshot of Data Sheet in the Excel Workbook............................ E-19

Figure E-6 Screenshot of Main Sheet of Excel Workbook................................. E-20

Figure E-7 Cobweb Graph for Selected Source Terms...................................... E-21

Figure E-8 Run 6-8 Combined Aleatory and Epistemic Uncertainty Conditional 

Individual LCF Risk (per Event) CCDF for the Radial Distances 

Considered................................................................................ E-23

Figure E-9 Run 3 Combined Aleatory and Epistemic Uncertainty Conditional 

Individual LCF Risk (per Event) CCDF and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual LCF Risk (per Event) CCDF for the Radial 

Distances Considered................................................................. E-24

Figure E-10 Run 6 Combined Aleatory and Epistemic Uncertainty Conditional 

Individual LCF Risk (per Event) CCDF and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual LCF Risk (per Event) CCDF for the Radial 

Distances Considered................................................................. E-25

Figure E-11 Run 9 Combined Aleatory and Epistemic Uncertainty Conditional 

Individual LCF Risk (per Event) CCDF and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual LCF Risk (per Event) CCDF for the Radial 

Distances Considered................................................................. E-26

Figure E-12 Run 12 Combined Aleatory and Epistemic Uncertainty Conditional 

Individual LCF Risk (per Event) CCDF and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual LCF Risk (per Event) CCDF for the Radial 

Distances Considered................................................................. E-27

Figure E-13 Run 15 Combined Aleatory and Epistemic Uncertainty Conditional 

Individual LCF Risk (per Event) CCDF and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual LCF Risk (per Event) CCDF for the Radial 

Distances Considered................................................................. E-28

Figure E-14 Runs 3-5 Epistemic Uncertainty Conditional, Mean, Individual LCF Risk 

(per Event) CCDFs and Run 1 Epistemic Uncertainty Conditional, Mean 

Individual LCF Risk (per Event) CCDF for the Radial Distances 

Considered................................................................................ E-33

Figure E-15 Runs 6-8 Epistemic Uncertainty Conditional, Mean, Individual LCF Risk 

(per Event) CCDFs and Run 1 Epistemic Uncertainty Conditional, Mean 

Individual LCF Risk (per Event) CCDF for the Radial Distances 

Considered................................................................................ E-34
E-3 

Figure E-16 Runs 9-11 Epistemic Uncertainty Conditional, Mean, Individual LCF 

Risk (per Event) CCDFs and Run 1 Epistemic Uncertainty Conditional, 

Mean Individual LCF Risk (per Event) CCDF for the Radial Distances 

Considered................................................................................ E-35

Figure E-17 Runs 12-14 Epistemic Uncertainty Conditional, Mean, Individual LCF 

Risk (per Event) CCDFs and Run 1 Epistemic Uncertainty Conditional, 

Mean Individual LCF Risk (per Event) CCDF for the Radial Distances 

Considered................................................................................. E-36

Figure E-18 Runs 15-17 Epistemic Uncertainty Conditional, Mean, Individual LCF 

Risk (per Event) CCDFs and Run 1 Epistemic Uncertainty Conditional, 

Mean Individual LCF Risk (per Event) CCDF for the Radial Distances 

Considered............................................................................... E-37

Figure E-19 Runs 3-5 Epistemic Uncertainty Conditional, Mean, Individual Prompt 

Fatality Risk (per Event) CCDFs and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual Prompt Fatality Risk (per Event) CCDF for 

the Radial Distances Considered.................................................. E-41

Figure E-20 Runs 6-8 Epistemic Uncertainty Conditional, Mean, Individual Prompt 

Fatality Risk (per Event) CCDFs and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual Prompt Fatality Risk (per Event) CCDF for 

the Radial Distances Considered.................................................. E-42

Figure E-21 Runs 9-11 Epistemic Uncertainty Conditional, Mean, Individual Prompt 

Fatality Risk (per Event) CCDFs and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual Prompt Fatality Risk (per Event) CCDF for 

the Radial Distances Considered.................................................. E-43

Figure E-22 Runs 12-14 Epistemic Uncertainty Conditional, Mean, Individual Prompt 

Fatality Risk (per Event) CCDFs and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual Prompt Fatality Risk (per Event) CCDF for 

the Radial Distances Considered................................................... E-44

Figure E-23 Runs 15-17 Epistemic Uncertainty Conditional, Mean, Individual Prompt 

Fatality Risk (per Event) CCDFs and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual Prompt Fatality Risk (per Event) CCDF for 

the Radial Distances Considered.................................................. E-45

Figure E-24 Run 1 Combined Aleatory and Epistemic Uncertainty Conditional 

Individual LCF Risk (per Event) CCDF and Run 1 Epistemic Uncertainty 

Conditional, Mean, Individual LCF Risk (per Event) CCDF for the Radial 

Distances Considered................................................................. E-46

Figure E-25 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 

15 with SRS and 95% Confidence Interval Upper and Lower Bounds for 

Runs 16 & 17 with SRS................................................................ E-48 

Figure E-26 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 

16 with SRS and 95% Confidence Interval Upper and Lower Bounds for 

Runs 15 & 17 with SRS................................................................ E-49

Figure E-27 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 

17 with SRS and 95% Confidence Interval Upper and Lower Bounds for 

Runs 15 & 16 with SRS................................................................ E-49
E-4 

Figure E-28 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 

15 with SRS and 95% Confidence Interval Upper and Lower Bounds for 

Runs 16 & 17 with SRS................................................................ E-50 

Figure E-29 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 

16 with SRS and 95% Confidence Interval Upper and Lower Bounds for 

Runs 15 & 17 with SRS................................................................ E-50 

Figure E-30 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 

17 with SRS and 95% Confidence Interval Upper and Lower Bounds for 

Runs 15 & 16 with SRS................................................................ E-51 

Figure E-31 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for 

Runs 15-17 with SRS and the Density Function for Run 15 with SRS..... E-51 

Figure E-32 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for 

Runs 15-17 with SRS and the Density Function for Run 15 with SRS..... E-52 

Figure E-33 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 

15 with LHS and 95% Confidence Interval Upper and Lower Bounds for 

Runs 16 & 17 with LHS................................................................. E-52 

Figure E-34 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 

16 with LHS and 95% Confidence Interval Upper and Lower Bounds for 

Runs 15 & 17 with LHS................................................................. E-53 

Figure E-35 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 

17 with LHS and 95% Confidence Interval Upper and Lower Bounds for 

Runs 15 & 16 with LHS................................................................. E-53 

Figure E-36 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for 

Run 15 with LHS and 95% Confidence Interval Upper and Lower 

Bounds for Runs 16 & 17 with LHS................................................. E-54 

Figure E-37 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 

16 with LHS and 95% Confidence Interval Upper and Lower Bounds for 

Runs 15 & 17 with LHS................................................................. E-54 

Figure E-38 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 

17 with LHS and 95% Confidence Interval Upper and Lower Bounds for 

Runs 15 & 16 with LHS................................................................ E-55 

Figure E-39 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for 

Runs 15-17 with LHS and the Density Function for Run 15 with LHS.... E-55 

Figure E-40 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for 

Runs 15-17 with LHS and the Density Function for Run 15 with LHS.... E-56 

Figure E-41 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for 

Low, Medium, and High Source Terms with LHS and the Conditional, 

Mean, Individual LCF Risk (per Event) CDF for the SOARCA UA with 

LHS Sampling........................................................................... E-57 

Figure E-42 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for 

Low, Medium, and High Source Terms with LHS and the Conditional, 

Mean, Individual LCF Risk (per Event) CDF for the SOARCA UA with 

LHS Sampling.......................................................................... E-58 
E-5 

Figure E-43 CAP17 Conditional, Mean, Individual LCF Risk (per Event) CCDF with 

LHS and MC Sampling for the Radial Distances Considered........... E-60 

Figure E-44 CAP17 Conditional, Mean, Individual Prompt Fatality Risk (per Event) 

CCDF with LHS and MC Sampling for the Radial Distances Considered. E-62 

Figure E-45 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for 

CAP17, CAP40, and 95% Confidence Interval Upper and Lower Bounds 

for CAP17 and CAP40.................................................................. E-63 

Figure E-46 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for 

CAP17, CAP40, and 95% Confidence Interval Upper and Lower Bounds 

for CAP17 and CAP40.................................................................. E-63 

Figure E-47 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for 

CAP17, CAP40 and the Density Function for CAP40.......................... E-64 

Figure E-48 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for 

CAP17, CAP40 and the Density Function for CAP40.......................... E-64 

Figure E-49 CDF of Failure Probability/Number of Valve Cycles.......................... E-66

Figure E-50 Typical LTSBO Drywell Characteristics......................................... E-69

Figure E-51 Peach Bottom Evacuation Routes................................................. E-75
E-6 

APPENDIX E – LIST OF TABLES

 Table Page

Table E-1 MACCS Runs to Source Term Crosswalk...................................... E-12

Table E-2 Run 1 Statistics.......................................................................... E-13

Table E-3 Run 2 Statistics.......................................................................... E-14

Table E-4 Parameters and Weighting (0.0 to 1.0) for Source Term Selection........ E-21

Table E-5 Average difference between the three separate LHS runs over all 

Aleatory Weather Distributions (1st to 99th percentile)....................... E-22

Table E-6 Conditional, mean, individual LCF risk (per event) average statistics for 

the MACCS Uncertainty Analysis for five circular areas (Run 1).......... E-29

Table E-7 Runs 3-5 conditional, mean, individual LCF risk (per event) average 

statistics for five circular areas...................................................... E-30

Table E-8 Runs 6-8 conditional, mean, individual LCF risk (per event) average 

statistics for five circular areas...................................................... E-30

Table E-9 Runs 9-11 conditional, mean, individual LCF risk (per event) statistics 

for five circular areas.................................................................. E-31

Table E-10 Runs 12-14 conditional, mean, individual LCF risk (per event) average 

statistics for five circular areas...................................................... E-31

Table E-11 Runs 15-17 conditional, mean, individual LCF risk (per event) average 

statistics for five circular areas...................................................... E-32

Table E-12 Conditional, mean, individual prompt-fatality risk (per event) average 

statistics for the MACCS Uncertainty Analysis for specified circular 

areas (Run 1) ........................................................................... E-38

Table E-13 Run 3-5 conditional, mean, individual prompt-fatality risk (per event) 

average statistics for specified circular areas................................... E-38

Table E-14 Run 6-8 conditional, mean, individual prompt-fatality risk (per event) 

average statistics for specified circular areas................................... E-39

Table E-15 Run 9-11 conditional, mean, individual prompt-fatality risk (per event) 

average statistics for specified circular areas................................... E-39

Table E-16 Run 12-14 conditional, mean, individual prompt-fatality risk (per event) 

average statistics for specified circular areas................................... E-40

Table E-17 Run 15-17 conditional, mean, individual prompt-fatality risk (per event) 

average statistics for specified circular areas................................... E-40

Table E-18 Percent Difference in the CDF between the Combined Aleatory and 

Epistemic Uncertainty LCF Risk to Mean Aleatory Uncertainty LCF Risk 

for Specified Radial Distances...................................................... E-47

Table E-19 Conditional, mean, individual LCF risk (per event) average statistics for 

the MACCS Uncertainty Analysis (CAP17) for five circular areas using 

LHS sampling............................................................................ E-59
E-7 

Table E-20 Conditional, mean, individual LCF risk (per event) average statistics for 

the MACCS Uncertainty Analysis (CAP17) for five circular areas using 

SRS/MC sampling...................................................................... E-60 

Table E-21 Conditional, mean, individual prompt fatality risk (per event) average 

statistics for the MACCS Uncertainty Analysis (CAP17) for six circular 

areas using LHS........................................................................ E-61 

Table E-22 Conditional, mean, individual prompt fatality risk (per event) average 

statistics for the MACCS Uncertainty Analysis (CAP17) for six circular

areas using MC.......................................................................... E-61 
E-8 

E.1 Motivation

As part of the NRC’s 606th meeting of the Advisory Committee on Reactor Safeguards (ACRS), 

this uncertainty analysis was discussed by the ACRS, NRC staff, and Sandia staff. From this 

meeting a series of additional questions were submitted to the NRC staff from the ACRS. The 

NRC and Sandia staff addressed these questions, and the results were discussed with the 

ACRS Regulatory Policies and Practices Subcommittee on September 16, 2013. The following 

questions were submitted by the ACRS:

2. MELCOR – MACCS1

 – Weather Uncertainty Integration: For the combined MELCORMACCS results, the report currently presents only results averaged over the weather trials. 

At a minimum, the report should also present results that include and display the full 

weather aleatory uncertainty. We would also like to discuss the results from the following 

requested analyses.

3. MACCS and Weather Uncertainties for Prompt227(Early) Fatalities: Select the MELCOR 

realization that produced the largest conditional prompt fatality consequences in the current 

SOARCA uncertainty results. For that realization, sample from the 350 MACCS input 

parameters, and for each epistemic sample generate 984 weather cases to derive an 

uncertainty distribution for the conditional prompt fatality consequences at each distance. 

Demonstrate convergence of the combined MACCS-weather uncertainty analysis results. 

Present the results from this analysis in two forms:

• Average over the weather samples as was done in the current report to show only the 

MACCS epistemic uncertainty.

• Present results that retain the full combined MACCS epistemic and weather aleatory 

uncertainty.

4. MACCS and Weather Uncertainties for Latent Cancer Fatalities 1: Select the MELCOR 

realization that produced the largest conditional latent cancer fatality consequences in the 

current SOARCA uncertainty results. For that realization, sample from the 350 MACCS

input parameters, and for each epistemic sample generate 984 weather cases to derive an 

uncertainty distribution for the conditional latent cancer fatality consequences at each 

distance. Demonstrate convergence of the combined MACCS weather uncertainty analysis 

results. Present the results from this analysis in two forms:

• Average over the weather samples as was done in the current report to show only the 

MACCS epistemic uncertainty.

• Present results that retain the full combined MACCS epistemic and weather aleatory 

uncertainty.

 

1 Note that the time, NRC and SNL were calling the MACCS2 code, “MACCS.” Subsequently the code is now simply 

being called “MACCS,” as reflected in the body of the report.

2 In this appendix, “prompt” and “early” are used interchangeably to describe early fatality risk.
E-9 

5. MACCS and Weather Uncertainties for Latent Cancer Fatalities 2: Select a MELCOR 

realization that produced a small, but non-zero, contribution to the conditional latent cancer 

fatality consequences in the current SOARCA uncertainty results. For that realization, 

sample from the 350 MACCS input parameters, and for each epistemic sample generate 

984 weather cases to derive an uncertainty distribution for the conditional latent cancer 

fatality consequences at each distance. Demonstrate convergence of the combined 

MACCS-weather uncertainty analysis results. Present the results from this analysis in two 

forms:

• Average over the weather samples as was done in the current report to show only the 

MACCS epistemic uncertainty.

• Present results that retain the full combined MACCS epistemic and weather aleatory 

uncertainty.

6. Input Parameter Uncertainties: We would like the staff to explain the technical justification 

for the uncertainties that are assigned for the following parameters. We would also like to 

understand the rationale for the type of distribution that is used to characterize the 

uncertainty. To facilitate planning, we have listed the parameters in the order of our general 

interests and priorities.

a. MELCOR Parameters:

I. SRVLAM – SRV stochastic failure to reclose

II. CHEMFORM – Iodine and cesium fraction

III. FL904A – Drywell liner failure flow area

IV. BATTDUR – Battery duration

V. SRVOAFRAC – SRV open area fraction

VI. SLCRFRAC – Main steam line creep rupture area fraction

VII. RDMTC, RDSTC – Radial debris relocation time constants

VIII. RRIDRFRAC, RODRFRAC – Railroad door open fraction

IX. H2IGNC – Hydrogen ignition criteria

X. RHONOM – Particle density

XI. FFC – Fuel failure criterion

XII. SC1141(2) – Molten clad drainage rate

b. MACCS Parameters:

I. DOSNRM, TIMNRM – Normal relocation

II. DOSHOT, TIMHOT – Hotspot relocation

III. ESPEED – Evacuation speed

IV. GSFAC – Shielding factor

V. GSHFAC – Groundshine
E-10

7. Other Issues: We would like to discuss the following modeling and analysis issues.

a. Surrogate Parameters: We would like to understand the technical bases for the 

selection of higher level "surrogate parameters" to account for the uncertainties and 

correlated effects from the lower level constituents that they represent in the models. In 

addition, we would like to understand how lower level parameters were combined to 

obtain an estimate and the uncertainty distribution for these lower level parameters. 

Should the MELCOR parameters for the in-core fuel degradation process be correlated 

and not independent?

b. Lower Head Penetration Failures: We would like to better understand why the 

sensitivity study in Section 6.4.2 provides a reasonable surrogate for understanding the 

effects from failure of the reactor vessel bottom head drain line.

c. Drywell Liner Failure: We would like to understand how the MELCOR drywell liner wall 

heatup and melt spreading model properly estimates the behavior of melt movement 

from the drywell pedestal leading to wall contact and failure. Is the presence of water 

considered in any way? If not, why not?

d. Operator Actions:

• Operators manually open SRV: The base case model assumes that the operators 

open a SRV at 1 hour after the initiating event. The sensitivity study in Section 6.4.1 

shows the effects from actions to open the valve at 0.5 hour, 2 hours, and 3 hours, 

and the effects if the operators do not open the valve. We would like to better 

understand the basis for the nominal 1-hour timing and how the open SRV is 

modeled in MELCOR for the base case model and the sensitivity study.

• Operators shed DC loads: We would like to understand the bases and the timing for 

the operator actions that are needed to extend the battery life to the maximum 

modeled duration of 8 hours.

The rest of this section provides the written discussions the NRC and Sandia staff provided the 

ACRS subcommittee to support the September 16, 2013 subcommittee meeting (the transcript 

of this meeting is available in Reference [E.1]). 
E-11

E.2 Discussion of MACCS Results

To address ACRS Questions 1 through 4, Sandia conducted a series of additional uncertainty 

MACCS analyses. Table E-1 provides a crosswalk of the MACCS analyses. Figure E-1 and 

Table E-2 show the Section 6.2 results. This figure and table is used as a comparison for the 

rest of this discussion. Figure E-2 and Table E-3 show a MACCS analysis using all 865 

SOARCA Uncertainty Analysis source terms with the SOARCA (NUREG/CR-7110 Volume 1) 

point estimates. This analysis was used to select three representative MELCOR source terms 

for additional analyses.
E-12

Table E-1: MACCS Runs to Source Term Crosswalk

MACCS Analysis Description Source

Term

Run 

Number

UAS_CAP17v364_2509

MACCS analysis with LHS inputs for combined 

MELCOR Replicates 1, 2, and 3 

(SOARCA Uncertainty Analysis Section 6.2 results)

All 865 Source 

Terms 1 

UAS_CAP20v364_2509 MACCS analysis with SOARCA Estimate inputs for 

combined MELCOR Replicates 1, 2, and 3

All 865 Source 

Terms 2 

UAS_CAP22v364_2509

MACCS analysis with LHS inputs for highest Prompt 

Fatality Risk source term determined from CAP 17 

(same LHS random seed as CAP 17)

Replicate 2 

Realization 291 3 

UAS_CAP23v364_2509

MACCS analysis with LHS inputs for highest Prompt 

Fatality Risk source term determined from CAP 17 

(different LHS random seed than CAP 22)

Replicate 2 

Realization 291 4 

UAS_CAP24v364_2509

MACCS analysis with LHS inputs for highest Prompt 

Fatality Risk source term determined from CAP 17 

(different LHS random seed than CAP 22 and CAP 23)

Replicate 2 

Realization 291 5 

UAS_CAP25v364_2509

MACCS analysis with LHS inputs for highest LCF Risk 

source term determined from CAP 17

(same LHS random seed as CAP 17)

Replicate 3 

Realization 46 6 

UAS_CAP26v364_2509

MACCS analysis with LHS inputs for highest LCF Risk 

source term determined from CAP 17

(different LHS random seed than CAP 25)

Replicate 3 

Realization 46 7 

UAS_CAP27v364_2509

MACCS analysis with LHS inputs for highest LCF Risk 

source term determined from CAP 17 

(different LHS random seed than CAP 25 and CAP 26)

Replicate 3 

Realization 46 8 

UAS_CAP28v364_2509

MACCS analysis with LHS inputs for low LCF Risk 

source term determined from CAP 20 

(same LHS random seed as CAP 17)

Replicate 3 

Realization 187 9 

UAS_CAP29v364_2509

MACCS analysis with LHS inputs for low LCF Risk 

source term determined from CAP 20 

(different LHS random seed than CAP 28)

Replicate 3 

Realization 187 10

UAS_CAP30v364_2509

MACCS analysis with LHS inputs for low LCF Risk 

source term determined from CAP 20 

(different LHS random seed than CAP 28 and CAP 29)

Replicate 3 

Realization 187 11

UAS_CAP31v364_2509

MACCS analysis with LHS inputs for medium LCF Risk 

source term determined from CAP 20 

(same LHS random seed as CAP 17)

Replicate 1 

Realization 75 12

UAS_CAP32v364_2509

MACCS analysis with LHS inputs for medium LCF Risk 

source term determined from CAP 20 

(different LHS random seed than CAP 31)

Replicate 1 

Realization 75 13

UAS_CAP33v364_2509

MACCS analysis with LHS inputs for medium LCF Risk 

source term determined from CAP 20 

(different LHS random seed than CAP 31 and CAP 32)

Replicate 1 

Realization 75 14

UAS_CAP34v364_2509

MACCS analysis with LHS inputs for high LCF Risk 

source term determined from CAP 20 

(same LHS random seed as CAP 17)

Replicate 1 

Realization 290 15

UAS_CAP35v364_2509

MACCS analysis with LHS inputs for high LCF Risk 

source term determined from CAP 20 

(different LHS random seed than CAP 34)

Replicate 1 

Realization 290 16

UAS_CAP36v364_2509

MACCS analysis with LHS inputs for high LCF Risk 

source term determined from CAP 20 

(different LHS random seed than CAP 34 and CAP 35)

Replicate 1 

Realization 290 17
E-13

Figure E-1: Run 1 Conditional Mean, Individual LCF Risk (per Event) CCDF for all 

Radial Distances Considered

Table E-2: Run 1 Statistics

0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.65E-04 2.79E-04 1.96E-04 1.26E-04 1.02E-04

Median 1.34E-04 1.87E-04 1.32E-04 8.67E-05 7.12E-05

5th Percentile 3.13E-05 4.89E-05 3.44E-05 2.24E-05 1.85E-05

95th Percentile 4.15E-04 7.73E-04 5.28E-04 3.38E-04 2.66E-04

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02

CCDF

Mean, Individual LCF Risk per Event

0-10 miles

0-20 miles

0-30 miles

0-40 miles

0-50 miles
E-14

Figure E-2: Run 2 Conditional Mean, Individual LCF Risk (per Event) CCDF for all 

Radial Distances Considered

Table E-3: Run 2 Statistics

0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 2.08E-04 3.42E-04 2.36E-04 1.49E-04 1.20E-04

Median 1.99E-04 2.50E-04 1.73E-04 1.11E-04 9.12E-05

5th Percentile 8.40E-05 1.03E-04 7.22E-05 4.62E-05 3.78E-05

95th Percentile 3.77E-04 9.41E-04 6.48E-04 3.98E-04 3.13E-04

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02

CCDF

Mean, Individual LCF Risk per Event

0-10 miles

0-20 miles

0-30 miles

0-40 miles

0-50 miles
E-15

E.3 Selection of the Three Representative MELCOR Realizations

E.3.1 INTRODUCTION

In order to test the influence of uncertain MACCS parameters by themselves to address ACRS 

Questions 1 through 4, three representative source terms needed to be selected. Each of them 

will be used as a reference source term on a Monte Carlo simulation in which only MACCS 

parameters will vary.

The selection of these source term required an initial MACCS run. In this run, all previously 865 

source terms have been used, while all MACCS parameters have been set to nominal value 

(SOARCA point estimates). This way it was possible to assess the influence of the source term 

when MACCS parameters are fixed.

A set of 11 results have then been used as metrics to select the three representative source 

terms:

• Latent Cancer Fatality (LCF) at 5 different locations (10, 20, 30, 40 and 50 miles)

• Fraction of inventory released for 5 radionuclides (Cs, I, Ba, Ce, Te)

• Release time

As three values needed to be selected, the ensemble of possibility (prob=1) was decomposed 

into three equiprobable groups ([0,1/3], [1/3,2/3] and [2/3,1]) and the mid-point quantile of each 

group was used as the ideal theoretical value (i.e., q1=1/6, q2=1/2 and q3=5/6)

Amongst the 865 set of results generated, three results were selected, such that their quantile 

position for the considered metrics are the closest to the theoretical representative quantile.

In other words:

• One realization such as the difference between its quantile position for all the metrics 

and the theoretical value of q1=1/6 is minimized

• One realization such as the difference between its quantile position for all the metrics 

and the theoretical value of q2=1/2 is minimized

• One realization such as the difference between its quantile position for all the metrics 

and the theoretical value of q3=5/6 is minimized

One additional constraint added to the problem is that the importance of the metrics is not 

equally likely. For instance, LCF results are considered more important (they are the final result 

of interest) than individual fraction of RN released and Release time is considered as the least 

important parameter. Furthermore, correlation amongst the outputs needs to be considered.

E.3.2 METHODOLOGY

Each of the 865 calculations performed generated a result for all the 11 metrics considered. For 

each realization the result for each metric was replaced by its quantile position, based on the 

865 results. (The value was ranked with respect to the 864 other values and normalized by 

865). Therefore, each realization was associated with 11 quantile positions (one for each 

metric).
E-16

QQii = �qq1,ii, qq2,ii, ⋯ , qq10,ii, qq11,ii ∗ �, = 1, ... ,865

Where i represents the realization number, Qi the set of quantiles associated with realization i 

and qj,i the quantile associated with metric j for realization i. 

As release time influence is inverse from the other metrics (the earlier the release time, the 

worse it is), a reverse quantile (q*=1-q) has been used for this metric. 

The importance of each metric is determined via a weight factor

WW = {ww1, ww2, ⋯ , ww11}

Where W represents the set of weights and wj the weight associated with metric j. 

Three normalized distances (based on the L2 norm) are estimated for each realization, one for 

each of the theoretical quantiles, via the following formula

ddii, = �∑ wwjj�qqjj,ii − qq �

2 11

jj=1

∑ wwjj

11

jj=1

 , = 1, ... ,865 and kk = 1,2 or 3

Where k represents the theoretical quantile reference number, qk the quantile for reference k

For each reference k the realization leading to the minimum of di,k is selected as representative 

for the set. It will be the one that minimizes the difference between the theoretical quantile and 

actual quantile (in the L2 norm sense) according to the weight of importance.

E.3.3 SELECTION OF THE WEIGHT 

The weights are selected for each metric to represent the importance of the metric relative to 

the others according to the analyst. As the distance result is normalized, the range of values 

used is left open to the analyst (as long as it is positive or null). A weight of 0.0 will lead to the 

metric not being considered.

One important factor to consider, when the weights are chosen, is the eventual correlations 

amongst the results. LCF results will be correlated (and some more strongly than other). For 

strongly correlated results (beyond 0.9 for instance), the group can be considered as a single 

metric, and the weights associated to each member of the group will be added to the influence 

to the group. As an example, LCF at 50 miles and LCF at 40 miles results have a correlation of 

0.999 (essentially correlation of 1). Associating a weight of 1 to both of these metric will be 

equivalent to associate a weight of 2 for the group consisting of these two metrics.

E.3.4 CHECKING OF RESULTS

Once the realizations are selected, one can check how good the selection is, with the selected 

set of weights. For this, two graphical methods are proposed.

The first one is a CDF comparison for each metric. The CDF resulting from the 865 values is 

plotted for each metric. On top, a CDF consisting of the three selected realizations is displayed. 

The analyst can then check how good the fit is between the two CDFs. A good fit will be 

obtained if the distance between the two CDFs is small. Another point of reference to evaluate 
E-17

the goodness of fit is to check whether the CDFs cross at or close to the selected quantiles (1/6, 

1/2 and 5/6). An example for LCF for a 50 miles radius is displayed in Figure E-3. The dashed 

lines indicate the quantiles position where the two CDFs are expected to cross.

Figure E-3: Example of CDFs Comparison in Linear Scale (left) and Semi-log Scale 

(right)

The second one uses a Cobweb to represent how far from the selected realizations are from the 

theoretical quantiles. An example can be seen in Figure E-4. The three selected realizations’ 

quantile curves are in color thick blue, green, and red lines, the theoretical quantiles in dotdashed dark lines and a set of 150 realizations are displayed in thin gray lines as reference (not 

all 865 realizations are plotted as it would make the cobweb hard to read).

E.3.5 USE OF THE EXCEL WORKBOOK

An excel workbook has been developed to perform the minimization and select the realizations 

(Selection_curves_SOARCA_PB-UA_v1.3.xlsx). In the Data Spreadsheet, the analyst copies 

the results of the 11 metrics for the 865 results under column B to L (see screenshot in 

Figure E-5).

In Main spreadsheet (see Figure E-6) the analyst can select the quantile desired in cells D4 to 

D6 (by default 1/6, 1/2, and 5/6) and the weights to be used in row 4, column K to U. The 

calculations are performed automatically and the resulting CDFs are displayed (using linear and 

log-scale on the abscissa) below in the same sheet. A correlation matrix is displayed in the area 

AJ3-AU14 to help select the appropriate weights.

Finally, the cobweb plots are available in the sheet Cobweb (see Figure E-4 for an example). 

The metrics have been listed from left to right according to their decreasing order of importance 

following the weights selected.
E-18

Figure E-4: Example of Cobweb Plot Result

0.00

0.20

0.40

0.60

0.80

1.00

50

miles

20

miles

10

miles

30

miles

40

miles

Cs Iodine Ba Ce Te (hr)
E-19

Figure E-5: Screenshot of Data Sheet in the Excel Workbook
E-20

Figure E-6: Screenshot of Main Sheet of Excel Workbook

E.3.6 Results

The selection of these three source terms are based on the Run 2 results for 11 input and 

output parameters. Each of these 11 parameters is assigned an importance factor based on 

their respective CDFs (i.e., conditional LCF risk, radionuclides, and release timing). The 

11 parameters are shown in Table E-4 with their respective weighting factor.

Conditional LCF risk at 50 miles was considered the most important metric and was associated 

with a value of 1.0. As 20-, 30- and 40-miles results are strongly correlated to this metric; their 

weight was fixed to a low value (0.3, 0.1, and 0.1, respectively). Result at 10-miles tends to be 

different so a higher weight (0.6) was associated to this metric.

With respect to radionuclides releases, Cesium was considered as the most important (weight 

of 0.6), followed by Iodine and Barium (weight of 0.3 each). Cerium and Tellurium releases 

were considered less important (weight of 0.1 each).

Finally, environmental release time was considered to have a small effect (weight of 0.1).

The source terms selected try to best represent 1/3 of the total CDF’s considered. The source 

terms selected try to best correspond to the 17th, 50th, and 83rd percentiles for each of the 

11 parameters considered. Figure E-7 shows a cobweb graph for the low (red line), medium 

(green line), and high (blue line) source terms selected. In Figure E-7, each of the source terms 

shows its respective representation to the parameters considered and its corresponding CDF 

information. 
E-21

Table E-4: Parameters and Weighting (0.0 to 1.0) for Source Term Selection

Conditional, Mean, Individual LCF Risk (per Event) at:

50 miles 20 miles 10 miles 30 miles 40 miles

1.0 0.3 0.6 0.1 0.1

Radionuclide Group

Cesium Iodine Barium Cerium Tellurium

0.6 0.3 0.3 0.1 0.1

Environmental Release Time (hour)

0.1

Figure E-7: Cobweb Graph for Selected Source Terms

E.4 Weather Uncertainty & MACCS Convergence

To answer ACRS Questions 1 through 4 for the five source terms considered (highest prompt 

fatality risk source term, highest LCF risk source term, and three high/medium/low source terms

selected by the methodology described in Section E.1), three Latin Hypercube Sampling (LHS) 

runs of 1,000 samples varying all 350 MACCS uncertain input variables were conducted. As 

part of this analysis, the distribution across the sampled weather is considered. Table E-5 

provides the average percent difference in results across the weather distribution for each of the 

0.0

0.2

0.4

0.6

0.8

1.0

50 miles 20 miles 10 miles 30 miles 40 miles Cs Iodine Ba Ce Te (hr) CDF
E-22

source terms considered and their associated Runs (i.e., see Table E-1 for a more detailed 

description of each Run). The largest deviation between the three LHS runs is observed for the 

0-10 mile radial distance to be the ‘low’ source term (4.5%) at the 99th percentile, and for the 

0-50 mile radial distance it is observed for the ‘medium’ source term (8.5%) at the 

99th percentile. 

Figure E-8 shows an example of the Table E-5 results for Run 6, 7, and 8 combined aleatory 

and epistemic uncertainty conditional individual LCF risk (per event) CCDFs for the 10- and 

50-mile radial distances. This figure further emphasizes how well converged the MACCS

results are for the source terms and sampled weather considered.

Figure E-9 through Figure E-13 show the 10- and 50-mile combined aleatory and epistemic 

uncertainty conditional LCF risk (per event) CCDFs for specified Runs compared to the 

epistemic uncertainty conditional, mean LCF risk (per event) CCDFs for Run 1. Based on these 

figures, the combined aleatory and epistemic results are similar to those from the SOARCA 

Uncertainty Analysis for the ‘medium’ source term determined from Section 2 (i.e., 5% average 

error between Run 1 and Runs 12-14 for the 0-10 mile radial distance (24% peak error at 

99th percentile), and 32% average error between Run 1 and Runs 12-14 for the 0-50 mile radial 

distance (72% peak error at 99th percentile)). 

Based on these analyses, it is judged that the MACCS model is well converged with respect to 

weather uncertainty for conditional LCF risk.

Table E-5: Average difference between the three separate LHS runs over all Aleatory 

Weather Distributions (1st to 99th percentile) 

Source Term

Conditional 

LCF Risk

0-10 miles

Conditional 

LCF Risk

0-50 miles

Highest Prompt Fatality Risk – Runs 3-5 0.8% 0.8%

Highest LCF Risk – Runs 6-8 0.8% 0.9%

Low – Runs 9-11 0.9% 0.8%

Medium – Runs 12-14 0.8% 0.9%

High – Runs 15-17 1.0% 0.6%

Overall Average 0.9% 0.8%

Prompt fatality risk was not able to be determined for the combined aleatory and epistemic 

results uncertainties because the large number of ‘zero’ risk results prevents the MACCS postprocessor from generating the convoluted CCDF.
E-23 

Figure E-8: Run 6-8 Combined Aleatory and Epistemic Uncertainty Conditional 

Individual LCF Risk (per Event) CCDF for the Radial Distances Considered

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.E-05 1.E-04 1.E-03 1.E-02

CCDF

Individual Latent Cancer Fatality Risk per Event

0-10 miles Run 6

0-10 miles Run 7

0-10 miles Run 8

0-50 miles Run 6

0-50 miles Run 7

0-50 miles Run 8
E-24

Figure E-9: Run 3 Combined Aleatory and Epistemic Uncertainty Conditional Individual 

LCF Risk (per Event) CCDF and Run 1 Epistemic Uncertainty Conditional, 

Mean Individual LCF Risk (per Event) CCDF for the Radial Distances 

Considered

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.E-06 1.E-05 1.E-04 1.E-03 1.E-02

CCDF

Individual Latent Cancer Fatality Risk per Event

0-10 miles Run 3

0-50 miles Run 3

0-10 miles Run 1

0-50 miles Run 1
E-25

Figure E-10: Run 6 Combined Aleatory and Epistemic Uncertainty Conditional Individual 

LCF Risk (per Event) CCDF and Run 1 Epistemic Uncertainty Conditional, 

Mean Individual LCF Risk (per Event) CCDF for the Radial Distances 

Considered

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.E-06 1.E-05 1.E-04 1.E-03 1.E-02

CCDF

Individual Latent Cancer Fatality Risk per Event

0-10 miles Run 6

0-50 miles Run 6

0-10 miles Run 1

0-50 miles Run 1
E-26

Figure E-11: Run 9 Combined Aleatory and Epistemic Uncertainty Conditional Individual 

LCF Risk (per Event) CCDF and Run 1 Epistemic Uncertainty Conditional, 

Mean Individual LCF Risk (per Event) CCDF for the Radial Distances 

Considered

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.E-06 1.E-05 1.E-04 1.E-03

CCDF

Individual Latent Cancer Fatality Risk per Event

0-10 miles Run 9

0-50 miles Run 9

0-10 miles Run 1

0-50 miles Run 1
E-27

Figure E-12: Run 12 Combined Aleatory and Epistemic Uncertainty Conditional 

Individual LCF Risk (per Event) CCDF and Run 1 Epistemic Uncertainty

Conditional, Mean Individual LCF Risk (per Event) CCDF for the Radial 

Distances Considered

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.E-06 1.E-05 1.E-04 1.E-03

CCDF

Individual Latent Cancer Fatality Risk per Event

0-10 miles Run 12

0-50 miles Run 12

0-10 miles Run 1

0-50 miles Run 1
E-28

Figure E-13: Run 15 Combined Aleatory and Epistemic Uncertainty Conditional 

Individual LCF Risk (per Event) CCDF and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual LCF Risk (per Event) CCDF for the Radial 

Distances Considered

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.E-06 1.E-05 1.E-04 1.E-03

CCDF

Individual Latent Cancer Fatality Risk per Event

0-10 miles Run 15

0-50 miles Run 15

0-10 miles Run 1

0-50 miles Run 1
E-29

E.5 Conditional Mean, Individual LCF Risk and Prompt Fatality Risk Results & Model 

Convergence

To answer ACRS Questions 1 through 4 for the five source terms considered, three LHS runs of 

1,000 samples varying all 350 MACCS uncertain input variables were conducted. Table E-6 

through Table E-11 provides the mean, conditional LCF risk (per event) statistical results for 

each of the source terms considered and their associated Runs (i.e., see Table E-1 for a more 

detailed description of each Run) for all radial distances considered. Figure E-14 through 

Figure E-18 show the 10- and 50-mile mean, conditional LCF risk (per event) CCDFs for the 

each source term considered. Again, these figures and tables show that the MACCS results are 

well converged for the source terms and for the three LHS sets considered. Based on these 

analyses and those discussed in Section E.4, it is determined that the MACCS model for the 

SOARCA Uncertainty Analysis for the Peach Bottom LTSBO is convergent with regards to 

conditional LCF risk for the uncertain inputs considered with respect to mean, conditional LCF 

risk. 

Table E-12 through Table E-17 provides the mean, conditional prompt fatality risk (per event) 

statistical results for each of the source terms considered and their associated Runs (i.e., see 

Table E-1 for a more detailed description of each Run) for all radial distances considered. 

Figure E-19 through Figure E-23 show the 3.5-mile mean, conditional prompt fatality risk (per 

event) CCDFs for the each source term considered. For Table E-15 and Figure E-21, there is 

only one non-zero conditional, mean, individual prompt fatality risk data point for Run 9; all other 

data points for Runs 9-11 are zero. Again, these figures show convergence the MACCS results 

are for the source terms and for the three LHS sets considered. However, for some of the

results (e.g., Runs 12-14) the limited number of non-zero conditional prompt fatality risk 

samples results in poor statistics and thus do not show a good convergence for the MACCS

model. Yet, for the higher source terms considered (e.g., Runs 6-8), there are a sufficient 

number of non-zero prompt fatality risk results to provide a high confidence in the convergence 

of the MACCS model for the SOARCA Uncertainty Analysis for the Peach Bottom LTSBO for 

the uncertain inputs considered with respect to mean, conditional prompt fatality risk.

Table E-6: Conditional, mean, individual LCF risk (per event) average statistics for the 

MACCS Uncertainty Analysis for five circular areas (Run 1)

0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.7x10-4 2.8x10-4 2.0x10-4 1.3x10-4 1.0x10-4

Median 1.3x10-4 1.9x10-4 1.3x10-4 8.7x10-5 7.1x10-5

5th percentile 3.1x10-5 4.9x10-5 3.4x10-5 2.2x10-5 1.9x10-5

95th percentile 4.2x10-4 7.7x10-4 5.3x10-4 3.4x10-4 2.7x10-4
E-30

Table E-7: Runs 3-5 conditional, mean, individual LCF risk (per event) average 

statistics for five circular areas

Run 3 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 2.60E-04 8.70E-04 5.93E-04 3.65E-04 2.88E-04

Median 2.29E-04 6.91E-04 4.67E-04 2.91E-04 2.30E-04

5th percentile 9.08E-05 2.22E-04 1.56E-04 1.04E-04 8.51E-05

95th percentile 5.19E-04 2.07E-03 1.38E-03 8.22E-04 6.39E-04

Run 4 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 2.60E-04 8.67E-04 5.89E-04 3.62E-04 2.86E-04

Median 2.24E-04 7.13E-04 4.84E-04 3.02E-04 2.42E-04

5th percentile 8.77E-05 2.11E-04 1.50E-04 1.00E-04 8.25E-05

95th percentile 5.50E-04 2.08E-03 1.42E-03 8.51E-04 6.65E-04

Run 5 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 2.61E-04 8.68E-04 5.91E-04 3.64E-04 2.88E-04

Median 2.27E-04 6.85E-04 4.68E-04 2.95E-04 2.34E-04

5th percentile 9.18E-05 2.32E-04 1.61E-04 1.04E-04 8.66E-05

95th percentile 5.62E-04 2.08E-03 1.42E-03 8.32E-04 6.40E-04

Table E-8: Runs 6-8 conditional, mean, individual LCF risk (per event) average 

statistics for five circular areas

Run 6 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 2.50E-04 1.33E-03 9.09E-04 5.51E-04 4.30E-04

Median 2.24E-04 1.05E-03 7.12E-04 4.32E-04 3.34E-04

5th percentile 9.57E-05 2.80E-04 1.95E-04 1.22E-04 9.79E-05

95th percentile 4.92E-04 3.35E-03 2.28E-03 1.36E-03 1.06E-03

Run 7 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 2.50E-04 1.33E-03 9.04E-04 5.47E-04 4.27E-04

Median 2.20E-04 1.08E-03 7.30E-04 4.43E-04 3.45E-04

5th percentile 9.00E-05 2.73E-04 1.87E-04 1.21E-04 9.81E-05

95th percentile 5.10E-04 3.36E-03 2.32E-03 1.39E-03 1.07E-03

Run 8 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 2.50E-04 1.33E-03 9.07E-04 5.50E-04 4.29E-04

Median 2.19E-04 1.01E-03 6.89E-04 4.16E-04 3.27E-04

5th percentile 9.33E-05 2.95E-04 1.99E-04 1.32E-04 1.05E-04

95th percentile 5.23E-04 3.26E-03 2.26E-03 1.35E-03 1.04E-03
E-31

Table E-9: Runs 9-11 conditional, mean, individual LCF risk (per event) statistics for 

five circular areas

Run 9 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.07E-04 1.18E-04 8.26E-05 5.41E-05 4.44E-05

Median 8.75E-05 1.03E-04 7.21E-05 4.73E-05 3.85E-05

5th percentile 2.34E-05 3.78E-05 2.68E-05 1.74E-05 1.36E-05

95th percentile 2.52E-04 2.40E-04 1.69E-04 1.10E-04 8.89E-05

Run 10 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.07E-04 1.18E-04 8.25E-05 5.40E-05 4.43E-05

Median 8.57E-05 1.05E-04 7.36E-05 4.82E-05 3.93E-05

5th percentile 2.24E-05 3.78E-05 2.65E-05 1.71E-05 1.39E-05

95th percentile 2.58E-04 2.41E-04 1.71E-04 1.16E-04 9.51E-05

Run 11 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.07E-04 1.18E-04 8.27E-05 5.41E-05 4.44E-05

Median 8.75E-05 1.03E-04 7.22E-05 4.68E-05 3.85E-05

5th percentile 2.30E-05 3.98E-05 2.72E-05 1.78E-05 1.42E-05

95th percentile 2.67E-04 2.39E-04 1.70E-04 1.13E-04 9.38E-05

Table E-10: Runs 12-14 conditional, mean, individual LCF risk (per event) average 

statistics for five circular areas

Run 12 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.58E-04 1.92E-04 1.33E-04 8.59E-05 7.01E-05

Median 1.35E-04 1.69E-04 1.17E-04 7.53E-05 6.13E-05

5th percentile 4.10E-05 6.52E-05 4.55E-05 2.88E-05 2.38E-05

95th percentile 3.43E-04 3.95E-04 2.73E-04 1.80E-04 1.44E-04

Run 13 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.59E-04 1.93E-04 1.33E-04 8.60E-05 7.01E-05

Median 1.31E-04 1.72E-04 1.18E-04 7.69E-05 6.24E-05

5th percentile 4.10E-05 6.56E-05 4.59E-05 2.91E-05 2.40E-05

95th percentile 3.64E-04 3.91E-04 2.69E-04 1.76E-04 1.46E-04

Run 14 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.59E-04 1.92E-04 1.33E-04 8.61E-05 7.03E-05

Median 1.35E-04 1.69E-04 1.16E-04 7.53E-05 6.15E-05

5th percentile 4.18E-05 6.71E-05 4.54E-05 2.88E-05 2.38E-05

95th percentile 3.63E-04 3.93E-04 2.73E-04 1.75E-04 1.44E-04
E-32

Table E-11: Runs 15-17 conditional, mean, individual LCF risk (per event) average 

statistics for five circular areas

Run 15 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 2.19E-04 4.18E-04 3.01E-04 1.94E-04 1.57E-04

Median 1.85E-04 3.57E-04 2.59E-04 1.70E-04 1.38E-04

5th percentile 5.86E-05 1.41E-04 1.00E-04 6.42E-05 5.30E-05

95th percentile 4.72E-04 8.87E-04 6.44E-04 4.15E-04 3.37E-04

Run 16 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 2.19E-04 4.17E-04 3.00E-04 1.94E-04 1.57E-04

Median 1.82E-04 3.71E-04 2.65E-04 1.72E-04 1.38E-04

5th percentile 5.94E-05 1.34E-04 9.63E-05 6.18E-05 5.10E-05

95th percentile 4.93E-04 8.59E-04 6.32E-04 3.98E-04 3.22E-04

Run 17 0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 2.19E-04 4.17E-04 3.01E-04 1.94E-04 1.57E-04

Median 1.86E-04 3.64E-04 2.59E-04 1.68E-04 1.37E-04

5th percentile 5.95E-05 1.39E-04 1.00E-04 6.28E-05 5.08E-05

95th percentile 5.04E-04 8.55E-04 6.25E-04 4.05E-04 3.27E-04
E-33

Figure E-14: Runs 3-5 Epistemic Uncertainty Conditional, Mean, Individual LCF Risk (per 

Event) CCDFs and Run 1 Epistemic Uncertainty Conditional, Mean 

Individual LCF Risk (per Event) CCDF for the Radial Distances Considered

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.0E-06 1.0E-05 1.0E-04 1.0E-03

CCDF

Mean, Individual LCF Risk per Event

0-10 miles Run 1

0-10 miles Run 3

0-10 miles Run 4

0-10 miles Run 5

0-50 miles Run 1

0-50 miles Run 3

0-50 miles Run 4

0-50 miles Run 5
E-34

Figure E-15: Runs 6-8 Epistemic Uncertainty Conditional, Mean, Individual LCF Risk (per 

Event) CCDFs and Run 1 Epistemic Uncertainty Conditional, Mean 

Individual LCF Risk (per Event) CCDF for the Radial Distances Considered

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.0E-06 1.0E-05 1.0E-04 1.0E-03

CCDF

Mean, Individual LCF Risk per Event

0-10 miles Run 1

0-10 miles Run 6

0-10 miles Run 7

0-10 miles Run 8

0-50 miles Run 1

0-50 miles Run 6

0-50 miles Run 7

0-50 miles Run 8
E-35

Figure E-16: Runs 9-11 Epistemic Uncertainty Conditional, Mean, Individual LCF Risk 

(per Event) CCDFs and Run 1 Epistemic Uncertainty Conditional, Mean 

Individual LCF Risk (per Event) CCDF for the Radial Distances Considered

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.0E-06 1.0E-05 1.0E-04 1.0E-03

CCDF

Mean, Individual LCF Risk per Event

0-10 miles Run 1

0-10 miles Run 9

0-10 miles Run 10

0-10 miles Run 11

0-50 miles Run 1

0-50 miles Run 9

0-50 miles Run 10

0-50 miles Run 11
E-36

Figure E-17: Runs 12-14 Epistemic Uncertainty Conditional, Mean, Individual LCF Risk 

(per Event) CCDFs and Run 1 Epistemic Uncertainty Conditional, Mean 

Individual LCF Risk (per Event) CCDF for the Radial Distances Considered

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.0E-06 1.0E-05 1.0E-04 1.0E-03

CCDF

Mean, Individual LCF Risk per Event

0-10 miles Run 1

0-10 miles Run 12

0-10 miles Run 13

0-10 miles Run 14

0-50 miles Run 1

0-50 miles Run 12

0-50 miles Run 13

0-50 miles Run 14
E-37

Figure E-18: Runs 15-17 Epistemic Uncertainty Conditional, Mean, Individual LCF Risk 

(per Event) CCDFs and Run 1 Epistemic Uncertainty Conditional, Mean 

Individual LCF Risk (per Event) CCDF for the Radial Distances Considered

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.0E-06 1.0E-05 1.0E-04 1.0E-03

CCDF

Mean, Individual LCF Risk per Event

0-10 miles Run 1

0-10 miles Run 15

0-10 miles Run 16

0-10 miles Run 17

0-50 miles Run 1

0-50 miles Run 15

0-50 miles Run 16

0-50 miles Run 17
E-38

Table E-12: Conditional, mean, individual prompt-fatality risk (per event) average 

statistics for the MACCS Uncertainty Analysis for specified circular areas 

(Run 1)

0-3.5 miles 0-7 miles 0-10 miles

Mean 3.5x10-8 8.3x10-9 4.8x10-9

Median 0.0 0.0 0.0

75th percentile 0.0 0.0 0.0

95th percentile 0.0 0.0 0.0

Table E-13: Run 3-5 conditional, mean, individual prompt-fatality risk (per event) 

average statistics for specified circular areas

Run 3 0-3.5 miles 0-7 miles 0-10 miles

Mean 3.42E-07 4.69E-08 9.53E-09

Median 0.0 0.0 0.0

75th percentile 2.02E-07 3.84E-09 0.0

95th percentile 1.53E-06 2.13E-07 1.24E-08

Run 4 0-3.5 miles 0-7 miles 0-10 miles

Mean 2.98E-07 4.18E-08 8.86E-09

Median 0.0 0.0 0.0

75th percentile 2.22E-07 1.11E-08 0.0

95th percentile 1.75E-06 2.33E-07 0.0

Run 5 0-3.5 miles 0-7 miles 0-10 miles

Mean 3.04E-07 4.67E-08 1.25E-08

Median 0.0 0.0 0.0

75th percentile 1.94E-07 8.17E-09 0.0

95th percentile 1.59E-06 2.06E-07 0.0
E-39

Table E-14: Run 6-8 conditional, mean, individual prompt-fatality risk (per event) 

average statistics for specified circular areas

Run 6 0-3.5 miles 0-7 miles 0-10 miles

Mean 7.44E-07 1.25E-07 3.12E-08

Median 1.25E-07 0.0 0.0

75th percentile 8.56E-07 9.84E-08 0.0

95th percentile 3.01E-06 5.52E-07 1.74E-07

Run 7 0-3.5 miles 0-7 miles 0-10 miles

Mean 6.68E-07 1.12E-07 2.92E-08

Median 1.30E-07 0.0 0.0

75th percentile 7.95E-07 9.42E-08 0.0

95th percentile 3.11E-06 5.50E-07 1.84E-07

Run 8 0-3.5 miles 0-7 miles 0-10 miles

Mean 6.99E-07 1.29E-07 4.08E-08

Median 1.25E-07 0.0 0.0

75th percentile 7.96E-07 8.64E-08 0.0

95th percentile 3.34E-06 5.37E-07 1.65E-07

Table E-15: Run 9-11 conditional, mean, individual prompt-fatality risk (per event) 

average statistics for specified circular areas

Run 9 0-3.5 miles 0-7 miles 0-10 miles

Mean 5.38E-11 0.0 0.0

Median 0.0 0.0 0.0

75th percentile 0.0 0.0 0.0

95th percentile 0.0 0.0 0.0

Run 10 0-3.5 miles 0-7 miles 0-10 miles

Mean 0.0 0.0 0.0

Median 0.0 0.0 0.0

75th percentile 0.0 0.0 0.0

95th percentile 0.0 0.0 0.0

Run 11 0-3.5 miles 0-7 miles 0-10 miles

Mean 0.0 0.0 0.0

Median 0.0 0.0 0.0

75th percentile 0.0 0.0 0.0

95th percentile 0.0 0.0 0.0
E-40

Table E-16: Run 12-14 conditional, mean, individual prompt-fatality risk (per event) 

average statistics for specified circular areas

Run 12 0-3.5 miles 0-7 miles 0-10 miles

Mean 1.67E-09 3.49E-10 0.0

Median 0.0 0.0 0.0

75th percentile 0.0 0.0 0.0

95th percentile 0.0 0.0 0.0

Run 13 0-3.5 miles 0-7 miles 0-10 miles

Mean 1.28E-11 3.24E-10 0.0

Median 0.0 0.0 0.0

75th percentile 0.0 0.0 0.0

95th percentile 0.0 0.0 0.0

Run 14 0-3.5 miles 0-7 miles 0-10 miles

Mean 7.48E-10 1.84E-10 0.0

Median 0.0 0.0 0.0

75th percentile 0.0 0.0 0.0

95th percentile 0.0 0.0 0.0

Table E-17: Run 15-17 conditional, mean, individual prompt-fatality risk (per event) 

average statistics for specified circular areas

Run 15 0-3.5 miles 0-7 miles 0-10 miles

Mean 1.87E-08 2.19E-09 2.66E-10

Median 0.0 0.0 0.0

75th percentile 0.0 0.0 0.0

95th percentile 0.0 0.0 0.0

Run 16 0-3.5 miles 0-7 miles 0-10 miles

Mean 2.24E-08 2.44E-09 2.79E-10

Median 0.0 0.0 0.0

75th percentile 0.0 0.0 0.0

95th percentile 0.0 0.0 0.0

Run 17 0-3.5 miles 0-7 miles 0-10 miles

Mean 1.33E-08 1.26E-09 7.09E-11

Median 0.0 0.0 0.0

75th percentile 0.0 0.0 0.0

95th percentile 0.0 0.0 0.0
E-41

Figure E-19: Runs 3-5 Epistemic Uncertainty Conditional, Mean, Individual Prompt 

Fatality Risk (per Event) CCDFs and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual Prompt Fatality Risk (per Event) CCDF for the 

Radial Distances Considered

0.001

0.01

0.1

1

1.0E-12 1.0E-11 1.0E-10 1.0E-09 1.0E-08 1.0E-07 1.0E-06 1.0E-05

CCDF

Mean, Individual Prompt Fatality Risk per Event

0-3.5 miles Run 1

0-3.5 miles Run 3

0-3.5 miles Run 4

0-3.5 miles Run 5
E-42

Figure E-20: Runs 6-8 Epistemic Uncertainty Conditional, Mean, Individual Prompt 

Fatality Risk (per Event) CCDFs and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual Prompt Fatality Risk (per Event) CCDF for the 

Radial Distances Considered

0.001

0.01

0.1

1

1.0E-12 1.0E-11 1.0E-10 1.0E-09 1.0E-08 1.0E-07 1.0E-06 1.0E-05

CCDF

Mean, Individual Prompt Fatality Risk per Event

0-3.5 miles Run 1

0-3.5 miles Run 6

0-3.5 miles Run 7

0-3.5 miles Run 8
E-43

Figure E-21: Runs 9-11 Epistemic Uncertainty Conditional, Mean, Individual Prompt 

Fatality Risk (per Event) CCDFs and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual Prompt Fatality Risk (per Event) CCDF for the 

Radial Distances Considered

Note: There is only one non-zero conditional, mean, individual prompt fatality risk data point for Run 9; 

all other data points for Runs 9-11 are zero.

0.001

0.01

0.1

1

1.0E-09 1.0E-08 1.0E-07 1.0E-06 1.0E-05

CCDF

Mean, Individual Prompt Fatality Risk per Event

0-3.5 miles Run 1
E-44

Figure E-22: Runs 12-14 Epistemic Uncertainty Conditional, Mean, Individual Prompt 

Fatality Risk (per Event) CCDFs and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual Prompt Fatality Risk (per Event) CCDF for the 

Radial Distances Considered

0.001

0.01

0.1

1.0E-10 1.0E-09 1.0E-08 1.0E-07 1.0E-06 1.0E-05

CCDF

Mean, Individual Prompt Fatality Risk per Event

0-3.5 miles Run 1

0-3.5 miles Run 12

0-3.5 miles Run 13

0-3.5 miles Run 14
E-45

Figure E-23: Runs 15-17 Epistemic Uncertainty Conditional, Mean, Individual Prompt 

Fatality Risk (per Event) CCDFs and Run 1 Epistemic Uncertainty 

Conditional, Mean Individual Prompt Fatality Risk (per Event) CCDF for the 

Radial Distances Considered

E.6 SOARCA Uncertainty Analysis Results for Conditional Individual LCF Risk

Figure E-24 shows Section 6.2 results (i.e., solid lines) for mean, individual LCF risk, and the 

combined aleatory and epistemic uncertainty (i.e., dashed lines) between the 1st and 

99th percentile for individual LCF risk at the 10-, 20-, and 50-mile radial distances. Table E-18 

shows the percent difference between the results presented in Figure E-24 at specified 

percentiles for the radial distances considered. In Figure E-24 for solid lines, what is displayed 

is an expected value over aleatory results, and for the dashed line, it is not. 

 

0.001

0.01

0.1

1.0E-11 1.0E-10 1.0E-09 1.0E-08 1.0E-07 1.0E-06 1.0E-05

CCDF

Mean, Individual Prompt Fatality Risk per Event

0-3.5 miles Run 1

0-3.5 miles Run 15

0-3.5 miles Run 16

0-3.5 miles Run 17
E-46

Figure E-24: Run 1 Combined Aleatory and Epistemic Uncertainty Conditional 

Individual LCF Risk (per Event) CCDF and Run 1 Epistemic Uncertainty 

Conditional, Mean, Individual LCF Risk (per Event) CCDF for the Radial 

Distances Considered

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02

CCDF

Individual LCF Risk per Event

0-10 miles Aleatory Mean

0-20 miles Aleatory Mean

0-50 miles Aleatory Mean

0-10 miles Epistemic & Aleatory

0-20 miles Epistemic & Aleatory

0-50 miles Epistemic & Aleatory
E-47

Table E-18: Percent Difference in the CDF between the Combined Aleatory and 

Epistemic Uncertainty LCF Risk to Mean Aleatory Uncertainty LCF Risk for 

Specified Radial Distances

Percentile 0-10 miles 0-20 miles 0-50 miles

99th 17% 34% 24%

95th 11% 14% 20%

80th 5% 3% 4%

60th 4% 14% 10%

50th 10% 18% 16%

40th 9% 24% 20%

20th 19% 36% 36%

5th 38% 48% 56%

1st 51% 70% 74%

E.7 Stability Analysis Using Bootstrap Approach

The ‘high’ source term (i.e., Replicate 1 Realization 290) has been selected to be used for a 

comparison between Simple Random Sampling (SRS) and Latin Hypercube Sampling (LHS) in 

order to validate the use of LHS. In addition to the three MACCS runs replicates of size 1000 

each using LHS (i.e., Runs 15-17 in Table E-1), another set of three replicates has been run 

using same sample size and random seed, but with SRS.

Conditional, mean, individual LCF risks (per event) for the 10-mile the 50-mile radial distance 

have been considered for this analysis. Each CDF has been estimated three times using a 

different random seed (i.e., Runs 15-17 in Table E-1 using SRS). Bootstrapping has been used 

on each of the three replicated CDFs, and for each distance radius considered, to generate a 

distribution of 1000 possible CDFs. This set of CDFs was used to estimate a 95% confidence 

interval (the confidence interval being centered, the 2.5th and 97.5th percentiles were used) for 

each replicate. These results are presented in Figure E-25 through Figure E-30 (note for these 

figures CAP 37 is Run 15 with SRS, CAP 38 is Run 16 with SRS, and CAP 39 is Run 17 with 

SRS).

In order to estimate the stability of results, one replicate’s CDF is displayed along with the 

confidence intervals for the two other replicates. Having the replicate CDF within the confidence 

interval defined by two other replicates (i.e., the other two replicates used a different random 

seed) can be considered a good test of stability.

Furthermore, the distribution of mean value based on bootstrap has been displayed for all three 

replicates, with the density estimated via binning for one of the replicates (Run 15 with SRS). 

This is presented in Figure E-31 and Figure E-32 for the 10-mile and 50-mile radial distances, 

respectively. This comparison also informs on the stability of the mean result for a sample of 

size 1000. Two things are considered at this level: 

1. How close are the means, and 

2. How close to a normal distribution is the density function, as the distribution of mean 

should tend to normal according to central limit theorem. 
E-48

Several analyses have demonstrated the faster convergence of LHS results compared to SRS 

(i.e., see Reference [E.2] for an example). One of the limitations of LHS compared to SRS is, 

however, with respect to the use of bootstrapping to estimate confidence intervals over 

estimators. Bootstrapping assumes that the set of observations used is from an independent 

and identically distributed population. While the LHS stratification enforces the identical 

distribution, it violates the independency statement; as each stratum is only used once. This 

means that each stratum already used cannot be used again and such action creates 

dependency in the sampling. 

While it would be hard to prove theoretically that the use of bootstrapping on LHS results is 

appropriate, an original sample size of 1000 can be considered large enough so that a selection 

of values (with replacement) will still lead to a good representation of the uncertainty in the CDF. 

Thus, bootstrapping has been used on the LHS results for Runs 15-17 in the same way it was 

used on SRS results in order to compare the stability and check if indeed the LHS results look 

more stable than conditional, mean, individual, LCF risk (per event) results when the same 

sample size is used. These results are presented in Figure E-33 through Figure E-38 for the 

10-mile and 50-mile radial distances (recall from Table E-1 CAP 34 is Run 15, CAP 35 is Run 

16, and CAP 36 is Run 17).

The distribution of mean value based on bootstrap has been displayed for all three replicates, 

with the density estimated via binning for one of the replicates (Run 15 with LHS). This is 

presented in Figure E-39 and Figure E-40 for the 10-mile and 50-mile radial distances, 

respectively.

Figure E-25: 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 15 

with SRS and 95% Confidence Interval Upper and Lower Bounds for Runs 

16 & 17 with SRS
E-49

Figure E-26: 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 16 

with SRS and 95% Confidence Interval Upper and Lower Bounds for Runs 

15 & 17 with SRS

Figure E-27: 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 17 

with SRS and 95% Confidence Interval Upper and Lower Bounds for Runs 

15 & 16 with SRS
E-50

Figure E-28: 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 15 

with SRS and 95% Confidence Interval Upper and Lower Bounds for Runs 

16 & 17 with SRS

Figure E-29: 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 16 

with SRS and 95% Confidence Interval Upper and Lower Bounds for Runs 

15 & 17 with SRS
E-51

Figure E-30: 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 17 

with SRS and 95% Confidence Interval Upper and Lower Bounds for Runs 

15 & 16 with SRS

Figure E-31: 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for Runs 

15-17 with SRS and the Density Function for Run 15 with SRS
E-52

Figure E-32: 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for Runs 

15-17 with SRS and the Density Function for Run 15 with SRS

Figure E-33: 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 15 

with LHS and 95% Confidence Interval Upper and Lower Bounds for Runs 

16 & 17 with LHS
E-53

Figure E-34: 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 16 

with LHS and 95% Confidence Interval Upper and Lower Bounds for Runs 

15 & 17 with LHS

Figure E-35: 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 17 

with LHS and 95% Confidence Interval Upper and Lower Bounds for Runs 

15 & 16 with LHS
E-54

Figure E-36: 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 15 

with LHS and 95% Confidence Interval Upper and Lower Bounds for Runs 

16 & 17 with LHS

Figure E-37: 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 16 

with LHS and 95% Confidence Interval Upper and Lower Bounds for Runs 

15 & 17 with LHS
E-55

Figure E-38: 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for Run 17 

with LHS and 95% Confidence Interval Upper and Lower Bounds for Runs 

15 & 16 with LHS

Figure E-39: 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for Runs 

15-17 with LHS and the Density Function for Run 15 with LHS
E-56

Figure E-40: 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for Runs 

15-17 with LHS and the Density Function for Run 15 with LHS

E.7.1 Low, Medium, & High Source Term Combined Analysis

From Section E.3, three source terms were selected to test the influence of uncertain MACCS

parameters by themselves. A comparison of these source terms’ conditional, mean, individual 

LCF risk results was conducted by weighting the three source terms’ LCF risks by 1/3 (i.e., each 

represents 1/3 of the source term uncertainty) to the SOARCA UA LCF risk results. Figure E-41 

and Figure E-42 show the comparison for the low source term (CAP29), medium source term 

(CAP32), and high source term (CAP35) with the SOARCA UA results (CAP17) at the 10- and 

50-mile radial distances, respectively. As seen in these figures, the source terms selected are a 

good representation of the 10-mile radial distance and of the 50-mile radial distance to ~80th

percentile where the ‘averaged’ estimate under predicts the LCF risk when compared to the 

SOARCA UA.
E-57

Figure E-41: 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for Low, 

Medium, and High Source Terms with LHS and the Conditional, Mean, 

Individual LCF Risk (per Event) CDF for the SOARCA UA with LHS 

Sampling
E-58

Figure E-42: 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for Low, 

Medium, and High Source Terms with LHS and the Conditional, Mean, 

Individual LCF Risk (per Event) CDF for the SOARCA UA with LHS 

Sampling

E.7.2 Bootstrap Comparison

During the July 10, 2013 ACRS meeting, an ACRS member asked why the NRC/SNL didn’t use 

simple random/Monte-Carlo (MC) sampling for the MACCS portion of the uncertainty analysis. 

Staff responded with the reasons why an LHS is traditionally preferred. But in addition, the 

MACCS code did not have the capability to do a simple random/MC sampling (abbreviated as 

MC in the figure legends). Current updates to the MACCS uncertainty code allow simple 

random sampling (SRS). Thus, a comparison of the SOARCA UA results (CAP17) to the 

CAP17 analysis using SRS/MC was conducted. Table E-19 and Table E-20 show the statistics 

for the conditional, mean, individual LCF risk (per event) results at specified radial distances for 

LHS and MC uncertainty sampling, respectively. Figure E-43 shows the comparison of CAP17 

CCDF LCF risk for LHS and MC results for the 10- and 50-mile radial distances. As seen from 

both the tables and figure, the LHS and MC results are very similar and would be considered in 

good agreement for conditional LCF risk.

Table E-21 and Table E-22 show the statistics for the conditional, mean, individual prompt 

fatality risk (per event) results at specified radial distances for LHS and MC uncertainty 
E-59

sampling, respectively. Figure E-44 shows the comparison of CAP17 CCDF prompt fatality risk 

for LHS and MC results for the 1.3-, 2-, and 3.5-mile radial distances. As seen from both the 

tables and figure, the LHS and MC results are very similar and would be considered in good 

agreement for conditional prompt fatality risk for the 1.3-mile and 2-mile radial distances. This is 

because there are a sufficient number of realizations that have a non-zero prompt fatality risk to 

provide a statistical comparison. Beyond 2 miles, there are few realizations that calculate a 

non-zero result and the statistics are less reliable.

For CAP17, the distribution of mean value based on bootstrap has been displayed for MC 

sampling (i.e., CAP40) and is presented in Figure E-45 and Figure E-46 for the 10-mile and 50-

mile radial distances, respectively. Additionally, Figure E-47 and Figure E-48 show the 

distribution of the mean values based on bootstrap with the density estimated via binning for 

CAP40. This comparison informs on the stability of the mean result for a sample of size 865. 

Two things are considered at this level: 

1. How close are the means, and 

2. How close to a normal distribution is the density function. 

An original sample size of 865 can be considered large enough so that a selection of values 

(with replacement) from a LHS sample will still lead to a good representation of the uncertainty 

in the CDF. Thus, bootstrapping has been used on the LHS results for CAP17 in the same way 

it was used on SRS results in order to compare the stability and check if indeed the LHS results 

look more stable than conditional, mean, individual, LCF risk (per event) results when the same 

sample size is used. These results are presented in Figure E-45 and Figure E-46 for the 10-

mile and 50-mile radial distances (i.e., recall from CAP17 is the Uncertainty Analysis results with 

LHS sampling and CAP40 is the Uncertainty Analysis results with MC sampling).

The distribution of mean value based on bootstrap has been displayed for CAP17 and CAP40, 

with the density estimated via binning for CAP40. This is presented in Figure E-47 and Figure 

E-48 for the 10-mile and 50-mile radial distances, respectively. 

As seen from Figure E-45 through Figure E-48, a reduction of variance in the mean for LHS 

sampling is seen (compared to SRS/MC); this is expected.

Table E-19: Conditional, mean, individual LCF risk (per event) average statistics for the 

MACCS Uncertainty Analysis (CAP17) for five circular areas using LHS 

sampling

0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.7x10-4 2.8x10-4 2.0x10-4 1.3x10-4 1.0x10-4

Median 1.3x10-4 1.9x10-4 1.3x10-4 8.7x10-5 7.1x10-5

5th percentile 3.1x10-5 4.9x10-5 3.4x10-5 2.2x10-5 1.9x10-5

95th percentile 4.2x10-4 7.7x10-4 5.3x10-4 3.4x10-4 2.7x10-4
E-60

Table E-20: Conditional, mean, individual LCF risk (per event) average statistics for the 

MACCS Uncertainty Analysis (CAP17) for five circular areas using SRS/MC 

sampling

0-10 miles 0-20 miles 0-30 miles 0-40 miles 0-50 miles

Mean 1.7E-04 2.9E-04 2.0E-04 1.3E-04 1.0E-04

Median 1.3E-04 1.9E-04 1.3E-04 8.7E-05 7.1E-05

5th percentile 3.0E-05 4.9E-05 3.4E-05 2.2E-05 1.8E-05

95th percentile 4.5E-04 8.8E-04 5.8E-04 3.8E-04 3.0E-04

Figure E-43: CAP17 Conditional, Mean, Individual LCF Risk (per Event) CCDF with LHS 

and MC Sampling for the Radial Distances Considered

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.0E-06 1.0E-05 1.0E-04 1.0E-03

CCDF

Mean, Individual LCF Risk per Event

0-10 miles CAP17-LHS

0-10 miles CAP17-MC

0-50 miles CAP17-LHS

0-50 miles CAP17-MC
E-61

Table E-21: Conditional, mean, individual prompt fatality risk (per event) average 

statistics for the MACCS Uncertainty Analysis (CAP17) for six circular areas 

using LHS

0-1.3 miles 0-2 miles 0-3 miles 0-3.5 miles 0-7 miles 0-10 miles

Mean 4.5x10-7 1.8x10-7 6.4x10-8 3.5x10-8 8.3x10-9 4.8x10-9

Median 0.0 0.0 0.0 0.0 0.0 0.0

75th percentile 0.0 0.0 0.0 0.0 0.0 0.0

95th percentile 1.9x10-6 7.4x10-7 5.3x10-10 0.0 0.0 0.0

Table E-22: Conditional, mean, individual prompt fatality risk (per event) average 

statistics for the MACCS Uncertainty Analysis (CAP17) for six circular areas 

using MC

0-1.3 miles 0-2 miles 0-3 miles 0-3.5 miles 0-7 miles 0-10 miles

Mean 4.6E-07 1.5E-07 5.6E-08 2.8E-09 2.4E-09 4.9E-10

Median 0.0 0.0 0.0 0.0 0.0 0.0

75th percentile 0.0 0.0 0.0 0.0 0.0 0.0

95th percentile 2.3E-06 5.6E-07 8.0E-08 0.0 0.0 0.0
E-62

Figure E-44: CAP17 Conditional, Mean, Individual Prompt Fatality Risk (per Event) 

CCDF with LHS and MC Sampling for the Radial Distances Considered

0.001

0.01

0.1

1

1.0E-12 1.0E-11 1.0E-10 1.0E-09 1.0E-08 1.0E-07 1.0E-06 1.0E-05

CCDF

Mean, Individual Prompt Fatality Risk per Event

0-1.3 miles CAP17-LHS

0-1.3 miles CAP17-MC

0-2 miles CAP17-LHS

0-2 miles CAP17-MC

0-3.5 miles CAP17-LHS

0-3.5 miles CAP17-MC
E-63

Figure E-45: 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for CAP17, 

CAP40, and 95% Confidence Interval Upper and Lower Bounds for CAP17 

and CAP40

Figure E-46: 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDF for CAP17, 

CAP40, and 95% Confidence Interval Upper and Lower Bounds for CAP17 

and CAP40
E-64

Figure E-47: 10-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for 

CAP17, CAP40 and the Density Function for CAP40

Figure E-48: 50-mile Conditional, Mean, Individual LCF Risk (per Event) CDFs for 

CAP17, CAP40 and the Density Function for CAP40
E-65

E.8 MELCOR Parameters

To address ACRS Question 5.a, NRC and Sandia staff conducted a thorough search through 

previous studies and lessons learned. The information provided in this section was 

complimentary to the discussions NRC and Sandia staff provided to the ACRS subcommittee on 

September 16, 2013. A detailed transcript of the verbal discussions can be found in the official 

transcript of the proceedings (ML14014A383). 

E.8.1 Question 5.a.I – SRVLAM

1. Very limited data exists on the probability of an SRV to fail to reclose; what little testing data 

is available is not thought to be representative of the environmental conditions that the SRV 

would experience in a severe accident progression. So the associated stochastic failure 

distribution in the uncertainty analysis is known to be uncertain. However, it is evidenced in 

documented SOARCA uncertainty calculations and in the results of the uncertainty analysis

that the range of the distribution specified leads on one end to cases where the lowest 

setpoint SRV fails open quite early (before the onset of core damage) and on the other end 

to cases quite late (such that a MSL rupture results). The fact that these extremes are 

captured is thought to be a good indication that the stochastic failure distribution specified in 

the uncertainty analysis is inclusive of the possible meaningful over-cycle failures that an 

SRV might suffer.

2. The SOARCA probability for SRV stochastic failure to reclose was adopted from the Peach 

Bottom IPE as 3.7x10-3 per demand which relates to failure after 270 cycles. 

3. A beta distribution with mean equal to the SOARCA failure-to-close probability of 

3.7x10-3 per demand was applied in the uncertainty analysis sampling of SRV stochastic 

failure criterion. The beta distribution is typically used to represent uncertainty in stochastic 

failure-on-demand parameters. The sampling resulted in a distribution skewed towards 

more cycles to failure relative to the SOARCA estimate as illustrated in the Figure E-49. 

4. As noted in Section 4.1.1, a stochastic failure rate of 9x10-3 per demand or below; the SRV 

will fail from thermal seizure and/or MSL creep rupture and the shape of the distribution 

below this value has no bearing on results.

5. Stochastic failures are treated as fully separable from elevated temperature effects in the 

uncertainty analysis as in the NUREG/CR-7110 Volume 1 Peach Bottom LTSBO MELCOR 

model. 

6. Differential thermal expansion of adjacent moving parts resulting in seizure, at temperatures 

exceeding design, is categorized as a ‘thermal’ failure in the uncertainty analysis. 

7. Failure due to plastic deformation of valve parts at severe temperatures is also categorized 

as a ‘thermal’ failure in the uncertainty analysis. 

8. The uncertainty analysis assumes a stochastic SRV failure to reclose always results in a 

fully open valve.

9. If an SRV were to fail closed, pressure relief would move up to the SRV with the next lowest 

pressure setpoint. Peach Bottom has 11 SRVs. The possibility that all of the SRVs could fail 

closed is considered remote and so is not addressed in the uncertainty analysis. 
E-66

10. Similarly, if an SRV were not to open on demand, pressure relief would move up to the SRV 

with the next lowest pressure setpoint. The possibility that all of the SRVs could fail to open 

is considered remote and so is not addressed in the uncertainty analysis. 

Figure E-49: CDF of Failure Probability/Number of Valve Cycles

E.8.2 Question 5.a.II – CHEMFORM

1. The peak gaseous iodine amounts recorded in four different Phebus experiments were 

fundamental in defining the five speciation combinations of cesium and iodine considered in 

the uncertainty analysis. A combination was devoted to each of the four recorded amounts 

and a 5th combination was formed by averaging the four recorded amounts of iodine 

together. Equal weighting in the parameter sampling was given to all but the 5th combination 

which was weighted four times greater than the other combinations reflecting that it was 

jointly formed from the iodine recorded in the four experiments.

2. With gaseous iodine (fraction of initial core inventory) defined for the five combinations, 

enough cesium was defined as CsI to involve all of the iodine not defined as gaseous (i.e., 

most all of the iodine).

3. Remaining cesium was defined in the different combinations to be either in the form of all 

CsOH, all Cs2MoO4, or half CsOH and half Cs2MoO4. 

4. With respect to cesium speciation, Combinations 3 and 5 closely match the SOARCA 

calculation. In the sampling of the chemical form of iodine and cesium, Combination 3 

results once in every eight realizations while Combination 5 results four times in every eight 
E-67

realizations. In five of every eight realizations then, the cesium speciation closely resembles 

the cesium speciation in the SOARCA calculation.

5. There is no speciation combination that matches the iodine and cesium speciation of the 

SOARCA calculation identically. Combination 3 comes closest with the smallest fraction of 

gaseous iodine (~0.3%) and 100% Cs2MoO4. SOARCA did not include any gaseous iodine.

6. In all cases, including the SOARCA case, 1% of the initial cesium inventory is defined to be 

elemental cesium residing in the fuel-cladding gap.

7. The discussion below are results of the Phebus studies that were used to inform the 

gaseous iodine used for this work:

a. Phebus FPT-0 

• Gaseous iodine: 

o 3% +/- 1.1% of initial iodine inventory (33% +/- 12.1%) of the total iodine found in 

containment during 13500 ~ 13700 sec, following first zircaloy oxidation phase)

o The gaseous iodine concentration level drops after the main zircaloy oxidation 

phase in few hours (2.5% of the initial bundle inventory, 0.039% of the total 

iodine in containment after core shutdown and 0.32+/-0.16% of the bundle 

inventory after containment isolation), due to steam condensation on the painted 

condenser and/or adsorption process on other containment surfaces.

• References: FPT0 Final Report Part D, 3-3 and FPT1 Final Report Section 5, 5.4.4.4

b. Phebus FPT-1 

• Gaseous iodine fraction:

o At first oxidation phase: At least 0.2 +/- 0.045% bundle inventory (corresponds to 

4.05 +/- 0.9% of the containment inventory) 

o After two oxidation phases, level drops to about 0.07+/-0.016% of the initial 

bundle inventory due to similar reasons as in FPT0.

• Reference: FPT1 Final Report Section 5, 5.4.4.4

c. Phebus FPT-2 

• Unlike the previous two tests, the gaseous iodine concentration in containment is 

minimum during or following the main oxidation phase. The gaseous iodine fraction

was determined from the following table: 

Time (sec) % gaseous Iodine of the 

initial bundle inventory

% gaseous Iodine of the total 

found in containment

10322-10387 0.011 0.209

13742-13848 0.128 0.392

16267-16453 0.298 0.615

16878-16918 0.196 0.375

20281-20583 0.083 0.146

• Reference: FPT2 Final Report Section 5, 5.4
E-68

d. Phebus FPT-3 

• Sharp increase of gaseous iodine and the peak observed at about ~ 14000 sec, just 

after the main oxidation phase (~9700 sec to ~11000 sec). Iodine concentration then 

drops due to depositions onto surfaces. The gaseous iodine fraction was determined 

from the following table: 

Time (sec) % gaseous Iodine of the 

initial bundle inventory

% gaseous Iodine of the total 

found in containment

9894-10208 0.28 63.11

10387-10512 0.42 32.91

10389-10703 1.49 98.79

11795-12097 7.57 60.4

15028-15135 7.26 22.83

17038-17210 2.85 8.6

18692-18963 2.12 6.22

• Reference: FPT3 Final Report 5.4, Table 5.4.2.10

e. Phebus FPT-4 

• The FPT4 test objectives didn’t include the study of iodine behavior in containment. 

E.8.3 Question 5.a.III – FL904A

1. Drywell liner shell melt-through occurs in the MELCOR model when molten-core debris 

contacts the drywell liner with a temperature of 1,700 K or higher (the melting temperature of 

carbon steel) for a period of five minutes. Stress induced in the liner due to pressurization of 

the drywell is not considered in the shell melt-through determination.

2. All of the uncertainty analysis realizations suffered a drywell liner melt-through as did the 

SOARCA calculation.

3. The drywell floor is characteristically dry in the LTSBO scenario (see the Figure E-50 for an

example).

4. Upon drywell shell liner melt-through in the SOARCA calculation, a 1.667-m long by 6-cm 

high (0.1-m2 area) slit was opened between the lower drywell and the main torus room at the 

elevation of the drywell floor.

5. In the uncertainty analysis sampling of melt-through size, the lower bound of 0.05 m2

(≈ 10 inch diameter hole) is half the SOARCA estimate and is the minimum observed critical 

zone determined for a damage index profile at 1143°C (2090°F) in NUREG/CR-6025. The 

upper bound (1.0 m2 ≈ 44-inch diameter hole) is determined as a sufficient flow area to 

provide containment depressurization within a few minutes, and is 14% greater than the 

maximum observed critical zone (0.88 m2

) determined for a damage index profile at 1260°C 

(2300°F) in NUREG/CR-6025.
E-69

Figure E-50: Typical LTSBO Drywell Characteristics

6. The hole opened in the drywell shell in the uncertainty analysis realizations, like in the 

SOARCA calculation, was 6 cm tall. It was as long as necessary to develop the sampled 

value of area. The hole was opened at a rate reflecting core-concrete debris moving as a 

stream to the liner and then along the liner in both directions at 0.72 m/min. The 0.72 m/min 

is the velocity observed in preliminary LTSBO calculations of core-concrete debris spreading 

on the drywell floor. At this velocity, it would take 35 sec to open a 0.05-m2 hole and 

11.57 minutes to open a 1-m2 hole.

7. Originally a uniform distribution was applied between these bounds, but the team felt this 

distribution did sample lower values often enough, and such as values closer the SOARCA 

value which is still thought to be the ‘best-practice’ nominal value. The team settled on 

applying a log-uniform distribution in the sampling of melt-through area, which still resulted

in a distribution skewed towards larger areas relative to the SOARCA estimate.

E.8.4 Question 5.a.IV – BATTDUR

See Section E.10.4 for further discussions regarding operator actions. 

E.8.5 Question 5.a.V – SRVOAFRAC

1. This parameter is the open area fraction of the lowest-setpoint SRV in the MELCOR model 

subsequent to it overheating to failure. This open fraction only applies to an overheating 

(thermal) failure of the valve to reclose (i.e., it does not apply to an over-cycling (stochastic) 

failure of the valve to reclose). Over-cycling failures are assumed to leave the valve in a fully 

open position.
E-70

2. Since heating of an SRV would predominately occur when it is flowing (i.e., when it is open),

it seems plausible that seizure of adjacent moving parts or deformation of valve parts would 

occur with the valve at least partway open.

3. A log-uniform distribution was employed in the sampling of SRVOAFRAC with mode 1.0, a 

minimum value of 0.1, and maximum value of 1.0. This sampling weighted larger area 

fractions more heavily than smaller fractions.

4. Sampling was skewed to higher values because the geometry of the SRV is such that it 

does not have to vertically traverse much of its stem length before reaching an open area 

close to fully open.

5. The possibility of an over-heating failure that leaves an SRV fully closed was not 

considered. If such were to happen, pressure relief would move on to the SRV with the next 

lowest pressure setpoint. There are 11 SRVs at Peach Bottom so the likelihood of all the 

SRVs failing closed seems remote.

E.8.6 Question 5.a.VI – SLCRFRAC

1. The intent in the uncertainty analysis was to open the MSL to the containment through an 

area equivalent to the full cross-sectional area of the pipe 85% of the time. However, the 

means through which the MSL rupture is accomplished in the Peach Bottom MELCOR

model (i.e., adjusting the flow area of 3 junctions), leads to an effective break area equal to 

the full area of the pipe for any value of SLCFRAC greater than or equal to 0.5. So, the MSL 

was actually opened fully to containment 96% of the time in the UA.

2. Applicable SOARCA Peer Review comments and resolutions are provided below:

a. Jeff Gabor – December 22, 2010 SOARCA Peer Review Memorandum

• Comment: The potential for Main Steam Line creep failure is not being considered 

as an uncertain parameter. The MSL rupture area for such a failure would likely be 

large and probably does not need to be evaluated as an uncertain parameter. I 

recommend that this uncertain parameter be replaced with a parameter that more 

directly relates to MSL creep failure.

• Resolution: The SOARCA team re-evaluated this phenomenon in regards to this 

comment. Our rationale is that the uncertainty in the parameters affecting the 

calculated potential for creep can be neglected in this assessment because prior 

experience (through sensitivity analyses) suggests the Larson-Miller (L-M) damage 

index transitions from zero to values well above unity within a very short time. The 

L-M parameter is not likely to be very sensitive because once the MSL enters creep 

conditions, the progression is very fast from 0 to 1. 

On the other hand, we consider the area of the rupture as an important uncertain 

parameter because it relates to the more important factor of how we model flow to 

and through the MSL, and associated heat transfer to wall piping. And after the 

October 2010 and December 2011 Peer Review meetings and feedback, we have 

re-assessed the distribution for the MSL rupture area. It is now skewed heavily to 

large open areas, with only a small residual probability (0.01) of an open area less 

than 10%.
E-71

b. David Leaver – December 22, 2010 SOARCA Peer Review Memorandum

• Comment: In the paragraph on Main steam line creep rupture area, should the 

uncertainty in the main steam line temperature be considered?

• Resolution: The main steam line structure temperature is calculated by the model 

and hence is not an uncertain input parameter. We consider the area of the rupture 

as an important uncertainty parameter. The rupture area is important because it 

affects containment response to MSL failure. Large areas generate relatively large 

pressure loads on the containment, and offer an opportunity for advancing the time 

of containment failure. The proposed SOARCA UA study considers the area of the 

rupture as an important uncertainty parameter because it relates to the more 

important factor of how we model flow to and through the MSL, and associated heat 

transfer to wall piping. After the October 2010 and December 2011 Peer Review 

meetings and feedback, we have re-assessed the distribution for the MSL rupture 

area. It is now skewed heavily to large open areas, with only a small residual 

probability (0.01) of an open area less than 10%.

In addition, uncertainty in the parameters affecting the calculated potential for creep 

is neglected in this assessment because prior experience (through sensitivity

analyses) suggests the L-M damage index transitions from zero to values well above 

unity within a very short time. The L-M parameter is not likely to be very sensitive 

because once the MSL enters creep conditions, the progression is very fast from 0.0

to 1.0. 

E.8.7 Question 5.a.VII – RDMTC and RDSTC

1. The improvements to fuel degradation modeling and 2-dimensional core modeling show a 

delayed heat-up followed by accelerated oxidation. The accelerated oxidation phase ends 

following molten Zircaloy breakout. Without Zircaloy, the subsequent heatup is primarily 

controlled by decay heat. The best-practice modeling of Zircaloy-oxide collapse creates a 

debris bed similar to TMI-2. The debris bed slows oxidation by creating blockages and 

inhibiting natural circulation. The debris bed gradually grows axially and radially, which 

eventually leads to core plate failure

2. These affect the rate of radial relocation from ring to ring of either solid debris material or 

molten materials that may be supported by complete underlying blockages. Significant 

changes (upwards) in the default values for these parameters were made in the 

Version 1.8.5 release of MELCOR, based mostly on recommendations from ORNL and on 

intuitive reasoning with respect to smooth behavior in the melt progression. The previous 

values (short time constants) produced sometimes-erratic behavior that did not seem 

physically reasonable. Siemens uncovered sensitivities here and explored ranges below 

those currently recommended in the MELCOR 1.8.5 defaults. At this point, we do not 

recommend varying these parameters for this study as sensitivities to hydrogen are not 

expected from variations about the currently used values. Additionally, the basis for variation 

of this parameter would be difficult to rationalize.

3. Applicable SOARCA Peer Review comment and resolution is provided below:

a. David Leaver – December 22, 2010 SOARCA Peer Review Memorandum
E-72

• Comment: Radial debris relocation time constants are another example of a 

parameter where there is no basis for the characterization of uncertainty. Also, there 

are two incomplete sentences at the bottom of the paragraph.

• Resolution: A technical basis has been added to Section 4.1.2 of the draft 

NUREG/CR report for this parameter and the editorial changes have been made.

The relocation time constant is meant to capture the rate of radial debris movement 

to the center and thus determine the time the debris moves to the lower plenum. This 

movement to the lower plenum then determines the time at which the lower plenum 

will fail. The distributions are based on expert judgment but are not based on TMI 

data since no data from TMI exists for radial debris relocation distribution. It is one of 

the few parameters to which a user has access to influence large scale movement 

and influences axial debris relocation as well. The time scale is a surrogate for the 

uncertainty in large scale movement. The range covers molten to solidus of 

core melt.

E.8.8 Question 5.a.VIII – RRIDRFRAC and RODRFRAC

1. Sampling of railroad door open fraction was bound between something relatively small and 

something relatively large. The doors are large, and so even the smallest open fraction in 

the sampling related to a fairly large hole (4’-10” square). Sampling was done uniformly for 

lack any knowledge of whether small or large openings are most likely. What showed to 

matter in the uncertainty calculations was whether these doorways opened; rather than how 

much they opened. Thus, the exact distributions were unimportant to the results.

E.8.9 Question 5.a.X – RHONOM

1. The average material density of the particulate released to the environment in the SOARCA 

LTSBO MELCOR calculation (6.45E+03 kg/m3

) served as the basis for the sampling of 

particle density in the uncertainty analysis calculations. Packing factors of 0.18 minus 25% 

variance (= 0.135) and 0.5 plus 25% variance (= 0.626) were applied to the average from 

the SOARCA calculation to define the lower and upper bounds of the sampling as 870 kg/m3

and 4,037 kg/m3

, respectively. A triangular distribution was invoked with mode equal to the 

MELCOR default density of 1,000 kg/m3 lending somewhat of a bias toward smaller 

densities in the sampling. At first, DASF was also identified as an uncertain parameter for 

sampling, but there was a worry about simultaneous varying both variables potentially 

leading to the modeling of unphysical conditions. After further deliberation and consultation 

with experts, the team concluded that assuming a DASF of 1 (perfectly spherical) and 

varying RHONOM should capture the effects of uncertainty stemming from both these 

related parameters.

E.8.10 Question 5.a.XI – FFC

1. The hydrogen uncertainty analysis done at Sandia in 2002 didn’t make use of a time-attemperature consideration for fuel rod collapse. It instead prescribed collapse at a threshold 

temperature considered to be distributed normally about a best-estimate value of 2,575 K 

with upper and lower bounds of 2,400 K and 2,700 K, respectively. The distribution was 

based on interpretations of results from the Phebus FPT-1 and FPT-2 tests. Further 

discussion will be provided by Sandia about why the team incorporated a time-at-
E-73

temperature collapse criteria for oxidized fuel rods at the ACRS subcommittee meeting. 

Maybe his explanation with a mentioning of the Phebus temperatures will satisfy the ACRS. 

E.8.11 Question 5.a.XII – SC1141(2)

1. SOARCA best practices for the value of SC1141(2) (the maximum melt flow rate per unit 

width after breakthrough) has been adjusted to 0.2 kg/m-s to yield an effective velocity of 

2 mm/s which reflects observations made in CORA experiments. 

2. The hydrogen uncertainty analysis done at Sandia in 2002 did not address SC1141(2). It 

does state that measurements taken from video observation of CORA experiments revealed

that while some free-falling molten droplets relocate very rapidly, most of the downward 

draining melt moves more on the order of millimeters per second.

E.9 MACCS Parameters

To address ACRS Question 5.b, NRC and Sandia staff conducted a thorough search through 

previous studies and lessons learned. The information provided in this section was 

complimentary to the discussions NRC and Sandia staff provided to the ACRS subcommittee on 

September 16, 2013. A detailed transcript of the verbal discussions can be found in the official 

transcript of the proceedings (ML14014A383). 

E.9.1 Question 5.b.I and 5.b.II – DOSNRM, TIMNRM, DOSHOT, and TIMHOT

Hotspot and normal relocation of the public are additional protective measures that may be 

modeled in the MACCS code. These are implemented after the initial evacuation and after 

plume arrival. The EPA Manual of Protective Action Guides (PAGs) (EPA 400: Table 2-1) 

recommends evacuation of the public if the projected dose range is from 1 to 5 rem, calculated 

as the projected sum of the effective dose over the early phase. These EPA PAGs have 

traditionally been implemented in MACCS as hotspot and normal relocation with hotspot set at 5 

rem and normal at 1 rem and typically apply to residents in areas beyond the emergency 

planning zone (EPZ). This is because the EPZ has been evacuated. However, the State or 

local authorities make the protective action decisions and can follow EPA PAGs or use different 

values. 

There are many opportunities for uncertainty in the dose and time values used in the analysis. 

In addition to authorities potentially selecting different values, the dose can be influenced by 

meteorology, shielding, infiltration of contamination indoors, and other factors.

The initial projected dose would typically be based on a dose model that includes atmospheric 

modeling, while later in the event, field surveys would provide actual data. The source of the 

model data is the site meteorological tower, which is located at least 10 miles from the relocated 

population who reside beyond the EPZ. There is uncertainty in applying calculating the 

relocation dose using meteorological data from a source 10 miles away. 

Dose to the public also depends on the shielding factors used in the analysis. MACCS allows a 

single value for sheltering which is intended to represent the typical shielding capacity of 

housing within the region. However, an average value may not be representative because 

housing types are not uniformly distributed. For instance, trailer parks and brick housing are not 

typically intermixed. The variation in housing stock and the distribution of types of housing are 

not standard introducing uncertainty when an average value is applied. Furthermore, the dose 
E-74

projection is calculated assuming the residents stay indoors for the entire time and does not 

consider the potential for equilibration of contamination indoors and outdoors through infiltration 

into the homes. This is another introduction of uncertainty. 

The selection of 0.5 rem for the normal relocation was based on input from the State; therefore, 

this value has high confidence. The 5 rem hotspot relocation is established from the EPA 

PAGs. There was an interest in understanding the sensitivity of hotspot and normal relocation. 

Thus, we only needed to establish a reasonable range to determine the contribution of these 

parameters to the risk. With the modes established, the team selected the upper and lower 

bounds shown in Table 4.2-14. 

The relocation times also do not need to be precise to identify the contribution to risk. 

Relocation is typically implemented beyond the EPZ and after plume arrival. A release of 

sufficient size such that relocation is required, has broad impacts in the area, and response 

agencies would have competing priorities. For Peach Bottom, evacuation of the EPZ has been 

completed for almost 50,000 people. Congregate care centers (Shelters) have been 

established, traffic control is in place, people are being monitored, field teams are confirming on 

ground doses, and Federal resources have arrived to support the local agencies. The timing of 

the relocation is important at this point, but not urgent, because this is a 4 day integrated dose. 

A few hours delay in relocation would not be expected to increase risk to residents beyond 

10 miles to a significant degree. Therefore, reasonable ranges were established based on 

when offsite resources would likely be available to implement relocation. The hotspot value of 

12 hours (after plume arrival) considers that the Federal Radiological Monitoring and 

Assessment Center (FRMAC) would be in place (or nearly in place) at this time and DOE 

resources could help with definition of hotspot areas and relocation of individuals. The State 

and county resources would have completed evacuation activities within the EPZ and could 

support relocation efforts beyond the EPZ. Hotspot relocation is completed first. The normal 

relocation value of 24 hours was established to provide ample time to complete the hotspot 

relocation recognizing the normal relocation for dose of 0.5 rem is not urgent. The upper and 

lower bounds were set at 200% and 50% of the mode of the relocation times to identify any 

sensitivity in the timing.

A triangle distribution was selected because the team had a mode (the nominal, most likely 

value) and upper and lower bounds. A normal distribution could have been applied, but was not 

selected because we had a nominal, most likely value for the mode. 

E.9.2 Question 5.b.III – ESPEED 

Evacuation speeds are developed using a traffic simulation model that analyzes the travel of 

vehicles over a roadway segment under specified conditions. Generally speaking, a roadway 

segment has a maximum capacity that may be calculated using Highway Capacity Manual 

methods based on the roadway characteristics (i.e., number of lanes, width of lanes, free-flow 

speed, intersection control, etc.) As the number of evacuating vehicles exceed the capacity, 

congestion occurs. 

There are three speeds assigned for each cohort including ESPEED early, ESPEED mid, and 

ESPEED late. ESPEED early reflects the initial speed of the cohort when they begin their 

evacuation. ESPEED late is the speed of the cohorts typically after they have exited the EPZ. 

ESPEED mid was the parameter evaluated in the uncertainty analysis because this represents 

the cohorts as they travel within the EPZ at times when congestion is present, specifically for 

the general public, which is the largest population group. 
E-75

The evacuating speed on any given roadway within the Peach Bottom EPZ is primarily 

influenced by the roadway (and intersection) capacity and the number of vehicles. As shown in 

Figure E-51, there are multiple evacuation routes, each of which may have a different 

evacuation speed. The MACCS model allows a single speed value for ESPEED mid for each 

cohort. 

Figure E-51: Peach Bottom Evacuation Routes

For the general public cohort (Cohort 1 in Table 4.2-16), the team develop the average 

evacuation speed for the entire EPZ of 3 mph, based on the traffic simulation model output and 

mobilization activities described in the ETE study. The team does not considering uncertainty in 

the traffic model. The team can establish an initial bound knowing the speed must be greater 

than 0.0 and less than the evacuation roadway speed limits which range from 20 to 55 mph (an 

average of about 35 mph). Therefore, the initial range is 0.0 to 35 mph with a mode of 3 mph. 

The team refined the bounds by using information from the ETE study, which describes 

congestion along the evacuation routes. For congestion to occur, the upper bound must be less 

than the average speed of 35 mph. The ETE study indicates that the evacuation speed in 

select areas is twice the average evacuation speed, or about 6 mph. For the upper bound the 

team rounded this value to 10 mph. To establish a lower bound, the team needed a value 

between 0.0 and 3 mph. It is not an option to select 0.0 mph, because this would effectively be 

a shelter in place. The team selected 1 mph to provide the greatest chance of observing an 

increase in risk. The speeds for the remaining cohorts were developed with similar rationale, 

and also considered when the cohort enters the roadway network. 

A triangular distribution was applied because the team has confidence in the mode and the 

team was able to define upper and lower bounds with some confidence. A normal distribution 

was considered but discounted because it is less likely speeds would be slower than the mode 

and more likely they would be greater than the mode. A discrete distribution is possible for 

evacuation speeds and could have been applied had the raw output from the traffic simulation 

model been available. However, even if the data were available, a distribution would have been 

developed for each evacuation route and then would have been averaged because MACCS

only allows one ESPEED and value for each cohort.
E-76

E.9.3 Question 5.b.IV – GSHFAC

In MACCS, shielding and protection factors are specified for each dose pathway and directly 

affect the dose received by individuals at each location. The shielding factors are used as 

multipliers on the dose that a person would receive if there were no shielding or protection. 

Thus, a shielding factor of one represents the limiting case of a person receiving the full dose 

(i.e., standing outdoors and completely unprotected from exposure); a shielding factor of zero 

represents the limiting case of complete shielding from the exposure. The shielding factors 

used in the MACCS calculation are clearly important because the doses received are directly 

proportional to these factors. As shown in Figure 4.2-3, the range of uncertainty of the shielding 

factors would be expected to have a significant impact on the overall outcome of a consequence 

analysis. 

While shielding factors for three dose pathways, groundshine, cloudshine, and inhalation, were 

treated as uncertain in the uncertainty analysis, groundshine is usually the most important of 

these pathways because of the dominant contribution of gamma radiation from the decay of 

Cs-137 (actually from its daughter, Ba-137m) during the long-term phase. Thus, it is important 

to treat the uncertainty of GSHFAC in the MACCS model in this uncertainty analysis. GSHFAC 

for the emergency phase was taken to be rank correlated with a similar parameter used in the 

long-term phase. This assumption makes sense because we also assume that the same 

building structures continue to be used (unless they are condemned) following the emergency 

phase.

Three types of activity, normal, sheltering, and evacuation, are evaluated for each dose 

pathway, resulting in nine sets of shielding factors. Normal activity refers to a combination of 

activities that are averaged over a week and over the population, including being indoors at 

home, commuting, being indoors at work, and being outdoors at home or at work. 

Values for GSHFAC are provided in Table 4.2-3b. Groundshine shielding factors are taken from 

a joint NRC/CEC study and were compiled by Bixler in NUREG/CR-7161. The values in 

Table 4.2-3b are taken directly from this NUREG/CR report, which faithfully represents the 

expert elicitation data. 

Values for GSHFAC are used in the uncertainty analysis with the further assumption that the 

distributions for normal activity and sheltering are correlated with a rank correlation coefficient 

(RCC) of 0.75. This correlation is applied for normal and sheltering activities for each of the 

dose pathways, including groundshine. There is no correlation between the three pathways. 

Each parameter (CSFACT, GSHFAC, PROTIN) can be specified for each of the six cohorts in 

WinMACCS. In the SOARCA analysis, the values listed in Table 1 were used. GSHFAC values 

for Cohorts 1, 2, 3, 5, and 6 were chosen to be identical. Cohort 4 is special facilities, which 

was assigned different shielding values in the SOARCA study. For this study, a single 

distribution was sampled and applied to all of the cohorts for simplicity. 

Uncertainty in groundshine doses has two components: uncertainty in the amount of shielding 

between an individual and the source of the groundshine (GSHFAC) and uncertainty in the 

energy deposited within a human organ for specified incident radiation. Distributions 

representing the uncertainty in the groundshine shielding factors (GSHFAC) are presented in 

Table 4.2-3b. Additional uncertainties of the deposition of radiation in individual organs stem 

from age, height, and weight variations of the population exposed to the radiation. Eckerman 

[E.3] recommended that a triangular distribution be used to represent uncertainty in dose 

coefficients. The parameters for that distribution are presented in Table 4.2-5. 
E-77

To simplify the implementation of uncertainty in the energy deposited within a human organ for 

a specified incident radiation, Eckerman [E.3] recommended that a single uncertainty 

distribution be applied as a multiplicative factor for all radionuclides and for all organs. 

Furthermore, Eckerman suggested that the uncertainty in groundshine dose coefficients are

highly correlated over the set of human all organs. As a result, it is possible to combine the 

uncertainty in the groundshine shielding factor and the uncertainty in the dose coefficients into a 

single uncertainty factor, which can be implemented as an overall uncertainty in the 

groundshine shielding factor (GSHFAC). Further, Eckerman recommended that the 

uncertainties in the groundshine shielding factor and in the groundshine dose coefficients 

should be treated as uncorrelated.

The distribution for groundshine shielding factor is presented in Table 4.2-3b. The parameters 

for the triangular distribution used to represent uncertainty in the dose coefficients for 

groundshine radiation are presented in Table 4.2.5. Piecewise uniform distributions for the 

overall uncertainty in GSHFAC are provided in Table 4.2-6 and plotted in Figure 4.2-5. These 

distributions are the ones used in the uncertainty analysis. The resulting rank correlation for the 

combined groundshine shielding factors were implemented using 0.76 for normal and 

sheltering, 0.2 for normal and evacuation, and 0.15 for sheltering and evacuation. 

E.10 Other Issues

To address ACRS Question 6, NRC and Sandia staff conducted a thorough search through 

previous studies and lessons learned. The information provided in this section was 

complimentary to the discussions NRC and Sandia staff provided to the ACRS subcommittee on 

September 16, 2013. A detailed transcript of the verbal discussions can be found in the official 

transcript of the proceedings (ML14014A383). 

E.10.1 Question 6.a – Surrogate Parameters

1. Zr breakout temperature: From the Sandia hydrogen uncertainty study conducted in 2002, 

“The MELCOR parameter that controls the retention of molten zircaloy within the outer ZrO2

shell is probably the most important factor affecting the total amount of hydrogen produced 

in the early stage of core degradation. The default value is 2400K, considered to be a most 

likely value based upon assessment of many experimental studies, including the Phebus 

FPT-1 test. Highly reducing (H2) conditions could encourage melt breakout at a lower 

temperature, as could protracted time encountered in the 2200K-2400K temperature range, 

owing to effects of oxygen profiles in the cladding oxide phase layers and on kinetics 

respectively. It is not considered likely that breakout could be delayed to temperatures 

higher than ~2500K owing to the strong tendency for Zr metal to dissolve its oxide and due 

to the fact that complete rod collapse by slumping and/or liquefaction seems to begin at 

about this temperature as evidenced from Phebus tests. A reasonable range for parameter 

variation is considered to be 2250K to 2550K, with a most probable value of 2400K. The 

Siemens report is consistent with this determination.”

2. In-vessel radial relocation time constants for molten and particulate debris: Certain 

parameters were correlated in the uncertainty analysis sampling. RDMTC and RDSTC, the 

time constants for radial relocation of molten and solid debris within the RPV, respectively, 

were correlated to prohibit combinations where solid debris relocated faster than liquid 

debris. Similarly, DHEADLIQ and DHEADSOL, the debris height required for lateral 

movement of core-concrete debris at the liquidus and solidus temperatures (of concrete), 
E-78

respectively, were correlated so that cooler debris never moved more readily than hotter 

debris.

E.10.2 Question 6.b – Lower Head Penetration Failures

The lower head penetration model in MELCOR is largely parametric but does employ important 

mechanistic heat transfer considerations. The model considers the limited contact area 

available for conduction between, for example, a guide tube and the lower head, i.e., the area of 

the circumferential weld securing and sealing the tube to the head. It also considers the surface 

area of the tube available for contact with core debris relocated to the lower plenum as well as 

the user-definable heat transfer coefficient between the tube and the debris. The mass of the 

tube is accounted for in calculating its heating. The temperature associated with failure of the 

tube/penetration is defined by the user.

The input specified to the penetration model in the standalone calculations of Section 6.4.2 was 

descriptive of instrument guide tubes and their associated penetrations. Given that a drain line 

is of somewhat different construct than an instrument guide tube, the calculations probably do 

not best address the specific interest the ACRS has expressed in the susceptibility and 

ramifications of the drain line overheating to failure. However, the construct and size of a guide 

tube penetration (1.5-in inner-diameter) and the 2-in drain line are not so different and the 

sampling of the number of penetrations enabled to fail resulted in a number of cases with initial 

leakage areas similar to the area of the 2-in drain line (i.e., leakage areas that were small). Little 

enough material passed through the small breaches in these cases that the calculations 

progressed to gross failure of the lower head. Key to the progression in these calculations to 

gross lower head failure may be that little ablation of the failed penetrations occurred likely due 

to the low-pressure situation of the RPV. Higher pressures would drive more material through 

the breach aggravating the ablation. SNL argues then that the stand-alone calculations 

undertaken to investigate the susceptibility of lower head penetrations to failure and the 

ramifications of their failure address the drain line fairly well.

E.10.3 Question 6.c – Drywell Liner Failure

Neither the drywell liner melt-through nor the core-concrete spreading models are mechanistic 

enough to claim that the phenomena they represent are accurately simulated. Both models are 

largely parametric and uncertainty exists in the key parameters. However, the dependencies 

within the models are understandable and the uncertain parameters serve as a means to 

investigate the importance of the phenomena relative to the metrics of the uncertainty analysis 

(e.g., relative to iodine and cesium releases to the environment). 

The presence of water in contact with the core-concrete debris is inherently considered in both 

models in that water would serve to cool the debris. Cool enough debris is prohibited from failing 

the drywell liner and the movement of core-concrete debris is slowed or stopped dependent 

upon how cool the debris becomes. However, the LTSBO scenario does not result in amounts 

of water making it to the drywell floor that quench or even significantly cool the debris. 

Consequently, the potential benefits of water interacting with the debris are not realized.
E-79

E.10.4 Question 6.d – Operator Actions

1. Operators manually open SRV: 

• When plant conditions stabilized in a LTSBO, Special Event Procedure SE-11 would call 

for a controlled depressurization of the RPV to 125 psig using the instructions in the 

RC/P Leg of Trip Procedure T-101. Depressurization would be accomplished by 

opening one or more SRVs or, if necessary, by manually opening other steam vent 

pathways, such as main steam line drains. The cooldown rate would be limited to less 

than 100°F per hour. In the SOARCA calculation, conditions were judged to be stable 

1.0 hours into the blackout, and a controlled depressurization was initiated by opening a 

single SRV. Variations about the 1-hr timing in the SOARCA calculation were 

investigated in the uncertainty analysis that were simply considered to be reasonable.

2. Operators shed DC loads:

• The load shedding is expected to extend battery life from 2 hours (with no load 

shedding) to 4 hours (with load shedding). This information was obtained through 

SOARCA-initiated communication with Peach Bottom system engineers. The action to 

shed loads is directed by applicable Special Event Procedure SE-11.

• As noted in Section 4.1.1, an upper limit of 8 hours was chosen based on input from the 

licensee. In 2008 to most recently in 2011, NRC staff had informal discussions with 

knowledgeable Peach Bottom personnel on what the range of battery duration may truly 

be. In some plant calculations, battery durations were shown to possibly last up to 

12 hours. However, plant personnel felt strongly that our public uncertainty analysis 

should not credit anything higher than 8 hours in the unmitigated LTSBO scenario. Staff 

explained the interpretation of higher percentiles (e.g., asked, as an example, whether 

they felt that there was truly less than one-in-a-hundred chance that the battery could 

last more than 8 hours). Even faced with this formulation, plant personnel were unwilling 

to place an upper bound at anything higher than 8 hours.

The unmitigated case credits automatic system responses and manual actions that would be 

directed by plant EOPs, such as operator reactor vessel depressurization and intervention to 

control RCIC injection flow (after its automatic actuation) to stabilize and maintain the level 

within a target range. The unmitigated case did not credit operator actions that are beyond the 

scope of EOPs – primarily, the mitigation measures installed in response to 10CFR50.54(hh). 

The following is the timeline of events and operator actions that were credited in the LTSBO 

unmitigated case with SE-11 procedures only:

Event Initiation and Initial Plant Response

• Control room receives indication that plant is in a station blackout condition requiring the 

operator to enter Special Event Procedure SE-11, “Station Blackout Procedure.” RCIC 

automatically starts when level drops to low-level setpoint with suction aligned to the 

CST.
E-80

10-15 minutes

• In accordance with SE-11, plant operations personnel initiate the following mitigation 

measures:

o Attempt to line up the Conowingo hydroelectric dam (i.e., station blackout line) as an 

alternative offsite power source, but the line is not available.

o Attempt manual start of emergency diesel generators, but none is available.

o Begin to shed non-essential loads from the emergency DC bus.

1 hour

• Actions to shed non-essential loads from DC bus is complete, battery life extended to an 

estimated 4 hours. 

2 hours

• Operator assumes remote manual control of RCIC flow.

4 hours

• DC power from station batteries is exhausted. The consequences of a loss of DC power 

are:

o Open SRV closes.

o Remote control of RCIC flow terminates. The system is assumed to continue 

operate at the conditions it experienced immediately prior to battery exhaustion. This 

effectively assumes the RCIC pump continues to operate at a constant rate, 

ultimately flooding the main steam line causing delayed termination of RCIC.

E.11 References

E.1 Nuclear Regulatory Commission, Official Transcript of Proceedings, Advisory Committee 

of Reactor Safeguards Regulatory Policies and Practices, September 16, 2013, 

Rockville, MD.

E.2 Helton, J.C., F.J. Davis, and J.D. Johnson, “A comparison of uncertainty and sensitivity 

analysis results obtained with random and Latin hypercube sampling,” Rel. Eng. & Sys. 

Safety 89(3), pages 305-330 (2005).

E.3 Eckerman, K., "Radiation Dose and Health Risk Estimation: Technical Basis for the 

State-of-the-Art Reactor Consequence Analysis (SOARCA) Project," Oak Ridge National 

Laboratory, Oak Ridge, TN, 2011.
APPENDIX F

GLOSSARY OF UNCERTAINTY ANLAYSIS TERMS

F-1 

This appendix is glossary defines terms as they are used in this study, and the same terms may 

be used differently in other studies. Note also that Appendix A in this report provides a 

description of probabilistic analysis methodology, including regression techniques, used in this 

study.

Additive Model – A regression technique where an estimation of the regression line is formed 

by a summation of a collection of one-dimensional arbitrary basis functions. An additive model 

considers the influence of the variables themselves and does not consider any possible 

interaction.

Aleatory – Inherent randomness in the properties or behavior of the system under study. 

Aleatory uncertainty cannot be reduced based on increased knowledge of the system under 

study.

Basis Function – Elementary elements used in the decomposition of a function in a specific 

space. Every continuous function can be constructed as a linear combination of basis functions. 

For example, a quadratic polynomial has basis functions of {1, xx, xx2}. Every quadratic 

polynomial has the form:

yy = aa ∗ 1 + bb ∗ xx + cc ∗ xx2

where 1, xx, and xx2 are the basis functions and aa, bb, and cc are coefficients of the basis functions 

that define the unique polynomial.

Beta Distribution – A family of continuous probability distributions defined on the interval [0,1] 

parameterized by two positive shape parameters (α and β) that control the shape of the 

distribution. Its probability density function is expressed as follow:

ff(tt) = Γ(αα + ββ)

Γ(αα)Γ(ββ)

ttαα−1(1 − tt)ββ−1

where Γ represents the gamma function:

Γ(ww) = � xxww−1ee−xxdd

∞

0

Beta distributions can serve as a model for the probability that a system or component is in 

operation for at least t units of time. Sometimes, two parameters (min and max) are added to 

the beta function parameters. These parameters scale the domain of definition from [0,1] to 

[min,max]. See illustrations below.
F-2 

Figure F-1: Example of Beta Probability Distribution Function

Figure F-2: Example of Beta Cumulative Distribution Function

Cliff-edge Effects – An instance in which a small change in an input can lead to a large change 

in the response of the system. 

Coefficient of Determination – This coefficient (noted as R2

) estimates the proportion of the 

variance of the output that is explained by the regression model under consideration. Thus, this 

coefficient provides an indication of how well a regression model replicates the observed 

outcomes. 

Complementary Cumulative Distribution Function (CCDF) – This function represents the 

probability for a value sampled from a probability distribution to be greater than a given quantile 

value. Given a real-valued random variable XX and a threshold value xx for a metric of interest, 

the complementary cumulative distribution function FF�(xx) is defined as:
F-3 

FF�(xx) = PP(XX > xx) = 1 − FF(xx)

where FF(xx) is the cumulative distribution function (CDF) defined by FF(xx) = PP(XX ≤ xx). 

Conjoint Influence – The influence of two or more input parameters acting together. This 

influence may have synergistic effects that would not be uncovered by studying the influence of 

each parameter individually. 

Correlation – A possible dependence between two random variables. Positive correlation 

between two variables implies that a high value (or low value) for one variable is more likely to 

be associated with a respectively high value (low value) for the other. Negative correlation will 

reverse this relation, meaning that low values of one variable will be associated with high values 

of the other. Correlation does not imply causation. Correlation determines the existence of a 

trend but does not assess the magnitude of the change in output with respect to the change in 

input.

Cumulative Distribution Function (CDF1

) - This function represents the probability for a value 

sampled from a probability distribution to be equal to or less than a given quantile value. For 

continuous variables, this function is the integral of the probability density function and is given 

by: 

FF(xx) = � ff(xx)dd

xx

−∞

where FF(xx) is the cumulative distribution function and FF(xx) = PP(XX ≤ xx). 

Deterministic – Describing a system in which no randomness is involved in the calculation of a 

given response. A set of constant inputs definitively predict the output. 

Discrete Distribution – A probability distribution where the random variable can have a set of 

distinct, finite values.

Epistemic – Uncertainty related to the lack of knowledge or confidence about the system under 

analysis. This type of uncertainty is produced by a lack of knowledge regarding the inputs or 

models under consideration. Epistemic uncertainty is usually considered as reducible 

uncertainty because increased knowledge should reduce it. Also called “state-of-knowledge” 

uncertainty.

Kaplan/Garrick ordered triplet representation for risk – This representation of risk poses 

three questions:

1) What can go wrong?

2) How likely is it to go wrong?

3) What are the consequences if the event occurs?

 

1 Not to be confused with core damage frequency (CDF) from a level 1 probabilistic risk assessment.
F-4 

This representation is used to assess inherent randomness in the system (i.e., aleatory 

uncertainty). Potential lack of knowledge (i.e., epistemic uncertainty) adds a fourth question to 

the original triplet which is:

4) How much confidence do we have in the answers to the first three questions?

The exploration of these questions is the basis for Probabilistic Risk Assessment (PRA) (see 

‘Probabilistic Risk Assessment’ below.) The Kaplan/Garrick ordered triplet representation is 

typically the NRC’s definition of the term “risk.”

Latin Hypercube Sampling (LHS) – A sampling technique in which each input variable is 

sampled in a stratified way in order to guarantee that all portions of the range of the variable’s 

distribution are represented. LHS samples a probability density function (PDF) by first dividing 

the PDF of each variable into NN bins of equal probability where NN is the sample size per variable 

chosen ahead of time. One value is then sampled from the random variable’s PDF in each of 

the NN bins. Thus, if there are random input variables, the input space is partitioned into × NN

hypercubes from which NN will be selected such that each variable will have exactly one value 

sampled in each of its defined strata (PDF interval). See illustrations below for one (x) and two 

(x, y) variables, where the red marks on the 2nd illustration represent one possible Latin 

Hypercube Sample of size N = 6.

Figure F-3: Example of One-variable LHS Sample Technique
F-5 

Figure F-4: Example of Two-variable LHS Sample Technique

Least Squares – An optimization technique that select the parameters of a model such that the 

difference between the estimation and empirical values (derived from observations or another 

model) is minimized according to the L2

-norm (i.e., the square root of the sum of square 

differences is minimized). 

Lognormal Distribution – A normal distribution over the logarithm of the random variable.

Log Triangular Distribution – A triangular distribution over the logarithm of the random 

variable. See illustrations under ‘Triangular Distribution’ below, where the only difference is 

that “log(x)” replaces “x” on the x axis.

Log Uniform Distribution – A uniform distribution over the logarithm of the random variable. 

See illustrations under ‘Uniform Distribution’ below, where the only difference is that “log(x)” 

replaces “x” on the x axis.

Mean – Estimates the expected value of a distribution of values. The mean value of a random 

variable is the arithmetic average of possible values as described by its probability density 

function. See illustration below for ‘mean,’ ‘median,’ and ‘mode,’ all of which are measures of 

central tendency, though they are all different.

Median – The median of a probability distribution corresponds to the middle value that 

separates a sample or a distribution into halves of equal likelihood. A random variable is 

equally likely to take on a value greater than the median or less than the median. In other 

words, the CDF(Median value) = CCDF(Median value) = 0.5. See illustration below for ‘mean,’ 

‘median,’ and ‘mode,’ all of which are measures of central tendency, though they are all 

different.

Mode – The most likely value for an uncertain variable. For a discrete distribution, the mode 

represents the most common (most likely) value in a set of values. For a continuous 

distribution, the mode represents the value at which the probability density function reaches its 
F-6 

maximum. See illustration below for ‘mean,’ ‘median,’ and ‘mode,’ all of which are measures of 

central tendency, though they are all different.

Figure F-5; Example of Mode/Median/Mean Differences

Monotonic – A monotonic function is a function which is either solely non-increasing or solely 

non-decreasing. A monotonic function cannot increase with increasing values of a dependent 

variable in one range and then decrease with increasing values of a dependent variable in a 

different range.

Monte Carlo simulation – A numerical technique that covers the uncertain input space 

(multidimensional space where each dimension represents a different random variable with its 

associated distribution) by sampling each probability distribution using random, or pseudorandom, numbers. This method is preferred over a direct discretization when the number of 

inputs is large because a regular discretization in each direction would lead to an impractically 

large number of simulations. The system model is then run repeatedly using a single set of 

values for the input variable vector at each repetition. With this process, Monte Carlo simulation 

produces a distribution of system model outputs (results) based on the input variable uncertainty 

as described by the input space. 

(Multiplicative) Interaction Term – In regression models, interaction (or higher order) terms are 

basis functions that do not solely depend on one parameter. They can involve interactions 

amongst just two parameters up to interactions that involve all parameters under study. They 

can be as simple as a multiplication of two parameters or fairly complex (division, power, log, 

etc.). These terms are ignored by additive regression models.

Normal distribution – The normal distribution is one of the most common probability 

distributions. As demonstrated by the central limit theorem, the normal distribution can be used 

to represent the distribution of the sum of random variables (if they follow the same distribution) 

or the distribution of the mean value. The normal distribution’s probability density function is 

defined from −∞ to +∞ and has a bell shape:

ff(xx|μμ, σσ) = 1

σσ√2ππ

ee−(xx−μμ)2

2σσ2

Where μμ and σσ represent respectively the mean and standard distribution and are the traditional 

parameters used to define a normal distribution.
F-7 

Percentile – Specific form of quantile for which the value is reported as a percentage (e.g. the 

0.01 quantile is the same as the 1st percentile). See ‘quantile’ for additional description. 

Piecewise Uniform Distribution – A distribution formed by distinct uniform distributions over 

intervals of the range of the probability density function. See illustration below.

Figure F-6: Example of Piecewise Uniform Probability Mass Function

Probabilistic Risk Assessment (PRA) – A systematic method for assessing three questions 

that the NRC uses to define "risk." These questions consider (1) what can go wrong, (2) how 

likely it is, and (3) what its consequences might be. (see Kaplan/Garrick ordered triplet 

representation for risk) These questions allow the NRC to understand likely outcomes, 

sensitivities, areas of importance, system interactions, and areas of uncertainty, which the staff 

can use to identify risk-significant scenarios. The NRC uses PRA to determine a numeric 

estimate of risk to provide insights into the strengths and weaknesses of the design and 

operation of a nuclear power plant. 

Probability Density Function (PDF) – A function that describes the likelihood that a 

continuous random variable takes on a value in an interval. A PDF has the properties that 1) a 

value on the function is greater than or equal to 0 and 2) the total integral probability is 1.

ff(tt) ≥ 0

� ff(tt)dd

∞

−∞

= 1

Probability Distribution – A mathematical representation of the uncertainty of a random 

variable in a probabilistic framework. Specification of a probability distribution can be done via 

probability density (or mass for discrete variable) function or a cumulative distribution function 

for instance. 
F-8 

Probability Mass Function (PMF) – A function that is equivalent to the probability density 

function for discrete variables (and for which integral is replaced with a regular sum).

Quantile – A quantile xxqq is the value of a random variable such that there is a probability qq that 

a sampled value will be equal or lower to xxqq. Specific quantiles include the median (for 

which qq = 0.5), quartiles (where qq =0.25 and 0.75 and represents the 1st and 3rd quartiles, 

respectively) and percentiles (in which qq is expressed as a percent from 0 to 100 instead of a 

probability between 0 and 1). 

Random Seed – An integer value (or vector) used to initialize the random number sequence of 

a pseudo random number generator. Random seeds are used so that the same sequences can 

be reproduced when the same random number generator is used. The use of different random 

seeds, even those close to each other, should lead to completely different and uncorrelated 

random number sequences.

Rank Correlation Coefficient – Also known as Spearman Correlation Coefficient, the rank 

correlation coefficient measures the degree of linearity in the relationship between two random 

variables after they have been rank-transformed (see ‘rank transformation’).

Rank Regression – Rank regression is a linear regression applied to rank values. The linear 

regression builds a linear function model between outputs and inputs using a least squares 

approach. Often, linear and rank regressions use a stepwise approach such that new 

parameters are added to the model only if they increase the strength of the regression model 

significantly enough such that the complexity of adding a parameter is overcome by the 

increase in variance explained. Rank Regression is solely used to estimate the influence of 

uncertainty in the input parameters on the output uncertainty and is not used for prediction. 

Rank Transformation – Rank transformation consists of replacing the actual value of a random 

variable by its rank in the total sample. Regression methods become non-parametric when 

working with rank values instead of with raw data. This allows for monotonic relations to be 

captured instead of simple linear relations and reduces the effect of outliers. 

Realization – An individual calculation using one sample of values for the input variable vector 

in Monte Carlo simulation. In other words, a Monte Carlo simulation where the system model is 

run N times has N realizations. Within a realization, the model is usually run deterministically 

and returns a unique set of output values

Regression – A measure of the relation between one variable (e.g., output or results of a 

model) and corresponding values of other variables (e.g., inputs to a model). Regression 

methods attempt to find a mathematical relationship between input variables and the output 

variable(s) of interest.

Replicates – A set of Monte Carlo simulations on the same system model, usually of the same 

sample size, that use different random numbers generated using a different random seed. For 

Monte Carlo simulations using simple random sampling, the results of replicates can be 

combined to form one larger data set for better statistics because all random samples are 

independent. 

Sensitivity Study – A set of studies that exercise a complex system under different conditions 

in order to 1) validate some assumptions, 2) explore alternative conceptual models or address 

differences in opinion, or 3) study one particular aspect of the complex system in greater detail. 

These studies are different from Monte Carlo simulations in that they require changing some 

options that have been considered to be constants in the study of reference and may study only 
F-9 

one variable or conceptual model in isolation. Such studies can be completed through either 

deterministic or probabilistic means. 

Sensitivity Analysis – An analysis that determines how sensitive an output is to a given input 

or set of inputs. Sensitivity analysis can be conducted using a deterministic set of model 

calculations (through a sensitivity study), or can be conducted probabilistically using Monte 

Carlo simulation and regression results that quantify how much the uncertainty in each analysis 

input contributes to the variance in the output under consideration. In this document, “sensitivity 

analysis” refers to the latter usage.

Simple Random Sampling (SRS) – A random sampling technique where for each time 

sampled, the probability that a particular value of a variable is chosen is proportional to the 

probability density function of the variable at that particular value. No further requirements are 

imposed on the sampling (unlike Latin Hypercube Sampling). 

Stochastic – A random occurrence. A stochastic simulation refers to a simulation in which 

randomness in uncertain input variables is used to calculate a system response.

Stochastic Failure – A failure that is caused by random processes.

Sum of Square Error (SSE) – The total sum of the squares of the differences between 

estimated and empirical values (i.e., observations, measurements, or an empirical model).

SSSS = ��yyii − ff(xxii)�

2

ii

A small SSE indicates a good fit between the predicted and observed values.

t-distribution – A probability distribution that can be used when determining the mean when the 

sample size is small and the data is normally distributed with an unknown standard deviation. 

The t-distribution describes samples drawn from a full data set. It can be used to assess the 

statistical difference between two means, confidence intervals in linear regressions.

Triangular distribution – A continuous distribution that takes the form of a triangle. The 

probability density for the range [a,b] reaches its mode at the location c and form a triangular 

shape:

ff(xx) =

⎩

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎧ 0 ffffff xx < aa

2(xx − aa)

(bb − aa)(cc − aa) ffffff aa ≤ xx < cc

2

bb − aa ffffff xx = cc

2(bb − xx)

(bb − aa)(bb − cc) ffffff cc < xx ≤ bb

0 ffffff xx > bb
F-10

Figure F-7: Example of Triangle Probability Distribution Function

Figure F-8: Example of Triangle Cumulative Distribution Function

Uncorrelated – A situation in which no linear dependence between sampled values for two 

variables is observed. 

Uniform Distribution – A distribution used when any value for a random variable defined on a 

range [a,b] is equally likely. The uniform probability density function forms a rectangle and is 

given by:

ff(xx) = �

1

bb − aa for xx ∈ [aa, bb]

0 otherwise
F-11

Figure F-9: Example of Uniform Probability Distribution Function

Figure F-10: Example of Uniform Cumulative Distribution Function

Variance – A measure of the dispersion of data about a mean, given by:

VV = σσ2 = ∑ (YYii − μμ) NN 2

ii=1

NN

where YYii is a particular data point, μμ is the mean, and NN is the number of data points. The 

variance characterizes the average spread squared of the data set.







 

 

NUREG/CR-7155 State-of-the-Art Reactor Consequence Analyses Project: Uncertainty analysis of the 

Unmitigated Long-term Station Blackout of the Peach Bottom Atomic Power Station