New Source Term Model for 

the RESRAD-OFFSITE Code 

Version 3

Office of Nuclear Regulatory Research

NUREG/CR-7127

ANL/EVS/TM/11-5
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New Source Term Model for 

the RESRAD-OFFSITE Code 

Version 3

Manuscript Completed: May 2013

Date Published: December 2013

Prepared by:

C. Yu, E. K. Gnanapragasam, J. J. Cheng, S. Kamboj, and S. Y. Chen

Argonne National Laboratory

9700 South Cass Avenue

Argonne, IL 60439

Ralph Cady, NRC Project Manager

NRC Job Codes N6731 and V6360

Office of Nuclear Regulatory Research

NUREG/CR-7127

ANL/EVS/TM/11-5

iii

Abstract

This report documents the new source term model developed and implemented in Version 3 of 

the RESRAD-OFFSITE code. This new source term model includes: (1) "first order release 

with transport" option, in which the release of the radionuclide is proportional to the inventory in 

the primary contamination and the user-specified leach rate is the proportionality constant, 

(2) "equilibrium desorption release" option, in which the user specifies the distribution coefficient 

which quantifies the partitioning of the radionuclide between the solid and aqueous phases, and 

(3) "uniform release" option, in which the radionuclides are released from a constant fraction of 

the initially contaminated material during each time interval and the user specifies the duration 

over which the radionuclides are released. The source term model implemented in RESRADOFFSITE Version 2 computes the release of radionuclides from the contaminated zone, as well 

as the concentration and distribution of the radionuclides within the contaminated zone. The 

model calculates the atmospheric release of particulates due to resuspension and that of 

volatiles due to diffusion and evapotranspiration, the surface water release due to erosion by 

runoff water, and the groundwater release due to leaching by infiltrating water. The release 

rates are used by the code to compute the transport of contaminants and exposure at offsite 

locations, whereas the concentration and distribution of radionuclides within the contaminated 

zone are used to compute the direct external exposure from the primary contamination, as well 

as any exposure from onsite activities. The newly developed source term models for RESRADOFFSITE code Version 3 also consider these releases and distribution in the primary 

contaminated zone. The new release mechanisms are not limited to treating soil materials as 

the source (primary contamination). Furthermore, the new release mechanisms are also not 

limited to uncontainerized sources because the new source release models assume that the 

releases are from a distinct phase of source material; once released into surrounding soils, they 

are transported in the soil in the region of primary contamination. The new source release 

models implemented in RESRAD-OFFSITE code Version 3 are compared with DUST-MS code

and the GoldSim software. The results of comparison are presented and discussed in the 

report. A detailed description of how to conduct sensitivity and probabilistic analyses using 

RESRAD-OFFSITE code is presented, and the results of using sensitivity and probabilistic 

analyses on the new source release input parameters are discussed. The revisions and 

additions to Version 3.1 included a time-delay feature for the source release mechanism. This 

time-delay feature provides the ability to model scenarios where the release of radionuclides is 

delayed and/or distributed over time. The “uniform release” option of Version 3.0 beta is now 

part of the time-distributed “equilibrium desorption release” option. The time–distributed, first–

order, rate-controlled release is an additional option available in Version 3.1. Another new 

feature in Version 3.1 facilitates the calculation of area factors for small areas of elevated 

activity. This area factor calculation was performed using the probabilistic analysis feature of 

the RESRAD-OFFSITE code.
iv

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v 

Table of Contents

Abstract ....................................................................................................................................iii

List of Figures ..........................................................................................................................ix 

List of Tables........................................................................................................................xxiii

Executive Summary..............................................................................................................xxv

Acknowledgments ..............................................................................................................xxvii

1. Introduction ....................................................................................................................... 1-1

1.1 Overview of the Source Release Model in RESRAD-OFFSITE Version 2..................1-1

1.2 Considerations for Expanding the Source Term Model..............................................1-2

1.3 The Proposed Approaches and the Implemented Source Term Models ....................1-2

1.4 Area Factors for Offsite Exposure Scenarios .............................................................1-4

2. Primary Contamination and the Source Term.................................................................... 2-1

2.1 Conceptualization of the Primary Contamination .......................................................2-1

2.2 Derivation of Mathematical Expressions for the Conceptual Primary 

Contamination Model.................................................................................................2-3

2.2.1 Thickness of the Primary Contamination........................................................2-3

2.2.2 Concentration of Radionuclides in the Primary Contamination.......................2-4

2.2.2.1 Concentration of Radionuclides in the Primary Contamination 

under the First Order Release Model...............................................2-4

2.2.2.2 Concentration of Radionuclides in the Primary Contamination 

under the Uniform Release Model ...................................................2-5

2.2.2.3 Concentration of Radionuclides in the Primary Contamination 

under the Equilibrium Desorption Model..........................................2-6

2.2.3 Surface Soil Mixing Model..............................................................................2-7

2.2.3.1 Density of Soil in the Mixing Zone....................................................2-7

2.2.3.2 Volume Fraction of Soil from the Primary Contamination in the 

Mixing Zone.....................................................................................2-8

2.2.3.3 Concentration of Radionuclides in the Surface Soil above the 

Primary Contamination....................................................................2-9

2.2.3.4 Three-Layer Model ........................................................................ 2-10

2.2.4 Release by Surface Runoff .......................................................................... 2-10

2.2.5 Release to Groundwater .............................................................................. 2-11

2.2.5.1 Transfer of Radionuclides to Soil Moisture under the

First Order Release Model ............................................................ 2-11

2.2.5.2 Transfer of Radionuclides to Soil Moisture under the Uniform 

Release Model .............................................................................. 2-12

2.2.5.3 Transport of Radionuclides from the Point of Transfer to the 

Bottom of the Primary Contamination for the Rate-Controlled 

Release Options............................................................................ 2-12

2.2.5.4 Release of Radionuclides to Groundwater under the 

Equilibrium Desorption Model........................................................ 2-12

2.2.6 Release to the Atmosphere in the Form of Dust........................................... 2-13

2.3 Implementation of the Models for the Primary Contamination.................................. 2-13
vi

Table of Contents (Continued)

2.3.1 Shape and Dimensions of the Primary Contamination ................................. 2-14

2.3.2 Thicknesses of the Primary Contamination, Cover, Clean Cover, 

Contaminated Mixing Zone, and Undisturbed Primary Contamination.......... 2-14

2.3.3 Concentration of Radionuclides in the Primary Contamination..................... 2-15

2.3.3.1 Concentration of Radionuclides in the Primary Contamination 

under the First-Order Release Model ............................................ 2-15

2.3.3.2 Concentration of Radionuclides in the Primary Contamination 

under the Uniform Release Model ................................................. 2-15

2.3.4 Depth of Penetration of the Mixing Zone ...................................................... 2-16

2.3.5 Density of Soil in the Mixing Zone ................................................................ 2-16

2.3.6 Volume Fraction of Soil from the Primary Contamination in the Mixing 

Zone ............................................................................................................ 2-17

2.3.7 Concentration of Radionuclides in the Surface Soil above the Primary 

Contamination.............................................................................................. 2-18

2.3.8 Release by Surface Runoff .......................................................................... 2-18

2.3.9 Transfer to Groundwater under the First-Order Release Model.................... 2-18

2.3.10 Transfer to Groundwater under the Uniform Release Model ........................ 2-19

2.3.11 Release to Groundwater under the Two Rate-Controlled Release 

Options ........................................................................................................ 2-19

2.3.12 Release to Groundwater under the Instantaneous Desorption

Equilibrium Release ..................................................................................... 2-19

2.3.13 Release to the Atmosphere in the Form of Dust........................................... 2-20

2.4 Users Guide to the Release Options in the RESRAD-OFFSITE Source

Term Model ............................................................................................................. 2-20

2.4.1 Source Release and Deposition Velocity Form ............................................ 2-20

2.4.1.1 Version 2 Release Methodology .................................................... 2-20

2.4.1.2 First-Order Release with Transport................................................ 2-22

2.4.1.3 Equilibrium Desorption Release..................................................... 2-22

2.4.1.4 Uniform Release............................................................................ 2-23

2.4.1.5 Release of Progeny Produced by Radiological

Transformations of an Initially Present Parent ............................... 2-23

2.4.1.6 Transport of the Radionuclides within the Primary 

Contamination ............................................................................... 2-23

2.4.1.7 Temporal Plots of the Different Release Options ........................... 2-24

2.5 Overriding the RESRAD-OFFSITE Source Term Model .......................................... 2-29

3. Benchmarking of Radionuclide Release Rates Calculated by RESRAD-OFFSITE

Version 3 and DUST-MS................................................................................................... 3-1

3.1 Conceptualization of Radioactive Sources within the Contaminated Zone for 

Release and Transport Modeling...............................................................................3-1

3.2 Release Options/Mechanisms ...................................................................................3-2

3.2.1 RESRAD-OFFSITE Version 3........................................................................3-3

3.2.2 DUST-MS ......................................................................................................3-3
vii

Table of Contents (Continued)

3.2.3 Options/Mechanisms Selected for Comparison..............................................3-4

3.3 Assumptions for Source Materials .............................................................................3-4

3.3.1 Release Sources in Different Comparison Cases...........................................3-4

3.3.2 Input Parameters Used for RESRAD-OFFSITE .............................................3-5

3.3.3 Input Parameters Used for DUST-MS............................................................3-6

3.4 Results of Comparison ..............................................................................................3-7

3.4.1 Case I – 0.3 m of Tc-99..................................................................................3-7

3.4.1.1 No Dispersion..................................................................................3-7

3.4.1.2 With Dispersion ...............................................................................3-9

3.4.2 Case II – 0.3 m of Cs-137 ............................................................................ 3-11

3.4.2.1 No Dispersion................................................................................ 3-12

3.4.2.2 With Dispersion ............................................................................. 3-13

3.4.3 Case III – 0.3 m of U-234 ............................................................................. 3-15

3.4.3.1 No Dispersion................................................................................ 3-15

3.4.3.2 With Dispersion ............................................................................. 3-19

3.4.4 Case IV – 3 m of Tc-99 ................................................................................ 3-22

3.4.4.1 No Dispersion................................................................................ 3-22

3.4.4.2 With Dispersion ............................................................................. 3-24

3.4.5 Case V – 3 m of U-234................................................................................. 3-26

3.4.5.1 No Dispersion................................................................................ 3-26

3.4.5.2 With Dispersion ............................................................................. 3-29

3.5 Summary of Comparison......................................................................................... 3-29

4. Sensitivity Analysis to Identify Influential Inputs................................................................. 4-1

4.1 Hypothetical Scenario to Illustrate Identification of Influential Inputs ..........................4-1

4.1.1 Site Layout and Dimensions...........................................................................4-1

4.1.1.1 Radionuclides in the Primary Contamination ...................................4-2

4.1.1.2 Preliminary Data for the Hypothetical Site........................................4-2

4.1.2 Initial Ranges or Distributions of Inputs ..........................................................4-3

4.1.3 Relationships or Correlations between Inputs ................................................4-4

4.2 Three-Point Single Input Sensitivity Analysis .............................................................4-5

4.2.1 Advantages and Disadvantages of Three-point Single-input Sensitivity 

Analysis .........................................................................................................4-7

4.2.2 Conclusion about the Use of 3-point Single-input Sensitivity Analysis............4-8

4.3 Multiple Input Sensitivity Analysis ............................................................................ 4-39

4.3.1 Advantages and Disadvantages of Multiple Input Sensitivity Analysis.......... 4-42

4.3.2 Conclusion about the Use of Sensitivity Analysis ......................................... 4-42

5. References........................................................................................................................ 5-1

Appendix A Letter Report – Proposed Approach for the Task of Expanding

the Source Term Model for RESRAD-OFFSITE............................................... A-1

Appendix B Additional Benchmarking of Radionuclide Release Rates ................................ B-1
viii

Table of Contents (Continued)

Appendix C Sensitivity Analysis Using Probabilistic RESRAD-OFFSITE............................. C-1

Appendix C.1 Hypothetical Scenario for Multi-Input Sensitivity Analysis............................. C-115

Appendix D Source Release with Time-delay Options in RESRAD-OFFSITE

Version 3.1....................................................................................................... D-1

Appendix E Users’ Guide to RESRAD-OFFSITE Code Area Factors.................................. E-1
ix

List of Figures

Figure 2.1 Source Release and Deposition Velocity Form – Version 2 Option ................ 2-21

Figure 2.2 Source Release and Deposition Velocity Form – New Release Options ........ 2-22

Figure 2.3 Distribution Coefficients Form ........................................................................ 2-23

Figure 2.4 Primary Contamination Form ......................................................................... 2-24

Figure 2.5 Temporal Profiles of Flux Out of the Primary Contamination for Different

Release Options ............................................................................................ 2-25

Figure 2.6 Temporal Profiles of Flux Out of the Primary Contamination for the

First-Order Release Option with Different Rates of Transport ........................ 2-26

Figure 2.7 Temporal Profiles of Flux Out of the Primary Contamination for the

Uniform Release Option with Different Rates of Transport............................. 2-27

Figure 2.8 Temporal Profiles of Flux Out of the Primary Contamination for the

Equilibrium Desorption Release Option with Different Rates of Transport...... 2-28

Figure 3.1 Conceptualization of Radioactive Sources Within the Contaminated Zone ...... 3-2

Figure 3.2 Various Designs for Subdividing the Domain of Analysis for DUST-MS 

Calculation....................................................................................................... 3-7

Figure 3.3 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case I

Concerning Release from a 0.3-m Tc-99 Source under the Equilibrium

Desorption Condition with No Dispersion ......................................................... 3-8

Figure 3.4 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case I

Concerning Release from a 0.3-m Tc-99 Source under the Uniform

Release Condition with No Dispersion ............................................................. 3-9

Figure 3.5 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case I

Concerning Release from a 0.3-m Tc-99 Source under the Equilibrium

Desorption Condition with a Dispersivity of 0.03 m......................................... 3-10

Figure 3.6 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case I

Concerning Release from a 0.3-m Tc-99 Source under the Equilibrium

Desorption Condition with a Dispersivity of 0.1 m........................................... 3-10

Figure 3.7 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case I

Concerning Release from a 0.3-m Tc-99 Source under the Uniform

Release Condition with a Dispersivity of 0.03 m............................................. 3-11

Figure 3.8 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case I

Concerning Release from a 0.3-m Tc-99 Source under the Uniform

Release Condition with a Dispersivity of 0.1 m............................................... 3-12

Figure 3.9 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case II

Concerning Release from a 0.3-m Cs-137 Source under the Equilibrium

Desorption Condition with No Dispersion ....................................................... 3-13

Figure 3.10 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case II

Concerning Release from a 0.3-m Cs-137 Source under the Uniform

Release Condition with No Dispersion ........................................................... 3-14

Figure 3.11 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case II

Concerning Release from a 0.3-m Cs-137 Source under the Equilibrium

Desorption Condition with a Dispersivity of 0.03 m......................................... 3-14
x 

List of Figures (continued)

Figure 3.12 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case II

Concerning Release from a 0.3-m Cs-137 Source under the Uniform

Release Condition with a Dispersivity of 0.03 m............................................. 3-15

Figure 3.13 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case III

Concerning Release of U-234 from a 0.3-m U-234 Source with No 

 Dispersion...................................................................................................... 3-16

Figure 3.14 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case III

Concerning Release of Th-230 from a 0.3-m U-234 Source with No 

 Dispersion...................................................................................................... 3-17

Figure 3.15 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case III

Concerning Release of Ra-226 from a 0.3-m U-234 Source with No

 Dispersion..................................................................................................... 3-17

Figure 3.16 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case III

Concerning Release of Pb-210 from a 0.3-m U-234 Source with No 

 Dispersion...................................................................................................... 3-18

Figure 3.17 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case III

Concerning Release of Po-210 from a 0.3-m U-234 Source with No 

 Dispersion...................................................................................................... 3-18

Figure 3.18 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case III

Concerning Release of U-234 from a 0.3-m U-234 Source with a Dispersivity

of 0.03 m........................................................................................................ 3-19

Figure 3.19 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case III

Concerning Release of Th-230 from a 0.3-m U-234 Source with a Dispersivity

of 0.03 m........................................................................................................ 3-20

Figure 3.20 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case III

Concerning Release of Ra-226 from a 0.3-m U-234 Source with a Dispersivity

of 0.03 m........................................................................................................ 3-20

Figure 3.21 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case III

Concerning Release of Pb-210 from a 0.3-m U-234 Source with a Dispersivity

of 0.03 m........................................................................................................ 3-21

Figure 3.22 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case III

Concerning Release of Po-210 from a 0.3-m U-234 Source with a Dispersivity

of 0.03 m........................................................................................................ 3-21

Figure 3.23 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case IV

Concerning Release from a 3-m Tc-99 Source under the Equilibrium

Desorption Condition with No Dispersion ....................................................... 3-23

Figure 3.24 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case IV

Concerning Release from a 3-m Tc-99 Source under the Uniform Release

Condition with No Dispersion ......................................................................... 3-23

Figure 3.25 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case IV

Concerning Release from a 3-m Tc-99 Source under the Equilibrium

Desorption Condition with a Dispersivity of 0.3 m........................................... 3-24
xi

List of Figures (continued)

Figure 3.26 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case IV

Concerning Release from a 3-m Tc-99 Source under the Equilibrium

Desorption Condition with a Dispersivity of 1 m ............................................. 3-25

Figure 3.27 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case IV

Concerning Release from a 3-m Tc-99 Source under the Uniform Release

Condition with a Dispersivity of 0.3 m............................................................. 3-25

Figure 3.28 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case IV

Concerning Release from a 3-m Tc-99 Source under the Uniform Release

Condition with a Dispersivity of 1 m ............................................................... 3-26

Figure 3.29 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case V

Concerning Release of U-234 from a 3-m U-234 Source with 

 No Dispersion ................................................................................................ 3-27

Figure 3.30 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case V

Concerning Release of Th-230 from a 3-m U-234 Source with 

 No Dispersion ................................................................................................ 3-27

Figure 3.31 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case V

Concerning Release of Ra-226 from a 3-m U-234 Source with 

 No Dispersion ................................................................................................ 3-28

Figure 3.32 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case V

Concerning Release of Pb-210 from a 3-m U-234 Source with 

 No Dispersion ................................................................................................ 3-28

Figure 3.33 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case V

Concerning Release of Po-210 from a 3-m U-234 Source with 

 No Dispersion ................................................................................................ 3-29

Figure 3.34 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case V

Concerning Release of U-234 from a 3-m U-234 Source with a 

 Dispersivity of 0.3 m....................................................................................... 3-30

Figure 3.35 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case V

Concerning Release of Th-230 from a 3-m U-234 Source with a 

 Dispersivity of 0.3 m....................................................................................... 3-30

Figure 3.36 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case V

Concerning Release of Ra-226 from a 3-m U-234 Source with a 

 Dispersivity of 0.3 m....................................................................................... 3-31

Figure 3.37 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case V

Concerning Release of Pb-210 from a 3-m U-234 Source with a 

 Dispersivity of 0.3 m....................................................................................... 3-31

Figure 3.38 Comparison of RESRAD-OFFSITE and DUST-MS Results for Case V

Concerning Release of Po-210 from a 3-m U-234 Source with a 

 Dispersivity of 0.3 m....................................................................................... 3-32

Figure 4.1 Layout of the Hypothetical Site......................................................................... 4-1

Figure 4.2 The Cross Section of the Primary Contamination and the Soil beneath It ........ 4-2
xii

List of Figures (continued)

Figure 4.3 Specifying the Lower and Higher Values to be Used for an Input Selected for

Sensitivity Analysis .......................................................................................... 4-6

Figure 4.4 Resetting the Sensitivity Analysis Range to Avoid Exceeding the Bounds

on the Inputs.................................................................................................... 4-7

Figure 4.5 Temporal Variation of Dose with the Volume of the Surface Water Body

Showing a Range of 48.3 mrem/year for the Peak Dose from

38.5 to 86.8 mrem/year.................................................................................... 4-9

Figure 4.6 Temporal Variation of Dose with the Mean Residence Time of Water in the

Surface Water Body showing a Range of 47.4 mrem/year for the Peak Dose

from 38.7 to 86.1 mrem/year.......................................................................... 4-10

Figure 4.7 Temporal Variation of Dose with the Duration of Release of 226Ra Showing

a Range of 20.4 mrem/year for the Peak Dose from 48.8 to 69.2 mrem/year . 4-11

Figure 4.8 Temporal Variation of Dose with the Density of the Primary Contamination

Showing a Range of 18.8 mrem/year for the Peak Dose from

49.3 to 68.1 mrem/year.................................................................................. 4-12

Figure 4.9 Temporal Variation of Dose with the Depth of Aquifer Contributing to the

Surface Water Body Showing a Range of 13.2 mrem/year for the Peak

Dose from 49.0 to 62.2 mrem/year................................................................. 4-13

Figure 4.10 Temporal Variation of Dose with the Distribution Coefficient of 210Pb in the First 

Unsaturated Zone Showing a Range of 12.9 mrem/year for the Peak Dose

from 51.5 to 64.4 mrem/year.......................................................................... 4-14

Figure 4.11 Temporal Variation of Dose with the Distribution Coefficient of 226Ra in the First 

Unsaturated Zone Showing a Range of 12.2 mrem/year for the Peak Dose

from 52.2 to 64.4 mrem/year.......................................................................... 4-15

Figure 4.12 Temporal Variation of Dose with the Evapotranspiration Coefficient Showing

a Range of 11.5 mrem/year for the Peak Dose from 47.6 to 59.1 mrem/year . 4-16

Figure 4.13 Temporal Variation of Dose with the Fraction of Fruit, Nonleafy Vegetables,

and Grain from the Contaminated Region Showing a Range of

9.8 mrem/year for the Peak Dose from 53.9 to 63.7 mrem/year..................... 4-17

Figure 4.14 Temporal Variation of Dose with the Irrigation Applied per Year to the Fruit,

Nonleafy Vegetables, and Grain Growing Areas Showing a Range

of 9.7 mrem/year for the Peak Dose from 53.9 to 63.6 mrem/year................. 4-18

Figure 4.15 Temporal Variation of Dose with the Wet Weight Crop Yield of Fruit,

Nonleafy Vegetables, and Grain in the Growing Areas Showing a Range

of 9.6 mrem/year for the Peak Dose from 54.0 to 63.6 mrem/year................. 4-19

Figure 4.16 Temporal Variation of Dose with the Translocation Factor for Fruit, Nonleafy

Vegetables, and Grain Showing a Range of 9.6 mrem/year for the Peak

Dose from 54.0 to 63.6 mrem/year................................................................. 4-20

Figure 4.17 Temporal Variation of Dose with the Foliar Interception Factor for Irrigation

in the Fruit, Nonleafy Vegetables, and Grain Growing Area Showing

a Range of 9.6 mrem/year for the Peak Dose from 54.0 to 63.6 mrem/year... 4-21
xiii

List of Figures (continued)

Figure 4.18 Temporal Variation of Dose with the x Dimension of the Primary Contamination

Showing a Range of 9.1 mrem/year for the Peak Dose

from 53.3 to 62.4 mrem/year.......................................................................... 4-22

Figure 4.19 Temporal Variation of Dose with the y Dimension of the Primary Contamination

Showing a Range of 9.1 mrem/year for the Peak Dose

from 53.3 to 62.4 mrem/year.......................................................................... 4-23

Figure 4.20 Temporal Variation of Dose with the Thickness of the Primary Contamination

Showing a Range of 8.2 mrem/year for the Peak Dose

from 53.9 to 62.1 mrem/year.......................................................................... 4-24

Figure 4.21 Temporal Variation of Dose with the Duration of the Growing Season of Fruit,

Nonleafy Vegetables, and Grain Showing a Range of 8.1 mrem/year

for the Peak Dose from 54.2 to 62.3 mrem/year............................................. 4-25

Figure 4.22 Temporal Variation of Dose with the Weathering Removal Constant for Fruit,

Nonleafy Vegetables, and Grain Showing a Range of 8.1 mrem/year

for the Peak Dose from 54.2 to 62.3 mrem/year............................................. 4-26

Figure 4.23 Temporal Variation of Dose with the Weathering Removal Constant for Fruit,

Nonleafy Vegetables, and Grain Showing a Range of 6.9 mrem/year

for the Peak Dose from 54.5 to 61.4 mrem/year............................................. 4-27

Figure 4.24 Temporal Variation of Dose with the Erodibility Factor of Soil in the Primary

Contamination Showing a Range of 5.0 mrem/year for the Peak Dose from

55.6 to 60.6 mrem/year.................................................................................. 4-28

Figure 4.25 Temporal Variation of Dose with the Irrigation Applied per Year to the Pasture

and the Silage Growing Areas Showing a Range of 4.0 mrem/year for the

Peak Dose from 56.2 to 60.2 mrem/year........................................................ 4-29

Figure 4.26 Temporal Variation of Dose with the Wet Weight Crop Yield from the Pasture

and the Silage Growing Areas Showing a Range of 4.0 mrem/year for the

Peak Dose from 56.2 to 60.2 mrem/year........................................................ 4-30

Figure 4.27 Temporal Variation of Dose with the Grain Intake by Cattle Raised for Meat

Showing a Range of 0.8 mrem/year for the Peak Dose

from 57.5 to 58.3 mrem/year.......................................................................... 4-31

Figure 4.28 Temporal Variation of Dose with the Longitudinal Dispersivity in the Saturated

Zone to the Surface Water Body Showing a Range of 0.0 mrem/year

for the Peak Dose from 57.8 to 57.8 mrem/year............................................. 4-32

Figure 4.29 Temporal Variation of Dose with the Dry Bulk Density of Soil in the Fruit,

Nonleafy Vegetables, and Grain Growing Area Showing a Range of

0.0 mrem/year for the Peak Dose from 57.8 to 57.8 mrem/year..................... 4-33

Figure 4.30 Temporal Variation of Dose with the Effective Porosity of the Primary

Contamination Showing a Range of 2.5 mrem/year for the Peak Dose

from 56.2 to 58.7 mrem/year.......................................................................... 4-34

Figure 4.31 Temporal Variation of Dose with the Total Porosity of the Primary

Contamination Showing a Range of 2.2 mrem/year for the Peak Dose

from 56.5 to 58.7 mrem/year.......................................................................... 4-35
xiv

List of Figures (continued)

Figure 4.32 Temporal Variation of Dose with the Field Capacity of the Primary

Contamination Showing a Range of 0.0 mrem/year for the Peak Dose

from 57.8 to 57.8 mrem/year.......................................................................... 4-36

Figure 4.33 Temporal Variation of Dose with the Leach Rate of 226Ra in Primary

Contamination for the First Order Release Example Scenario ....................... 4-37

Figure 4.34 Temporal Variation of Dose with the Distribution Coefficient of 226Ra in

Primary Contamination for the Equilibrium Desorption Release

Example Scenario.......................................................................................... 4-38

Figure 4.35 Step-by-step Analysis Tab of the Uncertainty and Probabilistic Analysis

 Form .............................................................................................................. 4-43

Figure 4.36 Specifying the Range for an Input Selected for Multiple Input

Sensitivity Analysis ........................................................................................ 4-44

Figure 4.37 Specified Range Adjusted to Conform to Bounds Built into the Code............. 4-45

Figure 4.38 Scatter Plot of Field Capacity against Total Porosity to Show the Effect of

Specifying a Correlation of 0.9 between Them............................................... 4-46

Figure 4.39 Specifying Correlation between Inputs ........................................................... 4-47

Figure 4.40 Specifying Relationships between Inputs ....................................................... 4-48

Figure 4.41 Scatter Plot of the Length Parallel to Aquifer Flow against the x Dimension

of the Primary Contamination......................................................................... 4-49

Figure 4.42 Cumulative Distribution Function of Peak Dose from the Identification Run

of the Preliminary Sensitivity Analysis ............................................................ 4-50

Figure 4.43 Regression Output of Preliminary Sensitivity Analysis with Inputs Sorted

in Descending Order of Influence................................................................... 4-51

Figure 4.44 Standardized Regression Coefficients of the Top 63 Inputs Sorted

in Descending Order of Importance ............................................................... 4-52

Figure 4.45 Standardized Regression Coefficients of All 222 Inputs Sorted

in Descending Order of Importance ............................................................... 4-53

Figure 4.46 Regression Output of Preliminary Sensitivity Analysis with Inputs Sorted

in Descending Order of Influence.................................................................. 4-54

Figure 4.47 Cumulative Distribution Function of Peak Dose from the 30-input

Verification Run of the Preliminary Sensitivity Analysis .................................. 4-55

Figure 4.48 Cumulative Distribution Function of Peak Dose from the 17-input

Verification Run of the Preliminary Sensitivity Analysis .................................. 4-56

Figure 4.49 Cumulative Distribution Function of Peak Dose from the 5-input

Verification Run of the Preliminary Sensitivity Analysis .................................. 4-57

Figure 4.50 Cumulative Distribution Function of Peak Dose from Identification and

Verification Runs............................................................................................ 4-58

Figure B.1 Modeling of a First Order Release with GoldSim.............................................. B-3

Figure B.2 Modeling of an Equilibrium Desorption Release with GoldSim ......................... B-4

Figure B.3 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I

Concerning Release from a 0.3-m Tc-99 Source under the Equilibrium

Desorption Condition with No Dispersion ......................................................... B-6
xv

List of Figures (continued)

Figure B.4 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I

Concerning Release from a 0.3-m Tc-99 Source under the Uniform

Release Condition with No Dispersion ............................................................. B-7

Figure B.5 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I

Concerning Release from a 0.3-m Tc-99 Source under the First Order

Release Condition with No Dispersion ............................................................. B-8

Figure B.6 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I

Concerning Release from a 0.3-m Tc-99 Source under the Equilibrium

Desorption Condition with a Dispersivity of 0.03 m........................................... B-9

Figure B.7 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I

Concerning Release from a 0.3-m Tc-99 Source Under the Equilibrium

Desorption Condition with a Dispersivity of 0.1 m........................................... B-10

Figure B.8 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I

Concerning Release from a 0.3-m Cs-137 Source under the Equilibrium

Desorption Condition with No Dispersion ....................................................... B-11

Figure B.9 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I

Concerning Release from a 0.3-m Cs-137 Source under the Uniform

Release Condition with No Dispersion ........................................................... B-12

Figure B.10 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I

Concerning Release from a 0.3-m Cs-137 Source under the First

Order Release Condition with No Dispersion ................................................. B-13

Figure B.11 Comparison of RESRAD-OFFSITE and GoldSim Results for Case III

Concerning Release of U-234 from a 0.3-m U-234 Source with No 

 Dispersion...................................................................................................... B-14

Figure B.12 Comparison of RESRAD-OFFSITE and GoldSim Results for Case III

Concerning Release of Th-230 from a 0.3-m U-234 Source with No 

 Dispersion...................................................................................................... B-15

Figure B.13 Comparison of RESRAD-OFFSITE and GoldSim Results for Case III

Concerning Release of Ra-226 from a 0.3-m U-234 Source with No 

 Dispersion...................................................................................................... B-16

Figure B.14 Comparison of RESRAD-OFFSITE and GoldSim Results for Case III

Concerning Release of Pb-210 from a 0.3-m U-234 Source with No 

 Dispersion...................................................................................................... B-17

Figure B.15 Comparison of RESRAD-OFFSITE and GoldSim Results for Case III

Concerning Release of Po-210 from a 0.3-m U-234 Source with No 

 Dispersion...................................................................................................... B-18

Figure C.1 Specifying Three-point Single-input Sensitivity Analysis for the Input 

 of Interest......................................................................................................... C-5

Figure C.2 Viewing Sensitivity Graphics ............................................................................ C-6

Figure C.3 Identifying Significant Exposure Pathways for the Base Case.......................... C-7

Figure C.4 Sensitivity of Predicted Dose from Drinking Water ........................................... C-7

Figure C.5 Sensitivity of Predicted Dose from Ingestion of Vegetables.............................. C-8
xvi

List of Figures (continued)

Figure C.6 Sensitivity of Predicted Dose from Ingestion of Meat ....................................... C-8

Figure C.7 Sensitivity of Predicted Dose from Ingestion of Milk ......................................... C-9

Figure C.8 Sensitivity of Predicted Dose from Direct Exposure to Waterborne

Accumulation in Soil......................................................................................... C-9

Figure C.9 Sensitivity of Predicted Dose from Ingestion of Fish....................................... C-10

Figure C.10 Specifying Distributed Sensitivity Analysis on an Input................................... C-13

Figure C.11 Viewing the Output of a Distributed Sensitivity Analysis on an Input .............. C-14

Figure C.12 Variation of Peak Predicted Dose with Hydraulic Conductivity

in the Saturated Zone .................................................................................... C-15

Figure C.13 Variation of Peak Predicted Dose from Drinking Water with

Hydraulic Conductivity in the Saturated Zone................................................. C-15

Figure C.14 Variation of Peak Predicted Dose from Ingestion of Vegetables

with Hydraulic Conductivity in the Saturated Zone ......................................... C-16

Figure C.15 Variation of Peak Predicted Dose from Ingestion of Meat with

Hydraulic Conductivity in the Saturated Zone................................................. C-16

Figure C.16 Variation of Peak Predicted Dose from Ingestion of Milk with

Hydraulic Conductivity in the Saturated Zone................................................. C-17

Figure C.17 Variation of Peak Predicted Dose from Direct Exposure to Waterborne

Accumulation in Soil with Hydraulic Conductivity in the Saturated Zone......... C-17

Figure C.18 Variation of Peak Predicted Dose from Ingestion of Fish with Hydraulic

Conductivity in the Saturated Zone ................................................................ C-18

Figure C.19 Option Box to be Checked to Flag the Code to Produce a Full Suite of

Temporal Plots for Each Probabilistic Simulation ........................................... C-23

Figure C.20 Relative Contributions of Exposure Pathways at 1984 m/yr Hydraulic

Conductivity ................................................................................................... C-24

Figure C.21 Total Dose at a Hydraulic Conductivity of 1984 m/yr in Saturated Zone......... C-24

Figure C.22 Relative Contributions of Exposure Pathways at 752.1 m/yr Hydraulic

Conductivity ................................................................................................... C-25

Figure C.23 Total Dose at a Hydraulic Conductivity of 752.1 m/yr in Saturated Zone ........ C-25

Figure C.24 Relative Contributions of Exposure Pathways at 732.1 m/yr Hydraulic

Conductivity ................................................................................................... C-26

Figure C.25 Total Dose at a Hydraulic Conductivity of 732.1 m/yr in Saturated Zone ........ C-26

Figure C.26 Relative Contributions of Exposure Pathways at 709.8 m/yr Hydraulic

Conductivity ................................................................................................... C-27

Figure C.27 Total Dose at a Hydraulic Conductivity of 709.8 m/yr in Saturated Zone ........ C-27

Figure C.28 Relative Contributions of Exposure Pathways at 299.2 m/yr Hydraulic

Conductivity ................................................................................................... C-28

Figure C.29 Total Dose at a Hydraulic Conductivity of 299.2 m/yr in Saturated Zone ........ C-28

Figure C.30 Relative Contributions of Exposure Pathways at 258 m/yr Hydraulic

Conductivity ................................................................................................... C-29

Figure C.31 Total Dose at a Hydraulic Conductivity of 258 m/yr in Saturated Zone........... C-29
xvii

List of Figures (continued)

Figure C.32 Relative Contributions of Exposure Pathways at 213.7 m/yr Hydraulic

Conductivity ................................................................................................... C-30

Figure C.33 Total Dose at a Hydraulic Conductivity of 213.7 m/yr in Saturated Zone ........ C-30

Figure C.34 Rate of Change of Peak Predicted Dose with Hydraulic Conductivity............. C-32

Figure C.35 Fractional Rate of Change of Peak Predicted Dose with Hydraulic

Conductivity ................................................................................................... C-34

Figure C.36 Shape of y = xk for select values of k ............................................................. C-35

Figure C.37 Dimensions of Plume Prior to Lateral Dispersion and Dimension of

Saturated Zone Contributing to the Surface Water Body................................ C-38

Figure C.38 Horizontal Distribution of Radionuclides in the Transverse Plane at the

 Location of the Surface Water Body............................................................... C-39 

Figure C.39 Vertical Distribution of Radionuclides in the Transverse Plane at the 

 Location of the Surface Water Body............................................................... C-39 

Figure C.40 Dimensions of the Initial Plume in the Saturated Zone and the Dimensions

of the Aquifer Contributing to the Well for Five Hydraulic Conductivities

in the Saturated Zone .................................................................................... C-41

Figure C.41 Variation in Dilution Factor with Hydraulic Conductivity in the 

 Saturated Zone .............................................................................................. C-42

Figure C.42 Horizontal Distribution of Radionuclides in the Transverse Plane at the 

Well................................... ....................................................................... C-43 

Figure C.43 Vertical Distribution of Radionuclides in the Transverse Plane at the 

Well................................... ....................................................................... C-43 

Figure C.44 Specifying Relationships between Inputs ....................................................... C-44

Figure C.45 Specifying the Dependent Input of a Relationship.......................................... C-44

Figure C.46 Adding an Independent Input to the Relationship........................................... C-45

Figure C.47 Adding an Arithmetic Operator and Selecting the Second Independent Input

to the Relationship ......................................................................................... C-46

Figure C.48 Completing the Specification of a Relationship and Transferring It to the

Relationship Table ......................................................................................... C-47

Figure C.49 Inputting Numerical Constants in a Relationship ............................................ C-47

Figure C.50 Using a Related Input in the Relationship of Another Input ............................ C-49

Figure C.51 Indirect Introduction of [ ] Using Placeholder Inputs, Enabling Creation

of Complex Relationships .............................................................................. C-49

Figure C.52 Relationship between Mean Residence Time of Water in the Surface

Water Body and the Hydraulic Conductivity in the Saturated Zone ................ C-50

Figure C.53 Variation with Hydraulic Conductivity of Peak Predicted Dose from

Ingestion of Fish When a Relationship Is Specified between Hydraulic

Conductivity and Mean Residence Time of Water in the Surface 

 Water Body.................................................................................................... C-51
xviii

List of Figures (continued)

Figure C.54 Variation with Hydraulic Conductivity of Peak Predicted Dose from All

Pathways When a Relationship Is Specified between Hydraulic

Conductivity and Mean Residence Time of Water in the Surface 

 Water Body.................................................................................................... C-52

Figure C.55 Specifying a Discrete Distribution on an Input................................................ C-54

Figure C.56 Pairing of Samples in a Two-input Probabilistic Analysis Where One Input

Has a Continuous Uniform Distribution and the Other a Discrete

Uniform Distribution ....................................................................................... C-55

Figure C.57 Variation of Peak Predicted Dose with Hydraulic Conductivity at Different

Discrete Values of Depth of Aquifer Contributing to the Well.......................... C-56

Figure C.58 Specifying a Continuous Linear Distribution................................................... C-57

Figure C.59 Samples from a Continuous Linear Distribution Showing a Greater

Concentration of Samples from One Part of the Range and Sparse

Sampling over the Rest of the Range............................................................. C-57

Figure C.60 Variation of Peak Predicted Dose with Hydraulic Conductivity at Discrete

Values for Depth of Aquifer Contributing to the Well ...................................... C-58

Figure C.61 Variation of Peak Predicted Dose with Hydraulic Conductivity in the

Range 200 to 800 m/yr at Discrete Values for Depth of Aquifer

Contributing to the Well.................................................................................. C-59

Figure C.62 Range of Peak Predicted Dose at Different Discrete Values for Depth of

Aquifer Contributing to the Well Caused by Variation of Hydraulic 

 Conductivity ................................................................................................... C-60

Figure C.63 Variation of Peak Predicted Dose with Hydraulic Conductivity—the Scatter

Shows the Effect of Sampling the Depth of Aquifer Contributing to the

Well and the Evapotranspiration Coefficient................................................... C-63

Figure C.64 Peak Predicted Dose at Three Values of Evapotranspiration Coefficient— 

the Range of Peak Predicted Dose Is Due to Sampling the Depth of Aquifer

Contributing to the Well and the Hydraulic Conductivity ................................. C-63

Figure C.65 Pairing of Samples in a Two-input Probabilistic Analysis Where Both

Inputs Have Continuous Distributions ............................................................ C-65

Figure C.66 Variation of Peak Predicted Dose with Hydraulic Conductivity—the

Scatter Shows the Effect of Sampling the Depth of Aquifer

Contributing to the Well.................................................................................. C-66

Figure C.67 Variation of Peak Predicted Dose with Depth of Aquifer Contributing

to the Well—the Scatter Shows the Effect of Sampling the

Hydraulic Conductivity ................................................................................... C-67

Figure C.68 Estimating the Range of Peak Predicted Doses at Any Given Value

of x-coordinate ............................................................................................... C-67

Figure C.69 Linear Regression on Standardized Raw and Ranked Data for the

Two-input Continuous Distribution Example................................................... C-68

Figure C.70 Linear Regression on Standardized Raw and Ranked Data for the

Second Two-input Continuous Distribution Example...................................... C-68
xix

List of Figures (continued)

Figure C.71 Variation of Peak Predicted Dose with Hydraulic Conductivity—the

Scatter Shows the Effect of Sampling the Depth of Aquifer Contributing

to the Well for the Second Example Case...................................................... C-69

Figure C.72 Variation of Peak Predicted Dose with Depth of Aquifer Contributing to

the Well—the Scatter Shows the Effect of Sampling the Hydraulic

Conductivity for the Second Case .................................................................. C-69

Figure C.73 Linear Regression on Standardized Raw and Ranked Data for the

Three-input Continuous Distribution Example ................................................ C-70

Figure C.74 Variation of Peak Predicted Dose with Hydraulic Conductivity—the

Scatter Shows the Effect of Sampling the Depth of Aquifer Contributing

to the Well and the Evapotranspiration Coefficient......................................... C-70

Figure C.75 Variation of Peak Predicted Dose with Depth of Aquifer Contributing to

the Well — the Scatter Shows the Effect of Sampling the Hydraulic

Conductivity and the Evapotranspiration Coefficient ...................................... C-71

Figure C.76 Variation of Peak Predicted Dose with Evapotranspiration Coefficient— 

the Scatter Shows the Effect of Sampling the Hydraulic Conductivity and

the Depth of Aquifer Contributing to the Well ................................................. C-71

Figure C.77 Scatter Plot of a Linear Relationship for a Case Involving Only a

Single Variable............................................................................................... C-72

Figure C.78 Scatter Plot of the Dependent Variable and the First Independent Variable

for a Case Involving a Linear Relationship with Two Independent Variables .. C-73

Figure C.79 Scatter Plot of the Dependent Variable and the Second Independent

Variable for a Case Involving a Linear Relationship with

Two Independent Variables ........................................................................... C-73

Figure C.80 Scatter Plot of the Dependent Variable and the First Independent

Variable for a Case Involving Linear and Nonlinear Relationships

with Three Independent Variables.................................................................. C-77

Figure C.81 Scatter Plot of the Dependent Variable and the Second Independent

Variable for a Case Involving Linear and Nonlinear Relationships

with Three Independent Variables.................................................................. C-77

Figure C.82 Scatter Plot of the Dependent Variable and the Third Independent

Variable for a Case Involving Linear and Nonlinear Relationships with

Three Independent Variables......................................................................... C-78

Figure C.83 Scatter Plot of the Rank of the Dependent Variable and the Rank of the

First Independent Variable for a Case Involving Linear and Nonlinear

Relationships with Three Independent Variables ........................................... C-78

Figure C.84 Scatter Plot of the Rank of the Dependent Variable and the Rank of the

Second Independent Variable for a Case Involving Linear and Nonlinear

Relationships with Three Independent Variables ........................................... C-79

Figure C.85 Scatter Plot of the Rank of the Dependent Variable and the Rank of the

Third Independent Variable for a Case Involving Linear and Nonlinear

Relationships with Three Independent Variables ........................................... C-79
xx

List of Figures (continued)

Figure C.86 Cumulative Distribution Function of One of the Inputs.................................... C-82

Figure C.87 Cumulative Distribution Function of the Output, the Peak Predicted Dose ..... C-83

Figure C.88 Regression Report......................................................................................... C-85

Figure C.89 Plot of the Standardized Regression Coefficients from the Regression

 Report............................................................................................................ C-86

Figure C.90 Scatter Plots of Peak Predicted Dose against Inputs Identified as the

Four Most Significant by the Regression Analysis .......................................... C-87

Figure C.91 Scatter Plots of Peak Predicted Dose against Inputs Identified as the

Second Set of Four Most Significant by the Regression Analysis................... C-88

Figure C.92 Scatter Plots of Peak Predicted Dose against Inputs Identified as the

Third Set of Four Most Significant by the Regression Analysis....................... C-89

Figure C.93 Scatter Plots of Peak Predicted Dose against Inputs Identified as the

Fourth Set of Four Most Significant by the Regression Analysis ................... C-90

Figure C.94 Scatter Plots of Peak Predicted Dose against Inputs Identified as the

Fifth Set of Four Most Significant by the Regression Analysis........................ C-91

Figure C.95 Scatter Plots of Peak Predicted Dose against Inputs Identified as the

Sixth Set of Four Most Significant by the Regression Analysis....................... C-92

Figure C.96 Scatter Plots of Peak Predicted Dose against Inputs Identified as the

Seventh Set of Four Most Significant by the Regression Analysis.................. C-93

Figure C.97 Scatter Plots of Peak Predicted Dose against Inputs Identified as the

Eighth Set of Four Most Significant by the Regression Analysis..................... C-94

Figure C.98 Scatter Plots of Peak Predicted Dose against Inputs Identified as the

Ninth Set of Four Most Significant by the Regression Analysis ...................... C-95

Figure C.99 Scatter Plots of Peak Predicted Dose against Inputs Identified as the

10th Set of Four Most Significant by the Regression Analysis........................ C-96

Figure C.100 Cumulative Distribution Function Plots from the Three Multi-input

Sensitivity Analyses ....................................................................................... C-97

Figure C.101 Cumulative Distribution Function of the Output, the Peak Predicted Dose,

When National Distributions Are Used to Obtain 500 Samples of Each

of the 203 Inputs .......................................................................................... C-101

Figure C.102 Plot of the Standardized Regression Coefficients from the Regression Report

of Sensitivity Analysis Using 500 Observations on National Distribution ...... C-102

Figure C.103 Cumulative Distribution Function of Peak Predicted Dose with 5000 Samples,

When National Distributions Are Used for the Inputs.................................... C-103

Figure C.104 Plot of the Standardized Regression Coefficients from the Regression Report

of Sensitivity Analysis Using 5000 Observations on National Distributions... C-104

Figure C.105 Regression Report of Sensitivity Analysis Using 5000 Observations on

National Distributions ................................................................................... C-105

Figure C.106 Cumulative Distribution Function of Peak Predicted Dose with 5000 Samples,

When National Distributions Are Used for the Inputs after Depressing

Erosion Release to Surface Water Body and Release to Atmosphere ......... C-108
xxi

List of Figures (continued)

Figure C.107 Regression Report of Sensitivity Analysis Using 5000 Observations on

National Distributions Inputs after Depressing Erosion Release to

Surface Water Body and Release to Atmosphere ........................................ C-109

Figure C.108 Cumulative Distribution Function Plot of the Input Samples for the

Thickness of the Unsaturated Zone ............................................................. C-110

Figure C.109 Cumulative Distribution Function Plot of the Input Samples for the

Distribution Coefficient for Radium in the Unsaturated Zone ........................ C-111

Figure C.110 Cumulative Distribution Function Plot of the Input Samples for the

Hydraulic Gradient of the Saturated Zone to the Surface Water Body.......... C-112

Figure C.111 Cumulative Distribution Function Plot of the Input Samples for the Hydraulic 

Conductivity of the Saturated Zone to the Surface Water Body.................... C-113

Figure C.1-1 Layout of the Hypothetical Site..................................................................... C-115

Figure C.1-2 The Cross Section of the Primary Contamination and the Soil beneath It .... C-115

Figure D.1 Specifying Inputs for the Version 2 Release Methodology................................ D-1

Figure D.2 Specifying Inputs for First-Order, Rate-Controlled Release of Material

That Initially Is Entirely in the Releasable Form.............................................. D-12

Figure D.3 Comparison of Pathway Doses Predicted by Version 3.1 with the

Doses Predicted by the Previously Benchmarked 3.0 Beta Version of

RESRAD-OFFSITE for a First-Order, Rate-Controlled Release..................... D-13

Figure D.4 Specifying Inputs for Equilibrium Desorption Release of Material

That Initially Is Entirely in the Releasable Form.............................................. D-14

Figure D.5 Comparison of Pathway Doses Predicted by Version 3.1 with the

Doses Predicted by the Previously Benchmarked 3.0 Beta Version of

RESRAD-OFFSITE for an Equilibrium Desorption Release ........................... D-15

Figure D.6 Specifying Inputs for Uniform Release of Material That Initially Is

Entirely in the Releasable Form ..................................................................... D-16

Figure D.7 Comparison of Pathway Doses Predicted by Version 3.1 with the

Doses Predicted by the Previously Benchmarked 3.0 Beta Version

of RESRAD-OFFSITE for a Uniform Release ................................................ D-17

Figure D.8 A First-Order Release with Radionuclide-Bearing Material Becoming

 Available Linearly Over Time ......................................................................... D-19

Figure D.9 A First-Order Release with Radionuclide-Bearing Material Becoming 

 Available Stepwise in Time ............................................................................ D-20

Figure D.10 An Instantaneous Equilibrium Desorption Release in Which

Radionuclide-Bearing Material Becomes Available for Release 

 Linearly in Time ............................................................................................. D-21

Figure D.11 An Instantaneous Equilibrium Desorption Release in Which

Radionuclide-Bearing Material Becomes Available for Release

Stepwise in Time............................................................................................ D-22

Figure E.1 Area Factors Form – Default Options............................................................... E-2

Figure E.2 Area Factors Form – Option to Specify the Range of the Y Dimension

of the Small Area of Elevated Contamination................................................... E-3
xxii

List of Figures (continued)

Figure E.3 Distribution of Area Using the Three Distribution Options for Sampling the 

Dimensions of the Small Area of Elevated Contamination: triangular skewed to 

the high end, uniform, and triangular skewed to the low end............................ E-4

Figure E.4 Area Factors Form – Generate Dose-Area Plot Command Button Activated.... E-6

Figure E.5 Scatter Plot of Dose against Area of Contamination for Cs-137 Where the

Direct External Exposure Is the Dominant Pathway ......................................... E-7

Figure E.6 Scatter Plot of Dose against Area of Contamination for Sr-90 for Which

Groundwater Transport Is the Dominant Route of Exposure. ........................... E-8

Figure E.7 Scatter Plot of Dose against Area of Contamination for Tc-99 for Which

Groundwater Transport Is the Dominant Route of Exposure. ........................... E-9
xxiii

List of Tables

Table 2.1: Input Files Used to Specify the Source Characteristics and Releases to 

 the Code ........................................................................................................ 2-29

Table 3.1: Assumptions for the Release Sources in Different Comparison Cases ............ 3-5

Table B.1: Properties of the Radioactive Species Considered in GoldSim Modeling ......... B-5

Table C.1: Peak Predicted Doses and Times of Peak Predicted Doses From

Different Exposure Pathways......................................................................... C-19

Table C.2: Effect of the Choice of the Representative Normalizing Value on the

Computed Fractional Rate of Change............................................................ C-33

Table C.3: Relationship between Fractional Rate of Change and the Shape of the

Curve of Peak Predicted Dose and the Input ................................................. C-35

Table C.4: One Hundred Samples of Data Used in Section 3.6.1 to Illustrate Linear

Regression on Raw Values............................................................................ C-74

xxv

Executive Summary

The RESRAD-OFFSITE computer code evaluates the radiological dose and excess cancer risk 

to an individual who is exposed while located within or outside the area of initial (primary) 

contamination. The RESRAD-OFFSITE code Version 2 was developed by adding offsite 

transport and offsite accumulation modules to the original and well-established RESRAD 

(onsite) code, which was designed for the evaluation of radiological doses to an onsite receptor 

from exposure to RESidual RADioactive materials in soil. The source release to groundwater 

model used in Version 2 (i.e., the first–order, rate-controlled leaching model, sometimes referred 

to as the exponential leaching model) is largely the same as the one used in the RESRAD 

(onsite) code. This model is retained in RESRAD-OFFSITE Version 3, which adds three new 

source release mechanisms.

The RESRAD-OFFSITE code Version 3 was improved by the addition of three release 

mechanisms to groundwater. The transport of the radionuclides in the primary contamination is 

modeled for all three new release options. The first release option, that is, the "first–order, 

release-with-transport" option, assumed that the release of the radionuclide is proportional to 

the inventory in the primary contamination; the user-specified leach rate is the proportionality 

constant. The waste forms/materials that resemble the “first order release with transport”

release option include dewatered sludge and ion-exchange resins. The second release option, 

that is, the "equilibrium desorption release" option, assumed that the release is controlled by the 

linear equilibrium partitioning between the solid and aqueous phase; the user specifies the 

distribution coefficient which quantifies the partitioning of the radionuclide between the solid and 

aqueous phases. The waste forms/materials that fit this specification include compacted lab 

trash, such as clothes or glove boxes, as well as small gadgets or tools. Under the third release 

option, that is, the "uniform release" option, the radionuclides are released from a constant 

fraction of the initially contaminated material during each time interval; the user specifies the 

duration over which the radionuclides are released. An example of waste forms/materials that 

may fit these descriptions is activated metal, which would corrode in the environment and 

release the imbedded radionuclides. The preexisting release methodology of the Version 2 

code is also retained; it is a first-order, release-without-transport option where the user may 

specify the leach rate or ask the code to estimate a leach rate from the specified distribution 

coefficient. The user-specified leach rate has to meet a non-negative distribution coefficient 

check. 

Two of the new source release models (i.e., equilibrium desorption release and uniform release) 

are comparable to two of the release mechanisms simulated by DUST-MS, a computer code 

designed for evaluating radionuclide releases from underground waste disposal units. The 

uniform release condition would result if the waste materials undergo constant dissolution upon 

contact with water, then release radionuclides contained within the materials. The equilibrium 

desorption release condition would result if radionuclides are distributed on the surface of the 

waste materials, then dissolve to water when the waste materials are rinsed by water. In the 

effort to benchmark the new source term models with DUST-MS, radionuclide release rates, 

which were obtained from the bottom of a contaminated zone/disposal unit and calculated under 

similar release conditions, were compared. The comparison with DUST-MS involved the 

development of five different cases that consider different sources containing different 

radionuclides, assuming different dimensions, and experiencing different water infiltration rates. 

Overall, the agreement between the RESRAD-OFFSITE results and DUST-MS results is very 

good, with both codes predicting the same or very similar profiles over time. Numerical 
xxvi

dispersion in the DUST-MS results was identified as potentially contributing to the disagreement 

in the release rates when no dispersion was considered. The mobility of radionuclides in the 

soil column and the radioactive decay half-life of radionuclides might also affect the agreement, 

with greater discrepancy in the release rates found for short-lived, fast-moving radionuclides 

than found for long-lived, slow-moving radionuclides.

The new source term model in RESRAD-OFFSITE code Version 3 was also compared with the 

Contaminant Transport Module for Radionuclides (RT Module) in GoldSim. To simulate the first 

order and uniform release, mass was introduced through the source element in the cell 

pathway. The waste material without any barrier was assumed to be contained in the source 

element and was assumed to degrade with a constant rate in the case of first-order release and 

with specified lifetime in the case of uniform release. The contaminants released from the 

source element were mixed in the cell element and were carried to the pipe element with the 

infiltrating water. The pipe element was assumed to be soil as the infill medium with known 

density and porosity. The contaminants were assumed to partition between the solid and liquid 

phases and transported through the advection process in the pipe element. The contaminant's 

outflow from the pipe element was linked to a sink element from which the release rates were 

obtained. To simulate the release of radionuclides under equilibrium desorption conditions, the 

initial inventory of radionuclides was uniformly distributed in the pipe (or aquifer, in the case of 

no dispersion) element. In the limited comparisons conducted, the results obtained with 

RESRAD-OFFSITE and GoldSim were, in general, in excellent agreement for all three source 

release options.

Multi-input probabilistic analysis and single input sensitivity analysis can be performed on the 

inputs that quantify the release. Examples of single input analysis and multiple input analysis 

are provided to illustrate how to perform these sensitivity analyses and to illustrate the sensitivity 

outputs that are available in the code. Appendix C discusses the sensitivity analyses in greater 

detail.

The revisions and additions to Version 3.1 of the code extend the idea of a uniform release, 

where the radionuclides in equal fractions of the contaminated material become available for 

release at equal time intervals to both release mechanisms, that is, first-order rate controlled 

and instantaneous desorption equilibrium. The revisions and additions also make it possible to 

model time-delay scenarios where the radionuclides become available for release at some time 

in the future. This delayed and time-distributed release option allows modeling of situations 

where the radionuclides are initially in an immobilized state due to engineered barriers or 

release-resistant waste forms, but might become available for release over a future period of 

time as the engineered barriers and/or waste forms deteriorate with time.

RESRAD-OFFSITE code Version 3.1 automates the calculation of area factors for offsite 

exposure scenarios using the probabilistic feature of the code. The area factor is defined as the 

ratio of the calculated dose from the large area of primary contamination divided by the dose 

from a small area of elevated activity (hot spot) for the same exposure scenario. Area factors 

can be used in conjunction with the Multi-Agency Radiation Survey and Site Investigation 

Manual (MARSSIM) to quickly determine cleanup criteria for small areas of elevated 

contamination.
xxvii

Acknowledgments

The authors would like to recognize John Randall and Wendy Reed, the U.S. Nuclear 

Regulatory Commission (NRC) Project Managers, for their effective project technical direction 

and helpful guidance in ensuring the high quality and timeliness of the work. We would like to 

thank Adam Schwartzman, Phil Reed, and Boby Eid, all of NRC, for reviewing and providing 

constructive comments on the draft report. We would also like to thank Dr. David LePoire of 

Argonne National Laboratory (Argonne) for his technical peer review of the final report and his 

constructive comments during the development of the new source term models. We would like 

to thank Terry Sullivan of Brookhaven National Laboratory for providing the DUST-MS source 

and executable codes and for helpful discussions on the source release mechanisms 

implemented in the DUST code. We would like to thank Mark Nutt of Argonne for his interest 

and support on the application of GoldSim. We also thank Andrea Manning and Suzanne 

Williams, technical editors at Argonne, and Linda Conlin and Vicki Skonicki of the Document 

Processing Center of Argonne’s Communications, Education, and Public Affairs Division for 

preparing the manuscript.

1-1 

1. Introduction

The RESRAD-OFFSITE Version 2 computer code was released in June 2007 (Yu et al. 2007). 

It is designed to evaluate the radiological dose and excess cancer risk to an individual who is 

exposed while located within or outside of the area of initial (primary) contamination. The 

primary contamination, which is the source of all of the releases modeled by the code, is 

assumed to be a layer of soil material. Just as with the RESRAD (onsite) code (Yu et al. 2001), 

the RESRAD-OFFSITE code Version 2 models the release from the primary contamination 

using a first-order exponential leaching model to estimate the release of contaminants. It then 

models the movement of contaminants from the area of primary contamination to agricultural 

areas, pastures, a dwelling area, a well, and a surface water body. The RESRAD-OFFSITE 

code also models the accumulation of the contaminants at those locations where appropriate. 

Any contribution of the contaminants from the water sources to the land-based locations is also 

modeled.

1.1 Overview of the Source Release Model in 

RESRAD-OFFSITE Version 2

The source release model used in RESRAD-OFFSITE Version 2 assumes a homogeneous 

distribution of radionuclides within an initially contaminated soil layer of uniform thickness. It 

accounts for radiological transformations (decay and ingrowth). The leaching of radionuclides in 

the contaminated layer by infiltration is modeled as a first-order, rate-controlled process 

occurring over the depth of the contamination. The code does not model the transport of the 

release within the contaminated zone; all of the material that is leached at any time is assumed 

to leave at the bottom of the contamination at that time. It also considers mixing in a surface 

layer. The concentration in the mixing layer is affected by erosion release to runoff and by 

leaching. Erosion is modeled by using the Universal Soil Loss Equation. Release to the 

atmosphere is computed by assuming that the clean dust that settles on the primary 

contamination is balanced by the release of an equal amount of contaminated dust.

RESRAD-OFFSITE has been used by the U.S. Nuclear Regulatory Commission (NRC) and its 

licensees; the U.S. Department of Energy (DOE) and its contractors; and other Federal 

agencies, health physicists, and risk assessors for the evaluation of contaminated sites, 

remediation alternatives, derivation of cleanup criteria, and performance assessments of waste 

disposal facilities. Recent decommissioning activities have involved evaluating the exposure to 

materials other than soil (e.g., slag, concrete, etc.). The current source term model (i.e., the 

first-order exponential leaching model) implemented in the RESRAD-OFFSITE code needs to 

be expanded to properly model various source release mechanisms. These release 

mechanisms may include surface wash off or surface rinse, diffusion, dissolution, and ionexchange. A proposal in the form of a Letter Report on expanding the source term model used 

in the RESRAD-OFFSITE code was submitted to NRC. This Letter Report is included in 

Appendix A. The new source release mechanisms/models are developed referencing the 

models used in the DUST-MS (Disposal Unit Source Term-Multiple Species) code 

(Sullivan 2001a). The existing contaminant transport models and the assumptions and 

algorithms of the RESRAD-OFFSITE code are taken into account when developing the new 

source term models. Some of the considerations are discussed in the next section.
1-2 

1.2 Considerations for Expanding the Source Term Model

The source term model implemented in RESRAD-OFFSITE Version 2 computes three releases 

from the contaminated zone, as well as the concentration and distribution of the radionuclides 

within the contaminated zone. The model calculates the atmospheric release of particulates 

due to resuspension and that of volatiles due to diffusion and evapotranspiration, the surface 

water release due to erosion by runoff water, and the groundwater release due to leaching by 

infiltrating water. The release rates are used by the code to compute the transport of 

contaminants and exposure at offsite locations, whereas the concentration and distribution of 

radionuclides within the contaminated zone are used to compute the direct external exposure 

from the primary contamination, as well as any exposure from onsite activities. The newly 

developed source term models consider these releases and distribution in the primary 

contaminated zone. 

Another consideration is the radionuclide decay and ingrowth chain. The new source term 

models consider not just the parent radionuclide but all radionuclides in the decay chain. The 

RESRAD-OFFSITE code Version 2 uses the radionuclide information in International 

Commission on Radiological Protection Publication 38 (ICRP-38) to construct the decay 

sequences of the radionuclide being analyzed. The codes in the RESRAD family are being 

modified to use the radionuclide information in ICRP-107. The user of the code specifies a 

cutoff half-life. The fate and transport of all transformation products that are of a half-life greater 

than or equal to the user-specified cutoff are modeled explicitly. Any transformation product that 

has a half-life that is less than that of the cutoff is assumed to be in secular equilibrium with its 

immediate parent whose half-life is greater than that of the cutoff.

In addition, it is desirable to be able to perform sensitivity analysis and probabilistic analysis on 

the input parameters of the new source term models. The newly implemented source term 

models do, in fact, allow users to perform both sensitivity and probabilistic analyses on new 

inputs. However, the probabilistic distribution functions for some input parameters under 

various conditions will still need to be developed.

1.3 The Proposed Approaches and the Implemented Source 

Term Models

Three approaches were proposed to NRC for adding the new release source options to the 

RESRAD-OFFSITE code (see Appendix A). The first is to derive the formulations for the 

desired mechanisms of release on the basis of DUST-MS code and implement the formulations 

in RESRAD-OFFSITE. The second is to link the DUST-MS code (executables) to 

RESRAD-OFFSITE. The third approach is to incorporate parts of the source code from 

DUST-MS regarding the desired source release mechanisms into the source code of 

RESRAD-OFFSITE. The pros and cons of these three approaches are discussed in detail in 

Appendix A; summaries of the advantages and disadvantages of each follow. 

Approach 1, which involves including the formulations of the various release options to 

uncontained contamination, will enhance the code while preserving all of the current capabilities 

of RESRAD-OFFSITE. This approach will provide more options for calculating release to 

groundwater while evaluating exposure from all of the current exposure pathways in 

RESRAD-OFFSITE. It will be possible to perform probabilistic and sensitivity analyses on all of 

the new inputs. 
1-3 

Approach 2, which involves the linking of the one-dimensional, finite-difference DUST code 

(executables) to RESRAD-OFFSITE, is expected to be the easiest to implement. All three 

approaches will require coding to the user interface to allow specification of the additional 

inputs. In addition, this approach will require coding to prepare the input file for DUST from the 

interface and coding to reformat the output of DUST to a form that is useable by 

RESRAD OFFSITE. Drawbacks include the inability to perform sensitivity and probabilistic 

analyses and the ability to model only the exposure from the release to groundwater. 

Approach 3, which involves incorporating the analytical formulations for container degradation 

and release into RESRAD-OFFSITE, will be more difficult to implement than Approach 2. It will 

be necessary to understand the coding to properly combine it with the transport formulations in 

RESRAD-OFFSITE so as to make the necessary changes to ensure that the imported coding is 

compatible with the FORTRAN complier used in RESRAD-OFFSITE. While it will be possible to 

perform sensitivity and probabilistic analyses, this approach will also be limited to modeling 

exposure from the release to groundwater. 

Although these three approaches are not mutually exclusive, different tasks need to be 

performed and efforts made to implement the different approaches for expanding the existing 

source term model. It would be preferable to include more than one approach to allow users the 

flexibility of choosing the option appropriate for their applications. Of the proposed approaches, 

the preferred task was to implement Approach 1 (provide more release options for uncontained 

contamination in soil). 

Approach 1 has the advantages of allowing users to perform both sensitivity and probabilistic 

analyses on the new input parameters, and it is the approach approved by NRC and 

implemented in RESRAD-OFFSITE Version 3.

The new source release mechanisms implemented in RESRAD-OFFSITE are described in 

detail in Chapter 2. These new release mechanisms are not limited to treating soil materials as 

the source (primary contamination). The release mechanisms are also not limited to 

uncontainerized sources because the new source release models assume that the releases are 

from a distinct phase of source material; once released into surrounding soils, they are 

transported in the primary contamination. The new source release models implemented in 

RESRAD-OFFSITE are compared with DUST-MS code, and the results are presented in 

Chapter 3. Additional comparisons were also conducted later with the GoldSim software, and 

these results are presented in Appendix B. Appendix C contains the detailed description of and

examples on how to conduct sensitivity and probabilistic analyses using RESRAD-OFFSITE 

code. The results of using sensitivity and probabilistic analyses on the new source release input 

parameters are presented in Chapter 4. This report is available from the RESRAD Web site in 

the Documents section (http://web.ead.anl.gov/resrad/documents/). It is also included in the 

RESRAD-OFFSITE Version 3 code in the Help button. The RESRAD-OFFSITE code Version 3 

can be downloaded from the RESRAD Web site: http://www.evs.anl.gov/resrad. 

Additional source term options were added to RESRAD-OFFSITE code Version 3.1 to consider 

the time-delay feature of source release mechanisms. These options consider two forms of 

contaminated material, one that is susceptible to releasing the radionuclides and the other that 

is not. Therefore, two time-delay periods are considered: (1) a period of time of no releases, 

and (2) a time period for the transition of contaminated material from one form to another. 

These additions were made after the preparation of the main body of this report and are 

described in Appendix D. Appendix D also includes some limited comparisons of the outputs of 

the Version 3.0 beta release options and the Version 3.1 release options.
1-4 

1.4 Area Factors for Offsite Exposure Scenarios 

Another new feature added to RESRAD-OFFSITE code Version 3.1 is the calculation of area 

factors for offsite exposure scenarios. The area factor is defined as the ratio of the calculated 

dose from the large area of primary contamination divided by the dose from a small area of 

elevated activity (hot spot) for the same exposure scenario. Area factors can be used in 

conjunction with the Multi-Agency Radiation Survey and Site Investigation Manual (MARSSIM) 

to quickly determine cleanup criteria for small areas of elevated contamination. The area 

factors are calculated using the probabilistic feature of the code. The interface of the code 

automates the calculation of air transport distances and directions, groundwater transport 

distances, and direct exposure distances for a number of small areas of elevated contamination 

sampled according to a number of user-specified conditions. The doses calculated for each of 

these small areas of elevated contamination are displayed graphically in the probabilistic output 

interface and are used to compute a table of area factors for each radionuclide in the primary 

contamination. The detailed users’ guide in Appendix E describes the area factor.
2-1 

2. Primary Contamination and the Source Term

This chapter consists of five sections. The first (Section 2.1) describes the manner in which 

RESRAD-OFFSITE conceptualizes the primary contamination, specifically its physical 

dimensions; the concentration of radionuclides within it; and the releases to the atmosphere, to 

surface erosion, and to groundwater as a function of time. Section 2.2 derives the expressions 

that result from the conceptual model, and Section 2.3 deals with the implementation of the 

solution or the evaluation of these expressions in the computational code. Section 2.4 

describes the input forms, the input, and how the inputs are used in the code to compute the 

releases. The last subsection (2.5) describes the method to override the source term model of 

the RESRAD-OFFSITE code. These formulations were extended further in RESRAD-OFFSITE 

Version 3.1 by adding a time-delay feature to the source release mechanism as described in 

Appendix D after the writing of the main body of this report. 

2.1 Conceptualization of the Primary Contamination

The initial contamination is assumed to be distributed uniformly throughout a soil layer. This 

contaminated layer is of uniform thickness and can have a clean cover of uniform thickness 

above it. The clean cover and the primary contamination may be eroded by surface runoff, and 

their thicknesses can decrease over time. Erosion occurs from a well-mixed surface layer. The 

thickness of the primary contamination is not affected until the thickness of the cover erodes to 

the thickness of this surface layer. The primary contamination is situated above the water table; 

it can be just above and in contact with the water table, or there can be up to five different 

intervening, partially saturated soil layers. The assumptions about the shape of the conceptual 

primary contamination vary across exposure and transport models. The atmospheric and 

groundwater transport modules assume rectangular shapes, although the shape specified for 

use by the two transport modes need not be identical. The external exposure module assumes 

either a circular shape or a polygonal shape for the primary contamination.

The current version of RESRAD-OFFSITE contains three new options to compute the release to 

groundwater. The “First Order Release with Transport” option is similar to the release 

mechanism that was available in the preceding versions of the code. The other two new options 

that are currently in the code are the “Uniform Release” and the “Equilibrium Desorption 

Release.” The preexisting release methodology is being retained for backward compatibility, 

and it is also the default release option for the new code, Version 3. 

Under the First Order Release with Transport option, the transfer to groundwater at any time is 

proportional to the radionuclide inventory at that time and occurs uniformly over the thickness of 

the primary contamination. Thus, the transfer to groundwater affects the concentration in the 

primary contamination but not its physical dimensions; the vertical concentration profile remains 

uniform over time. The proportionality constant, the leach rate, has to be specified by the user if 

this option is chosen.

The Uniform Release is the other rate-controlled option in the code. This option models a 

situation where the source weathers at a uniform rate; the radionuclides and their progeny 

contained within a constant fraction of the initial contamination are transferred to the soil 

moisture in a unit of time. This transfer also occurs uniformly over the thickness of the primary 

contamination. The vertical concentration profile remains uniform over time, and the 

dimensions of the contamination are not affected by the transfer. The concentration in the 
2-2 

primary contamination varies linearly with time because of this transfer, and exponentially with 

time because of radiological transformations. The user must specify the duration of the release 

if this option is chosen.

The infiltration that comes into contact with the contamination will become more contaminated 

as it passes through the primary contamination and will eventually attain the equilibrium 

concentration of the radionuclides. How long it takes to reach equilibrium and hence how deep 

it needs to travel before it reaches equilibrium depend on the rate at which the radionuclides are 

released from the soil solids into the infiltrating water and the rate at which the radionuclides 

sorb or precipitate back on the solids in the soil from the infiltrating water. The code uses the 

assumption of instantaneous equilibrium, one in which the forward and backward reaction rates 

are so fast that equilibrium is attained instantaneously, as soon as the clean infiltration contacts 

the top of the contamination. Under this assumption, the radionuclides are removed from the 

top of the contamination. In the Equilibrium Desorption Release model, the concentration in the 

infiltrating water is determined by the distribution coefficient and the concentration in the soil. 

The distribution coefficient also determines the rate at which the radionuclides are transported 

by the infiltration down through the primary contamination. The user must specify the 

distribution coefficient if this option is chosen. This situation is most easily and quickly modeled 

by treating it as an instantaneous release of radionuclide over the initial depth of contamination 

and by applying the groundwater transport model. The groundwater transport model gives the 

flux out of the bottom of the primary contamination. It is also possible to apply the groundwater 

transport model independently to compute the vertical concentration profile of each parent and 

progeny in the surface soil; however, this functionality has not been coded. Thus, the code 

computes only the release to groundwater under this option; it does not compute releases to the 

atmosphere nor erosion release by surface runoff.

The radionuclides are released to groundwater uniformly over the depth of the primary 

contamination under the rate-controlled release options—first-order release and uniform 

release. Thus, the release to groundwater affects the concentration in the primary 

contamination but not its physical dimensions. In instantaneous equilibrium-controlled 

groundwater release (i.e., solubility or adsorption/desorption) models, contaminants are 

removed from the top of the layer, leading to nonuniform concentration profiles in the vertical 

direction. Currently, the code computes the release to the atmosphere and to surface runoff 

only for the rate-controlled releases. The additional computations of concentration profile for the 

equilibrium desorption release will consume significant computation time; these can be coded to 

be performed only if the surface soil will become contaminated. The release of dust to the 

atmosphere and the release of contaminated soil to surface runoff occur from the well-mixed 

surface layer at the top of the primary contamination. Thus, these releases lower the total 

quantity of the radionuclides in primary contamination but not the concentration in the primary 

contamination below the surface layer. The release of H-3 and C-14 by evasion can occur from 

over the whole depth of the contamination; it is modeled in RESRAD-OFFSITE as being uniform 

over the entire depth of the primary contamination and affects the concentration in the primary 

contamination but not its physical dimensions. 

Transport of the radionuclides within the contaminated zone by the movement of infiltrating 

water is modeled for all three releases. If appropriate, the user can specify the distribution 

coefficient in the primary contamination to model the interaction of the radionuclide with the soil 

even when the release is not controlled by equilibrium desorption/adsorption in the soil.
2-3 

2.2 Derivation of Mathematical Expressions for the 

Conceptual Primary Contamination Model

The conceptual model has to be translated into mathematical expressions before it can be used 

in the computational code. The idealized descriptions of the previous section are expressed in 

mathematical terms in this section. 

2.2.1 Thickness of the Primary Contamination

The thickness of the primary contamination is computed as a function of time on the basis of the 

values of the initial thicknesses and erosion rates of the cover and the primary contamination as 

follows:

)0()( pc = TtT pc when cv ≤ tt , and (2.1) 

)()0()( pc pc pc cv TtT ε −−= tt when cv > tt , 

where

 Tpc(t) = thickness of the primary contamination at time t (m),

Tpc(0) = initial thickness of the primary contamination (m),

t = time since the site was characterized (yr),

tcv = Tcv(0)/εcv = time to erode the cover (yr),

Tcv(0) = initial thickness of the cover (m),

εcv = rate at which the cover is eroded (m yr‒1), and

εpc = rate at which the primary contamination is eroded (m yr‒1).

The erosion rate is computed using the Universal Soil Loss Equation. Section 12.10 of the 

Handbook of Hydrology (Shen and Julien 1993) has figures and tables for the first five factors in 

the following expression for erosion rate,

224 /( )10

6 ε KR LS PC ρ ××××××= (2.2) 

where

ε = erosion rate (m yr‒1

),

 R = annual rainfall erosion index, the rainfall erosivity factor, or the rainfall and runoff 

factor (yr‒1

),

 K = soil erodibility factor (tons/acre),

LS = slope length-steepness factor (dimensionless),

 C = cropping-management factor or the cover and management factor 

(dimensionless),

 P = conservation practice factor or the support practice factor (dimensionless),

224 = to convert tons per acre to gram per square meter (g m‒2 [tons/acre]‒1),

ρ = dry bulk density of the soil (g cm‒3), and

106 = to convert per cubic centimeter to per cubic meter (cm3 m‒3).
2-4 

2.2.2 Concentration of Radionuclides in the Primary Contamination

Radiological transformations and the release to infiltrating water diminish the concentration of 

radionuclides in soil in the primary contamination over time. The concentration of progeny 

radionuclides can increase over time if the transformation of the parent radionuclide produces 

more progeny radionuclides than are lost to the infiltrating water and by radiological 

transformations of the progeny. The vertical concentration profile of the radionuclides in the 

primary contamination for each release mechanism is derived in this sub-section. The 

implementation of the algorithms to compute the concentration profile is described in 

Section 2.3.

2.2.2.1 Concentration of Radionuclides in the Primary Contamination under the 

First Order Release Model

The transfer to the infiltrating water at any time is proportional to the concentration at that time. 

Because both rate-controlled leaching and radiological transformations are proportional to the 

concentration or inventory at that time, both of these processes will occur uniformly over the 

entire depth of the primary contamination if the initial concentration profile is uniform. Thus, the 

activity concentration of the radionuclide remains uniform over the primary contamination under 

the conceptual model of RESRAD-OFFSITE. Under these conditions, the activity 

concentrations of the radionuclide that is present initially and its progeny are obtained by solving 

the following series of equations, 

111

1 )( A

dt

dA

+−= μλ , and (2.3) 

1 )( ++−= kkkkk −

k AA

dt

dA λμλ for 2 ≤≤ nk , 

where

Ak(t) = activity concentration of the kth radionuclide of the transformation chain (pCi g‒1),

t = time since the site was characterized (yr), 

λk = radiological transformation constant of the kth radionuclide (yr‒1), and

μk = leach rate constant of the kth radionuclide (yr‒1). 

The term on the left is the change in activity concentration, and the terms on the right are the 

reductions of activity concentration due to radiological transformations and leaching, 

respectively, and the gain in activity concentration due to radiological transformations of the 

parent. The solutions obtained by multiplying the equation by ( μλ t) kk e + and evaluating the 

integral ∫ −

+ t

k

t dttAe kk

0 1

)( )( μλ , are of the form,

∑=

= −−

k

i

k ik ii

ttatA

1

, )( exp( μλ ) , (2.4) 

where

a ,ik = set of coefficients defined by )0( = Aa 11,1 , 
2-5 

iikk

ikk

ik

a

a

μλμλ

λ

−−+ = − ,1

, for all 1 <≤ ki , and

∑

−

=

−=

1

1

, ,

k

i

kk ik aa . 

For H-3 and C-14, the activity concentration is given by the equation,

= AtA )0()( exp( −−− εμλ ttvtt ))( , (2.5) 

where

εν(t) = evasion rate at timet (yr‒1) (see Appendix L of the User’s Manual for RESRAD 

Version 6 [Yu et al. 2001] for the time-dependent evasion rate and for a 

discussion of the H-3 and C-14 models).

2.2.2.2 Concentration of Radionuclides in the Primary Contamination under the 

Uniform Release Model

The release to the infiltrating water at any time is the product of two independent processes, 

one dependent and the other independent of time. The incremental volume of source from 

which radionuclides are transferred in each unit of time remains constant over the release 

duration; this process occurs uniformly over the depth of the primary contamination. 

Radiological transformations are proportional to the concentration or inventory at that time; this 

process will occur uniformly over the entire depth of the primary contamination if the initial 

concentration profile is uniform. Thus, the activity concentration of the radionuclide remains 

uniform over the primary contamination. Under these conditions, the activity concentrations of 

the radionuclide that is present initially and its progeny are obtained by solving the following 

series of equations, 

11

1 A

dt

dA −= λ , and (2.6) 

kkkk

k AA

dt

dA −1 −= λλ for 2 ≤≤ nk , 

where

Ak(t) = activity concentration of the kth radionuclide of the transformation chain (pCi g‒1),

t = time since the site was characterized (yr), 

λk = radiological transformation constant of the kth radionuclide (yr‒1), 

and then accounting for the release to groundwater.

The solutions obtained by multiplying the equation by t k e

λ and evaluating the integral 

∫ −

t

k

t dttAe k

0 1 )( λ , are of the form,
2-6 

∑=

−= −

k

i

ik i

release

k ta

T

t tA

1

, )1()( exp( λ ), (2.7) 

where

Trelease = duration of the release (years), 

a ,ik = set of coefficients defined by )0( = Aa 11,1 , 

ik

ikk

ik

a

a

λλ

λ

− = − ,1

, for all 1 <≤ ki , and

∑

−

=

−=

1

1

, ,

k

i

kk ik aa . 

For H-3 and C-14, the activity concentration is given by the equation,

A )0()1()( exp( ttvt ))( T

t tA

release

k −= −− ελ , (2.8) 

where

εν(t) = evasion rate at timet (yr‒1) (see Appendix L of the User’s Manual for RESRAD 

Version 6 [Yu et al. 2001] for the time-dependent evasion rate and for a 

discussion of the H-3 and C-14 models).

2.2.2.3 Concentration of Radionuclides in the Primary Contamination under the 

Equilibrium Desorption Model

The infiltrating water attains the equilibrium concentration of the radionuclide as soon as it 

comes into contact with the contaminated soil. Thus, the radionuclides will be removed from the 

leading edge of the primary contamination, and the thickness of the contamination will change 

with time. Because the different radionuclides can have different equilibrium distribution 

coefficients, the profile of the progeny may not be uniform over the thickness; a rapidly moving 

parent will produce more progeny at the lower part of the primary contamination than at the 

upper regions. The release to groundwater under this release mechanism is computed by 

modeling an instantaneous release of material uniformly over the thickness of the primary 

contamination at time zero and then letting the groundwater transport formulation compute the 

flux at all subsequent times. The concentration profile of the radionuclide over the thickness of 

the contamination at different times is not needed for the computation of the flux released to 

groundwater. The current draft code does not compute the concentration profile in the primary 

contamination at various times for this release mechanism. The concentration profile over the 

thickness of the primary contamination needs to be computed if direct exposure from the 

primary contamination or onsite exposure—or both—are to be computed. The concentration 

profile over the thickness of the primary contamination that eventually gets incorporated into the 

mixing layer will need to be computed if release to the atmosphere or release to surface runoff 

is to be modeled. While the concentration profile can be computed by using the formulations in 

the groundwater transport section of the RESRAD-OFFSITE manual (Sections 3.2.4 and 3.2.5), 

this step is not currently performed in the code. The calculations will be both memory- and 

computation time–intensive and will need to be coded so that they are performed only when 

necessary and so that memory and computation time requirements are minimized.
2-7 

2.2.3 Surface Soil Mixing Model

The releases to the atmosphere and to surface runoff occur from the surface soil layer. The 

concentration of radionuclides in surface soil differs from the concentration in the primary 

contamination because of mixing with any uncontaminated cover or with soil below the primary 

contamination. Because the contaminant concentrations are expressed in terms of mass of soil 

(and not in terms of the volume of soil), it is necessary to account for any differences in density 

among the different layers of soil. The formulations in this section apply for the two 

rate-controlled release mechanisms. The thickness of the primary contamination is dependent 

on the radionuclide and also varies with time as the radionuclides are released from the top to 

the infiltrating water for equilibrium-based releases. These processes need to be incorporated 

into the surface soil mixing model for the equilibrium desorption release mechanism.

2.2.3.1 Density of Soil in the Mixing Zone

The density of the mixing zone is computed by assuming that mixing occurs continuously (over 

time) over the specified mixing depth. If the thickness of the cover exceeds the depth of mixing, 

the mixing zone will be uncontaminated, and the density is not computed for this condition. The 

cover can erode with time, and the mixing zone will then penetrate the primary contamination. 

The density of the mixing zone for this condition is computed as follows.

When )( tTtTdtT )()( cv mix cv +≤< pc , the density is obtained by solving the equation 

)( pc mix

mix

mix dt

d d ρρε ρ −= with the appropriate initial condition. The term on the left is the 

change in mass within the mixing zone, the terms on the right are, in order, the mass entering 

the mixing zone from the primary contamination and the mass leaving the mixing zone due to 

erosion. 

The initial conditions are:

mix = ρρ cv )0( if cv mix )0( ≥ dT , and (2.9) 

( ) cv pc

mix

cv

mix pc d

T

ρρ += − ρρ )0( )0( if cv mix )0( < dT . 

The solution is easier to understand and is more compact when expressed as a function of the 

depth of penetration of the mixing zone into the primary contamination since initial mixing, rather 

than as a function of time. The expression for the density of the mixing zone is:

( ) ( ) mix pc pc mix pc pc mix ρ d )( )0( ρρρ exp −−+= / dd , (2.10) 

where

Tcv(t) = thickness of the cover after time t (m), 

dmix = depth of the mixing zone (m),

ρmix(dpc) = density of the mixing zone (g cm‒3), 

ρpc = density of the primary contamination (g cm‒3), 

ρcv = density of the clean cover (g cm‒3), and
2-8 

dpc = depth of penetration of the mixing zone into the primary contamination since 

initial mixing (m). 

Eventually, the cover and primary contamination will be eroded so that their combined thickness 

will be less than the depth of the mixing zone. Then the soil underlying the primary 

contamination will enter the mixing zone. Because it is too cumbersome to track the layers (any 

unsaturated zones first and then the saturated zone) that can enter the mixing zone over time, 

density changes are not modeled after the mixing zone penetrates the bottom of the primary 

contamination. However, if the initial thicknesses of the clean cover and the primary 

contamination are less than the post-release mixing depth, the code does compute the density 

at initial mixing, including consideration of the densities of the underlying layers that enter the 

mixing zone at time zero.

2.2.3.2 Volume Fraction of Soil from the Primary Contamination in the Mixing 

Zone

The quantity of radionuclides in the mixing zone is directly proportional to the volume of soil in 

the mixing zone that originated from the primary contamination. The mixing zone is 

uncontaminated as long as its depth is less than the thickness of the clean cover. The volume 

fraction of soil from the primary contamination in the mixing zone is evaluated when the depth of 

the mixing zone exceeds the thickness of the clean cover. It is evaluated by assuming that 

mixing occurs continuously (over time) over the specified mixing depth and that the volume 

fraction in the eroded soil is the same as the volume fraction in surface soil. 

When )( tTtTdtT )()( cv mix cv +≤< pc , the volume fraction of primary contamination in the mixing 

zone is obtained by solving the equation ( ) vm

vm f dt

df dmin ε 1−= , with the appropriate initial 

condition. The term on the left is the change in the volume of soil from the primary 

contamination in the mixing zone, and the terms on the right are, in order, the volume of soil that 

enters the mixing zone from the primary contamination and the volume of soil from the primary 

contamination that leaves the mixing zone due to erosion. The initial conditions are:

= 0)0( vm f if cv mix )0( ≥ dT , and (2.11) 

mix

cv

vm d

T f )0( 1)0( −= if cv mix )0( < dT . 

As in the case with the density in the preceding section (Section 2.2.3.1), the solution is easier 

to understand and is more compact when expressed as a function of the depth of penetration of 

the mixing zone into the primary contamination since initial mixing, rather than as a function of 

time. The expression for the volume fraction of primary contamination in the mixing zone is:

( ) ( ) vm pc vm pc mix df −−= f )0(11)( exp − / dd , (2.12) 

where

fνm(dpc) = volume fraction of primary contamination in the mixing zone.
2-9 

As the cover erodes, the mixing layer penetrates deeper into the primary contamination, and the 

volume fraction increases asymptotically toward unity as long as the bottom of the mixing zone 

stays within the primary contamination.

When the bottom of the mixing zone moves out of the primary contamination and into the 

underlying layers, the volume fraction will decrease. The volume fraction is computed under the 

assumption that the underlying soil is uncontaminated.1

When tTtTd )()( mix cv +> pc , the volume fraction of contamination in the mixing layer is obtained 

by solving the equation vm

vm

mix f dt

df d −= ε with the appropriate initial condition. The initial 

conditions are:

( ) pc mix

p f vm 1 exp −−= /)0( dT if cv mix )0( ≥ dT , 















 −+ −= −

mix

cv pc mix

mix

p cv

vm d

dTT

d

T f )0()0(

exp

)0( 1 if )0( )0()0( cv mix cv +<< TTdT pc , and 

mix

p pc

vm d

T

f )0( = if )0()0( mix cv +≥ TTd pc (2.13) 

The expression for the volume fraction of primary contamination in the mixing zone, now 

expressed in terms of the depth of penetration below the primary contamination for clarity and 

simplicity, is:

( ) upc mix

p

vm upc )( vm exp −= / ddfdf , (2.14) 

where

dupc = depth of penetration of the mixing zone into the layers underlying the primary 

contamination since initial mixing (m).

The algorithms in the code can accommodate a situation where there is no mixing layer. In 

such a situation, the combined modification factor is zero while there is a cover and unity when 

there is no cover.

2.2.3.3 Concentration of Radionuclides in the Surface Soil above the Primary 

Contamination

The concentration of radionuclides in surface soil is computed by applying two modification 

factors to the concentration in the primary contamination: the first considers the volumetric 

mixing within the mixing layer, and the other accounts for the differences in density. These 

modification factors are independent of the concentration in the primary contamination and can 

be treated separately: 

 

1 Because the code calculates only the flux of contaminants across the partially saturated zone 

boundaries and across the water table, and not the concentration profile in those layers, it is not 

possible to account for the contaminants in the underlying layer in this calculation and in the 

calculation of external direct radiation.
2-10

tAtftA t)(/)()()( sc = vm pc pc ρρ mix , (2.15) 

where

Asc(t) = activity concentration in surface soil after time t (pCi g‒1), and

Apc(t) = activity concentration in primary contamination after time t (pCi g‒1).

2.2.3.4 Three-Layer Model

The mixing model conceptualizes three layers for the source: (1) a clean cover, (2) the unmixed 

portion of the initial primary contamination, and (3) a mixing layer that is contaminated to a 

lesser extent than is the primary contamination. From the preceding sections (2.2.3.1, 2.2.3.2, 

and 2.2.3.3) that discuss the surface layer mixing model, it can be seen that no more than two 

of these layers can exist at any particular time. As long as the depth of the mixing zone is less 

than the depth of the clean cover, there will not be a contaminated mixing zone. Conversely, 

after the cover thickness decreases to the depth of the mixing zone, there will be no clean 

cover. With time, erosion could also bring about a situation in which the mixing zone breaks 

through the layer of initial contamination; then there would not be any initial contamination that 

is unmixed. These conditions are summarized below.

When cv mix )( ≥ dtT , then (2.16) 

tTtT )()( cv

c

cv = , tT = 0)( c

mix , and )0()( pc

um

pc = TtT , 

where

tT )( c

cv = thickness of the clean cover (m),

tT )( c

mix = thickness of the contaminated mixing layer (m), and

tT )( um

pc = thickness of the unmixed portion of the primary contamination (m).

When )( tTtTdtT )()( cv mix cv +≤< pc , then (2.17) 

tT = 0)( c

cv , mix

c

mix )( = dtT , and pc cv mix

um

pc )()()( −+= dtTtTtT . 

When cv pc mix )()( <+ dtTtT , then 

tT = 0)( c

cv , mix

c

mix )( = dtT , and tT = 0)( um

pc . 

2.2.4 Release by Surface Runoff

The activity of radionuclide released to surface water by the erosion of the surface soil above 

the primary contamination per unit of time is given by the product of the activity concentration in 

surface soil and the surface erosion rate. It is more easily computed as the product of the mass 

of primary contamination that is eroded per unit of time and the activity concentration in the 

primary contamination. The rate (g yr‒1) at which soil from the primary contamination is eroded 

is given by: 

)10)()(

6

pc vm pc tm = Af t ρε (2.18) 
2-11

where 

A = area of the primary contamination (m2), and

106 = to convert per cubic centimeter to per cubic meter (cm3 m‒3).

Then 

tAtmtR )()()( kpc

sr

k = , (2.19) 

where

tR )( sr

k = rate (activity per time) at which the kth radionuclide of the transformation chain is 

released by erosion (pCi yr‒1).

2.2.5 Release to Groundwater

The flux of radionuclides out of the primary contamination depends on two processes: the 

transfer of radionuclides from the solid phase of the soil to the soil moisture followed by the 

transport of the radionuclides in soil moisture from the point of the transfer to the bottom of the 

primary contamination. The transfer of the radionuclides to the soil moisture is first computed 

by using the activity concentrations in the soil for the two rate-controlled release options. This 

computation is followed by modeling the transport of the radionuclides in soil moisture. Both 

processes are modeled together for the equilibrium desorption release option. 

2.2.5.1 Transfer of Radionuclides to Soil Moisture under the First Order Release 

Model

The activity of radionuclide transferred by rate-controlled leaching to soil moisture per unit of 

time is given by the product of the total activity in soil and the first order leach rate. The transfer 

to groundwater under this release mechanism is given by:

( ) 6 )()( tTtTfAtAtT 10)()( um

pc

c

pckk vm mix

gw

k = ρμ + , (2.20) 

where

tT )( gw

k = rate (activity per time) at which the kth radionuclide of the transformation chain is 

transferred to groundwater (pCi yr‒1), and

106 = to convert per cubic centimeter to per cubic meter (cm3 m‒3).

with ∑=

= −−

k

i

k ik ii

ttatA

1

, )( exp( μλ ) , 

where

a ,ik = set of coefficients defined by )0( = Aa 11,1 , 
2-12

iikk

ikk

ik

a

a

μλμλ

λ

−−+ = − ,1

, for all 1 <≤ ki , and

∑

−

=

−=

1

1

, ,

k

i

kk ik aa . 

2.2.5.2 Transfer of Radionuclides to Soil Moisture under the Uniform Release 

Model

The activity of radionuclides transferred under this release mechanism to soil moisture per unit 

of time is the activity in incremental volume of soil that became susceptible to release during 

that time period. The release to groundwater under this release mechanism is given by:

( ) ' 6 )( 10)()( 1 )( tTtTfAtA T

tT um

pc

c

pck vm mix

rel

gw

k = ρ + , (2.21) 

with ∑=

= −

k

i

k ik i

tatA

1

,

' )( exp( λ ) , 

where

a ,ik = set of coefficients defined by )0( = Aa 11,1 , 

ik

ikk

ik

a

a

λλ

λ

− = − ,1

, for all 1 <≤ ki , and

∑

−

=

−=

1

1

, ,

k

i

kk ik aa . 

2.2.5.3 Transport of Radionuclides from the Point of Transfer to the Bottom of 

the Primary Contamination for the Rate-Controlled Release Options

The transport of the radionuclide from within the primary contamination is modeled using a 

modified form of the equations in Sections 3.2.4 and 3.2.5 of the RESRAD-OFFSITE manual. 

The quantity transferred from the original waste form to the soil is available in the previous two 

subsections (Sections 2.2.5.1 and 2.2.5.2). These transfers occur uniformly over the thickness 

of the primary contamination. This process is analogous to the uniform input pulse of 

contaminants into the water table below the length of the primary contamination as 

conceptualized in the groundwater transport models in Sections 3.2.4 and 3.2.5 of the 

RESRAD-OFFSITE manual. Those formulations are thus applicable with some modification to 

account for the different orientation and location and the fact that only longitudinal dispersion is 

modeled in the primary contamination—not lateral dispersion.

2.2.5.4 Release of Radionuclides to Groundwater under the Equilibrium 

Desorption Model

The flux to groundwater under this release mechanism is given by the formulations in Sections 

3.2.4 and 3.2.5 of the RESRAD-OFFSITE manual for an instantaneous pulse input. For a 
2-13

parent radionuclide, this rate is given by a modified form of equation 3.39 of the RESRADOFFSITE manual, 































 − −















 − =

−

tD

tV erf

tD

tVT erf TeV AtR AT c

z

c

c

z

cz c

cz

t

c

k pcpc

gw

k 2 4 4

10)0()0()( 6

λ

ρ

( ) ( )

















− −

− − − − − tD

tV

tD

tVT

cz

c t

z

pcpck

c

z

c

c

z

ccz

ee

T

e

t

D A AT 6 4 4

2 2

4 10)0()0(

λ

π

ρ . (2.22) 

where

tR )( gw

k = rate (activity per time) at which the kth radionuclide of the transformation chain is 

released to groundwater (pCi yr‒1), 

Vc = contaminant transport velocity (m yr‒1), and

c Dz = contaminant dispersion coefficient (m2

 yr‒1).

The expressions for the flux of the progeny produced in the primary contamination are more 

complicated and are obtained by using the formulations in Section 3.2.5.

2.2.6 Release to the Atmosphere in the Form of Dust

The activity of radionuclide released to the atmosphere per unit of time is given by the product 

of the activity concentration in surface soil and the rate at which dust is released from the area 

of primary contamination. The conceptual model assumes that there is no net change in the 

mass loading of dust above the region of primary contamination. Under this assumption, the 

rate at which dust is released from the primary contamination is equal to the rate at which dust 

settles out of the air onto the region of primary contamination:

7 1015576.3)( )( = )()( duduk ×

mix

pc

vm

du

k mtA Av

t

tftR

ρ

ρ , (2.23) 

where

tR )( du

k = rate (activity per time) at which the kth radionuclide of the transformation chain is 

released to the atmosphere as dust (pCi yr‒1), 

mdu = concentration of dust in the air above the area of primary contamination (g m‒3), 

and 

νdu = deposition velocity of dust in the area of primary contamination (m s‒1), and 

3.15576 × 107 is to convert per second to per year (s yr‒1). 

2.3 Implementation of the Models for the Primary 

Contamination

This section describes how the conceptual model (Section 2.1) or the expressions derived from 

the conceptual model (Section 2.2) are implemented in the computational code.
2-14

2.3.1 Shape and Dimensions of the Primary Contamination

The shape of the conceptual primary contamination in the horizontal plane depends on the 

exposure or transport model. The dimensions and orientation of the rectangular shape for the 

atmospheric transport model are specified in the site layout form or the map interface as 

described in Sections 4.3 and 4.4 of the user’s guide. The area of primary contamination is 

computed by the computational code as the product of the two dimensions. 

The groundwater transport model assumes that the primary contamination is rectangular in 

shape and with one pair of sides parallel to the direction of groundwater flow. The length of one 

of these sides is specified in the primary contamination form as described in Section 4.14 of the 

user’s guide. The length of the other pair of sides is computed by the computational code using 

the area of the primary contamination. 

Either a circular shape or a polygonal shape can be specified for the calculation of direct 

external radiation from the primary contamination, as described in Section 4.27 of the user’s 

guide. The polygon can have as many sides as necessary to approximate the shape of the 

actual contamination. Polygonal-shaped areas of primary contamination and circular-shaped 

ones involving a nonconcentric receptor are analyzed by finding the fractions of the areas of a 

set of 16 annular regions, concentric with the receptor, that are covered by the primary 

contamination. The computation of the fraction of the annular regions that contain the primary 

contamination is performed in the interface and not in the computational code. 

2.3.2 Thicknesses of the Primary Contamination, Cover, Clean Cover, 

Contaminated Mixing Zone, and Undisturbed Primary Contamination

The thickness of the cover is computed at each intermediate time on the basis of the values of 

the initial thickness and erosion rate of the cover as follows:

cv cv )0()( −= ε cvtTtT when Ttt cvcv cv =≤ )0( ε , and 

tT = 0)( cv when cv > tt . (2.24) 

The thickness of the primary contamination is computed at each intermediate time on the basis 

of the values of the initial thicknesses and erosion rates of the cover and the primary 

contamination as follows:

)0()( pc = TtT pc when cv ≤ tt , 

)()0()( pc pc pc cv TtT ε −−= tt when cv cv pc Ttttt cv cv Tpc pc =+≤< ε + )0()0( ε , and 

tT = 0)( pc when cv pc +> ttt . (2.25) 

The thicknesses of the clean cover, the unmixed portion of the initial primary contamination, and 

the contaminated mixing zone are computed at each intermediate time on the basis of the 

thicknesses of the cover and the primary contamination at that time and the depth of the mixing 

zone, as follows:

tTtT )()( cv

c

cv = , tT = 0)( c

mix , )0()( pc

um

pc = TtT when cv mix )( ≥ dtT , (2.26) 

tT = 0)( c

cv , mix

c

mix )( = dtT , and pc cv mix

um

pc )()()( −+= dtTtTtT
2-15

when )( tTtTdtT )()( cv mix cv +≤< pc , and 

tT = 0)( c

cv , mix

c

mix )( = dtT and tT = 0)( um

pc when cv pc mix )()( <+ dtTtT . 

2.3.3 Concentration of Radionuclides in the Primary Contamination

The activity concentrations of the radionuclides under the two rate-controlled release options 

are computed at each of the intermediate time points on the basis of the initial activity of the 

parent radionuclides and on the release rate constants and transformation constants of the 

radionuclides in the transformation chain.

2.3.3.1 Concentration of Radionuclides in the Primary Contamination under the 

First-Order Release Model

The activity concentrations of the radionuclides under this release option are computed using 

the following analytical expression:

∑=

= −−

k

i

k ik ii

ttatA

1

, )( exp( μλ ) , (2.27) 

where

ik a , = set of coefficients defined by 1,1 a = A1 (0),

iikk

ikk

ik

a

a

μλμλ

λ

−−+ = − ,1

, for all 1 <≤ ki , and

∑

−

=

−=

1

1

, ,

k

i

kk ik aa . 

2.3.3.2 Concentration of Radionuclides in the Primary Contamination under the 

Uniform Release Model

The activity concentrations of the radionuclides under this release option are computed using 

the following analytical expression:

∑=

−= −

k

i

ik i

release

k ta

T

t tA

1

, )1()( exp( λ ) if < Tt release , (2.28) 

and tA = 0)( k if ≥ Tt release

where

Trelease = duration of the release (years),

a ,ik = set of coefficients defined by )0( = Aa 11,1 , 

ik

ikk

ik

a

a

λλ

λ

− = − ,1

, for all 1 <≤ ki , and
2-16

∑

−

=

−=

1

1

, ,

k

i

kk ik aa . 

2.3.4 Depth of Penetration of the Mixing Zone

The expressions developed in Section 2.2 for the density of the mixing layer and for the volume 

fraction of soil from the primary contamination in the mixing zone were compact and easier to 

understand when stated in terms of the depth of penetration of the mixing zone, instead of in 

terms of time. The depth of penetration into the primary contamination following initial mixing is 

computed at each intermediate time as the difference between the sums of the thicknesses of 

the cover and primary contamination at the time of initial mixing and at the intermediate time. 

This algorithm is simple and has to deal with only two conditions:

[ tTtTtTtTtd ] ≥+−+= 0)()()()()( pc cv im pc im cv pc , while tTtTd )()( m cv +≤ pc , (2.29) 

where

cv im pc im pc m )0()()( +=+ dTtTtT if )0( m ≤ Td cv , 

)0()0()()( cv im pc im pc +=+ TTtTtT cv if )0( m > Td cv , and

 tim = the time of initial mixing, which does not need to be determined but is used for 

identification purposes. 

The depth of penetration of the mixing zone below the primary contamination is also computed 

in a similar manner using the following algorithm: 

[ tTtTtTtTtd )()()()()( ] upc cv pm pmpc cv +−+= pc when tTtTd )()( m cv +> pc , (2.30) 

where

cv pm pmpc m )()( =+ dtTtT if )0()0( m cv +≤ TTd pc , 

)0()0()()( cv pm pmpc pc +=+ TTtTtT cv if )0()0( m cv +> TTd pc , and

tpm = time at which the mixing layer contains the highest amount of soil from the 

primary contamination, which does not need to be determined but is used for 

identification purposes. 

2.3.5 Density of Soil in the Mixing Zone

The algorithms in the code consider two possible initial conditions for the mixing zone. 

Typically, the depth (or thickness) of the mixing zone will be smaller than the thickness of the 

clean cover; the mixing zone has the same properties as the cover under these conditions. If 

the depth of the mixing zone is specified to be greater than the depth of the clean cover, the 

code assumes immediate mixing of the material within the mixing zone at time zero. The initial 

density (at time zero) is calculated as follows:

mix = ρρ cv )0( if cv mix )0( ≥ dT , (2.31) 

( ) cv pc

mix

cv

mix pc d

T

ρρ += − ρρ )0( )0( if )0( )0()0( cv mix cv +≤< TTdT pc , and 
2-17

( ) ( ) ( ) sat pc

mix

sat

dm

N

is

us pc

mix

dm

cv pc

mix

cv

mix pc d

T

is

d

H is

d

T s

ρρ += ρρ +− ∑ )( ρρ +− − ρρ )0( )( )0( 

if cv pc mix )0()0( <+ dTT , 

where

Ns = number of partially saturated zones, 

H is)( dm = thickness of each partially saturated zone that is within the mixing zone at time 

zero (m),

is)( ρus = dry bulk density of the partially saturated zone (g cm‒3), 

sat Tdm = thickness of the saturated zone that is within the mixing layer at time zero (m), 

and

ρ sat = dry bulk density of the saturated zone (g cm‒3). 

The density of the mixing layer is computed at each intermediate time; the algorithm used was 

greatly simplified by the use of the depth of penetration instead of time as the independent 

variable. The density of the mixing layer is computed by using the following algorithm:

( ) ( ) mix pc pc mix pc pc mix ρ d )( )0( ρρρ exp −−+= / dd while tTtTd )()( pc cv +≤ pc . (2.32) 

2.3.6 Volume Fraction of Soil from the Primary Contamination in the Mixing Zone

The algorithms in the code consider two possible initial conditions for the mixing zone. If, as is 

the typical case, the depth (or thickness) of the mixing zone is less than the thickness of the 

clean cover, the mixing zone has the same properties as the cover. If the depth of the mixing 

zone is specified to be greater than that of the clean cover, the code assumes immediate mixing 

of the material within the mixing zone at time zero. The initial volume fraction of soil from the 

primary contamination in the mixing zone is calculated as follows:

= 0)0( vm f if cv mix )0( ≥ dT , (2.33) 

mix

cv

vm d

T f )0( 1)0( −= if )0( )0()0( cv mix cv +≤< TTdT pc , and 

mix

pc

vm d

T

f )0( )0( = if cv pc mix )0()0( <+ dTT . 

The volume fraction of soil from the primary contamination in the mixing zone is computed with 

the following algorithms at each intermediate time point:

( ) ( ) vm pc vm pc mix df −−= f )0(11)( exp − / dd when tTtTd )()( mix cv +≤ pc , and (2.34) 

( ) upc mix

p

vm upc )( vm exp −= / ddfdf when tTtTd )()( mix cv +> pc , 

where

( ) pc mix

p f vm 1 exp −−= /)0( dT if cv mix )0( ≥ dT , 
2-18















 −+ −= −

mix

cv pc mix

mix

p cv

vm d

dTT

d

T f )0()0(

exp

)0( 1 if )0( )0()0( cv mix cv +≤< TTdT pc , and

mix

p pc

vm d

T

f )0( = if cv pc mix )0()0( <+ dTT . 

The algorithms in the code can also accommodate a situation where there is no mixing zone. In 

such a situation, the combined modification factor is zero as long as there is a cover and unity 

when there is no cover.

2.3.7 Concentration of Radionuclides in the Surface Soil above the Primary 

Contamination

The concentration of radionuclides in surface soil is computed at each intermediate time by 

using the concentration in the primary contamination, the volume fraction of soil from the 

primary contamination in the mixing zone, and the dry bulk densities of the mixing zone and the 

primary contamination:

tAtftA t)(/)()()( sc = vm pc pc ρρ mix . (2.35) 

2.3.8 Release by Surface Runoff

The rate at which soil from the primary contamination is eroded is computed at each 

intermediate time as the product of the rate of erosion of the surface soil, the area of the primary 

contamination, the volume fraction of soil from the primary contamination in the mixing zone, 

and the dry bulk density of the primary contamination:

6 10)()( pc vm pc tm = Af t ρε , (2.36) 

where

ε = εcv when Tcv(t) > 0, and

ε = εpc when Tcv(t) = 0.

The rate at which the radionuclide is released to surface water by the erosion of the surface soil 

above the primary contamination is computed at each intermediate time as the product of the 

mass of primary contamination that is eroded per unit of time and the activity concentration in 

the primary contamination:

tAtmtR )()()( kpc

sr

k = . (2.37) 

2.3.9 Transfer to Groundwater under the First-Order Release Model

The rate at which the radionuclide is transferred to groundwater by rate-controlled leaching is 

computed at each intermediate time as the product of the total activity in soil and the release 

rate:

( ) 6 )()( tTtTfAtAtT 10)()( um

pc

c

pckk vm mix

gw

k = ρμ + . (2.38) 
2-19

2.3.10 Transfer to Groundwater under the Uniform Release Model

The rate at which the radionuclide is transferred to groundwater under the uniform release is 

computed at each intermediate time as the activity in incremental volume of soil that became 

susceptible to release during that time period:

( ) ' 6 )( 10)()( 1 )( tTtTfAtA T

tT um

pc

c

pck vm mix

rel

gw

k = ρ + . (2.39) 

2.3.11 Release to Groundwater under the Two Rate-Controlled Release Options

The transfer rate from the preceding two subsections is convolved with the transport equations 

in Sections 3.2.4 and 3.2.5 of the RESRAD-OFFSITE manual to obtain the release at the 

bottom of the primary contamination. The transport section of the code has been updated to 

allow subdivision of the primary contamination. If the primary contamination is subdivided, the 

number of intermediate time points used for the calculations must be sufficient to capture the 

variation in the fluxes across the boundaries of the subzones. This step can add appreciably to 

the computation time needed. The primary contamination should only be subdivided when 

necessary, that is, when both longitudinal dispersion and the different transport rates of the 

parent and the progeny have a significant impact on the progeny flux and when this progeny flux 

affects the dose to the receptor. Considering that the release is uniform over the thickness of 

the primary contamination, dispersion in general is not likely to be significant.

2.3.12 Release to Groundwater under the Instantaneous Desorption Equilibrium 

Release

Under the instantaneous desorption equilibrium release, the flux of the parent radionuclide at 

the bottom of the primary contamination is computed at each intermediate time using the 

instantaneous release expression:































 − −















 − =

−

tD

tV erf

tD

tVT erf TeV AtR AT c

z

c

c

z

cz c

cz

t

c

k pcpc

gw

k 2 4 4

10)0()0()( 6

λ

ρ

( ) ( )

















− −

− − − − − tDtV

tD

tVT

cz

c t

z

k pcpc

c

z

c

c

z

ccz

e e

T

e

t

D A AT 6 4 4

2 2

4 10)0()0(

λ

π

ρ . (2.40) 

The expression used for the progeny depends on whether the longitudinal dispersion or the 

radionuclide-specific transport rates dominate the transport. Section 3.2.5.1 of the RESRADOFFSITE manual deals with dispersion-dominant transport, and Section 3.2.5.2 addresses 

transport dominated by the different transport rates of the parent and progeny. The transport 

zone can be subdivided if both processes have a significant effect on the transport. If the 

primary contamination is subdivided, the number of intermediate time points must be sufficient 

to capture the variation of the fluxes across the boundaries of the subzones.
2-20

2.3.13 Release to the Atmosphere in the Form of Dust

The rate at which the radionuclide is released to the atmosphere is given by the product of the 

activity concentration in surface soil and the rate at which dust is released from the area of 

primary contamination:

7 1015576.3)( )( = )()( duduk ×

mix

pc

vm

du

k mtA Av

t

tftR

ρ

ρ . (2.41) 

2.4 Users Guide to the Release Options in the 

RESRAD-OFFSITE Source Term Model

This section describes the forms in the RESRAD-OFFSITE interface where the release options 

can be specified and forms in which some of the inputs that affect the release are located.

2.4.1 Source Release and Deposition Velocity Form

The release option for each radionuclide is specified in this form2 (Figure 2.1). This version of 

the code (Version 3) contains four release options: 

1. “Version 2 Release Methodology”;

2. “First-Order Release with Transport”;

3. “Equilibrium Desorption Release”; and

4. “Uniform Release.”

Each of these is discussed in the following subsections.

2.4.1.1 Version 2 Release Methodology

This option is provided to allow input files created using the previous release version of the code 

to be read and executed and for users who wish to continue to use the Version 2 (and 

RESRAD) release methodology. This option is chosen by checking the “Version 2 Release 

Methodology” check box on the form.
2-21

FIGURE 2.1 Source Release and Deposition Velocity

Form – Version 2 Option

The user can specify one or both of the inputs that become active when this option is chosen; 

“Specify First Order Leach Rate” and “Use Distribution Coefficient to Estimate First Order Leach 

Rate.” If the Specify First Order Leach Rate input is left unchanged at zero, the code will 

estimate that leach rate by using the expression: 

)0(

1

Tpcbdpc

I

K ρθ μ

+ = . (2.42) 

where

μ = first-order leach rate (yr‒1

),

I = infiltration rate (m yr‒1

),

θ pc = total moisture content of the primary contamination,

Kd = distribution coefficient (cm3

 g‒1), 

ρb = bulk density of the primary contamination (g cm‒3

), and

)0( Tpc = initial thickness of the primary contamination (m).

If a nonzero value is specified for the leach rate, the code will use it provided that the condition, 

≥ 0 − =

bpc

pcpc

d T

TI

K

ρμ

θμ

or 

T pcpc

I

θ μ ≤ (2.43) 

is satisfied. If not, the input for the leach rate is ignored, and the leach rate is estimated as in 

the case of an input of zero. Transport of the radionuclides within the primary contamination is 

not modeled when this release option is chosen.
2-22

2.4.1.2 First-Order Release with Transport

This option is chosen by first unchecking the “Version 2 release methodology” check box and 

then clicking the option button titled “First Order Release with Transport” on the form 

(Figure 2.2). This option is different from the Version 2 release methodology. The user must 

specify the leach rate if this option is chosen. The leach rate specified in the leach rate input 

box will be used directly by the code and is not subject to a calculated upper limit as in the case 

of the Version 2 methodology; a zero input for leach rate is taken at face value—no release—

and is not a flag for estimating leach rate. 

The radionuclides leach out into the soil moisture over the entire thickness of the primary 

contamination. The radionuclides that were leached out near the top of the contamination will 

need to travel almost the entire thickness of the contamination, whereas those that were 

leached out deeper in the contaminated zone will have to travel over shorter distances before 

they are released from the primary contamination into the soil below. The groundwater 

transport code is used to model this transport, and it accounts for the advective and dispersive 

transport in soil moisture, the partitioning of radionuclides between the solid and aqueous phase 

of soil, and for radiological transformations. The inputs that specify this transport are discussed 

in Section 2.4.1.6.

FIGURE 2.2 Source Release and Deposition Velocity

Form – New Release Options

2.4.1.3 Equilibrium Desorption Release

This option is chosen by first unchecking the “Version 2 release methodology” check box and 

then clicking the option button titled “Equilibrium Desorption Release” on the form (Figure 2.2). 

The user must specify the distribution coefficient, in either the source release form or the 

distribution coefficients form (Figures 2.2 and 2.3), if this option is chosen. All of the 

radionuclides in the soil are immediately available for release; however, how soon they are 
2-23

released from the bottom of the primary contamination depends on how quickly they can be 

transported to the bottom of the primary contamination.

FIGURE 2.3 Distribution Coefficients Form

2.4.1.4 Uniform Release

This option is chosen by first unchecking the “Version 2 release methodology” check box and 

then clicking the option button titled “Uniform Release” on the form (Figure 2.2). The user must 

specify the duration of the release if this option is chosen. An instantaneous release will be 

modeled if a duration of release of zero is specified, as this selection would be identical to the 

equilibrium desorption release. 

2.4.1.5 Release of Progeny Produced by Radiological Transformations of an 

Initially Present Parent

The release mechanism specified for the initially present parent is applied for the release of the 

progeny radionuclides that are produced in the primary contamination by the transformation of 

that parent. If the uniform release option is specified for the parent, then the release duration 

specified for the parent is used for the ingrowth progeny radionuclides, as well. If the parent is 

released by desorption equilibrium, then the distribution coefficient specified for the progeny will 

be used to determine the release of the ingrowth progeny. If the parent radionuclides are 

released by a first-order leach rate mechanism, the release of the ingrowth progeny will also be 

controlled by first-order leaching, and the leach rate specified for each progeny will be used to 

compute the progeny that is transferred to the soil moisture. Thus, it may be necessary to input 

values for leach rate, distribution coefficient, and the release duration for the same radionuclide

if different release mechanisms are chosen for the radionuclide and its parent radionuclide. 

2.4.1.6 Transport of the Radionuclides within the Primary Contamination

The transport of the radionuclides from the location where they enter the soil moisture to the 

bottom of the primary contamination is modeled for all three new release options. The 

distribution coefficient, which determines how quickly the radionuclides move, can be specified 
2-24

in the source release form or in the distribution coefficients form; changes made in one form will 

appear on the other form if both are open at the same time. Two inputs that only affect the 

modeling of the transport in the primary contamination, the longitudinal dispersivity in the 

primary contamination and the effective porosity of the primary contamination, can be specified 

in the primary contamination form (Figure 2.4).

FIGURE 2.4 Primary Contamination Form

2.4.1.7 Temporal Plots of the Different Release Options

Figures 2.5 through 2.8 show the temporal variations of the flux out of the primary contamination 

for the different release options with various types of transport. While these options add to the 

versatility of the code, the user has to make more decisions, not just about which release option 

to use but also about what values to use for the inputs that affect the release. To aid in this 

decision-making process, the code has the functionality to perform sensitivity analysis (both 

probabilistic sensitivity analysis and “one input at a time—three-point” deterministic sensitivity 

analysis) on all of the new inputs that affect release.
2-25

FIGURE 2.5 Temporal Profiles of Flux Out of the Primary Contamination for Different Release O
2-26

FIGURE 2.6 Temporal Profiles of Flux Out of the Primary Contamination for the First-Order Rele

Different Rates of Transport
2-27

FIGURE 2.7 Temporal Profiles of Flux Out of the Primary Contamination for the Uniform Releas

with Different Rates of Transport
2-28

FIGURE 2.8 Temporal Profiles of Flux Out of the Primary Contamination for the Equilibrium Des

Option with Different Rates of Transport
2-29

2.5 Overriding the RESRAD-OFFSITE Source Term Model

If all of the information that is computed by the RESRAD-OFFSITE source term model is 

available either from a more sophisticated model or from a series of measurements, the 

computational code can be flagged to suppress its source term module and to read in the time 

series of the information. The temporal series of source term and release information has to be 

in the format that is useable by the RESRAD-OFFSITE computational code. The names of the 

files containing the temporal source term and release data and their contents are described in 

Table 2.1.

The data files are structured on the basis of the number of parent-progeny combinations at the 

site. They contain a column of data for each parent-progeny combination. The order of the 

columns is determined as follows. The radionuclides that are initially present are sorted first 

alphabetically by their chemical symbol and then by the nominal atomic weight in the case of 

isotopes. The first column of data pertains to the first radionuclide in the sorted list. If that 

radionuclide has principal radionuclide progeny, there must be a column of data for each 

progeny in the order in which they occur in the transformation chain. If the radionuclide has 

more than one transformation thread, there must be additional columns of data for each 

transformation thread. Then there must be a column of data for the second initially present 

radionuclide in the sorted list, followed by a column each for its progeny in the order in which 

they occur in its transformation chain and so on for each radionuclide in the sorted list. The 

number of times that data are available determines the number of rows in the different files—

there must be a row for each time that data are available.

The computational code uses a linear interpolation between the specified times when 

performing the calculations. The input interface does not at present have a form to bypass the 

source module and accept these inputs because of the complexity of the format required for 

these input files.

TABLE 2.1 Input Files Used to Specify the Source Characteristics 

and Releases to the Code

File name Contents

SFSIN.DAT Temporal data of the concentration (Section 2.2.2), in pCi g‒1, of each 

initially present radionuclide and its principal radionuclide progeny in the 

unmixed region of the primary contamination.

CZTHICK3.DAT Temporal data of the composite modification factor for the concentration 

of radionuclides in the mixing zone (Section 2.2.3.3) and of the 

thicknesses, in m, of clean cover, contaminated mixing zone, and the 

unmixed portion of the contaminated zone (Section 2.2.3.4).

AQFLUXIN.DAT Temporal data of the flux, in pCi yr‒1, of each initially present radionuclide 

and its principal radionuclide progeny, to the groundwater pathway.

SWFLUXIN.DAT Temporal data of the eroded flux, in pCi yr‒1, of each initially present 

radionuclide and its principal radionuclide progeny and the mass of 

eroded soil, in g year‒1, to surface runoff. 

AIFLUXIN.DAT Temporal data of the flux, in pCi yr‒1, of each initially present radionuclide 

and its principal radionuclide progeny, to the atmosphere.

3-1 

3. Benchmarking of Radionuclide Release 

Rates Calculated by RESRAD-OFFSITE 

Version 3 and DUST-MS 

This chapter documents the comparison of radionuclide release rates calculated by Version 3 of 

RESRAD-OFFSITE vs. DUST-MS. The focus of comparison is on the release rates of 

radionuclides from the bottom of the contaminated zone that was assumed to contain 

radioactive source materials buried in soil. The newly developed source term model 

incorporated into the RESRAD-OFFSITE code Version 3 was used for the calculations.

The DUST-MS code was developed by Brookhaven National Laboratory more than a decade

ago. Its predecessor, DUST, which stands for Disposal Unit Source Term, was first available in 

1993 (Sullivan 1993). Later on, DUST was expanded to evaluate multiple species and was 

issued as DUST-MS in 2001 (Sullivan 2001a). Another version, DUSTMS-D, which allows 

consideration of distributed failure of waste containers, was also issued in the same year 

(Sullivan 2001b). The DUST codes (DUST, DUST-MS, and DUSTMS-D) are mostly used for 

evaluating radionuclide release rates from disposal units buried underground; the release rates 

then can be input to a groundwater transport model for further evaluation of potential 

groundwater contamination. The DUST code that was used for comparison with RESRADOFFSITE results was DUST-MS.

This benchmarking focused on the contaminant release rates; the transport of released 

contaminants outside of the primary contaminated zone is beyond the scope of this study. The 

comparison of release rates was performed for various sources with different dimensions and 

containing different radionuclides. 

3.1 Conceptualization of Radioactive Sources within the 

Contaminated Zone for Release and Transport Modeling

Radioactive sources within the contaminated zone could consist of waste materials such as 

sludge that was dispersed directly within soils, or waste materials such as activated metals that 

were contained by drums or canisters and buried underground. The radionuclides contained or 

imbedded in the waste materials have the potential of dissolving in water when water infiltrates 

soils or enters the waste containers through cracks or holes and makes contact with the waste 

materials. Upon dissolving in water, the radionuclides could be either carried directly downward 

through the soil column or indirectly carried outside of the containers and then downward 

through the soil column, and then transported to the bottom of the contaminated zone where 

release rates of radionuclides were calculated for this comparison. Both RESRAD-OFFSITE 

Version 3 and DUST-MS model the vertical transport of radionuclides in soils within the 

contaminated zone.

To model the release of radionuclides from waste materials, RESRAD-OFFSITE conceptualizes 

the waste materials as being distributed evenly over the depth of the contaminated zone. 

Figure 3.1 is a schematic presentation of the conceptualization. The release rates of 

radionuclides would depend on the interaction between the contaminants, waste materials, and 

water; therefore, the release rates would be different for different types of waste materials. 

Although currently the release rates of radionuclides to the surrounding soil are calculated 
3-2 

starting at time 0, meaning that immediate breaching of the waste containers occurs, a 

container integrity time period during which no release would occur can be considered by 

adjusting the initial radionuclide concentrations with ingrowth and decay factors that correspond 

to the container integrity time period, and then inputting the adjusted concentrations to 

RESRAD-OFFSITE code Version 3. 

Unlike RESRAD-OFFSITE, which analytically solves the mathematical equations describing the 

transport of radionuclides in soils, DUST-MS implements a numerical analysis method called 

finite difference (FD) to solve the same radionuclide transport equations. To use the FD 

method, users are required to subdivide the contaminated zone with a number of grids, which 

can be associated with release from radioactive waste materials. The distribution of the waste 

materials into these grids is determined by the users, with the amount over the grids adding up 

to the total inventory. Upon leaving the waste materials, radionuclides are assumed to partition 

between solid and liquid phases in equilibrium in the surrounding soil and to transport downward 

from one grid to another. The schematic presentation for the conceptualization of radioactive 

sources within the contaminated zone by DUST-MS is also shown in Figure 3.1.

The transition of the radionuclide concentration profile with the RESRAD-OFFSITE modeling is 

continuous over the depth of the contaminated zone, whereas the transition of the concentration 

profile with the DUST-MS modeling is step-wise. 

FIGURE 3.1 Conceptualization of Radioactive Sources 

Within the Contaminated Zone

3.2 Release Options/Mechanisms 

As the release rates of radionuclides from the source materials to the surrounding soils would 

be different for different materials, RESRAD-OFFSITE Version 3 and DUST-MS each provide 

users with different options for calculating the release rates.
3-3 

3.2.1 RESRAD-OFFSITE Version 3

RESRAD-OFFSITE Version 3 provides three new options for estimating the release rates of 

radionuclides from waste materials to the surrounding soils—first-order release, equilibrium 

desorption release, and uniform release. 

The first-order release considers the release rate of each radionuclide to be proportional to the 

remaining inventory of that radionuclide in the waste materials. The proportionality constant is 

characterized by a leach rate specified by the user. Waste materials that resemble this type of 

release may include dewatered sludge or resins used for ion-exchange.

The equilibrium desorption release assumes that all radionuclides would distribute between the 

solid and liquid phases of the surrounding soils from the beginning of simulation on the basis of 

equilibrium desorption. This assumption implies that radionuclides would be available for 

release from the waste materials and dissolve in water immediately when they are in contact 

with water. For this to happen, radionuclides would have to attach to the waste materials 

loosely and, most likely, on the surface. Waste materials that fit this specification may include 

compacted lab trash, such as clothes or glove boxes, as well as small gadgets or tools.

The uniform release option considers the dissolution of a constant fraction of the initial 

radionuclide inventory over time. However, because of the adjustment for radiological ingrowth 

and decay, the actual radioactivity released may be different as time progresses. Assuming the 

distribution of radionuclides throughout the waste materials is homogeneous, to be eligible for 

this option, a fixed portion of the waste materials would need to dissolve in water or disintegrate 

upon contact with water each year. This dissolution or disintegration of waste materials would 

then release the radionuclides contained or imbedded within. An example of waste materials 

that may fit these descriptions is activated metal, which would corrode in the environment and 

release the imbedded radionuclides.

3.2.2 DUST-MS

DUST-MS considers the mechanism by which radionuclides are released from the waste 

materials. Three mechanisms are provided for consideration—dissolution, rinse release, and 

diffusion. In addition to the three mechanisms, solubility can be specified to limit the amount of 

radionuclides dissolved in water. 

The dissolution mechanism accounts for constant dissolution of the waste materials, resulting in 

release of radionuclides. It is characterized by a fractional release rate, which is the inverse of 

the release duration used by RESRAD-OFFSITE for the uniform release option. The dissolution 

mechanism considered by DUST-MS is similar to the uniform release option considered by 

RESRAD-OFFSITE.

The rinse release mechanism assumes that radionuclides are distributed on the surface of the 

waste materials and would partition to and dissolve in water upon rinsing by water. This release 

mechanism is the same as that considered by RESRAD-OFFSITE for the equilibrium desorption 

option.

The diffusion mechanism assumes that release of radionuclides is controlled by diffusion, which 

applies to radionuclides dispersed in the bulk of porous waste materials. An example of waste 

materials that may assume this mechanism to release radionuclides is cement-solidified waste.
3-4 

3.2.3 Options/Mechanisms Selected for Comparison

On the basis of the above discussions, the release rates corresponding to the uniform release 

option of RESRAD-OFFSITE were calculated for comparison with those calculated by 

DUST-MS and corresponding to the dissolution mechanism, whereas the release rates 

corresponding to the equilibrium desorption option of RESRAD-OFFSITE were calculated for 

comparison with those calculated by DUST-MS and corresponding to the surface rinse 

mechanism. To match the assumption used by RESRAD-OFFSITE for the equilibrium 

desorption option, the partitioning factors of radionuclides within the waste materials was set to 

0 cm3

/g for the DUST-MS calculations.

Because there is no comparable match for the first-order release option of RESRAD-OFFSITE 

with the release mechanisms considered by DUST-MS, and the diffusion release mechanism 

considered by DUST-MS has not been incorporated into RESRAD-OFFSITE, comparison of the 

release rates associated with these two release options/mechanisms was not attempted.

3.3 Assumptions for Source Materials

For the comparison of radionuclide release rates, five different cases involving different source 

materials, as described in the following sections, were developed. The source materials could 

be of any specific waste forms. In the following sections, the terms “source materials,” “release 

sources,” and “waste forms” are used interchangeably.

3.3.1 Release Sources in Different Comparison Cases

The first three comparison cases, designated as Cases I, II, and III, involve radionuclides in the 

source material with a thickness of 0.3 m. For Case I, the source was assumed to contain 

Tc-99. For Case II, the source was assumed to contain Cs-137, which has a much shorter halflife than that of Tc-99. For the third case, Case III, the source was assumed to contain U-234, 

which would subsequently decay to Th-230, Ra-226, Pb-210, and Po-210. For Cases IV and V, 

the source was assumed to be 3-m thick; in Case IV, the source contains Tc-99, and in Case V, 

the source contains U-234. Because RESRAD-OFFSITE and DUST-MS simulate transport of 

radionuclides only in the vertical direction, the size of the cross sectional area would not affect 

the concentration profile of radionuclides over the thickness. Therefore, an area of 1 m2 was 

assumed for all of the release sources. The initial concentration of radionuclide in each source 

was assumed to be 100 pCi/g. In addition to the dimensions and initial concentration, the 

density of the waste form was assumed to be 1.5 g/cm3

, resulting in an initial total radioactivity 

of 4.5 x 10-5 Ci for Cases I, II, and III, and 4.5 x 10-4 Ci for Cases IV and V.

All of the waste forms were assumed to start releasing radionuclides at time 0 as a result of 

water infiltration. A water infiltration rate of 0.4 m/yr was assumed for Cases I and II, whereas a 

smaller water infiltration rate of 0.1 m/yr was assumed for Cases III, IV, and V.

Table 3.1 summarizes the assumptions made for the release sources in the five comparison 

cases. 
3-5 

TABLE 3.1 Assumptions for the Release Sources in

 Different Comparison Cases

Parameter Case I Case II Case III Case IV Case V

Area (m2) 1 1 1 1 1 

Thickness (m) 0.3 0.3 0.3 3 3 

Density (g/cm3) 1.5 1.5 1.5 1.5 1.5

Initial radionuclide Tc-99 Cs-137 U-234 Tc-99 U-234

Initial concentration (pCi/g) 100 100 100 100 100

Water infiltration rate (m/yr) 0.4 0.4 0.1 0.1 0.1

3.3.2 Input Parameters Used for RESRAD-OFFSITE

To obtain a water infiltration rate of 0.4 m for Cases I and II, the following input parameters were 

assumed: (1) the precipitation rate was 1 m/yr; (2) the irrigation rate was 0 m/yr; (3) the 

evapotranspiration coefficient was 0.5; and (4) the runoff coefficient was 0.2. To obtain an 

infiltration rate of 0.1 m for Cases III, IV, and V, the above settings were maintained, except for 

the runoff coefficient, which was increased to 0.8. All of the other parameters assumed the 

default values.

The parameter values specified for the contaminated zone were for the surrounding soil through 

which radionuclides transport toward the underlying groundwater table. A soil erodibility factor 

of 0 ton/acre was used to eliminate soil erosion over time. Both the total porosity and effective 

porosity were assumed to be 0.4. Although the value for the length of contamination parallel to 

aquifer flow parameter would not affect the calculated radionuclide release rates at the bottom 

of the contaminated zone, a value of 1 m was specified to reflect the assumption that the 

cross sectional area for the source was 1 m2

. 

The RESRAD-OFFSITE calculations were executed for a time frame of 500 years for Cases I 

and II, and a time frame of 10,000 years for Cases III, IV, and V. The number of graphic points 

varied from 512 for Cases I and II to 2,048 for Cases III, IV, and V. An exposure duration of 

12 years was specified for the first two cases, and the radionuclide release rates were reported 

every year. For the later cases, an exposure duration of 240 years was specified to obtain 

radionuclide release rate results every 5 years.

Various dispersivity values, along with various soil Kd values, were specified to obtain multiple 

sets of radionuclide release rates for comparison with DUST-MS results.

The calculated release rates of radionuclides from the contaminated zone were recorded in an 

output file, AQFLUXIN.DAT, which was opened to retrieve data after each execution.
3-6 

3.3.3 Input Parameters Used for DUST-MS

DUST-MS considers three release mechanisms along with solubility limits. The three release 

mechanisms can be considered simultaneously with designated fractions that specify the 

contribution of each mechanism to the overall radionuclide release rate; however, to simplify the 

comparison with RESRAD-OFFSITE results, only one release mechanism was considered in 

each execution of the code. Furthermore, only the dissolution and the rinse release 

mechanisms were used for comparison, because release of radionuclides through the diffusion 

mechanism has not been incorporated into the RESRAD-OFFSITE source term model. 

Because of the implementation of the FD method to solve the transport equations for 

radionuclides, the domain of analysis has to be subdivided into smaller grids to improve the 

precision in the calculation results. In addition, the initial condition for the entire domain and the 

conditions, which are applicable at any time period during the analysis for the upper and lower 

boundary, have to be specified. The DUST-MS analysis involves solving the dissolved 

radionuclide concentrations in the soil column of transport; therefore, the initial concentration for 

the entire domain was set to 0 pCi/L. The condition for the upper boundary was set such that 

no radionuclide would transport upward across the boundary, that is, the flux of radionuclide 

was 0 pCi/m2

/sec. The condition for the lower boundary was selected such that the lower 

boundary is far away so that no radionuclide would reach that boundary, that is, the dissolved 

concentration of any radionuclide would be 0 pCi/L. To make the lower boundary condition 

feasible, an unsaturated zone having the same properties as the contaminated zone but with a 

much greater thickness than that of the contaminated zone was added and included as part of 

the domain for analysis. 

Considering that the way the domain of analysis was subdivided into smaller grids might affect 

the precision of the calculation results, five different subdivisions, each with a different total 

number of grids, were designed. The first design was used for a 0.3-m contaminated zone, 

which was subdivided into 10 grids, with 10 m of unsaturated zone underlying it. The 

unsaturated zone was divided into three subzones, which were subdivided into 5, 5, and 

96 grids, respectively. In total, the first design has 116 grids, which were separated by 

117 nodes (one node at the top of the domain and another at the bottom of the domain). The 

second, third, and fourth designs were also for a 0.3-m contaminated zone with a 

10-m unsaturated zone but with different numbers of grids and nodes. The total numbers of 

nodes for these three designs were 223, 465, and 481, respectively. The last design was for a 

3-m source, along with a 100-m unsaturated zone. The distribution of nodes was the same as 

that of the third design, with a total of 465 nodes, except that the interval between two nodes 

was 10 times that of the third design. Figure 3.2 depicts the domain of analysis and the 

distribution of grids and nodes for the various designs. The maximum number of nodes allowed 

by DUST-MS is 500.
3-7 

FIGURE 3.2 Various Designs for Subdividing the Domain of Analysis

for DUST-MS Calculation

Input parameters required to run DUST-MS were selected so that they either matched or 

corresponded to the values used to run RESRAD-OFFSITE for this comparison. For Cases I 

and II, on the basis of RESRAD-OFFSITE input values, the corresponding moisture content in 

the soil column was 0.3157. For Cases III, IV, and V, the corresponding moisture content was 

0.2851. For Cases I and II, the DUST-MS calculated release rates were recorded every year for 

500 years. For Cases III, IV, and V, the release rates were recorded every 5 years for 

10,000 years. 

3.4 Results of Comparison

3.4.1 Case I – 0.3 m of Tc-99

Case I considers releases from a 0.3-m Tc-99 source. Annual release rates of Tc-99 in terms of 

pCi/yr were calculated over 500 years. The release rates were calculated with no dispersion, as 

well as with different levels of dispersion in the soil column. 

3.4.1.1 No Dispersion

Equilibrium desorption. Figure 3.3 compares the RESRAD-OFFSITE results obtained with 

the equilibrium desorption option with the DUST-MS results obtained with the rinse release 

mechanism. No dispersion in the soil column was involved. The partitioning factor of Tc-99 in 

the source material was set to 0 cm3

/g when the DUST-MS code was executed, so that all of the 

Tc-99 radionuclides in the source would dissolve in water when the source material was rinsed 

by water.

In Figure 3.3, RESRAD-OFFSITE results were plotted with solid lines, and DUST-MS results 

were plotted with dashed lines. For each soil Kd value, four sets of results were obtained with 

DUST-MS, corresponding to the different grid designs for the domain of analysis as discussed 
3-8 

in Section 3.3.3. The comparison shows that regardless of the soil Kd value, the DUST-MS 

results approach RESRAD-OFFSITE results as the number of grids increases. The 

discrepancy between the two could be caused by numerical dispersion in the DUST-MS results 

because no dispersion was assumed in this case (and DUST-MS showed dispersion in the 

results). As the number of grids increases, the numerical dispersion decreases in this case.

Uniform release. Figure 3.4 compares the RESRAD-OFFSITE results obtained with the 

uniform release option with the DUST-MS results obtained with the dissolution mechanism. The 

waste form was assumed to disintegrate uniformly with a disintegration (dissolution) fraction of 

0.01/yr for 100 years. 

Consistent with the observation made using the equilibrium desorption option, the DUST-MS 

results approach the RESRAD-OFFSITE results as the number of grids increases. The cause 

of discrepancy could also be explained by numerical dispersion in DUST-MS results.

FIGURE 3.3 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case I Concerning Release from a 0.3-m Tc-99 Source 

under the Equilibrium Desorption Condition with No Dispersion
3-9 

FIGURE 3.4 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case I Concerning Release from a 0.3-m Tc-99 Source 

under the Uniform Release Condition with No Dispersion

3.4.1.2 With Dispersion

Two dispersion levels were considered for the comparison, one with a dispersivity of 0.03 m, 

that is, 1/10 of the thickness of contaminated zone, and the other with a dispersivity of 0.1 m. 

The DUST-MS results were obtained with the subdivision design of 481 nodes.

Equilibrium desorption. Figure 3.5 shows the comparison of RESRAD-OFFSITE results 

obtained with the equilibrium desorption option with DUST-MS results obtained with the rinse 

release mechanism for a dispersivity of 0.03 m. The RESRAD-OFFSITE results and DUST-MS 

results agree very well with each other for all of the Kd values used. By increasing the 

dispersivity to 0.1 m, the RESRAD-OFFSITE results still agree fairly well with the DUST-MS 

results (see Figure 3.6), although the agreement slips a little.
3-10

FIGURE 3.5 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case I Concerning Release from a 0.3-m Tc-99 Source 

under the Equilibrium Desorption Condition with a Dispersivity 

of 0.03 m 

FIGURE 3.6 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case I Concerning Release from a 0.3-m Tc-99 Source 

under the Equilibrium Desorption Condition with a Dispersivity 

of 0.1 m 

Uniform release. As observed under the equilibrium desorption condition, under the constant 

release condition, the RESRAD-OFFSITE results agree very well with the DUST-MS results 

when the dispersivity is 0.03 m (see Figure 3.7). The agreement slips a little when the 
3-11

dispersivity is increased to 0.1 m (Figure 3.8); however, the agreement is still considered fairly 

well.

3.4.2 Case II – 0.3 m of Cs-137

Case II considers the release of Cs-137 from a 0.3-m source. Because Cs-137 has a much 

shorter decay half-life (30 years) as compared to that of Tc-99 (2.13 × 105 years), the influence 

of radioactive decay on the release rates would be more pronounced for Cs-137 than for Tc-99. 

The DUST-MS results were obtained with the grid design that has 481 nodes distributed in the 

domain of analysis.

FIGURE 3.7 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case I Concerning Release from a 0.3-m Tc-99 Source 

under the Uniform Release Condition with a Dispersivity of 0.03 m 
3-12

FIGURE 3.8 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case I Concerning Release from a 0.3-m Tc-99 Source 

under the Uniform Release Condition with a Dispersivity of 0.1 m 

3.4.2.1 No Dispersion

The comparison of RESRAD-OFFSITE results with the DUST-MS results starts with the 

condition when there is no dispersion of Cs-137 in the soil column.

Equilibrium desorption. Figure 3.9 shows the comparison between the RESRAD-OFFSITE 

equilibrium desorption results versus the DUST-MS rinse release results. The discrepancies 

between the two were considered to be caused by the numerical dispersion associated with the 

DUST-MS results. 

Without radioactive decay during transport, the release rate of radionuclides would stay 

constant for a period of time, that is, the time required for the radionuclides to transport from the 

top of the contaminated zone to the bottom of the contaminated zone, as seen in Figure 3.3 with 

the RESRAD-OFFSITE results for Tc-99. However, because of the significant radioactive 

decay of Cs-137, the release rate at the bottom of the contaminated zone cannot be maintained 

at the initial level, and the release rate would decrease over time until all Cs-137 radionuclides 

leave the contaminated zone, as shown in Figure 3.9.

Uniform release. The comparison of RESRAD-OFFSITE results and the DUST-MS results is 

shown in Figure 3.10 for a uniform release of 0.01/yr for 100 years. Again, because of the 

significant radioactive decay of Cs-137, the radionuclide release rate is not maintained at a 

constant level, even when a Kd value of 0 cm3

/g was assumed. Except for around the time of 

peak release rate with a Kd of 0 or 20 cm3

/g, the DUST-MS results are almost the same as 

those of RESRAD-OFFSITE.
3-13

3.4.2.2 With Dispersion

Equilibrium desorption. Figure 3.11 shows the comparison of RESRAD-OFFSITE results 

versus the DUST-MS results for an equilibrium desorption release. The two codes predict 

almost the same release rates over time when the dispersivity is 0.03 m.

Uniform release. Figure 3.12 shows the comparison of RESRAD-OFFSITE results versus the 

DUST-MS results for a uniform release. As in the comparison for the equilibrium desorption 

condition, the comparison for the uniform release condition shows that RESRAD-OFFSITE 

results and DUST-MS results are almost identical.

FIGURE 3.9 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case II Concerning Release from a 0.3-m Cs-137 Source 

under the Equilibrium Desorption Condition with No Dispersion
3-14

FIGURE 3.10 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case II Concerning Release from a 0.3-m Cs-137 Source 

under the Uniform Release Condition with No Dispersion

FIGURE 3.11 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case II Concerning Release from a 0.3-m Cs-137 Source 

under the Equilibrium Desorption Condition with a Dispersivity 

of 0.03 m
3-15

FIGURE 3.12 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case II Concerning Release from a 0.3-m Cs-137 Source 

under the Uniform Release Condition with a Dispersivity of 0.03 m 

3.4.3 Case III – 0.3 m of U-234

The comparison of release rates from a waste form containing U-234 involves comparing not 

only the release rate of U-234, but also the release rates of Th-230, Ra-226, Pb-210, and 

Po-210. The progeny radionuclides would be formed not only within the waste form, but also in 

the soil column during the transport of U-234. They may assume different Kd values from U234 and thereby transport with different speeds toward the bottom of the contaminated zone. 

The Kd values assumed for U-234 and its progeny radionuclides were 200, 6,000, 70, 100, and 

10 cm3

/g, respectively. 

When progeny radionuclides are formed within the waste form, they are assumed to be 

released through the same mechanism as is their parent radionuclide to the surrounding soils. 

To allow for more ingrowth of progeny radionuclides within the waste form, the water infiltration 

rate was reduced from 0.4 m/yr as used in Cases I and II to 0.1 m/yr. Furthermore, when 

calculating radionuclide release rates under the uniform release condition, a uniform release of 

0.00111/yr for 900 years was assumed. 

The DUST-MS results were obtained with the grid design of 481 nodes. 

3.4.3.1 No Dispersion

Figure 3.13 compares the release rates of U-234. Numerical dispersion might be the cause of 

discrepancies between the RESRAD-OFFSITE results and DUST-MS results.

Figure 3.14 compares the release rates of Th-230. The RESRAD-OFFSITE results and the 

DUST-MS results are almost identical. The release rates increase starting at time 0 as Th-230 

radionuclides are formed because of the decay of U-234. The Th-230 radionuclides formed 

would largely adsorb to soil particles and would stay in the soil column longer than would U-234 

radionuclides, because the Kd value assumed for Th-230 was much greater than that used for 
3-16

U-234. The adsorbed Th-230 radionuclides feed into the continuous release of Th-230 

radionuclides long after all U-234 radionuclides have left the source. 

Ra-226 radionuclides are formed as Th-230 radionuclides undergo radioactive decay. 

Figure 3.15 compares the release rates of Ra-226 calculated by RESRAD-OFFSITE vs. 

DUST-MS. The calculations show that the release rates of Ra-226 would increase from the 

beginning and reach maximum levels shortly after the release rates of U-234 peaked. After 

reaching the maximum levels, the release rates of Ra-226 would have decreased quickly, as the 

release rates of U-234, had there not been Th-230 radionuclides adsorbing to the soil particles 

and undergoing radioactive decay.

FIGURE 3.13 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case III Concerning Release of U-234 from a 0.3-m U-234 

Source with No Dispersion
3-17

FIGURE 3.14 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case III Concerning Release of Th-230 from a 0.3-m U-234 

Source with No Dispersion

FIGURE 3.15 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case III Concerning Release of Ra-226 from a 0.3-m U-234 

Source with No Dispersion

The decay of Ra-226 generates Pb-210. Because the Kd value assumed for Pb-210, 

100 cm3

/g, is close to the Kd value of 70 cm3/g assumed for Ra-226, the release rate profile of 

Pb-210 would be similar to the release rate profile of Ra-226, as shown in Figure 3.16. 

The last radioactive radionuclide in the decay chain of U-234 is Po-210, which has a short halflife of 0.38 year. Because of the short half-life, the total radioactivity level of Po-210 at any 

depth of the soil column is expected to be about the same as that of Pb-210. On the other 
3-18

hand, because Po-210 has a Kd value (10 cm3/g) 10 times smaller than that of Pb-210, the 

dissolution of Po-210 in the pore water is expected to be about 10 times greater than that of 

Pb-210, and so is the release rate of Po-210 versus the release rate of Pb-210. Comparing the 

release rates of Po-210 in Figure 3.17 with those of Pb-210 in Figure 3.16 confirms the above 

expectations. 

FIGURE 3.16 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case III Concerning Release of Pb-210 from a 0.3-m U-234 

Source with No Dispersion

FIGURE 3.17 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case III Concerning Release of Po-210 from a 0.3-m U-234 

Source with No Dispersion
3-19

In general, the release rates calculated by RESRAD-OFFSITE agree very well with those 

calculated by DUST-MS except for the release rate of Po-210. For Po-210, the profiles of 

release rates calculated by RESRAD-OFFSITE and DUST-MS are the same; however, the 

magnitudes vary slightly. The exact reason for this discrepancy is not known; perhaps it is 

related to the short half-life of Po-210, which could result in more numerical dispersion in the 

calculation results when using the same time step and grid design as for other radionuclides. 

Further benchmarking results presented in Appendix B seems confirm this point.

3.4.3.2 With Dispersion

Figures 3.18 through 3.22 compare the RESRAD-OFFSITE and DUST-MS results by 

considering a dispersivity of 0.03 m for all radionuclides in the soil column. Discrepancy is 

observed starting with the first progeny, Th-230, and continuing for the rest of the decay chain. 

However, the release rate profiles are similar and the agreement is considered acceptable, 

given the fact that the simulations were carried out for an extended time period of 10,000 years. 

Further benchmarking results of this case are presented in Appendix B.

FIGURE 3.18 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case III Concerning Release of U-234 from a 0.3-m U-234 

Source with a Dispersivity of 0.03 m
3-20

FIGURE 3.19 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case III Concerning Release of Th-230 from a 0.3-m U-234 

Source with a Dispersivity of 0.03 m

FIGURE 3.20 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case III Concerning Release of Ra-226 from a 0.3-m U-234 

Source with a Dispersivity of 0.03 m
3-21

FIGURE 3.21 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case III Concerning Release of Pb-210 from a 0.3-m U-234 

Source with a Dispersivity of 0.03 m

FIGURE 3.22 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case III Concerning Release of Po-210 from a 0.3-m U-234 

Source with a Dispersivity of 0.03 m
3-22

3.4.4 Case IV – 3 m of Tc-99

Cases I, II, and III consider a release source with a thickness of 0.3 m. In Case IV, a release 

source with 10 times that thickness was considered. Because of the greater thickness, 

transport of radionuclides within the soil column would take a longer time to reach the bottom of 

the contaminated zone. In addition, a smaller water infiltration rate of 0.1 m/yr, less than the

0.4 m/yr assumed for Cases I and II, was used. The smaller water infiltration rate would carry 

less radionuclides leaving the contaminated zone within the same period of time. As a result, 

the release of radionuclides from the bottom of the contaminated zone would last much longer 

in Case IV than in previous cases. 

The release source for Case IV was assumed to contain Tc-99. The DUST-MS calculations 

were performed with the last grid design discussed in Section 3.3.3, which includes a 

100-m unsaturated zone beneath the contaminated zone to make the assumed lower boundary 

condition, 0 pCi/L of dissolved radionuclide concentration, valid at all times. The grid design has 

465 nodes.

Both the equilibrium desorption condition and the uniform release condition were simulated. 

When the uniform release condition was simulated, the waste form was assumed to disintegrate 

with a rate of 0.001/yr for 1,000 years. 

3.4.4.1 No Dispersion

Equilibrium desorption. Figure 3.23 compares the RESRAD-OFFSITE results corresponding 

to the equilibrium desorption option with the DUST-MS results corresponding to the rinse 

release mechanism. In general, the agreement is good with the peak release rates calculated 

by both codes matching each other. The discrepancy is considered to result from the numerical 

dispersion in DUST-MS results, which was studied and discussed in Section 3.4.1.1.

Uniform release. Figure 3.24 compares the RESRAD-OFFSITE results corresponding to the 

uniform release option with the DUST-MS results corresponding to the dissolution mechanism. 

The peak release rates match each other. The discrepancy is considered also to be attributable 

to the numerical dispersion in DUST-MS results. 
3-23

FIGURE 3.23 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case IV Concerning Release from a 3-m Tc-99 Source 

under the Equilibrium Desorption Condition with No Dispersion

FIGURE 3.24 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case IV Concerning Release from a 3-m Tc-99 Source 

under the Uniform Release Condition with No Dispersion
3-24

3.4.4.2 With Dispersion

Equilibrium desorption. When there is dispersion in the soil column, agreement between the 

RESRAD-OFFSITE results and DUST-MS results improves as compared to when there is no 

dispersion. See Figure 3.25 for the comparison of RESRAD-OFFSITE and DUST-MS results 

with a dispersivity of 0.3 m, and Figure 3.26 for the comparison of RESRAD-OFFSITE and 

DUST-MS results with a dispersivity of 1 m. 

Uniform release. The improvement in agreement between the RESRAD-OFFSITE and 

DUST-MS results with the consideration of dispersion was also observed under the uniform 

release condition. This result is illustrated by comparing Figure 3.27 (with a dispersivity of 

0.3 m) and Figure 3.28 (with a dispersivity of 1 m) with Figure 3.24 (with no dispersion). 

FIGURE 3.25 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case IV Concerning Release from a 3-m Tc-99 Source 

under the Equilibrium Desorption Condition with a Dispersivity 

of 0.3 m 
3-25

FIGURE 3.26 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case IV Concerning Release from a 3-m Tc-99 Source under 

the Equilibrium Desorption Condition with a Dispersivity of 1 m 

FIGURE 3.27 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case IV Concerning Release from a 3-m Tc-99 Source 

under the Uniform Release Condition with a Dispersivity of 0.3 m 
3-26

 FIGURE 3.28 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case IV Concerning Release from a 3-m Tc-99 Source 

under the Uniform Release Condition with a Dispersivity of 1 m 

3.4.5 Case V – 3 m of U-234

Case V concerns a 3-m release source containing U-234. The release source was assumed to 

disintegrate with a rate of 0.001/yr for 1,000 years under the uniform release condition. A water 

infiltration rate of 0.1 m/yr was assumed. The Kd values assumed for U-234, Th-230, Ra-226, 

Pb-210, and Po-210 in soils were 50, 6,000, 70, 100, and 10 cm3

/g, respectively. The 

DUST-MS results were obtained with a grid design of 465 nodes.

3.4.5.1 No Dispersion

Figures 3.29 to 3.33 compare the RESRAD-OFFSITE and DUST-MS results when there is no 

dispersion in the soil column. As the comparison shows, the agreement for progeny release 

rates, except for Po-210, between RESRAD-OFFSITE and DUST-MS is very good. Some 

discrepancy is observed with the U-234 and Po-210 release rates. The former is thought to be 

attributable to numerical dispersion in the DUST-MS results, which could be reduced if the 

domain of analysis is subdivided into additional grids. However, the maximum number of nodes 

accepted by DUST-MS is 500. The actual reason for the discrepancy with Po-210 release rates 

is not yet clear. It could be related to the short decay half-life of Po-210, as well as the small Kd 

value that allows Po-210 radionuclides to transport faster in the soil column as compared to 

other radionuclides in the same decay chain. 
3-27

FIGURE 3.29 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case V Concerning Release of U-234 from a 3-m U-234 Source 

with No Dispersion

FIGURE 3.30 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case V Concerning Release of Th-230 from a 3-m U-234 Source 

with No Dispersion
3-28

FIGURE 3.31 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case V Concerning Release of Ra-226 from a 3-m U-234 Source 

with No Dispersion

FIGURE 3.32 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case V Concerning Release of Pb-210 from a 3-m U-234 Source 

with No Dispersion
3-29

FIGURE 3.33 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case V Concerning Release of Po-210 from a 3-m U-234 Source 

with No Dispersion

3.4.5.2 With Dispersion

Figures 3.34 to 3.38 compare the RESRAD-OFFSITE and DUST-MS results when dispersion in 

the soil column is considered. With a dispersivity of 0.3 m, the agreement with U-234 release 

rates is better than it is without dispersion. However, a greater discrepancy is observed with the 

release rates of Th-230, Ra-226, and Pb-210 when dispersion takes place. The agreement with 

the Po-210 release rates remains at about the same level.

3.5 Summary of Comparison

Comparisons of radionuclide release rates calculated by RESRAD-OFFSITE and DUST-MS were 

conducted for five different cases involving different source dimensions, radionuclides, water 

infiltration rates, and release mechanisms. Overall, the agreement between the RESRADOFFSITE results and DUST-MS results is very good, with both codes predicting the same or very 

similar profiles over time.

The cause of disagreement in release rates of parent radionuclides under the no-dispersion 

condition was studied with a 0.3-m Tc-99 source. The study showed that numerical dispersion in 

the DUST-MS results was responsible for the disagreement. The disagreement can be reduced by 

increasing node density when subdividing the domain of analysis for the DUST-MS calculations. 
3-30

FIGURE 3.34 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case V Concerning Release of U-234 from a 3-m U-234 Source 

with a Dispersivity of 0.3 m 

FIGURE 3.35 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case V Concerning Release of Th-230 from a 3-m U-234 Source 

with a Dispersivity of 0.3 m 
3-31

FIGURE 3.36 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case V Concerning Release of Ra-226 from a 3-m U-234 Source 

with a Dispersivity of 0.3 m 

FIGURE 3.37 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case V Concerning Release of Pb-210 from a 3-m U-234 Source 

with a Dispersivity of 0.3 m 
3-32

FIGURE 3.38 Comparison of RESRAD-OFFSITE and DUST-MS Results 

for Case V Concerning Release of Po-210 from a 3-m U-234 Source 

with a Dispersivity of 0.3 m 

The agreement between the RESRAD-OFFSITE results and DUST-MS results for parent 

radionuclides improves when dispersion in the soil column was considered. This improvement 

is observed with all of the comparison cases.

When the release source contains U-234, which decays to multiple progenies, the comparison 

shows that agreement between the RESRAD-OFFSITE results and DUST-MS results is better 

for the longer-lived progenies (Th-230, Ra-226, and Pb-210) than for the shorter-lived progeny 

(Po-210). The exact cause of this difference in agreement is not clear, but is thought to be 

related to the combination of a short half-life and greater mobility in the soil column. Even with 

some discrepancy, the agreement with the Po-210 release rates between RESRAD-OFFSITE 

and DUST-MS is still considered well acceptable. 

The comparisons demonstrate that the RESRAD-OFFSITE source term model calculates 

radionuclide release rates comparable to those calculated by DUST-MS under the release 

conditions that it is equipped to consider. Additional benchmarking results presented in 

Appendix B confirm this observation.
4-1

4. Sensitivity Analysis to Identify Influential Inputs

This chapter provides examples of identifying the inputs that contribute to the uncertainty of the 

radiological dose due to the uncertainty or variability of the inputs. Appendix C describes the 

three different methods available in RESRAD-OFFSITE to identify the influential inputs, the 

advantages and disadvantages of each of the three methods, and how each method can be

used. The hypothetical scenario used in Appendix C to illustrate the identification of influential 

inputs is expanded in this chapter to include the new source release options available in the 

RESRAD-OFFSITE code Version 3. 

4.1 Hypothetical Scenario to Illustrate Identification of 

Influential Inputs 

4.1.1 Site Layout and Dimensions

The layout of the hypothetical site and the section through the contaminated layer are depicted 

in Figures 4.1 and 4.2. 

FIGURE 4.1 Layout of the Hypothetical Site

Primary 

Contamination 

200 m x 200 m

Lake 

200 m x 300 m

Pasture

200 m x 200 m

Livestock feed 

grain

100 m x 200 m Nonleafy 

Vegetables

Leafy 

Vegetables

Dwelling

50 m x 50 m

North

Direction of Groundwater flow, East

490 m

570 

460 

630 

680 

580 

450 

410 

300 

100 

100 m x 100 m
4-2

FIGURE 4.2 The Cross Section of the Primary Contamination and the Soil beneath It

4.1.1.1 Radionuclides in the Primary Contamination

The radionuclides in the primary contamination and their concentrations are listed below:

226Ra: 35 pCi/g

210Pb: 35 pCi/g

210Po: 35 pCi/g

4.1.1.2 Preliminary Data for the Hypothetical Site

Preliminary data developed for this site are as given below. All other inputs are assumed to be 

at the preloaded (default) RESRAD-OFFSITE values for this preliminary analysis.

It is assumed that there is no cover on the pile. The preliminary data indicate that the release of 

the radionuclides from the waste pile is controlled by the rate of dissolution of the solids in which 

the radionuclides are embedded; the release duration is 10,000 years for all radionuclides. 

Alternatively, if a first order release option is to be used, leach rates for all radionuclides are 

0.0001 per year. If the release is to be modeled as being controlled by equilibrium desorption, a 

value of 1000 cm3

/g will need to be used for the distribution coefficients of all radionuclides in 

the contaminated zone.

The distribution coefficient of the radionuclides for partitioning between the solid phase and the 

moisture are as follows for the soil and conditions at the site: 

226Ra: 22 cm3

/g

210Pb: 5 cm3

/g

210Po: 5 cm3

/g

These distribution coefficients will be used for all transport zones and offsite locations for the 

preliminary analysis.

The average annual precipitation at this location is 1.25 m/yr. The primary contamination is not 

cultivated and is not irrigated. The preloaded (default) RESRAD-OFFSITE values for rainfall 

and runoff factor (160), slope length steepness factor (0.4), and support practice factor (1) are 

appropriate for this site. The cover management factor for the primary contamination is 0.04, 

and the runoff coefficient is 0.5. This value corresponds to an area that is 60% covered with 

weeds, short brush, and grass.

Primary Contamination 

200 m x 200 m x 2 m

200 m

Unsaturated zone 

5 m thick

Aquifer 100 m thick
4-3

The leafy vegetables are grown in a field that has 20% slope and is farmed along the contour; 

thus, a support practice factor of 0.9, a cover and management factor of 0.08, and a slope 

length steepness factor of 4 are appropriate.

The fruit, grain, nonleafy vegetables, and livestock feed grain are grown in relatively flat land; 

thus, slope length steepness factors of 0.4 and support practice factors of 1 are appropriate for 

both areas. The cover management factor is 0.04 for these two areas. A slope length 

steepness factor of 0.4 and a support practice factor of 1 are also appropriate for the pasture.

Assume for atmospheric transport purposes that this hypothetical site is located in Peoria, 

Illinois. The topographical map indicates that the ground level of the livestock feed grain 

growing area is 15 m above the ground level at the location of primary contamination. The 

corresponding differences in elevation for the leafy vegetable growing area and the dwelling site 

are 20 and 40 meters. All the other offsite locations are at approximately the same elevation as 

the ground in the vicinity of the primary contamination. A preliminary sensitivity analysis on the 

grid spacing for this site shows that a grid spacing of 125 m is adequate for the desired 

accuracy. 

The hydraulic gradient of the groundwater is 0.004 across the entire site, and the hydraulic 

conductivity is 105 m/yr. The longitudinal, horizontal lateral, and vertical lateral dispersivities to 

the surface water body are estimated to be 8, 0.8, and 0.05 m, respectively.

The surface water body is the source of all water used in this scenario. For groundwater 

transport purposes, the surface water body is 290 m along the groundwater flow line, from the 

down gradient edge of the primary contamination. The right and left edges of the surface water 

body are at 200 and 100 m from the groundwater flow line through the center of the primary 

contamination. This surface water body does not have any edible crustacea or fish.

The individual spends 0.5 of the time inside the dwelling, 0.2 of the time outdoors in the vicinity 

of the dwelling, 0.08 of the time in each of the vegetable plots and in the livestock grain field, 

and 0.01 of the time in the pasture. The remainder of time is spent away from the area.

A preliminary (deterministic) analysis of this scenario confirms that the long-term dose from this 

site results from the 226Ra that was at the site because of the short half-life of the other two 

radionuclides that are initially present at the site. The 210Pb and 210Po that were initially present 

would have transformed away at the time of the peak in the dose. Thus, these two 

radionuclides are left out of the probabilistic sensitivity analysis in order to avoid spending 

computation time on computations that do not affect the final results.

Users should perform a sensitivity analysis to find the inputs that have a significant impact on 

the dose so that the data-gathering effort can be focused on those inputs. Reasonable initial 

distributions or ranges for the inputs should be used, and any relationships or correlations 

between the inputs should be considered, if possible.

4.1.2 Initial Ranges or Distributions of Inputs

The values identified in the hypothetical scenario for the inputs are initial estimates. The actual 

value of the input is expected to lie within some range of this initial estimate. As the inputs vary 

across their ranges of values, the resulting predicted peak dose will take a range of values, as 

well. A majority of the inputs will have an insignificant influence on the dose; the dose will 

remain essentially the same regardless of what value these inputs take over their probable 
4-4

ranges. The remaining variables will have an influence on the dose; the dose will change 

noticeably as the values of these inputs change over their probable range. The purpose of a 

preliminary sensitivity analysis is to identify the inputs that cause the dose to vary over its range. 

It will usually be possible to break these inputs into groups on the basis of how much influence 

they exert on the variability of the dose. This analysis will allow resources to be focused on the 

more influential inputs to find more site-specific and (hopefully) narrower ranges or distributions 

for them. The initial estimates of the value and range of each input has to be found by using a 

small portion of the available resource. The initial estimates are usually based on the more 

easily obtainable site characteristics, for example, the soil type, climate, topography, and 

vegetation. The initial distributions will usually be uniform over the typical range appropriate for 

the easily obtainable site characteristics. 

The uncertainty of the value of an input is likely to be lower if an initial value was developed for it 

based on site characteristics rather than if it were left at the preloaded value in RESRADOFFSITE. Thus, if an initial estimate is given in this example scenario, a range of 10% on either 

side of the initial value will be used in most cases. However, there will be inputs for which it will 

be appropriate to use larger ranges, of 25% or even 50% on either side of the initial estimate, 

especially for inputs that span orders of magnitude, or where there is uncertainty about the 

conceptualization. For these reasons, 25% ranges will be specified for the release duration and 

the distribution coefficients in the transport zones and in the offsite locations; 50% ranges will be 

specified for the leach rates and, when modeling this as an equilibrium desorption release, for 

the distributions coefficient in the contaminated zone. In this preliminary sensitivity analysis 

example, a range of 50% will be used on either side of a preloaded RESRAD-OFFSITE value 

unless a smaller range is indicated by the nature of that input. Smaller ranges were specified 

for inputs that describe the standard receptor (10% range), the density or porosity of soil 

(25% range), and the ambient temperature (10% range).

4.1.3 Relationships or Correlations between Inputs

The RESRAD-OFFSITE inputs are not all independent; some of the inputs are correlated with 

others, and there may even be exact relationships between some of the inputs under certain 

circumstances. In this example scenario, the groundwater is shown to flow from west to east 

along the x dimension of the primary contamination. Thus, in this example, the length of 

contamination parallel to the aquifer flow is equal to the x dimension of the primary 

contamination—an exact relationship. In this example, the total porosity and the effective (in 

transport) porosity of the primary contamination are assigned the same initial preloaded 

RESRAD-OFFSITE value. They will also have identical ranges and distributions in this example 

scenario according to the discussion in Section 4.1.2. If these distributions are sampled 

independently, there will be many samples where the value for the effective porosity will exceed 

the value for total porosity. The only way to prevent this result is to specify that the effective 

porosity must be equal to total porosity in the contaminated zone: an exact relationship. 

There are many other inputs in RESRAD-OFFSITE which, while not related, are correlated. For 

example, consider the four inputs, dry bulk density, total porosity, effective (in transport) 

porosity, and field capacity of a soil layer. The field capacity, the volume fraction of pores that 

can hold water against gravity flow, has to be lower than the total porosity. Considering the 

initial values, 0.3 for field capacity and 0.4 total porosity, and the initial distributions of 0.225 to 

0.375 for field capacity and 0.3 to 0.5 for total porosity, it will be necessary to specify a positive 

correlation between these two inputs to ensure that the value used for field capacity is lower 

than the value used for total porosity in any of the simulations. Not all of the pores are effective 

in conducting moisture through the soil; thus, the effective porosity cannot exceed the total 
4-5

porosity. It is also likely that high total porosities should lead to high effective porosities. 

Hence, a positive correlation should be specified between total porosity and effective porosity. 

If total porosity is positively correlated with both field capacity and effective porosity, then field 

capacity and effective porosity must also be positively correlated. The more porous the soil, the 

lower its dry bulk density; these two inputs need to be inversely or negatively correlated. The 

dry bulk density would have to be negatively correlated with field capacity and effective porosity, 

as well, because they are positively correlated with total porosity. 

4.2 Three-Point Single Input Sensitivity Analysis

Section C.2 of Appendix C discusses the three-point single input sensitivity analysis and 

describes how to perform this analysis in RESRAD-OFFSITE. The sensitivity analysis is 

performed on a single input parameter at a time. The sensitivity analysis involves three 

simulations; the first with all of the inputs, including the one selected for sensitivity analysis, at 

their initially estimated values or at the preloaded RESRAD-OFFSITE values if initial estimates 

have not yet been developed for them; the second with a higher value for the input selected for 

sensitivity analysis while all of the other inputs are at the value used for the first simulation; and 

the third with a lower value for the input selected for sensitivity analysis while all of the other 

inputs are at the value used for the first simulation. The differences in the predicted dose 

among the three simulations are directly attributable to the three different values used for the 

selected input in the simulations. If the higher and lower values used in the second and third 

simulation for the input selected for sensitivity analysis are chosen to represent the probable 

range of that input, then the difference between the doses predicted for the two simulations is a 

measure of the influence of that input on dose. When an input is selected for sensitivity analysis 

(using the F9 key for example), the set sensitivity analysis range pops up as shown in 

Figure 4.3. The user can specify the factor (1.1 in Figure 4.3), which determines the lower and 

higher values to be used for that input in the two sensitivity analysis simulations. The lower 

value (181.81 in Figure 4.3) is obtained by dividing the base value, which is the value used for 

the input in the first simulation (200 in Figure 4.3), by the specified factor. The higher value 

(220 in Figure 4.3) is obtained by multiplying the base value by the specified factor. Factors of 

1.1, 1.25, and 1.5 were specified to simulate the 10%, 25%, and 50% ranges on either side of 

the base value. These factors would have produced the desired values at the upper end, but 

the lower values would have been approximately 9%, 20%, and 33% below the base value 

instead of the desired 10%, 25%, and 50%; however, this slate of values would not affect the 

conclusions. The lower and higher (or upper) values that will be used in the two sensitivity 

analysis simulations are displayed on the Set Sensitivity Analysis Range form.
4-6

FIGURE 4.3 Specifying the Lower and Higher Values to be Used for an Input 

Selected for Sensitivity Analysis

The interface checks to ensure that the two values computed for the sensitivity analysis 

simulations are within the upper and lower bounds that are in the code. If either the lower or 

higher values, computed by using the specified factor and the base value, violate the lower or 

upper bounds in the code for that input, another form pops up allowing the user to make a 

choice that satisfies the bounds, as shown in Figure 4.4.

Up to 25 inputs can be selected for sensitivity analysis in an input file. When this file is 

executed by the code, it first performs a simulation with all of the inputs set to the base value. It 

then performs a pair of simulations for each input selected for sensitivity analysis. An input file 

was created by using the data set out in Section 4.1 for the uniform release option. Twenty-five 

of these inputs were selected for sensitivity analysis. The temporal sensitivity plots and the 

difference between the peak doses for the pair of sensitivity simulations for each input selected 

are shown in Figures 4.5 through 4.29. The figures are arranged in decreasing order of 

influence based on the range of the peak dose. A second input file with 25 other inputs selected 

for sensitivity analysis was also created. Three of those plots are shown in Figures 4.30, 4.31, 

and 4.32. There are at least 224 inputs in this example scenario that are candidates for 

sensitivity analysis, so 9 input files would be needed to perform sensitivity analysis on all of 

them. Figures 4.7, 4.33, and 4.34 illustrate that sensitivity analysis can be performed on all 

three inputs that characterize the release mechanisms available in RESRAD-OFFSITE.
4-7

FIGURE 4.4 Resetting the Sensitivity Analysis Range to Avoid 

Exceeding the Bounds on the Inputs

4.2.1 Advantages and Disadvantages of Three-point Single-input Sensitivity 

Analysis

This sensitivity analysis is very easy to understand. Two simulations are performed for each 

input selected for sensitivity analysis; only the value of the selected input changes between the 

two simulations, whereas the values of all of the other inputs remain the same. The difference 

between the predicted doses for the two simulations is the direct result of the change in the 

value of the selected input. If the two values specified for the selected input are the limits of the 

likely range of that input for this scenario, the difference in the peak doses is a measure of the 

uncertainty in the peak dose due to the uncertainty in the value of the selected input. The 

influence of the selected input on dose can be seen from the pair of temporal dose curves from 

the two simulations plus the curve from the initial base value simulation. More effort is required 

to obtain a quantitative measure of this influence; specifically, users must view data and 

manually find the peak doses for the two simulations or export the data to a spreadsheet and 

then find the peaks.

The process of viewing the plots and then computing the difference between the peak doses of 

each pair of simulations is tedious when there are a large number of inputs as in this example 

scenario and therefore limits the usefulness of this method. This method would be easier to use 

if the code were to compute the differences between the peak doses of each pair of simulations 

and were to produce an ordered list of inputs based on that difference. If this automated 
4-8

process of ranking the inputs by their influence on the peak dose is implemented in the code, 

then it would also be necessary to remove the limit on the number of inputs that can be selected 

for three-point single-input sensitivity analysis.

The fact that only the value of the selected input is changed in the pair of simulations allows the 

effect of that input to be seen easily in the temporal plots. This clarity turns into a disadvantage, 

however, when there is some relationship between the inputs or if there is interaction between 

the inputs. Figures 4.30 and 4.31 illustrate the influence of the total porosity and the effective 

porosity of the soil in the primary contamination on dose. According to Figure 4.30, the peak 

dose decreases as the effective porosity in the primary contamination increases. Figure 4.31 

shows that the peak dose increases as the total porosity in the primary contamination increases. 

The influence of the two inputs appears to be similar in magnitude but opposite in direction. 

Recall that the effective porosity is the part of the total porosity of soil that is effective in the 

transport of water in soil. If there is uncertainty in these two porosities, it is reasonable to 

assume that the uncertainties will be correlated. In other words, if the total porosity were to be 

higher than the initially assigned value, it is likely that the effective porosity will also be higher 

than the initially assigned value. So when we change total porosity for the two simulations, we 

should also change effective porosity; they will have opposing effects on the peak dose, and the 

net result is likely to be a small change in the peak dose. However, we can only change the 

value of a single input in this sensitivity analysis. Sections C.3.2 and C.3.3 of Appendix C 

illustrate the interaction between inputs: changes to input A can cause a large change in the 

dose for certain values of inputs B, C, and D; whereas the same change in input A will have 

very little effect on the doses for other values of inputs B, C, and D. Thus, if there is uncertainty 

in inputs A, B, C, and D, then determining the effect of changes in the value of input A at a 

single combination of values of inputs B, C, and D only provides a partial picture of the effect of 

input A on the dose. 

4.2.2 Conclusion about the Use of 3-point Single-input Sensitivity Analysis

This sensitivity analysis is easy to understand and requires a small number of simulations, one 

more than twice the number of inputs being studied. Even though it does not consider 

relationships between inputs and the interactions between inputs, it is a useful tool especially in 

the preliminary stages of a sensitivity analysis when there might not be very much information 

about the relationships between the inputs. The main limitation to the usefulness of this method 

is the effort needed to view each plot in turn to find inputs that have an influence on the dose 

and then to calculate the difference between the peak doses in each pair of simulations to 

quantify the influence. If the following conditions were met, namely, that (1) there were no limits 

on the number of inputs that can be selected for sensitivity analysis, and (2) if the code were to 

compute the difference in the peak dose between pairs of simulations and (3) were to produce 

an ordered list of inputs on the basis of their influence, the three–point, single-input sensitivity 

analysis could be a more useful tool to identify the influential inputs in RESRAD-OFFSITE. 
4-9 

FIGURE 4.5 Temporal Variation of Dose with the Volume of the Surface Water Body Showing a 

of 48.3 mrem/year for the Peak Dose from 38.5 to 86.8 mrem/year
4-10

FIGURE 4.6 Temporal Variation of Dose with the Mean Residence Time of Water in the Surface W

Showing a Range of 47.4 mrem/year for the Peak Dose from 38.7 to 86.1 mrem/year
4-11

FIGURE 4.7 Temporal Variation of Dose with the Duration of Release of 226Ra Showing a Range 

of 20.4 mrem/year for the Peak Dose from 48.8 to 69.2 mrem/year
4-12

FIGURE 4.8 Temporal Variation of Dose with the Density of the Primary Contamination Showing 

of 18.8 mrem/year for the Peak Dose from 49.3 to 68.1 mrem/year
4-13

FIGURE 4.9 Temporal Variation of Dose with the Depth of Aquifer Contributing to the Surface W

Showing a Range of 13.2 mrem/year for the Peak Dose from 49.0 to 62.2 mrem/year
4-14

FIGURE 4.10 Temporal Variation of Dose with the Distribution Coefficient of 210Pb in the First Uns

Zone Showing a Range of 12.9 mrem/year for the Peak Dose from 51.5 to 64.4 mrem
4-15

FIGURE 4.11 Temporal Variation of Dose with the Distribution Coefficient of 226Ra in the First Uns

Zone Showing a Range of 12.2 mrem/year for the Peak Dose from 52.2 to 64.4 mrem
4-16

FIGURE 4.12 Temporal Variation of Dose with the Evapotranspiration Coefficient Showing a Ran

of 11.5 mrem/year for the Peak Dose from 47.6 to 59.1 mrem/year
4-17

FIGURE 4.13 Temporal Variation of Dose with the Fraction of Fruit, Nonleafy Vegetables, a

Contaminated Region Showing a Range of 9.8 mrem/year for the Peak Dose 

mrem/year
4-18

FIGURE 4.14 Temporal Variation of Dose with the Irrigation Applied per Year to the Fruit, Nonlea

Vegetables, and Grain Growing Areas Showing a Range of 9.7 mrem/year for the Pe

to 63.6 mrem/year
4-19

FIGURE 4.15 Temporal Variation of Dose with the Wet Weight Crop Yield of Fruit, Nonleafy Veget

and Grain in the Growing Areas Showing a Range of 9.6 mrem/year for the Peak Do

from 54.0 to 63.6 mrem/year
4-20

FIGURE 4.16 Temporal Variation of Dose with the Translocation Factor for Fruit, Nonleafy Vegeta

and Grain Showing a Range of 9.6 mrem/year for the Peak Dose from 54.0 to 63.6 m
4-21

FIGURE 4.17 Temporal Variation of Dose with the Foliar Interception Factor for Irrigation in the F

Nonleafy Vegetables, and Grain Growing Area Showing a Range of 9.6 mrem/year f

Peak Dose from 54.0 to 63.6 mrem/year 
4-22

FIGURE 4.18 Temporal Variation of Dose with the x Dimension of the Primary Contamination 

Showing a Range of 9.1 mrem/year for the Peak Dose from 53.3 to 62.4 mrem/year
4-23

FIGURE 4.19 Temporal Variation of Dose with the y Dimension of the Primary Contamination 

Showing a Range of 9.1 mrem/year for the Peak Dose from 53.3 to 62.4 mrem/year
4-24

FIGURE 4.20 Temporal Variation of Dose with the Thickness of the Primary Contamination Show

a Range of 8.2 mrem/year for the Peak Dose from 53.9 to 62.1 mrem/year
4-25

FIGURE 4.21 Temporal Variation of Dose with the Duration of the Growing Season of Fruit, 

Nonleafy Vegetables, and Grain Showing a Range of 8.1 mrem/year for the Peak Do

from 54.2 to 62.3 mrem/year
4-26

FIGURE 4.22 Temporal Variation of Dose with the Weathering Removal Constant for Fruit, 

Nonleafy Vegetables, and Grain Showing a Range of 8.1 mrem/year for the Peak Do

from 54.2 to 62.3 mrem/year
4-27

FIGURE 4.23 Temporal Variation of Dose with the Weathering Removal Constant for Fruit, 

Nonleafy Vegetables, and Grain Showing a Range of 6.9 mrem/year for the Peak Do

from 54.5 to 61.4 mrem/year
4-28

FIGURE 4.24 Temporal Variation of Dose with the Erodibility Factor of Soil in the Primary 

Contamination Showing a Range of 5.0 mrem/year for the Peak Dose 

from 55.6 to 60.6 mrem/year
4-29

FIGURE 4.25 Temporal Variation of Dose with the Irrigation Applied per Year to the Pasture and 

the Silage Growing Areas Showing a Range of 4.0 mrem/year for the Peak Dose 

from 56.2 to 60.2 mrem/year
4-30

FIGURE 4.26 Temporal Variation of Dose with the Wet Weight Crop Yield from the Pasture and 

the Silage Growing Areas Showing a Range of 4.0 mrem/year for the Peak Dose 

from 56.2 to 60.2 mrem/year
4-31

FIGURE 4.27 Temporal Variation of Dose with the Grain Intake by Cattle Raised for Meat Showing 

a Range of 0.8 mrem/year for the Peak Dose from 57.5 to 58.3 mrem/year
4-32

FIGURE 4.28 Temporal Variation of Dose with the Longitudinal Dispersivity in the Saturated 

Zone to the Surface Water Body Showing a Range of 0.0 mrem/year for the Peak Do

from 57.8 to 57.8 mrem/year
4-33

FIGURE 4.29 Temporal Variation of Dose with the Dry Bulk Density of Soil in the Fruit, 

Nonleafy Vegetables, and Grain Growing Area Showing a Range of 0.0 mrem/year 

for the Peak Dose from 57.8 to 57.8 mrem/year
4-34

FIGURE 4.30 Temporal Variation of Dose with the Effective Porosity of the Primary Contaminatio

Showing a Range of 2.5 mrem/year for the Peak Dose from 56.2 to 58.7 mrem/year
4-35

FIGURE 4.31 Temporal Variation of Dose with the Total Porosity of the Primary Contamination 

Showing a Range of 2.2 mrem/year for the Peak Dose from 56.5 to 58.7 mrem/year
4-36

FIGURE 4.32 Temporal Variation of Dose with the Field Capacity of the Primary Contamination 

Showing a Range of 0.0 mrem/year for the Peak Dose from 57.8 to 57.8 mrem/year
4-37

FIGURE 4.33 Temporal Variation of Dose with the Leach Rate of 226Ra in Primary Contamination 

for the First Order Release Example Scenario
4-38

FIGURE 4.34 Temporal Variation of Dose with the Distribution Coefficient of 226Ra in Primary 

Contamination for the Equilibrium Desorption Release Example Scenario
4-39

4.3 Multiple Input Sensitivity Analysis 

Section C.4 of Appendix C discusses the multiple input sensitivity analysis and describes how to 

perform this analysis in RESRAD-OFFSITE. The method involves specifying distributions—and 

not just ranges but probabilities associated with different parts of the range—for the inputs that 

are selected for sensitivity analysis. The code samples each distribution a specified number of 

times and then combines a sample from each of the distributions to produce a number of sets of 

inputs. Each sample is used in only one set of inputs, so the number of sets of inputs is equal 

to the number of times each distribution is sampled. If correlations are specified between 

inputs, the code takes those into account when it combines the samples from the distributions of 

those inputs to form the sets of inputs. Exact relations can also be specified between inputs in 

the step-by-step analysis mode (Figure 4.35). The code then performs the specified number of 

simulations using those sets of inputs. It is difficult visually to see the effect of an input on the 

dose in a scatter plot because all of the inputs change from simulation to simulation, unlike in 

the case of the single input sensitivity analysis. Even if it were possible to see the effect in the 

plots, viewing that many plots would be a tedious process. The code performs multivariable 

linear regression analysis between the peak dose of each simulation (the dependent variable) 

and the inputs (“independent” variables) and outputs a list of inputs in decreasing order of 

importance. The regression can be performed on the actual values of peak dose and inputs 

(raw), or it can be performed on the ranks assigned to the dose and the inputs. The ranks are 

simply the positions of the samples of input in a sorted list; thus, the smallest sample of each 

input would have a rank of 1, the second smallest sample of each input would have a rank of 2, 

and so on. The predicted peak dose also would be ranked from the least to the greatest. The 

linear regression on the ranks is useful if the relationship between the peak dose and the inputs 

is not linear but monotonic. The linear regression on the raw data can be used if the 

relationship is close to linear.

When an input is selected for multiple input sensitivity analysis using the Shift-F8 key, the 

“Uncertainty and Probabilistic Analysis” form pops up with a uniform distribution about the initial 

value of the input (Figure 4.36). The user can select from among ranges of 10%, 25%, or 50% 

on either side of the initial value; alternatively, the user can specify other distributions. If the 

present ranges (10%, 25%, or 50%) are chosen, the interface will check to ensure that the 

ranges remain within the bounds of the input. Thus, for example, a 50% range on either side of 

a 0.4 value for the erodibility input would require a range of 0.2 to 0.6. The upper bound for 

erodibility is set to 0.5 in the code. Thus, the interface sets a range of 0.2 to 0.5 when a 50% 

range is selected on a base value of 0.4 for the erodibility of soil (Figure 4.37). A total of 

222 inputs were selected for sensitivity analysis using the ranges in Section 4.1.2; a 10% range 

was specified for 42 of them, a 25% range was specified for 50 of them, and a 50% range was 

specified for the remaining 130 inputs.

The correlations between inputs can be specified by a correlation coefficient between the ranks 

of the data. Possible correlations between inputs of this example scenario were discussed in 

Section 4.1.3. Information will probably not be available about the extent of correlation at the 

stage of a preliminary analysis. One guide to estimating the degree of correlation is the physical 

constraint. The field capacity cannot exceed the total porosity; this constraint appears to have 

been met with a rank correlation coefficient of 0.9 between the two inputs, as can be seen in 

Figure 4.38. This figure contains 12,000 points; 4000 samples were obtained from each 

distribution, and the process was repeated three times. The points from the different repetitions 

are shown in different colors. The specification of correlation between inputs is shown in 

Figure 4.39. The inputs to be correlated have to be identified by the variable name. The 
4-40

variable name is displayed in the variable information bar at the bottom of the RESRADOFFSITE interface when the cursor is placed in an input box. When the variable is selected 

from the dropdown box, its descriptive title appears below the dropdown box. Pairwise 

correlations for all possible pairs were specified for a group of correlated inputs. For example, 

there are four properties of the first unsaturated zone that were correlated: dry bulk density, 

effective porosity, field capacity, and total porosity. It is possible to form six pairs from this 

group of four inputs: dry bulk density – effective porosity, dry bulk density – field capacity, dry 

bulk density – total porosity, effective porosity – field capacity, effective porosity – total porosity,

and field capacity – total porosity. When correlations are specified between inputs, it is best to 

generate the samples and view the scatter plots between the correlated inputs.

The two relationships discussed in Section 4.1.3 are specified in the related inputs tab 

(Figure 4.40) after generating the input samples. The variable name for the length of 

contamination parallel to the aquifer flow is LCZPAQ, and SOURCEXY(1) is the variable name 

of the x dimension of the primary contamination. The first expression in the table specifies that 

the value of length of contamination parallel to aquifer flow must be set to the sample value of 

the x dimension of the primary contamination for every simulation. Figure 4.41 confirms that 

this relationship is being used to generate the values for the length of primary contamination 

parallel to the aquifer flow. 

After all of the input samples have been generated, the next step is to perform the probabilistic 

simulation on the code to generate the output samples. A total of 12,000 simulations were 

performed in this example scenario; three repetitions each containing 4000 samples. The 

cumulative distribution function of peak dose is shown in Figure 4.42. The figure contains three 

curves, one for each repetition. The predicted peak dose ranges from 9 to 480 mrem/year and 

has a mean of 63 mrem/year. This range of uncertainty is a consequence of the uncertainty in 

the 224 inputs. The purpose of the sensitivity analysis is to identify the inputs that cause this 

uncertainty in the peak dose. 

Linear regression can be performed between the output samples of peak dose and the input 

samples, and the resulting standardized regression coefficients can be used to identify the 

inputs that cause the uncertainty in the peak dose. The code uses the standardized regression 

coefficients to sort the inputs in the order of influence from the most influential to the least 

influential. The list includes all 222 inputs selected for sensitivity analysis; the related inputs are 

not included in this list. A partial listing showing the top 50 inputs for the uniform release 

example scenario is shown in Figure 4.43. A bar chart of the standardized regression 

coefficients of the top 63 inputs is shown in Figure 4.44, while those of all 222 inputs are shown 

in Figure 4.45. The inputs at the top of the list have a large influence on the range of the peak 

dose. The impact of the input on the range of the peak dose decreases as we move down the 

list. We need to identify the point on the list below which the inputs have a negligible effect on 

the range of the dose. This identification will subsequently be confirmed by the comparison of 

the cumulative distribution function plots of two runs as discussed later in this section. The first 

5 inputs clearly have a very large influence on the uncertainty of the peak dose, and the next 12 

have a moderate influence (Figures 4.44 and 4.46). The last 160 inputs are judged not to 

contribute to the uncertainty in the peak dose: the standardized regression coefficient from at 

least two of the repetitions is 0.00, and that from the third repetition is 0.01, 0.00, or −0.01 

(Figure 4.45). Somewhere between the top 17 inputs and the bottom 160 inputs is a point 

below which the inputs have only a negligible effect on the uncertainty in the peak dose. The 

judgment regarding where this cut-off point falls will vary from analyst to analyst, but it needs to 

be defensible. For this illustration, the top 30 inputs (Figure 4.46) are judged to have some 

effect on the uncertainty of the predicted peak dose; the next 32 are judged to make a negligible 
4-41

contribution to the uncertainty of the predicted peak dose. The standardized regression 

coefficients from the three repetitions of any of the top 30 inputs are consistent, as they are 

within 0.01 of their mean values. The difference between the values from the three repetitions 

is not significant as compared to the mean of the three values. The mean of the standardized 

regression coefficients of the 30th input is 0.03, and a difference of 0.01 between the three 

values was considered insignificant especially in light of the fact that the standardized 

regression coefficients in the list have been rounded to a one-hundredth. Most importantly, this 

identification is supported by the close agreement between the cumulative distribution functions 

of two runs, the identification run, and the verification run. The identification run was the first run 

where all 222 inputs had the distributions specified in Section 4.1.2 together with the 

correlations and relationships developed in Section 4.1.3. For the verification run, the top 

30 inputs and the two inputs that were correlated to one of them retained the same distributions 

as in the identification run; the correlations and relations were also retained. The range of the 

uniform distribution of the 190 inputs that were judged to have either a negligible influence or no 

influence on the uncertainty of the predicted peak dose were reduced to 0.1% of the preliminary 

value; thus, the samples for these inputs ranged from 0.999 to 1.001 of their preliminary value 

(essentially the preliminary value). The reason for retaining the very narrow distributions for 

the190 insignificant inputs is to ensure that the samples of the 30 influential inputs and, more 

importantly, the grouping of those samples into sets of inputs in the verification run is the same 

as that in the identification run. The cumulative distribution function of the peak dose from the 

verification run of the 30 most significant inputs in Figure 4.47 is very similar to the cumulative 

distribution function of the 222-input identification run. The predicted peak doses for the 

verification run with the 30 most significant inputs range from 10 to 480 mrem/year and have a 

mean of 64 mrem/year, which is quite close to the values of 9, 480, and 63 obtained from the 

identification run. Thus, the top 30 inputs in this example scenario can be identified justifiably 

as the most significant, and available resources can be spent on gathering more site-specific 

values and distributions for these inputs. During this data-gathering process, it is likely that 

more site-specific values and distributions will also be found for some of the inputs that are 

related to or associated with the significant inputs. 

The sensitivity analysis would then have to be repeated with the newly gathered distributions or 

point values for the 30 significant inputs and for any of the other associated inputs; the 

remaining inputs would retain their values and distributions from the preliminary sensitivity 

analysis. This step will lead to the identification of another set of significant inputs, some of 

which might be different from those identified from the preliminary sensitivity analysis. More 

resources will need to be spent identifying site-specific values and distributions for the newly 

identified significant inputs. This iterative process is repeated until either the uncertainty in the 

peak dose of the last sensitivity analysis run is acceptable, or all inputs identified as being 

significant by the last sensitivity run already have site-specific distributions indicating that the 

uncertainty in peak dose cannot be reduced further.

The cumulative distribution function plots with the top 17 inputs and with the top 5 inputs are 

shown in Figures 4.48 and 4.49. The cumulative distribution functions of all 4 runs are plotted 

together in Figure 4.50. The cumulative distribution function plots of the 222-input identification 

run and the 30-input verification run are essentially indistinguishable. Even the curves from the 

17-input verification run and the 5-input verification run are remarkably close to that of the 

identification run. Two of the top 5 inputs had a range of 25%, and the other three had a 50% 

range. Three of the top 17 inputs were of the 10% range, and four were of the 25%-range 

variety. On the other end, 96 of the 130 inputs for which the 50% range was specified ended up 

in the “no influence” category. Thus, the use of different ranges do not necessarily skew the 

results; the range specified for each input needs to be the probable range for each input.
4-42

4.3.1 Advantages and Disadvantages of Multiple Input Sensitivity Analysis

This sensitivity analysis is more complex than that of the three-point sensitivity analysis. 

Distributions need to be specified for each input selected for sensitivity analysis, instead of just 

the endpoints of the ranges. The code samples each distribution many times; thus, the analyst 

has to specify how many times the distribution is to be sampled. The results will not be reliable 

if too few samples are chosen; this will be evident by the large differences between the results 

of the repetitions. If there are large differences between the results of the repetitions, the 

sensitivity analysis has to be repeated with a larger number of samples. Relations and 

correlations between the inputs can be specified. These are taken into account when forming 

the sets of inputs. A set of inputs is made up of one sample from each of these distributions; 

each sample is only used once. Thus, there are as many sets of inputs as there are samples. 

The code produces a sample of output, peak dose, for each set of inputs, so there are as many 

samples of output as there are for each input. The values of all of the inputs change from 

simulation to simulation. As a result, it is not easy to see the effect of an input on the variability 

in the peak dose from a scatter plot of the two; whereas an experienced analyst might be able to 

pick out many (but not all) of the important inputs from the scatter plots, most analysts would not 

be able to visually identify more than a few important inputs. Linear regression has to be 

performed between the output and the inputs in order to pick out all of the significant inputs. 

The linear regression output sorts the inputs in descending order of importance, thereby 

facilitating the identification of the significant inputs. Cumulative distribution function plots of the 

identification and verification runs can be compared to confirm the selection of the significant 

inputs. The multiple input sensitivity analysis requires a longer time to execute the code as 

compared to that required by the three-point sensitivity analysis. One the other hand, the 

significant inputs can be picked more easily from the sorted list of the regression output instead 

of having to view each figure in turn, as in the case of the three-point sensitivity analysis; this 

advantage is temporary until the code is able produce a sorted list for the three-point sensitivity 

analysis as well. The uncertainty of the peak dose can be obtained from the multiple input 

sensitivity analysis but not from the three–point, single-input sensitivity analysis.

4.3.2 Conclusion about the Use of Sensitivity Analysis

This sensitivity analysis is difficult to understand and requires a large number of simulations, the 

number of which has to be decided upon by the analyst. It considers relationships between 

inputs and the interactions between inputs. Although a significant execution time may be 

needed to generate the samples of peak dose, the sorted regression output allows the analyst 

to quickly judge the influential outputs. The process of verifying the selection of influential inputs 

can be made easier if the code were to narrow the distributions of the insignificant inputs. 

The inputs included in the first input file for the three–point, single-input sensitivity analysis were 

the top 22 from the list generated by the regression report, and the other three were from the 

no-influence category. There is good agreement between the ranking of the inputs by the two 

methods of sensitivity analysis. However, there are some significant differences, as well. Foliar 

interception factor for irrigation of fruit, grain, and nonleafy vegetables is judged to have no 

influence in the multiple input sensitivity analysis; it is 13th out of 25 in the three–point, singleinput sensitivity analysis file. Grain (kg/day) intake of meat livestock was judged to have some 

influence on the uncertainty in the dose by the multiple input sensitivity analysis, whereas it 

shows only a small effect on the temporal dose in the three–point, single-input sensitivity 

analysis. 
4-43

FIGURE 4.35 Step-by-step Analysis Tab of the Uncertainty and Probabilistic Analysis Form
4-44

FIGURE 4.36 Specifying the Range for an Input Selected for Multiple Input Sensitivity Ana
4-45

FIGURE 4.37 Specified Range Adjusted to Conform to Bounds Built into the Code
4-46

FIGURE 4.38 Scatter Plot of Field Capacity against Total Porosity to Show the Effect of Specifyin

a Correlation of 0.9 between Them
4-47

FIGURE 4.39 Specifying Correlation between Inputs
4-48

FIGURE 4.40 Specifying Relationships between Inputs
4-49

FIGURE 4.41 Scatter Plot of the Length Parallel to Aquifer Flow against the x Dimension 

of the Primary Contamination
4-50

FIGURE 4.42 Cumulative Distribution Function of Peak Dose from the Identification Run 

of the Preliminary Sensitivity Analysis
4-51

FIGURE 4.43 Regression Output of Preliminary Sensitivity Analysis with Inputs Sorted in Descen

Order of Influence
4-52

FIGURE 4.44 Standardized Regression Coefficients of the Top 63 Inputs Sorted in Descending 

Order of Importance
4-53

FIGURE 4.45 Standardized Regression Coefficients of All 222 Inputs Sorted in Descending 

Order of Importance
4-54

FIGURE 4.46 Regression Output of Preliminary Sensitivity Analysis with Inputs Sorted in Descen

Order of Influence
4-55

FIGURE 4.47 Cumulative Distribution Function of Peak Dose from the 30-input Verification Run 

of the Preliminary Sensitivity Analysis
4-56

FIGURE 4.48 Cumulative Distribution Function of Peak Dose from the 17-input Verification Run 

of the Preliminary Sensitivity Analysis
4-57

FIGURE 4.49 Cumulative Distribution Function of Peak Dose from the 5-input Verification Run 

of the Preliminary Sensitivity Analysis
4-58

FIGURE 4.50 Cumulative Distribution Function of Peak Dose from Identification and Verification 
5-1 

5. References

MARSSIM Manual, 2000, Multi-Agency Radiation Survey and Site Investigation Manual 

(MARSSIM), NUREG-1575, Rev. 1, EPA 402-R-97-016, Rev. 1, DOE/EH-0624, Rev. 1., 

August.

Shen, H.S., and P.Y. Julien, 1993, “Erosion and Sediment Transport,” in Handbook of 

Hydrology, Chapter 12, ed. D.R. Maidment, 12.1–12.61, New York: McGraw-Hill. 

Sullivan, T.M., 1993, Disposal Unit Source Term (DUST) Data Input Guide, NUREG/CR-6041, 

BNL-NUREG-52375, prepared for the U.S. Nuclear Regulatory Commission, Brookhaven 

National Laboratory, Upton, N.Y., April.

Sullivan, T.M., 2001a, DUST-MS Disposal Unit Source Term: Multiple Species Data Input 

Guide, Brookhaven National Laboratory, Upton, New York, Jan.

Sullivan, T.M., 2001b, DUSTMS-D Disposal Unit Source Term: Multiple Species-Distributed 

Failure Data Input Guide, Brookhaven National Laboratory, Upton, N.Y., Jan.

Yu, C., et al., 2001, User’s Manual for RESRAD Version 6, ANL/EAD-4, Argonne National 

Laboratory, Argonne, Ill., July.

Yu, C., et al., 2007, User’s Manual for RESRAD-OFFSITE Version 2, ANL/EVS/TM/07-1, 

Argonne National Laboratory, Argonne, Ill., June.

Appendix A

Letter Report – Proposed Approach for the Task 

of Expanding the Source Term Model 

for RESRAD-OFFSITE

January 22, 2010

A-1 

Appendix A

Letter Report – Proposed Approach for the Task

of Expanding the Source Term Model

for RESRAD-OFFSITE

A.1 Background 

RESRAD-OFFSITE inherits and expands upon the objective of RESRAD (onsite) code for 

modeling the environmental fate and transport of radionuclides in contaminated soil and 

evaluating subsequent human radiation exposures through consideration of multiple exposure 

pathways. Several enhancements were incorporated into RESRAD-OFFSITE to extend the 

location of human receptors beyond the contaminated area, where receptors considered by 

RESRAD (onsite) would be confined. These enhancements include a source mass balance and 

mixing model, an air dispersion model, a one-dimensional advection with three-dimensional 

dispersion groundwater transport model, an offsite soil accumulation model, and a surface water 

mixing and dilution model. In addition to the enhancement of fate and transport models, 

RESRAD-OFFSITE was also equipped with the option to specify the temporal fluxes of 

radionuclide releases to air, to surface runoff, and to groundwater. This feature bypasses the 

calculation of release rates by RESRAD-OFFSITE so that in addition to releases from 

contaminated soils, releases from other sources (e.g., waste disposed in soils, emissions from 

effluent stacks, or discharges from wastewater pipelines, etc.) can be evaluated as well.

The approach proposed in this letter report has three objectives: (1) to provide more release 

mechanisms for the user to choose from; (2) to allow specification of the fraction of inventory 

that will be released by each mechanism; and (3) to model situations where the initial 

contamination is in containers, in addition to the current conceptualization of the initial 

contamination being in soil. If all the proposed approaches are adopted, the code will be able to 

model the long-term performance of waste disposal facilities and be applied to evaluate different 

disposal methods.

Two computer codes, DUST (Disposal Unit Source Term) and BLT (Breach, Leach, and 

Transport), designed to estimate radionuclide release rates from disposal facilities, provide the 

technical background for these additions. A brief overview of these two computer codes is 

presented in this letter report, with an emphasis on their methodologies for calculating source 

release rates. 

A.2 Description of the Task Assignment

The task proposal approved by the U.S. Nuclear Regulatory Commission (NRC) for the task of 

expanding the source term model for RESRAD-OFFSITE is reproduced as follows:

Task 3 – Expand the source-term model for RESRAD-OFFSITE

RESRAD-OFFSITE uses a pathway analysis method to relate radionuclide concentrations in soil to doses 

received by a member of the critical population group. Recent decommissioning activities have involved 
A-2 

evaluating the exposure to materials other than soil (e.g., slags). In this task the contractor shall expand the 

current source term model to incorporate other source term release mechanisms or constraints such as:

• Solubility-Limits

• Surface-Wash Off or Surface Rinse

• Diffusion

• Dissolution / Uniform Dissolution

• Ion-Exchange

• Complex, non-uniform sources with variable size, depth, content, concentrations, and degradability

This task may be accomplished by incorporating previously developed codes (e.g., DUST, BLT), modifying 

the current source-term model within RESRAD-OFFSITE, or some other method suggested by the 

contractor and agreed upon by NRC. NRC will provide the source codes (e.g., DUST, BLT) to the 

contractor for incorporation into the RESRAD-OFFSITE code.

Subtask A – The contractor shall develop an approach for incorporating the mechanisms and constraints 

listed above into the current RESRAD-OFFSITE code.

Subtask B – Upon review and approval by NRC staff, the contractor shall incorporate the agreed upon 

approach for expanding the source term model into the RESRAD-OFFSITE software. 

Subtask C – The contractor shall perform verification testing on RESRAD-OFFSITE by developing test 

cases to evaluate the expanded source term capabilities. This includes entering input data, running the 

code, and verifying that the mathematical formulations are captured in the code and that the output correctly 

reflects these formulations.

Subtask D – The contractor shall submit a report for publication as a NUREG/CR consisting of the technical 

basis for the source term model, a User’s Guide, and documentation of the verification.

Subtask E – The contractor shall benchmark the expanded source term model against other codes that 

evaluate similar release mechanisms.

The anticipated level of effort for this task is 1,200 staff hours (or 8.0 staff months). This estimate is higher 

than the original NRC estimate of 600 staff hours (per NRC’s Statement of Work of September 12, 2008) 

based on the following rationale:

1. This task contains a substantial amount of effort (Subtask A through E),

2. This task entails a major increment in development to the existing RESRAD-OFFSITE Code; new 

modules are required to be developed to accommodate the requirements,

3. Interfacing with external codes (e.g., DUST, BLT) is needed to facilitate the task performance,

4. Additional code testing is required to ensure code functionality and maintain proper QA procedures.

In the case that the selected source term models or codes require significant modification of other parts of 

the RESRAD-OFFSITE code (e.g., the transport model needs to be changed from analytical solution to 

numerical solution), then significant increase in effort will be required.

The draft NUREG/CR report of this task (Task 3) is scheduled to appear 12 months after 

approval by NRC of the proposed approach (this letter report).
A-3 

A.3 Considerations for Expanding the Source Term Model

The source term model currently implemented in RESRAD-OFFSITE computes three releases 

from the contaminated zone and also the concentration and distribution of the radionuclides 

within the contaminated zone. The model calculates the atmospheric release of particulates 

due to resuspension and volatiles due to diffusion and evapotranspiration, the surface water 

release due to erosion by runoff water, and the groundwater release due to leaching by 

infiltrating water. The release rates are used by the code to compute the exposure at offsite 

locations, while the concentration and distribution of radionuclides within the contaminated zone 

are used to compute the direct external exposure from the primary contamination as well as any 

exposure from onsite activities.

The integration and implementation of the new methodology to improve the current source term 

model involve the consideration of preserving the functions of the current model. While the 

DUST and BLT codes provide methodologies to simulate groundwater releases from radioactive 

wastes disposal in soils with more realistic considerations of container disintegrations over time 

and transport of radionuclides within the contaminated zone (disposal cell), incorporating the 

methodologies entirely in RESRAD-OFFSITE would disable the functions of calculating 

atmospheric and surface water releases. If release from containerized contamination is to be 

modeled in RESRAD-OFFSITE, the code will need to have two options in order to preserve 

such functions. The first option is to use the RESRAD formulations for uniform contamination in 

uncontained soil and the second option is to consider the release to groundwater from 

containerized contamination. 

Another issue involved in the integration and implementation of the new methodology involves 

consistency and compatibility with the existing model. RESRAD-OFFSITE has transport models 

for both the unsaturated and saturated zones. These models are different from the ones 

included in the DUST and BLT codes. RESRAD-OFFSITE also implements a complicated 

methodology to track ingrowth and decay of radionuclides having multiple progeny radionuclides 

with different decay branches. Because the capability of handling radioactive decay and 

tracking parent and progeny radionuclides during environmental transport are critical in the 

evaluation of subsequent radiation exposures, it is desirable to preserve these functions while 

adding new capabilities to the code. 

Brief overviews and comparisons of the current source term model in RESRAD-OFFSITE and 

those used in DUST and BLT are presented in the following sections. After the overviews and 

comparisons, the pros and cons of the two different approaches (linking vs. inclusion) of 

expanding the current source term model are discussed, along with the proposal of tasks 

required for implementing these approaches. 

A.4 Overview of the Current Source Release Model 

in RESRAD-OFFSITE

The current source term model assumes a homogeneous distribution of radionuclides within an 

initially contaminated soil layer of uniform thickness. It accounts for radiological transformations 

(decay and ingrowth). The leaching of radionuclides in the contaminated layer by infiltration is 

modeled as a first order rate-controlled process occurring over the depth of the contamination. 

The code does not model the transport of the release within the contaminated zone; all of the 

material that is leached at any time is assumed to leave at the bottom of the contamination at 
A-4 

that time. It also considers mixing in a surface layer. The concentration in the mixing layer is 

affected by erosion release to runoff and by leaching. Erosion is modeled using the Universal

Soil Loss Equation. Release to the atmosphere is computed assuming that the clean dust that 

settles on the primary contamination is balanced by the release of an equal amount of 

contaminated dust.

A.5 Treatment of Radiological Transformations

in RESRAD-OFFSITE

The code currently uses the information in International Commission on Radiological 

Protection Publication 38 (ICRP-38) to construct the decay sequences of the radionuclide

being analyzed. The codes in the RESRAD family are being modified to use the information in 

ICRP-107. The user of the code specifies a cutoff half-life. The fate and transport of all 

transformation products that are of a half-life greater than or equal to the user-specified cutoff 

are modeled explicitly. Any transformation product that has a half-life that is less than the cutoff 

is assumed to be in secular equilibrium with its immediate parent whose half-life is greater than 

the cutoff. Depending on the radionuclide being analyzed and the choice of the cutoff half-life, 

the transformation products may form a single chain. If the radionuclide being analyzed or any 

of its progeny transform into multiple radionuclides, then, depending on the cutoff half-life, there 

is the possibility that the transformation sequence forms a complicated mesh or net rather than 

a linear chain. In this event, the RESRAD-OFFSITE code enumerates all of the potential 

transformation threads; each transformation thread starts with the radionuclide being analyzed 

and ends at one of the stable transformation products. The thread fraction associated with each 

transformation thread describes the fraction of the quantity of the radionuclide being analyzed 

that follows that transformation thread. The computational code in RESRAD-OFFSITE 

computes the radiological consequences of each of the transformation threads and combines 

them to model the exposure from the radionuclide being analyzed.

A.6 Impact of Some of the Desired Source Release-togroundwater Mechanisms and Processes on the 

Conceptual Model for the Contaminated Soil Layer 

and on Other Releases

Some of the desired processes and mechanisms for release from a contaminated soil layer to 

groundwater are: (1) advective and diffusive transport by water in the contaminated zone, 

(2) solubility equilibrium release, (3) solubility rate-controlled release, (4) adsorption-desorption 

equilibrium release, and (5) desorption rate-controlled release.

The different groundwater release mechanisms and processes lead to different concentration 

profiles over the depth of the contaminated soil layer. Thus, they also affect the other two 

releases in RESRAD-OFFSITE (release to the atmosphere and release by runoff to a surface 

water body) and the exposure from the primary contamination. 

The impact of the above five desired release mechanisms on the contaminated soil layer is

discussed as follows:

(1) Advective and diffusive transport by water in the contaminated zone. The unsaturated 

zone transport model can be used to model advective and diffusive transport in the 
A-5 

contaminated zone. All of the properties required for the unsaturated zone will have to be input 

for the contaminated zone as well.

(2) Solubility equilibrium release. The equilibrium solubility concentration of all isotopes (both 

stable and radioactive) of an element will change as the chemical conditions of the 

contaminated zone change over the time period of analysis. Information about the inventory of 

all stable and radioactive constituents of the contaminated zone and a whole host of chemical 

properties of the contaminated zone would have to be fed to a chemical equilibrium model to 

model the chemical conditions in the contaminated zone. The chemical equilibrium model 

would need to be run a number of times over the period of analysis. This level of detail is not 

compatible with the level of detail of the rest of RESRAD-OFFSITE. Such a level of detail would 

require a lot of current and future information about the site, also requiring a considerable 

computer resource to model the situation. A simple solubility equilibrium release model would 

use a constant release concentration for the radionuclide, which would be a user input. The 

clean water entering at the top of the contamination would rapidly dissolve the radionuclides 

there to reach the equilibrium concentration. The release would therefore occur at the top of the 

contaminated zone and would pass through the contaminated zone without apparent interaction 

with the soil in that zone; a distribution coefficient of zero would be appropriate for the zone. 

The removal of radionuclides by dissolution from the top would create a clean cover at the top. 

The rate at which the clean cover is created would differ from element to element. The creation 

of this clean cover would have to be tracked if onsite exposure or releases to the atmosphere or 

erosion releases by runoff are to be modeled.

(3) Solubility rate-controlled release. If the time the infiltrating water spends in the 

contaminated layer is shorter in comparison to the time needed to reach solubility equilibrium, 

the release might be governed by the rate of dissolution. The rate of dissolution of all isotopes 

(both stable and radioactive) of an element will change as the chemical conditions of the 

contaminated zone changes over the time period of the analysis. It will also change as the 

concentration in the infiltrating water increases as it percolates deeper into the contaminated 

zone. This level of detail is not compatible with the level of detail of the rest of RESRADOFFSITE. A simple solubility rate-controlled release would use an experimentally measured or 

computationally estimated release rate for the radionuclide, which would be a user input. This 

rate is assumed to be constant over time and over the depth of the contamination. The release 

would therefore occur over the entire depth of the contaminated zone and would pass through 

the contaminated zone without apparent interaction with the soil in that zone, so a distribution 

coefficient of zero would be appropriate for the zone. 

(4) Adsorption-desorption equilibrium release. The adsorption-desorption equilibrium 

concentration of all isotopes (both stable and radioactive) of an element, in the aqueous phase, 

will change as the chemical conditions of the contaminated zone change over the time period of 

the analysis. Information about the inventory of all stable and radioactive constituents of the 

contaminated zone and a whole host of chemical properties of the contaminated zone would 

have to be fed to a chemical equilibrium model to model the chemical conditions in the 

contaminated zone. The chemical equilibrium model would need to be run a number of times 

over the period of analysis. This level of detail is not compatible with the level of detail of the 

rest of RESRAD-OFFSITE. Such a level of detail would require a lot of current and future 

information about the site and would require a considerable computer resource to model the 

situation. A simple adsorption-desorption equilibrium release model would use a constant 

distribution coefficient for the radionuclide, which would be a user input. The radionuclides at 

the top of the contamination would rapidly desorb into the clean water entering the 

contaminated zone to reach the adsorption-desorption equilibrium concentration. The release 
A-6 

would therefore occur at the top of the contaminated zone and would pass through the 

contaminated zone without apparent interaction with the soil in that zone. The user-specified 

distribution coefficient would be applicable for the zone, but there would be no net adsorption by 

the rest of the contaminated zone as the concentration in the liquid phase is what would be in 

equilibrium with the nuclides in the solid phase. The removal of nuclides by desorption from the 

top would create a clean cover at the top. The rate at which the clean cover is created would 

differ from element to element. The creation of this clean cover would have to be tracked if 

onsite exposure or releases to the atmosphere or erosion releases by runoff are to be modeled.

(5) Desorption rate-controlled release. If the time the infiltrating water spends in the 

contaminated layer is short in comparison to the time needed to reach adsorption-desorption 

equilibrium, the release might be governed by the rate of desorption. The rate of desorption of 

all isotopes (both stable and radioactive) of an element will change as the chemical conditions 

of the contaminated zone changes over the time period of the analysis. It will also change as 

the concentration in the infiltrating water increases as it percolates deeper into the contaminated 

zone. This level of detail is not compatible with the level of detail of the rest of RESRADOFFSITE. A simple desorption rate-controlled release would use an experimentally measured 

or computationally estimated desorption rate for the radionuclide, which would be a user input. 

This desorption rate is assumed to be constant over time and over the depth of the 

contamination. The release rate, which is the product of the desorption rate and the 

radionuclide concentration, will vary with time, but will be constant over depth at any time. The 

release would therefore occur over the entire depth of the contaminated zone and would pass 

through the contaminated zone without apparent interaction with the soil in that zone, so a 

distribution coefficient of zero would be appropriate for the zone. This would be similar to the 

current leach rate model, but would need to include transport through the contaminated zone.

A.7 Overview of the Methodologies in DUST and BLT 

The above discussion applies to uncontained contaminated soil. Contaminants in containers 

will not be released until the walls of the container deteriorate and infiltrating water is able to 

penetrate the container. The two candidate codes suggested by the NRC for consideration to 

expand the current source term model evaluate the deterioration of the containers and the 

subsequent release by different release mechanisms. 

A.7.1 DUST Model

The DUST model was developed by Brookhaven National Laboratory (BNL) for the NRC 

(Sullivan 1993). It estimates contaminant release rates from the disposal facility by solving 

contaminant transport equations that describe mass balance in a finite volume along the depth 

of the disposal facility with considerations of convective flow, diffusion and dispersion, 

radiological decay, and release from waste containers [Eq. (1)]. Two models were implemented 

in DUST to obtain numerical solutions to the transport equations – one is called the Multi-Cell 

Mixing Cascade (MCMC) model; the other is called the Finite Difference (FD) model. The 

MCMC model divides the modeled domain into mixing cells along the transport path; 

concentration within each mixing cell is homogeneous, and each cell has the same size and 

transport properties. However, container performance and wasteform release may vary 

between mixing cells. By neglecting dispersion and diffusion, contaminant concentrations in 

each mixing cell are solved analytically and expressed as functions of time. 
A-7 

ingrowth due to radioactiv e decay parent of nuclide.

 source/sin k term used to modelrelease thefrom wasteform and xternal e sources, e.g., 

 adsorbed concentrat theion, mass unit per adsorbed mass solid; theof 

 radioactiv e decay constant;

 Darcy velocity;

 dispersivisity coefficient;

diffusion effective coefficient;

 ;

-diffusion the dispersion coefficient,

 solution concentration;

the moisture c volumetri content region theof (dimensionless);

 soil/water on distributi coefficient;

bulk density solid; theof

;1 

n retardatio coefficient,

where

)()()( (1) 

=

=

=

=

=

=

+=

=

=

=

=

=

+=

=

+−

∂

∂ − ∂∂

∂

∂ = ∂∂

q

S

V

a

D

Va

DD

D

C

K

K

R

R

CV RC q

xx

C D

x

CR

t

D

t

eff

Dt

eff

d

d

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λ

θ

θ

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θ

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θθ λθ

The FD model divides the modeled domain into finite regions called controlled volumes. A 

mass balance is performed for each controlled volume by approximating the derivative terms in 

Eq. (1) using finite differences. This results in a set of coupled algebraic equations that must be 

solved numerically to obtain contaminant concentrations. The FD model is a generalization of 

the MCMC model and permits differences in transport properties in each controlled volume. In 

addition to different transport properties, the FD model also allows the consideration of more 

general wasteform releases.

To solve the transport equation [Eq. (1)], information on fluid flow must be provided (to 

determine the Darcy velocity, VD). A constant infiltration rate is restricted for the MCMC model, 

while for the FD model, it can be a function of time through tabular input. In some cases, the 

gaseous pathway may be important. To consider gas flow, it is necessary to supply an average 

gas advection velocity in order to calculate the gaseous release. 

The source/sink term in Eq. (1) must be evaluated before the transport equation can be solved. 

This involves the consideration of container degradation. In the DUST model, two types of 

container failure are modeled—general failure and localized failure. In a general failure, the 

container prevents water ingress to the waste until failure, at which time the container no longer 

provides a barrier to water flow. The container failure time is provided by the users; for metallic 

containers, it can be estimated as the thickness of the container divided by the time-averaged 

corrosion rate. In addition to general failure, partial/localized failure prior to general failure can 

also be considered. For a partial/localized failure, only a small portion of the container will 
A-8 

permit water access to the wasteform. This reduction of water flow will impact the amount of 

contaminant released and available for transport. Consideration of a partial/localized failure is 

implemented through the calculation of the breached area with the specified number of localized 

failures per unit area of container, total container area, and two coefficients that are related to 

the soil conditions as well as container material. The partial/localized failure can be considered 

only when the FD model is selected. 

Regarding the release of contaminants from the wasteform, four release mechanisms are 

considered in the DUST code. They are (1) solubility-limited, (2) surface wash-off subject to 

partitioning, (3) diffusion, and (4) uniform release (e.g., dissolution). A combination of the four 

release mechanisms can be specified with the fractional amount of mass released by each 

mechanism. The solubility-limited release is modeled by allowing an instantaneous release of 

radionuclides into solution until the limit is reached or the entire inventory is released. Users 

must supply the solubility limit. The surface-rinse model assumes that the radionuclides in the 

wasteform are available for release as soon as water contact occurs. To use this option, a 

partitioning factor, which is an equilibrium ratio relating the amount of contaminant on the 

wasteform to the amount in solution, must be assigned. The diffusion mechanism can be 

considered only when the FD model is selected. Diffusion-controlled release is characterized by 

relatively high release rates at early times, which continually decrease over time. The release 

rate is calculated by analytically solving the diffusion equation corrected for decay, Eq. (2). The 

effective diffusion coefficient is supplied by the users. The uniform release mechanism is 

termed the dissolution mechanism in BLT. Besides the release of activated metals, which 

undergo corrosion in the environment, the release of a wide variety of waste 

streams/wasteforms may be described by this mechanism. To use this mechanism, a fractional 

release rate, which is the fraction of the mass in the wasteform that is released per unit time, 

must be specified. 

 the surface theof wasteform.

 the massflux at the surface theof wasteform ; and

 the massrelase per unit time;

diffusion effective the coefficient;

where

 

 (2) 

 

=

=

=

=

∂

∂ −=

∫ ⋅=

−∇⋅∇=

∂

∂

s

s

s

s

s

x

J

)t(Q

D

x

)x(C DJ

JdS)t(Q

CCD

t

C λ

 

As the waste containers fail, water enters through the breached area and flows out with the 

dissolved contaminants. The container water flow rate is calculated as the Darcy velocity 

multiplied by the ratio of the breached area to the total area. The failed container is treated as a 

mixing cell in which radionuclides released from the wasteform are uniformly mixed. The 

release rate from the container is the product of the water flow rate through the container and 

the mixing cell concentration as calculated based on the various release mechanisms.

Contaminant concentration in the water leaving the disposal area can be obtained by solving 

Eq. (1) with the MCMC or FD model. This concentration multiplied by the water infiltration rate 
A-9 

gives the release rate of radionuclides from the disposal facility, which can be input to RESRADOFFSITE for subsequent evaluation of transport in the underlying soils and groundwater 

aquifer. 

A.7.2 BLT Model

The BLT model (Suen and Sullivan 1990) is very similar to the DUST model. It was also 

developed by BNL for the NRC to calculate the release rates of contaminants from a shallow 

land burial facility. The release mechanisms considered by BLT are the same as those 

considered by DUST, except that the solubility limit considered in DUST is applied as a 

concentration limit for the surface rinse (wash-off) mechanism in BLT. While DUST employs the 

MCMC and FD methods to solve the governing differential equation (Eq. 1) for radionuclide 

transport, BLT employs a two-dimensional (2-D) finite element method to solve the equation. 

The BLT model consists of four individual compartments: (1) water flow through the waste 

disposal structure (typically a trench), (2) corrosion and subsequent breaching of waste 

containers, (3) leaching of radionuclides from the wasteform, and (4) transport of radionuclides 

to the boundary of the disposal structure. For the first and the last compartments, two existing 

2-D finite-element codes, FEMWATER and FEMWASTE, were modified and used. The 

implementation of the second and third compartments was accomplished by the design of two 

FORTRAN subroutines, one called BREACH and the other called LEACH. Together these two 

subroutines generate data for the source term, q, in Eq. (1) needed to solve the transport 

equation.

The BLT code was constructed on a revised version of FEMWASTE. To use BLT, a 

corresponding version of FEMWATER must first be executed with the pertinent geometry, 

hydraulic properties, and boundary conditions. The resulting information in water flow velocity 

and moisture content is then written into a file and used by BLT. Based on parameters input by 

the user (thickness of the waste container, surface area of the container, pitting parameters, 

area scale factor, number of pits per container, general corrosion rate, and clay content, pH, 

and aeration index of the soil) as well as the results from FEMWATER, the BREACH subroutine 

calculates the time and amount (in terms of breached area) of container corrosion, which are 

accessed by the LEACH subroutine to calculate the radionuclide release rate from the waste 

along with the wasteform parameters provided by the user. The BREACH and LEACH 

subroutines were directly incorporated into a modified version of FEMWASTE, so that the 

computed radionuclide release rates feed back directly to the contaminant transport portion of 

the code as time-dependent sources. The modified and extended code is abbreviated as BLT 

to distinguish it from the original FEMWASTE code. 

Three parallel radionuclide release mechanisms are modeled by the subroutine LEACH. They

are (1) the surface rinse process, which releases all of the radionuclides residing on the surface 

of the wasteform limited by their solubility; (2) the diffusion process, which accounts for the 

diffusional transport of radionuclides through the pore water within the wasteform; and (3) the 

dissolution process, which frees the radionuclides in the bulk solid by dissolving the solid phase. 

As mentioned previously, these three mechanisms are the same as the surface wash-off, 

diffusion, and uniform dissolution mechanism, respectively, considered in DUST.
A-10

A.8 Comparison of the Computational Methodology for 

Transport in RESRAD-OFFSITE with the Computational 

Methodologies for Transport in DUST and BLT

RESRAD-OFFSITE uses analytical expressions to model the transport of radionuclides in soil. 

Many of these analytical expressions are too complex to evaluate analytically and are evaluated 

numerically. This computational methodology is compatible with the one-dimensional, analytical 

MCMC model in DUST. Thus, the formulations and coding of MCMC would be best suited for 

inclusion in the RESRAD-OFFSITE code. The one-dimensional nature of the finite-difference 

methodology of DUST is compatible with the one-dimensional transport assumptions of 

RESRAD-OFFSITE in the unsaturated zone. Thus, if the codes are to be linked externally, 

either of the two methods in DUST would be compatible with RESRAD-OFFSITE. The 

analytical groundwater transport model that is currently in RESRAD-OFFSITE requires the 

contaminant input flux into the water table to be uniform over the footprint of the primary 

contamination. It therefore will not be able to use any spatially varying output from the 2-D 

finite-element formulations in BLT. If RESRAD-OFFSITE is to be linked with BLT for the release 

and transport from the initially contaminated area to the water table, it will also be necessary to 

link in a third code to model the transport in the aquifer. Thus, BLT is not a preferred candidate 

for direct linking with or inclusion in RESRAD-OFFSITE at this time.

A.9 Pros and Cons of Linking versus including the Coding 

Directly into the RESRAD-OFFSITE Code

Three approaches are proposed in the next section of this report to add the desired release 

options to the RESRAD-OFFSITE code. The first is to derive and implement the formulations 

for the desired mechanisms of release from contaminated soil. The second and third 

approaches involve using external codes that model these releases from contamination in 

containers. There are two ways of using an external code that already models the releases 

from containerized contamination: (1) link that code (executables) to RESRAD-OFFSITE, or 

(2) incorporate parts of the source code from that code into the source code of RESRADOFFSITE. The pros and cons of linking and including external codes to RESRAD-OFFSITE are 

discussed as follows. 

(1) The RESRAD-OFFSITE interface can be expanded to gather the inputs needed for the 

two candidate codes for computing release. The interface can write the inputs in the format 

required by the candidate codes and then launch it. When the release code has finished 

computations, the interface would read in the output, reformat it in the form needed by 

RESRAD-OFFSITE, and then launch RESRAD-OFFSITE. If the candidate code does not 

provide the full suite of releases (groundwater release, atmospheric release, and erosion 

release) or if it does not provide information about the concentration profile in the primary 

contamination, the exposure from those will not be computed by RESRAD-OFFSITE.

A deep understanding of the formulations of the candidate codes is not necessary, if they are to 

be linked through the RESRAD-OFFSITE interface to the RESRAD-OFFSITE computational 

code. The code is likely to run slowly because of the need to write the output from the release 

code to a file and the need to read the information from the file into RESRAD-OFFSITE. 

Probabilistic analysis will not be available on the inputs that affect the release.
A-11

(2) The source code or the formulations of the candidate code can be integrated into the 

RESRAD-OFFSITE computational code. The container degradation and nuclide release 

mechanisms in the candidate code can be integrated with the (unsaturated zone) transport 

mechanisms in RESRAD-OFFSITE. Parts of the candidate code can be placed with any 

necessary modification into the RESRAD-OFFSITE computational code. It likely will not be 

possible to model release to the atmosphere and the erosion release by runoff because of 

incompatibility between the two models.

The formulation and coding of the candidate codes must be understood in detail in order to 

integrate the formulations of the candidate code with the transport formulations in RESRADOFFSITE and in order to integrate the coding of the candidate code into the RESRAD-OFFSITE 

coding. The code will run faster than the first method (linking code) because the information 

about the releases and concentration profiles will be available within the code (in memory). It 

will be possible to perform a probabilistic analysis on the inputs that define the release.

A.10 Proposed Approaches

The three different approaches proposed here are not mutually exclusive. Different tasks need 

to be performed to implement the different approaches for expanding the existing source term 

model.

A.10.1 Approach 1: Include analytical expressions for the releases to the three 

media (air, runoff, and infiltration) from uncontained contamination in soil 

and the analytical expression for the vertical concentration profile within 

that contamination under the various groundwater release mechanisms.

This approach will include the derivation of analytical formulations to compute all of the releases 

and concentration profile information needed by RESRAD-OFFSITE for uncontained 

contamination in soil with respect to the release mechanisms described in pages A-5 through 

A-7 of this report. The RESRAD-OFFSITE code will then be modified to implement these 

analytical formulations. This would involve deriving formulations for the releases to atmosphere, 

groundwater, and surface runoff and also for the vertical concentration profile in soil and then 

adding code for the formulations.

The advantages and disadvantages of Approach 1 are as follows: (1) The capability of 

evaluating exposure from contamination in soil is enhanced. This also provides a means, if 

Approach 2 and/or 3 are adopted, for estimating exposure directly from the contamination in 

deteriorated containers and from release to the atmosphere from contamination in deteriorated 

containers. (2) The code will run in a reasonable amount of time on currently available personal 

computers. (3) The code will have the capability to perform both probabilistic and sensitivity 

analyses on the inputs that affect the release of the contamination. The probabilistic analysis 

will run in a tolerable amount of time. (4) None of the current capabilities of RESRAD-OFFSITE 

will be lost. (5) Need to derive a number of formulations. (6) Need to code the formulations. 

(7) Need to find a similar code to benchmark against.

A.10.2 Approach 2: Link the one-dimensional finite-difference DUST code to 

RESRAD-OFFSIE via the RESRAD-OFFSITE interface.

This approach will need the executables of the one-dimensional finite-difference DUST code. 

The RESRAD-OFFSITE interface will be expanded to gather all of the necessary inputs, to 
A-12

prepare an input file for DUST, and to execute DUST to produce the release from the 

contaminated layer. The interface will then reformat the DUST output (of the release) to the 

format required by RESRAD-OFFSITE and it will run the RESRAD-OFFSITE computational 

code, flagging it to suppress the source module and to read in the DUST output. 

The advantages and disadvantages of Approach 2 are as follows: (1) Additional coding will be 

needed to reformat the DUST output to the format that is required by RESRAD-OFFSITE, 

especially with regard to the transformation threads. (2) The execution time will likely be longer 

than for the third approach. (3) The code will not have the capability to perform a probabilistic or 

sensitivity analysis on the inputs that affect the deterioration of the container and the release of 

the contamination. (4) There is no need to recode the container degradation and release 

formulations. (5) Transport in the contaminated layer may not be modeled in a manner that is 

consistent with the modeling of transport in the unsaturated and saturated zones. (6) Direct 

exposure from the initial contamination will not be modeled. (7) There will be no release to the 

atmosphere and erosion release by runoff. (8) Only need to verify that the RESRAD-OFFSITE 

interface correctly creates the input file for DUST.

A.10.3 Approach 3: Include the analytical expressions for the deterioration of 

the container and the subsequent release into the RESRAD-OFFSITE 

code.

This approach will need the source code for the MCMC formulations from the DUST code, 

combine the container deterioration and release formulation/coding of DUST with the analytical 

groundwater transport formulations in RESRAD-OFFSITE, and incorporate it in the 

computational code of RESRAD-OFFSITE.

The advantages and disadvantages of Approach 3 are as follows: (1) All relevant 

transformation threads will be considered and combined in RESRAD-OFFSITE without the need 

for additional coding to keep track of the contributions of the threads. (2) The code will run in a 

reasonable amount of time on currently available personal computers. (3) The code will have 

the capability to perform both probabilistic and sensitivity analyses on the inputs that affect the 

deterioration of the container and the release of the contamination. The probabilistic analysis 

will run in a tolerable amount of time. (4) An informed RESRAD-OFFSITE user will be able to 

use this enhanced code. (5) There is no need to recode the container degradation and release 

formulations; it may be necessary to change some of the statements if DUST and RESRADOFFSITE were not written for the same version of FORTRAN or were not compiled with the 

same options. It will be necessary to code the combination for the release with the transport in 

the contaminated zone. (6) Transport in the contaminated layer will be modeled in a manner 

that is consistent with the modeling of transport in the unsaturated and saturated zones. (7) The 

code can be benchmarked against DUST.

If the source code of the MCMC formulations from the DUST code is not available, write the 

code for the analytical formulations in the references [Sullivan et al 1998, Sullivan, T.M., 2001] 

and combine with the groundwater transport formulations in RESRAD-OFFSITE. This likely will 

require more time than in the case where source codes are available.

A.11 Comparison of the Three Approaches

Approach 1, including the formulations of the various release options to uncontained 

contamination, will enhance the code while preserving all of the current capabilities of RESRAD-
A-13

OFFSITE. This will provide more options for release to groundwater while evaluating exposure 

from all of the current exposures pathways in RESRAD-OFFSITE. It will be possible to perform 

probabilistic and sensitivity analyses on all of the new inputs. 

Approach 2, linking of the one-dimensional finite-difference DUST code to RESRAD-OFFSITE, 

is expected to be the easiest to implement. All three approaches will require coding to the user 

interface to allow specification of the additional inputs. In addition, this approach will require 

coding to prepare the input file for DUST from the interface and coding to reformat the output of 

DUST to a form that is useable by RESRAD-OFFSITE. Drawbacks include the inability to 

perform sensitivity and probabilistic analyses and the ability to model only the exposure from the 

release to groundwater. 

Approach 3, incorporating the analytical formulations for container degradation and release into 

RESRAD-OFFSITE, will be more difficult to implement than Approach 2. It will be necessary to 

understand the coding to properly combine it with the transport formulations in RESRADOFFSITE, to make the necessary changes to ensure that the imported coding is compatible with 

the FORTRAN complier used in RESRAD-OFFSITE. While it will be possible to perform 

sensitivity and probabilistic analyses, this approach will also be limited to modeling exposure 

from the release to groundwater. 

It would be preferable to include more than one approach to allow users the flexibility of 

choosing the option appropriate for their site. The preferred proposed task is to implement 

Approach 1 (provide more release options for uncontained contamination in soil). If it is desired 

to include the ability to model the release from containerized contamination in 

RESRAD-OFFSITE, Approach 2 (link the one-dimensional finite-difference DUST code to 

RESRAD-OFFSITE) can be implemented. Some additional funding may be needed to complete 

both Approach 1 and 2. If it is also desirable to be able to perform a sensitivity/probabilistic 

analysis on the new inputs, then Approach 3 will have to be implemented. However, significant 

effort will be required to accomplish this task.

A.12 References and Bibliography for Appendix A

Suen, C.J., and T.M. Sullivan, 1990, BLT: A Source Term Computer Code for Low-level Waste 

Shallow Land Burial, BNL-NUREG-43927, DOE90-008520, Brookhaven National Laboratory, 

Upton, N.Y.

Sullivan, T.M., 1993, Disposal Unit Source Term (DUST) Data Input Guide, NUREG/CR-6041, 

BNL-NUREG-52375, Brookhaven National Laboratory, Upton, N.Y.

Sullivan, T.M., 2001, DUSTMS-D Disposal Unit Source Term: Multiple Species-Distributed 

Failure Data Input Guide, Brookhaven National Laboratory, Upton, N.Y.

Sullivan, T.M., C.R. Kempf, C.J. Suen, and S.M. Mughabghab, 1988, Development of a General 

Model to Predict the Rate of Radionuclide Release (Source Term) from a Low-level Waste 

Shallow Land Burial Facility, BNL-NUREG-40880, DOE88-007047, Brookhaven National 

Laboratory, Upton, N.Y.

Sullivan, T.M., R.J. MacKinnon, R.R. Kinsey, A. Aronson, and M. Divadeenam, 1996, BLT-MS 

(Breach, Leach, and Transport-Multiple Species) DATA INPUT GUIDE, NUREG/CR-6492, BNLNUREG-52509, Brookhaven National Laboratory, Upton, N.Y.

Appendix B 

Additional Benchmarking of Radionuclide 

Release Rates

B-1 

Appendix B 

Additional Benchmarking of Radionuclide

Release Rates

In Chapter 3, the source release rates calculated by the new source term model implemented in 

RESRAD-OFFSITE Version 3 code are compared with those obtained by the DUST-MS code. 

Although the results indicated very good agreement between these two codes, there are some 

minor discrepancies especially when longer decay chain results were compared. In these 

cases, it was difficult to pinpoint for certain exactly what caused the discrepancy. Hence, a third 

code, GoldSim, was employed to compare the release rates using the test cases described in 

Chapter 3. The GoldSim code is commercially available software designed as a generalpurpose Monte Carlo simulator for modeling complex systems in business, engineering, and 

science (GoldSim 2010a,b). It is equipped with a graphical user interface that helps users build, 

link, and dynamically simulate their models. GoldSim provides several specialized extension 

modules that provide additional features or functionality for particular applications. One of 

these, the Contaminant Transport Module for Radionuclides (RT Module), allows users to 

simulate the transport of contaminants in the environment and was used to generate source 

release rates for this comparison. The GoldSim calculations were not carried out for each 

comparison case under different conditions as presented in Chapter 3; however, the limited 

comparison with GoldSim results provides additional perspective to the RESRAD-OFFSITE 

source term model. 

B.1 Release and Environmental Transport Modeling with 

GoldSim 

The GoldSim (2010c) RT module solves for the movement of contaminant mass through the 

environmental system. It simulates the fate of mass within each system. The user can create 

an environmental system by defining a network of transport pathways, which are connected 

through mass flux links. There are two major mass flux links: advective and diffusive. The 

advective mass flux link was used in this comparison. 

In GoldSim, there are three ways to introduce mass into a system: (1) an initial mass that exists 

within the system from the beginning, (2) a continuous addition of mass whose rate can be 

directly specified to one or more pathways in the system, and (3) a discrete addition of mass 

that can be assigned to one or more pathways at specific times. In addition to the above three 

ways, the user can define sources with specific properties and, based on the properties, 

GoldSim computes the release rates of mass over time and feeds them to the pathways that are 

linked to/associated with the sources. 

The GoldSim transport pathways represent physical components through which contaminant 

species can move, such as aquifers, lakes, sediments, surface soil compartments, and the 

atmosphere. The Contaminant Transport Module of GoldSim provides five different pathway 

elements for use in modeling the transport of contaminants through these components. They 

are (1) cell, (2) aquifer, (3) pipe, (4) external, and (5) network elements. Three of these 

elements (cell, aquifer, and pipe) were used to construct source release and transport models 

for comparison with RESRAD-OFFSITE. 
B-2 

The Cell element is mathematically equivalent to a mixing cell and can be used to explicitly 

represent partitioning of contaminants among different phases/media, with the constraint of 

solubility limits.

The Aquifer element is intended to represent a feature that essentially behaves as a fluid 

conduit. It can be used to simulate vertical transport through an unsaturated zone or horizontal 

transport in aquifers, rivers, channels, and pipelines. The Aquifer element can contain only a 

single fluid medium; however, it can also contain a solid medium that can impact transport. The 

Aquifer element internally uses a set of linked Cell elements during the simulation, which are 

subsequently removed at the end of the simulation. In other words, the simulation approach 

used by the Aquifer element is similar to the finite difference approach used by DUST-MS, 

which subdivides the domain of analysis into multiple grids and assumes homogeneity for the 

solid and liquid phase, respectively, within each grid.

The intention for the Pipe element is the same as that for the Aquifer element. Mass is 

considered to enter at one end of the conduit, and travel through and disperse within the conduit 

before exiting at the other end of the conduit. However, the Pipe element uses a Laplace 

transform approach to provide analytical solutions to the equations governing one-dimensional 

advection, longitudinal dispersion, retardation, decay and ingrowth, and exchanges with 

immobile storage zones (e.g., matrix diffusion) as the mass moves through the conduit. This 

simulation approach is similar to that used by RESRAD-OFFSITE, which also solves the 

governing equations analytically.

B.1.1 First Order Release

To simulate the first order release condition with GoldSim, a Source element was used. The 

Source element contains waste materials with defined properties and characteristics. The 

waste materials release radionuclides to the surrounding environment.

The radionuclide inventory was assumed to be embedded in waste materials in some form 

(waste form) without any barrier. The waste form was assumed to degrade with a degradation 

rate of 0.01/yr (1% of the remaining waste form degraded every year) for Case I and Case II 

and with a degradation rate of 0.0011 for Case III. When the degraded waste form was 

exposed to infiltrating water, radionuclides were dissolved and carried to the next element 

through advection. This dissolving/carrying process was simulated by associating a Cell and a 

Pipe element with the Source. The Cell element mixes the radionuclides released from the 

waste form and distributes them to the Pipe element. 

The properties of the Cell element include the contaminant mass input from the source element, 

the volume of the water medium, and the flow rate of water to the Pipe element. The length, 

area, source zone length (to which the radionuclides released from the Cell element were 

distributed), dispersivity, and infill medium (soil) associated with the Pipe element were 

specified. 

Figure B.1 shows the model constructed for the first order release condition with GoldSim.
B-3 

FIGURE B.1 Modeling of a First Order Release with GoldSim

B.1.2 Equilibrium Desorption Release

To model the release of radionuclides under the equilibrium desorption condition with GoldSim, 

the Aquifer element was used when there is no dispersion, while the Pipe element was used 

when dispersion was considered. For both elements, it was assumed that initially, all 

radionuclides were uniformly distributed in a source zone (the initial inventory of radionuclide 

was specified) between the liquid and solid phases in the element. Outflow, equal to the yearly 

infiltration rate, was from the Aquifer or Pipe element to a Sink element, from which the release 

rates were obtained. 

The parameters specified for an Aquifer element were about the same as those specified for a 

Pipe element, which included length, area, dispersivity, and infill medium. For the outflow, only 

advection was considered to remove radionuclides in this comparison.

Figure B.2 shows the model constructed for the equilibrium desorption release condition with 

GoldSim.

Flow of Contaminants

Materials

3.14

16

Activity

Source2

Sink

Cell1 Pipe1

XX

flux_out
B-4 

FIGURE B.2 Modeling of an Equilibrium

Desorption Release with GoldSim

B.1.3 Uniform Release

To model the uniform release condition with GoldSim, a Pipe element was used to obtain the 

release rates. It was assumed that a constant fraction of the initial activity, after being adjusted 

for radioactive ingrowth and decay over time, was released every year from a Source element. 

The source element was associated with the Cell and Pipe elements, just as it was in the set up 

for the first order release condition. Outflow from the Pipe element, equal to the yearly 

infiltration rate, was then linked to a Sink element from which the release rates were obtained. 

B.2 Input Parameters Used with GoldSim Modeling 

The GoldSim models were constructed to obtain results for three comparison cases: Case I, II, 

and III. Input parameters required to run the models were selected so that they either matched 

or corresponded to the values used to run RESRAD-OFFSITE for this comparison. 

For Cases I and II, on the basis of RESRAD-OFFSITE input values, the infiltration rate was set 

at 0.4 m/yr; for Case III, it was kept at 0.1 m/yr. To simulate Cases I, II, and III, radioactive 

species—Tc-99, Cs-137, Po-210, Pb-210, Ra-226, Th-230, and U-234—were created with the 

properties specified in Table B.1. The half-lives and atomic weights were obtained from the 

RESRAD manual (Yu et al. 2001) because GoldSim does not have an inbuilt radionuclide decay 

database.

Material

Aquifer1

3.14

16

Activity

XX

Nuclide

Sink XX

Aquifer_flux
B-5 

TABLE B.1 Properties of the Radioactive Species Considered in GoldSim Modeling

Radionuclide Half-life (yr)1 Decay rate (yr-1)

Atomic weight 

(g/mol)1

Tc-99 2.13E+05 3.2542E-06 98.9

Cs-137 30 2.3105E-02 137

Pb-210 22.3 3.1083E-02 210.1

Po-210 0.37886 1.8296E+00 210.1

Ra-226 1600 4.3322E-04 226.1

Th-230 7.70E+04 9.0019E-06 230.1

U-234 2.45E+05 2.8350E-06 234.1

1 Half-lives and atomic weights were obtained from RESRAD manual (Yu et al. 2001).

 

The soil (a solid medium specified with the material tab) was assumed to have a density of 

1.5 g/cm3

, a porosity of 0.4, and various Kd values as were used for RESRAD-OFFSITE 

modeling. A data element, Activity, with a total activity of 4.5 × 107 pCi (100 pCi/g × 1.5 g/cm3

 × 

30 cm × 10,000 cm2

) for Tc-99, Cs-137, and U-234, respectively, was created. The initial 

activity for each of the U-234 progeny (Th-230, Ra-226, Pb-210, and Po-210) was set to zero. 

The equivalent mass of radioactive species, corresponding to the specified activity, was input as 

the inventory to the Source element to model the first order release and uniform release 

conditions. 

The parameters used for the Aquifer and Pipe elements were (1) length = 0.3 m; (2) area = 

1 m2

; (3) dispersivity = 0.03 m or 0.1 m; (4) number of cells (for the Aquifer element only) = 100, 

(5) source zone length (for the Pipe element only) = 0.3 m; and (6) infill medium = soil. To 

obtain release rates under the equilibrium desorption condition, the initial inventory set for the 

Pipe/Aquifer element was equal to the total activity of 4.5 × 107 pCi as specified for the Activity 

data element. 

Under the uniform release condition, for Cases I and II, the input rate from the Source element 

to the Pipe element was set at 0.01/yr for 100 years, whereas for Case III, the input rate was set 

at 0.0011/yr for 900 years. The rest of the parameters were kept at their default values.

The GoldSim simulations were carried out for a time period of 500 years for Cases I and II, and 

for a time period of 10,000 years for Case III. The radionuclide release rates were reported 

every year for Cases I and II and every five years for Case III. Various dispersivity values, 

along with various soil Kd values, were specified to obtain multiple sets of radionuclide release 

rates for comparison.
B-6 

B.3 Results of Comparison 

B.3.1 Case I: 0.3 m of Tc-99

Case I considers releases from a 0.3-m Tc-99 source. Annual release rates of Tc-99 in terms of 

pCi/yr were calculated over 500 years. The release rates were calculated with no dispersion, as 

well as with different levels of dispersion in the soil column. 

B.3.1.1 No Dispersion

Equilibrium desorption. Figure B.3 compares the RESRAD-OFFSITE results obtained with 

the equilibrium desorption option with the GoldSim results. No dispersion in the soil column was 

considered; however, with the GoldSim modeling, a very small dispersivity of 0.0015 m was 

automatically introduced and used in the simulation. The RESRAD-OFFSITE results were 

plotted with solid lines, whereas the GoldSim results were plotted with dashed lines. Although 

the comparison shows some discrepancy, the agreement between the RESRAD-OFFSITE 

results and the GoldSim results is considered well acceptable. The discrepancy between the 

two could be caused by numerical dispersion introduced in the GoldSim results, as they were 

obtained with an Aquifer element (GoldSim 2010c). 

FIGURE B.3 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I 

Concerning Release from a 0.3-m Tc-99 Source under the Equilibrium 

Desorption Condition with No Dispersion

Uniform release. Figure B.4 compares the RESRAD-OFFSITE results obtained with the 

uniform release option with the GoldSim results. The waste form was assumed to disintegrate 

uniformly with a disintegration fraction of 0.01/yr for 100 years. Good agreement was achieved 

0.00E+00

1.00E+05

2.00E+05

3.00E+05

4.00E+05

5.00E+05

6.00E+05

7.00E+05

8.00E+05

9.00E+05

0 100 200 300 400 500

Release rate (pCi/yr)

Time (yr)

RESRAD-OFFSITE, Kd = 50 cm3/g

RESRAD-OFFSITE, Kd = 88 cm3/g

RESRAD-OFFSITE, Kd = 200 cm3/g

GoldSim, Kd = 50 cm3/g

GoldSim, Kd = 88 cm3/g

GoldSim, Kd = 200 cm3/g
B-7 

between the RESRAD-OFFSITE results and the GoldSim results. The discrepancy could be 

caused by the small dispersivity introduced automatically to the Pipe element in the GoldSim 

simulation.

First Order release. Figure B.5 compares the RESRAD-OFFSITE results obtained with the 

first order release option with the GoldSim results. The waste form was assumed to follow a 

first order decay profile described by a rate constant of 0.01/yr. The GoldSim results almost 

match the RESRAD-OFFSITE results, except at times close to the peaks of the release profiles. 

Again, this discrepancy might be attributable to the small dispersivity introduced automatically to 

the Pipe element in the GoldSim simulation (as indicated by a Run Log warning message in 

GoldSim run).

FIGURE B.4 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I 

Concerning Release from a 0.3-m Tc-99 Source under the Uniform 

Release Condition with No Dispersion

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

3.50E+05

4.00E+05

4.50E+05

5.00E+05

0 100 200 300 400 500

Release rate (pCi/yr)

Time (yr)

RESRAD-OFFSITE, Kd = 0 cm3/g

RESRAD-OFFSITE, Kd = 20 cm3/g

RESRAD-OFFSITE, Kd = 50 cm3/g

RESRAD-OFFSITE, Kd = 88 cm3/g

RESRAD-OFFSITE, Kd = 200 cm3/g

GoldSim, Kd = 0 cm3/g

GoldSim, Kd = 20 cm3/g

GoldSim, Kd = 50 cm3/g

GoldSim, Kd = 88 cm3/g

GoldSim, Kd = 200 cm3/g
B-8 

FIGURE B.5 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I 

Concerning Release from a 0.3-m Tc-99 Source under the First Order 

Release Condition with No Dispersion

B.3.1.2 With Dispersion

Two dispersion levels were considered for the comparison, one with a dispersivity of 0.03 m, 

that is, 1/10 of the thickness of contaminated zone, the other with a dispersivity of 0.1 m. The 

comparison was made only for the equilibrium desorption option. 

Figure B.6 shows the comparison of RESRAD-OFFSITE results obtained with the equilibrium 

desorption option with GoldSim results for a dispersivity of 0.03 m. The agreement is 

considered well acceptable for all of the Kd values assumed, except for the sharp rise and 

decline at the beginning. By increasing the dispersivity to 0.1 m, the RESRAD-OFFSITE results 

still agree fairly well with the GoldSim results (see Figure B.7).

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

3.50E+05

4.00E+05

0 100 200 300 400 500

Release rate (pCi/yr)

Time (yr)

RESRAD-OFFSITE, Kd = 50 cm3/g

RESRAD-OFFSITE, Kd = 88 cm3/g

RESRAD-OFFSITE, Kd = 200 cm3/g

GoldSim, Kd = 50 cm3/g

GoldSim, Kd = 88 cm3/g

GoldSim, Kd = 200 cm3/g
B-9 

FIGURE B.6 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I 

Concerning Release from a 0.3-m Tc-99 Source under the Equilibrium 

Desorption Condition with a Dispersivity of 0.03 m

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

0 100 200 300 400 500

Release rate (pCi/yr)

Time (yr)

RESRAD-OFFSITE, Kd = 50 cm3/g

RESRAD-OFFSITE, Kd = 88 cm3/g

RESRAD-OFFSITE, Kd = 200 cm3/g

GoldSim, Kd = 50 cm3/g

GoldSim, Kd = 88 cm3/g

GoldSim, Kd = 200 cm3/g
B-10

FIGURE B.7 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I 

Concerning Release from a 0.3-m Tc-99 Source Under the Equilibrium 

Desorption Condition with a Dispersivity of 0.1 m

B.3.2 Case II: 0.3 m of Cs-137

Case II considers the release of Cs-137 from a 0.3-m source. Cs-137 was selected for 

comparison because of the shorter half-life of 30 years compared toTc-99’s half-life of 2.13 × 

105 years. The influence of half-life on the release rates would be more pronounced for Cs-137 

compared toTc-99. The comparison was performed only for the no-dispersion condition.

Equilibrium desorption. Figure B.8 compares the RESRAD-OFFSITE results obtained with 

the equilibrium desorption option with the GoldSim results. No dispersion in the soil column was 

specified, although GoldSim automatically introduced a small dispersivity of 0.0015 m to the 

simulation (as indicated by a Run Log warning message in GoldSim run). The RESRADOFFSITE results were plotted with solid lines, while the GoldSim results were plotted with 

dashed lines. The discrepancy between the two could be caused by numerical dispersion 

introduced in the GoldSim results, which were obtained with the use of an Aquifer element. 

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

3.00E+06

3.50E+06

4.00E+06

4.50E+06

0 100 200 300 400 500

Release rate (pCi/yr)

Time (yr)

RESRAD-OFFSITE,

Kd = 50 cm3/g

RESRAD-OFFSITE,

Kd = 88 cm3/g

RESRAD-OFFSITE,

Kd = 200 cm3/g

GoldSim, Kd = 50

cm3/g
B-11

FIGURE B.8 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I 

Concerning Release from a 0.3-m Cs-137 Source under the Equilibrium 

Desorption Condition with No Dispersion

Uniform release. Figure B.9 compares the RESRAD-OFFSITE results obtained with the 

uniform release option with the GoldSim results. The waste form was assumed to disintegrate 

uniformly with a disintegration (dissolution) fraction of 0.01/yr for 100 years. The small 

dispersivity introduced by GoldSim to the Pipe element might be responsible for the small

discrepancy between the GoldSim results and the RESRAD-OFFSITE results. 

First Order release. Figure B.10 compares the RESRAD-OFFSITE results obtained with the 

first order release option with the GoldSim results. The waste form was assumed to disintegrate 

following a first order mathematical form with a constant of 0.01/yr. Excellent agreement was 

achieved between the RESRAD-OFFSITE results and the GoldSim results. 

0.00E+00

1.00E+05

2.00E+05

3.00E+05

4.00E+05

5.00E+05

6.00E+05

7.00E+05

8.00E+05

9.00E+05

0 100 200 300 400 500

Release rate (pCi/yr)

Time (yr)

RESRAD-OFFSITE, Kd = 50 cm3/g

GoldSim, Kd = 50 cm3/g

RESRAD-OFFSITE, Kd = 88 cm3/g

GoldSim, Kd = 88 cm3/g

RESRAD-OFFSITE, Kd = 200 cm3/g

GoldSim, Kd = 200 cm3/g
B-12

FIGURE B.9 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I 

Concerning Release from a 0.3-m Cs-137 Source under the Uniform 

Release Condition with No Dispersion

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

3.50E+05

4.00E+05

4.50E+05

5.00E+05

0 100 200 300 400 500

Release rate (pCi/yr)

Time (yr)

RESRAD-OFFSITE, Kd = 0 cm3/g

GoldSim, Kd = 0 cm3/g

RESRAD-OFFSITE, Kd = 50 cm3/g

GoldSim, Kd = 50 cm3/g

RESRAD-OFFSITE, Kd = 88 cm3/g

GoldSim, Kd = 88 cm3/g

RESRAD-OFFSITE, Kd = 200 cm3/g

GoldSim, Kd = 200 cm3/g
B-13

FIGURE B.10 Comparison of RESRAD-OFFSITE and GoldSim Results for Case I 

Concerning Release from a 0.3-m Cs-137 Source under the First 

Order Release Condition with No Dispersion

B.3.3 Case III: 0.3 m of U-234

The comparison of release rates from a waste form containing U-234 involves comparing the 

release rates of U-234, Th-230, Ra-226, Pb-210, and Po-210, respectively. The progeny 

radionuclides would be formed not only within the waste form, but also during the transport of 

U-234 in the contaminated medium. The Kd values assumed for U-234 and its progeny 

radionuclides were 200, 6,000, 70, 100, and 10 cm3

/g, respectively. 

When progeny radionuclides are formed within the waste form, they are assumed to be 

released through the same mechanism as their parent radionuclide to the surrounding medium. 

In Case III, the water infiltration rate was reduced from 0.4 m/yr as in Cases I and II to 0.1 m/yr. 

Furthermore, under the uniform release condition, a uniform release rate of 0.0011/yr for 

900 years was assumed, and under the first order rate release condition, a rate constant of 

0.0011/yr was assumed.

Figure B.11 compares the release rates of U-234. Excellent agreement was displayed between 

the release rates calculated by RESRAD-OFFSITE and GoldSim under the uniform release 

condition and first order release condition. A slight discrepancy was observed in the release 

rates associated with the equilibrium desorption condition, which may be caused by numerical 

dispersion in the GoldSim results, because an Aquifer element was used in constructing the 

release model. 

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

3.50E+05

4.00E+05

4.50E+05

5.00E+05

0 100 200 300 400 500

Release rate (pCi/yr)

Time (yr)

RESRAD-OFFSITE, Kd = 0 cm3/g

GoldSim, Kd = 0 cm3/g

RESRAD-OFFSITE, Kd = 50 cm3/g

GoldSim, Kd = 50 cm3/g

RESRAD-OFFSITE, Kd = 88 cm3/g

GoldSim, Kd = 88 cm3/g

RESRAD-OFFSITE, Kd = 200 cm3/g

GoldSim, Kd = 200 cm3/g
B-14

Figures B.12, B.13, B.14, and B.15 compare the release rates of Th-230, Ra-226, Pb-210, and 

Po-210, respectively. The RESRAD-OFFSITE results and the GoldSim results match very well 

for all of these decay progenies under all three release conditions.

FIGURE B.11 Comparison of RESRAD-OFFSITE and GoldSim Results for Case III 

Concerning Release of U-234 from a 0.3-m U-234 Source 

with No Dispersion

0.00E+00

1.00E+04

2.00E+04

3.00E+04

4.00E+04

5.00E+04

6.00E+04

0 2000 4000 6000 8000 10000

Release rate (pCi/yr)

Time (yr)

RESRAD-OFFSITE, uniform release

GoldSim, uniform release

RESRAD-OFFSITE, equilibrium desorption

GoldSim, equilibrium desorption

RESRAD-OFFSITE, first order

GoldSim, first order
B-15

FIGURE B.12 Comparison of RESRAD-OFFSITE and GoldSim Results for Case III 

Concerning Release of Th-230 from a 0.3-m U-234 Source 

with No Dispersion

0.00E+00

5.00E+00

1.00E+01

1.50E+01

2.00E+01

2.50E+01

3.00E+01

3.50E+01

4.00E+01

0 2000 4000 6000 8000 10000

Release rate (pCi/yr)

Time (yr)

RESRAD-OFFSITE, uniform release

GoldSim, uniform release

RESRAD-OFFSITE, equilibrium desorption

GoldSim, equilibrium desorption

RESRAD-OFFSITE, first order

GoldSim, first order
B-16

FIGURE B.13 Comparison of RESRAD-OFFSITE and GoldSim Results for Case III 

Concerning Release of Ra-226 from a 0.3-m U-234 Source 

with No Dispersion

0.00E+00

5.00E+01

1.00E+02

1.50E+02

2.00E+02

2.50E+02

3.00E+02

0 2000 4000 6000 8000 10000

Release rate (pCi/yr)

Time (yr)

RESRAD-OFFSITE, uniform release

GoldSim, uniform release

RESRAD, equilibrium desorption

GoldSim, equilibrium desorption

RESRAD-OFFSITE, first order

GoldSim, first order
B-17

FIGURE B.14 Comparison of RESRAD-OFFSITE and GoldSim Results for Case III 

Concerning Release of Pb-210 from a 0.3-m U-234 Source 

with No Dispersion

0.00E+00

2.00E+01

4.00E+01

6.00E+01

8.00E+01

1.00E+02

1.20E+02

1.40E+02

1.60E+02

1.80E+02

0 2000 4000 6000 8000 10000

Release rate (pCi/yr)

Time (yr)

RESRAD-OFFSITE, uniform release

GoldSim, uniform release

RESRAD-OFFSITE, equilibrium desorption

GoldSim, equilibrium desorption

RESRAD-OFFSITE, first order

GoldSim, first order
B-18

FIGURE B.15 Comparison of RESRAD-OFFSITE and GoldSim Results for Case III 

Concerning Release of Po-210 from a 0.3-m U-234 Source 

with No Dispersion

B.4 References for Appendix B 

GoldSim, 2010a, Probabilistic Simulation Environment, User's Guide, Volume 1, GoldSim 

Technology Group, Issaquah, Wash., Version 10.5, Dec.

GoldSim, 2010b, Probabilistic Simulation Environment, User's Guide, Volume 2, GoldSim 

Technology Group, Issaquah, Wash., Version 10.5, Dec.

GoldSim, 2010c, Contaminant Transport Module, User's Guide, GoldSim Technology Group, 

Issaquah, Wash., Version 6.0, Dec.

Yu, C., et al., 2001, User’s Manual for RESRAD Version 6, ANL/EAD-4, Argonne National 

Laboratory, Argonne, Ill.

0.00E+00

2.00E+02

4.00E+02

6.00E+02

8.00E+02

1.00E+03

1.20E+03

1.40E+03

1.60E+03

1.80E+03

0 2000 4000 6000 8000 10000

Release rate (pCi/yr)

Time (yr)

RESRAD-OFFSITE, uniform release

GoldSim, uniform release

RESRAD-OFFSITE, equilibrium desorption

GoldSim, equilibrium desorption

RESRAD-OFFSITE, first order

GoldSim, first order
Appendix C 

Sensitivity Analysis Using Probabilistic 

RESRAD-OFFSITE

E. Gnanapragasam and C. Yu

C-1 

Appendix C

 Sensitivity Analysis Using 

Probabilistic RESRAD-OFFSITE

C.1 Introduction 

The RESRAD-OFFSITE code is an extension of the RESRAD (onsite) code (Yu et al. 2001)2

and has similarly enhanced ability to perform sensitivity and uncertainty (probabilistic) analyses 

(Yu et al. 2007).3 The sensitivity and probabilistic analyses using RESRAD (onsite) code are 

documented in various reports and publications, including Kamboj et al. (2000,4 20055). This 

report describes in detail the different ways in which sensitivity analysis can be performed using 

the probabilistic RESRAD-OFFSITE code. 

Sensitivity analysis attempts to quantify the influence of individual inputs on the predictions of 

the code. Often the influence of one parameter on the resultant predicted dose or risk is also 

dependent on the values of other parameters. The effect of the interaction between parameters 

on the sensitivity of dose to the parameters will be studied in this report.

RESRAD-OFFSITE has three methods for quantifying parameter sensitivity: the singleparameter method, the distributed single-parameter method, and the multiple-parameter 

method. The three methods quantify sensitivity differently and are not directly comparable. 

Some analyze the influence of the input on the predicted dose or risk, whereas others analyze 

its influence on the variability of the predicted dose or risk. Some account for the influence of 

other inputs. 

In almost all cases, the sensitivity of a parameter depends on the values of that parameter and 

the other parameters. Therefore, it is imperative to use site-specific parameter values when 

conducting sensitivity analyses. 

Sensitive parameters for radionuclides are sometimes dependent on the radiation type or 

exposure pathway. For Cs-137 and Co-60, for example, the external radiation pathway is 

usually the dominant pathway, unless there is a shield between the source and receptor. 

Hence, parameters related to the external pathway, such as the indoor and outdoor occupancy 

 

2 Yu, C., et al., 2001, User’s Manual for RESRAD Version 6, ANL/EAD-4, Argonne National Laboratory, 

Argonne, Ill., July.

3 Yu, C., et al., 2007, User’s Manual for RESRAD-OFFSITE Version 2, ANL/EVS/TM/07-1, Argonne 

National Laboratory, Argonne, Ill., June.

4 Kamboj, S., et al., 2000, “Probabilistic Dose Analysis Using Parameter Distributions Developed for 

RESRAD and RESRAD-BUILD Codes,” NUREG/CR-6676, ANL/EAD/TM-89, prepared by Argonne 

National Laboratory, Argonne, Ill., for U.S. Nuclear Regulatory Commission, Washington, D.C.

5 Kamboj, S., et al., 2005, “Deterministic vs. Probabilistic Analyses to Identify Sensitive Parameters in 

Dose Assessment Using RESRAD,” Operational Radiation Safety, supplement to Health Physics, 

pp. S104–S109, May.
C-2 

factors, are usually sensitive parameters for these radionuclides (Kamboj 2000)3

. A sensitivity 

analysis using one of the three methods described in this report will identify the sensitive 

parameters.

Sensitivity analysis also helps understand how the inputs are used by RESRAD-OFFSITE to 

predict dose and risk, and gives insight into the different methods of quantifying sensitivity. 

Sensitivity analysis is often a difficult subject for many of the professionals who perform dose or 

risk analysis. For this reason, this report contains many examples and is more in the form of a 

tutorial than a technical report. The case studies, and especially the in-depth look at the output 

from them, are written in first- and second-person problem-solving form rather than in the 

traditional style of a technical report. 

There are three different ways of performing sensitivity analysis in RESRAD-OFFSITE:

• Single-input sensitivity analysis using the F9 key—referred to as the three-point singleinput sensitivity analysis because it compares code predictions for three discrete values 

of the input being studied (see Section C.2.1).

• Single-input sensitivity analysis using the Shift-F8 key—referred to as the distributed 

single-input sensitivity analysis because it uses the probabilistic module to generate 

predictions for many values of the input being studied (see Section C.2.2). 

• Multiple-input sensitivity analysis using the Shift-F8 key—referred to as multiple-input 

sensitivity analysis using probabilistic feature of the code because it uses the 

probabilistic module to simultaneously analyze the sensitivity of multiple inputs (see 

Section C.4).

Section C.3 takes a deeper look at the case study in Section C.2. It also illustrates the methods 

commonly used to compare the influences of inputs. The reader is led through a natural 

progression from single-input sensitivity analysis to two- and three-input sensitivity analyses to 

multiple-input sensitivity analysis. Multiple-input sensitivity analysis is presented in Section C.4.
C-3 

C.2 Single-input Sensitivity Analysis 

C.2.1 Three-point Single-input Sensitivity Analysis

In the three-point single-input method of sensitivity analysis, all inputs other than the one being 

studied are held at their deterministic or point values. Three simulations of the code are 

performed, one with the input of interest at its point value (x), the second with it at a specified 

multiple of the original point value (mx), and the third with it at a specified fraction of the original 

point value (x/m). The same factor (m) is used to obtain the multiple and the fraction. Temporal 

predictions of the three simulations are shown on the same plot. The plotting program does not 

compute a numerical measure of sensitivity, but the numbers needed to compute sensitivity 

measures are in the data used by the plotting program. 

C.2.1.1 Performing a Three-point Single-input Sensitivity Analysis

The procedure for performing a three-point single-input sensitivity analysis in RESRADOFFSITE is listed below. A case study is given in Section C.2.1.2. 

1. Prepare an input file that contains site-appropriate deterministic values for all inputs. 

Assigned values must be appropriate for the site because the sensitivity of the predicted 

dose to an input depends on the values of all of the other inputs.

2. Place the cursor on the input upon which you want to perform three-point single-input 

sensitivity analysis. Select the input to be analyzed using the Form Options menu, the 

sensitivity icon on the tool bar, or, most conveniently, the F9 function key on the key 

board. This causes the Sensitivity Analysis Range form to pop up.

3. Select or type in the factor by which you want to modify (multiply, divide) the point value 

of the input in the Sensitivity Analysis Range form. Then click the OK button on that 

form.

4. Repeat Steps 2 and 3 for the other inputs of interest. Up to 25 inputs can be selected for 

sensitivity analysis in an input file.

5. Run the input file. The computational code will first perform a simulation with all inputs 

at their deterministic point values. It then continues seamlessly to perform a pair of 

simulations for the first input selected for sensitivity analysis. The first simulation of the 

pair is performed with the input in question set to a “high” value. The high value is equal 

to the deterministic point value multiplied by the factor specified in Step 2. The second 

of the pair is performed with the input in question set to a “low” value. The low value is 

equal to the deterministic point value divided by the factor specified in Step 2. RESRADOFFSITE then resets the input of interest to its original deterministic value in preparation 

for the next sensitivity analysis. The computational code will continue to perform 

additional pairs of simulations for each input chosen. 

6. A text report summarizing the deterministic doses is displayed when the simulations are 

completed. This text report does not contain information about the three-point singleinput sensitivity analysis. Close this report and view the deterministic graphics report. 

Click the Option button at the lower left side of the graphics pane to display the 

sensitivity output. Sensitivity of the output (predicted dose, risk, or concentration) to 
C-4 

each of the selected inputs can be viewed in turn using the dropdown selection box that 

is immediately below the option button.

C.2.1.2 Case Study

This simple illustration of the procedure for three-point single-input sensitivity analysis outlined 

in Section C.2.1.1 will allow users to try it for themselves if they wish to. For simplicity, it is 

assumed that most of the preloaded RESRAD-OFFSITE input values are site-appropriate. 

The simple scenario used for this case study is defined below. 

• The preloaded values of RESRAD-OFFSITE are assumed to be appropriate for the 

simple hypothetical scenario, except for the following: 

− Initial concentrations of 1 pCi/g for 210Pb, 210Po, and 226Ra in the primary 

contamination;

− Leach rates of 0.002 per year for 210Pb, 210Po, and 226Ra;

− Distribution coefficients in the unsaturated and saturated zones of 7 ml/g for Ra and 

10 ml/g for Pb;

− 100-m long, 100-m wide, 2-m thick contaminated soil;

− Hydraulic conductivity of 700 m/yr in saturated zone.

• Three-point single-input sensitivity analysis is to be performed on saturated hydraulic 

conductivity in the saturated zone using a modification factor of 3. 

The reader is assumed to be familiar with RESRAD-OFFSITE; therefore, we do not describe 

how to set up the site-appropriate point values in the code. Name this file “Three Point Single 

Input Sensitivity.ROF.”

The hydraulic conductivity in the saturated zone can be selected for sensitivity analysis after 

specifying the site-appropriate point value for that input. Press the F9 function key while the 

cursor is still in the input box for hydraulic conductivity in the saturated zone. The Set Sensitivity 

Analysis Range form pops up, as shown in Figure C.1. Click on the option button 

corresponding to a multiplication and division factor of 3. The three values that will be used to 

perform sensitivity analysis on the hydraulic conductivity in the saturated zone will be displayed 

in this form. 

The first simulation will use the site-appropriate values that were specified for all the inputs, 

including the 700 m/yr value for saturated hydraulic conductivity in the saturated zone. The 

second simulation will use a value of 2100 m/yr (= 700 × 3) for the saturated hydraulic 

conductivity and the site-appropriate values for all the other inputs. The third simulation will use 

a value of 233.3 m/yr (= 700 ÷ 3) for saturated hydraulic conductivity in the saturated zone and 

site-appropriate values for all the other inputs. All three simulations will be performed by the 

computational code when the “Run” command is issued. The Parent dose text report 

(summarizing the predicted dose at various times in the future) is displayed at the end of the 

run. This report does not contain results for the sensitivity analysis. Close the text report and 

open the deterministic graphics report to view the three-point single-input sensitivity output.
C-5 

FIGURE C.1 Specifying Three-point Single-input Sensitivity Analysis for the 

Input of Interest

The sensitivity graphics can be viewed by clicking on the option button on the bottom left of the 

graphic window. The resulting screen is shown in Figure C.2. The dropdown box lists all the 

inputs upon which sensitivity analyses were performed. In the example shown, just one input 

was selected for sensitivity analysis. The three temporal plots show that the peak predicted 

dose increases as the hydraulic conductivity decreases from 2100 m/yr through 700 m/yr to 

233.3 m/yr. 

One measure of sensitivity is the ratio between the fractional change in peak predicted dose 

and the fractional change in the value of the input. The data used to plot the three curves can 

be saved and viewed using the menu commands or toolbar icons. The peak predicted doses 

for the three simulations were found to be 11.6, 21, and 41.9 mrem/yr. The normalized 

sensitivity of predicted dose to hydraulic conductivity in the saturated zone over the range 

233.33 to 2100 m/yr is then computed as:

The sensitivity is negative because the predicted dose decreases as the value of the input 

increases. 

It is also possible to compute forward and backward sensitivities. The sensitivities of predicted 

dose to hydraulic conductivity in the ranges 700 to 2100 m/yr (forward sensitivity) and 233.3 to 

700 m/yr (backward sensitivity) are computed as follows:

71.0)6.1( 75.26

3.30

2/)21003.233(

21003.233

2/)6.119.41(

6.119.41

−=−÷=

+

− ÷

+

− Sensitivity = 
C-6 

Backward Sensitivity = 66.0)1( 45.31

9.20

2/)7003.233(

7003.233

2/)219.41(

219.41

−=−÷=

+

− ÷

+

− 

Forward Sensitivity = 58.0)1( 3.16

4.9

2100700( 2/)

2100700

2/)6.1121(

6.1121

−=−÷=

+

− ÷

+

− 

The three sensitivity calculations show that the sensitivity of predicted dose to hydraulic 

conductivity in the saturated zone is not uniform over the range 233.33 to 2100 m/yr. While the 

results give an indication of the variability of the sensitivity, more simulations would be needed 

to demonstrate how the sensitivity changes over the range. This will be investigated in 

distributed single-input sensitivity analysis (Section C.2.2). 

The temporal plots for each of the three simulations appear to be the sum of two curves that are 

offset in time. They are, in fact, the sum of predicted doses from 15 exposure and transport 

pathways, six of which make a visually significant contribution, as seen in Figure C.3. 

Sensitivity plots for the six exposure pathways are shown in Figures C.4 through C.9.

FIGURE C.2 Viewing Sensitivity Graphics
C-7 

FIGURE C.3 Identifying Significant Exposure Pathways 

for the Base Case

FIGURE C.4 Sensitivity of Predicted Dose from Drinking Water
C-8 

FIGURE C.5 Sensitivity of Predicted Dose from Ingestion of Vegetables 

(Waterborne Contamination)

FIGURE C.6 Sensitivity of Predicted Dose from Ingestion of Meat 

(Waterborne Contamination)
C-9 

FIGURE C.7 Sensitivity of Predicted Dose from Ingestion of Milk 

(Waterborne Contamination)

FIGURE C.8 Sensitivity of Predicted Dose from Direct Exposure 

to Waterborne Accumulation in Soil
C-10

FIGURE C.9 Sensitivity of Predicted Dose from Ingestion of Fish

The exposure pathways shown in Figures C.4 through C.8 occur as a result of the use of 

contaminated well water, while that shown in Figure C.9 occurs from contamination of a surface 

water body. The plots shown in Figures C.4 through C.8 all begin to rise at about the same 

time. The time of the peak predicted dose from these pathways depends on the relative 

contributions directly from well water and indirectly from the accumulation in soil following 

irrigation with well water. The predicted doses from the five pathways decrease with increasing 

hydraulic conductivity in the saturated zone. 

The plots in Figure C.9 start rising later than those in Figures C.4 through C.8 because of the 

longer distance to the surface water body. The predicted dose from this pathway rises with 

increasing hydraulic conductivity in the saturated zone. The higher predicted dose from the 

ingestion of fish in conditions of high hydraulic conductivity, as contrasted with the lower 

predicted dose from the five well-water-based pathways in conditions of high hydraulic 

conductivity, is investigated in Section C.3.

C.2.2 Distributed Single-input Sensitivity Analysis

In this method of analysis, all the inputs other than the one being studied are held at its 

deterministic or point value. Many simulations of the code are performed, each with the input of 

interest set to a (different) sample value obtained from the distribution specified for that input. 

The analyst specifies the number of simulations to be performed. A scatter plot shows the 

variation of peak predicted dose (or risk) with the variable of interest. Because of the large 

number of simulations that are typically performed, temporal predictions for all of the simulations 

are not shown on the same plot. It is, however, possible to view the temporal plots of each 

simulation individually, though this is not typically done because of the larger number of 

simulations. Flag the code prior to the run to save the plot data, if you want to view the temporal 

plot of each simulation. 
C-11

C.2.2.1 Performing a Distributed Single-input Sensitivity Analysis

The procedure for performing a distributed single-input sensitivity analysis in RESRADOFFSITE is as follows.

1. Prepare an input file that contains site-appropriate deterministic values for all inputs. 

Because the sensitivity of the predicted dose to an input of interest depends on the 

values of all of the other inputs, it is imperative that all inputs be assigned values that are 

appropriate for the site.

2. Place the cursor on the input upon which you want to perform distributed single input 

sensitivity analysis. Select the input of interest using the Shift-F8 function key. The 

“Parameter distributions” tab of the Uncertainty and Probabilistic Analysis form will 

appear.

3. Choose a distribution type. RESRAD-OFFSITE defaults to a uniform distribution, but in 

some cases it might be prudent to change this. Select a log-uniform distribution if the 

study range spans orders of magnitude. A continuous linear distribution might also be 

appropriate in some circumstances (Section C.3.5.2). Specify the lower and upper limits 

of the study range; click the Update Parameter Stats and Distribution button to save 

these limits. 

4. Do not select more than one input. Go to the “Sample specifications” tab of the 

Uncertainty and Probabilistic Analysis form and specify the desired number of 

observations. Set the number of repetitions to 1; repetitions are not necessary because 

the output of interest is a scatter plot and a distribution is being specified on only one 

input.

5. Run the input file. The computational code will first perform a deterministic simulation 

with all inputs at their deterministic point values. It then continues seamlessly to perform 

the specified number of probabilistic simulations for the input of interest. 

6. A text report summarizing the deterministic doses is displayed when the simulations are 

completed. This text report does not contain information about the distributed sensitivity. 

7. Close this report and view the probabilistic graphics. This displays the “Step by step 

analysis” tab of the Uncertainty and Probabilistic Analysis form. Select “View scatter 

plots of output vs. input.” The scatter plot shows how the output (peak predicted dose or 

peak risk) varies with the selected input.

C.2.2.2 Case Study

The simple scenario from Section C.2.1.2 is continued here. For simplicity, it is assumed that 

most of the preloaded RESRAD-OFFSITE input values are site-appropriate. The example 

scenario is restated here for easy reference:

• Name the file “Distributed Single Input Sensitivity.ROF.”

• The preloaded values are assumed to be appropriate for this example scenario, except 

for the following: 
C-12

− Initial concentration of 1 pCi/g each of 210Pb, 210Po, and 226Ra in the primary

contamination;

− Leach rates of 0.002 per year for 10Pb, 210Po, and 226Ra;

− Distribution coefficients in the unsaturated and saturated zones of 7 ml/g for Ra and 

10 ml/g for Pb;

− 100-m long, 100-m wide, 2-m-thick contaminated soil;

− Hydraulic conductivity of 700 m/yr in saturated zone.

• Distributed single-input sensitivity analysis is to be performed on saturated hydraulic 

conductivity using a uniform distribution over the range of 200 to 2000 m/yr. 

The hydraulic conductivity in the saturated zone can be selected for distributed sensitivity 

analysis after specifying the site-appropriate point value for the input of interest. Press the 

Shift-F8 function key while the cursor is still in the input box for hydraulic conductivity in the 

saturated zone. The “Parameter distributions” tab of the Uncertainty and Probabilistic Analysis 

form pops up, as shown in Figure C.10. 

Specify a minimum of 200 and a maximum of 2000 for limits of the uniform distribution for the 

hydraulic conductivity in the saturated zone; click the “Update parameter stats and distribution” 

button to save these limits. Go to the “Sample specification” tab of the Uncertainty and 

Probabilistic Analysis form. Set the number of observations to 100 and the number of 

repetitions to 1, instructing the code to sample 100 values uniformly in the interval of 200 to 

2000, and to perform 100 simulations using those sample values for hydraulic conductivity in the 

saturated zone. Repetitions are needed when distributions are specified for more than one 

input or when the output of interest is the cumulative distribution function of predicted dose (or 

risk). 

When performing a distributed single-input sensitivity analysis, the output of interest is the 

scatter plot between predicted dose (or risk) and the single-input for which a distribution is 

specified. All 100 simulations will be performed by the computational code when the “Run” 

command is issued. The text report (Parent dose) summarizing the deterministic dose at 

various times in the future is displayed at the end of the run. This report does not contain 

results of the distributed single-input sensitivity analysis. Close the report and view the 

probabilistic graphics. 
C-13

FIGURE C.10 Specifying Distributed Sensitivity Analysis on an Input

The scatter plot showing the sensitivity can be viewed by clicking on the “View scatter plots of 

output vs. input” button in the middle of the “Step by step analysis” tab shown in Figure C.11. 

The scatter plot of peak predicted dose from all pathways against hydraulic conductivity in the 

saturated zone for this example is shown in Figure C.12. The peak predicted dose increases as 

the conductivity increases from 200 to about 260 m/yr. The peak predicted dose then 

decreases rapidly as conductivity increases from about 260 to about 750 m/yr. A noticeable 

break in the curve occurs at a hydraulic conductivity of around 750 m/yr. The peak predicted 

dose continues to decrease as the hydraulic conductivity increases from about 750 to 

2000 m/yr, but at a slower rate. The data used to plot this curve are in the peak predicted dose 

data file (extension .pds)—“Distributed Single-Input Sensitivity.pds” in this case. These data 

can be used to compute the sensitivity between each pair of consecutive sample points, if 

necessary (see Section C.2.3). 

The scatter plots of peak predicted doses from the different exposure pathways against the 

hydraulic conductivity in the saturated zone can be viewed by clicking the up/down arrows in the 

probabilistic graphics output form. These are shown in Figures C.13 through C.18. The first 

five plots shown have similar shapes because they show the predicted doses from exposure 
C-14

pathways that involve contaminated well water: ingestion of well water (Figure C.13), ingestion 

of vegetables irrigated with well water (Figure C.14), ingestion of meat (Figure C.15) and milk 

(Figure C.16) from livestock that consumed well water and feed that was irrigated with well 

water, and external radiation from land irrigated with well water (Figure C.17). The peak 

predicted doses from these five pathways increase as the conductivity increases from 200 to 

about 260 m/yr. The predicted peak dose then decreases, rapidly at first and then at a 

continuously decreasing rate, as conductivity increases from about 260 to 2000 m/yr. 

The plot showing the influence of hydraulic conductivity on peak predicted dose from the 

ingestion of fish from the surface water body (Figure C.18) has a different shape than the plots 

of the five exposure pathways involving contaminated well water. The peak predicted dose from 

the ingestion of fish increases as the hydraulic conductivity in the saturated zone increases from 

200 to 2000 m/yr. The rate of increase is very rapid at first; it then diminishes as the hydraulic 

conductivity increases. The reasons for the differences in the shapes of the scatter plots of the 

pathways contaminated by the two sources of water are discussed in Section C.3. 

The plot of the peak predicted dose from all pathways (Figure C.12) is similar to the plot of the 

peak predicted dose from the five well-water-dependent pathways in the hydraulic conductivity 

range of 200 to about 750 m/yr. In fact, the data in the peak predicted dose data file (with 

filename extension .pds) and the probabilistic input sample data file (with filename extension 

.pin) indicate that those five pathways peak around the same time and that the peak predicted 

dose from all pathways is essentially the sum of the peak predicted doses from the five 

pathways, when the hydraulic conductivity ranges from 200 to about 750 m/yr (Table C.1). As 

the hydraulic conductivity increases beyond 750 m/yr, the peak predicted dose from all 

pathways exceeds the sum of the peak predicted doses from the five well-water-dependent 

pathways, but is less than the sum of the peak predicted doses for the six pathways listed in 

Table C.1. When the hydraulic conductivity is in the range 750 to 2000 m/yr, the peak predicted 

dose from all pathways occurs significantly later than for the five well-water-dependent 

pathways and is closer to the time of the peak predicted dose from the ingestion of fish. 

 FIGURE C.11 Viewing the Output of a Distributed Sensitivity Analysis

on an Input
C-15

FIGURE C.12 Variation of Peak Predicted Dose with Hydraulic 

Conductivity in the Saturated Zone

FIGURE C.13 Variation of Peak Predicted Dose from Drinking Water 

with Hydraulic Conductivity in the Saturated Zone
C-16

FIGURE C.14 Variation of Peak Predicted Dose from Ingestion 

of Vegetables (Waterborne Contamination) 

with Hydraulic Conductivity in the Saturated Zone

FIGURE C.15 Variation of Peak Predicted Dose from Ingestion of Meat 

(Waterborne Contamination) with Hydraulic Conductivity 

in the Saturated Zone
C-17

FIGURE C.16 Variation of Peak Predicted Dose from Ingestion of Milk 

(Waterborne Contamination) with Hydraulic Conductivity 

in the Saturated Zone

FIGURE C.17 Variation of Peak Predicted Dose from Direct 

Exposure to Waterborne Accumulation in Soil 

with Hydraulic Conductivity in the Saturated Zone
C-18

FIGURE C.18 Variation of Peak Predicted Dose from Ingestion of 

Fish with Hydraulic Conductivity in the Saturated Zone
C-19

TABLE C.1 Peak Predicted Doses and Times of Peak Predicted Doses From Different Exposur

Hydraulic 

Conductivity, m/yr

Simulation 

No.

All Pathways Water Ingestion

Plant 

(Water release)

Meat

(Water release)

Milk 

(Water release)

External Groun

(Water release

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/

yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time 

Peak

213.727448 65 39.872 317.871 23.0338 315.43 10.8382 319.824 2.37075 316.895 2.22203 319.336 1.47254 368.

231.355759 37 41.7195 299.805 24.1107 296.875 11.3347 301.758 2.47896 298.34 2.32962 300.781 1.54515 350.

237.567261 97 42.1328 293.945 24.3528 291.016 11.4451 295.898 2.50294 292.48 2.35426 294.922 1.56177 343.

258.008759 6 42.7195 276.855 24.7023 273.926 11.5981 279.297 2.53599 275.391 2.39195 277.832 1.58717 326.

276.414276 17 42.4395 263.672 24.5488 260.742 11.5167 266.113 2.51785 262.207 2.38025 264.648 1.57916 312.

299.234406 72 41.4044 249.512 23.9594 246.582 11.2296 251.953 2.45471 248.047 2.32655 250 1.54265 297.

319.006073 80 40.1579 238.77 23.2454 235.84 10.8865 241.699 2.37948 237.793 2.25982 239.258 1.49729 286.

328.45105 83 39.5027 234.375 22.8695 230.957 10.7066 236.816 2.34007 232.91 2.22438 234.375 1.4732 281.

346.223358 9 38.2211 226.074 22.1332 223.145 10.3552 229.004 2.26314 225.098 2.15468 226.563 1.4258 272.

374.722992 45 36.1491 214.844 20.9414 211.914 9.78806 217.773 2.13905 213.867 2.04121 214.844 1.34862 261.

386.024292 25 35.3473 210.938 20.4799 207.52 9.56881 213.867 2.0911 209.961 1.9971 210.938 1.31863 257.

411.100555 16 33.6372 203.125 19.4951 199.707 9.10153 206.055 1.98896 202.148 1.90276 202.148 1.25449 249.

422.747528 78 32.8804 199.707 19.0591 196.289 8.89485 202.637 1.94381 198.73 1.8609 198.73 1.22604 245.

445.124115 95 31.498 193.359 18.2624 189.941 8.51745 196.777 1.86139 192.383 1.78427 192.383 1.174 238.

462.823547 57 30.47 188.965 17.6697 185.547 8.23695 192.383 1.80015 187.988 1.72716 187.988 1.13525 234.

481.19635 1 29.4619 185.059 17.0883 181.152 7.96205 187.988 1.74015 184.082 1.67107 183.594 1.09723 229.

504.701752 93 28.2568 179.688 16.3932 176.27 7.63349 183.105 1.66846 179.199 1.60388 178.223 1.05174 225.

513.378479 42 27.8342 178.223 16.1493 174.805 7.51825 181.641 1.64332 177.246 1.58028 176.758 1.03578 223.

529.437073 77 27.0822 175.293 15.7153 171.875 7.31336 178.223 1.59863 174.316 1.53827 173.34 1.00739 220.

551.966003 87 26.0891 171.387 15.1421 167.48 7.04288 174.316 1.53964 170.41 1.48271 169.434 0.969903 216.

565.29834 91 25.5335 168.945 14.8213 165.527 6.89156 172.363 1.50664 168.457 1.45157 166.992 0.948925 214.

579.406982 49 24.9692 166.504 14.4954 163.086 6.73796 169.922 1.47315 166.016 1.41994 164.551 0.927634 211.

599.724426 64 24.1979 163.574 14.0498 160.156 6.52805 166.992 1.42738 163.086 1.37665 161.621 0.898532 208.

618.315735 55 23.5308 161.133 13.6642 157.715 6.34658 164.551 1.3878 160.645 1.33915 158.691 0.87337 206.

638.884766 26 22.8336 158.691 13.2612 154.785 6.15702 162.109 1.34646 158.203 1.29994 156.25 0.847086 203.

652.01825 92 22.4087 156.738 13.0155 153.32 6.04152 160.645 1.32127 156.25 1.27601 154.297 0.831076 202.

676.928101 11 21.6444 153.809 12.5733 150.391 5.83386 157.715 1.27598 153.809 1.23293 151.367 0.802277 199.

692.366821 12 21.1959 152.344 12.3137 148.926 5.71202 155.762 1.2494 151.855 1.20761 149.902 0.785383 197.
C-20

TABLE C.1 (Continued)

Hydraulic 

Conductivity, m/yr

Simulation 

No.

All Pathways Water Ingestion

Plant 

(Water release)

Meat

(Water release)

Milk 

(Water release)

External Groun

(Water release

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time 

Peak

709.79541 68 20.711 150.391 12.033 146.973 5.58039 154.297 1.22068 150.391 1.18023 147.949 0.767123 195.

732.122803 74 20.1215 148.438 11.6914 145.02 5.42032 151.855 1.18577 147.949 1.1469 145.508 0.744923 193.

752.093811 60 19.7361 254.883 11.4017 143.066 5.28466 150.391 1.15616 146.484 1.1186 143.555 0.726096 191.

765.409973 98 19.568 251.953 11.2162 141.602 5.19785 148.926 1.13722 145.02 1.10047 142.578 0.714051 190.

793.082581 30 19.2284 245.605 10.8496 139.648 5.02635 146.973 1.09981 143.066 1.06461 140.137 0.690241 188.

809.679382 15 19.031 242.188 10.6409 138.184 4.92878 145.508 1.07852 141.602 1.04419 138.672 0.676693 187.

817.123596 38 18.9441 240.723 10.5499 137.695 4.88628 145.02 1.06925 141.113 1.03528 138.184 0.670789 187.

839.900635 52 18.6834 236.328 10.2808 136.23 4.76059 143.555 1.04182 139.648 1.00893 136.23 0.653327 185.

863.278381 54 18.4245 231.934 10.0187 134.277 4.63817 142.09 1.01512 138.184 0.983236 134.766 0.636314 183.

871.421997 7 18.3363 230.957 9.93053 133.789 4.59703 141.602 1.00614 137.695 0.974592 134.277 0.630595 183.

889.124023 96 18.1482 227.539 9.74419 132.813 4.51006 140.137 0.987177 136.23 0.956318 132.813 0.618502 182.

903.143127 86 18.0025 225.586 9.60154 131.836 4.44349 139.648 0.972656 135.742 0.942317 131.836 0.609244 181.

930.153381 22 17.7299 221.191 9.33833 130.371 4.3207 137.695 0.945882 133.789 0.916476 130.371 0.59216 179.

938.296143 43 17.6496 219.727 9.26178 129.883 4.28498 137.207 0.938094 133.301 0.908956 129.883 0.587189 179.

967.092041 50 17.3734 215.82 9.00124 128.418 4.16347 135.742 0.911606 131.836 0.883348 128.418 0.570275 177.

980.122009 63 17.252 213.867 8.88818 127.441 4.11074 135.254 0.900114 131.348 0.872234 127.441 0.562933 177.

997.151611 35 17.0966 211.426 8.74471 126.953 4.04382 134.277 0.885532 130.371 0.85812 126.465 0.553615 176.

1013.97479 39 16.9465 209.473 8.6074 125.977 3.97975 133.301 0.871568 129.395 0.844602 125.977 0.544691 175.

1039.91357 5 16.7223 206.055 8.40464 124.512 3.8852 132.324 0.850973 128.418 0.824648 124.512 0.531519 174.

1048.34497 84 16.6513 205.078 8.341 124.512 3.8555 131.836 0.844504 127.93 0.818377 124.023 0.527381 173.

1065.34814 36 16.51 203.125 8.21518 123.535 3.79678 131.348 0.831716 127.441 0.805977 123.535 0.519201 173.

1085.15088 70 16.3487 200.684 8.07269 122.559 3.73032 130.371 0.817244 126.465 0.79194 122.559 0.509939 172.

1111.19568 76 16.1444 198.242 7.89407 121.582 3.64695 129.395 0.799094 125.488 0.774325 121.582 0.498322 171.

1119.3811 8 16.0814 197.266 7.83935 121.582 3.62145 128.906 0.793541 125 0.768937 121.094 0.494766 171.

1152.9635 20 15.8303 193.848 7.62331 120.117 3.52059 127.441 0.771584 123.535 0.74762 119.629 0.480709 169.

1167.8158 58 15.7231 192.383 7.53194 119.629 3.47795 126.953 0.762305 123.047 0.738606 119.141 0.474766 169.

1183.67175 3 15.6103 190.918 7.43625 119.141 3.43328 126.465 0.752588 122.559 0.729163 118.652 0.468542 168.

1203.81665 71 15.4708 188.965 7.31889 118.164 3.37846 125.488 0.740656 122.07 0.717573 117.676 0.460902 168.

1208.23889 32 15.4407 188.477 7.29369 118.164 3.3667 125.488 0.738099 121.582 0.715087 117.676 0.459263 167.
C-21

TABLE C.1 (Continued)

Hydraulic 

Conductivity, m/yr

Simulation 

No.

All Pathways Water Ingestion

Plant 

(Water release)

Meat

(Water release)

Milk 

(Water release)

External Groun

(Water release

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time 

Peak

1235.7533 34 15.256 186.035 7.13964 117.188 3.29476 124.512 0.722447 120.605 0.699875 116.699 0.449238 167.

1258.88123 14 15.1062 184.082 7.01574 116.211 3.2369 123.535 0.70986 120.117 0.687636 115.723 0.441177 166.

1269.42834 21 15.0396 183.594 6.96089 116.211 3.21129 123.535 0.70429 119.629 0.682222 115.723 0.437609 166.

1297.39136 31 14.8659 181.152 6.81885 115.234 3.14493 122.559 0.689854 118.652 0.668188 114.746 0.428365 165.

1299.31299 28 14.8543 181.152 6.80941 115.234 3.14052 122.559 0.688897 118.652 0.667256 114.746 0.427752 165.

1328.58472 10 14.6791 178.711 6.66741 114.258 3.07418 121.582 0.674465 117.676 0.653224 113.77 0.418512 164.

1338.29419 46 14.6225 178.223 6.6217 113.77 3.05283 121.094 0.66982 117.676 0.648708 113.281 0.41554 164.

1353.98828 79 14.5321 177.246 6.54909 113.281 3.01891 120.605 0.662443 117.188 0.641533 112.793 0.410818 164.

1374.4928 88 14.4167 175.781 6.45675 112.793 2.97576 120.117 0.653055 116.211 0.632407 112.305 0.404811 163.

1391.99585 18 14.3203 174.316 6.37999 112.305 2.93989 119.629 0.645254 115.723 0.624821 111.816 0.39982 163.

1406.14783 89 14.244 173.34 6.31946 111.816 2.91162 119.141 0.639107 115.723 0.618839 111.328 0.395886 162.

1428.97119 47 14.1227 171.875 6.2237 111.328 2.86687 118.652 0.629372 114.746 0.609375 110.84 0.38966 162.

1455.76257 66 13.9847 170.41 6.1153 110.84 2.81622 118.164 0.618359 114.258 0.598662 110.352 0.382617 161.

1471.4646 44 13.9057 169.434 6.05359 110.352 2.78739 117.676 0.612086 113.77 0.592562 109.863 0.378607 161.

1484.33765 19 13.8423 168.457 6.0042 109.863 2.76431 117.188 0.607064 113.281 0.58768 109.375 0.375401 161.

1500.2843 75 13.7642 167.48 5.94358 109.375 2.736 116.699 0.600908 113.281 0.58169 109.375 0.371467 160.

1529.224 48 13.6267 166.016 5.83731 108.887 2.68635 116.211 0.590105 112.305 0.571187 108.398 0.364566 160.

1549.78137 100 13.5312 165.039 5.76387 108.398 2.65204 115.723 0.582641 111.816 0.563929 107.91 0.359801 159.

1550.09094 90 13.5298 165.039 5.76282 108.398 2.65155 115.723 0.582533 111.816 0.563825 107.91 0.359732 159.

1571.17676 82 13.4342 163.574 5.68955 107.91 2.61733 115.234 0.575088 111.328 0.556585 107.422 0.35498 159.

1592.92505 33 13.338 162.598 5.61616 107.422 2.58305 114.746 0.567629 110.84 0.549332 106.934 0.350222 159.

1616.85938 29 13.234 161.133 5.53721 106.934 2.54618 114.258 0.559606 110.352 0.541531 106.445 0.345106 158.

1626.22607 2 13.1944 160.645 5.50719 106.934 2.53217 114.258 0.556557 110.352 0.538568 106.445 0.343163 158.

1653.32495 56 13.0811 159.668 5.42165 105.957 2.49224 113.281 0.547863 109.863 0.530116 105.957 0.337624 157.

1658.7533 94 13.0585 159.18 5.40466 105.957 2.4843 113.281 0.546136 109.375 0.528434 105.469 0.336522 157.

1679.25659 24 12.9752 158.203 5.34212 105.469 2.45511 112.793 0.539781 108.887 0.522257 105.469 0.332475 157.

1709.79932 51 12.8544 156.738 5.25181 104.98 2.41295 112.305 0.530604 108.398 0.513335 104.492 0.326632 157.

1714.51477 67 12.8361 156.738 5.23816 104.98 2.40659 112.305 0.529217 108.398 0.511989 104.492 0.325749 156.

1730.6283 40 12.774 155.762 5.19194 104.492 2.38502 111.816 0.524522 107.91 0.507422 104.492 0.322763 156.
C-22

TABLE C.1 (Continued)

Hydraulic 

Conductivity, m/yr

Simulation 

No.

All Pathways Water Ingestion

Plant 

(Water release)

Meat

(Water release)

Milk 

(Water release)

External Groun

(Water release

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time of 

Peak

Peak 

dose,

mrem/yr

Time of 

Peak

Peak 

dose, 

mrem/yr

Time 

Peak

1764.87146 4 12.6449 154.297 5.09625 104.004 2.34038 111.328 0.514798 107.422 0.497973 103.516 0.316579 156.

1768.25049 62 12.6324 154.297 5.08696 104.004 2.33604 111.328 0.513854 107.422 0.497056 103.516 0.315979 156.

1791.29834 69 12.5483 153.32 5.02499 103.516 2.30714 110.84 0.507558 106.934 0.490936 103.027 0.311978 155.

1803.01245 85 12.5063 152.832 4.99402 103.516 2.29271 110.84 0.504413 106.934 0.487882 103.027 0.309981 155.

1824.26672 53 12.4309 151.855 4.9387 103.027 2.26691 110.352 0.498793 106.445 0.482419 102.539 0.306411 155.

1850.21289 73 12.3411 150.879 4.87307 102.539 2.23631 109.863 0.492125 105.957 0.475939 102.051 0.302178 154.

1856.36206 99 12.32 150.879 4.8576 102.539 2.22911 109.863 0.490555 105.957 0.474414 102.051 0.301182 154.

1883.37854 61 12.2291 149.902 4.79146 102.051 2.19828 109.375 0.483837 105.469 0.467886 101.563 0.29692 154.

1903.48938 41 12.1629 148.926 4.7434 101.563 2.17588 108.887 0.478956 104.98 0.46314 101.074 0.293826 154.

1924.11035 27 12.0962 148.438 4.69511 101.074 2.1534 108.887 0.474053 104.492 0.458379 101.074 0.290719 154.

1938.86963 13 12.0491 147.949 4.66108 101.074 2.13754 108.398 0.470596 104.492 0.455019 100.586 0.288528 153.

1946.51367 59 12.0251 147.461 4.64377 101.074 2.12949 108.398 0.468838 104.492 0.453313 100.586 0.287416 153.

1976.03357 23 11.9335 146.484 4.57785 100.586 2.09879 107.91 0.462145 104.004 0.446809 100.098 0.283177 153.

1983.77808 81 11.9097 145.996 4.5607 100.586 2.09083 107.91 0.460404 103.516 0.445121 100.098 0.282078 153.
C-23

The interaction of the predicted doses from the well-water- and surface-water-dependent 

exposure pathways to predict the peak total dose can also be seen from temporal plots for each 

simulation. RESRAD-OFFSITE does not ordinarily save the data for the temporal plots of the 

individual simulations because writing the data to a file is time-consuming and most users are 

not likely to view the temporal plots. It is, however, possible to specify that the data be saved by 

checking the “Dose and risk at graphic time points” option box in the “Output specifications” tab 

(see Figure C.19). 

The example case, “Distributed Single-Input Sensitivity.ROF,” was rerun after checking the 

“Dose and risk at graphic time points” option box in the “Output specifications” tab. This 

produced 100 graphics output files—one for each of the simulations. Temporal plots of total 

predicted dose and component pathways for seven of the 100 simulations are shown in 

Figures C.20 through C.33. They correspond to (1) one point toward the upper end of the 

hydraulic conductivity range, (2) three points in the vicinity of the break in the curve, and 

(3) three points in the hydraulic conductivity range of 200 to 300 m/yr to capture the changes 

near the peak of the peak predicted dose. The probabilistic input sample data file (“Distributed 

Single-Input Sensitivity.pin,” in this case) contains the value of hydraulic conductivity used for 

each simulation. The first two columns in Table C.1 list the value of the hydraulic conductivity in 

the saturated zone and the simulation in which it was used.

FIGURE C.19 Option Box to be Checked to Flag the Code 

to Produce a Full Suite of Temporal Plots for Each 

Probabilistic Simulation
C-24

FIGURE C.20 Relative Contributions of Exposure Pathways 

at 1984 m/yr Hydraulic Conductivity

FIGURE C.21 Total Dose at a Hydraulic Conductivity of 1984 m/yr 

in Saturated Zone
C-25

FIGURE C.22 Relative Contributions of Exposure Pathways 

at 752.1 m/yr Hydraulic Conductivity

FIGURE C.23 Total Dose at a Hydraulic Conductivity of 752.1 m/yr 

in Saturated Zone
C-26

FIGURE C.24 Relative Contributions of Exposure Pathways 

at 732.1 m/yr Hydraulic Conductivity

FIGURE C.25 Total Dose at a Hydraulic Conductivity of 732.1 m/yr 

in Saturated Zone
C-27

FIGURE C.26 Relative Contributions of Exposure Pathways 

at 709.8 m/yr Hydraulic Conductivity 

FIGURE C.27 Total Dose at a Hydraulic Conductivity of 709.8 m/yr 

in Saturated Zone
C-28

FIGURE C.28 Relative Contributions of Exposure Pathways 

at 299.2 m/yr Hydraulic Conductivity 

FIGURE C.29 Total Dose at a Hydraulic Conductivity of 299.2 m/yr 

in Saturated Zone
C-29

FIGURE C.30 Relative Contributions of Exposure Pathways at 258 m/yr 

Hydraulic Conductivity

FIGURE C.31 Total Dose at a Hydraulic Conductivity of 258 m/yr 

in Saturated Zone
C-30

FIGURE C.32 Relative Contributions of Exposure Pathways 

at 213.7 m/yr Hydraulic Conductivity

FIGURE C.33 Total Dose at a Hydraulic Conductivity 

of 213.7 m/yr in Saturated Zone

When the hydraulic conductivity is 1984 m/yr, the highest value sampled in this example, the six 

major exposure pathways peak close together, as seen in Figure C.20. The exposure from 

drinking well water peaks at around 100 years, while the external radiation exposure from 

radionuclides in soil irrigated with well water peaks at around 150 years. The exposure 

pathways that receive contributions both from well water and from accumulation in soil following 

irrigation by well water peak at intervening times depending on the relative contributions of the 
C-31

two components. The exposure from the ingestion of fish from the surface water body also 

peaks at around 150 years, the surface water body being farther away than the well from the 

initial contamination. The six components combine to produce a total dose that peaks close to 

150 years (Figure C.21).

As the hydraulic conductivity decreases, the additional transport time to the surface water body 

causes the predicted peak dose from the ingestion of fish to move away from the predicted peak 

doses from the five well-water-dependent pathways (Figure C.22). At a hydraulic conductivity of 

752.1 m/yr, separation and relative magnitudes of the six peaks is such that the peak of the 

contribution from the six exposure pathways is only a little greater than the peak of the 

contributions from the five well-water-dependent exposure pathways (Figure C.23). At the nextlower hydraulic conductivity sampled in this case, 732.2 m/yr, the peak of the dose from all 

exposure pathways involves only contributions from the five well-water-dependent exposure 

pathways (Figures C.24 and C.25); the second peak that also involves contribution from the 

ingestion of fish is marginally less than the first peak. As the hydraulic conductivity decreases, 

the first peak becomes larger in relation to the second (Figures C.26 and C.27). The change in 

the exposure pathways that contribute to the peak predicted dose and the way in which these 

pathways vary with hydraulic conductivity in the saturated zone (Figures C.13 through C.18) are 

the reasons for the break in the curve, seen in Figure C.12, of peak predicted dose against 

hydraulic conductivity. 

Figures C.28 through C.33 show the contributions for the exposure pathways to the total 

predicted dose in vicinity of the peak in the curve of total dose against hydraulic conductivity 

(Figure C.12). They do not reveal why the peak predicted dose at a hydraulic conductivity of 

258 m/yr is higher than the peak predicted doses at hydraulic conductivities of 299.2 and 

213.7 m/yr. That requires a more in-depth look at the intermediate results, as described in 

Section C.3.

C.2.3 Comparison of the Two Methods of Performing Single-input Sensitivity in 

RESRAD-OFFSITE

The sensitivity of the peak predicted dose (or peak risk) to the input can be measured in many 

ways. This section discuss three alternatives for quantifying the sensitivity: (1) the rate of 

change of peak predicted dose with the input, (2) the fractional rate of change of peak predicted 

dose with the input, and (3) the range and distribution of the peak predicted dose when the input 

varies over its site-appropriate range of values. Each of these measures is appropriate for 

some purposes but not for others. The two methods of performing single-input sensitivity in 

RESRAD-OFFSITE are compared using these measures.

C.2.3.1 The Rate of Change of Peak Predicted Dose with the Input

The slope of the plot of peak predicted dose (or peak risk) against the input is a measure of how 

sensitive the peak predicted dose is to a change in the input. This will be constant over the 

range of input when the peak predicted dose is a linear function of the input over that range. 

While this is the case for some of the inputs in RESRAD-OFFSITE, the peak predicted dose is a 

nonlinear function of many of the inputs. Thus, the rate of change varies over the range of the 

input. The average rate of change over the two intervals 233.3 m/yr to 700 m/yr and 700 m/yr to 

2100 m/yr can be calculated using the three-point single-input sensitivity analysis data in 

WRESPLOT, the deterministic graphics viewer in RESRAD-OFFSITE. These data can be 

saved and viewed using the menu commands or toolbar icons in WRESPLOT, after displaying 
C-32

the three plots. The average rate of change in the interval between each pair of adjacent 

samples of the distributed single-input sensitivity analysis can be computed using the data in the 

peak predicted dose data file (with extension .pds) and the probabilistic input sample data file 

(with extension .pin). These calculated values are shown in Figure C.34. 

FIGURE C.34 Rate of Change of Peak Predicted Dose with Hydraulic Conductivity

Because the interval between the samples is small (no greater than 36 m/yr), the values 

computed using the distributed single-input sensitivity analysis are expected to closely 

approximate the slope of the peak predicted dose–hydraulic conductivity plot. The rates of 

change computed using the distributed single-point sensitivity analysis data change slowly over 

the range of 750 through 2000 m/yr, from –0.013 to –0.003 mrem/m. The average rate of 

change over the range of 700 to 2100 m/yr computed using the three-point single-input 

sensitivity analysis data, −0.0067 mrem/m, is in good agreement with rate of change computed 

using the distributed single-input sensitivity analysis data. The slope varies widely in the 200 to 

750 m/yr range. The rates of change computed using the data from the distributed single-input 

sensitivity analysis vary from 0.1 rapidly down to −0.073 and then gradually back up to 

−0.026 mrem/m. The average rate of change over the range of 233.3 to 700 m/yr, computed 

using the three-point single-input sensitivity analysis, is −0.045 mrem/m. Thus, the three-point 

single-input sensitivity analysis efficiently estimates the rate of change in the range where it is 

relatively constant, but does not when the slope changes rapidly or when the slope changes 

direction. The distributed single-input sensitivity analysis captures the variation of the rate of 

change over the range very well because the analyst is able to specify a larger number of 

simulations over the range. On the downside, the larger number of simulations requires a 

longer run time.

The slope of the peak predicted dose vs. input plot—that is, the rate of change of peak 

predicted dose with input—is a very good measure for comparing the sensitivities of peak 

predicted doses from different ranges of the same input. It is not an appropriate measure for

Rate of change of dose with hydraulic conductivity 

in the saturated zone

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 250 500 750 1000 1250 1500 1750 2000

Hydraulic conductivity in the saturated zone (m/y)

Rate of change (mrem/y)/(m/y)

Distributed Single Input Sensitivity 

Three point Single Input Sensitivity
C-33

comparing the sensitivity of peak predicted dose to two different inputs because there is no 

meaningful way to compare numbers with different units. 

C.2.3.2 Fractional Rate of Change of Peak Predicted Dose with Input

A fractional rate of change—that is, the rate of change normalized by some representative value 

of the peak predicted dose or the input—is dimensionless and permits comparison of the 

sensitivities to two different inputs. Normalizing the change in peak predicted dose by a 

representative value of peak predicted dose for that interval make it dimensionless; likewise, 

normalizing the change in the input by a representative value of input for that interval make it 

dimensionless as well. The only issue then is what is the representative value for the range; the 

values at one or the other of the two ends of the range, or the mean of the two values. The 

choice made for the representative value does not significantly affect the computation of the 

fractional rate of change when the range of the interval is small; this is usually the case for the 

distributed single-input sensitivity analysis. The interval in the three-point single-input sensitivity 

analysis can in general be large. Table C.2 illustrates how the choice of the representative 

normalizing value affects the computed fractional rate of change for the three-point single-input 

sensitivity example described in Section C.2.1.2.

TABLE C.2 Effect of the Choice of the Representative Normalizing Value on the 

Computed Fractional Rate of Change

Hydraulic conductivity, m/yr Peak predicted dose, mrem/yr

Fractional rate 

of change normalized by

Left end Right end Average Left end Right end Average Left end Right end Average

233.3 700 466.7 41.86 20.98 31.42 -0.25 -1.5 -0.66

700 2100 1400 20.98 11.57 16.28 -0.22 -1.2 -0.58

The fractional rates of change computed using the averages of the interval as the normalizing 

values are plotted in Figure C.35. The fractional rate of change starts off at a value of 0.6 at a 

hydraulic conductivity of 200 m/yr in the saturated zone. It falls rapidly at first with increasing 

hydraulic conductivity, levels out at a value of around −1 at a hydraulic conductivity of about 

500 m/yr, and steps up to a value of about −0.5 at a hydraulic conductivity of around 750 m/yr. 

The fractional rate of change computed using the two methods of single-input sensitivity 

analysis data are in agreement in the hydraulic conductivity range of 700 to 2100 m/yr. 
C-34

FIGURE C.35 Fractional Rate of Change of Peak Predicted Dose with 

Hydraulic Conductivity

Although normalization by a representative value makes this measure of sensitivity 

dimensionless and therefore a valid means of comparing the sensitivity of peak predicted dose 

to two or more different inputs, it also makes the interpretation of the comparison more difficult. 

The fractional sensitivity of peak predicted dose from the drinking well water to the hydraulic 

conductivity ranges from about −0.8 to −0.95 in the hydraulic conductivity range of 400 to 

2000 m/yr, while the peak predicted dose from that pathway decreases rapidly in the beginning 

of the range and more gradually at the end of the range (Figure C.13). The fractional sensitivity 

to hydraulic conductivity of peak predicted dose from the ingestion of fish ranges from about 

0.72 to 0.052 in the hydraulic conductivity range of 200 m/yr to 2000 m/yr, while the peak 

predicted dose from that pathway increases rapidly in the beginning of the range and more 

gradually at the end of the range (Figure C.18). 

C.2.3.2.1 Interpretation of Fractional Rate of Change of Peak Predicted Dose with 

the Input

This section derives the relationship between peak predicted dose and the input for a constant 

value of fractional rate of change. This relationship is then used to relate the value of the 

fractional rate of change, k , to the shape of the curve of peak predicted dose, y , against the 

input, x . 

Begin with the definition of the fractional rate of change, k

x

dx

y

dy / = . Rearranging and 

integrating ∫∫ = x

dx k

y

dy gives lnln += cxky , where c is the integration constant. This is 

equivalent to k = Cxy , where c = eC . Table C.3 summarizes the typical nature of this curve for 

various ranges of k. 

Fractional rate of change of dose with hydraulic 

conductivity in the saturated zone

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0 250 500 750 1000 1250 1500 1750 2000

Hydraulic conductivity in the saturated zone (m/y)

Fractional rate of change

Distributed Single Input Sensitivity

Three point Single Input Sensitivity
C-35

TABLE C.3 Relationship between Fractional Rate of Change and the Shape 

of the Curve of Peak Predicted Dose and the Input

Fractional rate of 

change Shape

1 < k Peak predicted dose increases nonlinearly with increasing value of input, slowly at first 

and more rapidly later.

1 Peak predicted dose increases linearly with increasing value of input.

0 < k < 1 Peak predicted dose increases nonlinearly with increasing value of input, rapidly at first 

and more gradually later.

k < 0 Peak predicted dose decreases nonlinearly with increasing value of input, rapidly at first 

and more gradually later.

k = −1 Peak predicted dose varies inversely with input; the shape is a rectangular hyperbola.

The curves for selected values of k are shown in Figure C.36. These curves illustrate that 

except for unity, a constant value of the normalized rate of change over the range of the input 

does not signify a constant sensitivity of peak predicted dose to the input over that range. 

These curves also indicate that depending on the range of the input, different values of the 

fractional rate of change indicate greater sensitivity. For example, a k of between 0 and 1 

indicates a greater sensitivity at low values of the range of x, when compared with a k >1; the 

situation is reversed at higher values of x, where a k >1 indicates a greater sensitivity than a k of 

0 to 1. Thus, the fractional rate of change is not necessarily a good indicator of the sensitivity. 

A more reliable indicator of sensitivity is needed.

FIGURE C.36 Shape of y = xk for select values of k

y = xk

0

0 x

y

-1

-0.5

0

0.5

1

1.5
C-36

C.2.3.3 The Range of the Peak Predicted Dose over the Site-appropriate Range

of the Input

The discussion in Sections C.2.3.1 and C.2.3.2 indicate the difficulties of using a derived 

measure of sensitivity. The range of the peak predicted dose is a direct measure of sensitivity. 

The response of peak predicted dose to changes in one input depends on the (point) values 

used for many of the other inputs (Section C.3). When performing sensitivity analysis, it is 

therefore imperative that site-appropriate values be used for all inputs if site-specific values 

have not yet been identified. Three point single-input sensitivity analysis can then be performed 

on a number of inputs using either site-appropriate ranges or site-specific ranges. The ranges 

of the peak predicted dose that result when each input is varied over its site-appropriate or sitespecific range can be used to determine the sensitivity of peak predicted dose to that input. 

Alternatively distributed single-input sensitivity analysis can then be performed on a number of 

inputs using either site-appropriate distributions or site-specific distributions. Some measure of 

the distribution of the peak predicted dose that result when each input is described by its siteappropriate or site-specific distribution can be used to determine the sensitivity of peak 

predicted dose to that input. The standard deviation of the peak predicted dose, which is 

composed of peak predicted dose of all the samples of the distribution, is a better measure of its 

distribution than the range which depends on only the two extreme predictions of peak dose.

C.3 Interactions between Inputs and Their Effect on the 

Sensitivity to Each Input 

This section takes a deeper look at the results of the example case presented in the previous 

section. This in-depth look serves many purposes:

• It helps answer the questions raised in Section C.2 about the manner in which the peak 

predicted doses from different exposure pathways vary with hydraulic conductivity in the 

saturated zone.

• It provides an example of how one might go about trying to understand the response of 

peak predicted dose to changes in other inputs under other situations.

• It highlights the interactions between inputs and suggests that the sensitivity of dose to 

one input depends on the values used for other inputs.

• It points to the need for using values that are either specific or at least appropriate for the 

site for all the inputs when performing sensitivity analysis. 

• It also shows the need for multiple-input sensitivity analysis and the need for specifying 

either correlations or relationships between some of the inputs.

C.3.1 Anticipated Influence of Saturated Hydraulic Conductivity on Transport 

Time

An increase in hydraulic conductivity in the saturated zone causes a corresponding rise in the 

Darcy velocity of flow in the saturated zone when the hydraulic gradient is held constant. Thus, 

the radionuclides are transported to the well and to the surface water body more quickly as the 

hydraulic conductivity increases, as is observed in the temporal plots from the three-point 

single-input sensitivity (Figures C.4 through C.9) and distributed single-input sensitivity analyses 

(Figures C.20, C.22, C.24, C.26, C.28, C.30, and C.32). The concentration of the radionuclide

in the water can change when the difference in transport time is significant in relation to the halflife of the radionuclide. As the hydraulic conductivity increased from 200 to 2000 m/yr, the 
C-37

transport time to the well decreased by more than 200 years and the transport time to the 

surface water body fell by more than 500 years. This decrease in travel time raises the 

concentration of 226Ra in the well by a factor of 1.1 and in the surface water body by a factor of 

1.3 as the saturated hydraulic conductivity increases from 200 to 2000 m/yr. 

Another consequence of a higher Darcy flow rate is that a greater quantity of water will flow 

through a given cross-section of the aquifer as the hydraulic conductivity increases. 

Conversely, the constant-flow-rate contaminated plume entering the saturated zone will initially 

occupy a smaller cross-section of the aquifer. The plume will spread out in the three directions 

(longitudinal, horizontal lateral, and vertical lateral) as it moves away from below the primary 

contamination and toward the well and surface water body. The quantity and concentration of 

the radionuclide in the well and in the surface water body will depend on how the radionuclide is 

distributed over the region of the aquifer that is intercepted by each source of water. This is 

discussed in the next two sections.

C.3.2 Influence of Saturated Hydraulic Conductivity on the Dose from Ingestion

of Fish

It is instructive to start with the dimensions of the plume in the saturated zone directly below the 

primary contamination prior to lateral dispersion. The width is equal to the width of the primary 

contamination, 100 m in this example. The thickness is computed by determining the thickness 

of the saturated zone required to convey the infiltration through the primary contamination—it is 

inversely proportional to the hydraulic conductivity in the saturated zone. The thicknesses and 

half the widths of the plumes for five hydraulic conductivities (210, 260, 300, 700, and 

2000 m/yr) are shown in Figure C.37. The dimensions of the saturated zone that feeds into the 

surface water body are also shown. In the absence of lateral dispersion, the entire plume would 

have entered the surface water body at hydraulic conductivities of 260 m/yr or greater. 
C-38

FIGURE C.37 Dimensions of Plume Prior to Lateral Dispersion and 

Dimension of Saturated Zone Contributing to the Surface 

Water Body

Longitudinal dispersion spreads the plume in the direction of flow; the effects of longitudinal 

dispersion can be seen in the temporal plots in WRESPLOT. Lateral dispersion spreads the 

plume in the vertical and horizontal directions perpendicular to the flow. Information about the 

transverse distribution of the radionuclides in the saturated zone at the locations of the well and 

the surface water body are written in the ASCII files “PROFILEW.OUT” and “PROFILES.OUT,” 

respectively. These files are written once for each run, so information for all the sensitivity 

simulations is not available. The code was run five times in the determinist mode, with the 

hydraulic conductivity in the saturated zone set to 210, 260, 300, 700, and 2000 m/yr, 

respectively. The horizontal and vertical distributions of 226Ra in the saturated zone at the 

location of the surface water body for these five runs are shown in Figures C.38 and C.39. 

Horizontal lateral dispersion spreads the plume from its initial width of 100 m to a width of about 

280 m at the surface water body. The surface water body in this example is at the plume 

centerline and is 300 m wide. Hence, horizontal lateral dispersion does not affect the quantity of 

radionuclides that are intercepted by the surface water body. Figure C.39 shows that vertical 

lateral dispersion has a significant effect on this quantity, however. At a hydraulic conductivity 

of 2000 m/yr in the saturated zone, the plume was conceptualized to be uniformly distributed 

over a depth of 1.25 m when it was directly below the primary contamination, as shown in 

Figure C.37. Vertical lateral dispersion spreads the radionuclide over a depth of about 25 m 

and reduces the concentration at the water table to approximately 0.15 of the initial value. 

The quantity of the radionuclides that remains within the depth of interception of the surface 

water body, 10 m in this example, can be found by integrating the area under the curves. In this 

Plume dimensions prior to lateral dispersion

0

2

4

6

8

10

12

0 40 80 120 160

Distance from plume centerline, meter

Depth below watertable, meter

210

260

300

700

2000

Aquifer contributing to

surface water body
C-39

example, 0.66, 0.71, 0.73, 0.80, and 0.81 of the plume is intercepted by the surface water body 

at hydraulic conductivities of 210, 260, 300, 700, and 2000 m/yr, respectively. This, too, leads 

to an increase in the peak predicted dose from the ingestion of fish with increasing hydraulic 

conductivity in the saturated zone—by a factor of 1.22 as the hydraulic conductivity increases 

from 200 to 2000 m/yr. Along with the factor of 1.3 increase discussed in Section C.3.1, it is a 

main reason for the shape of the plot of peak predicted dose from ingestion of fish against 

hydraulic conductivity (Figure C.18).

FIGURE C.38 (left) Horizontal Distribution of Radionuclides in the Transverse Plane at 

the Location of the Surface Water Body

FIGURE C.39 (right) Vertical Distribution of Radionuclides in the Transverse Plane at the 

Location of the Surface Water Body

The quantity of water entering the surface water body will increase in proportion to the hydraulic 

conductivity in the saturated zone, if the depth of interception is constant. This can be expected 

to affect the mean residence time of water in the surface water body. The mean residence time 

is an independent input in RESRAD-OFFSITE. It is not changed in the single-input sensitivity 

analysis on hydraulic conductivity in the saturated zone. From the discussion in this section, the 

sensitivity of peak predicted dose from the ingestion of fish to hydraulic conductivity can be 

expected to depend on the values specified for many inputs, including the mean residence time 

of water in the surface water body, the depth of interception and the width of the surface water 

body, and all the inputs that affect the quantity of water infiltrating through the primary 

contamination. This indicates the need for performing multiple-input sensitivity analysis and 

specifying a relationship between the hydraulic conductivity in the saturated zone and the mean 

residence time in the lake in this example. Section C.3.4 extends the example sensitivity 

analysis to include some of the interaction inputs discussed in this section.

Horizontal Concentration Profile

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150

Distance from plume centerline, meter

Factor for spreading of 226Ra due to horizontal lateral dispersion

210

260

300

700

2000

Vertical Concentration Profile

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40

Depth below water table, meter

Factor for spreading of 226Ra due to vertical lateral dispersion

210

260

300

700

2000
C-40

C.3.3 Influence of Saturated Hydraulic Conductivity on the Dose from Well-waterdependent Exposure Pathways

It is again helpful to start by comparing the dimensions of the plume in the saturated zone 

directly below the primary contamination prior to lateral dispersion, with the dimensions of the 

aquifer contributing to the well. The thickness of the aquifer contributing to the well is the depth 

of the well. The width of aquifer contributing to the well is computed from the well pumping rate, 

the depth, and the Darcy velocity. The dimensions of the initial plume into the saturated zone 

are computed as described in Section C.3.2. The concentration within the initial plume is 

assumed to be uniform. 

The dimensions of the two regions for five different hydraulic conductivities (210, 260, 300, 700, 

and 2000 m/yr) are compared in Figure C.40. If the effects of lateral dispersion were to be 

ignored, the dilution due to mixing of the plume with the clean water would simply be the fraction 

of the cross-sectional area of the aquifer contributing to the well that is contaminated. At a 

hydraulic conductivity of 210 m/yr, the plume thickness exceeds the depth of the well while the 

width of the aquifer contributing to the well exceeds the width of the undispersed plume. Thus, 

part of the plume passes below the well, while the well draws clean water from the two sides of 

the plume in addition to the contaminated water from the width of the plume. As the hydraulic 

conductivity increases, both the thickness of the plume and the width of the aquifer contributing 

to the well decrease. When the width of the aquifer contributing to the well decreases, a smaller 

proportion of water drawn into the well will be clean. The concentration in the well and thus the 

peak predicted dose from well-water-dependent pathways increases until either the width of the 

aquifer contributing to the well becomes equal to the width of the plume or the thickness of the 

aquifer contributing to the well becomes equal to the thickness of the plume. The former 

happens at a hydraulic conductivity of 250 m/yr in this example. The peak predicted dose 

remains constant until the other dimension of the plume and the portion of the aquifer 

contributing to the well become equal.
C-41

FIGURE C.40 Dimensions of the Initial Plume in the Saturated Zone and the Dimensions 

of the Aquifer Contributing to the Well for Five Hydraulic Conductivities 

in the Saturated Zone

The thickness of the plume becomes equal to the well depth at a hydraulic conductivity of 

255 m/yr in this example. As the hydraulic conductivity increases beyond this value, the 

thickness of the plume shrinks in comparison to the depth of the well below the water table, 

while the width of the plume exceeds the width of the aquifer contributing to the well. The peak 

predicted dose falls as clean water underlying the plume is drawn into the well while part of the 

210 m/y hydraulic conductivity in saturated zone

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70

Distance from plume centerline, meter

Depth below water table, meter

Initial plume

Aquifer contributing to well

260 m/y hydraulic conductivity in saturated zone

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70

Distance from plume centerline, meter

Depth below water table, meter

Initial plume

Aquifer contributing to well

300 m/y hydraulic conductivity in saturated zone

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70

Distance from plume centerline, meter

Depth below water table, meter

Initial plume

Aquifer contributing to well

700 m/y hydraulic conductivity in saturated zone

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70

Distance from plume centerline, meter

Depth below water table, meter

Initial plume

Aquifer contributing to well

2000 m/y hydraulic conductivity in saturated zone

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70

Distance from plume centerline, meter

Depth below water table, meter

Initial plume

Aquifer contributing to well
C-42

plume passes around the well. The change in dilution factor with hydraulic conductivity, 

computed by ignoring lateral dispersion, in the saturated zone for this example is shown in 

Figure C.41.

Lateral dispersion spreads the plume laterally, making the concentration profile nonuniform. 

Information from the output file “PROFILEW.OUT” for five determinist runs with the hydraulic 

conductivity in the saturated zone set to 210, 260, 300, 700, and 2000 m/yr were used to plot 

the horizontal and vertical distributions of 226Ra in the saturated zone at the well in Figures C.42 

and C.43. The code computes the dilution factor by multiplying the average factor for lateral 

horizontal dispersion over the width of the aquifer contributing to the well by the average factor 

for lateral vertical dispersion over the thickness of the aquifer contributing to the well. The 

change in dilution factor with hydraulic conductivity is shown in Figure C.41. 

When the thickness of the plume is small in comparison to the thickness of the aquifer 

contributing to the well and the width of the plume is large in comparison to the width of the 

aquifer contributing to the well, dispersion will not affect the quantity of radionuclides that reach 

the well. Nor will dispersion affect the quantity of radionuclides that reach the well when the 

thickness of the plume is large compared with the thickness of the aquifer contributing to the 

well and the width of the plume is small in comparison to the width of the aquifer contributing to 

the well. Lateral dispersion influences the peak predicted dose from well-water-related 

exposure pathways when one or both of the dimensions—the thicknesses or the widths of the 

plume and the region of aquifer contributing to the well—are of comparable magnitude. This is 

the case in the range of hydraulic conductivity over which the two curves in Figure C.41 deviate 

from each other. 

From the preceding discussion, the sensitivity of peak predicted dose from well-waterdependent exposure pathways to hydraulic conductivity can be expected to depend on the 

values specified for many inputs, including the depth and pumping rate of the well, the lateral 

dispersivities, and all the inputs that affect the quantity of water infiltrating through the primary 

contamination. This indicates the need for performing multiple-input sensitivity analysis. 

Section C.3.4 extends the example sensitivity analysis to include some of the interaction inputs 

discussed in this section.

FIGURE C.41 Variation in Dilution Factor with Hydraulic 

Conductivity in the Saturated Zone

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

200 400 600 800 1000 1200 1400 1600 1800 2000

Hydraulic conductivity in the saturated zone, m/y

Dilution factor

Ignoring lateral dispersion

including lateral dispersion
C-43

FIGURE C.42 (left) Horizontal Distribution of Radionuclides in the Transverse 

Plane at the Well

FIGURE C.43 (right) Vertical Distribution of Radionuclides in the Transverse 

Plane at the Well

C.3.4 Relationships between Inputs

Many of the inputs in the RESRAD-OFFSITE code are not independent. There may be 

analytical relationships between some variables. In the single-input sensitivity analysis example 

considered before, the quantity of water intercepted by the surface water body over a year is the 

product of the hydraulic gradient in the saturated zone, the hydraulic conductivity in the 

saturated zone, and the width and depth of the aquifer intercepted by the surface water body. 

The mean residence time of water in the surface water body is the volume of water in the 

surface water body divided by the quantity of water flowing in and out of the surface water body 

in a year. If the other inflows into the surface water body are fixed, these two combine to give 

the relationship between the mean residence time of water in the surface water body and the 

hydraulic conductivity in the saturated zone. This relationship must be included in the sensitivity 

analysis in order to accurately assess the sensitivity of peak predicted dose to the hydraulic 

conductivity. The distributed single-input sensitivity analysis example of Section C.2.2 can be 

expanded to include this relationship. Any input in the code can be expressed as a function of 

other (single-valued, distributed, or related) inputs in the “Related inputs” tab of the Uncertainty 

and Probabilistic Analysis form (Figure C.44). Currently, only the four operations—addition, 

subtraction, multiplication, and division—can be used to define the relationship. All the inputs to 

the RESRAD-OFFSITE code are included in the Input Variable dropdown box. This dropdown 

box and the operation keys are used to key in the relationships between the inputs. 

Horizontal Concentration Profile

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100

meter

Factor for spreading of 226Ra due to horizontal lateral dispersion

210

260

300

700

2000

Vertical Concentration Profile

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20

Distance below water table, meter

Factor for spreading of 226Ra due to vertical lateral dispersion

210

260

300

700

2000
C-44

FIGURE C.44 Specifying Relationships between Inputs

C.3.4.1 Specifying Relationships between Variables

Relationships can only be specified in “step by step” probabilistic analysis. Distributions must 

first be specified for all the probabilistic inputs. The input samples for the probabilistic 

distributions must then be generated in the “Step by step analysis” tab of the Uncertainty and 

Probabilistic Analysis form. A relationship is specified by first selecting the dependent input 

from the input variables dropdown box. This places the name of the input variable in the 

command button below the dropdown box. Clicking that command button transfers the name of 

the input into box above and adds an equal sign. These steps are illustrated in Figure C.45.

FIGURE C.45 Specifying the Dependent Input of a Relationship

The right-hand side of the relationship must begin with the name of an input or with a constant. 

Thus, only the input dropdown box is active and available for selection at this point. The input 

OFFLNAQF—which is the distance, in the direction perpendicular to the flow, from the center of 

the contamination to the left edge of the surface water body—is selected in the dropdown box 

and is transferred into the relationship specification box by clicking the command button as 

before. The next item that can be added to the specification of the relationship is an arithmetic 

operator. The buttons +, -, * and /, representing the arithmetic operations of addition, 

subtraction, multiplication, and division, become active while the input dropdown box becomes 

inactive at this point (Figure C.46). The expression in the relationship box equating one input to 
C-45

another is the simplest relationship. Therefore, the “Update relationship table” button also 

becomes active at this point.

FIGURE C.46 Adding an Independent Input to the Relationship

The width of the aquifer intercepted by the surface water body is the difference between the 

distances, in the direction perpendicular to the flow, from the center of the contamination to the 

left and right edges of the surface water body. The subtraction operator is selected next by 

clicking the “-” button. This deactivates the arithmetic operations buttons and the “Update 

relationship table” button, and activates the input dropdown box (Figure C.47).
C-46

FIGURE C.47 Adding an Arithmetic Operator and Selecting the Second 

Independent Input to the Relationship

The input OFFLNAQN—which is the distance, in the direction perpendicular to the flow, from 

the center of the contamination to the right edge of the surface water body—is selected next 

and transferred to the expression to complete the desired relationship for the width of the 

aquifer intercepted by the surface water body (Figure C.48). The width of the aquifer 

intercepted by the surface water body is not an input in the RESRAD-OFFSITE code. It is 

therefore not available in the dropdown box. That is why AGRIELEV(1) was chosen as a 

placeholder variable. This expression is accepted and transferred to the “Relationship table” 

(Figure C.49) by clicking the “Update relationship table” button (Figure C.48). As seen in 

Figure C.44, this relationship will be removed from the relationship table after it is used to define 

the relationship for mean residence time of water in the surface water body.

The additional quantity of water that is intercepted by the surface water body when the hydraulic 

conductivity is changed from its single deterministic value of 700 m/yr to a value sampled from 

the specified distribution is proportional to the difference between the sampled value and 700. 

Any numerical constant, in this case 700, can be typed into the input dropdown box, as 

illustrated in Figure C.49. The difference between the sampled value of the hydraulic 

conductivity in the saturated zone and the deterministic value of 700 is temporarily stored in 

AGRIELEV(2). This placeholder variable will also be removed from the relationship table. The 

rate at which water enters the surface water body in the deterministic case is equal to the 

deterministic volume divided by the deterministic mean residence time. 

The rate at which water enters the surface water body when the hydraulic conductivity is 

different from the deterministic value is the sum of the value in the deterministic case and the 

product of the hydraulic gradient, the difference in hydraulic conductivity (temporarily stored in 

AGRIELEV(2)), the width of aquifer intercepted by the surface water body (temporarily stored in 

AGRIELEV(1)), and the depth of aquifer intercepted by the surface water body. This is 

temporarily stored in AGRIELEV(3).
C-47

FIGURE C.48 Completing the Specification of a Relationship and Transferring It 

to the Relationship Table

FIGURE C.49 Inputting Numerical Constants in a Relationship

When an input is selected in the dropdown box, the code first checks whether a relationship has 

been specified for that input in the Relationship table. If it finds a relationship in the table, it will 

copy in that relationship into the relationship that is currently being created (Figure C.50). When 

the placeholder AGRIELEV(2) is selected in the dropdown box and transferred to the current 

relationship, HCSZ -700, which is the relationship defined for AGRIELEV(2) in the relationship 

table, is written in the current relationship that is being created for AGRIELEV(3). Likewise, 
C-48

when AGRIELEV(1) is selected in the dropdown box and transferred to the relationship, 

OFFLNAQF–OFFLNAQN, which is the relationship defined for AGRIELEV(1) in the relationship 

table, is written in the current relationship being created for AGRIELEV(3).

The relationship for the mean residence time of water can now be specified using the 

placeholder input AGRIELEV(3). Notice in Figure C.51 that when a previously defined related 

input is used in the specification of a related input, the expression for the previously defined 

input is enclosed in square braces in the specification of the current related input. Such use of 

placeholder inputs facilitates the creation of more complex relationships than would otherwise 

be possible with just the four arithmetic operators. A more direct way to create these complex 

relationships will be available in future versions of the code. The placeholder inputs, 

AGRIELEV(1), AGRIELEV(2), and AGRIELEV(3), are removed from the relationship table once 

the desired relationship for the mean residence time of water in the lake is transferred to the 

relationship table (Figure C.44).

The code computes the values for the related inputs as they are being specified. Consider, for 

example, the placeholder input AGRIELEV(2) (Figures C.49 and C.50). A number of memory 

spaces, equal to the number of simulations (i.e., observations × repetitions) are set aside for 

AGRIELEV(2) when it is defined as a dependent input. When the specification of this 

placeholder reaches the stage shown in Figure C.49, the value sampled for the hydraulic 

conductivity in the saturated zone for each simulation is placed in the memory set aside for this 

placeholder input. When the relationship AGRIELEV(2) = HCSZ − 700 is updated into the 

relationship table, 700 is subtracted from the quantities in those memory spaces. When the 

situation shown in Figure C.44 is reached there will be 100 values of mean residence time of 

water in the surface water body in the memory space set aside for TLAKE. These will be 

related to the probabilistic values sampled for the hydraulic conductivity in that simulation and to 

the deterministic values of the volume of the lake, the hydraulic gradient in the saturated zone 

from the contamination to the surface water body, and the width and depth of the aquifer 

intercepted by the surface water body. Figure C.52 plots against hydraulic conductivity the 

values computed for the mean residence time of water in the surface water body using the 

relationship.
C-49

FIGURE C.50 Using a Related Input in the Relationship of Another Input

FIGURE C.51 Indirect Introduction of [ ] Using Placeholder Inputs, Enabling Creation 

of Complex Relationships
C-50

FIGURE C.52 Relationship between Mean Residence Time of Water 

in the Surface Water Body and the Hydraulic Conductivity 

in the Saturated Zone

C.3.4.2 Influence of the Relationship on the Peak Predicted Dose

The computational code is launched from the “Step by step analysis” tab after all the 

relationships have been specified. The computational code then uses the values computed for 

the related inputs, the values sampled for the probabilistic inputs, and the deterministic values 

for the remaining inputs to run the simulations and generates a set of peak predicted doses and 

peak predicted risks. Figure C.53 shows the variation of peak predicted dose from the ingestion 

of fish with hydraulic conductivity in the saturated zone, when the relationship between the 

mean residence time of water in the surface water body and the hydraulic conductivity is 

specified: RESRAD-OFFSITE models the effects of the larger volume of water that passes 

through the surface water body as the hydraulic conductivity increases. 
C-51

FIGURE C.53 Variation with Hydraulic Conductivity of Peak Predicted 

Dose from Ingestion of Fish When a Relationship Is Specified 

between Hydraulic Conductivity and Mean Residence Time 

of Water in the Surface Water Body

There are three major considerations that affect the peak predicted dose from the ingestion of 

fish as the hydraulic conductivity increases:

1. The faster travel rate reduces the transport time, decreasing the loss from radiological 

transformations and causing the peak predicted dose from the ingestion of fish to 

increase with increasing hydraulic conductivity.

2. More of the plume passes through the depth of aquifer that is intercepted by the surface 

water body as the hydraulic conductivity increases, causing the peak predicted dose 

from the ingestion of fish to increase.

3. The increase in hydraulic conductivity also increases the amount of water that passes 

through the surface water body in a year, which tends to dilute the radionuclides in the 

surface water body and to flush them out more quickly, reducing accumulation. As a 

result, the peak predicted dose from ingestion of fish tends to decrease with increasing 

hydraulic conductivity. 

Initially, the first two processes dominate and the peak predicted dose from the ingestion of fish 

increases with hydraulic conductivity. As the hydraulic conductivity continues to rise, the third 

process becomes more important and at some point negates the increase from the first two 

processes. The peak predicted dose from the ingestion of fish then falls with increasing 

hydraulic conductivity. Figure C.18 shows the corresponding plot when this relationship was not 

specified. The third process was not modeled, leading to an increase in peak predicted dose 

with increasing hydraulic conductivity when the relationship was not specified (Sections C.3.1 

and C.3.2). 
C-52

Comparing the two figures shows that when the relationship is considered, the peak predicted 

dose from the ingestion of fish is higher when the hydraulic conductivity is less than the 

deterministic value, and lower when the hydraulic conductivity is higher than the deterministic 

value. 

Figure C.54 shows the variation of peak predicted dose from all exposure pathways with 

hydraulic conductivity in the saturated zone when the relationship between hydraulic 

conductivity and mean residence time of water in the surface water body is specified. 

(Figure C.12 shows the corresponding plot when this relationship is not specified.) The fish 

ingestion pathway makes a noticeable contribution to the peak predicted dose at hydraulic 

conductivities greater than about 750 m/yr in this example for the reasons discussed in 

Section C.2.2.2. As seen in the preceding paragraphs, this is also the range of hydraulic 

conductivity in which the doses in Figure C.53 are lower than the doses in Figure C.18. Recall 

that Figures C.53 and C.18 show the variation of peak predicted dose from the ingestion of fish 

with hydraulic conductivity with and without consideration of the relationship between the mean 

residence time of water in the surface water body and hydraulic conductivity, respectively. 

Thus, Figures C.54 and C.12 differ only at the higher values of hydraulic conductivity, and the 

curve in Figure C.54 is lower than that in Figure C.12 in that region.

FIGURE C.54 Variation with Hydraulic Conductivity of Peak Predicted Dose 

from All Pathways When a Relationship Is Specified between 

Hydraulic Conductivity and Mean Residence Time of Water 

in the Surface Water Body

C.3.5 Simultaneous Sensitivity Analysis on Two or More Inputs

Sections C.3.2 and C.3.3 conclude pointing out the need for performing multi-input sensitivity 

analysis. This section expands the distributed single-input sensitivity analysis example to 

illustrate how those can be performed and what outputs are available in RESRAD-OFFSITE to 

determine the sensitivities of peak predicted dose to the different inputs of interest. It 
C-53

progresses gradually to more complex cases to show the difficulties with graphical output, and 

the need to rely on multivariable regression analysis. 

C.3.5.1 Sensitivity Analysis on Two Inputs Using Continuous and Discrete 

Uniform Distributions

The discussion in Section C.3.3 suggests that the sensitivity of peak predicted dose to hydraulic 

conductivity in the saturated zone will depend on the values used for the inputs describing the 

well: the well depth and the well pumping rate. This section considers simultaneous sensitivity 

analyses on two inputs; simultaneous sensitivity analyses on three inputs will dealt with in a 

later section. The example considered in Section C.3.4 is expanded by including a discrete 

distribution for the depth of the aquifer contributing to the well. 

Begin with the input file used for the distributed single-input sensitivity analysis. Save the file 

under a different name (e.g., “Two Inputs One Discrete.ROF”). Go to the Saturated Zone 

Hydrology form and place the cursor on the input box for depth of aquifer contributing to the 

well.

Press the Shift-F8 function key. The “Parameter distributions” tab of the Uncertainty and 

Probabilistic Analysis form pops up, as shown in Figure C.55. 

Click on the Distribution dropdown box and select “Discrete Cumulative.” Use six entries to 

sample depths of 5, 6, 7, 8, 9, and 10 m with equal probability, as in Figure C.55; click the 

“Update parameter stats and distribution” button to save this distribution. The reason for using a 

discrete distribution instead of a continuous distribution will become apparent in Section C.3.5.4, 

where a continuous distribution is used for the depth of the aquifer contributing to the well. The 

number of observations needs to be increased in order to see the variation of peak predicted 

dose with hydraulic conductivity, now that sensitivity analysis is being performed on two inputs. 
C-54

FIGURE C.55 Specifying a Discrete Distribution on an Input

Go to the “Sample specification” tab of the Uncertainty and Probabilistic Analysis form. 

Increase the number of observations to 600. Click on the “Generate input samples” button on 

the “Step by step analysis” tab. The code samples 600 values uniformly in the interval 200 to 

2000 for hydraulic conductivity in the saturated zone. It also samples 600 values from the equal 

probability discrete distribution of 5, 6, 7, 8, 9, and 10 for the depth of aquifer contributing to the 

well—100 samples at each of the six values. It then combines the samples for the two inputs to 

make 600 pairs of values for hydraulic conductivity and depth of aquifer contributing to the well. 

The 600 pairs of values can be viewed by clicking the “View scatter plot of input vs. input” 

command button in the “Step by step analysis” tab. The resulting screen is shown in 

Figure C.56. Specify the relationship between the mean residence time of water in the surface 

water body and the hydraulic conductivity in the saturated zone as in Section C.3.4.1. Click on 

the “Generate output samples (RESRAD-O)” command button to launch the computational 

code.
C-55

FIGURE C.56 Pairing of Samples in a Two-input Probabilistic Analysis 

Where One Input Has a Continuous Uniform Distribution 

and the Other a Discrete Uniform Distribution

The variation of peak predicted dose from all exposure pathways with hydraulic conductivity can 

be visualized in the scatter plot of the two. Click the “View scatter plots of output vs. input” 

button. This displays the Probabilistic/Uncertainty Outputs form. Use the up/down arrows in the 

“X-axis” frame to change the variable to “Hydraulic conductivity of saturated zone.” This 

displays the plot shown in Figure C.57. The six “curves” correspond to the six discrete depths 

that were sampled to determine the extent of the aquifer contributing to the well. It is difficult to 

distinguish the curves in the low range of hydraulic conductivity. This is the region where the 

peak predicted dose is most sensitive to hydraulic conductivity—some of the curves are rising 

and others are falling, making it difficult to trace the trend in this region. One way to clarify the 

plot is to make the code sample more points in this region. 
C-56

FIGURE C.57 Variation of Peak Predicted Dose with Hydraulic Conductivity 

at Different Discrete Values of Depth of Aquifer Contributing 

to the Well

C.3.5.2 Sensitivity Analysis on Two Inputs Using a Continuous Linear 

Distribution and a Discrete Uniform Distribution

The values sampled by the code are spread evenly over the range when a uniform distribution 

is specified for hydraulic conductivity (Figure C.56). The peak predicted dose changes rapidly in 

the range of hydraulic conductivity 200 to 700 in Figure C.57. More values need to be sampled 

from this range to show the response of peak predicted dose in this region. This can be 

achieved by specifying a continuous linear distribution, as shown in Figure C.58. The code will 

obtain 60% of the samples for hydraulic conductivity from the range 200 to 700 m/yr and the 

remaining 40% of the samples from the range 700 to 2000 m/yr. Save the file under a different 

name (e.g., “Two Inputs One Discrete Refined.ROF”) and generate input samples. The 

resulting pairs of probabilistic inputs—hydraulic conductivity in the saturated zone and the depth 

of aquifer contributing to the well—are shown in Figure C.59. The points are very closely 

spaced in the 200 to 700 m/yr range of hydraulic conductivity and are sparsely spaced in the 

range 700 to 2000 m/yr. Specify the relationship between the mean residence time of water in 

the surface water body and the hydraulic conductivity in the saturated zone as in 

Section C.3.4.1. Click on the “Generate output samples (RESRAD-O)” button to launch the 

computational code.
C-57

FIGURE C.58 Specifying a Continuous Linear Distribution

FIGURE C.59 Samples from a Continuous Linear Distribution Showing a Greater 

Concentration of Samples from One Part of the Range and Sparse 

Sampling over the Rest of the Range

The variation of peak predicted dose from all exposure pathways with hydraulic conductivity can 

now be better visualized in the scatter plot (Figure C.60). Six “curves” correspond to the six 

discrete depths that were sampled to determine the extent of the aquifer contributing to the well. 

They have the same tendency: the peak predicted dose increases with hydraulic conductivity, 

reaches a maximum, and then decreases first rapidly and then more gradually with increasing 

hydraulic conductivity. The data for these plots are in the peak predicted dose data file (with 
C-58

extension .pds) and the probabilistic input sample data file (with extension .pin). These can be 

opened in a spreadsheet or transferred into a plotting program. 

Figure C.61 focuses on the region where the peak predicted dose changes rapidly. The 

sensitivity of peak predicted dose to hydraulic conductivity is highly dependent on the depth of 

aquifer contributing to the well in this range of hydraulic conductivity. This clearly illustrates the 

need for multi-input sensitivity analysis. A three-point single-input sensitivity analysis in the 

hydraulic conductivity range of 200 to 600 m/yr would have shown an increasing trend if 

performed with a 5-m depth of aquifer contributing to the well. It would have shown a 

decreasing trend when performed with a 10-m depth of aquifer contributing to the well. If a 

three-point single-input sensitivity analysis had been performed at an intermediate value of 

depth of aquifer contributing to the well, it would have shown a trend where the peak predicted 

dose falls on either side of the central value of hydraulic conductivity.

FIGURE C.60 Variation of Peak Predicted Dose with Hydraulic Conductivity 

at Discrete Values for Depth of Aquifer Contributing to the Well
C-59

Figure C.61 Variation of Peak Predicted Dose with Hydraulic Conductivity 

in the Range 200 to 800 m/yr at Discrete Values for Depth 

of Aquifer Contributing to the Well

The scatter plot of peak predicted dose against hydraulic conductivity in the saturated zone 

shown in Figure C.60 has six curves. A six-valued discrete distribution was specified for the 

depth of aquifer contributing to the well. It can therefore be inferred that each curve 

corresponds to a different depth. It is not usual to find distinct curves on this plot because (1) it 

is a scatter plot; (2) typically, the distributions for the other inputs are not discrete; and 

(3) distributions are specified for many inputs in a multi-input sensitivity analysis. There is, 

therefore, no labeling of the curves when they appear in this two-input (one continuous, one 

discrete) sensitivity analysis, which is a special case of multi-input sensitivity analysis. It is, 

however, possible to determine which curve corresponds to which depth by viewing the scatter 

plot of peak predicted dose against the depth of aquifer contributing to the well (Figure C.62). 

The highest value of peak predicted dose at the different depths of aquifer contributing to the 

well is approximately the same. The peak predicted dose has the greatest range when the 

depth of aquifer contributing to the well is 10 m. The range of the peak predicted dose decrease 

as the well depth decreases. This information helps identify the corresponding curves on 

Figure C.60.

Peak dose vs hydraulic conductivity at different well depths

20

25

30

35

40

45

200 300 400 500 600 700 800

Hydraulic conductivity m/y

peak dose from all exposure pathways mrem/y

5

6

7

8

9

10
C-60

Figure C.62 Range of Peak Predicted Dose at Different Discrete Values for 

Depth of Aquifer Contributing to the Well Caused by Variation of 

Hydraulic Conductivity

The scatter plot of peak predicted dose against the depth of aquifer contributing to the well 

(Figure C.62) does not show how the peak predicted dose varies with the depth of aquifer 

contributing to the well. There are points representing 100 different values of hydraulic 

conductivity at each well depth. Because the 100 hydraulic conductivity values used at each 

depth are different, it is not possible to see how the peak predicted dose varies with depth of the 

aquifer contributing to the well at a constant value of hydraulic conductivity in the saturated 

zone. However, the scatter plots of peak predicted dose against hydraulic conductivity 

(Figures C.60 and C.61) indicate how the peak predicted dose varies with the depth of the 

aquifer. 
C-61

The trend can be seen by looking at the peak predicted doses for the six curves at a specific 

value of hydraulic conductivity. When the hydraulic conductivity is in the range 500 to 

2000 m/yr, the peak predicted dose decreases as the depth of aquifer contributing to the well 

increases from 5 to 10 m. When the hydraulic conductivity is in the range 200 to 250 m/yr, the 

peak predicted dose increases as the depth of aquifer contributing to the well increases from 5 

to 10 m. When the hydraulic conductivity is in the range 250 to 500 m/yr, the peak predicted 

dose increases, reaches a maximum, and then decreases as the depth of aquifer contributing to 

the well increases from 5 to 10 m. 

Although we are able see the trend, we cannot visualize the shape of the relationship. That 

would require a sensitivity analysis with a continuous distribution for the depth of aquifer 

contributing to the well and a discrete distribution for the hydraulic conductivity. This is left for 

the reader to do as an exercise.

C.3.5.3 Sensitivity Analysis on Three Inputs Using a Continuous Linear 

Distribution for One and Discrete Uniform Distributions for the

Other Two

The discussion in Section C.3.3 suggested that the sensitivity of peak predicted dose to 

hydraulic conductivity in the saturated zone depends not only on the values used for the inputs 

describing the well, but also on the values used for the inputs that determine the infiltration 

through the primary contamination. This section expands the previous example further to 

consider simultaneous sensitivity analyses on three inputs. 

The example considered in Section C.3.5.2 is expanded by including a discrete distribution for 

the evapotranspiration coefficient. Begin with the input file used for the distributed single-input 

sensitivity analysis. Save the file under a different name (e.g., “Three Inputs Two 

Discrete.ROF”). Go to the Primary Contamination form containing the physical and hydrological 

inputs and place the cursor on the input box for evapotranspiration. Press the Shift-F8 function 

key. The “Parameter distributions” tab of the Uncertainty and Probabilistic Analysis form will 

appear. Click on the Distribution dropdown box and select “Discrete Cumulative.” Use three 

entries to sample evapotranspiration coefficients of 0.4, 0.5, and 0.6 with equal probability; click 

the “Update parameter stats and distribution” button to save this distribution. 

If the six discrete valued distribution specified in Section C.3.5.2 for the depth of aquifer 

contributing to the well were to be used, we would expect to see 6 × 3 curves. A larger number 

of simulations would be required to produce the 18 curves. It would also be difficult to make out 

the 18 curves in the same scatter plot, especially in the regions where the curves intersect or 

are close together. 

Go to the Saturated Zone Hydrology form and place the cursor on the input box for depth of 

aquifer contributing to the well. Press the Shift-F8 function key. The “Parameter distributions” 

tab of the Uncertainty and Probabilistic Analysis form pops up—change it to a discrete 

distribution with three equally probable values of 5, 7.5, and 10 m. This reduces the anticipated 

number of distinct curves in the scatter plot of peak predicted dose against hydraulic 

conductivity to nine.

Click on the “Generate input samples” button on the “Step by step analysis” tab. This launches 

the sampling code and produces the specified number of probabilistic input sets. Each 

probabilistic input set contains a sample from each of the three distributions specified for the 
C-62

three inputs. Specify the relationship between the mean residence time of water in the surface 

water body and the hydraulic conductivity in the saturated zone, as in Section C.3.4.1. Click on 

the “Generate output samples (RESRAD-O)” button to launch the computational code.

The scatter plot of peak predicted dose against each of the three probabilistic inputs and the 

related input can be viewed after the code finishes all the simulations. Click the “View scatter 

plots of output vs. input” button to display the Probabilistic/Uncertainty Outputs form. Use the 

up/down arrows in the X-axis frame to cycle thorough the four variables. The scatter plot of 

peak predicted dose against hydraulic conductivity in the saturated zone is shown in 

Figure C.63. There are three curves in the upper range of hydraulic conductivity—as shown in 

Section C.3.5.2, these correspond to the three discrete depths that were sampled to determine 

the extent of the aquifer contributing to the well. Each of these three curves splits into three 

curves in the lower range of hydraulic conductivity. These correspond to the three levels of 

evapotranspiration coefficient. The scatter plot of peak predicted dose against 

evapotranspiration coefficient, Figure C.64, indicates that the upper branch of the three curves 

corresponds to the higher evapotranspiration coefficient. 

The variation of peak predicted dose with hydraulic conductivity in the saturated zone is highly 

dependent on the values used for the depth of aquifer contributing to the well and for the 

evapotranspiration coefficient (Figure C.63). This clearly illustrates the need for multi-input 

sensitivity analysis and highlights the importance of using site-specific or at least siteappropriate values and distributions for all the inputs when performing sensitivity analysis.

The discussion in Section C.3.3 suggested some of the inputs that influence the sensitivity of 

peak predicted dose to hydraulic conductivity in the saturated zone. These include the depth of 

aquifer contributing to the well, the well pumping rate, the dispersivities in the saturated zone, 

the precipitation rate, the runoff and evapotranspiration coefficients, and irrigation rates. If 

discrete distributions with just two values were specified for each of these eight inputs, there 

could be 28 (= 256) curves on the scatter plot of peak predicted dose against hydraulic 

conductivity in the saturated zone. One obviously cannot differentiate among that many distinct 

curves on one plot. While the idea of performing a multi-input sensitivity analysis with a 

continuous distribution for one input and discrete distributions for the other inputs that affect the 

way the first input influences the peak predicted dose is a good way to understand that 

influence, it is only practical when the number of inputs is small. Even when the number of 

distinct curves is manageable, the number of simulations needed to produce the curves can be 

very large. There is also the need to know which inputs to include in the analysis. 

Such an analysis, where a continuous distribution is specified for one input and discrete 

distributions are specified for the other inputs, is useful only in understanding the variation of 

peak predicted dose with the input for which a continuous distribution was specified. A number 

of multi-input sensitivity analyses would have to be performed—each one with the continuous 

distribution on a different input—to gain insight into the manner in which an input of interest

affects peak predicted dose. 

While this method of multi-input sensitivity analysis might give insight into the influence of an 

input on the peak predicted dose, it does not provide an easy way to compare the relative 

influences of a number of inputs. The range of the peak predicted dose over the siteappropriate or site-specific range of the input is a possible measure of the importance of that 

input (Section C.2.3.3). But the range of the peak predicted dose varies from curve to curve in 

this method of sensitivity analysis. It is not possible to visually separate out the contributions of 

the different inputs to the range of the peak predicted dose in the scatter plot.
C-63

FIGURE C.63 Variation of Peak Predicted Dose with Hydraulic Conductivity—

the Scatter Shows the Effect of Sampling the Depth of Aquifer 

Contributing to the Well and the Evapotranspiration Coefficient

FIGURE C.64 Peak Predicted Dose at Three Values of Evapotranspiration 

Coefficient—the Range of Peak Predicted Dose Is Due 

to Sampling the Depth of Aquifer Contributing to the Well 

and the Hydraulic Conductivity

The relative influences of different inputs can be gauged from a single sensitivity analysis. If a 

single analysis is to be used, it is necessary to specify either site-appropriate or site-specific 

distributions for all the inputs. The site-appropriate or specific distributions are likely to be 

continuous. A commonly used technique of gauging the relative influences of different inputs 

involves the following steps:
C-64

• Step 1. Perform multi-input sensitivity analysis by specifying site-appropriate or sitespecific distributions for all the inputs.

• Step 2. Perform linear regression analysis between the output, the peak predicted dose, 

and the distributed inputs. Use the standardized regression coefficient or the 

standardized rank regression coefficient to identify the inputs that have a significant 

influence on the variability in the peak predicted dose. (Linear regression is discussed in 

Section C.3.6.)

• Step 3. Perform a second multi-input sensitivity analysis by specifying the same 

distributions as in Step 1 for only the inputs that were identified in Step 2. 

• Step 4. Compare the distributions of peak predicted dose that resulted from the two 

multi-input sensitivity analyses preformed in Steps 1 and 3. Repeat Steps 2 and 3 until 

the distribution of peak predicted dose resulting from Step 3 is close to the distribution of 

peak predicted dose resulting from Step 1.

This method is incorporated in the RESRAD-OFFSITE code. 

C.3.5.4 Sensitivity Analysis on Two Inputs Using Continuous Distributions

Two-input sensitivity analysis with a view to visually understanding how one of those inputs 

affects peak predicted dose was illustrated and discussed in Sections C.3.5.1 and C.3.5.2. This 

section deals with two-input sensitivity focused on evaluating the relative influence of the inputs. 

A key requirement is to use distributions that are appropriate for the site. The sensitivity 

analysis is usually performed before significant resources have been expended to develop sitespecific distributions; in fact, the sensitivity analysis identifies the significant inputs so that the 

limited resources can be focused on identifying site-specific distributions. Thus, distributions 

that are appropriate for the site, based on factors such as its location, climate, 

terrain/topography, soil type, and vegetation need to be used—it will be seen in this and 

subsequent sections that the influence of inputs depends on their distribution. Assume for this 

example that a uniform distribution from 200 to 2000 m/yr is appropriate for hydraulic 

conductivity and a uniform distribution from 5 to 10 is appropriate for the depth of aquifer 

contributing to the well. 

Open the file used in Section C.3.5.1, “Two Inputs One Discrete.ROF”, and save it as “Two 

uniform Inputs.ROF.” This has the desired distribution for hydraulic conductivity in the saturated 

zone, but not for the depth of aquifer contributing to the well. View the “Uncertainty/

Probabilistic Interface.” Go to the “Parameter distributions” tab of the Uncertainty and 

Probabilistic Analysis form. Click on “depth of aquifer contributing to the well” entry in the table 

on the left. Change the distribution to a uniform distribution from 5 to 10 m; click the “Update 

parameter stats and distribution” button to save these changes.

Click on the “Generate input samples” button on the “Step by step analysis” tab. The code 

samples 600 values uniformly in the interval 200 to 2000 for hydraulic conductivity in the 

saturated zone. It also samples 600 values uniformly in the interval of 5 to 10 m for the depth of 

aquifer contributing to the well. It then makes 600 pairs of values of hydraulic conductivity and 

depth of aquifer contributing to the well. The 600 pairs of values can be viewed by clicking the 

“View scatter plot of input vs. input” button in the “Step by step analysis” tab. The resulting 

screen is shown in Figure C.65. The pairs of values are distributed evenly over the entire space 

of the plot, a result of specifying uniform distributions for the two probabilistic inputs and 

requiring pairing with zero correlation.
C-65

Specify the relationship between the mean residence time of water in the surface water body 

and the hydraulic conductivity in the saturated zone as in Section C.3.4.1. Click on the 

“Generate output samples (RESRAD-O)” button to launch the computational code.

FIGURE C.65 Pairing of Samples in a Two-input Probabilistic Analysis 

Where Both Inputs Have Continuous Distributions

The scatter plot of peak predicted dose against each of the two probabilistic inputs and the 

related input can be viewed after the code finishes all the simulations. Click the “View scatter 

plots of output vs. input” button to display the Probabilistic/Uncertainty Outputs form. Use the 

up/down arrows in the X-axis frame to cycle thorough the three variables. The scatter plot of 

peak predicted dose against hydraulic conductivity in the saturated zone is shown in 

Figure C.66. This scatter plot shows a strong relationship between the peak predicted dose and 

the hydraulic conductivity. The 600 points are clustered within a band that first rises and then 

falls with increasing hydraulic conductivity. The width of the band in the direction parallel to the 

y-axis ranges from 6.5 to 16 mrem/year, compared with a 32.6 mrem/year range of the peak 

predicted dose (Figure C.68). The peak predicted dose at any saturated hydraulic conductivity 

varies over a range due to the effects of all the other distributed inputs. In this case, it quantifies 

the effect of the depth of the aquifer contributing to the well, which is the only other distributed 

variable.
C-66

FIGURE C.66 Variation of Peak Predicted Dose with Hydraulic 

Conductivity—the Scatter Shows the Effect of Sampling 

the Depth of Aquifer Contributing to the Well

The scatter plot of peak predicted dose against the depth of the aquifer contributing to the well 

is shown in Figure C.67. The 600 points are spread out over a wide band. The lower boundary 

of the band falls with increasing depth of aquifer contributing to the well; the upper boundary is a 

mild curve that first rises and then falls with increasing depth of aquifer contributing to the well. 

The width of the band in the direction parallel to the y-axis ranges from 25 to 32 mrem/year. 

The peak predicted dose at any depth of the aquifer contributing to the well varies over a range 

due to the effects of all the other distributed inputs. In this case, it quantifies the effect of the 

hydraulic conductivity in the saturated zone, the only other distributed variable in this analysis.

The range of the dose that is a consequence of the site-specific or site-appropriate distribution 

of an input is a direct indication of the influence of that input (Section C.2.3.3). In a twodistributed-input sensitivity analysis, the range of peak predicted dose that results from one of 

the distributed inputs can be determined from the scatter plot of peak predicted dose against the 

other distributed input. The range can be estimated from the scatter plot by clicking the mouse 

on the two ends of the band of points at the same x-value, as shown in Figure C.68. Thus, the 

peak predicted dose ranges from 21.8 to 38 mrem/yr as the depth of aquifer contributing to the 

well ranges from 5 to 10 m at a hydraulic conductivity of 653 m/yr—a range of 16.2 mrem/year. 

The range of the peak predicted dose at a few representative hydraulic conductivities can be 

obtained by applying this procedure on the plot shown in Figure C.66: 17.3 at 200, 7.7 at 360, 

16.2 at 650, 9.8 at 1100, 7.9 at 1550, and 6.6 at 2000. This gives an average range of 

11 mrem/yr attributable to the 5 to 10 m range of depth of aquifer contributing to the well. 

Applying the same procedure on the scatter plot of peak predicted dose against depth of aquifer 

contributing to the well (Figure C.67) gives a 30 mrem/yr range of peak predicted dose 

attributable to the 200 to 2000 m/yr range of hydraulic conductivity in the saturated zone. In this 

example, the variations in hydraulic conductivity cause almost three times as much variability in 

the peak predicted dose as the variations in the depth of aquifer contributing to the well: 

30 mrem/yr to 11 mrem/yr. 
C-67

FIGURE C.67 Variation of Peak Predicted Dose with Depth of Aquifer 

Contributing to the Well—the Scatter Shows the Effect 

of Sampling the Hydraulic Conductivity

FIGURE C.68 Estimating the Range of Peak Predicted Doses at Any Given Value 

of x-coordinate
C-68

Another way of estimating the contribution of each distributed input to the variability of the peak 

predicted dose is by performing linear regression analysis. The regression analyses available in 

RESRAD-OFFSITE are described in Section C.3.6. That section also discusses the different 

coefficients that result from those regression analyses. The regression output for this example 

is shown in Figure C.69. The output—the coefficient of determination—shows that the linear 

regression on the ranks of the peak predicted dose and the two inputs is able to explain 94% of 

the variation in the peak predicted dose in this example. The output—the standardized rank 

regression coefficients or SRRC—shows that the hydraulic conductivity in the saturated zone 

causes almost thrice the variability in peak predicted dose as the depth of aquifer contributing to 

the well: 0.91 compared with 0.34. 

FIGURE C.69 Linear Regression on Standardized Raw and Ranked Data 

for the Two-input Continuous Distribution Example

The variability in peak predicted dose that results from a distributed input depends on the 

distribution used for the input. This is illustrated by repeating the above analysis with a 

narrower distribution—uniform from 500 to 1000 m/day—for the hydraulic conductivity in the 

saturated zone. The regression output and the scatter plots, Figures C.70 through C.72, show 

that the variabilities in peak predicted dose from the two distributed inputs are about the same. 

Comparison of the results of the two analyses in this subsection again highlights the need to 

use site-specific or site-appropriate distributions when performing sensitivity analysis.

FIGURE C.70 Linear Regression on Standardized Raw and Ranked Data for the Second 

Two-input Continuous Distribution Example
C-69

FIGURE C.71 Variation of Peak Predicted Dose with Hydraulic 

Conductivity—the Scatter Shows the Effect 

of Sampling the Depth of Aquifer Contributing 

to the Well for the Second Example Case

FIGURE C.72 Variation of Peak Predicted Dose with Depth 

of Aquifer Contributing to the Well—the Scatter

Shows the Effect of Sampling the Hydraulic

Conductivity for the Second Case

C.3.5.5 Sensitivity Analysis on Three Inputs Using Continuous Distributions

A three-input sensitivity analysis using continuous distributions was performed by adding a 

uniform distribution of 0.4–0.6 for evapotranspiration. The relationship between the residence 

time in the lake and the saturated hydraulic conductivity was specified as in the previous 

example after generating the input samples. The regression output and scatter plots of peak 
C-70

predicted dose against the three inputs are shown in Figures C.73 through C.76. These will be 

discussed in Section C.3.6 to illustrate regression analyses.

FIGURE C.73 Linear Regression on Standardized Raw and Ranked Data 

for the Three-input Continuous Distribution Example

FIGURE C.74 Variation of Peak Predicted Dose with Hydraulic 

Conductivity—the Scatter Shows the Effect 

of Sampling the Depth of Aquifer Contributing 

to the Well and the Evapotranspiration Coefficient
C-71

FIGURE C.75 Variation of Peak Predicted Dose with Depth of Aquifer 

Contributing to the Well—the Scatter Shows the Effect 

of Sampling the Hydraulic Conductivity and the 

Evapotranspiration Coefficient

FIGURE C.76 Variation of Peak Predicted Dose with

Evapotranspiration Coefficient—the Scatter Shows

the Effect of Sampling the Hydraulic Conductivity 

and the Depth of Aquifer Contributing to the Well

C.3.6 Linear Regression

The peak dose predicted by the code depends on the values of the inputs: the peak predicted 

dose is the dependent variable, the inputs are the independent variables. If all but one of the 

inputs were fixed and only one input were allowed to vary, it would be easy see the relationship 

between the dependent and independent variables from a plot of the two (Figure C.77). If the 
C-72

relationship is strictly linear, then quantifying the relationship is straightforward. The relationship 

can be quantified using any two points on the plot. 

FIGURE C.77 Scatter Plot of a Linear Relationship 

for a Case Involving Only a Single Variable

Most of the situations in practice involve more than one independent variable. In this case it is 

difficult to see the relationship between the dependent and independent variables and 

quantifying the relationship is not trivial. Linear regression analysis is one of the methods that 

can be used to quantify the relationship in a multivariable case. The different types of linear 

regression options available in RESRAD-OFFSITE and the different coefficients in the 

regression output of the code are described in the following subsections.

C.3.6.1 Linear Regression on Raw Values

Figures C.78 and C.79 show scatter plots of a dependent variable against each of two 

independent variables. The first independent variable has a range of 0.2 to 0.4, while the 

second has a range of 0.2 to 0.8. In this example, the dependent variable is one less than five 

times the first independent variable plus three times the second independent variable. One 

hundred samples of the independent variables and the corresponding values of the dependent 

variable are shown in Table C.4. Although the dependent variable is a linear function of each of 

the independent variables, the plots of dependent variable against each independent variable 

are not straight lines because of the contribution of the other independent variable. Both plots 

show a tendency of the dependent variable increasing with increasing values of the independent 

variables. The relationship between the dependent variable and the independent variables in 

this example can be quantified using a linear regression analysis. 

Y = 5 X

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

X

Y
C-73

FIGURE C.78 (Left) Scatter Plot of the Dependent Variable and the First Independent 

Variable for a Case Involving a Linear Relationship with Two 

Independent Variables

FIGURE C.79 (Right) Scatter Plot of the Dependent Variable and the Second 

Independent Variable for a Case Involving a Linear Relationship 

with Two Independent Variables

The coefficient of determination of the linear regression on the data in this example (Table C.4) 

was 1.0; this coefficient is an indication of how much of the variation in the dose is explained by 

the linear regression. In this example the dependent variable is strictly a linear function of the 

two independent variables. Therefore, the regression between the dependent variable and the 

two independent variables was able to explain all the variation in the dependent variable in 

terms of the variation in the two independent variables, so the coefficient of determination 

was 1.

Y = 5 X1 + 3 X2 - 1

0

0.5

1

1.5

2

2.5

3

3.5

0.2 0.25 0.3 0.35 0.4

X1

Y

Y = 5 X1 + 3 X2 - 1

0

0.5

1

1.5

2

2.5

3

3.5

0.2 0.4 0.6 0.8

X2

Y
C-74

TABLE C.4 One Hundred Samples of Data Used in Section 3.6.1 to 

Illustrate Linear Regression on Raw Values

X1 X2 Y = 5 X1+3 X2 -1 X1 X2 Y = 5 X1+3 X2 -1 X1 X2 Y = 5 X1+3 X2 -1

0.30930 0.75332 2.80643 0.31508 0.65245 2.53277 0.32822 0.36408 1.73334

0.35477 0.78836 3.13894 0.27370 0.35838 1.44363 0.37387 0.39191 2.04511

0.34270 0.32052 1.67508 0.23660 0.64959 2.13178 0.36828 0.25533 1.60738

0.34448 0.47251 2.13992 0.26774 0.62248 2.20614 0.33953 0.78409 3.04991

0.32648 0.65787 2.60598 0.25471 0.26501 1.06857 0.31203 0.67937 2.59824

0.37681 0.33943 1.90235 0.38704 0.35577 2.00252 0.20348 0.41810 1.27171

0.23911 0.53951 1.81405 0.36208 0.63572 2.71759 0.26590 0.72329 2.49937

0.23124 0.48010 1.59653 0.32215 0.54773 2.25392 0.27460 0.45755 1.74568

0.22346 0.52169 1.68235 0.29332 0.31950 1.42511 0.32540 0.46672 2.02715

0.21625 0.75163 2.33613 0.29615 0.36849 1.58620 0.29044 0.52696 2.03308

0.34769 0.56596 2.43632 0.28203 0.20445 1.02350 0.39406 0.66622 2.96895

0.33050 0.78140 2.99670 0.34998 0.43280 2.04829 0.39321 0.27649 1.79550

0.35235 0.22642 1.44101 0.20153 0.33296 1.00651 0.35743 0.55594 2.45497

0.25664 0.60419 2.09580 0.36148 0.59171 2.58254 0.30215 0.62616 2.38924

0.39820 0.24120 1.71460 0.20645 0.23083 0.72472 0.27813 0.24969 1.13971

0.34127 0.49956 2.20504 0.22475 0.21393 0.76555 0.33244 0.29942 1.56047

0.22724 0.42613 1.41456 0.38047 0.69975 3.00163 0.26857 0.73646 2.55224

0.36436 0.57751 2.55435 0.33655 0.31362 1.62362 0.28523 0.39450 1.60968

0.35001 0.45956 2.12874 0.25022 0.69621 2.33974 0.37425 0.41001 2.10127

0.23482 0.27932 1.01207 0.30754 0.50867 2.06370 0.24059 0.44920 1.55054

0.20417 0.43580 1.32827 0.24441 0.72911 2.40940 0.37007 0.68544 2.90667

0.25912 0.37872 1.43177 0.22920 0.64310 2.07530 0.31765 0.53120 2.18187

0.38404 0.44306 2.24939 0.24216 0.21814 0.86521 0.24876 0.51573 1.79101

0.24648 0.59628 2.02124 0.28668 0.48430 1.88630 0.37811 0.40853 2.11616

0.32193 0.56945 2.31802 0.21322 0.67157 2.08083 0.30588 0.33091 1.52216

0.39734 0.50508 2.50192 0.38928 0.29530 1.83229 0.21103 0.77040 2.36633

0.33402 0.49210 2.14638 0.35847 0.74299 3.02131 0.23386 0.34800 1.21328

0.36776 0.55055 2.49044 0.31154 0.57829 2.29254 0.21427 0.30252 0.97892

0.28113 0.61754 2.25825 0.38336 0.71664 3.06671 0.29835 0.61064 2.32367

0.27657 0.38426 1.53563 0.30124 0.70825 2.63097 0.20849 0.58751 1.80499

0.31883 0.76158 2.87887 0.28857 0.71073 2.57505 0.29426 0.40256 1.67899

0.39157 0.24306 1.68701 0.27110 0.27058 1.16723 0.26282 0.79544 2.70045

0.22067 0.28673 0.96355 0.21941 0.21158 0.73180 0.25299 0.68777 2.32826

0.26134 0.76788 2.61035

The partial correlation coefficient between the dependent variable and the first independent 

variable was 1.0, as was the partial correlation coefficient between the dependent variable and 

the second independent variable. The partial correlation coefficient is a measure of how linear 

the relationship is between the dependent variable and one of the independent variables after 

accounting for the effects of all the other independent variables. In this case it is unity for both 

cases because the dependent variable is strictly linearly related to each of the independent 

variables. The correlation coefficients between the dependent variable and each of the two 

independent variables, on the other hand, would not be equal to unity because of the effects of 

the other dependent variable. The correlation coefficients were 0.49 (dependent variable and 
C-75

the first independent variable) and 0.88 (dependent variable and the second independent 

variable) in this example.

 

The regression coefficients for the first and second independent variables were 5 and 3, 

respectively. The regression analysis was able to determine the exact multipliers that were 

used to compute the dependent variable in this example because of the strict linear relationship 

that was used in the initial computations of the dependent variable. They would have been 

close to these values if the computation of the dependent variable had included some random 

error as well. 

The coefficient of determination can be used to gauge how well a particular regression explains 

the variations in the dependent variable. This can help decide whether to use those particular 

regression results to select a set of significant inputs. The partial correlation coefficients show 

how close the relationships between the dependent variable and each of the independent 

variables are to being linear, but they do not indicate how much influence each independent 

variable has on the variability of the predicted dose. The regression coefficients show how the 

dependent variable is related to the independent variables under a linear model. 

There are two related considerations that limit their use as indicators of the influence of the 

corresponding independent variable on the dependent variable: (1) the units of the correlation 

coefficient and (2) the spread or range of the independent variables. The regression 

coefficients are represented by i c s in the expression = ∑ XcY ii . The units of each regression 

coefficient i c are the units of the dependent variable, Y, divided by the units of the 

corresponding independent variable, Xi . 

If the independent variables are of different units, so will be the regression coefficients. It is not 

meaningful to use the numerical values of regression coefficients with different units to decide 

on the factors that have a significant influence on the predicted dose, because the numerical 

value can be changed simply by changing the units of the independent variable. For example, a 

regression coefficient can be changed by a factor of 1000 simply by changing the units of a 

length-based independent variable from m to km. 

The contribution of an independent variable to the variation of the dependent variable depends 

not only on the regression coefficient but also on the spread of the independent variable. If two 

independent variables are spread out in approximately the same manner, the one with the 

higher regression coefficient will have a larger influence on the variation of the dependent 

variable. If the regression coefficients of two independent variables are approximately the 

same, the one that is more spread out will have a larger influence on the variation of the 

dependent variable. 

The product of the regression coefficient and the measure of the spread of the variable gives a 

good indication of the effect of the independent variable on the variation of the dependent 

variable. One way to quantify the spread is by the range—this only describes how far apart the 

two extreme values are, and is not affected by how the other samples are distributed within that 

range. The standard deviation of the samples of an independent variable captures the spread 

of all the samples and is therefore a better measure of the spread. 

The numerical values of the regression coefficients for the two independent variables in this 

example are 5 and 3. They would be in the units of the dependent variable divided by the units 
C-76

of the corresponding independent variable. The standard deviations of the independent 

variables are 0.058 and 0.174, each in the units of the corresponding variable. The products of 

the correlation coefficients and the corresponding standard deviations are of the same units—

the units of the dependent variable—and can be compared to gauge the influence of the 

independent variables on the variability of the dependent variable. It is customary to divide

each of these products by the standard deviation of the dependent variable. The resulting 

nondimensional coefficients, or “standardized regression coefficients,” for the two independent 

variables in this example are 0.48 and 0.87, respectively. When the first independent variable is 

changed by a standard deviation of its distribution, the dependent variable is expected to 

change by 0.48 of its distribution according to the linear regression.

C.3.6.2 Linear Regression on the Ranks of the Values

Many of the inputs of RESRAD-OFFSITE influence the peak predicted dose in a nonlinear 

fashion. A linear approximation is applicable when the range of those inputs is small. The 

deviation from linearity increase as the range of the inputs grows larger. Figures C.80–C.82 

show scatter plots of a dependent variable against each of three independent variables. The 

dependent variable in this example is the sum of the first independent variable, the square of 

the second independent variable and the inverse of the third independent variable. A linear 

regression may not be able model the nonlinear relationship especially when the deviation from 

linearity is large. Each of the three plots shows the relationship between the dependent variable 

and the corresponding independent variable and also the scatter of the dependent variable due 

to the other two independent variables. 

The relationship between the dependent variable and the first independent variable is linear 

(Figure C.80). The contribution of the second independent variable to the dependent variable 

increases as that variable increases throughout its range. The contribution of the third 

independent variable to the dependent variable decreases through its range. These 

relationships are monotonic; there is a one to one relationship between the dependent and 

independent variables. Monotonic relationships can be linearized by using the ranks of the 

values instead of the raw values. The rank is the place of a value in a sorted list. Figures C.83–

C.85 show scatter plots of the ranks of the data of the dependent variable against the ranks of 

the data of each of the three independent variables. 

Linear regression can be performed on the ranks of the data. The resulting coefficient of 

determination indicates how much of the variation in the rank of the dependent variable is 

explained by the linear regression model on the ranks. If this is greater than the coefficient of 

determination of the regression on the raw data, the results of the regression on the ranks of the 

data can be used to select the inputs that have a significant influence on the dependent 

variable. The standardized rank regression coefficients are used to identify the inputs that have 

a significant influence in this case.
C-77

FIGURE C.80 Scatter Plot of the Dependent Variable 

and the First Independent Variable for a Case 

Involving Linear and Nonlinear Relationships

with Three Independent Variables

FIGURE C.81 Scatter Plot of the Dependent Variable 

and the Second Independent Variable 

for a Case Involving Linear and Nonlinear 

Relationships with Three Independent Variables

3X1

3X1 + 5(X2)

2

 + 1/X3

0

2

4

6

8

10

12

14

16

18

0 0.2 0.4 0.6 0.8 1

X1

Y

Y =

Y =

5(X3)

2

3X1 + 5(X2)

2

 + 1/X3

0

2

4

6

8

10

12

14

16

18

0 0.2 0.4 0.6 0.8 1

X2

Y

Y =

Y =
C-78

FIGURE C.82 Scatter Plot of the Dependent Variable 

and the Third Independent Variable 

for a Case Involving Linear and Nonlinear 

Relationships with Three Independent Variables

FIGURE C.83 Scatter Plot of the Rank of the Dependent 

Variable and the Rank of the First Independent 

Variable for a Case Involving Linear and Nonlinear 

Relationships with Three Independent Variables

1/X3

3X1 + 5(X2)

2

 + 1/X3

0

2

4

6

8

10

12

14

16

18

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

X3

Y

Y =

Y =

3X1

3X1 + 5(X2)

2

 + 1/X3

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Rank of X1

Rank of Y

Y =

Y =
C-79

FIGURE C.84 Scatter Plot of the Rank of the Dependent 

Variable and the Rank of the Second Independent 

Variable for a Case Involving Linear and Nonlinear 

Relationships with Three Independent Variables

FIGURE C.85 Scatter Plot of the Rank of the Dependent 

Variable and the Rank of the Third Independent 

Variable for a Case Involving Linear and Nonlinear 

Relationships with Three Independent Variables

5(X3)

2

3X1 + 5(X2)

2

 + 1/X3

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Rank of X2

Rank of Y

Y =

Y =

1/X3

3X1 + 5(X2)

2

 + 1/X3

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Rank of X3

Rank of Y

Y =

Y =
C-80

C.4 Multiple-input Sensitivity Analysis

The application of the sensitivity analysis tools that were described in the preceding two 

chapters to identify the sensitive inputs is illustrated by means of a hypothetical scenario in this 

chapter. The details of the hypothetical scenario are set out in Appendix C.I. The example 

scenario involves 203 distributed inputs. It is impractical to perform single-input sensitivity on 

each of these inputs even if one were not aware of the drawbacks associated with the use of 

single-input sensitivity analysis for the purpose of identifying the set of significant inputs 

(Sections C.2 and C.3). A multi-input sensitivity analysis involving all 203 distributed inputs can 

be performed to identify the distributed inputs that make a significant contribution to the 

variability in the output, the peak predicted dose. 

The number of times a distribution is sampled is termed the number of observations in 

RESRAD-OFFSITE; it is also referred to as the number of realizations. This must be large 

enough not only to ensure that the samples closely represent the distribution specified for each 

input, but also to ensure that they represent the multidimensional sample space of the 

203 inputs. Each distribution is sampled 500 times in this example. The analysis can be 

repeated with a different set of 500 samples. If the RESRAD-OFFSITE output for the different 

sets of samples agree (if they are statistically not different), then the number of samples chosen 

is sufficient for that analysis. The number of samples must be increased if the outputs from the 

repetitions are statistically different.

The multi-input sensitivity analysis can be performed in stages using the command buttons in 

the “Step by step analysis” tab of the Uncertainty/Probabilistic Analysis form or it can be 

performed all at once using the “run” command. In either case, the cumulative distribution 

function plots of the inputs can be used to judge whether the number of observations is 

sufficient to closely represent the distributions specified for the inputs. Figure C.86 is typical of 

the cumulative distribution function plots of the samples of the inputs used in this example. The 

plots for the three repetitions are indistinguishable, indicating that the number of observations is 

sufficient to closely represent the distributions used in this example. The cumulative distribution 

function plots of the samples of all the inputs must be checked to ensure that the plots of the 

repetitions are close. It is not as easy to verify that the number of observations chosen is 

sufficient to accurately represent the grouping in multidimensional space. One way to do this is 

to check the correlations between the samples of the inputs. Unfortunately, there are 20,503 

(= 203 × 202 ÷ 2) correlations between the 203 inputs—far too many numbers to look at for 

each repetition! A good check of whether the number of observations used is large enough is 

the cumulative distribution function of the output, the peak predicted dose. As seen in 

Figure C.87, the cumulative distribution functions of the peak predicted doses from three 

repetitions of this example are in good agreement.

C.4.1 Identification of Significant Inputs

RESRAD-OFFSITE has two aids to help identify the significant inputs: a regression report with 

the inputs sorted in descending order of significance and scatter plots of output against inputs. 

The scatter plots are available for all multi-input sensitivity analyses. The user chooses whether 

or not to perform regression analysis between the output and inputs, as well as whether to 

perform it on raw data, ranked data, or on both. If regression analysis is performed on both raw 

and ranked data, the code compares the coefficients of determination for the regression on the 

raw data and the regression the ranked data. The coefficient of determination measures how 

well a regression modeled the variation in the output (peak predicted dose). The absolute 
C-81

values of the standardized regression coefficients of the regression, raw or ranked, that has the 

higher coefficient of determination are used to sort the inputs in descending order of influence. 
C-82

FIGURE C.86 Cumulative Distribution Function of One of the Inputs
C-83

FIGURE C.87 Cumulative Distribution Function of the Output, the Peak Predicted Dose
C-84

C.4.2 Identifying Significant Inputs Using the Regression Report

Part of the sorted regression report is shown in Figure C.88. The coefficient of determination of 

the regression on the raw data is just slightly greater than the coefficient of determination of the 

regression on the ranked data. The inputs are therefore sorted by the absolute values of the 

standardized regression coefficients. The standardized regression coefficient indicates by how 

many standard deviations the dose changes, according to the linear regression model of the 

raw data, when the input changes by a standard deviation. The top two inputs in this example, 

both relating to the source of water, have standardized regression coefficients of close to 0.4. 

The next five inputs are around 0.3, followed by four inputs with coefficients of 0.2 to 0.1, and 

17 inputs with standardized coefficients of 0.08 to 0.05. It is easier to see this when the 

absolute values of the sorted standardized correlation coefficients are plotted in a bar chart, as 

in Figure C.89. The first 11 inputs are seen to have a significant influence on the variability in 

the dose; the next 19 have a moderate influence; and the following 10 have a mild influence. 

The remaining 160 inputs have very little influence on the variability in the dose at this stage. 

The standardized regression coefficients from the three repetitions are in good agreement, 

suggesting that the number of samples is sufficient.

C.4.3 Identifying Significant Inputs Using Scatter Plots

The scatter plots of peak predicted dose against each of the distributed inputs can also be used 

to identify which inputs have a significant influence on the peak predicted dose. Viewing the 

scatter plot of peak predicted dose against each distributed input in turn can be tedious when 

there are a large number of distributed inputs (203 in this case). The up/down scroll arrows in 

the X-axis frame at the upper right of the scatter plot (Figure C.90) help cycle through the 

scatter plot. If the distribution specified for the input warrants it, a logarithmic scale must be 

used for that input. This can slow down the viewing of the scatter plots. Scatter plots for inputs 

identified as having a significant, moderate, or mild influence on the peak predicted dose are 

shown in Figures C.90 through C.99. The 11 inputs that have a significant influence can be 

identified easily from the scatter plots (Figures C.90–C.92). It is difficult to identify the inputs 

that have a moderate influence on the peak predicted dose because of the scatter caused by 

variations in the other inputs.
C-85

FIGURE C.88 Regression Report
C-86

FIGURE C.89 Plot of the Standardized Regression Coefficients from the Regression Report

-0.05

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00

1 6 11 16 21 26 31 36 41 46 51 

Standardized regression coefficient

-0.05

0.10

0.05

0.00

61656973778185899397

101105109113117121125129133137141145149153157161165169173

repetition 1

repetition 2

repetition 3
C-87

FIGURE C.90 Scatter Plots of Peak Predicted Dose against Inputs Identified as the Four Most Sig

by the Regression Analysis
C-88

FIGURE C.91 Scatter Plots of Peak Predicted Dose against Inputs Identified as the Second Set 

of Four Most Significant by the Regression Analysis
C-89

FIGURE C.92 Scatter Plots of Peak Predicted Dose against Inputs Identified as the Third Set 

of Four Most Significant by the Regression Analysis
C-90

FIGURE C.93 Scatter Plots of Peak Predicted Dose against Inputs Identified as the Fourth Set 

of Four Most Significant by the Regression Analysis
C-91

FIGURE C.94 Scatter Plots of Peak Predicted Dose against Inputs Identified as the Fifth Set 

of Four Most Significant by the Regression Analysis
C-92

FIGURE C.95 Scatter Plots of Peak Predicted Dose against Inputs Identified as the Sixth Set 

of Four Most Significant by the Regression Analysis
C-93

FIGURE C.96 Scatter Plots of Peak Predicted Dose against Inputs Identified as the Seventh Set 

of Four Most Significant by the Regression Analysis
C-94

FIGURE C.97 Scatter Plots of Peak Predicted Dose against Inputs Identified as the Eighth Set 

of Four Most Significant by the Regression Analysis
C-95

FIGURE C.98 Scatter Plots of Peak Predicted Dose against Inputs Identified as the Ninth Set 

of Four Most Significant by the Regression Analysis
C-96

FIGURE C.99 Scatter Plots of Peak Predicted Dose against Inputs Identified as the 10th Set 

of Four Most Significant by the Regression Analysis
C-97

C.4.4 Verification of Selection of Significant Inputs

There are two ways of verifying that the set of input identified as having a significant influence 

on the variability in the dose is in fact responsible for the major part of the variability in the dose. 

The easier method is to perform a second multi-input sensitivity analysis after deleting the 

distributions on all but those inputs that were identified as having a significant influence. The 

more cumbersome method involves performing the second multi-input sensitivity analysis after 

drastically narrowing the ranges of the distributions for all but those inputs that were identified 

as having a significant influence. 

The advantage of the second method is that the sample values and, more importantly, the 

pairings of the samples of the initial multi-input sensitivity analysis are retained for the significant 

inputs. The closeness of the cumulative distribution function plots from the two multi-input 

sensitivity analyses confirms that none of the inputs that have a significant influence on the 

variability of the predicted dose has been left out. Figure C.100 compares the cumulative 

distribution function plots from (1) the multi-input sensitivity analyses on all inputs, (2) the multiinput sensitivity analyses on only the 11 inputs identified as significant, and (3) the multi-input 

sensitivity analysis with the original distributions for the 11 inputs identified as significant and 

narrower (by a factor of 100) distributions for those inputs that were not so identified.

FIGURE C.100 Cumulative Distribution Function Plots from the Three Multi-input 

Sensitivity Analyses

C.4.5 Implications of This Set of Influential Inputs 

Three of the 11 inputs identified as having a significant influence on the peak predicted dose in 

this example relate to the surface water body: volume of surface water body, mean residence 

time of water in surface water body, and depth of aquifer contributing to surface water body. 

Five pertain to the primary contamination: x-dimension of primary contamination, y-dimension of 

primary contamination, thickness of contaminated zone, dry bulk density of contaminated zone, 

and leach rate of Ra-226. Two are inputs that affect the rate of transport through the 

CDF of dose with all variables and only the significant variables

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120

Dose

Cumulative probability

All inputs

All inputs

All inputs

Only the significant inputs

Only the significant inputs

Only the significant inputs

Narrow distributions for the rest

Narrow distributions for the rest

Narrow distributions for the rest
C-98

unsaturated zone: Distribution coefficient of Ra-226 in Unsaturated Zone 1 and Distribution 

coefficient of Pb-210 in Unsaturated Zone 1. 

The remaining significant input is quantity of water for consumption by humans. Taken 

together, this indicates that the variability in the peak predicted dose in this example is mainly 

from the exposure and transport pathway that involves leaching from the contamination, 

transport through the unsaturated zone and groundwater to the surface water body, 

accumulation in the surface water body, and, finally, consumption of water.

The 19 inputs that were identified as having a moderate influence on the peak predicted dose in 

this example also fall into some broad groups. Three inputs relate to transport in the saturated 

zone: distance in the direction parallel to aquifer flow from downgradient edge of contamination 

to the surface water body, distance in the direction perpendicular to aquifer flow from center of 

contamination to left edge of the surface water body, and vertical lateral dispersivity of saturated 

zone to surface water body. 

Six inputs are used to compute the erosion release from the primary contamination to the 

surface water body: soil erodibility factor of contaminated zone, rainfall and runoff factor in area 

of primary contamination, cover and management factor in area of primary contamination, 

slope-length-steepness factor in area of primary contamination, support practice factor in area 

of primary contamination, and sediment delivery ratio. 

Six inputs are used in the modeling of the contamination and consumption of fruit, grain, and 

nonleafy vegetables: irrigation applied per year (m/yr) to fruit, grain, and nonleafy vegetable 

fields; foliage-to-food transfer coefficient of fruit, grain, and nonleafy vegetables; wet weight crop 

yield (kg/m2

) of fruit, grain, and nonleafy vegetables; weathering removal constant (1/year) of 

fruit, grain, and nonleafy vegetables; duration of growing season (years) of fruit, grain, and 

nonleafy vegetables; and fruit, grain, and nonleafy vegetables consumption rate. 

Four inputs are used in modeling exposure by the ingestion of meat: irrigation applied per year 

(m/yr) to pasture and silage fields, wet weight crop yield (kg/m2

) of pasture and silage, grain 

(kg/day) intake of meat livestock, and meat consumption rate. These show that the erosion 

release, transport through the saturated zone, ingestion of fruit, grain, and nonleafy vegetables, 

and ingestion of meat also contribute to the variability in the peak predicted dose.

C.4.6 Place of Multi-input Sensitivity Analysis in Probabilistic Analysis

Site-specific probabilistic analysis is usually an iterative or cyclic process. The first iteration is a 

multi-input sensitivity analysis using site-appropriate distributions for many of the inputs. Siteappropriate distributions are distributions that are expected to be appropriate for the site based 

on some general characteristic of the site. The general site characteristics include the location 

of the site, the climate at the site, the type of soil or soil classification at the site, the topography 

of the site, and the vegetation at the site. National distributions may be used for some inputs in 

this first iteration (e.g., for inhalation rate). The results of this first multi-input sensitivity analysis 

are sets of inputs deemed have a “significant,” “moderate,” and “mild” influence on the variability 

in the peak predicted dose. 

The next step involves finding site-specific distributions for the inputs identified as having a 

significant influence on the variability in the peak predicted dose. It might be possible to 

determine the site-specific distributions for some of the other inputs at a smaller incremental 

cost at the same time. It is therefore important to bear in mind the inputs that were identified as 
C-99

having a moderate or even mild influence on the variability in the peak predicted dose. Any 

relationships or correlations between these inputs will also be identified at this time.

The next iteration is another multi-input sensitivity analysis. The site-specific distributions found 

for the significant inputs and any that were found for the moderate inputs replace the 

distributions used in the preceding iteration. The relationships and correlations between the 

inputs are also specified for this iteration of probabilistic analysis. New sets of inputs that have 

a significant, moderate, and mild influence on the variability in the peak predicted dose will be 

identified from the output of this iteration. 

This process of identifying significant inputs then finding and using site-specific distributions for 

these significant inputs in the next iteration is repeated until the set of significant inputs identified 

in an iteration all have site-specific distributions specified for them. At this stage of probabilistic 

analysis site-specific distributions would have been identified and specified for all the important 

inputs, relationships between the inputs would have been specified, and correlations between 

inputs would have been identified and specified. 
C-100

C.4.7 Use of National Distributions for the First Iteration

It is tempting to use national distributions for the first iteration of the probabilistic analysis. This 

is tried out on the hypothetical scenario discussed in Appendix C.I. The cumulative distribution 

function plots of the peak predicted dose for the three repetitions with 500 observations each 

are shown in Figure C.101. A logarithmic scale is used for the x-axis, because the distribution 

for the peak predicted dose spans many orders of magnitude. Although the plots appear to be 

close, this is misleading because of the logarithmic axis. The three repetitions differ by up to 

56% in the upper half of the plot, compared with less than 5% difference between the repetitions 

in Figure C.87. The absolute values of the sorted standardized rank regression coefficients 

from the regression report are shown in Figure C.102.

There is good agreement between the standardized rank regression coefficients from the 

repetitions for the three most significant inputs. The differences between the coefficients from 

the repetitions become large in proportion to the average of the coefficients across the 

repetitions for the next seven significant inputs. The standardized rank regression coefficients 

for the 11th most significant input are –0.06, –0.04, and 0.01 from the three repetitions; the 

range is more than twice the mean and even changes sign. Standardized rank regression 

coefficients of –0.06 and –0.04 would have been significant, especially when the standard 

deviation of peak predicted dose is as high. The standard deviation of peak predicted dose in 

this example is in the 1000 to 2000 mrem/yr range (Figure C.101). The large differences 

between the standardized rank regression coefficients from the three repetitions call into 

question the reliability of these numbers. 

The differences between the cumulative distribution function plots for the repetitions and the 

differences between the standardized rank regression coefficients from the repetitions indicates 

the need to use a larger number of samples (observations) for each repetition. Thus, the 

analysis was repeated with 5000 observations; this reduced the differences between plots of the 

cumulative distribution function from the repetitions to 30%. The resulting cumulative 

distribution plots are in Figure C.103. Plots of the absolute values of the standardized rank 

regression coefficients from the regression report of inputs are shown in Figure C.104. Part of 

the regression report is shown in Figure C.105. 

There is much more consistency between the standardized rank regression coefficient in this 

case, which allows the 21 most significant inputs to be identified with confidence. The national 

distributions generally have a wide range, and the response of the dose is likely to be 

nonlinearly related to the inputs when the range of the inputs is large. This is evident in the 

small coefficients of determination, 0.10 to 0.13, for the regression analysis on the raw data 

from the repetitions. Using the ranks of the data will yield a linear relationship if the relationship 

between the raw data is monotonic. The relatively high coefficient of determination of 0.85 for 

the regression on the ranks of the data indicates that the relationship was close to monotonic. 

The standardized ranked regression coefficients from the regression are able to explain 85% of 

the variation in the ranks of the dose.
C-101

FIGURE C.101 Cumulative Distribution Function of the Output, the Peak Predicted Dose, W

Distributions Are Used to Obtain 500 Samples of Each of the 203 Inputs
C-102

FIGURE C.102 Plot of the Standardized Regression Coefficients from the Regression Repo

Analysis Using 500 Observations on National Distribution

-0.1

0

0.7

0.6

0.5

0.4

0.3

0.2

0.1

1 8 15 22 29 36 43 50 57 64 71 78 85 92 

Standardized regression coefficient

Series1

Series2

Series3
C-103

FIGURE C.103 Cumulative Distribution Function of Peak Predicted Dose with 5000 Samples

Distributions Are Used for the Inputs
C-104

FIGURE C.104 Plot of the Standardized Regression Coefficients from the Regression Repo

Analysis Using 5000 Observations on National Distributions

-0.1

0

0.7

0.6

0.5

0.4

0.3

0.2

0.1

1 8 15 22 29 36 43 50 57 64 71 78 85 92 

Standardized regression coefficient

Series1

Series2

Series3
C-105

FIGURE C.105 Regression Report of Sensitivity Analysis Using 5000 Observations on National D
C-106

Site-specific distributions can then be found for the inputs that were identified as significant in 

this first iteration. These site-specific distributions would then be used in the next iteration of 

multi-input sensitivity analysis. A new set of significant inputs is identified from this iteration of 

the multi-input sensitivity analysis and site-specific distributions are found for any for which 

national distributions were used in this iteration. If this iterative process were repeated until all 

the significant inputs identified in an iteration already had site-specific distributions specified 

from them, would the results be the same as the results from a probabilistic analysis that used 

site-appropriate distributions for the first iterations? Not necessarily, as can be seen in the 

following sections.

C.4.8 Implications of This Set of Influential Inputs from Using National 

Distributions

The 21 inputs identified fall into five categories. Eight of these inputs are used to model the 

erosion release from the primary contamination to the surface water body: y-dimension of 

primary contamination, x-dimension of primary contamination, cover and management factor in 

area of primary contamination, slope-length-steepness factor in area of primary contamination, 

rainfall and runoff factor in area of primary contamination, soil erodibility factor of contaminated 

zone, support practice factor in area of primary contamination, and sediment delivery ratio. 

Five inputs are used to compute the concentration in the surface water body: mean residence 

time of water in surface water body, volume of surface water body, Distribution coefficient of 

Po-210 in sediment in surface water body, Distribution coefficient of Ra-226 in sediment in 

surface water body, and Distribution coefficient of Pb-210 in sediment in surface water body. 

One input, water for consumption by humans, deals with the ingestion of water. Three inputs 

are part of the meat ingestion pathway: weathering removal constant (1/year) of pasture and 

silage, duration of growing season (years) of pasture and silage, and intake to animal product 

transfer factor of Po for meat. 

Four inputs are used to compute the exposure from the ingestion of fruit, grain, and nonleafy 

vegetables: soil-to-plant transfer factor of Ra for fruit, grain, and nonleafy vegetables; depth of 

soil mixing layer or plow layer (meters) of fruit, grain and nonleafy vegetables; duration of 

growing season (years) of fruit, grain, and nonleafy vegetables; and cover and management 

factor of fruit, grain, and nonleafy vegetable fields. 

This set of influential inputs has much in common with the one identified using the narrower 

“site-appropriate” distributions. The main exception is that this list does not have any inputs that 

relate to the leaching release and groundwater transport pathway. This brings up the question 

in the preceding subsection. The sensitivity analysis was repeated after reducing the influence 

of the erosion release to the surface water body and the release to the atmosphere. This was 

achieved by specifying very narrow distributions with very small values for the sediment delivery 

ratio and for the deposition velocity of dust in the area of primary contamination. 

The cumulative distribution function plots and the sorted regression report are shown in 

Figures C.106 and C.107. The contributions of the erosion release clearly decreased as 

evidenced by the eight orders of magnitude reduction in the peak predicted dose comparing 

Figures C.103 and C.106. This also shows that the contribution of the leaching and 

groundwater transport pathway is predicted to be even lower. The standardized rank regression 

coefficients for the 27th sorted input in the list are 0.00, 0.00, and 0.02 for the three repetitions; 

and 0.00, –0.01, and –0.02 for the 26th sorted input. Inputs 26 and 27, therefore, are not 

significant. There is good agreement between the standardized rank regression coefficients in 
C-107

the repetitions for the first 25 sorted inputs; therefore, these can reliably be included in the list of 

significant inputs. 

None of the inputs used to compute the leaching release or the transport by the groundwater 

pathways appears in this list. Some of the inputs that are used in the groundwater transport 

calculations have distributions with very wide ranges, as illustrated by the cumulative distribution 

function plots for the input samples for thickness of the unsaturated zone, the distribution 

coefficient of radium in the unsaturated zone, the hydraulic gradient, and the hydraulic 

conductivity in the saturated zone from the contamination to the surface water body 

(Figures C.108 through C.111). The distribution coefficient of radium in the saturated zone is 

similar to that shown in Figure C.109. Even with 5000 samples (observations), there apparently 

were no combinations of input samples that allowed the radionuclides to be transported to the 

surface water body in the 1000-year time frame of the analysis. Thus, when the national 

distributions were used, the groundwater-transport-related inputs would not be identified as 

being significant, even if they were in this example.
C-108

FIGURE C.106 Cumulative Distribution Function of Peak Predicted Dose with 5000 Samples

Distributions Are Used for the Inputs after Depressing Erosion Release to Su

and Release to Atmosphere
C-109

FIGURE C.107 Regression Report of Sensitivity Analysis Using 5000 Observations on Natio

Inputs after Depressing Erosion Release to Surface Water Body and Release 
C-110

FIGURE C.108 Cumulative Distribution Function Plot of the Input Samples for the Thicknes

of the Unsaturated Zone
C-111

FIGURE C.109 Cumulative Distribution Function Plot of the Input Samples for the Distributi

for Radium in the Unsaturated Zone
C-112

FIGURE C.110 Cumulative Distribution Function Plot of the Input Samples for the Hydraulic 

of the Saturated Zone to the Surface Water Body
C-113

FIGURE C.111 Cumulative Distribution Function Plot of the Input Samples for the Hydraulic 

of the Saturated Zone to the Surface Water Body
C-114

C.5 Summary and Conclusions

Three methods to perform sensitivity analysis on input parameters using the RESRADOFFSITE code have been demonstrated. The case studies presented are for illustration 

purposes only—parameter sensitivity may change from site to site. A summary of the 

advantages and drawbacks of each method follows:

• Three-point single-input sensitivity analysis can be performed easily and quickly. The 

temporal variations of predicted dose for the three simulations can be viewed on the 

same plot. Three-point single-input sensitivity analysis cannot take into account 

interactions among inputs, because just one input is analyzed at a time. It does not give 

a good indication of how the predicted dose varies over a range of input values because 

it uses only three simulations. It is also very tedious to compare the results when many 

inputs need to be analyzed.

• Distributed single-input sensitivity analysis can also be performed easily, but it takes 

more time than three-point single-input sensitivity analysis to perform because it uses 

more simulations. The large number of simulations can give a good indication of how 

the predicted dose varies over a range of the input. As with three-point single-input 

sensitivity analysis, distributed single-input sensitivity analysis does not take into account 

interactions among inputs. It is also very tedious to compare results when many inputs 

need to be analyzed.

• Multi-input sensitivity analysis can be performed using the probabilistic module in the 

code. Relationships and correlations among inputs can be specified. Interactions 

among inputs make it difficult to use output vs. input scatter plots to identify all the inputs 

that have a significant influence on the output. The standardized regression coefficients 

from a regression analysis between the raw or ranked values of the output and the input 

can be used to identify the inputs that have a significant influence on the predicted dose. 

A second multiple-input sensitivity analysis must then be performed to verify the 

identification of the significant inputs. Identification of significant inputs is an iterative 

process.

Although both methods of single-input sensitivity analysis (three-point and distributed) are useful 

in understanding how the RESRAD-OFFSITE code uses an input to model dose, they are 

usually not very useful for identifying the inputs that have a significant influence on predicted 

dose or risk. It should be emphasized that, whenever possible, site-appropriate distributions or 

ranges of parameter values must be used in the sensitivity analysis to identify the inputs that 

have a significant influence on the predicted dose. Some inputs that actually have a significant 

influence on the dose may not be identified as such if national distributions with wide ranges are 

used in the sensitivity analysis.
C-115

Appendix C.1 

Hypothetical Scenario for Multi-Input

Sensitivity Analysis

Site Layout and Dimensions 

The layout of the hypothetical site and the section through the contaminated layer are depicted 

in Figures C.1-1 and C.1-2. 

FIGURE C.1-1 Layout of the Hypothetical Site

FIGURE C.1-2 The Cross Section of the Primary Contamination and the Soil 

beneath It

Primary 

Contamination 

200 m x 200 m

Lake 

200 m x 300 m

Pasture

200 m x 200 m

Livestock feed 

grain

100 m x 200 m Nonleafy 

Vegetables

Leafy 

Vegetables

Dwelling

50 m x 50 m

North

Direction of Groundwater flow, East

490 m

570 m

460 

630 m

680 m

580 m

450 m

410 m

300 m

100 m

100 m x 100 m

Primary Contamination 

200 m x 200 m x 2 m

200 m

Unsaturated zone 

5 m thick

Aquifer 100 m thick
C-116

Radionuclides in the Primary Contamination

The radionuclides in the primary contamination and their concentrations are tabulated below.

226Ra: 35 pCi/g

210Pb: 35 pCi/g

210Po: 35 pCi/g

Preliminary Data for the Hypothetical Site

Preliminary data gathered for this site are as given below. All other inputs are assumed to be at 

the preloaded RESRAD-OFFSITE value for this preliminary analysis.

It is assumed that there is no cover on the pile. The preliminary data indicate that the release of 

the radionuclides from the waste pile is controlled by the rate of dissolution of the solids in which 

the radionuclides are embedded; the leach rates for all radionuclides are 0.0001 per year. The 

distribution coefficients for the radionuclides for both the unsaturated and saturated zones, and 

for all the offsite locations are as follows:

226Ra: 22 cm3

/g

210Pb: 5 cm3

/g

210Po: 5 cm3

/g

The average annual precipitation at this location is 1.25 m/yr. The primary contamination is not 

cultivated and is not irrigated. The cover management factor for the primary contamination is 

0.04 and the runoff coefficient is 0.5. This corresponds to an area that is 60% covered with 

weeds, short brush, and grass.

The leafy vegetables are grown in a field that has 20% slope and is farmed along the contour; 

so a support practice factor of 0.9, a cover and management factor of 0.08 and a slope length 

steepness factor of 4 are appropriate.

The fruit, grain, nonleafy vegetables and livestock feed grain are grown in relatively flat land. 

The cover management factor is 0.04 for these two areas.

Assume for atmospheric transport purposes that this hypothetical site is located in Peoria, 

Illinois. The topographical map indicates that the ground level of the livestock feed grain 

growing area is 15 m above the ground level at the location of primary contamination. The 

corresponding differences in elevation for the leafy vegetable growing area and the dwelling site 

are 20 and 40 meters. All the other offsite locations are at approximately the same elevation as 

the ground in the vicinity of the primary contamination. A preliminary sensitivity analysis on the 

grid spacing for this site shows that a grid spacing of 25 m is adequate for the desired accuracy. 

The hydraulic gradient of the groundwater is 0.004 across the entire site and the hydraulic 

conductivity is 105 m/yr. The longitudinal, horizontal lateral and vertical lateral dispersivities to 

the surface water body are estimated to be 8, 0.8 and 0.05 m respectively.

The surface water body is the source of all water used in this scenario. For groundwater 

transport purposes, the surface water body is 290 m along the groundwater flow line, from the 

down gradient edge of the primary contamination. The right and left edges of the surface water 

body are at 200 and 100 m from the groundwater flow line through the center of the primary 

contamination. This surface water body does not have any edible crustacea or fish.
C-117

The individual spends 0.5 of the time inside the dwelling, 0.2 of the time outdoors in the vicinity 

of the dwelling, 0.08 of the time in each of the vegetable plots and in the livestock grain field, 

and 0.01 of the time in the pasture. The remainder of time is spent away from the area.

A preliminary (deterministic) analysis of this scenario confirms that the long term dose from this 

site results from the 226Ra that was at the site because of the shorter half-life of the two other 

radionuclides that are initially present at the site. The 210Pb and 210Po that were initially present 

would have transformed away at the time of the peak in the dose. Thus, these two 

radionuclides are left out of the probabilistic sensitivity analysis in order to avoid spending 

computation time on computations that do not affect the final results.

Sections C.2 and C.3 emphasized the need to use site-appropriate if not site-specific 

distributions when performing sensitivity analysis. This is a hypothetical scenario. Rather than 

make up hypothetical “site-appropriate” distributions for this hypothetical sites, uniform 

distributions with a range of 20 percent of the point values, centered about the point values will 

be used for this example scenario. 

The exercise for this scenario is to perform sensitivity analysis to find the distributed inputs that 

have a significant impact on the dose.

Appendix D 

Source Release with Time-delay Options 

in RESRAD-OFFSITE Version 3.1

D-1 

Appendix D

Source Release with Time-delay Options 

in RESRAD-OFFSITE Version 3.1 

Version 3.1 of the RESRADOFFSITE code contains a 

range of options for the release 

of radionuclides to groundwater 

in addition to the original 

release option found in

Version 2. These options 

involve the following: 

• One of two release 

mechanisms, first-order ratecontrolled or instantaneous 

(equilibrium desorptioncontrolled) release; 

• A delay time during which 

there is no release to 

groundwater and possibly no 

release of particulates from 

the surface soil to either the 

atmosphere or to surface 

runoff; and 

• A transition time during which 

different proportions of the 

radionuclide-bearing material 

become exposed to the 

infiltrating moisture.

D.1 Version 2 

Release 

Methodology

The original source release 

model of the RESRADOFFSITE code Version 2 is the default 

option for Version 3 (Figure D.1) and is active when the “Version 2 Release Methodology” box is 

checked. In this case, the first-order leach rate specified in the first input box will be used 

provided that it is not zero and provided that it is less than the upper limit defined by the 

RESRAD methodology. Otherwise, the first-order leach rate is computed using the userspecified distribution coefficient. The value used by the code is shown in the input echo in the 

parent dose report (summary.rep).

FIGURE D.1 Specifying Inputs for the Version 2 

Release Methodology
D-2 

D.2 Conceptualization of New Release with Time-delay 

Options

The new release options conceptualize the material that contains the radionuclide as being in 

two states or forms: a form that is susceptible to releasing radionuclides to water that infiltrates 

the primary contamination and a form that is immune (not susceptible) to release. The form that 

is immune from releasing to infiltrating moisture can also be stipulated to be immune from 

releasing to the atmosphere. At any time period, a part of the radionuclide-bearing material can 

be in one form, and the remainder can be in the other form. The concentrations of the 

radionuclides contained in both the susceptible and immune forms change with time due to 

radiological transformations (both decay and ingrowth), whereas the concentration of the 

radionuclides in the susceptible form are also affected by the release to groundwater.

The concentration of the radionuclides (both parent and progeny) contained in the form that is 

immune to release is computed by the Bateman equation modified for the change in 

(releasable) form/state, as follows:

( ) ( ) ∑=

−= −

k

i

ik i

immune rel

k tatfts

1

1 , 1)( exp( λ ) , (D.1)

where

( )tsimmune

k is the concentration of the kth radionuclide of the transformation chain, in the material 

that is in the form that is immune to release (pCi/g),

( )tf rel

1 is the fraction of the radionuclide-bearing material that is in the releasable form 

(dimensionless),

a ,ik is a set of coefficients defined by the following:

)0(11,1 = sa , which is the initial concentration of radionuclide 1 in both forms (pCi/g),

ik

ikk

ik

a

a

λλ

λ

− = − ,1

, for all 1 <≤ ki , and

∑

−

=

−=

1

1

, ,

k

i

kk ik aa . 

λi is the radiological transformation rate of the ith radionuclide of the transformation chain (yr-1), 

and

t is the time since the determination of the inventory (yr).

The conceptual model envisions the material to be in the form immune to release for a userspecified period of time. This period of time, sometimes referred to as delay time, can be 

specified to be zero to model scenarios where some or all of the material is initially in the 

releasable form. The change of material from the release-immune form to the releasesusceptible form can be instantaneous (fraction at a specified time), or it can be continuous at a 

constant rate over a user-specified time (fraction/year), or it can even be a combination of the 

two. In this third scenario, a specified fraction of the material changes instantaneously at the 

beginning of the period of change followed by additional material changing at a constant rate 

over the period of change. For scenarios involving instantaneous changes, the user specifies 

the fractions of material that change to the releasable form at the different times and the time 
D-3 

interval between the instantaneous changes. The change at a constant rate is defined by 

specifying the period of change and the fractions of the material that has changed at the 

beginning and end of that time period.

The instantaneous increase in the activity of a radionuclide in the releasable form, which results 

from an instantaneous change in the form of the radionuclide-bearing material from the releaseimmune form to the releasable form, is given by:

( )∑ ( ) =

→ ∆= − +

k

i

um

pc

c

ik pci vm mix

unreleasable releasable rel

k C tTtTfAtatft

1

6

1 , )( exp( )ρλ 10)()( , (D.2)

where

C t)( unreleasable releasable

k

→ is the instantaneous change in activity of the kth radionuclide of the 

transformation chain at time t, from the release-immune form to the releasable form, in 

units of activity (pCi),

( )tf rel ∆ 1 is the instantaneous increase in the fraction of the parent radionuclide-bearing material 

that is in the releasable form, 

a ,ik is a set of coefficients defined by the following:

)0(11,1 = sa , the initial concentration of the first radionuclide in the transformation chain, 

in both forms (pCi/g),

ik

ikk

ik

a

a

λλ

λ

− = − ,1

, for all 1 <≤ ki , and

∑

−

=

−=

1

1

, ,

k

i

kk ik aa . 

λi is the radiological transformation rate of the ith radionuclide of the transformation chain (yr-1),

t is the time since the determination of the inventory (yr), 

ρ pc is the dry bulk density of the primary contamination (g/cm3

),

A is the area of the primary contamination (m2

), 

vm f is the volume fraction of the material from the primary contamination in the mixing layer,

tT )( c

mix is the thickness of the contaminated mixing layer (m),

tT )( um

pc is the thickness of the undisturbed primary contamination (m), and

6 10 is a conversion factor (cm3

/m3). 

The rate at which the activity of a radionuclide in the releasable form increases as a result of a 

continuous change of the radionuclide-bearing material from the release-immune form to the 

releasable form is given by the following:

( ) ( )∑ ( ) =

→ − + −

− =

k

i

um

pc

c

ik pci vm mix

dc

d

rel

c

rel

unreleasable releasable

k tTtTfAta

tt

tftf C t

1

6

,

1 1 )( exp( )ρλ 10)()(  , (D.3)

where
D-4 

C t)( unreleasable releasable

k

 → is the rate of change of the kth radionuclide, from the release-immune form 

to the releasable form (pCi/yr), 

( )tf rel

1 is the fraction of the parent radionuclide-bearing material that is in the releasable form,

dt is the time at which the radionuclide-bearing material first changes from the release-immune 

form to the releasable form (yr),

c t is the time as the radionuclide bearing material finishes changing from the release immune 

form to the releasable form (yr),

a ,ik is a set of coefficients defined by the following:

)0(11,1 = sa is the initial concentration of the first radionuclide in the transformation chain, 

in both forms (pCi/g),

ik

ikk

ik

a

a

λλ

λ

− = − ,1

, for all 1 <≤ ki , and

∑

−

=

−=

1

1

, ,

k

i

kk ik aa . 

λi is the radiological transformation rate (yr-1), 

t is the time since the determination of the inventory (yr),

ρ pc is the dry bulk density of the primary contamination (g/cm3

), 

A is the area of the primary contamination (m2

), 

vm f is the volume fraction of the material from the primary contamination in the mixing layer,

tT )( c

mix is the thickness of the contaminated mixing layer (m),

tT )( um

pc is the thickness of the undisturbed primary contamination (m), and

6 10 is a conversion factor (cm3

/m3). 

The concentration of the releasable form of the material varies with time and is influenced by the 

rate of release (leaching), the radiological transformation rates, and the rate of change from the 

release-immune form to the releasable form. The processes that are considered in modeling 

the concentration of the releasable form of a radionuclide are as follows. (The mathematical 

representations of the processes are written considering the activity of the releasable form of 

the radionuclide in the primary contamination over a time period of δt.) 

D.2.1 Change of Radionuclide-Bearing Material from Release-Immune Form to 

Releasable Form 

The change from the release-immune form to releasable form within the primary contamination 

is given by the following:

C ( ) tt unreleasable releasable

i δ  → , (D.4) 

where

unreleasable releasable Ci

 → is the time-dependent rate of change of the radionuclide from the releaseimmune form to the releasable form (pCi/yr). 
D-5 

D.2.2 Radiological Transformations 

The ingrowth of the releasable form within the primary contamination is given by the following:

tVts b

r

ii −1 )( δρλ , (D.5) 

where

λi is the radiological transformation rate of the radionuclide (yr-1),

)(1 tsr

i− is the releasable concentration of the parent radionuclide in primary contamination 

(pCi/g), 

ρb is the dry bulk density of primary contamination (g/cm3

), and

V is the volume of primary contamination (cm3

). 

The decay of the releasable form within the primary contamination is given by 

tVts b

r

ii )( δρλ . (D.6) 

where

λi is the radiological transformation rate of the radionuclide (yr

-1), 

ts )(r

i is the releasable concentration of the i

th radionuclide in primary contamination (pCi/g), 

ρb is the dry bulk density of primary contamination (g/cm3

), and

V is the volume of primary contamination (cm3

). 

D.2.3 First-order, Rate-controlled Leaching

The loss due to leaching is given by

tVts b

r

ii )( δρμ , (D.7) 

where

μi is the first-order rate at which the radionuclide is leached out of the mixing layer (yr-1),

ts )(r

i is the releasable concentration of the radionuclide in primary contamination (pCi/g), 

ρb is the dry bulk density of primary contamination (g/cm3), and

V is the volume of primary contamination (cm3

). 

The net effect of these processes is the change in the releasable activity in the primary 

contamination given by the following:

t

dt

tds V

r

i

b δρ )(

. (D.8) 

where
D-6 

ts )(r

i is the releasable concentration of the radionuclide in primary contamination (pCi/g), 

ρb is the dry bulk density of primary contamination (g/cm3

), and

V is the volume of primary contamination (cm3

). 

By equating the combined effects of the processes to the net change, we get the radioactivity

balance equation: 

C ( ) VtsVtsVtst

dt

tds V b

r

iib

r

iib

r

ii

unreleasable releasable

i

r

i ρb )()()( ρμρλρλ )( = + −1 − −  → . (D.9) 

This formulation simplifies to 

( ) ( ) )( )( )(

1 ts

V

C t

ts

dt

tds r

ii

b

unreleasable releasable

r i

iii

r

i

−

→

=++ + λ

ρ

μλ  . (D.10) 

This expression can be integrated from 0 to time t to obtain

( ) ( )

( ) ( ) ( ) ( ) ∫ ∫ +

−

→ + +−

+−

+− = + +

t

r t

i

t

i

t

unreleasable releasable t

i

b

t

r t

i

r

i C dtetsedtet

V

e

ests ii ii ii

ii

ii

0

1

0

)(

)0()( )( μλ μλ μλ

μλ

μλ λ

ρ

 (D.11) 

The form of C ( )t unreleasable releasable

i

 → needs to be known to solve this equation. It is assumed in the 

code thatC ( )t unreleasable releasable

i

 → has a linear variation between the known values at time points, as 

follows:

C ( ) ( ) Vtt bii

unreleasable releasable

i += ρβα  → , (D.12) 

where αi and βi are constants between each pair of the time points.

D.2.4 Releasable Concentration of the First Member of a Transformation Chain 

Representing the time-dependent deposition rate by a linear function of time and integrating6

yields: 

 

6 

( ) ( )

( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) 















+

− − +

− +

+

− = +

= + +

+ +

+−

+

+− +−

+

+−

+−

∫

2

11 11

11

11

0

1 1 11

0 1

1 )(

)0()(

11 11

11

11

11 11

11

11

11

μλ μλ β

μλ

α

ρβα

ρ

μλ μλ

μλ

μλ

μλ μλ

μλ

μλ

μλ

t t

i

t

t

i

r t t

t

t

b

b

t

r r t

te e

e

e

eets

t Ve dt

V

e

ests

 
D-7 

( )

( ) ( )

11

1

11

1

1

1 1

11

11

1

)0()( μλ

β μλ

β α μλ

μλ

+

+− 















+ −

= +

+−

+−

e t

ests

t

r r t . (D.13) 

Next, collecting the terms yields: 

r ( )t eCtAAts

1 11

1

1

1

0

1 1 )( +− μλ ++= , (D.14) 

where 

11

1 1

1 μλ

β

+

A = , 

11

1

1

11

1

11

11

1

1

0

1 μλμλ

α

μλ

μλ

β α

+ − + = +

+ −

= A A , and

0

1 1

11

11

1

1

1

1

1 sC )0( )0( As r r −= +

+ −

−= μλ

μλ

β α

 . 

D.2.5 Releasable Concentration of the Second Member of a Transformation Chain

The expression for the second member of the transformation chain is derived by building on the 

derivation for the first member of the chain, as follows:

( )

( ) ( )

( ) ( ) ∫ +− +

+−

+−

+

+

+− 















+ −

= +

t

t r t

t

r r t

dtetse

e t

ests

0

2 1

22

2

22

2

2

2 2

22 22

22

22

)(

1

)0()(

μλ μλ

μλ

μλ

λ

μλ

β μλ

β α

. (D.15) 

Substituting for the concentration of the first member and integrating7

gives the following:

 

7

 

( ) ( ) ( ) ( )

( ) ( )

( )

( )

1122

1

2 1

22

1

1

22

1

1

22

0

1

0

1

1

1

1

0

1

1 1

1

22 22 1122

22

11 22

μλ μλ μλλ

μλ

μλ μλ μλμλ

μλ

μλμλ

−−+

− +

+

− − +

+

+

− ++ =

+ + −−+

+

+− +

∫

o

t t t

t t

t t

L

e C e A te A

e AdteeCtAA
D-8 

( )

( ) ( )

( ) ( ) ( ) ( )

1122

1

12

22

1

1

22

1

0 1

1

2

22

2

22

2

2

2 2

11 22

22

22

22

1

1

)0()(

μλμλ

λ

μλ

μλ λ

μλ

β μλ

β α

μλ μλ

μλ

μλ

μλ

−−+

− +

+

+− 















+ −

+

+− 















+ −

= +

+− +−

+−

+−

+−

t t

t

t

r r t

ee C

e tA A A

e t

ests

. (D.16)

Collecting the terms yields:

r ( )t ( )t eCeCtAAts 11 2 22

2

1

2

1

2

0

2 2 )( +− μλ +− μλ ++= + , (D.17) 

where 

22

1

12

22

1 2

2 μλ

λ

μλ

β

+

+

+ = A A , 

22

1

2

22

0

12

22

2

22

22

1

0 1

1

2

22

22

2

2

0

2

μλμλ

λ

μλ

α

μλ

μλ λ

μλ

μλ

β α

+ − +

+

+ =

+

+ −

+

+

+ −

=

AA

A A

A

1122

1

1 12

2 μλμλ

λ

−−+ = C C , and 

1

2

0

2 2

2

2 )0( CAsC r −−= . 

D.2 6 Releasable Concentration of the jth Member of a Transformation Chain

Using the form of the expressions for the first and second members of the chains, the 

expression for the j

th member of the chain is obtained by induction. The concentration of the ith

member of the transformation chain in offsite soil is as follows:

( ) ∑=

+− ++=

i

k

k t

ii i

r

i kk eCtAAts

1

10 )( μλ . (D.18) 

Then, the concentration of the next member, j, of the transformation chain is given by: 
D-9 

( )

( ) ( )

( ) ( ) ∫ ∑ +

=

+− +−

+−

+−





 





+ ++

+

+− 















+ −

= +

t

t i

k

k t

ii i

t

j

jj

j

t

jj

j

j

r t

j

r

j

dteeCtAAe

e t

ests

jj kk jj

jj

jj

0 1

10

1

)0()(

μλ μλ μλ

μλ

μλ

λ

μλ

β μλ

β

α

. (D.19) 

Integration gives the following:

( ) ( ) ( )

( ) ( ) ( )

( )jj

ijj

t

jj

ijj

ijj

i

k kkjj

t t

k

ij

r t

j

r

j

e tA

A

A

ee

ests C

jj

kk jj

jj

μλ

λβ μλ

λβ λα

μλμλ

λ

μλ

μλ μλ

μλ

+

++− 















+

+

−+

+

−−+

− = +

+−

=

+− +−

+−

∑

1

1

0

1

1

)0()(

. (D.20) 

( )

( ) ( )

( ) ( ) ( ) ( )

∑=

+− +−

+−

+−

+−

−−+

− +

+

+− 















+ −

+

+

+− 















+ −

= +

i

k kkjj

t t

k

ij

jj

i

t

jj

i

i

j

jj

j

t

jj

j

j

r t

j

r

j

kk jj

jj

jj

jj

ee C

tAe A A

e t

ests

1

1

1

0 1

1

)0()(

μλμλ

λ

μλ

μλ λ

μλ

β μλ

β

α

μλ μλ

μλ

μλ

μλ

(D.21) 

Collecting the terms yields:

( ) ∑=

+− ++=

j

k

k t

jj j

r

j kk eCtAAts

1

10 )( μλ , 

where 

jj

jjj

jj

jj

jj

j

j

A A

A

μλ

λβ

μλ

λ

μλ

β

+

+ = +

+

+ = − −

1

1

1

1 1 , 

11

1 1

1 μλ

β

+

A = , 
D-10

,

10

1

0 1

1

1

0 1

1

0

jj

jjjj

jj

j

jj

jj

jj

j

jj

jj

j

j

j

jj

jj

j

j

j

AA

AA

A

A

A

μλ

λα

λμλ μ

λ

μλ

α

μλ

μλ λ

λ μ

μλ

β

α

+

−+ =

+ − +

+

+ =

+

+ −

+

+

+ −

=

−

−

−

−

11

1

1

11

1

11

11

1

1

0

1 μλμλ

α

μλ

μλ

β α

+ − + = +

+ −

= A A , 

kkjj

k

k jj

j

C

C

μλμλ

λ

−−+ = −1 for all ≠ jk , and

∑

−

=

−−=

1

1

0 )0(

j

k

k

j j

r

j

j

j CAsC , 0

1 1

11

11

1

1

1

1

1 sC )0( )0( As r r −= +

+ −

−= μλ

μλ

β α

 .

The release from the contaminated material into the infiltration water is computed by applying 

the first-order leach rate to the inventory of releasable radionuclides, as follows:

( ) ( ) 6 )( tTtTfAtstR 10)()( um

pc

c

pc vm mix

r

k = kk ρμ +

where 

tR )( k is the rate of release of the kth radionuclide, from the releasable form to the infiltrating 

water (pCi/yr).

μk is the first order release rate of the kth radionuclide from the releasable form to the infiltrating 

water (yr-1), 

t is the time since the determination of the inventory (yr),

ρ pc is the dry bulk density of the primary contamination (g/cm3

), 

A is the area of the primary contamination (m2

), 

vm f is the volume fraction of the material from the primary contamination in the mixing layer 

(dimensionless)

tT )( c

mix is the thickness of the contaminated mixing layer (m),

tT )( um

pc is the thickness of the undisturbed primary contamination (m),

6 10 is a conversion factor (cm3

/m3). 

The release rate for the equilibrium desorption release option can be obtained by using a very 

high value for the first-order leach rate. They can also be computed more directly as being 

equal to the rate of change from the release-immune form to the releasable form. The direct 
D-11

method is preferable because using a high leach rate to model the equilibrium desorption 

requires a much larger number of time points.

D.3 Three Release Options Described in Chapter 2 

The three release options of Version 3.0 beta discussed in Chapter 2 of this report—namely, 

First-Order Release with Transport, Equilibrium Release, and Uniform Release—are limiting 

cases of the more versatile releases in Version 3.1. 

D.3.1 Comparison of First-Order Release with Transport

The first-order release with transport discussed in Chapter 2 can be modeled in Version 3.1 

using the following procedures (and as illustrated in Figure D.2). First, uncheck the “Version 2 

Release Methodology” check box to activate the new release options. Verify that the four input 

boxes—Time at which radionuclide first becomes releasable (delay time), Fraction of 

radionuclide bearing material that is initially releasable, Time over which transformation to 

releasable form occurs, and Total fraction of radionuclide bearing material that is releasable are 

at their default values of 0, 1, 0, 1, respectively. Verify that the “First Order Rate Controlled 

Release with Transport” radio button is selected in the “Release mechanism” frame. Next, 

specify the desired leach rate in the “Initial Leach Rate” and “Final Leach Rate” input boxes. 

Finally, specify the distribution coefficient in the contaminated zone. 
D-12

FIGURE D.2 Specifying Inputs for First-Order, Rate-Controlled Release 

of Material That Initially Is Entirely in the Releasable Form 

The temporal plots of component (pathway) doses obtained from Version 3.1 for this case are 

compared with the temporal plots of component doses obtained for the first-order release with 

transport of Version 3.0 beta in Figure D.3. There are no differences between the two plots in 

Figure D.3.
D-13

FIGURE D.3 Comparison of Pathway Doses Predicted by Version 3.1 with the Doses 

Predicted by the Previously Benchmarked 3.0 Beta Version 

of RESRAD-OFFSITE for a First-Order, Rate-Controlled Release

D.3.2 Comparison of Equilibrium Release

The equilibrium release discussed in Chapter 2 can be modeled in Version 3.1 using the 

following procedures (and as illustrated in Figure D.4). First, uncheck the “Version 2 Release 

Methodology” check box to activate the new release options. Verify that the four input boxes—

Time at which radionuclide first becomes releasable (delay time), Fraction of radionuclide
D-14

bearing material that is initially releasable, Time over which transformation to releasable form 

occurs, and Total fraction of radionuclide bearing material that is releasable are at their default 

values of 0, 1, 0, 1, respectively. Click the “Instantaneous Equilibrium Desorption Release” 

radio button in the “Release mechanism” frame. Next, specify the desired distribution coefficient 

in the contaminated zone.

The temporal plots of component (pathway) doses obtained from Version 3.1 for the equilibrium 

desorption release discussed in Chapter 2 are compared with the temporal plots of component 

doses obtained from Version 3.0 beta in Figure D.5. There are no differences between the two 

plots in Figure D.5.

FIGURE D.4 Specifying Inputs for Equilibrium Desorption Release 

of Material That Initially Is Entirely in the Releasable Form
D-15

FIGURE D.5 Comparison of Pathway Doses Predicted by Version 3.1 with the Doses 

Predicted by the Previously Benchmarked 3.0 Beta Version of RESRADOFFSITE for an Equilibrium Desorption Release

D.3.3 Comparison of Uniform Release

The Uniform Release discussed in Chapter 2 can be modeled in Version 3.1 using the following 

procedures (and as illustrated in Figure D.6). First, uncheck the “Version 2 Release 

Methodology” check box to activate the new release options. Verify that the two input boxes

Time at which radionuclide first becomes releasable (delay time) and Fraction of radionuclide
D-16

bearing material that is releasable are at their default values of 0 and 1, respectively. Specify a 

value of 0 for the Fraction of radionuclide bearing that is initially releasable. Click the 

“Instantaneous Equilibrium Desorption Release” radio button in the “Release mechanism” 

frame. Next, specify the desired distribution coefficient in the contaminated zone and the Time 

over which transformation to releasable form occurs. 

The temporal plots of component (pathway) doses obtained from Version 3.1 for this case are 

compared with the temporal plots of component doses obtained from Version 3.0 beta of 

RESRAD-OFFSITE in Figure D.7. There are no differences between the two plots in 

Figure D.7.

FIGURE D.6 Specifying Inputs for Uniform Release of Material That

Initially Is Entirely in the Releasable Form
D-17

FIGURE D.7 Comparison of Pathway Doses Predicted by Version 3.1 with the Doses 

Predicted by the Previously Benchmarked 3.0 Beta Version of RESRADOFFSITE for a Uniform Release

D.4 General Release Options in Version 3.1 

There are four main general release options in Version 3.1, which are obtained by combining 

one of the two release mechanisms and one of the two temporal profiles of how the 

radionuclide-bearing material becomes susceptible to release. A first-order release in which 

radionuclide-bearing material becomes available for release linearly over time is specified, as 
D-18

shown in Figure D.8. No release occurs over a specified period of time—for the first 250 years, 

in this example. The radionuclides in a specified fraction of the material—one tenth in this 

example—become available for release at that time. Then, the radionuclides in another fraction 

of the material become available for release over a specified period of time—75% over the next 

100 years, in this example. Two first-order leach rates can be specified: the first applies at the 

beginning of the release, and the second applies after the end of the second period of time. 

The leach rate varies uniformly over time in the intervening period of time.

Next, a first-order release in which radionuclide-bearing material becomes susceptible for 

release stepwise over time is specified, as shown in Figure D.9. There are two differences 

between this case and the preceding case. First, the radionuclides in two specified fractions of 

the material become available for release at two specified times; for the inputs shown in this 

example, the radionuclides in 10% of the material become releasable at 250 years, whereas the 

radionuclides in another 75% of the material become susceptible to release in 350 years. 

Second, the radionuclides in the first fraction of material are released at the initial leach rate, 

whereas the radionuclides in the second fraction of material are released at the final leach rate. 

The leach rates for the radionuclides in the two fractions of material do not change over time.
D-19

FIGURE D.8 A First-Order Release with Radionuclide-Bearing Material 

Becoming Available Linearly Over Time
D-20

FIGURE D.9 A First-Order Release with Radionuclide-Bearing Material 

Becoming Available Stepwise in Time

Examples of instantaneous equilibrium desorption controlled releases in which radionuclidebearing material becomes available for release linearly over time or at two discrete times are 

shown in Figures D.10 and D.11. The radionuclides that become available for release at any 

time are distributed between the solids in the soil and the soil moisture according to the 

specified distribution coefficient at that time. If the primary contamination is conceptualized as a 

mixture of soil and an ion-exchange medium on which the radionuclides are adsorbed, then 

weighted values need to be input for the distribution coefficients and the physical characteristics 

of the primary contamination.
D-21 

FIGURE D.10 An Instantaneous Equilibrium Desorption

Release in Which Radionuclide-Bearing Material

Becomes Available for Release Linearly in Time
D-22

FIGURE D.11 An Instantaneous Equilibrium Desorption Release 

in Which Radionuclide-Bearing Material Becomes

Available for Release Stepwise in Time

D.5 Release of Progeny Radionuclides 

The same release mechanism specified for an initially present radionuclide is also applied to its

progeny but at the leach rates and distribution coefficients specified for the progeny. If users 

desire to model different mechanisms of release for the parent and progeny, then the first-order, 

rate-controlled release mechanism must be chosen and a very high leach rate must be specified 

for those radionuclides for which an instantaneous desorption release is desired. The time 

interval between intermediate time points will need to be made small enough to model the rapid 

release accurately.
D-23

D.6 Releases from the Surface Soil 

The RESRAD-OFFSITE code computes the release of particulates to the atmosphere and to 

runoff using the radionuclide concentration in the surface layer. By default, only the material in 

the release-susceptible form is released from the surface layer. The user can choose to include 

both the release-susceptible form and the release-immune form in the atmospheric release 

calculations. The radionuclides that are released into the soil moisture in the primary 

contamination can resorb onto the solids in soil; these radionuclides are not included in the 

calculations of the releases from the surface soil even though some of those radionuclides may 

still be within the mixing layer.

D.7 Connecting the Conceptual Options to Practical 

Situations

Section 3.2.1 of this report discusses which of the three options of Version 3 might best 

represent the release from different waste materials. This section expands on that topic to 

include the features added in RESRAD-OFFSITE Version 3.1. 

Engineered barriers, such as impermeable covers, waste containers, and grouting of the voids 

around and within the waste are designed to prevent water from infiltrating into the wastebearing material for certain periods of time. With the passage of time, however, some of these 

barriers, containers, and waste forms might deteriorate and moisture could penetrate them. The 

effect of engineered barriers in preventing release for a period of time can be modeled in 

RESRAD-OFFSITE by specifying a delay time. The period of time during which the engineered 

barrier is expected to be fully effective in preventing release should be entered in the delay time 

input captioned “Time at which radionuclides first become releasable.” 

When the engineered barrier starts to fail, it is likely to lose its integrity gradually. Most of a 

given barrier would still be effective when it first starts to deteriorate to the extent that moisture 

is able to start penetrating it. Only a small fraction of the waste material is likely to be exposed 

to this moisture at that time. This situation can be modeled by specifying the fraction of waste 

material that is exposed at the time when the barrier first fails in the input captioned “Fraction of 

radionuclide bearing material that is initially releasable.”

The engineered barrier could continue to deteriorate, and the amount of waste material that is 

subject to release would increase gradually with time. This somewhat compromised state can 

be modeled in RESRAD-OFFSITE by specifying the time period over which the barrier is 

expected to fail gradually in the input box captioned “Time over which transition to releasable 

form occurs” and by selecting the “linearly over time” option in the “Radionuclide bearing 

material becomes releasable” frame. If there are multiple engineered barriers, some of the 

waste would continue to be isolated. The input captioned, “Total fraction of radionuclide bearing 

material available for release” can be used to model this scenario.

Version 3.1 of RESRAD-OFFSITE also has the option to model the change in the releasable 

fraction of waste material as occurring stepwise in time. This option can be used to model 

situations where there are different types of waste material containing the same radionuclide in 

the disposal area.
D-24

Section 3.2.1 of the report discusses the choice of the release mechanisms—first-order, ratecontrolled release or instantaneous desorption-controlled release—that might be appropriate for 

modeling the release from different waste materials. Recall that the uniform release option 

discussed in that section is modeled in Version 3.1 by selecting the instantaneous desorption 

equilibrium release option in which radionuclide-bearing material becomes available for release 

linearly with time. For some wastes, either of these release mechanisms could apply depending 

on the chemical conditions of the waste and infiltrating moisture. Ion exchange resins could be 

used to illustrate this choice. If the partitioning between the resin and the infiltrating moisture 

occurs rapidly relative to the movement of moisture, then the instantaneous desorption 

equilibrium release option would be appropriate. If, on the other hand, the partitioning occurs 

slowly relative to the movement of moisture, the first-order, rate-controlled release option would 

be appropriate.

There are studies on source term releases for radionuclides on ion-exchange resins 

(Akers 2002, Robertson et al., 2000) and solubility and leaching of radionuclide releases from 

decommissioned sites (Felmy et al., 2002, 2003). These reports may be useful when using 

RESRAD-OFFSITE Version 3.1 source release models to simulate radionuclides’ release 

mechanisms from waste disposal sites.

D.8 References for Appendix D 

Akers, D.W., 2002, “Release of Radionuclides and Chelating Agents from Full-System 

Decontamination Ion-Exchange Resins,” NUREG/CR-6766, March.

Felmy, A.R., D. Rai, S.A. Hartley, and V.L. LeGore, 2002, “Solubility and Leaching of 

Radionuclides in Site Decommissioning Management Plan (SDMP) Slags,” NUREG/CR-6632, 

February.

Felmy, A.R., V.L. LeGore, and S.A. Hartley, 2003, “Solubility and Leaching of Radionuclides in 

Site Decommissioning Management Plan (SDMP) Soil and Ponded Wastes,” NUREG/CR-6821, 

June.

Robertson, D.E., S.L. Pratt, and C.W. Thomas, 2000, “Adsorption and Desorption Behavior of 

Selected 10 CFR Part 61 Radionuclides from Ion Exchange Resins by Waters of Different 

Chemical Composition,” NUREG/CR-6647, U.S. Nuclear Regulatory Commission, Washington, 

D.C., 20555-0001, July.
Appendix E

Users’ Guide to RESRAD-OFFSITE Code 

Area Factors

E-1 

Appendix E

Users’ Guide to RESRAD-OFFSITE Code 

Area Factors

The area factor is the ratio of the dose from the whole (large or wide) area of primary 

contamination divided by the dose from a small (hot spot or elevated activity) area within the 

large (wide) area. The small (elevated activity) area is referred to as the elevated measurement 

comparison (EMC) area in the Multi-Agency Radiation Survey and Site Investigation Manual 

(MARSSIM) (MARSSIM Manual 2000). The area factor can be used in conjunction with 

MARSSIM applications to determine the Derived Concentration Guideline Level (DCGL) for a 

small EMC area (i.e., DCGLEMC). In MARSSIM terminology, the DCGL for the large (wide) area 

is called DCGLW. The DCGL is inversely proportional to the corresponding dose; therefore the 

area factor is equivalent to the quotient of DCGLEMC divided by DCGLW, as shown in 

Equation E.1. The area factors are especially useful in field applications for quick determination 

of DCGLEMC, which is simply the product of area factor and the DCGLW. 

Area Factor = Dose from wide Area of primary contamination

Dose from small area of elevated activity

= DCGLEMC

DCGLW

 (E.1)

RESRAD-OFFSITE code Version 3 provides users with an easy and flexible way to obtain the 

area factors for an offsite receptor scenario using the probabilistic analysis feature of the code. 

The first step is to prepare an input file just as in the case of a regular RESRAD-OFFSITE run. 

The layout of the site is specified in the site layout form or in the map interface, and siteappropriate parameter values are included for all of the variables in the RESRAD-OFFSITE 

interface. The “Generate Area Factors” command is then chosen from the File menu to display 

the Area Factors form (Figure E.1). The user can then specify parameters related to area factor 

calculations. The X dimension of the small area of elevated contamination is always sampled. 

The Y dimension of the small area of elevated contamination can either be sampled or it can be 

made proportional to the X dimension. If the Y dimension is to be sampled, the correlation 

between the samples of the X and Y dimensions can be specified. The location of the small 

area of elevated contamination can be fixed at the center of the primary contamination, or it can 

be allowed to move within the confines of the original primary contamination.
E-2 

FIGURE E.1 Area Factors Form – Default Options

E.1 The Range of the X Dimension of the Small Area of 

Elevated Contamination

By default, the X dimension of the small area of elevated contamination will be obtained by 

sampling a triangular distribution skewed to the low end ranging from 1/50 to 1 times the 

X dimension of the primary contamination. The user can change the lower and upper limits; 

however, the upper limit may not exceed the X dimension of the primary contamination, that is, 

the X dimension of the small area of elevated contamination cannot be larger than the 

X dimension of the primary contamination (wide area).

E.2 The Range of the Y Dimension of the Small Area of 

Elevated Contamination

By default, the Y dimension for the small area of elevated contamination is set to be proportional 

to the X dimensions of the small area of elevated contamination. The default proportionality 

constant is the ratio of the Y dimension of the primary contamination to the X dimension of the 

primary contamination (Figure E.1). The user may change the proportionality constant; 

however, the code will not then check to ensure that the resulting Y dimension of the small area 

of elevated contamination is less than the Y dimension of the primary contamination.

Alternatively, the Y dimension can be sampled in the same manner as the X dimension. If this 

option is chosen (Figure E.2), by default the Y dimension will be sampled from a uniform 

distribution ranging from 1/50 to 1 times the Y dimension of the primary contamination. The 

user can change the lower and upper limits; however, as mentioned previously, the upper limit 

may not exceed the Y dimension of the primary contamination. In this case, the user can 
E-3 

specify the rank correlation coefficient between the X and Y dimensions of the small area of 

elevated contamination; the default value of 0.99 will produce results that are similar to the 

default proportionality option. A negative rank correlation coefficient would simulate small areas 

of elevated contamination that are elongated in either the X or Y directions.

FIGURE E.2 Area Factors Form – Option to Specify the Range of the 

Y Dimension of the Small Area of Elevated Contamination 

E.3 Distribution of the X and Y Dimensions of the Small Area 

of Elevated Contamination

Three options are available for the distribution of the dimensions of the small area of elevated 

contamination: (1) triangular distribution skewed to the high end, (2) uniform distribution, and 

(3) triangular distribution skewed to the low end. Option 1 (i.e., triangular distribution skewed to 

the high end) will result in uniform spacing of the sampled contamination area. This result can 

be seen from the cumulative distribution function of the area that was produced in the top graph 

of Figure E.3. 
E-4 

FIGURE E.3 Distribution of Area Using the Three Distribution Options for Sampling 

the Dimensions of the Small Area of Elevated Contamination: triangular 

skewed to the high end (top), uniform (bottom left), and triangular skewed 

to the low end (bottom right)

Option 2 (i.e., sampling the dimensions uniformly) will result in a distribution of the 

contamination area that is skewed to the lower end. The distribution of the sampled area will be 

skewed even more toward the low end if Option 3 (i.e., triangular distribution that is skewed to 

the low end) is selected. Either Option 2 or Option 3 would be appropriate if the areas of 
E-5 

elevated contamination are likely to be small and a user desires to sample a large number of 

small areas.

E.4 Location of the Center of the Small Area of Elevated 

Contamination

There are two choices for the location of the center (or centroid) of the small area of elevated 

contamination: it can be fixed at the center of the primary contamination, or it can be allowed to 

vary. The fixed option will produce a tighter curve between the dose and the small area of 

elevated contamination. Under the variable option, the small area of elevated contamination is 

constrained to be within the primary contamination. Thus, the center has to lie within a 

rectangle with dimensions that are the difference between the corresponding dimensions of the 

primary contamination and the small area of elevated contamination. The code samples two 

unit uniform distributions and uses those samples to locate the center of the small area of 

elevated contamination. A sample value of zero for the X location would place the left edge of 

the small area of elevated contamination on the left boundary of the primary contamination; a 

unit value would place the right edge of the small area of elevated contamination on the right 

boundary of the primary contamination. Likewise, a sample value of zero for the Y location 

would place the lower edge of the small area of elevated contamination on the lower boundary 

of the primary contamination; a unit value would place the top edge of the small area of elevated 

contamination on the upper boundary of the primary contamination. Because the calculated 

dose will vary with the location of the small area of elevated contamination, the first option

(centers fixed) could produce area factors that are higher than reasonable, whereas the second 

option (moving centers) will produce conservative area factors.

E.5 Number of Points on the Dose – Area Plot

This parameter specifies the number of times the distribution of the dimensions of the area of 

elevated contamination is to be sampled. The default value is 1,000. A smaller value can be 

used if the dose–area relationship is expected to be in a tight band or a single curve; this result 

will be the case if the Y dimension of the small area of elevated contamination is set to be 

proportional to the X dimension and the center is fixed. A larger value might be required if the 

dose–area relationship is expected to be in the shape of a wide band. This result could be the 

case when both dimensions of the small area of elevated contamination are sampled and/or the 

location of these small areas of elevated contamination was allowed to vary.

E.6 Generate Dimensions 

The Generate Dimensions command button is used to generate the layout—dimensions and 

location—of each sample of area of elevated contamination and the offsite transport distances 

from each sample of area of elevated contamination to the offsite receptor locations. The 

Generate Dimension command must be clicked after the user does the following: specifies the 

limits and type of distribution for the X dimension of the small area of elevated contamination, 

chooses the method of determining the Y dimension and specifying the required values for that 

method, selects the desired location option for the centers of the small areas of elevated 

contamination, and sets the number of samples. This command button first launches the 

probabilistic sampling code to sample all of the specified distributions. That information is then 

read by the interface, which uses the sampling results to develop the relationships for the offsite 
E-6 

transport distances. Three types of plots of the dimension that were generated can be viewed 

before proceeding to generate the dose from each area of elevated contamination: scatter plots, 

histograms, and cumulative distribution functions. These plots are used to verify that the 

desired layout and transport distances have been generated. The Generate Dose-Area Plot 

command button becomes active after the layout and transport distances have been generated 

(Figure E.4).

FIGURE E.4 Area Factors Form – Generate Dose-Area Plot Command

Button Activated

E.7 Generate Dose – Area Plot 

This command launches the computational code of RESRAD-OFFSITE to process the inputs for 

each of the sampled areas of elevated contamination, generating the dose from each of the

areas of elevated contamination. A scatter plot of dose against the area of elevated 

contamination is displayed at the end of the run. Four sample plots, obtained by using the four 

options, for three different radionuclides (i.e., Cs-137, Sr-90, and Tc-99) are shown in 

Figures E.5 through E.7. The four options are: (a) the Y dimensions of the small area of 

elevated contamination are proportional to the X dimension of the small area of elevated 

contamination with the center of the area of elevated contamination coinciding with the center of 

the whole area of primary contamination; (b) the Y dimensions of the small area of elevated 

contamination are proportional to the X dimension, and the area of elevated contamination is 

located within the whole area of primary contamination but is not constrained to be concentric; 

(c) the Y dimensions of the small area of elevated contamination are sampled and paired with 

the samples of the X dimension at a specified correlation and the center of the area of elevated 

contamination coincides with the center of the whole area of primary contamination; and (d) the 

Y dimensions of the small area of elevated contamination are sampled and paired with the 

samples of the X dimension at a specified correlation and the area of elevated contamination is 

located within the whole area of primary contamination but is not constrained to be concentric. 
E-7 

The area factor is the ratio of the dose from the large (wide) area of primary contamination 

divided by the dose from the smaller area of elevated contamination within the large (wide) 

area. The calculated area factors with the corresponding areas are saved in a file named 

“AreaFactorText.REP.” This file contains a list of up to 21 pairs of areas and area factors for 

each radionuclide analyzed. When more than 21 samples are used (the default is 1,000), the 

code groups the samples into 21 intervals based on area. Then the code determines the area 

within each interval for which the dose/area ratio is the greatest. These 21 areas and doses are 

used to generate the area factor text report, AreaFactorText.REP.

FIGURE E.5 Scatter Plot of Dose against Area of Contamination for Cs-137 Where the 

Direct External Exposure is the Dominant Pathway. (a) Top left, 

Y dimension is proportional to the X dimension; the center of the area of 

elevated contamination is located at the center of the area of primary 

contamination. (b) Bottom left, Y dimension is proportional to the 

X dimension; area of elevated contamination is located anywhere within the 

area of primary contamination. (c) Top right, X and Y dimensions are highly 

correlated (rank regression coefficient 0.99); the center of area of elevated 

contamination is located at the center of the area of primary contamination. 

(d) Bottom right, X and Y dimensions are highly correlated (rank regression 

coefficient 0.99); the area of elevated contamination is located anywhere 

within the area of primary contamination.
E-8 

FIGURE E.6 Scatter Plot of Dose against Area of Contamination for Sr-90 for Which 

Groundwater Transport Is the Dominant Route of Exposure. (a) Top left, 

Y dimension is proportional to the X dimension; the center of the area of 

elevated contamination is located at the center of the area of primary 

contamination. (b) Bottom left, Y dimension is proportional to the 

X dimension; the area of elevated contamination is located anywhere within 

the area of primary contamination. (c) Top right, X and Y dimensions are 

highly correlated (rank regression coefficient 0.99); the center of the area of 

elevated contamination is located at the center of the area of primary

contamination. (d) Bottom right, X and Y dimensions are highly correlated 

(rank regression coefficient 0.99); the area of elevated contamination is 

located anywhere within the area of primary contamination.
E-9 

Figure E.7 Scatter Plot of Dose against Area of Contamination for Tc-99 for Which 

Groundwater Transport Is the Dominant Route of Exposure. (a) Top left, 

Y dimension is proportional to the X dimension; the center of the area of 

elevated contamination is located at the center of the area of primary 

contamination. (b) Bottom left, Y dimension is proportional to the 

X dimension; the area of elevated contamination is located anywhere within 

the area of primary contamination. (c) Top right, X and Y dimensions are 

highly correlated (rank regression coefficient 0.99); the center of the area of 

elevated contamination is located at the center of the area of primary 

contamination. (d) Bottom right, X and Y dimensions are highly correlated 

(rank regression coefficient 0.99); the area of elevated contamination is 

located anywhere within the area of primary contamination.
E-10

E.8 Discussion 

The area factors generated by the RESRAD-OFFSITE code Version 3, as listed in the 

“AreaFactorText.REP” file, are for the specific scenario analyzed. They are derived on the basis 

of pathways selected and parameter values used for that particular case. Therefore, for 

different scenarios, the calculated area factors will most likely be different. Area factors, which 

are radionuclide-specific, describe the extent to which a radionuclide concentration can exceed 

the DCGLW and still comply with the release criteria. In the “AreaFactorText.REP” file, the area 

factors for different radionuclides are listed separately in tabular format. The radionuclidespecific area factor (AFi) for radionuclide i can be used with the wide area, radionuclide-specific 

DCGLWi to calculate the small area DCGLEMCi as in Equation E.2.

Area Factori = DCGLEMCi

DCGLWi

(E.2)

If there are multiple radionuclides in the contaminated area, the sum of fractions rule can be 

used to determine whether the dose criterion is exceeded or not.

E.9 Reference for Appendix E 

MARSSIM Revision 1, 2000, Multi-Agency Radiation Survey and Site Investigation Manual 

(MARSSIM), NUREG-1575, Rev. 1, EPA 402-R-97-016, Rev. 1, DOE/EH-0624, Rev. 1, August.



UNITED STATES 

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

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

OFFICIAL BUSINESS
NUREG/CR-7127 New Source Term Model for the RESRAD-OFFSITE Code Version 3