Verification of RESRAD-OFFSITE

Office of Nuclear Regulatory Research

NUREG/CR-7038

ANL-10/27
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Verification of RESRAD-OFFSITE

Manuscript Completed: October 2010

Date Published: November 2011

Prepared by

C. Yu

E. K. Gnanapragasam

J.-J. Cheng

S. Kamboj

B. M. Biwer

D. J. LePoire

Argonne National Laboratory

9700 South Cass Avenue

Argonne, IL 60439

John D. Randall, NRC Project Manager

NRC Job Code N6731

Office of Nuclear Regulatory Research

NUREG/CR-7038

ANL-10/27
iii 

Abstract 

This report documents the procedures used and the results obtained regarding the verification 

of the RESRAD-OFFSITE computer code. The RESRAD-OFFSITE code is an extension of the 

original RESRAD (onsite) code. The RESRAD-OFFSITE and RESRAD (onsite) codes share 

the same database and many models and modules. The RESRAD (onsite) code has already 

been extensively tested, verified, and validated. Many parameter values used in the RESRADOFFSITE code were taken from the RESRAD (onsite) database. These parameters include 

soil-plant transfer factors, meat and milk transfer factors, bioaccumulation factors, dose 

conversion factors, decay half-lives, and scenario-specific occupancy factors. The RESRAD 

(onsite) database is well documented and verified. Components of the RESRAD-OFFSITE 

code were verified by separately developed spreadsheets or benchmarked against the 

RESRAD (onsite) code. Independent verification was performed using calculations external to 

the RESRAD-OFFSITE code. Microsoft Excel spreadsheets were used to verify all the major 

portions of the RESRAD-OFFSITE code, including the source term model, groundwater 

transport model, air dispersion model, and accumulation in offsite soil and in food models. 

Paperwork Reduction Act Statement 

This NUREG does not contain information collection requirements and, therefore, is not subject 

to the requirements of the Paperwork Reduction Act of 1995 (44 USC 3501, et seq.). 

Public Protection Notification 

The NRC may not conduct or sponsor, and a person is not required to respond to, a request for 

information or an information collection requirement unless the requesting document displays a 

current valid OMB control number.
v 

Contents 

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

Executive Summary .................................................................................................................... xv

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

2.0 Source Term .................................................................................................................... 2-1

2.1 Mixing Model ........................................................................................................... 2-1

2.1.1 Thicknesses of Clean Cover, Contaminated Mixing Zone, and 

Undisturbed Primary Contamination ............................................................. 2-5

2.1.2 Composite Modification Factor for the Concentration of Nuclides in the 

Mixing Zone ................................................................................................ 2-10

2.2 Release by Surface Runoff ................................................................................... 2-17

2.2.1 Concentrations of Nuclide in the Unmixed Portion of the Primary 

Contamination ............................................................................................ 2-17

2.2.2 Release Rates of Nuclide through Runoff .................................................. 2-26

2.3 Release to Groundwater ....................................................................................... 2-33

2.4 Release to Air ....................................................................................................... 2-40

3.0 Groundwater Transport Model ......................................................................................... 3-1

3.1 Verification of Transport in the Unsaturated Zone .................................................. 3-1

3.1.1 Output Flux from a Decreasing Triangular Input Flux ................................... 3-5

3.1.2 Output Flux from an Increasing Triangular Input Flux ................................ 3-10

3.1.3 Description of the Excel Files Used in This Verification ............................. 3-15

3.2 Verification of Transport in the Saturated Zone to the Surface Water Body ......... 3-15

3.2.1 Output Flux from a Decreasing Triangular Input Flux ................................. 3-17

3.2.2 Output Flux from an Increasing Triangular Input Flux ................................ 3-23

3.2.3 Description of the Excel Files Used in This Verification ............................. 3-28

3.3 Verification of Transport in the Saturated Zone to the Well .................................. 3-28

3.3.1 Output Flux from a Decreasing Triangular Input Flux ................................. 3-30

3.3.2 Output Flux from an Increasing Triangular Input Flux ................................ 3-31

3.3.3 Description of the Excel Files Used in This Verification ............................. 3-36

4.0 Atmospheric Transport Model ......................................................................................... 4-1

4.1 Sector-Average Gaussian Plume Model ................................................................. 4-1

4.2 Area Model ............................................................................................................. 4-7

5.0 Accumulation at Offsite Locations and in Food ............................................................... 5-1

5.1 Accumulation in Offsite Surface Soil ....................................................................... 5-1

5.1.1 Accumulation in Offsite Surface Soil from Irrigation ..................................... 5-1

5.1.2 Accumulation in Offsite Surface Soil from Deposition of Contaminated 

Dust .............................................................................................................. 5-7

 
vi 

Contents (continued) 

5.1.3 Accumulation in Offsite Surface Soil for the Second Member of the 

Transformation Chain ................................................................................. 5-11

5.2 Accumulation in Surface Water............................................................................. 5-20

5.3 Accumulation in Plants ......................................................................................... 5-28

5.4 Accumulation in Meat and Milk ............................................................................. 5-38

5.5 Accumulation in Fish and Aquatic Foods .............................................................. 5-39

6.0 References ...................................................................................................................... 6-1

Figures 

2-1 Comparison of the RESRAD-OFFSITE Results and Spreadsheet Results for the 

Release Rates of Nuclide through Surface Runoff for Case I Concerning U-238 and 

Its Progenies .................................................................................................................. 2-27

2-2 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for 

Release Rates of Nuclide through Surface Runoff for Case VIII Concerning Ra-226 

and Its Progenies ........................................................................................................... 2-29

2-3 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Release Rates of Nuclide to Groundwater for Case I Concerning U-238 and Its 

Progenies .................................................................................................................... 2-34

3-1 Time Varying Flux Profile Represented as a Combination of Two Triangular Flux 

Distributions Shifted in Time ............................................................................................ 3-2

3-2 Decreasing Triangular Input Flux Profile ......................................................................... 3-5

3-3 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone 

Resulting from a Triangular Input Flux of 60Co of Unity at Time Zero and of Zero at 

the First Time Point at the Top of the Unsaturated Zone Using Spreadsheet 

Calculations ..................................................................................................................... 3-6

3-4 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone 

Resulting from a Triangular Input Flux of 90Sr of Unity at Time Zero and of Zero at the 

First Time Point at the Top of the Unsaturated Zone Using Spreadsheet Calculations .. 3-7

3-5 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone 

Resulting from a Triangular Input Flux of 63Ni of Unity at Time Zero and of Zero at 

the First Time Point at the Top of the Unsaturated Zone Using Spreadsheet 

Calculations ..................................................................................................................... 3-8

3-6 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone 

Resulting from a Triangular Input Flux of 14C of Unity at Time Zero and of Zero at the 

First Time Point at the Top of the Unsaturated Zone Using Spreadsheet Calculations .. 3-9
vii 

Figures (continued) 

3-7 Increasing Triangular Input Flux Profile ......................................................................... 3-10

3-8 Double Triangular Input Flux Profile .............................................................................. 3-10

3-9 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone 

Resulting from a Triangular Input Flux of 3

H of Zero at Time Zero and of Unity at the 

First Time Point at the Top of the Unsaturated Zone Using Spreadsheet 

Calculations ................................................................................................................... 3-11

3-10 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone 

Resulting from a Triangular Input Flux of 137Cs of Zero at Time Zero and of Unity at 

the First Time Point at the Top of the Unsaturated Zone Using Spreadsheet 

Calculations ................................................................................................................... 3-12

3-11 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone 

Resulting from a Triangular Input Flux of 226Ra of Zero at Time Zero and of Unity at 

the First Time Point at the Top of the Unsaturated Zone Using Spreadsheet 

Calculations ................................................................................................................... 3-13

3-12 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone 

Resulting from a Triangular Input Flux of 238U of Zero at Time Zero and of Unity at 

the First Time Point at the Top of the Unsaturated Zone Using Spreadsheet 

Calculations ................................................................................................................... 3-14

3-13 Decreasing Triangular Input Flux Profile ....................................................................... 3-17

3-14 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body 

Resulting from a Triangular Input Flux of 60Co of Unity at Time Zero and of Zero at 

the First Time Point at the Water Table Using Spreadsheet Calculations ..................... 3-19

3-15 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body 

Resulting from a Triangular Input Flux of 90Sr of Unity at Time Zero and of Zero at 

the First Time Point at the Water Table Using Spreadsheet Calculations ..................... 3-20

3-16 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body 

Resulting from a Triangular Input Flux of 63Ni of Unity at Time Zero and of Zero at 

the First Time Point at the Water Table Using Spreadsheet Calculations ..................... 3-21

3-17 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body 

Resulting from a Triangular Input Flux of 14C of Unity at Time Zero and of Zero at 

the First Time Point at the Water Table Using Spreadsheet Calculations ..................... 3-22

3-18 Increasing Triangular Input Flux Profile ......................................................................... 3-23

3-19 Double Triangular Input Flux Profile .............................................................................. 3-23

3-20 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water 

BodyFResulting from a Triangular Input Flux of 3

H of Zero at Time Zero and of 

Unity at the First Time Point at the Water Table Using Spreadsheet Calculations ........ 3-24
viii 

Figures (continued) 

3-21 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body 

Resulting from a Triangular Input Flux of 137Cs of Zero at Time Zero and of Unity at 

the First Time Point at the Water Table Using Spreadsheet Calculations ..................... 3-25

3-22 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body 

Resulting from a Triangular Input Flux of 226Ra of Zero at Time Zero and of Unity at 

the First Time Point at the Water Table Using Spreadsheet Calculations ..................... 3-26

3-23 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body 

Resulting from a Triangular Input Flux of 238U of Zero at Time Zero and of Unity at 

the First Time Point at the Water Table Using Spreadsheet Calculations ..................... 3-27

3-24 Decreasing Triangular Input Flux Profile ....................................................................... 3-31

3-25 Verification of RESRAD-OFFSITE Computed Concentration in the Well Resulting 

from a Triangular Input Flux of 60Co of Unity at Time Zero and of Zero at the First 

Time Point at the Water Table Using Spreadsheet Calculations ................................... 3-32

3-26 Verification of RESRAD-OFFSITE Computed Flux Concentration in the Well 

Resulting from a Triangular Input Flux of 90Sr of Unity at Time Zero and of Zero at 

the First Time Point at the Water Table Using Spreadsheet Calculations ..................... 3-33

3-27 Verification of RESRAD-OFFSITE Computed Concentration in the Well Resulting 

from a Triangular Input Flux of 63Ni of Unity at Time Zero and of Zero at the First 

Time Point at the Water Table Using Spreadsheet Calculations ................................... 3-34

3-28 Verification of RESRAD-OFFSITE Computed Concentration in the Well Resulting 

from a Triangular Input Flux of 14C of Unity at Time Zero and of Zero at the First 

Time Point at the Water Table Using Spreadsheet Calculations ................................... 3-35

3-29 Increasing Triangular Input Flux Profile ......................................................................... 3-36

3-30 Double Triangular Input Flux Profile .............................................................................. 3-36

3-31 Verification of RESRAD-OFFSITE Computed Flux Concentration in the Well 

Resulting from a Triangular Input Flux of 3

H of Zero at Time Zero and of Unity at 

the First Time Point at the Water Table Using Spreadsheet Calculations ..................... 3-37

3-32 Verification of RESRAD-OFFSITE Computed Flux Concentration in the Well 

Resulting from a Triangular Input Flux of 137Cs of Zero at Time Zero and of Unity 

at the First Time Point at the Water Table Using Spreadsheet Calculations ................. 3-38

3-33 Verification of RESRAD-OFFSITE Computed Flux Concentration in the Well 

Resulting from a Triangular Input Flux of 226Ra of Zero at Time Zero and of Unity 

at the First Time Point at the Water Table Using Spreadsheet Calculations ................. 3-39

 
ix 

Figures (continued) 

3-34 Verification of RESRAD-OFFSITE Computed Flux Concentration in the Well 

Resulting from a Triangular Input Flux of 238U of Zero at Time Zero and of Unity at 

the First Time Point at the Water Table Using Spreadsheet Calculations ..................... 3-40

4-1 Effective Release Height Calculation in RESRAD-OFFSITE .......................................... 4-5

4-2 Calculation of the Effective Wind Speed ......................................................................... 4-6

4-3 Vertical Dispersion Coefficient Calculation ...................................................................... 4-6

4-4 Calculation of the Depleted Source Strength Due to Wet and Dry Deposition ................ 4-6

4-5 Normalized Air Concentration Calculation in RESRAD-OFFSITE ................................... 4-7

4-6 Site Layout for Verification of the Area Averaged Normalized Air Concentration ............ 4-8

5-1 Accumulation of C-14 in Offsite Soil from Irrigation from Spreadsheet Calculations 

and from RESRAD-OFFSITE Code ................................................................................ 5-7

5-2 Offsite Surface Soil Accumulation from Irrigation ............................................................ 5-9

5-3 Accumulation of C-14 in Offsite Soil from Deposition from Spreadsheet Calculations 

and from RESRAD-OFFSITE Code .............................................................................. 5-11

5-4 Offsite Surface Soil Accumulation from Deposition ....................................................... 5-12

5-5 Accumulation of Sr-90 in Offsite Soil from Both Irrigation and Deposition from 

Spreadsheet Calculations and from RESRAD-OFFSITE Code..................................... 5-15

5-6 Offsite Surface Soil Accumulation from both Irrigation and Particulate Deposition for 

the First Member of Transformation Chain .................................................................... 5-16

5-7 Accumulation of Y-90 in Offsite Soil from Both Irrigation and Deposition from 

Spreadsheet Calculations and from RESRAD-OFFSITE Code..................................... 5-20

5-8 Offsite Surface Soil Accumulation from Both Irrigation and Particulate Deposition in 

the Second Member of the Chain .................................................................................. 5-23

5-9 Accumulation of Ra-226 in Surface Water from Spreadsheet Calculations and from 

RESRAD-OFFSITE Code .............................................................................................. 5-28

5-10 Accumulation in Surface Water for the First Member of Transformation Chain ............ 5-30

5-11 Accumulation of Pb-210 in Surface Water from Spreadsheet Calculations and from 

RESRAD-OFFSITE Code .............................................................................................. 5-32

5-12 Accumulation of U-238 in Fruit, Grain, and Nonleafy Vegetables from Spreadsheet 

Calculations and from RESRAD-OFFSITE Code .......................................................... 5-38

5-13 Plant Concentration Calculations for Fruit, Grain, and Nonleafy Vegetables ................ 5-40

5-14 Accumulation of U-238 in Leafy Vegetables from Spreadsheet Calculations and 

from RESRAD-OFFSITE Code...................................................................................... 5-41
x 

Figures (continued) 

5-15 Plant Concentration Calculations for Leafy Vegetables ................................................. 5-42

5-16 Accumulation of U-238 in Pasture and Silage from Spreadsheet Calculations and 

from RESRAD-OFFSITE Code...................................................................................... 5-43

5-17 Plant Concentration Calculations for Pasture and Silage .............................................. 5-44

5-18 Accumulation of U-238 in Grain from Spreadsheet Calculations and from 

RESRAD-OFFSITE Code .............................................................................................. 5-45

5-19 Plant Concentration Calculations for Grain.................................................................... 5-46

5-20 Accumulation of Cs-137 in Meat from Spreadsheet Calculations and from 

RESRAD-OFFSITE Code .............................................................................................. 5-49

5-21 Accumulation of Cs-137 in Milk from Spreadsheet Calculations and from 

RESRAD-OFFSITE Code .............................................................................................. 5-49

5-22 Meat Concentration Calculations ................................................................................... 5-50

5-23 Milk Concentration Calculations .................................................................................... 5-51

5-24 Fish and Aquatic Foods Concentration Calculations ..................................................... 5-53

5-25 Accumulation of Co-60 in Fish from Spreadsheet Calculations and from 

RESRAD-OFFSITE Code .............................................................................................. 5-53

5-26 Accumulation of Co-60 in Crustacea from Spreadsheet Calculations and from 

RESRAD-OFFSITE Code .............................................................................................. 5-54

Tables 

2-1 Parameters Used for Different Test Cases ...................................................................... 2-4

2-2 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Thicknesses of Clean Cover, Contaminated Mixing Zone, and Unmixed Portion of 

the Primary Contamination for Case III Concerning H-3, with Disagreements 

Highlighted ....................................................................................................................... 2-7

2-3 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Thicknesses of Clean Cover, Contaminated Mixing Zone, and Unmixed Portion of 

the Primary Contamination for Case IV Concerning C-14, with Disagreements 

Highlighted ....................................................................................................................... 2-8

 
xi 

Tables (continued) 

2-4 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Thicknesses of Clean Cover, Contaminated Mixing Zone, and Unmixed Portion of 

the Primary Contamination for Case VIII Concerning Ra-226, with Disagreement 

Highlighted ....................................................................................................................... 2-9

2-5 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Modification Factor for the Concentration of Nuclides in the Mixing Zone for Case II 

Concerning Cs-137, with Notable Disagreement Highlighted........................................ 2-13

2-6 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Modification Factor for the Concentration of Nuclides in the Mixing Zone for Case III 

Concerning H-3, with Notable Disagreement Highlighted ............................................. 2-14

2-7 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Modification Factor for the Concentration of Nuclides in the Mixing Zone for Case VI 

Concerning Ni-63 ........................................................................................................... 2-15

2-8 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Modification Factor for the Concentration of Nuclides in the Mixing Zone for Case VIII 

Concerning Ra-226, with Notable Disagreement Highlighted ....................................... 2-16

2-9 Calculations of the Radiological Decay Constants and Leach Rate Constants............. 2-20

2-10 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Concentration of Nuclide in the Unmixed Portion of the Primary Contamination for 

Case I Concerning U-238 and Its Progenies, with Notable Disagreement Highlighted . 2-21

2-11 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Concentration of Nuclide in the Unmixed Portion of the Primary Contamination for 

Case III Concerning H-3, with Notable Disagreements Highlighted .............................. 2-23

2-12 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Concentration of Nuclide in the Unmixed Portion of the Primary Contamination for 

Case IV Concerning C-14, with Notable Disagreements Highlighted ............................ 2-24

2-13 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Concentration of Nuclide in the Unmixed Portion of the Primary Contamination for 

Case V Concerning Co-60 ............................................................................................. 2-25

2-14 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Release Rates of Nuclide through Surface Runoff for Case I Concerning U-238 and 

Its Progenies, with Notable Disagreement Highlighted.................................................. 2-30

2-15 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Release Rates of Nuclide through Surface Runoff for Case VIII Concerning Ra-226 

and Its Progenies, with Notable Disagreements Highlighted ......................................... 2-32

 
xii 

Tables (continued) 

2-16 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Release Rates of Nuclide to Groundwater for Case I Concerning U-238 and Its 

Progenies, with Notable Disagreement Highlighted ...................................................... 2-36

2-17 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Release Rates of Nuclide to Groundwater for Case III Concerning H-3, with Notable 

Disagreements Highlighted ........................................................................................... 2-37

2-18 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Release Rates of Nuclide to Groundwater for Case IV Concerning C-14, with Notable 

Disagreements Highlighted ........................................................................................... 2-38

2-19 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Release Rates of Nuclide to Groundwater for Case VII Concerning Sr-90 ................... 2-39

2-20 Comparison of the RESRAD-OFFSITE Results and Spreadsheet Results for the 

Release Rates of Nuclide in the Form of Dust to the Air for Case I Concerning U-238 

and Its Progenies, with Notable Disagreement Highlighted........................................... 2-41

2-21 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the 

Release Rates of Nuclide in the Form of Dust to the Air for Case VIII Concerning 

Ra-226 and Its Progenies, with Notable Disagreements Highlighted ............................ 2-43

3-1 Nuclides Used in This Verification and Their Transformation Rates ............................... 3-3

3-2 RESRAD-OFFSITE Inputs and Intermediate Calculations That Pertain to Transport 

in the Unsaturated Zone .................................................................................................. 3-3

3-3 Value of the Two Exponentials for the Cases Used in This Verification .......................... 3-4

3-4 RESRAD-OFFSITE Inputs and Intermediate Calculations That Pertain to Transport 

in the Saturated Zone to the Surface Water Body ......................................................... 3-18

3-5 RESRAD-OFFSITE Inputs and Intermediate Calculations That Pertain to Transport 

in the Saturated Zone to the Well .................................................................................. 3-30

4-1 Baseline Site Layout and Atmospheric Transport Parameters Used to Verify 

RESRAD-OFFSITE Point-to-Point Air Dispersion Calculations ....................................... 4-2

4-2 Comparison of RESRAD-OFFSITE Normalized Air Concentrations with Spreadsheet 

Verification Calculations .................................................................................................. 4-3

4-3 Additional Comparison of RESRAD-OFFSITE Normalized Air Concentrations with 

Spreadsheet Verification Calculations ............................................................................. 4-4

5-1 Parameters Used in the Verification of Accumulation in Offsite Soil, Surface Water, 

Plant, Meat, Milk, and Aquatic Food ................................................................................ 5-3

5-2 Radionuclide-Specific Parameters Used in the Verification of Accumulation in Offsite 

Soil, Surface Water Body, Plant, Meat, Milk, and Aquatic Food ...................................... 5-4
xiii 

Tables (cont.) 

5-3 Spreadsheet Calculations for C-14 Accumulation in Offsite Surface Soil from 

Irrigation ........................................................................................................................... 5-6

5-4 Spreadsheet Calculations for C-14 Accumulation in Offsite Surface Soil from 

Deposition ...................................................................................................................... 5-10

5-5 Spreadsheet Calculations for Sr-90 Accumulation in Offsite Surface Soil from both 

Irrigation and Deposition ................................................................................................ 5-14

5-6 Spreadsheet Calculations for Y-90 Accumulation in Offsite Surface Soil from Both 

Irrigation and Deposition ................................................................................................ 5-19

5-7 Spreadsheet Calculations for Ra-226 Accumulation in Surface Water ......................... 5-27

5-8 Spreadsheet Calculations for Pb-210 Accumulation in Surface Water.......................... 5-29

5-9 Spreadsheet Calculations for U-238 Accumulation in Fruit, Grain, and Nonleafy 

Vegetables – Grown in Area 1 ....................................................................................... 5-34

5-10 Spreadsheet Calculations for U-238 Accumulation in Leafy Vegetables – Grown in 

Area 2 ............................................................................................................................ 5-35

5-11 Spreadsheet Calculations for U-238 Accumulation in Pasture and Silage – Grown in 

Area 3 ............................................................................................................................ 5-36

5-12 Spreadsheet Calculations for U-238 Accumulation in Grain – Grown in Area 4............ 5-37

5-13 Spreadsheet Calculations for Cs-137 Meat Concentration ............................................ 5-47

5-14 Spreadsheet Calculations for Cs-137 Milk Concentration ............................................. 5-48

5-15 Spreadsheet Calculations for Co-60 Accumulation in Fish and Aquatic Foods............. 5-52
xv 

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 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 RESRAD code has been extensively verified. The 

modules in RESRAD-OFFSITE that are also in RESRAD had already been verified by 

benchmarking an onsite exposure scenario against RESRAD. This verification report focuses 

on the verification of the modules that were added or modified when RESRAD-OFFSITE was 

developed; namely, the source term module which was modified by the incorporation of a 

surface soil mixing model to maintain (onsite and offsite) mass balance; the groundwater 

transport module which was modified to model dispersive transport and to allow the source of 

water to be away from the centerline of the plume; the new atmospheric transport module; the 

new modules to model the accumulation in surface soil at offsite locations and in the surface 

water body and the transfer to plant, meat, milk, and aquatic foods which were modified to 

include the transfer of nuclides from offsite locations in addition to the transfer from onsite 

locations. Spreadsheets were created using the formulations in the user’s manual. The code 

was verified by comparing its output against the spreadsheet calculations. 

The verification of the source term module consisted of verifying the temporal variation of the 

thicknesses of the clean cover, the contaminated mixing layer, and the undisturbed initial 

contamination; the temporal variation of the concentration in the undisturbed initial 

contamination; the temporal variation of the multiplication factor used to compute the 

concentration in the mixing layer; and the temporal variation of the rates at which the nuclides 

are released to the various media. Eight cases that covered a range of initial thicknesses of 

cover, mixing layer, and contamination and a range of erosion rates of the cover and 

contamination were used in this verification. A different nuclide was chosen for each case to 

cover a range of half-lives and a range of distribution coefficients, which are a measure of the 

affinity of the nuclides to the soil matrix. The two nuclides for which the code considers a vapor 

release, C-14 and H-3, were also included. There was mostly very good agreement between 

the RESRAD-OFFSITE output and spreadsheet output. Inconsequential differences were 

sometimes observed at specific times; namely, at the times at which the cover or the initial 

contamination eroded down to the thickness of the mixing layer and near time zero. These 

differences were due to the precision used by the code and the spreadsheet calculations for 

stored variables. All of the spreadsheet calculations were performed at double precision. Most 

of the variables in the computational code of RESRAD-OFFSITE are in single precision; only 

those variables that need to be at a higher precision are set to either double or quadruple 

precision. 
xvi 

The RESRAD-OFFSITE temporal outputs of the flux out of the unsaturated zone, the flux to the 

surface water body, and the concentration in the well were verified by comparison with the 

spreadsheet calculations. The same eight nuclides that were used for the verification of the 

source term module were used for the verification of the groundwater transport module. At least 

three different simulations with three different distribution coefficients were used for the 

verification, to cover a wide range of transport velocities. The precision of the error function built 

into the spreadsheet calculations was not sufficient at the range of arguments that were needed 

for the RESRAD-OFFSITE simulations. The evaluation algorithm used by RESRAD-OFFSITE 

for the error function had to be written into the spreadsheet calculations in order to perform the 

verification. The peak fluxes and peak concentrations computed by RESRAD-OFFSITE were 

verified by the Excel® calculations. 

The point-source-to-point-receptor normalized air concentrations (χ/Q values) computed by 

RESRAD-OFFSITE for five different combinations of distance, direction, wind speed, and 

stability classes were compared with spreadsheet-calculated values. The five χ/Q values were 

calculated under six different cases: three dispersion coefficient depositions combinations – 

using Brigg’s dispersion coefficients without either wet or dry deposition, using the PasquillGifford dispersion coefficient with only dry deposition, and using the Pasquill-Gifford dispersion 

coefficient with both wet and dry deposition – in conjunction with zero and non-zero heat release 

fluxes. The results for the thirty cases agreed within 2%; the difference was attributed to the 

fact that the spreadsheet calculations use a Simpson’s integration while RESRAD-OFFSITE 

uses Romberg integration. The spatial integration of the χ/Q value over the receptor area was 

verified for a case in which the receptor location straddled the wind sector boundary; the 

numbers agreed to within 0.2%. 

The accumulation in offsite soil was verified for the eight parent nuclides and selected progeny 

nuclides from the atmospheric deposition of dust and from irrigation water. The accumulation in 

the surface water body was also verified. The contamination of plants by root uptake, by foliar 

interception of dust, and by interception of irrigation water computed by RESRAD-OFFSITE 

agreed with the spreadsheet calculations. The calculations of the contamination of meat and 

milk by ingestion of the two types of livestock feed – grain and pasture and silage – by ingestion 

of soil associated with those two types of feed, and by the ingestion of livestock water were also 

verified. The spreadsheet-computed concentrations of nuclides in fish and crustacea agreed 

with the RESRAD-OFFSITE output. 
1-1 

1.0 Introduction 

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 models and parameters used in the RESRAD-OFFSITE code are described 

in detail in the RESRAD-OFFSITE User’s Manual (Yu et al. 2007). The RESRAD-OFFSITE 

code is an extension of the original RESRAD (onsite) code, which was designed for the 

evaluation of radiological doses to an onsite receptor from exposure to RESidual RADioactive 

materials in soil (Yu et al. 1993, 2001). 

The RESRAD-OFFSITE and RESRAD (onsite) codes share the same database and many 

models and modules. The RESRAD (onsite) code has already been extensively tested, verified, 

and validated, as documented in the RESRAD User’s Manual and other documents 

(Yu et al. 2001; Halliburton NUS 1994; Cheng et al. 1995; Gnanapragasam et al. 2000; 

Mills et al. 1997; Whelan et al. 1999a,b). 

Many parameter values used in the RESRAD-OFFSITE code were taken from the RESRAD 

(onsite) database. These parameters include soil-plant transfer factors, meat and milk transfer 

factors, bioaccumulation factors, dose conversion factors, decay half-lives, and scenariospecific occupancy factors. The RESRAD (onsite) database is well documented and verified 

(Yu et al. 2000, 2001, 2003). 

The RESRAD-OFFSITE code was developed following the RESRAD program’s quality 

assurance (QA) and quality control (QC) procedures. Some components of the code were 

verified by separately developed spreadsheets, or benchmarked against the RESRAD (onsite) 

code with respect to most of the equations used in the code. Additional benchmarking of the 

RESRAD-OFFSITE code against other peer codes was performed over the past several years. 

Some of the results were documented in the benchmarking report (Yu et al. 2006) and in other 

reports and peer-reviewed articles (Gnanapragasam and Yu 1997, Gnanapragasam et al. 2000; 

BIOMOVS II 1995, 1996). 

The purpose of this report had two objectives: (1) verify the proper operation of the code and 

(2) document the results using calculations outside the RESRAD-OFFSITE code. Independent 

verification was performed using calculations external to the RESRAD-OFFSITE code; Microsoft 

Excel spreadsheets were used to verify all the major portions of the program, including the 

source term (Chapter 2), groundwater transport model (Chapter 3), air dispersion model 

(Chapter 4), and accumulation in offsite soil and in food models (Chapter 5). All references 

cited are listed in Chapter 6.
1-2 
2-1 

2.0 Source Term 

RESRAD-OFFSITE analyzes the changes in radioactivity of the contamination source over time 

by accounting for the erosion, mixing, and leaching mechanisms, as well as the radiological 

ingrowth and decay factors. For gaseous radionuclides (H-3, C-14, and radon), the loss of 

radioactivity through gas diffusion is also considered in addition to the above mechanisms and 

factors. The effects of erosion and mixing are quantified in RESRAD-OFFSITE by tracking the 

changes in three thicknesses ⎯ the clean cover thickness, the penetration depth of mixing to 

the primary contaminated zone, and the thickness of the undisturbed primary contamination ⎯

as well as changes in the density of the mixing zone and in the volume fraction of the primary 

contaminated soil in the mixing zone. The effects of leaching, radiological ingrowth and decay, 

and loss through gas diffusion are analyzed independently of the erosion and mixing 

mechanisms, and are quantified by tracking the changes in radionuclide concentrations in the 

undisturbed primary contaminated soil. With the results obtained from quantifying the effects of 

the various mechanisms, the release rates of radionucludes from the contamination source to 

the surrounding environment are then calculated. 

This chapter documents the efforts to verify the release rate calculations in RESRAD-OFFSITE. 

Section 2.1 discusses the verification of the intermediate results related to the soil mixing model. 

Section 2.2 focuses on the release rates of radionuclides through surface runoff. Release rates 

of radionuclides to the underlying soils below the contamination source are the focus of 

Section 2.3, and the release rates of radionuclides to the air are the focus in Section 2.4. 

To verify the RESRAD-OFFSITE results, calculation spreadsheets were designed to implement 

the mathematical equations developed to model the changes in the contamination source, 

which are discussed in Chapter 2 of the RESRAD-OFFSITE User’s Manual (Yu et al. 2007). 

These spreadsheets simulate eight different test cases, each designed to consider a specific 

decay chain with different leaching potentials, erosion rates, and mixing depths. For most 

cases, the spreadsheets perform calculations for intermediate variables and radionuclide 

release rates every year for 1,000 years. To generate results for comparison with the 

spreadsheets, the RESRAD-OFFSITE code was executed with an input selection of 

1,024 graphic points and a maximum input time point of 994 years, which, along with an 

exposure duration of 30 years, instruct RESRAD-OFFSITE to record the intermediate and final 

results every year for 1,024 years. For the cases involving short-lived radionuclides, the time 

interval was reduced to 1⁄2 or 1⁄4 of a year, so that additional results were obtained for a one-year 

interval. 

2.1 Mixing Model 

RESRAD-OFFSITE considers mixing of soil at the surface level due to plowing or other human 

activities. Soils within the mixing depth are assumed to be homogeneously mixed and to have 

the same properties. In addition to mixing, surface soil could be eroded away; the erosion rate 

is determined by several parameters including the annual rainfall erosion index, soil erodability 

factor, slope length-steepness factor, cropping-management factor, and the conservation 
2-2 

practice factor. Because of erosion, the mixing zone, which is of constant depth, could be 

driven deeper into the soil column as time progresses. Depending on the initial thickness of the 

cover material and the cover erosion rate, the mixing zone could penetrate into the primary 

contamination zone and even to the uncontaminated vadose zone that lies underneath the 

primary contamination. As a result, the mixing zone could become contaminated with varying 

radionuclide concentrations over time. The radionuclide concentrations in the mixing zone 

determine the release rates of radionuclides through surface runoff and dust suspension/ 

resuspension, which result in releases of contaminated dust particles to the air. 

Soil mixing is modeled as a continuous process in RESRAD-OFFSITE. By considering mass 

balance, analytical equations were derived for the calculations of radionuclide concentrations in 

the mixing zone and in the undisturbed primary contamination zone, as well as several 

intermediate variables (see Chapter 2 of Yu et al. 2007). During the execution of RESRADOFFSITE, two output files are generated that record the calculations undertaken to model the 

soil mixing. These two files are CZTHICK3.DAT and SFSIN.DAT. CZTHICK3.DAT stores 

temporal data of the composite modification factor for the concentration of nuclides in the mixing 

zone and of the thicknesses of clean cover, the contaminated mixing zone, and the unmixed 

portion of the contaminated zone. SFSIN.DAT stores temporal data of the concentration of 

each initially present radionuclide and its principal progeny nuclide in the unmixed portion of the 

primary contamination. To verify the mixing model, the equations implemented by RESRADOFFSITE were coded into Microsoft Excel spreadsheets so that temporal data for the same 

variables recorded in the two output files were generated for comparison. 

Eight different test cases were developed for the verification of source term modeling. All eight 

test cases consider a contaminated area of 10,000 m2

 with an initial parent nuclide 

concentration of 100 pCi/g. The specific conditions considered in these test cases are listed in 

Table 2-1 and are discussed as follows: 

• Case I considers U-238 and its progeny nuclides. The half-life of U-238 is 4.47 × 109

years, and the RESRAD-OFFSITE default Kd value for U-238 is 50 cm3

/g, which is a 

measure of how readily U-238 adsorbs to soil particles. Because of the long half-life and 

the moderately large Kd value, changes in U-238 concentration in soil for the first 

1,000 years would be primarily caused by soil mixing. There is no clean cover, so 

penetration of the mixing zone (with a mixing depth of 15 cm) to the primary 

contamination starts at time 0. A high erosion rate of approximately 0.01 m/yr is 

assumed for the primary contamination zone; therefore, at approximately 185 years, the 

mixing zone would start to penetrate to the vadose zone that lies beneath the primary 

contamination. To verify RESRAD-OFFSITE’s ability to handle soil layers with different 

properties, the density of the primary contamination zone is set to a different value from 

that of the vadose zone; the contaminated zone has a density of 1.5 g/cm3

, while the 

vadose zone has a density of 1.7 g/cm3

. 

• Case II considers Cs-137, which has a short half-life of 30 years. The RESRADOFFSITE default Kd value for Cs-137 is 4,600 cm3

/g. Because of the large Kd value, 

release of Cs-137 through leaching is insignificant. The concentration of Cs-137 in the 

primary contamination zone would decrease quickly through radiological decay. In 
2-3 

addition to radiological decay, soil mixing would also affect the concentration; however, 

with a clean cover of 1 m on top of the contaminated zone and a mixing depth of 0.3 m, 

the effect of soil mixing would not be observed until 350 years later, when the erosion 

has reduced the cover thickness to 0.3 m. The erosion would continue even after the 

cover layer is gone and would completely remove the primary contaminated zone at the 

end of the simulation, which is 1,000 years. 

• Case III deals with H-3, which could be converted to tritiated water (HTO) upon contact 

with the environment; in turn, HTO can diffuse out from the contaminated area. 

RESRAD-OFFSITE employs the same special model as RESRAD (onsite) to deal with 

the loss of H-3 through gas diffusion, and the equations used to evaluate the loss were 

also coded into the spreadsheet. The loss through gas diffusion affects the remaining 

H-3 concentration in the primary contaminated zone. The RESRAD-OFFSITE default 

evasion depth of HTO was used in this test case, which is 0.3 m and equivalent to the 

thickness of the cover layer, so gas diffusion was inhibited at time 0. However, as soon 

as the cover layer starts to erode away, gas diffusion begins to proceed. The RESRADOFFSITE default Kd value for H-3 is 0 cm3

/g, which means that H-3 does not adsorb to 

soil particles; therefore, loss of H-3 through leaching is significant. Under this condition, 

the radioactivity of H-3 in soil is expected to be depleted in a short period of time. 

• Case IV deals with C-14. Like H-3, C-14 could be converted to CO2 and escape the 

contaminated zone through gas diffusion. The special model employed by RESRADOFFSITE to address the loss of C-14 through gas diffusion is the same as that 

employed by RESRAD (onsite). The equations used were coded into the spreadsheet. 

Because the default Kd value for C-14 is also 0 cm3

/g, the radioactivity of C-14 in soil is 

expected to diminish quickly. The other input parameters used for this test case are the 

same as those used for Case III. 

• Case V concerns Co-60, which has a short decay half-life of 5.27 years. Because the 

activity of Co-60 decreases quickly with time, a smaller time interval was chosen to 

obtain more recorded data for comparison. To observe the effect of soil mixing on the 

concentration of Co-60 in the mixing zone, no cover layer was considered above the 

primary contaminated zone. In this way, the mixing zone would penetrate to the primary 

contaminated zone immediately at time 0. 

• Case VI concerns Ni-63, which has a half-life of 96 years and a RESRAD-OFFSITE 

default Kd value of 1,000 g/cm3

. Like Cs-137, loss of radioactivity through leaching is 

insignificant because of the strong adsorption to soil particles. A thin cover layer and 

primary contamination zone, each with a thickness of 0.1 m, are specifically selected so 

that the mixing zone penetrates not only to the primary contamination zone but also to 

the vadose zone underneath the primary contamination from the very beginning. The 

soil mixing depth for this case is 0.3 m. 
2-4 

Table 2-1 Parameters Used for Different Test Cases 

Parameter Case I Case II Case III Case IV Case V Case VI Case VII Case VIII Radionuclide U-238 Cs-137 H-3 C-14 Co-60 Ni-63 Sr-90 Ra-226 

Kd of radionuclide (cm3/g) 50 4,600 0 0 1,000 1,000 30 70 

Time interval (yr) 1 1 1 1 0.25 1 0.5 1 Thickness of clean cover (m) 0 1 0.3 0.3 0 0.1 0.1 0.3 Thickness of primary contamination (m) 2 1 1 1 1 0.1 1 0.5 Thickness of vadose zone (m) 4 4 4 4 4 10 4 4 Density of clean cover (g/cm3) NA 1.6 1.6 1.6 NA 1.6 1.5 1.7 

Density of primary contaminated zone (g/cm3) 1.5 1.6 1.5 1.5 1.8 1.8 1.8 1.5 

Density of vadose zone (g/cm3) 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 

Nominal erosion rate of cover (m/yr) NA 0.002 0.001 0.001 NA 0.001 0 0.001 

Nominal erosion rate of primary contaminated 

zone (m/yr) 0.01 0.002 0 0 0.01 0.001 0 0.0005 

Soil mixing depth (m) 0.15 0.3 0.15 0.15 0.15 0.3 0.15 0.2 

Evasion depth for H-3 and C-14 (m) NA NA 0.3 0.5 NA NA NA NA Evasion rate for C-14 (1/yr) NA NA NA 2.0 NA NA NA NA 

NA ⎯ Not applicable.
2-5 

• Case VII considers Sr-90, a pure β emitter. The half-life of Sr-90 (29.12 years) is about 

the same as that of Cs-137; however, the default Kd value (30 g/cm3

) is much smaller 

than that of Cs-137 (4,600 g/cm3

). As a result, the remaining radioactivity in the primary 

contaminated zone is affected by both leaching and radiological decay. No erosion is 

assumed for both the cover layer and the primary contaminated zone, so the mixing 

zone would penetrate 0.05 m to the primary contaminated zone, but would not go farther 

as time passes. A time interval of 0.5 year is used for this case. 

• The last case, Case VIII, considers Ra-226, which generates radon by radiological 

decay. Like HTO for H-3 and CO2 for C-14, the formed radon gas can diffuse through 

the cover layer to the atmosphere. However, because the half-lives of radon and its 

progeny nuclides are short, they are treated as associated nuclides and do not affect the 

concentration of the next principal nuclide in the decay chain, Pb-210. The radon model 

incorporated in the RESRAD-OFFSITE code is the same as that in the RESRAD (onsite) 

code and does not affect the operation of the mixing model. Furthermore, the 

calculations associated with the radon model have been verified before (Halliburton 

NUS 1994); therefore, they are not repeated in this chapter. The thickness of the cover 

layer selected for this case is 1 m, followed by a thickness of 0.3 m for the primary 

contamination zone. Erosion rates for the cover layer and the primary contamination are 

different: the former is approximately 0.001 m/yr, while the latter is 0.0005 m/yr. The 

mixing depth is selected to be 0.2 m. 

2.1.1 Thicknesses of Clean Cover, Contaminated Mixing Zone, and Undisturbed 

Primary Contamination 

To calculate the thicknesses of clean cover, contaminated mixing zone, and undisturbed 

primary contamination, the thicknesses of the cover and primary contamination at each time 

point must be calculated first. Equations 2.19 and 2.20 from the RESRAD-OFFSITE User’s 

Manual (Yu et al. 2007) were used for calculating the thicknesses of the cover and primary 

contamination. Then Eq. 2.21 from the RESRAD-OFFSITE User’s Manual was used to obtain 

the target thicknesses listed in the CZTHICK3.DAT file. The equations used are listed here: 

Eq. 2.1 is Eq. 2.19 in the RESRAD-OFFSITE User’s Manual, Eq. 2.2 here is Eq. 2.20, and 

Eq. 2.3 is Eq. 2.21. 

 when 0 )(

 )0( )( and ,/)0( when 

cv cv

cv cv cv cvcv cv

tT tt

TtT Tttt

= >

−= ε =≤ ε

 (Eq. 2.1) 

pc pccv

pc pc pc cv cv cvpccv pccv pc

pc pc cv

tT ttt

TtT Ttttttt T

TtT tt

= +>

−−= =+≤≤ +

= ≤

 when 0)(

 when )()0()( and ,/)0(/)0(

 when )0()( , 

ε ε ε (Eq. 2.2) 
2-6 

cv pc mix

um

mix pc

c

mix

c

cv

cv cvmix pc

pc cv mix

um

mix pc

c

mix

c

cv

pc cv mix

um

pc

c

cv mix

c

cv

tTdtTtT dtTtT

tTtTdtT

dtTtTtTdtTtT

TtTtTtTtT dtT

= = = <+

+≤<

= = −+=

= = = ≥

)()( when 0)( and )( ,0)(

 )(when and ),()(

)()()( and ,)( ,0)(

)( when )0()( ,0)( ),()( ,

 (Eq. 2.3) 

where: 

for required time (yr),cover oferosion complete

cover (m/yr), rateerosion 

cover of thickness )0( (m), 0 at time

cover of thickness )( (m), at time

=

=

=

=

cv

cv

cv

cv

t

T

tT t

ε

tT primary of thickness )( contaminat t (m), at timeion pc =

= primary of thickness (0) contaminat (m), 0 at timeion Tpc

= primary contaminat (m/yr), rateerosion ion pc ε

= for required time primary oferosion complete contaminat (yr),ion pc t

tT cover clean of thickness )( t (m), at time c

cv =

tT contaminat of thickness )( t (m), at time zone mixing ed c

mix =

= and (m), zone mixing ofdepth dmix

tT = primary theofportion unmixed of thickness )( contaminat (m).ion um

pc

Comparison of the clean cover thickness, the thickness of the contaminated mixing zone, and 

the thickness of the unmixed portion of the primary contamination between those values listed in 

CZTHICK3.DAT and those calculated by the spreadsheets shows good agreement. Tables 2-2 

to 2-4 show the comparisons for Cases III, IV, and VIII where some disagreements were 

identified. These differences occur around the time at which the thickness of either the cover or 

the contaminated zone becomes equal to the thickness of the mixing layer; they are due to the 

differences in the precision to which the erosion rate is computed in the Excel spread sheet and 

the RESRAD-OFFSITE code. Excel uses double precision while RESRAD-OFFSITE uses 

single precision for most variables. 

Although these tables do not show it, one inconsequential difference between equation 2.3 

(equation 2.21 of the RESRAD-OFFSITE User’s manual) and the RESRAD-OFFSITE code was 

observed during this verification. The first line of equation 2.3 applies when the thickness of the 

cover is greater than the thickness of the mixing layer. The second line of equation 2.3 is 

applicable when the thickness of the cover is less than the thickness of the mixing layer. At the 

transition from the first to the second line, when the thickness of the cover is equal to the 

thickness of the mixing layer, both the first and second lines of equation 2.3 are equivalent. 

While the Users’ Manual places the equality on the first line of equation 2.21 (equation 2.3 

here), the code uses the second line at the point of transition. Because both forms are 

equivalent at the transition point, this does not affect the other results as seen in the remaining 

tables of this section. 
2-7 

Table 2-2 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results 

for the Thicknesses of Clean Cover, Contaminated Mixing Zone, and 

Unmixed Portion of the Primary Contamination for Case III Concerning H-3, 

with Disagreements Highlighted 

Thickness of Clean Cover 

(m) 

Thickness of 

Contaminated Mixing 

Zone (m) 

Thickness of the Unmixed 

Portion of Primary 

Contamination (m) 

Time 

(yr) 

RESRADOFFSITE Spreadsheet RESRADOFFSITE Spreadsheet RESRADOFFSITE Spreadsheet 

 

0 0.3 0.3 0 0 1 1 

1 0.299 0.299 0 0 1 1 

10 0.29 0.29 0 0 1 1 

20 0.28 0.28 0 0 1 1 

50 0.25 0.25 0 0 1 1 

100 0.2 0.2 0 0 1 1 

149 0.151 0.151 0 0 1 1 

150 0.15 0 0 0.15 1 1 

151 0 0 0.15 0.15 0.999 0.999 

200 0 0 0.15 0.15 0.95 0.95 

250 0 0 0.15 0.15 0.9 0.9 

300 0 0 0.15 0.15 0.85 0.85 

350 0 0 0.15 0.15 0.85 0.85 

400 0 0 0.15 0.15 0.85 0.85 

450 0 0 0.15 0.15 0.85 0.85 

500 0 0 0.15 0.15 0.85 0.85 

550 0 0 0.15 0.15 0.85 0.85 

600 0 0 0.15 0.15 0.85 0.85 

650 0 0 0.15 0.15 0.85 0.85 

700 0 0 0.15 0.15 0.85 0.85 

750 0 0 0.15 0.15 0.85 0.85 

800 0 0 0.15 0.15 0.85 0.85 

850 0 0 0.15 0.15 0.85 0.85 

900 0 0 0.15 0.15 0.85 0.85 

950 0 0 0.15 0.15 0.85 0.85 

1000 0 0 0.15 0.15 0.85 0.85 

 
2-8 

Table 2-3 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results 

for the Thicknesses of Clean Cover, Contaminated Mixing Zone, and 

Unmixed Portion of the Primary Contamination for Case IV Concerning C-14, 

with Disagreements Highlighted 

Thickness of Clean Cover 

(m) 

Thickness of 

Contaminated Mixing 

Zone (m) 

Thickness of the Unmixed 

Portion of Primary 

Contamination (m) 

Time 

(yr) 

RESRADOFFSITE Spreadsheet RESRADOFFSITE Spreadsheet 

RESRADOFFSITE Spreadsheet 

 

135 0.165 0.165 0 0 1 1 

136 0.164 0.164 0 0 1 1 

137 0.163 0.163 0 0 1 1 

138 0.162 0.162 0 0 1 1 

139 0.161 0.161 0 0 1 1 

140 0.16 0.16 0 0 1 1 

141 0.159 0.159 0 0 1 1 

142 0.158 0.158 0 0 1 1 

143 0.157 0.157 0 0 1 1 

144 0.156 0.156 0 0 1 1 

145 0.155 0.155 0 0 1 1 

146 0.154 0.154 0 0 1 1 

147 0.153 0.153 0 0 1 1 

148 0.152 0.152 0 0 1 1 

149 0.151 0.151 0 0 1 1 

150 0.15 0 0 0.15 1 1 

151 0 0 0.15 0.15 0.999 0.999 

152 0 0 0.15 0.15 0.998 0.998 

153 0 0 0.15 0.15 0.997 0.997 

154 0 0 0.15 0.15 0.996 0.996 

155 0 0 0.15 0.15 0.995 0.995 

156 0 0 0.15 0.15 0.994 0.994 

157 0 0 0.15 0.15 0.993 0.993 

158 0 0 0.15 0.15 0.992 0.992 

159 0 0 0.15 0.15 0.991 0.991 

160 0 0 0.15 0.15 0.99 0.99 

161 0 0 0.15 0.15 0.989 0.989 

162 0 0 0.15 0.15 0.988 0.988 

163 0 0 0.15 0.15 0.987 0.987 

164 0 0 0.15 0.15 0.986 0.986 

165 0 0 0.15 0.15 0.985 0.985 

166 0 0 0.15 0.15 0.984 0.984 
2-9 

Table 2-4 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet 

Results for the Thicknesses of Clean Cover, Contaminated Mixing Zone, 

and Unmixed Portion of the Primary Contamination for Case VIII Concerning 

Ra-226, with Disagreement Highlighted 

Thickness of Clean Cover 

(m) 

Thickness of 

Contaminated Mixing 

Zone (m) 

Thickness of the Unmixed 

Portion of Primary 

Contamination (m) 

Time 

(yr) 

RESRADOFFSITE Spreadsheet RESRADOFFSITE Spreadsheet RESRADOFFSITE Spreadsheet 

 

0 0.3 0.3 0 0 0.5 0.5 

1 0.299 0.299 0 0 0.5 0.5 

10 0.29 0.29 0 0 0.5 0.5 

30 0.27 0.27 0 0 0.5 0.5 

50 0.25 0.25 0 0 0.5 0.5 

99 0.201 0.201 0 0 0.5 0.5 

100 0 0 0.2 0.2 0.5 0.5 

101 0 0 0.2 0.2 0.499 0.499 

150 0 0 0.2 0.2 0.45 0.45 

200 0 0 0.2 0.2 0.4 0.4 

250 0 0 0.2 0.2 0.35 0.35 

300 0 0 0.2 0.2 0.3 0.3 

350 0 0 0.2 0.2 0.275 0.275 

400 0 0 0.2 0.2 0.25 0.25 

450 0 0 0.2 0.2 0.225 0.225 

500 0 0 0.2 0.2 0.2 0.2 

550 0 0 0.2 0.2 0.175 0.175 

600 0 0 0.2 0.2 0.15 0.15 

650 0 0 0.2 0.2 0.125 0.125 

700 0 0 0.2 0.2 0.1 0.1 

750 0 0 0.2 0.2 0.075 0.075 

800 0 0 0.2 0.2 0.05 0.05 

850 0 0 0.2 0.2 0.025 0.025 

900 0 0 0.2 0.2 4.47E-08 6.59E-08 

950 0 0 0.2 0.2 0 0 

1000 0 0 0.2 0.2 0 0 
2-10 

2.1.2 Composite Modification Factor for the Concentration of Nuclides in the 

Mixing Zone 

The composite modification factor for the concentration of nuclides in the mixing zone is used to 

obtain the concentration of nuclides in the mixing zone, which then can be used to calculate the 

nuclide release rates through runoff and to the atmosphere. The calculation of the composite 

modification factor involves several steps. First of all, the depths of penetration of the mixing 

zone into the primary contamination and into the vadose zone need to be known. These depths 

of penetration can be calculated with Eqs. 2.23 and 2.24 of the RESRAD-OFFSITE User’s 

Manual (Yu et al. 2007), which are shown as Eqs. 2.4 and 2.5 below: 

tTtTtTtTtd tTtTd ),()( while0)]()([)()()( pc impcimcv cv pc ≥+−+= cvmix +≤ pc (Eq. 2.4)

where: 

 ( ) ( ) (0) if (0),

( ) ( ) (0) (0) if (0), 

 ( ) depth of penentration of the mixing zone to the primary 

 contamination at t

+ =+ ≤

+ =+ >

=

cv im pc im pc mix mix cv

cv im pc im pc cv mix cv

pc

Tt Tt T d d T

Tt Tt T T d T

d t

ime after initial mixing (m), and

 time of initial mixing (yr). im =

t

t

 when )]()([)()()( tTtTdtTtTtTtTtd ),()( upc pmcv pmpc cv +−+= pc cvmix +> pc (Eq. 2.5)

where: 

primary thefrom soil contaminat (yr).ion 

 timei.e., layer mixing when the highest thecontains ofamount 

 zone, vadose the tozone mixing theofn penetratio initial of time

and (m),n penetratio intialafter at time 

zone vadose the tozone mixing theofn penetratio ofdepth )( 

),0()0( if )0()0()()(

),0()0( if )()(

=

=

+=+ +>

=+ +≤

pm

upc

pmcv pmpc pc cv cvmix pc

pmcv pmpc mix cvmix pc

t

t

td

TTdTTtTtT

TTddtTtT

After the penetration depths are known, the density of soil in the mixing zone is calculated 

(Eq. 2.26 in the RESRAD-OFFSITE User’s Manual) (Yu et al. 2007). The depth of penetration 

is used as an independent variable in the expression. 

(Eq. 2.6) ),()( while 

 )/exp())0(()(

tTtTd

d dd

cvpc pc

mixpcpcmix pc mixpc

+≤

ρ = ρ + ρ − ρ −
2-11 

where: 

 density of soil in the mixing zone when the penetration depth to the 

 primary contamination is dpc (g/cm3

). 

The initial density of soil in the mixing zone is calculated with Eq. 2.25 (Yu et al. 2007), which is 

listed as Eq. 2.7 as follows: 

,

)0( )(

)0(

)0()0( if 

)0( )( )())((

)0( (0) if )( and (0),)0(

,)0( if )0(

cv pc mix

sat pc

N

is

d

T

d us pc

isH

d pccv

T

mix pc

d pccv cv cvmix pc

T

mix pc

mix cv cv mix

dTT

is

TTdT

dT

s

mix

sat

dm

mix

dm

mix

cv

mix

cv

<+

+= +− −+−

+= − +≤<

= ≥

ρρ ρρ  ρρ ρρ

ρρ ρρ

ρρ

(Eq. 2.7)

where: 

bulk dry ).(g/cm zone saturated theofdensity 

0, at time (m)layer mixing e within this that zone vadose theof thickness 

bulk dry )( ),(g/cm zone vadose theofdensity 

)(H 0, at time (m) zone mixing e within this that zone eeach vados of thickness

),(g/cm 0 at time zone mixing in the soil ofdensity )0( 

3

3

3

=

=

=

=

=

sat

sat

dm

us

dm

mix

T

is

is

ρ

ρ

ρ

It should be noted that due to its complexity, the calculation of )( pcmix ρ d is not carried out 

further by RESRAD-OFFSITE after the mixing zone reaches the bottom of the primary 

contamination. The density after that is kept constant as the last calculated value. 

With the density of soil in the mixing zone known, the volume fraction of soil from the primary 

contamination in the mixing zone can be calculated. The equation used depends on whether 

the mixing zone has penetrated to the vadose zone. If it has not penetrated the vadose zone, 

the volume fraction is calculated as: 

 .)0()0( if )0( 

)0( if 1)0( and ),0()0(

,)0( if 0)0( 

 when )/exp())0(1(1( with),()(

)0(

)0(

)

d cv pc mix

T

vm

d cv cvmix pc

T

vm

vm cv mix

pcvm vm mixpc cvmix pc

f dTT

f TTdT

f dT

df f dd tTtTd

mix

pc

mix

cv

= <+

−= +≤<

= ≥

−−= − +≤

(Eq. 2.8)

)( pcmix ρ d =
2-12 

where: 

 when of valueinitial the)0( n.penetratio of beginning at the i.e., ,0

zone primary thedepth ton penetratio when the contaminat and , ision 

primary thefrom soil offraction volume)( contaminat mixing in theion 

= =

=

vm vm pc

pc

pcvm

f df

d

df

If the mixing zone has penetrated to the uncontaminated vadoze zone, then the following 

equations are used: 

( )

.

)0(

)0( )0()0(

 )0()0( if 

 exp1 )0( if and ),0()0(

,)0( if )/)0(exp(1 

 when )/exp()( with, )()(

d cv pc mix

p T

vm

d cv cvmix pc

dTT

d

p T

vm

pc mix cv mix

p

vm

upc mix cvmix pc

p

upcvm vm

f dTT

f TTdT

f dTdT

ddfdf tTtTd

mix

pc

mix

cv pc mix

mix

cv

= <+

−= − +≤<

−−= ≥

−= +>

−+ (Eq. 2.9)

where: 

penetratio zone. vadose then to

 when of valueinitial the of beginning at the i.e., 0,

zone and , is zone vadose thedepth ton penetratio when the

primary thefrom soil offraction volume)( contaminat mixing in theion 

= =

=

vm upc

p

vm

upc

upc

p

vm

f df

d

df

Finally, after vm f is calculated, the composite modification factor for the concentration of nuclides 

in the mixing zone, M mix , can be calculated as 

tftM t)(/ )()( mix = vm ρ ρ mixpc (Eq. 2.10)

Tables 2-5 to 2-8 compare values of the modification factor listed in the CZTHICK3.DAT file with 

those obtained with the spreadsheets. Table 2-5 shows the comparison for Case II concerning 

Cs-137. Table 2-6 shows the comparison for Case III concerning H-3. Tables 2-7 and 2-8 

show comparisons for Case VI and Case VIII concerning Ni-63 and Ra-226, respectively. In 

general, the results are identical; the few exceptions where there is a discrepancy are 

highlighted in yellow in the tables. These discrepancies appear at the time when the mixing 

zone just penetrates the primary contamination. At this time, the volume fraction of soil from the 

primary contamination in the mixing zone is very small. These discrepancies are explained by 

the different precisions used by RESRAD-OFFSITE and the Excel spreadsheets for storing 

numerical values. The Excel spreadsheet uses double precision while RESRAD-OFFSITE uses 

single precision for most variables. Double and quadruple precision is used for a few selected 

variables in RESRAD-OFFSITE. 
2-13 

Table 2-5 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for 

the Modification Factor for the Concentration of Nuclides in the Mixing Zone for 

Case II Concerning Cs-137, with Notable Disagreement Highlighted 

Time (yr) RESRAD-OFFSITE Spreadsheet 

 

349 0 0 

350 0 1.510E-07 

351 6.644E-03 6.645E-03 

352 1.324E-02 1.324E-02 

353 1.980E-02 1.980E-02 

354 2.631E-02 2.631E-02 

355 3.278E-02 3.278E-02 

375 1.535E-01 1.535E-01 

400 2.835E-01 2.835E-01 

425 3.935E-01 3.935E-01 

450 4.866E-01 4.866E-01 

475 5.654E-01 5.654E-01 

500 6.321E-01 6.321E-01 

525 6.886E-01 6.886E-01 

550 7.364E-01 7.364E-01 

575 7.769E-01 7.769E-01 

600 8.111E-01 8.111E-01 

625 8.401E-01 8.401E-01 

650 8.647E-01 8.647E-01 

675 8.854E-01 8.854E-01 

700 9.030E-01 9.030E-01 

725 9.179E-01 9.179E-01 

750 9.305E-01 9.305E-01 

775 9.412E-01 9.412E-01 

800 9.502E-01 9.502E-01 

825 9.579E-01 9.579E-01 

850 9.643E-01 9.643E-01 

851 9.579E-01 9.579E-01 

852 9.516E-01 9.516E-01 

853 9.452E-01 9.452E-01 

854 9.389E-01 9.390E-01 

855 9.327E-01 9.327E-01 

875 8.163E-01 8.163E-01 

900 6.910E-01 6.910E-01 

925 5.849E-01 5.849E-01 

950 4.951E-01 4.951E-01 

1000 3.548E-01 3.548E-01 
2-14 

Table 2-6 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for 

the Modification Factor for the Concentration of Nuclides in the Mixing Zone for 

Case III Concerning H-3, with Notable Disagreement Highlighted 

Time (yr) RESRAD-OFFSITE Spreadsheet 

 

149 0 0 

150 0 6.066E-08 

151 6.231E-03 6.232E-03 

152 1.243E-02 1.243E-02 

153 1.859E-02 1.859E-02 

154 2.471E-02 2.471E-02 

155 3.080E-02 3.080E-02 

160 6.071E-02 6.071E-02 

165 8.975E-02 8.975E-02 

170 1.179E-01 1.179E-01 

175 1.453E-01 1.453E-01 

180 1.719E-01 1.719E-01 

185 1.977E-01 1.977E-01 

190 2.227E-01 2.227E-01 

200 2.705E-01 2.705E-01 

210 3.156E-01 3.156E-01 

220 3.579E-01 3.579E-01 

230 3.978E-01 3.978E-01 

240 4.353E-01 4.353E-01 

250 4.705E-01 4.705E-01 

260 5.036E-01 5.036E-01 

270 5.347E-01 5.347E-01 

280 5.638E-01 5.638E-01 

290 5.913E-01 5.913E-01 

300 6.170E-01 6.170E-01 

350 6.170E-01 6.170E-01 

400 6.170E-01 6.170E-01 

500 6.170E-01 6.170E-01 

600 6.170E-01 6.170E-01 

700 6.170E-01 6.170E-01 

800 6.170E-01 6.170E-01 

900 6.170E-01 6.170E-01 

1000 6.170E-01 6.170E-01 

 
2-15 

Table 2-7 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for 

the Modification Factor for the Concentration of Nuclides in the Mixing Zone for 

Case VI Concerning Ni-63 

Time (yr) RESRAD-OFFSITE Spreadsheet 

 

0 3.60E-01 3.60E-01 

1 3.59E-01 3.59E-01 

2 3.58E-01 3.58E-01 

3 3.56E-01 3.56E-01 

4 3.55E-01 3.55E-01 

5 3.54E-01 3.54E-01 

6 3.53E-01 3.53E-01 

7 3.52E-01 3.52E-01 

8 3.51E-01 3.50E-01 

9 3.49E-01 3.49E-01 

10 3.48E-01 3.48E-01 

11 3.47E-01 3.47E-01 

12 3.46E-01 3.46E-01 

13 3.45E-01 3.45E-01 

14 3.44E-01 3.43E-01 

15 3.42E-01 3.42E-01 

16 3.41E-01 3.41E-01 

17 3.40E-01 3.40E-01 

18 3.39E-01 3.39E-01 

19 3.38E-01 3.38E-01 

20 3.37E-01 3.37E-01 

21 3.36E-01 3.35E-01 

22 3.34E-01 3.34E-01 

23 3.33E-01 3.33E-01 

24 3.32E-01 3.32E-01 

25 3.31E-01 3.31E-01 

26 3.30E-01 3.30E-01 

27 3.29E-01 3.29E-01 

28 3.28E-01 3.28E-01 

29 3.27E-01 3.27E-01 

30 3.26E-01 3.25E-01 

31 3.24E-01 3.24E-01 

32 3.23E-01 3.23E-01 

 
2-16 

Table 2-8 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results 

for the Modification Factor for the Concentration of Nuclides in the Mixing Zone 

for Case VIII Concerning Ra-226, with Notable Disagreement Highlighted 

Time (yr) RESRAD-OFFSITE Spreadsheet 

 

99 0 0 

100 0 2.491E-07 

101 4.404E-03 4.404E-03 

102 8.790E-03 8.790E-03 

103 1.316E-02 1.316E-02 

104 1.751E-02 1.751E-02 

105 2.185E-02 2.185E-02 

125 1.051E-01 1.051E-01 

150 2.004E-01 2.004E-01 

175 2.865E-01 2.865E-01 

200 3.640E-01 3.640E-01 

225 4.338E-01 4.338E-01 

250 4.964E-01 4.964E-01 

275 5.524E-01 5.524E-01 

325 6.256E-01 6.256E-01 

375 6.679E-01 6.679E-01 

425 7.055E-01 7.055E-01 

475 7.391E-01 7.391E-01 

525 7.689E-01 7.689E-01 

575 7.954E-01 7.954E-01 

625 8.189E-01 8.189E-01 

675 8.398E-01 8.398E-01 

725 8.583E-01 8.583E-01 

775 8.747E-01 8.747E-01 

825 8.892E-01 8.892E-01 

875 9.021E-01 9.021E-01 

899 9.077E-01 9.077E-01 

900 9.080E-01 9.080E-01 

901 9.057E-01 9.057E-01 

925 8.530E-01 8.530E-01 

950 8.013E-01 8.013E-01 

975 7.527E-01 7.527E-01 

1000 7.071E-01 7.071E-01 

 
2-17 

2.2 Release by Surface Runoff 

To know the release rates of radionuclides through surface runoff, the concentrations of 

nuclides in the mixing zone need to be calculated first. In RESRAD-OFFSITE, this is done by 

multiplying the concentrations of nuclides in the unmixed portion of the primary contamination 

with the composite modification factor for the concentration of nuclides in the mixing zone, 

which was discussed in the previous section. The concentrations of nuclides in the unmixed 

portion of primary contamination are calculated at each time point by taking into account loss 

through leaching and gas diffusion as well as changes through radiological ingrowth and decay. 

These concentrations are recorded for the principal nuclides in each decay chain and saved in 

the output file SFSIN.DAT. 

The release rates of nuclides through surface runoff can be obtained by multiplying the 

concentrations of nuclides in the mixing zone with the total mass of soil eroded away. This is 

equivalent to multiplying the eroded mass of soil that is from the primary contamination with the 

concentrations of nuclides in the unmixed portion of primary contamination. Temporal data of 

the eroded masses of soil that are from the primary contamination are recorded by RESRADOFFSITE and are saved, along with the data of the release rates of nuclide through surface 

runoff, in the output file named SWFLUXIN.DAT. 

2.2.1 Concentrations of Nuclide in the Unmixed Portion of the Primary 

Contamination 

Concentrations of nuclides in the unmixed portion of the primary contamination are adjusted 

constantly to account for loss through leaching and gas diffusion as well as changes through 

radiological ingrowth and decay. The following equations are used to consider each principal 

nuclide in a decay chain when there’s no loss through gas diffusion: 

)( (exp λ ,) ii

1

, atA tLt

k

i

k = ik −−

=

(Eq. 2.11)

where: 

,) 0 (Aa by defined tscoefficien ofset 

primary ofportion contaminat (pCi/g), at timeion 

)( concentrat unmixed in thechain decay ain nuclide principalth ofion 

, = = 11,1

=

ik

k

a

t

tA k

 ,1 allfor λλ

λ

,

1, a ki iikk

ikk

ik LL

a = ≤≤ −−+

−

 ,

1

1

,  ,

−

=

−=

k

i

kk ik aa

)0( concentrat parent theofion (pCi/g), 0 at time nuclide A1 =

 λi = radiological decay constant for ith principal nuclide in a decay chain (1/yr), and

 L constant rateleach i (1/yr).chain decay ain nuclide principalth for i =
2-18 

The radiological decay constant for a nuclide is calculated as i i t ,2/1 λ = /)2ln( , with 2/1t (yr) being 

the radiological decay half-life. The leach rate constant is a function of the water infiltration rate, 

volumetric water content, thickness, and retardation factor, and can be calculated with Eqs. E.3 

to E.8 from the RESRAD User’s Manual (Yu et al. 2001). 

( )( ) [ ]

( )

, 1 

, 

 ,

, 1 1 

 , 

32

1

0

θ

ρ

θ

θθ

i dpc

i

sat

i d

K

d

b K

I s

stssat

e rrrr

RT

I

i

R

R

RPR

IPCCI

L

+=

=

==

+−−=

=

+

(Eq. 2.12)

where: 

 (m/yr), rate irrigation

 precipitat (m/yr), rateion 

t,coefficien runoff 

 evapotranspiration t,coefficien

water (m/yr), rateon infiltrati

=

=

=

=

=

rr

r

r

e

I

P

C

C

I

 θ = volumetric water content primary in the contamination,

θ sat = saturated water content primary in the contamination,

conductivi hydraulic saturated primary in thety contaminat (m/yr),ion 

 ratio, saturation

porosity total primary in the contaminat ion,

=

=

=

sat

s

t

K

R

P

and , nuclidefor factor n retardatio

initial primary theof thickness contaminat (m),ion 

parameter lexponentia specificsoil primary for the contamination,

0

R i

T

-b

di =

=

=

 = di K soil/water distribution coefficient for nuclide i in the primary contamination /g).(cm

3

Table 2-9 shows calculations of the radiological decay and leach rate constants for the parents 

and their principal progeny nuclides concerned in Cases I-VIII when the density of the primary 

contamination is 1.5 g/cm3

. 

 
2-19 

For H-3 and C-14, Eq. 2.11 needs some modification to account for the loss through gas 

diffusion. The evasion rate constant, E , is introduced: 

( )

 when ).()(

0 when ),( )(

)( 

 when 0)( ,0

 exp)0()( , 

tTtCdE

tTCd

tT

tCd

E

tE Cd

AtA tELtt

dref

dref

dref

c dref

c

= >−

≤−≤ − ×=

= <−

= λ −−−

(Eq. 2.13)

where: 

evasion reference .(m) (0.3)depth 

and constant, rateevasion 

constant rateevasion for adjusted cover thic ),(yr kness -1

=

=

=

ref

c

d

E

E

EH−3 is calculated by taking into account the loss of HTO through evapotranspiration; therefore, 

the evapotranspiration rate, Et , is used: 

[ ] ( )

refst

t

H

et rrrr

dRP

E

E

IPCCE

 

 1

3 =

+−×=

−

(Eq. 2.14) 

For C-14, EC−14 is set to an empirical constant of 22/yr. Appendix L of the RESRAD User’s 

Manual (Yu et al. 2001) provides more information on the calculation of the evasion rates for 

H-3 and C-14. 

 
2-20 

Table 2-9 Calculations of the Radiological Decay Constants and Leach Rate 

Constantsa

Radionuclide 

Half-life 

t1/2 (yr) 

Kd 

(cm3/g) Rd 

Leach 

Rate 

Constant

L (1/yr) 

Radiological 

Decay 

Constant 

λ (1/yr) 

 

U-238 4.47E+09 50 234.70 3.32E-03 1.55E-10 

U-234 2.45E+05 50 234.70 3.32E-03 2.83E-06 

Th-230 7.70E+04 60000 280445.22 2.78E-06 9.00E-06 

Ra-226 1600 70 328.18 2.37E-03 4.33E-04 

Pb-210 22.3 100 468.41 1.66E-03 3.11E-02 

Po-210 0.379 10 47.74 1.63E-02 1.83E+00 

Cs-137 30 4600 21501.72 3.62E-05 2.31E-02 

Sr-90 29.12 30 141.22 5.52E-03 2.38E-02 

Ni-63 96 1000 4675.07 1.67E-04 7.22E-03 

Co-60 5.271 1000 4675.07 1.67E-04 1.32E-01 

C-14 5730 0 1.00 7.79E-01 1.21E-04 

H-3 12.35 0 1.00 7.79E-01 5.61E-02 a

 The parameters used in the calculations are: 

 Initial thickness of the contaminated zone (T0) 2 m 

Evapotranspiration coefficient (Ce) 0.5 

Runoff coefficient (Cr) 0.2 

Irrigation (Irr) 0.2 m/yr 

Precipitation (Pr) 1 m/yr 

Infiltration rate (I) 0.5 m/yr 

Saturated hydraulic conductivity (Ksat) 10 m/yr 

b parameter of the contaminated zone (b) 5.3 

Total porosity of the contaminated zone (Pt) 0.4 

Dry soil bulk density (r) 1.5 g/cm3

Saturation ratio (Rs) 0.802 

Moisture content (q) 0.321 

Tables 2-10 to 2-13 compare the concentrations of nuclides in the unmixed portion of the 

primary contamination listed in SFSIN.DAT with those obtained from the spreadsheets. 

Table 2-10 concerns U-238 and its progeny nuclides in Case I; Tables 2-11 and 2-12 concern 

H-3 in Case III and C-14 in Case IV, respectively; and Table 2-13 concerns Co-60 in Case V. In 

general, the results agree very well with each other except when the concentrations are very 

small. The discrepancies result from different precisions used for storing real numbers in 

RESRAD-OFFSITE and the spreadsheets. However, the discrepancies do not compromise 

agreement in the final dose results because the concentrations involved are extremely low and 

essentially make no dose contribution. 
2-21 

Table 2-10 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the Concentration o

Unmixed Portion of the Primary Contamination for Case I Concerning U-238 and Its Progenies, with Highlighted 

U-238 U-234 Th-230 Ra-226 Pb-210 

Time 

(yr) 

RESRADOFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet 

0 100 100 0 0 0 0 0 0 0 0 1 9.97E+01 9.97E+01 2.83E-04 2.83E-04 1.27E-09 1.27E-09 1.84E-13 1.84E-13 1.40E-15 1.40E-15 

2 9.93E+01 9.93E+01 5.63E-04 5.63E-04 5.08E-09 5.08E-09 1.47E-12 1.47E-12 2.25E-14 2.25E-14 3 9.90E+01 9.90E+01 8.42E-04 8.42E-04 1.14E-08 1.14E-08 4.94E-12 4.94E-12 1.13E-13 1.13E-13 4 9.87E+01 9.87E+01 1.12E-03 1.12E-03 2.02E-08 2.02E-08 1.17E-11 1.17E-11 3.54E-13 3.54E-13 5 9.84E+01 9.84E+01 1.39E-03 1.39E-03 3.15E-08 3.15E-08 2.28E-11 2.28E-11 8.58E-13 8.58E-13 

50 8.47E+01 8.47E+01 1.20E-02 1.20E-02 2.86E-06 2.86E-06 2.05E-08 2.05E-08 6.04E-09 6.04E-09 75 7.80E+01 7.80E+01 1.66E-02 1.66E-02 6.09E-06 6.09E-06 6.52E-08 6.52E-08 2.56E-08 2.56E-08 

100 7.18E+01 7.18E+01 2.03E-02 2.03E-02 1.03E-05 1.03E-05 1.46E-07 1.46E-07 6.84E-08 6.84E-08 125 6.60E+01 6.60E+01 2.34E-02 2.34E-02 1.52E-05 1.52E-05 2.69E-07 2.69E-07 1.43E-07 1.43E-07 150 6.08E+01 6.08E+01 2.58E-02 2.58E-02 2.07E-05 2.07E-05 4.38E-07 4.38E-07 2.54E-07 2.54E-07 175 5.59E+01 5.59E+01 2.77E-02 2.77E-02 2.68E-05 2.68E-05 6.57E-07 6.57E-07 4.08E-07 4.08E-07 200 5.15E+01 5.15E+01 2.92E-02 2.92E-02 3.32E-05 3.32E-05 9.26E-07 9.26E-07 6.07E-07 6.07E-07 225 4.74E+01 4.74E+01 3.02E-02 3.02E-02 3.98E-05 3.98E-05 1.25E-06 1.25E-06 8.53E-07 8.53E-07 250 4.36E+01 4.36E+01 3.09E-02 3.09E-02 4.67E-05 4.67E-05 1.61E-06 1.61E-06 1.15E-06 1.15E-06 275 4.01E+01 4.01E+01 3.13E-02 3.13E-02 5.37E-05 5.37E-05 2.03E-06 2.03E-06 1.48E-06 1.48E-06 300 3.69E+01 3.69E+01 3.14E-02 3.14E-02 6.07E-05 6.07E-05 2.49E-06 2.49E-06 1.87E-06 1.87E-06 350 3.13E+01 3.13E+01 3.10E-02 3.10E-02 7.48E-05 7.48E-05 3.54E-06 3.54E-06 2.76E-06 2.76E-06 400 2.65E+01 2.65E+01 3.00E-02 3.00E-02 8.85E-05 8.85E-05 4.73E-06 4.73E-06 3.81E-06 3.81E-06 450 2.25E+01 2.25E+01 2.86E-02 2.86E-02 1.02E-04 1.02E-04 6.04E-06 6.04E-06 4.98E-06 4.98E-06 500 1.90E+01 1.90E+01 2.69E-02 2.69E-02 1.14E-04 1.14E-04 7.43E-06 7.43E-06 6.25E-06 6.25E-06 550 1.61E+01 1.61E+01 2.51E-02 2.51E-02 1.26E-04 1.26E-04 8.88E-06 8.88E-06 7.60E-06 7.60E-06 600 1.36E+01 1.36E+01 2.32E-02 2.32E-02 1.37E-04 1.37E-04 1.04E-05 1.04E-05 8.99E-06 8.99E-06 650 1.16E+01 1.16E+01 2.13E-02 2.13E-02 1.46E-04 1.46E-04 1.19E-05 1.19E-05 1.04E-05 1.04E-05 700 9.79E+00 9.79E+00 1.94E-02 1.94E-02 1.56E-04 1.56E-04 1.34E-05 1.34E-05 1.18E-05 1.18E-05 
2-22 

Table 2-10 (cont.) 

U-238 U-234 Th-230 Ra-226 Pb-210 

Time 

(yr) 

RESRADOFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet 

750 8.30E+00 8.30E+00 1.76E-02 1.76E-02 1.64E-04 1.64E-04 1.49E-05 1.49E-05 1.32E-05 1.32E-05 800 7.03E+00 7.03E+00 1.59E-02 1.59E-02 1.71E-04 1.71E-04 1.63E-05 1.63E-05 1.46E-05 1.46E-05 850 5.95E+00 5.95E+00 1.43E-02 1.43E-02 1.78E-04 1.78E-04 1.77E-05 1.77E-05 1.60E-05 1.60E-05 900 5.04E+00 5.04E+00 1.28E-02 1.28E-02 1.84E-04 1.84E-04 1.90E-05 1.90E-05 1.73E-05 1.73E-05 950 4.27E+00 4.27E+00 1.15E-02 1.15E-02 1.89E-04 1.89E-04 2.03E-05 2.03E-05 1.85E-05 1.85E-05 

1000 3.62E+00 3.62E+00 1.02E-02 1.02E-02 1.94E-04 1.94E-04 2.15E-05 2.15E-05 1.97E-05 1.97E-05 
2-23 

Table 2-11 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for 

the Concentration of Nuclide in the Unmixed Portion of the Primary Contamination 

for Case III Concerning H-3, with Notable Disagreements Highlighted 

Time (yr) RESRAD-OFFSITE Spreadsheet 

 

0 1.00E+02 1.00E+02 

1 1.98E+01 1.98E+01 

2 3.88E+00 3.88E+00 

3 7.53E-01 7.53E-01 

4 1.44E-01 1.44E-01 

5 2.74E-02 2.74E-02 

6 5.16E-03 5.16E-03 

7 9.60E-04 9.60E-04 

8 1.77E-04 1.77E-04 

9 3.22E-05 3.22E-05 

10 5.81E-06 5.81E-06 

11 1.04E-06 1.04E-06 

12 1.83E-07 1.83E-07 

14 5.54E-09 5.54E-09 

16 1.61E-10 1.61E-10 

18 4.48E-12 4.48E-12 

20 1.20E-13 1.20E-13 

22 3.06E-15 3.06E-15 

24 7.52E-17 7.52E-17 

26 1.77E-18 1.77E-18 

28 4.01E-20 4.01E-20 

30 8.70E-22 8.70E-22 

32 1.81E-23 1.81E-23 

34 3.62E-25 3.62E-25 

36 6.92E-27 6.92E-27 

38 1.27E-28 1.27E-28 

40 2.24E-30 2.24E-30 

42 3.79E-32 3.79E-32 

44 6.15E-34 6.15E-34 

46 9.57E-36 9.57E-36 

48 1.43E-37 1.43E-37 

50 2.04E-39 2.04E-39 

52 2.81E-41 2.81E-41 

54 0.00E+00 3.70E-43 

56 0.00E+00 4.68E-45 

58 0.00E+00 5.67E-47 

60 0.00E+00 6.60E-49 

 
2-24 

Table 2-12 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for 

the Concentration of Nuclide in the Unmixed Portion of the Primary Contamination 

for Case IV Concerning C-14, with Notable Disagreements Highlighted 

Time (yr) RESRAD-OFFSITE Spreadsheet 

 

0 1.00E+02 1.00E+02 

1 1.41E+01 1.41E+01 

2 1.98E+00 1.98E+00 

3 2.76E-01 2.76E-01 

4 3.84E-02 3.84E-02 

5 5.32E-03 5.32E-03 

6 7.35E-04 7.35E-04 

7 1.01E-04 1.01E-04 

8 1.38E-05 1.38E-05 

9 1.89E-06 1.89E-06 

10 2.56E-07 2.56E-07 

11 3.47E-08 3.47E-08 

12 4.68E-09 4.68E-09 

14 8.39E-11 8.39E-11 

16 1.48E-12 1.48E-12 

18 2.58E-14 2.58E-14 

20 4.41E-16 4.41E-16 

22 7.42E-18 7.42E-18 

24 1.23E-19 1.23E-19 

26 2.00E-21 2.01E-21 

28 3.21E-23 3.22E-23 

30 5.08E-25 5.08E-25 

32 7.89E-27 7.90E-27 

34 1.21E-28 1.21E-28 

36 1.82E-30 1.82E-30 

38 2.69E-32 2.69E-32 

40 3.92E-34 3.92E-34 

42 5.62E-36 5.63E-36 

44 7.94E-38 7.95E-38 

46 1.10E-39 1.10E-39 

48 1.51E-41 1.51E-41 

50 2.03E-43 2.03E-43 

52 2.80E-45 2.69E-45 

54 0.00E+00 3.51E-47 

56 0.00E+00 4.50E-49 

58 0.00E+00 5.68E-51 

60 0.00E+00 7.05E-53 

 
2-25 

Table 2-13 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for 

the Concentration of Nuclide in the Unmixed Portion of the Primary Contamination 

for Case V Concerning Co-60 

Time (yr) RESRAD-OFFSITE Spreadsheet 

 

0.00 1.00E+02 1.00E+02 

0.25 9.68E+01 9.68E+01 

0.50 9.36E+01 9.36E+01 

0.75 9.06E+01 9.06E+01 

1.00 8.77E+01 8.77E+01 

1.25 8.48E+01 8.48E+01 

1.50 8.21E+01 8.21E+01 

1.75 7.94E+01 7.94E+01 

2.00 7.68E+01 7.68E+01 

2.25 7.43E+01 7.43E+01 

2.50 7.19E+01 7.19E+01 

2.75 6.96E+01 6.96E+01 

3.00 6.73E+01 6.73E+01 

3.25 6.52E+01 6.52E+01 

3.50 6.31E+01 6.31E+01 

3.75 6.10E+01 6.10E+01 

4.00 5.90E+01 5.90E+01 

4.25 5.71E+01 5.71E+01 

4.50 5.53E+01 5.53E+01 

4.75 5.35E+01 5.35E+01 

5.00 5.17E+01 5.17E+01 

. . . 

. . . 

. . . 

30.00 1.92E+00 1.92E+00 

30.25 1.86E+00 1.86E+00 

30.50 1.80E+00 1.80E+00 

30.75 1.74E+00 1.74E+00 

31.00 1.68E+00 1.68E+00 

31.25 1.63E+00 1.63E+00 

31.50 1.57E+00 1.57E+00 

31.75 1.52E+00 1.52E+00 

32.00 1.47E+00 1.47E+00 
2-26 

2.2.2 Release Rates of Nuclide through Runoff 

The rate at which soil from the primary contamination is eroded is computed at each 

intermediate time point with the following equation: 

, )( 10)( 6

vm pc tfAtm pc = ρε (Eq. 2.15)

where: 

contaminat of area )(mion 

primary thefrom is that mass eroded )( contaminat (g/yr), at timeion 

,0)( when 

 and ,0)( when 

2 =

=

= =

= >

A

tm t

tT

tT

pc

pc cv

cv cv

εε

ε ε

After the calculation of tm )( pc , nuclide release rates through surface runoff, tR )( sr

k , can be 

easily calculated as: 

tAtmtR )()()( kpc

sr

k = (Eq. 2.16)

The release rates of nuclide through surface runoff for Cases III (H-3), IV (C-14), and VII (Sr-90) 

are all zero. For Cases III and IV, it takes some time to erode the cover thickness to be less 

than the mixing depth, and by then the nuclides in the primary contamination had either diffused 

out or leached to the underlying vadose zone. For Case VII, the release rate is zero because 

there is no erosion of surface soil (erosion rate of cover is 0 m/yr). 

Listed records in SWFLUXIN.DAT are the same as those obtained with spreadsheets for 

Case II (Cs-137), Case V (Co-60), and Case VI (Ni-63). For Cases I (U-238) and Case VIII 

(Ra-226), discrepancies are found for a short period of time; they eventually disappear as time 

progresses. Figure 2-1 compares time profiles of the release rates of U-238 and its progeny 

nuclides in Case I. Table 2-14 highlights the comparison of the numerical values with which the 

graphics in Figure 2-1 are obtained. Figure 2-2 and Table 2-15 display comparisons of the 

release rates of Ra-226 and its progeny nuclides in Case VIII. 

Because the calculations in RESRAD-OFFSITE are sequential; any discrepancies observed in 

the earlier results can lead to discrepancies in the later results. In this section, the 

discrepancies in the release rates of nuclides through surface runoff are related to the 

discrepancies observed in Sections 2.1.1, 2.1.2, and 2.2.1. For both Tables 2-8 and 2-15, the 

observed discrepancy occurs at 100 years, while for both Tables 2-10 and 2-14, the observed 

discrepancy occurs at 1 year. 
2-27 

Figure 2-1 Comparison of the RESRAD-OFFSITE Results and Spreadsheet Results for the Release 

through Surface Runoff for Case I Concerning U-238 and Its Progenies 

0.00E+002.00E+094.00E+096.00E+098.00E+091.00E+101.20E+101.40E+101.60E+10

0 200 400 600 800 1000

time (yr)

Release rate of U-238 (pCi/yr) SWFLUXIN.DAT Spreadsheet

0.00E+005.00E+051.00E+061.50E+062.00E+062.50E+063.00E+063.50E+064.00E+064.50E+06

0 100 200 300 400 500 600 700 

time (yr)

Release rate of U-234 (pCi/yr) SWF

Spre

0.00E+005.00E+021.00E+031.50E+032.00E+032.50E+033.00E+033.50E+034.00E+034.50E+035.00E+03

0 100 200 300 400 500 600 700 800 900 1000

time (yr)

Release rate of Th-230 (pCi/yr) SWFLUXIN.DAT Spreadsheet

0.00E+002.00E+014.00E+016.00E+018.00E+011.00E+021.20E+02

0 100 200 300 400 500 600 700 

time (yr)

Release rate of Ra-226 (pCi/yr) SWF

Spre
2-28 

Figure 2-1 (cont.)

0.00E+001.00E+012.00E+013.00E+014.00E+015.00E+016.00E+017.00E+018.00E+01

0 100 200 300 400 500 600 700 800 900 1000

time (yr)

Release rate of Pb-210 (pCi/yr) SWFLUXIN.DAT Spreadsheet

0.00E+001.00E+012.00E+013.00E+014.00E+015.00E+016.00E+017.00E+018.00E+01

0 100 200 300 400 500 600 700 

time (yr)

Release rate of Po-210 (pCi/yr) SW

Spr

0.00E+002.00E+074.00E+076.00E+078.00E+071.00E+081.20E+081.40E+081.60E+08

0 100 200 300 400 500 600 700 800 900 1000

time (yr)

Eroded soil from primary contamination (g/yr) SWFLUXIN.DAT Spreadsheet
2-29 

Figure 2-2 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for Release 

through Surface Runoff for Case VIII Concerning Ra-226 and Its Progenies 

0.00E+001.00E+072.00E+073.00E+074.00E+075.00E+076.00E+077.00E+078.00E+079.00E+07

0 100 200 300 400 500 600 700 800 900 1000

Time (yr)

Release rate of Ra-226 (pCi/yr) SWFLUXIN.DAT Spreadsheet

0.00E+001.00E+072.00E+073.00E+074.00E+075.00E+076.00E+077.00E+078.00E+079.00E+071.00E+08

0 100 200 300 400 500 600 700 

Time (yr)

Release rate of Pb-210 (pCi/yr) S

S

0.00E+001.00E+072.00E+073.00E+074.00E+075.00E+076.00E+077.00E+078.00E+079.00E+071.00E+08

0 100 200 300 400 500 600 700 800 900 1000

Time (yr)

Release rate of Po-210 (pCi/yr) SWFLUXIN.DAT Spreadsheet

0.00E+001.00E+062.00E+063.00E+064.00E+065.00E+066.00E+067.00E+068.00E+069.00E+061.00E+07

0 100 200 300 400 500 600 700 

Time (yr)

Eroded soil from primary contamination (g/yr) SWFLU

Spread
2-30 

Table 2-14 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the Release Rat

through Surface Runoff for Case I Concerning U-238 and Its Progenies, with Notable Disagreeme

 U-238 U-234 Th-230 Ra-226 Pb-210 

Time 

(yr) 

RESRADOFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet 

0 1.50E+10 1.50E+10 0 0 0 0 0 0 0 0 1 1.50E+10 1.49E+10 4.24E+04 4.24E+04 1.91E-01 1.91E-01 2.76E-05 2.76E-05 2.10E-07 2.10E-07 

2 1.49E+10 1.49E+10 8.45E+04 8.45E+04 7.62E-01 7.62E-01 2.20E-04 2.20E-04 3.38E-06 3.38E-06 3 1.49E+10 1.49E+10 1.26E+05 1.26E+05 1.71E+00 1.71E+00 7.41E-04 7.41E-04 1.70E-05 1.70E-05 4 1.48E+10 1.48E+10 1.68E+05 1.68E+05 3.04E+00 3.04E+00 1.75E-03 1.75E-03 5.32E-05 5.32E-05 5 1.48E+10 1.48E+10 2.09E+05 2.09E+05 4.73E+00 4.73E+00 3.41E-03 3.41E-03 1.29E-04 1.29E-04 50 1.27E+10 1.27E+10 1.80E+06 1.80E+06 4.29E+02 4.29E+02 3.07E+00 3.07E+00 9.06E-01 9.06E-01 75 1.17E+10 1.17E+10 2.49E+06 2.49E+06 9.13E+02 9.13E+02 9.78E+00 9.78E+00 3.84E+00 3.84E+00 100 1.08E+10 1.08E+10 3.05E+06 3.05E+06 1.54E+03 1.54E+03 2.19E+01 2.19E+01 1.03E+01 1.03E+01 125 9.91E+09 9.91E+09 3.51E+06 3.51E+06 2.28E+03 2.28E+03 4.03E+01 4.03E+01 2.14E+01 2.14E+01 150 9.12E+09 9.12E+09 3.88E+06 3.88E+06 3.11E+03 3.11E+03 6.57E+01 6.57E+01 3.81E+01 3.81E+01 175 8.39E+09 8.39E+09 4.16E+06 4.16E+06 4.01E+03 4.01E+03 9.85E+01 9.85E+01 6.12E+01 6.12E+01 200 2.84E+09 2.84E+09 1.61E+06 1.61E+06 1.83E+03 1.83E+03 5.11E+01 5.11E+01 3.35E+01 3.35E+01 225 4.94E+08 4.94E+08 3.15E+05 3.15E+05 4.15E+02 4.15E+02 1.30E+01 1.30E+01 8.89E+00 8.89E+00 250 8.59E+07 8.59E+07 6.08E+04 6.08E+04 9.20E+01 9.20E+01 3.18E+00 3.18E+00 2.26E+00 2.26E+00 275 1.49E+07 1.49E+07 1.16E+04 1.16E+04 2.00E+01 2.00E+01 7.55E-01 7.55E-01 5.52E-01 5.52E-01 300 2.59E+06 2.59E+06 2.21E+03 2.21E+03 4.27E+00 4.27E+00 1.75E-01 1.75E-01 1.31E-01 1.31E-01 350 7.84E+04 7.84E+04 7.78E+01 7.78E+01 1.87E-01 1.87E-01 8.86E-03 8.86E-03 6.92E-03 6.92E-03 400 2.37E+03 2.37E+03 2.69E+00 2.69E+00 7.91E-03 7.91E-03 4.23E-04 4.23E-04 3.40E-04 3.40E-04 450 7.16E+01 7.16E+01 9.13E-02 9.13E-02 3.24E-04 3.24E-04 1.92E-05 1.92E-05 1.59E-05 1.59E-05 500 2.16E+00 2.16E+00 3.06E-03 3.06E-03 1.30E-05 1.30E-05 8.45E-07 8.45E-07 7.11E-07 7.11E-07 550 6.54E-02 6.54E-02 1.02E-04 1.02E-04 5.10E-07 5.10E-07 3.61E-08 3.61E-08 3.08E-08 3.08E-08 600 1.98E-03 1.98E-03 3.36E-06 3.36E-06 1.98E-08 1.98E-08 1.50E-09 1.50E-09 1.30E-09 1.30E-09 650 5.97E-05 5.97E-05 1.10E-07 1.10E-07 7.56E-10 7.56E-10 6.14E-11 6.14E-11 5.37E-11 5.37E-11 700 1.80E-06 1.80E-06 3.58E-09 3.58E-09 2.87E-11 2.87E-11 2.46E-12 2.46E-12 2.18E-12 2.18E-12 750 5.45E-08 5.45E-08 1.16E-10 1.16E-10 1.08E-12 1.08E-12 9.76E-14 9.76E-14 8.71E-14 8.71E-14 800 1.65E-09 1.65E-09 3.73E-12 3.73E-12 4.01E-14 4.01E-14 3.82E-15 3.82E-15 3.43E-15 3.43E-15 850 4.98E-11 4.98E-11 1.20E-13 1.20E-13 1.49E-15 1.49E-15 1.48E-16 1.48E-16 1.34E-16 1.34E-16 
2-31 

Table 2-14 (cont.) 

 U-238 U-234 Th-230 Ra-226 Pb-210 

Time 

(yr) 

RESRADOFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet 

900 1.50E-12 1.50E-12 3.83E-15 3.83E-15 5.49E-17 5.49E-17 5.68E-18 5.68E-18 5.16E-18 5.16E-18 950 4.55E-14 4.55E-14 1.22E-16 1.22E-16 2.01E-18 2.01E-18 2.16E-19 2.16E-19 1.97E-19 1.97E-19 1000 1.37E-15 1.37E-15 3.89E-18 3.89E-18 7.37E-20 7.37E-20 8.18E-21 8.18E-21 7.49E-21 7.49E-21 
2-32 

Table 2-15 Comparison of the RESRAD-OFFSITE Results and the 

Spreadsheet Results for the Release Rates of Nuclide through 

Surface Runoff for Case VIII Concerning Ra-226 and Its 

Progenies, with Notable Disagreements Highlighted 

Ra-226 Pb-210 Po-210 

Time 

(yr) 

RESRADOFFSITE Spreadsheet RESRADOFFSITE Spreadsheet RESRADOFFSITE Spreadsheet 

 

99 0 0 0 0 0 0 

100 0 1.57E+02 0 1.65E+02 0 1.60E+02 

101 2.74E+06 2.74E+06 2.88E+06 2.88E+06 2.80E+06 2.80E+06 

102 5.42E+06 5.42E+06 5.71E+06 5.71E+06 5.53E+06 5.53E+06 

103 8.03E+06 8.03E+06 8.47E+06 8.47E+06 8.21E+06 8.21E+06 

104 1.06E+07 1.06E+07 1.12E+07 1.12E+07 1.08E+07 1.08E+07 

105 1.31E+07 1.31E+07 1.38E+07 1.38E+07 1.34E+07 1.34E+07 

125 5.10E+07 5.10E+07 5.52E+07 5.52E+07 5.35E+07 5.35E+07 

150 7.48E+07 7.48E+07 8.24E+07 8.24E+07 7.99E+07 7.99E+07 

175 8.25E+07 8.25E+07 9.16E+07 9.16E+07 8.89E+07 8.89E+07 

200 8.10E+07 8.10E+07 9.02E+07 9.02E+07 8.76E+07 8.76E+07 

225 7.47E+07 7.47E+07 8.33E+07 8.33E+07 8.09E+07 8.09E+07 

250 6.61E+07 6.61E+07 7.39E+07 7.39E+07 7.17E+07 7.17E+07 

275 5.70E+07 5.70E+07 6.37E+07 6.37E+07 6.19E+07 6.19E+07 

300 2.41E+07 2.41E+07 2.70E+07 2.70E+07 2.62E+07 2.62E+07 

325 1.95E+07 1.95E+07 2.18E+07 2.18E+07 2.11E+07 2.11E+07 

350 1.57E+07 1.57E+07 1.75E+07 1.75E+07 1.70E+07 1.70E+07 

375 1.26E+07 1.26E+07 1.41E+07 1.41E+07 1.37E+07 1.37E+07 

400 1.01E+07 1.01E+07 1.13E+07 1.13E+07 1.09E+07 1.09E+07 

425 8.06E+06 8.06E+06 9.01E+06 9.01E+06 8.75E+06 8.75E+06 

450 6.43E+06 6.43E+06 7.19E+06 7.19E+06 6.98E+06 6.98E+06 

475 5.12E+06 5.12E+06 5.72E+06 5.72E+06 5.55E+06 5.55E+06 

500 4.07E+06 4.07E+06 4.55E+06 4.55E+06 4.42E+06 4.42E+06 

525 3.23E+06 3.23E+06 3.61E+06 3.61E+06 3.51E+06 3.51E+06 

550 2.56E+06 2.56E+06 2.86E+06 2.86E+06 2.78E+06 2.78E+06 

575 2.03E+06 2.03E+06 2.27E+06 2.27E+06 2.20E+06 2.20E+06 

600 1.60E+06 1.60E+06 1.79E+06 1.79E+06 1.74E+06 1.74E+06 

625 1.27E+06 1.27E+06 1.42E+06 1.42E+06 1.37E+06 1.37E+06 

650 1.00E+06 1.00E+06 1.12E+06 1.12E+06 1.09E+06 1.09E+06 

675 7.89E+05 7.89E+05 8.82E+05 8.82E+05 8.56E+05 8.56E+05 

700 6.22E+05 6.22E+05 6.95E+05 6.95E+05 6.75E+05 6.75E+05 

725 4.90E+05 4.90E+05 5.48E+05 5.48E+05 5.31E+05 5.31E+05 

750 3.86E+05 3.86E+05 4.31E+05 4.31E+05 4.18E+05 4.18E+05 

775 3.03E+05 3.03E+05 3.39E+05 3.39E+05 3.29E+05 3.29E+05 

800 2.38E+05 2.38E+05 2.67E+05 2.67E+05 2.59E+05 2.59E+05 

825 1.87E+05 1.87E+05 2.09E+05 2.09E+05 2.03E+05 2.03E+05 

850 1.47E+05 1.47E+05 1.64E+05 1.64E+05 1.60E+05 1.60E+05 

875 1.16E+05 1.16E+05 1.29E+05 1.29E+05 1.25E+05 1.25E+05 

900 9.06E+04 9.06E+04 1.01E+05 1.01E+05 9.83E+04 9.83E+04 

925 6.64E+04 6.64E+04 7.43E+04 7.43E+04 7.21E+04 7.21E+04 
2-33 

Table 2-15 (cont.) 

Ra-226 Pb-210 Po-210 

Time 

(yr) 

RESRADOFFSITE Spreadsheet RESRADOFFSITE Spreadsheet RESRADOFFSITE Spreadsheet 

 

950 4.87E+04 4.87E+04 5.44E+04 5.44E+04 5.28E+04 5.28E+04 

975 3.57E+04 3.57E+04 3.99E+04 3.99E+04 3.87E+04 3.87E+04 

1000 2.62E+04 2.62E+04 2.92E+04 2.92E+04 2.84E+04 2.84E+04 

2.3 Release to Groundwater 

Radionuclides in both the mixing zone and the unmixed portion of the primary contamination 

can dissolve in pore water and be carried through the vadose zone to the underlying 

groundwater table. The calculations of the release rates of nuclides, gw Rk , to the groundwater 

are performed using Eq. 2.32 in the RESRAD-OFFSITE User’s Manual (Yu et al. 2007): 

( ) 6 = tTtTfAtALR ×+ 10 )()( )( um

pc

c

pckk mixvm

gw

k ρ (Eq. 2.17)

The output file, AQFLUXIN.DAT, contains the calculation results. 

Comparison of the RESRAD-OFFSITE results and spreadsheet results are displayed in 

Figure 2-3 showing the temporal profiles for Case I concerning U-238 and its progeny nuclides 

and in Tables 2-16 to 2-19 showing numerical values for Case I, Case III (concerning H-3), 

Case IV (concerning C-14), and Case VII (concerning Sr-90), respectively. Overall, the 

agreement between the RESRAD-OFFSITE results and the spreadsheet results is very good. 

Differences are found when the release rates are very small and/or when they involve a distant 

progeny nuclide along the decay chain. The differences are caused by the different precisions 

used in RESRAD-OFFSITE and spreadsheets. For other cases, the release rates of nuclides to 

groundwater calculated by RESRAD-OFFSITE and the spreadsheets are the same. 
2-34 

Figure 2-3 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the Relea

Nuclide to Groundwater for Case I Concerning U-238 and Its Progenies 

0.00E+002.00E+094.00E+096.00E+098.00E+091.00E+101.20E+10

0 100 200 300 400 500 600 700 800 900 1000

Time (yr)

Releast rate of U-238 (pCi/yr) AQFLUXIN.DAT Spreadsheet

0.00E+002.00E+054.00E+056.00E+058.00E+051.00E+061.20E+06

0 100 200 300 400 500 600 700 

Time (yr)

Releast rate of U-234 (pCi/yr) AQF

Spre

0.00E+00

5.00E-021.00E-011.50E-012.00E-012.50E-013.00E-013.50E-014.00E-014.50E-015.00E-01

0 100 200 300 400 500 600 700 800 900 1000

Time (yr)

Releast rate of Th-230 (pCi/yr) AQFLUXIN.DAT Spreadsheet

0.00E+001.00E+002.00E+003.00E+004.00E+005.00E+006.00E+007.00E+008.00E+009.00E+00

0 100 200 300 400 500 600 700 

Time (yr)

Releast rate of Ra-226 (pCi/yr) AQF

Spre
2-35 

Figure 2-3 (cont.)

0.00E+00

5.00E-01

1.00E+001.50E+002.00E+002.50E+003.00E+003.50E+00

0 100 200 300 400 500 600 700 800 900 1000

Time (yr)

Releast rate of Pb-210 (pCi/yr) AQFLUXIN.DAT Spreadsheet

0.00E+005.00E+001.00E+011.50E+012.00E+012.50E+013.00E+013.50E+01

0 100 200 300 400 500 600 700 

Time (yr)

Releast rate of Po-210 (pCi/yr) AQ

Spr
2-36 

Table 2-16 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for the Release Rate

Groundwater for Case I Concerning U-238 and Its Progenies, with Notable Disagreement Highlight

U-238 U-234 Th-230 Ra-226 Pb-210 

Time 

(yr) 

RESRADOFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet 

0 9.96E+09 9.96E+09 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1 9.87E+09 9.87E+09 2.80E+04 2.80E+04 1.06E-04 1.06E-04 1.30E-05 1.30E-05 6.94E-08 6.94E-08 

2 9.79E+09 9.79E+09 5.55E+04 5.55E+04 4.19E-04 4.19E-04 1.03E-04 1.03E-04 1.11E-06 1.11E-06 3 9.71E+09 9.71E+09 8.26E+04 8.26E+04 9.36E-04 9.36E-04 3.46E-04 3.46E-04 5.56E-06 5.56E-06 4 9.63E+09 9.63E+09 1.09E+05 1.09E+05 1.65E-03 1.65E-03 8.15E-04 8.15E-04 1.73E-05 1.73E-05 5 9.55E+09 9.55E+09 1.35E+05 1.35E+05 2.56E-03 2.56E-03 1.58E-03 1.58E-03 4.17E-05 4.17E-05 

25 8.02E+09 8.02E+09 5.68E+05 5.68E+05 5.50E-02 5.50E-02 1.69E-01 1.69E-01 1.99E-02 1.99E-02 50 6.33E+09 6.33E+09 8.97E+05 8.97E+05 1.79E-01 1.79E-01 1.09E+00 1.09E+00 2.26E-01 2.26E-01 75 4.85E+09 4.85E+09 1.03E+06 1.03E+06 3.17E-01 3.17E-01 2.90E+00 2.90E+00 7.98E-01 7.98E-01 

100 3.57E+09 3.57E+09 1.01E+06 1.01E+06 4.27E-01 4.27E-01 5.19E+00 5.19E+00 1.71E+00 1.71E+00 150 1.51E+09 1.51E+09 6.43E+05 6.43E+05 4.32E-01 4.32E-01 7.80E+00 7.80E+00 3.17E+00 3.17E+00 200 1.41E+08 1.41E+08 8.02E+04 8.02E+04 7.63E-02 7.63E-02 1.82E+00 1.82E+00 8.36E-01 8.36E-01 250 4.27E+06 4.27E+06 3.03E+03 3.03E+03 3.83E-03 3.83E-03 1.13E-01 1.13E-01 5.63E-02 5.63E-02 300 1.29E+05 1.29E+05 1.10E+02 1.10E+02 1.78E-04 1.78E-04 6.23E-03 6.23E-03 3.27E-03 3.27E-03 350 3.90E+03 3.90E+03 3.87E+00 3.87E+00 7.81E-06 7.81E-06 3.16E-04 3.16E-04 1.73E-04 1.73E-04 400 1.18E+02 1.18E+02 1.34E-01 1.34E-01 3.30E-07 3.30E-07 1.50E-05 1.50E-05 8.49E-06 8.49E-06 450 3.56E+00 3.56E+00 4.54E-03 4.54E-03 1.35E-08 1.35E-08 6.85E-07 6.85E-07 3.96E-07 3.96E-07 500 1.08E-01 1.08E-01 1.53E-04 1.53E-04 5.41E-10 5.41E-10 3.01E-08 3.01E-08 1.77E-08 1.77E-08 550 3.26E-03 3.25E-03 5.07E-06 5.07E-06 2.13E-11 2.13E-11 1.28E-09 1.28E-09 7.69E-10 7.69E-10 600 9.84E-05 9.84E-05 1.67E-07 1.67E-07 8.24E-13 8.24E-13 5.35E-11 5.35E-11 3.25E-11 3.25E-11 650 2.97E-06 2.97E-06 5.47E-09 5.47E-09 3.15E-14 3.15E-14 2.18E-12 2.18E-12 1.34E-12 1.34E-12 700 8.98E-08 8.98E-08 1.78E-10 1.78E-10 1.19E-15 1.19E-15 8.78E-14 8.78E-14 5.44E-14 5.44E-14 750 2.71E-09 2.71E-09 5.77E-12 5.77E-12 4.48E-17 4.48E-17 3.48E-15 3.48E-15 2.17E-15 2.17E-15 800 8.20E-11 8.20E-11 1.86E-13 1.86E-13 1.67E-18 1.67E-18 1.36E-16 1.36E-16 8.56E-17 8.56E-17 850 2.48E-12 2.48E-12 5.97E-15 5.97E-15 6.20E-20 6.20E-20 5.27E-18 5.27E-18 3.34E-18 3.34E-18 900 7.49E-14 7.49E-14 1.91E-16 1.91E-16 2.29E-21 2.29E-21 2.02E-19 2.02E-19 1.29E-19 1.29E-19 950 2.26E-15 2.26E-15 8.81E+05 8.81E+05 8.39E-23 8.40E-23 7.70E-21 7.70E-21 4.92E-21 4.92E-21 

1000 6.84E-17 6.84E-17 8.74E+05 8.74E+05 3.07E-24 3.07E-24 2.91E-22 2.91E-22 1.87E-22 1.87E-22 
2-37 

Table 2-17 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results 

for the Release Rates of Nuclide to Groundwater for Case III Concerning H-3, 

with Notable Disagreements Highlighted 

Modification Factor 

Time (yr) RESRAD-OFFSITE Spreadsheet 

 

0 2.34E+12 2.34E+12 

1 4.63E+11 4.63E+11 

2 9.07E+10 9.07E+10 

3 1.76E+10 1.76E+10 

4 3.38E+09 3.38E+09 

5 6.42E+08 6.42E+08 

6 1.21E+08 1.21E+08 

7 2.24E+07 2.24E+07 

8 4.13E+06 4.13E+06 

9 7.53E+05 7.53E+05 

10 1.36E+05 1.36E+05 

11 2.42E+04 2.42E+04 

12 4.28E+03 4.28E+03 

14 1.30E+02 1.30E+02 

16 3.76E+00 3.76E+00 

18 1.05E-01 1.05E-01 

20 2.79E-03 2.79E-03 

22 7.16E-05 7.16E-05 

24 1.76E-06 1.76E-06 

26 4.15E-08 4.15E-08 

28 9.37E-10 9.37E-10 

30 2.03E-11 2.03E-11 

32 4.23E-13 4.23E-13 

34 8.45E-15 8.45E-15 

36 1.62E-16 1.62E-16 

38 2.97E-18 2.97E-18 

40 5.24E-20 5.24E-20 

42 8.86E-22 8.86E-22 

44 1.44E-23 1.44E-23 

46 2.24E-25 2.24E-25 

48 3.34E-27 3.34E-27 

50 4.78E-29 4.78E-29 

52 6.56E-31 6.56E-31 

54 0.00E+00 8.65E-33 

56 0.00E+00 1.09E-34 

58 0.00E+00 1.33E-36 

60 0.00E+00 1.54E-38 

 
2-38 

Table 2-18 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results 

for the Release Rates of Nuclide to Groundwater for Case IV Concerning C-14, 

with Notable Disagreements Highlighted 

Modification Factor 

Time (yr) RESRAD-OFFSITE Spreadsheet 

 

0 2.34E+12 2.34E+12 

1 3.29E+11 3.29E+11 

2 4.62E+10 4.62E+10 

3 6.45E+09 6.45E+09 

4 8.98E+08 8.98E+08 

5 1.24E+08 1.24E+08 

6 1.72E+07 1.72E+07 

7 2.36E+06 2.36E+06 

8 3.23E+05 3.23E+05 

9 4.41E+04 4.41E+04 

10 5.99E+03 5.99E+03 

11 8.11E+02 8.11E+02 

12 1.09E+02 1.09E+02 

14 1.96E+00 1.96E+00 

16 3.46E-02 3.47E-02 

18 6.02E-04 6.02E-04 

20 1.03E-05 1.03E-05 

22 1.73E-07 1.73E-07 

24 2.87E-09 2.87E-09 

26 4.68E-11 4.69E-11 

28 7.51E-13 7.52E-13 

30 1.19E-14 1.19E-14 

32 1.84E-16 1.85E-16 

34 2.82E-18 2.82E-18 

36 4.24E-20 4.25E-20 

38 6.29E-22 6.29E-22 

40 9.16E-24 9.17E-24 

42 1.31E-25 1.32E-25 

44 1.86E-27 1.86E-27 

46 2.58E-29 2.58E-29 

48 3.52E-31 3.53E-31 

50 4.75E-33 4.75E-33 

52 6.55E-35 6.29E-35 

54 0.00E+00 8.20E-37 

56 0.00E+00 1.05E-38 

58 0.00E+00 1.33E-40 

60 0.00E+00 1.65E-42 

 
2-39 

Table 2-19 Comparison of the RESRAD-OFFSITE Results and the Spreadsheet Results for 

the Release Rates of Nuclide to Groundwater for Case VII Concerning Sr-90 

Modification Factor 

Time (yr) RESRAD-OFFSITE Spreadsheet 

 

0.0 1.66E+10 1.66E+10 

0.5 1.63E+10 1.63E+10 

1.0 1.60E+10 1.60E+10 

1.5 1.58E+10 1.58E+10 

2.0 1.55E+10 1.55E+10 

2.5 1.53E+10 1.53E+10 

3.0 1.50E+10 1.50E+10 

3.5 1.48E+10 1.48E+10 

4.0 1.45E+10 1.45E+10 

4.5 1.43E+10 1.43E+10 

5.0 1.40E+10 1.40E+10 

. . . 

. . . 

. . . 

150.0 1.17E+08 1.17E+08 

150.5 1.15E+08 1.15E+08 

151.0 1.13E+08 1.13E+08 

151.5 1.12E+08 1.12E+08 

152.0 1.10E+08 1.10E+08 

152.5 1.08E+08 1.08E+08 

153.0 1.06E+08 1.06E+08 

153.5 1.04E+08 1.04E+08 

154.0 1.03E+08 1.03E+08 

154.5 1.01E+08 1.01E+08 

. . . 

. . . 

. . . 

300.0 8.29E+05 8.29E+05 

300.5 8.16E+05 8.16E+05 

301.0 8.02E+05 8.02E+05 

301.5 7.89E+05 7.89E+05 

302.0 7.76E+05 7.76E+05 

302.5 7.64E+05 7.64E+05 

303.0 7.51E+05 7.51E+05 

303.5 7.39E+05 7.39E+05 

304.0 7.27E+05 7.27E+05 

304.5 7.15E+05 7.15E+05 
2-40 

)( 

mix

ρ

where: 

 (s/yr).factor conversion 10 3.15576

and m/s), (0.001dust of velocity deposition 

,)g/m10(1 particles dust offactor loading mass 

(pCi/y), at timeair thedust to of form in thek nuclide of rate release )(

7

34-

=×

=

× =

=

du

du m

k

du t tR

ν

The calculated release rates for each time point are saved in the output file AIFLUXIN.DAT. 

comparison for Case VIII. 

RESRAD-OFFSITE results and the spreadsheet results for Case I, and Table 2-21 shows the 

discrepancies in the release rates through runoff. Table 2-20 shows the comparison between 

explanations for the discrepancies in the release rates to the air are the same as those for the 

using the same information, the concentrations of nuclides in the mixing layer. Therefore, the 

(Section 2.2). The coincidence is understandable because both release rates are calculated 

discrepancies occur at the same times as those observed in the release rates through runoff 

observed for Case I (concerning U-238) and Case VIII (concerning Ra-226). These 

Discrepancies between the RESRAD-OFFSITE results and the spreadsheet results are 

calculated by the spreadsheets. 

Case VII (concerning Sr-90), the release rates calculated by RESRAD-OFFSITE match those 

Cases II (concerning Cs-137), Case V (concerning Co-60), Case VI (concerning Ni-63), and 

in the primary contamination become zero due to loss through gas diffusion and leaching. For 

the cover thickness reduces to less than the mixing depth, the concentrations of H-3 and C-14 

air are zero, because the initial cover thickness is greater than the mixing depth, and by the time 

For Cases III (concerning H-3) and IV (concerning C-14), the releases in the form of dust to the 
2-41 

Table 2-20 Comparison of the RESRAD-OFFSITE Results and Spreadsheet Results for the Release Rates o

of Dust to the Air for Case I Concerning U-238 and Its Progenies, with Notable Disagreement High

U-238 U-234 Th-230 Ra-226 Pb-210 

Time 

(yr) 

RESRADOFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet 

0 3.16E+06 3.16E+06 0 0 0 0 0 0 0 0 1 3.15E+06 3.15E+06 8.92E+00 8.92E+00 4.02E-05 4.02E-05 5.80E-09 5.80E-09 4.41E-11 4.41E-11 

2 3.13E+06 3.13E+06 1.78E+01 1.78E+01 1.60E-04 1.60E-04 4.63E-08 4.63E-08 7.11E-10 7.11E-10 3 3.12E+06 3.12E+06 2.66E+01 2.66E+01 3.60E-04 3.60E-04 1.56E-07 1.56E-07 3.57E-09 3.57E-09 4 3.11E+06 3.11E+06 3.53E+01 3.53E+01 6.39E-04 6.39E-04 3.69E-07 3.69E-07 1.12E-08 1.12E-08 5 3.10E+06 3.10E+06 4.40E+01 4.40E+01 9.96E-04 9.96E-04 7.18E-07 7.18E-07 2.71E-08 2.71E-08 

25 2.90E+06 2.90E+06 2.06E+02 2.06E+02 2.38E-02 2.38E-02 8.56E-05 8.56E-05 1.44E-05 1.44E-05 50 2.67E+06 2.67E+06 3.79E+02 3.79E+02 9.02E-02 9.02E-02 6.46E-04 6.46E-04 1.91E-04 1.91E-04 75 2.46E+06 2.46E+06 5.23E+02 5.23E+02 1.92E-01 1.92E-01 2.06E-03 2.06E-03 8.07E-04 8.07E-04 

100 2.26E+06 2.26E+06 6.42E+02 6.42E+02 3.24E-01 3.24E-01 4.60E-03 4.60E-03 2.16E-03 2.16E-03 125 2.08E+06 2.08E+06 7.38E+02 7.38E+02 4.79E-01 4.79E-01 8.48E-03 8.48E-03 4.50E-03 4.50E-03 150 1.92E+06 1.92E+06 8.15E+02 8.15E+02 6.54E-01 6.54E-01 1.38E-02 1.38E-02 8.02E-03 8.02E-03 175 1.77E+06 1.77E+06 8.76E+02 8.76E+02 8.45E-01 8.45E-01 2.07E-02 2.07E-02 1.29E-02 1.29E-02 200 5.98E+05 5.98E+05 3.39E+02 3.39E+02 3.85E-01 3.85E-01 1.07E-02 1.07E-02 7.05E-03 7.05E-03 225 1.04E+05 1.04E+05 6.63E+01 6.63E+01 8.74E-02 8.74E-02 2.73E-03 2.73E-03 1.87E-03 1.87E-03 250 1.81E+04 1.81E+04 1.28E+01 1.28E+01 1.93E-02 1.93E-02 6.68E-04 6.68E-04 4.74E-04 4.74E-04 275 3.14E+03 3.14E+03 2.45E+00 2.45E+00 4.20E-03 4.20E-03 1.59E-04 1.59E-04 1.16E-04 1.16E-04 300 5.46E+02 5.46E+02 4.64E-01 4.64E-01 8.97E-04 8.97E-04 3.68E-05 3.68E-05 2.76E-05 2.76E-05 325 9.49E+01 9.49E+01 8.74E-02 8.74E-02 1.89E-04 1.89E-04 8.36E-06 8.36E-06 6.41E-06 6.41E-06 350 1.65E+01 1.65E+01 1.64E-02 1.64E-02 3.94E-05 3.94E-05 1.86E-06 1.86E-06 1.46E-06 1.46E-06 400 4.98E-01 4.98E-01 5.65E-04 5.65E-04 1.66E-06 1.66E-06 8.89E-08 8.89E-08 7.16E-08 7.16E-08 450 1.51E-02 1.51E-02 1.92E-05 1.92E-05 6.82E-08 6.82E-08 4.05E-09 4.05E-09 1.56E-08 1.56E-08 500 4.55E-04 4.55E-04 6.45E-07 6.45E-07 2.73E-09 2.73E-09 1.78E-10 1.78E-10 3.34E-09 3.34E-09 550 1.38E-05 1.38E-05 2.14E-08 2.14E-08 1.07E-10 1.07E-10 7.58E-12 7.58E-12 1.50E-10 1.50E-10 600 4.16E-07 4.16E-07 7.06E-10 7.06E-10 4.16E-12 4.16E-12 3.16E-13 3.16E-13 6.48E-12 6.48E-12 650 1.26E-08 1.26E-08 2.31E-11 2.31E-11 1.59E-13 1.59E-13 1.29E-14 1.29E-14 2.74E-13 2.74E-13 700 3.80E-10 3.80E-10 7.52E-13 7.52E-13 6.03E-15 6.03E-15 5.19E-16 5.19E-16 1.13E-14 1.13E-14 750 1.15E-11 1.15E-11 2.44E-14 2.44E-14 2.26E-16 2.26E-16 2.05E-17 2.05E-17 4.59E-16 4.59E-16 800 3.47E-13 3.47E-13 7.85E-16 7.85E-16 8.45E-18 8.45E-18 8.04E-19 8.04E-19 1.83E-17 1.83E-17 
2-42 

Table 2-20 (cont.) 

U-238 U-234 Th-230 Ra-226 Pb-210 

Time 

(yr) 

RESRADOFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet RESRAD- OFFSITE Spread- sheet 

850 1.05E-14 1.05E-14 2.52E-17 2.52E-17 3.13E-19 3.13E-19 3.11E-20 3.11E-20 7.22E-19 7.22E-19 900 3.17E-16 3.17E-16 8.07E-19 8.07E-19 1.15E-20 1.15E-20 1.20E-21 1.20E-21 2.81E-20 2.81E-20 950 9.57E-18 9.56E-18 2.57E-20 2.57E-20 4.24E-22 4.24E-22 4.55E-23 4.55E-23 1.09E-21 1.09E-21 
2-43 

Table 2-21 Comparison of the RESRAD-OFFSITE Results and the 

Spreadsheet Results for the Release Rates of Nuclide in the Form 

of Dust to the Air for Case VIII Concerning Ra-226 and Its 

Progenies, with Notable Disagreements Highlighted 

Ra-226 Pb-210 Po-210 

Time 

(yr) 

RESRADOFFSITE Spreadsheet RESRADOFFSITE Spreadsheet RESRADOFFSITE Spreadsheet 

 

99 0 0 0 0 0 0 

100 0 2.91E-01 0 3.05E-01 0 2.96E-01 

101 5.10E+03 5.10E+03 5.36E+03 5.36E+03 5.19E+03 5.19E+03 

102 1.01E+04 1.01E+04 1.06E+04 1.06E+04 1.03E+04 1.03E+04 

103 1.49E+04 1.49E+04 1.57E+04 1.57E+04 1.53E+04 1.53E+04 

104 1.97E+04 1.97E+04 2.08E+04 2.08E+04 2.02E+04 2.02E+04 

105 2.43E+04 2.43E+04 2.57E+04 2.57E+04 2.49E+04 2.49E+04 

125 9.59E+04 9.59E+04 1.04E+05 1.04E+05 1.01E+05 1.01E+05 

150 1.43E+05 1.43E+05 1.57E+05 1.57E+05 1.52E+05 1.52E+05 

175 1.59E+05 1.59E+05 1.76E+05 1.76E+05 1.71E+05 1.71E+05 

200 1.58E+05 1.58E+05 1.76E+05 1.76E+05 1.70E+05 1.70E+05 

225 1.47E+05 1.47E+05 1.64E+05 1.64E+05 1.59E+05 1.59E+05 

250 1.31E+05 1.31E+05 1.46E+05 1.46E+05 1.42E+05 1.42E+05 

275 1.14E+05 1.14E+05 1.27E+05 1.27E+05 1.23E+05 1.23E+05 

300 9.67E+04 9.67E+04 1.08E+05 1.08E+05 1.05E+05 1.05E+05 

325 7.84E+04 7.84E+04 8.76E+04 8.76E+04 8.50E+04 8.50E+04 

350 6.33E+04 6.33E+04 7.07E+04 7.07E+04 6.86E+04 6.86E+04 

375 5.09E+04 5.09E+04 5.69E+04 5.69E+04 5.52E+04 5.52E+04 

400 4.09E+04 4.09E+04 4.57E+04 4.57E+04 4.44E+04 4.44E+04 

425 3.27E+04 3.27E+04 3.66E+04 3.66E+04 3.55E+04 3.55E+04 

450 2.62E+04 2.62E+04 2.93E+04 2.93E+04 2.84E+04 2.84E+04 

475 2.09E+04 2.09E+04 2.33E+04 2.33E+04 2.27E+04 2.27E+04 

500 1.66E+04 1.66E+04 1.86E+04 1.86E+04 1.80E+04 1.80E+04 

525 1.32E+04 1.32E+04 1.48E+04 1.48E+04 1.43E+04 1.43E+04 

550 1.05E+04 1.05E+04 1.17E+04 1.17E+04 1.14E+04 1.14E+04 

575 8.33E+03 8.33E+03 9.31E+03 9.31E+03 9.03E+03 9.03E+03 

600 6.60E+03 6.60E+03 7.37E+03 7.37E+03 7.16E+03 7.16E+03 

625 5.22E+03 5.22E+03 5.83E+03 5.83E+03 5.66E+03 5.66E+03 

650 4.12E+03 4.12E+03 4.61E+03 4.61E+03 4.48E+03 4.48E+03 

675 3.26E+03 3.26E+03 3.64E+03 3.64E+03 3.53E+03 3.53E+03 

700 2.57E+03 2.57E+03 2.87E+03 2.87E+03 2.79E+03 2.79E+03 

725 2.03E+03 2.03E+03 2.27E+03 2.27E+03 2.20E+03 2.20E+03 

750 1.60E+03 1.60E+03 1.78E+03 1.78E+03 1.73E+03 1.73E+03 

775 1.26E+03 1.26E+03 1.41E+03 1.41E+03 1.36E+03 1.36E+03 

800 9.89E+02 9.89E+02 1.11E+03 1.11E+03 1.07E+03 1.07E+03 

825 7.78E+02 7.78E+02 8.70E+02 8.70E+02 8.44E+02 8.44E+02 

850 6.12E+02 6.12E+02 6.84E+02 6.84E+02 6.64E+02 6.64E+02 

875 4.80E+02 4.80E+02 5.37E+02 5.37E+02 5.21E+02 5.21E+02 

900 3.77E+02 3.77E+02 4.22E+02 4.22E+02 4.09E+02 4.09E+02 

925 2.77E+02 2.77E+02 3.09E+02 3.09E+02 3.00E+02 3.00E+02 
2-44 

Table 2-21 (cont.) 

Ra-226 Pb-210 Po-210 

Time 

(yr) 

RESRADOFFSITE Spreadsheet RESRADOFFSITE Spreadsheet RESRADOFFSITE Spreadsheet 

 

950 2.03E+02 2.03E+02 2.27E+02 2.27E+02 2.20E+02 2.20E+02 

975 1.49E+02 1.49E+02 1.66E+02 1.66E+02 1.61E+02 1.61E+02 

1000 1.09E+02 1.09E+02 1.22E+02 1.22E+02 1.18E+02 1.18E+02 
3-1 

3.0 Groundwater Transport Model 

Groundwater transport has three components: flux-to-flux transport in the unsaturated zone, 

pulse-to-flux transport in the saturated zone to the surface water body, and pulse-toconcentration transport in the saturated zone to the well. 

3.1 Verification of Transport in the Unsaturated Zone 

The equation for transport in the unsaturated zone that needs to be verified is the dispersiveadvective transport Eq. 3.59 of the RESRAD-OFFSITE User’s Manual (Yu et al. 2007). This 

equation is reproduced below as Eq. 3.1. 

































−

++ − −















−

++ −



















 



 



 ++

















+

−+

































−

+− − −















−

+− −



















 



 



 +−

















+

+=

)(4

)(4

)(4

)(4

2

4

exp

4 2

1

)(4

)(4

)(4

)(4

2

4

exp

4 2

1 ),(

1

1

2

2

2

2 2

2

1

1

2

2

2

2 2

2

1

2

ttD

ttDVz erf

ttD

ttDVz erf D

DVVz

DV

bz a

ttD

ttDVz erf

ttD

ttDVz erf D

DVVz

DV

bz tzf a

n

c

z

n

c

c z

n

c

z

n

c

c z

c

z

c

cc z

c

c z

n

c

z

n

c

c z

n

c

z

n

c

c z

c

z

c

cc z

c

c z

n

t

t

λ λ λ

λ

λ λ λ

λ (Eq. 3.1)

This is the output flux at a distance z at time 12 tttn >> , due to the input flux entering between 

times 1

t and 2t , and was obtained by the convolution 

( ) 

−

−















 − − = − −

1

2

4 exp 4

1 ),0(),(

tt 2

tt

c

z

c

c

z

n n

n

n

d

D

Vz

D

z tftzf τλτ

τ

τ

τ τπ

τ using a linear interpolation 

between the known input fluxes at times 1

t and 2t . 

 The coefficients a and b in Eq. 3.1 are given by Eq. 3.57 of the RESRAD-OFFSITE 

User’s Manual, which is reproduced below as Eq. 3.2. 

( ) ( )

12

1

2

12

2

1 2 1 ,0( ),0() ),0(

tt

tt tf

tt

tt tftttf n n

n −

−− + −

−− =≤−≤

τ τ

τ (Eq. 3.2)

Rearranging in terms of τ , ( ) τ batttf τ ,0 1 n 2 +=≤−≤ , 

 where 

12

1

2

12

2

1 ),0( ),0(

tt

tt tf

tt

tt tfa n n

−

− + −− = and 

12

1 2 ),0(),0(

tt

tftf b −− = . 

Any time-dependent input flux can be expressed as linear combination of two triangular flux 

distributions shifted in time, as illustrated in Figure 3-1. Thus, it is sufficient to verify the output 

flux from two triangular input fluxes, the first going from one to zero and the second going from 

zero to one in the first time interval. 
3-2 

Figure 3-1 Time Varying Flux Profile Represented as a Combination of Two Triangular Flux 

Distributions Shifted in Time 

The output fluxes of eight different nuclides (Table 3-1) that represent a wide spectrum of halflives were verified. The values used for the RESRAD-OFFSITE inputs that pertain to modeling 

the transport in the unsaturated zone are in Table 3-2. The inputs are in bold while the 

intermediate calculations are in italics. Four different runs with four different distribution 

coefficients were used for each of the nuclides to cover a wide range of conditions in this 

verification of transport in the unsaturated zone. Even so, this verification is not exhaustive; the 

Excel file that was used in this verification is available to verify other cases, should the need 

arise. 

 
3-3 

Table 3-1 Nuclides Used in This Verification and Their Transformation Rates 

 

Nuclide 60Co 3H 90Sr 137Cs 63Ni 226Ra 14C 238U 

Half-life, years 5.271 12.35 29.12 30 96 1600 5730 4.468 109

Transformation 

rate, 1/year 0.132 .0561 .0238 .0231 .00722 .000433 .000121 1.55 10-10

Table 3-2 RESRAD-OFFSITE Inputs and Intermediate Calculations That Pertain to 

Transport in the Unsaturated Zone 

 

Transport distance z (m) 4 

Darcy velocity Vd (m/yr) 0.5 

Saturated hydraulic conductivity Ksat (m/yr) 10 

Parameter b of Clapp-Hornberger 

equation 

b 5.3 

Saturation ratio Rs 0.8023 

Field capacity fc 0.3 

Total porosity pt 0.4 

Total moisture content θt 0.3209 

Effective porosity pe 0.2 

Effective moisture content θe 0.1605 

Dry bulk density ρb (g/cc) 1.5 

Distribution coefficient Kd (cc/g) 0 1 10 100 

Retardation factor Rd 1 5.674 47.74 468.4 

Contaminant transport velocity Vc (m/yr) 3.1160 0.5492 0.06527 0.006652 

Dispersivity D (m) 0.1 

Dispersion coefficient of contaminant Dc (m2

/yr) 0.3116 0.0549 0.00653 0.000665 

Time horizon (years) 4 20 200 2000 

Number of time points 128 

The expression of output flux contains two exponentials, a couple of differences between pairs 

of error functions, and two terms that involve the temporal variation of the input flux. The 

argument of the first exponential, c

z

c

zcc

D

DVVz

2

4 2 



 



 +− λ

, is negative and can be zero in cases 

where the transformation rate or the dispersion coefficient is miniscule compared to the 

contaminant transport rate. Thus, the first exponential is less than or equal to unity, as shown in 

the second column of Table 3-3. The argument of the second exponential, 

c

z

c

cc z

D

DVVz

2

4 2 



 



 ++ λ

, is positive and is greater than d

z . Thus, the value of the second 

exponential can be and is usually very large, as shown in the third column of Table 3-3. The 

second pair of error functions have to be evaluated to a much higher precision than the first pair. 

This is because the small differences between these two error functions are magnified by the 

much larger exponential multiplier. The error function that is available in Excel is not sufficiently 

precise for this purpose. The arguments of the second pair of error functions are typically large. 

 
3-4 

Table 3-3 Value of the Two Exponentials for the Cases Used in This Verification 























 



 



 +−

c

z

c

zcc

D

DVVz

2

4

exp

2 λ























 



 



 ++

c

z

c

zcc

D

DVVz

2

4

exp

2 λ

238U 

 Kd = 0 1 2.354E+17 

 Kd = 1 0.999999999 2.354E+17 

 Kd = 10 0.99999999 2.354E+17 

 Kd = 100 0.999999907 2.354E+17 

 

14C 

 Kd = 0 0.999844729 2.354E+17 

 Kd = 1 0.999119315 2.356E+17 

 Kd = 10 0.992615405 2.371E+17 

 Kd = 100 0.929968694 2.531E+17 

 

226Ra 

 Kd = 0 0.999444051 2.355E+17 

 Kd = 1 0.996849808 2.361E+17 

 Kd = 10 0.973817337 2.417E+17 

 Kd = 100 0.771968359 3.049E+17 

 

63Ni 

 Kd = 0 0.99077643 2.376E+17 

 Kd = 1 0.948834155 2.481E+17 

 Kd = 10 0.645521954 3.646E+17 

 Kd = 100 0.019232592 1.224E+19 

 

137

Cs 

 Kd = 0 0.970797583 2.425E+17 

 Kd = 1 0.845703411 2.783E+17 

 Kd = 10 0.254337486 9.255E+17 

 Kd = 100 1.81932E-05 1.294E+22 

 

90Sr 

 Kd = 0 0.969929157 2.427E+17 

 Kd = 1 0.84144947 2.797E+17 

 Kd = 10 0.244362118 9.633E+17 

 Kd = 100 1.38824E-05 1.696E+22 

 

3

H 

 Kd = 0 0.930607698 2.529E+17 

 Kd = 1 0.667174394 3.528E+17 

 Kd = 10 0.041344072 5.693E+18 

 Kd = 100 3.30086E-10 7.131E+26 

 

60Co 

 Kd = 0 0.845269484 2.785E+17 

 Kd = 1 0.392224955 6.001E+17 

 Kd = 10 0.00103154 2.282E+20 

 Kd = 100 5.79693E-18 4.061E+34 
3-5 

Thus, the expression ( )

( )





























+

 −+−≈

∏

=

= −

1

2

1

12

111)(

2

i

i

i

i j x

x

j

x

e xerf

π

 is used to evaluate the error 

functions in this case in both the RESRAD-OFFSITE code and in the Excel spreadsheet used 

for the verification. 

3.1.1 Output Flux from a Decreasing Triangular Input Flux 

The coefficients a and b for the input flux shown in Figure 3-2 are evaluated as: 

12

2

12

1

2

12

2

1 ),0( ),0(

tt

tt

tt

tt tf

tt

tt tfa n n n

−

− = −− + −− = and 

12 12

1 2 ),0(),0( 1

tttt

tftf b − = −− = . The expression 

for the output flux then becomes 

( )

( )

































− + + − −















− + + −

×























 



 



 ++

















+

− − −

− +

































− + − − −















− + − −

×























 



 



 +−

















+

− + −

−

=

)(

4

4

)(

1

4

)(

4

4

)(

1

4

2

4

exp

4

/

2

1

)(

4

4

)(

1

4

)(

4

4

)(

1

4

2

4

exp

4

/

2

1

),(

1

2

1

2

2

2

2

2

12

12

2

1

2

1

2

2

2

2

2

12

12

2

tt

D

DV

D tt

z erftt

D

DV

D tt

z erf

D

DVVz

DV

ttz

tt

tt

tt

D

DV

D tt

z erftt

D

DV

D tt

z erf

D

DVVz

DV

ttz

tt

tt

tzf

n c

z

c

c z

n c

z

n c

z

c

c z

n c

z

c

z

c

cc z

c

c z

n

n c

z

c

c z

n c

z

n c

z

c

c z

n c

z

c

z

c

cc z

c

c z

n

n

λ λ

λ

λ

λ λ

λ

λ

(Eq. 3.3)

This equation was evaluated in Excel files for 128 different values of time, nt ; the Excel files are 

described later. The situation was also modeled in the RESRAD-OFFSITE using the inputs 

shown in Table 3-2. In addition, the erosion rate of the contaminated zone was increased so 

that the contaminated zone erodes away before the second time point. This produces the 

desired triangular input flux. Thirty-two (eight nuclides, each at four different distribution 

coefficients) temporal profiles of output flux were verified. The verification of four of these flux 

profiles is illustrated in Figures 3-3, 3-4, 3-5, and 3-6. 

Figure 3-2 Decreasing Triangular Input Flux Profile 
3-6 

Figure 3-3 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone Resulting from 

Flux of 60Co of Unity at Time Zero and of Zero at the First Time Point at the Top of the Unsatu

Spreadsheet Calculations 

Output Flux from Decreasing Triangular Flux Input, 60C

0

0.005

0.01

0.015

0.02

0.025

0.5 1 1.5 2 

Time, years

Output Flux, pCi/year

RESRAD OFFSITESpread sheet calculations
3-7 

Figure 3-4 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone Resulting from 

Flux of 90Sr of Unity at Time Zero and of Zero at the First Time Point at the Top of the Unsatur

Spreadsheet Calculations 

Output Flux from Decreasing Triangular Flux Input, 90S

0

0.0020.0040.0060.008

0.01

0.0120.0140.0160.018

0.02

2.5 5 7.5 10 12.5 

Time, years

Output Flux, pCi/year

RESRAD OFFSITESpread sheet calculations
3-8 

Figure 3-5 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone Resulting from 

Flux of 63Ni of Unity at Time Zero and of Zero at the First Time Point at the Top of the UnsatuSpreadsheet Calculations 

Output Flux from Decreasing Triangular Flux Input, 63N

0

0.0020.0040.0060.008

0.01

0.0120.0140.0160.018

25 45 65 85 105 

Time, years

Output Flux, pCi/year

RESRAD OFFSITESpread sheet calculations
3-9 

Figure 3-6 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone Resulting from 

Flux of 14C of Unity at Time Zero and of Zero at the First Time Point at the Top of the Unsatura

Spreadsheet Calculations 

Output Flux from Decreasing Triangular Flux Input, 14C

0

0.005

0.01

0.015

0.02

0.025

250 450 650 850 1050 

Time, years

Output Flux, pCi/year

RESRAD OFFSITESpread sheet calculations
3-10 

3.1.2 Output Flux from an Increasing Triangular Input Flux 

The coefficients a and b for the input flux shown in Figure 3-7 are evaluated as 

12

1

12

1

2

12

2

1 ),0( ),0(

tt

tt

tt

tt tf

tt

tt tfa n n n

−

− = −− + −− = and 

12 12

1 2 ),0(),0( 1

tttt

tftf b −

− = −

− = . The expression for 

the output flux then becomes 

( )

( )

































− + + − −















− + + −

×























 



 



 ++

















+

− + −

− +

































− + − − −















− + − −

×























 



 



 +−

















+

− − −

−

=

)(

4

4

)(

1

4

)(

4

4

)(

1

4

2

4

exp

4

/

2

1

)(

4

4

)(

1

4

)(

4

4

)(

1

4

2

4

exp

4

/

2

1

),(

1

2

1

2

2

2

2

2

12

12

1

1

2

1

2

2

2

2

2

12

12

1

tt

D

DV

D tt

z erftt

D

DV

D tt

z erf

D

DVVz

DV

ttz

tt

tt

tt

D

DV

D tt

z erftt

D

DV

D tt

z erf

D

DVVz

DV

ttz

tt

tt

tzf

n c

z

c

c z

n c

z

n c

z

c

c z

n c

z

c

z

c

cc z

c

c z

n

n c

z

c

c z

n c

z

n c

z

c

c z

n c

z

c

z

c

cc z

c

c z

n

n

λ λ

λ

λ

λ λ

λ

λ

(Eq. 3.4)

This equation was evaluated in Excel files for 128 different values of time, nt ; the Excel files are 

described later. The situation was also modeled in the RESRAD-OFFSITE using the inputs 

shown in Table 3-2. It is not possible to obtain the desired increasing triangular input flux profile 

(Figure 3-7) using the release model of RESRAD-OFFSITE. The RESRAD-OFFSITE feature 

allowing an informed user to override the internal release model was utilized for this verification 

of the transport in the unsaturated zone. A double triangular input flux shown in Figure 3-8 was 

specified for the run. The increasing triangular input flux depicted in Figure 3-7 is equivalent to 

the difference between the double triangular input flux in Figure 3-8 and the decreasing 

triangular input flux in Figure 3-2 shifted by a time interval. Thus, the output flux corresponding 

to the increasing triangular input flux (Figure 3-7) is obtained as the difference between the 

output flux from the double triangular input flux (Figure 3-8) and the output flux from the 

decreasing triangular flux (Figure 3-2) shifted by a time interval. Thirty-two (eight nuclides, each 

at four different distribution coefficients) temporal profiles of output flux were verified. The 

verification of four of these flux profiles is illustrated in Figures 3-9, 3-10, 3-11, and 3-12. 

Figure 3-7 Increasing Triangular Input Flux Profile 

Figure 3-8 Double Triangular Input Flux Profile 
3-11 

Figure 3-9 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone Resulting fro

Flux of 3H of Zero at Time Zero and of Unity at the First Time Point at the Top of the Unsatura

Spreadsheet Calculations 

Output Flux from Increasing Triangular Flux Input, 3H

0

0.005

0.01

0.015

0.02

0.025

0.5 1 1.5 2 

Time, years

Output Flux, pCi/year

RESRAD OFFSITESpread sheet calculations
3-12 

Figure 3-10 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone Resulting fro

Flux of 137Cs of Zero at Time Zero and of Unity at the First Time Point at the Top of the Unsat

Spreadsheet Calculations 

Output Flux from Increasing Triangular Flux Input, 137C

0

0.0020.0040.0060.008

0.01

0.0120.0140.0160.018

0.02

2.5 5 7.5 10 12.5 

Time, years

Output Flux, pCi/year

RESRAD OFFSITESpread sheet calculations
3-13 

Figure 3-11 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone Resulting fro

Flux of 226Ra of Zero at Time Zero and of Unity at the First Time Point at the Top of the Unsat

Spreadsheet Calculations 

Output Flux from Increasing Triangular Flux Input, 226R

0

0.005

0.01

0.015

0.02

0.025

25 45 65 85 105 

Time, years

Output Flux, pCi/year

RESRAD OFFSITESpread sheet calculations
3-14 

Figure 3-12 Verification of RESRAD-OFFSITE Computed Flux Exiting an Unsaturated Zone Resulting fro

Flux of 238U of Zero at Time Zero and of Unity at the First Time Point at the Top of the Unsat

Spreadsheet Calculations 

Output Flux from Increasing Triangular Flux Input, 238U

0

0.005

0.01

0.015

0.02

0.025

0.03

250 450 650 850 1050 

Time, years

Output Flux, pCi/year

RESRAD OFFSITESpread sheet calculations
3-15 

3.1.3 Description of the Excel Files Used in This Verification 

Four Excel files, unsaturated 0.xls, unsaturated 1.xls, unsaturated 10.xls, and unsaturated 

100.xls, one for each value of the distribution coefficient, were used to verify the transport in the 

unsaturated zone. The first tab, “Ti,” contains the inputs that pertain to transport in the 

unsaturated zone and some intermediate calculations; the inputs are in bold. The tabs “AQ 1,” 

“AQ 2,” and “AQ 21” are the temporal input fluxes used in RESRAD-OFFSITE and correspond 

to Figures 3-2, 3-7, and 3-8. Tabs “WT 1” and “WT 21” are the RESRAD-OFFSITE outputs of 

flux out of the unsaturated zone corresponding to the input fluxes in tabs “AQ 1” and “AQ 21.” 

The temporal flux in tab “WT 2” was obtained by subtracting from the fluxes in tab “WT 21” the 

fluxes in tab “WT 1” shifted by a time step. 

The tab “Single Nuclide graph” compares the temporal output flux from RESRAD-OFFSITE with 

that calculated in the spreadsheet. The comparisons are captured in three plots: the first one, 

the one at the top anchored in cell “H4,” compares the output flux from a uniform input flux over 

the first time interval; the second plot in the middle, anchored in cell “H35,” compares the output 

flux from a decreasing triangular input flux over the first time interval; and the third plot at the 

bottom, anchored in cell “H66,” compares the output flux from a increasing triangular input flux 

over the first time interval. The plots pertain to the nuclide shown in cell “C1”; plots that pertain 

to the eight nuclides 60Co, 3

H, 90Sr, 137Cs, 63Ni, 226Ra, 14C, and 238U can be viewed by typing in 

the numbers, 2, 4, 9, 3, 5, 6, 1, and 11, respectively, in cell “A1.” Note that the nuclide name will 

change in cell “C1” but not in the title of the plots. Plots of all 64 verifications that were 

performed can be viewed in turn in this fashion. A subset of these plots were shown in 

Figures 3-3 to 3-6 and 3-9 to 3-12. 

3.2 Verification of Transport in the Saturated Zone to the 

Surface Water Body 

Two of the three equations of transport in the saturated zone to the surface water body that 

need to be verified are the dispersive-advective transport Eqs. 3.67 and 3.68 of the RESRADOFFSITE User’s Manual. These equations are reproduced below. 





−

−

−

−







 





 −−

−







 





 −+

− −

−

−

−

−

−

−

−





























− 















−

−− −















































 −−

−

























−+

















−

−− =−

1

2 2

1

4

2

4

2

1

1

1

1

1

4

4

2

4

2

2 ),(

mn

mn

c

x

c x

c

x

c x

mn

mn

tt

tt

D

V

L x

D

V

L x

x

c

x

mm

mn

tt

tt c

x

c

x

c

x

c

x

x

c

mm

mn

mn

e e d

L

D e

tt

tt

d

D

V

L

x

erf

D

V

L

x

erf L

eV

tt

tt

ttxf

τ

πτ

τ

τ

τ

τ

τ

τ τ

τ

τ

τ

τ

λτ

λτ

(Eq. 3.5a)
3-16 





−

−

−

−







 





 −−

−







 





 −+

− −

−

−

−

−

−

−





























− 















−

+− −















































 −−

−

























−+

















−

+− =−

1

2 2

1

4

2

4

2

1

1

2 1

4

4

2

4

2

2 ),(

mn

mn

c

x

c x

c

x

c x

mn

mn

tt

tt

D

V

L x

D

V

L x

x

c

x

mm

mn

tt

tt c

x

c

x

c

x

c

x

x

c

mm

mn

mn

e e d

L

D e

tt

tt

d

D

V

L

x

erf

D

V

L

x

erf L

eV

tt

tt

ttxf

τ

πτ

τ

τ

τ

τ

τ

τ τ

τ

τ

τ

τ

λτ

λτ

(Eq. 3.5b)

The first is the spatially integrated flux across a vertical plane in the saturated zone, at a 

distance x downgradient of the center of the primary contamination, at time >> mmn −1 ttt , due to 

an input flux that increases linearly from zero at time m−1 t to one at time mt . The second is the 

spatially integrated flux across the same vertical plane in the saturated zone, at the same time, 

due to the input flux that decreases linearly from one at time m−1 t to zero at time mt .

 The third 

equation that needs to be verified is Eq. 3.70 of the RESRAD-OFFSITE User’s Manual; this 

relates the spatially integrated fluxes in Eqs. 3.68 and 3.69 to the flux that enters a surface 

water body through a rectangular section of the aquifer of dimensions nf − yy by ds . This is 

reproduced below. 

z

zs

y

fnys

sw L

f

L

yyf xfxf , , ),( = )()( (Eq. 3.6)

where: 



















 − +

+ − − − + =

p

c

y

yn

p

c

y

yn

p

c

y

yf

p

c

y

yf

p

c

fnys y

tD

Ly Interf

tD

Ly Interf

tD

Ly Interf

tD

Ly InterftDyyf

16

2

16

2

16

2

16

2

),( ,

and 



















 − − + − − + =

p

c

z

z

p

c

z

z

p

c

z

zs

p

c

z

zs

p

c

zzs

tD

L

Interf

tD

L

Interf

tD

Ld

Interf

tD

Ld

InterftDf

4 4 4 4 ,

p t in these expressions is obtained from Eq. 3.49 of the RESRAD-OFFSITE User’s Manual: 

( )( )

( ) 2

22 2

4

4

c

c

x

c

c

x

c

x

c

x

p VD

nDnD xVD

t

+

+++− = λ

λ . (Eq. 3.7) 

The fluxes of eight different nuclides (Table 3-1) that represent a wide spectrum of half-lives 

were verified. The values used for the RESRAD-OFFSITE inputs that pertain to modeling the 

transport in the saturated zone to the surface water body are in Table 3-4. The inputs are in 

bold while the intermediate calculations are in italics. Three different runs with three different 
3-17 

distribution coefficients were used for each of the nuclides to cover a wide range of conditions 

in this verification of transport in the saturated zone. Even so this verification is not exhaustive; 

the excel file that was used in this verification is available to verify other cases should the 

need arise. 

3.2.1 Output Flux from a Decreasing Triangular Input Flux 

For the input flux shown in Figure 3-13, the expression for the output flux becomes 





−

−







 





 −−

−







 





 −+

−

−

−

−

−

−

















−

+− −















































 −−

−

























−+

















−

+− =

1

2

2 2

1

2

4

2

4

2

2

12

2

12

2

2

2

4

2

4

2

2 ),(

tt

tt

D

V

L x

D

V

L x

c

c

n x

x

c

tt

tt c

x

c

x

c

x

c

x

n

x

c

n

n

n

c

x

c x

c

x

c x

n

n

d e e

V

D

e

tt

tt

L

V

d

D

V

L

x

erf

D

V

L

x

erfe

tt

tt

L

V txf

τ

π τ

τ

τ

τ

τ

τ

τ τ

τ

τ

τ

τ

λτ

λτ

. (Eq. 3.8)

Figure 3-13 Decreasing Triangular Input Flux Profile 

This equation was evaluated in Excel files for 128 different values of time, nt ; the integral 

(convolution, to be more precise) had to be evaluated numerically. The Excel files are 

described later. The situation was also modeled in the RESRAD-OFFSITE code using the 

inputs shown in Table 3-4. In addition, the erosion rate of the contaminated zone was increased 

so that the contaminated zone erodes away before the second time point. This produces the 

desired triangular input flux profile. Twenty-four (8 nuclides, each at 3 different distribution 

coefficients) temporal profiles of output flux were verified. The verification of four of these flux 

profiles is illustrated in Figures 3-14, 3-15, 3-16, and 3-17. 

 
3-18 

Table 3-4 RESRAD-OFFSITE Inputs and Intermediate Calculations That Pertain to 

Transport in the Saturated Zone to the Surface Water Body 

 

Average transport distance X (m) 850 

Length of contamination Lx (m) 100 

Width of contamination Ly (m) 100 

Saturated hydraulic conductivity Ksat (m/yr) 500 

Hydraulic gradient .02 

Darcy velocity Vd (m/yr) 10 

Infiltration rate I (m/yr) 0.5 

Depth of initial penetration of the contamination into the 

saturated zone 

Lz (m) 5 

Total porosity pt 0.4 

Effective porosity pe 0.2 

Dry bulk density ρb (g/cc) 1.5 

Distribution coefficient Kd (cc/g) 0 1 10 

Retardation factor Rd 1 4.75 38.5 

Contaminant transport velocity Vc (m/yr) 50 10.53 1.299 

Longitudinal dispersivity dx (m) 20 

Longitudinal dispersion coefficient of contaminants Dcx (m2

/yr) 1000 210.5 25.97 

Lateral horizontal dispersivity dy (m) 3 

Lateral horizontal dispersion coefficient of contaminants Dcy (m2

/yr) 150 31.58 3.896 

Lateral vertical dispersivity dy (m) 0.15 

Lateral vertical dispersion coefficient of contaminants Dcy (m2

/yr) 7.5 1.579 0.1048 

Time to peak flux tp (yr) 14.5 54.3 211.9 

Distance from the plum centerline to right edge of 

surface waterbody 

yn (m) –150 

Distance from the plum centerline to left edge of surface 

waterbody 

yf (m) 150 

Depth of aquifer intercepted by surface water body ds (m) 5 

Time horizon (years) 32 128 1024 

Number of time points 128 
3-19 

Figure 3-14 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body Resulting from 

Flux of 60Co of Unity at Time Zero and of Zero at the First Time Point at the Water Table Usin

Calculations 

Flux to Surface Water Body from Decreasing Triangul

Pulse Input, 60Co

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

0.0004

0.00045

0.0005

0 5 10 15 20 25 3

Time, years

Flux, pCi/year

RESRAD OFFSITSpread sheet calc
3-20 

Figure 3-15 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body Resulting from 

Flux of 90Sr of Unity at Time Zero and of Zero at the First Time Point at the Water Table Usin

Calculations 

Flux to Surface Water Body from Decreasing Triangul

Pulse Input, 90Sr

0

0.0005

0.001

0.0015

0.002

0.0025

0 5 10 15 20 25 3

Time, years

Flux, pCi/year

RESRAD OFFSITSpread sheet calc
3-21 

Figure 3-16 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body Resulting from 

Flux of 63Ni of Unity at Time Zero and of Zero at the First Time Point at the Water Table Usin

Calculations 

Flux to Surface Water Body from Decreasing Triangula

Pulse Input, 63Ni

0

0.00020.00040.00060.0008

0.001

0.00120.00140.00160.0018

0 20 40 60 80 100 12

Time, years

Flux, pCi/year

RESRAD OFFSITSpread sheet calc
3-22 

Figure 3-17 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body Resulting from 

Flux of 14C of Unity at Time Zero and of Zero at the First Time Point at the Water Table Usin

Calculations 

Flux to Surface Water Body from Decreasing Triangula

Pulse Input, 14C

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 200 400 600 800 1000 

Time, years

Flux, pCi/year

RESRAD OFFSITESpread sheet calcu
3-23 

3.2.2 Output Flux from an Increasing Triangular Input Flux 

For the input flux shown in Figure 3-18, the expression for the output flux becomes 





−

−







 





 −−

−







 





 −+

− −

−

−

−





























− 















−

−− −















































 −−

−

























−+

















−

−− =

1

2

2 2

1

2

4

2

4

2

12

1

12

1

1

4

4

2

4

2

2 ),(

tt

tt

D

V

L x

D

V

L x

x

c

n x

tt

tt c

x

c

x

c

x

c

x

x

n c

n

n

n

c

x

c x

c

x

c x

n

n

e e d

L

D e

tt

tt

d

D

V

L

x

erf

D

V

L

x

erf L

eV

tt

tt

txf

τ

πτ

τ

τ

τ

τ

τ

τ τ

τ

τ

τ

τ

λτ

λτ

. (Eq. 3.9)

This equation was evaluated in Excel files for 128 different values of time, nt ; the integral 

(convolution, to be more precise) had to be evaluated numerically. The Excel files are 

described later. The situation was also modeled in the RESRAD-OFFSITE using the inputs 

shown in Table 3-4. It is not possible to obtain the desired increasing triangular input flux profile 

(Figure 3-18) using the release model of RESRAD-OFFSITE. The RESRAD-OFFSITE feature 

allowing an informed user to override the internal release model was utilized for this verification 

of the transport in the saturated zone. A double triangular input flux shown in Figure 3-19 was 

specified for the run. The increasing triangular input flux depicted in Figure 3-18 is equivalent to 

the difference between the double triangular input flux in Figure 3-19 and the decreasing 

triangular input flux in Figure 3-13 shifted by a time interval. Thus, the output flux corresponding 

to the increasing triangular input flux (Figure 3-18) is obtained as the difference between the 

output flux from the double triangular input flux (Figure 3-19) and the output flux from the 

decreasing triangular flux (Figure 3-13) shifted by a time interval. Twenty-four (eight nuclides, 

each at three different distribution coefficients) temporal profiles of output flux were verified. 

The verification of four of these flux profiles is illustrated in Figures 3-20, 3-21, 3-22, and 3-23. 

Figure 3-18 Increasing Triangular Input Flux Profile 

Figure 3-19 Double Triangular Input Flux Profile 
3-24 

Figure 3-20 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water BodyFResulting from 

Flux of 3H of Zero at Time Zero and of Unity at the First Time Point at the Water Table Using 

Calculations 

Flux to Surface Water Body from Increasing Triangula

Pulse Input, 3H

0

0.00020.00040.00060.0008

0.001

0.00120.00140.0016

0 5 10 15 20 25 3

Time, years

Flux, pCi/year

RESRAD OFFSITSpread sheet calc
3-25 

Figure 3-21 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body Resulting from 

Flux of 137Cs of Zero at Time Zero and of Unity at the First Time Point at the Water Table Usi

Calculations 

Flux to Surface Water Body from Increasing Triangula

Pulse Input, 137Cs

0

0.00010.00020.00030.00040.00050.0006

0 20 40 60 80 100 12

Time, years

Flux, pCi/year

RESRAD OFFSITSpread sheet calc
3-26 

Figure 3-22 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body Resulting from 

Flux of 226Ra of Zero at Time Zero and of Unity at the First Time Point at the Water Table Usi

Calculations 

Flux to Surface Water Body from Increasing Triangula

Pulse Input, 226Ra

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 20 40 60 80 100 12

Time, years

Flux, pCi/year

RESRAD OFFSITSpread sheet calc
3-27 

Figure 3-23 Verification of RESRAD-OFFSITE Computed Flux to the Surface Water Body Resulting from 

Flux of 238U of Zero at Time Zero and of Unity at the First Time Point at the Water Table Usin

Calculations 

Flux to Surface Water Body from Increasing Triangula

Pulse Input, 238U

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 200 400 600 800 1000 

Time, years

Flux, pCi/year

RESRAD OFFSITESpread sheet calcu
3-28 

3.2.3 Description of the Excel Files Used in This Verification 

Three excel files, saturated 0.xls, saturated 1.xls, and saturated 10.xls, one for each value of the 

distribution coefficient, were used to verify the transport in the saturated zone. The first tab, “Ti,” 

contains the inputs that pertain to transport in the saturated zone and some intermediate 

calculations; the inputs are in bold. The tabs “AQ 1,” “AQ 2,” and “AQ 21” are the temporal input 

fluxes used in RESRAD-OFFSITE and correspond to Figure 3-13, 3-18, and 3-19. “SWF 1” and 

“SWF 21” are the RESRAD-OFFSITE outputs of flux, out of the saturated zone into the surface 

water body, corresponding to the input fluxes in tabs “AQ 1” and “AQ 21.” The temporal flux in 

tab “SWF 2” was obtained by subtracting from the fluxes in tab “SWF 21” the fluxes in tab “SWF 

1” shifted by a time step. 

The tab “Single Nuclide graph” compares the temporal output flux from RESRAD-OFFSITE 

code with that calculated in the spreadsheet. The comparisons are captured in two plots: the 

first one, the one at the top, anchored in cell “J4,” compares the output flux from a decreasing 

triangular input flux over the first time interval; the second plot, anchored in cell “J35,” compares 

the output flux from an increasing triangular input flux over the first time interval. The plots 

pertain to the nuclide shown in cell “C1,” plots that pertain to the eight nuclides 60Co, 3

H, 90Sr, 

137Cs, 63Ni, 226Ra, 14C, and 238U can be viewed by typing in the numbers, 2, 4, 9, 3, 5, 6, 1, and 

11, respectively, in cell “A1” and then launching the computational macro by clicking Ctrl-a. The 

computational macro evaluates the convolutions using numerical integration; the numerical 

integration method used in the code is described in Section 3.3.14 of the RESRAD-OFFSITE 

User’s Manual. Note that the nuclide name will change in cell “C1” but not in the title of the 

plots. Plots of all 48 verifications that were performed can be viewed in turn in this fashion. A 

subset of these plots were shown in Figures 3-14 to 3-17 and 3-20 to 3-23. 

3.3 Verification of Transport in the Saturated Zone to the 

Well 

The general equation that needs to be verified is the dispersive-advective transport Eq. 3.71 of 

the RESRAD-OFFSITE User’s Manual. This equation is reproduced below. 

 = −

nt

nwt

xzyd

c

wwwell wywzw tf LLLV

V

ycctyxc

0

,,0 )( 2

)(),,( τ

(Eq. 3.10)

τ

τ

τ

τ

τ λτ d

D

VLx erf

D

VLx erfe c

x

cxw

c

x

cxw



































 −− −



















 −+

× −

4

2

4

2 , 

 
3-29 

where: 











− −+ − ++ =

p

c

y

yww

p

c

y

yww

w

p

c

y

wyw

tD

Ly Interf

tD

Ly Interf

tD

yc

16

2

16

2

)( ,

φ φ

φ









 −− +

+−

p

c

y

yww

p

c

y

yww

tD

Ly Interf

tD

Ly Interf

16

2

16

2 φ φ

and 



















 − − + − − + =

p

c

z

z

p

c

z

z

p

c

z

zw

p

c

z

zw

w

p

c

z

zw

tD

L Interf

tD

L Interf

tD

Ld Interf

tD

Ld Interf d

tD

c

4 4 4 4 ,

This is the concentration in a well located at a distance wx from the center of the primary 

contamination at time nt , due to the input flux ( )tf wt at the water table. 

The convolution is simplified to the two expressions (Eqs. 3.72 and 3.73) for the two triangular 

input fluxes considered in the previous sections. 



− −

−

−

−

−



































 −− −



















 −+

















−

−− =−

1

4

2

4

2

2 ),(

1

1

1

mn

mn

tt

tt c

x

cx

c

x

cx

zydx

c

mm

mn

mn d

D

VLx erf

D

VLx erf LLVLeV

tt

tt

ttxf τ

τ

τ

τ

τ τ λτ

 (Eq. 3.11) 



− −

−

−

−

− 

































 −− −



















 −+

















−

+− =−

1

4

2

4

2

2 ),(

1

2 1

mn

mn

tt

tt c

x

cx

c

x

cx

zydx

c

mm

mn

mn d

D

VLx erf

D

VLx erf LLVLeV

tt

tt

ttxf τ

τ

τ

τ

τ τ λτ

The first is due to the input flux that increases linearly from zero at time m−1 t to one at time mt . 

The second is due to the input flux that decreases linearly from one at time m−1 t to zero at 

time mt . 

The concentrations of eight different nuclides (Table 3-1) that represent a wide spectrum of halflives were verified. The values used for the RESRAD-OFFSITE inputs that pertain to modeling 

the transport in the saturated zone to the well are in Table 3-5. The inputs are in bold, while the 

intermediate calculations are in italics. Three different runs with three different distribution 

coefficients were used for each of the nuclides to cover a wide range of conditions in this 

verification of transport in the saturated zone. Even so, this verification is not exhaustive; the 

Excel file that was used in this verification is available to verify other cases, should the 

need arise. 
3-30 

Table 3-5 RESRAD-OFFSITE Inputs and Intermediate Calculations That Pertain to 

Transport in the Saturated Zone to the Well 

 

Average transport distance x (m) 850 

Length of contamination Lx (m) 100 

Width of contamination Ly (m) 100 

Saturated hydraulic conductivity Ksat (m/yr) 500 

Hydraulic gradient .02 

Darcy velocity Vd (m/yr) 10 

Infiltration rate I (m/yr) 0.5 

Depth of initial penetration of the contamination into 

the saturated zone 

Lz (m) 5 

Total porosity pt 0.4 

Effective porosity pe 0.2 

Dry bulk density ρb (g/cc) 1.5 

Distribution coefficient Kd (cc/g) 0 1 10 

Retardation factor Rd 1 4.75 38.5 

Contaminant transport velocity Vc (m/yr) 50 10.53 1.299 

Longitudinal dispersivity dx (m) 20 

Longitudinal dispersion coefficient of contaminants Dcx (m2

/yr) 1,000 210.5 25.97 

Lateral horizontal dispersivity dy (m) 3 

Lateral horizontal dispersion coefficient of 

contaminants 

Dcy (m2

/yr) 150 31.58 3.896 

Lateral vertical dispersivity dy (m) 0.15 

Lateral vertical dispersion coefficient of contaminants Dcy (m2

/yr) 7.5 1.579 0.1048 

Time to peak flux tp (yr) 14.5 54.3 211.9 

Distance from the plum centerline to well yw (m) 0 

Well pumping rate Uw (m3

/yr) 5,100 

Depth of aquifer intercepted by well dw (m) 5 

Width of aquifer intercepted by well φw (m) 51 

Time horizon (years) 32 128 1024 

Number of time points 128 

3.3.1 Output Flux from a Decreasing Triangular Input Flux 

For the decreasing input flux profile shown in Figure 3-24, the expression for the concentration 

in the well becomes 



−

−

−



































 −− −



















 −+

















−

+− =

1

2 4

2

4

2

2

1 ),(

12

2

2

tt

tt c

x

cx

c

x

n cx

x

c

zyd

n

n

n

d

D

VLx erf

D

VLx erfe

tt

tt

L

V

LLV txf τ

τ

τ

τ

τ τ λτ . 

 (Eq. 3.12) 

This equation was evaluated in Excel files for 128 different values of time, nt ; the integral 

(convolution, to be more precise) had to be evaluated numerically. The Excel files are 

described later. The situation was also modeled in the RESRAD-OFFSITE code using the 

inputs shown in Table 3-5. In addition, the erosion rate of the contaminated zone was increased 

so that the contaminated zone erodes away before the second time point. This produces the 

desired triangular input flux. Twenty-four (eight nuclides, each at three different distribution 
3-31 

coefficients) temporal profiles of output flux were verified. The verification of four of these flux 

profiles is illustrated in Figures 3-25, 3-26, 3-27, and 3-28. 

Figure 3-24 Decreasing Triangular Input Flux Profile 

3.3.2 Output Flux from an Increasing Triangular Input Flux 

For the increasing input flux profile shown in Figure 3-29, the expression for the concentration in 

the well then becomes 

τ

τ

τ

τ

τ τ λτ d

D

VLx erf

D

VLx erfe

tt

tt

L

V

LLV txf c

x

x c

c

x

x c

tt

tt

n

x

c

zyd

n

n

n



































 −− −



















 −+

















−

−− = 

−

−

−

4

2

4

2

2

1 ),(

1

2 12

1

1 

 (Eq. 3.13) 

This equation was evaluated in Excel files for 128 different values of time, nt ; the integral 

(convolution, to be more precise) had to be evaluated numerically. The Excel files are 

described later. The situation was also modeled in the RESRAD-OFFSITE code using the 

inputs shown in Table 3-5. It is not possible to obtain the desired increasing triangular input flux 

profile (Figure 3-29) using the release model of RESRAD-OFFSITE. The RESRAD-OFFSITE 

feature allowing an informed user to override the internal release model was utilized for this 

verification of the transport in the unsaturated zone. A double triangular input flux shown in 

Figure 3-30 was specified for the run. The increasing triangular input flux depicted in 

Figure 3-29 is equivalent to the difference between the double triangular input flux in 

Figure 3-30 and the decreasing triangular input flux in Figure 3-24 shifted by a time interval. 

Thus the output flux corresponding to the increasing triangular input flux (Figure 3-29) is 

obtained as the difference between the output flux from the double triangular input flux 

(Figure 3-30) and the output flux from the decreasing triangular flux (Figure 3-24) shifted by a 

time interval. Twenty-four (eight nuclides, each at three different distribution coefficients) 

temporal profiles of output flux were verified. The verification of four of these flux profiles is 

illustrated in Figures 3-31, 3-32, 3-33, and 3-34. 
3-32 

Figure 3-25 Verification of RESRAD-OFFSITE Computed Concentration in the Well Resulting from a Tria

60Co of Unity at Time Zero and of Zero at the First Time Point at the Water Table Using Spre

Concentration in Well from Decreasing Triangular Puls

Input, 60Co

0.0E+00

5.0E-091.0E-081.5E-082.0E-082.5E-083.0E-083.5E-084.0E-084.5E-085.0E-08

0 5 10 15 20 25 3

Time, years

Concentration, pCi/m

3

RESRAD OFFSITSpread sheet cal
3-33 

Figure 3-26 Verification of RESRAD-OFFSITE Computed Flux Concentration in the Well Resulting from 

Flux of 90Sr of Unity at Time Zero and of Zero at the First Time Point at the Water Table Usin

Calculations 

Concentration in Well from Decreasing Triangular Puls

Input, 90Sr

0.0E+00

5.0E-081.0E-071.5E-072.0E-072.5E-07

0 5 10 15 20 25 3

Time, years

Concentration, pCi/m

3

RESRAD OFFSITSpread sheet cal
3-34 

Figure 3-27 Verification of RESRAD-OFFSITE Computed Concentration in the Well Resulting from a Tria

63Ni of Unity at Time Zero and of Zero at the First Time Point at the Water Table Using Sprea

Concentration in Well from Decreasing Triangular Puls

Input, 63Ni

0.0E+00

2.0E-084.0E-086.0E-088.0E-081.0E-071.2E-071.4E-071.6E-071.8E-07

0 20 40 60 80 100 12

Time, years

Concentration, pCi/m

3

RESRAD OFFSITSpread sheet calc
3-35 

Figure 3-28 Verification of RESRAD-OFFSITE Computed Concentration in the Well Resulting from a Tria

14C of Unity at Time Zero and of Zero at the First Time Point at the Water Table Using Sprea

Concentration in Well from Decreasing Triangular Puls

Input, 14C

0.0E+00

5.0E-081.0E-071.5E-072.0E-072.5E-073.0E-07

0 200 400 600 800 1000 

Time, years

Concentration, pCi/m

3

RESRAD OFFSITESpread sheet calcu
3-36 

Figure 3-29 Increasing Triangular Input Flux Profile 

Figure 3-30 Double Triangular Input Flux Profile 

3.3.3 Description of the Excel Files Used in This Verification 

Three Excel files, saturated 0.xls, saturated 1.xls, and saturated 10.xls, one for each value of 

the distribution coefficient, were used to verify the transport in the saturated zone. The first tab, 

“Ti,” contains the inputs that pertain to transport in the saturated zone and some intermediate 

calculations; the inputs are in bold. The tabs “AQ 1,” “AQ 2,” and “AQ 21” are the temporal input 

fluxes used in RESRAD-OFFSITE and correspond to Figures 3-24, 3-29, and 3-30. Tabs 

“WellConc 1” and “WellConc 21” are the RESRAD-OFFSITE concentrations in the well 

corresponding to the input fluxes in tabs “AQ 1” and “AQ 21.” The temporal concentration in tab 

“WellConc 2” was obtained by subtracting from the concentrations in tab “WellConc 21” the 

concentrations in tab “WellConc 1” shifted by a time step. 

The tab “Single Nuclide graph” compares the temporal concentrations from RESRAD-OFFSITE 

with that calculated in the spreadsheet. The comparisons are captured in two plots: the first 

one, anchored in cell “J66”, compares the concentration in the well from a decreasing triangular 

input flux over the first time interval; the second plot, anchored in cell “J97,” compares the 

concentration in the well from a increasing triangular input flux over the first time interval. The 

plots pertain to the nuclide shown in cell “C1”; plots that pertain to the eight nuclides 60Co, 3

H, 

90Sr, 137Cs, 63Ni, 226Ra, 14C, and 238U can be viewed by typing in the numbers 2, 4, 9, 3, 5, 6, 1, 

and 11, respectively, in cell “A1” and then launching the computational macro by clicking Ctrl-a. 

The computational macro evaluates the convolutions using numerical integration; the numerical 

integration method used in the code is described in Section 3.3.14 of the RESRAD-OFFSITE 

User’s Manual. Note that the nuclide name will change in cell “C1” but not in the title of the 

plots. Plots of all 48 verifications that were performed can be viewed in turn in this fashion. A 

subset of these plots were shown in Figures 3-25 through 3-34. 
3-37 

Figure 3-31 Verification of RESRAD-OFFSITE Computed Flux Concentration in the Well Resulting from 

Flux of 3H of Zero at Time Zero and of Unity at the First Time Point at the Water Table Using 

Calculations 

Concentration in Well from Increasing Triangular Puls

Input, 3H

0.0E+00

2.0E-084.0E-086.0E-088.0E-081.0E-071.2E-071.4E-071.6E-07

0 5 10 15 20 25 3

Time, years

Concentration, pCi/m

3

RESRAD OFFSITSpread sheet cal
3-38 

Figure 3-32 Verification of RESRAD-OFFSITE Computed Flux Concentration in the Well Resulting from 

Flux of 137Cs of Zero at Time Zero and of Unity at the First Time Point at the Water Table Us

Calculations 

Concentration in Well from Increasing Triangular Puls

Input, 137Cs

0.0E+00

1.0E-082.0E-083.0E-084.0E-085.0E-086.0E-08

0 20 40 60 80 100 12

Time, years

Concentration, pCi/m

3

RESRAD OFFSITSpread sheet calc
3-39 

Figure 3-33 Verification of RESRAD-OFFSITE Computed Flux Concentration in the Well Resulting from a 

Flux of 226Ra of Zero at Time Zero and of Unity at the First Time Point at the Water Table Usi

Calculations 

Concentration in Well from Increasing Triangular Puls

Input, 226Ra

0.0E+00

5.0E-081.0E-071.5E-072.0E-072.5E-073.0E-07

0 20 40 60 80 100 12

Time, years

Concentration, pCi/m

3

RESRAD OFFSITSpread sheet calc
3-40 

Figure 3-34 Verification of RESRAD-OFFSITE Computed Flux Concentration in the Well Resulting from 

Flux of 238U of Zero at Time Zero and of Unity at the First Time Point at the Water Table Usin

Calculations 

Concentration in Well from Increasing Triangular Puls

Input, 238U

0.0E+00

5.0E-081.0E-071.5E-072.0E-072.5E-073.0E-07

0 200 400 600 800 1000 

Time, years

Concentration, pCi/m

3

RESRAD OFFSITESpread sheet calcu
4-1 

4.0 Atmospheric Transport Model 

The atmospheric transport model used in RESRAD-OFFSITE is a Gaussian plume dispersion 

model based on an area source release. The model is used to estimate the normalized air 

concentrations at area locations downwind of a contaminated site. Details of the model are 

presented in Yu et al. (2007). This section presents the results of the verification study 

performed to show that the model was implemented correctly in the RESRAD-OFFSITE code. 

RESRAD-OFFSITE assumes separate primary contamination source and receptor areas. For 

the calculation of downwind air concentrations, the source and receptor areas are first 

partitioned into grids having 1-m square resolution or greater. The center point of each grid 

square is used as the source or receptor point representing that small area. Air concentration 

calculations are performed for each receptor grid square for emissions from every source grid 

square, with an average chronic air concentration then calculated for each receptor grid square. 

The average air concentration over the entire receptor area is then taken to be the average 

value over all receptor grid squares. Each point-to-point calculation uses the appropriate wind 

direction and frequency for the specific points involved. Thus, no area source approximations 

are used. Rather, a series of point-to-point calculations are performed using a standard sectoraveraged Gaussian plume equation. The proper evaluation of the point-to-point calculations is 

verified in Section 4.1. Section 4.2 examines the concentration averaging over the entire 

receptor area. 

4.1 Sector-Average Gaussian Plume Model 

An arbitrary set of baseline conditions were used to exercise a range of calculations in the 

computer code as shown in Table 4-1. The point-to-point calculations assumed source and 

receptor areas of 1 m2

. Air concentrations as a function of distance, direction, elevation, and 

wind frequency were estimated for a single run of the program. 

The RESRAD-OFFSITE results were compared against spreadsheets using the code 

methodology as described in Yu et al. (2007). The normalized air concentrations (χ/Q values) 

calculated by the program can be found in the CHIOVERQ.OUT file after program execution in 

the directory containing the executable code. The first set of comparisons, as shown in 

Table 4-2, assumed a heat release flux (Qh = 90 cal/s) with a grid spacing of 1 m (90 cal/m2

-s) 

to exercise the plume rise portion of the code. This value is consistent with heat fluxes from 

ground surfaces due to solar heating from direct sunlight during the summer months in the 

western United States on a clear day (NREL 2008). 

The results in Table 4-2 are from three separate runs of the baseline verification input file. 

Run 1 was performed using Briggs rural dispersion coefficients with no dry or wet deposition 

assumed. Runs 2 and 3 were performed using the Pasquill-Gifford dispersion coefficients with 

dry deposition assumed. Wet deposition was not considered in Run 2 but was considered in 

Run 3. In all three cases, good agreement (< 2% difference) was shown between the 
4-2 

RESRAD-OFFSITE results and the parallel spreadsheet calculations, with excellent agreement 

(about 0.2% or less) for distances of 500 m or greater. 

A second set of runs were performed with the same baseline verification input file without the 

incorporation of plume rise (heat release term set to zero) and all receptor area elevations set to 

zero. Table 4-3 presents this second set of results, with good agreement (about 1% difference 

or less) between RESRAD-OFFSITE and independent spreadsheet results. In all cases, 

Runs 1 through 6, the differences in results could be considered to be within round-off error. 

Some differences may be due partially to the use of different integration methods in RESRADOFFSITE and the spreadsheet calculations, as discussed in the following example of a 

spreadsheet calculation. 

Table 4-1 Baseline Site Layout and Atmospheric Transport Parameters Used to Verify 

RESRAD-OFFSITE Point-to-Point Air Dispersion Calculations 

Receptor Area 

Distancea

(m) Directionb

Elevationc

(m) 

Directional 

Frequencyd

Stability 

Categorye

Wind 

Speed 

(m/s) 

 

Fruit, grain, nonleafy 

vegetables plot 100 North 0 0.05 A 0.89 

Leafy vegetables plot 200 South 5 0.10 B 2.46 

Pasture, silage growing area 500 East 10 0.25 D 6.93 

Grain fields 1,000 West 15 0.20 C 4.47 

Dwelling site 10,000 Northeast 20 0.40 F 9.61 

a

 Distance from the release point. 

b

 Direction from release point. Direction toward which the wind is blowing. c

 Elevation with respect to the release point. 

d

 Fraction of time the wind is blowing in a particular direction with a specific wind speed under a given stability category. e

 Pasquill-Gifford atmospheric stability category designations.

An example spreadsheet calculation from the verification spreadsheet is provided here to 

illustrate the process used to check the proper operation of the RESRAD-OFFSITE air 

dispersion model. The calculation considered is that for the normalized air concentration over 

the grain fields in Run 3. The effective release height (Figure 4-1) is first calculated in an 

iterative process with the effective wind speed (Figure 4-2), which are then used to calculate 

values for the vertical dispersion coefficient (Figure 4-3) and the downwind depleted source 

strength (Figure 4-4) due to wet and dry deposition. In Eq. 4.31 (in Figure 4-4), the dry 

deposition F(x) integral term was evaluated using a Simpson’s rule approach in the spreadsheet 

as a secondary check, whereas it is performed by a Romberg integration routine 

(Press et al. 1992) in the code. The sector average plume equation shown in Figure 4-5 is then 

used to calculate the normalized air concentration at the specified location downwind. The 

equation numbers in the figures refer to their numbering in Yu et al. (2007). 

 
4-3 

Table 4-2 Comparison of RESRAD-OFFSITE Normalized Air Concentrations (s/m3

) 

with Spreadsheet Verification Calculations (with Plume Rise)a

Receptor Area 

Spreadsheet 

Calculationb

Spreadsheet ×

Directional 

Frequencyb

RESRADOFFSITE % 

Difference 

Run 1 – Briggs rural dispersion coefficients, no dry or wet deposition 

Fruit, grain, nonleafy vegetables 

plot 

1.120E-03 5.600E-05 5.683E-05 1.48 

Leafy vegetables plot 1.698E-04 1.698E-05 1.690E-05 0.47 

Pasture, silage growing area 2.552E-05 6.380E-06 6.391E-06 0.17 

Grain fields 6.144E-06 1.229E-06 1.228E-06 0.07 

Dwelling site 5.218E-07 2.087E-07 2.087E-07 0.01 

 

Run 2 – Pasquill-Gifford dispersion coefficients with dry deposition, no wet deposition 

Fruit, grain, nonleafy vegetables 

plot 

1.538E-03 7.690E-05 7.807E-05 1.52 

Leafy vegetables plot 2.004E-04 2.004E-05 1.992E-05 0.60 

Pasture, silage growing area 3.115E-05 7.788E-06 7.797E-06 0.12 

Grain fields 7.256E-06 1.451E-06 1.449E-06 0.15 

Dwelling site 4.340E-07 1.736E-07 1.737E-07 0.06 

 

Run 3 – Pasquill-Gifford dispersion coefficients with dry and wet deposition 

Fruit, grain, nonleafy vegetables 

plot 

1.512E-03 7.560E-05 7.678E-05 1.56 

Leafy vegetables plot 1.980E-04 1.980E-05 1.968E-05 0.61 

Pasture, silage growing area 3.082E-05 7.705E-06 7.714E-06 0.12 

Grain fields 7.019E-06 1.404E-06 1.401E-06 0.20 

Dwelling site 4.273E-07 1.709E-07 1.711E-07 0.11 a

 Note that the number of significant figures used are for comparison purposes only to check the 

accuracy of the RESRAD-OFFSITE calculations. b

 The spreadsheet calculations do not incorporate the directional wind frequency, as shown in 

Table 4-1.
4-4 

Table 4-3 Additional Comparison of RESRAD-OFFSITE Normalized Air 

Concentrations (s/m3

) with Spreadsheet Verification Calculations (without 

Plume Rise)a 

Receptor Area 

Spreadsheet 

Calculationb

Spreadsheet ×

Directional 

Frequencyb

RESRADOFFSITE 

% 

Difference 

Run 4 – Pasquill-Gifford dispersion coefficients, no dry or wet deposition 

Fruit, grain, nonleafy vegetables 

plot 

1.572E-03 7.860E-05 7.937E-05 0.98 

Leafy vegetables plot 2.023E-04 2.023E-05 2.013E-05 0.49 

Pasture, silage growing area 3.142E-05 7.855E-06 7.869E-06 0.18 

Grain fields 7.342E-06 1.468E-06 1.467E-06 0.10 

Dwelling site 4.524E-07 1.810E-07 1.810E-07 0.02 

 

Run 5 – Pasquill-Gifford dispersion coefficients with dry deposition, no wet deposition 

Fruit, grain, nonleafy vegetables 

plot 

1.546E-03 7.730E-05 7.807E-05 1.00 

Leafy vegetables plot 2.005E-04 2.005E-05 1.994E-05 0.55 

Pasture, silage growing area 3.116E-05 7.790E-06 7.801E-06 0.14 

Grain fields 7.262E-06 1.452E-06 1.451E-06 0.10 

Dwelling site 4.357E-07 1.743E-07 1.744E-07 0.07 

 

Run 6 – Pasquill-Gifford dispersion coefficients with dry and wet deposition 

Fruit, grain, nonleafy vegetables 

plot 

1.521E-03 7.605E-05 7.678E-05 0.96 

Leafy vegetables plot 1.981E-04 1.981E-05 1.970E-05 0.56 

Pasture, silage growing area 3.083E-05 7.708E-06 7.718E-06 0.14 

Grain fields 7.025E-06 1.405E-06 1.403E-06 0.14 

Dwelling site 4.291E-07 1.716E-07 1.717E-07 0.03 a

 Note that the number of significant figures used are for comparison purposes only to check the 

accuracy of the RESRAD-OFFSITE calculations. Pasquill-Gifford dispersion coefficients were used 

for all runs. All receptor area elevations were set to zero. Plume rise was not considered. b

 The spreadsheet calculations do not incorporate the directional wind frequency as shown in 

Table 4-1. 
4-5 

Figure 4-1 Effective Release Height Calculation in RESRAD-OFFSITE 

Effective Release Height

0.62 (m) = 1.00 + 0.25 - ( 1. - 0.50 ) * [ min ( 1.25 15.00 ) (m) ] (4.1)

H h Δh Pc h + Δh Er - Ep

Unstable/Neutral Conditons (A-D)

x <= 10 * stack height

1.6

N/A = * [ 3.7 * 10-5 * 90 * 1000000 ]1/3 (4.2)

Δh (m) 4.47 (m4

/cal-s2) Qh (cal/s) x

2 (m2

)

UH (m/s)

x > 10 * stack height

1.6

0.25 = * [ 3.7 * 10-5 * 90 * 100 * 1.00 ]1/3 (4.3)

Δh (m) 4.47 (m4

/cal-s2) Qh (cal/s) h2 (m2)

UH (m/s)

Stable Conditions (E,F)

Still expanding [x <= 2.4*(UH/s1/2) and U >= Utest]

1.6

N/A = * [ 3.7 * 10-5 * 90 * 1000000 ]1/3 (4.4)

Δh (m) 4.47 (m4

/cal-s2) Qh (cal/s) x

2 (m2

)

UH (m/s)

Far limit [x > 2.4*(UH/s1/2) and U >= Utest]

 3.7 * 10-5 * 90 1/3

 (m4

/cal-s2) Qh (cal/s)

N/A = 2.9 * (4.5)

Δh (m) 4.47 * 0.001204

UH (m/s) s (s-2

)

Light wind, vertical rise (U < Utest)

 [ 3.7 * 10-5 * 90 ] 1/4

 (m4/cal-s2) Qh (cal/s)

N/A = 5.0 * (4.6)

Δh (m) [ 0.001204 ] 3/8

s (s-2)

s: stability parameter [g/Τ * dθ/dz]

9.80665

(m/s2

)

0.001204 = * 0.035 (4.7)

s (s-2) 285 dT/dz + l (o

K/m)

Ta(

o

K)

wind speed cut-off

0.020218 (m/s) = 0.195 * [ 3.7 * 10-5 * 90 ] 1/4 * [ 0.001204 ] 1/8 (4.8)

Utest (m4

/cal-s2) Qh (cal/s) s (s-2)
4-6 

Figure 4-2 Calculation of the Effective Wind Speed (iteration of Eq. 4.9 with Eqs. 4.2 to 4.5 to 

obtain consistent effective wind speed and release height values) 

Figure 4-3 Vertical Dispersion Coefficient Calculation 

Figure 4-4 Calculation of the Depleted Source Strength Due to Wet and Dry Deposition 

Effective Wind Speed

 If Heff <= 10 m

4.47 = 4.47

Ueff (m/s) U (m/s)

 else 0.1

0.62 p

Heff (m)

N/A = 4.47 * (4.9)

Ueff (m/s) U (m/s) 10.00

HAnem (m)

Pasquill-Gifford σz 

9.11E-01

61.1 = 1.13E-01 * ( 1,000 ) b + 0.00E+00 (4.34)

σz (m) a x (m) c

σz adjusted for buoyancy-induced dispersion

61.1 = ( 3.73E+03 + ( 0.25 / 3.5 ) 2

 )1/2 (4.36/4.37)

σze (m) σz

2

 (m2) Δh (m)

Washout Coefficient

1.48E-04 = 1.00E-03 * 1.48E-01 (4.29)

Vw (1/s) WC (1/s)(mm/h)-1 R (mm/h)

Depleted Source Strength (4.31)

1.48E-04 * 1000.0 0.0010

Vw (1/s) x (m) Vd (m/s)

9.56E-01 = 1.00E+00 * exp - + * 66.91

Qx (Ci) Q0 (Ci) 4.47 ( π / 2)1/2 * 4.47E+00

Ueff (m/s) Ueff (m/s) 

x

xF dx

0

)(
4-7 

Figure 4-5 Normalized Air Concentration Calculation in RESRAD-OFFSITE 

4.2 Area Model 

The site layout used for verification of the average normalized air concentration over a 

downwind receptor area is shown in Figure 4-6. RESRAD-OFFSITE computes the air 

concentration by averaging the values obtained from point-to-point estimates. In this case, a 

30 × 30 m receptor area is centered 70 m north and 15 m east of a release point. With a grid 

spacing set to 10 m in the atmospheric transport input, the code should split the area into nine 

10 × 10 m grids for evaluation. The calculation will involve computing the point-to-point air 

concentration from the release point to the center of each of the nine 10 × 10 m grid areas, 

summing the results, and dividing by nine to obtain the average air concentration. To verify 

proper operation, a separate set of nine individual calculations can be run, a calculation for 

transport from the release point to each of the nine distinct 10 × 10 m grid areas. The results 

can be manually summed and divided by nine for comparison with the calculation for the entire 

30 × 30 m area with a 10 m grid spacing. 

For the verification check, the receptor area was intentionally positioned straddling the dividing 

line between a wind direction of blowing towards the north and the north-northeast at the 

receptor location. Thus, a different portion of the wind frequency data for each stability class in 

the meteorological data file will be used when calculating air concentrations within the north and 

north-northeast sectors. The IL_CHICAGO.str meteorological file was used in this example. 

The normalized air concentration values (s/m3

) obtained from separate runs involving each of 

the nine individual 10 × 10 m areas are listed within their respective areas in Figure 4-6. The 

average air concentration is then calculated to be 2.753 × 10-4 s/m3

. A single run for the 

30 × 30 m area with a grid spacing set to 10 m as described above, computes a value of 

2.747 × 10-4 s/m3

. Thus, very good agreement is shown with about a 0.2% difference, well 

within any round-off errors that might be expected. 

 

Plume reflection not considered if

 ( 1 - 0.62 / 400 ) 1/2

Heff (m) L (m)

 σz(x) < = * 400 = 333.1 [TRUE] (4.15)

1.2 L (m) σz,no-mix (m) 

Then

9.56E-01 3.89E-01

Qx (Ci) Heff

2

 (m2)

7.019E-06 = * exp - (4.22)

Ca,no-mix (Ci/m3

) (2π)1/2 * 61.1 * 4.47E+00 * 1000 * tan(11.25o

) 2 * 3.73E+03

σz (m) Ueff (m/s) x (m) σz

2 (m2

)
4-8 

Figure 4-6 Site Layout for Verification of the Area Averaged 

Normalized Air Concentration 

(0,55)

(0,85)

(30,55)

(30,85)

(0,0)

2.440 x 10-4

2.877 x 10-4

2.440 x 10-4

2.260 x 10-4

1.823 x 10-4

2.493 x 10-4 3.114 x 10-4

4.113 x 10-4 3.214 x 10-4
5-1 

5.0 Accumulation at Offsite Locations 

and in Food 

Accumulation at offsite surface soil and food was verified in this section. The results of 

spreadsheet calculations were compared with RESRAD-OFFSITE code results for different 

processes involved in accumulation. For example, in verifying accumulation in offsite surface 

soil, the accumulation in offsite surface soil from irrigation and deposition of particulates was 

verified first, then the total accumulation calculations were verified. Similarly, the calculations 

were first verified for the first member of the decay chain, and later verification was done for the 

second member of the decay chain. To simplify spreadsheet calculations, storage times for 

surface water, well water, fruit, grain, nonleafy vegetables, leafy vegetables, pasture and silage, 

livestock feed grain, meat, milk, fish, and crustaceans and mollusks were changed to zero from 

their defaults in the code. The spreadsheets were created for eight radionuclides (H-3, C-14, 

Co-60, Ni-63, Sr-90, Cs-137, Ra-226, and U-238) to capture the variability in radionuclidedependent parameters. The subsequent sections show the results for one radionuclide only, 

but the calculations are done for all eight radionuclides in the Excel spreadsheets. Table 5-1 

lists the radionuclide-independent parameters used in the calculations, and Table 5-2 lists the 

radionuclide-dependent parameters used in the calculations. Section 5.1 discusses the 

accumulation in offsite surface soil. Section 5.2 focuses on the accumulation in surface water. 

Plant accumulation is discussed in Section 5.3. Meat and milk accumulation is discussed in 

Section 5.4, and Section 5.5 focuses on accumulation in fish and aquatic food. 

5.1 Accumulation in Offsite Surface Soil 

Offsite surface soil gets contaminated due to irrigation with contaminated water and deposition 

of contaminated dust. Radiological transformations, soil mixing in the surface layer, erosion, 

and equilibrium desorption release are included when calculating surface soil concentration at 

offsite locations. Accumulation in offsite surface soil is calculated as described in Section 5.1 of 

RESRAD-OFFSITE User’s Manual (Yu et al. 2007). 

5.1.1 Accumulation in Offsite Surface Soil from Irrigation 

The contaminant deposition rate (pCi/m2

/yr) at any time t of radionuclide i in offsite soil from 

irrigation water is given as (Eq. 5.11 in the RESRAD-OFFSITE User’s Manual): 















 −− = −

gw

gw

int

ir

i iir t

t

ftwqtD λ

λ )exp(1 1)()( (Eq. 5.1)

where: 

qir = irrigation rate (m/yr), 

tw )( ir

i = activity concentration of radionuclide i in contaminated irrigation water (pCi/m3

), 
5-2 

int f = foliar interception factor, 

λw = weathering constant (per yr), 

gt = duration of growing season (yr). 

The deposition rate of radionuclide i by irrigation water at any time t is approximated by a linear 

function given as (Eq. 5.12; Yu et al. 2007): 

tD t i )( α β ii ×+= (Eq. 5.2)

where α i and β i are constant between each pair of time points. 

The soil concentration of first member of transformation chain at any time t is given as (Eq. 5.15; 

Yu et al. 2007): 

o tLEo

eCtAAts

1 ( )

1

1

1

0

1 1

0 1 1 )( ++− +×+= λ (Eq. 5.3)

where 0 A1 , 1 A1 , and 1 C1 are given as: 

( ) 1 1

0

1 1

1 o oo

mixb LEd

A

++ = λρ

β (Eq. 5.4)

o oo oo

mixb LE

A

LEd

A

1 1

1

1

1 1

0

0 1

1 ( ) ++ − ++ = λρ λ

α (Eq. 5.5)

0

1

0

1

1

1 )0( −= AsC (Eq. 5.6)

where: 

0 ρ b = dry bulk density of soil at the offsite location (g/m3

), 

o d mix = mixing depth at offsite location (m), 

λ1 = decay constant of the first member of transformation chain (/yr), 

o E = fraction of the mixing zone that is eroded each year (/yr), 

o L1 = rate at which the nuclide is leached out of the mixing layer (/yr). 

 
5-3 

Table 5-1 Parameters Used in the Verification of Accumulation in Offsite Soil, Surface 

Water, Plant, Meat, Milk, and Aquatic Food 

General Parameters Values 

Deposition velocity (m/s) 0.001 

Storage time (d) 0 

Precipitation rate (m/yr) 1 

Offsite soil parameters in different agricultural areas 

Fraction of area directly over primary contamination 0 

Irrigation applied (m/yr) 0.2 

Evapotranspiration coefficient 0.5 

Runoff coefficient 0.2 

Mixing depth (m) 0.15 

Volumetric water content 0.3 

Dry bulk density (g/cm3

) 1.5 

Soil erodibility factor 0.4 

Slope-length-steepness factor 0.4 

Cover and management 0.003 

Support practice factor 1 

Surface water body parameters 

Volume of surface water body (m3

) 150,000 

Area of surface water body (m2

) 90,000 

Mean residence time of water (yr) 1 

Sediment delivery ratio 1 

Plant accumulation parameters 

Wet crop yield for fruit, grain, and leafy vegetables (kg/m2

) 0.7 

Wet crop yield for leafy vegetables (kg/m2

) 1.5 

Wet crop yield for pasture and silage (kg/m2

) 1.1 

Wet crop yield for grain (kg/m2

) 0.7 

Foliage to food transfer coefficient for fruit, grain, and leafy vegetables 0.1 

Foliage to food transfer coefficient for leafy vegetables 1.0 

Foliage to food transfer coefficient for pasture and grass 1.0 

Foliage to food transfer coefficient for grain 0.1 

Duration of growing season for fruit, grain, and leafy vegetables (yr) 0.17 

Duration of growing season for leafy vegetables (yr) 0.25 

Duration of growing season for pasture and grass (yr) 0.08 

Duration of growing season for grain, yr 0.17 

Weathering removal constant for all plant types (per yr) 20 

Foliar interception factor for irrigation for all plant typesa

 0.25 

Foliar interception factor for dust for all plant types 0.25 

Meat and milk accumulation parameters 

Beef cattle water intake (L/d) 50 

Dairy cow water intake (L/d) 160 

Beef cattle pasture intake (kg/d) 14 

Dairy cow pasture intake (kg/d) 44 

Beef cattle grain intake (kg/d) 54 

Dairy cow grain intake (kg/d) 11 

Beef cattle soil intake from pasture and silage (kg/d) 0.1 

Dairy cow soil intake from pasture and silage (kg/d) 0.4 

Beef cattle soil intake from grain (kg/d) 0.4 

Dairy cow soil intake from grain (kg/d) 0.1 

a For C-14 and H-3, the foliar interception factor for irrigation = 0.
5-4 

Table 5-2 Radionuclide-Specific Parameters Used in the Verification of Accumulation in Offsite Soil, Surfa

Plant, Meat, Milk, and Aquatic Food 

Radionuclide H-3 C-14 Co-60 Ni-63 Sr-90 Y-90 Cs-137 Ra-226 Pb-210 

Half life (yr) 12.35 5730 5.271 96 29.12 64 h 30 1600 22.3 Cut-off half life (d) 30 30 30 30 1 1 30 30 30 

Distribution coefficient (cm3/g) 0 0.1 1,000 1,000 30 720 4,600 70 100 

Distribution coefficient of sediment in surface 

water (cm3/g) 

0 0.1 1,000 1,000 30 720 4,600 70 100 

Plant root uptake transfer factor (pCi/kg per 

pCi/kg) 

NRa NR 0.08 0.05 0.3 0.0025 0.04 0.04 0.01 

Meat transfer factor (pCi/kg per pCi/d) NR NR 0.02 0.005 0.008 0.002 0.03 0.001 0.0008 Milk transfer factor (pCi/L per pCi/d) NR NR 0.002 0.02 0.002 2.00E-05 0.008 0.001 0.0003 Fish bioaccumulation factor (pCi/kg per pCi/L) 1 50,000 300 100 60 30 2,000 50 300 Crustacea bioaccumulation factor (pCi/kg per 

pCi/L) 

1 9,100 200 100 100 1,000 100 250 100 

a NR = not required. 
5-5 

The leach rate can be calculated as: 

o

d

o

b

o

c

o

mix

o

o

K

d

I

L

1

1

+ ρθ = (Eq. 5.7)

where: 

 o I = infiltration rate at the offsite location (m/yr), 

 o θ c = volumetric water content at offsite location, 

o Kd1 = distribution coefficient of radionuclide at offsite location cm3

/g. 

The infiltration rate is calculated as (Eq. 3.18; Yu et al. 2007): 

))1(()1( e +×−×−= qPCCI irrr (Eq. 5.8) 

where: 

Ce = evapotranspiration coefficient, 

Cr = runoff coefficient, 

Pr = precipitation rate m/yr. 

Table 5-3 shows the results of spreadsheet calculations for few time steps for the accumulation 

in offsite surface soil from irrigation. The verification was done for C-14 (initial concentration = 

1 pCi/g) and groundwater was used for irrigation. The results of spreadsheet calculations were 

compared with the RESRAD-OFFSITE results (Figure 5-1). For this comparison, the soil 

concentration in the fruit, grain, and non-leafy vegetable agricultural area was used. The 

parameters that were changed from their default values were: Kd was changed to 0.1 cm3

/g and 

the deposition velocity was set at 0. Figure 5-2 shows the individual steps of the calculation for 

one time step highlighted in Table 5-3. For this comparison radionuclide concentration in 

irrigation water was obtained from the code. There is practically no difference in the 

spreadsheet calculations and the results from RESRAD-OFFSITE code (see Table 5-3 and 

Figure 5-1). 
5-6 

Table 5-3 Spreadsheet Calculations for C-14 Accumulation in Offsite Surface Soil from Irrigation 

Time, yr 

Irrigation 

Water Conc. 

from Code 

(pCi/m3) 

Deposition 

from 

Irrigation 

Water 

(pCi/m2/yr) α1 β1 A11 A10 C11 

Soil Conc

Calculate

0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 

4.88E-01 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 9.77E-01 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 

1.46E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.95E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.44E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.93E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 3.42E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 3.91E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 4.39E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 4.88E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 5.37E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 5.86E+00 2.72E-06 5.44E-07 0.00E+00 1.11E-06 6.69E-13 -9.03E-14 9.03E-14 2.39E-13 

6.35E+00 2.70E-03 5.40E-04 5.44E-07 1.10E-03 6.63E-10 -8.92E-11 8.94E-11 2.37E-10 

6.84E+00 1.83E-01 3.66E-02 5.40E-04 7.39E-02 4.44E-08 -5.66E-09 5.90E-09 1.62E-08 

7.32E+00 1.43E+00 2.86E-01 3.66E-02 5.11E-01 3.06E-07 -1.94E-08 3.55E-08 1.31E-07 7.81E+00 6.19E+00 1.24E+00 2.86E-01 1.95E+00 1.17E-06 1.38E-08 1.17E-07 5.88E-07 

8.30E+00a 2.01E+01 4.02E+00 1.24E+00 5.71E+00 3.42E-06 2.80E-07 3.08E-07 1.96E-06 

8.79E+00 5.47E+01 1.09E+01 4.02E+00 1.41E+01 8.49E-06 1.27E-06 6.92E-07 5.43E-06 

a The calculations for the highlighted time step are shown in Figure 5-2. 
5-7 

Figure 5-1 Accumulation of C-14 in Offsite Soil from Irrigation from 

Spreadsheet Calculations and from RESRAD-OFFSITE 

Code 

5.1.2 Accumulation in Offsite Surface Soil from Deposition of Contaminated Dust 

The contamination deposition rate (pCi/m2

/yr) at any time t of radionuclide i in offsite soil from 

contaminated dust is given as (Eq. 5.13 in the RESRAD-OFFSITE User’s Manual): 

]

)exp(1 1)[()( int

w

gw

i idep

t

ftaVtD λ

−− λ = − (Eq. 5.9) 

where: 

Vdep = deposition velocity of the contaminated dust particle (m/yr), 

ta )(i = air concentration of radionuclide i above the agricultural area where plant is 

growing (pCi/m3

). 

The soil concentration in the offsite location from deposition of contaminated dust can be 

calculated in the same way, as described in Section 5.1.1. 

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

0.00E+00 1.00E+01 2.00E+01 3.00E+01 4.00E+01 5.00E+01 6.00E+01 7.00E+01

Time, yr

Concentration, pCi/g

Soil conc. calculated

Soil conc. from code
5-8 

Table 5-4 shows the results of spreadsheet calculations for few time steps for the accumulation 

in offsite surface soil from deposition. The verification was done for C-14. The results of 

spreadsheet calculations are compared with the RESRAD-OFFSITE results (Figure 5-3). For 

this comparison, the soil concentration in the fruit, grain, and nonleafy vegetable agricultural 

area was used. The irrigation rate in the agricultural area where fruit, grain, and nonleafy 

vegetables grow was set at 0 to only account for accumulation from deposition. Figure 5-4 

shows the individual steps of the calculation for one time step highlighted in Table 5-4. For this 

comparison, radionuclide concentration in air was obtained from the code. There is practically 

no difference in the spreadsheet calculations and the results from RESRAD-OFFSITE code 

(see Table 5-4 and Figure 5-3). 

For verifying the combined accumulation due to irrigation and deposition from contaminated 

dust, Sr-90 was selected (the results for other radionuclides are shown in the Excel 

spreadsheets). Table 5-5 shows the results of spreadsheet calculations for few time steps for 

the accumulation in offsite surface soil from irrigation and deposition. The verification was done 

for Sr-90 and surface water was used for irrigation. The cutoff half-life was changed to 1 day 

from its default setting of 30 days. All other parameters were kept at their default values. For 

this comparison, the soil concentration in the fruit, grain, and nonleafy vegetable agricultural 

area was used. The results of spreadsheet calculations are compared with the RESRADOFFSITE results (Figure 5-5). Figure 5-6 shows the individual steps of the calculation for one 

time step highlighted in Table 5-5. For this comparison, radionuclide concentrations in air and 

irrigation water were obtained from the code. There is practically no difference in the 

spreadsheet calculations and the results from RESRAD-OFFSITE code (see Table 5-6 and 

Figure 5-5). 
5-9 

Figure 5-2 Offsite Surface Soil Accumulation from Irrigation 
5-10 

Table 5-4 Spreadsheet Calculations for C-14 Accumulation in Offsite Surface Soil from Deposition 

Time 

Concentration 

in Air (pCi/m3) 

from Code 

Deposition 

Rate from Air 

(pCi/m2/yr) α1 β1 A11 A10 C11 

Soil Co

Calcula

0.00E+00 3.03E-07 9.46E-03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+

4.88E-01 4.63E-08 1.44E-03 9.46E-03 -1.64E-02 -9.85E-09 7.00E-09 -7.00E-09 2.01E-0

9.77E-01 7.07E-09 2.20E-04 1.44E-03 -2.51E-03 -1.50E-09 1.07E-09 9.38E-10 3.60E-

1.46E+00 1.08E-09 3.37E-05 2.20E-04 -3.83E-04 -2.30E-10 1.63E-10 1.97E-10 5.65E-

1.95E+00 1.65E-10 5.14E-06 3.37E-05 -5.84E-05 -3.50E-11 2.49E-11 3.16E-11 8.66E-

2.44E+00 2.52E-11 7.85E-07 5.14E-06 -8.92E-06 -5.35E-12 3.81E-12 4.86E-12 1.32E-

2.93E+00 3.84E-12 1.20E-07 7.85E-07 -1.36E-06 -8.17E-13 5.81E-13 7.42E-13 2.02E-

3.42E+00 5.87E-13 1.83E-08 1.20E-07 -2.08E-07 -1.25E-13 8.87E-14 1.13E-13 3.09E-

3.91E+00 8.96E-14 2.79E-09 1.83E-08 -3.17E-08 -1.90E-14 1.35E-14 1.73E-14 4.71E-

4.39E+00 1.37E-14 4.26E-10 2.79E-09 -4.85E-09 -2.91E-15 2.07E-15 2.64E-15 7.19E-

4.88E+00 2.09E-15 6.51E-11 4.26E-10 -7.40E-10 -4.44E-16 3.16E-16 4.04E-16 1.10E-

5.37E+00 3.19E-16 9.94E-12 6.51E-11 -1.13E-10 -6.78E-17 4.82E-17 6.16E-17 1.68E-

5.86E+00 4.87E-17 1.52E-12 9.94E-12 -1.72E-11 -1.03E-17 7.36E-18 9.41E-18 2.56E-

6.35E+00 7.43E-18 2.32E-13 1.52E-12 -2.63E-12 -1.58E-18 1.12E-18 1.44E-18 3.91E-

6.84E+00 1.13E-18 3.54E-14 2.32E-13 -4.02E-13 -2.41E-19 1.71E-19 2.19E-19 5.96E-2

7.32E+00 1.73E-19 5.40E-15 3.54E-14 -6.13E-14 -3.68E-20 2.62E-20 3.35E-20 9.11E-

7.81E+00 2.64E-20 8.24E-16 5.40E-15 -9.37E-15 -5.62E-21 4.00E-21 5.11E-21 1.39E-

8.30E+00a 4.03E-21 1.26E-16 8.24E-16 -1.43E-15 -8.58E-22 6.10E-22 7.80E-22 2.12E-2

8.79E+00 6.16E-22 1.92E-17 1.26E-16 -2.18E-16 -1.31E-22 9.31E-23 1.19E-22 3.24E-2

a The calculations for the highlighted time step are shown in Figure 5-4. 
5-11 

Figure 5-3 Accumulation of C-14 in Offsite Soil from Deposition from 

Spreadsheet Calculations and from RESRAD-OFFSITE Code 

5.1.3 Accumulation in Offsite Surface Soil for the Second Member of the 

Transformation Chain 

The soil concentration of second member of the transformation chain at any time t is given as 

(Eq. 5.18 in RESRAD-OFFSITE User’s Manual): 

o tLE tLE o o

eCtAAts eC

2 ( )

2

1 ( )

2

1

2

0

2 2

0 2 2 0 1 1 )( ++− ++− +×+= + λ λ (Eq. 5.10)

where 0 A2 , 1 A2 , 1 C2 , and 2 C2 are given as: 

o oo oo o

mixb LE

A

LE

A

LEd

A

2

0

2

1

2

2 2

0

12

2 2

0

0 2

2 ( ) ++ − ++

+

++ = λ λ

λ

λρ

α (Eq. 5.11)

o oo oo

mixb LE

A

LEd

A

2 2

1

12

2 2

0

1 2

2 ( ) ++

+

++ = λ

λ

λρ

β (Eq. 5.12)

o o LL

C C

1122

1

1 12

2

−−+ = λλ

λ (Eq. 5.13)

0.00E+00

5.00E-10

1.00E-09

1.50E-09

2.00E-09

2.50E-09

0.00E+00 1.00E+01 2.00E+01 3.00E+01 4.00E+01 5.00E+01 6.00E+01 7.00E+01

Time, year

Concentration, pCi/g

Soil conc. calculated

Soil conc. from code
5-12 

Offsite Surface Soil Accumulation from Paticulate Deposition 

 3.4 ═ 20 × 0.17 

 /yr yr 

 4.83E-02 ═ (1 ─ exp(- 3.4 ) ⁄ 20  1.26E-16 ═ 31557.6 × 4.034E-21 × (1 ─ 0.25 × 4.83E-0 pCi/m2/yr m/yr pCi/m3

α1 ═ 8.239E-16 

 -1.43E-15 ═ ( 1.26E-16 ─ 8.24E-16 ) ⁄ ( 8.30078 ─ 

β1 α1 t2 

 pCi/m2 pCi/m2/yr pCi/m2/yr yr  0.5 ═ ( 1 ─ 0.5 )  0.8 ═ ( 1 ─ 0.2 

Figure 5-4 Offsite Surface Soil Accumulation from Deposition 

λw gt gw λ t

gw λ t

int tD )( f i

tD )(i

Ce )1( −Ce

λw

w

gwt

λ

1 exp(−− λ )

ta )( Vdep i

1 exp

− 
5-13 

 0.5 ═ 0.5 × ( 0.8 × 1 + 0.2 )  m/yr m/yr m/yr  7.41E+00 ═ 0.5 ⁄ 0.15 ⁄ ( 0.3 + 1.5 ×  /yr m/yr m g/cm3 7.41E+00 ═ + 0.000121 + 7.65E-05 + 7.407407  /yr /yr /yr /yr  -8.58E-22 ═ -1.43E-15 ⁄ 225000 ⁄ 7.407605  A11 β1  pCi/g/yr pCi/m2 g/m2 /yr  6.10E-22 ═ 8.239E-16 ⁄ 225000 ⁄ 7.407605 ─ -8.6E-22 ⁄ 7.4076  A10 α1 A11  7.80E-22 ═ 1.39E-21 ─ 6.10E-22 

 C11 S10 A10  pCi/g pCi/g pCi/g/yr 

Figure 5-4 (cont.) 

)1( − Cr Cr

ir q

)1( −Ce )1( − Cr

o I Pr

o I o L1 omix d

o θ c

o ρ b

oo λ1 ++ LE 1 λ1 o E o L1

oo λ1 ++ LE 1

o

b mix d0 ρ

oo λ1 ++ LE 1 o b mix d0 ρ 

λ1 

+ 

E 
5-14 

 2.12E-22 ═ 6.10E-22 + -8.58E-22 × 0.48828 + 7.80E-22 × 0.02686  S1(t) A10 A11 t C11  pCi/g pCi/g pCi/g/yr yr pCi/g 

Figure 5-4 (cont.) 

Table 5-5 Spreadsheet Calculations for Sr-90 Accumulation in Offsite Surface Soil from both Irrigation and De

Time 

Sr-90 

Concentration 

in Irrigation 

Water (pCi/m3) 

Sr-90 

Concentration 

in Air from 

Code (pCi/m3) 

Influx 

Entering 

Offsite Soil 

(pCi/m2/yr) α1 β1 A11 A10 C11 

0.00E+00 0.00E+00 3.03E-05 9.46E-01 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 

4.88E-01 4.37E+01 2.99E-05 9.06E+00 9.46E-01 1.66E+01 7.58E-04 -7.73E-03 7.73E-03 

9.77E-01 6.97E+01 2.95E-05 1.39E+01 9.06E+00 9.83E+00 4.48E-04 -4.19E-03 4.20E-03 

1.46E+00 8.48E+01 2.91E-05 1.67E+01 1.39E+01 5.72E+00 2.61E-04 -2.04E-03 2.08E-03 1.95E+00 9.33E+01 2.86E-05 1.82E+01 1.67E+01 3.23E+00 1.47E-04 -7.52E-04 8.17E-04 2.44E+00 9.79E+01 2.82E-05 1.91E+01 1.82E+01 1.72E+00 7.85E-05 2.54E-05 7.38E-05 2.93E+00 1.00E+02 2.78E-05 1.95E+01 1.91E+01 8.12E-01 3.70E-05 4.90E-04 -3.56E-04 3.42E+00 1.01E+02 2.74E-05 1.96E+01 1.95E+01 2.62E-01 1.20E-05 7.65E-04 -5.96E-04 3.91E+00 1.01E+02 2.71E-05 1.96E+01 1.96E+01 -6.75E-02 -3.08E-06 9.25E-04 -7.23E-04 4.39E+00 1.00E+02 2.67E-05 1.94E+01 1.96E+01 -2.64E-01 -1.21E-05 1.02E-03 -7.81E-04 4.88E+00 9.92E+01 2.63E-05 1.92E+01 1.94E+01 -3.81E-01 -1.74E-05 1.06E-03 -7.99E-04 5.37E+00 9.81E+01 2.59E-05 1.90E+01 1.92E+01 -4.48E-01 -2.04E-05 1.09E-03 -7.94E-04 5.86E+00 9.69E+01 2.55E-05 1.88E+01 1.90E+01 -4.86E-01 -2.22E-05 1.09E-03 -7.75E-04 6.35E+00 9.56E+01 2.52E-05 1.85E+01 1.88E+01 -5.06E-01 -2.31E-05 1.09E-03 -7.48E-04 6.84E+00 9.43E+01 2.48E-05 1.83E+01 1.85E+01 -5.15E-01 -2.35E-05 1.09E-03 -7.17E-04 7.32E+00 9.30E+01 2.45E-05 1.80E+01 1.83E+01 -5.17E-01 -2.36E-05 1.08E-03 -6.85E-04 7.81E+00 9.17E+01 2.41E-05 1.78E+01 1.80E+01 -5.16E-01 -2.35E-05 1.06E-03 -6.53E-04 

8.30E+00a 9.04E+01 2.38E-05 1.75E+01 1.78E+01 -5.12E-01 -2.34E-05 1.05E-03 -6.21E-04 

8.79E+00 8.91E+01 2.34E-05 1.73E+01 1.75E+01 -5.07E-01 -2.31E-05 1.04E-03 -5.89E-04 

a The calculations for the highlighted time step are shown in Figure 5-6. 

E

e ( 

1 

λ 

+−
5-15 

Figure 5-5 Accumulation of Sr-90 in Offsite Soil from Both Irrigation 

and Deposition from Spreadsheet Calculations and from 

RESRAD-OFFSITE Code 

1

2

0

2

0

2

2

2 )0( −−= CAsC (Eq. 5.14) 

For verifying the offsite surface accumulation for the second member of the transformation 

chain, Sr-90 was selected and the concentration for its progeny Y-90 was verified. Table 5-6 

shows the results of spreadsheet calculations for a few time steps for the accumulation in offsite 

surface soil from irrigation and deposition. For this comparison, the soil concentration in the 

fruit, grain, and nonleafy vegetable agricultural area was used. The results of spreadsheet 

calculations are compared with the RESRAD-OFFSITE results (Figure 5-7). Figure 5-8 shows 

the individual steps of the calculation for one time step highlighted in Table 5-6. For this 

comparison, radionuclide concentrations in air and irrigation water were obtained from the code. 

There is practically no difference in the spreadsheet calculations and the results from RESRADOFFSITE code (see Table 5-6 and Figure 5-7). 

0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

5.00E-04

6.00E-04

7.00E-04

0.00E+00 1.00E+01 2.00E+01 3.00E+01 4.00E+01 5.00E+01 6.00E+01 7.00E+01

Time, yr

Concentration, pCi/g

Soil conc. calculated

Soil conc. from code
5-16 

 Offsite Surface Soil Accumulation from both Irrigation and Particulate Deposition for the First Member of Transformation Chain  3.4 ═ 20 × 0.17 

 /yr yr 

 4.83E-02 ═ (1 ─ exp(- 3.4 ) ⁄ 20  7.41E-01 ═ 31557.6 × 2.38E-05 × (1 ─ 0.25 × 4.83E-02 )  pCi/m2/yr m/yr pCi/m3 2.84E-01 ═ (1 ─ exp(- 3.4 ) ⁄ 3.4  1.68E+01 ═ 0.2 × 90.4078 × (1 ─ 0.25 × 2.84E-01 )  pCi/m2/yr m/yr pCi/m3

α1 ═ 17.78792 

Figure 5-6 Offsite Surface Soil Accumulation from both Irrigation and Particulate Deposition for the First Memb

Chain (the highlighted values correlate with the values in Table 5-5) 

λw gt gw λ t

gw λ t

int f

λw

w

gwt

λ

1 exp(−− λ )

ta )( dep i V

w

wt

λ

1 exp(−− λ 

gw λ t gw λ t

gw

gw

t

t

λ

1 exp(−− λ )

ir q

tw )( iri

gw

w

t

t

λ

1 exp(−− λ 

int f

i _)( airtD

i tD _)( irrigation
5-17 

-5.12E-01 ═ ( 1.75E+01 ─ 17.787916 ) ⁄ ( 8.3008 ─ 7

β1 α1 t2 t

 pCi/m2 pCi/m2/yr yr y 0.5 ═ ( 1 ─ 0.5 )  0.8 ═ ( 1 ─ 0.2  0.5 ═ 0.5 × ( 0.8 × 1 + 0.2 )  m/yr m/yr m/yr  7.36E-02 ═ 0.5 ⁄ 0.15 ⁄ ( 0.3 + 1.5 × 3 /yr m/yr m g/cm3 c 9.75E-02 ═ ( 0.023803 + 8E-05 + 0.0735835 )  /yr /yr /yr /yr 

-2.34E-05 ═ -0.51223 ⁄ 225000 ⁄ 0.0975 

 A11 β1  pCi/g/yr pCi/m2 g/m2 /yr 

1.05E-03 ═ 17.78792 ⁄ 225000 ⁄ 0.0975 ─ -2.34E-05 ⁄ 0.097463 

 A10 α1 A11 

Figure 5-6 (cont.) 

Ce )1( −Ce

)1( − Cr Cr

ir q

)1( −Ce )1( −Cr

o I Pr

o I o L1 omix d

o θ c

o ρ b o Kd1

oo λ1 ++ LE 1 λ1 o E o L1

oo λ1 ++ LE 1 o b mix d0 ρoo λ1 ++ LE 1 o b mix d0 ρ oo λ1 ++ LE 1

tD tot i _)(
5-18 

-6.21E-04 ═ 0.00043 ─ 1.05E-03 

 C11 S10 A10  pCi/g pCi/g pCi/g/yr 

4.48E-04 ═ 1.05E-03 + -2.34E-05 × 0.4883 + -6.21E-04 × 0.953525 

 S1(t) A10 A11 t C11  pCi/g pCi/g pCi/g/yr yr pCi/g 

Figure 5-6 (cont.) 

tLEo

e

( ) 0 1 1 λ ++−
5-19 

Table 5-6 Spreadsheet Calculations for Y-90 Accumulation in Offsite Surface Soil from Both Irrigation and D

Time 

Y-90 

Concentration 

in Irrigation 

Water 

(pCi/m3) 

Y-90 

Concentration 

in Air from 

Code (pCi/m3) 

Y-90 Influx 

Entering 

Offsite Soil 

(pCi/m2/yr) α2 β2 A21 A20 C21 C22 

0.00E+00 0.00E+00 0.00E+00 0.00E+00 

4.88E-01 4.37E+01 2.99E-05 9.05E+00 0.00E+00 1.85E+01 7.59E-04 -7.74E-03 7.74E-03 4.53E-08 

9.77E-01 6.96E+01 2.95E-05 1.39E+01 9.05E+00 9.83E+00 4.49E-04 -4.19E-03 4.20E-03 -9.48E-10 

1.46E+00 8.47E+01 2.91E-05 1.66E+01 1.39E+01 5.70E+00 2.61E-04 -2.05E-03 2.08E-03 -4.65E-12 1.95E+00 9.32E+01 2.87E-05 1.82E+01 1.66E+01 3.21E+00 1.47E-04 -7.52E-04 8.18E-04 6.19E-13 2.44E+00 9.77E+01 2.82E-05 1.90E+01 1.82E+01 1.71E+00 7.86E-05 2.54E-05 7.39E-05 8.00E-13 2.93E+00 9.99E+01 2.78E-05 1.94E+01 1.90E+01 7.96E-01 3.70E-05 4.90E-04 -3.56E-04 6.92E-13 3.42E+00 1.01E+02 2.74E-05 1.95E+01 1.94E+01 2.47E-01 1.20E-05 7.66E-04 -5.97E-04 5.70E-13 3.91E+00 1.00E+02 2.71E-05 1.95E+01 1.95E+01 -8.20E-02 -3.08E-06 9.26E-04 -7.24E-04 5.75E-13 4.39E+00 9.98E+01 2.67E-05 1.94E+01 1.95E+01 -2.78E-01 -1.21E-05 1.02E-03 -7.82E-04 4.35E-13 4.88E+00 9.88E+01 2.63E-05 1.92E+01 1.94E+01 -3.94E-01 -1.74E-05 1.07E-03 -8.00E-04 3.77E-13 5.37E+00 9.77E+01 2.59E-05 1.90E+01 1.92E+01 -4.61E-01 -2.05E-05 1.09E-03 -7.95E-04 2.74E-13 5.86E+00 9.64E+01 2.56E-05 1.87E+01 1.90E+01 -4.98E-01 -2.22E-05 1.10E-03 -7.75E-04 2.50E-13 6.35E+00 9.51E+01 2.52E-05 1.85E+01 1.87E+01 -5.17E-01 -2.31E-05 1.09E-03 -7.49E-04 2.70E-13 6.84E+00 9.38E+01 2.48E-05 1.82E+01 1.85E+01 -5.26E-01 -2.35E-05 1.09E-03 -7.18E-04 1.89E-13 7.32E+00 9.25E+01 2.45E-05 1.79E+01 1.82E+01 -5.28E-01 -2.36E-05 1.08E-03 -6.86E-04 1.73E-13 7.81E+00 9.12E+01 2.41E-05 1.77E+01 1.79E+01 -5.26E-01 -2.36E-05 1.07E-03 -6.53E-04 2.25E-13 

8.30E+00a 8.98E+01 2.38E-05 1.74E+01 1.77E+01 -5.22E-01 -2.34E-05 1.05E-03 -6.21E-04 1.86E-13 

8.79E+00 8.85E+01 2.35E-05 1.72E+01 1.74E+01 -5.17E-01 -2.31E-05 1.04E-03 -5.90E-04 1.29E-13 

a The calculations for the highlighted time step are shown in Figure 5-8. 
5-20 

Figure 5-7 Accumulation of Y-90 in Offsite Soil from Both 

Irrigation and Deposition from Spreadsheet 

Calculations and from RESRAD-OFFSITE Code 

5.2 Accumulation in Surface Water 

The contaminants can reach the surface water body from surface runoff, from contaminated 

groundwater flow, and by atmospheric deposition of contaminated dust. Radiological 

transformations and the removal of contaminant by the outflow of contaminated water are 

included when calculating surface water concentration, as described in Section 5.2 of the 

RESRAD-OFFSITE User’s Manual. The rate contaminants enter the surface water body can be 

given as: 

)(

)()()( )(

tV

AVtatfSDRtR tI sw

i

sw

depis

sr

sw i

i

++ = (Eq. 5.15) 

where: 

tR )( sr

i = release rate of nuclide i due to erosion of the surface soil above the primary 

contamination (pCi/yr), 

SDR = sediment delivery ratio, 

0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

5.00E-04

6.00E-04

7.00E-04

0.00E+00 1.00E+01 2.00E+01 3.00E+01 4.00E+01 5.00E+01 6.00E+01 7.00E+01

Time, yr

Concentration, pCi/g

Soil conc. calculated

Soil conc. from code
5-21 

tf )(s = flux of nuclide i carried by groundwater entering the surface water body (pCi/yr), 

ta )(i = air concentration of radionuclide i above the surface water body (pCi/m3

), 

sw A = surface area of the surface water body (m2

), 

tV )( sw

i = surface water body volume at time t (m3

) (given in Eq. 5.29 in RESRAD-OFFSITE 

User’s Manual): 

6 )( 10/)( i

d

sw sdsw

i += KtmVtV (Eq. 5.16) 

where: 

 t

dt

tdm

mtm

sd

sd sd Δ+=

)( )0()(

 (Eq. 5.16a)

 sw V = initial volume of water in the surface water body (m3

), 

tm )( sd = cumulative mass of contaminated soil deposited into surface water body (g), 

 i Kd = distribution coefficient of deposited radionuclide (cm3/g). 

The rate contaminants enter the water body can be approximated by a linear function of time t

given as: 

tI t ii

sw

i )( βα ×+= (Eq. 5.17) 

where α i and β i are constant between each pair of time points. 

The surface water concentration of the first member of the transformation chain at any time t is 

given as (Eq. 5.37 in the RESRAD-OFFSITE User’s Manual): 

sw t swsw

eCtAAtw

1 ( )

1

1

1

0

1 1 111 )( ++− λλλ +×+= (Eq. 5.18) 

where 0 A1 , 1 A1 , and 1 C1 are given as: 

sdsw

A A

111

1

0 11

1 λλλ

α

++

− = (Eq. 5.19) 

( ) 111

1 1

1 sdsw A

λλλ

β

++ = (Eq. 5.20) 

0

1 1

1

1 )0( AwC sw −= (Eq. 5.21) 
5-22 

where: 

sw λi = rate constant for the removal of nuclide i with the water flowing out of the surface water 

body (/yr), 

sd λi = equivalent rate constant for the change in partitioning caused by the additional mass of 

eroded soil into the surface water body (/yr), 

tV )(

q

sw

i

sw sw λi = (Eq. 5.22)

dt

tdm

V

K sd

sw

i

i

sd d

i

10 )( −6

λ = (Eq. 5.23)

mean residence time

V

q

sw

sw _ _ = (Eq. 5.24)

For verifying the surface water concentration from the initial contamination, Ra-226 was 

selected. Table 5-7 shows the results of spreadsheet calculations for few time steps for the 

accumulation in surface water. All parameters were kept at their default values. The results of 

spreadsheet calculations are compared with the RESRAD-OFFSITE results (Figure 5-9). 

Figure 5-10 shows the individual steps of the calculation for one time step highlighted in 

Table 5-7. For this comparison, additional mass deposition, erosion flux, air concentration 

above the surface water area, and flux from groundwater to surface water body were taken as 

input from the code. There is practically no difference in the spreadsheet calculations and the 

results from RESRAD-OFFSITE code (see Table 5-7 and Figure 5-9). The spreadsheet 

calculations for other radionuclides are provided in Excel spreadsheets. 

The surface water concentration of the second member of transformation chain at any time t is 

given as (Equation 5.40 in the RESRAD-OFFSITE User’s Manual): 

sw t t sdsw sdsw

eCtAAtw eC

2 ( )

2

1 ( )

2

1

2

0

2 2 111 222 )( ++− λλλ ++− λλλ +×+= + (Eq. 5.25)

where 0 A2 , 1 A2 , 1 C2 , and 2 C2 are given as: 

( () )

]

)(

)( [

( ) 222

1

2

222

0

12

2

1

222

0 2

2 sdsw sdsw

sw

sw

sdsw

A

A

tV

tV

A

λλλλλλ

λ

λλλ

α

++ − ++

+

++ = (Eq. 5.26)
5-23 

Offsite Surface Soil Accumulation from both Irrigation and Particulate Deposition in the Second Member of the Chain 

α2 ═ 1.77E+01

-5.22E01 ═ ( 1.74E+01 ─ 1.77E+01 ) ⁄ ( 8.30E+00 ─ 7.81E+00 ) 

β2 α2 t2 t1 

pCi/m2 pCi/m2/yr yr yr 

5.00E-01 ═ ( 1.00E+00 ─ 5.00E-01 ) 8.00E-01 ═ ( 1.00E+00 ─ 2.00E-01 ) 5.00E-01 ═ 5.00E-01 × ( 8.00E-01 × 1.00E+00 + 2.00E-01 ) 

m/yr m/yr m/yr 

3.09E-03 ═ 5.00E-01 ⁄ 1.50E-01 ⁄ ( 3.00E-01 + 1.50E+00 × 7.20E+02 ) 

/yr m/yr m g/cm3 cm3/g 

Figure 5-8 Offsite Surface Soil Accumulation from Both Irrigation and Particulate Deposition in the Se

Member of the Chain (the highlighted values correlate with the values in Table 5-6) 

Ce

)1( −Ce

)1( − Cr

Cr

ir q

)1( −Ce )1( −Cr

o I Pr

o I omix d

o θ c

o ρ b

i _)( tottD

o L2 o Kd 2
5-24 

9.49E+01 ═ ( 9.49E+01 + 7.65E-05 + 3.09E-03 ) 

-2.34E05 = -5.22E- 01 ⁄ 2.25E+05 ⁄ 9.49E+01 + 9.49E+01 × -2.34E- 05 ⁄ 9.49E+01 

A21 β2 A11 

pCi/g/yr pCi/m2 g/m2

1.05E-03 = ( 1.77E+01 ⁄ 2.25E+05 + 9.49E+01 × 1.05E-03 ─

-2.34E05 ) ⁄ 9.49E+0

A20 α2 A10 A21 

-6.21E04 = ( 9.49E+01 × -6.21E- 04 ) /( 9.49E+01 + 3.09E- 03 ─ 2.38E-02 ─ 7.36E-0

C21 C11 

1.86E-13 = 4.31E-04 ─ 1.05E-03 ─

-6.21E04 

C22 S20 A20 C21 

pCi/g pCi/g pCi/g/yr 

Figure 5-8 (cont.) 

o E

o

b mix d0 ρ

o

b mix d0 ρ

λ2

( ) 2 2oo λ ++ LE

o L2

( ) 2 2oo λ ++ LE ( ) 2 2oo λ2 λ ++ LE

( 

2 

λ 

+ 

λ2

λ2 λ2 o L2
5-25 

4.48E-04 = 1.05E-03 + 

-2.34E05 × 4.88E-01 + -6.21E- 04 × 9.54E- 01 + 1.86E-13 × 7.59E-2

S2(t) A20 A21 t C21 C22 

pCi/g pCi/g pCi/g/yr yr pCi/g pCi/g 

Figure 5-8 (cont.) 

tLEo

e

( ) 0 1 1 λ ++− 

e ( 

2 

λ 

+−
5-26 

( )

]

)(

)( [

( ) 222

1

12

2

1

222

1 2

2 sdsw

sw

sw

sdsw

A

tV

tV

A

λλλ

λ

λλλ

β

++

+

++ = (Eq. 5.27)

sw sdsw sdsw

sw C

tV

tV C

111222

1

12

2

1 1

2 ]

)(

)( [ λλλλλλ

λ

−−−++ = (Eq. 5.28)

1

2

0

2 2

2

2 )0( CAwC sw −−= (Eq. 5.29)

For verifying the surface water concentration for the second member of the transformation 

chain, Ra-226 was selected and the concentration for its progeny Pb-210 was verified. 
5-27 

Table 5-7 Spreadsheet Calculations for Ra-226 Accumulation in Surface Water 

Time V1sw Msd(t) λ1sw λ1sd

Erosion 

Flux from 

the Code

(pCi/yr) 

Additional 

Mass 

Deposited 

from the 

Code (g/yr) 

Air 

Concentration 

above SW 

Area from 

Code 

(pCi/m3) 

Flux from 

Groundwater 

to Surface 

Water Body 

from Code 

(pCi/yr) 

Flux 

Entering 

Surface 

Water Body 

(pCi/yr/m3) α1 β1 A11 A10 

0 150000 0.00E+00 1.00E+00 8.03E-05 1.72E+05 1.72E+05 1.37E-08 0.00E+00 1.15E+00 

0.4883 150006 8.40E+04 1.00E+00 8.03E-05 1.72E+05 1.72E+05 1.37E-08 0.00E+00 1.15E+00 1.15E+00 -3.31E-03 -3.31E-03 1.15E+00 -

0.9766 150012 1.68E+05 1.00E+00 8.03E-05 1.72E+05 1.72E+05 1.37E-08 0.00E+00 1.14E+00 1.15E+00 -3.31E-03 -3.30E-03 1.15E+00 1.4648 150018 2.52E+05 1.00E+00 8.03E-05 1.71E+05 1.72E+05 1.36E-08 0.00E+00 1.14E+00 1.14E+00 -3.30E-03 -3.30E-03 1.15E+00 1.9531 150024 3.36E+05 1.00E+00 8.03E-05 1.71E+05 1.72E+05 1.36E-08 0.00E+00 1.14E+00 1.14E+00 -3.30E-03 -3.29E-03 1.15E+00 2.4414 150029 4.20E+05 1.00E+00 8.03E-05 1.71E+05 1.72E+05 1.36E-08 0.00E+00 1.14E+00 1.14E+00 -3.29E-03 -3.29E-03 1.14E+00 2.9297 150035 5.04E+05 1.00E+00 8.03E-05 1.71E+05 1.72E+05 1.36E-08 0.00E+00 1.14E+00 1.14E+00 -3.29E-03 -3.29E-03 1.14E+00 

3.418 150041 5.88E+05 1.00E+00 8.03E-05 1.70E+05 1.72E+05 1.36E-08 0.00E+00 1.14E+00 1.14E+00 -3.28E-03 -3.28E-03 1.14E+00 

3.9063 150047 6.72E+05 1.00E+00 8.03E-05 1.70E+05 1.72E+05 1.35E-08 0.00E+00 1.13E+00 1.14E+00 -3.28E-03 -3.28E-03 1.14E+00 4.3945 150053 7.56E+05 1.00E+00 8.03E-05 1.70E+05 1.72E+05 1.35E-08 0.00E+00 1.13E+00 1.13E+00 -3.27E-03 -3.27E-03 1.14E+00 4.8828 150059 8.40E+05 1.00E+00 8.03E-05 1.70E+05 1.72E+05 1.35E-08 0.00E+00 1.13E+00 1.13E+00 -3.27E-03 -3.27E-03 1.14E+00 

5.3711a 150065 9.24E+05 1.00E+00 8.02E-05 1.69E+05 1.72E+05 1.35E-08 0.00E+00 1.13E+00 1.13E+00 -3.26E-03 -3.26E-03 1.13E+00 

5.8594 150071 1.01E+06 1.00E+00 8.02E-05 1.69E+05 1.72E+05 1.35E-08 0.00E+00 1.13E+00 1.13E+00 -3.26E-03 -3.26E-03 1.13E+00 6.3477 150076 1.09E+06 9.99E-01 8.02E-05 1.69E+05 1.72E+05 1.34E-08 0.00E+00 1.13E+00 1.13E+00 -3.25E-03 -3.25E-03 1.13E+00 6.8359 150082 1.18E+06 9.99E-01 8.02E-05 1.69E+05 1.72E+05 1.34E-08 0.00E+00 1.12E+00 1.13E+00 -3.25E-03 -3.25E-03 1.13E+00 7.3242 150088 1.26E+06 9.99E-01 8.02E-05 1.69E+05 1.72E+05 1.34E-08 0.00E+00 1.12E+00 1.12E+00 -3.24E-03 -3.24E-03 1.13E+00 7.8125 150094 1.34E+06 9.99E-01 8.02E-05 1.68E+05 1.72E+05 1.34E-08 0.00E+00 1.12E+00 1.12E+00 -3.24E-03 -3.24E-03 1.13E+00 8.3008 150100 1.43E+06 9.99E-01 8.02E-05 1.68E+05 1.72E+05 1.34E-08 0.00E+00 1.12E+00 1.12E+00 -3.24E-03 -3.24E-03 1.12E+00 

a The calculations for the highlighted time step are shown in Figure 5-10. 
5-28 

Figure 5-9 Accumulation of Ra-226 in Surface Water from Spreadsheet 

Calculations and from RESRAD-OFFSITE Code 

Table 5-8 shows the results of spreadsheet calculations for a few time steps for the 

accumulation in surface water for the second member of the chain (Pb-210). The results of 

spreadsheet calculations are compared with the RESRAD-OFFSITE results (Figure 5-11). For 

this comparison, erosion flux, air concentration above the surface water area, and flux from 

groundwater to surface water body were taken as input from the code. There is practically 

no difference in the spreadsheet calculations and the results from RESRAD-OFFSITE code 

(see Table 5-8 and Figure 5-11). The spreadsheet calculations for other radionuclides are 

provided in Excel spreadsheets. 

5.3 Accumulation in Plants 

Plant foods get contaminated due to root uptake from offsite contaminated soil, foliar uptake 

from overhead irrigation, and foliar uptake from contaminated dust in the agricultural area. 

RESRAD-OFFSITE has four food types: fruit, grain, and nonleafy vegetables; leafy vegetables; 

pasture and silage; and grain. Fruit, grain, and nonleafy and leafy vegetables are for human 

consumption, while pasture and silage and grain are for livestock intake. Accumulation in plant 

food is calculated as described in Section 5.3 of the RESRAD-OFFSITE User’s Manual. 

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

0 10 20 30 40 50 60 70

Time, yr

Concentration, pCi/m 3

First member surface water

conc. calculated 

First member surface water

conc. from code 
5-29 

Table 5-8 Spreadsheet Calculations for Pb-210 Accumulation in Surface Water 

Time, yr V2sw λ2sw λ2sd

Erosion 

Flux from 

the Code 

(pCi/yr) 

Air 

Concentration 

above SW 

Area from 

Code 

(pCi/m3) 

Flux from 

Groundwater 

to Surface 

Water Body 

from Code 

(pCi/yr) 

Flux 

Entering 

Surface 

Water 

Body 

(pCi/yr/m3) α2 β2 A21 A20 C21 C22 

0 1.50E+05 1.00E+00 1.15E-04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 

0.488 1.50E+05 1.00E+00 1.15E-04 2.59E+03 2.06E-10 0.00E+00 1.73E-02 0.00E+00 3.53E-02 3.42E-02 1.52E-03 -1.17E+00 1.16E+

0.977 1.50E+05 1.00E+00 1.15E-04 5.13E+03 4.08E-10 0.00E+00 3.42E-02 1.73E-02 3.47E-02 3.36E-02 1.88E-02 -7.15E-01 7.03E

1.465 1.50E+05 1.00E+00 1.15E-04 7.63E+03 6.07E-10 0.00E+00 5.09E-02 3.42E-02 3.41E-02 3.30E-02 3.57E-02 -4.39E-01 4.25E1.953 1.50E+05 1.00E+00 1.15E-04 1.01E+04 8.03E-10 0.00E+00 6.73E-02 5.09E-02 3.35E-02 3.24E-02 5.24E-02 -2.70E-01 2.56E2.441 1.50E+05 1.00E+00 1.15E-04 1.25E+04 9.95E-10 0.00E+00 8.33E-02 6.73E-02 3.30E-02 3.19E-02 6.88E-02 -1.66E-01 1.55E

2.93 1.50E+05 1.00E+00 1.15E-04 1.49E+04 1.18E-09 0.00E+00 9.92E-02 8.33E-02 3.24E-02 3.13E-02 8.49E-02 -1.02E-01 9.30E

3.418 1.50E+05 1.00E+00 1.15E-04 1.72E+04 1.37E-09 0.00E+00 1.15E-01 9.92E-02 3.18E-02 3.08E-02 1.01E-01 -6.25E-02 5.57E

3.906 1.50E+05 1.00E+00 1.15E-04 1.95E+04 1.55E-09 0.00E+00 1.30E-01 1.15E-01 3.13E-02 3.02E-02 1.16E-01 -3.84E-02 3.32E4.395 1.50E+05 9.99E-01 1.15E-04 2.17E+04 1.73E-09 0.00E+00 1.45E-01 1.30E-01 3.07E-02 2.97E-02 1.32E-01 -2.36E-02 1.96E4.883 1.50E+05 9.99E-01 1.15E-04 2.40E+04 1.91E-09 0.00E+00 1.60E-01 1.45E-01 3.02E-02 2.92E-02 1.47E-01 -1.45E-02 1.14E5.371 1.50E+05 9.99E-01 1.15E-04 2.61E+04 2.08E-09 0.00E+00 1.74E-01 1.60E-01 2.96E-02 2.87E-02 1.61E-01 -8.97E-03 6.43E5.859 1.50E+05 9.99E-01 1.15E-04 2.83E+04 2.25E-09 0.00E+00 1.88E-01 1.74E-01 2.91E-02 2.82E-02 1.76E-01 -5.55E-03 3.43E6.348 1.50E+05 9.99E-01 1.15E-04 3.04E+04 2.42E-09 0.00E+00 2.02E-01 1.88E-01 2.86E-02 2.77E-02 1.90E-01 -3.45E-03 1.62E6.836 1.50E+05 9.99E-01 1.15E-04 3.24E+04 2.58E-09 0.00E+00 2.16E-01 2.02E-01 2.81E-02 2.72E-02 2.04E-01 -2.16E-03 5.39E7.324 1.50E+05 9.99E-01 1.15E-04 3.45E+04 2.74E-09 0.00E+00 2.30E-01 2.16E-01 2.76E-02 2.67E-02 2.18E-01 -1.36E-03 -1.12E

7.813 1.50E+05 9.99E-01 1.15E-04 3.64E+04 2.90E-09 0.00E+00 2.43E-01 2.30E-01 2.71E-02 2.62E-02 2.31E-01 -8.79E-04 -4.99E

8.301 1.50E+05 9.99E-01 1.15E-04 3.84E+04 3.06E-09 0.00E+00 2.56E-01 2.43E-01 2.66E-02 2.58E-02 2.45E-01 -5.80E-04 -7.26E

8.789 1.50E+05 9.99E-01 1.15E-04 4.03E+04 3.21E-09 0.00E+00 2.69E-01 2.56E-01 2.62E-02 2.53E-02 2.58E-01 -3.97E-04 -8.57E

9.277 1.50E+05 9.99E-01 1.15E-04 4.22E+04 3.36E-09 0.00E+00 2.81E-01 2.69E-01 2.57E-02 2.48E-02 2.70E-01 -2.84E-04 -9.31E

9.766 1.50E+05 9.99E-01 1.15E-04 4.41E+04 3.51E-09 0.00E+00 2.93E-01 2.81E-01 2.52E-02 2.44E-02 2.83E-01 -2.15E-04 -9.69E

10.25 1.50E+05 9.99E-01 1.15E-04 4.59E+04 3.65E-09 0.00E+00 3.06E-01 2.93E-01 2.48E-02 2.40E-02 2.95E-01 -1.72E-04 -9.85E
5-30 

Figure 5-10 Accumulation in Surface Water for the First Member of Transformation Chain 

(the highlighted values correlate with the values in Table 5-7) 

The activity concentration in the edible part of the plant from root uptake of the contaminated 

offsite soil is given as (Eq. 5.44 in the RESRAD-OFFSITE User’s Manual): 

)()( 0 tsrtftp ii

offsoil

i = (Eq. 5.30) 

where: 

tp )( offsoil

i = activity concentration of radionuclide i in plant from root uptake at time t (pCi/kg), 
5-31 

i rtf = plant transfer factor (root uptake factor) of radionuclide i (pCi/kg per pCi/kg), 

)( 0 tsi = radionuclide i concentration in offsite soil where plant good is grown at time 

t (pCi/kg). 

The activity concentration in the edible part of the plant from foliar uptake from overhead 

irrigation is given as (Eq. 5.45 in the RESRAD-OFFSITE User’s Manual): 

)( )exp(1 )( int tw

t

t q

Y

ff tp ir

i

g

ir

w

oi tl gw

i λ

−− λ = (Eq. 5.31) 

where: 

tp )( oi

i = activity concentration of radionuclide i in the edible portion of the plant resulting 

 from foliar uptake of overhead irrigation (pCi/kg), 

int f = foliar interception factor, 

tl f = fraction of the contaminant that is translocated from the foliage to the edible part of 

the plant, 

Y = wet crop yield (kg/m2

), 

λ w = weathering constant (per yr), 

gt = duration of growing season (yr), 

qir = irrigation rate (m/yr), 

tw )( ir

i = activity concentration of radionuclide i in contaminated irrigation water (pCi/m3

). 
5-32 

Figure 5-11 Accumulation of Pb-210 in Surface Water from Spreadsheet 

Calculations and from RESRAD-OFFSITE Code 

The activity concentration in the edible part of the plant from foliar uptake from contaminated 

dust is given as (Eq. 5.51 in the RESRAD-OFFSITE User’s Manual): 

)( )exp(1 )( int taV

t

Y

ff tp idep

w

dust tl gw

i λ

−− λ = (Eq. 5.32) 

where: 

tp )( dust

i = activity concentration of radionuclide i at time t in the edible portion of the plant from 

foliar interception of dust (pCi/kg), 

 

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

8.00E-01

9.00E-01

0 10 20 30 40 50 60 70

Time, yr

Concentration, pCi/m 3

Second member surface

water conc. calculated

Second member surface

water conc. from code
5-33 

Vdep = deposition velocity of the contaminated dust particle (m/yr), 

ta )(i = air concentration of radionuclide i at time t above the agricultural area where plant is 

growing (pCi/m3

). 

U-238 was selected for this pathway verification. First, the plant concentration from the subpathways was calculated and finally added together to compare the results of the total plant 

concentration. The initial soil concentration in the primary contaminated area was 1 pCi/g. 

Surface water was the source of water for all uses. Other parameters were at their default 

values. The calculations were done for all four food types. The sub-pathways considered were: 

root uptake from offsite contaminated soil, foliar uptake from overhead irrigation, and foliar 

uptake from contaminated dust in the agricultural area. For this comparison, radionuclide 

concentration in soil, irrigation water, and air in the agricultural area where the plants were 

grown were obtained from the code. Tables 5-9 to 5-12 show the spreadsheet calculations for 

U-238 accumulation in four different food types grown in four different agricultural areas. 

Figure 5-12 shows the U-238 accumulations in fruit, grain, and nonleafy vegetables grown in 

agricultural area 1 from both spreadsheet calculations and from the RESRAD-OFFSITE code. 

Figure 5-13 shows the individual steps of the calculation for one time step highlighted in 

Table 5-9 for U-238 accumulation in fruit, grain, and nonleafy vegetables. 

Figure 5-14 shows the U-238 accumulations in leafy vegetables grown in agricultural area 2 

from both spreadsheet calculations and from the RESRAD-OFFSITE code. Figure 5-15 shows 

the individual steps of the calculation for one time step highlighted in Table 5-10 for U-238 

accumulation in leafy vegetables. 

Figure 5-16 shows the U-238 accumulations in pasture and silage grown in agricultural area 3 

from both spreadsheet calculations and from the RESRAD-OFFSITE code. Figure 5-17 shows 

the individual steps of the calculation for one time step highlighted in Table 5-11 for U-238 

accumulation in pasture and silage. 

Figure 5-18 shows the U-238 accumulations in grain grown in agricultural area 4 from both 

spreadsheet calculations and from the RESRAD-OFFSITE code. Figure 5-19 shows the 

individual steps of the calculation for one time step highlighted in Table 5-12 for U-238 

accumulation in grain. 

There is practically no difference in the RESRAD-OFFSITE code results and spreadsheet 

calculations for all plant types. 

 
5-34 

Table 5-9 Spreadsheet Calculations for U-238 Accumulation in Fruit, Grain, and 

Nonleafy Vegetables – Grown in Area 1 

Time 

(year) 

Soil 

Conc. 

from 

Code 

(pCi/g) 

Irrigation 

Water 

Conc. 

from 

Code 

(pCi/L) 

Air Conc. 

from 

Code 

(pCi/m3

) 

Plant 

Conc. 

from 

Root 

Uptake 

(pCi/g) 

Plant 

Conc. 

from 

Irrigation 

(pCi/g) 

Plant 

Conc. 

from 

Dust 

(pCi/g) 

Fruit, 

Grain, 

Nonleafy 

Conc. 

Calculated 

(pCi/kg) 

Fruit, 

Grain, 

Nonleafy 

Conc. 

from 

Code 

(pCi/kg) 

 

0.00E+00 0.00E+00 0.00E+00 3.03E-07 0.00E+00 0.00E+00 1.65E-08 1.65E-05 1.65E-05 

4.88E-01 1.09E-07 4.43E-04 3.03E-07 2.72E-10 8.99E-07 1.65E-08 9.16E-04 9.16E-04 

9.77E-01 3.58E-07 7.14E-04 3.02E-07 8.94E-10 1.45E-06 1.65E-08 1.47E-03 1.47E-03 

1.46E+00 6.88E-07 8.79E-04 3.02E-07 1.72E-09 1.79E-06 1.64E-08 1.80E-03 1.80E-03 

1.95E+00 1.06E-06 9.80E-04 3.01E-07 2.66E-09 1.99E-06 1.64E-08 2.01E-03 2.01E-03 

2.44E+00 1.46E-06 1.04E-03 3.01E-07 3.66E-09 2.11E-06 1.64E-08 2.13E-03 2.13E-03 

2.93E+00a 1.88E-06 1.08E-03 3.00E-07 4.69E-09 2.19E-06 1.64E-08 2.21E-03 2.21E-03 

3.42E+00 2.29E-06 1.10E-03 3.00E-07 5.73E-09 2.23E-06 1.63E-08 2.26E-03 2.26E-03 

3.91E+00 2.70E-06 1.11E-03 2.99E-07 6.76E-09 2.26E-06 1.63E-08 2.28E-03 2.28E-03 

4.39E+00 3.11E-06 1.12E-03 2.99E-07 7.78E-09 2.27E-06 1.63E-08 2.30E-03 2.30E-03 

4.88E+00 3.51E-06 1.12E-03 2.98E-07 8.78E-09 2.28E-06 1.63E-08 2.31E-03 2.31E-03 

5.37E+00 3.90E-06 1.13E-03 2.98E-07 9.76E-09 2.29E-06 1.62E-08 2.31E-03 2.31E-03 

5.86E+00 4.29E-06 1.13E-03 2.97E-07 1.07E-08 2.29E-06 1.62E-08 2.31E-03 2.31E-03 

6.35E+00 4.67E-06 1.12E-03 2.97E-07 1.17E-08 2.28E-06 1.62E-08 2.31E-03 2.31E-03 

6.84E+00 5.03E-06 1.12E-03 2.97E-07 1.26E-08 2.28E-06 1.62E-08 2.31E-03 2.31E-03 

7.32E+00 5.39E-06 1.12E-03 2.96E-07 1.35E-08 2.28E-06 1.61E-08 2.31E-03 2.31E-03 

7.81E+00 5.75E-06 1.12E-03 2.96E-07 1.44E-08 2.28E-06 1.61E-08 2.31E-03 2.31E-03 

8.30E+00 6.09E-06 1.12E-03 2.95E-07 1.52E-08 2.27E-06 1.61E-08 2.30E-03 2.30E-03 

a

 The calculations for the highlighted time step are shown in Figure 5-13. 

 
5-35 

Table 5-10 Spreadsheet Calculations for U-238 Accumulation in Leafy Vegetables – 

Grown in Area 2 

Time 

(year) 

Soil 

Conc. 

from 

Code 

(pCi/g) 

Irrigation 

Water 

Conc. 

from 

Code 

(pCi/L) 

Air Conc. 

from 

Code 

(pCi/m3

) 

Plant 

Conc. 

from 

Root 

Uptake 

(pCi/g) 

Plant 

Conc. 

from 

Irrigation 

(pCi/g) 

Plant 

Conc. 

from 

Dust 

(pCi/g) 

Leafy 

Conc. 

Calculated 

(pCi/kg) 

Leafy 

Conc. 

from 

Code 

(pCi/kg) 

 

0.00E+00 0.00E+00 0.00E+00 2.35E-07 0.00E+00 0.00E+00 6.14E-08 6.14E-05 6.14E-05 

4.88E-01 1.06E-07 4.43E-04 2.35E-07 2.66E-10 2.93E-06 6.13E-08 2.99E-03 2.99E-03 

9.77E-01 3.56E-07 7.14E-04 2.34E-07 8.90E-10 4.73E-06 6.12E-08 4.79E-03 4.79E-03 

1.46E+00 6.89E-07 8.79E-04 2.34E-07 1.72E-09 5.82E-06 6.11E-08 5.89E-03 5.89E-03 

1.95E+00 1.07E-06 9.80E-04 2.33E-07 2.67E-09 6.49E-06 6.10E-08 6.55E-03 6.55E-03 

2.44E+00 1.47E-06 1.04E-03 2.33E-07 3.69E-09 6.90E-06 6.09E-08 6.96E-03 6.96E-03 

2.93E+00a 1.89E-06 1.08E-03 2.33E-07 4.73E-09 7.14E-06 6.08E-08 7.21E-03 7.21E-03 

3.42E+00 2.31E-06 1.10E-03 2.32E-07 5.78E-09 7.29E-06 6.07E-08 7.35E-03 7.35E-03 

3.91E+00 2.73E-06 1.11E-03 2.32E-07 6.82E-09 7.37E-06 6.06E-08 7.44E-03 7.44E-03 

4.39E+00 3.14E-06 1.12E-03 2.31E-07 7.85E-09 7.42E-06 6.05E-08 7.48E-03 7.48E-03 

4.88E+00 3.55E-06 1.12E-03 2.31E-07 8.87E-09 7.44E-06 6.04E-08 7.51E-03 7.51E-03 

5.37E+00 3.95E-06 1.13E-03 2.31E-07 9.86E-09 7.45E-06 6.03E-08 7.52E-03 7.52E-03 

5.86E+00 4.34E-06 1.13E-03 2.30E-07 1.08E-08 7.45E-06 6.02E-08 7.52E-03 7.52E-03 

6.35E+00 4.72E-06 1.12E-03 2.30E-07 1.18E-08 7.45E-06 6.01E-08 7.52E-03 7.52E-03 

6.84E+00 5.09E-06 1.12E-03 2.30E-07 1.27E-08 7.44E-06 6.00E-08 7.51E-03 7.51E-03 

7.32E+00 5.45E-06 1.12E-03 2.29E-07 1.36E-08 7.43E-06 5.99E-08 7.51E-03 7.51E-03 

7.81E+00 5.81E-06 1.12E-03 2.29E-07 1.45E-08 7.42E-06 5.98E-08 7.50E-03 7.50E-03 

8.30E+00 6.16E-06 1.12E-03 2.29E-07 1.54E-08 7.41E-06 5.97E-08 7.49E-03 7.49E-03 

a

 The calculations for the highlighted time step are shown in Figure 5-15. 

 
5-36 

Table 5-11 Spreadsheet Calculations for U-238 Accumulation in Pasture and Silage – 

Grown in Area 3 

Time 

(year) 

Soil Conc. 

from 

Code 

(pCi/g) 

Irrigation 

Water 

Conc. 

from 

Code 

(pCi/L) 

Air Conc. 

from Code 

(pCi/m3

) 

Plant 

Conc. 

from Root 

Uptake 

(pCi/g) 

Plant 

Conc. 

from 

Irrigation 

(pCi/g) 

Plant 

Conc. 

from Dust 

(pCi/g) 

Pasture, 

Silage 

Conc. 

Calculated 

(pCi/kg) 

Pasture 

Silage 

Conc. 

from Code 

(pCi/kg) 

 

0.00E+00 0.00E+00 0.00E+00 4.59E-08 0.00E+00 0.00E+00 1.31E-08 1.31E-05 1.31E-05 

4.88E-01 8.66E-08 4.43E-04 4.59E-08 2.16E-10 1.00E-05 1.31E-08 1.01E-02 1.01E-02 

9.77E-01 3.05E-07 7.14E-04 4.58E-08 7.63E-10 1.62E-05 1.31E-08 1.62E-02 1.62E-02 

1.46E+00 6.01E-07 8.79E-04 4.57E-08 1.50E-09 1.99E-05 1.31E-08 2.00E-02 2.00E-02 

1.95E+00 9.41E-07 9.80E-04 4.56E-08 2.35E-09 2.22E-05 1.31E-08 2.22E-02 2.22E-02 

2.44E+00 1.30E-06 1.04E-03 4.56E-08 3.26E-09 2.36E-05 1.30E-08 2.36E-02 2.36E-02 

2.93E+00a 1.68E-06 1.08E-03 4.55E-08 4.19E-09 2.44E-05 1.30E-08 2.45E-02 2.45E-02 

3.42E+00 2.05E-06 1.10E-03 4.54E-08 5.13E-09 2.49E-05 1.30E-08 2.50E-02 2.50E-02 

3.91E+00 2.43E-06 1.11E-03 4.53E-08 6.07E-09 2.52E-05 1.30E-08 2.53E-02 2.53E-02 

4.39E+00 2.80E-06 1.12E-03 4.53E-08 7.00E-09 2.54E-05 1.30E-08 2.54E-02 2.54E-02 

4.88E+00 3.16E-06 1.12E-03 4.52E-08 7.91E-09 2.55E-05 1.29E-08 2.55E-02 2.55E-02 

5.37E+00 3.52E-06 1.13E-03 4.51E-08 8.80E-09 2.55E-05 1.29E-08 2.55E-02 2.55E-02 

5.86E+00 3.87E-06 1.13E-03 4.50E-08 9.68E-09 2.55E-05 1.29E-08 2.55E-02 2.55E-02 

6.35E+00 4.22E-06 1.12E-03 4.50E-08 1.05E-08 2.55E-05 1.29E-08 2.55E-02 2.55E-02 

6.84E+00 4.55E-06 1.12E-03 4.49E-08 1.14E-08 2.55E-05 1.29E-08 2.55E-02 2.55E-02 

7.32E+00 4.88E-06 1.12E-03 4.48E-08 1.22E-08 2.55E-05 1.28E-08 2.55E-02 2.55E-02 

7.81E+00 5.20E-06 1.12E-03 4.48E-08 1.30E-08 2.54E-05 1.28E-08 2.54E-02 2.54E-02 

8.30E+00 5.51E-06 1.12E-03 4.47E-08 1.38E-08 2.54E-05 1.28E-08 2.54E-02 2.54E-02 

a

 The calculations for the highlighted time step are shown in Figure 5-17. 
5-37 

Table 5-12 Spreadsheet Calculations for U-238 Accumulation in Grain – Grown in 

Area 4 

Time 

(year) 

Soil 

Conc. 

from 

Code 

(pCi/g) 

Irrigation 

Water 

Conc. 

from 

Code 

(pCi/L) 

Air Conc. 

from 

Code 

(pCi/m3

) 

Plant 

Conc. 

from 

Root 

Uptake 

(pCi/g) 

Plant 

Conc. 

from 

Irrigation 

(pCi/g) 

Plant 

Conc. 

from 

Dust 

(pCi/g) 

Grain 

Conc. 

Calculated 

(pCi/kg) 

Grain 

Conc. 

from 

Code 

(pCi/kg) 

 

0.00E+00 0.00E+00 0.00E+00 1.19E-07 0.00E+00 0.00E+00 6.50E-09 6.50E-06 6.50E-06 

4.88E-01 9.66E-08 4.43E-04 1.19E-07 2.41E-10 8.99E-07 6.49E-09 9.06E-04 9.06E-04 

9.77E-01 3.33E-07 7.14E-04 1.19E-07 8.33E-10 1.45E-06 6.47E-09 1.46E-03 1.46E-03 

1.46E+00 6.52E-07 8.79E-04 1.19E-07 1.63E-09 1.79E-06 6.46E-09 1.79E-03 1.79E-03 

1.95E+00 1.02E-06 9.80E-04 1.18E-07 2.54E-09 1.99E-06 6.45E-09 2.00E-03 2.00E-03 

2.44E+00 1.41E-06 1.04E-03 1.18E-07 3.52E-09 2.11E-06 6.44E-09 2.12E-03 2.12E-03 

2.93E+00a 1.81E-06 1.08E-03 1.18E-07 4.52E-09 2.19E-06 6.43E-09 2.20E-03 2.20E-03 

3.42E+00 2.21E-06 1.10E-03 1.18E-07 5.53E-09 2.23E-06 6.42E-09 2.25E-03 2.25E-03 

3.91E+00 2.61E-06 1.11E-03 1.18E-07 6.53E-09 2.26E-06 6.41E-09 2.27E-03 2.27E-03 

4.39E+00 3.01E-06 1.12E-03 1.18E-07 7.52E-09 2.27E-06 6.40E-09 2.29E-03 2.29E-03 

4.88E+00 3.40E-06 1.12E-03 1.17E-07 8.50E-09 2.28E-06 6.39E-09 2.30E-03 2.30E-03 

5.37E+00 3.78E-06 1.13E-03 1.17E-07 9.46E-09 2.29E-06 6.38E-09 2.30E-03 2.30E-03 

5.86E+00 4.16E-06 1.13E-03 1.17E-07 1.04E-08 2.29E-06 6.37E-09 2.30E-03 2.30E-03 

6.35E+00 4.53E-06 1.12E-03 1.17E-07 1.13E-08 2.28E-06 6.36E-09 2.30E-03 2.30E-03 

6.84E+00 4.89E-06 1.12E-03 1.17E-07 1.22E-08 2.28E-06 6.35E-09 2.30E-03 2.30E-03 

7.32E+00 5.24E-06 1.12E-03 1.16E-07 1.31E-08 2.28E-06 6.34E-09 2.30E-03 2.30E-03 

7.81E+00 5.58E-06 1.12E-03 1.16E-07 1.40E-08 2.28E-06 6.33E-09 2.30E-03 2.30E-03 

8.30E+00 5.92E-06 1.12E-03 1.16E-07 1.48E-08 2.27E-06 6.32E-09 2.29E-03 2.29E-03 

a

 The calculations for the highlighted time step are shown in Figure 5-19. 
5-38 

Figure 5-12 Accumulation of U-238 in Fruit, Grain, and Nonleafy Vegetables from 

Spreadsheet Calculations and from RESRAD-OFFSITE Code 

5.4 Accumulation in Meat and Milk 

Accumulation in meat and milk at offsite locations is calculated as described in Section 5.4 of 

the RESRAD-OFFSITE User’s Manual. Assuming that agricultural areas are not in the primary 

contamination zone, accumulation is given as (Eq. 5.52 in the RESRAD-OFFSITE User’s 

Manual): 

twqtsqtpqimftm )]()()([)( if

i

w

ing

o

i

s

i ing

p

i = ingi ++ (Eq. 5.33) 

where: 

tm )(i = activity concentration of radionuclide i in meat or milk at time t (pCi/kg), 

i imf = meat or milk transfer factor of radionuclide i (pCi/kg per pCi/d), 

p

ing q = plant ingestion rate by the livestock (kg/d), 

tp )(i = radionuclide i concentration in plant food (pCi/kg), 

s qing = soil ingestion rate by the livestock (kg/d), 

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

0 5 10 15 20 25 30 35 40 45 50

Time, years

Fruit, Grain, Non-leafy concentration, pCi/kg

Fruit, Grain, Non-leafy Conc.

Calculated

Fruit, Grain, Non-leafy Conc. From

code
5-39 

)( 0 tsi = radionuclide i concentration in soil ingested by livestock at time t (pCi/kg), 

w qing = water ingestion rate by the livestock (kg/L), 

tw )( if

i = radionuclide i concentration in water ingested by livestock at time t (pCi/L). 

Livestock eat grains as well as pasture and silage, and the soil ingested would be from both 

agricultural areas where livestock feed is grown. Cs-137 was selected for this pathway 

verification. The initial soil concentration in the primary contaminated area was 1 pCi/g. 

Surface water was the source of water for all uses. Other parameters were at their default 

values. First the accumulation from the sub-pathways was calculated and finally added together 

to compare the results of the total meat and milk concentrations (see Tables 5-13 and 5-14). 

The sub-pathways considered were: pasture and silage ingestion, grain ingestion, soil ingestion 

from pasture and silage agricultural area, soil ingestion from grain agricultural area, and water 

ingestion. For this comparison, radionuclide concentration in plant, soil, and water was obtained 

from the code. Figure 5-20 shows the Cs-137 accumulations in meat, and Figure 5-21 shows 

the Cs-137 accumulation in milk. Figure 5-22 shows the individual steps of the calculation for 

one time step highlighted in Table 5-13 for Cs-137 accumulation in meat. Figure 5-23 shows 

the individual steps of the calculation for one time step highlighted in Table 5-14 for Cs-137 

accumulation in milk. 

There is practically no difference in the RESRAD-OFFSITE code results and spreadsheet 

calculations for meat and milk accumulation. 

5.5 Accumulation in Fish and Aquatic Foods 

Accumulation in fish and aquatic food is calculated as described in Section 5.5 of the RESRADOFFSITE User’s Manual by the following equation: 

)( twbaftaqf )( sw

i ×= ii (Eq. 5.34) 

where: 

taqf )(i = activity concentration of radionuclide i in aquatic food at time t (pCi/kg), 

tw )( sw

i = surface water concentration at any time t (pCi/L), and 

bafi = bioaccumulation factor in fish or aquatic food (pCi/kg per pCi/L). 
5-40 

 

 Plant Concentration Calculations – Fruit, Grain, and Non-leafy Vegetables 

 

 3.4 ═ 20 × 0.17 

 

 

 /yr yr 

 

 4.83E-02 ═ (1 ─ exp(- 3.4 ) ⁄ 20 

 

 

 

 yr /yr 

 

 3.57E-02 ═ 0.25 × 0.1 ⁄ 0.7 

 

 

 

 (m2/kg) kg/m2 

 

 Root uptake from off-site contaminated soil 

 4.69E-06 ═ 2.50E-03 × 1.88E-03 (5.30) 

 

 

 (pCi/kg) 

pCi/kg per 

pCi/kg (pCi/kg) 

 

 Foliar uptake from overhead irrigation 

 2.19E-03 ═ 3.57E-02 × 4.83E-02 × 1.08E+00 × 0.2 ⁄ 0.17 (5.31) 

 

 

 

 (pCi/kg) (m2/kg) (yr) (pCi/m3) (m) (yr) 

 

 Foliar uptake from contaminated dust 

 1.64E-05 ═ 3.57E-02 × 4.83E-02 × 3.00E-07 × 31557.6 (5.32) 

 

 

 

 (pCi/kg) (m2/kg) (yr) (pCi/m3) (m/yr) 

 

Figure 5-13 Plant Concentration Calculations for Fruit, Grain, and Nonleafy Vegetables 

tp )( offsoil

i i rtf )( 0 tsi

λw g

λ t gw t

gw λ t

w

gwt

λ

1 exp(−− λ ) λw

Y

ffint tl

int f tl f

Y

gt ir q

tw )( ir

w i

gwt

λ

1 exp(−− λ )

Y

ffint tl

tp )( oi

i

w

gwt

λ

1 exp(−− λ )

Y

ffint tl

tp )( dust

i

Vdep ta )(i
5-41 

Figure 5-14 Accumulation of U-238 in Leafy Vegetables from Spreadsheet 

Calculations and from RESRAD-OFFSITE Code 

Cobalt-60 was selected for this pathway verification. The initial concentration was 1 pCi/g. The 

rest of the parameters were at their default values. The surface water concentration at different 

times was obtained from the code. Table 5-15 shows the results from the spreadsheet 

calculations and compares the results from the code for different time steps. Figure 5-24 shows 

the accumulation concentration calculations in fish and aquatic food. Figure 5-25 compares the 

results for fish concentration, and Figure 5-26 compares the spreadsheet calculated results for 

crustacea concentration. 

0.00E+00

1.00E-03

2.00E-03

3.00E-03

4.00E-03

5.00E-03

6.00E-03

7.00E-03

8.00E-03

0 10 20 30 40 50

Time, years

Leafy concentration, pCi/kg

Leafy Conc. Calculated

Leafy Conc. From code
5-42 

Figure 5-15 Plant Concentration Calculations for Leafy Vegetables 
5-43 

Figure 5-16 Accumulation of U-238 in Pasture and Silage from Spreadsheet 

Calculations and from RESRAD-OFFSITE Code 

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

0 10 20 30 40 50

Time, years

Pasture Silage concentration, pCi/kg

Pasture, Silage Conc. Calculated

Pasture Silage Conc. From code
5-44 

Figure 5-17 Plant Concentration Calculations for Pasture and Silage 
5-45 

Figure 5-18 Accumulation of U-238 in Grain from Spreadsheet 

Calculations and from RESRAD-OFFSITE Code 

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

0 10 20 30 40 50

Time, years

Grain concentration, pCi/kg

Grain Conc. Calculated

Grain Conc. From code
5-46 

Figure 5-19 Plant Concentration Calculations for Grain 
5-47 

Table 5-13 Spreadsheet Calculations for Cs-137 Meat Concentration 

Time 

(year) 

Pasture 

Conc. 

(pCi/kg) 

Grain 

Conc. 

(pCi/kg) 

Water Conc. 

(pCi/L) 

Soil 

Conc. in 

Grain 

Area 

(pCi/g) 

Soil 

Conc. in 

Pasture 

Area 

(pCi/g) 

Meat 

Conc. 

from 

Pasture 

Intake 

(pCi/kg) 

Meat 

Conc. 

from 

Grain 

Intake 

(pCi/kg) 

Meat 

Conc. 

from 

Water 

Intake 

(pCi/kg) 

Meat Conc. 

from Soil 

Intake with 

Grain 

(pCi/kg) 

Meat Conc

from Soil 

Intake with 

Pasture 

(pCi/kg) 

0.00E+00 1.31E-05 6.50E-06 0.00E+00 0.00E+00 0.00E+00 5.52E-06 1.05E-05 0.00E+00 0.00E+00 0.00E+00 4.88E-01 9.93E-03 8.98E-04 4.37E-04 9.58E-08 8.58E-08 4.17E-03 1.46E-03 6.56E-04 1.15E-06 2.57E-07 9.77E-01 1.58E-02 1.43E-03 6.97E-04 3.30E-07 3.02E-07 6.65E-03 2.32E-03 1.05E-03 3.96E-06 9.07E-07 1.46E+00 1.93E-02 1.76E-03 8.49E-04 6.44E-07 5.94E-07 8.10E-03 2.85E-03 1.27E-03 7.73E-06 1.78E-06 1.95E+00 2.13E-02 1.95E-03 9.37E-04 1.00E-06 9.27E-07 8.94E-03 3.16E-03 1.41E-03 1.20E-05 2.78E-06 2.44E+00 2.24E-02 2.06E-03 9.85E-04 1.38E-06 1.28E-06 9.41E-03 3.34E-03 1.48E-03 1.66E-05 3.85E-06 2.93E+00 2.30E-02 2.13E-03 1.01E-03 1.78E-06 1.65E-06 9.65E-03 3.45E-03 1.51E-03 2.13E-05 4.94E-06 3.42E+00 2.32E-02 2.16E-03 1.02E-03 2.17E-06 2.01E-06 9.76E-03 3.51E-03 1.53E-03 2.60E-05 6.04E-06 3.91E+00 2.33E-02 2.18E-03 1.02E-03 2.56E-06 2.38E-06 9.78E-03 3.54E-03 1.53E-03 3.07E-05 7.14E-06 4.39E+00 2.32E-02 2.19E-03 1.02E-03 2.95E-06 2.74E-06 9.75E-03 3.55E-03 1.53E-03 3.54E-05 8.22E-06 4.88E+00 2.31E-02 2.19E-03 1.01E-03 3.33E-06 3.10E-06 9.70E-03 3.56E-03 1.52E-03 3.99E-05 9.29E-06 5.37E+00a 2.29E-02 2.19E-03 1.00E-03 3.70E-06 3.44E-06 9.62E-03 3.55E-03 1.51E-03 4.44E-05 1.03E-05 

5.86E+00 2.27E-02 2.19E-03 9.95E-04 4.07E-06 3.78E-06 9.54E-03 3.54E-03 1.49E-03 4.88E-05 1.14E-05 6.35E+00 2.25E-02 2.18E-03 9.85E-04 4.42E-06 4.12E-06 9.45E-03 3.53E-03 1.48E-03 5.31E-05 1.24E-05 6.84E+00 2.23E-02 2.17E-03 9.74E-04 4.77E-06 4.44E-06 9.36E-03 3.52E-03 1.46E-03 5.73E-05 1.33E-05 7.32E+00 2.21E-02 2.17E-03 9.64E-04 5.11E-06 4.76E-06 9.26E-03 3.51E-03 1.45E-03 6.14E-05 1.43E-05 7.81E+00 2.18E-02 2.16E-03 9.53E-04 5.44E-06 5.07E-06 9.17E-03 3.50E-03 1.43E-03 6.53E-05 1.52E-05 8.30E+00 2.16E-02 2.15E-03 9.43E-04 5.77E-06 5.37E-06 9.07E-03 3.48E-03 1.41E-03 6.92E-05 1.61E-05 

a The calculations for the highlighted time step are shown in Figure 5-22. 
5-48 

Table 5-14 Spreadsheet Calculations for Cs-137 Milk Concentration 

Time 

(year) 

Pasture 

Conc. 

(pCi/kg) 

Grain 

Conc. 

(pCi/kg) 

Water 

Conc. 

(pCi/L) 

Soil 

Conc. in 

Grain 

Area 

(pCi/g) 

Soil 

Conc. in 

Pasture 

Area 

(pCi/g) 

Milk 

Conc. 

from 

Pasture 

Intake 

(pCi/kg) 

Milk 

Conc. 

from 

Grain 

Intake 

(pCi/kg) 

Milk 

Conc. 

from 

Water 

Intake 

(pCi/kg) 

Milk 

Conc. 

from Soil 

Intake 

with Grain 

(pCi/kg) 

Milk Conc. 

from Soil 

Intake 

with 

Pasture 

(pCi/kg) 

0.00E+00 1.31E-05 6.50E-06 0.00E+00 0.00E+00 0.00E+00 4.63E-06 5.72E-07 0.00E+00 0.00E+00 0.00E+00 4.88E-01 9.93E-03 8.98E-04 4.37E-04 9.58E-08 8.58E-08 3.50E-03 7.91E-05 5.60E-04 7.66E-08 2.75E-07 9.77E-01 1.58E-02 1.43E-03 6.97E-04 3.30E-07 3.02E-07 5.57E-03 1.26E-04 8.92E-04 2.64E-07 9.67E-07 1.46E+00 1.93E-02 1.76E-03 8.49E-04 6.44E-07 5.94E-07 6.79E-03 1.55E-04 1.09E-03 5.15E-07 1.90E-06 1.95E+00 2.13E-02 1.95E-03 9.37E-04 1.00E-06 9.27E-07 7.49E-03 1.71E-04 1.20E-03 8.02E-07 2.97E-06 2.44E+00 2.24E-02 2.06E-03 9.85E-04 1.38E-06 1.28E-06 7.89E-03 1.81E-04 1.26E-03 1.11E-06 4.10E-06 2.93E+00 2.30E-02 2.13E-03 1.01E-03 1.78E-06 1.65E-06 8.09E-03 1.87E-04 1.29E-03 1.42E-06 5.27E-06 3.42E+00 2.32E-02 2.16E-03 1.02E-03 2.17E-06 2.01E-06 8.18E-03 1.91E-04 1.31E-03 1.74E-06 6.45E-06 3.91E+00 2.33E-02 2.18E-03 1.02E-03 2.56E-06 2.38E-06 8.20E-03 1.92E-04 1.31E-03 2.05E-06 7.62E-06 4.39E+00 2.32E-02 2.19E-03 1.02E-03 2.95E-06 2.74E-06 8.17E-03 1.93E-04 1.30E-03 2.36E-06 8.77E-06 4.88E+00 2.31E-02 2.19E-03 1.01E-03 3.33E-06 3.10E-06 8.13E-03 1.93E-04 1.30E-03 2.66E-06 9.91E-06 5.37E+00a 2.29E-02 2.19E-03 1.00E-03 3.70E-06 3.44E-06 8.07E-03 1.93E-04 1.29E-03 2.96E-06 1.10E-05 

5.86E+00 2.27E-02 2.19E-03 9.95E-04 4.07E-06 3.78E-06 8.00E-03 1.93E-04 1.27E-03 3.25E-06 1.21E-05 6.35E+00 2.25E-02 2.18E-03 9.85E-04 4.42E-06 4.12E-06 7.92E-03 1.92E-04 1.26E-03 3.54E-06 1.32E-05 6.84E+00 2.23E-02 2.17E-03 9.74E-04 4.77E-06 4.44E-06 7.84E-03 1.91E-04 1.25E-03 3.82E-06 1.42E-05 7.32E+00 2.21E-02 2.17E-03 9.64E-04 5.11E-06 4.76E-06 7.76E-03 1.91E-04 1.23E-03 4.09E-06 1.52E-05 7.81E+00 2.18E-02 2.16E-03 9.53E-04 5.44E-06 5.07E-06 7.68E-03 1.90E-04 1.22E-03 4.36E-06 1.62E-05 8.30E+00 2.16E-02 2.15E-03 9.43E-04 5.77E-06 5.37E-06 7.60E-03 1.89E-04 1.21E-03 4.62E-06 1.72E-05 

a The calculations for the highlighted time step are shown in Figure 5-23. 
5-49 

Figure 5-20 Accumulation of Cs-137 in Meat from Spreadsheet Calculations 

and from RESRAD-OFFSITE Code 

Figure 5-21 Accumulation of Cs-137 in Milk from Spreadsheet Calculations and 

from RESRAD-OFFSITE Code 

0.00E+00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

1.00E-02

1.20E-02

1.40E-02

1.60E-02

0.00E+00 1.00E+01 2.00E+01 3.00E+01 4.00E+01 5.00E+01

Time, years

Meat concentration, pCi/kg

T otal Meat concentration

calculated

Meat concentration From

code

0.00E+00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

1.00E-02

1.20E-02

0.00E+00 1.00E+01 2.00E+01 3.00E+01 4.00E+01 5.00E+01

T ime, years

Milk concentration, pCi/L

T otal Milk concentration

calculated

Milk concentration From code
5-50 

Meat Concentration Calculations 

 

Meat concentration from pasture 

intake 

 

9.62E-03 ═ 0.03 × 14 × 2.29E-02 (Eq. 5.33) 

 

 

pCi/kg pCi/kg per pCi/d kg/d pCi/kg 

 

Meat concentration from grain intake 

 

3.55E-03 ═ 0.03 × 54 × 2.19E-03 (Eq. 5.33) 

 

 

pCi/kg pCi/kg per pCi/d kg/d pCi/kg 

 

Meat concentration from soil intake in pasture agricultural area 

 

1.03E-05 ═ 0.03 × 0.1 × 3.44E-03 (Eq. 5.33) 

 

 

pCi/kg pCi/kg per pCi/d kg/d pCi/kg 

 

Meat concentration from soil intake in grain agricultural area 

 

4.44E-05 ═ 0.03 × 0.4 × 3.70E-03 (Eq. 5.33) 

 

 

pCi/kg pCi/kg per pCi/d kg/d pCi/kg 

 

Meat concentration from water intake 

 

1.51E-03 ═ 0.03 × 50 × 1.00E-03 (Eq. 5.33) 

 

 

pCi/kg pCi/kg per pCi/d L/d pCi/kg 

 

Figure 5-22 Meat Concentration Calculations 

 

tm )(i

i imf p qing tp )(i

tm )(i

i imf p

ing q tp )(i

tm )(i

i imf

tm )(i

i imf

tm )(i

i imf

s qing

s qing

ts )( o

i

ts )( o

i

w

ing q tw )( if

i
5-51 

Milk Concentration Calculations 

 

Milk concentration from pasture intake 

8.07E-03 ═ 0.008 × 44 × 2.29E-02 (Eq. 5.33) 

 

 

pCi/kg pCi/kg per pCi/d kg/d pCi/kg 

 

Milk concentration from grain intake 

1.93E-04 ═ 0.008 × 11 × 2.19E-03 (Eq. 5.33) 

 

 

pCi/kg pCi/kg per pCi/d kg/d pCi/kg 

 

Milk concentration from soil intake in pasture agricultural 

area 

 

1.10E-05 ═ 0.008 × 0.4 × 3.44E-03 (Eq. 5.33) 

 

 

pCi/kg pCi/kg per pCi/d kg/d pCi/kg 

 

Milk concentration from soil intake in grain agricultural 

area 

 

2.96E-06 ═ 0.008 × 0.1 × 3.70E-03 (Eq. 5.33) 

 

 

pCi/kg pCi/kg per pCi/d kg/d pCi/kg 

 

Milk concentration from water intake 

1.29E-03 ═ 0.008 × 160 × 1.00E-03 (Eq. 5.33) 

 

 

pCi/kg pCi/kg per pCi/d L/d pCi/kg 

 

Figure 5-23 Milk Concentration Calculations 

 

tm )(i

i imf p qing tp )(i

tm )(i

i imf p qing tp )(i

tm )(i

i imf

tm )(i

i imf

tm )(i

i imf

s qing

s qing

ts )( o

i

ts )( o

i

w

ing q tw )( if

i
5-52 

Table 5-15 Spreadsheet Calculations for Co-60 Accumulation in Fish and Aquatic 

Foods

Time 

(year) 

Surface 

Water Conc. 

from Code 

(pCi/L) 

Fish Conc. 

Calculated 

(pCi/kg) 

Crustacea 

Conc. 

Calculated 

(pCi/kg) 

Fish Conc. 

from Code 

(pCi/kg) 

Crustacea 

Conc. from 

Code 

(pCi/kg) 

 

0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 

0.49 4.16E-04 1.25E-01 8.31E-02 1.25E-01 8.31E-02 

0.98 6.29E-04 1.89E-01 1.26E-01 1.89E-01 1.26E-01 

1.46a 7.27E-04 2.18E-01 1.45E-01 2.18E-01 1.45E-01 

1.95 7.61E-04 2.28E-01 1.52E-01 2.28E-01 1.52E-01 

2.44 7.59E-04 2.28E-01 1.52E-01 2.28E-01 1.52E-01 

2.93 7.38E-04 2.21E-01 1.48E-01 2.21E-01 1.48E-01 

3.42 7.07E-04 2.12E-01 1.41E-01 2.12E-01 1.41E-01 

3.91 6.72E-04 2.02E-01 1.34E-01 2.02E-01 1.34E-01 

4.39 6.35E-04 1.90E-01 1.27E-01 1.90E-01 1.27E-01 

4.88 5.98E-04 1.79E-01 1.20E-01 1.79E-01 1.20E-01 

5.37 5.63E-04 1.69E-01 1.13E-01 1.69E-01 1.13E-01 

5.86 5.29E-04 1.59E-01 1.06E-01 1.59E-01 1.06E-01 

6.35 4.96E-04 1.49E-01 9.93E-02 1.49E-01 9.93E-02 

6.84 4.66E-04 1.40E-01 9.31E-02 1.40E-01 9.31E-02 

7.32 4.37E-04 1.31E-01 8.74E-02 1.31E-01 8.74E-02 

7.81 4.10E-04 1.23E-01 8.20E-02 1.23E-01 8.20E-02 

8.30 3.84E-04 1.15E-01 7.69E-02 1.15E-01 7.69E-02 

8.79 3.60E-04 1.08E-01 7.21E-02 1.08E-01 7.21E-02 

9.28 3.38E-04 1.01E-01 6.76E-02 1.01E-01 6.76E-02 

9.77 3.17E-04 9.51E-02 6.34E-02 9.51E-02 6.34E-02 

10.25 2.97E-04 8.92E-02 5.94E-02 8.92E-02 5.94E-02 a

 The calculations for the highlighted time step are shown in Figure 5-24. 

 
5-53 

 

 Fish Concentration Calculations for Co-60 

 

 2.18E-01 ═ 300 × 7.27E-04 (Eq. 5.34) 

 

 

 (pCi/kg) pCi/kg per pCi/L pCi/L 

 Crustacea Concentration Calculations for Co-60 

 1.45E-01 ═ 200 × 7.27E-04 (Eq. 5.34) 

 

 

 (pCi/kg) pCi/kg per pCi/L pCi/L 

 

Figure 5-24 Fish and Aquatic Foods Concentration Calculations 

Figure 5-25 Accumulation of Co-60 in Fish from Spreadsheet Calculations and 

from RESRAD-OFFSITE Code 

0

0.05

0.1

0.15

0.2

0.25

0 2 4 6 8 10 12 14 16 18 20

Time, years

Fish concentration, pCi/kg

Fish conc. Calculated

Fish conc. From code

taqf )(i tw )( sw bafi i

taqf )(i tw )( sw bafi i
5-54 

Figure 5-26 Accumulation of Co-60 in Crustacea from Spreadsheet 

Calculations and from RESRAD-OFFSITE Code 

0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

1.40E-01

1.60E-01

0 2 4 6 8 10 12 14 16 18 20

Time, years

Crustacea concentration, pCi/kg

Crustacea conc. calculated

Crustacea conc. from code
6-1 

6.0 References 

BIOMOVS (Biosphere Model Validation Study) II, 1995, Long-Term Contaminant Migration and 

Impacts from Uranium Mill Tailings — Comparison of Computer Models Using a Hypothetical 

Dataset, BIOMOVS II Technical Report No. 4, Biosphere Model Validation Study Steering 

Committee, Swedish Radiation Protection Institute, Stockholm, Sweden. 

BIOMOVS II, 1996, Long-Term Contaminant Migration and Impacts from Uranium Mill Tailings 

— Comparison of Computer Models Using a Realistic Dataset, BIOMOVS II Technical Report 

No. 5, Biosphere Model Validation Study Steering Committee, Swedish Radiation Protection 

Institute, Stockholm, Sweden. 

Cheng, J.J., et al., 1995, Benchmarking Analysis of Three Multimedia Models: RESRAD, 

MMSOILS, and MEPAS, DOE/ORO-2033, U.S. Department of Energy, Washington, D.C. 

Gnanapragasam, E., and C. Yu, 1997, Analysis of BIOMOVS II Uranium Mill Tailings Scenario 

1.07 with the RESRAD Computer Code, ANL/EAD/TM-66, Argonne National Laboratory, 

Argonne, Ill. 

Gnanapragasam, E., et al., 2000, “Comparison of Multimedia Model Predictions for a 

Contaminant Plume Migration Scenario,” J. Contaminant Hydrology 46(1–2):17–38. 

Halliburton NUS (Halliburton NUS Corporation), 1994, Verification of RESRAD: A Code for 

Implementing Residual Radioactive Material Guidelines, Version 5.03, HNUS-ARPD-94-174, 

Gaithersburg, Md. 

Mills, W.B., et al., 1997, “Multimedia Benchmarking Analysis for Three Risk Assessment 

Models: RESRAD, MMSOILS, and MEPAS,” Risk Analysis 17(2):187–201. 

NREL (National Renewable Energy Laboratory), 2008, “Concentrating Solar Power Resource 

Maps,” Sept. Available at http://www.nrel.gov/csp/maps.html. Accessed July 1, 2009. 

Press, W.H., et al., 1992, Numerical Recipes in FORTRAN, The Art of Scientific Computing, 

Cambridge University Press, New York. 

Whelan, G., et al., 1999a, “Benchmarking of the Saturated-Zone Module Associated with Three 

Risk Assessment Models: RESRAD, MMSOILS, and MEPAS,” Environmental Engineering 

Science 16(1):67–80. 

Whelan, G., et al., 1999b, “Benchmarking of the Vadose-Zone Module Associated with Three 

Risk Assessment Models: RESRAD, MMSOILS, and MEPAS,” Environmental Engineering 

Science 16(1):81–91. 
6-2 

Yu, C., et al., 1993, Manual for Implementing Residual Radioactive Material Guidelines Using 

RESRAD, Version 5.0, ANL/EAD/LD-2, Argonne National Laboratory, Argonne, Ill. 

Yu, C., et al., 2000, Development of Probabilistic RESRAD 6.0 and RESRAD-Build 3.0 

Computer Codes, NUREG/CR-6697, ANL/EAD/TM-98, Argonne National Laboratory, Argonne, 

Ill., Nov. 

Yu, C., et al., 2001, User’s Manual for RESRAD Version 6, ANL/EAD-4, Argonne National 

Laboratory, Argonne, Ill. 

Yu, C., et al., 2003, User’s Manual for RESRAD-BUILD Version 3, ANL/EAD/03-1, Argonne 

National Laboratory, Argonne, Ill., June. 

Yu, C., et al., 2006, Benchmarking of RESRAD-OFFSITE: Transition from RESRAD (onsite) to 

RESRAD-OFFSITE and Comparison of RESRAD-OFFSITE Predictions with Peer Codes, 

ANL/EVS/TM/05-1, Argonne National Laboratory, Argonne, Ill., June. 

Yu, C., et al., 2007, User’s Manual for RESRAD-OFFSITE Version 2, ANL/EVS/TM/07-1, 

DOE/HS-0005, NUREG/CR-6937, DOE/HS-0005, Environmental Science Division, Argonne 

National Laboratory, Argonne, Ill., June. 
BIBLIOGRAPHIC DATA SHEET

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NUREG/CR-7038

November Verification of RESRAD-OFFSITE 2011

N6731

Technical C. Yu, E.K. Gnanapragasam, J.-J. Cheng, S. Kamboj, B.M. Biwer, and D.J. 

LePoire

12/08-10/10

Division of Risk Analysis 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555 

Argonne National Laboratory 

9700 South Cass Avenue 

Argonne, IL 60439-4832

This report documents the procedures used and the results obtained regarding the verification of the 

RESRAD-OFFSITE computer code. The RESRAD-OFFSITE code is an extension of the original RESRAD 

(onsite) code. The RESRAD-OFFSITE and RESRAD (onsite) codes share the same database and many models 

and modules. The RESRAD (onsite) code has already been extensively tested, verified, and validated. Many 

parameter values used in the RESRAD-OFFSITE code were taken from the RESRAD (onsite) database. These 

parameters include soil-plant transfer factors, meat and milk transfer factors, bioaccumulation factors, dose 

conversion factors, decay half-lives, and scenario-specific occupancy factors. The RESRAD (onsite) database is 

well documented and verified. Components of the RESRAD-OFFSITE code were verified by separately 

developed spreadsheets or benchmarked against the RESRAD (onsite) code. Independent verification was 

performed using calculations external to the RESRAD-OFFSITE code. Microsoft Excel spreadsheets were used 

to verify all the major portions of the RESRAD-OFFSITE code, including the source term model, groundwater 

transport model, air dispersion model, and accumulation in offsite soil and in food models.

RESRAD-OFFSITE, environmental transport, uptake, dose 


UNITED STATES 

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

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NUREG/CR-7038 Verification of RESRAD-OFFSITE November 2011