Synthesis of Distributions 

Representing Important 

Non-Site-Specific 

Parameters in Off-Site 

Consequence Analyses

Office of Nuclear Regulatory Research

NUREG/CR-7161

SAND2010-3380P
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Synthesis of Distributions 

Representing Important 

Non-Site-Specific 

Parameters in Off-Site 

Consequence Analyses

Manuscript Completed: October 2012

Date Published: April 2013

Prepared by: 

N. E. Bixler, E. Clauss, and C. W. Morrow

Sandia National Laboratories

Albuquerque, New Mexico 87185-0734

J. A. Mitchell, C. Navarro, J. Barr, NRC Project Managers 

NRC Job Codes N6159, Y6628, and V6227

Office of Nuclear Regulatory Research

NUREG/CR-7161

SAND2010-3380P

iii 

ABSTRACT 

The United States and the Commission of European Communities conducted a series of expert 

elicitations to obtain distributions for uncertain variables used in health consequence analyses 

related to accidental release of nuclear material. The distributions reflect degrees of belief for 

non-site-specific parameters that are uncertain and are likely to have significant or moderate 

influence on the results. The present work presents the effort to develop ranges of values and 

degrees of belief that fairly represent the divergent opinions of the experts while maintaining the 

resulting parameters within physical limits. Where necessary, there is a discussion of correlation 

coefficients that should be included when the uncertainty is used in a calculation. The 

methodology used a resampling of the experts' values and was based on the assumption of equal 

weights of the experts' opinions. Various statistical properties of the distributions, the median, 

the mean, and the mode, are presented so that the user can choose a parameter value when only a 

point estimate is desired. 

Paperwork Reduction Act Statement 

This NUREG/CR 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 requrest for 

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

current valid OMB control number. 

v 

TABLE OF CONTENTS 

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

EXECUTIVE SUMMARY ....................................................................................................... xix

ACKNOWLEDGMENTS ......................................................................................................... xxi

ACRONYMS AND INITIALISMS ........................................................................................ xxiii 

1.0 BACKGROUND .......................................................................................................... 1 

1.1 Methodology ....................................................................................................... 2 

2.0 EVALUATION OF DISPERSION DATA .................................................................. 7 

2.1 Distributions for Stability Class A/B ................................................................ 10 

2.1.1 Crosswind Dispersion ....................................................................... 11 

2.1.2 Vertical Dispersion ........................................................................... 16 

2.2 Distributions for Stability Class C .................................................................... 19 

2.2.1 Crosswind Dispersion ....................................................................... 19 

2.2.2 Vertical Dispersion ........................................................................... 23 

2.3 Distributions for Stability Class D .................................................................... 26 

2.3.1 Crosswind Dispersion ....................................................................... 26 

2.3.2 Vertical Dispersion ........................................................................... 30 

2.4 Distributions for Stability Class E/F ................................................................. 33 

2.4.1 Crosswind Dispersion ....................................................................... 33 

2.4.2 Vertical Dispersion ........................................................................... 37 

2.5 Comparisons with Tadmor and Gur Data ......................................................... 40 

2.6 Correlations Between the Dispersion Data ....................................................... 44 

3.0 DRY DEPOSITION .................................................................................................... 45 

3.1 Distributions of Dry Deposition Data ............................................................... 45 

3.2 Correlations Between Dry Deposition Data ..................................................... 66 

4.0 WET DEPOSITION .................................................................................................... 67 

4.1 Distributions of Wet-Deposition Data .............................................................. 67 

4.2 Correlations Between Wet Deposition Data ..................................................... 82 

5.0 LATENT HEALTH EFFECTS ................................................................................... 83 

5.1 Distributions of Risk Factors for Late Health Effects ...................................... 83 

5.2 Correlations Between Risk Factors for Late Health Effects ............................. 90 
vi 

6.0 EARLY HEALTH EFFECTS ...................................................................................... 91 

6.1 Distributions of Early Health Parameters ......................................................... 91 

6.2 Correlations Between Early Health Parameters ................................................ 97 

7.0 FOOD-CHAIN PARAMETERS ................................................................................. 99 

7.1 Distributions of Animal Feed Parameters ......................................................... 99 

7.2 Correlations Between Animal Feed Parameters ............................................. 109 

7.3 Distributions of Concentration Ratios ............................................................ 110 

7.4 Correlations Between Concentration Ratios ................................................... 113 

7.5 Distributions of Transfer Coefficients ............................................................ 113 

7.6 Correlations Between Transfer Coefficients ................................................... 120 

8.0 CONCLUSIONS ........................................................................................................ 121 

9.0 REFERENCES .......................................................................................................... 123 
vii

LIST OF FIGURES

Figure 1.1. Illustration of the evaluation of a PDF and mode (shown as a bright

pink square) of the distribution using m = 2, 4, 6, 8, and 10 in

Equation (1.1) .........................................................................................................6

Figure 2-1. Illustration of the functional dependence of on given

in Equation (2.4) .....................................................................................................9

Figure 2-2. Illustration of differences between crosswind dispersion in cartesian

and polar coordinate systems ................................................................................12

Figure 2-3. Expert and resampled data for  at 1 km downwind and 

Pasquill-Gifford stability class A/B ......................................................................13

Figure 2-4. Expert and resampled data for  at 3 km downwind and

Pasquill-Gifford stability class A/B ......................................................................13

Figure 2-5. Expert and resampled data for  at 10 km downwind and

Pasquill-Gifford stability class A/B ......................................................................14

Figure 2-6. Expert and resampled data for  at 30 km downwind and

Pasquill-Gifford stability class A/B ......................................................................14

Figure 2-7. Comparison of resampled expert data for  and

Pasquill-Gifford stability class A/B with the calculated values

using the parameters in Table 2-1 .........................................................................15

Figure 2-8. Comparison of resampled expert data for  and Pasquill-Gifford

stability class A/B with the calculated values using the parameters

in Table 2-1 ...........................................................................................................15

Figure 2-9. Expert and resampled data for z at 0.5 km downwind and

Pasquill-Gifford stability class A/B ......................................................................16

Figure 2-10. Expert and resampled data for z at 1 km downwind and

Pasquill-Gifford stability class A/B ......................................................................17

Figure 2-11. Expert and resampled data for z at 3 km downwind and

Pasquill-Gifford stability class A/B ......................................................................17

Figure 2-12. Comparison of resampled expert data for z and Pasquill-Gifford

stability class A/B with the calculated values using the parameters

in Table 2-1 ...........................................................................................................18

Figure 2-13. Comparison of resampled expert data for z and Pasquill-Gifford

stability class A/B with the calculated values using the parameters

in Table 2-1 ...........................................................................................................18

Figure 2-14. Expert and resampled data for  at 1 km downwind and

Pasquill-Gifford stability class C ..........................................................................20

Figure 2-15. Expert and resampled data for  at 3 km downwind and

Pasquill-Gifford stability class C ..........................................................................20

Figure 2-16. Expert and resampled data for  at 10 km downwind and

Pasquill-Gifford stability class C ..........................................................................21

Figure 2-17. Expert and resampled data for  at 30 km downwind and

Pasquill-Gifford stability class C ..........................................................................21

z CL  z
viii

LIST OF FIGURES (continued)

Figure 2-18. Comparison of resampled expert data for  and Pasquill-Gifford

stability class C with the calculated values using the parameters

in Table 2-2 ...........................................................................................................22

Figure 2-19. Comparison of resampled expert data for  and Pasquill-Gifford

stability class C with the calculated values using the parameters

in Table 2-2 ...........................................................................................................22

Figure 2-20. Expert and resampled data for z at 0.5 km downwind and

Pasquill-Gifford stability class C ..........................................................................23

Figure 2-21. Expert and resampled data for z at 1 km downwind and

Pasquill-Gifford stability class C ..........................................................................24

Figure 2-22. Expert and resampled data for z at 3 km downwind and

Pasquill-Gifford stability class C ..........................................................................24

Figure 2-23. Comparison of resampled expert data for z and Pasquill-Gifford

stability class C with the calculated values using the parameters

in Table 2-2 ...........................................................................................................25

Figure 2-24. Comparison of resampled expert data for z and Pasquill-Gifford

stability class C with the calculated values using the parameters

in Table 2-2 ...........................................................................................................25

Figure 2-25. Expert and resampled data for  at 1 km downwind and

Pasquill-Gifford stability class D ..........................................................................27

Figure 2-26. Expert and resampled data for  at 3 km downwind and

Pasquill-Gifford stability class D ..........................................................................27

Figure 2-27. Expert and resampled data for  at 10 km downwind and

Pasquill-Gifford stability class D ..........................................................................28

Figure 2-28. Expert and resampled data for  at 30 km downwind and

Pasquill-Gifford stability class D ..........................................................................28

Figure 2-29. Comparison of resampled expert data for  and Pasquill-Gifford

stability class D with the calculated values using the parameters

in Table 2-3 ...........................................................................................................29

Figure 2-30. Comparison of resampled expert data for  and Pasquill-Gifford

stability class D with the calculated values using the parameters

in Table 2-3 ...........................................................................................................29

Figure 2-31. Expert and resampled data for z at 0.5 km downwind and

Pasquill-Gifford stability class D ..........................................................................30

Figure 2-32. Expert and resampled data for z at 1 km downwind and

Pasquill-Gifford stability class D ..........................................................................31

Figure 2-33. Expert and resampled data for z at 3 km downwind and

Pasquill-Gifford stability class D ..........................................................................31

Figure 2-34. Comparison of resampled expert data for z and Pasquill-Gifford

stability class D with the calculated values using the parameters

in Table 2-3 ...........................................................................................................32
ix

LIST OF FIGURES (continued)

Figure 2-35. Comparison of resampled expert data for z and Pasquill-Gifford

stability class D with the calculated values using the parameters

in Table 2-3 ...........................................................................................................32

Figure 2-36. Expert and resampled data for  at 1 km downwind and

Pasquill-Gifford stability class E/F .......................................................................34

Figure 2-37. Expert and resampled data for  at 3 km downwind and

Pasquill-Gifford stability class E/F .......................................................................34

Figure 2-38. Expert and resampled data for  at 10 km downwind and

Pasquill-Gifford stability class E/F .......................................................................35

Figure 2-39. Expert and resampled data for  at 30 km downwind and

Pasquill-Gifford stability class E/F .......................................................................35

Figure 2-40. Comparison of resampled expert data for  and Pasquill-Gifford

stability class E/F with the calculated values using the parameters

in Table 2-4 ...........................................................................................................36

Figure 2-41. Comparison of resampled expert data for  and Pasquill-Gifford

stability class E/F with the calculated values using the parameters

in Table 2-4 ...........................................................................................................36

Figure 2-42. Expert and resampled data for z at 0.5 km downwind and

Pasquill-Gifford stability class E/F .......................................................................37

Figure 2-43. Expert and resampled data for z at 1 km downwind and

Pasquill-Gifford stability class E/F .......................................................................38

Figure 2-44. Expert and resampled data for z at 3 km downwind and

Pasquill-Gifford stability class E/F .......................................................................38

Figure 2-45. Comparison of resampled expert data for z and Pasquill-Gifford

stability class E/F with the calculated values using the parameters

in Table 2-4 ...........................................................................................................39

Figure 2-46. Comparison of resampled expert data for z and Pasquill-Gifford

stability class E/F with the calculated values using the parameters

in Table 2-4 ...........................................................................................................39

Figure 2-47. Comparison between the Tadmor and Gur crosswind dispersion data

and the processed expert data for the eleven quantile values given in

Table 2-1 for stability classes A and B .................................................................40

Figure 2-48. Comparison between the Tadmor and Gur vertical dispersion data

and the processed expert data for the eleven quantile values given in

Table 2-1 for stability classes A and B .................................................................41

Figure 2-49. Comparison between the Tadmor and Gur crosswind dispersion data

and the processed expert data for the eleven quantile values given in

Table 2-2 for stability class C ...............................................................................41

Figure 2-50. Comparison between the Tadmor and Gur vertical dispersion data

and the processed expert data for the eleven quantile values given in

Table 2-2 for stability class C ...............................................................................42
x

LIST OF FIGURES (continued)

Figure 2-51. Comparison between the Tadmor and Gur crosswind dispersion data

and the processed expert data for the eleven quantile values given in

Table 2-3 for stability class D ...............................................................................42

Figure 2-52. Comparison between the Tadmor and Gur vertical dispersion data

and the processed expert data for the eleven quantile values given in

Table 2-3 for stability class D ...............................................................................43

Figure 2-53. Comparison between the Tadmor and Gur crosswind dispersion data

and the processed expert data for the eleven quantile values given in

Table 2-4 for stability classes E and F ..................................................................43

Figure 2-54. Comparison between the Tadmor and Gur vertical dispersion data

and the processed expert data for the eleven quantile values given

in Table 2-4 for stability classes E and F ..............................................................44

Figure 3-1. Expert and resampled data for deposition velocity corresponding to

0.1 m particles over an urban terrain and a wind speed of 2 m/s .......................48

Figure 3-2. Expert and resampled data for deposition velocity corresponding to

0.1 m particles over an urban terrain and a wind speed of 5 m/s .......................48

Figure 3-3. Expert and resampled data for deposition velocity corresponding to

0.3 m particles over an urban terrain and a wind speed of 2 m/s .......................49

Figure 3-4. Expert and resampled data for deposition velocity corresponding to

0.3 m particles over an urban terrain and a wind speed of 5 m/s .......................49

Figure 3-5. Expert and resampled data for deposition velocity corresponding to

1 m particles over an urban terrain and a wind speed of 2 m/s ..........................50

Figure 3-6. Expert and resampled data for deposition velocity corresponding to

1 m particles over an urban terrain and a wind speed of 5 m/s ..........................50

Figure 3-7. Expert and resampled data for deposition velocity corresponding to

3 m particles over an urban terrain and a wind speed of 2 m/s ..........................51

Figure 3-8. Expert and resampled data for deposition velocity corresponding to

3 m particles over an urban terrain and a wind speed of 5 m/s ..........................51

Figure 3-9. Expert and resampled data for deposition velocity corresponding to

10 m particles over an urban terrain and a wind speed of 2 m/s ........................52

Figure 3-10. Expert and resampled data for deposition velocity corresponding to

10 m particles over an urban terrain and a wind speed of 5 m/s ........................52

Figure 3-11. Expert and resampled data for deposition velocity corresponding to

0.1 m particles over a meadow and a wind speed of 2 m/s ................................53

Figure 3-12. Expert and resampled data for deposition velocity corresponding to

0.1 m particles over a meadow and a wind speed of 5 m/s ................................53

Figure 3-13. Expert and resampled data for deposition velocity corresponding to

0.3 m particles over a meadow and a wind speed of 2 m/s ................................54

Figure 3-14. Expert and resampled data for deposition velocity corresponding to

0.3 m particles over a meadow and a wind speed of 5 m/s ................................54

Figure 3-15. Expert and resampled data for deposition velocity corresponding to

1 m particles over a meadow and a wind speed of 2 m/s ...................................55
xi

LIST OF FIGURES (continued)

Figure 3-16. Expert and resampled data for deposition velocity corresponding to

1 m particles over a meadow and a wind speed of 5 m/s ...................................55

Figure 3-17. Expert and resampled data for deposition velocity corresponding to

3 m particles over a meadow and a wind speed of 2 m/s ...................................56

Figure 3-18. Expert and resampled data for deposition velocity corresponding to

3 m particles over a meadow and a wind speed of 5 m/s ...................................56

Figure 3-19. Expert and resampled data for deposition velocity corresponding to

10 m particles over a meadow and a wind speed of 2 m/s .................................57

Figure 3-20. Expert and resampled data for deposition velocity corresponding to

10 m particles over a meadow and a wind speed of 5 m/s .................................57

Figure 3-21. Expert and resampled data for deposition velocity corresponding to

0.1 m particles over a forrest and a wind speed of 2 m/s ...................................58

Figure 3-22. Expert and resampled data for deposition velocity corresponding to

0.1 m particles over a forrest and a wind speed of 5 m/s ...................................58

Figure 3-23. Expert and resampled data for deposition velocity corresponding to

0.3 m particles over a forrest and a wind speed of 2 m/s ...................................59

Figure 3-24. Expert and resampled data for deposition velocity corresponding to

0.3 m particles over a forrest and a wind speed of 5 m/s ...................................59

Figure 3-25. Expert and resampled data for deposition velocity corresponding to

1 m particles over a forrest and a wind speed of 2 m/s ......................................60

Figure 3-26. Expert and resampled data for deposition velocity corresponding to

1 m particles over a forrest and a wind speed of 5 m/s ......................................60

Figure 3-27. Expert and resampled data for deposition velocity corresponding to

3 m particles over a forrest and a wind speed of 2 m/s ......................................61

Figure 3-28. Expert and resampled data for deposition velocity corresponding to

3 m particles over a forrest and a wind speed of 5 m/s ......................................61

Figure 3-29. Expert and resampled data for deposition velocity corresponding to

10 m particles over a forrest and a wind speed of 2 m/s ....................................62

Figure 3-30. Expert and resampled data for deposition velocity corresponding to

10 m particles over a forrest and a wind speed of 5 m/s ....................................62

Figure 3-31. Comparison of resampled expert data for dry deposition velocity

over urban terrain and wind speed of 2 m/s with the calculated values

using the parameters in Table 3-1 .........................................................................63

Figure 3-32. Comparison of resampled expert data for dry deposition velocity

over urban terrain and wind speed of 5 m/s with the calculated values

using the parameters in Table 3-1 .........................................................................63

Figure 3-33. Comparison of resampled expert data for dry deposition velocity

over meadow and wind speed of 2 m/s with the calculated values

using the parameters in Table 3-1 .........................................................................64

Figure 3-34. Comparison of resampled expert data for dry deposition velocity

over meadow and wind speed of 5 m/s with the calculated values

using the parameters in Table 3-1 .........................................................................64
xii

LIST OF FIGURES (continued)

Figure 3-35. Comparison of resampled expert data for dry deposition velocity

over forrest and wind speed of 2 m/s with the calculated values using

the parameters in Table 3-1 ..................................................................................65

Figure 3-36. Comparison of resampled expert data for dry deposition velocity

over forrest and wind speed of 5 m/s with the calculated values using

the parameters in Table 3-1 ..................................................................................65

Figure 4-1. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 0.1 m particles and a rainfall intensity of 0.3 mm/hr ..............70

Figure 4-2. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 0.1 m particles and a rainfall intensity of 2 mm/hr .................70

Figure 4-3. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 0.1 m particles and a rainfall intensity

of 0.05 mm/10 min ................................................................................................71

Figure 4-4. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 0.1 m particles and a rainfall intensity

of 0.33 mm/10 min ................................................................................................71

Figure 4-5. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 0.1 m particles and a rainfall intensity

of 1.67 mm/10 min ................................................................................................72

Figure 4-6. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 0.3 m particles and a rainfall intensity of 0.3 mm/hr ..............72

Figure 4-7. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 0.3 m particles and a rainfall intensity of 2 mm/hr .................73

Figure 4-8. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 0.3 m particles and a rainfall intensity

of 0.05 mm/10 min ................................................................................................73

Figure 4-9. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 0.3 m particles and a rainfall intensity

of 0.33 mm/10 min ................................................................................................74

Figure 4-10. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 0.3 m particles and a rainfall intensity

of 1.67 mm/10 min ................................................................................................74

Figure 4-11. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 1 m particles and a rainfall intensity of 0.3 mm/hr .................75

Figure 4-12. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 1 m particles and a rainfall intensity of 2 mm/hr ....................75

Figure 4-13. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 1 m particles and a rainfall intensity

of 0.05 mm/10 min ................................................................................................76

Figure 4-14. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 1 m particles and a rainfall intensity

of 0.33 mm/10 min ................................................................................................76
xiii

LIST OF FIGURES (continued)

Figure 4-15. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 1 m particles and a rainfall intensity

of 1.67 mm/10 min ................................................................................................77

Figure 4-16. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 10 m particles and a rainfall intensity of 0.3 mm/hr ...............77

Figure 4-17. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 10 m particles and a rainfall intensity of 2 mm/hr ..................78

Figure 4-18. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 10 m particles and a rainfall intensity

of 0.05 mm/10 min ................................................................................................78

Figure 4-19. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 10 m particles and a rainfall intensity

of 0.33 mm/10 min ................................................................................................79

Figure 4-20. Expert and resampled data for wet deposition rate (R in units of s-1)

corresponding to 10 m particles and a rainfall intensity

of 1.67 mm/10 min ................................................................................................79

Figure 4-21. Correlated values (fit) and resampled expert data for removal rate

at a rainfall intensity of 0.3 mm/hr as a function of particle size .........................80

Figure 4-22. Correlated values (fit) and resampled expert data for removal rate

at a rainfall intensity of 2 mm/hr as a function of particle size ............................80

Figure 4-23. Correlated values (fit) and resampled expert data for removal rate

at a rainfall intensity of 0.05 mm/10 min as a function of particle size ................81

Figure 4-24. Correlated values (fit) and resampled expert data for removal rate

at a rainfall intensity of 0.33 mm/10 min as a function of particle size ................81

Figure 4-25. Correlated values (fit) and resampled expert data for removal rate

at a rainfall intensity of 1.67 mm/10 min as a function of particle size ................82

Figure 5-1. Expert and resampled data for the risk factor for a bone cancer

fatality to a person receiving 1 Gy low-LET radiation over 1 min .......................84

Figure 5-2. Expert and resampled data for the risk factor for a colon cancer

fatality to a person receiving 1 Gy low-LET radiation over 1 min .......................84

Figure 5-3. Expert and resampled data for the risk factor for a breast cancer

fatality to a person receiving 1 Gy low-LET radiation over 1 min .......................85

Figure 5-4. Expert and resampled data for the risk factor for a leukemia fatality

to a person receiving 1 Gy low-LET radiation over 1 min ...................................85

Figure 5-5. Expert and resampled data for the risk factor for a liver cancer

fatality to a person receiving 1 Gy low-LET radiation over 1 min .......................86

Figure 5-6. Expert and resampled data for the risk factor for a lung cancer

fatality to a person receiving 1 Gy low-LET radiation over 1 min .......................86

Figure 5-7. Expert (excluding values of zero) and resampled data for the risk

factor for a pancreas cancer fatality to a person receiving 1 Gy

low-LET radiation over 1 min ...............................................................................87
xiv

LIST OF FIGURES (continued)

Figure 5-8. Expert and resampled data for the risk factor for a skin cancer

fatality to a person receiving 1 Gy low-LET radiation over 1 min .......................87

Figure 5-9. Expert and resampled data for the risk factor for a stomach cancer

fatality to a person receiving 1 Gy low-LET radiation over 1 min .......................88

Figure 5-10. Expert and resampled data for the risk factor for a thyroid cancer

fatality to a person receiving 1 Gy low-LET radiation over 1 min .......................88

Figure 5-11. Expert and resampled data for the risk factor for other cancer

fatality to a person receiving 1 Gy low-LET radiation over 1 min .......................89

Figure 5-12. Expert and resampled data for the risk factor for all cancer

fatalities to a person receiving 1 Gy low-LET radiation over 1 min ....................89

Figure 6-1. Expert and resampled data for the threshold dose corresponding

to hematopoietic syndrome for a person receiving 100 Gy/hr

low-LET radiation to the whole body....................................................................93

Figure 6-2. Expert and resampled data for LD50 corresponding to hematopoietic

syndrome for a person receiving 100 Gy/hr low-LET radiation to

the whole body ......................................................................................................93

Figure 6-3. Expert and resampled data for the threshold dose corresponding

to gastrointestinal syndrome for a person receiving 100 Gy/hr

low-LET radiation to the whole body....................................................................94

Figure 6-4. Expert and resampled data for LD50 corresponding to gastrointestinal

syndrome for a person receiving 100 Gy/hr low-LET radiation to

the whole body ......................................................................................................94

Figure 6-5. Expert and resampled data for the threshold dose corresponding

to pulmonary syndrome for a person receiving 1 Gy/hr beta radiation

to the lungs ............................................................................................................95

Figure 6-6. Expert and resampled data for LD50 corresponding to pulmonary

syndrome for a person receiving 1 Gy/hr beta radiation to the lungs ...................95

Figure 6-7. Expert and resampled data for the threshold dose corresponding to

pneumonitis for a person receiving 1 Gy/hr beta radiation to the lungs ...............96

Figure 6-8. Expert and resampled data for D50 corresponding to pneumonitis

for a person receiving 1 Gy/hr beta radiation to the lungs ....................................96

Figure 7-1. Expert and resampled data for consumption rate

(kg/day on a dry basis) of pasture grass by dairy cattle ......................................102

Figure 7-2. Expert and resampled data for consumption rate

(kg/day on a dry basis) of silage/hay by dairy cattle ..........................................102

Figure 7-3. Expert and resampled data for consumption rate

(kg/day on a dry basis) of cereals by dairy cattle ...............................................103

Figure 7-4. Expert and resampled data for consumption rate

(kg/day on a dry basis) of soil by dairy and beef cattle ......................................103

Figure 7-5. Expert and resampled data for consumption rate

(kg/day on a dry basis) of pasture grass by beef cattle .......................................104
xv

LIST OF FIGURES (continued)

Figure 7-6. Expert and resampled data for consumption rate

(kg/day on a dry basis) of silage/hay by beef cattle ............................................104

Figure 7-7. Expert and resampled data for consumption rate

(kg/day on a dry basis) of cereals by beef cattle .................................................105

Figure 7-8. Expert and resampled data for consumption rate

(kg/day on a dry basis) of pasture grass by sheep ...............................................105

Figure 7-9. Expert and resampled data for consumption rate

(kg/day on a dry basis) of silage/hay by sheep ...................................................106

Figure 7-10. Expert and resampled data for consumption rate

(kg/day on a dry basis) of cereals by sheep ........................................................106

Figure 7-11. Expert and resampled data for consumption rate

(kg/day on a dry basis) of soil by sheep ..............................................................107

Figure 7-12. Expert and resampled data for consumption rate

(kg/day on a dry basis) of cereal by pigs ............................................................107

Figure 7-13. Expert and resampled data for consumption rate

(kg/day on a dry basis) of soil by pigs ................................................................108

Figure 7-14. Expert and resampled data for consumption rate

(kg/day on a dry basis) of cereal by poultry .......................................................108

Figure 7-15. Expert and resampled data for consumption rate

(kg/day on a dry basis) of soil by poultry ...........................................................109

Figure 7-16. Expert and resampled data for grain to soil concentration ratio

(Bq/kg Fresh Plant Mass / Bq/kg Dry Soil Mass) for Sr ....................................111

Figure 7-17. Expert and resampled data for grain to soil concentration ratio

(Bq/kg Fresh Plant Mass / Bq/kg Dry Soil Mass) for Cs ....................................112

Figure 7-18. Expert and resampled data for root to soil concentration ratio

(Bq/kg Fresh Plant Mass / Bq/kg Dry Soil Mass) for Sr ....................................112

Figure 7-19. Expert and resampled data for root to soil concentration ratio

(Bq/kg Fresh Plant Mass / Bq/kg Dry Soil Mass) for Cs ....................................113

Figure 7-20. Expert and resampled data for beef transfer coefficient

at steady state (Bq/kg / Bq/d) for strontium ........................................................115

Figure 7-21. Expert and resampled data for beef transfer coefficient

at steady state (Bq/kg / Bq/d) for cesium ............................................................115

Figure 7-22. Expert and resampled data for milk transfer coefficient

at steady state (Bq/l / Bq/d) for strontium ..........................................................116

Figure 7-23. Expert and resampled data for milk transfer coefficient

at steady state (Bq/l / Bq/d) for cesium ...............................................................116

Figure 7-24. Expert and resampled data for milk transfer coefficient

at steady state (Bq/l / Bq/d) for iodine ...............................................................117

Figure 7-25. Expert and resampled data for poultry transfer coefficient

at steady state (Bq/kg / Bq/d) for strontium ........................................................117

Figure 7-26. Expert and resampled data for poultry transfer coefficient

at steady state (Bq/kg / Bq/d) for cesium ...........................................................118
xvi

LIST OF FIGURES (continued)

Figure 7-27. Expert and resampled data for egg transfer coefficient

at steady state (Bq/kg / Bq/d) for strontium ........................................................118

Figure 7-28. Expert and resampled data for egg transfer coefficient

at steady state (Bq/kg / Bq/d) for cesium ...........................................................119

Figure 7-29. Expert and resampled data for egg transfer coefficient

at steady state (Bq/kg / Bq/d) for iodine .............................................................119
xvii

LIST OF TABLES

Table 1-1: Resampled data for two experts. .............................................................................4

Table 1-2: Example of merged and sorted data and estimation of mode. ................................4

Table 2-1: Values for cross-wind and vertical dispersion coefficients for

Pasquill-Gifford stability class A/B. .....................................................................10

Table 2-2: Values for cross-wind and vertical dispersion coefficients for

Pasquill-Gifford stability class C. .........................................................................19

Table 2-3: Values for cross-wind and vertical dispersion coefficients for

Pasquill-Gifford stability class D. .........................................................................26

Table 2-4: Values for cross-wind and vertical dispersion coefficients for

Pasquill-Gifford stability class E/F. ......................................................................33

Table 3-1: Values of regression coefficients in Equation (3.1) for dry

deposition velocity. ..............................................................................................46

Table 3-2: Values of dry deposition velocity in cm/s for z0 = 10 cm, v = 5 m/s. ...................47

Table 4-1: Values for the wet deposition coefficients in Equation (4.1) for

1 m particles. .......................................................................................................68

Table 4-2: Values of regression coefficients in Equation (4.2) for the

wet deposition coefficient C1. ...............................................................................69

Table 5-1: Risk factors for latent cancer fatalities. ................................................................83

Table 6-1: Coefficients for quantifying early health effects. .................................................92

Table 7-1: Daily consumption by beef and dairy cattle. ......................................................100

Table 7-2: Daily consumption by sheep, pigs, and poultry. .................................................101

Table 7-3: Ratio of concentration in foodstuff to concentration in soil (Bq/kg

fresh plant mass / Bq/kg dry soil mass). .............................................................110

Table 7-4: Ratio of concentration in foodstuff to daily ingestion level. ..............................114

xix

EXECUTIVE SUMMARY

The U.S. Nuclear Regulatory Commission (NRC) developed the MELCOR Accident 

Consequence Code System, Version 2, (MACCS2) specifically to evaluate offsite consequences 

from a hypothetical release of radioactive material into the atmosphere. The code models 

atmospheric transport and dispersion, emergency response actions, exposure pathways, health 

effects, and economic costs. There are a large number of input parameters required for the 

MACCS2 code, some of which have a range of possible values and varying level of uncertainty. 

This document presents distributions developed to provide analysts using MACCS2 guidance on 

the most appropriate values to use for these parameters.

The NRC and the Commission of European Communities (CEC) conducted a series of studies with 

panels of experts from the United States and the CEC (References 1 through 6). During those 

studies, the experts were asked to provide their own ranges of values and degrees of belief for a 

large number of input parameters used in offsite consequence codes. The parameters were those 

that the authors of the studies decided were (1) uncertain in value, (2) likely to be significant or 

moderate in their influence on the calculated results, and (3) applicable to all sites (that is, not sitespecific). 

The present study, performed by Sandia National Laboratories, uses the results of the previous 

studies by combining the varying expert opinions of each parameter to form a single distribution 

for each parameter. The distribution for each parameter is developed in a way that fairly represents 

the experts' divergent opinions while maintaining the parameter within physical limits. A 

resampling method was used with equal weight assigned to each expert. These distributions 

provide guidance to analysts using the MACCS2 code regarding the input values that should be 

used for these parameters.

In several cases, correlation coefficients are necessary to maintain physical relationships among 

groups of parameters when the full distribution is used in an uncertainty study. The suggested 

correlation coefficients, where necessary, are discussed at the end of each section. 

Different offsite consequence measures (e.g., early fatality risk, latent cancer fatality risk, or costs) 

are dependent in different ways on the input parameters evaluated. For use in consequence 

analyses in which only a point estimate is desired, the medians, means, and modes of the 

distributions are provided to allow the user to select an appropriate value. If results at one or more 

specific quantile levels are desired, it is preferable to conduct an uncertainty study in which all of 

the relevant parameters are sampled over their entire distributions and the results are evaluated at 

each of the appropriate quantile levels. MACCS2, and its graphical user interface and 

preprocessor, WinMACCS, have been tailored to perform such evaluations. 

xxi

ACKNOWLEDGMENTS

The authors thank Jocelyn Mitchell for initiating and supporting this work, for offering guidance 

as the work progressed, and for providing valuable comments on the contents of this report. We 

deeply regret that she was not able to see the completion of this work. 

xxiii

ACRONYMS AND INITIALISMS

CDF Cumulative Distribution Function

CEC Commission of European Communities

COSYMA COde SYstem from MAria

D50 Dose at which 50% of the public experience a health effect

EC European Commission

LD50 Lethal Dose for 50% of the public

LHS Latin Hypercube Sampling

MACCS2 MELCOR Accident Consequence Code System, Version 2

NRC U.S. Nuclear Regulatory Commission

PDF Probability Distribution Function

RSM ReSampling Method

SOARCA State-of-the-Art Reactor Consequence Analyses project

1

1.0 BACKGROUND

An expert elicitation was conducted jointly by the United States Nuclear Regulatory Commission

(NRC) and the Commission of the European Communities (CEC) to obtain distributions for

uncertain variables used in health consequence analyses related to accidental release of nuclear

materials into the atmosphere. The distributions reflect degrees of belief for parameters that are

uncertain and are likely to be significant or moderate in their influence on the calculated results.

The results of the elicitation are given in References 1through 6. The references explain that the

approach was jointly formulated and was based on two important ground rules: (1) the current

code models would not be changed because both the NRC and European Commission (EC) were

interested in the uncertainties in the predictions produced by MACCS (the NRC's off-site consequence code) [Reference 7] and the Code System from Maria (COSYMA) (the EC's off-site consequence code), respectively, and (2) the experts would be asked only to assess physical quantities

that hypothetically could be measured in experiments. The reasons for these ground rules are that

(1) the codes have already been developed and applied in the US and the EC risk assessments, and

(2) eliciting physical quantities avoids ambiguity in definitions of variables; more important, the

physical quantities elicited are not tied to any particular model, and thus have a much wider

potential application. The study involved several phases: preparation stage, expert training meetings, preparation of the assessments and written rationale, expert elicitation sessions, and processing of the elicited results. The values elicited from each of the experts for each of the parameters

are given in the references. 

This present work represents the effort to develop ranges of values and degrees of belief that fairly

represent the divergent opinions of the experts, while maintaining the resulting parameters within

physical limits. The development is performed specifically with the MACCS2 code in mind; only

the set of parameters that can be used as MACCS2 input parameters is evaluated in this report.

The purpose for this work is to facilitate a more comprehensive evaluation of uncertainty in future

consequence analyses. Typically, evaluation of uncertainty in consequence analysis has been limited to the influence of weather, a type of aleatory uncertainty, but has not been extended to other

input parameters that are not well quantified. The purpose of this report is to assimilate distributions for important parameters that are site independent and are not well quantified so that future

consequence analyses can more thoroughly assess the inherent uncertainty, both from weather and

from other sources of uncertainty related to lack of knowledge. Specifically, the distributions

developed in this report are intended to be used in the State-of-the-Art Reactor Consequence

Analysis (SOARCA) uncertainty analysis, which is being performed by Sandia National Laboratories for the NRC.

Within each of References 1 through 6, each expert who participated in the process is assigned a

letter in order to preserve confidentiality. In most cases, a subset of the experts provided an opinion on a specific parameter. The relationship between the expert and the letter used to designate

that expert is preserved throughout the original documents. The same letter designations are used

in this report as well. Thus, the set of letters representing the experts’ opinions in Sections 2

through 7 of this report differ from plot to plot, depending on which subset of experts provided an

opinion on the parameter shown in the plot.
2

Some previous work has been done along the lines of the work presented here. Wheeler et al.

[Reference 8] evaluated the uncertainty of a set of parameters relevant to the safety analysis of the

Cassini Mission. This effort did not consider all of the parameters needed for consequence codes

like MACCS2 and only considered a few percentile levels (5%, 50%, and 95%). Furthermore, this

study did not attempt to provide correlations of input parameters, such as aerosol size, to the

uncertain outputs, such as deposition velocity. In these regards, the current study is more comprehensive than the one conducted by Wheeler et al. and should prove to have a broader range of

applicability.

1.1 Methodology

Some expert data were elicited for the following quantile values: 0.00, 0.05, 0.50, 0.95, and 1.00;

however, most expert data were only elicited for the 0.05, 0.50, and 0.95 quantiles. In this work,

we take each elicited opinion as being equally likely since we have no basis for considering the

opinion of one expert more credible than another. This means that each expert’s data are represented by an equal number of resampled points. While equal weighting seems straightforward on

the surface, it is somewhat more complicated than might be expected in cases where some experts

provided values for the 0.00 and 1.00 quantiles while other experts did not.

The initial concept for treating nonhomogeneous expert data was to normalize over quantile

ranges so that each quantile range would receive the same number of data points. This concept

results in more resampling points per expert for the extreme ranges, from 0.00 to 0.05 and 0.95 to

1.00, than for the intermediate range, 0.05 to 0.95, since only a small number of experts contributed values in the extreme ranges and most contributed values in the intermediate range. To illustrate this point, consider a case of eight experts providing values for the 0.05, 0.5, and 0.95

quantiles, but a subset of three providing values for the 0 and 1 quantile levels. If eight resample

points were evaluated for each of the three experts providing opinions in the ranges 0.00 to 0.05

and 0.95 to 1.00 and three resample points were chosen for each expert from 0.05 to 0.95, then the

result is that all quantile ranges are represented by the same density of resample points and all

experts are treated equally over ranges where they supplied data. However, the values of the three

experts have a greater weight in the extreme ranges.

While the initial concept seems like a very good one, it has one fatal shortcoming for the analysis

at hand. Only in the report on dispersion and deposition were the experts asked to provide 0.00

and 1.00 quantile values; in the other reports, the experts were not asked to provide these values.

In these cases, the initial resampling concept would only be able to produce distributions over the

0.05 to 0.95 quantile range, which is unacceptable because sampling algorithms (e.g., standard

Monte Carlo or Latin Hypercube Sampling (LHS)) require a complete probability distribution to

be defined. 

The second concept for treating nonhomogeneous expert data is to estimate the missing values

using some simple algorithm. The algorithm that was adopted was to divide the expert’s 0.05

quantile value by 2 to get the 0.00 quantile value and to multiply the expert’s 0.95 quantile value

by 2 to get the 1.00 quantile value. The factor of two was chosen because it approximately fit the

values for the experts who did provide the 0.00 and 1.00 quantile values. The second concept
3

seems a bit more arbitrary than the first concept; it was chosen here because it could be extended

to the evaluation of all the expert elicitation data.

A second choice that had to be made in order to perform the resampling is the type of interpolation to be used to represent the expert data. The choice here is the simplest one, linear interpolation. Once the resampled data are created, they are ordered and assigned a quantile value. This

process is illustrated in Tables 1-1 and 1-2 for a simplified example in which there are only two

experts. For some of the parameters, data at a given quantile level are fitted using linear regression to calculate the coefficients used to describe the overall trends. The results are provided in

the following sections.

In each of the subsequent sections, results are tabulated at a set of quantile levels: 0.00, 0.01, 0.05,

0.10, 0.25, 0.50, 0.75, 0.90, 0.95, 0.99, and 1.00. In addition, means and modes are included in the

tabulations. Means are computed simply as the arithmetic average of the set of resampled values.

Calculation of the modes is described below.

The mode corresponds to the peak in the probability distribution function (PDF). The PDF is the

derivative of the cumulative distribution function (CDF). Problems arise in the calculation of the

PDF and the determination of the mode when the CDF is not smooth. Some compromises must be

made to determine the PDF and its peak, the mode, in a reasonable fashion. This is illustrated in

the remainder of this section.

Table 1-2 shows an example of the method used to determine the mode of a distribution. The third

column shows the values used to determine the mode (i.e., the derivative of the CDF) which is

calculated using the following formula with m = 8:

(1.1)

where

n = a subscript representing the point being evaluated

m = an integer representing the number of points to be included in the difference

i = a dummy index

Mn,m = is a finite difference approximation to a derivative

Q = a quantile value

D = a resampled data point from the original expert data

The mode of the distribution shown in Table 1-2 corresponds to the peak value of M, which is

4.691. 

Mn m

Qn i + Qn i –   –

i = 1 m



Dn i + Dn i –   –

i = 1 m



= ---------------------------------------------------
4

Table 1-1: Resampled data for two 

experts.

Quantile

Expert

A B

0.0 4.300 3.784

0.1 4.477 4.520

0.2 4.522 4.606

0.3 4.566 4.691

0.4 4.611 4.776

0.5 4.657 4.862

0.6 4.729 4.953

0.7 4.792 5.033

0.8 4.865 5.124

0.9 4.937 5.215

1.0 5.667 5.954

Table 1-2: Example of merged and sorted 

data and estimation of mode.

Quantile (Q) Ordered Data (D) M

0.000 3.784

0.048 4.300

0.095 4.477

0.143 4.520

0.190 4.522

0.238 4.566

0.286 4.606

0.333 4.611

0.381 4.657 1.065

0.429 4.691 1.276

0.476 4.729 1.274

0.524 4.776 1.191

0.571 4.792 .0980

0.619 4.862 0.794

0.667 4.865

0.714 4.937

0.762 4.953

0.810 5.033

0.857 5.124

0.905 5.215

0.952 5.667

1.000 5.954
5

The summation in Equation (1.1) can be over a single point or over a large number of points, depending on the selection of the value of m. Few points provide large fluctuations in the value of M

due to noise in the data. A large number smooths the result but looses the local character of the data. After evaluating values of m from 2 to 10, m = 8 was selected for this work. 

The difficulties associated with finding the mode of a resampled distribution are illustrated in Figure 1.1 for crosswind dispersion under stability classes A and B. Because of the interpolation

scheme used to represent the few data points provided by each of the experts, the data used for

resampling have discontinuities in slope. When all of the experts’ data are assembled, the slope

has a number of peaks and valleys, as illustrated in the figure. 

When m = 2, the calculation of the slope is extremely noisy, as shown in the first plot in Figure

1.1. The bright pink square is the location of the tallest peak in the plot and would correspond to

the mode if this method were used to estimate the PDF. The second plot uses m = 4 and is clearly

much smoother than the one for m = 2, but still fairly noisy. Notice that the location of the mode in

this plot is dramatically different than in the plot for m = 2. The plot with m = 6 is smoother yet,

but produces an estimate for the mode that is identical to the previous plot. This trend continues

for m = 8 and m = 10. The estimated values of the mode are nearly the same, but not identical for

m = 4 through 10. 

A choice of either m = 8 or 10 would have provided reasonable estimates of the mode in the subsequent sections. The choice of m = 8 was selected after evaluating the experts’ data for a number

of parameters. This choice was used consistently throughout each of the subsequent sections.
6

Figure 1.1. Illustration of the evaluation of a PDF and mode (shown as a bright pink square) of

the distribution using m = 2, 4, 6, 8, and 10 in Equation (1.1)
7

2.0 EVALUATION OF DISPERSION DATA

MACCS2 allows two approaches for evaluating dispersion as a function of downwind distance.

The first, and probably the more widely used, is based on a lookup table provided by the user.

However, this approach is inconvenient for representing uncertain dispersion values. The second

approach is much more convenient for expressing degree of belief and uses power-law equations

for and , which are defined as follows:

(2.1)

(2.2)

where

= crosswind dispersion parameter (m)

= vertical dispersion parameter (m)

a = linear coefficient for crosswind dispersion (m)

c = linear coefficient for vertical dispersion (m)

x = downwind distance (m)

x0 = downwind distance scale, 1 m

b = exponential parameter for crosswind dispersion (dimensionless)

d = exponential parameter for vertical dispersion (dimensionless)

Here, distributions for a, b, c, and d are calculated to reflect the degree of belief expressed during

the expert elicitation process. The distributions are calculated for Pasquill-Gifford stability classes

A/B, C, D, and E/F. The basic methodology used to calculate the coefficients in Equations (2.1)

and (2.2) begins by resampling the expert data for each expert. 

A final difficulty with the expert data arose in evaluating the parameters associated with vertical

dispersion, c and d, because the experts were not asked to provide directly. Instead, the experts

were asked to provide the ratio of off-centerline to centerline concentrations. Standard equations

for a Gaussian plume, which assume reflective planes at the ground surface and at the mixing layer height, are used to calculate given concentration ratio for values between 0 and 1, not including the endpoints. The value of approaches 0 when the concentration ratio approaches 0

and it approaches infinity when the concentration ratio approaches 1. Values of this ratio greater

than 1 do not have any physical meaning in the context of a Gaussian plume model. 

The Gaussian plume equation is [Reference 9]:

(2.3)

y z

y a

x

x0

----     b

=

z c

x

x0

----     d

=

y

z

z

z

z



Q

---- 1

2yzu --------------------- 1

2

-- y

y

-----     2

– 1

2

-- 2nh H– – z

z

---------------------------     2

exp – 1

2

-- 2nh H z + –

z

----------------------------     2

+ exp –

n = –



= exp 
8

where

= concentration of released contaminant (kg/m3 or Bq/m3)

Q = source rate of released contaminant (kg/s or Bq/s)

u = wind speed at plume centerline (m/s)

n = a dummy index used for summation

y = crosswind distance from the plume centerline (m)

z = vertical distance from the ground (m)

h = height of the mixing layer (m), which is taken to be 1500 m

H = height of the plume centerline (m), which is given as 10 m

From Equation (2.3), the ratio of the concentration at a vertical elevation z to the centerline concentration is

(2.4)

Equation (2.4) is used to calculate values of given expert values of . This calculation

is done iteratively because of the highly nonlinear dependence on . 

Figure 2-1 shows the dependence of on when z = 60 m and H = 0 m. This figure

clearly depicts the difficulty of calculating given a value of close to unity. In fact,

there is no unique value of when is unity. The statement that is approximately unity (i.e., rounds to unity for some finite number of significant digits) implies that 

must be greater than or equal to some minimum value. For example, using the parameters chosen

to generate Figure 2-1, > 180 m if is 1.0, > 580 m if is 1.00, and >

1240 m if is 1.000.



z

CL

----------

1

2

-- 2nh H– – z

z

---------------------------     2

exp – 1

2

-- 2nh H z + –

z

----------------------------     2

+ exp –

–





1

2

-- 2nh – 2H

z

-----------------------     2

exp – 1

2

-- 2nh

z

---------     2

+ exp –

–





= ----------------------------------------------------------------------------------------------------------------------------------

z z CL 

z

z CL  z

z z CL 

z z CL  z CL 

z

z z CL  z z CL  z

z CL 
9

Figure 2-1. Illustration of the functional dependence of on given in Equation

(2.4)

Unfortunately, a significant number of the elicited values for were 1. Depending on the expert,

the elicited values were provided with 1, 2, or 3 significant digits. The most likely explanation for

concentration ratios of 1 is simply that, to the number of significant digits provided by the experts,

the number rounded to 1. As explained above, this corresponds only to a lower bound on the value

of . Even worse, a number of experts provided concentration ratios greater than 1. 

The approach adopted was to exclude data for if the expert provided concentration ratios

greater than 1 because such values are inadmissible with a Gaussian plume model. The choice of

which experts to include was done by stability class (i.e., an expert was excluded in the evaluation

of for a stability class if any of his values exceeded 1). Experts who provided values of 1 for

the concentration ratio were not excluded. Instead, a simple algorithm was adopted to estimate 

in these cases. If the concentration ratio of 1 corresponded to the 0.00 or 1.00 quantile, then the

factor-of-2 approach described above was used to fill in the value of . In other words, the value

assigned to at the 0.00 quantile was half the value of at the 0.05 quantile; the value assigned to at the 1.00 quantile was twice the value of at the 0.95 quantile. In several cases,

experts provided concentration ratios of 1 for the 0.95 quantile. In one case, an expert provided

values of 1 at all quantile levels. In general, values of 1 at the 0.95 quantile level were filled in by

scaling the 0.50 quantile value by 1.5, a value that seemed to fit the overall trend. The one case in

which an expert provided values of 1 at all quantile levels is discussed below in the section on the

A/B stability class.

0.0

0.2

0.4

0.6

0.8

1.0

0 200 400 600 800 1000

z (m)

zCL

z CL  z

z

z

z

z

z

z

z z

z z
10

Initially, an attempt was made to develop distributions for all four of the coefficients (a, b, c, and

d) in Equations (2.1) and (2.2). This turned out to generate distributions for b and d that were neither monotonically increasing nor decreasing with quantile level. This is permissible in principle

because the parameter combinations for (a,b) and (c,d) can lead to a monotonic distribution of

dispersion coefficients even if the correlations of b and d are not monotonic. However, since values of b and d must be sampled, the lack of montonicity is problematic. The simplest solution was

to force c and d to have a single value for each stability class. This treatment, although less general, produced correlations that agreed very well with the original data, as demonstrated below.

2.1 Distributions for Stability Class A/B

Table 2-1 provides values for a, b, c, and d from Equations (2.1) and (2.2) when the Pasquill-Gifford stability class is either A or B (here, the two classes are combined and referred to as A/B).

These values were calculated using linear regression to match the expert data as closely as possilbe. The figures in this section that show curves labeled “Fit” were generated using the parameter

values in this table. To interpolate values between the quantile levels provided in the table, it is

preferable to interpolate the logarithms of a and c linearly.

Table 2-1: Values for cross-wind and vertical dispersion coefficients for PasquillGifford stability class A/B.

Quantile

Crosswind Dispersion Parameters Vertical Dispersion Parameters

a (m) b 

(dimensionless) c (m) d (dimensionless)

0.00 0.0650 0.866 0.0056 1.277

0.01 0.1515 0.866 0.0089 1.277

0.05 0.2586 0.866 0.0132 1.277

0.10 0.3381 0.866 0.0166 1.277

0.25 0.4861 0.866 0.0252 1.277

0.50 0.7507 0.866 0.0361 1.277

0.75 1.1379 0.866 0.0598 1.277

0.90 1.6222 0.866 0.0800 1.277

0.95 2.0731 0.866 0.0961 1.277

0.99 3.2179 0.866 0.1336 1.277

1.00 4.0698 0.866 0.1951 1.277

Mean 0.7393 0.866 0.0370 1.277

Mode 0.6282 0.866 0.0401 1.277
11

2.1.1 Crosswind Dispersion

The crosswind dispersion values specified in the expert elicitation are in terms of . The

MACCS2 code, which uses a polar coordinate system, requires crosswind dispersion values in

terms of , which is expressed in units of distance along an arc at a specified radius rather than

along lines perpendicular to the wind direction. The physical picture is illustrated in Figure 2-2. In

the past, no distinction was made between and when defining the input parameters for

MACCS2 (i.e., was simply set equal to ). Not making this distinction is acceptable provided that crosswind dispersion, , is significantly less than the downwind distance, x; this distinction is important when crosswind dispersion is similar to downwind distance; it is crucial when

crosswind dispersion is significantly greater than downwind distance. Values of are converted

to values of as follows:

(2.5)

The angle in a polar coordinate system is , which from Equation (2.5) equals .

Equation (2.5) defines so that the point (x, /x) in a polar coordinate system lies on a straight

line from the origin to the point (x, ) in a cartesian coordinate system. Notice that the polar formulation is not identical to the original cartesian formulation. In fact, there is no simple way to

maintain consistency between the two coordinate systems. The scheme adopted is certainly preferable to simply setting the value of equal to . To see that this is so, imagine the case where

 is much greater than the downwind distance, x. In a cartesian coordinate system, the point (x,

) always lies downwind of the point of release (i.e., to the right of the y axis). In the polar coordinate system, the point (x, /x) would approach the y axis if is defined by Equation (2.5);

on the other hand, the point (x, /x) in a polar coordinate system could lie anywhere on a circle

of radius x, including points which are upwind of the point of release. This latter picture makes no

physical sense and should be rejected.

y



y 

 y

y

y



 x y =  atan   x

y atan   x   x

 



 y

y



 

y
12

Figure 2-2. Illustration of differences between crosswind dispersion in cartesian and polar coordinate systems

Figures 2-3 through 2-6 display the expert data for each of the eight experts and the resampled

data (labeled RSM throughout the report for resampling method) that were created for this study.

Missing values in the expert data are determined using the algorithm described in Section 1. The

original data for are converted to using Equation (2.5). The figures show the resampled

data span the entire ranges of values provided by the experts. This is a significant advantage over

other methods that were considered, which all employed least-square fitting of the original data.

Figures 2-7 and 2-8 compare the final results tabulated in Table 2-1 with the resampled data

shown in Figures 2-3 through 2-6. In Figure 2-7, the comparisons are made at fixed quantile level.

In Figure 2-8, the comparisons are made at fixed downwind distances. The agreement is generally

quite good. 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Downwind Distance (km)

Crosswind Distance (km)

y



y 
13

Figure 2-3. Expert and resampled data for  at 1 km downwind and Pasquill-Gifford

stability class A/B

Figure 2-4. Expert and resampled data for  at 3 km downwind and Pasquill-Gifford

stability class A/B

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000 10000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)

0.0

0.2

0.4

0.6

0.8

1.0

100 1000 10000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)
14

Figure 2-5. Expert and resampled data for  at 10 km downwind and Pasquill-Gifford

stability class A/B

Figure 2-6. Expert and resampled data for  at 30 km downwind and Pasquill-Gifford

stability class A/B

0.0

0.2

0.4

0.6

0.8

1.0

100 1000 10000 100000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)

0.0

0.2

0.4

0.6

0.8

1.0

100 1000 10000 100000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)
15

Figure 2-7. Comparison of resampled expert data for  and Pasquill-Gifford stability

class A/B with the calculated values using the parameters in Table 2-1

Figure 2-8. Comparison of resampled expert data for  and Pasquill-Gifford stability

class A/B with the calculated values using the parameters in Table 2-1

3

4

5

6

7

8

9

10

11

6 7 8 9 10 11

ln(x)

 ln(

 )

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Experts - 100%

Fit - 100%

ln(



)

ln()

0.0

0.2

0.4

0.6

0.8

1.0

4 5 6 7 8 9 10 11

ln(

y)

Cumulative Probability

Experts - 1 km

Fit - 1 km

Experts - 3 km

Fit - 3 km

Experts - 10 km

Fit - 10 km

Experts - 30 km

Fit - 30 km

ln()
16

2.1.2 Vertical Dispersion

Figures 2-9 through 2-11 display the expert data for each of the eight experts and the resampled

data (RSM) that were created for this study. Missing values in the expert data are determined using the algorithm described in Section 1. The figures show that the resampled data span the entire

ranges of values provided by the experts. This is a significant advantage over other methods that

were considered, which all employed least-square fitting of the original expert data.

Figures 2-12 and 2-13 compare the final results reported in Table 2-1 with the resampled data

shown in Figures 2-9 through 2-11. In Figure 2-12, the comparisons are made at fixed quantile

level. In Figure 2-13, the comparisons are made at fixed downwind distances. The agreement is

remarkably good. 

Figure 2-9. Expert and resampled data for z at 0.5 km downwind and Pasquill-Gifford

stability class A/B

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

z (m)
17

Figure 2-10. Expert and resampled data for z at 1 km downwind and Pasquill-Gifford

stability class A/B

Figure 2-11. Expert and resampled data for z at 3 km downwind and Pasquill-Gifford

stability class A/B

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000 10000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

z (m)

0.0

0.2

0.4

0.6

0.8

1.0

100 1000 10000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

z (m)
18

Figure 2-12. Comparison of resampled expert data for z and Pasquill-Gifford stability

class A/B with the calculated values using the parameters in Table 2-1

Figure 2-13. Comparison of resampled expert data for z and Pasquill-Gifford stability

class A/B with the calculated values using the parameters in Table 2-1

2

3

4

5

6

7

8

9

10

11

6.0 6.5 7.0 7.5 8.0

ln(x)

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Fit - 100%

Experts - 100%

ln(

z) 0.0

0.2

0.4

0.6

0.8

1.0

3456789

Cumulative Probability

Experts - 0.5 km

Fit - 0.5 km

Experts - 1 km

Fit - 1 km

Experts - 3 km

Fit - 3 km

ln(z)
19

2.2 Distributions for Stability Class C 

Table 2-2 provides values for a, b, c, and d from Equations (2.1) and (2.2) when the PasquillGifford stability class is C. To interpolate values between the quantile levels provided in the table,

it is preferable to interpolate the logarithms of a and c linearly.

2.2.1 Crosswind Dispersion

Figures 2-14 through 2-17 display the expert data for each of the eight experts and the resampled

data that were created for this study. Missing values in the expert data are determined using the algorithm described in Section 1. The original data for are converted to using Equation (2.5).

The figures show that the resampled data span the entire ranges of values provided by the experts.

This is a significant advantage over other methods that were considered, which all employed

least-square fitting of the original data.

Figures 2-18 and 2-19 compare the final results tabulated in Table 2-2 with the resampled data

shown in Figures 2-14 through 2-17. In Figure 2-18, the comparisons are made at fixed quantile

level. In Figure 2-19, the comparisons are made at fixed downwind distances. The agreement is

remarkably good. 

Table 2-2: Values for cross-wind and vertical dispersion coefficients for PasquillGifford stability class C.

Quantile

Crosswind Dispersion Parameters Vertical Dispersion Parameters

a (m) b 

(dimensionless) c (m) d (dimensionless)

0.00 0.0631 0.865 0.0487 0.859

0.01 0.0963 0.865 0.0683 0.859

0.05 0.1564 0.865 0.0871 0.859

0.10 0.2000 0.865 0.1106 0.859

0.25 0.2805 0.865 0.1491 0.859

0.50 0.4063 0.865 0.2036 0.859

0.75 0.5939 0.865 0.3492 0.859

0.90 0.8257 0.865 0.5287 0.859

0.95 0.9735 0.865 0.7039 0.859

0.99 1.3720 0.865 1.2540 0.859

1.00 2.0763 0.865 1.8861 0.859

Mean 0.4031 0.865 0.2274 0.859

Mode 0.4379 0.865 0.1514 0.859

y 
20

Figure 2-14. Expert and resampled data for  at 1 km downwind and Pasquill-Gifford

stability class C

Figure 2-15. Expert and resampled data for  at 3 km downwind and Pasquill-Gifford

stability class C

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000 10000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)
21

Figure 2-16. Expert and resampled data for  at 10 km downwind and Pasquill-Gifford

stability class C

Figure 2-17. Expert and resampled data for  at 30 km downwind and Pasquill-Gifford

stability class C

0.0

0.2

0.4

0.6

0.8

1.0

100 1000 10000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)

0.0

0.2

0.4

0.6

0.8

1.0

100 1000 10000 100000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)
22

Figure 2-18. Comparison of resampled expert data for  and Pasquill-Gifford stability

class C with the calculated values using the parameters in Table 2-2 

Figure 2-19. Comparison of resampled expert data for  and Pasquill-Gifford stability

class C with the calculated values using the parameters in Table 2-2 

3

4

5

6

7

8

9

10

6 7 8 9 10 11

ln(x)

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Experts - 100%

Fit - 100%

ln(



) 0.0

0.2

0.4

0.6

0.8

1.0

3 4 5 6 7 8 9 10

Cumulative Probability

Experts - 1 km

Fit - 1 km

Experts - 3 km

Fit - 3 km

Experts - 10 km

Fit - 10 km

Experts - 30 km

Fit - 30 km

ln()
23

2.2.2 Vertical Dispersion

Figures 2-20 through 2-22 display the expert data for each of the eight experts and the resampled

data that were created for this study. Missing values in the expert data are determined using the algorithm described in Section 1. The figures show that the resampled data span the entire ranges of

values provided by the experts. This is a significant advantage over other methods that were considered, which all employed least-square fitting of the original data.

Figures 2-23 and 2-24 compare the final results tabulated in Table 2-2 with the resampled data

shown in Figures 2-20 through 2-22. In Figure 2-23, the comparisons are made at fixed quantile

level. In Figure 2-24, the comparisons are made at fixed downwind distances. The agreement is

remarkably good. 

Figure 2-20. Expert and resampled data for z at 0.5 km downwind and Pasquill-Gifford

stability class C

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

z (m)
24

Figure 2-21. Expert and resampled data for z at 1 km downwind and Pasquill-Gifford

stability class C

Figure 2-22. Expert and resampled data for z at 3 km downwind and Pasquill-Gifford

stability class C

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

z (m)

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000 10000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

z (m)
25

Figure 2-23. Comparison of resampled expert data for z and Pasquill-Gifford stability

class C with the calculated values using the parameters in Table 2-2

Figure 2-24. Comparison of resampled expert data for z and Pasquill-Gifford stability

class C with the calculated values using the parameters in Table 2-2

2

3

4

5

6

7

8

6.0 6.5 7.0 7.5 8.0 8.5

ln(x)

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Experts - 100%

Fit - 100%

ln(

z) 0.0

0.2

0.4

0.6

0.8

1.0

2345678

Cumulative Probability

Experts - 0.5 km

Fit - 0.5 km

Experts - 1 km

Fit - 1 km

Experts - 3 km

Fit - 3 km

ln(z)
26

2.3 Distributions for Stability Class D

Table 2-3 provides values for a, b, c, and d from Equations (2.1) and (2.2) when the Pasquill-Gifford stability class is D. To interpolate values between the quantile levels provided in the table, it

is preferable to interpolate the logarithms of a and c linearly.

2.3.1 Crosswind Dispersion

Figures 2-25 through 2-28 display the expert data for each of the eight experts and the resampled

data that were created for this study. Missing values in the expert data are determined using the algorithm described in Section 1. The original data for are converted to using Equation (2.5).

The figures show that the resampled data span the entire ranges of values provided by the experts.

This is a significant advantage over other methods that were considered, which all employed

least-square fitting of the original data.

Figures 2-29 and 2-30 compare the final results tabulated in Table 2-3 with the resampled data

shown in Figures 2-25 through 2-28. In Figure 2-29, the comparisons are made at fixed quantile

level. In Figure 2-30, the comparisons are made at fixed downwind distances. The agreement is

generally very good. 

Table 2-3: Values for cross-wind and vertical dispersion coefficients for PasquillGifford stability class D.

Quantile

Crosswind Dispersion Parameters Vertical Dispersion Parameters

a (m) b 

(dimensionless) c (m) d (dimensionless)

0.00 0.0341 0.881 0.0421 0.751

0.01 0.0562 0.881 0.0752 0.751

0.05 0.0961 0.881 0.1161 0.751

0.10 0.1253 0.881 0.1404 0.751

0.25 0.1845 0.881 0.1821 0.751

0.50 0.2779 0.881 0.2636 0.751

0.75 0.4282 0.881 0.4224 0.751

0.90 0.6080 0.881 0.6048 0.751

0.95 0.7570 0.881 0.7504 0.751

0.99 1.1511 0.881 1.4634 0.751

1.00 1.7618 0.881 3.6880 0.751

Mean 0.2765 0.881 0.2796 0.751

Mode 0.2865 0.881 0.1842 0.751

y 
27

Figure 2-25. Expert and resampled data for  at 1 km downwind and Pasquill-Gifford

stability class D

Figure 2-26. Expert and resampled data for  at 3 km downwind and Pasquill-Gifford

stability class D

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000 10000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)
28

Figure 2-27. Expert and resampled data for  at 10 km downwind and Pasquill-Gifford

stability class D

Figure 2-28. Expert and resampled data for  at 30 km downwind and Pasquill-Gifford

stability class D

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000 10000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)

0.0

0.2

0.4

0.6

0.8

1.0

100 1000 10000 100000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)
29

Figure 2-29. Comparison of resampled expert data for  and Pasquill-Gifford stability

class D with the calculated values using the parameters in Table 2-3

Figure 2-30. Comparison of resampled expert data for  and Pasquill-Gifford stability

class D with the calculated values using the parameters in Table 2-3

2

3

4

5

6

7

8

9

10

6 7 8 9 10 11

ln(x)

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Experts - 100%

Fit - 100%

ln(



) 0.0

0.2

0.4

0.6

0.8

1.0

3 4 5 6 7 8 9 10

Cumulative Probability

Experts - 1 km

Fit - 1 km

Experts - 3 km

Fit - 3 km

Experts - 10 km

Fit - 10 km

Experts - 30 km

Fit - 30 km

ln()
30

2.3.2 Vertical Dispersion

Figures 2-31 through 2-33 display the expert data for each of the eight experts and the resampled

data that were created for this study. Missing values in the expert data are determined using the algorithm described in Section 1. The figures show that the resampled data span the entire ranges of

values provided by the experts. This is a significant advantage over other methods that were considered, which all employed least-square fitting of the original data.

Figures 2-34 and 2-35 compare the final results tabulated in Table 2-3 with the resampled data

shown in Figures 2-31 through 2-33. In Figure 2-34, the comparisons are made at fixed quantile

level. In Figure 2-35, the comparisons are made at fixed downwind distances. The agreement is

remarkably good. 

Figure 2-31. Expert and resampled data for z at 0.5 km downwind and Pasquill-Gifford

stability class D

0.0

0.2

0.4

0.6

0.8

1.0

1 10 100 1000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

z (m)
31

Figure 2-32. Expert and resampled data for z at 1 km downwind and Pasquill-Gifford

stability class D

Figure 2-33. Expert and resampled data for z at 3 km downwind and Pasquill-Gifford

stability class D

0.0

0.2

0.4

0.6

0.8

1.0

1 10 100 1000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

z (m)

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000 10000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

z (m)
32

Figure 2-34. Comparison of resampled expert data for z and Pasquill-Gifford stability

class D with the calculated values using the parameters in Table 2-3

Figure 2-35. Comparison of resampled expert data for z and Pasquill-Gifford stability

class D with the calculated values using the parameters in Table 2-3

1

2

3

4

5

6

7

8

6.0 6.5 7.0 7.5 8.0 8.5

ln(x)

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Experts - 100%

Fit - 100%

ln(

z) 0.0

0.2

0.4

0.6

0.8

1.0

12345678

Cumulative Probability

Experts - 0.5 km

Fit - 0.5 km

Experts - 1 km

Fit - 1 km

Experts - 3 km

Fit - 3 km

ln(z)
33

2.4 Distributions for Stability Class E/F 

Table 2-4 provides values for a, b, c, and d from Equations (2.1) and (2.2) when the Pasquill-Gifford stability class is E or F. To interpolate values between the quantile levels provided in the table, it is preferable to interpolate the logarithms of a and c linearly.

2.4.1 Crosswind Dispersion

Figures 2-36 through 2-39 display the expert data for each of the eight experts and the resampled

data that were created for this study. Missing values in the expert data are determined using the algorithm described in Section 1. The original data for are converted to using Equation (2.5).

The figures show that the resampled data span the entire ranges of values provided by the experts.

This is a significant advantage over other methods that were considered, which all employed

least-square fitting of the original data.

Figures 2-40 and 2-41 compare the final results tabulated in Table 2-4 with the resampled data

shown in Figures 2-36 through 2-39. In Figure 2-40, the comparisons are made at fixed quantile

level. In Figure 2-41, the comparisons are made at fixed downwind distances. The agreement is

remarkably good. 

Table 2-4: Values for cross-wind and vertical dispersion coefficients for PasquillGifford stability class E/F.

Quantile

Crosswind Dispersion Parameters Vertical Dispersion Parameters

a (m) b 

(dimensionless) c (m) d (dimensionless)

0.00 0.0212 0.866 0.0533 0.619

0.01 0.0376 0.866 0.0756 0.619

0.05 0.0575 0.866 0.1141 0.619

0.10 0.0768 0.866 0.1310 0.619

0.25 0.1193 0.866 0.1598 0.619

0.50 0.2158 0.866 0.2463 0.619

0.75 0.3730 0.866 0.4617 0.619

0.90 0.5458 0.866 0.8180 0.619

0.95 0.6583 0.866 1.1260 0.619

0.99 0.9467 0.866 2.2051 0.619

1.00 1.5307 0.866 4.5386 0.619

Mean 0.2081 0.866 0.2874 0.619

Mode 0.2169 0.866 0.1458 0.619

y 
34

Figure 2-36. Expert and resampled data for  at 1 km downwind and Pasquill-Gifford

stability class E/F

Figure 2-37. Expert and resampled data for  at 3 km downwind and Pasquill-Gifford

stability class E/F

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000 10000



Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)
35

Figure 2-38. Expert and resampled data for  at 10 km downwind and Pasquill-Gifford

stability class E/F

Figure 2-39. Expert and resampled data for  at 30 km downwind and Pasquill-Gifford

stability class E/F

0.0

0.2

0.4

0.6

0.8

1.0

10 100 1000 10000



Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)

0.0

0.2

0.4

0.6

0.8

1.0

100 1000 10000 100000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

 (m)
36

Figure 2-40. Comparison of resampled expert data for  and Pasquill-Gifford stability

class E/F with the calculated values using the parameters in Table 2-4 

Figure 2-41. Comparison of resampled expert data for  and Pasquill-Gifford stability

class E/F with the calculated values using the parameters in Table 2-4

2

3

4

5

6

7

8

9

10

6 7 8 9 10 11

ln(x)

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Experts - 100%

Fit - 100%

ln(



) 0.0

0.2

0.4

0.6

0.8

1.0

2 4 6 8 10

Cumulative Probability

Experts - 1 km

Fit - 1 km

Experts - 3 km

Fit - 3 km

Experts - 10 km

Fit - 10 km

Experts - 30 km

Fit - 30 km

ln()
37

2.4.2 Vertical Dispersion

Figures 2-42 through 2-44 display the expert data for each of the eight experts and the resampled

data that were created for this study. Missing values in the expert data are determined using the

algorithm described in Section 1. The figures show that the resampled data span the entire ranges

of values provided by the experts. This is a significant advantage over other methods that were

considered, which all employed least-square fitting of the original data.

Figures 2-45 and 2-46 compare the final results tabulated in Table 2-4 with the resampled data

shown in Figures 2-42 through 2-44. In Figure 2-45, the comparisons are made at fixed quantile

level. In Figure 2-46, the comparisons are made at fixed downwind distances. The agreement is

generally very good. 

Figure 2-42. Expert and resampled data for z at 0.5 km downwind and Pasquill-Gifford

stability class E/F

0.0

0.2

0.4

0.6

0.8

1.0

1 10 100 1000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

z (m)
38

Figure 2-43. Expert and resampled data for z at 1 km downwind and Pasquill-Gifford

stability class E/F

Figure 2-44. Expert and resampled data for z at 3 km downwind and Pasquill-Gifford

stability class E/F

0.0

0.2

0.4

0.6

0.8

1.0

1 10 100 1000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

z (m)

0.0

0.2

0.4

0.6

0.8

1.0

1 10 100 1000

Cummulative Probability

I

J

K

L

M

N

O

P

RSM

z (m)
39

Figure 2-45. Comparison of resampled expert data for z and Pasquill-Gifford stability

class E/F with the calculated values using the parameters in Table 2-4

Figure 2-46. Comparison of resampled expert data for z and Pasquill-Gifford stability

class E/F with the calculated values using the parameters in Table 2-4

0

1

2

3

4

5

6

7

8

9

6.0 7.0 8.0 9.0 10.0 11.0

ln(x)

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Experts - 100%

Fit - 100%

ln(

z) 0.0

0.2

0.4

0.6

0.8

1.0

01234567

Cumulative Probability

Experts - 0.5 km

Fit - 0.5 km

Experts - 1 km

Fit - 1 km

Experts - 3 km

Fit - 3 km

ln(z)
40

2.5 Comparisons with Tadmor and Gur Data

The data reported in Tables 2-1 through 2-4 are compared with the Tadmor and Gur (T&G) data

used in one of the standard sample problems distributed with the MACCS2 code, Sample Problem

A [Reference 7], in Figures 2-47 through 2-54. The Tadmor and Gur representation for dispersion

has been widely used in reactor consequence analyses, including NUREG-1150, and therefore has

both current and historical significance. The comparisons are generally quite favorable. For the

crosswind dispersions, the 0.50 quantile curve from this work agrees well in all cases with the

Tadmor and Gur curve or curves (Figures 2-47, 2-49, 2-51, and 2-53). For the vertical dispersions,

the agreement is very good for the C and the E/F stability classes (Figures 2-50 and 2-54). The expert data for vertical dispersion at the 0.50 quantile level agrees very well with the Tadmor and

Gur B stability class curve (Figure 2-48); the Tadmor and Gur curve for the A stability class is

close to the 1.00 quantile level curve from the expert elicitation (also Figure 2-48). The Tadmor

and Gur curve for vertical dispersion and the D stability class is close to the 0.05 quantile level

curve from the expert elicitation (Figure 2-52). 

In all cases but one, the Tadmor and Gur curves are very nearly parallel to the ones obtained in

this study. The single exception is for vertical dispersion in the A and B stability classes, where

the Tadmor and Gur curve for stability class A is significantly steeper than those obtained from

the expert data (Figure 2-48). This means that vertical dispersion can occur more rapidly under

the original Tadmor and Gur formulation for stability class A than would be obtained using the

combined stability class A and B from this work, even at the 1.00 quantile level. The significance

of this difference for a calculation in which weather sampling is performed depends on the probability of stability class A occurring in the meteorological conditions at a specific site.

Figure 2-47. Comparison between the Tadmor and Gur crosswind dispersion data and the

processed expert data for the eleven quantile values given in Table 2-1 for stability classes A and B

1.E+2

1.E+3

1.E+4

1.E+5

1.E+6

0.0E+0 5.0E+5 1.0E+6 1.5E+6 2.0E+6

Downwind Distance (m)

Crosswind Dispersion (m)

T&G A

T&G B

0.00

0.01

0.05

0.25

0.50

0.75

0.95

0.99

1.00
41

Figure 2-48. Comparison between the Tadmor and Gur vertical dispersion data and the

processed expert data for the eleven quantile values given in Table 2-1 for stability classes A and B

Figure 2-49. Comparison between the Tadmor and Gur crosswind dispersion data and the

processed expert data for the eleven quantile values given in Table 2-2 for stability class C

1.E+1

1.E+2

1.E+3

1.E+4

0.E+0 1.E+4 2.E+4 3.E+4

Downwind Distance (m)

Vertical Dispersion (m)

T&G A

T&G B

0.00

0.01

0.05

0.25

0.50

0.75

0.95

0.99

1.00

1.E+2

1.E+3

1.E+4

1.E+5

1.E+6

0.0E+0 5.0E+5 1.0E+6 1.5E+6 2.0E+6

Downwind Distance (m)

Crosswind Dispersion (m)

T&G C

0.00

0.01

0.05

0.25

0.50

0.75

0.95

0.99

1.00
42

Figure 2-50. Comparison between the Tadmor and Gur vertical dispersion data and the

processed expert data for the eleven quantile values given in Table 2-2 for stability class C

Figure 2-51. Comparison between the Tadmor and Gur crosswind dispersion data and the

processed expert data for the eleven quantile values given in Table 2-3 for stability class D

1.E+1

1.E+2

1.E+3

1.E+4

0.E+0 1.E+4 2.E+4 3.E+4

Downwind Distance (m)

Vertical Dispersion (m)

T&G C

0.00

0.01

0.05

0.25

0.50

0.75

0.90

0.95

0.99

1.00

1.E+2

1.E+3

1.E+4

1.E+5

1.E+6

0.0E+0 5.0E+5 1.0E+6 1.5E+6 2.0E+6

Downwind Distance (m)

Crosswind Dispersion (m)

T&G D

0.00

0.01

0.05

0.25

0.50

0.75

0.95

0.99

1.00
43

Figure 2-52. Comparison between the Tadmor and Gur vertical dispersion data and the

processed expert data for the eleven quantile values given in Table 2-3 for stability class D

Figure 2-53. Comparison between the Tadmor and Gur crosswind dispersion data and the

processed expert data for the eleven quantile values given in Table 2-4 for stability classes E and F

1.E+1

1.E+2

1.E+3

1.E+4

0.E+0 1.E+4 2.E+4 3.E+4

Downwind Distance (m)

Vertical Dispersion (m)

T&G D

0.00

0.01

0.05

0.25

0.50

0.75

0.95

0.99

1.00

1.E+2

1.E+3

1.E+4

1.E+5

1.E+6

0.0E+0 5.0E+5 1.0E+6 1.5E+6 2.0E+6

Downwind Distance (m)

Crosswind Dispersion (m)

T&G E

T&G F

0.00

0.01

0.05

0.25

0.50

0.75

0.95

0.99

1.00
44

Figure 2-54. Comparison between the Tadmor and Gur vertical dispersion data and the

processed expert data for the eleven quantile values given in Table 2-4 for stability classes E and F

2.6 Correlations Between the Dispersion Data

It is logical to assume that crosswind and vertical dispersion are correlated for a given stability

class. For example, vertical dispersion is likely to be large if crosswind dispersion is determined

to be large since both are governed by the size and magnitude of turbulent eddies. It is not obvious

that the correlation coefficient should be unity, but it should not be much less than unity. A correlation coefficient of 0.9 to 1.0 between crosswind and vertical dispersion for each stability class

seems reasonable.

Furthermore, it seems reasonable that dispersion should be correlated between the stability classes. If this were not so, the dispersion values for a more stable class could exceed those for a less

stable class. Again, a correlation coefficient of 0.9 to 1.0 between the stability classes seems reasonable. 

1.E+1

1.E+2

1.E+3

1.E+4

0.E+0 1.E+4 2.E+4 3.E+4

Downwind Distance (m)

Vertical Dispersion (m)

T&G E

T&G F

0.00

0.01

0.05

0.25

0.50

0.75

0.90

0.95

0.99

1.00
45

3.0 DRY DEPOSITION

Dry deposition velocities in MACCS2 are treated as being dependent on aerosol size, but as being

independent of wind conditions and surface roughness. In the expert solicitation, both wind speed

and surface roughness were considered as variables. The experts provided data for two wind

speeds, 2 and 5 m/s, and for three surface roughnesses, corresponding to prairie, forest, and urban

terrains. 

The approach used in this work is to retain important dependencies so that the user can decide

what is most appropriate for their specific situation. The final results for dry deposition velocities

account for particle size, wind speed, surface roughness, and degree of belief. Because only particle size can be accounted for in the current MACCS2 dry deposition model, the user is required to

choose representative values of wind speed, surface roughness, and quantile. Evaluation of the

expert results indicates that quantile is significantly more important than surface roughness or

wind speed.

3.1 Distributions of Dry Deposition Data

Dry deposition velocity is represented using linear regression with the following equation:

(3.1)

where

vd = deposition velocity (cm/s)

dp = hydrodynamic particle diameter (m)

z0 = surface roughness (m)

v = wind speed (m/s)

The regression coefficients, a through g, are tabulated for each of eleven quantiles in Table 3-1.

The regression was performed over the following parameter ranges: 0.1 to 10 m for dp, 5 to 60

cm for z0, and 2 to 5 m/s for v. Using Equation (3.1) with parameters from Table 3-1 should provide reasonable results over these ranges. The reader is cautioned not to extrapolate too far

beyond these parameter ranges. The behavior of the correlation is generally better at the 0.5 quantile and worse at the tails of the distribution. Extrapolation beyond a factor of two beyond (above

or below) the parameter ranges provided above is generally discouraged. For surface roughness,

even a factor of two above the indicated range (120 cm) is too much and results in non-monotonic

behavior with quantile level (i.e., the 0.9 quantile may be larger than the 0.95 quantile). It is the

reader’s responsibility to verify that any extrapolation in the parameter ranges provides reasonable deposition velocities. 

Table 3-2 shows values for deposition velocity as a function of aerosol diameter corresponding to

typical choices for surface roughness (z0 = 10 cm) and wind speed (v = 5 m/s). Figures 3-1

through 3-30 show comparisons between the original experts’ data and the resampling method

(RSM) results from this work. Figures 3-31 through 3-36 show comparisons of the resampled

expert data with curves (labeled “Fit”) constructed from Equation (3-1) using the coefficients in

Table 3-1. The agreement between the expert and correlated data is generally very good. 

vd ln  ab dp   ln c dp   ln 2 d dp   ln 3e z 0 f z 0

2 = + + + + ++ g v
46

It is not entirely obvious how to interpolate the data in Table 3-1 between quantile levels. Given

the fact that many of the quantities in the table are negative, a simple linear interpolation is probably best.

Table 3-1: Values of regression coefficients in Equation (3.1) for dry deposition velocity. 

Quantile

Regression Coefficients

abcde f g

0.00 -6.482 1.578 -0.068 0.015 -0.056 1.235 0.071

0.01 -5.991 1.448 0.183 -0.057 -1.469 4.259 0.086

0.05 -5.504 1.121 0.284 -0.048 1.110 0.270 0.160

0.10 -5.111 1.033 0.282 -0.042 3.063 -2.703 0.155

0.25 -4.369 0.981 0.256 -0.050 3.490 -2.995 0.178

0.50 -3.112 0.992 0.190 -0.072 5.922 -6.314 0.169

0.75 -2.082 0.843 0.204 -0.045 7.768 -8.251 0.170

0.90 -1.468 0.950 0.259 -0.041 8.209 -6.243 0.218

0.95 -1.319 1.002 0.272 -0.041 16.239 -18.056 0.230

0.99 -0.601 0.934 0.266 -0.032 24.575 -31.551 0.216

1.00 0.574 0.976 0.242 -0.042 22.313 -28.886 0.191

Mean -2.582 0.949 0.255 -0.040 15.984 -18.716 0.211

Mode -4.838 1.003 0.333 -0.019 0.697 0.467 0.092
47

Table 3-2: Values of dry deposition velocity in cm/s for z0 = 10 cm, v = 5 m/s.

Quantile

Aerosol Diameter (m)

0.1 0.3 1. 3. 10

0.00 3.4·10-5 2.9·10-4 2.2·10-3 1.2·10-2 6.9·10-2

0.01 6.5·10-4 8.7·10-4 3.5·10-3 2.0·10-2 1.3·10-1

0.05 6.2·10-3 4.3·10-3 1.0·10-2 4.6·10-2 3.4·10-1

0.10 1.2·10-2 8.1·10-3 1.7·10-2 7.2·10-2 5.0·10-1

0.25 3.2·10-2 2.1·10-2 4.3·10-2 1.6·10-1 8.6·10-1

0.50 1.2·10-1 7.9·10-2 1.8·10-1 6.0·10-1 2.0·100

0.75 4.3·10-1 3.1·10-1 5.9·10-1 1.8·100 7.0·100

0.90 1.1·100 7.3·10-1 1.5·100 5.4·100 3.1·101

0.95 2.5·100 1.7·100 3.6·100 1.4·101 9.2·101

0.99 9.7·100 7.0·100 1.4·101 5.1·101 3.3·102

1.00 2.1·101 1.5·101 3.2·101 1.2·102 6.6·102

Mean 6.3·10-1 4.4·10-1 8.9·10-1 3.3·100 1.9·101

Mode 9.9·10-3 6.8·10-3 1.4·10-2 5.9·10-2 6.3·10-1
48

Figure 3-1. Expert and resampled data for deposition velocity corresponding to 0.1 m

particles over an urban terrain and a wind speed of 2 m/s

Figure 3-2. Expert and resampled data for deposition velocity corresponding to 0.1 m

particles over an urban terrain and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
49

Figure 3-3. Expert and resampled data for deposition velocity corresponding to 0.3 m

particles over an urban terrain and a wind speed of 2 m/s

Figure 3-4. Expert and resampled data for deposition velocity corresponding to 0.3 m

particles over an urban terrain and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
50

Figure 3-5. Expert and resampled data for deposition velocity corresponding to 1 m particles over an urban terrain and a wind speed of 2 m/s

Figure 3-6. Expert and resampled data for deposition velocity corresponding to 1 m particles over an urban terrain and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
51

Figure 3-7. Expert and resampled data for deposition velocity corresponding to 3 m particles over an urban terrain and a wind speed of 2 m/s

Figure 3-8. Expert and resampled data for deposition velocity corresponding to 3 m particles over an urban terrain and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
52

Figure 3-9. Expert and resampled data for deposition velocity corresponding to 10 m

particles over an urban terrain and a wind speed of 2 m/s

Figure 3-10. Expert and resampled data for deposition velocity corresponding to 10 m

particles over an urban terrain and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-2 1.E-1 1.E+0 1.E+1 1.E+2 1.E+3

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-2 1.E-1 1.E+0 1.E+1 1.E+2 1.E+3

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
53

Figure 3-11. Expert and resampled data for deposition velocity corresponding to 0.1 m

particles over a meadow and a wind speed of 2 m/s

Figure 3-12. Expert and resampled data for deposition velocity corresponding to 0.1 m

particles over a meadow and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
54

Figure 3-13. Expert and resampled data for deposition velocity corresponding to 0.3 m

particles over a meadow and a wind speed of 2 m/s

Figure 3-14. Expert and resampled data for deposition velocity corresponding to 0.3 m

particles over a meadow and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
55

Figure 3-15. Expert and resampled data for deposition velocity corresponding to 1 m particles over a meadow and a wind speed of 2 m/s

Figure 3-16. Expert and resampled data for deposition velocity corresponding to 1 m particles over a meadow and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
56

Figure 3-17. Expert and resampled data for deposition velocity corresponding to 3 m particles over a meadow and a wind speed of 2 m/s

Figure 3-18. Expert and resampled data for deposition velocity corresponding to 3 m particles over a meadow and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
57

Figure 3-19. Expert and resampled data for deposition velocity corresponding to 10 m

particles over a meadow and a wind speed of 2 m/s

Figure 3-20. Expert and resampled data for deposition velocity corresponding to 10 m

particles over a meadow and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-2 1.E-1 1.E+0 1.E+1 1.E+2 1.E+3

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
58

Figure 3-21. Expert and resampled data for deposition velocity corresponding to 0.1 m

particles over a forrest and a wind speed of 2 m/s

Figure 3-22. Expert and resampled data for deposition velocity corresponding to 0.1 m

particles over a forrest and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
59

Figure 3-23. Expert and resampled data for deposition velocity corresponding to 0.3 m

particles over a forrest and a wind speed of 2 m/s

Figure 3-24. Expert and resampled data for deposition velocity corresponding to 0.3 m

particles over a forrest and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
60

Figure 3-25. Expert and resampled data for deposition velocity corresponding to 1 m particles over a forrest and a wind speed of 2 m/s

Figure 3-26. Expert and resampled data for deposition velocity corresponding to 1 m particles over a forrest and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
61

Figure 3-27. Expert and resampled data for deposition velocity corresponding to 3 m particles over a forrest and a wind speed of 2 m/s

Figure 3-28. Expert and resampled data for deposition velocity corresponding to 3 m particles over a forrest and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-2 1.E-1 1.E+0 1.E+1 1.E+2 1.E+3

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-2 1.E-1 1.E+0 1.E+1 1.E+2 1.E+3

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
62

Figure 3-29. Expert and resampled data for deposition velocity corresponding to 10 m

particles over a forrest and a wind speed of 2 m/s

Figure 3-30. Expert and resampled data for deposition velocity corresponding to 10 m

particles over a forrest and a wind speed of 5 m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.E-1 1.E+0 1.E+1 1.E+2 1.E+3 1.E+4

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-1 1.E+0 1.E+1 1.E+2 1.E+3 1.E+4

Deposition Velocity (cm/s)

Cummulative Probability

A

B

C

D

E

F

G

H

RSM
63

Figure 3-31. Comparison of resampled expert data for dry deposition velocity over urban

terrain and wind speed of 2 m/s with the calculated values using the parameters in Table 3-1

Figure 3-32. Comparison of resampled expert data for dry deposition velocity over urban

terrain and wind speed of 5 m/s with the calculated values using the parameters in Table 3-1

1.E-5

1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

1.E+1

1.E+2

1.E+3

0.1 1.0 10.0

Particle Diameter (micron)

Deposition Velocity (cm/s)

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Experts - 100%

Fit - 100%

1.E-5

1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

1.E+1

1.E+2

1.E+3

0.1 1.0 10.0

Particle Diameter (micron)

Deposition Velocity (cm/s)

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Experts - 100%

Fit - 100%
64

Figure 3-33. Comparison of resampled expert data for dry deposition velocity over meadow and wind speed of 2 m/s with the calculated values using the parameters in

Table 3-1

Figure 3-34. Comparison of resampled expert data for dry deposition velocity over meadow and wind speed of 5 m/s with the calculated values using the parameters in

Table 3-1

1.E-5

1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

1.E+1

1.E+2

1.E+3

0.1 1.0 10.0

Particle Diameter (micron)

Deposition Velocity (cm/s)

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Experts - 100%

Fit - 100%

1.E-5

1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

1.E+1

1.E+2

1.E+3

0.1 1.0 10.0

Particle Diameter (micron)

Deposition Velocity (cm/s)

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Experts - 100%

Fit - 100%
65

Figure 3-35. Comparison of resampled expert data for dry deposition velocity over forrest

and wind speed of 2 m/s with the calculated values using the parameters in

Table 3-1

Figure 3-36. Comparison of resampled expert data for dry deposition velocity over forrest

and wind speed of 5 m/s with the calculated values using the parameters in

Table 3-1

1.E-5

1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

1.E+1

1.E+2

1.E+3

1.E+4

0.1 1.0 10.0

Particle Diameter (micron)

Deposition Velocity (cm/s)

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Experts - 100%

Fit - 100%

1.E-5

1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

1.E+1

1.E+2

1.E+3

1.E+4

0.1 1.0 10.0

Particle Diameter (micron)

Deposition Velocity (cm/s)

Experts - 0%

Fit - 0%

Experts - 5%

Fit - 5%

Experts - 50%

Fit - 50%

Experts - 95%

Fit - 95%

Experts - 100%

Fit - 100%
66

3.2 Correlations Between Dry Deposition Data

Sampling for dry deposition velocities could be performed by sampling any or all of the parameters in Equation 3.1; this includes hydrodynamic particle diameter, surface roughness, wind

speed, and quantile level. Quantile level enters Equation 3.1 implicitly through the values of the

linear coefficients, a, b c, d, e, f, and g. However, it is reasonable that, for each realization, the

same value of surface roughness, wind speed, and quantile level be selected for each of the hydrodynamic particle diameters used in the calculation. This ensures that the expected relationship

between deposition velocity and particle diameter is preserved within each realization. This

approach amounts to assuming a perfect correlation between the deposition velocities for a set of

aerosol diameters. In practice, a correlation coefficient between 0.9 and 1.0 is probably sufficient

to ensure a reasonable relationship between aerosol size and deposition velocity. 

A simpler approach for sampling deposition velocities is to assume fixed values for each of the

aerosol diameters, surface roughness, and wind speed. In this case, the aerosol diameters would

be fixed and a set of deposition velocities would be sampled for each aerosol diameter. This

approach is sufficient because quantile level has a much stronger influence on deposition velocity

than any of the other variables in Equation 3.1. Again, it is reasonable to assume a correlation

coefficient between 0.9 to 1.0 between each of the distributions representing the set of aerosol

diameters to ensure that a correct relationship between aerosol size and deposition velocity exists

within each of the realizations.
67

4.0 WET DEPOSITION

4.1 Distributions of Wet-Deposition Data

Wet deposition is modeled in MACCS2 using the following formula:

(4.1)

where

R = the fractional rate at which aerosols are removed from the plume (s-1)

C1 = an empirical, linear coefficient (s-1

)

I = rain intensity (mm/hr)

C2 = an empirical exponent (dimensionless)

The first attempt to analyze the expert data allowed both C1 and C2 to be functions of quantile.

The values of C1 turned out to increase monotonically with quantile; the values of C2 did not. Because C1 and C2 are correlated, the results could not be implemented with latin hypercube sampling (LHS). As a result, a single value of C2 was obtained, independent of quantile. The results

are shown in Table 4-1.

The more general result obtained from the experts’ data for C1 is a correlation of the following

form:

(4.2)

The regression coefficients in Equation (4.2) are displayed in Table 4-2 for each quantile level.

The correlation is over the particle diameter range of 0.1 to 10 m that was used in the expert elicitation process. The values of C1 should not be extrapolated too far below or above this range.

Even a factor of two above the indicated range in particle diameter (20 m) is too much and produces non-physical results. It is the reader’s responsibility to verify that any extrapolation in the

parameter range provides reasonable wet deposition removal rates. 

Plots showing comparisons between the expert data and the resampled data are shown in Figures

4-1 through 4-20. Comparisons between the correlations and the resampled data are provided in

Figures 4-21 through 4-25. Curves labeled “Fit” on Figures 4-21 through 4-25 were generated using the parameter values in Table 4-2. 

It is not entirely obvious how to interpolate the data in Tables 4-1 and 4-2 between quantile levels.

Given the fact that many of the quantities in the tables are negative, a simple linear interpolation is

probably best.

R C1I

C2 =

C1 ab dp ln c dp    ln 2 d dp    ln 3 = +  + +
68

Table 4-1: Values for the wet deposition coefficients 

in Equation (4.1) for 1 m particles.

Quantile

Wet Deposition Parameters

C1 (s-1) C2 (dimensionless)

0.00 2.73·10-8 0.664

0.01 2.92·10-7 0.664

0.05 9.13·10-7 0.664

0.10 1.73·10-6 0.664

0.25 5.36·10-6 0.664

0.50 1.89·10-5 0.664

0.75 9.84·10-5 0.664

0.90 2.59·10-4 0.664

0.95 5.79·10-4 0.664

0.99 3.78·10-3 0.664

1.00 1.14·10-2 0.664

Mean 2.21·10-5 0.664

Mode 4.49·10-5 0.664
69

Table 4-2: Values of regression coefficients in Equation 

(4.2) for the wet deposition coefficient C1.

Quantile

Regression Coefficients

abcd

0.00 -17.415 1.948 -0.306 -0.159

0.01 -15.045 2.701 -0.124 -0.270

0.05 -13.907 2.740 -0.034 -0.288

0.10 -13.269 2.812 -0.009 -0.307

0.25 -12.136 2.529 0.075 -0.296

0.50 -10.875 1.600 0.122 -0.145

0.75 -9.227 1.242 0.092 -0.126

0.90 -8.259 0.877 0.082 -0.076

0.95 -7.454 1.305 0.034 -0.157

0.99 -5.579 1.536 -0.058 -0.217

1.00 -4.472 0.297 -0.031 -0.043

Mean -10.721 1.820 0.066 0.271

Mode -10.012 0.995 0.163 -0.051
70

Figure 4-1. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 0.1 m particles and a rainfall intensity of 0.3 mm/hr

Figure 4-2. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 0.1 m particles and a rainfall intensity of 2 mm/hr

0.0

0.2

0.4

0.6

0.8

1.0

1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1) 

Cummulative Probability

B

C

D

E

F

G

H

RSM
71

Figure 4-3. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 0.1 m particles and a rainfall intensity of 0.05 mm/10 min

Figure 4-4. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 0.1 m particles and a rainfall intensity of 0.33 mm/10 min

0.0

0.2

0.4

0.6

0.8

1.0

1.E-7 1.E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-7 1.E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

ln(R)

Cummulative Probability

B

C

D

E

F

G

H

RSM
72

Figure 4-5. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 0.1 m particles and a rainfall intensity of 1.67 mm/10 min

Figure 4-6. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 0.3 m particles and a rainfall intensity of 0.3 mm/hr

0.0

0.2

0.4

0.6

0.8

1.0

1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM
73

Figure 4-7. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 0.3 m particles and a rainfall intensity of 2 mm/hr

Figure 4-8. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 0.3 m particles and a rainfall intensity of 0.05 mm/10 min

0.0

0.2

0.4

0.6

0.8

1.0

1.E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM
74

Figure 4-9. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 0.3 m particles and a rainfall intensity of 0.33 mm/10 min

Figure 4-10. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 0.3 m particles and a rainfall intensity of 1.67 mm/10 min

0.0

0.2

0.4

0.6

0.8

1.0

1.E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM
75

Figure 4-11. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 1 m particles and a rainfall intensity of 0.3 mm/hr

Figure 4-12. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 1 m particles and a rainfall intensity of 2 mm/hr

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM
76

Figure 4-13. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 1 m particles and a rainfall intensity of 0.05 mm/10 min

Figure 4-14. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 1 m particles and a rainfall intensity of 0.33 mm/10 min

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM
77

Figure 4-15. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 1 m particles and a rainfall intensity of 1.67 mm/10 min

Figure 4-16. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 10 m particles and a rainfall intensity of 0.3 mm/hr

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM
78

Figure 4-17. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 10 m particles and a rainfall intensity of 2 mm/hr

Figure 4-18. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 10 m particles and a rainfall intensity of 0.05 mm/10 min

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM
79

Figure 4-19. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 10 m particles and a rainfall intensity of 0.33 mm/10 min

Figure 4-20. Expert and resampled data for wet deposition rate (R in units of s-1) corresponding to 10 m particles and a rainfall intensity of 1.67 mm/10 min

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-3 1.E-2 1.E-1 1.E+0

R (s-1)

Cummulative Probability

B

C

D

E

F

G

H

RSM
80

Figure 4-21. Correlated values (fit) and resampled expert data for removal rate at a rainfall intensity of 0.3 mm/hr as a function of particle size

Figure 4-22. Correlated values (fit) and resampled expert data for removal rate at a rainfall intensity of 2 mm/hr as a function of particle size

1.E-10

1.E-9

1.E-8

1.E-7

1.E-6

1.E-5

1.E-4

1.E-3

1.E-2

0.1 1.0 10.0

Particle Size (micro m)

Removal Rate (1/s)

Fit - 0%

Experts - 0%

Fit - 5%

Experts - 5%

Fit - 50%

Experts - 50%

Fit - 95%

Experts - 95%

Fit - 100%

Experts - 100%

1.E-10

1.E-9

1.E-8

1.E-7

1.E-6

1.E-5

1.E-4

1.E-3

1.E-2

1.E-1

0.1 1.0 10.0

Particle Size (micro m)

Scavenging Rate (1/s)

Fit - 0%

Experts - 0%

Fit - 5%

Experts - 5%

Fit - 50%

Experts - 50%

Fit - 95%

Experts - 95%

Fit - 100%

Experts - 100%
81

Figure 4-23. Correlated values (fit) and resampled expert data for removal rate at a rainfall intensity of 0.05 mm/10 min as a function of particle size

Figure 4-24. Correlated values (fit) and resampled expert data for removal rate at a rainfall intensity of 0.33 mm/10 min as a function of particle size

1.E-10

1.E-9

1.E-8

1.E-7

1.E-6

1.E-5

1.E-4

1.E-3

1.E-2

1.E-1

0.1 1.0 10.0

Particle Size (micro m)

Removal Rate (1/s)

Fit - 0%

Experts - 0%

Fit - 5%

Experts - 5%

Fit - 50%

Experts - 50%

Fit - 95%

Experts - 95%

Fit - 100%

Experts - 100%

1.E-10

1.E-9

1.E-8

1.E-7

1.E-6

1.E-5

1.E-4

1.E-3

1.E-2

1.E-1

0.1 1.0 10.0

Particle Size (micro m)

Removal Rate (1/s)

Fit - 0%

Experts - 0%

Fit - 5%

Experts - 5%

Fit - 50%

Experts - 50%

Fit - 95%

Experts - 95%

Fit - 100%

Experts - 100%
82

Figure 4-25. Correlated values (fit) and resampled expert data for removal rate at a rainfall intensity of 1.67 mm/10 min as a function of particle size

4.2 Correlations Between Wet Deposition Data

Because a single correlation is currently used to represent wet deposition for all aerosol bins in

MACCS2, no correlation of the wet deposition values is needed. However, if a model were used

in which wet deposition parameters were needed for each aerosol bin, the coefficients should be

correlated to preserve the correct relationship between wet deposition and aerosol size. A correlation coefficient between wet deposition parameters of 0.9 to 1.0 is reasonable.

1.E-9

1.E-8

1.E-7

1.E-6

1.E-5

1.E-4

1.E-3

1.E-2

1.E-1

0.1 1.0 10.0

Particle Size (micro m)

Removal Rate (1/s)

Fit - 0%

Experts - 0%

Fit - 5%

Experts - 5%

Fit - 50%

Experts - 50%

Fit - 95%

Experts - 95%

Fit - 100%

Experts - 100%
83

5.0 LATENT HEALTH EFFECTS

MACCS2 allows users to construct relationships between doses to an individual organ (or an

effective dose to the whole body) and the risk of induction of a specific cancer related to that

organ. The category, “other,” captures the risk of other type of cancers not specifically included in

the list. The category, “all cancers,” is the total of all types of cancers induced by the radiation

exposure. The constant of proportionality between dose and an induced health effect is called a

risk factor. NUREG/CR-6555 [Reference 5] documents an expert elicitation of such risk factors.

The data from this expert elicitation is evaluated in this section.

5.1 Distributions of Risk Factors for Late Health Effects

Table 5-1 provides a summary of the results. The values in the table correspond to the risk to an

individual exposed to 1 Gy of low-LET radiation over a 1-min time period. This corresponds to a

whole-body dose of 1 Sv (100 rem). The values in the table are population averaged, assuming an

equal number of male and female members of the population.

Values are tabulated at 11 quantile levels and for the mean and mode. Figures 5-1 through 5-12

compare the aggregated distributions, using the resampling methodology, with the distributions

provided by each of the experts for each of the 12 cancer categories.

Table 5-1: Risk factors for latent cancer fatalities.

Quantile

Risk of a Latent Cancer Fatality (1/Gy)

Bone Colon Breast Leukemia Liver Lung Pancreas Skin Stomach Thyroid Other All 

Cancers

0.00 0 4.0·10-5 5.0·10-5 1.0·10-4 0 7.0·10-5 0 0 0 0 0 1.5·10-2

0.01 0 2.8·10-4 9.0·10-4 1.5·10-3 1.8·10-5 6.4·10-4 0 0 1.0·10-4 2.3·10-5 1.7·10-3 1.8·10-2

0.05 3.7·10-5 1.4·10-3 1.9·10-3 3.4·10-3 1.2·10-4 5.1·10-3 5.4·10-5 1.6·10-5 3.5·10-4 8.4·10-5 5.7·10-3 3.4·10-2

0.10 6.2·10-5 2.5·10-3 2.5·10-3 4.5·10-3 2.1·10-4 7.2·10-3 1.5·10-4 5.1·10-5 6.3·10-4 1.4·10-4 8.5·10-3 4.2·10-2

0.25 1.2·10-4 5.3·10-3 4.5·10-3 6.6·10-3 4.1·10-4 1.4·10-2 5.8·10-4 1.9·10-4 1.4·10-3 3.0·10-4 1.5·10-2 6.2·10-2

0.50 4.2·10-4 1.0·10-2 9.2·10-3 9.5·10-3 8.6·10-4 2.6·10-2 2.1·10-3 4.5·10-4 3.2·10-3 6.3·10-4 2.7·10-2 9.6·10-2

0.75 1.2·10-3 1.8·10-2 2.0·10-2 1.4·10-2 2.3·10-3 4.4·10-2 5.8·10-3 9.7·10-4 7.3·10-3 1.8·10-3 5.3·10-2 1.6·10-1

0.90 6.1·10-3 2.8·10-2 3.6·10-2 1.8·10-2 1.1·10-2 6.6·10-2 9.1·10-3 2.3·10-3 1.9·10-2 5.9·10-3 9.0·10-2 2.3·10-1

0.95 1.0·10-2 3.5·10-2 4.7·10-2 2.5·10-2 1.9·10-2 8.4·10-2 1.2·10-2 3.2·10-3 3.5·10-2 1.3·10-2 1.2·10-1 2.9·10-1

0.99 1.9·10-2 5.8·10-2 6.1·10-2 3.9·10-2 3.6·10-2 1.3·10-1 1.9·10-2 5.5·10-3 7.1·10-2 5.6·10-2 2.0·10-1 4.9·10-1

1.00 3.0·10-2 8.0·10-2 1.0·10-1 7.0·10-2 7.6·10-2 2.0·10-1 2.8·10-2 1.0·10-2 1.5·10-1 1.2·10-1 2.8·10-1 7.0·10-1

Mean 1.9·10-3 1.3·10-2 1.5·10-2 1.1·10-2 3.8·10-3 3.3·10-2 3.7·10-3 8.7·10-4 8.2·10-3 3.5·10-3 4.1·10-2 1.2·10-1

Mode 6.1·10-5 4.7·10-3 3.1·10-3 8.0·10-3 3.9·10-4 1.2·10-2 1.5·10-4 1.4·10-5 8.6·10-4 2.1·10-4 1.6·10-2 7.2·10-2
84

Figure 5-1. Expert and resampled data for the risk factor for a bone cancer fatality to a

person receiving 1 Gy low-LET radiation over 1 min

Figure 5-2. Expert and resampled data for the risk factor for a colon cancer fatality to a

person receiving 1 Gy low-LET radiation over 1 min

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1

Risk of Bone Cancer Fatality (1/Gy)

Quantile

A

B

C

D

E

F

G

H

I

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1

Risk of Colon Cancer Fatality (1/Gy)

Quantile

A

B

C

D

E

F

G

H

I

RSM
85

Figure 5-3. Expert and resampled data for the risk factor for a breast cancer fatality to a

person receiving 1 Gy low-LET radiation over 1 min

Figure 5-4. Expert and resampled data for the risk factor for a leukemia fatality to a person receiving 1 Gy low-LET radiation over 1 min

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1

Risk of Breast Cancer Fatality (1/Gy)

Quantile

A

B

C

D

E

F

G

H

I

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1

Risk of Leukemia Fatality (1/Gy)

Quantile

A

B

C

D

E

F

G

H

I

RSM
86

Figure 5-5. Expert and resampled data for the risk factor for a liver cancer fatality to a

person receiving 1 Gy low-LET radiation over 1 min

Figure 5-6. Expert and resampled data for the risk factor for a lung cancer fatality to a

person receiving 1 Gy low-LET radiation over 1 min

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1

Risk of Liver Cancer Fatality (1/Gy)

Quantile

A

B

C

D

E

F

G

H

I

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

Risk of Lung Cancer Fatality (1/Gy)

Quantile

A

B

C

D

E

F

G

H

I

RSM
87

Figure 5-7. Expert (excluding values of zero) and resampled data for the risk factor for a

pancreas cancer fatality to a person receiving 1 Gy low-LET radiation over 1

min

Figure 5-8. Expert and resampled data for the risk factor for a skin cancer fatality to a

person receiving 1 Gy low-LET radiation over 1 min

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1

Risk of Pancreas Cancer Fatality (1/Gy)

Quantile

A

B

C

D

E

F

G

H

I

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-6 1.E-5 1.E-4 1.E-3 1.E-2

Risk of Skin Cancer Fatality (1/Gy)

Quantile

A

B

C

D

E

F

G

H

I

RSM
88

Figure 5-9. Expert and resampled data for the risk factor for a stomach cancer fatality to

a person receiving 1 Gy low-LET radiation over 1 min

Figure 5-10. Expert and resampled data for the risk factor for a thyroid cancer fatality to a

person receiving 1 Gy low-LET radiation over 1 min

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

Risk of Stomach Cancer Fatality (1/Gy)

Quantile

A

B

C

D

E

F

G

H

I

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

Risk of Thyroid Cancer Fatality (1/Gy)

Quantile

A

B

C

D

E

F

G

H

I

RSM
89

Figure 5-11. Expert and resampled data for the risk factor for other cancer fatality to a

person receiving 1 Gy low-LET radiation over 1 min

Figure 5-12. Expert and resampled data for the risk factor for all cancer fatalities to a person receiving 1 Gy low-LET radiation over 1 min

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

Risk of All Other Cancer Fatalities (1/Gy)

Quantile

A

B

C

D

E

F

G

H

I

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-2 1.E-1 1.E+0

Risk of All Cancer Fatalities (1/Gy)

Quantile

A

B

C

D

E

F

G

H

I

RSM
90

5.2 Correlations Between Risk Factors for Late Health Effects

It is not obvious that the health risks associated with doses to the human organs are interrelated.

Cancer incidents and fatalities are estimated independently for each type of cancer. Therefore, the

risk factors provided in Table 5-1 should be treated as being uncorrelated.
91

6.0 EARLY HEALTH EFFECTS

6.1 Distributions of Early Health Parameters

MACCS2 allows users to construct relationships between acute doses to an individual organ and

the risk of induction of an early injury or fatality related to that organ. The relationship between

dose and an induced health effect is represented by a Weibull function, which has three parameters: a threshold, a D50 or LD50 value, and a shape factor, . The form of this equation is as follows:

(6.1)

NUREG/CR-6545 [Reference 4] documents an expert elicitation of the relationship between dose

and induced early health effects. The data from this expert elicitation are evaluated in this section.

Four specific health effects are considered in this report. Table 6-1 provides a summary of the results. The values in Table 6-1 for a given health effect should be treated as having a correlation

coefficient of 1. That is, the same quantile values should be used for all three parameters associated with a health effect. Furthermore, the parameters associated with the pulmonary syndrome and

pneumonitis should be treated as having a correlation coefficient of 1 because it would not make

sense for pneumonitis to require higher doses than the pulmonary syndrome.

The first health effect considered is hematopoietic syndrome, a type of early fatality. The expert

data are for a whole-body dose rate of 100 Gy/hr. Following the radiation exposure, the person is

assumed to receive supportive medical treatment. 

The second health effect considered is gastrointestinal syndrome, also a type of early fatality. The

expert data are for a whole-body dose rate of 100 Gy/hr. Following the radiation exposure, the

person is assumed to receive supportive medical treatment. 

The third health effect considered is pulmonary syndrome, also a type of early fatality. The expert

data are for a lung dose rate of 1 Gy/hr of beta radiation to a person under the age of 40. Supportive medical treatment is assumed following the exposure.

The fourth health effect considered is pneumonitis, an early health effect that is generally nonfatal. The expert data are for a lung dose rate of 1 Gy/hr of beta radiation to a person under the age

of 40. Again, supportive medical treatment is assumed following the exposure.

Two of the three parameters in the Weibull function were elicited directly: dose threshold and D50

or LD50. The other elicited values were D10 and D90. The shape factor is calculated using the following equation:

(6.2)

R 1 2 ln  D

D50

--------     

–      = – exp

 ln  0.5

ln  0.9 -----------------     ln D50D10 ----------     =  ln
92

Values are tabulated in Table 6-1 at 11 quantile levels and for the mean and mode of the distribution. Figures 6-1 through 6-8 compare the aggregated distributions, using the resampling methodology, with the distributions provided by each of the experts for each of the 4 early health effects.

It is not entirely obvious how to best interpolate the data in Table 6-1 between quantile levels.

Since all of the quantities in the table are positive, a logarithmic interpolation can be used and is

likely to most faithfully reproduce the intention of the experts. 

Table 6-1: Coefficients for quantifying early health effects.

Quantile

Weibull Factors for Early Health Effects

Hematopoietic 

Syndrome

Gastrointestinal 

Syndrome Pulmonary Syndrome Pneumonitis

LDth 

(Sv)

LD50 

(Sv)  LDth (Sv)

LD50 

(Sv)  LDth (Sv)

LD50 

(Sv)  Dth (Sv)

D50 

(Sv) 

0.00 0.67 2.0 2.4 2.0 4.8 3.2 5.3 10.0 3.7 2.7 5.0 3.5

0.01 0.80 2.4 2.5 2.9 6.2 3.2 6.7 12.0 3.8 3.5 7.3 3.6

0.05 1.11 3.3 2.8 3.8 7.9 3.4 8.6 16.6 4.4 4.4 8.9 4.0

0.10 1.32 3.7 3.2 4.5 8.5 3.6 9.6 17.8 4.7 5.1 10.3 4.6

0.25 1.72 4.4 4.2 5.4 10.0 6.0 11.5 19.9 5.6 6.5 12.9 5.1

0.50 2.32 5.6 6.1 6.5 12.1 9.3 13.6 23.5 9.6 9.2 16.6 7.3

0.75 3.56 7.2 10.2 7.7 14.9 11.0 18.4 33.6 13.8 11.3 20.3 14.8

0.90 4.63 8.9 13.2 8.8 17.7 16.0 22.1 42.0 16.9 14.3 25.7 19.3

0.95 5.26 10.3 14.3 9.5 19.1 18.0 24.0 45.0 18.7 16.6 31.1 22.1

0.99 6.19 11.8 15.8 13.0 23.3 19.5 32.4 55.7 21.4 20.7 36.5 65.4

1.00 8.55 16.5 16.0 15.0 30.0 19.9 37.5 76.5 21.7 28.5 55.5 83.8

Mean 2.70 6.0 7.4 6.6 12.7 9.3 15.1 27.3 10.1 9.5 17.5 11.1

Mode 2.18 5.6 6.0 6.5 10.3 4.4 12.0 20.1 4.8 6.6 16.4 4.7
93

Figure 6-1. Expert and resampled data for the threshold dose corresponding to hematopoietic syndrome for a person receiving 100 Gy/hr low-LET radiation to the

whole body

Figure 6-2. Expert and resampled data for LD50 corresponding to hematopoietic syndrome for a person receiving 100 Gy/hr low-LET radiation to the whole body

0.0

0.2

0.4

0.6

0.8

1.0

1.E-1 1.E+0 1.E+1

Threshold Dose (Sv)

Quantile

A

B

C

D

E

F

G

H

I

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E+0 1.E+1 1.E+2

LD50 (Sv)

Quantile

A

B

C

D

E

F

G

H

I

RSM
94

Figure 6-3. Expert and resampled data for the threshold dose corresponding to gastrointestinal syndrome for a person receiving 100 Gy/hr low-LET radiation to the

whole body

Figure 6-4. Expert and resampled data for LD50 corresponding to gastrointestinal syndrome for a person receiving 100 Gy/hr low-LET radiation to the whole body 

0.0

0.2

0.4

0.6

0.8

1.0

1.E+0 1.E+1 1.E+2

Threshold Dose (Sv)

Quantile

A

B

C

D

E

F

G

H

I

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E+0 1.E+1 1.E+2

LD50 (Sv)

Quantile

A

B

C

D

E

F

G

H

I

RSM
95

Figure 6-5. Expert and resampled data for the threshold dose corresponding to pulmonary syndrome for a person receiving 1 Gy/hr beta radiation to the lungs

Figure 6-6. Expert and resampled data for LD50 corresponding to pulmonary syndrome

for a person receiving 1 Gy/hr beta radiation to the lungs

0.0

0.2

0.4

0.6

0.8

1.0

1.E+0 1.E+1 1.E+2

Threshold Dose (Sv)

Quantile

A

B

C

D

E

F

G

H

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E+0 1.E+1 1.E+2

LD50 (Sv)

Quantile

A

B

C

D

E

F

G

H

RSM
96

Figure 6-7. Expert and resampled data for the threshold dose corresponding to pneumonitis for a person receiving 1 Gy/hr beta radiation to the lungs

Figure 6-8. Expert and resampled data for D50 corresponding to pneumonitis for a person receiving 1 Gy/hr beta radiation to the lungs

0.0

0.2

0.4

0.6

0.8

1.0

1.E+0 1.E+1 1.E+2

Threshold Dose (Sv)

Quantile

A

B

C

D

E

F

G

H

RSM
97

6.2 Correlations Between Early Health Parameters

It is not obvious that the acute health risks associated with doses to the human organs are interrelated. Therefore, the risk factors provided in Table 6-1 should be treated as being uncorrelated for

different organs. However, the values in Table 6-1 for a given health effect should be treated as

having a correlation coefficient of 1. That is, the same quantile values should be used for all three

parameters associated with a health effect. Furthermore, the parameters associated with the pulmonary syndrome and pneumonitis should be treated as having a correlation coefficient of 1 because it would not make sense for pneumonitis to require higher doses than the pulmonary

syndrome.

99

7.0 FOOD-CHAIN PARAMETERS

A large number of food chain parameters are included in the COMIDA2 food-chain model. All of

the parameters relevant to the COMIDA2 food-chain model that were evaluated in the expert elicitation are described in this section. 

7.1 Distributions of Animal Feed Parameters

The first category of data evaluated in this section is the quantity of feed consumed by livestock

that are most commonly consumed as meat or animal products in the United States. Three types of

food consumption as well as consumption of soil by five categories of livestock are evaluated. All

consumption rates are calculated on a dry basis. Cattle, sheep, and poultry are assumed to live predominantly outdoors; pigs are assumed to live predominantly in a barn. The values at 11 quantile

levels and for the mean and mode are shown in Tables 7-1 and 7-2. Figures 7-1 through 7-15 show

comparisons between the expert data and the resampled curves from which the data in Tables 7-1

and 7-2 are extracted.

It is not entirely obvious how to best interpolate the data in Tables 7-1 and 7-2 between quantile

levels. Since some of the quantities in both of the tables are zero, it is probably best to use a simple linear interpolation. 
100

Table 7-1: Daily consumption by beef and dairy cattle.

Quantile

Dry Quantity Consumed (kg/dy)

Dairy Cattle Beef Cattle

Pasture 

Grass

Silage/

Hay Cereals Soil Pasture Grass

Silage/

Hay Cereals Soil

0.00 1.0 0.1 0.0 0.01 1.5 0.0 0.0 0.01

0.01 2.0 0.1 0.0 0.01 2.4 0.0 0.0 0.01

0.05 3.2 0.4 0.1 0.01 3.5 0.0 0.0 0.01

0.10 4.5 1.0 0.5 0.02 4.6 1.0 0.1 0.02

0.25 7.0 2.8 2.7 0.09 6.2 3.4 1.5 0.09

0.50 12.0 5.9 5.7 0.26 8.2 8.1 6.3 0.26

0.75 16.6 11.4 9.7 0.70 10.6 10.2 9.3 0.70

0.90 20.5 19.6 14.8 1.24 12.8 12.4 11.1 1.24

0.95 23.7 22.6 16.6 1.67 14.7 14.4 12.8 1.67

0.99 40.0 30.1 26.4 2.92 24.0 23.3 21.1 2.92

1.00 50.0 50.0 38.0 5.00 30.0 30.0 28.0 5.00

Mean 12.7 8.2 6.9 0.50 8.8 7.5 6.0 0.50

Mode 5.1 0.2 0.0 0.01 7.5 0.0 0.0 0.01
101

Table 7-2: Daily consumption by sheep, pigs, and poultry.

Quantile

Dry Quantity Consumed (kg/dy)

Sheep Pigs Poultry

Pasture 

Grass

Silage/

Hay Cereals Soil Cereals Soil Cereals Soil

0.00 0.20 0.00 0.00 0.01 0.3 0.00 0.015 0.000

0.01 0.27 0.00 0.00 0.01 0.5 0.00 0.026 0.000

0.05 0.45 0.00 0.00 0.01 0.9 0.00 0.044 0.000

0.10 0.56 0.15 0.10 0.02 1.1 0.00 0.054 0.000

0.25 0.86 0.44 0.44 0.05 1.5 0.01 0.074 0.001

0.50 1.29 0.97 0.86 0.12 2.3 0.03 0.101 0.005

0.75 1.81 1.66 1.44 0.21 10.8 0.14 0.134 0.015

0.90 2.29 2.29 1.94 0.33 13.7 0.32 0.172 0.034

0.95 2.73 2.55 2.36 0.45 14.7 0.41 0.196 0.049

0.99 4.52 4.46 3.89 0.75 20.4 0.75 0.303 0.096

1.00 6.00 6.00 5.00 1.00 32.0 1.00 0.404 0.160

Mean 1.42 1.14 1.01 0.16 5.2 0.10 0.11 0.013

Mode 1.06 0.00 0.00 0.03 1.3 0.00 0.10 0.000
102

Figure 7-1. Expert and resampled data for consumption rate (kg/day on a dry basis) of

pasture grass by dairy cattle

Figure 7-2. Expert and resampled data for consumption rate (kg/day on a dry basis) of silage/hay by dairy cattle

0.0

0.2

0.4

0.6

0.8

1.0

1 10 100

Pasture Grass Consumption (kg/day)

Cumulative Probability

H

I

J

K

L

M

N

O

P

Q

RSM

0.0

0.2

0.4

0.6

0.8

1.0

0.01 0.1 1 10 100

Silage/Hay Consumption (kg/day)

Cumulative Probability

H

J

K

M

N

O

RSM
103

Figure 7-3. Expert and resampled data for consumption rate (kg/day on a dry basis) of

cereals by dairy cattle

Figure 7-4. Expert and resampled data for consumption rate (kg/day on a dry basis) of

soil by dairy and beef cattle

0.0

0.2

0.4

0.6

0.8

1.0

1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Cereal Consumption (kg/day)

Cumulative Probability

H

I

J

K

L

M

N

O

Q

RSM

0.0

0.2

0.4

0.6

0.8

1.0

0.001 0.01 0.1 1 10

Soil Consumption (kg/day)

Cumulative Probability

H

I

J

K

L

M

N

P

Q

RSM
104

Figure 7-5. Expert and resampled data for consumption rate (kg/day on a dry basis) of

pasture grass by beef cattle

Figure 7-6. Expert and resampled data for consumption rate (kg/day on a dry basis) of silage/hay by beef cattle

0.0

0.2

0.4

0.6

0.8

1.0

1 10 100

Pasture Grass Consumption (kg/day)

Cumulative Probability

H

I

J

K

L

M

N

P

Q

RSM

0.0

0.2

0.4

0.6

0.8

1.0

0.01 0.1 1 10 100

Silage/Hay Consumption (kg/day)

Cumulative Probability

H

I

K

L

N

RSM
105

Figure 7-7. Expert and resampled data for consumption rate (kg/day on a dry basis) of

cereals by beef cattle

Figure 7-8. Expert and resampled data for consumption rate (kg/day on a dry basis) of

pasture grass by sheep

0.0

0.2

0.4

0.6

0.8

1.0

0.01 0.1 1 10 100

Cereal Consumption (kg/day)

Cumulative Probability

H

I

K

L

N

RSM

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10

Pasture Grass Consumption (kg/day)

Cumulative Probability

H

I

J

K

L

N

P

Q

RSM
106

Figure 7-9. Expert and resampled data for consumption rate (kg/day on a dry basis) of silage/hay by sheep

Figure 7-10. Expert and resampled data for consumption rate (kg/day on a dry basis) of

cereals by sheep

0.0

0.2

0.4

0.6

0.8

1.0

0.01 0.1 1 10

Silage/Hay Consumption (kg/day)

Cumulative Probability

H

I

K

L

N

RSM

0.0

0.2

0.4

0.6

0.8

1.0

0.01 0.1 1 10

Cereal Consumption (kg/day)

Cumulative Probability

H

I

K

L

N

RSM
107

Figure 7-11. Expert and resampled data for consumption rate (kg/day on a dry basis) of

soil by sheep

Figure 7-12. Expert and resampled data for consumption rate (kg/day on a dry basis) of

cereal by pigs

0.0

0.2

0.4

0.6

0.8

1.0

0.001 0.01 0.1 1

Soil Consumption (kg/day)

Cumulative Probability

H

I

J

K

L

N

P

Q

RSM

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100

Cereal Consumption (kg/day)

Cumulative Probability

K

N

P

Q

RSM
108

Figure 7-13. Expert and resampled data for consumption rate (kg/day on a dry basis) of

soil by pigs

Figure 7-14. Expert and resampled data for consumption rate (kg/day on a dry basis) of

cereal by poultry

0.0

0.2

0.4

0.6

0.8

1.0

0.0001 0.001 0.01 0.1 1

Soil Consumption (kg/day)

Cumulative Probability

H

I

K

N

P

Q

RSM

0.0

0.2

0.4

0.6

0.8

1.0

0.01 0.1 1

Cereal Consumption (kg/day)

Cumulative Probability

H

I

J

K

L

M

N

P

Q

RSM
109

Figure 7-15. Expert and resampled data for consumption rate (kg/day on a dry basis) of

soil by poultry

7.2 Correlations Between Animal Feed Parameters

It is clear that the quantities in Tables 7-1 and 7-2 for a specified livestock type must be correlated. For example, a dairy cow that consumes 50 kg/dy of pasture grass would not also consume the

maximum quantities of hay and cereals. So, the various categories of food consumption must be

negatively correlated. The correlations are made more difficult by the fact that there are three food

categories from which the total should be more or less constant. Also, consumption of soil by cattle and sheep is likely to be correlated with consumption of pasture grass and to a lesser extent silage/hay; cereals are likely to be eaten from some type of feed trough that would limit the

consumption of soil. As a suggestion, the correlation between pasture grass and hay consumption

should be strongly inversely correlated (i.e., -0.9 to -1.0) for both dairy and beef cattle. The correlation between grains and the other two feed categories should be weak (i.e., -0.5 to 0.5). The correlation between soil and the three feed categories should also be weak. 

Consumption of cereals by pigs and poultry is even more difficult to interpret. The expert elicitation process did not prescribe an alternative food source to grains, but the animals are presumably

given some other type of feed if grain is not available. The only other type of feed allowed for

poultry in COMIDA2 is legumes, but this would not normally be a significant portion of the food

source for chickens. Thus, the large uncertainty in the daily intake of grains by chickens (and also

pigs) seems difficult to justify. Since no alternative food source is suggested, it is not obvious

0.0

0.2

0.4

0.6

0.8

1.0

0.0001 0.001 0.01 0.1 1

Soil Consumption (kg/day)

Cumulative Probability

H

I

J

K

N

P

Q

RSM
110

whether or not the daily intake of soil by chickens (and pigs) should be correlated with the intake

of grains. Therefore, a weak correlation (i.e., -0.5 to 0.5) between consumption of grains and soil

is reasonable. 

7.3 Distributions of Concentration Ratios

The second category of data evaluated in this section is the ratio of grain and root concentrations

to elemental concentrations in the surrounding soil. The values at 11 quantile levels are shown in

Table 7-3. Figures 7-16 through 7-19 show comparisons between the expert data and the resampled curves from which the data in Table 7-3 are extracted.

Table 7-3: Ratio of concentration in foodstuff to concentration in soil (Bq/kg fresh plant 

mass / Bq/kg dry soil mass). 

Quantile

Ratio of Concentration in 

Foodstuff to Concentration 

in Soil (Dimensionless)

Grain Root

Sr Cs Sr Cs

0.00 0.00 0.00 0.000 0.00000

0.01 0.00 0.00 0.000 0.00000

0.05 0.01 0.01 0.000 0.00000

0.10 0.01 0.02 0.000 0.00000

0.25 0.04 0.03 0.000 0.00000

0.50 0.13 0.07 0.006 0.00000

0.75 0.29 0.16 0.017 0.00007

0.90 0.42 0.33 0.075 0.00086

0.95 0.93 0.50 0.121 0.00197

0.99 2.73 0.91 0.197 0.00454

1.00 5.25 1.73 0.347 0.00600

Mean 0.27 0.14 0.023 0.00032

Mode 0.01 0.03 0.000 0.00000
111

It is not entirely obvious how to best interpolate the data in Table 7-3 between quantile levels.

Since some of the quantities are zero, it is probably best to use a simple linear interpolation. 

Figure 7-16. Expert and resampled data for grain to soil concentration ratio (Bq/kg Fresh

Plant Mass / Bq/kg Dry Soil Mass) for Sr

0.0

0.2

0.4

0.6

0.8

1.0

0.001 0.01 0.1 1 10

Grain to Soil Concentration Ratio 

(dimensionless)

Cumulative Probability

A

B

C

E

F

RSM
112

Figure 7-17. Expert and resampled data for grain to soil concentration ratio (Bq/kg Fresh

Plant Mass / Bq/kg Dry Soil Mass) for Cs

Figure 7-18. Expert and resampled data for root to soil concentration ratio (Bq/kg Fresh

Plant Mass / Bq/kg Dry Soil Mass) for Sr

0.0

0.2

0.4

0.6

0.8

1.0

0.001 0.01 0.1 1 10

Grain to Soil Concentration Ratio 

(dimensionless)

Cumulative Probability

A

B

C

E

F

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1E-07 1E-06 1E-05 0.0001 0.001 0.01 0.1 1

Root to Soil Concentration Ratio 

(dimensionless)

Cumulative Probability

B

C

E

F

RSM
113

Figure 7-19. Expert and resampled data for root to soil concentration ratio (Bq/kg Fresh

Plant Mass / Bq/kg Dry Soil Mass) for Cs

7.4 Correlations Between Concentration Ratios

Since the chemical properties of cesium and strontium are different, there is no reason to assume

that the concentration ratios for these elements should be correlated. There could be some correlation between the uptake of these elements by grains and roots, but the only defensible assumption

is that they are also uncorrelated. Thus, it is reasonable that these four distributions be treated as

completely uncorrelated.

7.5 Distributions of Transfer Coefficients

The third category of data evaluated in this section is a set of transfer coefficients. These are quantities with dimensions of d/kg or d/l that reflect the equilibrium ratio of the activity in foodstuffs

to the daily activity intake of the animal generating the foodstuff. Foodstuffs considered are beef,

milk, poultry, and eggs. The elements considered are strontium and cesium; iodine is also included for milk and eggs. The values at 11 quantile levels are shown in Table 7-4. Figures 7-20

through 7-29 show comparisons between the expert data and the resampled curves from which the

data in Table 7-4 are extracted.

0.0

0.2

0.4

0.6

0.8

1.0

0.0000001 0.000001 0.00001 0.0001 0.001 0.01

Root to Soil Concentration Ratio 

(dimensionless)

Cumulative Probability

C

F

RSM
114

Table 7-4: Ratio of concentration in foodstuff to daily ingestion level. 

It is not entirely obvious how to best interpolate the data in Table 7-4 between quantile levels.

Since some of the quantities are zero, it is probably best to use a simple linear interpolation. 

Quantile

Ratio of Activity in Foodstuff to Daily Ingestion Level

Beef (d/kg) Milk (d/l) Poultry 

(d/kg) Eggs (d/kg)

Sr Cs Sr Cs I Sr Cs Sr Cs I

0.00 0.000 0.001 0.0002 0.000 0.000 0.00 0.2 0.0 0.03 0.0

0.01 0.000 0.003 0.0002 0.000 0.001 0.00 0.2 0.0 0.03 0.0

0.05 0.000 0.007 0.0004 0.001 0.001 0.00 0.4 0.0 0.07 0.0

0.10 0.000 0.009 0.0005 0.001 0.001 0.01 0.7 0.0 0.10 0.3

0.25 0.001 0.018 0.0010 0.002 0.003 0.02 1.6 0.1 0.22 1.4

0.50 0.003 0.039 0.0019 0.005 0.006 0.06 3.9 0.2 0.48 2.6

0.75 0.008 0.057 0.0032 0.010 0.015 0.30 8.9 0.4 0.80 3.8

0.90 0.011 0.088 0.0042 0.020 0.027 1.05 12.0 0.9 1.59 5.4

0.95 0.016 0.120 0.0056 0.030 0.036 2.29 15.9 2.5 2.03 7.7

0.99 0.079 0.196 0.0100 0.138 0.068 6.03 25.6 9.8 3.31 11.4

1.00 0.200 0.400 0.0140 0.400 0.100 8.00 50.0 17.2 5.00 20.0

Mean 0.006 0.046 0.0023 0.011 0.011 0.44 5.9 0.6 0.67 3.0

Medium 0.000 0.053 0.0007 0.001 0.001 0.01 0.5 0.0 0.07 0.0
115

Figure 7-20. Expert and resampled data for beef transfer coefficient at steady state (Bq/kg

/ Bq/d) for strontium

Figure 7-21. Expert and resampled data for beef transfer coefficient at steady state (Bq/kg

/ Bq/d) for cesium

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

Transfer Coefficient (d/kg)

Cummulative Probability

H

I

J

K

L

N

O

P

Q

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-3 1.E-2 1.E-1 1.E+0

Transfer Coefficient (d/kg)

Cummulative Probability

H

I

J

K

L

M

N

O

P

Q

RSM
116

Figure 7-22. Expert and resampled data for milk transfer coefficient at steady state (Bq/l /

Bq/d) for strontium 

Figure 7-23. Expert and resampled data for milk transfer coefficient at steady state (Bq/l /

Bq/d) for cesium 

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1

Transfer Coefficient (d/l)

Cummulative Probability

H

I

J

K

L

M

N

O

P

Q

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0

Transfer Coefficient (d/l)

Cummulative Probability

H

I

J

K

L

M

N

O

P

Q

RSM
117

Figure 7-24. Expert and resampled data for milk transfer coefficient at steady state (Bq/l /

Bq/d) for iodine 

Figure 7-25. Expert and resampled data for poultry transfer coefficient at steady state (Bq/

kg / Bq/d) for strontium

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1

Transfer Coefficient (d/l)

Cummulative Probability

H

I

J

K

L

M

N

O

P

Q

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1

Transfer Coefficient (d/kg)

Cummulative Probability

H

I

J

K

L

N

P

Q

RSM
118

Figure 7-26. Expert and resampled data for poultry transfer coefficient at steady state (Bq/

kg / Bq/d) for cesium 

Figure 7-27. Expert and resampled data for egg transfer coefficient at steady state (Bq/kg /

Bq/d) for strontium 

0.0

0.2

0.4

0.6

0.8

1.0

1.E-1 1.E+0 1.E+1 1.E+2

Transfer Coefficient (d/kg)

Cummulative Probability

H

I

J

K

L

N

P

Q

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Transfer Coefficient (d/kg)

Cummulative Probability

H

I

J

K

L

N

P

Q

RSM
119

Figure 7-28. Expert and resampled data for egg transfer coefficient at steady state (Bq/kg /

Bq/d) for cesium 

Figure 7-29. Expert and resampled data for egg transfer coefficient at steady state (Bq/kg /

Bq/d) for iodine 

0.0

0.2

0.4

0.6

0.8

1.0

1.E-2 1.E-1 1.E+0 1.E+1

Transfer Coefficient (d/kg)

Cummulative Probability

H

I

J

K

L

M

N

P

Q

RSM

0.0

0.2

0.4

0.6

0.8

1.0

1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2

Transfer Coefficient (d/kg)

Cummulative Probability

H

I

J

K

L

M

N

P

Q

RSM
120

7.6 Correlations Between Transfer Coefficients

Since the chemical properties of cesium, strontium, and iodine are quite different, there is no reason to assume that the transfer coefficients for these elements should be correlated. While there

could be some correlation between the accumulation of these elements in beef, milk, poultry, and

eggs, the only defensible assumption is that they are also uncorrelated. Thus, it is reasonable that

the distributions for these foodstuffs be treated as completely uncorrelated.
121

8.0 CONCLUSIONS 

The results of the expert elicitation conducted by the NRC and the CEC have been evaluated to

provide ranges of values and degrees of belief for parameters in off-site consequence analyses that

are likely to have significant or moderate influence on the calculated results. This present work

represents the effort to fairly represent the divergent opinions of the experts while maintaining the

resulting parameters within physical limits. This evaluation also includes correlation coefficients

between variables when appropriate. The medians, means, and modes of the distributions are presented so that the user can choose a value when only a point estimate calculation is needed.

123

9.0 REFERENCES

1. F.T. Harper, et al., “Probabilistic Accident Consequence Uncertainty Analysis, Dispersion

and Deposition Uncertainty Assessment,” NUREG/CR-6244, NRC, Washington, DC, January 1995.

2. F.T. Harper, et al., “Probabilistic Accident Consequence Uncertainty Analysis, Food Chain

Uncertainty Assessment,” NUREG/CR-6523, NRC, Washington, DC, June 1997.

3. F.T. Harper, et al., “Probabilistic Accident Consequence Uncertainty Analysis, Uncertainty

Assessment for Deposited Material and External Doses,” NUREG/CR-6526, NRC, Washington, DC, December 1997.

4. F.T. Harper, et al., “Probabilistic Accident Consequence Uncertainty Analysis, Early Health

Effects Uncertainty Assessment,” NUREG/CR-6545, NRC, Washington, DC, December

1997.

5. F.T. Harper, et al., “Probabilistic Accident Consequence Uncertainty Analysis, Late Health

Effects Uncertainty Assessment,” NUREG/CR-6555, NRC, Washington, DC, December

1997.

6. F.T. Harper, et al., “Probabilistic Accident Consequence Uncertainty Analysis, Uncertainty

Assessment for Internal Dosimetry,” NUREG/CR-6571, NRC, Washington, DC, April

1998.

7. D. Chanin and M.L. Young, “Code Manual for MACCS2, User's Guide,” NUREG/CR6613, NRC, Washington, DC, May 1998.

8. T. A. Wheeler, G. D. Wyss, and F. T. Harper, “Cassini Spacecraft Uncertainty Analysis Data

and Methodology Review and Update, Volume 1: Updated Parameter Uncertainty Models

for Consequence Analysis,” SAND2000-2719/1, Sandia National Laboratories, Albuquerque, NM, 2000.

9. D. B. Turner, “Workbook of Atmospheric Dispersion Estimates, An Introduction to Dispersion Modeling,” 2nd Ed., Lewis Publishers, CRC Press, Boca Raton, 1994.




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NUCLEAR REGULATORY COMMISSION

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OFFICIAL BUSINESS
NUREG/CR-7161 Synthesis of Distributions Representing Important Non-Site-Specific 

Parameters in Off-Site Consequence Analyses