United Nations Scientific Committee on the Effects of Atomic Radiation

ATTACHMENT A-12

APPROACH FOR ASSESSING UNCERTAINTIES AND
VARIABILITY IN ESTIMATED DOSESUNSCEAR 2020/2021 Report, Annex B, Levels and effects of radiation exposuredue to the accident at the Fukushima Daiichi Nuclear Power Station: implicationsof information published since the UNSCEAR 2013 Report
Content
This attachment describes:− The general approach adopted for evaluating and propagating uncertainties in estimating
doses to the public from the accident at the Fukushima Daiichi Nuclear Power Station(FDNPS);− How the general approach has been applied in estimating uncertainties and variability indoses for each of the significant pathways of exposure; and− How the approach has been applied in estimating the distribution of doses in particulargroups of the population (municipalities, prefectures, evacuated areas, etc.) from all
pathways of exposure and in estimating the uncertainty in the average doses for the samegroups.
Notes
The designations employed and the presentation of material in this publication do not imply theexpression of any opinion whatsoever on the part of the Secretariat of the United Nations
concerning the legal status of any country, territory, city or area, or of its authorities, orconcerning the delimitation of its frontiers or boundaries.
Information on Uniform Resource Locators (URLs) and links to Internet sites contained in thepresent publication are provided for the convenience of the reader and are correct at the time ofissue. The United Nations takes no responsibility for the continued accuracy of that informationor for the content of any external website.
© United Nations, April 2022. All rights reserved, worldwide.
This publication has not been formally edited.

CONTENTS
I. GENERAL APPROACH FOR EVALUATING AND PROPAGATINGUNCERTAINTIES ............................................................................................................... 5
II. APPLICATION OF THE GENERAL APPROACH FOR EVALUATING AND
PROPAGATING UNCERTAINTIES ................................................................................... 7
A. Assessment of uncertainties and variability in doses to residents from radionuclides
in the air ............................................................................................................................ 7
B. Assessment of uncertainties and variability in doses to evacuees from radionuclides
in the air .......................................................................................................................... 10
C. Assessment of uncertainties and variability in external doses from depositedradionuclides .................................................................................................................. 13
D. Assessment of uncertainties and variability in dose from ingestion .............................. 15
E. Combination of doses from different exposure pathways .............................................. 16
REFERENCES ........................................................................................................................... 17

ANNEX B, ATTACHMENT A-12: APPROACH FOR ASSESSING UNCERTAINTIES AND VARIABILITY IN ESTIMATED DOSES

I.

5

GENERAL APPROACH FOR EVALUATING UNCERTAINTIES1.
The approach adopted by the Committee and described in this attachment is in accordancewith the Joint Committee for Guides in Metrology [JCBM, web], in particular with the ISO/IEC
Guide 98-3 Supplement 1 [JCGM, 2008a].
2.
The uncertainties of doses D have been evaluated by probability density functions (PDF),
which take into account the uncertainties and variabilities of the input quantities on which thedoses depend, including any model parameters unless otherwise noted.
� of
3.
The PDFs quantify the probabilities for the unknown and unknowable true values 𝐷𝐷
the doses given the information about the input quantities. Note that the superscripted ~ is used
to indicate a true value of a quantity [ISO, 2019] (see [JCGM, 2012] for the terminology). The
PDFs represent Bayesian probabilities. They cannot be handled by frequentistic statistics
because these cannot handle Type B uncertainties, which dominate the uncertainties of the doses.
4.
The uncertainties take into account the observed variability of input quantities, forexample the deposition densities of radionuclides, as well as the uncertainties of other input
quantities, the values of which are unknown (e.g., consumption rates, occupation factors etc.).
While the former are taken into account as Type A uncertainties, the latter are Type B
uncertainties for which PDFs are assigned from other sources, for example from the literature,general knowledge, and expert judgement. Both types of uncertainty are equally relevant andhave been taken into account in estimating the overall uncertainties. Mathematically, there is nodifference between variability and uncertainty.
5.

For any model of evaluation of a dose D:
𝐷𝐷 = 𝐺𝐺(𝑋𝑋1 , . . . , 𝑋𝑋𝑚𝑚 ) = 𝐺𝐺(𝑿𝑿)(A-12.1)

with a model function G, the uncertainties could be evaluated according to ISO/IEC Guide 98-3
[JCGM, 2008b] or ISO/IEC Guide 98-3 Supplement 1 [JCGM, 2008a]. The ISO/IEC Guide 98-3
[JCGM, 2008b] uses normal (Gaussian) distributions and an approximation based on a Taylor
expansion truncated after the first order term. However, given the complexity of the model
equations and the non-Gaussian character of many input quantities, the ISO/IEC Guide 98-3
Supplement 1 [JCGM, 2008a] is to be preferred and has been adopted by the Committee in its
assessment. It applies to any distribution type and allows the calculation of posterior PDF of themeasurand (here the dose) using Monte Carlo methods (see also [ISO, 2019] for details of suchprocedures).
6.
To derive the PDF of a dose, D, PDFs of the input quantities relevant to its estimation
have to be established; this process is described in section II for the different exposure pathways.
Then, a joint probability distribution, 𝑓𝑓𝑋𝑋 (𝑥𝑥�|𝑥𝑥), can be formed, which, for independent input
quantities, is given by:
�|𝒙𝒙) = ∏𝑚𝑚
𝑓𝑓𝑿𝑿 (𝒙𝒙�𝑖𝑖 |𝑥𝑥𝑖𝑖 )1 𝑓𝑓𝑋𝑋𝑖𝑖 (𝑥𝑥(A-12.2)

with 𝑥𝑥 being any available and relevant information and 𝑥𝑥𝑖𝑖 being the subset of information
available for 𝑋𝑋𝑖𝑖 . A joint probability distribution has to be assigned to those 𝑋𝑋𝑖𝑖 that are notindependent and inserted in equation A-12.2 for the respective input quantities (see [JCGM,
2008b] for further details). For the evaluation of the uncertainties of doses, the Committee has

6

ANNEX B, ATTACHMENT A-12: APPROACH FOR ASSESSING UNCERTAINTIES AND VARIABILITY IN ESTIMATED DOSES

assumed that the different exposure pathways are statistically independent so that no correlations
had to be taken into account.
� �𝑥𝑥) can then be calculated from the joint probability
7.
The probability distribution 𝑓𝑓𝐷𝐷 (𝐷𝐷distribution 𝑓𝑓𝑋𝑋 (𝑥𝑥�|𝑥𝑥) using the model equation 𝐷𝐷 = 𝐺𝐺(𝑋𝑋) and the so-called Markov equation:� �𝒙𝒙) = ∫+∞ 𝑓𝑓𝑿𝑿 (𝜉𝜉|𝒙𝒙) ⋅ 𝛿𝛿(𝐷𝐷� − 𝐺𝐺(𝜉𝜉)) 𝑑𝑑 𝜉𝜉
𝑓𝑓𝐷𝐷 (𝐷𝐷−∞(A-12.3)

8.
In practice, the evaluation of the integral of equation A-12.3, is performed by conducting
𝑛𝑛𝑀𝑀 Monte Carlo trials. In each trial, a set of random numbers 𝑥𝑥1,𝑖𝑖 , . . . , 𝑥𝑥𝑛𝑛,𝑖𝑖 is drawn from each of
the PDFs 𝑓𝑓𝑋𝑋𝑖𝑖 (𝑥𝑥�𝑖𝑖 |𝑥𝑥𝑖𝑖 ) of the input quantities and the respective doses 𝐷𝐷𝑖𝑖 = 𝐺𝐺(𝑥𝑥1,𝑖𝑖 , . . . , 𝑥𝑥𝑛𝑛,𝑖𝑖 ) are�⃗𝑀𝑀 = �𝐷𝐷1 , . . . , 𝐷𝐷𝑛𝑛 � is ordered ascendingly
calculated according to equation A-12.1. The vector 𝐷𝐷
𝑀𝑀�⃗𝑀𝑀 . 𝐷𝐷
�⃗𝑀𝑀 is a discreteand then cumulative probabilities 𝑖𝑖/𝑛𝑛𝑀𝑀 are assigned to the 𝐷𝐷𝑖𝑖 of 𝐷𝐷𝑦𝑦�� �𝑥𝑥) = ∫ 𝑓𝑓𝐷𝐷 (𝜂𝜂|𝑥𝑥) 𝑑𝑑𝑑𝑑 of 𝐷𝐷. From this posterior
representation of the distribution function 𝐹𝐹𝐷𝐷 (𝐷𝐷−∞distribution function all required moments of the PDF can be derived numerically.
9.
This process has been used by the Committee to derive PDFs of the doses from eachexposure pathway. For the calculation of the total dose, E, summed over the different exposure
pathways, 𝐸𝐸 = 𝐸𝐸ext + 𝐸𝐸ing + 𝐸𝐸inh , the PDF of the total dose was also calculated by Monte Carlotrials with samples drawn from the PDFs of the doses from each pathway, 𝑓𝑓𝐸𝐸𝑖𝑖 (𝐸𝐸�𝑖𝑖 �𝒙𝒙) (𝑖𝑖 =ext, ing, inh). The Committee has used the same procedure for the estimation of PDFs of theeffective doses and absorbed doses in various organs.
10.
For all calculated doses (effective dose and absorbed doses in various organs) and dose
rates uncertainties were evaluated and the PDF have been reported as graphs of the PDFs or bysuitable moments of the distributions, such as means, medians and specified percentiles. Sensitivity
analyses were not performed, but the relevance of the individual sources of uncertainty can be
judged from the data given for the individual cases. Detailed descriptions of the calculations andthe models of evaluation are given in attachments A-1, A-2, A-3, A-9 and A-10.
11.
A similar process, based on Monte Carlo simulations, has been used to derive the PDF
of the average dose in the population group (and therefore the mean and 95th percentile upperbound) from the PDFs of the doses from each exposure pathway, in this case by calculating the
average dose in the population group summed over the exposure pathways in each Monte Carlotrial. Again, the same procedure has been used for average effective doses and absorbed doses
in various organs. The PDFs of the average doses have been used, in particular, for theassessment of the health implications of the estimated doses (see attachment A-23), where theCommittee has carried out power calculations using the average dose in a specified populationgroup (e.g., adults living in a municipality) and the 95th percentile upper bound of this dose.

ANNEX B, ATTACHMENT A-12: APPROACH FOR ASSESSING UNCERTAINTIES AND VARIABILITY IN ESTIMATED DOSESII.

APPLICATION OF THE GENERAL APPROACH FOREVALUATING AND PROPAGATING UNCERTAINTIESA.

Assessment of uncertainties and variability in doses to residents
from radionuclides in the air

7

12.
The Committee’s aim was to make realistic estimates of doses and, for this purpose, it has
used the best models and input data available to it. However, there are uncertainties associated withthese estimates because of variability of input quantities, incomplete knowledge or information,
imperfect models and the many assumptions that had to be made as a consequence.
13.
Figure A-12.I shows the key modelling steps in assessing doses to the public for residents(i.e., those who were not evacuated) in Fukushima Prefecture and neighbouring prefectures fromthe exposure pathways of inhalation and external exposure from radionuclides in the air. The
estimated doses from inhalation and from external exposure from the plume are largely based on
measured levels of deposition density of radionuclides on the ground:(a) As a first step, the concentrations of 137Cs in air were estimated from the measured levelsof deposition density of 137Cs on the ground using the ratios of estimates fromatmospheric transport, dispersion and deposition modelling (ATDM) of the timeintegrated activity concentrations in air to the deposition density (for the reference
radionuclide 137Cs) as a function of location (see attachments A-9 and A-10 for further
details);(b) Then, concentrations of 131I (separately for elemental, organic and aerosol-bound forms),132
Te/132I and 134Cs in air were derived from the estimated concentrations of 137Cs in air
using the ratios of the concentrations of these radionuclides in air to the concentration of137
Cs in air determined from ATDM. Because the ATDM did not provide estimates of
the concentrations in air for the short-lived radionuclide, 133I, its concentrations were
derived from 131I concentrations using the ratio of 133I to 131I at 14:46 on 11 March 2011
from Nishihara et al. [Nishihara et al., 2012] and correcting for the different physicalhalf-lives of the two isotopes;(c) External exposure to radionuclides in the air and exposure from inhalation were thenassessed from the radionuclide concentrations in air, using: age-dependent breathing rates(for inhalation dose); reduction factors to take account of the reduction in theconcentrations of radionuclides, and shielding, inside buildings; occupancy factors toaccount for the proportion of time spent indoors for the various age and social groups of
the Japanese population; and relevant dose coefficients.
14.
The main sources of uncertainty and variability that were judged by the Committee tosignificantly influence uncertainties in the estimated doses to residents from exposure toradionuclides in the air are:(a) Spatial variability of the deposition density of deposited radionuclides;(b) Relationship between the deposition density of 137Cs and its time-integrated
concentration in air as a function of location (the bulk deposition velocity);(c) Ratios of the concentrations of 131I (separately for elemental, organic and aerosol-boundforms), 133I, 132Te/132I and 134Cs in air relative to the concentration of 137Cs in air;(d) Factor by which the concentration of radionuclides in air inside buildings is reduced
compared with the concentration outdoors;

8

ANNEX B, ATTACHMENT A-12: APPROACH FOR ASSESSING UNCERTAINTIES AND VARIABILITY IN ESTIMATED DOSES(e) Breathing rate of reference individuals in the exposed population (adult male, adultfemale, 10-year-old child, and 1-year-old infant); and(f) Dose coefficients for intakes of radioiodine and radiotellurium by inhalation.
Note that variability as a result of age has been addressed by considering three representative
age groups separately to produce dose distributions for each age group. Dose distributions forthe population as a whole have then been obtained from the distributions for each age groupusing the age profile of the population obtained from census data.
Figure A-12.I. Key modelling steps in assessing doses from inhalation and external exposure
from the plume for residents

15.
The Committee has taken explicit account of each of these uncertainties or variabilities
when evaluating uncertainties in its estimates of dose. It recognizes, however, that numerous
other sources of uncertainty or variability will also have contributed to uncertainties in its
estimated doses (e.g., uncertainties in the measurements of deposition densities of radionuclides,in the assumed occupancy factor, in the dose coefficients for intakes by inhalation ofradionuclides other than radioiodine and radiotellurium, and uncertainties due to imperfectionsin the models used, etc.). However, based on expert judgement and a limited scoping analysis,
the Committee has concluded that the exclusion of these additional sources of uncertainty would
not materially affect its estimates of uncertainties in doses (e.g., the uncertainties in the measured
deposition densities are small compared with their spatial variability and can be neglected whenestimating overall uncertainties in doses).
16.
Deposition densities of radionuclides on the ground (and, similarly, derived concentrationsof radionuclides in air) generally exhibit large spatial variability within a given municipality 1 andhave a significant impact on the distribution of individual doses within a given population group.
The approach used for uncertainty modelling describes this variability directly by estimating the
distribution of deposited activity from all deposition measurements within each municipality. The
spatial variability of the deposition densities within a given municipality is, in general, lognormally distributed and far exceeds uncertainties associated with measurements – hence the latter1

Or prefecture.

ANNEX B, ATTACHMENT A-12: APPROACH FOR ASSESSING UNCERTAINTIES AND VARIABILITY IN ESTIMATED DOSES9

not being explicitly included in the Monte Carlo analysis. Uncertainties associated with theassumption that each measurement at a specific location can be taken to be representative of theaverage 137Cs deposition density over the area around the measurement location were taken as lognormally distributed with an estimated geometric standard deviation (GSD) = 1.5.
17.
The uncertainty of the ratios of time-integrated activity concentrations in air to thedeposition density were assessed by estimating the distribution of these values (as derived fromthe ATDM results) within a circular area of 3 km around the location of each deposition
measurement. This distribution of ratios was then applied to the deposition density at eachmonitoring location, resulting in a distribution of calculated air concentrations for 137Cs. When
there is only dry deposition, the uncertainty in the bulk deposition velocity will simply be areflection of the uncertainty around the dry deposition velocity assumed in the ATDM. The
largest fluctuations in the bulk deposition velocity arise when there is rainfall or snowfall (i.e.,
when there is wet as well as dry deposition) and such fluctuations will be captured by the spatial
variability if there is rainfall at one location and no rainfall at a nearby location. A scoping
analysis has indicated that the uncertainties in the bulk deposition velocity encompass a wide
range where there is some wet deposition, and the Committee therefore considers that its
approach has sufficiently captured the modelling uncertainties in the ATDM (for the purpose of
estimating doses to residents).
18.
Uncertainties in the ratios of the concentrations of 131I (separately for elemental, organic
and aerosol-bound forms), 132Te/132I and 134Cs in air relative to the concentration of 137Cs in air
were assumed to follow a log-normal distribution with a geometric standard deviation of 1.5(based on expert judgement). Additionally, the uncertainty of the gaseous and the aerosol-boundfraction was described by a normal distribution with an estimated standard deviation of 0.3. The
uncertainty in the 133I/131I ratio at a given location was modelled by a log-normal distribution
with a geometric standard deviation of 1.2 (based on expert judgement).
19.
For the reduction in exposures from being indoors, the Committee has used new dataexperimentally derived for Japanese houses [Hirouchi et al., 2018]. The measured reduction
factors ranged from less than 0.1 to approximately 1. The Committee has used a reduction factorof 0.5 as a central estimate, with an uncertainty described by a triangular distribution withminimum = 0.1, peak = 0.5 and maximum = 0.95 (as proposed by [Ohba et al., 2020]). The
application of the reduction factor takes into account variabilities in the amount of time people
spend indoors and outdoors according to the age group (represented by the occupancy factor),and the percentages of the population in different occupation categories (indoor worker, outdoor
worker, pensioner), taken from the published literature and based on national statistical data forJapan (see attachment A-1 for further details).
20.
To estimate uncertainty in breathing rates, the Committee has assumed the breathing rates
to be log-normally distributed about the International Commission on Radiological Protection(ICRP) standard values of the age-dependent breathing rates, with GSD = 1.3, as assigned by theUnited States National Cancer Institute [NCI, 1997].
21.
The uncertainty in the Japan-specific dose conversion coefficients for iodine andtellurium isotopes was explicitly modelled by assuming a triangular distribution with minimum
value = dose coefficient for Kelp-rich diet, peak value = dose coefficient for typical Japanesediet, and maximum value = dose coefficient for Western pattern diet.
22.
As an example, figure A-12.II indicates how variability and uncertainty were consideredwith a probabilistic Monte Carlo approach for assessing doses from inhalation of 131I for
residents in municipalities in Fukushima Prefecture and neighbouring prefectures. For each

10

ANNEX B, ATTACHMENT A-12: APPROACH FOR ASSESSING UNCERTAINTIES AND VARIABILITY IN ESTIMATED DOSES

location where a deposition measurement exists a distribution of potential doses was calculated
taking into account the uncertainty of the various model parameters as described in paragraphs
16 to 21 above. Finally, all these distributions were numerically combined to give an overall
distribution of doses within one municipality by weighting each location-specific dose
distribution with the ratio of the population around this location to the total population of themunicipality. The resulting overall dose distribution describes the potential distribution ofindividual doses within one municipality.
Figure A-12.II. Illustrative example of the modelling of variability (blue distribution) and
uncertainty (red distributions) in the assessment of doses from inhalation of 131I for residents

B.

Assessment of uncertainties and variability in doses to evacuees
from radionuclides in the air

23.
Figure A-12.III shows the key modelling steps in assessing doses to evacuees frominhalation and external exposure from the plume. The key difference compared with theassessment of doses to residents is that estimates of exposure were based not on concentrationsof radionuclides in air derived from measured deposition densities but on concentrations
estimated directly from the source term and ATDM of Terada et al. [Terada et al., 2020]. Thiswas because for evacuees information was needed about the time dependence of theconcentrations of radionuclides in the air.

ANNEX B, ATTACHMENT A-12: APPROACH FOR ASSESSING UNCERTAINTIES AND VARIABILITY IN ESTIMATED DOSES

11

Figure A-12.III. Key modelling steps for the assessment of doses from inhalation and external
exposure from the plume for evacuees

24.
In this case, the main sources of uncertainty and variability that were judged by theCommittee to significantly influence uncertainties in the estimated doses from exposure toradionuclides in the air are:(a) Uncertainties and spatial variability of the modelled concentrations of radionuclides inair;(b) Ratio of the concentration of the short-lived 133I in air relative to the concentration of 131I
in air;(c) Uncertainties in evacuation routes;(d) Factor by which the concentration of radionuclides in air inside buildings is reduced
compared with the concentration outdoors;(e) Breathing rate of reference individuals in the exposed population (adult male, adultfemale, 10-year-old child, 1-year-old infant); and(f) Dose coefficients for intakes of radioiodine and radiotellurium by inhalation.
25.
As with doses to residents, the Committee judged that not taking explicit account of theuncertainties in the assumed occupancy factor, in the dose coefficients for intakes by inhalationof radionuclides other than radioiodine and radiotellurium, and uncertainties due toimperfections in the models used would not materially affect the estimates of uncertainties indoses. Other, additional, sources of uncertainty were not considered, including, specifically,
uncertainties due to incomplete knowledge about the release rates of radionuclides over time andthe weather conditions during the releases.
26.
The exact timing of evacuation is a further, potentially important, source of uncertainty.
In the evacuation scenarios defined by [Ohba et al., 2020], the timing of evacuation is specified
with a 6-hour resolution. A limited scoping analysis has been performed which showed that theestimated doses to evacuees for 20 of the 40 evacuation scenarios were insensitive to the exact
timing of the evacuation within these 6-hour periods. For the other 20 scenarios, the estimateddoses would be significantly higher in most cases (and significantly lower in a few cases) if itwere assumed that the evacuation started 6 hours later than indicated in the scenarios specified
by [Ohba et al., 2020] – see attachment A-22 for more details. While this scoping analysis

12

ANNEX B, ATTACHMENT A-12: APPROACH FOR ASSESSING UNCERTAINTIES AND VARIABILITY IN ESTIMATED DOSES

demonstrated the potential importance of uncertainty in the timing of the evacuation, theCommittee was unable to include it explicitly in its uncertainty analysis in the absence of further
information on the uncertainty associated with this quantity.
27.
Each evacuation scenario was modelled as a series of discrete time steps starting at theoriginal location on 11 March 2011, progressing along the evacuation route (simplified as astraight line between the original location and the destination location after evacuation) andending at the destination location. For each time step the nearest ATDM grid cell was identified
and the air concentration at this grid cell at the relevant time was taken to be the air concentration
for the time step. The time-integrated air concentration for the entire modelling period was thenobtained by summing the air concentrations over all of the time steps.
28.
An assessment of the uncertainties in the concentrations of released radionuclides in air
derived directly from ATDM is not straightforward, particularly given that the source term and
ATDM have been derived by optimizing the agreement between the ATDM results and theconsiderable amount of measurement data, albeit largely of deposition density measurements.
The comparison between ATDM estimates and the measurements of 137Cs concentrations in air
derived from SPM monitoring stations described in attachment A-9 indicates agreement withina factor of ten for about 70% of the measurements within or close to Fukushima Prefecture. Sucha comparison, based on the time integrated concentration over the entire period of the releases
from the FDNPS and all of the 23 measurements of air concentrations in or near to Fukushima
Prefecture, would indicate a log-normal distribution with a GSD of about 5 for the PDF of air
concentrations due to source term and ATDM uncertainties. Focusing on the few airconcentration measurements within the evacuated areas and on the time periods when theevacuations were taking place leads to better agreement and could support the use of a lower
GSD (see attachment A-9). However, the available measurements of concentrations of 137Cs inair, and particularly those within the areas that were evacuated, are too sparse to provide a robust
estimate of the uncertainties in the air concentrations of radiocaesium derived directly from
ATDM. Of greater interest for inhalation doses are the air concentrations of radioiodine. Thesemay be associated with greater uncertainty because radioiodine was assumed to be released inthree different physico-chemical forms, in defined relative proportions, each with different
deposition characteristics; there is even less information available to quantify these uncertainties.
The Committee has therefore used expert judgement to quantify the uncertainties in theconcentrations of all radionuclides in air estimated directly from ATDM. The uncertainty of air
concentration estimates from ATDM at a given location have been assumed to be represented
by a combination of: (a) the spatial variation of the air concentration derived from ATDM withina circular area with a radius of 3 km; and (b) a log-normal uncertainty distribution with a GSD
of 3. A scoping calculation has shown that the 95th percentile of the distribution of doses toevacuees is relatively insensitive to the choice of GSD in the range of 3 to 5.
29.
The uncertainty in evacuation routes was considered by assessing doses for a number ofparallel evacuation routes (within a 3-km radius around the straight line connecting the start point
and the destination of the evacuation as provided by Ohba et al. [Ohba et al., 2020]) and deriving
the distribution of doses from the doses for these different routes.
30.
Uncertainties in the reduction factor for the concentration of radionuclides in the air
inside buildings, in the breathing rate, in the ratio of the gaseous and the aerosol-bound fractionof iodine, in the 133I/131I ratio and in the dose conversion factor for radioisotopes of iodine andtellurium were taken into account in the same manner as for residents (see section II.A). A sample
size of 10,000 was used for the Monte Carlo simulations.

ANNEX B, ATTACHMENT A-12: APPROACH FOR ASSESSING UNCERTAINTIES AND VARIABILITY IN ESTIMATED DOSES

13

31.
Figure A-12.IV indicates, as an example, how variability and uncertainty was consideredwith a Monte Carlo approach for assessing doses to evacuees from inhalation of 131I.
Figure A-12.IV. Illustrative example of the modelling of variability (blue distributions, left) and
uncertainty (red distributions, right) in the assessment of doses from inhalation of 131I for
evacuees

C.

Assessment of uncertainties and variability in external doses from
deposited radionuclides

32.
Doses to members of public from exposure to radioactive material deposited in theterrestrial environment following the accident at FDNPS were calculated as summarized below(also described in more detail in attachment A-1).
33.
The integrated doses for various age and social population groups, for evacuees and those
returning subsequently to their homes were estimated using the following equation:
𝑡𝑡2

𝐷𝐷(𝑡𝑡1 , 𝑡𝑡2 |𝑎𝑎0 ) = 𝑐𝑐 � 𝐷𝐷̇(𝑥𝑥|𝑎𝑎0 )d𝑥𝑥
𝑡𝑡1

(A-12.4)

where 𝐷𝐷̇(𝑡𝑡|𝑎𝑎0 ) is the rate of the dose quantity of interest, effective or organ equivalent dose; 𝑎𝑎0
is the age when accidental radiation exposure started for the considered population group; times
𝑡𝑡1 and 𝑡𝑡2 bound the exposure period; and the unit conversion coefficient 𝑐𝑐 depends on theselected dimensions of the quantities used (time, deposition density, dose rate coefficients, decay
data, and half-lives).

14

ANNEX B, ATTACHMENT A-12: APPROACH FOR ASSESSING UNCERTAINTIES AND VARIABILITY IN ESTIMATED DOSES34.

The dose rate was evaluated as:𝐷𝐷̇(𝑡𝑡|𝑎𝑎0 ) = 𝑟𝑟(𝑡𝑡)𝑞𝑞Cs-137 � 𝜌𝜌𝑚𝑚 𝑒𝑒 −𝜆𝜆𝑚𝑚 𝑡𝑡 𝑑𝑑̇𝑚𝑚 (𝑎𝑎 + 𝑡𝑡) � 𝑓𝑓𝑗𝑗 (𝑡𝑡)𝑝𝑝𝑗𝑗 (𝑎𝑎 + 𝑡𝑡)
𝑚𝑚(A-12.5)

𝑗𝑗

where 𝑞𝑞Cs-137 is the deposition density of 137Cs (Bq/m2) on 15 March 2011 (the assumed time ofthe deposition); 𝑟𝑟(𝑡𝑡) is the empirical two-exponential function describing dose reduction due tonatural processes of redistribution (downward migration, weathering, run-off); 𝜌𝜌𝑚𝑚 is the ratio ofthe deposition density of radionuclide m to that of 137Cs on 15 March 2011 (unitless); 𝜆𝜆𝑚𝑚 is its
radioactive decay rate (s−1); 𝑑𝑑̇𝑚𝑚 (𝑎𝑎 + 𝑡𝑡) is the corresponding age-dependent dose rate coefficient
for radionuclide m including also the effect of its radioactive progeny; 𝑓𝑓𝑗𝑗 (𝑡𝑡) is the timedependent location factor, i.e. a ratio of the ambient dose rate in air in a specific location, j, tothat above open ground undisturbed from the moment of deposition (unitless); and 𝑝𝑝𝑗𝑗 (𝑎𝑎 + 𝑡𝑡) is
the fraction of time spent by the individual of age 𝑎𝑎 + 𝑡𝑡 in the location j.
35.
The sources of uncertainty and variability that the Committee has included in assessing
the uncertainties in the estimated doses from external exposure to deposited radionuclides are:(a) Spatial variability of the deposition density of 137Cs (𝑞𝑞Cs-137 );(b) Dose rate reduction factor (𝑟𝑟(𝑡𝑡));(c) Ratio of the deposition density of radionuclide m to that of 137Cs (𝜌𝜌𝑚𝑚 );(d) Dose rate coefficient for radionuclide m (𝑑𝑑̇𝑚𝑚 (𝑎𝑎 + 𝑡𝑡));(e) Location factor (𝑓𝑓𝑗𝑗 (𝑡𝑡)); and(f) Occupancy factor (𝑝𝑝𝑗𝑗 (𝑎𝑎 + 𝑡𝑡)).

36.
The Committee has taken explicit account of each of these uncertainties or variabilities
when evaluating uncertainties in its estimates of dose. Other sources of uncertainty or variability(e.g., uncertainties in the measurements of deposition densities of radionuclides, anduncertainties due to imperfections in the models used) have again been judged not to materiallyaffect its estimates of uncertainties in doses.
37.
The spatial variability of the deposition density was based on the spatial variability of themeasurement data. The uncertainty associated with assuming that the 137Cs deposition density
measured at a particular location is representative of the area averaged value has been taken to
be log-normally distributed with an estimated GSD of 1.5. The dose rate coefficients [ICRP,
2020] were assumed to follow normal distributions with the 95% confidence interval specified
by a relative uncertainty of 20%. The empirical dose rate reduction function was assumed to be
log-normally distributed with a GSD of 1.2, for integration periods of 1 and 10 years after theaccident, and with a GSD of 1.3 for longer integration periods, to address higher uncertainty due
to extrapolation of the fitted function beyond the data-supported domain. Isotopic ratios ρm werealso assumed to be log-normally distributed with a GSD of 1.1 for all radionuclides except for
131
I, for which the uncertainty in the mean value was expressed by a GSD of 1.5 to reflect thehigher variability observed in the measured data. Uncertainty specific to location and occupancy
factors was evaluated as corresponding to log-normally distributed quantities with a GSD of 1.2;
correspondingly, the uncertainty of the combined factor was taken as represented by a GSD of
1.3, assuming statistical independence of both factors. Sample size in the stochastic simulations
was chosen equal to 10,000.

ANNEX B, ATTACHMENT A-12: APPROACH FOR ASSESSING UNCERTAINTIES AND VARIABILITY IN ESTIMATED DOSES

15

38.
This Monte Carlo technique was applied to generate PDFs for different ages, types ofoccupancy and periods of exposure. The main statistical properties of the generated PDFs for the
cumulative external doses from deposited radionuclides are summarized in table A-12.1.
Specifically, the ratios of the estimated geometric mean (GM) and 5th and 95th percentiles tothe corresponding arithmetic mean (AM) of a generated distribution were calculated. These
ratios for different population groups were found to be very similar, so only the group-averaged
values are shown in table A-12.1.
Table A-12.1. Statistical characteristics of the uncertainty PDFs, expressed as a ratio to thecorresponding arithmetic mean, associated with estimates of cumulative external doses from
deposited radionuclides
Exposure period

5th percentileGM

AM

95th percentile

1 year

0.54

0.94

1

1.66

10 years

0.54

0.94

1

1.66

Lifetime

0.49

0.93

1

1.76

D.

Assessment of uncertainties and variability in dose from ingestion

39.
The assessment of uncertainties and variability in doses from ingestion is based to alarge extent on Murakami and Oki [Murakami and Oki, 2014]. In this study variations inindividual ingestion doses to adults in the first year were estimated by Monte Carlosimulations, which took account of:(a) Variability in radionuclide concentrations in drinking water;(b) Uncertainty in the daily consumption of drinking water;(c) Variability in radionuclide concentrations in foods; and(d) Uncertainty in the daily consumption of each foodstuff.
40.
Other sources of uncertainty considered, but not explicitly assessed, by Murakami andOki included the treatment of measurements that were below the minimum detection limits anddifferences in individual behaviours. They compared their results with the results of marketbasket and duplicate diet studies to validate their approaches, and also estimated doses for a moreconservative scenario regarding the source of some foods, but estimated doses for this scenario
were not included in the percentile intervals adopted by the Committee.
41.
Murakami and Oki [Murakami and Oki, 2014] assumed the uncertainties in the daily
consumption of drinking water and in the daily consumption of each foodstuff were log-normally
distributed, based on the results of surveys and other research; variabilities in radionuclide
concentrations were based on measurement data. The Committee has used the uncertainties
estimated by Murakami and Oki (table 2 in [Murakami and Oki, 2014],) together with expert
judgement to derive percentile intervals (5–95%) for doses from ingestion (of 131I, 134Cs and137
Cs). These were conservatively estimated to be 0.3 and 3.0 times the average doses. This isequivalent to a geometric standard deviation of about 1.9. For doses from ingestion of drinking
water to evacuees prior to their evacuation, smaller uncertainty ranges were assumed (a ratio of
1.7 between 95% and average values), equivalent to a geometric standard deviation of about 1.4.
Given the relatively small contribution of ingestion doses to the total doses, the Committee
considers that applying these assumptions to all doses from foodstuffs is justified.

16

ANNEX B, ATTACHMENT A-12: APPROACH FOR ASSESSING UNCERTAINTIES AND VARIABILITY IN ESTIMATED DOSES

E.

Combination of doses from different exposure pathways

42.
As indicated in section I, the doses to members of the public from each of the exposure
pathways described above have been combined to estimate total doses in the population groups
considered (groups of evacuees according to each evacuation scenario, residents ofmunicipalities in Fukushima Prefecture and four neighbouring prefectures, residents ofprefectures in all other prefectures) by applying a Monte Carlo approach to generate samples ofindividual doses from each pathway separately and then adding up the sampled doses to give asample of total dose (assuming statistical independence between the various pathways). The
main statistical properties (e.g., mean, median, 95% coverage interval) were then derived fromthe resulting distributions of total doses. These statistical properties are presented in detail foreach population group in attachments A-13 to A-19.
43.
A Monte Carlo approach has similarly been applied to estimate the distribution (andstatistical properties) of the average dose in each population group. These distributions of theaverage doses have been used, inter alia, for the purposes of the power calculations used to assess
the health implications of the exposures (see attachment A-23 for further details).

ANNEX B, ATTACHMENT A-12: APPROACH FOR ASSESSING UNCERTAINTIES AND VARIABILITY IN ESTIMATED DOSES

17

REFERENCES
Hirouchi, J., S. Takahara, H. Komagamine et al. Investigation of reduction factor of internal
exposure for sheltering in Japan. ASRAM2018. Asian Symposium on Risk Assessment
and Management, Xiamen, China, 2018.
ICRP. Dose coefficients for external exposures to environmental sources. ICRP Publication 144.
Annals of the ICRP 49(2). International Commission on Radiological Protection,
Elsevier Ltd., 2020.
ISO. Determination of the characteristic limits (decision threshold, detection limit and limits ofthe coverage interval) for measurements of ionizing radiation – Fundamentals andapplication – Part 2: Advanced applications. International Organization forStandardization. ISO 11929-2:2019 (2019).
JCGM. Guides in metrology. GUM: Guide to the expression of uncertainty in measurement.
Joint Committee for Guides in Metrology. [Internet] Available from(https://www.bipm.org/en/publications/guides/).
JCGM. Uncertainty of measurement. Part 3: Guide to the expression of uncertainty inmeasurement (GUM:1995). Supplement 1: Propagation of distributions using a Monte
Carlo method. Joint Committee for Guides in Metrology (JCGM 101:2008). ISO/IEC
Guide 98-3/Suppl.1:2008 (2008a).
JCGM. Uncertainty of measurement. Part 3: Guide to the expression of uncertainty inmeasurement (GUM:1995). Joint Committee for Guides in Metrology (JCGM
100:2008). ISO/IEC Guide 98-3:2008 (2008b).
JCGM. International vocabulary of metrology – Basic and general concepts and associated terms(VIM), 3rd edition. Joint Committee for Guides in Metrology (JCGM 200:2012).
ISO/IEC Guide 99 (2012).
Murakami, M. and T. Oki. Estimated dietary intake of radionuclides and health risks for the
citizens of Fukushima City, Tokyo, and Osaka after the 2011 nuclear accident. PLOS
ONE 9(11): e112791 (2014).
NCI. Estimated exposures and thyroid doses received by the American people from iodine-131
in fallout following the Nevada atmospheric nuclear bomb tests. DHHS/NIH/NCI,
National Cancer Institute, Bethesda, 1997.
Nishihara, K., H. Iwamoto and K. Suyama. Estimation of fuel compositions in FukushimaDaiichi Nuclear Power Plant. JAEA-Data/Code 2012-018. Japan Atomic Energy
Agency, Tokaimura, 2012.
Ohba, T., T. Ishikawa, H. Nagai et al. Reconstruction of residents' thyroid equivalent doses frominternal radionuclides after the Fukushima Daiichi nuclear power station accident. Sci
Rep 10(1): 3639 (2020).
Terada, H., H. Nagai, K. Tsuduki et al. Refinement of source term and atmospheric dispersion
simulations of radionuclides during the Fukushima Daiichi Nuclear Power Station
accident. J Environ Radioact 213: 106104 (2020).
UNSCEAR. Sources, Effects and Risks of Ionizing Radiation. Volume I: Report to the General
Assembly and Scientific Annex A. UNSCEAR 2013 Report. United Nations ScientificCommittee on the Effects of Atomic Radiation. United Nations sales publication
E.14.IX.1. United Nations, New York, 2014.