Uncertainties in probabilistic nuclear accident consequence
analysis
Authors: M P Little  
Published: August 2002

National Radiological Protection Board, Chilton, Didcot, Oxon OX11 0RQ, UK
For all nuclear installations there is a small probability of an accident occurring
which could lead to a release of radionuclides into the environment, despite the
design intent to build the nuclear plant in such a way as to reduce that possibility
to a low level. It is therefore important as a part of the process of licensing of
nuclear sites to evaluate the probability of such accidents, and what the
radiological consequences of an accident might be.
For this reason, in the last 25 years considerable effort has gone into the
development of computer codes to assess the probability distributions of the
radiological consequences of various sorts of nuclear accidents. Among the first such
probabilistic accident consequence codes were CRAC, developed by the United States
Nuclear Regulatory Commission (USNRC 1975), and MARC (Clarke and Kelly 1981),
developed by the National Radiological Protection Board (NRPB). More recent examples
of such codes include UFOMOD (Ehrhardt et al 1988), CONDOR (1993),
COSYMA (CEC 1991), sponsored by the European Commission (EC), and MACCS (Jow
et al 1990), sponsored by the USNRC. As currently modelled, the
probability distributions of the radiological consequences of various sorts of
nuclear accidents are solely a function of the range of atmospheric conditions that
could occur at the time of the accident.
The efforts involved in developing these codes have not always been matched by the
sophistication of the methods used to assess and propagate uncertainties through the
various models in each of these codes. Earlier uncertainty analyses (e.g. those for
the predecessors of the most current codes, COSYMA and MACCS) have used probability
distributions assembled largely by the code developers (Fischer et
al 1990, Jones et al 1995). For this reason the EC and
USNRC sponsored a joint assessment of uncertainty for such codes, primarily for the
models contained in COSYMA and MACCS. The results of this exercise are described in
the paper by Goossens and Harper (1998) in this issue.
The Bayesian methodology employed is unusual: it involved assembling eight more or
less separate panels of experts to assess uncertainty distributions on what are, in
principle, empirically measurable quantities in these specialised areas (atmospheric
dispersion; deposition; behaviour of deposited material and its related doses;
foodchain on animal transfer and behaviour; foodchain on plant/soil transfer and
processes; internal dosimetry; early health effects; late health effects). As the
experts were not asked directly about uncertainties in model parameter values, it is
necessary to propagate these elicited uncertainties on `measurable' variables
backwards through the models built into the various codes to obtain the desired model
parameter uncertainty distributions. This is the subject of ongoing research, and is
not described by Goossens and Harper (1998). The advantage of eliciting uncertainties
in `measurable' quantities rather than, for example, in the values of model
parameters is that the resulting uncertainty distributions can be propagated through
a variety of different types of model, so that the results of the exercise can be
applied to codes other than COSYMA or MACCS. A further advantage is that one can
elicit uncertainties from experts who do not necessarily use the particular models
built into these codes.
In addition to these features, this method of determining uncertainties has other
advantages, including the synthesis it affords of a variety of different sorts of
uncertainty, including both sampling (e.g. Poisson) uncertainty in model parameters
and uncertainties in the form of each model. Even within the area of late health
effects, the novelty of this approach should be contrasted with the previous efforts
at assessing uncertainty by the Biological Effects of Ionizing Radiations (BEIR V)
committee (National Research Council 1990) and by the National Council on Radiation
Protection and Measurements (NCRP 1997), who considered individual components of
uncertainty in some detail. These components include such things as:

sampling error;

model uncertainty (e.g. use of relative risk or absolute risk models or
some hybrid of the two (Muirhead and Darby 1987));

errors in dose estimates in the exposed groups (e.g. random errors in dose
estimates for the Japanese atomic bomb survivors (Pierce et
al 1990), systematic errors in neutron dose estimates for the
Hiroshima survivors (Straume et al 1992));

uncertainties in extrapolation of risks across populations (e.g. from the
Japanese population to a EC/US population with rather different underlying
cancer risks);

uncertainties in extrapolation from high dose and high dose-rate exposure
to low dose and low dose-rate exposure; and

uncertainties in extrapolation from the current period of follow-up in
exposed groups (e.g. 45 years in the atomic bomb survivors) to the end of
life (relating to model uncertainty).

Perhaps the most problematic source of uncertainty in the area of late health
effects is model uncertainty, and arguably this is the most serious shortcoming of
previous attempts at determining uncertainties in late health effects. There are
other ways of dealing with this aspect of uncertainty, among the more promising
techniques recently proposed being the hierarchical Bayesian modelling methods of
Richardson and Gilks (1993a, b).
Despite the novelty of the method, the results of the exercise in various areas are
reassuring. In the late health effects panel, for example, the best estimate (50
percentile) of the aggregate high dose-rate cancer risk for the specified EC/US
population is 10.2% Sv-1, with 90% uncertainty interval 3.5%-28.5% (Little
et al 1997). This compares with the aggregate cancer risk
calculated by BEIR V (National Research Council 1990) for a current US population of
7.9% Sv-1, the risk calculated by the International Commission on
Radiological Protection (ICRP 1991) (the average of risks for current UK and US
populations) of 12.05% Sv-1 and the risk estimated by the United Nations
Scientific Committee on the Effects of Atomic Radiation (UNSCEAR 1994) for a current
Japanese population of 12.0% Sv-1. [It should be noted that the measure of
cancer risk used by BEIR V (National Research Council 1990) is excess cancer
deaths, in contrast to the measure risk of exposure-induced
death (REID) (Thomas et al 1992) used in the EC/USNRC
elicitation exercise and by the other committees discussed above. The measure of
total excess cancer deaths generally gives values about 20-25% lower than the REID
measure since the former quantity does not include that fraction (20-25% for most
populations) of people developing a radiation-induced cancer who would have developed
some sort of cancer anyway.] In the BEIR V report (National Research Council 1990)
there is considerable discussion of uncertainty in fatal cancer risk estimates, which
they judge to be dominated by sampling uncertainty (in the Japanese atomic bomb
survivor data). Considering only sampling uncertainties, BEIR V estimated the 90%
confidence intervals for the high dose-rate cancer risk as 6.4%-10.8%
Sv-1. The NCRP (1997) estimated a low dose-rate cancer risk of 4.0%
Sv-1, and considered a large number of factors (most of the list given
above) in determining a 90% confidence range of 1.2%-8.8% Sv-1. The NCRP
central estimate of the dose and dose-rate effectiveness factor (DDREF) is 2 (NCRP
1997), so that their best estimate of high dose and high dose-rate risk is 8.0%
Sv-1, with an approximate 90% confidence range of 2.4%-17.6%
Sv-1. This confidence range would of course be tighter if the
uncertainties involved in extrapolation to low dose rates were omitted; these
comprised the largest part (40%) of the total uncertainty evaluated by the NCRP
(1997). It is worth noting the similarity of the central estimates of these other
bodies compared with those of Little et al (1997), as well as the
rather wider range of uncertainty bounds coming from the analysis of Little
et al (1997).
A critical aspect of the method described by Goossens and Harper (1998) is the
choice of experts. Goossens and Harper imply that the `best experts' were selected
after CVs were solicited from a shortlist of experts compiled from the open
literature. A glance at the various panels demonstrates that many have substantial
overlap with the ICRP, in particular the internal dosimetry panel. It might be argued
that by selecting from such an apparently small pool of experts the resulting
elicited uncertainty distributions could be too narrow. However, in certain areas
(e.g. internal dosimetry, late health effects) the available pool of `experts' is
small, and to widen the selection would introduce bias, as well as an unreasonable
widening in the uncertainty intervals.
Another potential problem in this sort of elicitation exercise is the difficulty
most people have in taking account of the different sorts of uncertainty, and in
particular those that arise from sources other than sampling error. The experts
attended various training sessions, one of the aims of which was to familiarise them
with the concept of uncertainty. Experience of the training meeting for the late
health effects panel suggests that the experts were providing rather wider
uncertainty intervals at the end of the exercise than at the beginning, but it may be
that the elicited uncertainty intervals are still too narrow.
Despite these caveats, this large project has already yielded some useful findings.
It will be interesting to see the results of the next stage of the analysis, when the
elicited distributions are propagated backwards to obtain model parameter
uncertainties, which will be used to calculate uncertainties in the radiological
consequence components of nuclear accident codes.

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