Dose calculation and probabilistic assessment

Estimation of the level of radiological impact due to potential exposure normally involves [6, 27]:

 for doses in the range of deterministic effects – calculation of mean absorbed doses to the organ or tissue, weighted by an appropriate relative biological effectiveness (RBE);

 for doses in the range of stochastic effects:

- calculation of equivalent dose to certain organs (thyroid, fetus);

- calculation of effective dose resulting from the sum of the committed effective doses from internal exposure pathways and the effective doses from external exposure.

In probabilistic assessments the results of estimation of the health effects are traditionally presented in a set of complementary cumulative distribution functions (CCDF) providing information on the likelihood and magnitude of consequence of the release associated with an AOO or an accident. CCDF can be introduced as

𝑃(𝐶) = ∫ 𝑝(𝑡)𝑑𝑡 (2)

where 𝑃(𝐶) is the conditional probability of having consequence equal and higher than C; and 𝑝(𝑡) is a function of density of consequences (∫ 𝑝(𝑡)𝑑𝑡 = 1).

The CCDF are normally displayed as a set of log-log graphs of exceeded probability versus consequences [6, 18]. A point on a CCDF curve gives the conditional probability⁴ that a consequence will equal or exceed a given magnitude (Figure 5). The probability of consequence at a specific location will be considered as conditional, as it is assumed that a release had already occurred.

Ref [28] explains that “the conditional probability is the probability that an event will occur, given the occurrence of an earlier defined event. E.g. the probability of dying as the consequence of an exposure to radiation is conditional on the occurrence of the exposure and

4 Although it is not strictly correct the relative frequencies calculated in the consequence models are generally

on its magnitude. Conditional probabilities must be used with care, since they can be manipulated and combined only if the conditions applying to them remain unchanged”.

FIG.5. Example of a CCDF

The point marked with red dashed lines on Figure 5 means that the consequence value C or a greater value is expected with the probability P.

In the results of calculation, the CCDF can be presented as a set of standard percentiles, e.g.

90^th percentile, 95^th percentile, 99^th percentile etc. The values of percentiles can be defined from the CCDF and the n^th percentile of consequences is the value of consequence 𝐶 , which can be determined from Eq. (3):

𝑃(𝐶 ) = 1 − (3)

where 𝑃(𝐶 ) is the probability of the occurrence of consequence equal or higher to 𝐶 , and n is the number of percentile. E.g. the 97^th percentile of the dose from potential exposure is the dose value which will be accrued (or exceeded) by an individual with the probability of 3%.

One assessment typically produces a series of CCDFs for different locations, different types of dose and different groups of individuals.

Different criteria may be set up for different types of facilities in different countries. Ref [11]

requires that “the likelihood and magnitude of potential exposures, their likely consequences and the number of individuals who may be affected by them” shall be assessed. In some countries national criteria for assessment of potential exposure may be based on the restrictions of probability of exposure and restriction of doses. In other countries national requirements may be focused on a single aggregated parameter called risk or a combination of both (e.g. in UK).

Definition of risk can also vary in different situations.

The ICRP provides recommendations on annual public dose limits for radiation exposure from normal operation that correspond to an annually committed probability of premature death of a few 10^-5 and implied limit of the probability of death linked to the threshold of the region of unacceptable risk. Based on these recommendations, Ref [28] assumes that the annual individual risk from potential exposure should be of similar magnitudes to the restrictions for normal exposures and that risk from potential exposure, expressed as the annual probability of death attributable to a single installation, should not exceed 10^-5. However, it is clarified that

“individual risk expressed in terms of potential exposure would only be the determining factor for the safety of nuclear power plants for doses, should they occur, of less than about 10 mSv”.

For larger doses the potential exposure will still play a part, but societal consequences, especially of intervention, will increasingly prove to be more limiting. The term societal risk is used to represent the total impact of an accident including the risk to individuals, the number of individuals at risk, the economic impact of such things as the counter-measures needed to protect individuals, including food bans, and the loss of production and the loss of the capital value of the installation.

Ref [28] explores the relationship between individual risk and societal risk and the relevant criteria. It concludes that societal risk is more than the sum of individual risks. For accidents causing serious damage to an NPP or having off-site consequences, individual risk is considered not sufficiently limiting because of the many aspects of societal impact.

In this project every participant has used his national criteria and requirements for the assessment exercise. This report is not intended to criticise national regulations but rather to make a record of the current status and to compare requirements in different Member States.

Potential transboundary impacts are not considered in this report.

Other simpler approaches for presenting the results of the potential exposures involve calculating the resulting dose from the accident scenario to a representative person used for assessing doses, including dose reductions due to protective actions if relevant, and estimating the risk using risk factors. Ref [6] discusses definition and use of risk.

3 EXERCISE ON ASSESSMENT OF RADIOLOGICAL ENVIRONMENTAL