# Probabilistic Techniques in Radiation Dose Assessment

In the present study, we used a probabilistic approach to assess the doses to the public living in areas contaminated by radioactive materials released from the 1F Plant. Probabilistic approach in exposure assessments, which are a well-established Fig. 18.2 Schematic illustrating the application of probabilistic approach to assess radiation doses

method to describe a diverse set of environmental hazards, can yield a fuller characterization of the information on the dose distributions in the population [4–8]. Application of this approach needs statistically characterized data on the contributors, such as the concentrations of radionuclides in environmental media data and habits data relevant to the exposure pathways .

Figure 18.2 illustrates the general process of applying a probabilistic approach to assess radiation doses. One sample from each input distribution is selected based on the statistical characteristics, and the set of samples is entered into the model. The process is repeated until the specified numbers of model iterations have been completed. As a result, it is possible to represent a distribution of the output of a model by generating sample values for the model input. In the present study, we used the probabilistic distributions of surface activity of 137Cs and time the people spent outdoors as input of the calculations of doses.

Table 18.2 Parameters for location factors of cesium for an urban environment 

 Type of location al,1 al,2 Tl (years) Virgin land 0.32 0.68 1.4 Dirt surface 0.50 0.25 2.2 Asphalt 0.56 0.12 0.9

# Models for Assessing Doses from External and Internal Exposures

#### 18.2.3.1 External Exposure to Deposited Radionuclides

The effective dose received by population group j from groundshine E gd

municipality listed in the evacuation scenarios is represented by in each where j is the index for population types; l is the index for location types; E" gd (t ) is the effective dose rate from groundshine at locations of virgin land in the urban environment (Sv h1); fl(t) is the location factor for urban locations of type l, pl,in (or out), j is the ratio of time spent indoors (or outdoors) at location type l to that of the assessment period; and sgd is the shielding factor for groundshine.

The index l for location types represents virgin land, dirt surfaces, and asphalt, which are classified according to the characteristics of the ground surface [9–11]. The location factors are defined by dividing the dose rates at a given location by those at an open undisturbed field [9–11]. The location factors are represented as a function of the time elapsed after the contamination, as follows: where al,1, al, 2, and Tl are fitting parameters for the location factors of cesium. The values of these parameters are listed in Table 18.2; they were determined from data obtained from the Chernobyl accident .

The ratio of time spent at location type l for the assessment period was defined as a fraction of the average time spent in a day at location l, as follows: where tl,in(or out), j is the time spent indoors (or outdoors) in a day at location l by an individual of population group j.

In the present study, the calculations were performed for indoor workers, outdoor workers, and pensioners on the assumption that they live in the urban areas. It is assumed that indoor workers and pensioners spend all day in areas paved with asphalt. However, it is assumed that outdoor workers spend their working hours in areas classified as dirt surfaces in an urban environment.

The values of tl,in(or out), j were determined by generating random numbers in accordance with the probabilistic distribution functions obtained from the surveys in Fukushima Prefecture. In the survey we measured time spent indoors and outdoors for the three population groups of indoor workers, outdoor workers, and pensioners. The indoor workers surveyed were from the Fukushima City office and the outdoor workers were from the Northern Fukushima affiliate of Contractors Association and Japan Agricultural Cooperatives. In the present study, data surveyed for the month of February, March, and April 2012 were used.

To determine the distribution form of time spent outdoors of each population group, normality tests were performed for time spent outdoors in a day and its logarithmic values. When the normality was examined for the logarithmic values of that of indoor workers, the results of the p values were more than 5 %. Log-normal distribution was thus assumed for the time spent outdoors by indoor workers. Hereafter, the significance level of 5 % is used to determine whether the null hypothesis is rejected. The results of similar analyses performed for time spent outdoors of the other population groups indicated that the distribution was normal for outdoor workers and log-normal for pensioners. The statistical values to determine the probabilistic distribution functions of tl,in(or out), j are listed in Table 18.3.

The shielding factor sgd for gamma radiation from deposited radionuclides is defined as the ratio of ambient doses inside a house to those outside. Figure 18.3

shows the correlation between the ambient dose rate measured inside and outside houses. The dosimetric surveys were made for 130 households in Fukushima Prefecture during a period between October 2 and November 11, 2012. The breakdown of building types is as follows: 124 oneor two-story wood frame houses, and 6 concrete houses with one or more stories. The calculations were performed using a shielding factor sgd of 0.4. This value were determined conservatively based on the ratio of the ambient dose rate measured inside and those measured outside (Fig. 18.3).

The effective dose rate from groundshine at locations of virgin land is given by the following form: where r(t) is the attenuation function of dose rate from migration of 137Cs into the soil; Ci is the ratio of the surface activity density of radionuclide i to that of 137Cs; ACs137 (0) is the initial value of the surface activity density of 137Cs (Bq m−2); λi is the decay constant for radionuclide i (h−1); and kgd,i is the effective dose coefficient from surface density activity ((Sv h−1)/(Bq m−2)).

Table 18.3 Statistical values to determine the probabilistic distribution functions of time spent outdoors for each population group

 Population groupa Distribution form Mean (h) Deviation Indoor worker Outdoor worker Pensioner Log-normal Normal Log-normal 0.57b 6.97c 1.27b 3.28d 2.90e 3.37d

aIndoor worker means Fukushima City office workers; outdoor worker includes construction workers

and farmersbGM cAM dGSDeSD

Fig. 18.3 Correlation between ambient dose equivalent rates measured inside and outside houses The attenuation function r(t) is given by the following equation [2, 9–12]: The parameter values were p1 = 0.34, p2 = 0.66, T1 = 1.5 years, and T2 = 50 years [2, 12].

Radioactive fallout and contamination in most of the contaminated areas of Fukushima Prefecture were estimated to have occurred on March 15 or 16, 2011 because the gamma dose rate in air suddenly increased over the background radiation rates during these days . In the present study, the doses were assessed

Table 18.4 Composition of radionuclides deposited on March 15, 2011 aActivity of 132I and 140La was derived from that of the parent nuclide, i.e., 132Te and 140Ba, assuming radioactive equilibrium

with the assumption that the contamination occurred at 00:00 on March 15, 2011. The ratio of the surface activity density of each radionuclide i to that of 137Cs was determined according to the report of WHO . The relative isotopic composition of deposited radionuclides is listed in Table 18.4.

Equation (18.4) was calculated using values of ACs137 (0) produced by the random number generator according to the distributions of the measured surface density of 137Cs for each municipality listed in the evacuation scenarios. The distributions of the surface activity density of 137Cs on March 15, 2011 were derived from the monitoring data measured by MEXT  . The soil samples were collected from a 5-cm surface layer within 80 km of the 1F Plant. In principle, the measurements were conducted at a single location per 2 × 2 km2 grid for these areas. The details of the surface density of 137Cs are discussed in Sect. 18.2.4. The effective dose coefficients were obtained from a U.S. Environmental Protection Agency (EPA) report .

#### 18.2.3.2 External Exposure to the Radioactive Cloud

The effective dose received by population group j from cloudshine E cd is represented by where pin, j is the ratio of time spent indoors; pout, j is the ratio of time spent outdoors;

E cd is the effective dose from cloudshine outdoors (Sv); and scd for cloudshine from radionuclides in the radioactive cloud.

The ratio of time spent indoors or outdoors was calculated as the total time spent indoors or outdoors in various locations per day. To calculate the external doses

cd

from the radioactive cloud, Eout, it was necessary to convert the surface density of

radionuclides to time-integrated activity concentrations in air. Noble gases, which do not deposit on the ground surfaces, were not included in the calculations.

The effective dose from cloudshine outdoors, Eoutcd, is represented as follows: where Vi is the bulk deposition velocity of radionuclide i (m s−1) and kcd,i is the effective dose coefficient for air submersion of radionuclide i (Sv/(Bq s m−3).

The deposition velocity Vi is determined according to the method in the WHO preliminary report . The areas in which the surface density of 137Cs, ACs137, is higher than or equal to 30 kBq m−2 were treated as being contaminated through wet deposition, with deposition velocities of VI-131 = 0.07 m s−1 for 131I and Vother = 0.01 m s−1 for other radionuclides. If the surface density ACs137 is less than 30 kBq m−2, then the contamination originated from dry deposition with deposition velocities of VI-131 = 0.01 m s−1 for 131I and Vother = 0.001 m s−1 for other radionuclides. The doses from cloudshine and inhalation were calculated using the surface densities of 137Cs in the municipality where the inhabitants stayed while the radioactive plumes passed. The value of 0.6 was used as the shielding factor scd for gamma radiation from the radioactive plume . The effective dose coefficients kcd,i were obtained from

an EPA report .

#### 18.2.3.3 Internal Exposure Through Inhalation of Radionuclides

The effective dose received by the population group j from internal exposure through

inh

inhalation of radionuclide i in the radioactive cloud Ej is represented by where Einh is the effective dose from inhalation of radionuclide i in the radioactive cloud (Sv); f is the filtering factor for a house.

To prevent underestimation of doses in the calculation, the value of 1 was adopted for the filtering factor f. Einh is given as where B is the breathing rate for adults (L day−1) and kinh,i is the effective dose coefficient for inhalation of radionuclides i (Sv Bq−1).

The value of 22.2 L day−1 was adopted as the breathing rate of adults from the recommendation of the International Commission on Radiological Protection (ICRP) Publication 71 . The effective dose coefficients for inhalation were also obtained from the same publication .

•  The data presented in this paper used Japan Time [i.e., Greenwich mean time (GMT) plus 9 h]
•  MEXT is the abbreviation for the Ministry of Education, Culture, Sports, Science and Technology of Japan
•  The soil samples had been collected prior to the rainy season in Japan, from June 6 to June 14 and from June 27 to July 8, 2011, so that the level of contamination could be observed before any changes occurred on the soil surface