Estimation of Effective Dose from External Exposure in The Six Prefectures adjacent to Fukushima Prefecture

. The Fukushima Daiichi Nuclear Power Plant accident caused a release of radionuclides. Radionuclides were deposited on the ground not only in Fukushima prefecture but also in nearby prefectures. Since the accident, measurement of radiation in environment such as air dose rate and deposition density of radionuclides has been performed by many organizations and universities. In particular, Japan Atomic Energy Agency (JAEA) has been performing observations of air dose rate using a car-borne survey system continuously and over wide areas. In our study, using the data measured by JAEA, we estimated effective dose from external exposure in the six prefectures adjacent to Fukushima prefecture. Since car-borne survey was started a few months later after the accident, measured air dose rate in this method is mainly contributed by 137 Cs and 134 Cs whose half-lives are relatively long. Therefore, based on air dose rate of 137 Cs and 134 Cs and the ratio of deposition density of short-half-life nuclides to that of 137 Cs and 134 Cs, we also estimated effective dose contributed from not only 137 Cs and 134 Cs but also other short-half-life nuclides. We compared the effective dose estimated by the method above with that of UNSCEAR and measured data using personal dosimeters in some areas.


Introduction
The Fukushima Daiichi Nuclear Power Plant accident caused a release of radionuclides. Radionuclides were deposited on the ground not only in Fukushima prefecture but also in nearby prefectures. Since the accident, measurement of radiation in environment such as air dose rate and deposition density of radionuclides has been performed by many organizations and universities. In particular, Japan Atomic Energy Agency (JAEA) has been performing observations of air dose rate using a car-borne survey system continuously and over wide areas. There has been 11 times surveys performed as of March 2016 [1].
In our study, considering some factors such as time spent indoor and outdoor, background and radiation reduction by house, and using the data of air dose rate measured by JAEA [2], we estimated effective dose from external exposure in the six prefectures adjacent to Fukushima prefecture (Iwate pref., Miyagi pref., Ibaraki pref., Tochigi pref., Gunma Pref. and Chiba Pref.).
United Nations Scientific Committee on the Effects of Atomic Radiation has also estimated effective dose using measured date of radiation in environment [3]. In their method, density of radionuclides is used. There is a similarity between UNSCEAR's method and ours in terms of using measured data in environment. However, although the data that we use has been measured continuously, the data that UNSCEAR used was the one that was measured only one time.
There is also another approach such as measurement using personal dosimeters. This kind of survey was performed some places, such as Tochigi pref., Kashiwa city in Chba pref. and Marumori town in Miyagi pref [4] [5] [6] .
In the case of Marumori town in Miyagi pref., this town was divided into three areas (Area-A,B,C) and measurement of external dose was performed using personal dosimeter. There were a few hundred children as examinee, and the measurement had been continued for two years since September 2011. In this survey, other data such as time spent indoor and outdoor, body height and bodily weight. In the relevant survey, radiation reduction factor of typical types of house in the nearby areas was also measured [7]. For purpose of reference, typical measured data are shown in the Table. 1 for three areas. Measurement using personal dosimeter has the advantage that the date measured contains various sorts of uncertainties such as time spend indoor and outdoor and type of houses, therefore it is not necessary to introduce any conversion coefficients or assumptions. On the other hand, examinees have to attach dosimeters to their bodies, and therefore it is difficult to keep measuring for years against many examinees.
In our study, we estimated effective dose from external exposure based on measured air dose rate by car-borne survey by JAEA, and compered its vale to the one estimated by UNSCEAR and the one measured using personal dosimeters in Marumori town in Miyagi Pref.

Methods
In our study, we annualized measured air dose rate with two models. By fitting with the models, timedependent function of air dose rate. Maltiplying some conversion factors and subtracting background, air dose rate can be converted to effective dose rate contributed from nuclides that were released by The Fukushima Daiichi Nuclear Power Plant accident. Integrating this, accumulative effective dose from external exposure can be obtained (See Fig. 1

Models of decrease of air does rate
Air dose rate decreases because of physical decay and weathering effect. In the case of physical decay, air dose rate decay at the pace determined by half-life of each nuclide. Weathering effect is a natural phenomenon where rainfall promotes nuclide to penetrate into the soil, therefore this depends on weather condition or soil characteristics of each area.
In this study, we use two models to analyze decrease of air dose rate. The first model is given by the equation (1). In this model, it is assumed that decrease of air dose rate can be simply expressed by one exponential function.
The second model is given by the equation (2) using the parameters listed in the Table. 2 [8]. In this model, decay of nuclide and weathering are considered.
According to the previous studies, weathering effect can be expressed as the second term in equation (2) under the assumption that this effect can be divided into two elements whose contributions are normalized, where fast f is fraction of fast element, and fast T and slow T are half-life of fast and slow elements [9]. The third term in equation (2) coresponds to physical decay of 137 Cs and 134 Cs, where k is ratio of 137 Cs to 134 Cs contributing to air dose under the assumption that the initial value of deposition density of each nuclide is same, and 134 O and 7 13 O are decay constants of each nuclide.

Conversion to effective dose
Considering some factors such as time spent indoor and outdoor, background and radiation reduction of houses, air dose rate can be converted to effective dose rate as shown in equation (3). In this study, by substracting the background which was measured in the area of interest before the accident, we estimated the dose added by the nulides released by The Fukushima Daiichi Nuclear Power Plant accident the accident.
In car-borne survey, measurement is conducted on streets with detectors set in the car. The measured air dose rate is the one on streets. Because of traffics of cars, nuclides deposited on streets are easier to be removed or penetrate into soil than in living environment, therefore air dose rate measured by car-borne survey tends to be smaller air dose rate measured in living environment. It is shown that the former is approximately 1.2 times lareger than the latter by man-borne survey conducted nearby the street where car-borne surevy was also conducted [10] [12]. According to this, indoor workers spend 0.57 hours outdoor on average. In this study, although the targeted prefectures are not Fukushima prefecture, we used this value.
Radiations are reduced indoor because of shielding effect of houses. In this study, we adapted the value 0.4 for reduction factor s [13].
For conversion factor between air dose rate and effective dose, we adapted the value 0.6, where the target that we estimate is assumed to be adult [14].  Table. 3)

Effective dose considering short-half-life nuclides
Since car-borne survey was started a few months later after the accident, measured air dose rate in this method is mainly contributed by 137 Cs and 134 Cs whose half-lives are relatively long. Therefore, based on air dose rate of 137 Cs and 134 Cs and the ratio of deposition density of short-half-life nuclides to that of 137 Cs and 134 Cs, we also estimated effective dose contributed from not only 137 Cs and 134 Cs but also other short-half-life nuclides.

Fig. 2. Estimation flow of contribution of short-halflife nuclides
The initial value ) 0 ( air D can be obtained by plugging in 0 into t in eqution (1) or (2). This value can be considerd as sum of the contribution of 137 Cs, 134 Cs and background as shown in equation (5).
is air dose rate contributed from 137 Cs in the soil and Assumuing that the initial value of deposition densityof 137 Cs and 134 Cs is same ( parameter 2 A can be eliminated, then the equation below is obtained.
Defining the ratio of initial deposition density of each nuclide i to that of 137 Cs ( 1 Although this ratio has been studied in many previous studies, in this study, we adapted the same values as UNSCEAR (   (9), where half As shown in 2.2, by multiplying some factors (defining its product as 4 , 3 i f in equation (10) ),  (10) this can be converted to effective dose that considers time spent indoor and outdoor, and reduction factor is obtained as shown in equation (11).

Fig. 3. Prefectures targeted in this study
In the first model, parameters b a, and c were free. In the second model,  Table. 3 were used.
The parameters for Miyagi Pref., Tochigi Pref. and Ibaraki Pref. were derermined by fitting as shown in the Table. 7 and Table. 8. For the three prefectures (Miyagi, Ibraki and Tochigi Pref.), averaged measured data and time-dependent degrease of air dose rate drawn by the determined parameters are shown in Fig. 4 ~Fig. 6.  In the three prefectures (Miyagi, Ibraki and Tochigi Pref.) where measured data of air dose rate were relatively small, there were some cases where fitting parameters were not determined appropriately. In order to avoid this, we used the fitting parameters in the other prefecture ( b in the first model, and fast T in the second model) and fixed the parameter ( fast f in the second model).
The parameters determined for these three prefectures are shown in Table. 9 and Table. 10.  Averaged measured data and time-dependent degrease of air dose rate drawn by the determined parameters are shown in Fig. 7~Fig. 9. Years after the Accident (y) Air Dose Rate (μSv/h) Fig. 9. Air does rate (Chiba Pref.)

Effective dose (considering 137 Cs and 134 Cs)
Based on the time-dependent degrease of air dose rate shown in 3.1, we estimated accumulated effective dose (considering only 137 Cs and 134 Cs) by equation (3) and (4). Fig. 10~Fig. 12 show the estimated results for Miyagi Pref., Ibaraki Pref. and Tochigi Pref. For the three prefectures where some parameters were fixed with the values determined in the other prefecture or fixed with the typical value, the estimated results are shown in Fig. 13~Fig. 15. For the first model in Iwate Pref. and Gunma Pref., air dose rate decreases to the background level. In this case, when integrateing by equation (4), interval of integration was confined till air dose rate gets the background level.

Estimation in Marumori Town in Miyagi Pref.
As shown in 1., there were some cases where measurement using personal dosimeters were conducted. In particular, in Marumori Town in Miyagi Pref., measurement had been conducted for relatively long [6]. In order to compare results, we estimated effective dose in this town.
First, we analysed averaged measured date of air dose rate in this town as the same way shown above, however here we used the first model here. Estimation of effective dose based on air dose rate was done almost the same way above exept for some small changes below.
z Distributions of parameters were considered as possible, and ten thouthands sets of randam numbers of the distributions were generated. z Conversion factor was changed, because examinees in Marumori Town were children. z Background was not sabstructed in equation (3) because accumulated value by personal dosimeters includes background. z Interval of integration ) , ( 2 1 T T in equation (4) was changed to adjust to the condition of measurement using personal dosimeters in Marumori Town. The parameters used here are listed in Table. 11. Estimated results are shown in Fig. 20~Fig. 22. The values written in these figures with dashed lines are the typical value measured with personal dosimeter in each area in Marumori Town (Table. 1) [6].

Comparison with estimation of UNSCEAR
Estimated effective dose in this study and that of UNSCEAR are listed in Table. 12. In this list, these values does not include background. Although UNSCEAR estimated at the level of cities, towns and villages, in this study we estimated at the level of prefectures. Therefore, estimated values of UNSCEAR were shown minimum and maximum values given by cities, towns or villages belonging to each prefecture. [18] [19].  [19].
We estimated efective dose in Nasu Town by the same way as shown above. The resulut is shown in Fig. 23. In this figure, in order to compare with the estimation of UNSCEAR, the curve of UNSCEAR estimation that we calucurated based on the medhod of UNSCEAR in this study is also shown [15]. -Nasumachi (model1) ---Nasumachi (model2) … UNSCEAR Year after the Accident (y) Effective Dose (mSv)  In the UNSCEAR method, measured deposition density was used for input data. This measurement was conducted only one time within a few months after the accident. The number of measurement points was quite fewer than that of car-borne survey. In addition, some parameters used in UNSCEAR method are based on Chernobyl accident, therefore it is possible that environmental characteristics in Japan are not reflected enough. Fig. 24 shows the ratio of contribution from effective dose each nuclides to the total. Years after the Accident (y) Effective Dose (mSv) Fig. 24. Contribution from each nuclide to effective dose This graph shows that within a few months after the accident the contribution from 132 Te, 132 I and 131 I is relatively large, and the contribution from 137 Cs and 134 Cs gets more dominant as time passes. At three years after the accident, the ratio of 137 Cs and 134 Cs to the total exceeds 80 percent. This suggests that estimated effective dose considering not only 137 Cs and 134 Cs but also other short-half-life nuclides is about 1.2 times larger than the one considering only 137 Cs and 134 Cs.

Comparison with measurement using personal dosimeters
Estimating effective dose in Marumori Town in Miyagi Pref., we considered distribution for some parameters. Therefore estimated value also has its distribution. Comparing the distributions of estimated value with typical measured value using personal dosimeters for three cases, it is shown that the latter value is within the distribution and corresponds to about 1.2 to 1.3 times lager value than the mode of each distribution. Although the distribution and typical measured values are in good agreement, it is necessary to be aware that they are basically different. There are some assumptions and some conversion factors that have uncertainty behind estimated values, although measured values using personal dosimeters are reflected by real behavioural pattern of each examinee.