Mapping of the cumulative β-ray dose on the ground surface surrounding the Fukushima area

A large amount of the fission products released by the Fukushima Daiichi Nuclear Power Plant (FDNPP) accident on 11 March 2011 was deposited in a wide area from Tohoku to northern Kanto. A map of the estimated cumulative β-ray dose (70 μm dose equivalent) on the soil surface for one year after the FDNPP accident has been prepared using previously reported calculation methods and the 2-km mesh survey data by MEXT. From this map of estimated dose, areas with a high cumulative β-ray dose on the soil surface for one year after the FDNPP accident were found to be located in the Akogi-Teshichiro to Akogi-Kunugidaira region in Namie Town, and in the southern Futaba Town to the northern Tomioka Town region. The highest estimated cumulative β-ray dose was 710 mSv for one year at Akogi-Teshichiro, Namie Town.


INTRODUCTION
The nuclear accident at the Fukushima Daiichi Nuclear Power Plant (FDNPP) occurred after the enormous earthquake and associated tsunami on 11 March 2011. A large amount of fission products was released and deposited over a wide area from the Tohoku region to the northern Kanto region [1][2][3][4]. The deposited radionuclides were mainly 129m Te, 129 Te, 131 I, 132 Te, 132 I, 134 Cs, 136 Cs and 137 Cs. These radionuclides emit both γ rays and β rays. Because β rays do not contribute to the effective dose, dose evaluations have been focused on γ rays. However, β rays contribute to the skin dose for humans, the whole-body dose for small insects, and the total dose for plant leaves.
In our previous publication, the time variation in the β-ray dose rate and the cumulative β-ray dose as 70 μm dose equivalent were estimated for the conditions of an initial 137 Cs deposition of 1000 kBq/m 2 , using a Monte Carlo calculation [5]. In the current study, the deposition ratios of 129m Te, 129 Te, 131 I, 132 Te, 132 I and 134 Cs to 137 Cs were taken into account, values for which ratios were mainly taken from the Iitate Village contamination study [5]. For example, the 131 I/ 137 Cs ratio was assumed to be 9.2 at the time of deposition [4]. However, the 131 I/ 137 Cs ratio has a range of values for the various areas between the northwestern region and the southern region of the FDNPP [1,2].
In addition, the Ministry of Education, Culture, Sports, Science and Technology (MEXT) conducted a 2-km mesh contamination study from June to August 2011 [6]. This study started three months after the main deposition occurred on 15 March 2011. Therefore, the short-half-life radionuclides, such as 132 I and 132 Te (half-life: 3.204 days), had already decayed out. 131 I was also decayed by a factor of 2000 due to its short half-life (8.021 days). In the MEXT study, 131 I radioactivity was detected in only 19% of 2181 soil sampling locations. Consequently, the 131 I/ 137 Cs ratio is available for only 415 locations in the Fukushima prefecture.
The purpose of this paper was to evaluate the cumulative β-ray dose (70 μm dose equivalent) for one year after the FDNPP accident on the ground surface and to create a β-ray dose map of contaminated areas in the Fukushima prefecture, using our previous β-ray calculation method [5] coupled with the MEXT 2-km mesh soil data [6].   [6] interpolated with a multilevel B spline interpolation by SAGA-GIS [10].

MATERIALS AND METHODS
Calculation technique for the cumulative soil surface β-ray dose for one year A previously published β-ray dose calculation technique [5,7,8] was used in this study. The transport of β-rays was simulated with Monte Carlo N-Particle transport code version 4C (MCNP-4C) [9]. Betaray sources were uniformly distributed in a surface soil layer of 5-mm thickness. Beta-ray energy spectra were used for the radionuclides: 129m Te, 129 Te, 131 I, 132 Te, 132 I, 134 Cs and 137 Cs [5]. Energy deposition in the air cell is accumulated as a function of height from the soil surface. The initial β-ray dose rate for each of seven radionuclides was calculated. Then, seven values of β-ray dose rates for the radionuclide i at the time of deposition ( _ D  134 Cs and 137 Cs [5]. In our study, in the calculation process for the cumulative β-ray dose, radionuclide ratios of 131 I/ 137 Cs and 129m I/ 137 Cs were treated as two parameters of: r I and r T , respectively. Also, 129 Te/ 137 Cs and 132 I/ 137 Cs ratios were scaled to the 129m Te/ 137 Cs ratio by factors of 0.7 and 8.3, respectively. Therefore, a relation of 129 Te/ 137 Cs = 0.7 x 129m Te/ 137 Cs and 132 I/ 137 Cs = 8.3 x 129m Te/ 137 Cs were used here,     where T i is the half-life of radionuclide i, and r I and r T are 131 I/ 137 Cs and 131 I/ 137 Cs ratios, respectively. After this calculation, the relationships between the cumulative soil surface β-ray dose for one year and conditions of deposition density of 137 Cs were determined. The cumulative soil surface β-ray dose for one year (D A ) was calculated by: where A137 Cs is the 137 Cs deposition density (kBq/m 2 ) taken from the MEXT 2-km mesh soil contamination data [6]. The dose conversion factor from Gy to Sv for β-rays was assumed to be 1 in this analysis.
129m Te/ 137 Cs ratio interpolation The 129m Te/ 137 Cs ratio was obtained from the MEXT data (which includes 2181 sampling locations) at 797 locations. However, both ratios of 129m Te/ 137 Cs and 131 I/ 137 Cs were obtained at only 175 locations. At the locations without 129m Te/ 137 Cs data, 129m Te/ 137 Cs data were interpolated with geographic information techniques (GIS): a multilevel B spline interpolation by SAGA-GIS [10]. The resultant 129m Te/ 137 Cs map is shown in Fig. 1.

RESULTS AND DISCUSSION
The time dependence of the β-ray dose (70-μm dose equivalent) rate on the ground surface is shown in Fig. 2a for a fixed value of r T = 1.0, with parameter values of r I = 5, 9.2, 20, 40, 100 and 200. The 131 I contribution diminishes about 80 days after deposition due to the decay from Fig. 2a. Figure 2b shows the time dependence of the β-ray dose rate for a fixed r I of 9.2 with various r T of 0.1, 0.5, 1, 5, 10 and 50. In case of r T being >5, small increases in the β-ray dose appear from 20 days. This increase is caused by the contribution of β-rays from 129,129m Te nuclides, which have a half-life of 33.6 days. For detailed calculation methods, please refer to the previous publication [5]. The cumulative β-ray dose on the ground surface can be obtained by integrating the time-dependent dose rate as Eq. 2. Results of cumulative β-ray dose calculation for various sets of r I and r T values are plotted in Fig. 3, respectively. The cumulative dose per 137 Cs deposition of 1000 kBq/m 2 is increasing with the 131 I/ 137 Cs ratio. The least square fitted function was determined to be D(r I , r T ) = 1.1165 r I + b, as shown in Fig. 3. The fitted parameter values of b for several values of r T are listed in Table 1. The fitted parameter: b was re-fitted by linear function and determined to be b(r T ) = 31.032 r T + 50.009. The fitted result is shown in Fig. 4. Finally, the cumulative βray dose on the ground surface per initial 137 Cs deposition for one year, D(r I , r T ), can be expressed as a function of r I and r T as: Dðr I ; r T Þ ¼ 1:1165 Á r I þ 31:032r T þ 50:009: Eq: 4 The cumulative soil surface β-ray dose for one year was calculated for 415 MEXT sampling locations using Eq. 4. The representative 72 locations selected from 415 locations are listed in Table 2. The calculated results show that higher cumulative β-ray doses appear around the Akogi region in Namie Town and from Futaba Town to northern Tomioka Town. The values for cumulative soil surface β-ray dose were estimated to be 710 mSv at Namie-Akogi-Teshichiro, 477 mSv at Namie-Akogi-Kunugidaira, 246 mSv at Futaba-Ishiguma and 620 mSv at Tomioka-Osuge. Also, the southern Iitate Village had a relatively high cumulative β-ray dose of 100-150 mSv. In Fukushima City, the cumulative soil surface β-ray dose around the eastern region was estimated to be 20-60 mSv higher than that around the western region (4-10 mSv). On the other hand, areas with a high 131 I/ 137 Cs ratio of 69 ± 39 (maximum: 285) around Iwaki City showed a relatively low deposition density of 137 Cs of 20-50 kBq/m 2 ; thus, the cumulative β-ray dose showed slightly lower values: ∼1-24 mSv. The map of the estimated cumulative soil surface β-ray dose is shown in Fig. 5, edited by interpolating the results with the multilevel B spline interpolation using SAGA-GIS [10]. Three higher cumulative β-ray dose regions can be clearly seen in the Akogi-Teshichiro and Akogi-Kunugidaira regions in Namie Town, and also from Futaba Town to northern Tomioka Town. Compared with the cumulative γ-ray dose map produced by MEXT [11], the β-ray dose is slightly larger than the γ-ray dose around Iwaki City. This is due to the 129m,129 Te contributions, which have longer half-lives (33.6 days) than 131 I (8.021 days) and higher β-ray emission rates of ∼90% compared with the γ-ray emission rates (<10%).
As already stated in the Introduction, our estimation used the 70-μm dose equivalent as the skin dose for humans. These estimates are based on the assumption that people stay outside houses or buildings continuously for a year. Therefore, this skin dose is not strictly accurate for humans; however, the doses are fairly accurate for organisms living in the outside environment, such as small insects, plant leaves, etc.

CONCLUSION
The cumulative soil surface β-ray dose was calculated using the 2-km mesh soil contamination data by MEXT and our previously published β-ray dose calculation technique. From that, an estimated cumulative soil surface β-ray dose map was produced. As a result of this map, areas estimated to have a higher cumulative β-ray dose on the soil surface for the first year after the FDNPP accident were found to be located in the Akogi-Teshichiro to Akogi-Kunugidaira region in Namie Town and from Futaba Town to northern Tomioka Town. The highest estimated cumulative β-ray dose was 710 mSv for one year at Akogi-Teshichiro, Namie Town.