## Materials and Methods  
### Projection of Absorbed Dose  
First, a situation of land contamination caused by fall-out \({}^{137}\)Cs deposited onto the ground is assumed. In this situation, external exposure to \(\gamma\)-rays from the \({}^{137}\)Cs source in the ground surface is the main concern; internal exposure from radiocesium is supposed to be quite small as confirmed from the Fukushima Daiichi accident [3; 4; 18]; [PERSON] et al. [18] \begin{table}
\begin{tabular}{c c} \hline \hline
**Early and Intermediate Phase** & **Long-Term Phase** \\ \hline
100 mSv or below for the entire duration of & Lower half of the 1 to 20 mSv per year band \\  & with the objective to progressively reduce \\  & both the early and intermediate phases 1 & exposure to levels towards the lower end of the \\  & band or below, if possible \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Updated reference levels for guiding the optimization of protection of members of the public during the successive phases of a nuclear accident [8]. reported that most of the committed effective doses from radiocesium (\({}^{137}\)Cs and \({}^{134}\)Cs) determined based on whole-body-counter measurements were less than 0.1 mSv for most of the examined residents (125 adults and 49 children) who lived near the Fukushima Daichi nuclear power station at the time of the accident. Assuming that the whole-body absorbed dose of a resident in the initial year, \(D(0)\), was well known through in situ measurements at the respective site, the chronological change of annual absorbed dose rate at time = t from radiocesium deposited onto the ground can be calculated as follows:  
\[D(t)=(D(0)-D_{BKG})\cdot\exp(-\lambda_{137}\cdot t)\cdot f(t) \tag{1}\]  
where \(D_{BKG}\) is the background dose rate at the site; \(\lambda_{137}\) is the physical decay constant of \({}^{137}\)Cs; and \(f(t)\) is the attenuation function which is related to the cesium mobility in the surface soil layer. As the value of \(D_{BKG}\), 0.05 uSv h\({}^{-1}\) (0.44 mSv y\({}^{-1}\)) was employed from a previous study on the external dose assessment of the evacuee in Fukushima Prefecture [19]. It is empirically known that the observed dose-rate changes can be approximated well with \(f(t)\) composed of a sum of two exponential functions, i.e., short-term and long-term decay components, as follows [2; 20; 21; 22; 23]:  
\[f(t)=\alpha\cdot exp\left(-\frac{ln2}{T_{S}}\cdot t\right)+(1-\alpha)\cdot exp \left(-\frac{ln2}{T_{L}}\cdot t\right) \tag{2}\]  
where \(\alpha\) is a fraction of the short-term component; \(T_{S}\) and \(T_{L}\) are environmental half-lives for short-term and long-term decay components, respectively, that characterize the disappearing rates from the respective local environment due to the natural removal phenomena and human activities for reusing the land. It is expected that the values of site-specific \(T_{S}\) and \(T_{L}\) could be derived from the on-site radiation monitoring data obtained for initial days by using the areal monitoring posts, monitoring vehicles, portable detectors, monitoring airplane, etc., as demonstrated at the Fukushima Daichi accident [24]. In the present analyses, the environmental half-life of the long-term decay component (\(T_{L}\)) was assumed to be 50 years in reference to the relevant work of [PERSON] et al. [20] in regard to the Chernobyl accident and also the assessment of United Nations Scientific Committee on the effects of atomic radiation (UNSCEAR) regarding the Fukushima Daichi accident [2]. As to the fraction (\(\alpha\)) and environmental half-life (\(T_{S}\)) of the short-term component, large variations depending on the land-surface properties have been observed in the area affected by the Fukushima Daiichi accident [3; 22; 23]. Here, the 5 th percentile, median and 95 th percentile values of the \"other than forest\" undisturbed area in the evacuation zone were chosen from the paper of [PERSON] et al.