## 4 Discussion
### Temporal Decrease of \({}^{137}\)Cs Concentration in Sediment and River Water  
[PERSON] et al. [17] measured the dissolved \({}^{137}\)Cs component on three rivers at sites downstream of the catchments under normal flow conditions every two months during 2011-2013 in the Yamakiya District, Fukushima. They observed a rapid decrease of \({}^{137}\)Cs concentration during the initial flush until the end of 2011, with effective half-lives of 0.10-0.21 y, and thereafter, a slow decrease of \({}^{137}\)Cs as the second phase with effective half-lives of 0.69-1.5 y in the three catchments. [PERSON] et al. [18] studied behaviors of suspended sediments and \({}^{137}\)Cs in the Ogaki Dam reservoir on the Ukedo River, Fukushima, during a heavy rainfall caused by the typhoon on 15 September 2013. Their simulation results were interpreted that the reservoir play a role to delay and buffer the transport of radiocesium in heavy rainfall events. After Chernobyl accident, long-term radiological monitoring of river water were performed at two rivers, the Pripyat and the Dnieper Rivers, in Ukraine for 1986-2001 by [PERSON] et al. [20] and five rivers in Finland for 1986-1996 by [PERSON] and [PERSON] [23]. The \({}^{137}\)Cs concentration decreased exponentially in the first 5-6 years, then it declined slowly. We have estimated the effective half-lives of the Pripyat and the Dnieper Rivers fitting with an exponential function:  
\[y=A_{0}\exp(-\lambda t) \tag{1}\]  
Figure 9: (**a**) \({}^{137}\)Cs depth profile over the floodplain at the Kinoene Bridge at the S1 site on the Odaka River. (**b**) \({}^{137}\)Cs depth profile over the floodplain at the S2 site. where \(A_{0}\) (Bq\(\cdot\)kg\({}^{-1}\)) is an initial deposition, \(\lambda\) (y\({}^{-1}\)) is annual decrease rate, and \(t\) (y) is the elapsed time from initial deposition. The effective half-life is derived as \(T_{e}=\ln 2\)\(\lambda^{-1}\) using the annual decrease rate \(\lambda\). The effective half-lives were 1.5-1.6 y for the Pripyat and the Dnieper Rivers in Ukraine. Two rivers in Finland, the Kymijohl and the Kokenmaenjoki Rivers, which were located in high radioactive contamination areas, were also fitted with an exponential function. The estimated effective half-lives were 1.1-1.0 y, similar to the case of Ukraine. We have also estimated the effective half-lives of the \({}^{137}\)Cs decrease of sediments in Minami-Soma City shown in Figure 4a, with fitting with an exponential function. The results are given in Table 4. The annual decrease rates for sediment were 0.33-0.46 y\({}^{-1}\) and the associated effective half-lives were 1.5-2.1 y, except for the Odaka River which had a longer effective half-life of 4.7 y. The annual decrease rate and effective half-life were also estimated for the average concentration of \({}^{137}\)Cs in river water shown in Figure 4b. The results are also given in Table 4. The effective half-lives were 0.9-2.1 y except for the Odaka River which had a longer effective half-life of 3.7 y. The effective half-lives for the three dammed rivers agree with the second phase data are reported by [PERSON] et al. [17]. As shown in Figure 2, the Ohta, the Mizunashi, and the Mano Rivers are dammed at upstream, and \({}^{137}\)Cs supplied from the Abukuma mountain range to the river has accumulated in the dam reservoir. Since present sampling sites were all located in the downstream area of the dams, the temporal \({}^{137}\)Cs decrease in sediments and river water is demonstrated with a single exponential function. In contrast, the Odaka River is not dammed upstream, thus, the \({}^{137}\)Cs decrease is represented not only by a simple exponential function, but an additional transfer component from the forest and the plain to the river might exist. One possibility to represent the temporal decrease of \({}^{137}\)Cs on the Odaka River with two components is as follows:  
\[y=A_{0}\exp(-\lambda_{s}t)+Bt\exp(-\lambda_{t}t) \tag{2}\]  
where \(B\) and \(\lambda_{t}\) are two additional parameters.