Thirty-Year Prediction of ¹³⁷Cs Supply from Rivers to Coastal Waters off Fukushima Considering Human Activities

Abstract

The Fukushima Daiichi Nuclear Power Plant accident caused an accumulation of ¹³⁷Cs in coastal sediment. The ¹³⁷Cs supply from rivers to the ocean can affect the long-term fate of ¹³⁷Cs in coastal sediment. Since the Fukushima coastal river basins include large decontaminated and evacuation order areas, considering the decontamination work and resumption of agriculture is important for predicting the ¹³⁷Cs supply. We conducted a 30-year prediction of the ¹³⁷Cs supply from the Fukushima coastal rivers to the ocean using a distributed radiocesium prediction model, considering the effects of human activities. In river basins with decontaminated and evacuation order areas, human activities reduced the total ¹³⁷Cs outflow from agricultural lands, urban lands, and forest areas to the rivers and the ¹³⁷Cs supply to the ocean by 5.0% and 6.0%, respectively. These results indicated that human activities slightly impacted the ¹³⁷Cs outflow and supply. The ¹³⁷Cs supply from rivers impacted by the accident to the coastal sediment was estimated to correspond to 11–36% of the total ¹³⁷Cs in the coastal sediment in the early phase of the accident. Therefore, the ¹³⁷Cs supply from rivers to the ocean is important for the long-term behavior of ¹³⁷Cs in coastal sediment.

1. Introduction

The accident at the Fukushima Daiichi Nuclear Power Plant (FDNPP) released significant quantities of radioactive materials into the environment, which included various radionuclides, most of which have a half-life of less than one year. However, there is concern about the impacts of ¹³⁷Cs, which has a long half-life (30.1 years) and remains in the environment for a long time. Since ¹³⁷Cs released into the environment can be taken up by organisms and affect them, clarifying the environmental fate of ¹³⁷Cs using numerical simulation is important to evaluate its effects on organisms. Cesium-137 was transported to the ocean by three means through (1) direct discharge from the FDNPP, (2) deposition on the surface water from the atmosphere, and (3) supply from rivers after deposition on the land surface [1,2]. Studies have reported that the direct discharge from the FDNPP and the deposition on the surface water caused significant contamination after the accident [1,3].

Kusakabe et al. [4] and Takata [5] showed that the ¹³⁷Cs concentration in seawater at nearshore stations off Fukushima after the accident decreased exponentially, although it was much higher than before the accident. Preventing visible leakage by injecting water glass and the dilution effect of seawater caused the rapid decrease [5]. The ¹³⁷Cs concentrations in seabed sediment at most nearshore stations off Fukushima decreased between 2011 and 2015 at a rate of approximately 30% per year [6,7] and decreased more slowly thereafter at approximately 12% per year [2]. These results showed that the ¹³⁷Cs concentration in seabed sediment at nearshore stations off Fukushima decreased much slower than in seawater. Therefore, ¹³⁷Cs could remain in seabed sediment for a long period of time.

Studies have shown that the relative impact of the ¹³⁷Cs supply from rivers on ¹³⁷Cs in seabed sediment could increase as the ¹³⁷Cs accumulated on seabed sediment in the early phase of the accident has decreased [2,8]. Uchiyama et al. [9] analyzed ¹³⁷Cs settled on the seafloor using a 3D ocean circulation and sediment transport model considering the supply of particulate ¹³⁷Cs from the Niida River. Their study estimated that 76.6% of the ¹³⁷Cs supply from the river due to flooding in 2013 was settled on coastal areas shallower than 25 m. Suzuki et al. [10] estimated the ¹³⁷Cs concentrations in coastal sediment off Fukushima using numerical modeling, considering the supply of particulate ¹³⁷Cs from rivers. Their study suggested that the particulate ¹³⁷Cs supply from rivers is important for determining the temporal trend of ¹³⁷Cs concentrations in coastal sediment. These results showed that the particulate ¹³⁷Cs supply from rivers impacts the long-term behavior of ¹³⁷Cs in coastal sediment. Therefore, predicting the long-term supply of particulate ¹³⁷Cs from rivers is necessary to clarify the long-term fate of ¹³⁷Cs in coastal sediment.

The Fukushima coastal river basins are within 70 km of the FDNPP and include the evacuation order area. The Abukuma River basin is the largest basin near the FDNPP, located 30–100 km from the FDNPP. Although the Fukushima coastal and Abukuma River basins were decontaminated, the Fukushima coastal river basins include Special Decontamination Areas where large-scale decontamination was conducted due to high radiation doses [11]. The Abukuma River and Fukushima coastal rivers supply ¹³⁷Cs to the coastal waters off Miyagi and the Fukushima Prefecture, respectively. Both monitoring [12,13] and simulation studies [14] indicated that the ¹³⁷Cs supply from the Fukushima coastal rivers was comparable to that from the Abukuma River. Therefore, predicting the long-term supply of ¹³⁷Cs from the Abukuma and the Fukushima coastal rivers to the ocean is important.

Taniguchi et al. [12,13] estimated the ¹³⁷Cs supply from the Abukuma River to the ocean and the contributions of the supply according to land uses by monitoring for approximately six years after the accident. By using a model that considered the characteristics of ¹³⁷Cs behavior in land uses, Ikenoue et al. [15] reproduced the estimated supply from the Abukuma River to the ocean based on Taniguchi et al. [12,13] and predicted the supply for the following 24 years. Since the contribution of the ¹³⁷Cs supply from urban land and disturbed agricultural lands (disturbed croplands and paddy fields) to the ocean was estimated to be 80–85% of the total supply [12,15], these studies indicated that land uses and human activities remarkably affected the ¹³⁷Cs supply from the river to the ocean. Although agriculture was suspended in the evacuation zones after the accident, it gradually resumed as the decontamination work progressed. Therefore, in the Fukushima coastal river basins, including the evacuation order area, resuming agriculture and the associated land-use changes could significantly impact the ¹³⁷Cs supply to the ocean. Feng et al. [16] monitored the impact of decontamination and the associated land-cover change on the concentrations of ¹³⁷Cs and suspended sediment in the Niida River downstream. They showed that the upstream decontamination caused persistently excessive suspended sediment loads downstream, though with reduced ¹³⁷Cs concentrations. Therefore, their study indicated that the decontamination work affected the ¹³⁷Cs and suspended sediment supply from the rivers to the ocean. Pratama et al. [17] estimated the ¹³⁷Cs supply from the Abukuma River to the ocean for 100 years after the accident, considering the impact of decontamination using simulations. They estimated that the decontamination work reduced the 100-year ¹³⁷Cs supply by 2.6% compared to that without decontamination. Since the Fukushima coastal river basins have been decontaminated on a larger scale than the Abukuma River basin and the decontamination work was conducted preferentially on urban lands and agricultural lands (croplands and paddy fields) [11], the decontamination work could significantly reduce the ¹³⁷Cs supply from the Fukushima coastal rivers to the ocean. These results show that it is important to consider the decontamination work and the resumption of agriculture as human activities to predict the long-term supply of ¹³⁷Cs from the Fukushima coastal rivers to the ocean.

Several studies have estimated the ¹³⁷Cs supply from the Abukuma and Fukushima coastal rivers to the ocean [12,13,14,15,17,18,19,20,21,22,23,24]. However, none of them conducted a long-term prediction of the ¹³⁷Cs supply from the Fukushima coastal rivers to the ocean, considering the decontamination work and the resumption of agriculture. We focus on the effects of these human activities and provide useful insights into the long-term behavior of ¹³⁷Cs in highly contaminated areas. In this study, a 30-year prediction of the ¹³⁷Cs supply from the Fukushima coastal rivers to the ocean was conducted using a distributed radiocesium prediction model, considering the decontamination work and the resumption of agriculture.

2. Materials and Methods

2.1. Model

2.1.1. Distributed Radiocesium Prediction Model

We applied a distributed radiocesium prediction model to the Fukushima coastal river basins. The model used in this study was an improved version of a model developed by Ikenoue et al. [15] to consider the sedimentation at the dam and the erosion and sedimentation in the floodplain. The details of the improvements are described in Section 2.1.2 and Section 2.1.3. This model comprises a hydrological model, a sediment transport model, and a ¹³⁷Cs transport model. These models calculate the water flow, soil erosion and sediment transport, and the transport of washed-off ¹³⁷Cs adsorbed on the eroded soil particles, respectively.

The hydrological model is based on Kojiri et al. [25] and represents the water cycle processes, such as snowmelt, snowfall, infiltration, surface runoff, subsurface flow, and groundwater flow. The computational domain is divided into grids with a horizontal resolution of 1 km × 1 km, and each computational grid comprises river and land, divided into four land-use categories: croplands, forest areas, urban lands, and paddy fields.

The sediment transport model calculates the suspended sediment transport based on a one-dimensional equation, considering advection, diffusion, sedimentation, resuspension, and the lateral inflow of suspended sediment [15]. The sediment and ¹³⁷Cs transport models in this study divide the land into seven land-use categories to represent the processes described in Section 2.1.3. In these models, croplands were divided into disturbed and undisturbed croplands, and paddy fields were similarly divided. Furthermore, we added one new land-use category (floodplain). The assumption that the parameters of disturbed and undisturbed land use in the hydrological model are the same is one of the model limitations.

The ¹³⁷Cs transport is modeled assuming it does not dissolve in the river water [15] since the particulate form dominates the ¹³⁷Cs transport. The ¹³⁷Cs transport model simulates the particulate ¹³⁷Cs associated with suspended sediment. To reflect the characteristics of the ¹³⁷Cs migration processes in land uses, the model considers wash-off from paddy fields based on observation, ¹³⁷Cs migration in forest areas between compartments, downward migration in undisturbed soils, and wash-off from paved grounds and roofs based on observation.

2.1.2. Sedimentation at the Dam

The monitoring studies reported that more than 80% of ¹³⁷Cs inflows into the dam were accumulated by sedimentation [26,27]. In most of the Fukushima coastal river basins with dams, it is important to consider the sedimentation at the dam to predict the ¹³⁷Cs supply from the rivers to the ocean since the ¹³⁷Cs depositions in the upstream areas of the dams are greater than in the downstream areas. In the model developed by Ikenoue et al. [15], it was assumed that the inflow of suspended sediment to the dam would be discharged from the dam without a sedimentation process. Sedimentation at the dam is greatly influenced by the flow field in the dam and the operation of the dam. Since representing these processes in detail is difficult, we use trap efficiency ($TE$) in this study. $TE$ is an important parameter for quantifying sedimentation at the dam and is defined as the ratio of the amount of suspended sediment that settles to the amount of suspended sediment inflow [28]. Therefore, this study calculates the outflow of suspended sediment from the dam by multiplying the inflow to the dam by $1-TE$. $TE$ is calculated based on Siyam [29] as follows.

$$TE=\mathrm{e}\mathrm{x}\mathrm{p}(-\beta \frac{I}{C}),$$

(1)

where $TE$ is the trap efficiency (−), β is a sedimentation parameter (−), $I$ is the annual average inflow (m³), and $C$ is the amount of water that the dam can store (m³). In this study, 15 dams are considered and $C$ depends on the size, usage, and shape of the dam. β is a newly introduced parameter in this study and was calibrated to reproduce the sedimentation process at the dam. $TE$ was obtained based on $I$, which converted the calculated inflow to the dam into an annual average for each time step from the model developed by Ikenoue et al. [15].

2.1.3. Erosion and Sedimentation in the Floodplain

Studies have indicated that extreme flood events have caused erosion and sedimentation in the floodplain [30,31]. These processes notably influence downstream areas with large floodplain areas. Therefore, considering the erosion and sedimentation in the floodplain is necessary to predict the ¹³⁷Cs supply from the rivers to the ocean. The erosion rate in the floodplain is calculated based on Clark and Wynn [32] as follows.

$${\epsilon }_{er}=\left(\genfrac{}{}{0pt}{}{k_d{({\tau }_a-{\tau }_c)}^a}{0}\right)\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{n} {\tau }_a\left(\genfrac{}{}{0pt}{}{>{\tau }_c}{\le {\tau }_c}\right),$$

(2)

$$k_d=2.0\times {10}^{-7}{{\tau }_c}^{-0.5},$$

(3)

$${\tau }_c=3.54\times {10}^{-28.1D_{50}},$$

(4)

$${\tau }_a=\left(\genfrac{}{}{0pt}{}{{\rho }_{w}gi\frac{A_{fl}}{S_{fl}}\times {10}^{-3}}{0}\right)\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{n} H_r\left(\genfrac{}{}{0pt}{}{>H_{fl}}{\le H_{fl}}\right),$$

(5)

where ${\epsilon }_{er}$ is the erosion rate in the floodplain (m s⁻¹), $k_d$ is the erodibility coefficient (m³ N⁻¹ s⁻¹), ${\tau }_a$ is the shear stress in the floodplain (Pa),${\tau }_c$ is the critical shear stress in the floodplain (Pa), $a$ is the constant (−), $D_{50}$ is the mean particle size of soil (m), ${\rho }_w$ is the water density (g m⁻³), $g$ is the gravitational acceleration (m s⁻²), $i$ is the channel slope (−), $A_{fl}$ is the stream cross-sectional area in the floodplain (m²), $s_{fl}$ is the wetted perimeter in the floodplain (m), $H_r$ is the water depth (m), and $H_{fl}$ is the water depth to the low water channel (m). ${\tau }_c$ is a parameter used to determine ${\epsilon }_{er}$ and should be obtained experimentally. However, due to the lack of data in the Fukushima coastal river basins, we assumed that the empirically derived Equation (4) can be applied to the target basins. The variables on the left side in Equations (2)–(5), $a$, $A_{fl}$, $S_{fl},$ and $H_{fl}$ are newly introduced parameters and variables in this study, and $D_{50}$, ${\rho }_w$, $g$, $i$, and $H_r$ were defined in the model developed by Ikenoue et al. [15]. ${\tau }_a$ is determined based on the calculated values from the hydrological model and the cross-sectional shape of a river. The wetted perimeter is defined as the total length of the surface of the channel bottom and sides that is in direct contact with the water in the cross-section of the river channel. The erosion in the floodplain based on Equation (2) and the erosion in other land uses based on the Universal Soil Loss Equation (USLE) [33] were used to estimate the lateral inflow of sediment as follows.

$$f_{SSfl}={\epsilon }_{er}{s}_{fl}{\rho }_{Bfl},$$

(6)

$$f_{ss}={\sum }_l{f}_{ssl},$$

(7)

where $f_{ss}$ is the lateral inflow load per grid length of the sediment (g m⁻¹ s⁻¹), ${\rho }_{Bfl}$ is the bulk density of the floodplain soil (g m⁻³), $fl$ is the floodplain in land-use categories, and $l$ is the land-use categories. The sedimentation rate in the floodplain is calculated based on the settling velocity of suspended sediment in the rivers proposed by Rubey [34] as follows:

$${Sed}_{fl}=w_f{C}_{SS}\frac{A_{fl}}{H_r-H_{fl}},$$

(8)

$${\epsilon }_{sed}=\frac{{Sed}_{fl}}{s_{fl}{\rho }_{Bfl}},$$

(9)

where ${Sed}_{fl}$ is the settled sediment load (g m⁻¹ s⁻¹), $w_f$ is the settling velocity of the suspended sediment (m s⁻¹), $C_{ss}$ is the suspended sediment concentration in the river (g m⁻³), and ${\epsilon }_{sed}$ is the sedimentation rate in the floodplain (m s⁻¹). The variables on the left side in Equations (6), (8), and (9), and ${\rho }_{Bfl}$ are newly introduced parameters and variables in this study, and $f_{ss}$, $w_f$, and $C_{SS}$ were defined in the model developed by Ikenoue et al. [15].

Cs-137 in the floodplain is divided into ¹³⁷Cs in the sediment and soil layers. Cs-137 in the sediment layer refers to the ¹³⁷Cs settled on the floodplain after the accident when the water depth exceeds the depth to the low water channel. Cs-137 in the soil layer refers to the ¹³⁷Cs deposited on the soil from the atmosphere after the accident. We assumed the following for ¹³⁷Cs in two layers. The ¹³⁷Cs concentration in the sediment layer is constant regardless of the depth from the land surface due to mixing sediment. Similar to undisturbed soil, the ¹³⁷Cs concentration in the sediment layer is expressed based on the diffusion equation [15]. The thickness of the sediment layer ($d_{flsed}$) varies due to sedimentation and erosion in the floodplain. When $d_{fsed}$ is greater than 0, the eroded ¹³⁷Cs concentration in the floodplain is calculated as follows.

$$\frac{\partial }{\partial t}{d}_{flsed}={\epsilon }_{sed}-{\epsilon }_{er},$$

(10)

$$\frac{\partial }{\partial t}{(R}_{flsed}{d}_{flsed})={R_{riv}\epsilon }_{sed}-{R_{flsed}\epsilon }_{er},$$

(11)

$$E_{rfl}=R_{flsed},$$

(12)

where $d_{flsed}$ is the sediment layer thickness (m), and $R_{flsed}$, $R_{riv}$, and $E_r$ are the ¹³⁷Cs concentrations (Bq g⁻¹) in the sediment layer, suspended sediment, and eroded soil, respectively. The erosion of the soil layer begins when all the sediment layers are eroded. When all the sediment layers are eroded, the eroded ¹³⁷Cs concentration in the floodplain is calculated as follows.

$$E_{rfl}=\frac{{R_{riv}\epsilon }_{sed}+R_{flsoil}({\epsilon }_{er}-{\epsilon }_{sed})}{{\epsilon }_{er}},$$

(13)

where $R_{flsoil}$ is the ¹³⁷Cs concentration (Bq g⁻¹) in the eroded soil of the soil layer. Based on Equations (6), (12), and (13), the lateral inflow load of ¹³⁷Cs is expressed as follows.

$$f_{Cs}=\frac{{\sum }_l{{Er}_l\times f}_{SSl}\times A_l}{{\sum }_l{A}_l},$$

(14)

where $A_l$ is the catchment area (m²). The variables on the left side in Equations (10)–(12) and $R_{flsoil}$ are newly introduced variables in this study, and $E_r$, $f_{Cs}$, $R_{riv}$, and $A_l$ were defined in the model developed by Ikenoue et al. [15].

2.2. Computational Conditions

2.2.1. Computational Domain and Period

The Fukushima coastal river basins are within 70 km of the FDNPP (Figure 1). The distributed radiocesium prediction model was applied to the Fukushima coastal river basins for 30 years, from January 2011 to December 2040. The model was also applied to the Abukuma River basin under similar computational conditions. Assuming climate change does not have a notable impact on ¹³⁷Cs transport [15], the meteorological data from 2011 to 2020 were repeatedly applied to reflect the scale of flooding each year. The transport of ¹³⁷Cs was analyzed starting on July 2, 2011, the reference date of the reconstructed fallout map [35]. Based on the reconstructed fallout map (Figure 1), the initial depositions were set at 1094, 85, 100, 127, 5, and 1411 TBq for the forest areas, croplands, urban lands, paddy fields, floodplain, and the Fukushima coastal river basins, respectively [35]. The initial ¹³⁷Cs depositions in each river basin are as follows; Uda: 13 TBq, Mano: 49 TBq, Niida: 219 TBq, Ota: 66 TBq, Odaka: 28 TBq, Ukedo: 623 TBq, Meada: 91 TBq, Kuma: 138 TBq, Tomioka: 48 TBq, Ide: 14, Kido: 51 TBq, Natsui: 49 TBq, and Same: 24 TBq. The performance of the model was evaluated at observatories in the Fukushima coastal rivers (Figure 1), i.e., 13 sites (Nakamura, Ojimadazeki, Haramchi, Kitamachi, Ota, Kawahata, Odaka, Ukedo, Takase, Kuma, Tomioka, Nakakabeya, and Matsubara) for the river discharge and ¹³⁷Cs. We used the river discharge data at the observatories of the Fukushima Prefecture for Nakamura, Ojimadazeki, Haramchi, Kitamachi, Ota, Odaka, Ukedo, Takase, Tomioka, Nakakabeya, and Matsubara [36]. We observed the water level at Kawahata and Kuma using the same method as the Fukushima Prefecture and obtained the river discharge data. Figure S1 shows the outline of the computational domain in the Abukuma River basin. The initial depositions were set at 520 TBq for the Abukuma River basin.

2.2.2. Input Data

The radar precipitation data from the Japan Meteorological Agency were used as the precipitation inputs for the hydrological and sediment transport models. The other input data used in the hydrological, sediment transport, and ¹³⁷Cs transport models were based on Ikenoue et al. [15]. The relative land-use distributions in the Fukushima coastal river basins (Figure 2) were 78.8%, 5.7%, 5.3%, 9.8%, and 0.5% for the forest areas, croplands, urban lands, paddy fields, and floodplain, respectively. The cross-sectional shapes of the river were determined based on the Ministry of Land, Infrastructure, Transport, and Tourism [37]. The parameters related to the vertical distribution of the ¹³⁷Cs concentrations in the soil layer of the floodplain were set to the same values as the undisturbed cropland soil determined by Ikenoue et al. [15].

2.2.3. Decontamination Work and Resumption of Agriculture

We considered the impact of the decontamination work by decreasing the ¹³⁷Cs wash-off from the decontaminated area. Based on Kurokawa et al. [38] and the decontamination guidelines [39], we determined the decrease rate of the ¹³⁷Cs wash-off from the decontaminated area (

Table 1. Decrease rates of the ¹³⁷Cs wash-off from the decontaminated area. In the forest areas, only the organic soil was set to be decontaminated.

Land Uses	Decrease Rate (%)	References
Croplands and paddy fields in Special Decontamination Areas	80	[38]
Croplands and paddy fields outside Special Decontamination Areas	50	[39]
Urban lands	100	[39]
Forest areas (organic soil)	100	[39]

). Based on the decontamination guidelines [39], we assumed that the ¹³⁷Cs wash-off was prevented due to decontamination. The decontamination in the floodplain was only conducted in some places, such as parks and playgrounds. We did not consider decontamination in the floodplain because of the limited decontaminated area and the lack of information on the decontamination work. Although the decontamination work in areas except for the difficult-to-return zone was conducted from 1.5 years to seven years after the accident, the decontamination work in the difficult-to-return zone was conducted beginning six years after the accident, primarily in urban areas [11]. The simulation results based on Ikenoue et al. [15] showed that the major ¹³⁷Cs outflow from urban lands to the river stopped five years after the accident. Considering these results and the lack of information on the decontamination work in the difficult-to-return zone, we did not consider decontamination in the difficult-to-return zone. After the accident, the evacuation zones were set up as Special Decontamination Areas and agriculture was suspended. In some areas that were not evacuation zones, agriculture was also suspended. As the decontamination work progressed, agriculture gradually resumed in areas outside the difficult-to-return zones. Undisturbed agricultural lands (undisturbed croplands and paddy fields) change into disturbed agricultural lands when continuing agriculture.

Feng et al. [16] indicated that the decontamination work of undisturbed agricultural lands increased the erodibility due to soil disturbance. They estimated that the erodibility of the undisturbed agricultural land soil immediately after and two years after decontamination was 1.98 and 1.3 times larger than before decontamination, respectively. The erodibility of the decontaminated agricultural land soil was determined, assuming that this change in erodibility is linear until the erodibility reaches the same value as before decontamination. The erodibility of soil where agriculture has been resumed and soil where agriculture and decontamination have not been conducted were set at the same values as the disturbed and undisturbed agricultural lands, respectively. Based on the Ministry of the Environment (MOE) [11] and the Ministry of Agriculture, Forestry, and Fisheries (MAFF) [40], the decontaminated and resumption of agriculture area rates were determined, respectively, assuming that the progress rate in decontamination and resumption of agriculture is linear. The decontaminated area and resumption area for agriculture were divided based on each municipality, Special Decontamination Areas, and the difficult-to-return zone. We assumed that agriculture resumed preferentially from decontaminated areas. We evaluated the impacts of decontamination and the resumption of agriculture in 10 target river basins (Mano, Niida, Ota, Odaka, Ukedo, Maeda, Kuma, Tomioka, Ide, and Kido) with decontaminated areas and resumption areas for agriculture. The relative land-use distributions in the 10 target river basins were 75.3%, 6.8%, 5.2%, 11.9%, and 0.8% for forest areas, croplands, urban lands, paddy fields, and floodplain, respectively. Figure 3 shows the decontaminated and resumption of agriculture area rates in the 10 target river basins based on the MOE [11] and MAFF [40]. The area rates of decontaminated croplands, urban lands, paddy fields, and forest areas from 1.5 years to seven years after the accident were 49.7%, 49.1%, 57.3%, and 12.9%, respectively (Figure 3a). Over the 12 years after the accident, the area rates of resumption area for agriculture area in croplands and paddy fields reached 16.6% and 41.4%, respectively (Figure 3b). Changes of these rates were affected by the timing of lifting evacuation orders and shipping restrictions. Since the area rate of resumption area for agriculture is constant over 12 years and those after 12 years are future information, it was assumed that the rate is constant thereafter.

This study conducted five calculations to evaluate the impacts of (1) sedimentation at the dam, (2) erosion and sedimentation in the floodplain, (3) decontamination work, and (4) the resumption of agriculture on ¹³⁷Cs supplies from the rivers to the ocean. In the Base, V1, V2, L1, and L2 cases, we considered the effects of (1, 2, 3, 4), (2, 3, 4), (1, 3, 4), (1, 2, 3), and (1, 2), respectively. The Base, V1, and V2 cases were used for the model validation, and the Base, L1, and L2 cases were used for evaluating the impacts of the decontamination work and the resumption of agriculture.

3. Results and Discussion

3.1. Model Validation

The hydrological model performance for simulating the daily river discharge was evaluated using the statistical indices [41] shown in Equations (15)–(17).

$$\mathrm{R}\mathrm{S}\mathrm{R}=\frac{\sqrt{{\sum }_{i=1}^N{(O_i-M_i)}^2}}{\sqrt{{\sum }_{i=1}^N{(O_i-\stackrel{-}{O})}^2}},$$

(15)

$$\mathrm{P}\mathrm{B}\mathrm{I}\mathrm{A}\mathrm{S}=\frac{{\sum }_{i=1}^N{(O}_i-M_i)\times 100}{{\sum }_{i=1}^N{O}_i},$$

(16)

$$\mathrm{N}\mathrm{S}\mathrm{E}=1-\frac{{\sum }_{i=1}^N{\left(O_i-M_i\right)}^2}{{\sum }_{i=1}^N{(O_i-\stackrel{-}{O})}^2},$$

(17)

where $M$ is the calculated value, $O$ is the observed value, $N$ is the number of samples (−), an overline indicates a sample mean, $\mathrm{R}\mathrm{S}\mathrm{R}$ is the root mean square error standard deviation ratio (−), $\mathrm{P}\mathrm{B}\mathrm{I}\mathrm{A}\mathrm{S}$ is the percentage bias (%), and $\mathrm{N}\mathrm{S}\mathrm{E}$ is the Nash–Sutcliffe model efficiency coefficient (−).

Table 2. Statistical indices of the daily discharge from January 2011 to December 2017 at each observatory.

Observatory	Observed (m3 s−1)	Calculated (m3 s−1)	RSR (−)	|PBIAS| (%)	NSE (−)
Nakamura	2.87	3.14	0.56	9.7	0.69
Ojimadazeki	2.52	4.57	0.72	58.5	0.47
Haramachi	5.95	7.34	0.62	23.4	0.62
Odaka	0.98	0.92	0.54	5.8	0.71
Kawahata	2.21	2.01	0.43	8.7	0.82
Ukedo	6.53	6.01	0.61	8.0	0.63
Takase	9.86	12.1	0.55	22.7	0.7
Kuma	2.92	3.73	0.48	28.1	0.77
Tomioka	1.69	2.07	0.71	22.9	0.5
Nakakabeya	20.92	25.51	0.58	22.0	0.66
Matsubara	18.3	21.43	0.71	17.1	0.49

shows the statistical indices of the daily discharge from January 2011 to December 2017 at each observatory. The hydrological model performance was evaluated at 11 sites in the Fukushima coastal rivers (Figure 1) using the daily observation data of the river discharge based on the Fukushima Prefecture [36] and our monitoring. For a monthly time step, Moriasi et al. [41] proposed that the model simulation can be judged as satisfactory if the RSR ≤ 0.70, |PBIAS| < 25%, and NSE > 0.50 for the river discharge. The model simulations are poorer for shorter time steps than longer ones [42]. Despite the evaluation for a daily time step, the statistical indices at seven sites except for Ojimadazeki, Kuma, Tomioka, and Matsubara satisfied the criteria based on Moriasi et al. [41]. Considering that the criteria were strict regarding the values for a daily time step, the model performance at Ojimadazeki, Kuma, Tomioka, and Matsubara was considered acceptable.

In validating the suspended sediment, Nakanishi et al. [21] estimated that the cumulative export of the total suspended sediment at the Ukedo and Takase observatories between July 2013 and December 2019 was 358 Gg, based on observation. In the Base, V1, and V2 cases, the calculated cumulative export of suspended sediment in the same period was estimated to be 431, 447, and 189 Gg, respectively. The sedimentation at the dam reduced the cumulative export at the Ukedo observatory by 13.5%, and the erosion and sedimentation in the floodplain increased the export at the Ukedo and Takse observatories by a factor of 5.1 and 1.9, respectively. The sedimentation at the dam contributed little to the cumulative export at the Ukedo observatory since the upstream area has low erodibility due to large forest areas, and the downstream basin of the dam has a floodplain. Due to the large-scale erosion in the floodplain associated with the flooding from Typhoon Etau in September 2015 and Typhoon Hagibis in October 2019, the erosion and sedimentation in the floodplain had a more significant impact on the cumulative export at Ukedo and Takase than the sedimentation at the dam. These results suggested that the erosion and sedimentation in the floodplain significantly influence the suspended sediment export. Although the model in the Base case overestimated the export compared to the estimated value based on observation, it captured the trend of the estimated value.

Figure 4 shows the monthly and cumulative exports of the total ¹³⁷Cs at the Mano, Haramachi, Kitamchi, Ota, Odaka, Ukedo, Takase, and Matsubara observatories based on observation [12,13] and calculations using the model. Based on the monthly estimated and calculated export, the NSE and the coefficient of determination (R²) were 0.91 and 0.95, 0.89 and 0.92, and 0.57 and 0.79 for the Base, V1, and V2 cases, respectively (Figure 4a). By considering the erosion and sedimentation in the floodplain and the sedimentation at the dam, we improved the export caused by Typhoon Etau 4.5 years after the accident and the overestimation in the overall export, respectively (Figure 4a,b). The sedimentation at the dam slightly impacted the suspended sediment export since the upstream areas with large forest areas have low erodibility. However, the sedimentation at the dam had a significant impact on ¹³⁷Cs because the ¹³⁷Cs depositions in the upstream areas were much greater than in the downstream areas. Therefore, the model in the Base case reproduced the temporal trends of the ¹³⁷Cs export well. The model in the Base case best reproduced the exports of suspended sediment and ¹³⁷Cs of the models in the three cases. Based on the river discharge and export of suspended sediment and ¹³⁷Cs, the overall model performance was acceptable. Similarly, the model performance for suspended sediment and ¹³⁷Cs export in the Abukuma River was evaluated (Figure S2) [12,13,24] and considered to be acceptable.

3.2. Evaluation of the Impacts of Decontamination Work and Resumption of Agriculture

This study provided the first simulation results for the long-term fate of ¹³⁷Cs in the Fukushima coastal river basins, considering the decontamination work and the resumption of agriculture. We calculated the ¹³⁷Cs outflow from agricultural lands, urban lands, and forest areas to rivers and the ¹³⁷Cs supply from rivers to the ocean to evaluate the impacts of the decontamination work and the resumption of agriculture. Since ¹³⁷Cs transported from the land to the rivers is supplied to the ocean through sedimentation at dams, floodplain, and riverbeds, the supply is smaller than the outflow. This study evaluated the variation rates of the calculated values in the Base case relative to that in the L1 and L2 cases as the impacts of the decontamination work and the resumption of agriculture. The variation rates relative to the calculated values in L1 and L2 represent the impacts of the resumption of agriculture after the decontamination work, and the decontamination work and resumption of agriculture, respectively. Figure 5 shows the cumulative outflows of the total ¹³⁷Cs to 10 target rivers according to land use and the variation rates of cumulative outflows in the Base case relative to those in L1 and L2. The total ¹³⁷Cs outflow from four land uses in the Base, L1, and L2 cases was estimated to be 24.8, 24.6, and 26.1 TBq, respectively (Figure 5a). The total ¹³⁷Cs outflow from four land uses in the Base case was 0.7% higher and 5.0% lower compared to the total outflow in L1 and L2. The decontamination work and the resumption of agriculture reduced the outflow from croplands and paddy fields by 16.6% and 15.1%, respectively. However, the resumption of agriculture after the decontamination work increased the outflow from croplands and paddy fields by 5.7% and 5.0%, respectively (Figure 5b). Since agriculture resumed preferentially from decontaminated areas, the decontamination work reduced the increase in the ¹³⁷Cs outflow from agricultural lands. These results suggested that the resumption of agriculture slightly impacted the outflow from agricultural lands to rivers. Since ¹³⁷Cs in urban lands was rapidly washed off within the first year after the accident [15] and forest areas had a tiny, decontaminated area (Figure 3a), the decontamination work reduced the outflow from urban lands and forest areas by only 3.4% and 2.8%, respectively (Figure 5b). The outflow from agricultural lands and paddy fields with large, decontaminated areas was small, whereas the decontamination work slightly affected urban lands and forest areas with large outflows. Therefore, the decontamination work and the resumption of agriculture slightly impacted the total outflow from four land uses to the rivers.

The cumulative supply of ¹³⁷Cs from 10 target rivers to the ocean in the Base, L1, and L2 cases was estimated to be 16.8, 17.0, and 17.9 TBq, respectively (Figure 6). The cumulative supply of ¹³⁷Cs to the ocean in the Base case was 1.1% and 6.0% lower, respectively, compared to the cumulative supply in L1 and L2. The difference between the detachment (resuspension and erosion) from the riverbed or floodplain and sedimentation in the floodplain or riverbed was estimated to be 0.43 and 0.82 TBq for the Base and L1 cases, respectively. Overall, since the resumption of agriculture was primarily conducted in the downstream areas where ¹³⁷Cs deposition was small, the reduction in the ¹³⁷Cs concentrations settled on the riverbed and floodplain decreased the resuspension from the riverbed and the ¹³⁷Cs outflow associated with soil erosion from the floodplain. The cumulative outflow to the rivers and the supply to the ocean indicated that the decontamination work and the resumption of agriculture slightly affected the total outflow to the rivers and the ¹³⁷Cs supply to the ocean.

3.3. Overall Evaluation of the Fukushima Coastal River Basins

Figure 7 shows the cumulative ¹³⁷Cs supply to the ocean from each river in the Base case, and

Table 3. The cumulative ¹³⁷Cs supply to the ocean from each river 30 years after the accident and the ratio to each initial deposition.

River Name	Supply (TBq)	Ratio (%)
Ukedo	13.8	2.2
Kuma	6.2	4.5
Niida	4.5	2.0
Maeda	2.4	2.7
Tomioka	2.1	4.4
Natsui	1.6	3.3
Kido	1.2	2.4
Mano	1.0	2.1
Odaka	1.0	3.5
Uda	0.6	4.9
Ide	0.4	3.2
Ota	0.3	0.5
Same	0.2	1.0

shows the cumulative ¹³⁷Cs supply from each river 30 years after the accident and the ratio to each initial deposition. The cumulative ¹³⁷Cs supply from the Ukedo, Kuma, Niida, Maeda, and Tomioka rivers accounted for 81.8% of the total cumulative ¹³⁷Cs supply. The ¹³⁷Cs supply from the Kuma, Maeda, and Tomioka rivers was large in the early phase of the accident because their basins had a high ¹³⁷Cs deposition in urban lands. The overall trend was estimated to be the larger ¹³⁷Cs supply from the river with the high deposition basin. Except for the basins with a high deposition in urban lands in the downstream area of the dam (Kuma and Tomioka river basins), sedimentation at the dam suppressed the ratios of the ¹³⁷Cs supply to the initial deposition. The ¹³⁷Cs supplies from the Ota and Same rivers, which have dams near their downstream areas, were significantly suppressed by the sedimentation at the dams. These results indicate that the sedimentation at the dam and ¹³⁷Cs deposition significantly influenced the ¹³⁷Cs supply from the rivers to the ocean.

Figure 8 shows the temporal variation of the cumulative ¹³⁷Cs outflows to the rivers in the Fukushima coastal river basins, according to land use in the Base case. The cumulative ¹³⁷Cs outflow from forest areas and urban lands dominated the 2.5 years after the accident, and the outflow from forest areas dominated after that (Figure 8) due to the high deposition in forest areas and the rapid wash-off of ¹³⁷Cs from urban lands. Furthermore, the decontamination work and undisturbed soil suppressed the ¹³⁷Cs outflow from agricultural lands. The ¹³⁷Cs wash-off events from the floodplain occurred three times within ten years after the accident. Since the ten years of meteorological data were repeatedly applied to the model, nine wash-off events occurred during the computational period. However, as the concentrations of ¹³⁷Cs that settled on the floodplain decreased, the ¹³⁷Cs wash-off from the floodplain decreased. In the Abukuma River basin, the ¹³⁷Cs outflow from forest areas and urban lands dominated the first year after the accident, and the contribution of the ¹³⁷Cs outflow from disturbed agricultural lands gradually increased after the first year [15]. In both the calculated results of the Abukuma River [15] and Fukushima coastal river basins in this study, the major ¹³⁷Cs outflow from urban lands and forest areas occurred in the first five years after the accident and slowly washed off after that. Similar trends were obtained from both calculated results that the ¹³⁷Cs outflow from agricultural lands continued to increase. These results indicated the same temporal trends of the ¹³⁷Cs outflow from each land use to the rivers in both basins. In the Fukushima coastal river basins, due to the high deposition in forest areas and the suppression of the outflow from agricultural lands by the decontamination work and the undisturbed soil, the cumulative ¹³⁷Cs outflows in both basins differed.

Figure 9 shows the cumulative ¹³⁷Cs supply from the Fukushima coastal and Abukuma rivers to the ocean in the Base case. The cumulative ¹³⁷Cs supply from the Fukushima coastal and Abukuma Rivers to the ocean 30 years after the accident was estimated to be 35.6 and 23.4 TBq, respectively. The total ¹³⁷Cs supply from the Fukushima coastal and Abukuma rivers to the ocean was estimated to be 59.0 TBq, corresponding to 3.1% of the total initial deposition in the Fukushima coastal and Abukuma River basins. Otosaka and Kato [43] estimated that the total ¹³⁷Cs in the seabed sediment off Fukushima was 100–300 TBq as of October 2011 based on the observed ¹³⁷Cs concentrations. Otosaka [2] estimated that 80% of this value existed in the coastal areas shallower than 100 m. These results indicate that the total sedimentary ¹³⁷Cs in the coastal areas off Fukushima was 80–240 TBq as of October 2011. Based on a laboratory experiment, Takata [23] estimated that the ¹³⁷Cs desorbed by seawater from suspended sediment in the river was 5.5–11%. The calculated ¹³⁷Cs supply to the ocean between October 2011 and December 2040 was 35.5–37.7 TBq based on the desorption rate, and 76.6% of the ¹³⁷Cs supply from the rivers was settled on the coastal areas based on Uchiyama et al. [9]. Therefore, the particulate ¹³⁷Cs was estimated to supply 27.2–28.9 TBq to the coastal areas shallower than 25 m. Although the supply from the rivers to the coastal areas shallower than 100 m was greater than those shallower than 25 m, these supplies were assumed to be equivalent in this study. Considering these results, the supply of particulate ¹³⁷Cs to the coastal sediment between October 2011 and December 2040 corresponded to 11–36% of the total amount of sedimentary ¹³⁷Cs in the coastal area off Fukushima as of October 2011. Since ¹³⁷Cs accumulated in seabed sediment has been decreasing [2,6,7], these results suggested that the ¹³⁷Cs supply from the rivers to the ocean is an important process for the long-term behavior of ¹³⁷Cs in coastal sediments.

4. Conclusions

This study conducted a 30-year prediction of the ¹³⁷Cs supply from the Fukushima coastal rivers to the ocean using a distributed radiocesium prediction model, considering the decontamination work and the resumption of agriculture as human activities. This model sufficiently reproduced the river discharge and the export of suspended sediment and ¹³⁷Cs. In the river basins with decontaminated areas and resumption areas for agriculture, the total ¹³⁷Cs outflow from croplands, urban lands, paddy fields, and forest areas to the rivers between the decontamination start date (July 2012) and calculation end date (December 2040) was reduced by 5.0% due to the decontamination work and the resumption of agriculture. The decontamination work and the resumption of agriculture reduced the outflow from croplands and paddy fields to the rivers by 16.6% and 15.1%, respectively. Despite the increase in the ¹³⁷Cs outflow due to the resumption of agriculture, resuming priority agriculture in the decontaminated areas was estimated to reduce the increase in the ¹³⁷Cs outflow from croplands and paddy fields. Due to the rapid wash-off from urban lands before the decontamination work and the small, decontaminated area in forest areas, the decontamination work reduced the outflow from urban lands and forest areas to the rivers by 3.4% and 2.8%, respectively. The outflow from agricultural lands and paddy fields with large, decontaminated areas was small, whereas the decontamination work slightly affected urban lands and forest areas with large outflows. Between the decontamination start and calculation end dates, the decontamination work and the resumption of agriculture reduced the cumulative supply of ¹³⁷Cs from the river basins with decontaminated areas and resumption areas of agriculture by 6.0%. The cumulative outflow to the rivers and the supply to the ocean indicated that the decontamination work and the resumption of agriculture slightly affected the ¹³⁷Cs supply and outflow. Although this study focused on the changes in land use due to the resumption of agriculture, we did not consider the impact of changes in land use due to rural and urban development on the ¹³⁷Cs supply. Therefore, a long-term simulation should consider the impacts of these effects on the ¹³⁷Cs supply in future studies. The cumulative ¹³⁷Cs supply from the Fukushima coastal rivers to the ocean 30 years after the accident was estimated to be 35.6 TBq. Based on the calculated results of the Fukushima coastal and Abukuma rivers, the supply of particulate ¹³⁷Cs from the rivers to the coastal sediment affected by the accident between October 2011 and December 2040 corresponded to 11–36% of the total amount of sedimentary ¹³⁷Cs in the coastal area as of October 2011.

Since ¹³⁷Cs accumulated in seabed sediment has decreased, the simulation results suggested that the ¹³⁷Cs supply from the rivers to the ocean is important for the long-term behavior of ¹³⁷Cs in coastal sediment. This study provided simulation results for the long-term supply of ¹³⁷Cs from the rivers to the ocean and helpful information about the impacts of decontamination work and the resumption of agriculture on the ¹³⁷Cs supply. Predicting the long-term supply of ¹³⁷Cs from the rivers to the ocean is important for clarifying the long-term fate of ¹³⁷Cs in coastal sediment. In future studies, a long-term simulation of the environmental fate of ¹³⁷Cs in coastal sediment will be conducted using the calculated supply of ¹³⁷Cs from the rivers to the ocean in this study and an oceanic dispersion model.