Where to Act in the Landscape to Minimize Sedimentation and Contamination of the River System

1. Introduction

After the Fukushima Daiichi Nuclear Power Plant accident on March 11, 2011, more than 2.7 PBq of fallout Radiocaesium (¹³⁷Cs, RC) was deposited on the landscape [1]. The ¹³⁷Cs, the most critical radionuclide for long-term exposure, caused widespread and persistent contamination across the Fukushima Prefecture. ¹³⁷Cs binds strongly to soil particles and is transported as contaminated sediment, which causes additional exposure to living organisms in downhill and downstream areas [2]. Moreover, the use of river water for irrigation and other purposes can further spread contamination [2]. The local government initiated a decontamination program that significantly reduced surface contamination, but this increased soil erosion and transport of low-contaminated sediment into river systems [3].

The behavior of sediment and ¹³⁷Cs in soil and river networks in the Fukushima prefecture has been widely studied [4,5], indicating that substantial amounts of particulate ¹³⁷Cs leave the catchments and enter the Pacific Ocean [2,6,7,8]. In the Niida catchment, researchers demonstrated a clear link between upstream decontamination works and the increased suspended sediment loads in the rivers [3]. Between 2013 and early 2017, approximately 11.9% of the land in the Niida watershed underwent decontamination through topsoil removal. As a result, suspended sediment loads in the river increased by up to 237.1% in 2016 compared to pre-remediation levels in 2013 [9]. The loss of vegetation cover explains the increase in erosion and suspended sediment in the rivers. This suggests that rapid re-vegetation, e.g., through afforestation, of decontaminated sites could have helped mitigate the magnitude and persistence of contaminated sediment losses.

Herewith, afforestation is defined as a silvicultural activity that is adapted, in terms of tree species, planting density and other management, to the local environmental conditions and that results in the rapid development of a protective soil cover that significantly reduces the erosion potential compared to the original land cover type. In afforested regions, the amount of sediment production and transport is smaller than in regions with other land cover, such as agriculture.

Several mathematical models have been proposed to model sediment production, transport and accumulation [10,11,12,13]. Since the underlying data, such as elevation and land use, are often represented as discrete data (raster maps), often discrete models are used.

Given the scale of the necessary interventions and the ineffectiveness of re-vegetation in areas that contribute little sediment to the river channels, mitigation efforts must be spatially optimized to maximize impact [14]. Indeed, the intervention effectiveness heavily depends on the spatial context, and the efforts must explicitly account for spatial interaction (also known as spatial inter-dependency) between sites. In this context, spatial interaction refers to the phenomenon that intervention at a site alters the state and behavior of downstream sites, influencing the effectiveness of subsequent interventions. Hence, spatial optimization methods should be used to determine the sites where intervention, e.g., afforestation, should take place to minimize the accumulation of both sediment and ¹³⁷Cs at target sites, e.g., at a river outlet.

Several optimization methods have been proposed to identify optimal sites for afforestation within a river catchment while reducing sediment export at target locations, such as the catchment outlet, explicitly accounting for spatial interaction, and considering a budget constraint. Vanegas et al. [15] presented an integer programming formulation that used a simple flow-routing model and a convex piecewise linear transport function, although its implementation in Lingo proved effective only for very small datasets. Therefore, Vanegas [16] proposed the Cellular Automata-based Heuristic for Minimizing Flow (CAMF), which integrates a sediment production and transportation model with an iterative approach based on a steepest ascent hill-climbing algorithm. A genetic-algorithm-based approach was proposed by Domingues et al. [17]; however, such approaches generally require large populations and many iterations, leading to high computational costs and providing no guarantee of reaching the global optimum.

CAMF has been applied and extended in several studies [18,19,20]. Recently, Castillo Reyes et al. [21] introduced an accelerated version of CAMF that incorporates modifications to the steepest ascent hill-climbing approach with negligible effects on the accuracy of the results. The selection of sets of compact and contiguous sites has been explored in other studies [18,22]. In addition to afforestation, CAMF has been applied in the context of deforestation [23] to identify critical areas where deforestation would significantly increase sediment production, as well as areas where deforestation would have minimal impact.

For the dual-objective optimization of afforestation interventions in ¹³⁷Cs-contaminated catchments, we extend in this paper the CAMF heuristic to simultaneously minimize sediment export and ¹³⁷Cs export while preserving the spatially explicit nature of CAMF. We also extend the sediment production, transport and accumulation models to account for radionuclide transport processes. As case study we consider the Niida catchment in the Fukushima region of Japan, to select sites for afforestation in which have the greatest potential to simultaneously reduce the loss of sediment and spatially variable associated ¹³⁷Cs at the outlet of the river.

The paper is organized as follows. Section 2 recalls the CAMF method, including the sediment production and transport model, the calculation of sediment accumulation, and emphasizing the ¹³⁷Cs concentration. It also describes the modifications implemented in CAMF to address the dual objectives of reducing both sediment and ¹³⁷Cs yield, and presents the case study focused on the Niida river catchment in the Fukushima region. Section 3 and Section 4 describe the results and provide a discussion of the main findings, respectively. Finally, Section 5 concludes the paper.

2. Materials and Methods

This section presents the sediment production, transport and accumulation models used in the current implementation of CAMF, and how the ¹³⁷Cs concentration in the sediment is estimated. Afterward, we present the CAMF iterative process to identify optimal sites for intervention, considering both the sediment loss and ¹³⁷Cs concentration. Since the increase in sediment loss in the Niida river catchment was caused by the removal of the protective vegetation cover and topsoil, the intervention considered is the rapid afforestation of decontaminated zones.

2.1. Sediment Production, Transport and Accumulation

The CAMF method uses a discrete raster representation of elevation, land use, sediment production, and sediment transport in the region. For this study, per-cell ¹³⁷Cs deposition and topsoil concentration after decontamination are also considered as part of the raster representation.

The sediment production model used is aligned with the Revised Universal Soil Loss Equation (RUSLE) [11] and the sediment transport with WATEM/SEDEM [13]. The mean annual sediment production for each cell of the raster-based representation is calculated with RUSLE as follows:

$$\alpha =R\times K\times LS\times C\times P$$

(1)

with $\alpha$ the mean annual soil loss ($tonh{a}^{-1}y{r}^{-1}$), R the rainfall erosivity factor ($\mathit{MJ}mmh{a}^{-1}{h}^{-1}y{r}^{-1}$), K the soil erodibility factor ($tonh{\mathit{MJ}}^{-1}m{m}^{-1}$), $LS$ the two-dimensional slope and slope length factor (−), C the cover management factor (−), and P the erosion control practice factor (−).

The sediment transport from a cell to its neighboring down-slope cell(s) is modeled using the Transport Capacity (TC) approach proposed in Verstraeten et al. [14] as follows:

$$\tau =K_{tc}\times R\times K\times (LS-4.12\times S_g^{0.8})$$

(2)

where $\tau$ is the transport capacity ($tonh{a}^{-1}y{r}^{-1}$), $K_{tc}$ is the transport capacity coefficient, R, K, and $LS$ are is in Eq. 1, $S_g$ is the local slope (-).

Three levels of $K_{tc}$ are defined: $K_{tc,low}$, $K_{tc,high}$, and $K_{tc,limit}$. The values $K_{tc,low}$ and $K_{tc,high}$ are specific to the catchment and depend on the C-factor: cells with a C-factor $\le K_{tc,limit}$ are assigned $K_{tc,low}$, while those with a C-factor $>K_{tc,limit}$ receive $K_{tc,high}$. Both values require calibration for each catchment. When a cell is afforested, its land use changes from the original state to forest land. As a result, the C-factor decreases and the transport capacity coefficient $K_{tc}$ may decrease from $K_{tc,high}$ to $K_{tc,low}$.

Thus, sediment flow in each cell i is simulated using the locally produced sediment, ${\alpha }_i^k$, and the transport capacity, ${\tau }_i^k$. Since the land use of cells can change, the superscript k indicates whether the cell is not yet afforested ($k=1$) or whether the cell is afforested ($k=2$). Since the sediment production after afforestation, ${\alpha }_i^2$, is calculated based on the updated C-factor value, ${\alpha }_i^2<{\alpha }_i^1$, and the sediment transport is calculated using the updated $K_{tc}$.

In this case study, the Fractional Deterministic Eight-Neighbor (FD8) variant of the Multiple Flow Direction (MFD) model is used. In this approach, cell connectivity along the flow pathway is represented as an acyclic graph, and a topological sorting algorithm determines the order in which cells are traversed to compute sediment transport [22,24].

For each cell i, the Sediment Accumulation, ${\mathit{SA}}_i$, and the outgoing sediment, $S{O}_i$, are calculated by traversing the acyclic graph. To this end, the total amount of sediment present in the cell (incoming sediment + produced sediment, ${\alpha }_i^k$) is compared to the transport capacity ${\tau }_i^k$, which leads to one of two possible outcomes:

• ${\mathit{SA}}_i$ is smaller than the transport capacity ${\tau }_i^k$. In this case, the total amount of sediment in the cell, ${\mathit{SA}}_i$, is transported to down-slope cell(s).
• ${\mathit{SA}}_i$ is larger than the transport capacity ${\tau }_i^k$. In this case, the outgoing sediment from cell i, is equal to ${\tau }_i^k$.

Therefore,

$${\mathit{SO}}_i=\left\{\begin{array}{cc}{\mathit{SA}}_i,\hfill & \mathrm{if}{\mathit{SA}}_i\le {\tau }_i^k\hfill \\ {\tau }_i^k,\hfill & \mathrm{if}{\mathit{SA}}_i>{\tau }_i^k\hfill \end{array}\right.$$

(3)

• ¹³⁷Cs concentration in sediment

We assume that the amount of spatially variable ¹³⁷Cs deposition is available in raster representation, see [25] for the data for the Niida river catchment. To relate ¹³⁷Cs deposition to concentration in sediment, a solid entrainment coefficient for the particular land use type, denoted by $S_c$, is used [26]. Hence, ${\mathit{CC}}_i$, the ¹³⁷Cs concentration in sediment for cell i, is estimated as

$${\mathit{CC}}_i=S_c\times D_{cs-137,i}$$

(4)

where $S_c$ is the solid entrainment coefficient for the particular land use type ($m^{2}k{g}^{-1}$), and $D_{cs-137,i}$ is the initial deposition of ¹³⁷Cs at cell i in the catchment ($Bq{m}^{-2}$) [25].

Following the principles of sediment movement, ¹³⁷Cs travels with the soil particles. Therefore, the amount of ¹³⁷Cs leaving cell i, and ultimately the catchment, is related to the amount of sediment accumulated in the cell, ${\mathit{SA}}_i$, the concentration of ¹³⁷Cs in the sediment, ${\mathit{CC}}_i$, and the transport capacity in the cell, ${\tau }_i^k$.

The ¹³⁷Cs movement is simplified by assuming that the ¹³⁷Cs concentration in the sediment in a cell is homogeneous, and when it reaches another cell it will be mixed (becomes homogeneous again) with the sediment in that cell. Thus, the amount of ¹³⁷Cs transported from cell j to cell i, is equal to

$${\mathit{D}}_{ji}\times {\mathit{CC}}_j$$

(5)

where ${\mathit{D}}_{ji}$ is the amount of sediment flowing from cell j to cell i.

Once the sediment accumulated in cell i, ${\mathit{SA}}_i$, has been computed, the corresponding accumulated ¹³⁷Cs activity in the mixed sediment is computed by mass balance as

$${\mathit{CA}}_i={\alpha }_i^k\times {\mathit{CC}}_i^0+\sum _{j\in U_i}{D}_{ji}\times {\mathit{CC}}_j$$

(6)

where $U_i$ is the set of upstream cells delivering sediment to cell i, ${\mathit{CC}}_j$ is the ¹³⁷Cs concentration in the sediment delivered from cell j, ${\alpha }_i^k$ is the sediment locally produced in cell i, and ${\mathit{CC}}_i^0$ is the ¹³⁷Cs concentration in the locally produced sediment. The homogeneous ¹³⁷Cs concentration in the sediment accumulated in cell i is then obtained as

$${\mathit{CC}}_i=\left\{\begin{array}{cc}{\displaystyle \frac{{\mathit{CA}}_i}{{\mathit{SA}}_i}},\hfill & \mathrm{if}{\mathit{SA}}_i>0,\hfill \\ 0,\hfill & \mathrm{otherwise}.\hfill \end{array}\right.$$

(7)

2.2. The Iterative Procedure in CAMF

In CAMF, only a subset of cells, called candidate cells, can be afforested. These are typically cells with high erosion potential, such as agricultural or bare land. In this study, candidate cells correspond to decontaminated areas.

The iterative CAMF procedure selects a user-defined number of candidate cells for afforestation, which acts as a constraint. We first describe the constrained single-objective optimization procedure used to maximize sediment yield reduction at target locations in the catchment (e.g., the outlet). We then explain how this procedure is modified to maximize ¹³⁷Cs yield reduction. Finally, we describe how the constrained multi-objective optimization procedure, based on the Distance to the Ideal Point (DIST2IP), is integrated into CAMF.

A) Single-objective optimization procedure

The optimization procedure in CAMF iteratively selects cells based on their potential effect on sediment yield reduction, $\mathit{SYR}$, at target locations in the catchment (e.g., the outlet). In each iteration t, the following steps are performed to select cells for afforestation [24]:

1.

For each candidate cell i, its afforestation is considered independently, by changing the local sediment production ${\alpha }_i^1$ to ${\alpha }_i^2$, and the local sediment transport capacity ${\tau }_i^1$ to ${\tau }_i^2$. The sediment production and transport model is integrated to evaluate the corresponding sediment loss at the target cell(s), called the sediment yield, $\mathit{SY}$. Afforestation of the cell reduces the amount of sediment delivered to its down-slope neighbors, and this reduction is propagated from the cell down to the cells on the pathway. The resulting sediment yield, ${\mathit{SY}}_i^t$, is compared with ${\mathit{SY}}^0$, the initial sediment yield before any cell is afforested, and the corresponding sediment yield reduction in iteration t, ${\mathit{SYR}}_i^t$ , is given by

$${\mathit{SYR}}_i^t={\mathit{SY}}^0-{\mathit{SY}}_i^t$$

(8)

2.

The cells are then ranked in descending order based on their $\mathit{SYR}$ values.

3.

The cell with the highest $\mathit{SYR}$ value is added to the set of selected cells for afforestation.

This procedure is repeated until a fixed number of candidate cells is selected for afforestation, or a cumulative $\mathit{SYR}$ is achieved. This iterative process allows for explicit accounting of the spatial interaction between the cells.

To also consider the amount of ¹³⁷Cs concentration in sediment, we introduce the formulations described in Section 2.1 to compute the cumulative ¹³⁷Cs in sediment. Step 1 of the above procedure is extended as follows. The ¹³⁷Cs yield at target cell(s), $\mathit{CY}$, and the ¹³⁷Cs yield reduction, $\mathit{CYR}$, due to the tentatively afforestation of cell in iteration t, are computed as follows, assuming that ${\mathit{CY}}^0$ is the $\mathit{CY}$ at the initial situation, and $\mathit{CCY}$ is the ¹³⁷Cs concentration at the target cell(s).

$${\mathit{CY}}_i^t={\mathit{SY}}_i^t\times {\mathit{CCY}}_i^t$$

(9)

$${\mathit{CYR}}_i^t={\mathit{CY}}^0-{\mathit{CY}}_i^t$$

(10)

To maximize ¹³⁷Cs yield reduction at the target locations, cells are selected based on their potential effect on ¹³⁷Cs yield reduction, by replacing $\mathit{SYR}$ by $\mathit{CYR}$ in steps 2 and 3.

Algorithm 1 presents the modifications to the algorithm presented by Castillo-Reyes et al. [24], to compute both the sediment yield, $\mathit{SY}$, and the ¹³⁷Cs yield, $\mathit{CY}$.

Algorithm 1 Compute the sediment yield $\mathit{SY}$, and the 137Cs yield $\mathit{CY}$

Input: local sediment production ${\alpha }^k$; local transport capacity ${\tau }^k$, with k indicating the values before the afforestation ($k=1$) or after the afforestation ($k=2$); local 137Cs concentration in sediment $\mathit{CC}$; target cells p   for each cell i in the sorted graph S do     1. ${\mathit{SA}}_i\leftarrow {\alpha }_i^k$        ▹$\mathit{SA}$ stores the sediment accumulation for every cell     2. ${\mathit{CA}}_i\leftarrow {\alpha }_i^k\times {\mathit{CC}}_i$    ▹$\mathit{CA}$ stores the cumulative 137Cs concentration in sediment for every cell     for each ancestor j of cell i do         if ${\mathit{SA}}_j\le {\tau }_j^k$ then            3. $D_j\leftarrow {\mathit{SA}}_j$         else            4. $D_j\leftarrow {\tau }_j^k$         end if         5. $D_{ji}\leftarrow D_j\times F_{ji}$    ▹$F_{ji}$ is the fraction of sediment delivered from cell j to its neighbor cell i         6. ${\mathit{SA}}_i\leftarrow {\mathit{SA}}_i+D_{ji}$         7. ${\mathit{SA}}_j\leftarrow {\mathit{SA}}_j-D_{ji}$         8. ${\mathit{CA}}_i\leftarrow {\mathit{CA}}_i+D_{ji}\times {\mathit{CC}}_j$     end for     if ${\mathit{SA}}_i>0$ then         9. ${\mathit{CC}}_i\leftarrow {\displaystyle \frac{{\mathit{CA}}_i}{{\mathit{SA}}_i}}$     else         10. ${\mathit{CC}}_i\leftarrow 0$     end if end for   11.${\displaystyle \mathit{SY}\leftarrow \sum _p{\mathit{SA}}_p\mathrm{in}\mathrm{target}\mathrm{cells}p}$ 12.${\displaystyle \mathit{CY}\leftarrow \sum _p{\mathit{CA}}_p\mathrm{in}\mathrm{target}\mathrm{cells}p}$ Output: sediment yield, $\mathit{SY}$; 137Cs yield, $\mathit{CY}$

B) Multi-Objective Optimization

To adapt CAMF to simultaneously minimize $\mathit{SY}$ and $\mathit{CY}$, and thus maximize $\mathit{SYR}$ and $\mathit{CYR}$, we propose a multi-objective approach for selecting afforestation sites. This dual-objective optimization identifies sites that provide the best joint performance for both $\mathit{SYR}$ and $\mathit{CYR}$.

Distance to the Ideal Point (DIST2IP) is a concept often used in Multi-Criteria Decision-Making (MCDM), particularly in compromise programming and ideal-point methods [27,28,29,30]. It refers to the distance of a given solution or alternative from a theoretical Ideal Point (IP), a vector with the best possible values for each of the considered criteria. It is also related to the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) [31,32].

We propose to use the shortest distance from the IP to select sites for afforestation based on the maximal and minimal values for $\mathit{SYR}$ and $\mathit{CYR}$. In each iteration t of CAMF, after computing the $\mathit{SYR}$ and the $\mathit{CYR}$ values due to the tentative afforestation of each candidate cell, the following steps are considered:

1.

Normalization of the data. Since the reductions in sediment and ¹³⁷Cs yields are on different scales, both values are normalized to the range $[0,1]$, where 0 represents the worst value and 1 the best. For each cell i:

$$x_{i,\mathit{syr}}={\displaystyle \frac{{\mathit{SYR}}_i^t-{\mathit{SYR}}_{min}^t}{{\mathit{SYR}}_{max}^t-{\mathit{SYR}}_{min}^t}}$$

(11)

$$x_{i,\mathit{cyr}}={\displaystyle \frac{{\mathit{CYR}}_i^t-{\mathit{CYR}}_{min}^t}{{\mathit{CYR}}_{max}^t-{\mathit{CYR}}_{min}^t}}$$

(12)

where ${\mathit{SYR}}_{min}^t$ and ${\mathit{SYR}}_{max}^t$ are the minimum and maximum values obtained due to afforesting all cells independently in iteration k, and similarly for ${\mathit{CYR}}_{min}^t$ and ${\mathit{CYR}}_{max}^t$.

2.

Definition of the IP. The IP is a vector whose coordinates are given by the optimal values for the different criteria [29], i.e. maximum $\mathit{SYR}$, and maximum $\mathit{CYR}$. After normalization, IP becomes

$$\mathrm{IP}=(1,1)$$

3.

Combine the values by calculating the Euclidean Distance to IP. For each cell i, compute its DIST2IP

$$\mathit{DIST}\mathit{2}{\mathit{IP}}_i=\sqrt{{(1-x_{i,\mathit{syr}})}^2+{(1-x_{i,\mathit{cyr}})}^2}$$

(13)

4.

Rank the cells in ascending order according to their DIST2IP.

5.

The cell(s) with the lower DIST2IP value are added to the set of cells selected for afforestation.

Algorithm 2 shows the modifications added to the heuristic optimization process in CAMF presented in [24].

Algorithm 2 Determine the cells to be selected for maximizing both $\mathit{SYR}$ and $\mathit{CYR}$

Input: Number of cells to be selected n   1.$S\leftarrow \varnothing$     ▹S stores the cells selected 2.$t\leftarrow 0$ while size of $S<n$ do     3. $t\leftarrow t+1$     for each candidate cell i that has not been selected do         4. Compute ${\mathit{SYR}}_i^t$ and ${\mathit{CYR}}_i^t$ by tentatively afforesting cell i     end for     5. Compute $x_{i,\mathit{syr}}$ and $x_{i,\mathit{cyr}}$ by normalizing ${\mathit{SYR}}_i^t$ and ${\mathit{CYR}}_i^t$ values     6. Compute the DIST2IP based on $x_{i,\mathit{syr}}$ and $x_{i,\mathit{cyr}}$     7. Rank cells in ascending order according to their DIST2IP     8. Put cell(s) with lowest DIST2IP in solution set S end while   Output: Set of selected cells S

2.3. Case Study: Niida Catchment

The Niida river catchment covers $\approx 198k{m}^2$ and it is located ±$40km$ from the Fukushima Daiichi Nuclear Power Plant. A Digital Elevation Model (DEM) with a resolution of $10m\times 10m$ was obtained from the Geospatial Information Authority of Japan and resampled to a resolution of $20m\times 20m$, Figure 1. The topography is almost mountainous [3], with altitudes reaching $\approx 930m$ a.s.l.

The extent of the DEM is 708 × 1,339 cells of which 695,426 cells cover the catchment. The zones that have been decontaminated until 2014 (29,056 cells) were selected as candidate cells for intervention [9]. These cells cover $\approx 11.6k{m}^2$ [3] and are mainly located near the river, Figure 1.

The mean annual sediment production per cell is computed using RUSLE, with parameters retrieved from previous studies for the region [3,9,34,35,36,37]. The rainfall erosivity factor R is set to $2,191$$mmh{a}^{-1}{h}^{-1}y{r}^{-1}$, being an average value from several measurements carried out from 2013 to 2018 in the Haramachi station (red dot in Figure 1)[3] and discussed in [25]. The K-factor is set to 0.039 for all cells, as in [37] and [9]. Given that there are no registers of support practices to control erosion, the P-factor is set to 1 for all cells in the catchment.

The use of spatially uniform values for the R and K factors is a simplification of the erosion modeling. Spatially distributed observations of rainfall erosivity and soil properties were not available. Therefore, average values previously adopted and validated in studies of the same catchment [3,9,37] were used. Since the objective of this study is to evaluate the effectiveness of optimization heuristics to select intervention locations rather than to provide precise predictions of sediment production and transport, uniform R and K factors are used as acceptable approximations.

The actual values for the C-factor shown in Table 1 were taken from [25,34,35] and assigned to each cell of the particular land cover type (Figure 2) obtained from the World-cover Land Cover product 2020 [9,38].The $LS$-factor was computed according to Desmet and Govers [39], the slope angle values were cut off at $50\%$ as in Abrams et al. [9], see Figure 3 (left).

In each cell the outgoing sediment is modeled using the transport capacity function, Eq. 3, with the same parameter values as those used to estimate the erosion risk using RUSLE. The $K_{tc}$ coefficients were taken from the calibration carried out in Abrams et al. [9] using measurements of sediment loads from 2013 to 2018 and the Nash–Sutcliffe model efficiency coefficient. Hence, $K_{tc,limit}$ is set to 0.01, while $K_{tc,low}=2$ and $K_{tc,high}=6$.

Figure 3 shows the maps representing the $LS$-factor, the sediment production ${\alpha }^1$ and the transport capacity ${\tau }^1$ before afforestation.

The magnitude of the spatially variable ¹³⁷Cs deposition is shown in the map of Figure 4.

Eq. 4 was used to estimate the ¹³⁷Cs concentration in the sediment produced in each cell, based on the land use type, in consecutive years after the Fukushima Daiichi nuclear accident, as in [37]. The values of the solid entrainment coefficient to compute the ¹³⁷Cs concentration in sediment, $S_c$, are shown in Table 1, whereby “bare land” was set equal to the “agriculture” land use type.

Part of the decontamination works carried out during 2012–2014 were done on agricultural land [25]. They consisted of the removal of vegetation and the topsoil layer ($\pm 5cm$), adapting the land cover from its original type to bare land. Measurements of air dose rate showed a decrease of 20%–70% of the original contamination [1], therefore Abrams [25] assumed that the decontamination works reduced the initial ¹³⁷Cs concentration in sediment by 50%, as shown in the map of Figure ??.

3. Results

We used both the single-objective and multi-objective optimization in CAMF to minimize $\mathit{SY}$ and $\mathit{CY}$ at the outlet of the catchment, when up to 1,000 cells (<5% of the candidate cells) of the zones decontaminated between 2012 and 2014, are afforested. The simulated initial values for sediment yield ${\mathit{SY}}^0$, and ¹³⁷Cs yield ${\mathit{CY}}^0$ at the outlet are 50,166 $tony{r}^{-1}$ and $1.81990208\times {10}^{11}$$Bqy{r}^{-1}$, respectively.

These simulated ${\mathit{SY}}^0$ and ${\mathit{CY}}^0$ are compared with observations reported by Bin et al. [3] and Abrams [25] for the Haramachi monitoring station, in Table 2. The observed values are the average annual sediment and ¹³⁷Cs yield measured between 2013 and 2018, which is consistent with the period used to derive the average rainfall erosivity factor R, adopted in this study from [25]. The ${\mathit{SY}}^0$ estimated with CAMF is close to the observed average of 48,837 $tony{r}^{-1}$. While the agreement is strong for ${\mathit{SY}}^0$ (2.7% difference), the larger discrepancy in ${\mathit{CY}}^0$ (≈ 60%), is probably due to the assumption of homogeneous mixing of ¹³⁷Cs within sediments.

3.1. Sediment Yield Reduction vs. ¹³⁷Cs Yield Reduction

Table 3 presents the values for $\mathit{SYR}$ and $\mathit{CYR}$ after afforesting up to 1,000 cells for three scenarios: 1) selecting cells that maximize $\mathit{SYR}$, 2) selecting cells that maximize $\mathit{CYR}$, and 3) integrating both objectives by selecting the cells using $\mathit{DIST}\mathit{2}\mathit{IP}$ as shown in Algorithm 2, which accounts for trade-offs between $\mathit{SYR}$ and $\mathit{CYR}$.

The results highlight the trade-offs between the three scenarios. Selection based on $\mathit{SYR}$ consistently produces the highest cumulative sediment yield reduction values for any given number of cells, but also the lowest ¹³⁷Cs yield reduction values (e.g., afforesting 100 cells: $\mathit{SYR}=$ 5,364 $tony{r}^{-1}$ vs. 4,491 $tony{r}^{-1}$ for selection based on $\mathit{CYR}$ and 4,704 $tony{r}^{-1}$ for selection based on $\mathit{DIST}\mathit{2}\mathit{IP}$). In contrast, selection based on $\mathit{CYR}$ maximizes ¹³⁷Cs reduction, achieving the highest $\mathit{CYR}$ values of all scenarios, but with significantly lower sediment reduction (e.g., afforesting 100 cells: $\mathit{CYR}=$$8.39342\times {10}^9$$Bqy{r}^{-1}$ vs. $6.84943\times {10}^9$$Bqy{r}^{-1}$ for selection based on $\mathit{SYR}$ and $8.36963\times {10}^9$$Bqy{r}^{-1}$ for selection based on $\mathit{DIST}\mathit{2}\mathit{IP}$). Notably, the effect is largest when few cells are selected for afforestation and decreases as the number of selected cells increases, which is expected, as described in [21].

Selection based on $\mathit{DIST}\mathit{2}\mathit{IP}$ provides an intermediate outcome, resulting in $\mathit{SYR}$ and $\mathit{CYR}$ values that are close to the maxima for each objective while avoiding the strong imbalances observed in the single-objective optimization. This indicates that $\mathit{DIST}\mathit{2}\mathit{IP}$ effectively balances sediment and ¹³⁷Cs reduction goals by selecting cells that perform well in both dimensions.

The latter is confirmed in the plots shown in Figsures Figure 5 and Figure 6, illustrating the cumulative values of $\mathit{SYR}$ and $\mathit{CYR}$ with respect to the number of cells selected for afforestation, for the three scenarios. Selection based on $\mathit{SYR}$ results in substantially smaller $\mathit{CYR}$ values than in the two other scenarios (e.g. $\approx 18\%$ smaller when 100 cells are selected). Selection based on $\mathit{CYR}$ results in lower $\mathit{SYR}$ values than selection based on $\mathit{SYR}$ ($\approx 9-16\%$ smaller). The $\mathit{DIST}\mathit{2}\mathit{IP}$ selection scenario results in $\mathit{SYR}$ values that are $\approx 8-12\%$ smaller than in the single-objective $\mathit{SYR}$ optimization scenario, but with negligibly smaller $\mathit{CYR}$ values ($\le 0.3\%$) than with the single-objective $\mathit{CYR}$ selection.

Figure 6 shows relative performance plots indicating how much each scenario ($\mathit{SYR}$, $\mathit{CYR}$, $\mathit{DIST}\mathit{2}\mathit{IP}$) loses compared to the best-performing scenario. The lines corresponding to $\mathit{SYR}$ and $\mathit{CYR}$ consistently stay at 100%, which is expected since selecting cells based on $\mathit{SYR}$ is designed to maximize $\mathit{SYR}$, and similarly for the selection by $\mathit{CYR}$. The plot on the right shows a strong performance in $\mathit{CYR}$ when using $\mathit{DIST}\mathit{2}\mathit{IP}$, consistently being very close to the maximum. This is a very interesting result, which suggests that, in this specific optimization problem and for this specific case study, the compromise using $\mathit{DIST}\mathit{2}\mathit{IP}$ is highly effective, providing nearly the same level of $\mathit{CYR}$ as the selection purely based on $\mathit{CYR}$, while still maintaining good performance in $\mathit{SYR}$, as shown in the left plot.

The maps in Figure 7 show the geographic distribution of the selected cells in relation to the candidate cells identified for afforestation. The first map (Figure 7(a)) shows the spatial location of the cells selected using the $\mathit{DIST}\mathit{2}\mathit{IP}$ scenario, while the second one (Figure 7(b)) provides the spatial coincidence of the cells across the three scenarios, showing the cells that were selected in common and those uniquely selected by each of the scenarios: $\mathit{SYR}$, $\mathit{CYR}$ and $\mathit{DIST}\mathit{2}\mathit{IP}$ respectively. Generally, the most optimal cells for afforestation are located near the river, because afforestation leads not only to a reduction in sediment production, but also to a reduction of transport capacity, halting part of the sediment moving downward from upper situated cells [25]. The cells located close to the river and within the sediment flow path to the river retain the sediment from up-slope cells, as also observed in [22].

An important observation in the map of Figure 7(b) is that there are no cells uniquely selected by the $\mathit{DIST}\mathit{2}\mathit{IP}$ method. This means that every single one of the 1,000 cells selected by $\mathit{DIST}\mathit{2}\mathit{IP}$ is also selected by the $\mathit{SYR}$-based selection, the $\mathit{CYR}$-based selection, or both. Hence, in this case study, the IP compromise is “contained” within the union of the two single-objective selections. Therefore, the multi-objective compromise does not require selecting cells that were not already considered important by at least one of the single-objective scenarios. However, this result should not be interpreted as a general property of the DIST2IP approach. In catchments with different environmental characteristics, or when considering pollutants whose transport pathways differ substantially from those of sediment, stronger conflicts between objectives may emerge.

3.2. Characteristics of the Cells Selected for Afforestation

The box-plots in Figure 8 present the cumulative frequency of the characteristics of the 1,000 selected cells for afforestation using the $\mathit{DIST}\mathit{2}\mathit{IP}$ scenario. The analysis reveals that these cells are concentrated in a relative narrow range of elevations, from around 400 m to 500 m. However, there is a significant number of selected cells at higher elevations, with a notable cluster around 600–625 m. This suggests that while most of the selected cells are in the lower-to-mid elevation ranges, the optimization procedure also finds significant benefits from planting at higher elevations, possibly due to other factors at those specific locations.

On average, the selected cells have a LS-factor between 0.1 and 1. However, the values are widely distributed, from values less than 0.1 to more than 100. Most of the selected cells have a high LS-factor value.

The initial local sediment production for the selected cells covers an extremely wide range, from very low values to more than 100 $tonh{a}^{-1}y{r}^{-1}$, with an average between 1 to 10 $tonh{a}^{-1}y{r}^{-1}$. Notably, a large portion of the selected cells have very high initial sediment production values. However, the cell in the catchment with the highest sediment production is not among the 1,000 selected cells, indicating that optimal afforestation sites are not necessarily the highest sediment producers; sediment routing and connectivity are also important factors [21].

The last box-plot confirms that the median distance to the river is quite small, indicating that afforestation can effectively act as a trap for sediment and contamination just before they reach the main channel, as visualized in Figure 7.

4. Discussion

This study illustrated that land use and land management planners must be aware of and take into account the off-site effects of interventions in the landscape, aiming at one or multiple objectives. The decontamination practices in the Niida catchment are a clear example of site-specific interventions where on-site impacts (reduction of local contamination) have large off-site impacts (increased erosion and resulting low contaminated sediment loss at the outlet). Off-site effects are due to spatial interaction: an intervention at a given location affects not only the characteristics and properties of that location but also those of other, even distant, locations in the landscape. These off-site impacts are especially pertinent for flow phenomena such as water and sediment. A consequence is that location does matter for the effectiveness of interventions, impacting the generation, transportation, and accumulation of materials, not only in terms of the location-specific (on-site) characteristics but also regarding the off-site effects. This confirms that applying measures to areas that hardly contribute sediment to river channels is inefficient [14].

When afforestation is used as the intervention to maximally reduce the export of sediment and associated contaminants from the catchment, we showed that cells, representing sites, can be iteratively ranked and selected from high-impact cells to lower-impact cells. The spatial distribution of the highest-ranked intervention sites is in line with many studies that indicate the riparian zone as an efficient area for retaining sediment from surface runoff [40,41,42]. Similar patterns were found by Domingues et al. [17], who used a genetic algorithm to optimize the allocation of forest restoration zones to minimize soil losses in watersheds. The result confirms the critical importance of implementing and maintaining decontamination and erosion-control measures near channel networks.

In this study, CAMF identified the cells for which afforestation was most efficient in terms of sediment yield reduction and ¹³⁷Cs export in a spatially explicit way, taking full account of spatial interaction. For the Niida catchment, the results showed that targeting the most impactful sites could considerably reduce sediment yield, $\mathit{SY}$, and ¹³⁷Cs yield, $\mathit{CY}$, at the outlet of the catchment. By afforesting only ≈4% of the candidate cells corresponding to ≈40$ha$ of the more than ≈12$k{m}^2$ decontaminated zones, a 22% reduction in $\mathit{SY}$ and a 6% reduction in $\mathit{CY}$ at the outlet could be obtained.

In this case study, when reductions in both $\mathit{SY}$ and $\mathit{CY}$ were considered, the $\mathit{DIST}\mathit{2}\mathit{IP}$ method was highly effective for selecting cells. It provided solutions on the optimal trade-off curve, as shown in Figure 9, whereas single-objective optimization led to suboptimal outcomes for the other objective.

These results suggest that using DIST2IP in CAMF in the decision-making process could support more effective and efficient schemes for the management of decontaminated land. Consequently, future remediation initiatives should include the off-site implications of the decontamination or other interventions by pre-assessing the prospective sediment dynamics in the remediated locations to assure the sustainability of the remediation, as proposed by Bin et al. [3].

Nevertheless, some characteristics of the CAMF heuristic and the models used to estimate sediment production and transport must be considered. For the case study presented in this research, we used RUSLE to compute the yearly sediment production per cell in the catchment. RUSLE should be used with caution since it has initially been developed from an agricultural point of view for simple topographic situations. RUSLE has been widely applied for spatial soil-erosion assessment, but its predictions are sensitive to input data, spatial resolution, and the parameterization of land cover and topographic factors; therefore, model parameters should be tested and, where possible, calibrated for the specific study area [11,22,43,44]. However, as mentioned in [21], it is possible to use other models to estimate soil erosion in CAMF, as the sediment production maps are computed offline beforehand, and then indicated as inputs.

Similarly, the use of a simple transport function to describe sediment flow between cells is a simplification of a complex process involving sediment detachment, transport, deposition, and spatial connectivity [45,46,47]. Due to the range of different (stochastic) processes involved in sediment transport, it is unlikely that simple relationships accurately quantify the process [46]. In addition, no formal uncertainty analysis was conducted to assess the sensitivity of the results to uncertainties in the input parameters and datasets. Given the importance of uncertainty quantification in environmental modeling and decision support [48], future research could evaluate how uncertainty affects the identification of priority intervention sites. However, for planning of erosion mitigation measures, the understanding of patterns within the landscape are more important than obtaining exact values, as argued in [17,21].

Our implementation of DIST2IP assumes equal importance of sediment and ¹³⁷Cs yield reduction. However, this can be extended to account for different management priorities through the introduction of weights in the distance calculation. Such an extension would allow decision-makers to emphasize one objective over another depending on the decision-making context.

CAMF considers a direct reduction in sediment production after afforestation, which may overestimate the initial impact [49]. Even so, when afforestation is complemented with soil covering practices such as mulching or rapid re-vegetation, these assumptions are reasonable. In addition, determining the ¹³⁷Cs concentration in sediment based on a conversion factor can be seen as too simplistic. More complex Bayesian models are proposed by Delmas et al. [50]. However, for the long-term timescale that is considered, the approach is fit for purpose. Moreover, considering the reality of afforestation, clustering afforestation sites through a region-growing approach as proposed in [22] would reduce the operational difficulty and costs.

Radioactive decay of ¹³⁷Cs was not considered in this study because the current version of the CAMF heuristic does not consider a temporal dimension. Hence, contamination is treated as static in time, while in reality, ¹³⁷Cs concentrations decrease over time due to both physical decay and ongoing environmental processes. Future work could incorporate time by running RUSLE for a sequence of years, updating sediment production and transport capacity as vegetation develops after afforestation, while also accounting for radioactive decay. This would allow CAMF to evaluate how priority intervention areas evolve through time.

Although the proposed method was demonstrated for the reduction of sediment and ¹³⁷Cs export, its applicability is not limited to radioactive contamination or to two criteria. CAMF combined with DIST2IP can be extended to environmental problems involving other pollutants, such as nitrogen or phosphorus, transported through hydrological and sediment connectivity pathways. It can also be applied to more than two criteria exhibiting spatial interaction, or to combinations of criteria with and without spatial interaction. For example, cost can be included as an on-site criterion, although afforestation costs may also depend partly on accessibility and therefore on the afforested or non-afforested status of surrounding cells. The same principle applies as long as the effects of interventions on the selected criteria can be estimated.

5. Conclusions

CAMF, originally designed for spatially targeting interventions aimed at sediment yield reduction only, was effectively adapted to address dual objectives, such as the simultaneous reduction of sediment yield and ¹³⁷Cs contaminated sediment export. We reported results for the Niida river catchment, affected by the accident at the Nuclear Power Plant in Fukushima, Japan.

This study confirms that, due to spatial variability and spatial interaction, the effectiveness of afforestation as a post-decontamination intervention to reduce sediment and associated radionuclide export from catchments affected by ¹³⁷Cs deposition, is highly location-specific. We demonstrated that the multi-objective optimization procedure in CAMF is suitable to identify those locations in the catchment for which the intervention has the highest desired impact.

Selecting cells purely based on their capacity to reduce sediment yield maximizes sediment control, but results in a substantially lower ¹³⁷ Cs yield reduction. In contrast, selecting cells based on ¹³⁷Cs yield reduction, minimizes ¹³⁷Cs yield but sacrifices sediment control. The Distance to the Ideal Point consistently delivers a (near-optimal) balance between sediment and ¹³⁷Cs yield reduction. This demonstrates its potential as a practical compromise strategy in multi-objective environmental planning in contexts where both objectives have similar importance. When one objective is considered more important, this preference could be incorporated by introducing weights in the calculation of DIST2IP, allowing the compromise solution to reflect different management priorities.

In ¹³⁷Cs contaminated catchments such as the Niida river catchment, targeted and timely afforestation guided by a multi-objective solution would have simultaneously mitigated downstream sediment fluxes and reduced the transport of ¹³⁷Cs, thereby enhancing long-term ecological safety.