# Soil-to-river Cesium-137 transfer in a catchment coupling the SWAT model and a mass balance equation

François Guillory, Hugo Lepage, Sabine Sauvage, José-Miguel Sánchez-Pérez, Clément Fabre, Patrick Boyer, David Mourier

► To cite this version:

François Guillory, Hugo Lepage, Sabine Sauvage, José-Miguel Sánchez-Pérez, Clément Fabre, et al. Soil-to-river Cesium-137 transfer in a catchment coupling the SWAT model and a mass balance equation. Journal of Environmental Radioactivity, 2026, 291, pp.107849. 10.1016/j.jenvrad.2025.107849. hal-05448858

HAL Id: hal-05448858

https://hal.science/hal-05448858v1

Submitted on 8 Jan 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
<figure><img src="image_2.png" /></figure>

# Soil-to-river Cesium-137 transfer in a catchment coupling the SWAT model and a mass balance equation

François Guillory<sup>a, *,</sup> Hugo Lepage<sup>a</sup>, Sabine Sauvage<sup>b</sup>, José-Miguel Sánchez<sup>b</sup>, Clément Fabre<sup>b, c</sup>, Patrick Boyer<sup>a</sup>, David Mourrier<sup>a</sup>

## ABSTRACT

Nuclear accidents and atmospheric tests have released large quantities of radionuclides into the environment. Among them, Cesium-137 ($^{137}$Cs) is of major concern due to its long-term persistence. To support post-accidental management, predictive tools are needed to assess its environmental transfers. This study presents a novel approach to simulate the transfer of $^{137}$Cs from soils to the river outlet in a watershed impacted by radioactive atmospheric fallout. The Soil and Water Assessment Tool (SWAT) was coupled with a trace metal transfer equation to simulate daily concentrations of $^{137}$Cs in suspended sediments in the Ardèche watershed (2138 km², France). The total $^{137}$Cs stock in soils was estimated at 7.7 TBq based on a soil sampling campaign. Modelled $^{137}$Cs concentrations range from 0 to 43.0 Bq kg⁻¹, whereas measured values range from 3.5 to 20.1 Bq kg⁻¹. The discrepancies are mainly due to limitations in SSC observations used for model calibration, as well as the particle-trap sampling method, which tends to underestimate the actual concentrations. Moreover, results indicate that 83 % of the annual $^{137}$Cs transport occurs in the particulate phase with 75 % of the total annual $^{137}$Cs flux at the outlet exported during the top 10 % highest flow days. On average, 263.0 GBq y⁻¹ of $^{137}$Cs are eroded from the watershed soils, the river exports 1.62 GBq y⁻¹ of $^{137}$Cs at the outlet and stores 256.0 GBq y⁻¹ within the river itself and floodplain. This corresponds to an annual export of only 0.02 % of the total $^{137}$Cs soil stock.

## 1. Introduction

Atmospheric nuclear tests and nuclear accidents, such as Chernobyl in 1986 and Fukushima in 2011, have released significant quantities of artificial radionuclides into the environment. These radioactive elements, with varying half-lives, are dispersed through different transfer pathways, affecting soil and water systems. Understanding their spatial and temporal distribution is crucial for effective management and environmental protection (Gilbin et al., 2021).

Among these radionuclides, Cesium-137 ($^{137}$Cs) is of particular concern due to its persistence in the environment (Kitamura et al., 2014) and its toxicity at high doses to humans and living organisms (Lestaevel et al., 2010). Soil erosion significantly influences $^{137}$Cs mobility at the catchment scale, as most of $^{137}$Cs still remains in the top few centimeters of soils, decades after the accidents of Chernobyl and Fukushima Dai-ichi (Bunzl et al., 1995; Krstić et al., 2004; IAEA, 2006; Kurihara et al., 2018; Konoplev, 2022). Soil erosion mainly affects the contaminated upper layers, making soils continuous sources of pollution for both

continental and marine hydrosystems (Evrard et al., 2015; Lepage et al., 2016; Buesseler et al., 2017). Land use significantly affects $^{137}$Cs migration, with limited movement in forests (Evrard et al., 2015) and higher mobility in agricultural lands due to enhanced erosion and plowing (Lepage et al., 2015; Golosov and Ivanov, 2020). Kitamura et al. (2014) found that up to 99 % of $^{137}$Cs inventory remains within studied coastal catchments during the first year (without considering radioactive half-life), emphasizing the need to study the redistribution of contamination.

After a nuclear accident, $^{137}$Cs exists in two phases: a liquid phase (mainly dissolved cesium) and a particulate phase fixed to particles (particulate cesium) (Park et al., 2019). Water-soluble and exchangeable forms dominate the initial deposition (Hilton et al., 1991) which is gradually transformed into more stable and nonexchangeable particulate forms through fixation processes (Sawhney, 1972; Krstić et al., 2004). The liquid-to-particulate concentration ratio values reflect this progressive fixation, with initially low values indicating higher mobility, that increase over time as $^{137}$Cs becomes less exchangeable. The ratio

<footnote><sup>a</sup> Nuclear Safety and Radiation Protection Authority, PSE-ENV, STAAR/LRTA, BP 3, Saint Paul Lez Durance, 13115, France</footnote>

<footnote><sup>b</sup> Centre de Recherche sur la Biodiversité et l'Environnement (CRBE), Université de Toulouse, CNRS, IRD, Toulouse INP, Université Toulouse 3 - Paul Sabatier (UT3), Toulouse, France</footnote>

<footnote><sup>c</sup> Tour du Valat, Arles, France</footnote>

<footnote>This article is part of a special issue entitled: ICRER-2024 published in Journal of Environmental Radioactivity.</footnote>

<footnote>* Corresponding author.
E-mail address: francois.guillory@gmail.com (F. Guillory).</footnote>
between particulate and dissolved ¹³⁷Cs is often described using a dis- tribution coefficient (Kd), which assumes equilibrium, reversibility, and trace conditions. Although this simplification is widely used in modeling ¹³⁷Cs migration and bioavailability, it must be applied with caution, especially in dynamic environments where these assumptions may not be held. The Kd varies based on the surrounding river soil composition, mineralogy, organic matter content, and hydrological conditions (Garneau et al., 2017). Tomczak et al. (2021) highlighted that particle size and mineral composition significantly affect cesium partitioning in fluvial environments. During floods, most ¹³⁷Cs is transported in par- ticulate form, while under base flow conditions, the dissolved fraction becomes more significant. Temperature and litter fall have minimal influence on this ratio in the Japanese temperate climate (Ochiai et al., 2015). Riverbed sediments can also contribute to dissolved ¹³⁷Cs con- centrations, particularly in colder periods (Nakanishi and Sakuma, 2019), and bottom sediments of lakes or ponds may be remobilized during certain events (Funaki et al., 2022) or release dissolved ¹³⁷Cs under anoxic conditions (Funaki et al., 2020).

Given the complexity of ¹³⁷Cs behavior in the environment, various modeling approaches have been developed to simulate its transfer through rivers. These range from simple parametric models using transfer functions (Delmas et al., 2017; Konoplev et al., 2016) and models describing solid/liquid partitioning using distribution co- efficients (Kd) (Sakuma et al., 2018) to more sophisticated hydrological models incorporating sediment transport and erosion processes (Kinouchi et al., 2015). It is important to distinguish that Kd-based models do not simulate erosion or surface runoff processes themselves but can be coupled with erosion models to represent the redistribution of ¹³⁷Cs between dissolved and particulate phases. Some tools used to model ¹³⁷Cs concentrations consider multiple land-use compartments like the Soil and Water Assessment Tool (Pratama et al., 2015), while others dynamically updates soil contamination maps during rainfall events (WaterSed - Vandromme et al., 2023). The WEP model (Kinouchi et al., 2015) incorporates land use, vegetation, and human activities such as irrigation. Other models, like Nays2D (Yamada et al., 2015) and approaches by Iwasaki et al. (2015), focus on sediment accumulation in riverbeds. Ikenoue et al. (2023) developed a model assuming that ¹³⁷Cs moves exclusively through sediment transport, incorporating advection, diffusion, sedimentation, and resuspension processes.

The main difficulty in developing a complex model lies in the cali-
bration and validation steps, which involve numerous parameters. The
challenge is to achieve a realistic representation of the key processes
governing ¹³⁷Cs dynamics while keeping the parameterization as limited
as possible. Building on these previous studies, this study extends pre-
vious findings and current approaches.

In this study, the hydro-agro-environmental model SWAT was used to simulate ¹³⁷Cs in particulate and dissolved phases transported by the Ardèche River during a 7-year period (2016–2022), a medium-length tributary of the Rhône River (France). This region was affected by radioactive atmospheric fallout from the Chernobyl accident in 1986 and atmospheric nuclear testing. Developed by the U.S. Department of Agriculture (USDA), SWAT has been extensively applied worldwide for hydrological and sediment transfer simulations (Gassman et al., 2007; Wang et al., 2019; Aloui et al., 2023). However, its application to radionuclide transport remains at an early stage of development. Only a few studies, such as Pratama et al. (2015), have attempted to couple SWAT-derived hydrological and sediment data with radionuclide-specific models to simulate ¹³⁷Cs dynamics, highlighting the emerging nature of this research direction.

Investigating the transfer of ¹³⁷Cs in a catchment without a nuclear power plant, such as the Ardèche catchment, provides an opportunity to better quantify the wash-off and transport of historical atmospheric fallout. In this context, analyzing the dynamic contribution of tributaries to the Rhône is essential for refining the assessment of the relative inputs from industrial sources and legacy deposits (Tomczak et al., 2021). To address this, an exploratory modeling approach that derives ¹³⁷Cs

concentrations from hydro-sedimentary data generated by SWAT and
results from a soil campaign was applied. A key innovative aspect of this
study lies in the spatialization of the results, including the production of
maps highlighting areas of ¹³⁷Cs soil loss and ¹³⁷Cs storage within the
river system.

The study aims to evaluate whether the combination of a hydrological-erosion model with a¹³⁷Cs-specific empirical model can reproduce the observed dynamics of ¹³⁷Cs within the river network. It further seeks to quantify the total amount of ¹³⁷Cs exported from the catchment during the study period, distinguishing between dissolved and particulate forms and examining how these exports vary under different hydrological conditions. Finally, the work explores the spatial and temporal evolution of ¹³⁷Cs distribution across the catchment, providing insights into the processes governing radionuclide transfer under varying land use and flow regimes.

To address the objectives outlined above, a sequential modeling framework that combines hydrological and radionuclide transfer processes was developed. The SWAT model was first used to simulate hydrological dynamics and sediment transport at the sub-catchment scale over the 2016–2022 period. Outputs from SWAT, including sediment fluxes by particle size were then used as inputs to a ¹³⁷Cs-Kd model. A dedicated coupling procedure was implemented to assign initial ¹³⁷Cs soil mass activities to each sub-catchment based on spatial interpolation of field measurements. This approach allows simulation of radionuclide behavior in both particulate and dissolved phases, providing a basis for assessing the transfer of ¹³⁷Cs from soils to the river network.

2. Material and methods

2.1. *Study site*

The Ardèche River, located in France, is a medium-length tributary (125 km) of the Rhône River, with a catchment area of 2138 km² (Fig. 1A). The whole Rhône catchment has been impacted by radioactive fallout, particularly from the Chernobyl accident (Meusburger et al., 2020).

The average monthly discharge at the Ardèche outlet (Saint-Martin d'Arèche) for the period 1955-2022 varies from about 9.2 m³ s⁻¹ in July to 150.0 m³ s⁻¹ in December (https://www.hydro.eaufrance.fr/; station: V506 4010; accessed: 10/10/2023). The instantaneous flow varies from 0.3 m³ s⁻¹ during severe droughts to 4500.0 m³ s⁻¹ in cases of major floods. The catchment is prone to Cévenol episodes that cause intense autumn rainfall leading to flash floods (Boudevillain et al., 2011; Naulet et al., 2005; Nuissier et al., 2008). During the low-water period in summer, dam releases maintain the flow to 10 % of the mean annual discharge (around 6.0 m³ s⁻¹) for approximately 19 % of the time for tourism, navigation and for minimum ecosystem functioning in the river (AUCEA, 2007).

The catchment can be divided into two distinct parts based on ge-
ology and associated soils. In the headwaters, the bedrock consists of
plutonic and metamorphic rocks formed during the Variscan orogeny
(420-250 Ma). These extremely hard and erosion-resistant rocks shape a
mountainous landscape (Fig. 1B) with peaks reaching up to 1699 m.
Soils developed on these rocks, classified according to the French AFES
(Association Française pour l'Étude du Sol) system as Alocrisols and
Podzols (equivalent to Arenosols and Podzols in the WRB - World
Reference Base for Soil Resources system), are relatively shallow but still
show moderate susceptibility to erosion, reflecting the interaction be-
tween a resistant geology and pedogenetic and climatic processes
(Fig. 1C). In contrast, the eastern part of the catchment is underlain by
softer sedimentary formations from the Jurassic and Cretaceous periods
(201-65.5 Ma), which favor water infiltration and the development of
karst systems. The soils in this region are more alkaline and include
Regosols, Rendosols, and Fersialsols (equivalent to Leptosols, Calcisols
and Luvisols), typical of limestone environments (Fig. 1C).

Land cover (Fig. 1D) in the catchment is predominantly forested (51
<figure><img src="image_3.png" /><figcaption>Fig. 1. (A) The Ardèche catchment, soil sampling points, hydrography, hydrologic gauges, dams, catchment exit; (B) topographic map DB-Alti® from the Institut Géographique National (IGN) © IGN, (C) the soil map from the European Soils Database of the European Soil Data Centre (ESDAC) © European Commission; (D) and the land cover map Corine Land Cover from the European Environment Agency (EEA) © European Environment Agency.</figcaption></figure>

%), mainly located in the western and central mountainous areas, where steep slopes and higher rainfall favor dense deciduous (63 %) and coniferous (22 %) forests (supplementary materials: Table 1).

Shrublands and grasslands (31 %) also dominate upland areas. In contrast, cultivated lands (16 %) are concentrated in the lower elevations of the eastern sedimentary domain, where fertile Rendosols and

<table><caption>**Table 1**

overview of swat data inputs, data for calibration and validation, and their sources.</caption><thead><tr><th></th><th>Format</th><th>Description</th><th>Spatial resolution</th><th>Temporal resolution</th><th>Data sources</th></tr></thead><tbody><tr><td>Topographic map</td><td>Raster</td><td>Elevation</td><td>25 m-25 m</td><td>2001</td><td>https://geoservices.ign.fr/bdalti</td></tr><tr><td>Land use map</td><td>Raster</td><td>Land use classification</td><td>1: 100 000</td><td>2012</td><td>https://www.data.gouv.fr/fr/datasets/corine-land-cover-occupation-des-soils-en-france/</td></tr><tr><td>Soils map</td><td>Vector</td><td>Pedology</td><td>1: 1 000 000</td><td>2001</td><td>https://esdac.jrc.ec.europa.eu/content/european-soil-database-v20-vector-and-attribute-data</td></tr><tr><td>Meteorology</td><td>Data</td><td>Meteorological data</td><td>Grided: 8 km-8 km</td><td>1980-2021; Daily</td><td>https://donneespubliques.meteofrance.fr/</td></tr><tr><td>Hydrology</td><td>Data</td><td>Water flow</td><td>11 gauges</td><td>2013-2022; Daily/hourly</td><td>https://hydro.eaufrance.fr/</td></tr><tr><td>Sediment</td><td>Data</td><td>SSC</td><td>1 station</td><td>2016-2022; Instantaneous</td><td>https://bdoh.irstea.fr/OBSERVATOIRE-DES-SEDIMENTS-DU-RPHONE/</td></tr></tbody></table>
Fersialsols overlying limestone provide favorable conditions for agriculture. Importantly, these cultivated areas are spatially connected to the river network (Fig. 1A, D), occupying valley bottoms and floodplains where soils are deeper and more productive.

## 2.2. Coupling between SWAT and ¹³⁷Cs model

The layering of the different models and input-output data is presented in Fig. 2 to allow a better understanding of the modelling approach. Coupling between SWAT model and ¹³⁷Cs model is performed in two steps. Foremost, SWAT simulates daily sediment fluxes by sub-catchment and by particle size class (clay, silt, sand, aggregates). These sediment outputs are then enriched with ¹³⁷Cs activity values assigned to each sub-catchment, based on soil contamination measurements. For each particle size class, ¹³⁷Cs concentration is computed using ¹³⁷Cs model. These values are used to simulate transfer and storage of ¹³⁷Cs in suspended sediments (SS), riverbed, and floodplain. The equations governing ¹³⁷Cs behavior are not embedded directly in SWAT but are applied externally based on SWAT's outputs. This approach preserves the hydrological realism of SWAT while enabling radionuclide-specific modeling. This allows, for each sub-catchment, to calculate ¹³⁷Cs concentration in SS from soil erosion but also the ¹³⁷Cs concentration in the sediments stored in the river and in the floodplain, given that all sub-catchments interact according to SWAT's operational structure.

## 2.3. The SWAT model

SWAT is an open-source, hydro-agronomic modelling software developed by the USDA and Texas A&M AgriLife Research. It is designed to simulate hydrology (surface and groundwater) and water quality (suspended matter, contaminants, or nutrients ...), and predict the environmental impact of various anthropogenic practices, including agriculture, dam operations, and point-source pollution (Arnold et al.,

1998, 2012). The model is physically based and works on an integration principle of geographic and climatic information. SWAT is a semi-distributed model that works at scale of the Hydrologic Response Unit (HRU). Each HRU is defined by a single land use type, a single soil type and a category of slopes of a few degrees of difference. Hydro-biogeochemical calculations are performed by SWAT at HRU scale and are then aggregated into sub-catchments. For each sub-catchment there is a river section with its own flow characteristics depending on slope, the width of the stream, its roughness and many other parameters related to hydrodynamic processes.

The landscape contribution to sediment transport in SWAT is modelled through upland erosion and sediment delivery to streams. Hillslope erosion is calculated using Modified Universal Soil Loss Equation (Eq. (1)) (MUSLE) (Williams, 1975), which considers rainfall energy, runoff volume, soil erodibility, slope gradient, and land cover management to estimate daily soil loss.

Once eroded, sediment is routed through overland flow paths, where deposition and enrichment processes modify particle size distribution based on transport energy. The model accounts for selective transport, with finer particles like clay and silt traveling further than sand and gravel. Sediment reaching the channel network is then subject to in-stream transport processes, linking upland erosion dynamics with riverine sediment fluxes. This integration allows SWAT to assess the impact of land management practices on sediment yield and aquatic ecosystems:

$$A = 11,8 \cdot (Q \cdot q_p)^{0,56} \cdot K \cdot L \cdot S \cdot C \cdot P \qquad \text{Eq. 1}$$

here:

* A (t) is the sediment yield for a given storm event.

* Q (m³) is the surface runoff volume.

* Q.qp (m³ s⁻¹) is the peak runoff rate.

* K (t ha h ha⁻¹ MJ⁻¹ mm⁻¹) is the soil erodibility factor.

<figure><img src="image_4.png" /><figcaption>Fig. 2. Schematic representation of the coupling between SWAT and the ¹³⁷Cs model. Geographic (DEM, pedology, land use) and weather data (precipitation, temperature, wind, solar radiation, humidity) are used as inputs for SWAT, which simulates daily water and sediment fluxes by sub-catchment (si) and by particle size class (ip, i.e. clay, silt, sand, aggregates). These fluxes are then combined with ¹³⁷Cs activity values derived from soil contamination measurements to compute radionuclide transfer and storage in the river system (suspended sediments, bed sediments, and dissolved fraction).</figcaption></figure>
* LS (dimensionless) is the topographic factor, combining effects of slope length and steepness.

* C (dimensionless) is the cover and management factor, accounting for the influence of vegetation and land use.

* P (dimensionless) is the support practice factor, representing the effectiveness of erosion control practices such as contouring or terracing.

At this point, the eroded soil particles are linked to a¹³⁷Cs soil contamination map and the information of origin of the material is kept in memory until the breakdown into different classes of particles.

SWAT models sediment transport by quantifying inflow and outflow for each reach. The incoming sediment consists of the outflow from the upstream section combined with sediment contributions from sub-catchment erosion. Using Kodoatie (2000) equation, SWAT provides a detailed breakdown of sediment size fractions transported through each reach, including clay (2 µm), silt (10 µm), sand (200 µm), gravel (2000 µm), small aggregates (30 µm), and large aggregates (500 µm). Each particle is then assigned to a¹³⁷Cs value based on its size and its sub-catchment of origin according to operation of Tomczak equilibrium formula. Kodoatie model (Kodoatie, 2000) estimates maximum sediment concentration in stream (Eq. (2)) based on hydrogeomorphologic variables:

$$ conc_{sed, ch, mx} = \left( \frac{a v_{ch}^{b} y^{c} S^{d}}{Q_{in}} \right) \cdot \left( \frac{W + W_{btm}}{2} \right) \qquad \text{Eq. 2} $$

here:

* $v_{ch}$ (m.s⁻¹) is the mean flow velocity.

* y (m) is the mean flow depth.

* S (m.m⁻¹) is the bed slope.

* $Q_{in}$ (m³) is the volume of water entering the reach in the day.

* W (m) is the width of the channel at the water level, and $W_{btm}$ bottom width of the channel.

* The parameters a, b, c, and d are regression coefficients based on the grain size distribution of bed material. To estimate these parameters, SWAT requires D50 values of the grain size distribution of bed material for each reach.

This technique has demonstrated strong performance in SWAT (Wilk et al., 2022), as it is based on the well-established Kodoatie (2000) equations. For small aggregates (SMAG) and large aggregates (LAG), the fractions used are equal to the respective fractions of sediment sizes present in sub-catchments soils as defined in Foster et al. (1985) were used. In other words, LAGs are composed of the same proportions of sand, silt, and clay as the soils, while SMAG are composed exclusively of silt and clay, maintaining the same proportions as in soils.

The Kodoatie model in SWAT refines Posada's (1995) equation through nonlinear optimization and field data, making it applicable to channels with bed materials ranging from silt to gravel. The equation incorporates flow velocity, depth, slope, discharge, and channel width, with regression coefficients dependent on sediment size. By accounting for these factors, the model helps predict sediment transport dynamics, crucial for understanding erosion and deposition processes in river systems. It should be noted that SMAG and LAG are created solely through soil erosion. Gravels are generated solely through channel erosion. The sand, silt, and clay fractions are produced through both soil and channel erosion.

SWAT determines whether to compute erosion or resuspension based on total sediment production of the sub-catchment. If erosion is triggered, the model first checks whether sediment deposited on the previous day is available for resuspension. If no sediment is available, it then evaluates whether the shear stress exerted on the channel bed exceeds critical shear stress, determining the erosion rate accordingly. Conversely, if the shear stress remains below critical threshold but is still

sufficient to mobilize previously deposited particles, the model calculates resuspension. Sediment deposition for different particle sizes is estimated using the equations of Stokes (1851) and Einstein (1905) equations. When total deposition exceeds total erosion, the river is in a depositional state; otherwise, it is in an erosional state.

SWAT also simulates floodplain deposition using Bagnold and Beech's (1977) sediment transport equations. The model assumes that fine particles (silt and clay) are deposited in floodplains in proportion to their cross-sectional areas. The sediment transport capacity is calculated based on stream power and compared to the actual sediment load to determine deposition. Excess water spreads into floodplain when flow higher than bankfull stage, at which point velocity drops, and transport capacity is reduced. A settling equation based on Stokes' law that takes floodplain size, velocity, and flow depth into account is used to estimate deposition. Deposition efficiency is dependent on residence time and shear stress because silt has a low settling velocity. Unlike sediments in main channel, silt and clay are considered to be permanently eliminated from system once they settle in the floodplain and are not remobilized in subsequent time steps. Finally, all storage zones for each granulometric class, whether in the river or in the floodplain, as well as resuspension zones are clearly identified, and the information related to ¹³⁷Cs contamination of the particles is also incorporated.

The complete mass balance equations (Eq. (3)) for sediment routing are as follows:

$$ sed_{ch} = sed_{ch,i} - sed_{dep} + sed_{deg} \quad \text{where:} \qquad \text{Eq. 3} $$

$$ sed_{ch,i} = sand_{ch,i} + silt_{ch,i} + clay_{ch,i} + SMAG_{ch,i} + LAG_{ch,i} $$

$$ sed_{dep} = sand_{ch,i} \cdot Pdep_{sand} + silt_{ch,i} \cdot Pdep_{silt} + clay_{ch,i} \cdot Pdep_{clay} + SMAG_{ch,i} \cdot Pdep_{SMAG} + LAG_{ch,i} \cdot Pdep_{LAG} + gravel_{ch,i} \cdot Pdep_{gravel} $$

$$ sed_{deg} = Bnk_{deg} + Bed_{deg} $$

where:

$$ Bnk_{deg} = Bnksand + Bnksilt + Bnkclay + Bnkgravel $$

$$ Bed_{deg} = Bedsand + Bedsilt + Bedclay + Bedgravel $$

here:

* $sed_{ch}$ (t) is the amount of SS in the reach.

* $sed_{ch,i}$ (t) is the amount of SS entering the reach at the beginning of the time period.

* $sed_{dep}$ (t) is the amount of sediment deposited in the reach segment.

* $sed_{deg}$ (t) is the amount of sediment contribution from bank and bed erosion in the reach segment.

* $Pdep$ () is the percentage of sediments (sand, silt, clay, and gravel) that get deposited.

Two specific conditions of this project must be clearly explained:

* A Microsoft Access database is generated when creating a SWAT project. It includes all SWAT attribute tables, as well as correspondence codes such as physicochemical information for all soil types. For this study, the database was extended by adding new soil types representative of southern French soils, including all soils cited in Fig. 1 to better reflect the conditions of the study area.

* A fine discretization was adopted in order to achieve the most precise spatial scale possible and to align delineation of sub-catchments with the locations of the hydrological measurement stations in the Ardèche. The project includes 5679 HRUs and 283 sub-catchments. Sources and types of data used in modeling are given in Table 1.

SWAT was first run, and results were extracted at the sub-catchment scale, including resuspension and deposition fluxes by particle size class.
These sub-catchments were then assigned ¹³⁷Cs mass activity value, estimated by inverse distance weighted interpolation applied by land use type and integrated according to proportion of each land use type within each sub-catchment. This information defined initial conditions required to implement the ¹³⁷Cs model.

## 2.4. Cesium-137 model

Soil mass activity (Bq kg⁻¹) is required by the ¹³⁷Cs model and to evaluate the ¹³⁷Cs stock in the Ardèche catchment (Eq. (6)). This approach will also enable quantification of the proportions of ¹³⁷Cs exported from the catchment and assessment of the temporal evolution of catchment contamination.

### 2.4.1. Spatialized initial conditions

To apply the ¹³⁷Cs partitioning model between SS and dissolved forms, all initial conditions must be expressed on a consistent scale. In particular, the soil sampling campaign provides the mass activity in soils, which serves as one of the model's initial conditions. These measurements were scaled to the sub-catchment level to achieve a detailed spatial distribution. Only the contamination of the superficial 0–5 cm soil layer was considered to characterize soil mass activity, as no significant soil erosion occurs below this layer (Morgan, 2005).

The soil mass activity in each sub-catchment is defined as Eq. (4):

$$A_s = \sum_{i \in \{F, U, C\}} \left( P_{i,s} \cdot \frac{\sum_{j=1}^{3} \left( \frac{A_{ij}}{d_{ij}} \right)}{\sum_{j=1}^{3} \left( \frac{1}{d_{ij}} \right)} \right) \quad \text{Eq. 4}$$

where:

* $A_s$ (Bq m⁻²) is the total soil mass activity estimated for sub-catchment s.

* $i \in \{F, U, C\}$ refers to land use types: $F$ = forested, $U$ = undisturbed, $C$ = cultivated.

* $P_{i,s}$ (%) is the percentage of land use type i within sub-catchment s.

* $A_{ij}$ (Bq m⁻²) is the measured ¹³⁷Cs soil activity at sampling point j, corresponding to land use i.

* $d_{ij}$ (m) is the distance between sub-catchment s (centroid) and sampling point j of land use type i.

* The expression $\frac{\sum_{j=1}^{3} \left( \frac{A_{ij}}{d_{ij}} \right)}{\sum_{j=1}^{3} \left( \frac{1}{d_{ij}} \right)}$ (Bq m⁻²) represents a distance-weighted average of the three closest sampling points for land use type i.

### 2.4.2. Total stock

To estimate the total ¹³⁷Cs stock, an average inventory for three main land-use types was calculated and multiplied by area occupied by each category (Eq. (5)):

$$\text{Total stock} = \sum (\text{Land use area}_i \times \text{Contamination}_i) \quad \text{Eq. 5}$$

where:

* Land use area_i (m²) is surface of the sub-catchments of each land use.

* Contamination in Bq m⁻² (Bq m⁻²) is ¹³⁷Cs activity, obtained by converting values from Bq kg⁻¹ using the method described in Supplementary materials (Section 5.1: Conversion of mass activity to surface activity).

The calculated ¹³⁷Cs stock decreases each year due to soil erosion and radioactive decay. Accounting for radioactive decay allows for a comparison between ¹³⁷Cs removed from the watershed by erosion and ¹³⁷Cs lost through its radioactive half-life. The same decay calculation

also applies to ¹³⁷Cs stored in the river, which decreases over time according to the same principle.

Using radioactive half-life of ¹³⁷Cs (30.1 years), the decay of soil mass activity is calculated as follows (Eq. (6)):

$$\text{Soil mass activity (t)} = \text{Soil mass activity (t}_0) \cdot \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}} \quad \text{Eq. 6}$$

where:

Soil mass activity(t) (Bq) is the activity at time t.

* $A_0$ (Bq) is the initial activity.

* $t$ is time elapsed.

* $T_{1/2}$ is half-life of ¹³⁷Cs.

The reference year for the initial activity is 2016. Values for 2016 were reconstructed from the 2022 measurements, and annual decay was then applied year by year in the model to simulate period 2016–2022.

### 2.4.3. Solid/liquid fractionation

The modeling of ¹³⁷Cs concentration in SS and water is based on equations described by Tomczak et al. (2021) (Eq. (7)). These equations require parameters related to hydro-sedimentary conditions (water flow, SS concentration (SSC), particle size and the concentration of ¹³⁷Cs in the soils of the catchment. This approach also uses Kd and considers an exchange zone between the particles and surrounding liquid medium, as shown in Fig. 3. The radius for each sediment class was set as the mean of the respective size ranges defined by SWAT: 2 µm for clay, 10 µm for silt, and 200 µm for sand (Neitsch et al., 2011). The relationships between ¹³⁷Cs concentration and specific surface area follow a power law function (R² > 0.9) (He and Walling (1996), which supports reliable modeling of behavior of particulate ¹³⁷Cs in a non-nuclearized catchment.

For Eq. 7.A, for a given particle size category p, suspended sediments SS (kg m⁻³) are divided into reactive $[SSp]r$ and non-reactive $[SSp]nr$ fractions based on particle size $r_p$. The partitioning factor $\gamma_p$ is calculated as follows:

$$\gamma_p = \left(1 - \frac{\mathcal{Q}}{r_p}\right)^3 \quad \text{if } r_p > \mathcal{Q} \text{ and } \gamma_p = 0 \text{ if } r_p \le \mathcal{Q} \quad \text{Eq. 7.A}$$

here:

* $\mathcal{Q}$ (µm) represents thickness of the reactive layer. We set $\mathcal{Q}$ at 1 µm according to Tomczak et al. (2021).

* $r_p$ (µm) is radius of the particles.

The equations for reactive and non-reactive fractions are (Eq 1.B):

$$[SSp]r = (1 - \gamma_p)[SSp] \quad \text{Eq. 7.B} \\ [SSp]nr = \gamma_p[SSp]$$

## 2 - Total ¹³⁷Cs Concentration in SS

Total ¹³⁷Cs concentration in suspended sediments $CSS$ (Bq kg⁻¹) is derived by summing ¹³⁷Cs concentration across all particle sizes $p$ (Eq. 7.C):

$$C_{ss} = \sum_{p} [SSp] \cdot CSS_{p} \quad \text{Eq. 7.C}$$

## 3 - ¹³⁷Cs Concentration for each particle size

For each particle size $p$, ¹³⁷Cs concentration $CSS$, $p$ is calculated using the following formula (Eq. 7.D):
<figure><img src="image_5.png" /><figcaption>Fig. 3. schematic functioning of ¹³⁷Cs model. Given a soil ¹³⁷Cs concentration, the flow, the D50, and SSC, the model will predict dissolved ¹³⁷Cs concentrations and particulate ¹³⁷Cs concentrations. Adapted from Tomczak et al. (2021).</figcaption></figure>

$$ C_{ss,p} = \frac{(K_{d_2} \cdot C_{\omega} \cdot [SSp] \cdot r + C_{soil} \cdot [SSp] \cdot nr)}{[SSp]} \qquad \text{Eq. 7.D} $$

here:

* $K_{d_2}$ (L kg⁻¹) is the solid-liquid distribution coefficient of the reactive layer. We set it at 68 000 according to Tomczak et al. (2021).
* $C_{\omega}$ (Bq L⁻¹) is concentration of ¹³⁷Cs in water phase.
* $C_{soil}$ (Bq kg⁻¹) represents ¹³⁷Cs concentration in soil particles.
* 4 - ¹³⁷Cs in water Phase

The concentration of ¹³⁷Cs (Bq L⁻¹) in water phase $C_{\omega}$ is calculated by summing the contributions from reactive particles (Eq. 7.E):

$$ C_{\omega} = \frac{\sum_{p} [SSp] \cdot r \cdot C_{soil}}{1 + K_{d_2} \cdot \sum_{p} [SSp] \cdot r} \qquad \text{Eq. 7.E} $$

¹³⁷Cs concentration in the reactive sediment fraction $C_{ss,r}$ is then given by (Eq. 7.F):

$$ C_{ss,r} = K_{d_2} \cdot C_{\omega} \qquad \text{Eq. 7.F} $$

## 2.5. Observed data

### 2.5.1. SWAT inputs

#### 2.5.1.1. DEM.
A high-resolution DEM created in 2001 by the Institut Géographique National (IGN) (© IGN, France) with a 25 m resolution was used for the delineation of sub-catchments and the computation of slopes. The DEM is essential for accurately defining drainage patterns and catchment areas within the region under study (Fig. 1).

#### 2.5.1.2. Pedology.
The soil data (2001) were derived from the European Soil Database (ESDB) (© European Commission) at the scale of 1:1 000 000, using the 1985 FAO-UNESCO soil legend and related soil characteristics (Fig. 1). Soil characteristics, such as texture, organic matter content, and permeability, are critical for modelling soil-water interactions, infiltration rates, and nutrient cycling processes.

#### 2.5.1.3. Land use.
Land use data from the Corine Land Cover 2012 dataset, along with soil characteristics (© European Environment Agency) were integrated into SWAT. These datasets provided key information on land cover types and soil properties that are essential for understanding surface runoff, infiltration, and groundwater recharge.

#### 2.5.1.4. Meteorology.
Meteorological data were obtained from the French "Système d’Analyse Fournissant des Renseignements

Atmosphériques à la Neige" (SAFRAN) (Durand et al., 2009) a model that uses actual measurements from meteorological stations and provide them in the form of a grid with a point every 8 km. It provided daily values for precipitation, minimum and maximum temperatures, wind speed, solar radiation, and relative humidity for 39 grid stations located in the Ardèche catchment from 1980 to 2022. The Penman-Monteith method, integrated within SWAT, was used to simulate evapotranspiration.

### 2.5.2. Data for model evaluation

#### 2.5.2.1. River flow.
River discharge data were sourced from the Banque Hydro database (Banque Hydro, French Ministry for Ecological Transition and Solidarity) (available at: http://www.hydro.eaufrance.fr/, accessed on: [10/10/2023], which provided monthly streamflow data from 10 gauging stations, including the outlet at Saint-Martin d'Ardèche, along the river network (Fig. 1a). Daily average data on flow for each station were extracted.

#### 2.5.2.2. SSC.
SSC data were provided by the Rhône Sediments Observatory (Lepage et al., 2022) using a turbidimeter that measures every 10 min (Fig. 1). Turbidity measurements are converted into SS loads via a calibrated curve derived from 44 manual water samples.

#### 2.5.2.3. D50.
Median grain size (D50) data were obtained from the BDOH database (Base de Données sur les Observatoires de l'Homme et de l'Environnement) (Thollet et al., 2021).

#### 2.5.2.4. Particulate ¹³⁷Cs.
To measure the concentration of particulate ¹³⁷Cs (supplementary materials: Table 2), SS samples are monthly collected (since 2016) using a metal trap fixed approximately 0.5 m above the water surface at Saint-Martin d'Ardèche, within the Rhône Sediment Observatory (Lepage et al., 2022). The trap is sometimes removed during low water levels in summer, and as it is collected once a month, it may incorporate several successive floods. The deposited matter is then collected and subjected to gamma analysis as described in Lepage et al. (2022).

The study duration of 7 years (2016–2022) was chosen because it corresponds to the period covered by ¹³⁷Cs concentration observations in SS (Table 2).

#### 2.5.2.5. Soil ¹³⁷Cs activity.
Soil contamination was assessed by drilling cores in March 2022 using a 7.9 cm diameter manual steel corer, which divided into three layers (0–5 cm; 5–15 cm; 15–30 cm). To determine the 31 sampling points, land use, soil types, geological information and a radioactive fall-out map (Roussel-Debel et al., 2007) were considered to characterize the distribution of ¹³⁷Cs in the catchment (Fig. 1a)
<table><caption>**Table 2**
SWAT calibrated parameters: hydrology, sediments and D50.</caption><thead><tr><th></th><th>Input</th><th>Parameter</th><th>Description</th><th>Min. value</th><th>Max. value</th><th>Calibrated value</th></tr></thead><tbody><tr><td rowspan="10">Hydrology</td><td>.mgt</td><td>CN2</td><td>Function of permeability, LU and prev soil humidity</td><td>-10 %</td><td>+10 %</td><td>83.5 (+10 %)</td></tr><tr><td>sol</td><td>SOL_AWC</td><td>Available capacity of the soil layer</td><td>-0.04</td><td>+0.04</td><td>0.237 (+0.04)</td></tr><tr><td>.bsn</td><td>ESCO</td><td>Soil evaporation compensation factor</td><td>0</td><td>1</td><td>0.95</td></tr><tr><td>.gw</td><td>GW_REVAP</td><td>Shallow aquifer to overlying unsaturated zone</td><td>0.02</td><td>0.2</td><td>0.02</td></tr><tr><td>.gw</td><td>REVAPMN</td><td>Shallow aquifer to deep aquifer</td><td>0</td><td>1000</td><td>600</td></tr><tr><td>.gw</td><td>GWQMN</td><td>Shallow aquifer to return flow</td><td>0</td><td>5000</td><td>1200</td></tr><tr><td>.hru</td><td>SURLAG</td><td>Soil to river water concentration time</td><td>0.1</td><td>24</td><td>0.1 (forced)</td></tr><tr><td>.rte</td><td>CH_COV (1)</td><td>Main channel erodibility ratio</td><td>-0.05</td><td>0.6</td><td>0.6</td></tr><tr><td>.rte</td><td>CH_COV (2)</td><td>Tributary channels erodibility ratio</td><td>0.001</td><td>1</td><td>1</td></tr><tr><td>.rte</td><td>CHN EQN</td><td>Sediment routing methods</td><td>1 to 4 (whole number)</td><td>2</td><td>2</td></tr><tr><td rowspan="6">Suspended Sediments</td><td>.bsn</td><td>PRF</td><td>Peak rate adjustment for sediment routing</td><td>0</td><td>2</td><td>0</td></tr><tr><td>.bsn</td><td>IDEG</td><td>Constant update of channel dimensions</td><td>Inactive/active</td><td></td><td>Active</td></tr><tr><td>.mgt</td><td>USLE_P</td><td>Ratio of soil loss Slope&lt;20 % = x1 &gt;20 % = x2</td><td>0</td><td>1</td><td>x1 = 0.65 x2 = 0.95</td></tr><tr><td>sub</td><td>CH_N (1)</td><td>Manning's "n" value for the main channel</td><td>0.01</td><td>30</td><td>0.3</td></tr><tr><td>.rte</td><td>CH_N (2)</td><td>Manning's "n" value for the tributary channels</td><td>-0.01</td><td>0.3</td><td>0.3</td></tr><tr><td>.rte</td><td>CH_BNK_D50</td><td>Median particle size of channel bank sediment</td><td>1</td><td>10000</td><td>50</td></tr><tr><td rowspan="2">SS D50</td><td>.rte</td><td>CH_BED_D50</td><td>Median particle size of channel bed sediment</td><td>1</td><td>10000</td><td>500</td></tr></tbody></table>

(supplementary materials: Table 3).

To minimize hyper-local variations, three replicates were taken at each point, spaced 10 m apart, and subsequently mixed. Depressions and sunken areas were excluded to avoid sampling zones with higher concentrations of ¹³⁷Cs. In many instances, it was not possible to sample deeper than 5 cm due to the presence of coarser substrates or rocks. In the laboratory, soil cores were homogenized and sieved to a 2 mm mesh size. Approximately 300 g of soil were then dried and subjected to analysis similarly to particulate ¹³⁷Cs.

## 2.6. Model performance evaluation

The performance in simulating flow, SSC and ¹³⁷Cs particulate concentrations was assessed using several of the most common statistical indicators for such studies. The Percent Bias (Pbias; Moriasi et al., 2007), the Nash–Sutcliffe model Efficiency (NSE; Nash and Sutcliffe, 1970) and the coefficient of determination (R²; Fisher, 1921) were employed. Additionally, a visual inspection of the model versus observed hydrographs and SSC time series was conducted to assess the model's performance.

The Pbias is defined as Eq. (8):

$$ Pbias = \frac{\sum_{i=1}^{n} (O_i - P_i)}{\sum_{i=1}^{n} O_i} \cdot 100 \qquad \text{Eq. 8} $$

where:

* $O_i$ is the observed value.

* $P_i$ is the predicted value.

<table><caption>**Table 3**
statistical indices by hydrological observation station for daily flow modelling on the period 2020–2022.</caption><thead><tr><th>Station</th><th>R<sup>2</sup></th><th>NSE</th><th>Pbias</th></tr></thead><tbody><tr><td>F</td><td>0.57</td><td>0.53</td><td>0.97</td></tr><tr><td>G</td><td>0.64</td><td>0.58</td><td>-11.53</td></tr><tr><td>H</td><td>0.6</td><td>0.52</td><td>15.10</td></tr><tr><td>I</td><td>0.4</td><td>-0.59</td><td>-246.11</td></tr><tr><td>J</td><td>0.55</td><td>0.23</td><td>-14.31</td></tr><tr><td>A</td><td>0.6</td><td>-0.44</td><td>-14.40</td></tr><tr><td>B</td><td>0.55</td><td>-0.36</td><td>24.32</td></tr><tr><td>D</td><td>0.76</td><td>-0.09</td><td>5.69</td></tr><tr><td>E</td><td>0.69</td><td>0.29</td><td>12.48</td></tr><tr><td>K</td><td>0.76</td><td>0.54</td><td>-7.91</td></tr><tr><td>L</td><td>0.87</td><td>0.87</td><td>-1.36</td></tr></tbody></table>

Pbias measures the average tendency of the simulated data to be larger or smaller than their observed counter parts.

The NSE is calculated as Eq. (9):

$$ NSE = 1 - \frac{\sum_{i=1}^{n} (O_i - P_i)^2}{\sum_{i=1}^{n} (O_i - \bar{O})^2} \qquad \text{Eq. 9} $$

where:

* $\bar{O}$ is the observed value.

* $\bar{P}$ is the predicted value.

NSE compares the accuracy of predictions relative to the observed data mean.

The coefficient of determination (R²) is given by Eq. (10):

$$ r^2 = \frac{\sum_{i=1}^{n} (O_i - \bar{O}) \cdot (P_i - \bar{P})}{\left( \sum_{i=1}^{n} (O_i - \bar{O})^2 \right) \cdot \left( \sum_{i=1}^{n} (P_i - \bar{P})^2 \right)} \qquad \text{Eq. 10} $$

The R² value indicates the proportion of the variance in the observed data that is predictable from the simulated data.

## 2.7. SWAT calibration

Model calibration was performed by adjusting parameters to improve the accuracy of hydrological simulations (streamflow and SSC; Table 2). Seven parameters were manually adjusted for the calibration of hydrology according to the knowledge of the catchment: CN2, SOL_AWC, ESCO, GW_REVAP, REVAPMN, GWQMN, and SURLAG. All parameters were adjusted within acceptable ranges reflecting the real observed conditions in the Ardèche catchment, despite the inclusion of minimum and maximum (Table 2) values based on commonly accepted SWAT literature. SSC modelling required calibration of eight parameters: CH_COV (1), CH_COV (2), CHN EQN, PRF, IDEG, USLE_P, CH_N (1), and CH_N (2).

Hydrology was calibrated using river discharge data from 1980 to 2000 and validated from 2000 to 2022. SSC was calibrated from 2016 to 2019 and validated from 2019 to 2022 using measured SSC data. Particulate ¹³⁷Cs concentrations in suspended sediments were calibrated from 2016 to 2019 and validated from 2019 to 2022 using measured ¹³⁷Cs data. Table 2 summarizes the parameter values used in the model calibration process.
# 3. Results and discussion

## 3.1. Soil mass activity

### 3.1.1. Surface soils $^{137}$Cs contamination

Measures of $^{137}$Cs concentration in soils revealed significant variability in $^{137}$Cs concentrations across the three land-use categories (supplementary materials: Table 3). For forested and undisturbed soils, most $^{137}$Cs was concentrated in the upper soil layers, whereas cultivated soils showed a more uniform vertical distribution. In the 0–5 cm layer (Fig. 4), concentrations ranged from 2.9 Bq kg$^{-1}$ to 22.5 Bq kg$^{-1}$ for cultivated soils, with an average of 10.4 Bq kg$^{-1}$ σ = 7.0 Bq kg$^{-1}$ (σ equals standard deviation) (median = 8.8 Bq kg$^{-1}$, Q1-Q3 = 4.2–14.7 Bq kg$^{-1}$). In undisturbed land use, $^{137}$Cs concentrations ranged between 15.5 Bq kg$^{-1}$ and 107.0 Bq kg$^{-1}$, with an average of 50.8 Bq kg$^{-1}$ σ = 29.9 Bq kg$^{-1}$ (median = 47.6 Bq kg$^{-1}$, Q1-Q3 = 31.9–66.2 Bq kg$^{-1}$). Forest land use showed the highest variability, with concentrations ranging from 14.8 Bq kg$^{-1}$ to 160.0 Bq kg$^{-1}$, and an average of 65.3 Bq kg$^{-1}$ σ = 46.4 Bq kg$^{-1}$ (median = 47.3 Bq kg$^{-1}$, Q1-Q3 = 32.4–91.3 Bq kg$^{-1}$). However, the mean inventory (concentration of $^{137}$Cs for the entire soil core, expressed in Bq m$^{-2}$) was similar across the three land uses, with a wider range for cultivated soils.

The values calculated by applying regrowth correction up to 1986, considering an effective half-life of 30.1 years, are similar to measurements taken between 1987 and 1992 by Renaud et al. (1997). The average for the Ardèche department was measured at 6251.0 Bq m$^{-2}$, with values ranging from 2065.0 to 12260.0 Bq m$^{-2}$ while for the

Ardèche catchment the calculated values in this study range from 407.0 to 19748.0 Bq m$^{-2}$, with an average of 7597.0 Bq m$^{-2}$.

### 3.1.2. Surface soils $^{137}$Cs contamination mapping

$^{137}$Cs contamination values per sub-catchment (Fig. 5) range from 6.8 Bq kg$^{-1}$ to 114.7 Bq kg$^{-1}$ with an average of 46.2 Bq kg$^{-1}$ σ = 24.1 Bq kg$^{-1}$ at the starting date (01/01/2016). The western part of the catchment shows more heterogeneous and higher values while the eastern part is more homogeneous with lower values.

$^{137}$Cs contamination values per sub-catchment (Fig. 5) range from 6.8 Bq kg$^{-1}$ to 114.7 Bq kg$^{-1}$ with an average of 46.2 Bq kg$^{-1}$ σ = 24.1 Bq kg$^{-1}$ at the starting date (01/01/2016). The western part of the watershed shows the highest and most heterogeneous contamination levels. This pattern is mainly explained by topography and associated rainfall regime: crystalline mountains in the west are exposed to intense Cévenol precipitation events (Renaud et al., 2003), which favor higher initial deposition of $^{137}$Cs and its retention in surface soils. In addition, steep slopes enhance erosion and local redistribution, contributing to the observed variability. In contrast, the eastern part of the watershed, underlain by sedimentary formations with gentler relief, receives significantly less rainfall and is more affected by agricultural practices. Plowing accelerates the vertical migration of cesium, making part of the stock inaccessible to the 0–5 cm layer considered here. As a result, contamination appears more homogeneous and generally lower in the eastern sub-catchments. The displayed values correspond to topsoil concentrations and are dynamically updated according to radioactive decay of $^{137}$Cs.

### 3.1.3. Total stock calculation

Total $^{137}$Cs stock of the Ardèche catchment was estimated at 7.7 TBq as of 01/01/2016. This value was obtained using a weighted mean approach: for each sub-catchment, the average contamination of the three closest sampling points of each land-use category was multiplied by the corresponding surface area. This provided an integrated estimate consistent with the objective of assessing the total stock at the catchment scale.

In the literature, total inventories are often derived from fallout deposition maps or atmospheric dispersion models (e.g FLEXPART; Yasunari et al., 2011). The approach adopted here is simpler but conceptually similar, since it integrates contamination values across the main land-use types. The main limitation is that it assumes land-use averages are representative of spatial variability, which may not always hold in heterogeneous landscapes (Ito et al., 2020).

Moreover, the 7.7 TBq value may underestimate the true total stock of the catchment. Because since the initial fallout, years of erosion, resuspension, and sediment redistribution have occurred and the field campaign was designed to characterize contamination in eroding soils and intentionally to avoid potential accumulation zones (slope-enclosed areas), possibly excluding localized contamination hotspots.

## 3.2. Daily flow, SSC, particulate $^{137}$Cs concentration, KDA and fluxes modelling

### 3.2.1. Flow and SSC modelling

The modelling of daily flow at Saint-Martin d'Ardèche (Fig. 6A and B) near the outlet matches observations closely ($R^2$ = 0.87, NSE = 0.87, Pbias = -1.36) especially during floods, with rise and fall times of floods consistent with observations (Fig. 6). However, there are discrepancies in flood amplitude and low flows. Some flood peaks are underestimated, while others are overestimated, with differences of up to 400 m$^3$ s$^{-1}$ for major events. If we consider all flood peaks above 200 m$^3$ s$^{-1}$ and which represent the highest value over a 5-day sliding window, the peaks are underestimated or overestimated by about 30 % on average. At low flows between 5 m$^3$ s$^{-1}$ and 10 m$^3$ s$^{-1}$ (Fig. B), the model underestimates the observed values.

Statistical indices were also calculated at the 10 other stations in the

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** A) Surface soil concentration of $^{137}$Cs by type of land use during the 2022 soil campaign on 31 sampling sites in the Ardèche catchment. B) Soil contamination in Bq m$^{-2}$ in the three major types of land use.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 5. First layer of soil (0–5 cm) spatialized results of the field campaign done in 2022 by sub-catchment and values from punctual sampling.</figcaption></figure>

catchment (Table 3). The most accurate results were observed at the last station before the outlet (Station K, $R^2$ = 0.76; NSE = 0.54; Pbias = -7.91) while the least accurate (Station I, $R^2$ = 0.4; NSE = -0.59; Pbias = -246.11) were obtained at the station located a few hundred meters from a dam. Overall, the further downstream the stations are in the catchment, the better indices are.

The discrepancies observed during low-flow periods are primarily related to dam operations, which occur approximately 19 % of the time. In addition, regular water releases generate short-term fluctuations (the crenelated appearance of the curve) that the model does not capture.

Since the calibration was performed at the outlet, the agreement between simulated and observed flows is highest there. Although SWAT includes a dam module, explicit modeling of dams was not implemented here, as calibration already yielded satisfactory performance at the outlet.

### 3.2.2. Suspended sediments and ¹³⁷Cs concentrations calibration and validation

Simulation of SSC in the Ardèche River near the outlet (Saint-Martin d'Ardèche) (Fig. 7) shows a wide range of daily values up to 1000 mg L⁻¹. Most modelled peaks fall within the range of 100 mg L⁻¹ to 300 mg L⁻¹, with approximately two peaks per month during the wet season and almost no peaks from June to September over the period from 2016 to 2022. When comparing SWAT-modelled daily SSC values with those observed, the following statistical indices were obtained ($R^2$ = 0.013; NSE = -3.23; PBIAS = 16 %).

Although simulated peaks align in amplitude with observed ones (Fig. 7), some discrepancies remain. Rare instances occur where simulated peaks are present but not observed, and vice versa. Overall, the model accurately captures the baseline level of SSC during low flow periods. However, the comparison does not fully validate this model ($R^2$ = 0.013; NSE = -3.23; PBIAS = 16 %).

This weak statistical agreement is mainly due to the nature of the observational dataset, rather than a structural flaw in the model because SWAT has been widely validated for simulating SSC in diverse hydrological settings (Pinto et al., 2013; Bée et al., 2024; Yen et al., 2017), even under data-scarce conditions (Yuan et al., 2019).

In fact, the turbidity-to-SSC relationship was established using a very limited number of discrete water samples, collected mostly during baseflow conditions. With 95 % of SSC data falling between 0.5 mg L⁻¹ and 15.0 mg L⁻¹, and only two samples exceeding 20.0 mg L⁻¹, the dataset does not represent flood or high sediment transport events adequately. As a result, continuous SSC time series derived from turbidity is inherently biased towards low-flow periods and is not suitable for capturing peak sediment concentrations during high flows. This likely explains the negative NSE and poor $R^2$, despite the model's ability to reproduce the timing and intensity of sediment load peaks.

While the SSC dataset is too limited to formally validate the model using standard performance metrics, the general agreement in peak occurrence and the expected seasonal pattern reinforces confidence in model outputs. Some isolated turbidity anomalies unlinked to discharge may result from local disturbances at the sensor site (i.e intense kayaking activity in summer), which further complicates direct comparison with modelled values.

Given these constraints, we consider SWAT-simulated SSC to be more reliable than the observational series for capturing erosion-driven sediment dynamics at the catchment scale.

### 3.2.3. Particle size modelling

The evolution of modelled daily fluxes of different particle size fractions (sand, silt, clay, SMAG, and LAG) exhibits substantial temporal variability (Fig. 8). Fine particles dominate the total flux over the 7-year
<figure><img src="image_8.png" /><figcaption>Fig. 6. Daily observed and SWAT simulated flow at the output – A zoom during 2018–2021 period and B 2000–2022 daily 1:1 chart.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Daily observed and SWAT simulated SSC and corresponding hydrology at the outlet from 2016 to 2018.</figcaption></figure>

simulation period, with clay contributing $2.3 \times 10^5$ t (93 %), silt $1.1 \times 10^4$ t (4 %), SMAG $3.3 \times 10^3$ t (1 %), and sand $2.6 \times 10^3$ t (1 %). Very few LAG particles were transported ($2.2 \times 10^{-2}$ t, 0 %), and no gravel was simulated ($5.3 \times 10^{-16}$ t, 0 %). The total amount of exported sediments amounts to $3.6 \times 10^4$ t y$^{-1}$.

Observed D50 values ranged from 19.06 µm to 40.71 µm, with a mean of 26.30 µm σ = 5.4 µm, indicating moderate variability in particle size among samples. Fine particles, particularly clay and silt, constitute the dominant fraction, which is critical for understanding $^{137}$Cs transport due to the strong sorption of this radionuclide onto finer sediments.

Analysis of the modelled daily sediment fluxes by particle size class (Fig. 8) reveals a strong dominance of the clay fraction, which accounts for 93 % of the total sediment mass over the 7-year simulation period. Silt and sand contribute far less (4 % and 1 % respectively), with SMAG and LAG fractions being negligible. This result indicates that finer particles are more easily detached and transported in suspension during runoff events, whereas coarser fractions tend to settle rapidly. In the Ardèche catchment, clay-rich soils are mainly found in the eastern sedimentary domain (e.g., Fersialsols, Rendosols), while upland soils such as Podzols and Alocrisols are comparatively poor in clay. The
values ranging from 0 t ha⁻¹ yr⁻¹ to 3.8 t ha⁻¹ yr⁻¹, with an average of 0.7 t ha⁻¹ yr⁻¹ σ = 1.0 t ha⁻¹ yr⁻¹ (median = 0.1 t ha⁻¹ yr⁻¹, Q1-Q3 = 0.0–0.9 t ha⁻¹ yr⁻¹). A total of 8.0 × 10⁶ t y⁻¹ of soil was eroded during the simulated period.

Erosion rates exhibited clear contrasts between land uses. As expected, cultivated areas showed relatively low erosion rates (mean = 0.4 t ha⁻¹ yr⁻¹) while forested HRUs presented higher values (mean = 0.7 t ha⁻¹ yr⁻¹) despite their protective vegetation cover. This apparently counter-intuitive result can be explained by the interplay between topography, soils, rainfall, and the structure of the MUSLE equation used in SWAT.

Forests in the Ardèche catchment are predominantly located on steep mountain slopes (supplementary materials: Fig. 1), which directly amplify the LS factor and therefore the sediment transport capacity. These areas also coincide with the highest rainfall zones of the catchment (supplementary materials: Fig. 2), where intense Cévenol storms increase runoff and soil detachment (R factor). In addition, forest soils are mostly shallow, acidic Alocrisols with relatively low aggregate stability, which enhances erodibility (K factor). Finally, forests display the highest P values (mean = 0.88; supplementary materials: Table 4), reflecting the absence of conservation practices in SWAT. Altogether, these conditions push nearly all MUSLE parameters toward their upper range, which explains why erosion remains significant even under dense canopy cover. Similar values have been reported on Mediterranean soils under forest cover (Meliho et al., 2019), with a value of 4.2 t ha⁻¹ yr⁻¹.

Conversely, cultivated HRUs are mainly found on flatter valley bottoms and floodplains, developed on deep Calcosols and Rendosols that promote infiltration and reduce surface runoff, thereby lowering the R term of MUSLE. The gentler slopes also minimize LS, while the land-use composition, 40 % dense crops (AGRL), 20 % vineyards (GRAP), and 25 % pastures (PAST), contribute to moderate C values due to seasonal or permanent ground cover. Cultivated lands also display the lowest mean P values (0.76; supplementary materials: Table 4), consistent with reduced erosion control needs in such terrain. The combination of low LS, low R, and low P values jointly explains the comparatively small erosion rates obtained for cultivated areas. Furthermore, a study on soil erosion and conservation potential of row crops (Arnhold et al., 2014) has shown that for flat soils and continuous cover (meadow or intercrops under vines), values between 0.4 t ha⁻¹ yr⁻¹ and 0.7 t ha⁻¹ yr⁻¹ are common.

Overall, these results are coherent with previous findings in southern France (Kirkby et al., 2004; Van der Knijff et al., 2000) and consistent with the Cévenol context of the Ardèche catchment. While forests appear more erodible than cultivated lands in the model, this outcome reflects their geomorphological position and the spatial distribution of MUSLE parameters rather than a contradiction to the protective role of vegetation.

A total of 8.0 × 10⁶ t y⁻¹ of sediments was eroded from the catchment during the simulation period, of which 3.6 × 10⁴ t y⁻¹ were exported at the outlet. This yields a Sediment Delivery Ratio (SDR) of 0.0045 (0.45 %). The SDR estimated for the Ardèche catchment is low but consistent with international literature. Several studies (de Vente et al., 2013; Wu et al., 2017) show an exponential decrease in SDR with increasing watershed area, often falling below 1 % for catchments larger than 1000 km². The studies of Sedighi et al. (2021) and Alatorre et al. (2012) confirm the key role of vegetation cover, gentle slopes, and internal sediment trapping in this reduction. In the case of the Ardèche, although hillslope erosion can be intense, most of the sediment is effectively trapped within the system. In the north-western mountainous part of the catchment, material is rapidly deposited on short, steep slopes, while in the eastern lowlands, the wide alluvial plain and meandering channel network promote additional storage. This transition from mountain to plain, combined with significant in-channel deposition and the presence of several dams, strongly reduces sediment connectivity and explains the very low SDR.

### 3.2.5. $^{137}$Cs concentrations modelling

The main graph and the inset graph show the modelled and observed concentrations of $^{137}$Cs in SS at Saint-Martin d'Ardèche for the period 2016–2022 (Fig. 10). The modeling produced daily $^{137}$Cs concentrations ranging up to 43.0 Bq kg⁻¹. Observations, integrated over roughly a month, are overlaid with simulations averaged over the same periods. The monthly modelled concentrations (red line) exhibit several significant peaks, often exceeding 28.0 Bq kg⁻¹ and reaching up to 43.0 Bq kg⁻¹. In contrast, observed concentrations (black line) are more stable, with a mean of 9.0 Bq kg⁻¹ σ = 2.8 Bq kg⁻¹. Over the observation period, the following indices were obtained R² = 0.09; NSE = -0.36; PBIAS = -879 %.

The modelled $^{137}$Cs concentrations fall within a reasonable range (of the same order of magnitude as the observations), and the model successfully reproduces the general trends of $^{137}$Cs transport in suspended sediments. However, several factors limit the accuracy and interpretation of the results, as summarized below:

* SSC validation: The validation of SSC remains challenging due to the scarcity of observations during high-flow events, when sediment transport is most active. Nevertheless, SSC has been successfully simulated in numerous SWAT studies, suggesting that the model's underlying conceptual framework is robust.

* Sediment composition: The modelled sediment fluxes are clay-dominated (93 %), whereas the observed samples indicate silt dominance. This discrepancy likely results from sediment trap efficiencies during flood events. Despite this, both the modeling approaches and existing literature support the predominance of clay in sediment transport, lending credibility to the simulation results.

* Data reliability: The quality and reliability of the observed $^{137}$Cs data must also be considered. Submerged traps tend to underestimate the finest sediment fractions, which is critical since $^{137}$Cs preferentially adsorbs onto these particles.

### 3.2.6. Dissolved concentrations and fluxes

The simulated dissolved concentration of $^{137}$Cs at the outlet of the Ardèche River (Saint-Martin-d'Ardèche) exhibits relatively low values overall. The mean concentration is $1.4 \times 10^{-4}$ Bq L⁻¹ σ = $1.2 \times 10^{-4}$ Bq L⁻¹, with a maximum of $6.3 \times 10^{-4}$ Bq L⁻¹ and a minimum of $5.7 \times 10^{-8}$ Bq L⁻¹, indicating moderate variability over simulated period. The resulting flux is $0.3$ GBq year⁻¹, or $1.9$ GBq for the whole period.

Over the seven-year simulation period, the modelled $^{137}$Cs flux at the watershed outlet reached 11.1 GBq, corresponding to an average annual export of $1.6$ GBq yr⁻¹. Of this total, $9.2$ GBq of $^{137}$Cs were transported in the particulate phase, representing 83 % of the total flux, even though particulate transport dominated over dissolved transport on only 35 % of the simulated days. This exported activity corresponds to a 0.14 % reduction in the watershed's total $^{137}$Cs inventory over the seven-year period.

For comparison, during the same timeframe, radioactive decay led to a loss of approximately 1.6 TBq of $^{137}$Cs, or 17 % of the initial watershed stock. Although this export rate (0.14 % over 7 years) is lower than values reported in post-accidental contexts (e.g., Bonnett, 1990; Taniguchi et al., 2019), this difference likely reflects the fact that the study represents a late-post-Chernobyl period, more than three decades after deposition, when $^{137}$Cs has largely stabilized within soils.

Although no direct observations are available to validate the simulated dissolved $^{137}$Cs concentrations at the outlet of the Ardèche River, it is still possible to draw a comparison with measurements taken at the Rhône River outlet (Tomczak et al., 2021). The simulated concentrations for the Ardèche are noticeably lower, with a mean of $1.4 \times 10^{-4}$ Bq L⁻¹ σ = $1.2 \times 10^{-4}$ Bq L⁻¹, whereas the observed concentrations at the Rhône outlet are generally higher, around $3 \times 10^{-4}$ Bq L⁻¹ to $4 \times 10^{-4}$ Bq L⁻¹. This difference may partly reflect the influence of liquid discharges from nuclear facilities along the Rhône River, which increase $^{137}$Cs levels in that system. However, it may also stem from modeling
<figure><img src="image_10.png" /><figcaption>**Fig. 10.** Daily observed and modelled SS <sup>137</sup>Cs concentrations at the outlet of the Ardèche (Saint-Martin d'Ardèche), 2019–2022. Modeling allowed us to calculate daily <sup>137</sup>Cs concentrations (light red line). However, since observations (black line) were integrated over a month, we also integrated the modelled results to match this temporal resolution (red line). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

uncertainties, since the simulated dissolved <sup>137</sup>Cs concentrations in the Ardèche are derived from the modelled particulate concentrations, which are not perfectly constrained. In addition, the *Kd* value of 68 000 L kg<sup>-1</sup>, adopted from measurements on the Rhône, may not be fully representative of the Ardèche River, even though it is one of its tributaries. Variations in sediment characteristics and geochemical conditions could result in a different *Kd* and therefore different partitioning between dissolved and particulate phases.

Fluxes align with values reported in the literature (IRSN, 2012; Tsukada et al., 2017) for a catchment without nuclear discharge, with

83 % of the yearly <sup>137</sup>Cs flux transferred at the catchment outlet occurring in particulate form. This means that the transfer is largely driven by the SS load in the river. If we define the 'flood' state as the top 10 % of daily flow rates, setting the threshold at 118.3 m<sup>3</sup> s<sup>-1</sup>, then 75 % of the <sup>137</sup>Cs flux at the outlet occurs during these 10 % of days.

### 3.2.7. Spatialized outputs

SWAT enables the modelling of spatial outputs. Considering the limitations and uncertainties discussed above, a total of 1.8 TBq or 263.6 GBq y<sup>-1</sup> of <sup>137</sup>Cs was eroded from the soil and transmitted to the river

<figure><img src="image_11.png" /><figcaption>**Fig. 11.** <sup>137</sup>Cs transfer at the catchment scale, yearly average (2016–2022).</figcaption></figure>
for 7 years period (Fig. 11).

Fig. 11 illustrates the contribution of each sub-catchment to the river, expressed in becquerels per year. Over the seven-year simulation period, a total of 1.7 TBq of $^{137}$Cs was stored in the river, corresponding to an average of 255.8 GBq yr$^{-1}$. In contrast, only 14.6 GBq accumulated in the floodplain during the same period (approximately 2.1 GBq yr$^{-1}$, shown in light blue).

The northwestern part of the catchment shows both higher erosion and higher in-river storage, as this mountainous area produces large sediment loads (transporting $^{137}$Cs) from steep slopes that are rapidly deposited once they reach the river network. In contrast, the south-eastern plain presents much lower storage values, as most of the material has already settled upstream. Overall, the Ardèche catchment behaves as a storage-dominated system, where most eroded material is retained within the catchment rather than exported out of it.

It should be noted, however, that these spatialized results must be interpreted with caution. No direct field data (e.g., sediment cores, local erosion measurements) are available to validate the modelled spatial patterns of $^{137}$Cs storage and erosion. Nevertheless, the model was hydrologically calibrated at 11 gauging stations and validated for suspended sediment and $^{137}$Cs concentrations at the outlet. Since the model follows the well-established SWAT equations and parameter values were kept within environmentally realistic ranges, the simulated spatial distribution can be considered physically consistent and representative of the Ardèche catchment behavior, even if local uncertainties remain.

## 4. Conclusion

This study aimed to assess the transfer of $^{137}$Cs from soils to rivers by developing and applying a coupled modeling framework that combines SWAT with a trace-metals mass balance equation. The methodology allowed for the simulation of both particulate and dissolved phases of $^{137}$Cs transport over a seven-year period (2016–2022) in the Ardèche River catchment, which has been affected by historical atmospheric fallout from Chernobyl and nuclear testing. The coupling approach relied on SWAT outputs of hydrological and sediment fluxes, which were enriched with spatially distributed soil $^{137}$Cs inventories to compute daily $^{137}$Cs concentrations and fluxes.

The total $^{137}$Cs stock in the catchment was estimated at 7.7 TBq in 2016, decreasing by 17 % over seven years due to radioactive decay and by 0.14 % through erosion. The model indicated that 83 % of exported $^{137}$Cs was associated with the particulate phase, emphasizing the dominant role of sediment transport in radionuclide mobility. Flood events, which represented only 10 % of the time, accounted for 75 % of total $^{137}$Cs fluxes, confirming their key influence on contaminant export. Spatially, the western mountainous sub-catchments displayed the highest soil inventories and erosion-driven transfers, whereas eastern agricultural areas exhibited lower surface activities due to plowing and vertical migration of $^{137}$Cs. Temporally, a strong seasonality was observed, with episodic remobilization during Cévenol floods and limited transfers under baseflow conditions.

However, it is important to consider these results within the context of available observational data, which produced limited accuracy statistics for daily $^{137}$Cs concentrations at the outlet ($R^2$ = 0.09; NSE = -0.36; PBIAS = -879 %). The scarcity of high-frequency SSC and $^{137}$Cs measurements, as well as the use of sediment traps integrating several events, constrains quantitative validation but does not invalidate the model's ability to reproduce key spatial and temporal patterns of radionuclide redistribution.

Overall, the proposed approach provides a physically based and spatially explicit approach to investigate radionuclide dynamics in catchments affected by radioactive fallout. Future research could benefit from integrating in situ sediment tracing, improving temporal resolution of $^{137}$Cs monitoring, and coupling with biogeochemical or isotopic models to better constrain exchange processes between particulate and dissolved phases. The framework could also be extended to

larger river systems or to other contaminants governed by similar erosion-transport-deposition mechanisms.

### CRediT authorship contribution statement

**François Guillory:** Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Hugo Lepage:** Writing – original draft, Visualization, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation. **Sabine Sauvage:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Formal analysis, Conceptualization. **José-Miguel Sánchez:** Writing – review & editing, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Conceptualization. **Clément Fabre:** Visualization, Validation, Software, Methodology, Investigation, Data curation. **Patrick Boyer:** Validation, Methodology. **David Mourrier:** Resources, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

This study was supported by the Rhône Sediment Observatory (OSR), a multi-partner research program partly funded by the 'Plan Rhône' and by the European Regional Development Fund (ERDF).

The authors thank the "Nuclear, Risk, Society" Federative Project of the NEEDS (Nuclear: Energy, Environment, Waste, Society) program for its support of this research.

Thanks to F. Eyrolle for her help. Thanks to F. Thollet and F. Giner for field samplings, sample treatment and analyses.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jenvrad.2025.107849.

### Data availability

Data will be made available on request.

### References

Alatorre, L.C., Beguería, S., Lana-Renault, N., Navas, A., García-Ruiz, J.M., 2012. Soil erosion and sediment delivery in a mountain catchment under scenarios of land use change using a spatially distributed numerical model. Hydrol. Earth Syst. Sci. 16, 1321–1334. https://doi.org/10.5194/hess-16-1321-2012.

Aloui, S., Mazzoni, A., Elomri, A., Aouissi, J., Boufekane, A., Zghibi, A., 2023. A review of soil and water assessment tool (SWAT) studies of mediterranean catchments: applications, feasibility, and future directions. J. Environ. Manag. 326 (B), 116799. https://doi.org/10.1016/j.jenvman.2022.116799.

Arnold, S., Lindner, S., Lee, B., Martin, E., Kettering, J., Nguyen, T.T., Koellner, T., Ok, Y.S., Huwe, B., 2014. Conventional and organic farming: soil erosion and conservation potential for row crop cultivation. Geoderma 219–220, 89–105. https://doi.org/10.1016/j.geoderma.2013.12.023.

Arnold, J.G., Srinivasan, R., Muttiah, Rs, Williams, J.R., 1998. Large area hydrologic modeling and assessment part I: model development. J. Am. Water Resour. Assoc. 34, 73–89. https://doi.org/10.1111/j.1752-1688.1998.tb05961.x.

Arnold, J.G., Moriasi, D.N., Gassman, P.W., Abbaspour, K.C., White, M.J., Srinivasan, R., Santhi, C., Harmel, R.D., van Griensven, A., Van Liew, M.W., Kannan, N., Jha, M.K., 2012. SWAT: model use, calibration, and validation. ASABE 55 (4), 1491–1508. https://doi.org/10.13031/2013.42256.

AUCEA, 2007. Plan de gestion des étiages du bassin versant de l'Ardeche. Schéma d'Aménagement et de Gestion des Eaux du bassin versant de l'Ardeche. Bureau d'Étude AUCEA, Toulouse. Juin, 2007. http://www.ardeche-eau.fr.
Bagnold, R., Beech, M., 1977. Bed load transport by natural rivers. Water Resour. Res. 13, 303–312. https://doi.org/10.1029/WR0131002p0030.

Bée, S., St-Hilaire, A., van den Heuvel, M., 2024. Modeling sediment concentrations and loads for two small agricultural watersheds in prince-Edward-island (Canada): present conditions and a future scenario. Front. Water 6, 1337907. https://doi.org/10.3389/frwa.2024.1337907.

Bonnett, P.J.P., 1990. A review of the erosional behaviour of radionuclides in selected drainage basins. J. Environ. Radioact. 11 (3). https://doi.org/10.1016/0265-931x (90)90018-q.

Boudevillain, B., Delrieu, G., Galabertier, B., Bonnifait, L., Bouilloud, L., Kirstetter, P.-E., Mosini, M.-L., 2011. The Cévennes-Vivarais Mediterranean Hydrometeorological Observatory database. Water Resour. Res. 47 (7). https://doi.org/10.1029/2010WR010353.

Buesseler, K., Dai, M., Aoyama, M., Benitez-Nelson, C.A., Charmasson, S., Higley, K., Maderich, V., Masquè, P., Morris, P.J., Oughton, D., Smith, J.N., 2017. Fukushima Daichi-derived radionuclides in the ocean: transport, fate, and impacts. Ann. Rev. Mar. Sci 9, 173–203. https://doi.org/10.1146/annurev-marine-010816-060733.

Bunzl, K., Kracke, W., Schimmack, W., Auerswald, K., 1995. Migration of fallout 239+ 240Pu, 241Am and ¹³⁷Cs in the various horizons of a forest soil under pine. J. Environ. Radioact. 28, 17–34. https://doi.org/10.1016/0265-931X(94)00066-6.

Delmas, M., Garcia-Sanchez, L., Nicoulaud-Gouin, V., Onda, Y., 2017. Improving transfer functions to describe radiocesium wash-off fluxes for the Niida River by a Bayesian approach. J. Environ. Radioact. 167, 100–109. https://doi.org/10.1016/j.jenvrad.2016.11.002.

Durand, Y., Laternser, M., Giraud, G., Etchevers, P., Lesaffre, B., Mérindol, L., 2009. Reanalysis of 44 yr of climate in the French Alps (1958–2002): methodology, model validation, climatology, and trends for air temperature and precipitation. J. Appl. Meteorol. Climatol. 48 (3), 429–449.

Einstein, A., 1905. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. Phys. 322 (8), 549–560. https://doi.org/10.1002/andp.19053220806.

Evrard, O., Laceby, J.P., Lepage, H., Onda, Y., Cerdan, O., Ayrault, S., 2015. Radiocesium transfer from hillslopes to the Pacific Ocean after the Fukushima Nuclear Power Plant accident: a review. J. Environ. Radioact. 148, 92–110. https://doi.org/10.1016/j.jenvrad.2015.06.018.

Fisher, R.A., 1921. On the probable error of a coefficient of correlation deduced from a small sample. Metron 1, 3–32.

Foster, G.R., Young, R.A., Neibling, W.H., 1985. Sediment composition for nonpoint source pollution analyses. Trans. ASABE (Am. Soc. Agric. Biol. Eng.) 28, 133–139. https://apisemanticscholar.org/CorpusID:109196414.

Funaki, H., Sakuma, K., Nakanishi, T., Yoshimura, K., Katengeza, E.W., 2020. Reservoir sediments as a long-term source of dissolved radiocaesium in water system; a mass balance case study of an artificial reservoir in Fukushima, Japan. Sci. Total Environ. 743, 140668. https://doi.org/10.1016/j.scitotenv.2020.140668.

Funaki, H., Tsuji, H., Nakanishi, T., Yoshimura, K., Sakuma, K., Hayashi, S., 2022. Remobilisation of radiocaesium from bottom sediments to water column in reservoirs in Fukushima, Japan. Sci. Total Environ. 812, 152534. https://doi.org/10.1016/j.scitotenv.2021.152534.

Garneau, C., Sauvage, S., Sánchez-Pérez, J.-M., Lofts, S., Brito, D., Neves, R., Probst, A., 2017. Modelling trace metal transfer in large rivers under dynamic hydrology: a coupled hydrodynamic and chemical equilibrium model. Environ. Model. Software 89, 77–96. https://doi.org/10.1016/j.envsoft.2016.11.018.

Gassman, P.W., Reyes, M.R., Green, C.H., Arnold, J.G., 2007. Soil and Water Assessment Tool: historical development, applications, and future research directions. Trans. ASABE 50, 1211–1250. https://doi.org/10.13031/2013.23637.

Gilbin, R., Arnold, T., Beresford, N.A., Berthomieu, C., Brown, J.E., de With, G., Horemans, N., Madruga, M.J., Masson, O., Merroun, M., Michalik, B., Muikku, M., O'Toole, S., Mrdakovic Popic, J., Nogueira, P., Real, A., Sachs, S., Salbu, B., Stark, K., Steiner, M., Sweeke, L., Vandenhove, H., Vidal, M., Vives i Battle, J., 2021. An updated strategic research agenda for the integration of radioecology in the European radiation protection research. J. Environ. Radioact. 237, 106697. https://doi.org/10.1016/j.jenvrad.2021.106697.

Golosov, V., Ivanov, M., 2020. Quantitative Assessment of Lateral Migration of the Chernobyl-derived ¹³⁷Cs in contaminated teCritories of the East European Plain. Springer. https://doi.org/10.1007/978-981-15-3568-0-4.

Harhash, M., Schroeder, H., Zavarsky, A., Kamp, J., Linkhorst, A., Lauschke, T., Dierkes, G., Ternes, T.A., Duester, L., 2023. Efficiency of five samplers to trap suspended particulate matter and microplastic particles of different sizes. Chemosphere 233, 139479. https://doi.org/10.1016/j.chemosphere.2023.139479.

He, Q., Walling, D.E., 1996. Interpreting particle size effects in the adsorption of 137Cs and unsupported 210Pb by mineral soils and sediments. J. Environ. Radioact. 30, 117–137. https://doi.org/10.1016/0265-931X(96)89275-7.

Hilton, J., Cambray, Rs, Green, N., 1991. Chemical fractionation of radioactive caesium in airborne particles containing bomb fallout, Chernobyl fallout and atmospheric material from the Sellafield site. J. Environ. Radioact. 13, 267–279.

Hoffmann, T.O., Baulig, Y., Fischer, H., Blöthe, J., 2020. Scale breaks of suspended sediment rating in large rivers in Germany induced by organic matter. Earth Surf. Dyn. 8, 661–678. https://doi.org/10.5194/esurf-8-661-2020.

IAEA, 2006. Environmental Consequences of the Chernobyl Accident and Their Remediation: Twenty Years of Experience. International Atomic Energy Agency.

IRSN, 2012. Le césmièt-137 et l'environnement. Institut de Radioprotection et de Sûreté Nucléaire (IRSN). France. https://www.irsn.fr/FR/connaissances/Installations_nu-cleares/impact-environnement/radionucleides-environnement/Documents/Cesiu-m-137-environnement-IRSN.pdf.

Ikenoue, T., Shimadera, H., Nakanishi, T., Kondo, A., 2023. Thirty-year simulation of environmental fate of ¹³⁷Cs in the Abukuma River basin considering the

characteristics of ¹³⁷Cs behavior in land uses. Sci. Total Environ. 876, 162846. https://doi.org/10.1016/j.scitotenv.2023.162846.

Ito, E., Miura, S., Aoyama, M., Shichi, K., 2020. Global 137Cs fallout inventories of forest soil across Japan and their consequences half a century later. J. Environ. Radioact. 225, 106421. https://doi.org/10.1016/j.jenvrad.2020.106421.

Iwasaki, T., Nabi, M., Shimizu, Y., Kimura, I., 2015. Computational modeling of ¹³⁷Cs contaminant transfer associated with sediment transport in Abukuma River. J. Environ. Radioact. 139, 416–426. https://doi.org/10.1016/j.jenvrad.2014.05.012.

Kinouchi, T., Yoshimura, K., Omata, T., 2015. Modeling radiocesium transport from a river catchment based on a physically-based distributed hydrological and sediment erosion model. J. Environ. Radioact. 139, 407–415. https://doi.org/10.1016/j.jenvrad.2014.07.022.

Kirkby, M.J., Jones, R.J.A., Irvine, B., Gobin, A., Govers, G., Cerdan, O., Van Rompaey, A. J.J., Le Bissonnais, Y., Daroussin, J., King, D., Montanarella, L., Grimm, M., Vieillefont, V., Puigdefabregas, J., Boer, M., Kosmas, C., Yassoglou, N., Tsara, M., Mantel, S., Van Lynden, G.J., Huting, J., 2004. Pan-European Soil Erosion Risk Assessment: the PESERA Map, Version 1, October 2003. Explanation of Special Publication Ispra 2004 Eur S Bureau, No. 73, S.P.104.73.

Kitamura, A., Yamaguchi, M., Kurikami, H., Yui, M., Onishi, Y., 2014. Predicting sediment and cesium-137 discharge from catchments in eastern Fukushima. Anthropocene 5, 22–31. https://doi.org/10.1016/j.ancene.2014.07.001.

Van der Knijff, J.M., Jones, R.J.A., Montanarella, L., 2000. Soil erosion risk assessment in Europe. Eur S Bureau Res Report No. 11, EUR 19044 EN.

Kodoate, R.J., 2000. Sediment Transport Relations in Alluvial Channels. Colorado State University. Unpublished PhD Thesis.

Konoplev, A., Golosov, V., Laptev, G., Nanba, K., Onda, Y., Takase, T., Wakiyama, Y., Yoshimura, K., 2016. Behavior of accidentally released radiocesium in soil-water environment: looking at Fukushima perspective. J. Environ. Radioact. 151, 568–578. https://doi.org/10.1016/j.jenvrad.2015.06.019.

Konoplev, A., 2022. Fukushima and Chernobyl: similarities and differences of radiocesium behavior in the soil-water environment. Toxics 10, 578. https://doi.org/10.3390/toxics10100578.

Krstić, D., Nikezić, D., Stevanović, N., Jelić, M., 2004. Vertical profile of ¹³⁷Cs in soil. Appl. Radiat. Isot. 61, 1487–1492. https://doi.org/10.1016/j.apradiso.2004.03.118.

Kurihara, M., Onda, Y., Kato, H., Loffredo, N., Yasutaka, T., Coppin, F., 2018. Radiocesium migration in the litter layer of different forest types in Fukushima, Japan. J. Environ. Radioact. 187, 81–89. https://doi.org/10.1016/j.jenvrad.2018.01.027.

Lepage, H., Evrard, O., Onda, Y., Lefèvre, I., Laceby, J.P., et al., 2015. Depth distribution of ¹³⁷Cs in paddy fields across the Fukushima pollution plume in 2013. J. Environ. Radioact. 147, 157–164. https://doi.org/10.1016/j.jenvrad.2015.05.003.

Lepage, H., Laceby, J.P., Bonté, P., Joron, J.-L., Onda, Y., Lefèvre, I., Ayrault, S., Evrard, O., 2016. Investigating the source of radiocesium contaminated sediment in two Fukushima coastal catchments with sediment tracing techniques. Anthropocene 13, 57–68. https://doi.org/10.1016/j.ancene.2016.01.004.

Lepage, H., Gruat, A., Thollet, F., Le Coz, J., Coquery, M., Masson, M., Dabrin, A., Radakovitch, O., Labille, J., Ambrosi, J.-P., Delanghe, D., Raimbault, P., 2022. Concentrations and fluxes of suspended particulate matter and associated contaminants in the Rhone River from Lake Geneva to the Mediterranean Sea. Earth Syst. Sci. Data 14 (5), 2369–2384. https://doi.org/10.5194/essd-14-2369-2022.

Lestaveil, P., Racine, R., Bensoussan, H., Rouas, C., Gueguen, Y., Dublineau, I., Bertho, J.-M., Gourmelon, P., Jourdain, J.-R., Souidi, M., 2010. Césium ¹³⁷ : propriétés et effets biologiques après contamination interne. Méd. Nucléaire 34 (2), 108–118. https://doi.org/10.1016/j.mednuc.2009.12.003.

Masson, M., Angot, H., Le Bescond, C., Launay, M., Dabrin, A., Miège, C., Le Coz, J., Coquery, M., 2018. Sampling of suspended particulate matter using particle traps in the Rhone River: relevance and representativeness for the monitoring of contaminants. Sci. Total Environ. 637–638, 538–549. https://doi.org/10.1016/j.scitotenv.2018.04.343.

Meusburger, K., Evrard, O., Alewell, C., Borrelli, C., Cinelli, G., Ketterer, M., Mabit, L., Panagos, P., van Oost, K., Ballabio, C., 2020. Plutonium-aided reconstruction of caesium atmospheric fallout in European topsoils. Sci. Rep. 10, 11858. https://doi.org/10.1038/s41598-020-68736-2.

Melho, M., Nouira, A., Benmansour, M., Boulmane, M., Khattabi, A., Mhammdi, N., Benkdad, A., 2019. Assessment of soil erosion rates in a Mediterranean cultivated and uncultivated soils using fallout 137Cs. J. Environ. Radioact. 208–209, 106021. https://doi.org/10.1016/j.jenvrad.2019.106021.

Morgan, R.P.C., 2005. Soil Erosion and Conservation, third ed. Blackwell Publishing, Oxford. https://doi.org/10.1111/j.1365-2389.2005.0756x.f.

Nakanishi, T., Sakuma, K., 2019. Trend of ¹³⁷Cs concentration in river water in the medium term and future following the Fukushima nuclear accident. Chemosphere 215, 272–279. https://doi.org/10.1016/j.chemosphere.2018.10.017.

Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models part I — a discussion of principles. J. Hydrol. 10 (3), 282–290. https://doi.org/10.1016/0022-1694(70)90255-6.

Naulet, R., Lang, M., Ouarda, T.B.M.J., Cœur, D., Bobée, B., Recking, A., Moussay, D., 2005. Flood frequency analysis on the Ardèche river using French documentary sources from the last two centuries. J. Hydrol. 313, 58–78.

Neitsch, S.L., Arnold, J.G., Kiniry, J.R., Williams, J.R., 2011. Soil & Water Assessment Tool: Theoretical Documentation Version 2009. Texas Water Resources Institute.

Nussier, O., Ducrocq, V., Ricard, D., Lebeaupin, C., Anquetin, S., 2008. A numerical study of three catastrophic precipitating events over southern France. I: Numerical framework and synoptic ingredients. Q. J. R. Meteorol. Soc. 134, 111–130.

Ochiai, S., Ueda, S., Hasegawa, H., Kakiuchi, H., Akata, N., Ohtsuka, Y., Hisamatsu, S., 2015. Effects of radiocesium inventory on ¹³⁷Cs concentrations in river waters of
Fukushima, Japan, under base-flow conditions. J. Environ. Radioact. 144, 86-95.
https://doi.org/10.1016/j.jenvrad.2015.03.005.

Park, S.-M., Alessi, Ds, Baek, K., 2019. Selective adsorption and irreversible fixation behavior of cesium onto 2:1 layered clay mineral: a mini review. J. Hazard. Mater. 369, 569-576. https://doi.org/10.1016/j.jhazmat.2019.02.061.

Pinto, D.B.F., Silva, A.M., Beskow, S., de Mello, C.R., Coelho, G., 2013. Application of the Soil and Water Assessment Tool (SWAT) for sediment transport simulation at a headwater watershed in Minas Gerais State, Brazil. Trans. ASABE (Am. Soc. Agric. Biol. Eng.) 56 (2), 697-709. https://doi.org/10.13031/2013.42668.

Posada-G., L., 1995. Transport of Sands in Deep Rivers. PhD Dissertation, Department of Civil Engineering, Colorado State University, Fort Collins, Colorado, 158 pp.

Pratama, A.M., Yoneda, M., Shimada, Y., Matsui, Y., Yamashiki, Y., 2015. Future projection of radiocesium flux to the ocean from the largest river impacted by Fukushima Daiichi Nuclear Power Plant. Sci. Rep. 5, 8408. https://doi.org/10.1038/srep08408.

Renaud, P., Beaugelin, K., Maubert, H., Ledenvic, P., 1997. Consequences radio écologiques et dosimétriques de l'accident de Tchernobyl en France. Rapport IPSN, 97-03.

Renaud, P., Pourcelot, L., Métivier, J.M., Morello, M., 2003. Mapping of 137Cs deposition over eastern France 16 years after the Chernobyl accident. Sci. Total Environ. 309 (1-3), 257-264. https://doi.org/10.1016/S0048-9697(03)00049-4.

Rhoton, F.E., Emmerich, W.E., Nearing, M.A., McChesney, D.S., Ritchie, J.C., 2011. Sediment source identification in a semiarid watershed at soil mapping unit scales. Catena 87 (2), 172-181. https://doi.org/10.1016/j.catena.2011.05.002.

Roussel-Debel, S., Renaud, P., Métivier, J.-M., 2007. ¹³⁷Cs in French soils: deposition patterns and 15-year evolution. Sci. Total Environ. 374 (2-3), 388-398. https://doi.org/10.1016/j.jscitotenv.2006.12.037.

Sakuma, K., Tsuji, H., Hayashi, S., Funaki, H., Malins, A., Yoshimura, K., Kurikami, H., Kitamura, A., Iijima, K., Hosomi, M., 2018. Applicability of Kd for modelling dissolved ¹³⁷Cs concentrations in Fukushima river water: Case study of tce upstream Ota River. J. Environ. Radioact. 184-185, 53-62. https://doi.org/10.1016/j.jenvrad.2018.01.001.

Sawhney, B.L., 1972. Selective sorption and fixation of cations by clay minerals: a review. Clays Clay Miner. 20 (2), 93-100. https://doi.org/10.1346/CCMN.1972.0200208.

Sedighi, F., Khaledi Darvishan, A., Zare, M.R., 2021. Effect of watershed geomorphological characteristics on sediment redistribution. Geomorphology 375, 107559. https://doi.org/10.1016/j geomorph.2020.107559.

Stokes, G.G., 1851. On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Philos. Soc. 9, 8.

Taniguchi, K., Onda, Y., Smith, H.G., Blake, W., Yoshimura, K., Yamashiki, Y., Kuramoto, T., Saito, K., 2019. Transport and redistribution of radiocesium in Fukushima fallout through rivers. Environ. Sci. Technol. 53 (21). https://pubs.acs.org/doi/10.1021/acs.est.9b02890.

Thollet, F., Le Bescond, C., Lagouy, M., Gruat, A., Grisot, G., Le Coz, J., Coquery, M., Lepage, H., Gairoard, S., Gattacceca, J.C., Ambrosi, J.-P., Radakovitch, O., Dur, G., Richard, L., Giner, F., Eyrolle, F., Angot, H., Mourier, D., Bonnefoy, A., Dugué, V.,

Launay, M., Troudet, L., Labille, J., Kieffer, L., 2021. Observatoire des Sédiments du Rhône. INRAE. https://doi.org/10.17180/OBS.OSR.

Tomczak, W., Boyer, P., Eyrolle, F., Radakovitch, O., Krimissa, M., Lepage, H., Amielh, M., Anselmet, F., 2021. Modelling of solid/liquid fractionation of trace metals for suspended sediments according to the hydro-sedimentary conditions of rivers - application to ¹³⁷Cs in the Rhône River (France). Env. I Mod. & Soft. 145, 105211. https://doi.org/10.1016/j.envsoft.2021.105211.

Tsukada, H., Nihira, S., Watanabe, T., Takeda, S., 2017. The 137Cs activity concentration of suspended and dissolved fractions in irrigation waters collected from the 80 km zone around TEPCO's Fukushima Daiichi Nuclear Power Station. J. Environ. Radioact. 178-179, 354-359. https://doi.org/10.1016/j.envrad.2017.08.002.

Vandromme, R., Hayashi, S., Tsuji, H., Evrard, O., Grangeon, T., Landemaine, V., Laceby, J.P., Wakiyama, Y., Cerdan, O., 2023. Lessons learnt on the impact of an unprecedented soil decontamination program in Fukushima on contaminant fluxes. Proc. Natl. Acad. Sci. U.S.A. 120 (43), e2301811120. https://doi.org/10.1073/pnas.2301811120.

de Vente, J., Poesen, J., Verstraeten, G., Govers, G., Vanmaercke, M., Van Rompaey, A., Arabkhedri, M., Boix-Fayos, C., 2013. Predicting soil erosion and sediment yield at regional scales: where do we stand? Earth Sci. Rev. 127, 16-29. https://doi.org/10.1016/j.earscirev.2013.08.014.

Wang, Y., Jiang, R., Xie, J., Zhao, Y., Yan, D., Yang, S., 2019. Soil and water assessment tool (SWAT) model: a systemic review. J. Coast Res. 93, 22-30. https://doi.org/10.2112/SI93-004.1.

Williams, J.R., 1975. Sediment-Yield Prediction with Universal Equation Using Runoff Energy Factor. USDA ARS-S-40, 244. Agricultural Research Service, Southern Region, U.S. Department of Agriculture, Washington DC.

Wilk, P., Szlapa, M., Hachaj, Ps, et al., 2022. From the source to the reservoir and beyond—tracking sediment particles with modeling tools under climate change predictions (Carpathian Mts.). J. Soils Sediments 22, 2929-2947. https://doi.org/10.1007/s11368-022-03287-9.

Wu, L., Liu, X., Ma, X., 2017. Research progress on the watershed sediment delivery ratio. Int. J. Environ. Stud. 75 (9), 1-15. https://doi.org/10.1080/00207233.2017.1392771.

Yamada, S., Kitamura, A., Kurikami, H., Yamaguchi, M., Malins, A., Machida, M., 2015. Sediment and ¹³⁷Cs transport and accumulation in the Ogaki Dam of eastern Fukushima. Environ. Res. Lett. 10 (1), 14013.

Yasunari, T.J., Stohl, A., Hayano, R.S., Burkhart, J.F., Eckhardt, S., Yasunari, T., 2011. Cesium-137 deposition and contamination of Japanese soils due to the Fukushima nuclear accident. Proc. Natl. Acad. Sci. USA 108 (49), 19530-19534. https://doi.org/10.1073/pnas.1112058108.

Yen, H., Lu, S., Feng, Q., Wang, R., Gao, J., Brady, D.M., Sharifi, A., Ahn, J., Chen, S.-T., Jeong, J., et al., 2017. Assessment of optional sediment transport functions via the complex watershed simulation model SWAT. Water 9, 76. https://doi.org/10.3390/w9020076.

Yuan, L., Forshay, K.J., 2019. Using SWAT to evaluate streamflow and lake sediment loading in the Xinjiang River Basin with limited data. Water 12 (1), 39. https://doi.org/10.3390/w12010039.