Benoît Guyot

Charline Wiegert

Fatima Meite

Pablo Alvarez- Zaldivar

Eric Pernin

J'aimerai

sa bonne humeur quotidienne

The rapid population growth since the beginning of 20 th century induced substantial changes in farming practices. The predominance of intensive cropping in France make it the first user of pesticides in Europa.

Once sprayed on field, pesticides are likely to enter aquatic systems through many different ways and then, to interact with sediment. However, scientific community lacks of knowledges about these interactions and pollutant fate within aquatic systems is partially understood.

To account for the complexity of this system, we implemented a coupled lab-scale experiments and modelling approach. In this way, identified relevant processes were both studied under laboratory controlled conditions and modelled in VENSIM®. Moreover, the use of Compound Specific Isotope Analysis (CSIA) allowed us to individually assess the role of each process in complex systems involving multiple intertwined degradation pathways.

During this work, one hydrolysis experiment was conducted and lead to derive half-life values and carbon enrichment factors. Then, it appeared that under natural conditions (𝑝𝐻 = 7 and 𝑇 = 20°𝐶), studied pesticides were stable with less than 50% degradation after 49 days.. However, under more alkaline or acid conditions and at higher temperatures (𝑝𝐻 = 2 or 12 and 𝑇 = 30°𝐶) half-life values significantly decreased (from 6 days to atrazine to 18 days for Butachlor). Enrichment factors were also determined with great accuracy for 4 in 7 of the studied pesticides.

In-silico experiments, relying on existing dataset were also conducted. They aimed at assessing the model ability to compute diffusion and sorption as well as to check its ability to simulate complex systems.

The diffusion experiment validated the model ability to simulate pesticide diffusion through the sediment layer. It also proved that after 100 days of simulation, only the first centimeters of sediments (< 16 𝑐𝑚) are likely to be affected by pollutant contaminations when considering diffusion as the only transport process.

The sorption experiment showed that ageing is likely to accumulate a huge fraction (>50%) of the initial pesticide mass after 200 days of incubation. Then, because ageing decreases the pollutant availability for degradation, it can't be neglected when assessing persistence of pesticides in the environment. Then, we showed that neglecting the ageing process when calculating half-life values is likely to lead to a 20% under-estimation of the persistence of pesticides within the environment. In addition, thanks to a good fit with measured carbon isotopic composition, the model proved to be capable of mechanistically predicting the fate of pesticide within the water-sediment interface.

Résumé

Dissipation des micropolluants à l'interface eau-sédiment des systèmes aquatiques : Approche combinée entre modélisation et expériences en laboratoire.

La croissance démographique rapide observée depuis le début du 20 ème siècle s'est traduite par une modification profonde des pratiques agricoles. Sur le territoire national, la prédominance de l'agriculture intensive place la France en tête du classement Européen des utilisateurs de pesticides.

A la suite de leur application, les pesticides migrent vers les différents compartiments de la matrice environnement et contaminent les systèmes aquatiques. Cependant, ces phénomènes sont encore mal connus.

Une approche couplée entre modélisation et expérience de laboratoire nous a permis d'appréhender la complexité de cette interface. Les processus identifiés comme prédominants ont été étudiés au laboratoire et modélisés sous VENSIM®. L'utilisation de l'Analyse isotopique composé spécifique a de plus ouvert les portes à une compréhension mécaniste du comportement des pesticides au sein de l'interface eau-sédiment.

Au cours de ce travail, une expérience d'hydrolyse a été conduite au laboratoire et a permis l'obtention de temps de demi-vie et de facteur d'enrichissement isotopique pour plusieurs pesticides. Dans les conditions environnementales moyennes (𝑝𝐻 = 7 et 𝑇 = 20°𝐶) les pesticides étudiés se sont révélés stables avec moins de 50% de dégradation après 49 jours. Dans des conditions alcalines et acides et à des températures supérieures ( 𝑝𝐻 = 2 or 12 and 𝑇 = 30°𝐶 ), les temps de demi-vie ont significativement chutés (6 jours pour l'Atrazine, 18 jours pour le Butachlor). Des valeurs d'enrichissement isotopique ont ainsi pu être obtenues pour 4 des 7 pesticides étudiés.

Trois expériences in-silico reposant sur des sets de données expérimentaux réalisés en parallèle de ce travail ont permis d'évaluer les capacités du modèle développé à résoudre les équations physiques.

L'expérience de diffusion a validé la résolution de l'équation de Fick et a montré qu'en conditions statiques seuls les premiers centimètres de sédiments (< 16 𝑐𝑚) sont affectés par les contaminations. L'expérience de sorption a permis de valider le formalisme « two sites one rate » et a montré qu'après 200 jours d'incubation dans les sols, la fraction non biodisponible (agée) peut représenter jusqu'à 50% de la masse initiale de pesticides. Enfin, nous montrons que ne pas intégrer l'ageing dans le calcul des temps de demi-vie amène à sous-estimer de 20% la persistance des pesticides dans l'environnement. Grâce à une correspondance satisfaisante entre enrichissement mesuré et simulé le modèle se révèle capable de prédire avec certitude l'importance de chaque processus dans le devenir global du pesticide. ) [START_REF] Meybeck | Carbon, nitrogen, and phosphorus transport by world rivers. Meybeck, M[END_REF] [START_REF] Meybeck | Carbon, nitrogen, and phosphorus transport by world rivers. Meybeck, M[END_REF]

Table of content

Table of figures

Table of tables

I/ Introduction 1 Study context

Anthropogenic activities coupled with massive use of water caused water contamination with numerous synthetic and geogenic compounds [START_REF] Schwarzenbach | Environmental Organic Chemistry / Edition[END_REF]. In addition, over the next decades, climate change and population growth are likely modifying the hydrological cycle, resulting in a global water quality deterioration [START_REF] Jackson | Water in a Changing World[END_REF]. Thus in the early 1990s, numerous countries worldwide (united nations) recognized micropollutant contaminations as one of the great environmental challenges the world faces [START_REF] Wania | Peer Reviewed: Tracking the Distribution of Persistent Organic Pollutants[END_REF] These anthropogenic or natural substances referred to as micropollutants or "emerging contaminants" represent a wide variety of molecules from pharmaceuticals to plant protection products (PPP) via consumer care products. They mostly originate from agricultural inputs and treated effluents from domestic or industrial waste water treatment plants [START_REF] Elsner | Compound-specific isotope analysis (CSIA) of micropollutants in the environment -current developments and future challenges[END_REF][START_REF] Luo | A review on the occurrence of micropollutants in the aquatic environment and their fate and removal during wastewater treatment[END_REF].

Plant protection products (PPP), commonly referred to as "pesticides" are well identified as partly responsible for surface water pollution. Classified in three different classes (fungicide, insecticide and herbicide) they are widely and massively used throughout the word for increasing crop productivity. Despite a steady decrease in European PPP consumption for the last decades, in 2003 Eurostats reported a total of 220 000 tonnes of PPP used in Europe (25 members), 28% of which in France (European Commission and Eurostats, 2007). Due to their persistence, these molecules can be transported "over hundreds of kilometres" and are then ubiquitously found in French surface water [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF][START_REF] Schwarzenbach | Environmental Organic Chemistry / Edition[END_REF][START_REF] Wania | Peer Reviewed: Tracking the Distribution of Persistent Organic Pollutants[END_REF]. In 2013, pesticides were measured in 92% of the national surveillance grid (Commissariat général au développement durable, 2015). These observations are consistent with the assertion that the use of intensive cropping is intrinsically linked to high rate of pollutions in surface and underground water [START_REF] Gutowski | A comparative assessment of the transformation products of S-metolachlor and its commercial product Mercantor Gold(®) and their fate in the aquatic environment by employing a combination of experimental and in silico methods[END_REF].

Micropollutants are thus named because they are detected in low concentrations in the environment (from 𝑛𝑔/𝐿 to 𝜇𝑔/𝐿) [START_REF] Elsner | Compound-specific isotope analysis (CSIA) of micropollutants in the environment -current developments and future challenges[END_REF][START_REF] Luo | A review on the occurrence of micropollutants in the aquatic environment and their fate and removal during wastewater treatment[END_REF]. However, despite these low concentrations, the occurrence of micropollutants in the aquatic environment has proved negative effects including short-term and long-term toxicity, endocrine disrupting effects and antibiotic resistance of microorganisms [START_REF] Luo | A review on the occurrence of micropollutants in the aquatic environment and their fate and removal during wastewater treatment[END_REF]. Thus, considering that more than 65% of the national drinking water production relies on surface water pumping (Commissariat général au développement durable, 2016), micropollutant in water resources represent a thorny topic for public health.

In this way, international commissions, national government and even local policies play a prominent role in addressing this issue of pollution. Through the Water Framework Directive (WFD) and its objective to reach a good ecological and chemical status for surface waters, the EU defines a list of priority substances (including among biocides as Atrazine or Alachlor) subjected to be forbidden by the next two decades. Based on the Ecophyto plan, launched in 2008, France aims at halving the use of pesticides by 2025. In this way, since the first of January 2017, the use of PPP is forbidden in public areas all over the country. In addition, thanks to international environmental quality standards, pesticide thresholds in surface or underground water intended for human consumption are limited to 0.1 𝜇𝑔. 𝐿 -1 for a single pesticide and to 0.5 𝜇𝑔. 𝐿 -1 for a bulk of pesticides (WFD). In France, 4.5% of the population undergoes regular threshold overrun (ARS, 2014).

Then, understanding behaviour of pesticides in environmental compartments appears as a sine qua non condition to move forward and improve national and international management strategies [START_REF] Honti | Deriving Persistence Indicators from Regulatory Water-Sediment Studies -Opportunities and Limitations in OECD 308 Data[END_REF].

Description of the water-sediment interface

The aim of this first section is to introduce the basic knowledges of water-sediment interface and pesticide as well as processes involved in pollutant cycling. Secondly, on the basis of the above, most suited methods of investigation are presented with their complementarities.

Historically the environmental behaviour of pesticides has been studied at large scales, under specific conditions, within isolated compartments and with limited considerations for the interactions between the different compartments (e.g., atmosphere-water or water-sediment interfaces) (Figure 2).

The water-sediment interface is a relevant compartment to study due to its frequent exposure to pollution and its complex and still poorly understood interactions with contaminants (Figure 3). Indeed, pesticides entering aquatic systems may originate from several sources and pathways as spray drift, surface runoff, field drainage or even groundwater discharge [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF]. Then, partitioning between overlying water and sediment is complex and dynamic, as shown in two recent studies [START_REF] Alvarez | Bottom sediment as a source of organic contaminants in Lake Mead, Nevada, USA[END_REF] and [START_REF] Lu | Fate and transport of polychlorinated biphenyls (PCBs) in the River Thames catchment -Insights from a coupled multimedia fate and hydrobiogeochemical transport model[END_REF]. The role of sediment for pesticide dissipation or storage, and as sources and sinks of pesticides over space and time remains unclear. In particular, these publications highlight the fact that in river and lake systems, the sediment layer might act either as a pollutant reservoir or as a "secondary contaminant source" when overlying water concentration decreases. Considering that the interface is dynamic [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF][START_REF] Meybeck | Carbon, nitrogen, and phosphorus transport by world rivers. Meybeck, M[END_REF], it must be studied as a thin horizon. Indeed, characteristics as Dissolved Oxygen (𝐷𝑂) concentrations, 𝑝𝐻, Temperature, etc. face sharp and quick variations within a few millimetres in the interface (Figure 4). For example, DO concentration depleted rapidly within the first 4 𝑚𝑚 of sediment [START_REF] Honti | Deriving Persistence Indicators from Regulatory Water-Sediment Studies -Opportunities and Limitations in OECD 308 Data[END_REF][START_REF] Shrestha | Simulation Studies to Explore Biodegradation in Water-Sediment Systems: From OECD 308 to OECD 309[END_REF][START_REF] Wang | Microscale chemical features of sediment-water interface in Hongfeng Lake[END_REF]. Through chemical equilibria, such fluctuations also can alter other parameters, such as 𝑝𝐻 or 𝐸 (𝑉). Thus, pollutant degradation pathways driven by physicochemical characteristics at the water-sediment interface, may change within a few millimetres, and, in turn, impact the degradation rates. Traditional approaches relying on simplistic and global description of the water or the sediment compartment can hardly enable reliable predictions of pollutant behaviour. A comprehensive characterisation of the interface is required to capture the complexity and the diversity of the involved processes.

In this study, the water-sediment interface has been conceptually split in two interdependent compartments; the surface water and the sediment compartment. These compartments are both biphasic (water + Suspended Solids (SS) and sediment + interstitial water) (Figure 4).

Surface water

According to [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF], "natural water contains suspended matter, dissolved organic and inorganic matter, and many kinds of aquatic biota". Then, 2 phases are distinguished in this compartment; the liquid and the solid phase.

 The liquid phase is composed of a mix of water and dissolved elements (from nutrients to organic pollutants).

 The solid phase is solely composed of SS issued from bank erosion and surface runoff.

Liquid phase: surface water

To describe this phase, numerous parameters are required summarized in the Table 1. They represent either the pollutant concentrations or the state conditions of the water.

Solid phase: suspended solid

The term SS refers to the material that is big enough not to be considered as dissolved matter and small enough to be held in suspension (D>2 μm). Amount of SS is evaluated in mass (𝑚𝑔) or concentration (𝑚𝑔 𝑜𝑟𝑔𝑎𝑛𝑖𝑐 𝑚𝑎𝑡𝑡𝑒𝑟 . 𝐿 -1 ) of inorganic and organic matter which is held in the water column of a stream, river, lake or reservoir by turbulence [START_REF] Bilotta | Understanding the influence of suspended solids on water quality and aquatic biota[END_REF]. They originate from different processes such as soil erosion due to surface runoff or bank and bed erosion. Thus, the SS characteristics highly depend on catchment's geophysical and entropic characteristics as well as seasonal river flow variation [START_REF] Ongley | Physical and geochemical characteristics of suspended solids, Wilton Creek, Ontario[END_REF] (Table 2). SS are relevant to consider because pesticides are likely to interact with it (sorption) [START_REF] Weber | Sorption of hydrophobic compounds by sediments, soils and suspended solids-II. Sorbent evaluation studies[END_REF].

Sediment compartment

The sediment compartment is a porous media composed of a solid phase (aggregated and trapped SS) and a liquid phase (interstitial water). Geochemistry of the interstitial porewater significantly differs from overlying water (Higher DO gradient [START_REF] Shrestha | Simulation Studies to Explore Biodegradation in Water-Sediment Systems: From OECD 308 to OECD 309[END_REF][START_REF] Wang | Microscale chemical features of sediment-water interface in Hongfeng Lake[END_REF], higher bacterial activity, different concentrations in nutrients...). On this basis, it "is deeply involved in the partitioning of pesticide to sediment." [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF].

Liquid phase: interstitial water

Parameters describing the interstitial porewater are equivalent to the overlying water. Nonetheless, mean values and ranges significantly differ and face higher heterogeneity within the sediment column (e.g. higher organic matter content and lower DO concentrations due to bacterial activity).

Solid phase: sediment

Solid phase is mainly described via physical and geological parameters. Given that sediment is composed of aggregated grains of SS, structural parameters are included in its description (Table 4).

𝛕 (%)

Tortuosity: "Ratio between the real flow path length and the straight distance between the two points of the soil" [START_REF] Kutílek | Soil hydrology[END_REF] τ = P 1 3 [START_REF] Millington | Permeability of porous solids[END_REF] ω (%) Water content: Ratio between volume of water contained in the soil and total volume of soil Sediment = saturated media  ω = 100%

Additional compartments

Depending on the scale and the degree of complexity of the study, it may be relevant to integrate additional compartments to the representation. Several authors attempted to integrate bioaccumulative compartments such as aquatic plants [START_REF] Diepens | Uptake, translocation, and elimination in sediment-rooted macrophytes: a model-supported analysis of whole sediment test data[END_REF] or biotic organisms [START_REF] Webster | Development and application of models of chemical fate in Canada[END_REF]. In addition, because compartments such as atmosphere or underground water are believed to play a prominent part in large-scale transportation of micropollutants, they are often studied as pollutant input in rivers (see Water -sediment models overview).

This description highlights the complexity and the heterogeneity of the water-sediment interface. Thus, the representation of the interface has to integrate this variability via a multicompartmental and multiphasic description. These considerations bring us to wonder which of these parameters are involved in pesticide degradation, and in what extent?

Influence of destructive and non-destructive process

The "partitioning" of micropollutants within the water-sediment interface involves both nondestructive and destructive processes. Furthermore, pollutant degradation might be either biotic (mediated by microorganism) or abiotic (driven by chemical or photochemical reactions) [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF].

Destructive processes

According to the United States Environmental Protection Agency (EPA), destructive processes refer to "chemical or biological breakdown of a complex compound into simpler compounds". Hence, degradation often leads to a "loss of specific properties" and the rise of potentially hazardous transformation products [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF][START_REF] Porto | Biodegradation of Pesticides[END_REF].

Destructive processes account for both biotic and abiotic degradation. These two types of degradation differ in terms of mechanisms, controlling factors and kinetics.

 Biotic processes are usually assumed to be predominant route of degradation in the environment. Through biotransformation and potentially mineralization, pesticides might be used by chimio-organotrophes bacteria as an energy source for bacterial growth, or transformed through co-metabolism as a side effect of enzyme activity [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF][START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF]. Because biodegradation may results from a plethoric diversity of bacterial communities and enzymes activities, rates and pathways of degradation are various and difficult to predict in the environment [START_REF] Porto | Biodegradation of Pesticides[END_REF][START_REF] Schwarzenbach | The Challenge of Micropollutants in Aquatic Systems[END_REF]. However, depending on the environmental conditions (oxic, anoxic) and on molecule chemical structures, oxidative (e.g. dealkylation, hydrolysis) or reductive (e.g. dechlorination, dehalogenation) reactions are expected [START_REF] Elsner | Compound-specific isotope analysis (CSIA) of micropollutants in the environment -current developments and future challenges[END_REF][START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF][START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF].

 Abiotic processes are mediated by hydrolysis, redox reactions or photolytic reactions.

Although abiotic and biotic degradation mechanisms are different, degradation pathways and TP products might be similar [START_REF] Honti | Deriving Persistence Indicators from Regulatory Water-Sediment Studies -Opportunities and Limitations in OECD 308 Data[END_REF].

Influencing factors are often well identified and easily measured in the environment (e.g. temperature, pH, light, DOC) [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF]. Then, relationships between physicochemical parameters and degradation rates can be set up.

Note that [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF] explicitly identify 𝑝 𝐻 , Dissolved Organic Carbon (𝐷𝑂𝐶), Particulate Organic Carbon (𝑃𝑂𝐶) and Temperature as main factors influencing destructive processes within the watersediment interface.

Non-destructive process

On the other hand, non-destructive process do not lead to pollutant mass reduction. Pollutant is partially moved from one compartment (or phase) to another without creation of Transformation Product (TP). Diffusion and sorption represent the main non-destructive process and are driven by concentration gradient and environmental matrix properties. Similarly to destructive processes, intercompartment transfers are likely to results in a decrease in pollutant concentration within specific compartments but does not result from pollutant mass reduction.

Previous considerations show that in terms of concentrations, destructive and non-destructive processes may have similar effects and then can't be detangled unless combining concentration monitoring (GC/MS) with mass balance modelling. However, mass balance approach is hard to achieve in situ and is not suitable for determining contribution of each processes among the wide panel of destructive mechanism. In this way, the use Compound Specific Isotope Analysis (CSIA) becomes relevant [START_REF] Honti | Deriving Persistence Indicators from Regulatory Water-Sediment Studies -Opportunities and Limitations in OECD 308 Data[END_REF].

Introduction to Compound Specific Isotope Analysis

Nowadays, CSIA is a well handled and efficient tool for "proving, characterizing and assessing degradation of industrial organic pollutants within contaminated aquifers" [START_REF] Lutz | A modelbased assessment of the potential use of compound-specific stable isotope analysis in river monitoring of diffuse pesticide pollution[END_REF][START_REF] Thullner | Quantification of organic pollutant degradation in contaminated aquifers using compound specific stable isotope analysis -Review of recent developments[END_REF] that has rarely been applied to pesticides due to both analytical and conceptual constraints. Because CSIA makes possible to detect degradation without mass balance or metabolites measurement [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF], [START_REF] Lutz | A modelbased assessment of the potential use of compound-specific stable isotope analysis in river monitoring of diffuse pesticide pollution[END_REF] suggests to deploy CSIA to surface water. However, assessing routes, rates and fraction of degradations required CSIA data to be measured for each compound under specific conditions. Data are available in the literature for historical groundwater pollutants (hydrocarbons). At the opposite, for more recent molecules such as pesticides, data are still lacking. [START_REF] Elsner | Compound-specific isotope analysis (CSIA) of micropollutants in the environment -current developments and future challenges[END_REF] reviewed the very first available values of isotope fractionation for several organic compounds from herbicides to insecticides via TPs, mostly in lab and controlled experimental systems.

CSIA "relies on the observation of shifts in ratios of stable isotopes for carbon (...) that are involved in the breakage or generation of chemical bonds during the degradation of organic contaminants [START_REF] Meckenstock | Stable isotope fractionation analysis as a tool to monitor biodegradation in contaminated acquifers[END_REF]". In other words, when degradation occurs, lower energy bonds (involving light isotopes) are broken first, resulting in an enrichment of heavy isotopes within the remaining fraction (Figure 5). Thus, an increase in 𝛿 13 𝐶 = 𝐶 13 𝐶 12 isotope ratios in a parent compounds provide evidences of its degradation [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF].

existing between pesticide degradation and Carbon heavy isotope enrichment (Rayleigh equation). Example extracted from hydrolysis experiment dataset for Alachlor (this study).

The Rayleigh equation is used to correlate the variations in isotopic ratio to the degraded fraction (1):

𝐥𝐧( 𝜹 𝟏𝟑 𝑪 𝒕 𝜹 𝟏𝟑 𝑪 𝟎 ) = (𝛂 -𝟏) * 𝐥𝐧 ( 𝑪 𝒕 𝑪 𝟎 ) (1)
Where 𝐶 𝑡 is the concentration of light and heavy carbon at 𝑡𝑖𝑚𝑒 = 𝑡 and 𝛼 -1 = 𝜖, the enrichment factor in ‰, specific to each compound under defined conditions. Thanks to this formalism, we are capable of quantifying degradation in the environment without mass balance measurement (initial 𝛿 13 𝐶 0 and 𝜖 are sufficient input data).

Moreover, because different destructive processes show specific isotopic fractionation magnitudes, it is possible to detangle and to identify processes responsible for degradation. Destructive and nondestructive processes are also easily discriminated (non-destructive processes are believed not to fractionate).

However, because environmental matrixes are complex, several destructive processes are likely to simultaneously take place. In this case, 2D CSIA (e.g. carbon and nitrogen) could be useful to discriminate the simultaneous processes [START_REF] Elsayed | Using compound-specific isotope analysis to assess the degradation of chloroacetanilide herbicides in labscale wetlands[END_REF].

Considering the complexity of natural aquatic systems (matrix heterogeneity, non-steady state conditions, time dependency ...), CSIA measurements may become difficult to reach when applied in situ. In this way, reactive transport models incorporating isotope fractionation can help for interpretation of isotope ratios on the field scale". Moreover, event-based studies at larger spatial and longer time scales may be conducted, supporting enhanced understanding of pesticide behaviour within aquatic systems [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF].

Modelling the water-sediment interface: state of the art

The gap between current knowledge and natural functioning of the water -sediment interface is wide. [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF] and [START_REF] Meybeck | Carbon, nitrogen, and phosphorus transport by world rivers. Meybeck, M[END_REF] describe the water-sediment interface as an heterogeneous system composed of two interdependent and multiphase compartments, with high spatial and temporal variability and involving numerous processes controlling pesticides degradation. At the opposite, [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF] shows that current representation of the interface is more simplistic. "Beyond the outcome of regulatory testing, current approaches are limited in their ability to," mechanistically understand involved processes and to assess prevailing ones among others. In other words, up to now, water -sediment interface is studied under specific conditions and in controlled environment. In addition, current lab scale experiments do not allow us to individually assess the role played by each process. However, as suggested by [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF] and [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF], laboratory scale experiments might prove useful for deriving CSIA indicators and understanding pesticide behaviour if regulatory protocols are improved (EFSA, 2015;[START_REF] Honti | Deriving Persistence Indicators from Regulatory Water-Sediment Studies -Opportunities and Limitations in OECD 308 Data[END_REF]. An efficient approach will then consist in coupling enhanced lab-scale experiment with numerical modelling. Indeed, complex interactions can be numerically solved and suited laboratory scale experiments will bring reliable data for model calibration.

In order to design the best suited modelling tool, prerequisites for model structure are derived from the previous considerations:

o The model is multi-compartmental in a bid to assess with confidence the inter-compartment exchanges alongside the water sediment column;

o Vertical discretisation of the column is required in order to represent depth dependent variations;

o Destructive and non-destructive processes (biotic and abiotic) are covered; o CSIA must be integrated in order to detangle the numerous degradation pathways; o Mechanistic understanding of pesticide behaviour requires a physically based model. In this way, factors controlling degradation and transportation are more easily measured at experiment or catchment scale than conceptual parameters;

o According to the pesticides properties (notably degradation rates, see Table 8), a daily or hourly time step is highly recommended and continuous simulation will be helpful to evaluate pesticide fate over an agricultural season or years for example;

The aim of this discussion is to determine whether or not a model complying with our requirements is already available. A comparison of existing models is realised to highlight the upsides or lacks of current tools and to lead us to the best suited model design.

Water -sediment models overview

The following state of the art relies on a comparison of existing models according to the methodology proposed by [START_REF] Quilbe | Selecting a pesticide fate model at the watershed scale using a multi-criteria analysis[END_REF], based on a multi-criteria analysis considering 3 aspects : model purposes, model characteristics and model applicability.

model purposes can be distinguished:

o Research models  They represent all the known processes with high accuracy. o Management models  Thanks to a convenient user interface, they provide stakeholders with relevant information to make a choice. Note that these models are sometimes also designed for research purposes.

o Screening models  They offer an easy way to assess the general behaviour of a pesticide within a specific environment.

o Multimedia models  Often based on the fugacity concept, they offer a representation of the environment in compartment. Numerous models designed for specific purposes are available in the literature. We focused on 9 of them, covering a wide range of characteristics. Because some models were either described through specific applications or thanks to the user's manual, information were cross checked in a bid to strengthen the analysis.

1/Model purposes

Five in nine of the selected models are multimedia fugacity models (Table 5). This approach is usefull as a first approximation at large scale [START_REF] Quilbe | Selecting a pesticide fate model at the watershed scale using a multi-criteria analysis[END_REF], but can only account for the chemical transfer between large regions [START_REF] Pistocchi | Spatially explicit multimedia fate models for pollutants in Europe: State of the art and perspectives[END_REF]. EQC and ChemRANGE both are the simplest form of multimedia model whereas ChemCAN and especially CalTOX and GB-PMBM are the more advanced version of multimedia fugacity models (level III and IV). Note that according to the Ministère de l'Environnement de l'Energie et de la Mer (MEEM) [START_REF] Bonnard | Le logiciel de calcul CALTOX (Ministère de l'Ecologie et du Développement Durable)[END_REF], CalTOX is frequently used to assess population exposure to pollutant, especially in France.

CalTOX X > 10 -3 Lumped Compartmental (0D) X (<40) - CE-QUAL- W2 X Catchment scale Lumped Compartmental (with subdivisions, 0.5D) X (>100) - ChemCAN X 10 4 < 𝑆 < 10 6 Lumped Compartmental (0D) - X (<40) ChemRAN GE X World Semi distributed Compartmental (0D) - X (<30) EQC X 10 6 Lumped Compartmental (0D) - X (<30) GB-PMBM X 10 4 < 𝑆 < 10 6 Semi distributed (grid) Compartmental (0D) - X (~60) InCa X X > 1 Semi distributed (river sections) 0D X (?) - PegOpera X 10 < 𝑆 < 10 4 Semi distributed (river sections) 0D X (?) - QUAL2EU X
Catchment scale (from local to regional/national) Semi distributed (river sections) 0D X (>100) -4 of them (except GB-PMBM -Level IV) operate in steady state conditions considering "inter-and intra-media transfer rates, as representative values constant in time, which hampers the possibility of capturing mechanisms of transfer strongly dependent on time variations of environmental processes which may be very relevant [START_REF] Lammel | Multicompartmental fate of persistent substances. Comparison of predictions from multi-media box models and a multicompartment chemistryatmospheric transport model[END_REF]" [START_REF] Pistocchi | Spatially explicit multimedia fate models for pollutants in Europe: State of the art and perspectives[END_REF].

Fugacity models are suited for large scale studies and optimal spatial distribution of model domain ranges from catchment to word size (e.g. GB-PMBM  ~400 𝑘𝑚 2 grid cell [START_REF] Tian | Modelling historical budget of alphahexachlorocyclohexane in Taihu Lake, China[END_REF] or ChemRange  ring of boxes aligned around the globe [START_REF] Lammel | Multicompartmental fate of persistent substances. Comparison of predictions from multi-media box models and a multicompartment chemistryatmospheric transport model[END_REF]). These divisions allow users to study larger zone and to apply different parameters depending on environment variation.

Multi-media fugacity models have high degree of simplification in describing spatial variation of landscape and time variation. It shouldn't be seen as a realistic type of model but as an evaluative way to describe coarse variations in pesticide concentrations [START_REF] Mackay | An introduction to multimedia models[END_REF].

For the 4 physically based models, selected processes are represented with physical formalism (e.g. Fick's law, Monod's law, Langmuir's isotherm …). Required parameters have physical meaning and are measurable in-situ or in laboratory. Then, they can be easily adjusted with time and space making physically based models more suitable for dynamic and distributed studies. However, model parametrization requires much more input data than fugacity models. None of the selected models are vertically distributed, and compartments (air, water and sediment) are considered as homogeneous within the entire column (except CE-QUAL-W2 and InCa models, respectively subdividing the water column in epilimnion, thermocline and hypolimnion and the sediment layer).

Although fully distributed models are powerful, they are more complex to implement and calibrate than lumped models. Their massive needs in input data and in computational time make them less suitable for this study study [START_REF] Quilbe | Selecting a pesticide fate model at the watershed scale using a multi-criteria analysis[END_REF]. In addition, their complexity is likely to increase when numerous processes are taking into account.

To summarize this section, the selected fugacity models are not suited to our study because of their high degree of simplification. In addition, most advanced physically based models might reveal too complex to calibrate with few input data. In addition, in both multimedia and physically based models, considering compartments as homogeneous layer with depth hampers the accurate representation of prevailing processes within the thin water -sediment interface. The optimal model lays between these two types of models, coupling a compartmental division/subdivision of the interface with a physically based representation of relevant processes. Such model thus needs to be developed.

4/Processes to model

According to [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF], "the model to be used should scientifically reflect the observed degradation pathway of a pesticide by focusing on significant paths while avoiding overparametrization". Moreover, "additional complexity will generally require additional numbers of parameters to be defined, the values of which will require calibration" and then additional data to collect [START_REF] Beven | A manifesto for the equifinality thesis[END_REF]. Then, the choice of the relevant processes to model is essential to ensure the reliability and the simplicity of the model.

Processes

Numbers of model integrating the process

Surface water

Water cycle

Physical

Flowing water 6

Runoff 6

Evaporation 2

Percolation 1

Lateral diffuse runoff 1

Biogeochemical

Eutrophication cycle 4

Pesticide cycle

Physical

Advective exchanges 7

Water/air partitioning 9

Fractionation 3 Sorption 5

Settling 7

Photolysis 6

Biological

Biodegradation 8

Chemical

Hydrolysis 8

Sediment

Pesticide cycle Physical

Water/sediment diffusion 6

Sorption 5

Re-suspension 5

Ageing 3

Hydrolysis 7

Lixiviation 3

Table 7 summarises the most frequently used processes among the selection of models (complete and detailed table available in Appendix 1). It leads us to pinpoint the most relevant processes to model. Then, in surface water, factors controlling the rapid transportation of pollutant should be implemented: hydrological cycle, advective exchanges and SS settling/resuspension. In addition, due to its substantial influence on physicochemical conditions, it appeared significant to consider the eutrophication cycle. Photolysis, hydrolysis and biodegradation revealed to be the most used destructive processes. In the other hand, in sediment, settling/resuspension and diffusion accounted for interactions between sediment and surface water. Diffusion was also used to represent transfers through the sediment layer. In the end, biodegradation and hydrolysis should be used as destructive processes

In several models, supplementary compartments are represented; atmosphere, underground water, soil, biomass (aquatic plants and fish). Because these compartments do not to play a prominent role in pesticide fate within the water -sediment interface, they are not included here in a preliminary step. Nonetheless, they might be represented as external sources of pollutant. Indeed, the atmosphere compartment is for example believed to be the main pathway for long range transport of pollutants over the world (UNEP).

It is worth noting that some models first designed to work with conventional pollutants (nutrients, heavy metals …) can be easily adapted to emerging micro-pollutant as shown in [START_REF] Deliège | PEGASE, an integrated river/basin model dedicated to surface water quality assessment: application to cocaine[END_REF] where cocaine's behaviour in surface water was described with PegOpera.

None of these 9 models integrates CSIA analyses. Due to equifinality, authors are often not capable of detangling which degradation processes or transport pathways are responsible for pollutant removal. "The fact that more than one combination of model equations and parameters yield equally satisfactory results" [START_REF] Beven | A manifesto for the equifinality thesis[END_REF], hinders modellers from achieving a comprehensive contaminant behaviour.

Model designing conclusions

Previous considerations advocate for the use of a physically based and compartmental model including processes mentioned in Table 7. A new model was designed because no suitable model was already available in the literature.

Here, we should distinguish the final version of the model which will results from my future thesis work and the preliminary version of this model which is presented in this work. Then, the final version of this model will integrate the selected processes and compartments shown in Figure 6. For each process, formalism will be implemented in accordance with laboratory experiments. In this way, complete model parametrization is possible and equifinality issue tackled.

The preliminary work presented here, has been restricted to the assessment of pesticide fate within the water -sediment interface under specific but relevant conditions:

 Static environments as lakes or ponds (no dynamic system as rivers) is considered because hydrodynamic would have required to implement very complicated tool.

 Transportation processes have been reduced to diffusion in accordance with the static representation of the interface.

 Destructive processes focused on hydrolysis because it is referenced as an important process to consider and because time scale of the laboratory experiment was suitable with the time dedicated to this work.

 Non-destructive processes were reduced to sorption/desorption/ageing because it is assiduously studied worldwide and notably in the LHyGeS and because ageing was suspected to play one of the most prominent but hidden role within the interface.

Additional destructive processes such as photolysis, biodegradation and biogeochemical cycle have been discussed but are not implemented yet.

Scientific questions, objectives and overall approach

According to the previous considerations, it appears crucial to evaluate the behaviour of pesticides within the water-sediment column. Although current methods for assessing pesticides behaviour insitu are already developed, they are not fully suited for water-sediment interface studies. Moreover, they do not allow to mechanistically understand the fate of pesticides and then to more accurately predict their dynamics.

Therefore, this work wish to address the following questions:

 What are the main pathways of pesticides degradation within the water -sediment interface?  How can CSIA measurements and numerical modelling help for process-based interpretation of pesticide fate within the water -sediment interface?

The main objective of this work was then to develop a reactive model for process-based interpretation of pesticide fate within the water -sediment interface. To achieve this objective we relied on an innovative way of modelling in co-designing laboratory scale experiments with model implementation.

The pre-selection of relevant processes to be modelled gives an overview of the system functioning. Then, potential mathematical formalisms will be investigated in accordance with experimental capabilities. Model implementation will incorporate experimental designing and results from individual experiments. The experimental results will be confronted with model simulation to evaluate the goodness of the representation at the water-sediment interface.

II/ Material and methods

1) Studied pesticides

As shown in the Study context paragraph, PPP have become a worldwide issue of increasing concern for human health and environment. Studied pesticides were chosen to represent a wide range of environmental behaviours (hydrophobicity, solubility, etc), include mainly pesticide of the widely used class of aniline pesticide and based on their occurrence in both surface and ground-water worldwide. Moreover, analytical methods had to be already developed in laboratory for selected molecules.

Structural description

Six anilines (Acetochlor, Alachlor, Butachlor, Metalaxyl, S-Metolachlor, Pendimethalin) and 1 triazine (Atrazine) molecules were selected in the experimental studies (Table 5); and. This panel of pesticides covers a wide range of chemical family, uses (herbicides and fungicides), degradation and transportation behaviours (Table 8). Persistence (sediment-water half life, 𝐷𝑇 50 ) and hydrophobicity respectively represent the capabilities of a chemical to sustainably remain at the interface or to percolate through the water table.

Among this panel Alachlor and Atrazine are classified as priority substances by the directive 2013/39/eu of the WFD. In addition, between 2009 and 2013, S-Metolachlor and Atrazine ranked 5 th and 11 th in French's top 15 most frequently measured pesticides in surface water (Commissariat général au développement durable, 2015). Although atrazine has been forbidden in France since 2003, Atrazine's transformation product (TP) (desethylatrazine) is one of the most frequently found pesticide in surface water since 2009. Even if TPs are becoming better identified, their behaviours under environmental conditions have still not been investigated extensively [START_REF] Gutowski | A comparative assessment of the transformation products of S-metolachlor and its commercial product Mercantor Gold(®) and their fate in the aquatic environment by employing a combination of experimental and in silico methods[END_REF][START_REF] Porto | Biodegradation of Pesticides[END_REF].

Chemical description of the studied pollutants is relevant because it provides first insight on the possible pathways of degradation. Indeed, destructive processes are believed to be driven by 1) environmental conditions and 2) structural affinity of pollutants to specific transformations [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF]. Then, specific transformations require to be identified and described to investigate the fate of pesticides in the environment.

2) Model framework

As presented in the state of the art, a physically based multimedia model is used. The interface is represented through two vertically discretized compartments: surface water and sediment. It accounts for static environment where diffusive processes prevail and includes both destructive and conservative processes (hydrolysis and sorption/desorption/ageing).

The model computes the non-steady state equation of mass balance within both compartments. Production and degradation terms respectively represents pollutant input (continuous or event contamination) and pollutant degradation. Retroactions on state variables are not already implemented at this stage but are intended to be in the future.

The choice of a physically based model induced an important effort of parameterization. In this way, experiments were designed to derive ranges for these parameters, and in the other way, formalisms were selected to involve only measurable or easily derivable parameters. Thanks to this coupled approach, model will be easily adapted to different situations.

Mass balance equation

The mass balance equation (Eq. 2) is computed within each compartment for each time step:

𝒅𝑪 𝒊 𝒅𝒕 (𝒛, 𝒕) = 𝒅𝒊𝒇𝒇𝒖𝒔𝒊𝒐𝒏(𝒛, 𝒕) ± 𝚽(𝐳, 𝐭) (2)
𝐶 𝑖 is the pesticide concentration (𝑚𝑔/𝐿 or 𝑚𝑔/𝑔) whether in the water compartment (𝑖 = 𝑤) or in the sediment compartment ( 𝑖 = 𝑠 ), then 𝐶 𝑡𝑜𝑡 = 𝐶 𝑤 + 𝐶 𝑠 . Moreover, because both compartments are composed of solid and liquid phase, we note 𝐶 𝑖 𝑙 (resp. 𝐶 𝑖 𝑠 ) the concentrations of pollutant in liquid phase (resp. in solid phase) for compartment 𝑖, in other words 𝐶 𝑖 = 𝐶 𝑖 𝑙 + 𝐶 𝑖 𝑠 .

Pollutant diffusion

Molecular diffusion is the only transport process of chemicals through compartments considered in this study. Considering the huge spatial variability of reaction kinetics within the watersediment column, it becomes of importance to properly assess how deep and fast a chemical will move through the column after a contamination event Fick's law (Eq. 3) is used to model pollutant diffusion through water and sediment.

𝒅𝑪 𝒊 𝒅𝒕 = 𝑫 𝒋,𝒊 𝒅 𝟐 𝑪 𝒊 𝒅𝒛 𝟐 (3)
𝐷 𝑗,𝑖 is the Fick's diffusion coefficient (𝑚 2 /𝑠) for the compound 𝑗 in compartment 𝑖. This value is theoretically calculated with the following equation [START_REF] Schwarzenbach | Environmental Organic Chemistry / Edition[END_REF]:

𝐷 𝑤𝑎𝑡𝑒𝑟 =
13.26 * 10 -5 𝜂 1.14 * 𝑉 0.589 , with { 𝜂 = 𝐷𝑦𝑛𝑎𝑚𝑖𝑐 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 (𝑘𝑔. 𝑚 -1 . 𝑠 -1 ) 𝑉 = 𝑀𝑜𝑙𝑎𝑟 𝑣𝑜𝑙𝑢𝑚𝑒 (𝑐𝑚 3 . 𝑚𝑜𝑙 -1 ) (4)

According to [START_REF] Li | Accuracy of Empirical Correlations for Estimating Diffusion Coefficients in Aqueous Organic Mixtures[END_REF], this empirical correlation accounting for water viscosity and molecule's size is accurate in aqueous mixtures for organic compounds.

In porous media, 𝐷 𝑤𝑎𝑡𝑒𝑟 is corrected with porosity and tortuosity (𝜏) [START_REF] Millington | Permeability of porous solids[END_REF]:

𝐷 𝑝𝑜𝑟𝑜𝑢𝑠 = 𝐷 𝑤𝑎𝑡𝑒𝑟 * 𝑃 * 𝜏 2 , and for saturated media 𝜏 = 𝑃 1 3

According to [START_REF] Van Beinum | Pesticide Sorption and Diffusion in Natural Clay Loam Aggregates[END_REF] "diffusion of small solutes in the aggregates can be described by pore diffusion with a theoretical tortuosity" with accuracy if "there is no additional constrictivity caused by the molecular size of the pesticide". Moreover, this correction is used in others RTM as Min3P for example.

Pollutant availability: Adsorption/desorption/ageing "The fate of pesticides after application onto a field is highly controlled by the extent of interaction with the soil. Sorption onto the soil matrix controls the availability of the compound for transport to surface waters and groundwater" [START_REF] Van Beinum | Pesticide Sorption and Diffusion in Natural Clay Loam Aggregates[END_REF]. Because sorption is known to be quicker than numerous destructive processes, it is likely to mitigate pollutant concentration available for biodegradation, hydrolysis or photolysis [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF]. As a result, not implementing sorption in the model would potentially leads to overestimate the final degraded pollutant mass.

Sorption used to be represented as a thermodynamic equilibrium between a dissolved phase and a solid phase. However, since several authors observed an increase in the apparent sorption coefficient over time, it is necessary to incorporate non equilibrium terms to the traditional formalism [START_REF] Barriuso | Solvent extraction characterization of bioavailability of atrazine residues in soils[END_REF][START_REF] Gulkowska | Time-dependent sorption of two novel fungicides in soils within a regulatory framework[END_REF]. In this way, [START_REF] Wauchope | Pesticide soil sorption parameters: theory, measurement, uses, limitations and reliability[END_REF] suggests that there are at least three time scales involved in sorption; A fast sorption (equilibrium sorption) occurring during the first minutes to hours (24h), a slower sorption (time dependent sorption) lasting for hours to days and finally a very slow process (from weeks to years) referred to as ageing (Figure 7).

"Two sites one rate" (Figure 7) and equivalent methods are the most widespread numerical schemes developed in accordance with the previous description (EFSA, 2015). The guidance on how aged sorption studies for pesticides should be conducted, analysed and used in regulatory assessments sorption studies (EFSA, 2015) were proposed and successfully applied on two novel fungicides (penflufen and fluxapyroxad) by [START_REF] Gulkowska | Time-dependent sorption of two novel fungicides in soils within a regulatory framework[END_REF]. Earlier, a similar numerical formalism and experimental protocol accurately assessed bioavailability of persistent organic pollutant in soil [START_REF] Fragoulis | A model assessing bioavailability of persistent organic pollutants in soil[END_REF].

Sorption mass balance (Eq. 5) is implemented to distribute pollutant fraction among the 4 boxes. In this way, pesticide is made available or unavailable for degradation and transportation.

Equilibrium sorption (Eq. 6): This compartment account for reversible exchanges between the liquid phase and the solid phase. It relies on the Freundlich's adsorption isotherm since it provides satisfactory results for thermodynamic sorption/desorption [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF] Where 𝑞 𝑖 𝑒𝑞 is the amount of pollutant sorbed in the compartment 𝑖 (𝑚𝑔/𝑔) at the equilibrium, 𝐾 𝐹 𝐸𝑄 is the equilibrium Freundlich constant and Langmuir's relationship are implemented in case they prove more successful than Freundlich isotherm.

Time dependent sorption (Eq. 7) shows lower ability for sorption. Mathematical coefficients are used to slow down the process (𝑘 𝑑𝑒𝑠 < 1) as well as to mitigate the final sorbed quantity (negative term in the differential equation).

Aged fraction and NER formation (Eq. 8): Depending on the authors, this compartment might be used either to represent pesticide degradation during the aged sorption study (EFSA, 2015) or to represent degradation and the formation of non-extractable residues [START_REF] Gulkowska | Time-dependent sorption of two novel fungicides in soils within a regulatory framework[END_REF]. In both cases it leads to an irreversible decrease in available mass of pesticides represented via a first order kinetic:

With 𝒒 𝑨𝒈𝒆𝒅 = ∫ 𝒅𝑴 𝑷 𝒅𝒕 𝒅𝒕, the quantity of aged pollutant.

Destructive processes

Hydrolysis (Eq. 9) is described via a first order removal kinetics with dependency on 𝑝 𝐻 and temperature [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF].

𝑪 𝒊 𝒍 (𝒕) = 𝑪 𝒊 𝟎 𝒍 * 𝐞 -𝐤 𝐡𝐲𝐝𝐫𝐨𝐥𝐲𝐬𝐢𝐬 * 𝐭 (9)
Temperature, 𝑝𝐻 and humic substances (𝐷𝑂𝐶) are believed to have strong influences on the hydrolysis rate of organic pollutants [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF][START_REF] Kuivila | Degradation Rates of Six Pesticides in Water from the Sacramento River, California By[END_REF]Liqiang et al., 1994) (Eq. 10).

𝑙𝑜𝑔 [𝑘] = 𝑘 𝐻 3 𝑂 + [𝐻 3 𝑂 + ] + 𝑘 𝑂 [𝐻 2 𝑂] + 𝑘 𝑂𝐻 -[𝑂𝐻 -] 𝑘 ℎ𝑦𝑑𝑟𝑜𝑙𝑦𝑠𝑖𝑠 = ∑ 𝐴 𝑖 * 𝑒 -𝐵 𝑖 𝑇 𝑖∈[𝐻 + ,𝐻 2 𝑂,𝑂𝐻 -] (10)
With 𝑘 𝐻 3 𝑂 + (resp. 𝑘 𝑂 , 𝑘 𝑂𝐻 -) defined as the specific acid (resp. neutral and basic) catalyzed hydrolysis rate. The Arrhenius law is used for temperature dependency with 𝐴 𝑋 the preexponential factor and 𝐸 𝑎 the activation energy expressed in 𝐽. 𝑚𝑜𝑙 -1 (both characteristic of the studied pollutant and reaction). Hydrolysis calibration will then requires several 𝑝𝐻, temperature and 𝐷𝑂𝐶 concentrations to be tested.

𝒅𝒒 𝒊

Future processes to be implemented

This study preliminarily covers hydrolysis as degradative process. Investigations of the impact other major processes (settling/resuspension, photolysis, biodegradation and eutrophication cycle) have been conducted but are not presented here as a main result. However, because they were identified to play a prominent role in pesticide degradation within the water-sediment interface, discussions on these processes are reported in Appendix 2.

Carbon stable isotope ratios

As recommended by [START_REF] Alvarez | Bottom sediment as a source of organic contaminants in Lake Mead, Nevada, USA[END_REF] Then (1 + 𝜖) represents the "difference between the reaction rates for light and heavy isotope" [START_REF] Alvarez-Zaldívar | Biogeochemical modelling of in situ biodegradation and stable isotope fractionation of intermediate chloroethenes in a horizontal subsurface flow wetland[END_REF].

In the document, Carbon isotope compositions are expressed in 𝐶 13 𝛿 = 𝑅 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 -𝑅 𝑅 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 with 𝑅 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 = 𝑅 𝑉𝑃𝐷𝐵 = 0.011237.

Model's conceptual scheme

The selected processes have then to be distributed in the different compartments where they may take place. The Figure 8 shows the potential inter-compartments fluxes of pollutant (non-destructive processes) and the processes involved in mass reduction (destructive processes). It highlights the predominance sorption which is likely to take place in each of the four compartments (Figure 8).

3) Modelling environment

Numerous open source programming languages could be used to implement the selected formalism; Visual Basic for Application (VBA), FORmula TRAnslator (FORTRAN), C … However, these languages require numerical integration scheme to be implemented (Euler explicit/implicit, Runge Kutta 2/4 …) as well as a strict prioritisation of processes. Nonetheless, when well established, they might prove really efficient and convenient. Due to this, and as a first in watersediment modelling we decided to use the closed source software VENSIM®, designed to study dynamic systems (population model, financial modelling …).

VENSIM® is a convenient modelling environment for system dynamics in several respects. Several numerical integration schemes are implemented (from Euler implicit to RK4). Automatic calibration (sum of the differences between computed variable and measured data) and Monte Carlo sensitivity analysis are natively embedded. Live connections with Microsoft Excel® allows to easily set up the model without using VENSIM®'s toolboxes. Graphical interpretation of simulations can be immediately performed within the software but export of output data to Excel is also possible for deeper analyses.

Designing system dynamics in VENSIM® allows to deal with high level nonlinear problems. In this way, It has already been applied in numerous fields as various as energy producing strategies, hydrological systems or even eutrophication models [START_REF] Afshar | Development of a Complex System Dynamic Eutrophication Model: Application to Karkheh Reservoir[END_REF][START_REF] Li | A system dynamics approach to a comprehensive assessment of water strategies: A case study of North China[END_REF].

However, this software only accounts for time discretisation. Spatial discretisation has to be artificially implemented using subscripts function (see Diffusion experiment paragraph). Nonetheless, VENSIM is not convenient and suitable to create a 2D mesh.

Figure 9 shows VENSIM's user interface with the sketch of the diffusion process. On view is associated to each process, easing the global overview. In VENSIM, boxes always represent integrated variables. Other variables are computed from equalities or represent input parameters (from excel sheet or implemented in VENSIM).

4) Experiments design and model implementation

In accordance with the time allowed to this work, only one lab-scale experiment focusing on hydrolysis was conducted (named hydrolysis experiment). In parallel and as a first approach, two in-silico simulations relying on lab scale experiments previously conducted by researchers in LHyGeS were designed (sorption experiment by Meite et al., in preparation and global experiment by Torabi et al., in preparation). In the end of this work the model will be suitable to predict pesticide fate in systems similar to Figure 10. Using these 4 experiments, model predictability were assessed for each studied process, i.e. hydrolysis, diffusion, degradation, sorption/desorption/ageing. Further investigations will lead me to design suited lab-scale experiments for each process during my PhD work which will follow the Master thesis.

The laboratory scale experiment conducted during this work allowed to derive half-life values and carbon isotope enrichment factors under specific conditions as well as to validate the first order degradation kinetic. 2 in 3 of the in-silico experiments relied on experimental data and aimed at 1) validating the sorption formalism and 2) validating the global model predictions. The last one was conducted in order to optimize the computation of diffusion.

Hydrolysis experiment

This experiment aims at deriving hydrolysis 𝐷𝑇 50 and 𝜖 depending on variations in 𝑝𝐻, temperature and 𝐷𝑂𝐶 concentration. Protocol from the Organisation for Economic Co-operation and Development (OECD) was adapted to our needs in order to derive valuable and universal parameters. Each parameter is individually studied (Figure 11).

According to [START_REF] Meybeck | Carbon, nitrogen, and phosphorus transport by world rivers. Meybeck, M[END_REF], "Dissolved Organic Carbon (𝐷𝑂𝐶) varies from 1 𝑚𝑔 𝐶 /𝐿 in the mountainous alpine environments to 20 𝑚𝑔 𝐶 /𝐿 in some Taiga rivers. The world DOC average is 5.75 𝑚𝑔 𝐶 /𝐿". Then, the range of 𝐷𝑂𝐶 concentrations studied is 0, 5, 10 and 20 𝑚𝑔 𝐶 /𝐿.

The OECD (2004) proposes a range of pH from 4 to 9. This range is wide enough to cover natural values. In Alsace, 𝑝𝐻 50 = 7.9 and 𝑝𝐻 10 = 7.4 and 𝑝𝐻 90 = 8.3 (AERM data analysis, between 2007 January and 2015 December). However, some pesticides are not significantly degraded under these conditions (i.e. atrazine between 4 and 10 [START_REF] Kuivila | Degradation Rates of Six Pesticides in Water from the Sacramento River, California By[END_REF][START_REF] Mill | Hydrolysis of Organic Chemicals[END_REF]). Hence the idea to widen the experiment from 𝑝𝐻 = 2 to 𝑝𝐻 = 12 via 𝑝𝐻 = 4, 7 and 9.

Studied temperatures were laboratory temperature and lower oven's temperature (𝑇 = 20 and 30°𝐶) even if this range is slightly higher than the temperature distribution in Alsace (AERM).

Experimental design

According to OECD ( 2004), the batch experiment is performed in 1𝐿 glass containers (avoid sorption) under dark (avoid photolysis) and sterile conditions (avoid biodegradation). In this way, brown Schott bottles are covered with aluminium foil and autoclaved. Buffered solutions were used to keep a constant 𝑝𝐻 all along the experiment (final 𝑝𝐻 were 2.11, 4.07, 7.10, 9.01, 12.21 ±0.01 ) . Buffered solution was filtered through a 0.22 𝜇𝑚 pore diameter Millipore membrane. 17.0, 36.7 and 70.1 ± 0.1 𝑚𝑔 𝐻𝑢𝑚𝑖𝑐 𝑎𝑐𝑖𝑑𝑠 of humic acid salts (Sigma® Humic acid sodium salt -technical grade -H16752) were dissolved in 0.1𝑀 𝑁𝑎𝑂𝐻 solution followed by 45 minutes sonication as recommended by [START_REF] Mazzuoli | The Analysis of the Seasonal, Spatial, and Compositional Distribution of Humic Substances in a Subtropical Shallow Lake[END_REF]. Final 𝐷𝑂𝐶 concentrations were 4.9, 10.7 and 20.3 ± 0.1 𝑚𝑔 𝐶 . 𝐿 -1 ). One pollutant concentration was tested for each compound (from 2.3 to 4.1 𝑚𝑔/). These concentrations are much higher than natural concentrations (from 𝑛𝑔. 𝐿 -1 to 𝜇𝑔. 𝐿 -1 , AERM data base) but were specifically set for CSIA quantification after 90% degradation. Pesticides used was Sigma-Aldrich® pure active compounds solution/powder (analytical grade purity > 95.9% , GC-area). In this way, interactions with adjuvant used in commercial formulations were enabled. Vials were incubated in temperature-controlled environments at 𝑇 = 20 ± 1°𝐶 and 𝑇 = 30 ± 1°𝐶. Vials were analysed in series (≠sacrificed over time) at variable sample times and each modality was duplicated.

Analytical methods

Solid-Phase Extraction (SPE) of a variable volume (from 20 to 60 𝑚𝐿 ) of experiment solution was carried out using SolEx C18 cartridges according to the chloroacetanilide extraction protocol developed by Wiegert et al., in preparation.

Pesticides concentrations were analysed in GC-MS consisting of a Gas Chromatograph coupled with a Mass Spectrometer (Thermo Fisher Scientific). The reproducibility of triplicate concentration measurements was < 20%.

Carbon isotope compositions were analysed in GC-IRMS consisting of a GC coupled with Isotopic Ratio Mass Spectrometer (Thermo Fischer Scientific, Appendix 3). The oxidation furnace of the . The reproducibility of carbon isotopic composition measurements was < 5%. 𝐶𝑂 2 reference gas was calibrated to VPDB standards.

Well characterised in-house pesticides mix standards with known concentrations and isotopic compositions were analysed at least each 12 injections to control the quality of measurements.

Diffusion experiment

VENSIM® do not natively handle spatial discretisation. However the diffusion equation (Eq. 3) depends on time and space. Then, in order to implement diffusion in VENSIM®, the use of subscripts was required. "Subscripts allow a single variable to represent more than one thing" (VENSIM® online support). For example, thanks to the subscript "isotopologue" the concentration in 𝐶 12 was computed in the exact same way that the concentration in 𝐶 13 (with different parameterization only). As regards the diffusion process, a subscript representing water or sediment horizon at different depth within the interface was created. In this way, VENSIM® was capable of computing pesticide exchange between layers as well as pesticide degradation or sorption for each layer.

Due to the use of subscripts to model the diffusion process, the adjustment of layer number is time consuming and formalism used to calculate exchange rate at each time step is simplistic. Then, this experiment aims at 1) determining whether or not the used formalism is suitable for diffusion calculation as well as 2) determining the number of layers required, depending on compounds ability to move through the column in order to optimize computing time and to ensure a good fit to theoretical mass balance.

Methodology and experimental design

The reference solution of the diffusion equation used to assess the goodness of the fit to mass balance is solved in Microsoft Excel 2010® with a maximum number of time step and layers while wide ranges are tested in VENSIM® (Table 9). In this way, a VBA code was implemented using a Forward-Time Central-Space method. 28, 56, 112, 225, 450, 900, 1800, 3600 30 Space discretization (cm) 3.3, 1.7, 0.8, 0.4, 0.2, 0.1 0.1

As previously seen, high exchange rate and high bacterial and chemical activities make the first centimetres of sediment very important in pesticide behaviour. Then the modelled domain is composed of 20 cm of sediment. The diffusion coefficient is set at 3.06 * 10 -7 𝑐𝑚 2 . 𝑠 -1 which correspond to the Atrazine diffusion coefficient calculated Eq. 4 and is corrected for saturated porous media thanks to Millington and Quirk's formula with 𝜏 = 𝑃 1 3 and 𝑃 = 45% (average porosity for silty/loamy soil [START_REF] Kutílek | Soil hydrology[END_REF]). Simulation time is set at 100 days (water-sediment 𝐷𝑇 50 of the Atrazine equals 80 days). Pollutant is continuously spiked (e.g. WWTP discharge) on top of the sediment layer with Dirichlet boundary condition set at 10 𝑚𝑔 𝑎𝑡𝑟𝑎𝑧𝑖𝑛𝑒 /𝐿. A Neumann's zero-flux condition is set at the bottom of the sediment layer. Initial conditions are ∀ 𝑙𝑎𝑦𝑒𝑟𝑠 (𝑒𝑥𝑐𝑒𝑝𝑡 𝑡𝑜𝑝 𝑙𝑎𝑦𝑒𝑟), 𝐶 𝑝𝑒𝑠𝑡𝑖𝑐𝑖𝑑𝑒 (𝑇 0 ) = 0 𝑚𝑔. 𝐿 -1 .

The reference solution is computed with a first order central difference in time and a second order central difference in space. In VENSIM®, time dependency is solve with Euler implicit integration scheme (exacerbate potential error in time and allows quicker computation) and space dependency with explicit backward difference. Two criteria are studied over time to assess the resolution efficiency:

 global mass balance error, ∑ (C i Excel -C i Vensim ) * (layer thickness)

Layer number i=1

 pollutant distribution in the end of the simulation.

Sorption/desorption experiment

The "two sites one rate" formalism has been previously validated in several publications and for different pesticides ((EFSA, 2015;[START_REF] Gulkowska | Time-dependent sorption of two novel fungicides in soils within a regulatory framework[END_REF]. We tested this module on a dataset issued from a soil degradation experiment conducted by Meite et al., in preparation. The uncertainty associated to the parameterization of the different compartments as well as the uncertainties associated to soil extraction methods will be discussed.

Experimental design

This laboratory soil experiment consisted in spiking a well characterised soil (Alteckendorf soil, silt 60.2%, Sand 24.2%, clay 15.6% and organic carbon 4.47%) with several pesticides (including Atrazine, Metalaxyl, S-Metolachlor and Pendimethalin) and heavy metals, and in monitoring their dissipation kinetics. We focused on the S-Metolachlor as it is consistent with the global experiment.

Both biotic and abiotic (sterilised) soil incubations were conducted in the dark, at 𝑇 = 20°𝐶 for 200 days with initial S-Metolachlor concentrations of 5 𝜇𝑔. 𝑔 𝑑𝑟𝑦 𝑠𝑜𝑖𝑙 -1

. As regards to the 𝑝𝐻 of soil solution no hydrolysis was assumed (see Hydrolysis experiment results). Then, in the abiotic blank experiment only sorption is likely to occur.

The soil was extracted with ethyl-acetate solvent (Wiegert et al., in preparation). Extraction recovery for S-Metolachlor in Alteckendorf soil at 40% of water content equals 21% (tested after 7 days of incubation).

Model parameterization

The extracted fraction associated to the protocol was not precisely characterised. Basically, 𝐶𝑎𝐶𝑙 2 extractions are believed to recover the equilibrium sorbed fraction and solvent extraction (methanol) to recover the equilibrium and the non-equilibrium fraction (see Results and discussions). Because ethyl-acetate soil extraction lies somewhere in between (mild solvent extraction) we assumed and tested the 2 following hypothesis (Eq. 11 and Eq. 13): According to EFSA ( 2015), default values used in the "two sites one rate" formalism were set at 0.300 for 𝑓 𝑛𝑒 and 0.0004 for 𝑘 𝑑𝑒𝑠 with constraining ranges from 0.001 to 100 for 𝑓 𝑛𝑒 and from 4 * 10 -6 to 0.0200 for 𝑘 𝑑𝑒𝑠 ("arbitrary but realist values"). While no initial value was proposed for 𝑘 𝑡 , default value was chosen at 8 * 10 -5 (365 days) and limited to 180 days and 730 days according to the time scale associated to ageing by [START_REF] Wauchope | Pesticide soil sorption parameters: theory, measurement, uses, limitations and reliability[END_REF].

Combined experiment: simultaneous ageing, biodegradation and hydrolysis processes

This experiment aimed at showing the capabilities of the model to predict the behaviour of pesticides when several processes occurred simultaneously. This simulation relied on a dataset derived from an experiment assessing the "Dissipation of butachlor and S-metolachlor in agricultural soil microcosms" and conducted by Ehssan Torabi (PhD student at University of Tehran and cooperation with the LHyGeS, publication in preparation). In this work 𝐷𝑇 50 and enrichment values (𝜖) were derived for Butachlor and S-Metolachlor.

Experimental design

Two well characterised soils were used (Arable land form Alteckendorf, Alsace and paddy soil from Guilan Province, Iran, silt 72.0%, Sand 0.1%, clay 27.9% and organic matter 5.36%) characterisation by Charline Wiegert). Because this experiment accounted for abiotic and biotic degradation, a first order biodegradation equation was added to the model as a first approach to represent biotic degradation (Appendix 2 shows how the biodegradation should be eventually implemented).

We focused on the paddy soil (10𝑔) with moisture content maintained to 100% (similar to lake sediments). The soil was homogeneously spiked with S-Metolachlor, incubated under dark conditions at 30 °𝐶 for 85 days. The experiment was conducted on biotic and abiotic soil (autoclaved). As reported by Ehssan Torabi, to avoid a prominent effect of adsorption on soil (high fraction of carbon in soil), we used data extracted from the soil spiked with the higher concentration of pesticide (150 𝜇𝑔. 𝑔 -1 ). In this way, 𝐷𝑇 50 and 𝜖 derived from biotic and abiotic experiments were attributed to hydrolysis and biodegradation and to hydrolysis only, respectively.

Model parameterization

According to [START_REF] Van Breukelen | Extending the Rayleigh equation to allow competing isotope fractionating pathways to improve quantification of biodegradation[END_REF], enrichment factors were corrected to account for competing pathways in the biotic experiment (Eq. 13):

{ 𝐹 = 𝑘 ℎ𝑦𝑑𝑟𝑜𝑙𝑦𝑠𝑖𝑠 𝑘 ℎ𝑦𝑑𝑟𝑜𝑙𝑦𝑠𝑖𝑠 + 𝑘 𝑏𝑖𝑜𝑑𝑒𝑔𝑟𝑎𝑑𝑎𝑡𝑖𝑜𝑛 1 + 𝜖 𝑡𝑜𝑡𝑎𝑙 = 𝐹 * (1 + 𝜖 ℎ𝑦𝑑𝑟𝑜𝑙𝑦𝑠𝑖𝑠 ) + (1 -𝐹) * (1 + 𝜖 𝑏𝑖𝑜𝑑𝑒𝑔𝑟𝑎𝑑𝑎𝑡𝑖𝑜𝑛 ) (13)
With 𝑘 ℎ𝑦𝑑𝑟𝑜𝑙𝑦𝑠𝑖𝑠 , respectively 𝑘 𝑏𝑖𝑜𝑑𝑒𝑔𝑟𝑎𝑑𝑎𝑡𝑖𝑜𝑛 the degradation rate associated to hydrolysis and biodegradation respectively. Thus, the biodegradation and hydrolysis were first parameterised with the dataset provided in Table 10. Sorption parameters were reused from the calibration of previous sorption experiment. 1. At first glance, because no influence of sorption was assumed the remaining fraction was interpreted as the ratio of the non-degraded fraction to the initial mass (Eq. 14)

𝑋 𝑛𝑖𝑡𝑖𝑎𝑙 -𝑋 𝑑𝑒𝑔𝑟𝑎𝑑𝑒𝑑 𝑋 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 (14)
In this configuration, the model is expected to fit well with the observations. This first simulation is then used as a reference for the second one. 2. In a second phase, the sorption/desorption/ageing process is enabled and the remaining fraction becomes (Eq. 15)

𝑋 𝑛𝑖𝑡𝑖𝑎𝑙 -𝑋 𝑑𝑒𝑔𝑟𝑎𝑑𝑒𝑑 -𝑋 𝑎𝑔𝑒𝑑 𝑋 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 . ( 15
)
Calibrated parameters from the sorption experiment are used.

III/ Results and discussions

1) Hydrolysis experiment

As the hydrolysis experiment is still running, the presented set of data is likely to face slight modifications until the last sampling time. Up to now, 6 sampling time (after 5, 14, 27, 35, 41 and 49 days) have been realised which approximately represents a dataset of 600 values (300 analyses in GC-MS, 300 in GC-IRMS). Experimental reproducibility showed that duplicates measurements for quantification had variation coefficient <20%). Results are reported in Table 11.

Significant degradations were mostly observed for 𝑝𝐻 higher than 9 for Atrazine, Acetochlor, Alachlor, S-Metolachlor and Butachlor with more than 85% of degradation after 49 days at 𝑇 = 30°𝐶 and more than 40% at 𝑇 = 30°𝐶. At 𝑝𝐻 = 12, degradation of Metalaxyl was too fast to be observed (below the quantification limit after 5 days). Under acid conditions (𝑝𝐻 = 2), Atrazine also showed a huge potential of degradation with a reduction in concentration of 40% to 90% for 𝑇 = 20°𝐶 and 𝑇 = 30°𝐶 respectively (Figure 13). Acetochlor, Alachlor and S-Metolachlor faced weaker but noticeable degradation. All studied pesticides were stable at 𝑝𝐻 = 7 (degradation < 10%), and our results could not highlight any effect of 𝐷𝑂𝐶 on the hydrolysis rate.

𝐷𝑇 50 were calculated when at least 50% of degradation was observed in the end of the experiment. Linear regression was applied to fit the data to first order hydrolysis equation (ln ( 𝐶(𝑡) 𝐶 0 ) = 𝑘 ℎ𝑦𝑑𝑟𝑜𝑙𝑦𝑠𝑖𝑠 * 𝑡) and Fischer test was computed to assess the regression confidence (confidence level set at 95% ). For 𝑇 = 30°𝐶 , Atrazine 𝐷𝑇 50 was 6 days while 𝐷𝑇 50 of chloroacetanilides ranged around 20 days. Temperature proved to be an important influencing factor of the hydrolysis kinetic. Indeed, at pH = 12 and after 49 days, from 1.5 to more than 2 times more degradation was observed at 𝑇 = 30°𝐶 than 𝑇 = 20°𝐶 and 𝐷𝑇 50 were at least halved with 𝑇 = 30°𝐶 (Figure 12 and Table 11). Carbon isotopic enrichments were observed when degraded fraction was significant. Enrichment factors were calculated according to the Rayleigh model (1) thanks to linear regression (Figure 13). At 𝑝𝐻 = 12, CSIA of the three chloroacetanilides revealed similar average while Atrazine showed higher value ( 𝜖 = -4.4‰ ± 0.6 at 𝑝𝐻 = 2 and 𝑇 = 30°𝐶 and 𝜖 = -4.8‰ ± 0.3 at 𝑝𝐻 = 12). [START_REF] Meyer | C and N Isotope Fractionation Suggests Similar Mechanisms of Microbial Atrazine Transformation Despite Involvement of Different Enzymes (AtzA and TrzN)[END_REF] reports similar values for Atrazine's hydrolysis at 𝑇 = 60°𝐶; 𝑝𝐻 = 3  𝜖 = -4.8‰ ± 0.4 and 𝑝𝐻 = 12  𝜖 = -3.7‰ ± 0.4 . This observation advocates for similar mechanisms of bond cleavage between Acetochlor, Alachlor and Butachlor.

Taking into account the measurement uncertainties, enrichment factors for 𝑇 = 20°𝐶 and 𝑇 = 30°𝐶 were not significantly different. Then, temperature plays a catalytic role but do not modify the degradation mechanisms.

No significant variations in 𝜖 and 𝐷𝑇 50 were observed for Atrazine at 𝑝𝐻 = 2 and 𝑝𝐻 = 12. Then, carbon CSIA measurement alone is suitable for demonstrating the hydrolysis of Atrazine but not for determining under which conditions it happens and then which TPs are likely to be released in the environment. According to [START_REF] Elsayed | Using compound-specific isotope analysis to assess the degradation of chloroacetanilide herbicides in labscale wetlands[END_REF][START_REF] Meyer | C and N Isotope Fractionation Suggests Similar Mechanisms of Microbial Atrazine Transformation Despite Involvement of Different Enzymes (AtzA and TrzN)[END_REF], the use of "multi-element CSIA" could allow us to tackle this issue. In this way, [START_REF] Meyer | C and N Isotope Fractionation Suggests Similar Mechanisms of Microbial Atrazine Transformation Despite Involvement of Different Enzymes (AtzA and TrzN)[END_REF] significant variations in Nitrogen enrichment (𝜖 𝑁𝑖𝑡𝑟𝑜𝑔𝑒𝑛 (𝑝𝐻3) = 2.5 ± 0.2 and 𝜖 𝑁𝑖𝑡𝑟𝑜𝑔𝑒𝑛 (𝑝𝐻12) = -0.9 ± 0.2) highlighted the different bonds cleavage mechanisms between alkaline and acid hydrolysis. This experiment also highlighted the rapid formation of TPs for Acetochlor, Alachlor and Butachlor (chromatogram in Appendix 5). Well characterised TPs might provide supplementary evidences of parent compounds degradation in the environment and preferential pathways. Moreover, because TPs are an issue for public health concern, being able to predict their formation in environmental matrices may be relevant [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF]. In this way, further investigations might be conducted to characterise the observed TPs and parameterise their formation kinetics. In Vensim, the degradation kinetic and the enrichment in heavy isotope are well simulated when parameterised with previously calculated 𝐷𝑇 50 and 𝜖. For Atrazine, 𝜖 𝐶 = -4.8‰, 𝐷𝑇 50 = 6 𝑑𝑎𝑦𝑠, 𝐶 0 = 10 𝑚𝑔. 𝐿 -1 and after 𝑡 = 5 * 𝐷𝑇 50 :

 𝜖 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 = 8.0 ‰ and 𝜖 𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑒𝑑 = 8.0 ‰ and 𝐶 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 = 0.31 𝑚𝑔. 𝐿 -1 and 𝐶 𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑒𝑑 = 0.31 𝑚𝑔. 𝐿 -1 .

This experiment highlighted the high degradation rates of several chloroaceanilides at high temperature and strongly acid or alkaline 𝑝𝐻. Natural average 𝑝𝐻 in most world rivers is known to range between 6 and 8.2. However, water chemistry shows that numerous parameters can be responsible for sharp 𝑝𝐻 variations (dissolved 𝐶𝑂 2 , eutrophication level, surrounding mineral environment …). For instance, the Loire River, faces 𝑝𝐻 exceeding 9.2 during summer algal blooms or the Rio Negro shows 𝑝𝐻 ranging from 2.9 to 4.2 [START_REF] Meybeck | Carbon, nitrogen, and phosphorus transport by world rivers. Meybeck, M[END_REF]. Then, it results that hydrolysis may not be the dominant pathway controlling chloroacetanilides degradation within the water-sediment interface under natural conditions. In addition, according to the equation 10 studying hydrolysis at strong acid and alkaline pH as well as at neutral pH allow us to establish a relationship between hydrolysis rate and water 𝑝𝐻 from 2 to 12. This relationship will prove useful when retroactions will be implemented in the model.

The experiment also showed that carbon CSIA should be backed with nitrogen CSIA in order to identify and eventually predict the formation of TPs in the environment with a dual isotope approach.

Future experiments

As shown in Figure 6, several processes still required laboratory assessment. Photolysis and biodegradation will be both tested under laboratory experiments in the beginning of my thesis work (first year). Dynamic processes such as river flow or flow through the sediment layer should be implemented during the second year. Then, the model will be tested at catchment scale on rivers pre-selected with the Agence de l'Eau Rhin-Meuse (AERM) (third year).

2) Diffusion experiment

The potential deviation of VENSIM® resolution compared with the reference solution was assessed considering the most adverse initial and boundary conditions:  Dirichlet boundary conditions forced the total mass of pesticides within the column to increase with time and then exacerbated potential deviation to final mass balance.

 Studying only the sediment column (low diffusion coefficient) forced concentration gradients to remain high longer than in the water column, increasing potential deviation due to the resolution scheme.

The reference solution was computed in Excel® because the integration scheme is easy to control in it. Number of layer and time steps are set up in entering the desired value in the attributed cells while in Vensim® the entire code has to be modified.

Excel computation:

After 100 days of simulation, final mass of pesticide in the sediment column (sum of masses in each compartments) equalled 49.4 𝑚𝑔 𝐴𝑡𝑟𝑎𝑧𝑖𝑛𝑒 (defined as the reference value) and the pollutant reaches a depth of 16.1 𝑐𝑚 with significant value (𝐶 𝑎𝑡𝑟𝑎𝑧𝑖𝑛𝑒 > 𝐶 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 100

).

Vensim® computation:

Spatial discretization played a prominent role in pesticide distribution. Indeed, final mass of pesticide within the sediment column ranged from 99.7% (for 200 layers) to 71.0% (for 6 layers) of the reference value. However, general distribution pattern of pesticides remained unchanged:

The model associates to each layer the value of pollutant concentration computed at the bottom of this layer. In other words for a six layers sediment column, the homogeneous concentration in the first layer equals the concentration computed at the first node (depth of 20 6 = 3.33 cm) (Figure 14). In this way, reducing the number of layers slowed down the diffusion and then leaded to underestimation of total mass of pesticide within the sediment column.

Because diffusion is a slow process, spatial variations of concentrations are slights and almost linear. Then, in order to reduce the mass balance error when reducing the number of layer, it might prove useful to evaluate concentrations at middle point (green area and black points in Figure 14). Thanks to this method, with 6 layers the maximum mass balance error is shrink to 2.7% (97.3% of the reference value).

However, additional gradients influencing pollutant behaviour should be considered when representing the interface. Microbially mediated reactive processes might be inhibited by either the absence or presence of dissolved oxygen in the sediment [START_REF] Alvarez-Zaldívar | Biogeochemical modelling of in situ biodegradation and stable isotope fractionation of intermediate chloroethenes in a horizontal subsurface flow wetland[END_REF]. Then, because the 𝑂 2 depleted within the first millimetres of sediment [START_REF] Honti | Deriving Persistence Indicators from Regulatory Water-Sediment Studies -Opportunities and Limitations in OECD 308 Data[END_REF][START_REF] Shrestha | Simulation Studies to Explore Biodegradation in Water-Sediment Systems: From OECD 308 to OECD 309[END_REF][START_REF] Wang | Microscale chemical features of sediment-water interface in Hongfeng Lake[END_REF], a precise spatial discretization would be required. Then, non-uniform spatial discretization might prove useful in terms of gradient representation and mass balance compliance.

At the opposite, time step does not significantly influence diffusion computation (𝐶 𝑣 = 𝜎 𝜇 = 10 -5 ). Then, time step will be favourably increased as long as it does not impact computation of other processes. [START_REF] Van Beinum | Pesticide Sorption and Diffusion in Natural Clay Loam Aggregates[END_REF] showed that due to huge molecular size of pesticides, measured values of the effective diffusion coefficients for three organic molecules (azoxystrobin, chlorotoluron, and cyanazine) were from 3 to 6 fold lower than theoretical values (calculated with [START_REF] Millington | Permeability of porous solids[END_REF]). Simulations with 𝐷 = 𝐷 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 6

results in halving the initial mass balance showing slower diffusion through the sediment layer. This experiment showed the ability of VENSIM® to accurately compute the diffusion equation. The boundary conditions tested in this experiment strengthened the diffusion of the pesticide through the sediment column. Then, under environmental conditions, it is unlikely to observe significant pollutant concentrations deeper than in the few first centimetres. Optimisation of the resolution (middle point computation) provides good fit with the reference solution and allows user to reduce the number of layers to compute. However, because numerous degradative processes show sharp spatial variations within the first millimetres of sediment, coarse discretisation might hide relevant processes. Considering the huge uncertainty associated to the theoretical diffusion coefficient for a specific pesticide, we will preferably use a welldocumented value or set up lab-scale experiments to determine this value.

The model could not yield acceptable fit to the measured data when assuming all but the aged fraction extracted (sum of squared residuals =43.09 after 22 simulations while it equals 0.10 in the first configuration).

The final optimized set of parameters is as following; 𝒇𝒏𝒆 = 5.195, 𝒌 𝒅𝒆𝒔 = 0.0034 ℎ -1 and 𝒌 𝒂𝒈𝒊𝒏𝒈 = 0.00015 ℎ -1 = 192 𝑑𝑎𝑦𝑠 . 𝑓𝑛𝑒 increased meaning that the pesticide storage capacity of the non-equilibrium compartment raised while 𝑘 𝑑𝑒𝑠 increased, leading to an acceleration of the sorption/desorption process. These rises in parameters are consistent with the remarks of the EFSA, (2015) which recognises that the default values rank rather low in the distribution of available values. Finally, the calibrated ageing half-life complies time scale of [START_REF] Wauchope | Pesticide soil sorption parameters: theory, measurement, uses, limitations and reliability[END_REF].

The main issue associated to this formalism is the characterisation of the extraction method. In this experiment, it resulted in uncertainties on the choice of the objective function and then in uncertainties on the calibrated parameters. The non convergence of the model calibrated with the aged fraction, leads us to conclude that the soil extraction protocol is not able to extract aged pesticide. In the meantime, the good fit with the first calibration indicates that the extracted fraction roughly corresponds to the equilibrium sorption. However, it doesn't allow us to precisely set the limit betweenextracted and non extracted fractions. This issue is discussed in the guidance on how aged sorption experiments should be conducted and different protocols for extracting readily available (equilibrium sorption), poorly available (time dependent sorption, calibration of 𝑘 𝑑𝑒𝑠 and 𝑓𝑛𝑒) and aged (aged-sorbed, calibration of 𝑘 𝑎𝑔𝑒𝑑 ) fractions are proposed. Other authors also tested different protocols [START_REF] Barriuso | Solvent extraction characterization of bioavailability of atrazine residues in soils[END_REF]EFSA, 2015;[START_REF] Gulkowska | Time-dependent sorption of two novel fungicides in soils within a regulatory framework[END_REF][START_REF] Park | Assessment of bioavailability of soilsorbed atrazine[END_REF].

4) Global experiment

In this experiment multiple processes were tested together to check model's capability to work simulate complex system. Available data issued from the experiment provided 𝐷𝑇 50 and enrichment values calculated without considering ageing. However, because it was conducted over 85 days and as seen in the sorption experiment, ageing was expected to play a significant role. This role was assessed with simulations including sorption/desorption/ageing, hydrolysis and biodegradation.

The first simulation was conducted without the ageing and suited well to the experimental data. In a general manner it underestimated to a small proportion the remaining fraction. The correction of the 𝐷𝑇 50 values proved to be efficient. Indeed simulation with non-corrected values leads to a sum of squared residuals twice as much as with the corrected values. The final isotopic shift was expected to range between 5.2 and 5.4 ‰. The simulated isotopic shift after 85 days of incubation equalled 5.7‰. The good fit with concentrations as well as with the final isotopic enrichment shows that the model is capable of predicting the role of each destructive process as regards to the global degradation. Thus, it would be possible to derive 𝐷𝑇 50 , respectively enrichment factors if only enrichment factors, respectively 𝐷𝑇 50 are known for each involved process.

Because this solution fitted well with the measurements, it was used as the reference solution for the second simulation. The aim of this second part is to highlight the potential effect of the ageing process on 𝐷𝑇 50 and enrichment values measurements. Before calibration (solid blue line), we observed a global decrease in the remaining fraction compared to the reference solution. Although, the degradation kinetics remained unchanged, this discrepancy was attributed to a progressive increase in the aged fraction (12% of the initial value after 85 days). Compared with the sorption experiment this value is significantly lower.

In order to compare 𝐷𝑇 50 and 𝜖 values including or not the effect of aged sorption, a calibration on the 𝐷𝑇 50 was successfully achieved (finak variations < 0.2% with the reference solution). The fitted parameters are the following; 𝐷𝑇 50 ℎ𝑦𝑑𝑟𝑜𝑙𝑦𝑠𝑖𝑠 = 160 𝑑𝑎𝑦𝑠 -1 and 𝐷𝑇 50 𝑏𝑖𝑜𝑑𝑒𝑔𝑟𝑎𝑑𝑎𝑡𝑖𝑜𝑛 = 36 𝑑𝑎𝑦𝑠 -1 .

The new half-life values ranged higher than the previous one. Indeed, when ageing is disabled, the remaining fraction solely depends on the degraded mass and the half-life is associated with the decrease in this remaining fraction 𝑋 𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 = 𝑓(𝑋 𝑑𝑒𝑔𝑟𝑎𝑑𝑒𝑑 ) . At the opposite, when ageing is enabled, the remaining fraction depends both on the degraded mass and on the aged fraction 𝑋 𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 = 𝑓(𝑋 𝑑𝑒𝑔𝑟𝑎𝑑𝑒𝑑 𝑒𝑓𝑓 , 𝑋 𝑎𝑔𝑒𝑑 ). Then because the remaining fraction stay constant, 𝑋 𝑑𝑒𝑔𝑟𝑎𝑑𝑒𝑑 𝑒𝑓𝑓 < 𝑋 𝑑𝑒𝑔𝑟𝑎𝑑𝑒𝑑 and half-life value increases.

This observation leads us to several conclusions:

 Not considering the sorption/desorption/ageing process in an experiment designed to derive half-life values generate a systematic error resulting in an overestimation of the degradation rate.

 Not considering the aged fraction leads to underestimate the persistence of pesticide in the environment.

In this way, [START_REF] Honti | Deriving Persistence Indicators from Regulatory Water-Sediment Studies -Opportunities and Limitations in OECD 308 Data[END_REF] propose to use the 𝐷𝑒𝑔𝑇 50 which is defined as the time until 50% of the parent chemical as diseappeared from the system. In this case 𝐷𝑒𝑔𝑇 50 = 32 𝑑𝑎𝑦𝑠 which is 7 days longer than the initially measured 𝐷𝑇 50 .

The final shift in carbon isotope after calibration decreased (from 5.7 to 4.3‰). Indeed, because degradation rate decreased, isotopic enrichment consequently decreased. Then, in experiments influenced by ageing, measured enrichment factors must be corrected to account for this decrease. If not, they will be under-estimated. However, unless one of the two process was previously individually assessed the current calibration methodology does not allow for accurate correction of 𝜖 values. Further investigations should be triggered in this way. Nonetheless, the evolution of the isotopic composition over time shows an inflection reflecting that in the end of the experiment, degradation was almost completed (slope → 0 ). Then, final distribution of pollutant within the different compartments (hydrolysed, biodegraded and aged) is close to its equilibrium state. Finally, this experiment showed that ageing is an important process to consider for deriving reliable half-life values and enrichment factors. Indeed, the aged fraction is likely to accumulate a fraction of the initial mass of contaminant and then to slow down destructive processes.

Compared with the sorption experiment, ageing is highly mitigated in mass by destructive processes and only 12% of the initial mass were aged after 85 days of incubation here while more than 50% were aged after 200 days in the first experiment. In our case half-life values corrected for integrating ageing were 3 days higher for biodegradation and 27 days higher for hydrolysis. Because we were not able to calibrate the model with both remaining fraction and isotopic enrichment, we can only conclude that enrichment factors derived from the experiment are slightly under-estimated. In the end, if the sorption process is well characterised, this model can be used for correcting 𝐷𝑇 50 values. Currently correcting 𝜖 values would requires at least one of the two destructive process to be individually characterised, which advocates for the coupling of numerical modelling and lab-scale experiment.

IV/ Conclusion and perspectives

This work highlights the lack of knowledge about the fate of pesticides within the watersediment interface. Considering the complexity of its representation, cutting edge tools are required to understand and identified main pathways of pesticide degradation within the interface. Then, the developed model is a first step toward an improved understanding of this dynamic interface.

Under static conditions, the developed model proved its ability to individually represent three groups of processes: Diffusion, sorption/desorption/ageing and hydrolysis. Moreover, the last experiment showed that the model is also capable of providing good fit when simultaneous process occurred. This tool could be used to correct values derived from soil degradation experiments conducted as recommended in international guidelines.

The application of this model on the sorption experiment and the paddy soil study underscored some relevant conclusions. Supported with results of the hydrolysis experiment, abiotic degradation will probably not be the main pathway of degradation of the selected groups of pesticides under environmental conditions. On the other hand, ageing is likely to significantly mitigate pesticide bioavailability over a time scale of hundreds of days and affect biodegradation extent. As reported in the literature and confirmed by the diffusion experiment, pesticides are not expected to percolate deep within the sediment column as a result of diffusion only.

The hydrolysis experiment provided insights into potential abiotic pathways of degradation for six chloroacetanilides and one triazine pesticides. It allowed us to derive valuable 𝐷𝑇 50 and 𝜖 values for strong acid and alkaline environments but will eventually be extended to the complete range of 𝑝𝐻 between 2 and 12 and temperature between 20 to 30°C. It also highlighted the apparition of dominant TPs, which may give further insights on degradation pathways occurring in the environment.

Numerous perspectives were discussed during this work. [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF] lists a few methods as promising for pesticide fate studies. Among these are the use of 2D CSIA in order to more accurately differentiate destructive processes [START_REF] Elsayed | Using compound-specific isotope analysis to assess the degradation of chloroacetanilide herbicides in labscale wetlands[END_REF]. First, N CSIA tests are currently conducted on our hydrolysis experiment by Jérémy Masbou (researcher LHyGeS). 2D CSIA could then be easily implemented in VENSIM. TPs could also be integrated into the model as they indicate degradation. Moreover, predicting the formation of TPs might be useful for risk assessment as they are likely to easily percolate to groundwater and to show higher toxicity than their parent products [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF].

Another perspective is also the integration of ESIA, which provides similar insights than CSIA and which should be implemented with the same formalism as CSIA of chiral pesticides.

Because the coupled numerical modelling and lab-scale experiment methodology might be difficult to set up, integrating Quantitative Structure-Activity Relationship (QSAR) capable of predicting pollutant affinity with different process could ease the application of the model in different places.

Finally, the model should be transposed into dynamic systems, such as rivers. However, this adaptation will probably requires to use another modelling environment because VENSIM does not natively handle spatial discretisation. .

𝑌 is the stoichiometric coefficient for substrate consumption (-) to be determined.

For Michaelis-Menten kinetics, the global formalism is the same but the parameters are different.

For degradation of the sorbed bioavailable fraction, a first order kinetics is fitted and used [START_REF] Fragoulis | A model assessing bioavailability of persistent organic pollutants in soil[END_REF]. Moreover, if data describing the molecule biodegradation are insufficient (TEA or equations unknown) the first order degradation kinetic must be used.

Destructive abiotic processes

Photolysis is described via a first order removal kinetics. As no physically based equation is currently available in the literature, it is relevant to determine 𝐷𝑇 50 ℎ𝑦𝑑𝑟𝑜𝑙𝑦𝑠𝑖𝑠 value for a wide range of influential parameters (photoperiod, light emission spectrum, atmosphere and water column absorbance, geometric isomerization of the pollutant (S/R), DOM concentration of the water [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF][START_REF] Kochany | Sunlight Photodegradation of Metolachlor in Water[END_REF]. Il apparait donc primordial de comprendre le devenir des polluants dans l'environnement afin d'orienter les politiques nationales et internationales de gestion de la ressource en eau vers les stratégies les plus adaptées à chaque situation et les plus efficaces [START_REF] Honti | Deriving Persistence Indicators from Regulatory Water-Sediment Studies -Opportunities and Limitations in OECD 308 Data[END_REF].

𝑑𝐵

Description de l'interface eau-sédiment

L'objectif de cette première partie est de rappeler l'état des connaissances en matière de pollution par les pesticides des écosystèmes aquatiques. A ce titre, l'étude se focalise sur l'interface eau-sédiment et sur les processus majoritaires gouvernants le devenir des pesticides dans cette zone. Seront présentées ensuite les méthodes d'investigations les plus adaptées à cette étude.

Historiquement, le devenir des pesticides dans l'environnement a été étudié dans des conditions très spécifiques ou au contraire de manière très globale sans intégrer les particularités propres à chaque compartiment et aux interactions qui les lient (e.g. interfaces atmosphère-eau ou encore eau-sédiment) (Figure 2). L'interface eau-sédiment est particulièrement intéressante à étudier au regard de sa forte exposition aux pollutions et de la complexité encore peu étudiée des interactions qu'elle entretient avec les différentes substances (Figure 3). Effectivement, les pesticides pénètrent les systèmes aquatiques selon de nombreuses voies passant des dérives lors de l'épandage agricole au ruissellement de surface ou au drainage agricole ou encore par le biais des nappes phréatique [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF]. Dès lors, la répartition des polluants entre le sédiment et l'eau de surface est très complexe et dynamique comme le montre deux études récentes [START_REF] Alvarez | Bottom sediment as a source of organic contaminants in Lake Mead, Nevada, USA[END_REF][START_REF] Lu | Fate and transport of polychlorinated biphenyls (PCBs) in the River Thames catchment -Insights from a coupled multimedia fate and hydrobiogeochemical transport model[END_REF]. En effet, il a été montré que dans les lacs et les rivières, en fonction des concentrations en pesticides présentes dans les sédiments et dans l'eau, les sédiments sont susceptibles d'agir comme puit de polluant ou comme source « secondaire de contaminant ».

De plus, en prenant en compte la dynamique de cette interface [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF][START_REF] Meybeck | Carbon, nitrogen, and phosphorus transport by world rivers. Meybeck, M[END_REF], elle doit être étudiée comme une couche fine (Figure 4). En effet, certains paramètres comme l'Oxygène dissous, le 𝑝𝐻 ou encore la température varient très rapidement dans les premiers millimètres de sédiments (4 mm) [START_REF] Honti | Deriving Persistence Indicators from Regulatory Water-Sediment Studies -Opportunities and Limitations in OECD 308 Data[END_REF][START_REF] Shrestha | Simulation Studies to Explore Biodegradation in Water-Sediment Systems: From OECD 308 to OECD 309[END_REF][START_REF] Wang | Microscale chemical features of sediment-water interface in Hongfeng Lake[END_REF]. Ainsi, puisque les conditions physico-chimiques régissent les cinétiques de dégradation des pesticides, il apparaît primordial d'intégrer cette variabilité spatiale.

Ainsi, les approches traditionnelles s'appuyant sur des représentations globales et non spatialement distribuées de cette interface révèlent leurs limites lorsqu'il s'agit d'apporter une compréhension mécaniste des phénomènes impliqués. Ce travail tente donc un développement plus étendu de l'interface eau-sédiment.

Conceptuellement, l'interface a été divisée en deux compartiments interdépendants ; l'eau de surface et les sédiments. Chacun de ces compartiments est bi-phasiques (eau + solides en suspensions et sédiments + eau interstitielle).

Eau de surface :

Selon [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF], les "eaux naturelles contiennent de la matière en suspension, de la matière organique et inorganique dissoute ainsi qu'une grande diversité de biomasse aquatique ». A cet égard, les deux phases distinctes de ce compartiment sont les suivantes :

 La phase liquide composée du mélange d'eau et d'éléments dissous (depuis les nutriments jusqu'aux micropolluants).

 La phase solide uniquement composée des éléments en suspensions issus de l'érosion des berges ou du ruissellement de surface.

Phase liquide : Les paramètres nécessaires à la caractérisation de cette phase sont synthétisés en Table 1. Ils permettent à la fois une caractérisation des différents polluants et des conditions physico-chimiques de l'eau.

Phase solide : Le terme matière en suspension fait référence au matériel de taille supérieure aux éléments dissous et inférieure aux éléments qui décantent ( 𝐷 > 2 𝜇𝑚 ). La quantité de matière en suspension est exprimée indifféremment en masse ( 𝑚𝑔 ) ou en concentration (𝑚𝑔 𝑚𝑎𝑡𝑖è𝑟𝑒 𝑜𝑟𝑔𝑎𝑛𝑖𝑞𝑢𝑒 . 𝐿 -1 ) maintenus en suspension dans la colonne d'eau par les turbulences [START_REF] Bilotta | Understanding the influence of suspended solids on water quality and aquatic biota[END_REF]. Ils trouvent leurs origines de processus aussi diverses que l'érosion des sols ou des berges. Ainsi, leurs caractéristiques dépendent à la fois du socle géochimique de la région concernée mais aussi des variations hydrologiques saisonnières [START_REF] Ongley | Physical and geochemical characteristics of suspended solids, Wilton Creek, Ontario[END_REF] (Table 2). Cette phase occupe une place importante dans le devenir des contaminants puisque les molécules organiques sont susceptibles d'interagir avec (soprtion) [START_REF] Weber | Sorption of hydrophobic compounds by sediments, soils and suspended solids-II. Sorbent evaluation studies[END_REF].

Sédiments :

Ce compartiment est un milieu poreux composé de solides en suspensions agrégés et emprisonnés et d'une phase liquide (eau interstitielle). Les physico-chimie de l'eau interstitielle varie sensiblement de celle de l'eau de surface (concentrations en oxygène dissous inférieurs, [START_REF] Shrestha | Simulation Studies to Explore Biodegradation in Water-Sediment Systems: From OECD 308 to OECD 309[END_REF][START_REF] Wang | Microscale chemical features of sediment-water interface in Hongfeng Lake[END_REF], activité bactérienne supérieure, concentrations en nutriments …). C'est dans ce contexte que selon [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF] le compartiment sédiment est notablement impliqué dans la distribution des pesticides au sein de l'interface eau-sédiment.3

Phase liquide : Ici, les paramètres utilisés sont identiques à ceux de la phase liquide de l'eau superficielle mais leurs gammes de valeurs diffèrent.

Phase solide : La phase solide est principalement décrite par des critères géophysiques. Des critères mécaniques sont ajoutés pour tenir compte de l'aspect solide de ce compartiment (Table 4).

Compartiments additionnels :

Selon l'échelle de l'étude et le degré de complexité recherché, certains auteurs intègrent d'avantage de compartiments à leurs études. C''est ainsi que la biomasse est parfois prise en compte ; plantes aquatiques [START_REF] Diepens | Uptake, translocation, and elimination in sediment-rooted macrophytes: a model-supported analysis of whole sediment test data[END_REF] ou encore microorganismes [START_REF] Webster | Development and application of models of chemical fate in Canada[END_REF]. De plus, puisque l'atmosphère et l'eau souterraine sont connues comme étant des vecteurs à l'échelle mondiale des micropolluants, ils sont aussi souvent étudiés comme le prouve la partie état de l'art et modélisation.

Cette description met en évidence la complexité et l'hétérogénéité de l'interface eausédiment. C'est pourquoi cette étude se doit d'intégrer cette variabilité en favorisant une approche multi-compartiments et multiphasique. Nous en venons donc à nous demander lesquels de ces paramètres sont impliqués dans les voies de dégradations des pesticides et dans quelles mesures ?

Influence des processus destructifs et non destructifs

Deux types de processus doivent être distingués ici ; les processus destructifs (réductions de la masse) et les processus non destructifs (conservation de la masse). On distingue parmi les processus destructifs, ceux médiés par la biomasse (processus biotique) de ceux influencés par les réactions chimiques (processus abiotiques).

Processus destructifs :

Selon l'Environmental Protection Agency (EPA), les processus destructifs réfèrent à « toutes les réactions chimiques ou biologiques impliquant la destruction de molécules complexes en molécules plus simples ». Des changements de propriétés chimiques et physiques peuvent donc être observés ainsi que l'apparition de produits de dégradation dangereux [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF][START_REF] Porto | Biodegradation of Pesticides[END_REF].

Dégradation biotique : Ils sont les processus dominants dans l'environnement. En effet, les bactéries chimio-organotrophes sont capables d'utiliser les pesticides comme source d'énergie ou de les dégradés comme conséquence indirect de leur activité via co-métabolisme [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF][START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF]. Prédire la voie métabolique privilégiée n'est pas une tâche aisée puisque les communautés bactériennes présentes dans l'environnement sont extrêmements diversifiées [START_REF] Porto | Biodegradation of Pesticides[END_REF][START_REF] Schwarzenbach | The Challenge of Micropollutants in Aquatic Systems[END_REF]. Cependant, des tendances se dégagent en fonction des conditions physico-chimiques (oxique/anoxique) ; conditions oxydantes (e.g. dealkylation, hydrolyse) ou conditions réductives (e.g. dechlorination, dehalogénation) [START_REF] Elsner | Compound-specific isotope analysis (CSIA) of micropollutants in the environment -current developments and future challenges[END_REF][START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF][START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF].

Dégradation abiotique : Ce type de dégradation est principalement attribué à l'hydrolyse, aux réactions d'oxydoréduction ou encore aux réactions photolytiques. Malgré que les voies de L'équation de Rayleigh est utilisée pour corréler les variations du rapport isotopique aux variations de concentration (1).

De plus, puisque chaque processus est associé à un facteur d'enrichissement spécifique, il devient possible d'identifier et de différencier la part de chaque processus destructif dans la dégradation globale du composé. Les processus destructifs sont donc facilement différenciés des processus non-destructifs qui ne modifient pas la composition isotopique des composés.

Cependant, puisque les matrices environnementales sont diverses, plusieurs processus dont les facteurs d'enrichissement diffèrent peu peuvent potentiellement opérer en même temps, rendant leur identification difficile même avec l'AICS. L'identification peut-être rendue possible grâce à l'étude simultanée de l'enrichissement en isotope lourd du carbone ainsi qu'en isotope lourd de l'azote par exemple (2D-AICS) [START_REF] Elsayed | Using compound-specific isotope analysis to assess the degradation of chloroacetanilide herbicides in labscale wetlands[END_REF].

Analyser simultanément enrichissement en carbone et en azote peut rapidement devenir complexe. Ainsi, incorporer à un modèle numérique la prédiction de l'enrichissement peut faciliter les analyses à l'échelle d'un bassin versant. Cette méthode rendrait aussi possible les analyses sur le plus long terme et/ou à de plus grandes échelles permettant une meilleure compréhension du devenir des contaminants dans les systèmes aquatiques [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF].

Modélisation de l'interface eau-sédiment : état de l'art

La représentation conceptuelle actuelle de l'interface eau-sédiment est particulièrement simplificatrice par rapport à son fonctionnement réel : Système hétérogène aux fortes variabilités spatiales et temporelles impliquant un nombre important de processus de dégradation et de diffusion [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF][START_REF] Meybeck | Carbon, nitrogen, and phosphorus transport by world rivers. Meybeck, M[END_REF]. A l'opposé, [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF] montre que la connaissance actuelle de cette interface est plus simple : Très peu d'étude mécaniste des processus impliqués mais au contraire des études en milieux contrôlés et selon des conditions très spécifiques. Les expériences de laboratoires actuelles ne permettent généralement pas d'étudier le rôle de chaque processus individuellement. Cependant, dans des conditions plus adaptées (EFSA, 2015;[START_REF] Honti | Deriving Persistence Indicators from Regulatory Water-Sediment Studies -Opportunities and Limitations in OECD 308 Data[END_REF] (EFSA, 2015;[START_REF] Honti | Deriving Persistence Indicators from Regulatory Water-Sediment Studies -Opportunities and Limitations in OECD 308 Data[END_REF], ces expériences pourraient être un très bon outil pour comprendre le devenir des pesticides au sein de cette interface, ainsi que pour obtenir des valeurs importantes d'enrichissement isotopique [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF][START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF]. L'approche la plus pertinente semble donc être de coupler la modélisation à l'expérimentation en laboratoire. Afin de construire le modèle le plus adapté à nos besoins, quelques prérequis sont extraits des discussions précédentes :  Le modèle doit être multi-compartimental afin d'évaluer avec précision les échanges le long de la colonne eau-sédiment ;

 La colonne doit être verticalement discrétisée afin d'intégrer les variabilités spatiales avec la profondeur ;

 Les processus destructifs et non-destructifs doivent être pris en compte ;

Pour résumer cette section, les modèles de fugacité sélectionnés ne sont pas adaptés à nos besoins du fait de leur trop grande simplicité. A l'opposé, les modèles à base physique les plus avancés pourraient in fine se révéler trop complexes à calibrer. De plus, puisque tous les modèles considèrent les compartiments comme homogènes le long de la colonne eau-sédiment, ils ne permettront pas de révéler la variabilité des processus le long de la colonne. Ainsi, le modèle optimal réside en une hybridation de ces deux types de modèles, intégrant une représentation multi-compartimentale non homogène et basée sur une représentation mathématique à base physique. Un tel modèle nécessite donc d'être développé.

Processus à modéliser

Selon [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF], le modèle utilisé doit se concentrer uniquement sur les voies de dégradation les plus importants, permettant alors d'éviter l'écueil de sur-paramétrisation. Plus de complexité nécessitera aussi d'avantage de paramètres à calibrer et ainsi d'avantage de paramètres à mesurer in-situ [START_REF] Beven | A manifesto for the equifinality thesis[END_REF]. Ainsi, le choix des processus les plus importants dans la dégradation des pesticides à l'interface eau-sédiment est essentielle pour assurer une simplicité et une fiabilité optimale du modèle à développer. La Table 7 résume l'ensemble des processus les plus couramment utilisés au sein du panel de modèles étudiés (table complète disponible en annexe 1) et nous permet de conclure sur les processus à prendre en compte : Dans les eaux de surface les processus influençant le transport rapide des polluants devront être modélisés (cycle hydrologique, transport par advection, décantation des particules en suspensions ou remise en suspension). Le cycle d'eutrophisation joue lui aussi un rôle important par l'influence qu'il a sur la physico-chimie de l'eau. Les processus destructifs les plus couramment représentés sont la photolyse, l'hydrolyse ainsi que la biodégradation.

Dans les sédiments, ce sont les processus de décantation ou remise en suspension ainsi que de diffusion qui réalisent les échanges avec l'eau de surface. La biodégradation et l'hydrolyse sont les deux seuls processus destructifs restants. Dans de nombreux modèles, d'avantages de compartiments sont représentés à l'image de l'atmosphère, l'eau souterraine, le sol ou encore la biomasse (poissons ou plantes). Puisque ces compartiments n'interagissent pas immédiatement avec l'interface eau-sédiment ils ne sont pas considérés dans cette étude. Cependant, puisque certains d'entre eux sont considérés comme des vecteurs majeurs de polluants à l'échelle mondiale (atmosphère, UNEP), ils pourront dans un premier temps être représentés comme des sources ponctuelles/diffusives de polluant.

Notons que certains modèles originellement développés pour l'étude des polluants conventionnels (nutriments, métaux lourds …) sont facilement adaptable aux micropolluants comme montré par [START_REF] Deliège | PEGASE, an integrated river/basin model dedicated to surface water quality assessment: application to cocaine[END_REF] qui étudie le devenir de la cocaïne dans les eaux de surface grâce à PegOpera.

Enfin, notons qu'aucun de ces 9 modèles n'intègre l'AICS. Ainsi, à cause de l'équifinalité, certains auteurs ne sont pas capables d'identifier la responsabilité de chaque processus dans la dégradation global modélisée. Plusieurs combinaisons de paramètres peuvent mener à des résultats identiquement bons sans qu'ils n'aient la même signification physique [START_REF] Beven | A manifesto for the equifinality thesis[END_REF]. Le comportement des pesticides ne peut donc pas être étudié dans ces cas.

Conclusions sur l'état de l'art

Les discussions précédentes prônent pour l'utilisation d'un modèle multimédias à base physique, incluant l'ensemble des processus identifiés en Table 7. Puisque ce modèle n'existe pas encore, il doit être implémenté.

Il nous faut distinguer ici ce qu'on appelle le modèle final qui sera le résultat de mon futur travail de thèse, du modèle préliminaire que l'on développe dans cette étude. En Figure 6 est donc présentée la structure du modèle final. Chaque processus implémenté fera l'objet d'une coconstruction en parallèle d'une expérience de laboratoire destinée à obtenir des gammes de paramètres applicables dans les conditions les plus diverses possibles. On s'affranchira alors de l'équifinalité ainsi que de la sur paramétrisation.

Pour le modèle préliminaire l'étude est réduite aux conditions suivantes :  L'environnement considéré est statique comme des lacs, des marres, des zones humides etc… L'implémentation de la dynamique aurait nécessité des outils beaucoup plus compliqués et n'aurait pas apporté de plus-value dans le contexte des expériences réalisées ;

 Les processus de transport sont donc réduits à la diffusion seule ;  Les processus destructifs se sont reportés sur l'hydrolyse puisque l'étude expérimentale de ce processus était compatible avec le temps attribué à cette étude.

 Les processus non-destructifs sont limités à la sorption/désorption/ageing puisque son influence et largement reportée dans la littérature.

D'autres processus destructifs comme la photolyse, la biodégradation ou le cycle d'eutrophisation ont été discutés mais pas encore implémentés.

  Abstract ............................................................................................................................................... Résumé ................................................................................................................................................ Acronyms AERM: Agence de l'eau Rhin-Meuse CSIA: Compound Specific Isotope Analysis DO: Dissolved Oxygen DOC: Dissolved Organic Carbon EPA: Environmental Protection Agency GC-MS: Gas chromatography-mass spectrometry GC-IRMS: Gas chromatography-Isotope Ratio Mass Spectrometry POC: Particulate Organic Carbon SDAGE: Schémas Directeurs d'Aménagement et de Gestion des Eaux SIERM : Système d'Information sur l'Eau Rhin-Meuse SS: Suspended Solids TP: Transformation product UNEP: United Nations Environment Programme WFD: Water Framework Directive 𝐷𝑇 50 : Half-life value (days) 𝜖: Isotopic enrichment factor (‰) 𝐾 𝑜𝑐 : Soil Organic Carbon-Water Partitioning Coefficient (𝑚𝑔 𝑝𝑜𝑙𝑙𝑢𝑡𝑎𝑛𝑡 . 𝑔 𝑐𝑎𝑟𝑏𝑜𝑛 -1

Figure 1 :

 1 Figure 1: The river Souffel in Griesheim-sur-Souffel (Alsace), surrounded by two fields of intensive cropping. This river is classified as bad ecological and chemical status (SDAGE 2015) and concentrations of Acetochlor regularly exceed reference threshold (SIERM). Drouin Guillaume on 18 June 2017. ............................................................................................................................................... Figure 2: Temporal evolution of number publications assessing pesticides environmental behavior within individual and coupled compartments. Search in ISI Web of Science from 1975 to 2017, [pesticide] AND [behavior] AND [(water) OR (soil) OR (sediment) OR (atmosphere) OR (water AND interface) OR (sediment AND interface)]. n=2064, 1626, 332, 96, 35 and 4 respectively). ................... Figure 3: Main compartments (boxes), sources of pollution and partitioning fluxes (arrows) of an aquatic ecosystem. ................................................................................................................................ Figure 4: Zoom in the schematic cross section of the thin water-sediment interface. ........................Table 1: Key parameters for surface water (Data for Alsace, extracted from AERM database). Relevant parameters involved in equations solved in the model are in bold. ....................................... Table 2: Key parameters for suspended solids phase (Mean values for Alsace extracted from Eaufrance and variability from[START_REF] Meybeck | Carbon, nitrogen, and phosphorus transport by world rivers. Meybeck, M[END_REF]). ................................................................................ Table 3: Typical values for interstitial porewater phase ....................................................................... Table 4: Key parameters for sediment phase ....................................................................................... Figure 5: (a) Illustration of the reduction in concentration coupled with changes in 𝟏𝟑𝑪𝟏𝟐𝑪 and (b) the relationship existing between pesticide degradation and Carbon heavy isotope enrichment (Rayleigh equation). Example extracted from hydrolysis experiment dataset for Alachlor (this study). ............................................................................................................................................................... Table 5: Model purposes and general information ............................................................................... Table 6: Applicability of the selected model, mathematical formalism and number of required input parameters ............................................................................................................................................ Table 7: List of the most frequently used processes among the selected models discussed above. Water cycle refers to hydrodynamic and macro pollutant pathways. ..................................................

  Figure 1: The river Souffel in Griesheim-sur-Souffel (Alsace), surrounded by two fields of intensive cropping. This river is classified as bad ecological and chemical status (SDAGE 2015) and concentrations of Acetochlor regularly exceed reference threshold (SIERM). Drouin Guillaume on 18 June 2017. ............................................................................................................................................... Figure 2: Temporal evolution of number publications assessing pesticides environmental behavior within individual and coupled compartments. Search in ISI Web of Science from 1975 to 2017, [pesticide] AND [behavior] AND [(water) OR (soil) OR (sediment) OR (atmosphere) OR (water AND interface) OR (sediment AND interface)]. n=2064, 1626, 332, 96, 35 and 4 respectively). ................... Figure 3: Main compartments (boxes), sources of pollution and partitioning fluxes (arrows) of an aquatic ecosystem. ................................................................................................................................ Figure 4: Zoom in the schematic cross section of the thin water-sediment interface. ........................Table 1: Key parameters for surface water (Data for Alsace, extracted from AERM database). Relevant parameters involved in equations solved in the model are in bold. ....................................... Table 2: Key parameters for suspended solids phase (Mean values for Alsace extracted from Eaufrance and variability from[START_REF] Meybeck | Carbon, nitrogen, and phosphorus transport by world rivers. Meybeck, M[END_REF]). ................................................................................ Table 3: Typical values for interstitial porewater phase ....................................................................... Table 4: Key parameters for sediment phase ....................................................................................... Figure 5: (a) Illustration of the reduction in concentration coupled with changes in 𝟏𝟑𝑪𝟏𝟐𝑪 and (b) the relationship existing between pesticide degradation and Carbon heavy isotope enrichment (Rayleigh equation). Example extracted from hydrolysis experiment dataset for Alachlor (this study). ............................................................................................................................................................... Table 5: Model purposes and general information ............................................................................... Table 6: Applicability of the selected model, mathematical formalism and number of required input parameters ............................................................................................................................................ Table 7: List of the most frequently used processes among the selected models discussed above. Water cycle refers to hydrodynamic and macro pollutant pathways. ..................................................

Figure 6 :

 6 Figure 6: Final representation of the sediment-water interface model accounting for destructive and non-destructive processes. Orange font refer to processes not already tested, green font refer to processes tested and implemented in this work ................................................................................... Table 8: Physicochemical properties of studied pesticides, expected behaviours and available analytical methods ................................................................................................................................ Figure 7: Conceptual representation of the adsorption/desorption/ageing process. Adapted from (EFSA, 2015) ...........................................................................................................................................Figure 8: Schematic representation of processes interactions within the different compartments. Dotted arrows indicate pollutant degradation or reduction in bioavailability. Complete scheme accounting for all relevant processes available in Appendix 4 .............................................................. Figure 9: Representation of the diffusion process in VENSIM. ............................................................. Figure 10: Implemented and tested processes along this work. Used dataset in callouts. .................. Figure 11: Tested modalities for hydrolysis experiment ....................................................................... Table 9: Time and spatial discretization tested in VENSIM® and VBA .................................................. Table 10: Hydrolysis and biodegradation parameters for S-Metolachlor used for the global experiment. ........................................................................................................................................... Figure 12: Fitted and simulated concentration exponential decrease as a function of a) pH and b) Temperature.......................................................................................................................................... Figure 13: Fitted and simulated double logarithmic plot according to the Rayleigh equation for Atrazine at pH=12 and T=20 and 30°C. ................................................................................................. Table 11: Calculated half-life (in days) and enrichment factors (in ‰) and their associated errors. For compounds degraded less than 50%, 𝑫𝑻𝟓𝟎 are visually assessed and only represent order of magnitude. (O) Number of outlier points. ............................................................................................ Figure 14: Simulated pollutant distribution within the sediment column in VENSIM. Hatched area represents the reference solution distribution, Orange area represents VENSIM distribution with 6 layers, green area and black points represent the computation at middle point and black line represents VENSIM distribution with 200 layers ................................................................................... Figure 15: "Two sites one rate" model calibration assuming extraction of equilibrium and nonequilibrium fraction. Black triangle represents the outlier point. ......................................................... Figure 16: Schematic representation of proposed extraction protocols in the EFSA's guidance, extracted from EFSA, (2015) .................................................................................................................. Figure 17: Calibrated simulation with enabled ageing process. The grey line shows the simulation with enabled ageing but before calibration, the red line shows the simulation with enabled ageing and after calibration. Red line and reference solution are undistinguishable. ............................................ Figure 18: Evolution of the carbon fractionation expressed in ‰ over the experiment. Blue line correspond to the simulation without ageing and red line to the simulation after calibration with ageing. ...................................................................................................................................................

Figure 12 :

 12 Figure 6: Final representation of the sediment-water interface model accounting for destructive and non-destructive processes. Orange font refer to processes not already tested, green font refer to processes tested and implemented in this work ................................................................................... Table 8: Physicochemical properties of studied pesticides, expected behaviours and available analytical methods ................................................................................................................................ Figure 7: Conceptual representation of the adsorption/desorption/ageing process. Adapted from (EFSA, 2015) ...........................................................................................................................................Figure 8: Schematic representation of processes interactions within the different compartments. Dotted arrows indicate pollutant degradation or reduction in bioavailability. Complete scheme accounting for all relevant processes available in Appendix 4 .............................................................. Figure 9: Representation of the diffusion process in VENSIM. ............................................................. Figure 10: Implemented and tested processes along this work. Used dataset in callouts. .................. Figure 11: Tested modalities for hydrolysis experiment ....................................................................... Table 9: Time and spatial discretization tested in VENSIM® and VBA .................................................. Table 10: Hydrolysis and biodegradation parameters for S-Metolachlor used for the global experiment. ........................................................................................................................................... Figure 12: Fitted and simulated concentration exponential decrease as a function of a) pH and b) Temperature.......................................................................................................................................... Figure 13: Fitted and simulated double logarithmic plot according to the Rayleigh equation for Atrazine at pH=12 and T=20 and 30°C. ................................................................................................. Table 11: Calculated half-life (in days) and enrichment factors (in ‰) and their associated errors. For compounds degraded less than 50%, 𝑫𝑻𝟓𝟎 are visually assessed and only represent order of magnitude. (O) Number of outlier points. ............................................................................................ Figure 14: Simulated pollutant distribution within the sediment column in VENSIM. Hatched area represents the reference solution distribution, Orange area represents VENSIM distribution with 6 layers, green area and black points represent the computation at middle point and black line represents VENSIM distribution with 200 layers ................................................................................... Figure 15: "Two sites one rate" model calibration assuming extraction of equilibrium and nonequilibrium fraction. Black triangle represents the outlier point. ......................................................... Figure 16: Schematic representation of proposed extraction protocols in the EFSA's guidance, extracted from EFSA, (2015) .................................................................................................................. Figure 17: Calibrated simulation with enabled ageing process. The grey line shows the simulation with enabled ageing but before calibration, the red line shows the simulation with enabled ageing and after calibration. Red line and reference solution are undistinguishable. ............................................ Figure 18: Evolution of the carbon fractionation expressed in ‰ over the experiment. Blue line correspond to the simulation without ageing and red line to the simulation after calibration with ageing. ...................................................................................................................................................

  ). ................................................................................ Table 3: Typical values for interstitial porewater phase ....................................................................... Table 4: Key parameters for sediment phase ....................................................................................... Table 5: Model purposes and general information ............................................................................... Table 6: Applicability of the selected model, mathematical formalism and number of required input parameters ............................................................................................................................................

  ) and enrichment factors (in ‰) and their associated errors. For compounds degraded less than 50%, 𝑫𝑻𝟓𝟎 are visually assessed and only represent order of magnitude. (O) Number of outlier points. ............................................................................................

Figure 2 :

 2 Figure 2: Temporal evolution of number publications assessing pesticides environmental behavior within individual and coupled compartments. Search in ISI Web of Science from 1975 to 2017, [pesticide] AND [behavior] AND [(water) OR (soil) OR (sediment) OR (atmosphere) OR (water AND interface) OR (sediment AND interface)]. n=2064, 1626, 332, 96, 35 and 4 respectively).

Figure 3 :

 3 Figure 3: Main compartments (boxes), sources of pollution and partitioning fluxes (arrows) of an aquatic ecosystem.

Figure 4 :

 4 Figure 4: Zoom in the schematic cross section of the thin water-sediment interface.

Figure

  Figure 5: (a) Illustration of the reduction in concentration coupled with changes in 𝑪 𝟏𝟑 𝑪 𝟏𝟐 and (b) the relationship existing between pesticide degradation and Carbon heavy isotope enrichment (Rayleigh equation). Example extracted from hydrolysis experiment dataset for Alachlor (this study).

3

  main model characteristics should be considered: o Mathematical representation (conceptual, empirical, physically based) o Time and spatial distribution o Number of processes modelled (physical, chemical and biological).3 criteria assessing the model applicability require attention: o Spatial scale o Complexity of the required data and the calibration process o Validation of the model

Figure 6 :

 6 Figure 6: Final representation of the sediment-water interface model accounting for destructive and non-destructive processes. Orange font refer to processes not already tested, green font refer to processes tested and implemented in this work

Figure 7 :

 7 Figure 7: Conceptual representation of the adsorption/desorption/ageing process. Adapted from (EFSA, 2015)

Figure 8 :

 8 Figure 8: Schematic representation of processes interactions within the different compartments. Dotted arrows indicate pollutant degradation or reduction in bioavailability. Complete scheme accounting for all relevant processes available in Appendix 4

Figure 9 :

 9 Figure 9: Representation of the diffusion process in VENSIM.

Figure 10 :

 10 Figure 10: Implemented and tested processes along this work. Used dataset in callouts.

Figure 11 :

 11 Figure 11: Tested modalities for hydrolysis experiment

  to a temperature of 1000 °C. A TG-5MS column (60 m × 0.25 mm ID, 0.25 µm film thickness) was used for chromatographic separation, with helium as the carrier gas at a flow rate of 1.5 𝑚𝐿. min -1

Figure 12 :

 12 Figure 12: Fitted and simulated concentration exponential decrease as a function of a) pH and b) Temperature

Figure 13 :

 13 Figure 13: Fitted and simulated double logarithmic plot according to the Rayleigh equation for Atrazine at pH=12 and T=20 and 30°C.

Figure 14 :

 14 Figure 14: Simulated pollutant distribution within the sediment column in VENSIM. Hatched area represents the reference solution distribution, Orange area represents VENSIM distribution with 6 layers, green area and black points represent the computation at middle point and black line represents VENSIM distribution with 200 layers

Figure 16 :

 16 Figure 16: Schematic representation of proposed extraction protocols in the EFSA's guidance, extracted from EFSA, (2015)

Figure 17 :

 17 Figure 17: Calibrated simulation with enabled ageing process. The grey line shows the simulation with enabled ageing but before calibration, the red line shows the simulation with enabled ageing and after calibration. Red line and reference solution are undistinguishable.

Figure 18 :

 18 Figure 18: Evolution of the carbon fractionation expressed in ‰ over the experiment. Blue line correspond to the simulation without ageing and red line to the simulation after calibration with ageing.

Table 1 :

 1 Key parameters for surface water (Data for Alsace, extracted from AERM database). Relevant parameters involved in equations solved in the model are in bold. .......................................

Table 2 :

 2 Key parameters for suspended solids phase (Mean values for Alsace extracted from Eaufrance and variability from

Table 1 :

 1 Key parameters for surface water (Data for Alsace, extracted from AERM database). Relevant parameters involved in equations solved in the model are in bold. .......................................

Table 2 :

 2 Key parameters for suspended solids phase (Mean values for Alsace extracted from Eaufrance and variability from

Table 7 :

 7 List of the most frequently used processes among the selected models discussed above. Water cycle refers to hydrodynamic and macro pollutant pathways. ..................................................

Table 8 :

 8 Physicochemical properties of studied pesticides, expected behaviours and available analytical methods ................................................................................................................................

Table 9 :

 9 Time and spatial discretization tested in VENSIM® and VBA ..................................................

Table 10 :

 10 Hydrolysis and biodegradation parameters for S-Metolachlor used for the global experiment. ...........................................................................................................................................

Table 11 :

 11 Calculated half-life (in days

Table 1 : Key parameters for surface water (Data for Alsace, extracted from AERM database). Relevant parameters involved in equations solved in the model are in bold. Description Parameters Mean range Variability (𝑷 𝟏𝟎 < 𝑉𝑎𝑙𝑢𝑒 < 𝑷 𝟗𝟎 ) Concentrations

 1

		𝐶 𝑛𝑢𝑡𝑟𝑖𝑒𝑛𝑡𝑠 (𝑚𝑔/𝐿) 𝑪 𝒑𝒐𝒍𝒍𝒖𝒕𝒂𝒏𝒕 (𝒎𝒈/𝑳) {		𝑛𝑔/𝐿 < 𝐶 𝑝𝑜𝑙𝑙𝑢𝑡𝑎𝑛𝑡 < 𝜇𝑔/𝐿
		𝑇𝐴/𝑇𝐴𝐶 (𝑚𝑒𝑞/𝐿) { 𝑫𝑶𝑪 (𝒎𝒈 𝑪 /𝑳)	𝐷𝑂𝐶 50 = 5	1 < 𝐷𝑂𝐶 < 20
			𝑻 (°𝑪)
	State variables:		𝒑 𝑯 𝐸 (𝑉)	𝑝 𝐻 50 = 7.9	7.4 < 𝑝 𝐻 < 8.3
			{ 𝜌 (𝑘𝑔. 𝑚 -3 ) 𝜎(𝑆. 𝑚 -1 )	𝑇 50 = 11.8	4.6 < 𝑇 < 18.6
			𝐶𝑂𝐷 (𝑚𝑔 𝑂 2 /𝐿)	𝐵𝑂𝐷 5 50 = 2.3	0.5 < 𝐵𝑂𝐷 5 < 42
	Degradation and redox activity	{	𝐵𝑂𝐷 5 (𝑚𝑔 𝑂 2 /𝐿)
			𝐷𝑂 (𝑚𝑔 𝑂 2 /𝐿)	𝐷𝑂 50 = 10	7.4 < 𝐷𝑂 < 12.6
	Physical characteristics	𝑉 𝑤𝑎𝑡𝑒𝑟 (𝑚/𝑠) 𝑫𝒆𝒑𝒕𝒉 (𝑫)(𝒎) {

Table 2 : Key parameters for suspended solids phase (Mean values for Alsace extracted from Eaufrance1 and variability from (Meybeck, 1982)).

 2

	Characteristic	Parameters	Meaning	Mean range	Variability (𝑷 𝟏𝟎 < 𝑉𝑎𝑙𝑢𝑒 < 𝑷 𝟗𝟎 )
	Geometry	𝑫 (𝒎𝒎) 1	𝐷 is the diameter of one grain	𝐷 50 = 35 𝑚𝑚	1 < 𝐶 𝑠 < 600
			Particulate Organic Carbon:
		POC (𝒎𝒈 𝑪 /𝑳)1	Measurement of the total carbon	𝐶 𝑐 50 = 7.2 𝑚𝑔 𝐶 /𝐿	1 < 𝐶 𝑐 99% < 30
	Geochemical		concentration within the sample
	composition	𝑪 𝒔 (𝒎𝒈/𝑳) 2	Measurement of the Total Suspended Solid concentration	𝐶 𝑠 50 = 800 𝑚𝑔/𝐿	5 < 𝐶 𝑠 < 50 000 𝐶 𝑠 99% < 5000

Table 3 : Typical values for interstitial porewater phase

 3

	Description	Parameters	Variability
			Aerobic pore water: 4 -20
	Concentrations	𝑫𝑶𝑴 (𝒎𝒈/𝑳)	Anaerobic pore water: 10 -390
			(Katagi, 2006)
	Degradation and redox activity	𝑫𝑶 (𝒎𝒈 𝑶 𝟐 /𝑳)	0% 𝐷𝑂 𝑤𝑎𝑡𝑒𝑟 < 𝐷𝑂 𝑠𝑒𝑑𝑖𝑚𝑒𝑛𝑡 < 100% 𝐷𝑂 𝑤𝑎𝑡𝑒𝑟

Table 4 : Key parameters for sediment phase Description Parameters Meaning Variability

 4

	Geochemical composition	𝐟𝐨𝐜 (%)	Fraction of organic carbon: Ratio between organic carbon and organic matter contained in sediment	0.5 < 𝑓𝑜𝑐 < 10 (OECD, 2002; Wauchope et al., 2002)
				Texture	Porosity (%)
				Sandy	56 -36
				Silty	56 -39
		𝛟 (%)	Porosity: Relative volume of pores	Loamy	55 -30
				Clayey	70 -35
				(Kutílek and Nielsen, 1994)
	Geometry

Table 6 : Applicability of the selected model, mathematical formalism and number of required input parameters

 6

	Model	Formalism Conceptu al Physic al	Spatial scale (𝒌𝒎 𝟐 )	Spatial distribution Horizontal Vertical	Required data (number) Measura Conceptu ble al

Table 7 : List of the most frequently used processes among the selected models discussed above. Water cycle refers to hydrodynamic and macro pollutant pathways.

 7

Table 8 : Physicochemical properties of studied pesticides, expected behaviours and available analytical methods

 8 𝐻 14 𝐶𝑙𝑁 5 𝐶 14 𝐻 20 𝐶𝑙𝑁𝑂 2 𝐶 14 𝐻 20 𝐶𝑙𝑁𝑂 2 𝐶 17 𝐻 26 𝐶𝑙𝑁𝑂 2 𝐶 15 𝐻 21 𝑁𝑂 4 𝐶 15 𝐻 22 𝐶𝑙𝑁𝑂 2 𝐶 13 𝐻 19 𝑁 3 𝑂 4

	Active substance	Atrazine	Acetochlor	Alachlor	Butachlor	Metalaxyl	S-Metolachlor	Pendimethalin
	General description
	Usage 2	Herbicide	Herbicide	Herbicide	Herbicide	Fungicide	Herbicide	Herbicide
	Approved/not in France 3 (end date)	Not approved (2003)	Not approved (2013) Not approved (2008) Not approved	Approved	Approved	Approved
	Priority substance	Yes (Hazardous)	No	Yes	No	No	No	No
	Chemical properties
	Chemical family	Triazine	Chloroacetamide	Chloroacetamide	Chloroacetamide Phenylamide	Chloroacetamid e	Dinitroaniline
	Chemical structure
	Chemical formula 𝐶 8 Major transformation products2 , 4 Deethylatrazine, hydroxyatrazine	2-[(2-ethyl-6-methylphenyl)amino]-2-oxoethanesulfonic acid, N-(ethoxymethyl)-N-(2-ethyl-6-methylphenyl)acetami	alachlor ethane sulphonate, alachlor oxanilic acid	/	(R)-2-((2,6-Dimethyl-phenyl)-(2-methoxy-acetyl)-amino)-propionic acid, N-(2,6-dimethylphenyl)-N-	Metolachlor oxanilic acid (MOXA), metolachlor ethane sulfonic acid (MESA)	2-methyl-3,5-dinitro-4-(pentan-3ylamino)benzoi c acid
			de			(methoxyacetyl)al
						anine
	Environmental behaviour
	Persistence (Water-
	sediment 𝑫𝑻 𝟓𝟎 -	80	19.7	2	56	32.1	47.5	16
	days)2

  [START_REF] Thullner | Quantification of organic pollutant degradation in contaminated aquifers using compound specific stable isotope analysis -Review of recent developments[END_REF], carbon stable isotope fractionation was implemented "by modelling stable isotopologues as separate chemical species" (𝐶 𝑡𝑜𝑡𝑎𝑙 = 12 𝐶+ 13 𝐶). The differential of the Rayleigh equation gives us for 𝑅 ≪ 1 and 12 𝐶 ≫ 13 𝐶:

	𝑑 13 𝐶 13 𝐶	= (1 + 𝜖) *	𝑑 12 𝐶 12 𝐶	→ 𝒌 𝒉𝒆𝒂𝒗𝒚 = (𝟏 + 𝝐) * 𝒌 𝒍𝒊𝒈𝒉𝒕

Table 9 : Time and spatial discretization tested in VENSIM® and VBA VENSIM® VBA Time discretization (s)

 9

  1. Measured concentrations result from pesticide in interstitial water and pesticide readily available ( 𝐶 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 𝐶 𝑤𝑎𝑡𝑒𝑟 + 𝑋 𝑒𝑞 ). With no expected degradation 𝐶 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 (𝑡) = 𝐶 0 and then, 𝑪 𝟎 -𝑪 𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 = 𝑿 𝒏𝒆𝒒 + 𝑿 𝒂𝒈𝒆𝒅 (11) With 𝑋 𝑒𝑞 the fraction of equilibrium sorption, 𝑋 𝑛𝑒𝑞 the fraction of nonequilibrium sorption and 𝑋 𝑎𝑔𝑒𝑑 the fraction of aged sorption. 2. Measured concentrations result from pesticide in interstitial water, pesticide readily available and pesticide moderately available ( 𝐶 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 𝐶 𝑤𝑎𝑡𝑒𝑟 + 𝑋 𝑒𝑞 + 𝑋 𝑛𝑒𝑞 ). With no expected degradation 𝐶 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 (𝑡) = 𝐶 0 and then, 𝑪 𝟎 -𝑪 𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 = 𝑿 𝒂𝒈𝒆𝒅 (12) Available data, did not enable to calibrate the Freundlich isotherm. Then, a linear isotherm was assumed with data from PAN database, 𝐾 𝑜𝑐 = 190.

Table 10 : Hydrolysis and biodegradation parameters for S-Metolachlor used for the global experiment.

 10

		Biodegradation	Hydrolysis
		𝑫𝑻 𝟓𝟎 (days)	𝝐 (‰)	𝑫𝑻 𝟓𝟎 (days)	𝝐 (‰)
	Raw values	25	-3,4	107	-2,1
	Corrected values	33	-3,8	107	-2,1
	Data issued from this work are expressed in remaining fraction (%):

  and 𝐾 𝑂 2 𝑖𝑛ℎ𝑖𝑏. the calibrated inhibition factor (𝑚𝑔 𝑂 2 /𝐿). Note that for anaerobic bacteria,

	𝐾 𝑂 2 𝑖𝑛ℎ𝑖𝑏. 𝐾 𝑂 2 𝑖𝑛ℎ𝑖𝑏. +[𝑂 2 ] becomes	[𝐶 𝑖 𝑙 ] 𝑖𝑛ℎ𝑖𝑏. +[𝑂 2 ] 𝐾 𝑂 2

  Alachlor). D'autres initiatives nationales sont à noter, notamment le plan Ecophyto lancé en 2008 et visant à diminuer de moitié l'usage des pesticides d'ici à 2025. Ainsi, depuis 2017, l'usage des pesticides est interdit dans les lieux publics. En matière d'eau de consommation, les réglementations internationales définissent des valeurs seuils au-delà desquelles l'usage des eaux brutes n'est plus autorisé à des fins alimentaires. Ainsi, une eau brute dont les concentrations excèdent 0.1 𝜇𝑔. 𝐿 -1 pour une substance et 0.5 𝜇𝑔. 𝐿 -1 pour la somme de toutes les substances détectées ne pourra pas être traitées et distribuée dans les réseaux d'eau potable. A noter notamment qu'en 2014, selon l'Agence Régionale de Santé (ARS), évaluait à 4.5% la population nationale soumise à des dépassements réguliers de ce seuil.

	l'
	𝑑𝑡	= 𝜇 𝑚𝑎𝑥 *	[𝐶 𝑖 𝑙 ] 𝐾 𝑆 * [𝐶 𝑖 𝑙 ]	*	[𝐶 𝑇𝐸𝐴 𝑙 𝐾 𝑇𝐸𝐴 * [𝐶 𝑇𝐸𝐴 ] 𝑙	]	*	𝑖𝑛ℎ𝑖𝑏. 𝐾 𝑂 2 𝑖𝑛ℎ𝑖𝑏. + [𝑂 2 ] 𝐾 𝑂 2	* 𝐵 -𝑘 𝑑𝑒𝑐𝑎𝑦 * 𝐵
	𝒅𝑪 𝒊 𝒍 𝒅𝒕	= -	𝟏 𝒀	* (𝝁 𝒎𝒂𝒙 *	[𝑪 𝒊 𝒍 ] 𝑲 𝑺 * [𝑪 𝒊 𝒍 ]	*	[𝑪 𝑻𝑬𝑨 𝒍 𝑲 𝑻𝑬𝑨 * [𝑪 𝑻𝑬𝑨 ] 𝒍	]	*	𝒊𝒏𝒉𝒊𝒃. 𝑲 𝑶 𝟐 𝑲 𝑶 𝟐 𝒊𝒏𝒉𝒊𝒃. + [𝑶 𝟐 ] ) * 𝑩	(16)

http://www.naiades.eaufrance.fr/

PPDB, 2017 http://sitem.herts.ac.uk/aeru/ppdb/)

E-phy (https://ephy.anses.fr/)

[START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF]

Remerciements

CE-QUAL-W2, GB-PMBM, InCa, QUAL2EU, are mainly used as research tools. They compute two different modules in the meantime, accounting for the hydrological cycle and the pollutant cycle. Note that CE-QUAL-W2 does not account for pesticide fate simulation but for eutrophication cycle model

PegOpera is the only model especially designed for resource management. It is fitted with 4 submodels dedicated to the hydrological cycle, the water quality cycle, the thermal variation and the pollutant discharge management.

-3/Model characteristics, applicability and required data

The 5 multimedia models rely on the fugacity concept. In each compartment the model solves a linear system of equations representing the considered processes. Each process is set with transfer and degradation rates, specific to the studied components and environment (𝐶 𝑖 = 𝑍 𝑖 * 𝑓 𝑖 with 𝐶 𝑖 the concentration of pollutant 𝑖, 𝑍 𝑖 its fugacity capacity and 𝑓 𝑖 the fugacity of the pollutant in studied compartment). In this case, model parametrisation requires less input data but parameters do not have physical meaning and can't be measured.

3) Sorption experiment

In this experiment we tried to fit the "two sites one rate" formalism with experimental data. Concentrations of extracted pesticide over time were compared with simulated concentrations assuming mild or strong extraction.

The measured value after 1 day of incubation was not consistent with the rest of the dataset. Then, it was considered as an outlier for the calibration procedure. For convenience, all concentrations are expressed in 𝑚𝑔. 𝐿 -1 and the grey line represents the sum of the concentration in liquid phase and the equilibrium sorption.

Assuming the extraction of both equilibrium and non-equilibrium fractions, the model provides good fit to measurements. In the beginning, the non-equilibrium sorption soars to a threshold around 4.5 𝑚𝑔. 𝐿 -1 (1.9 𝜇𝑔. 𝑔 -1 ). In the meantime and until approximatively 60 days, the aged fraction increases in subtracting pesticide to both water and non-equilibrium fraction. After 60 days and to the end non-equilibrium fraction is forced to desorbe to compensate the ageing process. In other words, the pollutant is transferred from a reversible to an irreversible compartment. In the end, non-equilibrium sorption accounts for approximately a quarter of the initial mass, while the aged fraction accumulated more than half of the initial pesticide mass. If most of them agree to define the 𝐶𝑎𝐶𝑙 2 extraction as a way to recover equilibrium sorbed fraction, there is a fierce debate on which protocol should be used to extract non equilibrium and aged-sorbed fraction. Solvent extraction seems to be required for poorly available fractions but the solvent to choose, the quantity to apply, the time to wait, etc. are still at stakes as illustrated in Figure 16. [START_REF] Barriuso | Solvent extraction characterization of bioavailability of atrazine residues in soils[END_REF] and [START_REF] Park | Assessment of bioavailability of soilsorbed atrazine[END_REF] propose two successive methanol extractions, with 4 hours shaking for extracting Atrazine in clay soil while [START_REF] Gulkowska | Time-dependent sorption of two novel fungicides in soils within a regulatory framework[END_REF] proposes a methanol extraction at 80°𝐶 and 100 bar for extracting penflufen and fluxapyroxad from different type of soils. This panel of available methods advocates for a choice case-by-case of the extraction method (Tiktak, 2015).

Then, the compartmental resolution of sorption leads to ambiguity when trying to precisely describe borders to each box. In this way, different approaches based on continuous description (as intra-particle diffusion) were tested [START_REF] Van Beinum | Pesticide Sorption and Diffusion in Natural Clay Loam Aggregates[END_REF].

The last identified issue to tackle is that some authors use the third compartment as a representation of the biodegraded fraction during aged sorption experiments (EFSA, 2015) while others consider this rate as the sum of the "transformation rate coefficient" and "the formation of non-extractable residues" [START_REF] Gulkowska | Time-dependent sorption of two novel fungicides in soils within a regulatory framework[END_REF]. Nonetheless, because this compartment is a one way exchange box, aged fraction is permanently stuck within this compartment and will accumulate to the infinite, which has no physical meaning.

Altogether, this experiment confirmed the ability of the "two sites one rate" formalism implemented in VENSIM® to predict the trend of sorption/desorption/ageing process. It also showed that after 200 days of incubation, the aged fraction of S-Metolachlor in Alteckendorf soil is expected to account for more than 50% of the initial mass. This huge storage of pesticides in soil might cause punctual contaminations due to soil destructuring (ploughing, intense rain event …). Moreover, because aged pesticides are less available for degradation, it is likely to significantly increase the persistence of organic pollutants in the environment [START_REF] Fragoulis | A model assessing bioavailability of persistent organic pollutants in soil[END_REF].

Appendices Appendix 1: Detailed processes list and number of time used

Processes

CalTOX ChemCAN ChemRANGE EQC GB-PMBM InCa PegOpera QUAL2EU CE-QUAL-W2 Frequence

Appendix 2: Supplementary information on future processes to be implemented

Destructive biotic processes

In aqueous phase, when pollutant is metabolized as an energy source for bacterial growth, the Monod kinetics (16) is believed to be appropriated. At the opposite, when cometabolism is responsible for pollutant degradation, Michaelis-Menten kinetics is used [START_REF] Liqiang | The influential factors of hydrolysis of organic pollutants in environment[END_REF].

As the oxic conditions in the first centimeters of sediments are likely to suddenly change with depth [START_REF] Honti | Deriving Persistence Indicators from Regulatory Water-Sediment Studies -Opportunities and Limitations in OECD 308 Data[END_REF][START_REF] Wang | Microscale chemical features of sediment-water interface in Hongfeng Lake[END_REF], the inhibitory effect of 𝑂 2 is taking into account, as first proposed by [START_REF] Henze | Activated Sludge Model No 1 (IAWPRC)[END_REF]. [START_REF] Alvarez-Zaldívar | Biogeochemical modelling of in situ biodegradation and stable isotope fractionation of intermediate chloroethenes in a horizontal subsurface flow wetland[END_REF] also proposed to use inhibition factor for terminal electron acceptor (TEA):

Where 𝜇 𝑚𝑎𝑥 is the maximum specific growth rate of the bacteria (𝑑𝑎𝑦 -1 ), 𝐵 is the bacteria concentration (absorbance), 𝑘 𝑑𝑒𝑐𝑎𝑦 is the first order decaying rate (𝑑𝑎𝑦 -1 ), 𝐾 𝑆 (resp. 𝐾 𝑇𝐸𝐴 ) the concentration (𝑚𝑔/𝐿) of substrate (resp. TEA) when 𝜇 = 𝜇 𝑚𝑎𝑥

Example of biogeochemical cycle: Atrazine

As destructive reactions result in substrate, 𝑂 2 , 𝑝 𝐻 , etc variations, these changes have to be assessed. Well-known atrazine biochemical system equations are developed here.

(La [START_REF] Cecilia | Kinetics of atrazine, deisopropylatrazine, and deethylatrazine soil biodecomposers[END_REF] proposed a comprehensive description of the atrazine biodegradation cycle. Since metabolites decomposition is likely to play a prominent part in the biogeochemical cycle, it is considered in this formalism. Aerobic (dechlorination and dealkylation) and anaerobic (oxidation) degradation of the atrazine happen as following:

 Under aerobic conditions:

with 𝐶𝐻 2 𝑂 the 𝐶 source for bacteria growth.

 Under anaerobic conditions:

La [START_REF] Cecilia | Kinetics of atrazine, deisopropylatrazine, and deethylatrazine soil biodecomposers[END_REF] considers different pools of bacteria (from 1 isolated bacteria type to artificially recomposed microbial community) for parameterization. Then, the proposed parameterization data should only be used if the microbial communities present in the experiment are similar to the one reported in the literature. (𝑡 = 𝑇 0 )). S-Metolachlor proved to be the more stable of the tested mix.

Appendix 6: Traduction Française de l'introduction

Contexte de l'étude

L'activité humaine associée à l'utilisation massive des ressources en eau conduit à des pollutions de l'eau par de multiples composés synthétiques [START_REF] Schwarzenbach | Environmental Organic Chemistry / Edition[END_REF]. De plus, les prédictions de changement climatique et d'augmentation de la population seront liées à une modification du cycle hydrologique de l'eau et par conséquent à une dégradation générale de la qualité de l'eau [START_REF] Jackson | Water in a Changing World[END_REF]. C'est ainsi que dès le début des années 1990, les pays des nations unies ont reconnu les contaminations de l'eau par les micropolluants comme l'une des préoccupations mondiales majeure à venir [START_REF] Wania | Peer Reviewed: Tracking the Distribution of Persistent Organic Pollutants[END_REF].

Ces molécules artificielles ou naturelles couramment nommées micropolluants ou « contaminants émergents » sont représentées par une large variété de substances depuis les produits pharmaceutiques jusqu'aux pesticides en passant par les produits de beauté. Dans nos systèmes aquatiques, ces substances sont préférentiellement issues de l'agriculture et des eaux usées domestiques et industrielles traitées [START_REF] Elsner | Compound-specific isotope analysis (CSIA) of micropollutants in the environment -current developments and future challenges[END_REF][START_REF] Luo | A review on the occurrence of micropollutants in the aquatic environment and their fate and removal during wastewater treatment[END_REF].

Les produits phytopharmaceutiques, couramment nommés "pesticides", sont clairement identifiés comme partiellement responsables des pollutions des eaux de surface. Hiérarchisés en trois grandes classes selon leur objectif (fongicide, insecticide et herbicide), ils sont largement employés pour garantir et augmenter les rendements de production en agriculture intensive. Malgré une utilisation décroissante en Europe depuis quelques dizaines d'années, Eurostats a reporté en 2003 une consommation en pesticide de 220 000 tonnes pour l'Europe (25 membres), dont 28% du total en France (European Commission and Eurostats, 2007). La persistance avérée de ces substances dans l'environnement, leur procure la capacité d'être transportés sur plusieurs milliers de kilomètres et en fait des substances omniprésentes dans les rivières Françaises [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF][START_REF] Schwarzenbach | Environmental Organic Chemistry / Edition[END_REF][START_REF] Wania | Peer Reviewed: Tracking the Distribution of Persistent Organic Pollutants[END_REF]. A ce titre, en 2013, des pesticides ont été détectés dans 92% des rivières Françaises (Commissariat général au développement durable, 2015). Les pratiques agricoles apparaissent ainsi comme largement responsables des fort taux de pollutions aux pesticides observés en rivières et dans les eaux souterraines [START_REF] Gutowski | A comparative assessment of the transformation products of S-metolachlor and its commercial product Mercantor Gold(®) and their fate in the aquatic environment by employing a combination of experimental and in silico methods[END_REF].

Les micropolluants sont nommés ainsi en accord avec les faibles concentrations dans lesquelles ils sont mesurés dans l'environnement (de l'ordre du 𝑛𝑔/𝐿 au 𝜇𝑔/𝐿) [START_REF] Elsner | Compound-specific isotope analysis (CSIA) of micropollutants in the environment -current developments and future challenges[END_REF][START_REF] Luo | A review on the occurrence of micropollutants in the aquatic environment and their fate and removal during wastewater treatment[END_REF]. Malgré ces faibles concentrations, leur toxicité à court et long terme est avérée : citons l'exemple des perturbateurs endocriniens ou encore des effets de résistance aux antibiotiques des microorganismes [START_REF] Luo | A review on the occurrence of micropollutants in the aquatic environment and their fate and removal during wastewater treatment[END_REF]. Ainsi, puisque plus de 65% de la production nationale d'eau potable repose sur des prélèvements d'eau de surface (Commissariat général au développement durable, 2016), les pollutions aux micropolluants inquiètent les pouvoirs publics responsables de la santé de leurs citoyens.

C'est dans ce contexte que les institutions internationales et nationales ont mis en oeuvre des lois de police afin de limiter les problèmes de pollution. Au niveau Européen, la Directive Cadre sur l'Eau (DCE) en est un bon exemple puisqu'elle impose aux pays membres de l'UE l'atteinte du bon état écologique des masses d'eau d'ici à 2027 ainsi que l'interdiction de l'usage de certains pesticides classés comme substances prioritaires dangereuses (notamment l'Atrazine et dégradations soient différentes que pour les processus biotiques, les produits de transformation peuvent être identiques [START_REF] Honti | Deriving Persistence Indicators from Regulatory Water-Sediment Studies -Opportunities and Limitations in OECD 308 Data[END_REF]. Les facteurs contrôlant ces réactions sont bien identifiés (e.g. température, pH, luminosité, DOC) [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF] et les relations liants ces paramètres aux vitesse de dégradation connues.

En ce sens, [START_REF] Katagi | Behavior of Pesticides in Water-Sediment Systems[END_REF] identifie avec certitude le 𝑝𝐻 la teneur en carbon organique et la température comme les facteurs principaux d'influenç au sein de l'interface eau-sédiment.

Processus non-destructifs :

Dans le cas de ces processus, aucune réduction de la masse n'est observée. Les polluants sont transférés d'un compartiment ou d'une phase à un autre. Les deux processus prédominants sont la sorption et la diffusion qui sont dirigés par les concentrations et les caractéristiques de la matrice environnementale. Cependant, de la même manière que les processus destructif, il est possible d'observer des diminutions de concentrations liées à ces processus qui laisseraient faussement penser à une dégradation.

Les considérations précédentes nous montrent qu'en termes de concentration les processus destructifs et non-destructifs peuvent avoir des effets similaires. Ils ne peuvent ainsi pas toujours être différenciés en s'appuyant uniquement sur des analyses de concentrations. L'approche par bilan de masse permet de s'affranchir de ce verrou mais est difficilement applicable à l'échelle des bassins versants par exemple. Ainsi, Honti et Fenner (2015) proposent l'utilisation de l'Analyse Isotopique Composé Spécifique (AICS) comme solution au problème.

Introduction à l'Analyse Isotopique Composé Spécifique

Jusqu'à aujourd'hui l'AICS a fait ses preuves pour différenciés les processus de dégradation des polluants organiques industriels en eau souterraine [START_REF] Lutz | A modelbased assessment of the potential use of compound-specific stable isotope analysis in river monitoring of diffuse pesticide pollution[END_REF][START_REF] Thullner | Quantification of organic pollutant degradation in contaminated aquifers using compound specific stable isotope analysis -Review of recent developments[END_REF]. Cependant, son application aux eaux de surface reste lacunaire. Cette solution apparit prometteuse puisqu'elle offre l'avantage de détecter les processus de dégradation sans avoir recours au bilan de masse ou à l'analyse des produits de dégradation [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF]. Cependant, pour une analyse complète des voies de dégradation en milieu naturel, des études préalables du comportement de chaque molécule étudiée dans toutes les conditions environnementales envisageables doivent-être menées [START_REF] Lutz | A modelbased assessment of the potential use of compound-specific stable isotope analysis in river monitoring of diffuse pesticide pollution[END_REF]. Cependant, si ces données sont souvent disponibles pour les polluants des eaux de surface (hydrocarbures), seules quelques-unes sont disponibles pour les pesticides. [START_REF] Elsner | Compound-specific isotope analysis (CSIA) of micropollutants in the environment -current developments and future challenges[END_REF] représente le premier recueil de facteurs d'enrichissement pour plusieurs pesticides, principalement en conditions contrôlées.

L'AICS repose sur l'observation des dérives des compositions isotopiques du carbone au cours de la dégradation du composé [START_REF] Meckenstock | Stable isotope fractionation analysis as a tool to monitor biodegradation in contaminated acquifers[END_REF]. En d'autres termes, la destruction préférentielle des liaisons chimiques à faible énergie (isotope léger -isotope léger) entraine un enrichissement en isotopes lourds dans la fraction non dégradée (Figure 5). Ainsi, une augmentation du ratio isotopique 𝛿 13 𝐶 = 𝐶 13 𝐶 12 d'un composé mère prouve l'apparition d'un phénomène destructif [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF].

 L'AICS permettra de déconvoluer chacun des processus ;  L'étude mécanistique de chacun des processus requière l'utilisation d'un modèle à base physique. La variabilité spatiale influencera donc les vitesses de réaction ou de transport le long de la colonne.

 Un pas de temps horaire ou journalier devra être utilisé selon les comportements attendus des différents processus (voir Table 8).

L'objectif de cette discussion est donc de déterminer si un modèle répondant à l'ensemble des critères présentés ci-dessus est actuellement disponible. Une comparaison d'une sélection de 9 modèles est donc réalisée.

Vue d'ensemble des modèles disponibles

Cette comparaison est réalisée selon la méthodologie proposée par [START_REF] Quilbe | Selecting a pesticide fate model at the watershed scale using a multi-criteria analysis[END_REF], s'appuyant sur une analyse multicritère évaluant 3 aspects: les objectifs du modèle, ses caractéristiques et son domaine d'application.

Commençons par distinguer les 4 objectifs des modèles :

 Modèle pour la recherche  Représentation avec le plus haut degré de complexité de tous les processus connus. Objectif des modèles : 5 des 9 modèles sont des modèles multi-compartimentaux (Table 5). Cette approche est très efficace comme première approche pour des études à grande échelle [START_REF] Quilbe | Selecting a pesticide fate model at the watershed scale using a multi-criteria analysis[END_REF] mais n'est adapté à l'évaluation des échanges entre grandes régions uniquement [START_REF] Pistocchi | Spatially explicit multimedia fate models for pollutants in Europe: State of the art and perspectives[END_REF]. EQC et ChemRANGE sont les deux modèles les plus simples

Appendix 7: Traduction Française de la conclusion

Ce travail a mis en évidence le manque de connaissances relatives au devenir des pesticides au sein de l'interface eau-sédiment. Au vu de la complexité de cette matrice environnementale, des outils de pointes sont requis afin d'identifier les voies de dégradations prioritaires. Le modèle développé fait office d'approche préliminaire vers une meilleure compréhension de la dynamique de l'interface eau-sédiment.

En conditions statiques, le modèle développé a montré sa capacité à reproduire individuellement chacun des processus suivants ; Diffusion, sorption/désorption/ageing et hydrolise. La dernière expérience met de plus en évidence les capacités du modèle à gérer les processus simultanément. Il serait donc envisageable d'utiliser cet outils à des fins d'analyse des résultats issus des expériences visant à déterminer des temps de demi-vie.

L'application du modèle sur l'expérience de sorption et sur le sol de rizière apporte des conclusions intéressantes. L'expérience d'hydrolyse montre que dans les conditions environnementales classiques ce processus n'est probablement pas dominant pour les composés étudiés. A l'opposé, le processus d'ageing a montré son implication forte dans la diminution de la biodisponibilité et ainsi de la biodégradation des pesticides après plusieurs centaines de jours d'incubation. Comme reporté dans la littérature, le modèle a montré que les pesticides ne pénètrent pas les couches profondes de sédiment en considérant le processus de diffusion comme seul vecteur de transport. L'expérience d'hydrolyse apporte de nouvelles connaissances sur le potentiel de dégradation abiotic des six chloroacetanilides et du triazine étudiés. Les valeurs de demi-vie et d'enrichissement isotopique mesurées en condition alcalines et acides permettront par analyse statistique d'obtenir des valeurs pour la gamme environnementale complète. L'apparition massive de produits de dégradation permettra aussi une étude plus pointue de leur formation.

De nombreuses perspectives ont été discutées au cours de ce travail. Comme proposé par [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF], l'usage du 2D-AICS permettra à termes une discrimination encore plus précise des différents processus destructifs [START_REF] Elsayed | Using compound-specific isotope analysis to assess the degradation of chloroacetanilide herbicides in labscale wetlands[END_REF]. C'est notamment dans cette optique que Jérémy Masbou (chercheur CNRS au LHyGeS) mène à l'heure actuelle des tests d'enrichissement isotopique sur l'azote sur notre expérience d'hydrolyse. Le 2D-AICS sera très facilement intégré au modèle actuel au même titre que les cinétiques d'apparition des produits de transformation. La prédiction du comportement des produits de transformation est aussi un enjeu majeur pour les études de risque puisque certains d'entre eux sont parfois plus toxiques que les molécules mères et percolent beaucoup plus facilement vers les eaux souterraines utilisées comme eau de consommation [START_REF] Fenner | Evaluating Pesticide Degradation in the Environment: Blind Spots and Emerging Opportunities[END_REF]. Une perspective proche est l'introduction de l'Analyse Isotopique Enantiomérique Spécifique (AIES) qui fournit des informations similaires à l'AICS en se basant cette fois-ci sur la conformation géométrique des produits de dégradation.

Résumé

The predominance of intensive cropping in France make it the first user of pesticides in Europa. Pesticides are likely to enter aquatic systems through many different ways and then, to interact with sediment.

We implemented a coupled lab-scale experiments and modelling approach (VENSIM®). The use of Compound Specific Isotope Analysis (CSIA) allowed us to assess the role of each process One hydrolysis experiment was conducted and lead to derive half-life values and carbon enrichment factors.

In-silico experiments, relying on experimental dataset were conducted to assess the model ability to compute diffusion and sorption as well as to check its ability to simulate complex systems.

The model proved to be functional and showed the important role of ageing in the environment.

Mots-clés: Water-sediment interface, pesticides behaviour, CSIA, isotope, modelling, VENSIM