Faiez Zannad

Steven Macari

Drug treatment with empagliflozin was beneficial in people with heart failure with preserved ejection fraction: plain language summary of the EMPEROR-Preserved study

What is this summary about?

This summary describes a study of a new pill for treating chronic heart failure called empagliflozin (brand name Jardiance®). The study is called EMPEROR-Preserved and was published in the New England Journal of Medicine. Chronic heart failure is a condition where the heart does not pump blood around the body properly. Heart failure causes symptoms such as shortness of breath, tiredness and build-up of too much water in the body (fluid retention). These symptoms often need hospital treatment and increase the risk of early death.

What was the EMPEROR-Preserved study?

The EMPEROR-Preserved study looked at how empagliflozin works in people living with a type of heart failure called heart failure with preserved ejection fraction. In this type of heart failure, the lower left chamber (ventricle) of the heart is too stiff to fill with enough blood during each heartbeat.

What happened during the study?

Almost 6000 people living with preserved ejection fraction heart failure were asked to take either a pill containing empagliflozin or a placebo, an identical pill lacking empagliflozin, daily. The choice of pill for each participant was randomly assigned. The study was double-blinded, meaning that neither the participants nor their doctors knew which pill the participants were taking.

What were the results?

After an average of 26 months of treatment, empagliflozin reduced the risk of participants needing hospital treatment for complications of heart failure by about 30%. Side effects were generally similar in participants who took empagliflozin and in those who took the placebo, except for genital infections like thrush, which happened in more people who took empagliflozin (2.2%) than in those who took the placebo (0.7%).

What do the results mean?

A previous study called EMPEROR-Reduced found that empagliflozin had similar benefits in participants with heart failure with reduced ejection fraction. Therefore, the overall evidence shows that empagliflozin can help people with heart failure whether it is caused by reduced ejection fraction or preserved ejection fraction.

• Empagliflozin: em-pa-gli-FLOE-zin • Jardiance: jar-DEE-ans

The hearts of people with chronic heart failure do not pump enough blood around the body. This means that their organs do not receive enough oxygen and nutrients, and also means that waste products such as carbon dioxide are not removed quickly enough.

People with chronic heart failure generally have one or more of the following symptoms: • Shortness of breath (in severe cases, this occurs even when resting) • Fluid retention (edema), causing swollen legs and stomach and difficulty breathing • Reduced physical strength and stamina • Fatigue, tiredness and sluggishness • Difficulty performing daily tasks • Difficulties with memory and concentration Chronic heart failure can be classified according to how badly it affects a person -one common method is the New York Heart Association (NYHA) Functional Classification.

Adapted from Zannad F, Macar S. Drug treatment with empagliflozin lowered risk for hospitalization in people with heart failure with reduced ejection fraction: plain language summary of the EMPEROR-Reduced study. Future Cardiol. doi:10.2217/fca-2023-0090 (2023) (Epub ahead of print).

What is chronic heart failure with preserved ejection fraction?

Who sponsored this study?

The EMPEROR-Preserved study was sponsored by Boehringer Ingelheim and Eli Lilly and Company Diabetes Alliance. This plain language summary may be helpful for healthcare professionals who want to learn more about chronic heart failure, as well as people living with heart failure and their family and friends.

The purpose of this plain language summary is to help you to understand the findings from recent research. Empagliflozin (brand name Jardiance®) is used to treat the condition under study that is discussed in this summary. Approval varies by country; please check with your local provider for more details. The results of this study may differ from those of other studies. Health professionals should make treatment decisions based on all available evidence, not on the results of a single study.

Who is this article for?

What is the purpose of this plain language summary? Class I No symptoms and no limitation in ordinary physical activity, e.g., shortness of breath when climbing stairs, etc.

Class III

Marked limitation in activity due to symptoms, even during less-than-ordinary activity, e.g., walking short distances (20-100 meters). Comfortable only at rest.

NYHA classification of heart failure

Class IV Severe limitations. Experience symptoms even while at rest. Mostly bedbound patients. There are two main types of chronic heart failure, depending on the heart's ejection fraction. Ejection fraction is the percentage of blood pumped out of the lower left chamber of the heart (the left ventricle) at each heartbeat.

• Heart failure with reduced ejection fraction is where the left ventricle does not contract strongly enough with each heartbeat, so the heart does not empty (eject) enough of its blood volume at each heartbeat • Heart failure with preserved ejection fraction is where the left ventricle -although capable of pumping out enough of its volume at each heartbeat -is too small and stiff to actually fill with enough blood during each heartbeat. Preserved ejection fraction is defined as a left ventricular ejection fraction of more than 40%, meaning that at least 40% of the blood within their hearts was pushed out with every heartbeat

What is empagliflozin?

Empagliflozin is a medicine originally developed to treat people with type 2 diabetes. It is called an SGLT2 inhibitor because it attaches to a protein in the kidneys called sodium-glucose transporter 2 (SGLT2).

Empagliflozin causes the kidneys to lose sugar (glucose) in the urine (pee) in people with type 2 diabetes, which lowers their dangerously high blood glucose levels and reduces their risk of heart and kidney complications.

Studies have suggested that empagliflozin may also have positive effects on the heart and kidneys even in people without diabetes, without lowering their blood sugar.

Plain language summary of the EMPEROR-Preserved study Plain Language Summary of Publication The EMPEROR-Preserved study tested whether empagliflozin improved the health and well-being of people with heart failure with preserved ejection fraction.

The study mainly measured the following issues in participants:

• Hospitalization and/or re-hospitalization for heart failure • Death from heart disease • How well the kidneys were working (kidney function)

• Quality of life. This was evaluated through a questionnaire called the Kansas City Cardiomyopathy Questionnaire (KCCQ)

• Side effects (unintended problems caused by a medication)

What did the EMPEROR-Preserved study look at?

The EMPEROR-Preserved study only included people with symptoms of chronic heart failure with a left ventricular ejection fraction of more than 40%, meaning that at least 40% of the blood within their hearts was pushed out with every heartbeat.

They also had to have NYHA classes II to IV heart failure.

Who took part in this study? What were the results of the study?

Empagliflozin had the following effects, on average:

Approximately 6000 participants in this study were given either a daily pill containing empagliflozin or a placebo, an identicallooking pill that didn't contain empagliflozin.

The pill that was given to each participant was randomly chosen (randomization). The study was double-blinded (neither the participants nor the researchers knew whether the participant was receiving the empagliflozin pill or the placebo pill).

The use of randomization and double-blinding means that, at the end of the study, any differences in results between participants taking empagliflozin and those taking placebo are very likely to be because of empagliflozin itself (not simply due to chance or other differences between the participants in each group or the results for each group being interpreted differently).

The study was designed so that each of these two groups of participants had approximately the same number of participants with or without type 2 diabetes.

After starting to take the pills, participants had regular check-ups for just over 2 years, on average. Plain language summary of the EMPEROR-Preserved study Plain Language Summary of Publication

  Class IIMild symptoms (mild shortness of breath and/or chest pain/angina) and slight limitation during ordinary activity.Plain Language Summary of Publication Zannad and Macari future science group www.futuremedicine.com 10.2217/fca-2023available to treat heart failure with reduced ejection fraction; however, until now there were no medicines with strongly proven benefits for heart failure with preserved ejection fraction.Adapted from Zannad F, Macar S. Drug treatment with empagliflozin lowered risk for hospitalization in people with heart failure with reduced ejection fraction: plain language summary of the EMPEROR-Reduced study. Future Cardiol. doi:10.2217/fca-2023-0090 (2023) (Epub ahead of print)

•

  Reduced the need for hospitalization for heart failure • Improved quality of life (as measured with the KCCQ questionnaire) • Did not damage the kidneys • Slowed further loss of kidney function, and • Had similar effects in people with or without type 2 diabetes These results were similar regardless of participant age, sex, ethnicity or other characteristics.

Characteristics of the people who participated in the EMPEROR-Preserved study

	67% had an ejection
	fraction of 50% or more
	Average ejection fraction
	was 54%
	51% had atrial brillation,
	a type of irregular heart
	beat
	The average body mass index (BMI) was 30 kg/m 2 55% had a BMI less than 30 45% had a BMI 30 or more	50% had reduced kidney function Average estimated glomerular ltration rate (eGFR) was
		61 ml/min/1.73 m 2
		(eGFR is one of the
		common ways to
		measure kidney function)

82% had NYHA function- al class II heart

failure 18% class III Less than 1% class IV 23% had previously been admitted to hospital because of heart failure 91%

of participants had high blood pressure.

	Plain Language Summary of Publication Zannad and Macari
	Sex
	55% male
	45% female
	Age
	Average age 72 years 64% aged 70 years or more 36% aged less than 70 years	The average systolic blood pressure (SBP) was 132 mmHg (SBP is the
		blood pressure caused
	Race	by the heart beating)
	76% White
	14% Asian
	4% Black
	Location
	45% from Europe
	25% Latin America
	12% Asia	49% had type 2 diabetes
	11% North America	51% did not have diabetes

www.futuremedicine.com 10.2217/fca-2023-0091

Acknowledgments

The authors and study sponsors thank all the people who participated in the study.

Financial disclosure

Faiez Zannad received personal consulting fees or fees for participating in running clinical trials from Boehringer Ingelheim during the conduct of the EMPEROR-Preserved study, from Applied Therapeutics, AstraZeneca, Bayer, Cardior, Cellprothera, Cereno Pharmaceutical, CVRx, Janssen, Merck, Novartis and Vifor Fresenius outside the submitted work, and other support from Cardiorenal and CVCT outside the submitted work. Steven Macari has worked on projects with AstraZeneca, Bayer, Boehringer Ingelheim, CLS Vifor, CVCT, Global Heart Hub, INSERM CIC-P CHRU de Nancy -INI CRCT, Kidney Disease Clinical Trialists, Optim'IC, Pfizer, Novartis, Servier and The Heart Failure Policy Network. Steven Macari did not receive any financial remuneration for this Plain Language Summary of Publication. The authors have no other relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript apart from those disclosed.

The EMPEROR-Preserved study shows that treating people with heart failure and preserved ejection fraction with empagliflozin:

• Lowers their risk of needing hospital treatment for complications of heart failure • Protects their kidneys • Lowers fluid retention (build-up of too much water in the body)

• Can improve their quality of life • Lowers blood sugar in those who also have type 2 diabetes • Has few side effects A previous study called EMPEROR-Reduced found that empagliflozin had similar benefits in people with heart failure with reduced ejection fraction. Therefore, empagliflozin may help people with heart failure whether it is caused by reduced ejection fraction or preserved ejection fraction.

What do the results of this study mean?

What side effects were seen?

Overall, empagliflozin did not cause many side effects in the EMPEROR-Preserved study (most medical problems during the study happened in at least as many participants taking the placebo pill as those taking the empagliflozin pill).

Kidney failure, a common complication of heart failure, was the most common side effect, and happened at the same rate in participants taking empagliflozin and those taking placebo (around 12 participants out of 100 [12%]).

Low blood pressure (hypotension), another common side effect experienced by people with heart failure, happened at least once in about 10 out of 100 (10.4%) of participants taking empagliflozin and almost 9 out of 100 (8.6%) of those taking placebo. Where can I find more information about this study?

This summary is based on the article titled 'Empagliflozin in heart failure with a preserved ejection fraction' .

• Anker et al. N. Engl. J. Med. 385, 1451-1461(2021) • You can read the full article for free at https://www.nejm.org/doi/full/10.1056/NEJMoa2107038

The reason for the EMPEROR-Preserved study and its experimental design has been discussed in detail in a previous article.

Competing interests disclosure

Faiez Zannad was one of the authors of the original article in the New England Journal of Medicine (N. Engl. J. Med. 385, 1451Med. 385, -1461Med. 385, [2021]]). The authors have no other competing interests or relevant affiliations with any organization or entity with the subject matter or materials discussed in the manuscript apart from those disclosed.

Writing disclosure

Writing assistance for this plain language summary was provided by Giles Brooke, PhD, of Elevate Scientific Solutions, and was supported financially by Boehringer Ingelheim.


Marcin Lefik
email: marcin.lefik@p.lodz.pl

Krzysztof Komeza
email: krzysztof.komeza@p.lodz.pl

Member, IEEE Ewa Napieralska Juszczak
email: ewa.napieralskajuszczak@univ-artois.fr

IEEE Senior Member

Senior Member, IEEE Noureddine Takorabet
email: noureddine.takorabet@univ-lorraine.fr

Farid Meibody-Tabar
email: farid.meibody-tabar@univ-lorraine.fr

Hamed Elmadah

Comparison of the Reluctance and Permanent Magnet Synchronous Machine operating at High Temperatures

Keywords: Fluid dynamics, Permanent magnet machines, Synchro-reluctant machine, High Temperature, Thermal analysis

The paper describes 3D analysis of the thermal field in permanent magnet synchronous machine and reluctance synchronous machine able to work at high internal temperature (HT° machine). 3D coupled fluid-thermal model of projected machine is created to obtain the distribution of thermal field and air flow and to calculate the average temperature of the most sensitive parts such as coils and permanent magnets. The influence of the surface state of the machine housing on its heating is examined. The points of the highest temperature inside analyzed machine are localized too. The comparison of thermal properties and the possibility of working at high temperatures for both kinds of machines has been carried out.

I. INTRODUCTION

THE HT° ELECTRIC MACHINES are designed for special purposes. They are used in environments where the ambient temperature is much higher than typical ones. Of course, this also causes an increase the temperature inside the motor housing. For example, the Permanent Magnet Synchronous Machine (PMSM) designed for working in the vicinity of the aircraft turbines, where the ambient temperature is about 200°C, will work with an internal temperature estimated to 450-500°C at thh hottest point. In order to work continuously at such internal temperatures it is necessary to use inorganic Electrical Insulation Systems (EIS) and to adapt the machine design to this inorganic technology [START_REF] Iosif | An insulation solution for coils of high temperature motors (500°C)[END_REF][START_REF] Liu | Thermal stability and performance data for SmCo 2:17 high-temperature magnets on ppm focusing structures[END_REF][START_REF] Cozonac | Materials characterization and geometry of a high temperature induction machine[END_REF][START_REF] Iosif | Assessment and improvements of inorganic insulation for high temperature low voltage motors[END_REF]. With this topology, two main options are possible: a synchronous permanent magnet machine, or a reluctance synchronous machines which produces torque from variations of the reluctance of the magnetic circuit [START_REF] Pyrhoonen | Design of Rotating Machines[END_REF][START_REF] Belhadi | Switched reluctance motor with magnetic slot wedges for automotive traction application[END_REF][START_REF] Lipo | Synchronous reluctance machines-A viable alternative for a.c. drives?[END_REF]. In the case of a machine with permanent magnets special SmCo permanent magnets must be used and these magnets have a relatively high electrical conductivity in comparison to the classical ones. During the design process of these HT° PMSM a particular attention must be paid to thermal strength of the winding insulation and the operating temperature of permanent magnets. The HT° motor, made with rigid inorganic coils, requires a specific design of the stator with rectangular teeth and opened slots. The slotting effect is much higher than for a classical machine; the only available magnets have a higher electric conductivity, the machine design must take these effects into consideration adding magnetic wedges between the stator teeth and segmenting the magnets. Thus, the design calculations of those electromechanical transducers require specific electromagnetic and thermal analyzes, which allow calculating additionally the thermal effects of power losses.

The paper describes the thermal analysis of HT° PMSM and HT° Synchronous Reluctance Machine (SRM) operating at high ambient temperatures using 3D field calculations. The machine is run at the rated speed of 5650 rpm. To analyze this phenomenon the 3D coupled thermal-fluid (CFD) model is used. The distribution of the temperature field and average temperature of the windings and permanent magnets (in the case of PMSM) are calculated. In addition, points with the highest value of the temperature (hot points) are localized. The impact of color and surface condition of the motor housing on the temperature distribution, the influence of the type of the material used for magnetic wedges, conductivity and segmentation of the permanent magnets on the power losses in the magnets is examined. This allowed the optimal way to choose the material and design to develop a prototype of the machine.

II. CHOICE OF TOPOLOGY OF HT° MACHINES.

As part of this project consists in studying the feasibility of such a machine with its power supply that can work durably in a warm environment. The choice of structure of the machine can be guided by different aspects mainly related to the materials used to the manufacture of active parts.

In general, it is recommended to avoid machines with brushes. The rotor in this case is powered via a sliding contact system. Indeed, two major difficulties are inherent in this type of machines. The first being the wear and the oxidation of the parts in contact which risks being accentuated by the effect of heat and thermal cycles. The second concerns the presence of a winding at rotor made of rigid inorganic materials that would be subjected to mechanical stress and vibration in addition to the constraints related to the temperature. The cage induction machine is rejected because of the need to use distributed windings that require some flexibility of the coils. Of course, it is still possible to use rigid coils but at the expense of compactness. The induction machine is still a track which can be explored in the future.

Aside from asynchronous machines, standard brushless machines that can be tested are permanent magnet machines or variable reluctance machines. The choice is made on a synchronous machine with permanent magnets and / or a synchronous reluctance machine (SRM) so that one same dental winding stator can be used with two different rotor structures in architecture and materials. This makes it possible to have an alternative solution in the case where the rotor with permanent magnets has temperature resistance problems beyond certain limits. In synchronous magnet machines, two magnet mounting technologies are possible: surface mounting and embedded inside the rotor. The first option is the easiest to achieve but it place the magnets close to the stator coils, therefore at a high temperature.

The second solution places the magnets inside the rotor core; the flux is concentrated towards the air gap by soft magnetic parts. The magnet temperature is lower. In both cases, the design of the rotor must provide for a direct evacuation of the heat created in the magnets by the eddy currents. In the case of the synchronous machine with wound rotor we will find a stator winding and rotor winding with inorganic insulated wire. Joule losses will be accentuated in high temperature. The sliding connection system that connects the rotor coils to the circuit outside is quite tricky to achieve at conventional temperatures. It is not reasonable to consider it in HT. The only reasonable structure the Permanent Magnet Synchronous Machine (MSAP) which uses special SmCo alloys with a preference for the embedded magnet machine.

Synchronous reluctance machines have very different structures. Our machine uses the same basic physical principle as all the others: the torque results by the variations of the magnetic energy stored in the motor at a given instant. In a conventional synchronous machine, the distributed windings are traversed by a balanced three-phase current system. The stator creates a rotating magneto motive force (mmf) with a sinusoidal spatial distribution. Induction in the air gap results from this mmf. The mmf brought by the rotor (magnets or direct current in the excitation coils) and the geometry of the gap. When the rotor has salient poles, the natural spatial variations of the induction create a reluctant torque when the rotor mmf is zero. This effect can be amplified by varying the amplitude of the stator mmf, the geometry of the rotor and the anisotropy of the magnetic materials of the rotor. Therefore, the SRM is a special case of salient pole synchronous machine; the magnetic energy in the gap is only provided by stator currents; a part of the reactive power is used for magnetizing the machine. With this structure, the magnets are no longer useful, which is very interesting because it eliminates this technological lock. However, this topology needs larger stator mmf and a reduced air-gap. Thermal expansions can create mechanical problems. On the other hand, this topology needs to use a larger number of turns for the stator windings which increases the difficulty of designing the coils. This structure can operate at higher temperatures than the PMSM but with a lower power factor and lower energy efficiency. This type of machine, however, remains the only solution for the highest temperatures.

The figure 1 gives an idea of the two topologies envisaged for the electric motor. The study is first focused on the permanent magnet machine with the two variants of magnet placed on the surface or magnets inserted in the rotors. These machines have the advantage of following similar rules as to the choice of the number of stator slots and number of poles so that a stator of a PMSM can be used for variable reluctance machine provided that the number of turns or the voltage level is adapted. The most important criterion that led to this choice is the possibility of using prefabricated rigid coils insulated by inorganic materials. The shape of the stator slots must be adapted to these rigid coils and their insertion. For the magnet machine placed on the surface, it is sufficient to adapt the height of the magnets and their arrangement so that they produce the necessary flux. Particular attention is paid to losses in magnets due to the magnetic reaction of the armature or to the effect of the stator teeth. A segmentation of each magnet in 4 pieces (2 in the azimuthal direction and 2 in the axial direction) is sufficient to reduce these losses without increase the complexity of manufacturing and assembly. Figure 2 gives some elements on the design of the magnet rotor placed on the surface.

Regarding the inserted magnet rotor (flux concentration), we kept the same number of poles so as to keep the same stator winding. The peculiarity of this topology lies in the sizing or design of flux barriers. Indeed, it is essential to limit the flow of rotor leakage to take full advantage of the flux of magnets. The chosen topology is described in Figure 3. The slots provided for inserting the magnets into the magnetic circuit of the rotor is open on the lower side (shaft side) so that the flux does not loop back by the non-magnetic rotor. The upper side of these slots (air gap side) is closed by a band narrow to form a flux barrier by saturating itself. The thickness of this band is dimensioned from so that it holds mechanically but is very magnetically saturated. In the same way as for magnets placed on the surface, the inserted magnets are also subdivided into 4 pieces to limit the losses and heating. Naturally, the topology with inserted magnets better protects magnets that are not directly exposed to the armature reaction field or to the heat flux that may come from the stator following an over-heating.

III. MATHEMATICAL MODEL

CFD analysis model it is a 3D thermo-fluid coupled mathematical model, which is based on Computational Fluid Dynamics method. This mathematical model uses Navier-Stockes equations which in case of the turbulent fluid flow take a form of Reynolds-averaged Navier-Stokes equations (RANS equations). RANS equations for the steady flow can be written as follows [START_REF] Gryboś | Fundamentals of fluid dynamics. Part 1[END_REF][START_REF] Melka | A Validated Numerical Model of Heat and Mass Transfer in a PM BLDC Electric Motor[END_REF]:

(1) (2)
(3)

Equations ( 1), ( 2) and ( 3) are written for averaged values of fluid velocity v, pressure p, temperature T and mass density ρ. RANS equations cannot be solved without turbulence model. In analyzed case k-ε turbulent model was used. It is two equations model, which include two extra transport equations to represent the turbulent properties of the flow [START_REF]Release 17.2, Help System, Theory Guide[END_REF]. For analyzed HT° machine it is necessary to take into account the rotor rotation and radiation which have a significant contribution in the heat flow. The rotor rotation can be solved using the moving reference frame equations, whereas the rest of machine's parts can be solved with the stationary frame equations [START_REF]Release 17.2, Help System, Theory Guide[END_REF]. Radiation can be included by additional radiation model (Discrete Ordinates or Surfaceto-Surface). This method can be used to calculate the radiation inside the machine. For external walls the simplest approach is using mixed boundary condition for energy equation ( 2) with the surface emissivity coefficient ε r . The convective component of this boundary condition can be determined from empirical formula which is based on dimensionless Rayleigh and Nusselt numbers. 3D coupled thermal-fluid model is prepared using Ansys Fluent package. This model includes such parts as shaft, bearings and housing. These elements participate in the heat flow in the machine; therefore, they must not be omitted. Ansys Fluent package uses the finite volume method. The finite volume mesh of the HT° machine model has over 5 million elements.

Heat sources in the analyzed machine are the power losses. To analyze of the losses the time-stepping 3D finite element method (FEM) is used. The power losses in the core, permanent magnets and windings of HT machine were calculated. The detailed description used for calculating the losses is presented in the paper [START_REF] Gryboś | Fundamentals of fluid dynamics. Part 1[END_REF]. In equation ( 3) the heat source is presented as heat source density Q which can be calculated from following formula:

(4)
where ΔP is power losses taken from electromagnetic analysis and V is a volume of motor's part where the power losses were generated.

In order to obtain excitation for the thermal model, calculations of the electromagnetic field were made using the Opera program [START_REF] Komeza | Analysis of the Impact of the Design of HT Machines on the Cogging Torque and Losses in Permanent Magnets[END_REF][START_REF] Komeza | Numerical Analysis of Thermal and mechanical Field in the High Temperature Permanent Magnet Synchronous Machine[END_REF]. For the purpose of the 3D simulation a quarter of the machine has been considered to benefit from the magnetic symmetry. The windings are modelled by connections to external resistances. The time stepping analysis was performed assuming constant speed of rotation of the rotor. The 3D mesh contains 4.264778 million elements in total. In the conductive areas, the elements size was chosen to be less than one-third of the penetration depth. Moreover, the distribution of the density of the mesh is greater than to correctly reproduce the effect of rotation of the rotor relative to the stator. To reduce the computation times the simulations were performed on a virtual machine with eight cores. Next the core losses are calculated as an average value taken from all available time snapshots. A number of sample points in time were chosen to allow for the subsequent Discrete Fourier Transform (DFT) analysis. Using the values of components of magnetic flux density in each mesh element calculated at sample

0 = ∇v τ ρ µ ∇ + - ∇ = ∇ F v p 2 ( ) 0 ' ' 1 2 = ∇ - ∇ - + + ∇ T T Q D T c c v v ρ ρ λ V P Q Δ =
points, the DFT analysis was performed in order to assess the contribution of higher harmonics. The number of calculated harmonics was selected according to the Nyquist-Shannon sampling theorem as half of the number of sample points. The calculation of losses necessitated extrapolation of the specific loss characteristic of the material for frequencies above 5000Hz. This extrapolation used the measured values in the range 50-5000Hz and had the form:

w Fe = k e f 2 B α + k h f B β (5)
In the case of the Vacoflux 48 material the coefficients in ( 5) have the following values: k h =2.22256E-02, k e =1.358143E-5, α=2.72582, β=1.14622. The losses generated by the higher harmonics account for only 11.4% of the fundamental loss, which suggests that the magnetic circuit has been properly configured.

IV. SOME RESULTS AND CONCLUSIONS

Using the coupled thermal-fluid-electromagnetic model the repartition of the temperature outside and inside the machine for the various designs and material were calculated. Figure 4 shows an example result of the distribution of the temperature in the all PMSM machine for 2 variants surface mounted magnets and embedded magnets with and without wedges. Basing on the results of simulations three prototypes were constructed, the first one is a PMSM with the surface mounted permanent magnets, second one with interior magnets in the rotor and third one is a SRM. The comparison of simulation results and measurement has shown good compatibility, temperature differences do not exceed 6°C. The tests carried out allowed us to state that synchronous motors with permanent magnets can be used in the case of an ambient temperature of not more than 300°C. For higher temperatures we recommend using of the variable reluctance machine. The comparison of simulation and measurements results and comparison of ownership and selection of a suitable machine for specific working conditions will be presented in the full version of the paper.

Fig. 1 .

 1 Fig.1. Different topologies of the machines (a) PMSM with embedded magnets, (b) PMSM with surface magnets, (c) VRM

Fig. 2 . 3 .

 23 Fig.2. Soft magnetic circuit with magnets on the surface. Fig.3. Soft magnetic circuit with embedded magnets.

Fig. 4 .

 4 Fig.4. Temperature distribution in the motor -cross section XY: a) variant 1 with wedges, b) variant 1 without wedges, c) variant 2 with wedges, d) variant 2 without wedges


Guillaume Métayer
email: guillaume.metayer@inrae.fr

Cécile Dagès

David Crevoisier

Jean-Stéphane Bailly

Marc Voltz

Performance of a pesticide fate model for predicting multiyear surface runoff contamination in a Mediterranean vineyard

Keywords: Mhydas-Pesticide, Diuron, Glyphosate, Ageing, Calibration, Validation Highlights 

Characterization of the risk of water contamination by pesticide runoff is an essential issue in the assessment of the environmental impact of pesticide use in agriculture. Models are valuable tools for this purpose. However, the use of pesticide runoff models implies that they can simulate the intra-and interannual variations in runoff contamination with a sufficient accuracy. In this study, we aimed to assess the performance of a modelling approach coupling Richards and convection-dispersion equations with the uniform mixing cell concept and an overland flow routine to predict the between-and within-year variability of the pesticide concentration in runoff water at the outlet of an agricultural field within a Mediterranean context. The model performance was evaluated by calibrating and validating model predictions to observed concentrations of two herbicides, diuron and glyphosate. The temporal structure of the model performance was analysed over 10 and 9 years for diuron and glyphosate, respectively. The results showed a favourable average model performance for runoff pesticide concentration prediction over approximately ten years. However, the annual performance largely varied, suggesting that at least 3 years of data are required to obtain reasonably precise runoff pesticides estimates in terms of the Nash-Sutcliffe efficiency in a Mediterranean climate. Although limited differences in the prediction performance were found between the two compounds, the within-year fluctuation of the predictions was more accurate for glyphosate than for diuron. This is interpreted by ageing effects that affect diuron sorption but not glyphosate sorption.

Furthermore, the study results indicated that the parameters critical to precise 2 estimation depend on the simulation objectives. The main parameter values to be determined include the pesticide half-life time when estimating chronic exposure to pesticide runoff and the sorption coefficient and mixing depth when predicting the maximum observed concentration during a given season.

Introduction

Pesticides are widely used in agriculture. Nearly 2 million tons is consumed per year worldwide [START_REF] Sharma | Worldwide pesticide usage and its impacts on ecosystem[END_REF]. Their application leads to widespread contamination of different environmental compartments, including surface waters. In France, at least one pesticide compound was measured at 93% of surface water monitoring points in 2021 [START_REF] Eaufrance | Naïades, données sur la qualité des eaux de surface[END_REF]. Runoff is considered a major pathway of surface water contamination [e.g., [START_REF] Wauchope | Pesticide runoff: methods and interpretation of field studies[END_REF], [START_REF] Louchart | Herbicide transport to surface waters at field and watershed scales in a Mediterranean vineyard area[END_REF] and [START_REF] Reichenberger | Mitigation strategies to reduce pesticide inputs into ground-and surface water and their effectiveness; A review[END_REF]], influenced by many factors that vary in space and time [START_REF] Shipitalo | Atrazine, deethylatrazine, and deisopropylatrazine in surface runoff from conservation tilled watersheds[END_REF][START_REF] Calvet | Les pesticides dans les sols. Conséquences agronomiques et environnementales[END_REF], such as the type of compound, topography, date and modality of application, climate, soil, and agricultural practices (e.g., tillage). The characterization of the risks of water contamination by pesticide runoff is thus an essential issue in the assessment of the environmental impact of pesticide use in agriculture. In situ monitoring approaches can only be employed in a limited number of situations due to their cost and difficulty of implementation.

Mathematical modelling represents a valuable alternative [START_REF] Ma | Integrating system modeling with field research in agriculture: applications of the root zone water quality model (RZWQM)[END_REF][START_REF] Shrestha | Evaluation of the Root Zone Water Quality Model (RZWQM) using field-measured data from the tropical zone, Thailand[END_REF] to characterize the risks of contamination under variable conditions. Models can thus be used to assess environmental exposure to pesticides in waters as part of regulatory assessment of the environmental risk resulting from the use of pesticide substances at the European scale [START_REF] Focus | Focus surface water scenarios in the EU evaluation process under 91/414/EEC[END_REF][START_REF] Boivin | Environmental risk assessment of pesticides: state of the art and prospective improvement from science[END_REF]. They can also be employed to assess the risks of contamination of water due to agricultural practices [START_REF] Zhang | Modeling effectiveness of agricultural BMPs to reduce sediment load and organophosphate pesticides in surface runoff[END_REF][START_REF] Baffaut | Long-term simulated runoff and water quality from grain cropping systems on restrictive layer soils[END_REF][START_REF] Oh | Development of surface water exposure scenarios for risk assessment of pesticides in Korea[END_REF] or to predict the evolution of these risks under changing climatic conditions [e.g., Gagnon et al. (2015)]. In these applications, the variation in the concentration in runoff water has often been simulated over a large number of years to account for climate variability, thereby estimating mean or maximum time-weighted average pesticide concentrations or pesticide mass losses by runoff. This suggests that pesticide runoff models can simulate the intra-and interannual variations in runoff concentrations and losses with a sufficient accuracy.

Pesticide fate and transport models currently applied in pollution risk assessment can be divided broadly into two main categories [START_REF] Siimes | A review of available pesticide leaching models: Selection of models for simulation of herbicide fate in Finnish sugar beet cultivation[END_REF] according to the description of soil moisture and water transport in soil: (a) capacity models [e.g., the pesticide root zone model (PRZM)- [START_REF] Carsel | The Pesticide Root Zone Model (PRZM): A procedure for evaluating pesticide leaching threats to groundwater[END_REF]; Groundwater Loading Effects of Agricultural Management Systems (GLEAMS)- [START_REF] Leonard | Gleams: Groundwater Loading Effects of Agricultural Management Systems[END_REF]; Agricultural Policy/Environmental eXtender (APEX)- [START_REF] Williams | APEX Users Guide. Version 2110[END_REF]; and dynamic agricultural non-point source assessment tool (DANSAT)- [START_REF] Cho | A comprehensive modeling approach for BMP impact assessment considering surface and groundwater interaction[END_REF]] and (b) models using the Richards' equation [e.g., the root zone water quality model (RZWQM)- [START_REF] Hanson | RZWQM: Simulating the effects of management on water quality and crop production[END_REF]; MACRO-Larsbo et al. (2005); and Pesticide Emission Assessment at Regional and Local scales (PEARL)- [START_REF] Van Den Berg | PEARL model for pesticide behaviour and emissions in soil-plant systems[END_REF]].

Capacity models mainly estimate surface runoff, at a daily time step by applying the empirical Soil Conservation Service (SCS)-curve-number method (e.g., GLEAMS, APEX, and PRZM) whereas Richards based models may estimate surface runoff at sub-daily variable time steps by applying the soil infiltration excess approach (e.g., MACRO, PEARL, and RZWQM) followed by an overland flow description. For simulating pesticide transport, convection is represented by all models with diffusion whereas hydraulic dispersion is generally only represented by Richards type models [START_REF] Siimes | A review of available pesticide leaching models: Selection of models for simulation of herbicide fate in Finnish sugar beet cultivation[END_REF]. Pesticide losses into surface waters are generally calculated in both model types based on the mixing cell concept, in which rainwater mixes uniformly or variably over a specific depth, and chemical equilibrium is assumed between the water and solid phases (e.g., GLEAMS, APEX, and DANSAT). Moreover, all models represent sorption and degradation processes in the soil, most often assuming linear or Freundlich partition coefficient and first-order kinetics, respectively.

The accuracy of surface runoff models in the prediction of pesticide transport by runoff has been demonstrated at the laboratory scale and through modelling exercises, but their performance in practical applications, such as at the field scale, is less clear [START_REF] Young | Field-scale evaluation of pesticide uptake into runoff using a mixing cell and a non-uniform uptake model[END_REF]. The available plot-scale performance tests aiming to continuously reproduce the temporal dynamics of pesticide runoff contamination under actual rainfall conditions are relatively limited. We identified performance tests of the following models: APEX, DANSAT, GLEAMS, PRZM and RZWQM. These tests are most often based on simulations lasting between one and three cropping seasons [START_REF] Leonard | Gleams: Groundwater Loading Effects of Agricultural Management Systems[END_REF][START_REF] Ma | Measured and RZWQM predicted atrazine dissipation and movement in a field soil[END_REF][START_REF] Ghidey | Evaluation of the Root Zone Water Quality model using field-measured data from the Missouri MSEA[END_REF][START_REF] Malone | Modeling surface and subsurface pesticide transport under three field conditions using PRZM-3 and GLEAMS[END_REF][START_REF] Connolly | Simulating Endosulfan Transport in Runoff from Cotton Fields in Australia with the GLEAMS Model[END_REF][START_REF] Malone | Modeling hydrology, metribuzin degradation and metribuzin transport in macroporous tilled and no-till silt loam soil using RZWQM[END_REF][START_REF] Miao | Modeling the Effects of Tillage Management Practices on Herbicide Runoff in Northern Italy[END_REF][START_REF] Cho | Evaluating cell-based components of DANSAT for predicting surface and subsurface transport of pesticides[END_REF][START_REF] Mudgal | Apex model assessment of variable landscapes on runoff and dissolved herbicides[END_REF][START_REF] Chen | Numerical simulation of agricultural sediment and pesticide runoff: RZWQM and PRZM comparison[END_REF][START_REF] Baffaut | Long-term simulated runoff and water quality from grain cropping systems on restrictive layer soils[END_REF]. Only [START_REF] Chinkuyu | Prediction of pesticide losses in surface runoff from agricultural fields using GLEAMS and RZWQM[END_REF] and [START_REF] Plotkin | Apex calibration and validation of water and herbicide transport under U.S Southern Atlantic Coastal Plain Conditions[END_REF] performed model evaluations over longer time periods, at 5 and 8 years, respectively. The results shown are remarkably diverse with respect to both the performance criteria used and the performance observed. Concerning the performance criteria adopted, models have been most often evaluated in terms of their ability to reproduce daily exported masses [START_REF] Ma | Measured and RZWQM predicted atrazine dissipation and movement in a field soil[END_REF][START_REF] Connolly | Simulating Endosulfan Transport in Runoff from Cotton Fields in Australia with the GLEAMS Model[END_REF][START_REF] Chinkuyu | Prediction of pesticide losses in surface runoff from agricultural fields using GLEAMS and RZWQM[END_REF][START_REF] Cho | Evaluating cell-based components of DANSAT for predicting surface and subsurface transport of pesticides[END_REF][START_REF] Mudgal | Apex model assessment of variable landscapes on runoff and dissolved herbicides[END_REF][START_REF] Chen | Numerical simulation of agricultural sediment and pesticide runoff: RZWQM and PRZM comparison[END_REF][START_REF] Baffaut | Long-term simulated runoff and water quality from grain cropping systems on restrictive layer soils[END_REF] or daily concentrations [START_REF] Ghidey | Evaluation of the Root Zone Water Quality model using field-measured data from the Missouri MSEA[END_REF][START_REF] Malone | Modeling surface and subsurface pesticide transport under three field conditions using PRZM-3 and GLEAMS[END_REF][START_REF] Malone | Modeling hydrology, metribuzin degradation and metribuzin transport in macroporous tilled and no-till silt loam soil using RZWQM[END_REF][START_REF] Miao | Modeling the Effects of Tillage Management Practices on Herbicide Runoff in Northern Italy[END_REF][START_REF] Chinkuyu | Prediction of pesticide losses in surface runoff from agricultural fields using GLEAMS and RZWQM[END_REF]. The main performance statistics computed include Pearson's correlation coefficient (r) and its related coefficient of determination (R 2 ), Nash-Sutcliffe efficiency (NSE) and percent bias (PBIAS), but only the two latter were recommended by [START_REF] Moriasi | Model evaluation guidelines for systematic quantification of accuracy in watershed simulations[END_REF] for use in watershed model evaluation. Concerning the performance observed, R 2 , NSE and absolute PBIAS for mass loss predictions varied between 0.001 and 0.99, between -8.74 and 0.96 and between 4 and 98.4%, respectively, whereas R 2 and NSE for concentration predictions varied between 0.001 and 0.94 and between -4.98 and 0.8, respectively (Fig. S1).

According to the performance ratings proposed by [START_REF] Moriasi | Hydrologic and water quality models: Performance measures and evaluation criteria[END_REF], the previously observed performance statistics ranged from unsatisfactory to very good, indicating that the accuracy of pesticide runoff models remains highly uncertain even under calibration. This applies not only to mass loss predictions but also to concentration predictions in surface runoff water, as a worst-case proxy for the concentration in surface waters. Surface runoff concentrations are essential to regulatory exposure risk assessment [START_REF] Final | Generic guidance for FOCUS surface water Scenarios[END_REF]. Given the variations in the testing setups, the number of model evaluations is insufficient to allow the determination of possible differences in performance between the models applied. Indeed, the performance is intrinsically variable due to the large range of uncertainty sources in pesticide fate modelling, including the modeller's subjectivity [please refer to the review by [START_REF] Dubus | Sensitivity analyses for four pesticide leaching models[END_REF]]. However, we hypothesize that too-short evaluation periods with respect to the natural temporal variation in pesticide transfer conditions inhibit comprehensive examination of the prediction performance of a given pesticide runoff model, which partly explains the high variation in the observed performance statistics. Thus, the main aim of the present work was to evaluate the performance of a model coupling Richards' and convection-dispersion equations with the uniform mixing cell concept and an overland flow routine to predict the between-and within-year variability of the pesticide concentration in runoff in an agricultural plot. Such a model is implemented in MHYDAS-Pesticide 1.0, a physically based hydrological model. , 2022). Diuron shows a strong seasonal increasing trend in sorption [START_REF] Louchart | Aging effects on the availability of herbicides to runoff transfer[END_REF] due to the ageing phenomenon, while glyphosate experiences sorption evolution only within a few days after application [START_REF] Padilla | Time-dependent sorption and desorption of glyphosate in soils: Multi-reaction modeling[END_REF].

MHYDAS-

Materials and methods

Field measurements

The meteorological and hydrological monitoring protocols are part of the duties of the OMERE observatory, which have been presented in detail by [START_REF] Molénat | OMERE: a long-term observatory of soil and water resources, in interaction with agricultural and land management in Mediterranean hilly catchments Vadose[END_REF].

• Meteorological and surface runoff data

The reference crop evapotranspiration (ET0) was estimated at hourly time steps according to the method proposed by [START_REF] Allen | Crop evapotranspirationguidelines for computing crop water requirements[END_REF] and(b)]. A rainfall or runoff event is defined as a period during which rainfall or discharge, respectively, can be continuously measured. These events are highly variable in terms of i) their duration, ranging from 5 min to 5 days for rainfall and from 5 min to 1.5 days for runoff, ii) their peak flow rate, between 0.01 and 44.4 L.s -1, and iv) their runoff volume, between 1.6 and 67000 L. The average runoff coefficient is 0.26 and reaches 0.4 for rainfall events with a rainfall height larger than 40 mm.

• Herbicide concentration in runoff

The observed during the first rainfall events following pesticide application.

Model description

MHYDAS-Pesticide-1.0 is a fully distributed mechanistic model that can simulate the hydrological fate of a pesticide compound in a heterogeneous cultivated landscape [START_REF] Crevoisier | MHYDAS-Pestides-1.0 : Modélisation Hydrologique Distribuée des AgroSystèmes -Eau et Pesticides. Rapport dans le cadre du projet collaboratif PollDiff Captage 2018-2021[END_REF]. In this study, MHYDAS-Pesticide-1.0 was applied at the scale of the agricultural field described in section 2.1.1. A homogeneous field was assumed.

A brief description of the numerical representation of the main physico-chemical processes assessed in this study is presented hereafter. A more detailed description of the processes represented by MHYDAS-Pesticide-1.0 is available in Crevoisier et al.

(2021).

Hydrological processes

The model simulates the soil water balance, soil infiltration excess and surface runoff propagation. Water movement in soil and infiltration excess are simulated by solving the Richards' equation with the Ross method [START_REF] Ross | Modeling soil water and solute transport -Fast, simplified numerical solutions[END_REF][START_REF] Crevoisier | Evaluation of the Ross fast solution of Richards' equation in unfavourable conditions for standard finite element methods[END_REF]. [START_REF] Schaap | A Modified Mualem-van Genuchten formulation for improved description of the hydraulic conductivity near saturation[END_REF]. Surface runoff is assumed to correspond to infiltration excess once the maximum ponding height is reached. Then surface runoff is propagated to the oulet of the field by overland flow using the diffuse wave model, a simplification of the Saint-Venant system (1871), which is solved with the Hayami method [START_REF] Moussa | Analytical Hayami Solution for the diffusive wave flood routing problem with lateral inflow[END_REF].

Pesticide fate processes

The main pesticide fate processes simulated involve compound reactive transfer in soil and remobilization and transport by runoff. Vertical transport in soil is represented by convection-dispersion equation. An instantaneous sorption equilibrium relationship is assumed between the liquid-and solid-phase concentrations. In this study, the relationship was represented by a linear model. Compound degradation was represented by first-order kinetics for both the solid and liquid soil phases. The degradation rate was adjusted depending on the soil water content according to Walker's equation [START_REF] Walker | A simulation model for prediction of herbicide persistence[END_REF]. To calculate the concentration in runoff, uniform and instantaneous mixing between runoff and the topsoil mixing cell was considered.

The latter can contain several elements of the grid representing the soil profile.

Model performance evaluation

Model setup and input parameters

The soil profile was simulated to a depth of 1.2 m with free drainage as the boundary condition at the profile bottom. The profile was discretized into 39 grid elements whose vertical widths ranged from 0.001 m to 0.1 m (Table S1). Three soil layers were distinguished according to the soil surveyor description. The hydraulic properties of the two subsoil layers were estimated from measurements stored in the OMERE database (Table S1). The soil hydraulic parameters of the surface layer, namely the hydraulic conductivity (Ks) and the ponding height, were estimated by calibration over 5 years and validated on the remaining monitoring years (see details in supplementary materials Text page S5 and Table S2). The pesticide fate parameters, namely, the sorption coefficient (K D ), compound half-life (t 1/2 ), exponent of Walker's function (b) and thickness of the mixing layer (z mix ), considered to be calibration parameters and were subject to the investigations described hereafter. The climatic (rainfall and reference evapotranspiration) and agronomic (applied pesticide mass per unit area) forcings were fixed using the data observed in the OMERE observatory presented in section 2.1. The applied herbicide mass was fully and uniformly incorporated into the 0.001 m top grid element of the discretized soil profile. To fix realistic initial conditions to the simulations, a warm-up period of 18 months of the model was run prior to all simulations. No pesticide application was considered during the warm-up.

Calibration of pesticide fate parameters

Prior sensitivity analysis

The sensitivity to the pesticide fate parameters (K D , t 1/2 , b, z mix ) was first jointly analysed to determine their respective influence on the model outputs, thereby identifying the most influential parameters for calibration. These parameters were chosen because of their high variability depending on the environmental conditions and the difficulty of transposing laboratory values (e.g., K D and t 1/2 ) [START_REF] Calvet | Les pesticides dans les sols. Conséquences agronomiques et environnementales[END_REF] or the absence of a consensus reference value, e.g., zmix [START_REF] Bruce | A model for runoff of pesticides from small upland watersheds[END_REF][START_REF] Ahuja | The depth of rainfall-runoff-soil interaction as determined by 32 P[END_REF]. In model sensitivity analysis to t 1/2 and K D , the ranges of the studied values for glyphosate were obtained from the range of values cited by the PPDB (2022), while those for diuron were obtained from measurements in the study field [START_REF] Baer | Comportement des pesticides dans les sols : Evaluation et simulation de la dissipation au champ[END_REF] for t 1/2 and Louchart and Voltz, 2007 for K D ). The chosen ranges of z mix and b were the same for both compounds to include most values found in the literature. (e.g., [START_REF] Ahuja | The depth of rainfall-runoff-soil interaction as determined by 32 P[END_REF] and [START_REF] Bruce | A model for runoff of pesticides from small upland watersheds[END_REF] for z mix and [START_REF] Boesten | Behaviour of herbicides in soil: simulation and experimental assessment[END_REF] for exponent b). Table 1 shows the boundaries of the tested values for these two compounds.

Regarding t 1/2 , K D and b, the parameter space was sampled according to a complete and balanced statistical design with a sampling method based on domain tessellation in polygons and sample generation by randomly drawing from each polygon [START_REF] Faivre | Analyse de sensibilité et exploration de modèles : Application aux sciences de la nature et de l'environnement[END_REF]. This sampling approach sufficiently covered the parameter space, allowing the execution of analysis of variance (ANOVA). Specifically, for each of the three parameters, the range of variation was divided into 6 levels of equal magnitude, and each level was then combined with all levels of the other parameters. For a given combination of levels of the parameters, the parameter values were determined via a random draw within the levels. Thus, the values of t 1/2 , K D and b varied for each combination of levels. In regard to z mix , random values could not be drawn in intervals since a unique grid was adopted to discretize the soil profile to ensure the same resolution of the Richards' equation for all runs. Accordingly, the range of variation in z mix was deterministically sampled involving 6 values determined in regular intervals over the logarithmic scale of the z mix values. The soil profile discretization was adapted so that all 6 values corresponded to a node of the grid. Parameter space sampling was repeated twice to increase the number of combinations assessed. In total, 2592 simulations were run per compound over 3-year, from March 2002 to March 2005.

These 3 years were chosen since observations were available for both diuron and glyphosate and thereby the simulations performed could also be used for subsequent calibration of model parameters. Moreover the duration was set at 3 years in order to include a sufficient number of runoff events.

ANOVA was then conducted to assess the average contribution (main effect or firstorder effect) of each model parameter and the contribution of the interactions (interaction effect or higher-order effect than the first-order effect) between the parameters to the overall outcome variance, i.e., the sum of the squared differences between each simulation and the overall mean. Since applications of ANOVA in model sensitivity analysis have been extensively described by many authors [START_REF] Ginot | Combined use of local and ANOVA-based global sensitivity analyses for the investigation of a stochastic dynamic model: Application to the case study of an individual-based model of a fish population[END_REF][START_REF] Saltelli | Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index[END_REF], we invite the reader to consult these papers for more details. In this application, ANOVA was applied to the simulated log-transformed concentrations of each runoff event during the 3-year period, in order to analyze the influence of parameters at different times after herbicide application. The main effects of the parameters and their second-, third-and fourth-order interaction effects were estimated, with the order corresponding to the number of parameters in the interaction.

Parameter set identification

For identifying the pesticide fate parameter values that allowed the most accurate simulations, the the simulations run during the sensitivity analysis for the 2002-2005 period were compared with the observed glyphosate and diuron concentrations during the same period. Accordingly, the sampling of the parameter space for parameter identification was thus identical to the sampling done for the sensitivity analysis.

The simulation performance was quantified, was quantified, as recommended by [START_REF] Moriasi | Hydrologic and water quality models: Performance measures and evaluation criteria[END_REF] and [START_REF] Althoff | Goodness-of-fit criteria for hydrological models: Model calibration and performance assessment[END_REF], using a statistical criterion of accuracy, namely, NSE, and a correctness criterion, namely, PBIAS. NSE compares the model performance in reproducing the observed values to that of another model comprising a simple average of the observations. The value varies between -∞ and 1, which is the optimal value, and can be calculated with equation ( 2): No attempt was made to select a unique optimal set of parameter values since, as will be shown in the results section, several sets of parameters could yield a similar and satisfactory fit of the observed data. Among all sampled parameter sets, those yielding NSE and PBIAS values over the calibration period (03/2002 to 03/2005) greater than 0.65 and less than 5%, respectively, were selected. According to the performance ratings proposed by [START_REF] Moriasi | Hydrologic and water quality models: Performance measures and evaluation criteria[END_REF] (Table 2) all parameter combinations satisfying the latter criteria are rated as "very good" in terms of solute concentration simulations. In the case of diuron, only one combination met this criterion. Additional simulations were therefore conducted by refining the initial tessellation of the parameter space according by a new grid of values (Table S3) around the only combination identified. This allowed to select, similar to glyphosate, a set of combinations generating a sufficient prediction performance during the calibration period.

NSE=1-[ ∑ i=1 n (Y i obs -Y i simu )² ∑ i =1 n (Y i obs -Y mean (obs) )² ] (2)

Model performance analysis

First, the overall performance of the model was assessed by predicting concentrations outside the calibration period with the selected combinations of pesticide parameter values during the calibration approach. To do so, simulations were run continuously over the entire datasets, i.e. between September 1993 and March 2009 for diuron and between September 2000 and March 2014 for glyphosate, and model performance was computed for the years of data not used for calibration, namely 7 and 6 years for diuron and glyphosate respectively (Table 3). The goodness of fit of the model predictions was quantified using the same criteria as for calibration (see section

2.3.2).

Second, the temporal structure of the model performance was analysed to assess the model's ability to reproduce the inter-and intra-annual variations in the compound concentration in surface runoff water. This analysis was performed with the parameter sets selected after calibration and with all available data records, including the calibration and validation periods, i.e., 10 and 9 years, respectively, for diuron and glyphosate. To analyse the interannual variability of the prediction performance, the NSE and PBIAS criteria were calculated per year of evaluation. Then, the accuracy of the mean model performance was estimated as a function of the number of evaluation years by computing the theoretical standard error of the sample mean of the annual NSE and PBIAS values. The theoretical standard error values were computing using the standard deviation value estimated from the sample of evaluation years used in this work, according to the following classical equation [equation ( 4)]:

SE= σ √n with σ = √ ∑ i =1 n ( x i -x)² n-1 (4)
x i : PBIAS or NSE in year i calculated with the original or log-transformed concentration values of diuron or glyphosate;

x : Mean annual PBIAS or NSE value calculated with the original or log-transformed concentration values of diuron or glyphosate;

σ : Standard deviation of the annual PBIAS or NSE values estimated from the sample of evaluation years;

n : Number of years used for evaluation; and SE : Standard error of the estimated mean annual PBIAS or NSE value.

To analyse the intra-annual variability of the prediction performance and accuracy, the relative error (RE) was estimated for each predicted runoff concentration, according to equation ( 5 A time permutation test [START_REF] Legendre | Numerical Ecology[END_REF] was then conducted to assess the temporal variation in the median RE of runoff events grouped by two-month intervals following herbicide application. In addition, a Wilcoxon signed-rank test was performed to determine whether the median RE of each two-month interval significantly differed from 0 at the 5% significance level.

Results

Sensitivity analysis

The sensitivity of the log-transformed simulated runoff event concentrations to the considered parameters and their interactions was satisfactorily represented by the ANOVA model, which could explain at least 79% of the total variation in the concentrations during all runoff events regardless of the duration after herbicide application (Fig. 2).

However, the main effects of the parameters, as shown in Fig. 2, were very heterogeneous with time after herbicide application. The half-life, t 1/2 , was globally the most influential parameter at the annual scale. Its influence increased with increasing time after application, and it explained more than 80% of the variability of the simulated concentrations from 50 days after application. In contrast, K D and z mix were the most influential parameters for runoff events occurring a few days after herbicide application for both diuron and glyphosate. The influence of Walker's exponent was negligible for all simulated events. The main effect of each parameter also varied according to the compound studied, reflecting differences in the influences of the processes driving the fate of each compound. Overall, despite a smaller considered range of K D values for diuron than that for glyphosate, K D was more influential for diuron than for glyphosate. For a simulated runoff event 30 days after herbicide application, K D accounted for nearly 30% of the variability explained by the main effects for diuron, against nearly 14% for glyphosate. Moreover, for diuron K D, the influence remained notable up to 100 days, whereas for glyphosate, it remained notable only up to 50 days. For diuron, the main effect of K D was always higher than that of z mix and decreased less rapidly, while for glyphosate, the main effects of K D and z mix were similar for all runoff events. These differences are related with K D ranges explored since other parameter ranges are quite similar. It must be noted that the interaction effects eventually imposed a greater influence for glyphosate than for diuron and exhibited a peak approximately 50 and 180 days after application for glyphosate and diuron, respectively.

These results suggest that the runoff contamination level is mainly controlled by degradation mechanisms except for runoff events occurring shortly after application, during which the sorption mechanism is the most influential.

Identified parameter sets and global model performance

Application of the selection criteria presented in section 2.4.2. allowed us to identify 389 and 16 parameter sets for diuron and glyphosate, respectively, allowing very favourable reproduction of runoff contamination during the calibration period, according to the thresholds set by [START_REF] Moriasi | Hydrologic and water quality models: Performance measures and evaluation criteria[END_REF]. The ranges of the values for these parameter sets are listed in Table 1. The selected K D and t 1/2 values differed between the two compounds, while all the selected z mix values were lower than 1 cm.

In line with the compound properties, the selected K D values for diuron were significantly lower than those for glyphosate. In contrast, the adjusted half-lives were systematically smaller for diuron than for glyphosate, which ranks differently based on the data in the PPDB. The variability of the K D and t 1/2 values selected for diuron was smaller than that for glyphosate. This difference was particularly marked for K D . The standard deviations of the sets of selected K D values were 2.7 and 67.6 L.kg -1 for diuron and glyphosate, respectively. The variability of the parameter values satisfying the performance criteria could be explained by the positive correlation between t 1/2 and K D and the negative correlation between z mix and K D (Table 4). Simultaneous calibration of these parameters therefore led to the nonuniqueness issue in model calibration. The correlations between K D and t 1/2 and between z mix and K D indicate strong compensation effects between these pairs of model parameters in the simulation of the removal of pesticide compounds from the soil by runoff water. The correlation between z mix and K D was much higher for glyphosate than for diuron. This could be explained by a similar evolution of the sensitivity to z mix and K D for glyphosate but not for diuron, for which the influence of z mix on the simulated concentrations was more than two times less than that of K D from 40 days after application. Thus, as 90% of the runoff events occurred after this time, the vast majority of the runoff concentrations were simulated for diuron at a time when the sensitivity to z mix was lower than that to K D , allowing no compensation.

The values of the performance criteria regarding the simulated concentrations [Fig.

3(a)

] for the selected parameter sets were slightly higher for diuron, with an NSE value up to 0.8 versus 0.69 for glyphosate, while the performance levels based on the logtransformed concentrations were higher but equivalent between these compounds, at

Between-year variation in the prediction performance

The interannual variability of the model performance could be high depending on the compound and performance criterion (Fig. 4). It could also be observed that the model performance variability was generally smaller for the log-transformed concentrations than for the original concentrations, except for PBIAS obtained for diuron with standard deviations of 29.5% and 34.4% for the original and log-transformed concentrations, respectively. For glyphosate, the standard deviations of the annual PBIAS were 18.8% and 15% for the original and log-transformed concentrations, respectively. Concerning the annual NSE, the standard deviations were 0.24 and 0.11 for the original and log-transformed diuron concentrations, respectively, and they were 0.19 and 0.13 for the original and log-transformed glyphosate concentrations, respectively. Thus, the model performance was mostly more variable for diuron than for glyphosate, in particular in regard to the variations in the annual PBIAS values. For diuron, the year 1998 was particularly notable for a high annual |PBIAS| value (69%)

and a low NSE value (0.14), based on the mean concentrations.

Within-year variation in the prediction performance

In general, the intra-annual variability of the runoff concentrations was reproduced well by the model, even if the performance differed according to the compound, while the maximum difference between the predicted and measured concentrations could reach up to a factor of 6 (Fig. S2). Fig. 6 shows the distribution of the RE values for each 2-month interval after herbicide application. On average, the median RE was low for both compounds: it approached -15% and -8% for diuron and glyphosate, respectively. However, the Wilcoxon test results showed that for diuron and runoff events occurring between the 3 rd and 4 th months, between the 9 th and 10 th months, and between the 11 th and 12 th months after application, the median RE significantly differed from 0 (Table 5). In particular, the diuron concentrations measured between the 3 rd and 4 th months were overestimated by the model. Furthermore, the permutation test indicated that the median RE was time dependent for diuron. In contrast, for glyphosate, the median RE never significantly differed from 0, and accordingly, the permutation test did not indicate a time dependence of the median RE for glyphosate.

Discussion

According to the performance thresholds of [START_REF] Moriasi | Hydrologic and water quality models: Performance measures and evaluation criteria[END_REF], the prediction performance for the surface runoff pesticide concentration of MHYDAS-Pesticide was very good or good on average over the multi-year evaluation period. In regard to the available tests of pesticide surface runoff models (Fig. S1), our evaluation results ranked among the best as compared to the few other tests of field-scale concentration predictions [e.g., [START_REF] Ghidey | Evaluation of the Root Zone Water Quality model using field-measured data from the Missouri MSEA[END_REF]; [START_REF] Malone | Modeling hydrology, metribuzin degradation and metribuzin transport in macroporous tilled and no-till silt loam soil using RZWQM[END_REF][START_REF] Chinkuyu | Prediction of pesticide losses in surface runoff from agricultural fields using GLEAMS and RZWQM[END_REF]] and the more numerous assessments of mass loss predictions [START_REF] Mudgal | Apex model assessment of variable landscapes on runoff and dissolved herbicides[END_REF][START_REF] Plotkin | Apex calibration and validation of water and herbicide transport under U.S Southern Atlantic Coastal Plain Conditions[END_REF][START_REF] Chen | Numerical simulation of agricultural sediment and pesticide runoff: RZWQM and PRZM comparison[END_REF][START_REF] Baffaut | Long-term simulated runoff and water quality from grain cropping systems on restrictive layer soils[END_REF]. This result indicates that no major temporal prediction bias appeared over almost ten years of runoff simulations for either diuron or glyphosate. Moreover, all concentrations were simulated with the right order of magnitude despite the wide range of the observed concentrations. It confirms the capacity of the adopted modelling approach to simulate both the between-and within-year variations in the pesticide concentration in runoff water, provided calibration was performed satisfactorily over a few years.

Concerning the variation in the between-year prediction performance, it must first be recognized that in this case study, all observed annual performance values for both diuron and glyphosate ranked satisfactory or higher according to the classification of [START_REF] Moriasi | Hydrologic and water quality models: Performance measures and evaluation criteria[END_REF], apart one year for diuron that exhibited unsatisfactory NSE and PBIAS. However, the annual performance still largely varied between individual years.

The potential sources of variation can be diverse, including sources of environmental origin, such as variations in climatic conditions or soil surface states (organic matter content, soil structure, and soil water content) and sources of experimental origin (uncertainties in the applied pesticide amounts and number of observed runoff events). Unfortunately, even with ten years of model prediction evaluation, it was barely possible to precisely identify and discriminate the variation sources. However, examination of the contribution of the prediction error of each runoff event to the annual NSE and PBIAS values revealed that for many years, one or a few events with high concentrations close to application contributed the most (Figs. S3 to S6). This explains the slightly better prediction performance criteria for the log-transformed concentrations than for the original concentrations. Eventually, the high variation in the performance between individual years suggests that a significant part of the observed variation in the performance in the literature may result from evaluation periods that are too short (Fig. S1). As a rule of thumb, our calculations indicated that at least 3 years of test data are required to obtain estimates of the runoff model performance with a reasonable NSE precision in a Mediterranean climate.

Concerning the within-year variations in the prediction errors, they did not significantly differ from zero for glyphosate, while the opposite was observed for diuron for some periods. This difference may be explained by the difference in the sorption and/or degradation behaviour between these two compounds. The assumptions of stable sorption properties and first-order degradation kinetics throughout the pesticide fate simulation period seemed valid for glyphosate, whereas they must be questioned for diuron. Indeed, the change with time after application of the log-transformed diuron concentrations did not exhibit linear behaviour overall but rather a nonlinear trend including a relatively steep decrease up to 80 days after application and a more moderate decrease thereafter (Fig. 7). Accordingly, a bilinear regression could achieve a better fit than a simple linear regression (Fig. 7). Hence, after calibration, the RE values of the diuron predictions differed from zero for some periods. To explain this nonlinear behaviour, the first hypothesis is that the degradation rate decreases in summer due to a decrease in the soil water content. However, this hypothesis is not consistent with the sensitivity analysis results, which showed that considering the effect of the soil water content on the degradation rate generates a negligible influence regardless of the time after application (Fig. 2). The second hypothesis entails a major effect of diuron ageing on the change in diuron sorption in soil notably influencing the concentrations observed in runoff water. Many studies have indeed shown the influence of ageing of various pesticide compounds on K D evolution [START_REF] Laabs | Sorption and aging of corn and soybean pesticides in tropical soils of Brazil[END_REF][START_REF] Regitano | Influence of soil aging on sorption and bioavailability of simazine[END_REF][START_REF] Louchart | Aging effects on the availability of herbicides to runoff transfer[END_REF][START_REF] Motoki | Effect of time-dependent sorption on the dissipation of water-extractable pesticides in soils[END_REF]. In particular, it has been determined from soil and water diuron content data acquired at the same study site that the apparent K D of diuron increases in two stages, with an initial rapid increase up to 60-90 days after application and a subsequent slower increase [START_REF] Louchart | Aging effects on the availability of herbicides to runoff transfer[END_REF]. The diuron ageing effect could therefore explain the diuron concentration overestimation for events occurring in the third and fourth months after herbicide application and consequently the concentration underestimation after the ninth month after application. In general, the increase in K D due to the ageing effect is considered to particularly concern nonionic compounds with a particular affinity for soil organic matter [START_REF] Motoki | Effect of time-dependent sorption on the dissipation of water-extractable pesticides in soils[END_REF], such as diuron. To improve the model performance in simulating diuron concentrations in runoff, the process of the increase in K D could be included and assessed in the future. Modelling of K D evolution under the ageing effect of compounds has been the subject of increasing interest in recent years, particularly in groundwater contamination assessment [START_REF] Boesten | Effects of aged sorption on pesticide leaching to groundwater simulated with PEARL[END_REF]European Commission, 2021). However, in the present case, the expected improvement is limited in view of the admittedly significant but slight differences in the overall prediction performance between diuron and glyphosate.

Finally, the study results also provide hints for the parameterisation of this type of runoff model. First, the sensitivity analysis clearly showed that the parameters that must be precisely estimated depend on the simulation objectives. If the modelling objective is to estimate chronic exposure to pesticides in runoff water over one or several cropping seasons, the main parameter value to be determined is the pesticide half-life time. Half-life time has often been shown as one of the pesticide fate parameters with the greatest influence [START_REF] Cryer | Regional sensitivity analysis using a fractional factorial method for the USDA model GLEAMS[END_REF][START_REF] Chinkuyu | Sensitivity analysis of GLEAMS using multi-objective sensitivity analysis procedure[END_REF][START_REF] Dubus | Sensitivity analyses for four pesticide leaching models[END_REF][START_REF] Luo | Management-oriented sensitivity analysis for pesticide transport in watershed-scale water quality modeling using SWAT[END_REF]. However, if the objective is to predict the maximum observed concentrations during a given season, the sorption coefficient, K D , and the mixing depth, z mix , jointly impose a greater influence than t 1/2 . Maximum concentrations mainly occur shortly after application before the occurrence of significant degradation. Second, a nonuniqueness phenomenon was observed in parameter selection. The calibrated K D and z mix values were highly correlated and exhibited similar influences on the model outputs. Thus, high indeterminacy existed in the depth of the mixing layer, which in turn allowed us to choose the same mixing depth for the different compounds. These results suggest that there is a nonuniqueness issue in calibration based on the uniform mixing concept. [START_REF] Dubus | Calibration of pesticide leaching models: Critical review and guidance for reporting[END_REF] already recognized that pesticide fate models are subject to inherent nonuniqueness issues due to the compensation effect between parameters, and they considered it a research priority to identify the data requirements for effective and robust calibration of these models. Here, with only runoff event concentration data, although over several years, calibration of a unique optimal set of parameter values would not have been justified. This also puts into question the data needs for model validation and comparison. For example, [START_REF] Young | Field-scale evaluation of pesticide uptake into runoff using a mixing cell and a non-uniform uptake model[END_REF], in their field-scale evaluation of models of pesticide uptake into runoff, could not discriminate between the uniform mixing and nonuniform uptake concepts since they both could satisfactorily predict 99 pesticide runoff events observed in different experiments after specific calibration.

Conclusions

In this study, we aimed to evaluate the prediction performance of MHYDAS-Pesticide-1.0in the simulation of pesticide concentrations in event runoff water at the field scale.

The availability of long-term monitoring data enabled us to estimate the overall model performance and its temporal variation. Several results were obtained. This study first shows that simulations of pesticide concentrations in surface runoff at the field scale by Richards and convection-dispersion equations coupled with the uniform mixing concept are likely to provide consistent predictions under natural Mediterranean rainfall conditions over a large number of years at the runoff event resolution.It must however be recognized that the satisfactory long-term performance of this model was estimated in rather favourable conditions, namely a single field with a stable topsoil structure and soil management and after a prior calibration of the model parameters over 3 years. The potential sources of variations in model predictions were thus less than all those that were listed by [START_REF] Dubus | Sensitivity analyses for four pesticide leaching models[END_REF]. Nevertheless, even in this case, there was high variation in the prediction performance among individual years, indicating that to obtain robust estimates of the performance, monitoring data over several climate and application cycles should be adopted in evaluation studies. In this case study, which certainly corresponds to a worst case given the intrinsic variability of the Mediterranean climate, at least 3 annual cycles are advisable. The study results also indicated that the very large within-year variation in the pesticide concentrations in runoff water could be satisfactorily predicted. Differences in the within-year prediction performance were noted between the considered compounds, possibly due to ageing effects on sorption. However, these differences were small, suggesting that, in this case study, the omission of ageing processes in the model was not a major source of prediction uncertainty. Finally, the study provides guidelines concerning pesticide runoff model parameterisation. If the model is applied in predicting the average concentration in runoff water, the compound degradation rate is of paramount influence, whereas if it is applied in predicting peak concentrations known to occur soon after application, the sorption coefficient and the mixing zone depth are the most influential model parameters.

CRediT authorship contribution statement

  Pesticide was applied to a Mediterranean vineyard plot where the pesticide concentrations in surface runoff water were monitored from 1995 to 2014. After calibration, the model prediction performance was evaluated by comparison with the observed concentrations outside the calibration years of two herbicides, glycin from 1994 to 2014. The specific objectives were (i) to estimate the number of years of data acquisition required to determine the average model prediction performance with reasonable accuracy, ii) to identify potential patterns of the temporal change in the prediction performance and iii) to analyse the influence of model parameters according to the modelling objectives.

  diuron concentration in runoff was measured over 11 years between 1995 and 2000 and then between 2002 and 2009, whereas the glyphosate concentration was monitored over 9 years between 2002 and 2005 and then between 2008 and 2014.Water was sampled via two automatic samplers (Sigma Model 800SL; American Sigma, Medina NY) with a capacity of 24 samples of 330 mL, controlled in two distinct modes. In one mode, sampling was triggered by water level variations in the Venturi flume. In the other mode, samples were collected at regular time intervals of 20 min.This system makes it possible to record runoff rise, peak and decrease and ensures regular sampling throughout the entire runoff duration as much as possible. Until the end of 2000, each sample was individually analysed, and then, since 2001, individual samples were accumulated in the same container for each runoff event. Samples, whether individual or cumulative, were collected within approximately 24 hours of the end of the sampling period and then stored at less than 4°C before analysis by a specialised laboratory. For diuron, concentrations were determined by high performance liquid chromatography (HPLC) separation and diodes bar ultraviolet detection before 2006 and by HPLC and mass spectrometric detection afterwards. For glyphosate, concentrations were determined using derivatization prior to gas chromatography and mass spectrometric detection before 2006 and prior to liquid chromatography and mass spectrometric detection afterwards. Regarding runoff events with several samples, the average runoff concentration was estimated by weighting the concentration measured for each sample by the water volume during the sampling time.A total of 79 average runoff event concentrations were obtained for glyphosate, and 132 event concentrations were obtained for diuron. The flux-weighted average runoff event concentrations of glyphosate and diuron varied by several orders of magnitude during the monitoring period, namely, between 0.2 and 120 µg.L -1 and between 0.1 and 702 µg.L -1 , respectively[Fig. 1(d)]. The highest concentration values were

Fluxes

  at the soil surface interface are controlled by a classical atmospheric condition like in other models solving Richards equation (e.g. HYDRUS, Simunek et al. 2013). This boundary condition switches from a Neumann (flux) to a Dirichlet (head) boundary condition when the climatic forcing (rainfall or potential evaporation rate) exceeds the maximum potential soil flux at the soil interface as estimated by Darcy's equation. In case of excess infiltration, ponding is assumed to occur up to a maximum height. The relationships between water content, pressure head and hydraulic conductivity are expressed by the modified Mualem-van Genuchten model (Schaap

Y

  i obs : the i th observation of the studied variable of interest (the original runoff concentration or the log-transformed concentration); Y i sim : the i th simulated value; Y mean(obs) : the mean of the observed values; and n: the total number of observed values. PBIAS quantifies the average over-or underestimation of the observations by the simulations. A positive value indicates that the model overpredicts the variable of interest on average, and a negative value indicates that the model underestimates the variable overall [equation (3computed for both the original runoff pesticide concentrations and their log-transformed values. As stressed by Krause et al. (2005), the calculation with log-transformed values reduces the sensitivity of these performance criteria to extreme error values. As a result, given the large range of concentration values and the many low values, criteria based on log-transformed values are sensitive to all concentrations, whereas criteria based on concentrations are mostly sensitive to high concentrations occurring soon after application.

  runoff concentration of diuron or glyphosate; and C obs : Observed runoff concentration of diuron or glyphosate.

  approximately 0.88. Regarding validation, the overall model performance remained stable or decreased depending on the performance criterion considered and the compound. Concerning the log-transformed concentrations, the model performance was very similar to that during the calibration period and remained high for both compounds [Fig.3(d)]. The NSE values exceeded 0.77, while the PBIAS values varied between -20% and -8%. In regard to the predicted concentrations over the validation period, the model performance was lower than that during the calibration period, either slightly for glyphosate with a maximum NSE value of 0.74 and a minimum | PBIAS| value of 26% or markedly for diuron with a maximum NSE value of 0.52 and a minimum |PBIAS| value of45% [Fig. 3(b)].

Fig. 5

 5 Fig. 5 shows the evolution of the standard error of the mean annual PBIAS and NSE values as a function of the number of years used for model evaluation. A large number of years of data is required to accurately measure the average model performance in reproducing the interannual variability of the pesticide concentration in runoff. With three years of data used for performance evaluation in reproducing runoff concentrations, the standard errors of the mean annual NSE and PBIAS valuesreached up to 0.14 and 17%, respectively, which are higher than the ranges of the PBIAS values chosen to define the classes of the simulation performance defined by[START_REF] Moriasi | Hydrologic and water quality models: Performance measures and evaluation criteria[END_REF], namely, 10%. To ensure a sufficient estimation accuracy for NSE and PBIAS to categorize the model performance according to the classification of Moriasi, the standard errors should be less than 0.15 and 10% for NSE and PBIAS, respectively. Thus, for example, at least 3 years of data are required to obtain a standard error of the mean annual NSE less than 0.15 for all analysed compounds and variables, and at least 12 years of data are required to obtain a standard error of the mean annual PBIAS less than 10% for all analysed compounds and variables. The number of years of data needed to reach these thresholds varies, however, depending

2.1. Site description and field measurements

	2.1.1.

Field site and studied compounds

	The entire surface area of the field was chemically treated with herbicides currently or
	formerly used in viticulture, namely, with diuron, a preemergence herbicide, between
	1995 and 2008, and with glyphosate, a postemergence herbicide, between 2001 and
	2013. Frequently found in surface water monitoring networks, diuron was banned in
	France in 2008. The diuron and glyphosate doses applied, as estimated from farmers'
	statements or our measurements prior to spraying, varied between 1 and 2.3 kg.ha -1
	and between 2 and 2.7 kg.ha -1 , respectively [Fig. 1(c)]. Diuron is a moderately
	hydrophobic and moderately water-soluble compound (35.6 mg.L -1 according to the
	Pesticide Properties DataBase (PPDB) [PPDB, 2022)], while glyphosate is a strongly
	The field site is located in the Roujan experimental catchment (Herault, 60 km west of hydrophilic and highly water-soluble compound (100000 mg.L -1 ; PPDB, 2022). The
	Montpellier, 43°30'N, 3°19'E), which belongs to the Mediterranean Observatory of the values of the sorption coefficient (K f ) and the Freundlich sorption parameter 1/n range
	Rural Environment and Water (Observatoire Méditerranéen de l'Environnement Rural respectively from 4.48 to 15.52 L.kg -1 and 0.67 to 0.89 for diuron, and from 18.1 and
	et de l'Eau or OMERE) observatory (Molénat et al., 2018). The climate is a subhumid 166.4 L.kg -1 and 0.54 to 0.78 for glyphosate (PPDB
	Mediterranean climate with a prolonged dry season in summer and precipitation, often
	stormy, mainly occurring in spring and autumn. The average annual rainfall over the
	09/1994 to 09/2014 period was 659 mm, which is also marked by high interannual
	variations (from 414 to 1377 mm) and high intra-annual variations (the rainfall from
	June to August equals the average rainfall in October, which is the rainiest month). The
	rainfall intensity can be very high (with a maximum intensity over 5 min close to 240
	mm.h -1 ), resulting in dominant Hortonian runoff processes.
	The study field is a 1200 m 2 area entirely planted with vines. Its slope varies between
	7% and 15% (Chahinian et al., 2005). The field is hydrologically isolated from its
	neighbouring plots via a girdling ditch.The substratum belongs to the Miocene marine
	deposits. The soil is a calcaric cambisol (IUSS-WRB, 2014). The main properties of the
	0-5 cm layer are a bulk density of 1.44 g.cm -3 , a pH measured in water of 8.5, a soil
	organic carbon content of 1.06%, a CaCO3 content of 24% and a silty sand texture
	[18.6% clay (0-2 μm), 55.4% silt (2-50 μm) and 26% sand (50-2000 μm)].

Acknowledgements

We thank the OMERE observatory (http://www.obs-omere.org) for providing the data used in this work. We also thank Laurent Prévot, scientist at the French National Research Institute for Agriculture, Food and Environment (INRAE), Sandrine Negredo, assistant engineer at INRAE, and Olivier Huttel, engineer at INRAE for their help in checking the experimental data.

Declaration of competing interest

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

Funding

The PhD grant of the senior author was provided by the French National Research Institute for Agriculture, Food and Environment (INRAE) and the Occitanie Region, whereas the study was conducted as part of the POLLDIFF CAPTAGE Project funded by the Occitanie Region and European Regional Development Fund (FEDER) (grant LR 0014594/2017-007745-01)