Saeko Tachikawa
email: saekotac@iis.u-tokyo.ac.jp

Jose Ordonez-Miranda

Yunhui Wu
email: yunhui@iis.u-tokyo.ac.jp

Laurent Jalabert
email: jalabert@iis.u-tokyo.ac.jp

Roman Anufriev
email: anufriev@iis.u-tokyo.ac.jp

Sebastian Volz
email: volz@iis.u-tokyo.ac.jp

Masahiro Nomura
email: nomura@iis.u-tokyo.ac.jp

High Surface Phonon-Polariton in-Plane Thermal Conductance along Coupled Films

Keywords: surface phonon-polaritons, multilayered structure, thermal conductance, polar materials

Surface phonon-polaritons (SPhPs) are evanescent electromagnetic waves that can propagate distances orders of magnitude longer than the typical mean free paths of phonons and electrons. Therefore, they are expected to be powerful heat carriers capable of significantly enhancing the in-plane thermal conductance of polar nanostructures. In this work, we show that a SiO 2 /Si (10 µm thick)/SiO 2 layered structure efficiently enhances the SPhP heat transport, such that its in-plane thermal conductance is ten times higher than the corresponding one of a single SiO 2 film, due to the coupling of SPhPs propagating along both of its polar SiO 2 nanolayers. The obtained results thus show that the proposed three-layer structure can outperform the in-plane thermal performance of a single suspended film while improving significantly its mechanical stability.

Introduction

As the microfabrication technology has rapidly progressed and the integration density of electrical circuits has been enhanced dramatically, the local heating has become a critical issue because it can damage the electrical devices or lower their performance [START_REF] Semenov | Impact of self-heating effect on long-term reliability and performance degradation in CMOS circuits[END_REF]. The nanoscale heat transfer has been investigated due to its importance in both fundamental physics and in semiconductor industries [START_REF] Nomura | Thermal phonon engineering by tailored nanostructures[END_REF][START_REF] Volz | Heat conduction in nanostructured materials[END_REF][START_REF] Cahill | Nanoscale thermal transport[END_REF][START_REF] Giri | A Review of Experimental and Computational Advances in Thermal Boundary Conductance and Nanoscale Thermal Transport across Solid Interfaces[END_REF]. The thermal fluxes drop down with the sizes scaled down to nano-metric dimensions [START_REF] Chen | Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons; Google-Books-ID: M3n3lUJpYDYC[END_REF][START_REF] Braun | Size effects on the thermal conductivity of amorphous silicon thin films[END_REF][START_REF] Volz | Nanophononics: State of the art and perspectives[END_REF], therefore the thermal management is in great need.

Surface phonon-polaritons (SPhPs) attracted enormous attention in the past decade as an additional heat carrier. SPhPs are electromagnetic surface modes generated by the coupling between electromagnetic waves and optical phonons located at the interface of polar dielectric materials [START_REF] Yang | Long-range surface modes supported by thin films[END_REF][START_REF] Greffet | Coherent emission of light by thermal sources[END_REF][START_REF] Chen | Surface phonon-polariton mediated thermal conductivity enhancement of amorphous thin films[END_REF][START_REF] Chen | Measurement of silicon dioxide surface phonon-polariton propagation length by attenuated total reflection[END_REF][START_REF] Chen | Heat flow in thin films via surface phonon-polaritons[END_REF]. Studies on SPhPs have been conducted especially on polar materials, such as SiC [START_REF] Chen | Heat flow in thin films via surface phonon-polaritons[END_REF][START_REF] Huber | Focusing of surface phonon polaritons[END_REF][START_REF] Francoeur | Local density of electromagnetic states within a nanometric gap formed between two thin films supporting surface phonon polaritons[END_REF][START_REF] Joulain | Radiative thermal rectification between SiC and SiO 2[END_REF], SiO 2 [START_REF] Chen | Surface phonon-polariton mediated thermal conductivity enhancement of amorphous thin films[END_REF][START_REF] Chen | Measurement of silicon dioxide surface phonon-polariton propagation length by attenuated total reflection[END_REF][START_REF] Joulain | Radiative thermal rectification between SiC and SiO 2[END_REF][START_REF] Gluchko | Focusing of surface phonon-polaritons along conical and wedge polar nanostructures[END_REF][START_REF] Gluchko | Thermal excitation of broadband and long-range surface waves on SiO2 submicron films[END_REF][START_REF] Ordonez-Miranda | Anomalous thermal conductivity by surface phonon-polaritons of polar nano thin films due to their asymmetric surrounding media[END_REF], and hBN [START_REF] Zhao | Enhanced photon tunneling by surface plasmon-phonon polaritons in Graphene/hBN heterostructures[END_REF][START_REF] Zhang | Hybrid phonon-polaritons at atomically-thin van der Waals heterointerfaces for infrared optical modulation[END_REF][START_REF] Nikitin | Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab[END_REF][START_REF] Yang | Boundary-Induced Auxiliary Features in Scattering-Type Near-Field Fourier Transform Infrared Spectroscopy[END_REF]. SPhPs propagate with infrared frequencies over distances in the range of hundreds of micrometers along the interface of nanostructures [START_REF] Gluchko | Thermal excitation of broadband and long-range surface waves on SiO2 submicron films[END_REF]. Therefore, they could be additional energy carriers capable of enhancing the in-plane thermal conductivity [START_REF] Gluchko | Focusing of surface phonon-polaritons along conical and wedge polar nanostructures[END_REF][START_REF] Ordonez-Miranda | Anomalous thermal conductivity by surface phonon-polaritons of polar nano thin films due to their asymmetric surrounding media[END_REF], especially when it decreases as the system size reduces to the nano scale [START_REF] Chen | Surface phonon-polariton mediated thermal conductivity enhancement of amorphous thin films[END_REF][START_REF] Chen | Measurement of silicon dioxide surface phonon-polariton propagation length by attenuated total reflection[END_REF][START_REF] Chen | Heat flow in thin films via surface phonon-polaritons[END_REF]. Chen et al. have reported that the SPhP thermal conductivity of a 40 nm-thick thin film of amorphous SiO 2 suspended in air is 4 Wm -1 K -1 at 500 K, which is higher than its bulk phonon thermal conductivity [START_REF] Chen | Surface phonon-polariton mediated thermal conductivity enhancement of amorphous thin films[END_REF]. An experimental demonstration was also conducted by Tranchant et al. [START_REF] Tranchant | Two-Dimensional Phonon Polariton Heat Transport[END_REF]. They reported that the in-plane thermal conductivity of a SiO 2 film increases by more than 50% of that of bulk SiO 2 for a film thickness less than 50 nm.

However, a suspended thin film of a polar material is technically challenging to achieve and is not a practical geometry, thus a film on a substrate or a multilayered structure was then investigated [START_REF] Ordonez-Miranda | Anomalous thermal conductivity by surface phonon-polaritons of polar nano thin films due to their asymmetric surrounding media[END_REF][START_REF] Ordonez-Miranda | Thermal conductivity of nano-layered systems due to surface phonon-polaritons[END_REF][START_REF] Lim | Thermal-Conductivity Enhancement by Surface Electromagnetic Waves Propagating along Multilayered Structures with Asymmetric Surrounding Media[END_REF]. Multilayered structures were found to achieve higher thermal conductivity than a single film for certain conditions [START_REF] Ordonez-Miranda | Thermal conductivity of nano-layered systems due to surface phonon-polaritons[END_REF]. Lim et al. [START_REF] Lim | Thermal-Conductivity Enhancement by Surface Electromagnetic Waves Propagating along Multilayered Structures with Asymmetric Surrounding Media[END_REF] developed an analytical algorithm to scan the crucial parameters to optimize materials in multilayered configurations.

Here, we report SPhP dispersion relation of a structure consisting of a 10 µm-thick silicon (Si) layer sandwiched between two SiO 2 layers (the three-layer structure). We demonstrate that this configuration exalts the coupling between polaritonic layers inside the Si film. When the Si layer thickness is within the cross-plane decay length of SPhPs in each polar film, the surface polaritons are indeed expected to couple without diminishing completely in the cross-plane direction and to carry thermal energy inside the system efficiently in the in-plane direction. Previous studies were focused on very thin nanofilms, where the SPhP dispersion relation was linearized and yielded only one solution (branch) [START_REF] Ordonez-Miranda | Anomalous thermal conductivity by surface phonon-polaritons of polar nano thin films due to their asymmetric surrounding media[END_REF][START_REF] Ordonez-Miranda | Thermal conductivity of nano-layered systems due to surface phonon-polaritons[END_REF][START_REF] Lim | Thermal-Conductivity Enhancement by Surface Electromagnetic Waves Propagating along Multilayered Structures with Asymmetric Surrounding Media[END_REF]. In this study, we calculate the SPhP dispersion relation without using any analytical simplification and find several branches contributing to the SPhP thermal conductance. We found a higher thermal conductance due to SPhPs for the three-layer structure compared to that of a single SiO 2 film thicker than 150 nm. This conductance becomes more than ten times higher for SiO 2 films thicker than 600 nm. The novelty of this work lies in the discovery that the coupling of SPhPs propagating in each SiO 2 layer of the SiO 2 /Si/SiO 2 structure is able to enhance its ability to transport thermal energy, which results in a thermal conductance higher than the corresponding one of a single SiO 2 film. This work provides insights into the design of the SPhPs supporting structures of large dimensions, which are mechanically stable, but can still yield a high SPhPs in-plane thermal conductance. Note that, throughout the manuscript, the contribution of acoustic phonons are not considered in the thermal conductance calculations.

Method and Model

The SPhP dispersion relation of the three-layer structure, shown in Figure 1b, is derived in order to calculate the in-plane thermal conductance of the structure due to SPhPs. Figure 1a shows the scheme of a single suspended film of thickness d, surrounded by vacuum, and Figure 1b displays the specific structure of a Si layer of thickness h, sandwiched between SiO 2 films of thickness d. The SiO 2 films and Si are assumed to be nonmagnetic (Relative magnetic permeability µ = 1). The SiO 2 has a frequency-dependent relative permittivity 2 (ω), while Si has a relative permittivity of 3 = 11.7, which assumed as non-absorptive in the infrared range, surrounded by non-absorptive media with a permittivity of 1 such as vacuum. The thermal conductance generated by SPhPs in this structure G is given by [START_REF] Chen | Surface phonon-polariton mediated thermal conductivity enhancement of amorphous thin films[END_REF],

G = W 4πL ∞ 0 hωΛβ R ∂ f 0 ∂T dω. (1)
where f 0 is the Bose-Einstein distribution function, T the temperature of the structure, and h the reduced Planck's constant, ω is the angular frequency, W and L are the system width and length, respectively. We assume the in-plane wave vector along the interfaces as a complex wave vector, denoted β as β = β R +iβ I . The propagation length of SPhPs Λ is defined by

Λ = 1 2β I . ( 2
)
By solving Maxwell's equations with proper boundary conditions at each interface, we can obtain the dispersion relation for β of the three-layer structure as [START_REF] Ordonez-Miranda | Thermal conductivity of nano-layered systems due to surface phonon-polaritons[END_REF][START_REF] Yeh | The Essence of Dielectric Waveguides[END_REF]

tanh(p 3 h) = - 2S 23 [S 12 + tanh(p 2 d)][S 12 tanh(p 2 d) + 1] [S 12 + tanh(p 2 d)] 2 S 2 23 + [S 12 tanh(p 2 d) + 1] 2 .
(

) 3
where S nm = p n m /p m n , the transverse wave vector p n in the medium referred to as by n is

p 2 n = β 2 -n k 2 0 . ( 4
)
with n being the relative permittivity of medium n = 1, 2, 3, and the wave vector in vacuum k 0 = ω/c, where c is the speed of light in vacuum. This dispersion relation leads to the in-plane wave vector β. Note that we did not use any simplification when solving this dispersion relation, therefore the term tanh(p 3 h) yields more than one solution. It means that several SPhPs branches exist in this structure.

Knowing this β, one can obtain the in-plane thermal conductance of this structure by summing up the thermal conductances given by each branch.

Here, we consider silicon dioxide (SiO 2 ) as the polariton active media. The relative permittivity of SiO 2 is complex and frequency-dependent. The real part R and imaginary part I of the relative permittivity 2 (ω) of SiO 2 can be obtained from experimental data reported for the complex index of refraction [START_REF] Palik | Handbook of Optical Constants of Solids[END_REF], as shown in Figure 2. The main peaks of I at about 87 Trad/s and 202 Trad/s indicate that the SiO 2 absorbs significant energy from the electromagnetic field at those frequencies. By contrast, the minimum of I at 174 Trad/s shows that these fields can propagate relatively large distances within the SiO 2 , at this frequency. On the other hand, the two dips of R at 89 Trad/s and 207 Trad/s are associated with the SPhP resonance frequencies and therefore the major contribution to the SPhP thermal conductance is expected to arise from the vicinity of the minimum of I and the main dip of R , as shown below.

Results

The dispersion relation of β R is plotted in Figure 3. There are five branches, named as the 1st-5th branches, within this frequency range. All the branches are below the light line, which means that they are evanescent in the cross-plane direction in this frequency range. The in-plane propagation length of each branch is plotted in Figure 4a. The first branch has the longest propagation length at frequencies above 90 Trad/s and this latter length is even longer than the in-plane propagation length of SPhPs in a single SiO 2 film. This behavior leads to the high thermal conductance of the first branch in the structure.

The thermal conductance of each branch is plotted in Figure 4b. The first branch with the longest propagation length shows the largest thermal conductance. However, the thermal conductance given by the second branch is equivalent to approximately 16% of the total thermal conductance, and the contribution of the second branch is not negligible. For comparison, we calculated the thermal conductance dependence on the SiO 2 thickness, shown in Figure 5. The SiO 2 thickness is varied from 1 µm down to 10 nm and both the thermal conductance by SPhPs of the three-layer structure and of the single SiO 2 film are plotted. The thermal conductance of the three-layer structure is higher than that of the single SiO 2 film for SiO 2 film thickness > 150 nm. When the SiO 2 film is thicker than 600 nm, the thermal conductance is more than one order of magnitude higher than that of the single SiO 2 film.

Discussion

For most of the studies of SPhPs, thin enough layers (|p 3 |h 1, |p 2 |d 1) were considered. This justified the assumption of tanh(x) → x, reducing the dispersion relation equation into a linear relation yielding a single solution. In this study, Si thickness of 10 µm is considered as not thin enough to apply the assumption, so that the equation was calculated numerically, resulting in several different solutions or branches. The higher the order of the branch, the shorter the propagation length. Therefore, each branch contributes to thermal transport at different levels. The first branch has the longest propagation length over nearly all the frequency range, even longer than that of a 1 µm-thick single film. It provides the most significant contribution of approximately 70% to the thermal conductance. The second branch and the third branch contribute to ∼16% and ∼5% of the thermal conductance, respectively. In the structure of relatively large dimensions, there is more than one branch to take into account in the calculation of the thermal conductance. The branches with longer propagation lengths pushed the thermal conductance higher than that of the single SiO 2 film case. However, the reduction of SiO 2 thickness enhances the thermal transport by SPhP in in-plane due to less absorption in the polar materials and this effect has less impact on the three-layer structure, for its low effective volume of the polar material among the total volume. Therefore, as plotted in Figure 5, the thermal conductance of the three-layer structure cannot defeat that of the single SiO 2 film, for SiO 2 thickness smaller than 150 nm. Yet, this result shows that bulk structure can give higher thermal conductance by carefully choosing the material and the configuration without thinning the suspended film to create a mechanically unstable and non-realistic structure. As for Si thickness dependence, as the thickness of the Si layer reduces, the coupling between the SPhPs propagating along the top and bottom SiO 2 layers strengthens, with both layers tend to act like a single thicker one, which increases the absorption of energy by SiO 2 and hence decreases the SPhP thermal conductance.

We also calculated the cross-plane wave vectors in each media of the three-layer structure and compared them to the one of the single SiO 2 film case for SiO 2 thickness of 1 µm. In Figure 6, the cross-plane decay length δ in Si (δ 3-layer,3 ) and in vacuum at the vicinity of the three-layer structure (δ 3-layer,1 ) are plotted in addition to the δ in vacuum at the vicinity of the single SiO 2 film (δ f ilm,1 ). It shows that δ 3-layer,3 is longer than δ f ilm,1 , indicating that SPhPs in the top SiO 2 layer and the SPhPs at the bottom SiO 2 layer are coupled inside Si. Note that δ 3-layer,3 is very long so that almost not decaying within 10 µm thick Si. On the other hand, δ 3-layer,1 is shorter compared to δ f ilm,1 . Figure 7 shows the Poynting vector distribution along the cross-plane direction at ω= 174 Trad/s. As predicted in Figure 6, for the three-layer structure, the wave in the cross-plane direction decays more quickly than for the single SiO 2 film case and is more confined at the interface between SiO 2 and vacuum. The energy is more distributed inside the structure instead of spreading into the vacuum surroundings. When the in-plane thermal conductance by SPhPs of the structure is concerned, SPhPs of two films coupled inside Si which propagates without being absorbed in Si, and energy strongly confined around the structure can effectively yield higher value than the summation of the SPhPs thermal conductance of two individual single SiO 2 films. The three-layer structure supports SPhPs with long propagation lengths, and thus yields a significant SPhPs thermal conductance even with relatively thick SiO 2 layers which are normally not effective in enhancing SPhPs thermal transport. Although the SiO 2 thickness reduction leads to a substantial impact in the single film case and the thermal conductance for the single film exceeds that of the three-layer structure with SiO 2 thinner than 150 nm, suspended films with this range of thicknesses are difficult to handle and barely realistic in terms of applications.

Conclusions

We have calculated the dispersion relation of SPhPs in a SiO 2 /Si (10 µm)/SiO 2 three-layer structure involving two coupled polaritonic nanofilms. Several branches exist in the structure with different in-plane propagation lengths and the total thermal conductance is a sum of the thermal conductance given by each branch. The three-layer structure exhibits higher SPhP thermal conductance than a single SiO 2 film when SiO 2 is thicker than 150 nm in both structures. Furthermore, the SPhP thermal conductance of the structure is ten times higher than the one of a single SiO 2 film thicker than 600 nm. Finally, we have demonstrated that the energy decay in the cross-plane direction inside Si was almost negligible, whereas more confinement in the vicinity of the SiO 2 layer for the structure has been found through a cross-plane wave vectors analysis. This work shows that the coupling of two polaritonic nanofilms generates a substantial gain in electromagnetic heat flux, while ensuring strong mechanical stability.

Figure 1 .

 1 Figure 1. Scheme of (a) a single SiO 2 film and (b) a three-layer structure (SiO 2 /Si/SiO 2 ).

2 Figure 2 .

 22 Figure 2.Real and imaginary parts of the relative permittivity of SiO 2 reported in Ref[START_REF] Palik | Handbook of Optical Constants of Solids[END_REF].

Figure 3 .

 3 Figure 3. Dispersion relations of SPhPs propagating along a SiO 2 (1 µm)/Si (10 µm)/SiO 2 (1 µm) structure.

Figure 4 .

 4 Figure 4. (a) The in-plane propagation length and (b) thermal conductance of SPhPs. The structure consists of the layered system, SiO 2 (1 µm)/Si (10 µm)/SiO 2 (1 µm).

Figure 5 .

 5 Figure 5. A comparison of the SPhPs thermal conductances of the SiO 2 /Si (10 µm)/SiO 2 three-layer structure and of a single SiO 2 film at 300, 500 and 700 K, for different SiO 2 thicknesses.

Figure 6 .

 6 Figure 6. Cross-plane decay length in different media: Si (red solid line) and vacuum (black solid line) of the three-layer structure, and vacuum in the vicinity of the single film structure (black dashed line).

Figure 7 .

 7 Figure 7. Normalized Poynting vector along the cross-plane direction for (a) the single SiO 2 film and (b) the three-layer structure surrounded by vacuum.

Acknowledgments:

The authors thank Sergei Gluchko for the conceptional discussions and Shiyun Xiong for the analytical discussions. We also appreciate the JSPS Core-to-Core Program (A. Advanced Research Networks) for promoting our collaborative works.

Funding: This research is funded by CREST JST Grant Number JPMJCR19Q3 and JPMJCR19I1, KAKENHI Grants Numbers 15H05869 and 17H02729.

Author Contributions: S.T. and J.O.-M. built up the model and conducted the investigation and analysis. S.T. prepared the original draft and Y.W. worked on editing and visualization. J.O.-M., Y.W., R.A., L.J., S.V. and M.N. contributed on discussion of results. This work was supervised by S.V., administrated by S.V. and M.N. All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest:

The authors declare no conflict of interest.


Honggang Zhang

Bo Sun

Song Hu

Hongyan Wang

Yajuan Cheng

Shiyun Xiong

Sebastian Volz

Yuxiang Ni

Novel phonon resonator based on surface screw thread for suppressing thermal transport of Si nanowires

We propose a novel phonon resonator for hindering the thermal transport of nanowires (NWs), based on a screw threadlike helical nanowall. Results from molecular dynamic simulations reveal that the thermal conductivity and phonon transmission of the screw threadlike Si NWs continuously decrease with an increase in the period density of the helical nanowall. The reduction can reach as high as 36% for the NW with six circles of the helical nanowall, which is much larger than in the case of NWs with straight nanowalls (12%) and nanopillars (15%). This phenomenon is due to that the helical nanowall has a larger contact area with the base structure, which leads to a larger volume of the resonating substructure with a constant height and width. Phonon dispersion relations show the formation of flat bands, which confirms the occurrence of phonon resonances due to the surface screw threadlike structures. The phonon spatial distribution reveals mode localization in the helical resonator at the resonant frequency. With regard to suppressing the phonon propagation, the helical nanowall as a phonon resonator exhibits superiority over the straight nanowalls or conventional nanopillars, because (1) it may be easier to fabricate a larger contact area with the base structure and (2) it avoids the problem of nanopillars or nanowalls touching each other, which maintains the ability of generating localized modes. The obtained results provide a novel design of efficient surface phonon resonators to realize nanowires with ultralow thermal conductivity.

I. INTRODUCTION

Semiconductor nanowires (NWs) exhibit many attracting properties owing to their confined dimension with nanoscale characteristic lengths [1]. For example, silicon nanowires with diameters on the order of their phonon mean free paths or less show impeded thermal transport due to phonon boundary scattering [2]. The suppressed phonon propagation in NWs is beneficial to applications in thermoelectrics [3], where the energy conversion efficiency is inversely proportional to the thermal conductivity.

A phonon is a collective quantization of the lattice waves. The superposition of phonons of multiple frequencies existing in the solid forms wave packets, which can be considered as particles as long as they are much smaller than the crystal size [START_REF] Chen | Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons and Photons[END_REF]. Conventionally, the design of low-thermally conducting NWs is based on the phonon particle picture, by utilizing * These authors contributed equally to this work.

† yuxiang.ni@swjtu.edu.cn the phonon scattering mechanisms, such as phonon-boundary scattering [START_REF] Rojo | [END_REF][6][7], phonon-imperfection scattering [8][9][10][11][12][13], and phonon-impurity scattering [14][15][16]. Phonons with lower frequencies (long wavelengths) will ignore the spatial structural patterns, thus in general only phonons with a relatively high frequency (typically above 1 ∼ 2 THz) can be scattered efficiently. Meanwhile, in most cases, grain boundaries, imperfections, and impurities are unfavorable for the electronic transport, which negates the increase of thermoelectric efficiency.

On the other hand, manipulating the thermal transport based on the wave nature of phonons, particularly by local resonance, has intrigued research interests in recent years [17]. By adding pillars on the base structure, standing waves that hybridize with phonons in the base structure can be introduced, which leads to flat bands in the phonon dispersion relation [18,19]. Inspired by this idea, a series of nanophononic metamaterials (NPMs) with resonant structures were proposed to achieve low thermal conductivity. Xiong et al. [20] systematically studied the heat transport in Si based resonant structures. Their molecular dynamic (MD) simulations show that the branched NWs can produce numerous resonances in a broad frequency range, and the phonon group velocities were reduced accordingly. Further investigations on oxidized Si membranes show that surface amorphous structures can also produce phonon resonances [21]. Giri et al. used fullerenes as phonon resonators to functionalize carbon nanotubes (CNT) and graphene, and tunable thermal conductivities of individual CNTs and graphene were obtained [22,23]. By introducing phonon resonators, the thermal rectification can also increase up to 470% under small temperature bias in pristine/branched graphene nanoribbon junctions [24].

Despite the progress made in the thermal transport manipulation with local resonance, further enhancing the impact of the resonators is challenging. It is reported that the phonon transport suppression in Si membranes can be enhanced with increasing volume of the nanopillars, by changing their height and contact area with the main structure [25][26][27]. However, enlarging the nanopillar size leads to the extreme case of connective nanopillars, which forms a uniform waveguide and favors the thermal transport in the host structure. For example, by replacing the nanopillars by nanowalls (parallel to the phonon transport direction) on a Si membrane, the localized modes almost disappeared and the thermal conductivity reduction decreased [27]. A similar trend was also found for nanopatterned Si membrane systems [28]. In this regard, it is necessary to design a connective resonator structure in order to increase the contact area with the base structure, while maintaining the ability of generating localized modes.

In this work, we propose using a helical nanowall as a phonon resonator for NWs. There are two important advantages of helical nanowall resonators compared with conventional nanopillars or straight nanowalls: (1) The helical nanowall is consecutive, which provides larger contact area with the base structure; (2) the curved nature of the helical nanowall makes it a poor phonon waveguide, which ensures the generation of localized modes. Besides, the screw threadlike NWs are already obtained experimentally in recent years [29,30]. Our MD simulations show that, compared with the pristine Si NW, the screw threadlike Si NW exhibits a 36% reduction in thermal conductivity (κ), much larger than in the case of NWs with straight nanowall (12%) and nanopillars (15%). Phonon analyses such as dispersion relations, group velocity, phonon transmission, and phonon spatial distribution are conducted to gain more insights into the underling physical mechanisms.

II. METHOD A. Computational models

The atomistic models of Si nanowires are illustrated in Fig. 1. Cylindrical Si NWs are obtained by cleaving the bulk Si supercells along the [100] direction. The radius of the cross section (1.48 nm) and the total length (38 nm) are fixed in all the NW models. Helical nanowall, i.e., the screw thread, is then added to the main NWs. We label the NWs according to the period number of the helical nanowall on NWs with a fixed length (38 nm). For example, 2P corresponds to the NW with two circles of the helical nanowall [Fig. 1 on the thermal transport of NWs, we design a set of NWs from 1P to 6P. The width of the helical nanowall is 0.32 nm and the height is set between 0.5 and 3.5 nm.

B. Thermal conductivity calculation of screw threadlike Si NWs

We compute the thermal conductivity (κ) along the NWs by using the nonequilibrium molecular dynamics (NEMD) with the LAMMPS package [31]. The Stillinger-Weber (SW) potential is employed to describe the covalent Si-Si bond [32]. Free boundary conditions are applied at the boundaries transverse to the direction of the heat current flow, while atoms at both ends of the structures are fixed. Adjacent to the two fixed areas, sections with a length L bath = 10 nm are set as the hot and cold heat baths, as illustrated in Fig. 2. To reach the equilibrium state, a 500 ps simulation run is performed in the canonical ensemble (NVT) at 300 K, followed by a 200 ps run in the microcanonical ensemble (NVE), with a time step of 1 fs. Subsequently, the Langevin thermostat is applied to the groups of atoms in the thermal baths to achieve temperatures T hot = T + T and T cold = T -T , respectively. Here T is set to 300 K and T is 60 K. A 2 ns run was performed to reach the steady state and another 8 ns run to time average the local temperature and heat flux along the wires. The thermal conductivity κ along the wires is calculated from the temperature gradient ∇T and the heat flux Q/S determined from a steady state according to Fourier's Law:

κ = Q S∇T . ( 1
)
Here, Q is the thermal power across a cross-sectional area S perpendicular to the transport direction. It should be noted that both the cross-sectional area of the NW and the helical FIG. 2. Schematic illustration of a Si nanowire model (3P) for NEMD simulations.

nanowall are included in S. In our study, the size (length) effect in NEMD is not removed in the computations, since our purpose is to compare the trend of the relative κ change rather than to obtain the absolute value of the thermal conductivity.

C. Phonon transmission spectra calculations

To uncover the physical mechanism of the phonon transport in our models, phonon analyses were performed based on MD simulations. We use the same NEMD simulation set to calculate the phonon transmission spectra [Trans(ω)], by using the method developed by K. Saaskilahti et al. [33,34]. The frequency resolved heat flux between any atoms i and j can be expressed as:

q i-→ j ≈ - 2 t simu ω α,β∈{x,y,z} Im vα i (ω) * K αβ i j vβ j (ω) , ( 2
)
where t simu and ω are the simulation time and the frequency, respectively. vα i and vβ j are the Fourier transformed atomic velocities of atom i in direction α and atom j in direction β, respectively. For calculating the flux spectra, the force constant matrix is calculated with the finite displacement method by Lammps, i.e., after relaxing the structures to the potential minimum, atom i is moved in the directions ±x, ±y, and ±z with a small value ( = 0.01 Å). After each displacement, the forces F of each atoms are calculated. As a result, the element of the force constant matrix can be evaluated as:

K αβ i j = F β- j -F β+ j 2 , (3)
here F β- j and F β+ j denote the force on atom j in β direction when atom i is displaced to -α and +α directions, respectively. The heat current across any interface separating adjacent atom sets L and R can be obtained by summing over atoms in each set:

q(ω) = i∈L j∈R q i-→ j (ω). (4)
The phonon transmission function can thus be defined according to the spectral heat current as:

Trans(ω) = q(ω) k B T , ( 5
)
where T is the temperature difference of the two thermal baths in NEMD simulations.

D. Phonon dispersion relation, group velocity, and spatial distribution calculations

The phonon dispersion relations and the group velocity of the nanowires were obtained based on the harmonic lattice dynamics [35]. The normal-mode eigenvector components ε and their corresponding eigenfrequencies ω were obtained by solving the lattice dynamics equation,

D(k)ε = ω 2 ε. ( 6
)
D(k) is the atomic mass normalized dynamical matrix, which is calculated from the second derivative of the Stillnger-Weber potential used in MD simulations. One period of the NW with helical nanowall (the repeating unit) was chosen as the unit cell in our calculations. Phonon group velocity was then derived according to the dispersion relations.

The spatial distribution of the phonon modes within a given frequency range of the models was calculated as follows [24]:

φ i,ω = ω∈ α ε * iα,ω ε iα,ω j ω∈ α ε * iα,ω ε iα,ω , (7)
where α and i correspond to the Cartesian component (x, y, or z) and the atom index, respectively. denotes a frequency range and we considered 0.25 ± 0.2 THz and 14.5 ± 0.2 THz in this study.

III. RESULTS AND DISCUSSION

A. Thermal conductivity and phonon transmission spectra of screw threadlike Si NWs

Figure 3(a) shows the calculated thermal conductivity (κ) of the screw threadlike Si NWs as a function of different period density of helical nanowall at 300 K. It can be seen that the screw threadlike surface has obvious impact on the thermal conductivity of Si NWs. κ decreases from 6.7 W/mK (pristine) to 5.5 W/mK (1P). With the increasing period density of the helical nanowalls, κ continuously decreases, suggesting that a larger contact area of the base structure and the resonator is more efficient in suppressing the phonon propagation. A 35% reduction in κ is obtained for 6P NW compared with the pristine one. We attribute the thermal transport impedance in the screw threadlike Si NWs to the standing waves generated by the helical nanowalls that hybridize with the phonons (especially with low frequency) in the base NW. Evidences from the phonon dispersion relations and the group velocity will be shown later in the following section. It is interesting to note that by changing the atomic type of the helical nanowall from Si to Ge, κ can be further decreased from 5.4 W/mK to 4.7 W/mK.

To have a deeper understanding of the κ reduction, we calculated the phonon transmission spectra, as shown in Fig. 3(b). Overall, the phonon transmission spectrum decreases with increasing period density of the helical nanowall, which complies well with the thermal conductivity results. It should be noted that, for 4P and 6P models, there is obvious decrease of the transmission spectra in the low-frequency regime (below 4 THz), indicating the importance of the resonant effect at low frequencies. Such phenomenon was not observed in our previous studies on phonon-imperfection scattering [13] and phonon-impurity scattering [36], in which cases the transmission spectra almost remain unaltered in the low-frequency regime, and the ballistic transport is obvious due to the long-wavelength nature of these phonons. When the atomic type of the helical nanowall is changed from Si to Ge, the corresponding phonon transmission is further suppressed in the high frequency range (above 4 THz), as shown in the inset of Figure 3(b). This result implies that, to further suppress the phonon transport, the phonon resonance can be combined with other phonon hindering mechanisms such as introducing acoustic impedance.

We now evaluate the impact of the height and width of the helical nanowall on the NW thermal conductivity. As demonstrated in Fig. 4, κ monotonically decreases with the height of the screw thread. This phenomenon is expected because taller nanowall exhibits more local resonance modes (vibrons) than a thinner one and therefore more strongly affects the phonon propagation for a given length of NW section. On the other hand, κ is not sensitive to the width of the helical nanowall, as shown in Table I. This phenomenon may be due to the competition between the increased room for phonon propagation and the increased number of localized modes.

B. Analyses of phonon dispersion relation, group velocity, and spatial distribution

To confirm the phonon resonance effect of the helical nanowalls, we compare the phonon dispersion relations of pristine Si NW and 1P screw threadlike Si NW in Figs. 5(a tween the LA mode and the resonant phonon can be observed.

The standing waves that hybridize with the low-frequency phonons in the main NW lead to flat bands in the phonon dispersion relation. Therefore, reduction is observed for the phonon group velocity of the screw threadlike Si NW, compared with that of the pristine Si NW, as shown in Fig. 5(d).

To have an intuitive image of the phonon resonance, we calculated the spatial distribution of phonon modes from Eq. ( 7). According to the phonon dispersion relations, 0.25 THz is a resonant frequency, while 14.5 THz is an ordinary frequency where no phonon resonance occurs. For the NWs with helical nanowall, we calculated the phonon spatial distribution of the modes within the frequency ranges of 0.25 ± 0.2 THz and 14.5 ± 0.2 THz, as illustrated in Figs. 5(f) and 5(g). The phonon spatial distribution of a pristine NW is also calculated for comparison [Fig. 5(e)].

Here, the range ±0.2 THz is considered to ensure the inclusion of the resonant modes (if any) around the corresponding frequency. The color bar indicates the portion of the local mode energy over the total energy, at a given frequency range. Figure 5(e) shows that phonons distribute uniformly in the pristine NW. When the helical nanowall is added, phonons with the resonant frequency are mostly localized in the helical nanowall, and only a few atoms in the main NW participate in the vibration [Fig. 5(f)]. In contrast, Fig. 5(g) shows that the spatial distribution of an ordinary mode (around 14.5 THz) is relatively uniform, indicating that the phonon vibration is not affected by the resonators at this frequency.

C. Comparison between the impacts of helical and straight nanowalls on NW thermal conductivity

In this section, from two aspects, we will highlight the advantages of using helical nanowall as phonon resonators to suppress the phonon propagation in NWs. Firstly, we compare the thermal conductivity of Si NWs with resonators of helical and straight nanowalls, respectively, in order to show the advantage of the curved nature of the resonator. Secondly, we evaluate the impact of the continuity of the nanowalls on the NW thermal conductivity. Computational models are built as demonstrated in Fig. 6. Helical (3P) and straight nanowalls are introduced to Si NW [Figs. 6(a) and 6(c)], and then a set of atoms is removed from the nanowalls, leaving nanowall sections (nanopillars) with equal spaces [Figs. 6(b) and 6(d)]. Note that the straight nanowall is placed along the NW axis, which is parallel to the heat transport direction under consideration.

Figure 7 shows the thermal conductivity of Si NWs with resonators of helical and straight nanowalls as a function of the volume fraction (n v ) of the removed atoms. At n v = 0, both straight and helical nanowalls are consecutive, and κ of the helical nanowall case is about 10% smaller than that of the straight one. This discrepancy can be due to the fact that a large part of the localized modes in NWs with straight nanowall disappeared, as shown in Fig. 5(c). The dispersion diagram of Si NW with straight nanowall is relatively close to that of the pristine NW [Fig. 5(a)]. In this case, the straight nanowall is a uniform waveguide along the axial direction [27]. Phonon resonance would not occur without the localized modes, and therefore, the thermal conductivity is larger. When the nanowall revolves around the nanowire, phonon propagation along the curved nanowall is more difficult, and localized modes can be generated and then couple with the low-frequency modes in the main wire [Fig. 5(b)]. In this regard, the curved nature of the nanowall is important for phonon resonators.

As n v increases, in both straight and helical cases, κ first slightly decreases and then increases and finally converges to n v = 1 (the pristine NW). The slight decrease in κ stems from the breakdown of the nanowall continuity, which blocks the phonon transmission along the nanowall. As more atoms are removed, the contact area between the resonators and the host NW decreases, and the resonator impact on κ is weakened, which leads to the κ increase. It can be clearly seen that κ of NWs with helical nanopillars is still lower than that of the straight nanopillar cases, owing to the larger volumetric size of the helical nanopillars relative to the straight ones at the same n v . As n v further grows, the difference in κ between the two cases gets smaller, until κ of both cases converge to the value of the pristine NW. The results revealed by Fig. 7 prove that the helical resonators are more beneficial for suppressing the phonon transport than conventional nanopillars.

IV. CONCLUSIONS

In this study, we propose using the helical nanowall as a resonator for nanowires. Our molecular dynamics simulations show that, compared with the pristine Si NW, the screw threadlike Si NW exhibits a 36% reduction in thermal conductivity (6P), much larger than in the case of NWs with a straight nanowall (12%) and nanopillars (15%). Phonon transmission spectra show the hindering of phonon transport in the whole frequency range. Phonon analysis such as dispersion relations, group velocity, and phonon spatial distribution confirm the phonon resonance effect in the screw threadlike Si nanowires. We conclude that the helical nanowall as a phonon resonator exhibits superiority over the straight nanowall or conventional nanopillars, owing to its large contact area with the base structure while maintaining the ability of generating localized modes. The radius of NWs (1.48 nm) and the height of the nanowall (0.5-3.5 nm) in our theoretical models can be scaled to the experimentally synthesized screw threadlike NWs (5 nm for both the NW radius and the height of the nanowall [29]). Therefore, the findings in this study should be valuable to the design of efficient surface phonon resonators for nanowires, which is important for their applications in thermoelectrics and thermal insulators, where low thermal conductivity is desired.

  FIG. 1. Atomistic models of Si nanowires: (a) pristine, and (b),(c) with helical nanowall.

FIG. 3 .

 3 FIG. 3. (a) Thermal conductivity of Si NWs varying with the period density of the helical nanowall. The red dot indicates the thermal conductivity of the model with Ge helical nanowall (the main NW is still Si). The height of the nanowall is set to 1 nm. (b) Phonon transmission spectra of Si NWs with different period density of the helical nanowall. The inset compares the transmission spectra of the models with Si and Ge nanowalls, respectively.

  FIG.4. The thermal conductivity of Si NWs against the height of the helical nanowall.

FIG. 5 .

 5 FIG. 5. (a)-(c) Phonon dispersion relations in the frequency range [0, 3] THz for the pristine Si NW, 1P screw threadlike Si NW, and Si NW with surface straight nanowall, respectively. (d) Averaged phonon group velocities of the different models. (e)-(g) Spatial distribution of the modes in the pristine and the screw threadlike NWs with the resonant frequency (ω = 0.25 THz) and ordinary frequency (ω = 14.5 THz).

FIG. 6 .

 6 FIG. 6. Models of Si NWs with (a) helical (3P) and (c) straight nanowalls, and the corresponding NWs (b) and (d) with nanowall sections with equal spaces after the removal of certain atoms. (e) Side view of the NW with straight nanowall.

FIG. 7 .

 7 FIG. 7. The thermal conductivity of Si NWs with resonators of helical and straight nanowalls as a function of the volume fraction of the removed atoms.

TABLE I .

 I Thermal conductivity of Si NWs against the width of the helical nanowall (2P).

	Width (nm)	0.32	0.64	0.96
	κ (W/mK)	5.1	5.0	5.2

ACKNOWLEDGMENTS Y.N. acknowledges the support of National Natural Science Foundation of China (NSFC) Grant No. 11774294, and the R&D Program for International S&T Cooperation and Exchanges of Sichuan province (Grant No. 2018HH0088). S.X. acknowledges the financial support from National Natural Science Foundation of China (Grant No. 11804242).

This work is also supported by the Fundamental Research Funds for the Central Universities (2682019CX67). The authors thank Prof. Jie Chen from Tongji University for useful discussions.


Thomas Grangeon
email: t.grangeon@brgm.fr

Valeria Ceriani

Olivier Evrard

Aurélie Grison

Rosalie Vandromme

Arthur Gaillot

Olivier Cerdan

Sébastien Salvador-Blanes

Quantifying hydro-sedimentary transfers in a lowland tile-drained agricultural catchment

Keywords:

Soil erosion, runoff and sediment connectivity are strongly impacted by anthropogenic features in lowland agricultural catchments. Among these landscape features, the role played by tile drainage on water and sediment transfers and hillslope-to-river connectivity in drained catchments remains poorly understood. This study quantified water and sediment transfers in a tile drained catchment of central France by combining high frequency rainfall, discharge and sediment concentration measurements at the outlet of a set of 10 tile drained plots (34 ha) and at the medium-sized (120 km 2 ) catchment scale. Over the monitoring period, including a dry and a wet year compared to average conditions (one year with 112% of the mean annual rainfall and one year with 64% of the mean annual rainfall), 36 rainfall-flood events were recorded and analyzed. The high frequency analysis of water and sediment transfers in tile-drained plots showed a high seasonal variability and the occurrence of two transfer pathways in the soil column including the slow drainage of saturated soils and the occurrence of preferential flow pathways through the soil column. Indeed, 13 of the 36 recorded flood events showed hydrographs with two components, reflecting these two pathways: slow transfers in the soil columns and fast transfers through soil macropores and/or cracks. Indeed, at the beginning of the flood event, a highmagnitude peak overlaid on the hydrograph. On average, this fast peak contributed 15% of the water and sediment fluxes. The sediment dynamics in tile drains was suggested to depend on sediment storage and exhaustion processes occurring in the tile drain network.

Introduction

In Europe, agricultural landscapes were strongly modified following WWII to increase agricultural productivity through the removal of hedges, land consolidation and stream redesigning programs [START_REF] Souchère | Grassland and crop trends: role of the European Union Common Agricultural Policy and consequences for runoff and soil erosion[END_REF][START_REF] Evrard | Modelling the impact of land use change and rainfall seasonality on sediment export from an agricultural catchment of the northwestern European loess belt[END_REF]. The agricultural areas were also extended in lowland areas with the installation of tile drainage systems to convert wetlands into arable land. A review conducted by [START_REF] Montagne | Soil drainage as an active agent of recent soil evolution: a review[END_REF] demonstrated that these changes may act as geomorphic agents, which outlines the need to consider their role in catchment sediment dynamics. Installing tile drainage systems may have extensive environmental implications [START_REF] Blann | Effects of agricultural drainage on aquatic ecosystems: a review[END_REF] because they may increase transfers of sediments from plots to rivers, which may have deleterious impacts on downstream environments [START_REF] Owens | Fine-grained sediment in river systems: environmental significance and management issues[END_REF][START_REF] Kemp | The impact of fine sediment on riverine fish[END_REF]. Indeed, tile drainage creates new pathways for water, sediment and associated pollutants resulting in the loss of on-site nutrients such as phosphorous [START_REF] Ulén | Field-scale phosphorous losses from a drained clay soil in Sweden[END_REF][START_REF] Macrae | Intra-annual variability in the contribution of tile drains to basin discharge and phosphorous export in a first-order agricultural catchment[END_REF][START_REF] Ulén | Particulate-facilitated leaching of glyphosate and phosphorous from a marine clay soil via tile drain[END_REF]. Furthermore, tile drains may also lead to offsite impacts including the enhanced export of pesticides [START_REF] Kladivko | Pesticide transport to subsurface tile drains in humid regions of North America[END_REF]. A specific problem occurring in these drained systems is associated with the fact that fluxes occurring in tile drains may bypass soil conservation measures (e.g. grass buffer strips) designed to prevent runoff and sediment transfers from cultivated land to the river channel (Le [START_REF] Bissonnais | Grass strip effects on runoff and soil loss[END_REF]. These fluxes are therefore directly delivered to the river systems, resulting in an increased connectivity between plots and river systems, which may directly affect the water quality [START_REF] Rozemeijer | Direct measurements of the tile drain and groundwater flow route contributions to surface water contamination: from field-scale concentration patterns in groundwater to catchment-scale surface water quality[END_REF]. Moreover, it was demonstrated that a direct connection between the soil surface and tile drainage systems may occur [START_REF] Akay | Experimental investigation of direct connectivity between macropores and subsurface drains during infiltration[END_REF][START_REF] Frey | Dual permeability modelling of tile drain management influences on hydrologic and nutrient transport characteristics in macroporous soil[END_REF], resulting in the limited retention and degradation of contaminants within the soil column [START_REF] Stone | Preferential flow estimates to an agricultural tile drain with implications for glyphosate transport[END_REF].

So far, most studies dealing with water and sediment transfers from tile drainage have been conducted at the plot scale (e.g. [START_REF] Turunen | Modelling water balance and effects of different subsurface drainage methods on water outflow components in a clayey agricultural field in boreal conditions[END_REF][START_REF] Muma | Assessment of the impact of subsurface agricultural drainage on soil water storage and flows of a small watershed[END_REF]. They demonstrated that suspended sediment concentrations in subsurface drain flows could exhibit large variations and represent a large proportion of sediment fluxes [START_REF] Deasy | Pathways of runoff and sediment transfer in small agricultural catchments[END_REF]. Experimental studies were designed to investigate this issue both in the field and in the laboratory (e.g. [START_REF] Turtola | Surface runoff, subsurface drainflow and soil erosion as affected by tillage in a clayey Finnish soil[END_REF][START_REF] Van Den Bogaert | Aggregation and dispersion behavior in the 0-2-µm fraction of Luvisols[END_REF]. For instance, [START_REF] Uusitalo | Particulate phosphorous and sediment in surface runoff and drainflow from clayey soils[END_REF] measured concentrations ranging from 540 to 1240 mg⋅l -1 . [START_REF] Chapman | Sediment delivery from agricultural lands to rivers via subsurface drainage[END_REF] measured concentrations up to 2600 mg⋅l -1 . Based on this extensive research, very detailed numerical models were developed to simulate water and sediment transfers in drained plots [START_REF] Warsta | Modelling soil erosion in a clayey, subsurface-drained agricultural field with a threedimensional FLUSH model[END_REF][START_REF] Turunen | Computational assessment of sediment balance and suspended sediment transport pathways in subsurface drained clayey soils[END_REF]. However, the role of preferential flows in the transfers of water, associated fertilizers and pesticides in drained systems remains unclear (Nagy et al., 2020a(Nagy et al., , 2020b)). Moreover, the upscaling of these results from the plot to the catchment scales remains unresolved to date [START_REF] De Vente | Predicting soil erosion and sediment yield at the basin scale: scale issues and semi-quantitative models[END_REF][START_REF] Evrard | Seasonal evolution of runoff generation on agricultural land in the Belgian loess belt and implications for muddy flood triggering[END_REF][START_REF] Delmas | Erosion and sediment budget across scale: a case study in a catchment of the European loess belt[END_REF][START_REF] Fiener | Filling the gap between plot and landscape scaleeight years of soil erosion monitoring in 14 adjacent watersheds under soil conservation at Scheyern, Southern Germany[END_REF]. There is a lack of quantitative assessments of the impacts of tile drainage on water and sediment fluxes at the catchment scale, despite the fact that previous studies outlined the need to monitor drained catchments in order to improve our understanding of these preferential transfer pathways [START_REF] Li | Water and nutrient balances in a large tiledrained agricultural catchment[END_REF][START_REF] Hansen | Importance of including small-scale tile drain discharge in the calibration of a coupled groundwater-surface water catchment model[END_REF][START_REF] King | Effects of subsurface drainage on streamflow in an agricultural headwater watershed[END_REF].

Previous studies investigating sediment transfers in tile drained catchments mainly relied on sediment fingerprinting approaches [START_REF] Russell | Suspended sediment sources in two small lowland agricultural catchments in the UK[END_REF][START_REF] Walling | Establishing sediment budgets for two small lowland agricultural catchments in the UK[END_REF][START_REF] Walling | The catchment sediment budget as a management tool[END_REF][START_REF] Foucher | Quantifying the dominant sources of sediment in a drained lowland agricultural catchment: the application of a thoriumbased particle size correction in sediment fingerprinting[END_REF][START_REF] Gall | Investigating the temporal dynamics of suspended sediment during flood events with 7 Be and 210 Pb xs measurements in a drained lowland catchment[END_REF]. This technique consists in the measurement of conservative properties in potential sources and in sediment collected in the main river to quantify the respective contributions of these potential sources to the material transiting the river [START_REF] Haddachi | Sediment fingerprinting in fluvial systems: a review of tracers, sediment sources and mixing models[END_REF][START_REF] Collins | Sediment source fingerprinting as an aid to catchment management: a review of the current state of knowledge and a methodological decision-tree for end-users[END_REF]. They demonstrated that contributions from tile drains may be very variable, even at the flood event scale. However, these studies often combined tile drains with other sediment sources (e.g. channel banks in [START_REF] Cooper | High-temporal resolution fluvial sediment source fingerprinting with uncertainty: a Bayesian approach[END_REF]or surface cropland in Foucher et al., 2015), underlining the complexity and the variety of processes involved in sediment transfers from tile drains.

In contrast, very few studies quantified water and sediment transfers from tile drains at the catchment scale based on high resolution (<15minutes time step) drain and river monitoring, although the importance of quantifying these fluxes at very detailed temporal resolutions was demonstrated in contrasted environmental contexts [START_REF] Meybeck | Global variability of daily total suspended solids and their fluxes in rivers[END_REF][START_REF] Navratil | Global uncertainty analysis of suspended sediment monitoring using turbidimeter in a small mountainous river catchment[END_REF][START_REF] De Girolamo | Temporal variability of suspended sediment transport and rating curves in a Mediterranean river basin: the Celone (SE Italy)[END_REF]. Although [START_REF] King | Effects of subsurface drainage on streamflow in an agricultural headwater watershed[END_REF] quantified water transfers from multiple tile drains with a high temporal resolution and evaluated their contribution to the entire catchment water budget, they did not measure suspended sediment fluxes. [START_REF] Cooper | High-temporal resolution fluvial sediment source fingerprinting with uncertainty: a Bayesian approach[END_REF] combined high temporal resolution rainfall and water monitoring with sediment fingerprinting to construct time series of tile drain contributions. They however restricted their analysis to eight rainfall events only and did not quantify sediment fluxes with a high frequency. [START_REF] Grangeon | Hydro-sedimentary dynamics of a drained agricultural catchment: a nested monitoring approach[END_REF] quantified water and sediment dynamics with a high temporal resolution at both the drained plot and the catchment scales, in an area where 41% of the surface is drained. They measured concentrations ranging from a few to 1600 mg⋅l -1 , and estimated fluxes from tile drains to represent 0-63% of the catchment fluxes, with a mean of 13%. They also hypothesized that sediment fluxes mainly consisted of the flush of material stored in channels, but did not analyze the potential sediment storage in tile drains. However, their analysis was restricted to data from a single tile drain, which may lead to representativity issues and prevent the extrapolation of their results to larger and/or contrasted catchments. The objective of the current study was therefore to analyze the tile drain functioning, based on a set of drained plots to increase the analysis representativity. In particular, the processes leading to the seasonal and flood event scale variations in water and suspended sediment dynamics will be analyzed. To this end, water and suspended sediment dynamics at the outlet of multiple tile drains were monitored with a high temporal resolution (10 minute time step) over two contrasted hydrological years.

Materials and methods

The Bonnée River catchment

The Bonnée catchment is a medium-sized (120 km 2 at the monitoring station) headwater catchment tributary of the Loire River (France), mainly covered with cropland and forest.

Forest dominates in catchment upper parts while lower parts are mainly covered with cropland (Fig. 1a). Wheat, maize, sugar beet, rapeseed and sunflower are the main crops cultivated in the region. The tile drained area is ranging from 30% to 50% of the utilized agricultural land in this part of France [START_REF] Tournebize | Gérer les eaux de drainage agricole: du génie hydraulique au génie écologique[END_REF][START_REF] Vincent | Principes techniques et chiffres du drainage agricole -De la tuyautique à l'hydro-diplomatie[END_REF]. Elevation ranges from 103 to 176 m. Catchment topography is mainly Fig. 2. a) Zoom on the localization of the monitoring stations. Note that the pipes originating from the eastern plots cross the Bonnée river. b) Fluxes from the tile drain network are collected in a sump, which is monitored with a water height probe. They are then pumped into a basin (lower panel) and then delivered to the main Bonnée river network. c) The water height in the sump was used to calculate discharge from the tile drain network. d) Pictures of the pumping outlet and basin. They were taken during high and low flows and illustrate the observed variations in turbidity from the tile drain network. composed of a sequence of three plateaus, separated by steeper gradient steps: slope first, fifth (median) and ninth deciles amount to 0.3%, 1.7% and 7.1%, respectively, calculated from a 5-m resolution DEM. Highest slopes are mainly found in upper parts, under forests. Soils are mainly sandy and clayey and are developed on alluvial deposits. The climate is temperate (Cfb) according to the Köppen-Geiger climate classification [START_REF] Peel | Updated world map of the Köppen-Geiger climate classification[END_REF][START_REF] Beck | Present and future Köppen-Geiger climate classification maps at 1-km resolution[END_REF] with mean monthly temperatures ranging from 3 • C to 18 • C. The mean annual rainfall amounts to 637 mm at the nearby Orléans station, according to the national weather service, based on 30-year records . Monthly means are ranging from 45 mm to 65 mm, with higher values recorded from October to December and in May, and lower values recorded during summer.

River channel redesigning and tile drain network

The river channel was channelized between 1960 and 1970. The goal was to reduce the water transfer time to the outlet to decrease soil saturation, increase the agricultural productivity and reduce the inundation risk [START_REF] Spaling | Conceptual model of cumulative environmental effects of agricultural land drainage[END_REF]. Consequently, the original (i.e. natural) river channel was disconnected (the natural water channel became higher than the redesigned one) and abandoned. To redirect the water flow into the original river channel and initiate the ecological restoration of the river to comply with the European Water Framework Directive, a small dam built between 1960 and 1970 was enhanced (up to 1.90 m) in 2013 (Fig. 1b).

It increased the water height in the upstream river section and resulted in water flowing both within the natural and the redesigned channels. However, it also increased the water height above some of the tile drains outlet, which made them inoperative. Therefore, a unique manmade, sewer-like network was installed to allow tile drain functioning, collecting water flowing from a set of 10 fields equipped with tile drains, covering a surface area of 34 ha (Fig. 2a). At the outlet of this network, water and sediment were collected in a sump (Fig. 2b). They were then pumped up into a wetland in order to trap sediment and contaminants before supplying 'clean' water to the river network. This sewer network therefore completely isolated tile drain fluxes from the river flow, providing a unique opportunity to monitor water and sediment fluxes from a set of tile drained cultivated fields during both baseflow and flood events.

Tile drain characteristics were variable across the set of fields monitored in the current research. They were all made of perforated PVC pipes. The pipe diameters ranged from 45 to 700 mm, and they were buried between 30 cm and 1.8 m below the soil surface.

Hydrological monitoring station

Two monitoring stations were installed to measure the water and sediment fluxes in both the Bonnée River and in the tile drain network. The river station was installed next to the tile drain network (Fig. 3) and was located 1 km upstream of the dam.

Each station was equipped with a water height (Nivelco Nivopress NKK) and a turbidity probe (Neotek Ponsel, 0-4000 NTU). An automatic sampler (Teledyne ISCO 3700) was used to collect river water and suspended sediment samples, mainly during flood events. An automatic pluviometer (Précis Mécanique 3029) was installed to monitor rainfall. Water height, turbidity and rainfall were monitored with a 10-minute resolution from September 2017 to July 2019. Because of several technical problems (e.g. probe failures), only the period from December 2017 to July 2019 was investigated in the current research.

Water discharge measurements in the main river

In the river, 11 streamflow measurements were performed during low and high flow periods in order to derive relationships to convert water height into discharge. However, a simple least square regression between water height and discharge did not allow fitting the relationship. High flows were underestimated, which was problematic because they transport most of the sediment fluxes [START_REF] Navratil | Global uncertainty analysis of suspended sediment monitoring using turbidimeter in a small mountainous river catchment[END_REF]. A nonlinear fitting procedure taking into account streamflow measurement uncertainties was therefore developed and resulted in a rating curve able to capture the highest discharges. The detailed procedure and the corresponding rating curve are provided as supplementary material.

When the highest storm event occurred (mid-February 2017 and during a large event in July 2018), the dam was opened by the local authorities to prevent flooding. In both cases, the water height time series was linearly interpolated when the dam was opened. The water height time series was not considered for analysis in February 2017. In July 2018, as the dam opening was performed during the falling limb of the hydrograph, the event was considered for analysis.

Water discharge measurements at the tile drain network outlet

Because of a low water height in the tile drain network and limited probe resolution (respectively in the order of 1-10 cm with 1 cm resolution), water height was measured in the sump, collecting fluxes from the entire tile drainage network. Due to fast water height variations, especially during flood events, it was monitored with a 15-second time step. The water volume time series in the sump, resulting from both tile drain network discharge and the sump pumping, was estimated from water height time series using the well-defined geometry of the sump (Fig. 2c). The volume calculated during the rising limb provided water input from the tile drain network, while the falling limb (resulting from pumping) were removed. Consequently, the discharge time series was calculated for rising limb periods and interpolated across pumping periods (Fig. 2). The resulting discharge time series was then interpolated at a 10-minute time step to match the recording time step of the other measurements.

Soil and sediment sampling and analysis

Suspended sediment sampling and analysis

Suspended sediment was sampled using the ISCO 3700 device based on water level thresholds and time intervals during flood events, both in the tile drain network and in the Bonnée river. This procedure was adapted based on the monitored water level before a forecasted flood event. In general, it consisted of one sampling per hour when the water level increased by more than 5 cm. The sampled water volume was fixed at 500 ml, although small (±10 ml) variations were measured. Therefore, the volume was systematically measured in the laboratory. River water was filtered with 0.45 µm-mesh filters and oven-dried at 105 • C for 24 h to obtain suspended sediment concentrations. These measurements were used to establish a suspended sediment concentrationturbidity rating curve. It was used to convert turbidity into suspended sediment concentration time series. The turbidity-concentration relationship was good for the Bonnée river and the tile drain network (R 2 = 0.93, n = 93 and R 2 = 0.88, n = 44, respectively). The sample concentrations were comprised between 8 and 3100 mg⋅l -1 for the Bonnée river. Due to technical issues (flood event flashiness and noise on the raw measured turbidity), sample concentrations for the tile drain network varied between 3 and 210 mg⋅l -1, . Consequently, the concentration was extrapolated for less than 6% of the monitoring period.

Soil surface observations

Finally, during the two-year monitoring period, a monthly visual inspection of the soil surface was performed on the drained plots to document the density of the soil cover by vegetation, crusting stage, surface roughness and the occurrence of soil cracks, as all these characteristics were shown to control the runoff and erosion behavior of cultivated plots [START_REF] Cerdan | Incorporating soil surface crusting processes in an expert-based runoff model: sealing and Transfer by Runoff and Erosion related to Agricultural Management[END_REF].

Flood event separation

Flood events were defined according to the methodology presented in [START_REF] Grangeon | Hydro-sedimentary dynamics of a drained agricultural catchment: a nested monitoring approach[END_REF]. Flood events were identified based on the ratio between quick flow and base flow (calculation based on the methodology proposed by [START_REF] Chapman | Comment on "Evaluation of automated techniques for base flow and recession analyses[END_REF]. The correspondence of flood events occurring both in the tile drain network and in the main river was verified. Then, single storm events were defined as events cumulating more than 1 mm precipitation. Flood events were then associated with rainfall events, and when multiple storm events were recorded during a single flood event, they were grouped into a single event. This procedure resulted in a dataset of 36 coupled storm-flood events occurring in both the river and the tile drain network between December 2017 and June 2019. The following analysis is based on these 36 flood events, although some supplementary individual events were recorded only in the Bonnée River or in the tile drain network.

Data analysis

For these 36 individual flood events, several characteristics were calculated including rainfall depth (mm), duration (h), mean and maximal intensity (mm⋅h -1 ), flood event volume (m 3 ), total, rising and falling limb durations (h), mean and maximal discharge (m 3 ⋅s -1 ), runoff coefficient (%), antecedent rainfall (rainfall depth cumulated over the previous 48 h, mm), mean and maximal concentration (mg⋅l -1 ), sediment load (kg). Specific peak discharge was calculated by dividing the peak discharge by the catchment or tile drain network area. Sediment loads were obtained through the integration of the product of the water discharge and the sediment concentration time series.

Results were considered separately for winter (December to February), spring (March to May), summer (June to August) and autumn (September to November). A correlation matrix using Pearson correlation coefficients was used to analyze the statistical relationships between these variables.

The statistical analysis will be used to investigate (i) the tile drainage network dynamics and (ii) the global catchment dynamics.

Results and discussion

Rainfall and river catchment dynamics

During the monitoring period, two contrasted hydrological years (defined as years starting on September 1st) were recorded (Fig. 4).

The 2017-2018 hydrological year concentrated most of the rainfall and flood events. Moreover, during the monitoring period, most of the storm events occurred in winter and in spring (Table 1). From 1st January to 31th March the total rainfall amounted 254 mm, corresponding to 162% of the long-term average over the same period (157 mm).

These floods contributed 60% and 83% of the annual water fluxes in the river and the tile drain network, and 62% and 92% of the sediment fluxes. The flashiness of the water and sediment fluxes was previously demonstrated for headwater catchments (e.g. [START_REF] Navratil | Global uncertainty analysis of suspended sediment monitoring using turbidimeter in a small mountainous river catchment[END_REF] and for tile drained areas [START_REF] King | Effects of subsurface drainage on streamflow in an agricultural headwater watershed[END_REF][START_REF] Grangeon | Hydro-sedimentary dynamics of a drained agricultural catchment: a nested monitoring approach[END_REF], underlining the importance of conducting a high resolution monitoring in these systems.

Of note, heavy rainfall was observed in July 2018 after a dry period: only 7 mm was recorded in the previous 3 weeks. More than 42 mm was then recorded in less than 6 h. At a 10-minute time step, the maximum rainfall intensity reached 37 mm⋅h -1 . This event generated a significant flood event, even leading to the flooding of a nearby village (located about 10 km away from the monitoring station), and corresponding to the highest peak discharges observed throughout the entire study period. This event suggested the occurrence of infiltration-excess overland flow in this lowland medium-sized catchment.

Furthermore, the river baseflow remained at a high level during 2017-2018, especially during winter (62% of the annual total water fluxes). This high contribution from baseflow underlines the high soil moisture levels observed during this period of long-lasting and continuous rainfall, also characterized by a low evapotranspiration. Accordingly, discharge from tile drains was high during this period. Moreover, eight flood events occurred during winter following low rainfall amounts (<10 mm), while flood events were never triggered by such a low rainfall amount during the other seasons. These observations, combined with the distribution of rainfall and the number of flood events recorded during seasons and over the monitoring period, indicated that this period was prone to saturation-excess runoff.

Although a quantitative study of the relative importance of infiltration-and saturation-excess could not be performed because of the lack of monitoring data across the entire catchment, this information, combined with the calculation of the water balance (calculation provided in the supplementary material), demonstrated that both infiltration-and saturation-excess processes were involved in flood generation in the study area. This interpretation is in line with the findings of [START_REF] Saffarpour | Multiple runoff processes and multiple thresholds control agricultural runoff generation[END_REF] and [START_REF] Grangeon | Hydro-sedimentary dynamics of a drained agricultural catchment: a nested monitoring approach[END_REF], although the current research suggested their combined occurrence at a much larger scale. The occurrence of soil saturation in a drained catchment had important implications on the hydrological regime and on flow occurrence in the tile network. It will also affect sediment connectivity across the catchment by allowing runoff, and therefore sediment transport, to occur more regularly and to take place on parts of the hillslopes that would not be prone to infiltration-excess runoff.

Tile drainage network water dynamics

A constant low flow (≈1 × 10 -3 m 3 ⋅s -1 ) was observed and measured over the entire monitoring period in the tile drainage network (Fig. 5a).

It reflected the constant inflow of water from a local spring. As the corresponding discharge was constant and low, with the absence of suspended sediment in the flow, it was considered negligible in this study. In 2017-2018, tile drainage water discharge exhibited much higher values, the 25th decile of the discharge time series was 75% The quick response of the tile drainage flow to rainfall suggests the occurrence of a direct connection between the soil surface and the rest of the soil column, increasing water and sediment vertical connectivity across the soil profile. On the contrary, late in spring and during summer, transfers from the tile drainage system were ephemeral, with successive periods of low and high flows, corresponding to highly variable transfers and connectivity levels across the soil column.

Although a link was found between the discharged volume from tile drains and the rainfall depth (Fig. 6), two relationships had to be derived for winter, on the one hand, and the remaining seasons, on the other hand.

R 2 amounted to 0.62 and 0.42, respectively, and both regressions were significant at the 5% level. This result reflects the seasonal behavior of tile drain systems in the study area, despite the relatively high connectivity maintained throughout the entire year between soils and the drain network. This seasonal behavior reflects variations in the soil surface properties (e.g. soil crusting may prevent water infiltration into the soil, although in this study, infiltration capacity could not be measured), the sparse soil cover by vegetation as observed through qualitative soil surface observations (Fig. 7) and the low temperatures. Indeed, all of these factors directly influence the soil moisture content.

During rainfall events, a quick response of discharge was observed in the tile drainage network throughout the monitoring period (Fig. 5b, the quick flow is highlighted by the gray shaded area). A peak in the discharge time series was regularly measured, and overlaid on the rising limb of floods occurring during the soil saturation period. When focusing on the 36 identified flood events, 13 of them were characterized by the occurrence of two clearly different peaks, as illustrated in Fig. 5b, in both time and magnitude: a rapid and high-magnitude peak occurring at the beginning of the event overlaying on the global, longer and lower flood signal. Overall, 46% of the flood events displaying this double peak occurred during spring and 38% occurred in summer. As they were mainly recorded during spring and summer, this quick flow component is assumed to be controlled by flow occurring in soil macropores and shrink-swell cracks, which is in line with the results of previous studies [START_REF] Kladivko | Pesticide and nutrient movement into subsurface tile drains on a silt loam soil in Indiana[END_REF][START_REF] Øygarden | Soil erosion via preferential flow to drainage systems in clay soil[END_REF]. This hypothesis was also confirmed by field observations made during the current research (Fig. 7).

It is also possible that these peaks did occur in winter, although they were diluted by the higher magnitude of the winter flood events. Quantifying precisely the contribution of these two peaks over multiple hydrological conditions would provide an interesting perspective for future research.

In addition to these coupled river-tile drain flood events, 12 other events displaying this quick discharge component were measured in the tile drains only. All these events were observed during spring and summer. Our results demonstrated that, in addition to transfers triggered by soil saturation, preferential flow occurring through soils cracks and macropores may occur in the soil column. Various flow conditions and connectivity levels in the tile drains were therefore observed throughout the year. This result may have an important impact on the transfer time of water, sediment and the associated contaminants. [START_REF] Stone | Preferential flow estimates to an agricultural tile drain with implications for glyphosate transport[END_REF] previously measured this type of behavior in the US (Indiana) at the outlet of a single tile drain from a unique field, during two flood events. They demonstrated the important implications of these preferential flows, accounting for 11% to 51% of the total flood flow, on glyphosate transfers. Our study demonstrates, using high frequency and long time series that these preferential flows occur frequently. Moreover, their occurrence was confirmed at larger scales (multiple drained fields and flood events) and in another environmental context, suggesting that it may be a generalized behavior of tile drainage. On average, at the flood event scale, preferential flow (occurring through macropores and cracks), calculated as the volume measured during the fast peak relative to the total flood volume, supplied 10-15% of the water fluxes to the total tile drainage network. It was estimated by isolating this peak on the hydrograph and calculating the relative water volume, compared to the total flood event volume. Therefore, the substances applied to the fields may be transferred with these preferential flows to the river channel with limited effects of soil retention and degradation.

Tile drainage suspended sediment dynamics and transfers to the river

The dynamics of suspended sediment concentrations from tile drains were very episodic and they displayed a contrasted behavior over the two monitored years (Fig. 5a). At the beginning of the monitoring period, when the baseflow remained at a high level, suspended sediment concentration displayed regular peaks, in response to rainfall events. This period of significant transport lasted for several months, until early March 2018. Then, the subsequent sediment concentration peaks occurred mainly when rainfall events were significant and after long periods without high flow periods in the tile drain network. During the 2017-2018 hydrological year, suspended sediment loads ranged from 6 × 10 -4 to 9 t⋅km -2 at the event scale for the tile drainage network (34 ha), while it was ranging from 1 × 10 -3 to 2 × 10 -1 t⋅km -2 during the 2018-2019 hydrological year. In addition to these fluxes, peak concentrations were also analyzed focusing on significant storm events, arbitrarily defined by suspended sediment concentrations higher than 250 mg⋅l -1 . Thirty events with such high concentrations were recorded during the 2017-2018 hydrological year while during the 2018-2019 hydrological year, with only 56% of the 2017-2018 cumulative rainfall, less than 20 of these high concentration events were recorded. However, relatively high peaks of suspended sediment concentrations were also observed during this 2018-2019 monitoring year. Over these two years, respectively 71% and 57% of the events displaying high suspended sediment concentration peaks were measured during winter, corresponding to periods of high flows. Moreover, during storm events, fast sediment transportcalculated during the fast peak of the rising limb in a similar way as it was performed for water in Section 3.2 -represented, on average, 15% of the sediment load. The concentrations measured in the tile drain network were in agreement with those found in other studies conducted at a tile drain outlet located in an agricultural catchment in a comparable environment in France [START_REF] Grangeon | Hydro-sedimentary dynamics of a drained agricultural catchment: a nested monitoring approach[END_REF]. The high concentrations, along with the significance of fast transport from tile drains, highlight the potential major impact of tile drainage on the catchment sediment dynamics. A statistical analysis was performed on suspended sediment fluxes from the tile drainage network and those from the river (correlation table provided in supplementary material). For the Bonnée River catchment, it revealed that, among the variables analyzed (describing rainfall and flood event characteristics, see Section 2.6), the specific peak discharge correlated reasonably well with the specific sediment load of the Bonnée River catchment (Fig. 8).

The determination coefficient was higher using a linear relationship (R 2 = 0.68), but a power law is presented in this study, based on a previous study analyzing this relationship over multiple catchments [START_REF] Duvert | Towards prediction of suspended sediment yield from peak discharge in small erodible mountainous catchments (0.45-22 km 2 ) of France, Mexico and Spain[END_REF]. However, for the tile drainage network, the relationship with the specific peak discharge was very variable in time, depending upon both the season and the monitored year. Indeed, no relationship was found during winter (r = 0.40) when the base flow was high, with the regular outflow of water from the drain pipes. It indicated that increase in peak flow, which should have resulted in increased transport capacity and therefore increased sediment fluxes, was limited by another factor that we hypothesized to be sediment storage between storm events, when water flow in drains was low. Accordingly, there was a clear progressive decrease in the specific suspended sediment load as winter progressed (R 2 = 0.78). It corresponded to a shift in the suspended sediment concentration dynamics (Fig. 5a) from high concentrations and regular sediment peaks to limited sediment concentrations and peaks. This result suggests that suspended sediments fluxes from the tile drain network were controlled by sediment storage and exhaustion in the tile drainage network, and its progressive evolution throughout the year.

The relationship between specific peak discharge and specific sediment load was good (R 2 = 0.68) for the tile drain network during spring, autumn and summer of the first monitored year (i.e. from March to December 2018). It corresponded to a decrease in the base flow, responding to a decreased water transfer and therefore a lower transport capacity through the soil column down to the pipes. We therefore hypothesized that sediment from tile drains was likely to accumulate, leaving stored sediment available for resuspension during the subsequent flood events.

During the second monitored year, alternating periods of relatively low or null base flow were observed, and associated suspended sediment loads remained very low: on average, over the two winter seasons, suspended sediment loads were 22 times lower in 2018-2019 compared to 2017-2018. This drop in sediment fluxes was also reflected by the low concentrations measured (Fig. 5), displaying only a fewalthough significantsuspended sediment concentration peaks. Most of these peaks occurred early in winter. Material accumulated during periods of ephemeral flow through the soil column allowed soil particles to be mobilized and transported to the drain network. This hypothesis may explain why, in the current research, a good relationship was not found between drain water flow and sediment load when considering the entire data set (R 2 = 0.5), which confirms results obtained by [START_REF] Chapman | Sediment delivery from agricultural lands to rivers via subsurface drainage[END_REF]. Interestingly, this relationship was higher when tested separately for winter and for the other seasons (Fig. 9).

A large scattering was observed in the relationship between specific sediment load and rainfall depth (R 2 = 0.16) over the winter period, reflecting all the processes that may control sediment load: particle detachment and transfer over the soil column, sediment accumulation and subsequent erosion and the associated sediment selectivity. During the other seasons, when baseflow was low and when significant sediment loads remained episodic, the relationship between the specific sediment load and rainfall depth increased (R 2 = 0.64), reflecting a higher degree of connectivity, associated with a direct transfer of sediments with flowing water.

Limitations and implications of this study

In similar lowland drained catchments with gentle slopes, tile drains are usually immersed during flood events. The studied catchment configuration provided an original framework to isolate and analyze water and sediment fluxes from multiple tile drains throughout the year and in contrasted hydrological conditions (baseflow and flood events). ) Specific peak discharge (m 3 .s -1 .km -2 ) Fig. 8. Relationship between specific sediment load and specific peak discharge for the Bonnée river. However, due to this particular configuration, it was not possible to investigate in detail the interactions between river/ditches and tile drain flows, which are likely to occur in similar catchments. This could be usefully addressed in future investigations. Moreover, the two studied years were either wet or dry. It offered contrasted conditions to study the tile drains dynamics, which should have provided data of the tile drain network functioning under "extreme" conditions. However, because only two monitoring years could be recorded, the effects of successive wet, mean or dry years could not be investigated. Therefore, monitoring tile-drained catchments over longer periods should provide valuable insights into tile drain dynamics, especially regarding the hypothesized processes of sediment storage and exhaustion. Medium to long-term water and sediment high-resolution monitoring is indeed extremely scarce in the literature [START_REF] Esteves | Medium term high frequency observation of discharges and suspended sediment in a Mediterranean mountainous catchment[END_REF] and, to the best of our knowledge, do not exist in the case of tile drain.

The current study however used an original experimental set-up to measure water and sediment flow originating from tile drains, using high frequency monitoring. Such data sets, extremely scarce in the literature, provided insights into the hydrographs and sedigraphs generated from multiple drained plots under contrasted monitoring conditions including both a wet and a dry year. Based on this unique monitoring, a conceptual diagram of tile drain functioning is proposed (Fig. 10).

Conclusions

Water and suspended sediment dynamics were characterized during two hydrological years in a drained agricultural lowland catchment. A specific drainage collection network allowed the detailed quantification of water and sediment fluxes originating from a 34-ha surface area of drained fields. The results showed the very dynamic behavior of the tile drainage system. At the event scale, suspended sediment loads from the tile drains were significant, ranging from 6 × 10 -4 t⋅km -2 to 9 t⋅km -2 . The occurrence of double transfer pathways in the tile drains, previously demonstrated in the literature although for individual plots, was confirmed in this study for multiple plots, suggesting that this process may be widely significant in tile-drained environments. Water and sediment fluxes occurring during the fast stages of tile drain flood events were calculated to be in the order of 15% of the total flood event fluxes. The data suggests that the succession of deposition and resuspension stages of sediment stored in the drainage network play a significant role on sediment dynamics in the tile drain system.

Although these results may reflect the behavior of an individual catchment, the original experimental set up allowed insights into the hydrographs and sedigraphs of multiple drained plots. In the future, the factors controlling the sediment storage originating from the cultivated topsoil layer to the tile drains during ephemeral flow conditions should be further quantified, for instance through the measurement of shortlived fallout radionuclides characterized by contrasting half-lives (e.g. 7 Be, 210 Pb xs ) or alternative low-cost measurements (e.g. color, magnetic susceptibility). Furthermore, the impacts of these transfers and their dynamics on sediment and contaminant exports from agricultural drained catchments should be further quantified in these lowland environments.

Fig. 1 .

 1 Fig. 1. a) Location of the Bonnée River catchment with its confluence with the Loire River. The situation of hydrological monitoring stations and soil sampling locations is indicated with the black and red dots, respectively. Land use data were extracted from Corine Land Cover (2018). b) Longitudinal view of the main river bed. Both the original and modified river channels are indicated. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 3 .

 3 Fig. 3. Hydro-sedimentary monitoring stations in the tile drain network and the Bonnée River. The distance between the two stations is approximately 4 m.

Fig. 4 .

 4 Fig. 4. Rainfall (black line) and water discharge (blue line) recorded at the Bonnée River monitoring station between 2017 and 2019. The green dots correspond to the suspended sediment samples collected using the ISCO sampler. The gray area corresponds to a period of dam opening; data for this period were not considered. Hydrological years are indicated with arrows in the upper part of the figure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 5 .Fig. 6 .

 56 Fig. 5. a) Rainfall and discharge time series measured at the outlet of the tile drainage network. b) A zoom on the situation observed during a flood event that started on 21st May 2018 illustrates the behavior of discharge during an individual flood event with the successive occurrence of fast, as illustrated by the gray shaded area, and slow discharge stages.

Fig. 7 .

 7 Fig. 7. Progressive development of soil cracks on one of the studied drained plots. Cracks progressively developed from the end of winter to become fully developed in summer.

Fig. 9 .

 9 Fig.9. Relationship between specific sediment load and rainfall depth, for winter (blue) and the other seasons (green) for the tile drain network. (For interpretation of the references to color in this figure legend, the reader is referred to the web this article.)

Fig. 10 .

 10 Fig. 10. Conceptual diagram of sediment transfers through tile drains.

Table 1

 1 Main hydrological characteristics of the monitored period. The flood event percentage is relative to the entire monitoring period (2017-2019).

	Hydrological	Recorded rainfall (mm) -	Flood events recorded over	Winter flood events during	Spring flood events during	Autumn and summer flood
	year	Percentage of the long	the monitoring period	the hydrological year	the hydrological year	events during the hydrological
		term average (%)	(number-percentage)	(number-percentage)	(number-percentage)	year (number-percentage)
	2017-2018	716 mm -112%	23-64%		14-61%	7-30%	2-9%
	2018-2019	408 mm -64%		13-36%		6-46%	3-23%	4-31%
							)
		Discharge m 3 .s -1 )	0.01 0.02 0.03 0.04 0				0 8000 6000 4000 2000	Suspended sediment concentr on (mg.l -1	0 3 6 9 12 15	Rainfall depth (mm)
		01/12/2017 23/03/2018 13/07/2018 02/11/2018 22/02/2019 14/06/2019
			0.008				0
		Discharge m 3 .s -1	0.006 0.004 0.002				2 4 6	Rainfall depth (mm)
			0				8
			21/05/2018	22/05/2018	23/05/2018	24/05/2018

Acknowledgments

The reviewers provided very detailed comments that greatly contributed to improve the manuscript. This work received financial support from the Loire-Brittany Water Agency in the framework of the Describe research project, under the supervision of Xavier Bourrain, Jean-Noël Gauthier and Anne Colmar. Anthony Foucher is warmly acknowledged for providing the artwork used in Fig. 10.

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.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi. org/10.1016/j.catena.2020.105033.