S Michau
email: michau@lspm.cnrs.fr

S Prasanna

K Longo

Hassouni

A Michau

P Swaminathan

S Longo

K Hassouni

Particle charge fluctuation and its consequences on aerosol dynamics in dusty plasmas: from continuous to discrete statistical models

Keywords: dusty plasma, particle charging, nanoparticle

published or not. The documents may come

Particle charge fluctuation and its consequences on aerosol dynamics in dusty plasmas: from continuous to discrete statistical models

A.

Introduction

Formation of solid particles may take place in non equilibrium plasmas under a variety of discharge conditions [START_REF] Boufendi | Dusty plasma for nanotechnology[END_REF]2,[START_REF] Hassouni | Formation of soot particles in Ar/H2/CH4 microwave discharges during nanocrystalline diamond deposition: A modeling approach[END_REF]. In some cases these (nano)particles are produced on purpose for their functionnal properties [START_REF] Mariotti | Low-Temperature Atmospheric Pressure Plasma Processes for "Green" Third Generation Photovoltaics[END_REF]. In other cases they are form accidentally produced and may be be detrimental for the targetted plasma process [START_REF] Boufendi | Dusty plasma for nanotechnology[END_REF]. In both situations, whether one need to optimize or avoid the production of particles, it is necessary to understand the plasmas and aerosol dynamics processes involved in particle production [START_REF] Michau | On the Competition Between the Phenomena Involved in the Aerosol Dynamics in Sputtering Nonequilibrium Plasma[END_REF]. In particular, particle coagulation seems to be a key process that governs the particle density and structures, and shapes the particle size-distribution [START_REF] Arnas | Experimental study of different carbon dust growth mechanisms[END_REF]. It was early recognized that particle coagulation in discharge plasma can only take place if charge fluctuation enables the production of large enough amount of neutral or positively charged particles [START_REF] Matsoukas | Particle charging in low-pressure plasmas[END_REF]. Surprisingly, the incorporation of this effect as a driver of the coagulation kinetics in dusty plasmas models were performed only quite recently by very few groups [START_REF] Gelbard | Sectional representations for simulating aerosol dynamics[END_REF][START_REF] Michau | Aerosol dynamics in a sputtering DC discharge[END_REF]. Most of the approaches used in dusty plasma modeling are based on a continuous statistical description of the charge fluctuation. This which assumes that, the charging beeing an ergodic Poisson process, the charge distribution is Gaussian [START_REF] Matsoukas | Particle charging in low-pressure plasmas[END_REF]. This approach works fine as long as the mean charge value is much larger than the charge fluctuation magnitude, which is typically the case for large particles and large electron temperature discharge conditions [START_REF] Boufendi | Dusty plasma for nanotechnology[END_REF]. It becomes questionable for small particles and/or low electron temperature conditions when the mean charge value is of the same order as the fluctuation magnitude. Analyzing the accuracy of this continuous statistical model and proposing other, hopfully more accurate, approaches to estimate the charge distribution for small particles is of prime importance as far as coagulation kinetics is concerned. Indeed, small particles are the only one that can show a large fraction of neutral or positively charged particles. Their charge distribution therefore governs the coagulation kinetics. The first objective of this paper is related to this last point. More specifically, we compare the charge distributions inferred from a continuous and discrete statistical models for particle of different sizes. We investigate how expliciteley taking into account the discrete nature of the Poisson charging process in a dusty plasma model affect the predicted particle size distributions. We also analyse how the charging processes is affected by the ion current enhancement due to ion-neutral elastic collisions in the torr regime.

In all these studies we describe the aerosol dynamics using a sectional model that enables predicting the size distribution without any assumption and with a good accuracy. This approach has the drawback to present a relativeley important complexity. In particular, it can be hardly used in multidimensional dusty plasma models. Therefore, based on the results obtained using the sectional approach, we proposeinvstigate, in the second part of the paper, an alternative models that makes use of a modal approach in order to determine the typical bimodal size-distributions obtained in the investigated dusty plasmas.

The paper is organized as follows: section 2 gives a brief description of typical discharges considered in this work, section 3 presents the different charging models as well as a sensitivity study of the predicted charge and particle disctributions to these models, section 4 presents the simplified modal approaches used to describe the aerosol dynamics and determine the bimodal size distributions that are typically obtained in the investigated plasma, section 5 gives a brief summary of the results and discusses some research perspectives that may be drawn from this work.

Brief description of the studied Plasma Discharges and of the dusty plasma model used for their investigation

Studied plasmas discharges

In this study, we consider a sputtering argon DC discharge with a graphite catode. This that discharge has been extensively used to produce carbon nanoparticles [START_REF] Arnas | Experimental study of different carbon dust growth mechanisms[END_REF]. The inter-electrode distance is 14 cm, the pressure is 60 Pa and the discharge current is set to 80 mA. The graphite cathode is sputtered by fast ions and neutrals, which produces carbon atoms and small amounts of C2 and C3 clusters. These clusters undergo molecular aggregation, attachment and charge transfer processes which results in the nucleation of solid particles. These nanoparticles grow up to ~40 nm diameter by molecular deposition of clusters on their surface and coagulation [START_REF] Arnas | Experimental study of different carbon dust growth mechanisms[END_REF].

Numerical Modelling

A dDusty plasma model [START_REF] Michau | On the Competition Between the Phenomena Involved in the Aerosol Dynamics in Sputtering Nonequilibrium Plasma[END_REF] was previously developped to describe this discharge. It consists of three modules describing (i) the DC discharge dynamic equilibrium, (ii) the molecular growth of clusters and (iii) the aerosol dynamics. The last module used the so-called sectional model that accounts for a large number of size bins (or 'sections') over 1-100 nm size domain along with a charge distribution for each size bin [START_REF] Gelbard | Sectional representations for simulating aerosol dynamics[END_REF] [START_REF] Agarwal | Sectional modeling of nanoparticle size and charge distributions in dusty plasmas[END_REF]. The advantage of this kind of model is to accuratly take into account the influence of the particle size on the non-linear aerosol dynamic processes. The counterpart of this precision accuracy is the numerical expense which makes it difficult to extend this approach to very large, 2D or 3D simulations.

The developped one-dimensionnal dusty plasma model have shown good agreement with experimental results, especially in the description of the particle size distribution [START_REF] Michau | Nanoparticle formation and dusty plasma effects in DC sputtering discharge with graphite cathode[END_REF]. In particular we showed that particle formation and growth is only possible in the elctric field reversal region where negative species are trapped. We also showed that the particle nucleation takes place during the whole discharge duration so that the particle size distribution is controlled by the combination of three processes : nucleation, surface sticking and coagulation. Typical distributions show high particle densities for the small size domain, just above the nucleus size, and the large size domain that determine the mean diameter. Intermediate size particles are highly depleted which were attributed to coagulation. In other words, coagulation is responsible for the creation of two modes in the particle size distribution : a nucleation mode and a core distribution mode. All the aerosol dynamics phenomena, i.e., transport, nucleation, coagulation, surface-sticking of clusters, are controlled by the particle charge and more precisely charge fluctuation. We described the charge fluctuation dynamic by assuming that the charging process is ergodic in nature and by using a charge distribution as suggested by Matsoukas [START_REF] Matsoukas | Particle charging in low-pressure plasmas[END_REF].

In the previous version of the model, following Matsoukas et al [START_REF] Matsoukas | Particle charging in low-pressure plasmas[END_REF], we made use of a continuous statistical approach and assumed that the Poisson charging process results in a gaussian charge distribution. The standard deviation of this distribution depends on the plasma parameter and particle size. It determines the charge fluctuation and the fraction of neutral and even positively charged particles that can play a key-role in the growth mechanism, especially through coagulation with the negatively charged particles of the core distribution [START_REF] Michau | Aerosol dynamics in a sputtering DC discharge[END_REF].

Particle Charging Model: sensitivity studies

In Matsoukas et al approach [START_REF] Matsoukas | Particle charging in low-pressure plasmas[END_REF] the mean charge of a given particle is obtained assuming OML equilibrium ( j e , q = j i , q ) and the charge distribution obtained on the basis of continuous statistics is however valid for large particles that carry a significant number of elementary charges, in which case the charge fluctuation magnitude is small compared to the mean-value of the particle charge. This becomes questionable in the case of small particles or/and moderate electron temperature plasmas when, the charge fluctuation magnitude is comparable to the mean value of the charge carried by the particles. In this case, the charge fluctuation phenomenon cannot be described using a continuous charge distribution and the discrete nature of the charging processes has to be explicitly taken into account.

For this purpose, we first developed a discrete OML model for particle charging [START_REF] Prasanna | Effect of charge fluctuation on nanoparticle heating in dusty plasma[END_REF]. In this model, the charge distribution is discretised using a set of integer charge states that expand over a large enough charge-domain. The discrete Poisson charging processes is solved for each charge state in terms of the normalized charge population, q, at charge q. The dynamic of q depends on the electron, je,q,, and ion ji,q, currents collected by the particles of a surface Sp following the expression:

j (|e , q+ j i , q ) φ q 1 S p d φ q dt = j e ,q +1 φ q +1 + j i ,q -1 φ q -1 - Eq 1
Usually for the particle size considered in this work, i.e., 10-100 nm, the electron and ion currents are inferred from the OML theory assuming a collisionless sheath. Recent A recent work by Chahl and Gopalakrishnan [START_REF] Chahl | High potential, near free molecular regime Coulombic collisions in aerosols and dusty plasmas[END_REF] shows however that ion-neutral elastic collisions may be significant enough to increase the ion capture section and to enhance the ion collection current even at fairly low pressure. We therefore also considered this collision-induced ion current enhancement and analysed its impact on the charging kinetics and charge fluctuation.

Figures 1 shows the charge distribution calculated for 1nm (a) and 10nm particle (b) using using the continuous charging model assuming OML theory [START_REF] Matsoukas | Particle charging in low-pressure plasmas[END_REF], the discrete charging statistical model (Eq 1) either assuming collisionless charging model (denoted discrete) or taking into account the collision-induced enhancement of ion collection current (denoted CG). It appears that the three charging models are in good agreement for large particles (10 nm diameter) even-though the charging level, with a mean value of 2, is fairly low. The situation is different in the case of small particles, i.e. 1 nm diameter for which the three charging models give significantly different results. In particular, the mean charge-value, below one elementary charge, is smaller than the charge fluctuation amplitude.

The detailed charge distribution, especially the fraction of neutral and positively charged particles, plays a key-role in the growth process of the particle since collisions with negative species, i.e., coagulation with the dominant large negative particle or surface deposition of negative cluster, are only effective for non-negatively charged small particles. Figure 2 depicts the fraction of non-negative particles as a function of the particle diameter computed with the different charging models. It appears that continuous and discrete collisionless charging models yield similar values for the fraction of non-negative particles with size below 5 nm. However, the continuous model significantly underestimates the population of non-negative particles with diameter values above 5 nm. In particular, the discrete model yields a nonnegative particle fraction above 1% up to 10 nm size particles. On the opposite, the continuous model predicts a very sharp depletion, i.e. more than two orders of magnitude, of the non-negative particle fraction in the size range between 5 and 7 nm. On the other hand, the discrete collisional charging model predicts larger amount of neutral particles as compared to the collisionless model for sizes below 5 nm. The fraction of non-negative particle with sizes greater than 5 nm predicted by this model is however significantly smaller than that determined assuming collisionless discrete charging model, i.e., almost one order of magnitude for a 10 nm diameter.

We implemented these different charging models in the aerosol module of the 1D dusty plasmsa model discussed in reference [START_REF] Michau | Aerosol dynamics in a sputtering DC discharge[END_REF] and [2] and [START_REF] Michau | Aerosol dynamics in a sputtering DC discharge[END_REF]. Since our aims is mainly to analyse the sensitivity of aerosol dynamics to the adopted charging model, the simulation performed and discussed in this article are not fully self consistent. The discharge conditions and cluster dynamics are taken from previous simulation [START_REF] Michau | Aerosol dynamics in a sputtering DC discharge[END_REF] and only the aerosol module is solved in order to emphasize the effect of the charging model on particle growth. The three models show similar trends. Nucleation starts around 50 s after the discharge ignition. It causes a steep increase of the particle density until ~150 s time-period. Then, the density remains almost constant, while the mean diameter keeps increasing monotonically at a rate of approximately ~10 nm/min during the whole discharge phase.

Both the collisionless and collisional discrete charging models yield an increased mean diameter and a reduced total density as compared to the continuous OML charging model. This result is a consequence of the larger coagulation rate induced by the enhanced fraction of neutral particles that is obtained when discrete charging model is used.

Figure 4 presents the obtained particle size distributions for the considered charging models for plasma durations of 100s and 300s. The three models show similar time evolution of the size distribution : these are monomodal distributions for time duration below 150 s and becomes bimodal above. The bimodal distributions is are composed of a first very narrow mode in the size range close to the diamater of the smallest nucleus, i.e. 1 nm, and a much wider second mode with a log-normal distribution shape. Continuous and discrete OML yield similar estimates for the particle density of the nucleation mode. This is not the case for the core distribution mode, the population of which, is overestimated by the continuous charging model. This difference is due to the larger fraction of the non-negative particles and the subsequent enhanced coagulation kinetics predicted by the discrete model. On the other hand, the density values predicted using the collisional discrete (CG) model for both the nucleation and the large size modes are smaller than those obtained with the other charging models. This model therefore yields an enhanced coagulation kinetics and larger values of the mean diameter as compared to the other models. This result is explained by the largest value predicted for the fraction of neutral small particles contained in the nucleation mode by the collisional discrete (CG) model.

Simplified approach for aerosol dynamics modelling

The simulations discussed in the previous sections are based on a discrete sectional representation of the particle size distribution. This method has two advantages: it does not require any assumption on the shape of the particle size distribution and it shows a very good accuracy. This method It requires however a high size resolution to minimize the numerical diffusion that can alter the accuracy of the numerical approximation of the molecular deposition flux term in the aerosol dynamic equation [START_REF] Seigneur | Simulation of Aerosol Dynamics: A Comparative Review of Mathematical Models[END_REF]. The numerical cost associated with this high accuracy makes this approach barely feasible for large dusty plasma simulations, and one has to look for simplified approaches. Since, the particle size distribution obtained in the investigated plasmas always show one or two log-normal modes [START_REF] Mariotti | Low-Temperature Atmospheric Pressure Plasma Processes for "Green" Third Generation Photovoltaics[END_REF], it is possible to adapt a parametrized model based on log-normal mode size distributions originally developped for air armospheric aerosol systems to simplify the description of the aerosol dynamics in our plasmas [START_REF] Arnas | Experimental study of different carbon dust growth mechanisms[END_REF]. In this approach, the size distribution of each mode is approximated by an analytical log-normal distribution which can be completely fully described by three parameters, namely the particle density in the mode (Ni), the average particle diameter (dpi) and the standard deviation (i) for each mode. The three distribution parameters can be determined by solving a combination of three moments, M0, M3, and M6, of the General Dynamics Equation. A charging dynamics equation (Eq 1) has to be solved for each mode. For each mode, the dynamic equation takes into account particle transport, particle nucleation, particle growth by deposition of molecular species and coagulation processes either between two particles belongings to the same mode, i.e. intra-modal coagulation, or between particle belongings to different modes, i.e. inter-modal coagulation [START_REF] Whitby | Modal Aerosol Dynamics Modeling[END_REF]. However, in this so-called Whitby's model, the modes that characterize the distribution have to be prescribed a priori. The major consequence of this, is that the appearance of a distribution mode during the growth process cannot be accounted for. Since in our case the larger mode appears only 150 s after the discharge ignition, we extended Whitby's model to account for the creation of new particle in the larger mode from intra-modal coagulation. To treat this issue, Megaridis and Dobbins [START_REF] Michau | On the Competition Between the Phenomena Involved in the Aerosol Dynamics in Sputtering Nonequilibrium Plasma[END_REF] proposed a modeling approach for bimodal distribution where coagulation processes occuring in the small size mode yield a full particle transfer to the larger size mode, i.e., the core distribution mode. We also therefore adapted this approach to our situation by assuming that coagulation between particles belonging to the nucleation mode results in a particle in the large-size mode, i.e., the core distribution mode. Figure 5 shows the particle size distributions obtained in the same conditions as discussed above and for 300 s discharge duration using either the sectional model, the modal model without transfer, i.e., Whitby's model [START_REF] Whitby | Modal Aerosol Dynamics Modeling[END_REF], and a the modal model with full transfer by coagulation from the nucleation mode to the core distribution mode, i.e., Megaridis model [START_REF] Megaridis | A Bimodal Integral Solution of the Dynamic Equation for an Aerosol Undergoing Simultaneous Particle Inception and Coagulation[END_REF]. The results clearly show that bimodal distribution cannot be obtained when no transfer is considered between the two distribution modes. Whistby's model is in particular not able to predict the presence of the nucleation mode, which leads to the underestimation of the coagulation kinetics. We also notice that the particle size distribution predicted by Withby's model shows slightly higher density and lower mean diameter as compared with the distribution obtained from the sectional model. Figure 5 also shows that Megaridis model is capable of capturing the bimodal shape of the distribution. However, the nucleation mode predicted by this model shows much larger density over a larger size domain as compared with the one determinedde by the sectional model. This results is consistent with the much smaller density value obtained for the core distribution mode when using Megaridis model. This result It is at least partly due to a significant underestimation of the rate of inter-mode particle transfer through the growth by cluster deposition on particle surface. The evaluation of this transfer rate in Megaridi's is not straitforward since it requires defining relevent size criteria that may be used to evaluate intermode trasnfer transfer kinetics through cluster deposition on particle surface. As a final alternative, we also analyzed a simplified bimodal approach proposed by Jeong et al [START_REF] Gelbard | Sectional representations for simulating aerosol dynamics[END_REF]. In this case, the nucleation mode is approximated by a single size distribution with a diameter-value that corresponds to the size of smallest solid nucleus, while no approximation is used for the larger mode. Therefore, all the growing particle of the nucleation mode are transfered to the larger mode. This model is therefore able to take into account the key-role of the nucleation mode in the coagulation process with a much simpler mathematical formulation as compared to Whitby's and Megaridi's models. Further, since neutral and positively charged particles produced by charge fluctuation essentially belong to the nucleation mode, the particles belonging to the large size mode being always negatively charged, the coagulation process can be accurately described by taking into account the charge fluctuation for the only nucleation mode. Figure 6 shows the particle size distributions obtained at 300 s with the sectional model and the bimodal model proposed by Jeon et al. [START_REF] Jeong | A bimodal moment model for the simulation of particle growth[END_REF]. It appears that the simplified approach, yields a good estimates for both the density of the nucleation mode and the size distribution of the large size mode. The only difference resides in the fact that the large size distribution mode obtained by the sectional model is larger than the one inferred from the simplified modal approach. This is probably due to the fairly different treatment of particle growth kinetics by surface-deposition of clusters. This effect is indeed considered for each bin in the sectional model which therefore accounts for the enhancement of this growth route for the larger sizes, i.e., the growth rate is a linear function of the surface. This effect also explains the asymmetric shape of the large size distribution obtained from the sectionnal model, i.e., the core distribution is more populated above the mean dimater than below. The large size distribution obtained using the bimodal approach of Jeon et al. exhibits a less asymmetric shape. Note however, that the shape asymmetry observed when the sectional approach is at least also partly due to the numerical diffusion that appears in the numerical approximation of the aerosol dynamic equations when stable non-symmetric upwinding is used to evaluate the convective growth flux due to surface-deposition of clusters. We believe therefore that the 'actual' large size distribution would be somewhat between the distributions destermined by the sectional model and by the modal approach of Jeon et al. In any case, the particle density-values and the partice mean-diameters obtained by the two approaches are in good agreement. This may be clearly seen Figure 7 that shows the time-evolution of the number density of for both nucleation and large size modes obtained from Jeong's model along with the total particle density obtained from the sectional model. The particle density of the core distribution obtained from Jeong's and sectional models are in good agreement. They show very similar time-evolutions. The time-evolution of the nucleation mode density cleary reveals the different regimes that take place during particle gowth. Between 50 s and 100 s we see a similar density-values for both modes, which is indicative of unimodal distribution. For time periods greater than 100 s, there is a decrease of the density of the particles belonging to the nucleation mode that are consummed in the coagulation with larger particles. This is consistent with the bimodal nature of the distribution shown in Figure 6. Notwithstanding its limitations, Jeong's modal model appears to be the best alternative to the sectional model. It yields the distribution parameters with fairly good accuracy, requires a low computational cost and makes use of relatively simple mathematical expressions for the closure terms of moments and charge fluctuation.

Conclusion

The modeling study performed in this work clearly shows that it is necessary to explicitly taking take into account the discrete nature of the charge fluctuation along with the collisional ion current enhancement of ion current as far as charge fluctuation evaluation is concerned. The fraction of neutral and positiveely charged particles are is significanty enhanced by theses effects. This in turn leads to a significant enhancement of the coagulation kinetics, which results to a threefold decrease of the particle density. We also showed that a simplified method originally developped for modeling atmospheric aerosol dynamic may be well adapted to describe the bimodal particle size-distributions that are typically obtained in non equilibrium plasmas.

By validating fairly straightfirward straightforward and useful approaches that enables accurately describing the charge fluctuation for the small particles and predicting the bimodal nature of the particle size distribution, the present work open up interesting perspectives as far as multidimensional fully self consistent dusty plasma model development is concerned.

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Figure 1 :

 1 Figure 1 : Calculated Normalized charge distributions for 1 nm-size (a) and 10 nm-size (b) particles using the continuous statistical model proposed by Matsoukas [10] (continuous), the discrete statistical collision-less model (discrete) and the discrete statistical collisional model (CG). The discharge conditions are those of reference [5]. The cold electron density and temperature used in the simulation corresponds to the value obtained at the field reversal, i.e., ne=10 11 cm -3 and Te=0.1 [14].

Figure 2 :

 2 Figure 2 : Calculated non-negative fractions of dust particle as function of their size using the continuous statistical model proposed by Matsoukas [10] (continuous), the discrete statistical collision-less model (discrete) and the discrete statistical collisional model (CG). The discharge conditions are those of reference [5]. The cold electron density and temperature used in the simulation corresponds to the value obtained at the field reversal, i.e., ne=10 11 cm -3 and Te=0.1 [14]Figrure 3 depicts the time-evolutions of the total density and mean-diameter of the particles at the maximum density position (the field reversal position 2).

Figure 3 :

 3 Figure 3: Time evolutions of the total density and mean diameter of the produced dust particles calculated using the continuous statistical model proposed by Matsoukas [10] (continuous), the discrete statistical collision-less model (discrete) and the discrete statistical collisional model (CG). The discharge conditions are those of reference [5]. The cold electron density anddensity and temperature used in the simulation corresponds to the value obtained at the field reversal, i.e., ne=10 11 cm -3 and Te=0.1 [14]

Figure 4 :

 4 Figure 4 : Particle size distributions obtained from the dusty plasma model, at the maximum electron density position for discharge durations of 100 s (a) and 300 s (b), using the continuous statistical model proposed by Matsoukas [10] (continuous), the discrete statistical collision-less model (discrete) and the discrete statistical collisional model (CG). The simulated discharge conditions are those of reference [14].

Figure 5 :

 5 Figure 5 : Particle size distributions obtained from the dusty plasma model, at the maximum electron density position and for discharge durations of at 300 s, using the sectional model, Whitby's bimodal approach and Magaridis's bimodal model. The simulated discharge conditions are those of reference [14].

Figure 6 :

 6 Figure 6 : Particle size distributions obtained from the dusty plasma model, at the maximum electron density position and for discharge durations of at 300 s, using the sectional model and Jeong's bimodal model. The simulated discharge conditions are those of reference [14].

Figure 7 :

 7 Figure 7 : Time-evolution of particle densities (a) and mean diameter (b) obtained from the dusty plasma model, at the maximum electron density position, using the sectional model and Jeong's bimodal model. The densities of both the nucleation and core distribution modes are given in the case of Jeong's model. The simulated discharge conditions are those of reference [14].

Acknowledgements

.


C F Barros

B Muzeau

Raoul François

V L'hostis

V L'

Hostis Corrosion

Corrosion behavior of Mg-Zr alloy in alkaline solutions and in Na-geopolymer

Keywords: magnesium, UNGG, geopolymer, galvanic corrosion, pH

Introduction

The reprocessing of spent fuels from UNGG (Uranium Natural Graphite Gas) nuclear reactors in France generated cladding wastes mainly composed of Mg alloys. The management of these wastes involves their immobilization in a hydraulic binder with high pH interstitial solution (pH =12.5). As a result, the use of geopolymers as binders is being studied at the CEA for conditioning this metallic waste [START_REF] Lambertin | Mg-Zr alloy behavior in basic solutions and immobilization in Portland cement and Na-geopolymer with sodium fluoride inhibitor[END_REF].

The choice of the immobilization matrix is not straightforward due to the characteristic reactivity of these alloys, which is caused by several aspects [START_REF] Guo | A Review of Magnesium/Magnesium Alloys Corrosion and its Protection[END_REF]. First, magnesium corrosion is strongly influenced by the pH, and thermodynamics predicts a passivation of Mg alloys with pH higher than 10.50 due to the formation of a superficial protective film of Mg(OH) 2 [8]. However, understanding the kinetics of formation for this passivating layer is important to the comprehension of the corrosion mechanisms of Mg in alkaline media. In addition, the electrochemical potential of Mg places this metal as an anode with respect to several materials [START_REF] Pourbaix | Atlas of electrochemical equilibria in aqueous solutions[END_REF] (e.g. residual graphite materials initially present in the fuel assemblies or steel from the container), which can create galvanic couplings and accelerate corrosion. Furthermore, magnesium corrosion results in hydrogen production [START_REF] Song | Corrosion Mechanisms of Magnesium Alloys[END_REF], which must be understood to better manage the immobilization of the magnesium waste in a geopolymer matrix. The geopolymer used in this study was obtained by activation of an alumino-silicate source by sodium hydroxide solution in the presence of sodium fluoride (NaGeo/NaF). Fluoride is used here as a corrosion inhibitor for the Mg-Zr alloy [START_REF] Lambertin | Mg-Zr alloy behavior in basic solutions and immobilization in Portland cement and Na-geopolymer with sodium fluoride inhibitor[END_REF] [START_REF] Gulbrandsen | The passive behavior of Mg in alkaline fluoride solutions. Electrochemical and electron microscopical investigations[END_REF].

The aim of this work is to provide, through electrochemistry and gravimetric measurements, information about the corrosion processes that will occur once the alloy is in contact with its immobilization matrix, either in the case of general corrosion or in a galvanic coupling situation.

Experimental approach

This work is divided in two main axes. The first one focuses on the study of the general and galvanic corrosions of Mg in alkaline solutions by electrochemical methods (OCP, ZRA and polarization curves), covering the study of the effect of the pH, ions and conductivity. The second axis studies the corrosion of Mg in the geopolymer by gravimetric measurements.

Corrosion of Mg-Zr in alkaline solutions

The reference electrolyte chosen for this study is an interstitial solution of the geopolymer used for the immobilization of Mg waste. The pH, conductivity and the ions present in this solution will interfere in different ways during the corrosion process and, in order to understand the impact of these factors on the corrosion mechanisms, an individual study of each one of them was carried out.

The effect of the pH and the conductivity was studied directly in the case of galvanic coupling with graphite during 90 days by ZRA (Zero Resistance Ammeter). This technique allowed us to measure the current between Mg-0.5%Zr and graphite, where Mg becomes the anode and graphite the cathode, with a surface ratio Mg-Zr/Graphite of 1/1. Our pH range is between 10.45 (close to the equilibrium pH of Mg(OH) 2 ) and 13.70 (close to the pH of the pore solution of activated slag, which is also used for storing Mg nuclear wastes). The corrosion rates and hydrogen evolution were subsequently calculated from the coupling current measured by ZRA.

Corrosion of Mg-Zr in the geopolymer

This test allowed us to access the average corrosion rates over hydration time for a maximum period of 373 days. Three cases were evaluated: general corrosion of Mg-0.5%Zr and galvanic corrosion of Mg-0.5%Zr/Steel S235JR and Mg-0.5%Zr/Graphite.

For the execution of this test the samples were weighed before and after the exposure to a corrosive environment for a certain time. For Mg alloys, the NF ISO 8407 (2014-05-02) standard specifies the solution used for removing the formed corrosion products.

Results

Galvanic corrosion of Mg in alkaline solutions

The conductivity increases with pH (values ranging from 0.072 to 242.7 mS.cm -1

). However, this parameter does not have the same major impact on the corrosion rate as the pH. An optimum pH value was observed for values higher than 12 (Figure 1.a), where the corrosion rate was kept under 15 μm.year -1

, so binders with a pH above this value are relevant for embedding Mg-Zr alloys. The highest corrosion rate was observed for pH between 10.45 and 11.44. In this case, Mg(OH) 2 precipitates in a heterogeneous manner. For the pH with a lower corrosion rate (above 11.90) Mg(OH) 2 precipitates homogeneously in a thin layer on the surface of Mg (Figure 1.b). This difference in the homogeneity of the Mg(OH) 2 layer is related to the concentration of ions OH -present in the solution : lower concentrations favor the growth of preexisting Mg(OH) 2 crystals, causing heterogeneous precipitations on the surface; higher concentrations favor the nucleation of new growth sites, generating a thinner and homogeneous layer on the surface which is apparently more protective than the Mg(OH) 2 layer formed at lower pH.

Mg corrosion in geopolymer mortar

The evolution of the average corrosion for the general corrosion of Mg-0.5%Zr and the galvanic corrosion of Mg-0.5%Zr/Steel S235JR and Mg-0.5%Zr/Graphite is shown in table 1. The samples were embedded in a Na-Geo/NaF geopolymer up to 373 days. In all cases the average corrosion rate decreased with time, the coupling Mg-0.5%Zr/Graphite inducing the highest corrosion rate values. This difference is less evident when comparing these values to the ones obtained until 28 dayshowever, even if the coupling Mg-0.5%Zr/Graphite induces higher corrosion rates than the other cases, these values remain low (2.3 µ.year -1

).

Average corrosion rate (µ.year -1 )

Conclusions

Based on our results for the pH effect, the optimal pH for reducing Mg-Zr corrosion and hydrogen evolution is around 12.50. This confirms the results obtained previously in the coating matrix and shows the good choice of this material for immobilizing this type of waste even in a situation of a galvanic coupling with graphite, which induces the highest corrosion rates. The pH is a major parameter to understand the corrosion of magnesium, because small variations strongly affect the kinetics of corrosion and the formation of a passive layer on the surface of the metal. It was also found that graphite is the most penalizing coupling for Mg-Zr, presenting nonetheless a small corrosion rate.

Figure 1 :

 1 Figure 1: (a) Comparison of the galvanic corrosion rates between Mg-Zr/Graphite (ratio 1:1) at 3, 28 and 90 days in alkaline solutions at different pH. (b) SEM images of the Mg surface after 90 days at pH 10.45 and 12.35.

Table 1 : Average corrosion rates for the general corrosion of Mg-Zr and the galvanic corrosion of Mg- Zr/Steel S235JR and Mg-Zr/Graphite obtained by gravimetric methods.

 1

		3 days	28 days	90 days	373 days
	General Corrosion	29.4 ± 5.7	6.7 ± 1.1	2.4 ± 0.3	1.0 ± 0.4
	Mg-0.5%Zr / Graphite	37.8 ± 8.3	8.2 ± 1.6	5.9 ± 0.7	2.3 ± 0.1
	Mg-0.5%Zr/Steel S235JR	27.9 ± 9.4	5.8 ± 0.2	2.2 ± 0.5	0.6 ± 0.1

Acknowledgment

Authors thank ORANO for the financial support.


Ondoa Gregoire Abessolo

Magnus Larson
email: magnus.larson@tvrl.lth.se.

Rafael Almar
email: rafael.almar@ird.fr.

Bruno Castelle
email: bruno.castelle@u-bordeaux.fr.

Edward J Anthony
email: anthony@cerege.fr.

J Reyns
email: j.reyns@unesco-ihe.org.

MODELING REGIONAL COASTAL EVOLUTION IN THE BIGHT OF BENIN, GULF OF GUINEA, WEST AFRICA

The Bight of Benin coast is marked by the presence of three deepwater harbours which have affected the stability of the shoreline. In addition, several studies pointed out the overall diminution of sand supply due to the dams on Volta river channel and climate change effects. The combination of all these factors leads to a mixture of natural and artificial components affecting the coastline evolution in regional and long term scales. Here, we modeled the shoreline in the Bight of Benin, using the CASCADE model. The results show that the overall shape is well maintained and shoreline changes pretty well reconstructed. But, unresolved detailed information did not allowed to consider cross-shore sediment exchange and marked deviations can be observed. However, the CASCADE model can be used to investigate regional and long term solutions for decisions-makers in the concerned countries.

Introduction

In coastal management, a major issue is to understand the processes causing the variability of the coasts at different time scales. The damages and losses observed during extreme events and flooding are often a result of inadequate coastal management strategies. The long-term and large-scale adjustments of the shoreline to changes in wave climate, sea level rise, and sediment supply at open coasts can result into intensive erosion, threatening coastal societies, economical values, and valuable nature ecosystems [START_REF] Ranasinghe | Assessing climate change impacts on open sandy coasts: a review[END_REF][START_REF] Doody | Living with Coastal Erosion in Europe: Sediment and Space for Sustainability: Results from the EUROSION Study[END_REF]). Facing the increasingly intensive occupation of the coastal areas, it is of significant value to be able to predict the impact of such factors at several different time and space scales [START_REF] French | Coastal geomorphology: trends and challenges[END_REF], leading to a need of managing the coastal area regionally and not locally. The regional modeling that spans decades to centuries can be used to address the full consequences and interactions of engineering activities, as well as the widescale influence of natural processes and features [START_REF] Larson | Overview of regional coastal processes and controls[END_REF].

In the Bight of Benin, West Africa, Gulf of Guinea, recent studies [START_REF] Anthony | Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part 2: Sources and patterns of sediment supply, sediment cells, and recent shoreline variations[END_REF][START_REF] Giardino | A quantitative assessment of human interventions and climate change on the West African sediment budget[END_REF], Dada et al. 2015[START_REF] Almar | Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part1: Wave climate variability and impacts on the longshore sediment transport[END_REF] have focused on understanding the observed disturbance of the shoreline stability over the last few decades. Three main observations have been made: (i) this wave-dominated coast is particularly exposed to erosion and flooding due to wave climate and sea level rise [START_REF] Giardino | A quantitative assessment of human interventions and climate change on the West African sediment budget[END_REF][START_REF] Almar | Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part1: Wave climate variability and impacts on the longshore sediment transport[END_REF]; (ii) the stability of this coast has been strongly affected by the breakwaters at several deep-water harbors (Lome, Cotonou, and Lagos) and groins [START_REF] Anthony | Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part 2: Sources and patterns of sediment supply, sediment cells, and recent shoreline variations[END_REF][START_REF] Giardino | A quantitative assessment of human interventions and climate change on the West African sediment budget[END_REF][START_REF] Laibi | Longshore drift cell development on the human-impacted Bight of Benin sand barrier coast, West Africa[END_REF]); (iii) existing river dams and decrease in rainfall reduced the sediment supply from the Volta and Niger rivers [START_REF] Anthony | Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part 2: Sources and patterns of sediment supply, sediment cells, and recent shoreline variations[END_REF][START_REF] Giardino | A quantitative assessment of human interventions and climate change on the West African sediment budget[END_REF]. The prediction of the spatial and temporal responses of this coastal system is therefore important to decisions-makers in the concerned countries, which are low-income countries with 70% of the population in the coastal zone.

Several models have been developed for this purpose, encompassing in their description hundreds of kilometers of the coast (Larson, Kraus and Hanson 2002;[START_REF] Jiménez | A long-term (decadal scale) evolution model for microtidal barrier systems[END_REF]Hanson et al. 2008;[START_REF] Hoan | A mathematical model of spit growth and barrier elongation[END_REF][START_REF] Ranasinghe | Climate change impact assessment for inlet-interrupted coastlines[END_REF]). However, these models have typically simplified the representation of the cross-shore exchange sediment exchange, employing sources and sinks with schematized values in time and space (Larson, Kraus and Hanson 2002). To improve the predictive capability of these models, longshore and cross-shore processes have been combined in a more rigorous manner, using physics-based formulations [START_REF] Robinet | Modélisation de l'évolution long-terme du trait de côte le long des littoraux sableux dominés par l'action des vagues[END_REF][START_REF] Vitousek | A model integrating longshore and cross-shore processes for predicting longterm shoreline response to climate change: CoSMoS-COAST[END_REF]). However, further simplifications are required as simulations are performed for large areas over long time periods [START_REF] Larson | Simulating crossshore material exchange at decadal scale. Theory and model component validation[END_REF]). The regional coastal evolution model, known as CASCADE (Larson, Kraus and Hanson 2002) can be applied to stretches of coastline covering hundreds of kilometers, encompassing several barrier islands separated by inlets, including such phenomena as inlet creation, ebb-and flood-tidal shoal development, bypassing bars between beaches and inlets, channel dredging, regional trends in the shape of the coast, relative change in sea level, wind-blown sand, storms, periodic beach nourishment, and shore-protection structures such as groins and seawalls. Moreover, in the most recent development of the model complex cross-shore material exchange can be included [START_REF] Larson | Simulating crossshore material exchange at decadal scale. Theory and model component validation[END_REF]). These exchanges include dune erosion, wind-blown sand, overwash, berm erosion, and longshore bar development based on simplified physics-based relationships.

The overall objective of this work is to implement and develop the CASCADE model in the Bight of Benin, taking into account the main factors of shoreline variability of the area, to provide information for engineers, planners, and managers working on the decadal to century scale. First, background material and data were compiled for the study site with the purpose of calibrating the model. Second, the impact of the main harbors was considered and sediment transfer modeled. In a final step, the modeled

The Bight of Benin coast

The Bight of Benin in the Gulf of Guinea, West Africa, is the embayment located between the Volta River delta in the west (Ghana) and the Niger River delta (Nigeria) in the east, exhibiting a mildly embayed sand barrier system [START_REF] Anthony | Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part 2: Sources and patterns of sediment supply, sediment cells, and recent shoreline variations[END_REF]. The Volta River delta and the Niger River delta are among the three largest deltas in West Africa. The total length of the considered coastline is about 400 km, ranging between 1° to 5°E in longitude, and 5 to 7°N latitude.

The coast is a microtidal open-environment, facing the South Atlantic Ocean and exposed to a dominant long swell-wave component that travels far from mid-to high latitudes 45-60° in the South Atlantic and to the wind-sea component locally generated in the tropical band, 6°N to 15°S [START_REF] Almar | Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part1: Wave climate variability and impacts on the longshore sediment transport[END_REF]. This wave climate (mean values: Hs = 1.36 m; Tp = 9.4 s) drives an easterly longshore sediment transport ranging between 0 up to 1.2 million m3/year, depending on the location, according to [START_REF] Allersma | Coastal conditions in West Africaa review[END_REF], [START_REF] Anthony | Morphosedimentary evolution of a deltasourced, driftaligned sand barrier-lagoon complex, western Bight of Benin[END_REF] and [START_REF] Almar | Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part1: Wave climate variability and impacts on the longshore sediment transport[END_REF]. [START_REF] Anthony | Morphosedimentary evolution of a deltasourced, driftaligned sand barrier-lagoon complex, western Bight of Benin[END_REF] identified the Volta River as the single most important fluvial sediment source for much of the sand barrier system of the Bight of Benin, with minor additional inputs [START_REF] Anthony | Sedimentation in a tropical, microtidal, wave-dominated coastal-plain estuary[END_REF] from the Mono River in Benin. However, the Volta river discharge has been markedly reduced due to the decrease in rainfall over the Sahel since 1975 [START_REF] Oguntunde | Hydroclimatology of the Volta River Basin in West Africa: Trends and variability from 1901 to 2002[END_REF], as well as the construction of the Akosombo dam between 1961 and 1965, approximately 100 km upstream from the sea [START_REF] Anthony | Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part 2: Sources and patterns of sediment supply, sediment cells, and recent shoreline variations[END_REF]) and another smaller dam at Kpong, 24 km downstream of the Akosombo dam, constructed between 1977 and 1982. Three deepwater harbours have been constructed at the main cities on the bight coast: Lagos (1957), Cotonou (1962), andLomé (1967). Recently, several groins have been built along the coast. An example is given by the field of nine groins of 100 m lengths and 20 m width over a distance of 3.5 km, constructed near the city of Anèho (Togo) between 2012 and 2014.

The continental shelf is narrow, with widths of 15 to 33 km [START_REF] Anthony | Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part 2: Sources and patterns of sediment supply, sediment cells, and recent shoreline variations[END_REF][START_REF] Giardino | A quantitative assessment of human interventions and climate change on the West African sediment budget[END_REF]. Tides are semi-diurnal with a tidal range of approximately 0.3 m and 1.8 m for neap and spring tides, respectively, whereas sea level rise is about +3.3 mm/year. The sediment size is medium-to-coarse sand, from 0.4 to 1 mm, with a median grain size D50 = 0.6 mm.

Methods

Observed Regional Shoreline and Wave data (1990-2015)

Shoreline evolution in the Bight of Benin was determined using the LANDSAT 4-8 satellite images. Three images for each of the years 1990, 2000, 2005, 2010, and 2015 were chosen and downloaded from the USGS data portal Earth Explorer to offer large individual coverage as well as robust and accurate determinations of shoreline change rates (accuracy 30 x 30 m). Rates of changes in shoreline position were digitized using the ArcMap extension module Digital Shoreline Analysis System (DSAS), version 4.3, coupled with ArcGIS®10. Details can be found in [START_REF] Anthony | Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part 2: Sources and patterns of sediment supply, sediment cells, and recent shoreline variations[END_REF] Hindcasted time series of waves, part of the ERA-Interim dataset [START_REF] Sterl | Climatology, variability and extrema of ocean waves-the web-based KNMI/ERA-40 Wave Atlas[END_REF], were extracted at seven different stations (see Fig. 1b) along the coast over the 1990-2015 period.

Mathematical Modeling of Coastline Evolution: CASCADE

The CASCADE model simulates coastal evolution at the regional scale covering 100s of km and several decades. A typical coastal setting to which CASCADE may be applied is barrier islands separated by inlets with and without jetties, where the sediment is transferred around the inlets through the ebb-shoal complex [START_REF] Larson | Overview of regional coastal processes and controls[END_REF]. Sediment sources and sinks that vary in time and space are included in the model as well as a wide range of cross-shore processes, including dune erosion, overwash, wind-blown sand, bar-berm material exchange, erosion during storms and sea level rise. Focus was on reproducing the evolution around the main harbors in the area including Lagos, Cotonou, and Lomé.

Results

Model setup and implementation

CASCADE was implemented for a stretch of coastline along the Bight of Benin extending from a location just east of the Volta River to a location just west of Niger River. The modeled stretch is 374 km long, including the cities of Lome (Togo), Cotonou (Benin), and Lagos (Nigeria), which all have major harbors with structures that severely influence the sediment transport, causing downdrift erosion on a large scale [START_REF] Anthony | Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part 2: Sources and patterns of sediment supply, sediment cells, and recent shoreline variations[END_REF][START_REF] Laibi | Longshore drift cell development on the human-impacted Bight of Benin sand barrier coast, West Africa[END_REF]). In addition, some of these harbors border lagoons or river mouths that further complicate the sediment transport and coastal evolution. However, in the present, initial phase of modeling, no effort was made to reproduce shoals and bars that might be present around the harbors, but they were described through a shore-perpendicular structures that block the sediment transport. After more information has been collected on the detailed morphology and its evolution around the harbors, it will be possible to add modeling of the shoals and bars, which will improve the description of the coastal evolution and lead to better resolution of the governing processes in these areas.

As a starting point in the modeling of this complex region, the boundaries of the modeling area were placed some distance away from the river deltas where historically (i.e., during the time period of observation, 1990-2015) no shoreline change was observed. This implies that a boundary condition corresponding to no longshore transport gradient can be employed, allowing sediment to be freely transported in and out over a boundary. Although such a boundary condition may work for the time period of study, simulations over longer periods, when significant changes to the system occur, may not reproduce the expected behavior. For example, major changes in the river sediment discharge that have occurred will in general not be described by the model with this type of boundary condition. A more extensive model approach should include the Volta and Niger River Deltas and the sediment discharge from major tributaries in the deltas.

The calculation grid employed a length step of 1000 m with a time step of 6 hr; the latter corresponded to the time resolution of the wave input. The positive x-axis is directed from east to west, implying that an observer standing on the beach facing the ocean consider transport to the right to be positive (westward). In total seven offshore wave stations were used as input with linear interpolation between the stations when wave conditions were assigned along the grid (input waves varied spatially). The typical water depth at the stations is 40 m, being more or less deep water. Since very limited information was available on the profile characteristics along the grid, the cross-shore sediment exchange routines were not activated, but the profile shape was kept constant. A median grain size of 0.5 mm was used throughout the grid; this was also due to lack of detailed information on the alongshore variation.

The simulations were performed with standard values in the model and comparison with the observed changes between 2000 and 2015 were performed. The shoreline from 1990 was not included in the simulation since this shoreline indicated significant general accumulation along most of the grid up until year 2000. This accumulation was typically in the range of 100 to 200 m; no clear mechanism has been identified so far that explains this seaward of movement of the shoreline. Thus, it could not be described by the model.

Simulation results

The simulated shoreline evolution from 2000 to 2015 is displayed in Fig. 2 together with the measured shoreline at the end of the simulation. The calculated and observed shoreline change between 2000 and 2015 is also shown, since the scale of the bight makes it difficult to appreciate the detailed evolution of the shoreline. The influence of the tree harbors at Lome, Cotonou, and Lagos are easily identified with distinct areas of erosion and accumulation. Although qualitatively the shoreline response predicted by the model agrees with the observations, marked deviations occur locally and the magnitudes differ. Particularly the shoreline response around Lagos is not well resolved and the observed magnitude of seaward shoreline advance is much larger than the modeled. It is expected that more detailed information about morphology around the harbors will improve the simulations and form a basis for systematic model calibration and validation. The simulations also demonstrated that the model can maintain the overall shape of the bight, which tends to be difficult in this type of long-term simulations where diffusive processes smooth out shoreline gradients. The derived mean annual transport rate along the bight is shown in Fig. 3 based on the simulation period 2000-2015. The large-scale transport pattern is predicted satisfactorily with the model calculation yielding local values in the expected range and in agreement with previous investigations [START_REF] Almar | Response of the Bight of Benin (Gulf of Guinea, West Africa) coastline to anthropogenic and natural forcing, Part1: Wave climate variability and impacts on the longshore sediment transport[END_REF]. The net transport is to the east along most part of the bight, except for in the eastern part where the net transport is to the west (note that westward transport is taken positive, as previously explained).

Conclusion

Several recent works observed show that, for the last thirty years, the shoreline in the Bight of Benin has been destabilized, because of the progressively diminishing sand supply from the Volta river downstream of the Akosombo dam, the presence of the three harbors and climate change. In this study, the main objective is to model the evolution of the coast in the Bight of Benin, Gulf of Guinea. The results of implementing the CASCADE model on the coast of the Bight of Benin shows that the overall shape of the bight coast is well maintained. However, marked deviations are observed, particularly around Lagos harbor, as cross-shore sediment exchange routines were not activated. More detailed information about morphology and sediment supply around the harbors may improve the simulations. Moreover, it must be quite possible to derive the contributions of all the factors responsible of shoreline changes in the Bight of Benin, and therefore study what infrastructural solutions are adequate for this coast, in regional and long term scale.

Fig. 1 .

 1 Fig. 1. The Bight of Benin in the Gulf of Guinea, with the three main harbors at Lomé, Cotonou and Lagos. Red points stand for stations where wave characteristics were extracted.

Fig. 2 .

 2 Fig. 2. Simulation of regional coastal evolution of the Bight of Benin between 2000 and 2015 with CASCADE. Calculated and measured shorelines at the end of the simulation period (2015) together with measured initial shoreline (2000). The calculated and measured shoreline change, from 2000 to 2015, is also displayed.

Fig. 3 .

 3 Fig. 3. Calculated annual net longshore transport rate based on the simulation between 2000 and 2015.

Acknowledgements

This publication was made possible through support provided by the IRD (French Institute of Research for Development).


Ibaceta Rai

Jennifer Vega

Giovanni Montaño

Jose Coco

Tom Antolinez

Karin Beuzen

Laura Bryan

Bruno Cagigal

Mark Castelle

Evan Davidson

Goldstein

Jennifer Montaño

Giovanni Coco

Jose A A Antolinez

Tom Beuzen

Karin Bryan

Laura Cagigal

Bruno Castelle

Mark Davidson

Evan Goldstein

Rai Ibaceta Vega

Deborah Idier

Bonnie Ludka

Sina Masoud Ansari

Fernando Mendez

Brad Murray

Nathaniel Plant

Arthur Robinet

Ana Rueda

Nadia Senechal

Josh Simmons

Kristen Splinter

Scott Stephens

Ian Townend

Sean Vitousek

Kilian Vos

SHORECASTS: A BLIND-TEST OF SHORELINE MODELS

Introduction

Understanding processes regulating beach erosion and recovery remains a fundamental challenge in coastal research due to the inherent uncertainty in predicting the future "drivers" (e.g., wave characteristics) and to our limited understanding of interactions between drivers and response (e.g., sediment transport). Still, given the ongoing climatic changes and that most of the world's population lives near the coast, it is imperative to improve predictive capability of shoreline change. In fact, driven by the pressure from decision-makers, managers, politicians and the public, research efforts to understand and predict shoreline evolution have recently increased.

From a modelling perspective, several approaches have been proposed (Fig. 1), but two approaches seem particularly suited to predict shoreline change over the medium scale (seasonal to inter-annual): (a) Hybrid models (usually based on the equilibrium concept) and (b) machine learning. So far, a number of numerical models have been implemented for the prediction of shoreline evolution but there are very few studies that have attempted a detailed comparison of their predictive skill. The objective of our study is to test the ability of such models in predicting shoreline evolution seasonal to inter-annual scales. Here, we report on a novel approach to prediction and model testing based on a non-competitive competition (Shorecast) and subsequent workshop (Shoreshop 2018) specifically carried to bridge this gap. Overall, contributors from 15 institutions participated to the Shorecast competition and contributed to the discussion on advances in shoreline evolution models.

Data

In order to develop the Shorecast competition, data from a variety of sources had to be obtained and compiled. The cornerstone of the dataset is the eighteen years (1999-2017) of daily video shoreline position of Tairua Beach (NZ). Tairua Beach (Fig. 2) is an embayed beach of ~1200 m length located on the Coromandel Peninsula of New Zealand's North Island. Tairua beach faces northeast and is usually exposed to waves characterized by 1-3 m significant height and 10 s period, and approaching predominantly from NE. The tidal range is around 2 m. The beach is generally steep with sand of mean diameter of about 0.35 mm. The beach is highly dynamic and displays rhythmic longshore bar patterns frequently being modified by the formation of rips channels. The wave (significant wave height, peak wave period and direction) and tide characteristics were obtained from numerical modelling. We used SLR predictions until 2100 for the specific area.

Methods

The Participants to the Shorecast were asked to predict shoreline evolution at Tairua beach for the period 2014-2017, by using data to train their models from (1999-2014). For the Shorecast, we only provided the wave characteristics for the period 2014-2017, but not the shoreline evolution. This ensured that participants would not be biased by knowing the "result" and so avoided that the competition was reduced to a parameter fitting/calibration exercise.

Results

Overall, 19 models among Equilibrium Model types (12) and Machine Learning techniques (7) were used to predict shoreline behavior. Interestingly, almost all models displayed agreement with the observations, but they also indicated shortcomings that future research will need to address. Fig. 3 shows two examples: a Hybrid model (cyan line) and a Machine Learning model (magenta line). As can be seen in Fig. 3, upper panel, both models are able to capture seasonal to interannual changes in shoreline position. However, the Hybrid model was also able to predict faster shoreline changes. In general, many of the models reproduced the overall mean trend and seasonality but often failed to reproduce these large variations at faster time-scales as those induced by storms. Additionally, models showed a better performance during the hindcast period. In general, predictions followed a smooth trend, showing less variability during the prediction period (Fig. 3, bottom panel). Differences during hindcast and shorecast models performance were more evident for machine learning models than for hybrid models (Fig. 3, bottom panel).

Conclusion

We used observations of shoreline change at Tairua beach (New Zealand) to perform a "blind" test of numerical models. Our objective was to test model performance avoiding the possibility of calibration. Results indicate that both modelling methodologies can reproduce shoreline change over the medium term. All participants to the blind test appreciated the value of attempting uncalibrated predictions and it is hopeful that future studies will attempt similar tests.

  hal.archives-ouvertes.fr/hal-02394970 Submitted on 11 Dec 2019

Fig. 1 .

 1 Fig. 1. Classification of numerical models for shoreline change.

Fig. 2 .

 2 Fig. 2. a) and b) Tairua beach location c) Camera view of Tairua beach (courtesy of NIWA and Waikato Regional Council).

Fig. 3 .

 3 Fig. 3. Top panel: Hindcast prediction from 2003 -2006. Bottom panel: Shorecast prediction. Example of a Hybrid model (cyan) and of Machine learning model (magenta). The black line indicates the observed shoreline position.

Acknowledgements

We wish to thank all people and institutions that have made this research possible by making data available. In particular, we wish to thank the Waikato Regional Council, NIWA, George Payne and B. Blossier for their work in the codes for the video images, R. Bell (NIWA) for the tide and SLR data, and MetOcean for the wave hindcast. Funding from the Auckland Hazard Hub and a project awarded to GC (Climate change impacts on weather-related hazards) are gratefully acknowledged.


est destinée au dépôt

  Apnoeic oxygenation via high-flow nasal cannula oxygen combined with non-invasive ventilation preoxygenation for intubation in hypoxaemic patients in the intensive care unit: the single-centre, blinded, randomised controlled OPTINIV trial Samir Jaber, Marion Monnin, Mehdi Girard, Matthieu Conseil, Moussa Fafa Cisse, Julie Carr, Martin Mahul, Jean Marc Delay, Fouad Belafia, Gerald Chanques, et al. To cite this version: Samir Jaber, Marion Monnin, Mehdi Girard, Matthieu Conseil, Moussa Fafa Cisse, et al.. Apnoeic oxygenation via high-flow nasal cannula oxygen combined with non-invasive ventilation preoxygenation for intubation in hypoxaemic patients in the intensive care unit: the single-centre, blinded, randomised controlled OPTINIV trial. Intensive Care Medicine, 2016, 42 (12), pp.1877 -1887. 10.1007/s00134-016-4588-9. hal-01781330


est destinée au dépôt

  Rise in RBC aggregability and concomitant decrease in blood pressure 10 days after injection of the long acting erythropoietin analogue methoxy polyethylene glycol-epoetin-β (MIRCERA®) Céline Joré, Jean-Frédéric Brun, Emmanuelle Varlet-Marie To cite this version: Céline Joré, Jean-Frédéric Brun, Emmanuelle Varlet-Marie. Rise in RBC aggregability and concomitant decrease in blood pressure 10 days after injection of the long acting erythropoietin analogue methoxy polyethylene glycol-epoetin-β (MIRCERA®). Clinical Hemorheology and Microcirculation, 2017, 64 (4), pp.809 -816. 10.3233/CH-168015. hal-01818441


Matthieu De Schipper
email: a.deschipper@tudelft.nl

J Hopkins
email: j.a.hopkins@tudelft.nl

M Wengrove
email: meagan.wengrove@oregonstate.edu

I Saxoni
email: i.saxoni@student.tudelft.nl

M Kleinhans
email: m.g.kleinhans@uu.nl

N Senechal
email: n.senechal@epoc.u-bordeaux1.fr

B Castelle
email: b.castelle@epoc.u-bordeaux1.fr

F Ribas

B G Ruessink
email: b.g.ruessink@uu.nl

B Murphy
email: b.j.murphy@hull.ac.uk

S Mclelland
email: s.j.mclelland@hull.ac.uk

MODEX: LABORATORY EXPERIMENT EXPLORING SEDIMENT SPREADING OF A MOUND UNDER WAVES AND CURRENTS

The dispersal of sand from submerged mounds in the nearshore is driven by the interplay of processes such as converging and recirculating flows, changing roughness, bed slope effects and wave focusing/refraction. This morphological diffusivity is key to understanding sand bars in shallow seas, tidal inlets, estuaries, and the nearshore response to human interventions such as nourishments and dredging. Most of the work on the evolution of submerged mounds has been based on fluvial studies, focusing on flow without waves. In these cases, circular mounds tend to deform to crescentic (barchan) shapes. In contrast, observations of sandbars and berms in the nearshore subjected to waves show much more complex translation and deformation behavior. This contribution introduces the laboratory MOrphological Diffusivity Experiment (MODEX) aimed at examining morphological diffusivity under different forcing conditions. The experiment particularly addresses the linkages between small scale (local) effects (e.g. bed slope, bedforms) on the adjustment of sandy mounds.

Introduction

Morphological diffusivity, or the tendency of large morphological shapes to flatten due to feedback under flow conditions, is key to understanding the behavior of sand bars in shallow seas, tidal inlets, estuaries, and the nearshore response to human interventions such as nourishments and dredging. The diffusivity and feedback can be the result of wave angle variations alongshore, converging and recirculating flows, changing roughness, bed slope effects and wave focusing/refraction (e.g. Pelnard-Considère, 1956;[START_REF] Moulton | A surfzone morphological diffusivity estimated from the evolution of excavated holes[END_REF][START_REF] De Schipper | The influence of sea state on formation speed of alongshore variability in surf zone sand bars[END_REF][START_REF] Smit | Formation and evolution of nearshore sandbars[END_REF][START_REF] Price | Morphological coupling in multiple sandbar systems-a review[END_REF]. The understanding and predicting ability of this three-dimensional behavior is currently impeded by 1) a lack of data and 2) incomplete understanding of the underlying physical processes that govern the behavior on larger scales (e.g. bed slope effects, [START_REF] Baar | Sediment transport of fine sand to fine gravel on transverse bed slopes in rotating annular flume experiments[END_REF]. As a result, the morphodynamic models used to understand natural behavior (e.g. rhythmic sand bars) show a strong dependence on the parameterization of morphodynamic diffusivity (e.g. [START_REF] Dubarbier | Mechanisms controlling the complete accretionary beach state sequence[END_REF].

The lack of data on three-dimensional morphological diffusivity originates from the difficulty of experimenting in the natural system, viz. the signal-to-noise ratio of observed diffusivity in natural situations is low. During normal conditions, bed level changes are dominated by day-to-day variation in forcing, obstructing a clear view on the overall diffusivity. Yet, this behavior is often exploited to validate numerical models. A classical test case is the Gaussian Hump test of de [START_REF] De Vriend | 2DH mathematical modelling of morphological evolutions in shallow water[END_REF], showing the morphological diffusivity for a bed with constant roughness in a unidirectional current (i.e. no waves). This test case is often used for model validation (e.g. [START_REF] Lesser | Development and validation of a three-dimensional morphological model[END_REF][START_REF] Cowles | A block-structured adaptive mesh refinement solver for morphodynamic modeling[END_REF] and replicated in the lab by Garcia-Hermosa (2008). Overall these tests reveal that circular mounds reshape into crescentic (barchan) shapes. In contrast, observations of mounds subjected to waves such as sandbars and berms in the nearshore show much more complex behavior with translation and deformation. The diffusivity under waves and currents was experimented first in [START_REF] Moulton | A surfzone morphological diffusivity estimated from the evolution of excavated holes[END_REF], suggesting that bed slope may explain most of the behavior. Yet due to the complex nature of field experiments, the evolution could not be related to forcing in detail.

This contribution introduces the laboratory MOrphological Diffusivity Experiment (MODEX) aimed at examining morphological diffusivity under different types of forcing conditions. To examine three-dimensional morphological diffusivity, an experiment similar to the theoretical Gaussian Hump test case [START_REF] De Vriend | 2DH mathematical modelling of morphological evolutions in shallow water[END_REF] was designed. The experiment particularly addresses the linkages between small scale (local) effects (e.g. bed slope, bedforms) on the adjustment of sandy mounds. Following the experiment the research is focused amongst others on 1) spreading rates, 2) prediction skill using numerical models, 3) ripple formation and 4) linking ripple scale with overall spreading. MODEX is a collaboration between Delft University of Technology, Utrecht University, Oregon State University, CNRS, Université de Bordeaux, Universitat Politècnica de Catalunya and the University of Hull and made possible through the Hydralab+ program of the E.U. Data is made available on a repository to facilitate a wide use. This contribution describes the experiment setup, the execution of the test program and the initial results. The [START_REF] Hopkins | Observations and numerical model results of morphodynamic feedback owing to wavecurrent interaction[END_REF] and [START_REF] Lee | Wave driven sand ripple formation and evolution on a mound[END_REF] contributions to this Coastal Sediments 2019 conference present more detailed results of sub-projects.

Methodology

Experimental Setup

The experiment was executed over a 7-week period at the Total Environment Simulator (TES), a flume in Hull, United Kingdom in May and June 2018. The TES has the possibility to produce waves, currents and combined flows (waves + following currents) and suited to the installation of a wide planar sand bed. The flume basin is 12 m in length and 6 m in width, with eight wave paddles located at one end and recirculating flow (Figure 1). For the experiment, the basin was filled with a 0.1 m thick layer of sand with a D50 of 215 µm. Water level was raised to a water depth of 0.4 m above the main bed with fresh water. To allow for waves to be dissipated, a beach-like structure was constructed on the downstream end of the flume. The slope of this beach was approximately 1:5 and the surface was covered by artificial grass to increase the roughness. The beach structure was mounted 0.2 m above the bed level to allow for the current to flow into the recirculation system. Additionally, the beach was perforated by 0.032 m holes approximately 0.08 m apart (centre-to-centre) to attain a surface permeability of about 10 to 15 % for the flow to pass through. For each test a mound was constructed in the center of the flume. The dimensions of the mound are based on a gaussian with standard deviation of 0.3 m (~ 1.5 m diameter) and 0.2 m height at its peak, resulting of a mound height to ambient water depth of 0.5 at the start. The mound was designed to be axial symmetric and constructed using a mold consisting of an outer rim and a rotating profile board around the center to obtain similar initial bed conditions prior to each test (Figure 2). After each of the nine tests, the bed of the full flume was flattened to remove ripples and recreate a similar initial condition.

Experimental Program

The various tests focus on subjecting the mound to various wave and current conditions and monitoring its morphological response (Table 1). The wave conditions were tailored to the limitations of the wavemaker and in the nonbreaking regime. The forcing conditions were chosen such that transport were mostly in the bedload regime. In combined experiments the ratio of currents and wave forcing was chosen based on estimates of shear stress, such that waves and currents approximately result in similar stress or that one of the two dominates (Table 1).

Observation Techniques

A wide range of measurement devices was employed above and around the mound to capture the bed response and the concurrent forcing during the experiment (Figure 3 and Figure 4).

• Bed level measurements were taken using laser scanning, rotary pencil beam sonars and ultrasonic bed altimeters to capture the deformation and translation of the mounds in detail.

Laserscanning: A FARO Focus X330 scanner was used before and after each test when the flume was drained. It was programmed at a resolution of 3 mm at 10 m distance (175 million points per scan) and set up at six stations on the edges of the sandy bed to avoid objects being in the shadow of instruments. The six scans were then stitched together in the FARO SCENE software using five permanent targets installed in the TES. The reported registration errors of the combined 3D point-cloud on these targets are about 2 mm. With the CloudCompare software the 3D point-clouds were cut manually to contain the sandy bed only and then gridded to a rectangular grid with 5 mm resolution in the horizontal.

Rotary pencil beam sonars: Two Marine Electronics 3D Sand Ripple Profiling Logging Sonar (RPS) devices were used to map the bed while the flume was filled with water. The RPS devices contain a 1.0 MHz narrow beam sonar that rotates around its zenith angle to create a swath, followed by rotating in the planform. This resulted in a circular bed level image with a diameter of about 1 m. RPS devices were mounted on a moving traverse and lowered into the water between runs for scans. The backscatter data from the instruments was post-processed following [START_REF] Wengrove | Wave and current ripple formation and migration during storms[END_REF]. More on the RPS results can be found in [START_REF] Hopkins | Observations and numerical model results of morphodynamic feedback owing to wavecurrent interaction[END_REF].

Ultrasonic bed altimeters: 12 Seatek 2 MHz ultrasonic altimeters were used to obtain local bed information while the flume was filled with water (also during flow and waves). These altimeters with small transducer diameter (1 cm) and narrow beam width (1.8 degrees), effectively provide a point measurement of bed elevation on an intra bedform scale. Sampling frequency was equal to 1 Hz (based on three pings per sample).

• Hydrodynamics were measured using wave gauges, Acoustic Doppler Velocimeter (ADV) point measurement devices and near-bed ADV profiling devices.

Wave gauges: surface elevations were recorded at seven locations using HR Wallingford resistance wave gauges. The wave gauges were of the twin rod type and require calibration with changing water temperature and salinity. Therefore, daily calibration of wave gauges was done while filling and lowering the still water level of the flume. Sampling frequency was equal to 29 Hz.

ADV: Six Nortek ADVs were used to obtain mid-depth values of flow and wave orbital motion. Sampling frequency of the ADVs was equal to 25 Hz.

Profiling ADVs: To obtain high detail velocity profiles of near bed velocities, four Nortek Vectrino profilers were installed along the centerline of the mound. These devices provide a 3.5 cm profile of velocities. By synchronizing the devices in pairs they were able to map velocity structures larger than the individual sampling ranges. Sampling frequency was equal to 50 Hz. Additionally the Vectrino devices provide estimates of the bed level underneath the transducer head. During the tests the transducers were positioned 2 -8 cm (varying between different tests) above the bed and lowered (or raised) as the bed eroded (accreted).

• Sediment concentration.

To obtain estimates of sediment concentrations an acoustic backscatter (ABS) device was mounted upstream of the mound. The AQUASCAT 1000R device was used with 1, 2, 3 and 5 MHz transducers. Sampling frequency was equal to 128 Hz.

• Additional imagery data Four GoPro cameras were used for additional data. Three GoPro Hero4 devices were mounted overhead to provide an overview of the water surface (1/30 Hz). An additional GoPro Hero6 camera was used for subaqueous imagery. This Hero6 camera was mounted perpendicular to the mound to observe ripple formation at 5 second interval while the forcing acted on the mound.

Canon EOS 600 DSLR and smartphone camera images were also used for documenting the bed ripples and the experiment as a whole. Most instruments were mounted off a gantry spanning across the flume, such that the bed was not disturbed. For observations of hydrodynamics before the mound a separate frame was installed with a wave gauge, ADV and the ABS. Near the beach a second overhead frame was used to mount a wave gauge and an ADV (Figure 3 and5). A test consists of six to ten runs (i.e. bursts) of forcing. During these runs the flow, waves or both were activated and the hydrodynamics and altimeters were recording. After each run the RPS devices were lowered into the water column to obtain a measurement of bed level. The length of the runs varies between 5 to 30 minutes depending on the rate at which the mound lowers. Occasionally the final runs of a test were longer to provide the bed more time to evolve. Once the mound was approximately at half its height the tests were ended (Figure 6).

Preliminary results

Findings based on the experiment will be discussed at the conference, Hopkins et al. ( 2019) and [START_REF] Lee | Wave driven sand ripple formation and evolution on a mound[END_REF] contributions and subsequent publications.

General observations are given here.

Reproducibility

Crucial in comparing various tests in the experiment is a near similar initial bed. This is investigated using the pre-test laserscans. A profile comparison across the flume shows the initial mounds for all tests. Standard deviations between initial bathymetries (|zb,i-zb,j|, with i and j indicating different tests) are on average 0.0040 m (and maximum 0.0066 m). These differences are likely to be caused by a slight lateral shift of the mound position rather than differences in the shape itself (Figure 7)

Spreading

The overall behavior of the mound varies based on the forcing. Wave-only tests displayed a nearly invariant center of the mound, with a spreading to all sides.

To assess the spreading, Gaussian fits are made to the pre-and post-test bed levels:

(1)

where zb is the bed level (m); H(t) the height of the mound (m); sx and sy are the width of the mound in the direction of wave propagation and perpendicular to the wave propagation (m). Using a least-squares fitting procedure the best fitting Gaussian can then be found for each of the bed level scans.

For the wave only tests the best fit statistics of the mounds are displayed in Table 2. Fits to the pre-test mounds all have a height of around 0.19 m and a width of around 0.30 m, sufficiently matching the desired shape. The post-test fits show the relation between forcing and increase in widths of the mounds. The largest dispersion of sediment is found for the most energetic wave conditions in Test 3. Current-only tests show more resemblance to the formation of barchan dunes, as reported by Garcia-Hermosa (2008). In these current-only tests the center of mass of the mound is moved down-current and an asymmetric profile formed with a steep lee side.

Fig. 1 .

 1 Fig. 1. Side (top) and plan view (bottom) schematic of the TES facility during MODEX (Not to scale).

Fig. 2 .

 2 Fig. 2. Mound profile (top panel) and construction method in the flume.

Fig. 3 .

 3 Fig. 3. Laserscan point-cloud of the sandy bed with the mound prior to a test. Beach is visible at the right side in green. Overhead gantry (visible by the yellow and black hazard tape) was used to mount instruments off the bed.

Fig. 4 .

 4 Fig. 4. Instruments used during MODEX (from left to right). Top row: Laser scanner, Ultrasonic altimeters and the two RPS scanners. Middle row: Wave rod and ADV, four near bed profiling Vectrinos. Bottom row: ABS transducers, submerged GoPro camera and overhead GoPro camera.

Fig. 5 .

 5 Fig. 5. Top view schematic with detail of instrument positions. Note that the RPS devices were located on a traverse and were moved laterally to map the full extent of the mound. Note that wave rod #7 was removed from the experiment prior to test T1.

Fig. 6 .

 6 Fig. 6. Sequence of measurements and operations during an individual test.

Fig. 7 .

 7 Fig. 7. Differences between initial bed levels between individual tests. Along flume profile across the pre-test laser scans. Colors indicate the profiles prior to different tests.

  Fitting results for the mounds in the laser scans prior and post the wave-only tests. Amp indicates the amplitude of the mound Bedforms A range of bedforms were formed from an initially smooth topography during each of the tests. Depending on the forcing type, ripples were more straightcrested or linguoid-like. The various ripple patterns visible after the test show changing orientation and sizes, indicative of variations in the larger scale flow (Figure 8).

Fig. 8 .

 8 Fig. 8. Ripple patterns observed after Test 8 with waves and currents. Image facing the beach with a 30 cm ruler on the mound remains for scale.

Table 1 .

 1 Forcing conditions used during different tests of the experiment. Θ refers to the expected non-dimensional shear stress (Shields parameter) for waves Θw or currents Θc used to create a dominance of either of the two. Currents follow from the imposed flow rate divided by the wet cross-section (6 by 0.4 m). Values are the imposed values, observed values near the centre of the mound given in bold.

	Tests	Wave forcing	Flow rate	Total time
	date	(monochromatic)		(intervals)
	T1 Waves only (low)	T=1s, H=0.11 m	-	150 min
	16 & 17 May	(0.10 m)
	(day of year 136 &137)
	T2 Waves only (medium)	T=1.2s, H=0.14 m	-	90 min
	21 & 22 May (141 & 142)	(0.12 m)		(9 x 10)
	T3 Waves only (high)	T=1.3s, H=0.16 m	-	60 min
	24 & 25 May (144 & 145)	(0.12 m)		(9 x 6.66)
	T4 Current only (large)	-	900 l/s, 0.38m/s	35 min
	30 May (150)			(10 + 5 x 5 )
	T5 Current only (medium)	-	700 l/s, 0.29m/s	40 min
	1 June (152)			(8 x 5)
	T6 Wave+Currents (low energy)	T=0.85s, H=0.07 m	400 l/s, 0.17m/s	125 min
	5 June (156)	(0.055m)		(5+5+10+15
				+30+30+30)
	T7 Wave+Currents (Θw ≈ Θc)	T=1.2s, H=0.14 m	500l/s, 0.21m/s	45 min
	7 June (158)	(0.10 m)		(9 x 5)
	T8 Wave+Currents (Θw < Θc)	T=1.0s, H=0.11 m	580 l/s, 0.24m/s	47 min
	11 June (162)			(2 + 9 x 5)
	T9 Wave+Currents (Θw > Θc)	T=1.3s, H=0.16 m	420 l/s, 0.18m/s	45 min
	13 June (164)			(9 x 5)

Table 2 .

 2

Acknowledgements

The MODEX project was supported by the European Community's Horizon 2020 Programme through the grant to the budget of the Integrated Infrastructure Initiative Hydralab+, Contract no. 654110. The experiment would not have been possible without the nearly unlimited dedication, expertise and flexibility of the Total Environment Simulator staff, Hannah Williams and Laura Jordan. The scientific team also consisted of Anne Baar (Utrecht University), and Seok-Bong Lee (Oregon State University) who worked meticulously and enthusiastic to collect the data. Matthieu de Schipper is financed by NWO Domain Applied and Engineering Sciences under project code 15058.