J Barglik
email: jerzy.barglik@polsl.pl

S Golak

Electromagnetic stirring of liquid metal in crucible furnace

Keywords: induction crucible furnace, electromagnetic stirring, magnetohydrodynamics, mechanical efficiency

Mathematical modeling of electromagnetic stirring process in aninduction crucible furnace is presented. The model is based on one way coupled electromagnetic and flow phenomena. The paper is focused on calculation of distribution of electromagnetic and flow fields in the sub-domain of molten metal. Based upon these calculations the distribution of the Lorentz force and velocity of liquid metal are determined. It makes it possible to provide a theoretical analysis of the mechanical efficiency of the induction crucible furnace considered as an electromagnetic stirrer. An illustrative example dealing with a one-phase induction crucible stirrer is analyzed. The results show that the mechanical efficiency of the device reach quite small values.

Introduction

Induction crucible furnaces are widely used in different branches of modern industry. Apart from melting and preheating of metals they are mostly used for melting, preheating and homogenization of the compositions of liquid metals in such metallurgical processes like casting or refining. Due to high energy consumption, such processes should be precisely optimized. One of the important objectives of such an optimization is to obtain an appropriate intensity of stirring, which is usually expressed by an average flow velocity. However, in the case of large electromagnetic stirrers used in steel and/or non-ferrous metals industry, their mechanical efficiency, defined as the ratio of the energy used for acceleration of metal to the total power supplied to the inductor, has very interesting properties. Therefore, it is necessary to carry out an effective evaluation of the mechanical work done by the induction crucible furnace considered as a stirrer.Whilethe classic rotating electrical machines or linear movable elementsrepresent rigid bodies, which allows even purely analytical determination of their efficiency, electromagnetic stirring is much more complicated in this respect. The device of this type works with conductive liquid that is to be set into motion. Due to non-uniform distribution of electromagnetic forces, forces of friction along the crucible walls, and often turbulent flow of molten metal,determination of the mechanical efficiency of the crucible furnace should be based on knowledge of the spatial distribution of mechanical power dissipated in the entire volume of the device.

Mathematical model of electromagnetic stirring

The mathematical model consists of two partial differential equations describing electromagnetic and flow fields in the crucible. The presented study covers the period of operation of the furnace after melting metal and stabilizing the velocity field. This allows introducing some simplifications in the electromagnetic model (with acceptably small deterioration of the accuracy of results) to achieve the solution in reasonable time, using sequential coupling of electromagnetic field and hydrodynamic field. Coupling of this type first provides the distribution of electromagnetic forces, and then simulation of the hydrodynamics. Analysis of the electromagnetic field is based on Maxwell's equations supplemented with generalized Ohm's law. The model is simplified using the transition from the time domain to the frequency domain. Electromagnetic field analysis starts from the approach working with the phasor of the magnetic vector potential A [1]. In order to allow for the sequential model, the electromagnetic coupling with the hydrodynamic model does not include the impact of temperature on the physical properties of metal, as well as the eddy current density due to movement of molten metal in magnetic field [2]  

s 1 jω μ        A A J , (1)
where μ denotes the magnetic permeability, Ais thephasor of the magnetic vector potential, σstands for theelectric conductivity, andJ s isthe phasor of thefield current density.

Phasors of magnetic flux density B and eddy current densityJmay be determined from equation (1) after taking account the relations (2) and (3).

   BA , (2)
                  v v v v f g , ( 5
) 0    v , ( 6
)
where vdenotes the velocity, η, ρare the dynamic viscosity and density, p stands for the pressure, and f e is the volumetric density of the Lorentz force, and g represents the gravity acceleration.

Due to high values of the Reynolds number, the flow should be analyzed as turbulent. This number is on the order of 10 4 -10 5 . This necessitates to include an appropriate model of turbulence. Our analysis was based on a widely used modelk-ε characterized by a relatively short time of computation.

Neglecting the influence of temperature on electric conductivity of metal and neglecting the influence of velocity of melt on eddy currents distribution in it allows using a computationally efficient, sequential model working only with coupling of electromagnetic and flow fields [3][4][5][START_REF] Barglik | 10th International Scientific Conference: Electric Power Engineering[END_REF]. Figure 1 shows a simplified diagram of this way of coupling.

For devices in which the free surface is significantly dependent on electromagnetic field (mainly small stirrers and stirrers working light metals such as aluminum), this coupling scheme should be implemented in a series of calculations including changes of free surface shape of the metal bath [START_REF] Golak | [END_REF][8][9][10]. For larger furnaces stirrers and heavier metals at higher, such as steel, the phenomenon of the meniscus occurs on a relatively small scale, so does not affect significantly on the mechanical power in a separate stirrer and can be omitted in order to minimize the computation time.

Fig. 1: Schematic model of one-way coupling of electromagnetic and hydrodynamic model

Mechanical efficiency of the electromagnetic stirrer

We defined the mechanical efficiency  m of electromagnetic stirring as a ratio of the generated mechanical power P m in the flowing metal to the power P i delivered to the inductor m m i P P   [START_REF] Golak | [END_REF] The specific mechanical power p m and its total value P m are given by formulae ( 8) and ( 9)

m p  e fv , ( 8
) mm d V P p V   (9)
provided that a small influence of the convection is neglected.

Illustrative example

Determination of the mechanical efficiency was investigated for the case of single-phase stirring of steel in the crucible furnace with the height of 400mm, lower diameter of 370mm and upper diameter of 400mm. The inductor was powered by current of amplitude of 1000A and frequency of 50Hz.

Based on the model of the electromagnetic field (1) we obtained a series of fields acting in molten metal. These distributions are depicted in Fig. 2. The field of the Lorentz forces is shown in Fig. 2a The final flow field distribution after stabilization of flow velocity obtained from the hydrodynamic model is shown in Fig. 2b. Two toroidal vortices are well visible, which is typical for single-phases stirring. The highest velocities were observed near the walls and the upper surface, but they do not differ much from the average volume velocity (see Table 1), resulting in a relatively uniform mixing. Based on the obtained field distribution of electromagnetic forces and velocity field, we determined the spatial distribution of mechanical power density generated in the liquid metal. In order to improve readability of the figures, this distribution is presented in two separate areas. Figure 3c shows the section in with emitted mechanical power and Fig. 2d with absorbed mechanical power. Emitted mechanical power occurs in the domains where the dot product ( 8) is positive, in other words, where the angle between vectors f e and vis between 0 and 90°, while power is absorbed in areas where the dot product (8) is negative, i.e., where the angle between vectorsf e and vis between 90° and 180°. While the occurrence of emission of the mechanical power is restricted just to the area near the wall of the crucible, the same quantity is absorbed near the free surface and also near the bottom of the crucible. The effect of these phenomena is extremely low mechanical efficiency of the mixer, especially if it is compared with the efficiency of heating (see Table 1). The results obtained for the solved sample mixer provided a very low mechanical efficiency of this device. The reason is that a significant part of energy is used for heating both the inductor and, above all, liquid metal, while just its small part is changed to work exerted by the electromagnetic forces. As a result, the efficiency of the mechanical mixer is about three orders lower than the electrical efficiency, which in the case of equipment, whose primary task is to perform mechanical work and make the molten metal flow, is very unfavorable. Low efficiency of mechanical stirring gives a high potential for optimization of these devices in order to increase its value as much as possible.

  of the above equations of magnetic induction and eddy current density allows determining the time-average specific electromagnetic forces, acting in molten metal.where B * is the complex conjugate ofB.The flow of liquid metal in the stirrer is described by the set of Navier-Stokes and the continuity equations for the incompressible

Fig. 2 :

 2 Fig. 2: Distributions of the fields in the crucible: a)Lorentz forcefield, b)the velocity field, c) emitted mechanical power, d) absorbed mechanical power.

Table 1 :

 1 Important calculated parameters of molten metal in the crucibleConclusionsEstimation of the mechanical efficiency of electromagnetic stirring helps to evaluate the effectiveness of the crucible furnace and allows its optimizing in this respect.

	Parameter

Acknowledgment

Thepaper was realized within the framework of the grant project NN 508 388637 supported by the Polish Ministry of Science and Higher Education.


Li Qiulin

Wei Liu

Investigation on the Removal of Inclusions from Aluminum Melt Using Alternating Combined Magnetic Field

Keywords: combined magnetic field, alternating rotating magnetic field, agglomeration, inclusions

In this article, the primary silicon particles precipitated from Al-Si hypereutectic alloy during the solidification process are regarded as inclusions in the aluminum melt which need to be eliminated. The effect of alternating combined magnetic field (CMF) composed of downward travelling magnetic field (TMF) and alternating rotating magnetic field (RMF) on the removal of inclusions formed in the aluminum is investigated. The results indicated that the particles of inclusions had agglomerated into clusters obviously and migrated to the top of the melt to be removed under alternating CMF. In comparison, alternating CMF has a better removing effect than that of oriented CMF composed of oriented RMF and downward TMF. With the increasing of the current and the frequency for the alternating RMF included in the alternating CMF, the effect of elimination by alternating CMF is improved. The best removing effect condition for the alternating CMF is at the alternating time 10s.

Introduction

Due to their low density, high strength, high thermal conductivity and high electrical conductivity characteristics, aluminum alloys have been widely used in many fields, such as aerospace, marine engineering, automobile industry, and construction industry, etc. However, the presence of inclusions in aluminum alloys has significant harmful effects on their mechanical properties, which also lead to defects increase and corrosion resistance weaken [1,2]. Therefore there must be feasible and effective method to reduce the inclusions in aluminum alloys.

Traditional methods like gravity sedimentation, bubble method, flotation and filtration have low efficiency in removing little inclusions, particularly for those smaller than 20μm ones, and have difficulty to industrialize.

A practical way to remove small inclusions is to force groups of particles to aggregate with each other into large inclusions, which can be dislodged easily. Miki Yuji [3] discovered that there are many inclusions aggregation pairs in steel ingot treated by oriented rotating magnetic field (RMF), which enhanced the productivity of removing oxide inclusions. Lu Dehong [4] also found the phenomenon of primary silicon particles aggregating under RMF during the solidification of a hypereutectic Al-Si alloy. He Yanjie's researches [5,6] discovered that combined magnetic field (CMF) composed of downward travelling magnetic field (TMF) and RMF had a better removing effect than TMF or RMF individually. R. Alireza [7] found that primary silicon particles would aggregate in some degree, under electromagnetic vibration during the solidification of a hypereutectic Al-Si alloy. Han Yecong [8] further verified the effect of electromagnetic vibration on agglomeration of primary silicon particles, and investigated the effect of frequency and current on the influence of agglomeration scientifically.

In this study, primary silicon particles precipitating during the solidification of A390 aluminum alloy are regarded as inclusions. An alternating CMF of downward TMF and alternating RMF (magnetic field direction changes periodically) is introduced. The effect of such CMF to remove inclusions is investigated systematically.

Experimental

In this investigation, the commercial hypereutectic Al-Si alloy A390 is used, whose specific chemical composition is shown in table 1. The alloy rod sample with a diameter of 25mm is placed in a crucible with a diameter of 26mm, and is raised to the middle of electric oven by a servo motor. After the sample is heated to 720 °C to be completely melted and remained in this state for 20min, then the heating motor power is adjusted to cool the sample to 640°C at a constant cooling rate of 8°C/s. When the temperature is reduced to 640°C, the heat motor is turned off and the excitation source is switched on. Therefore, a magnetic field is imposed on the sample until the temperature reduced to 580°C. Then the magnetic field is turned off, the sample is pulled down and cooled to room temperature. After being milled and polished, the microstructures and macro distributions of the solidified samples are observed.

Tab.1 Chemical composition of hypereutectic Al-Si alloy (wt%

) Si Cu Fe Mg Zn Ti Al 18~2 0 <0.1 <0.1 <0.1 <0.1 <0.1 YY

Results

The distributions of primary silicon under different magnetic fields are shown in Fig. 1. In the case of sample without magnetic field (Fig. 1a), the primary silicon particles distribute uniformly in the sample basicly. By comparing Fig. 1b and Fig. 1c with Fig. 1d, one can finds that sample treated by alternating CMF has a larger area of silicon-particle-free region than those treated by TMF or RMF individually, which indicates that alternating CMF has a stronger inclusion removing effect.

Discussion

The diagram of the CMF removal mechanism of primary silicon particles is shown in Fig.5 [6]. TMF downward can create an annular flow filed [9-12] in both paratropicplane and diatropicplane of the melt, shown as region I and region II. When an oriented CMF is applied, primary silicon particles in region II will migrate to region I, under a centrifugal force provided by oriented RMF, with a great migration velocity, collide and agglomerate with each other into larger particles in the center of melt. Meanwhile, large particles in region I will migrate to the upper of melt, under their buoyancy and flow filed produced by TMF. When an alternating CMF is applied, alternating RMF can not only drive particles migrating radially, but also promote particles to collide and agglomerate tangentially. Collision in tangential direction of melt, caused by alternating RMF, can increase the collision probability of particles; produce lager agglomerate clusters consisting of silicon particles, which migrate faster to the upper region of melt, under their buoyancy and flow filed produced by TMF. Thus, alternating CMF has a better cleaning efficiency than oriented CMF.

The velocity of silicon particle increases with the increasing of the frequency or current of alternating RMF [12],

which also enhances particle collision and agglomeration. Therefore, with the increase of the frequency or current of alternating RMF, the particles tend to agglomerate into clusters and migrate to the top of melt. So the removing efficiency of inclusions is increased. If the alternating time is too short, the primary silicon particles have not enough time to accelerate to an equilibrium velocity, which means the distance the particles can reach is short and the collision probability of particles is low. As if the alternating time is too long, longer than the required time for particle accelerating to equilibrium velocity, It has no effect to enhance collision probability. On the contrary, when the total time of magnetic field treatment is constant, alternating time increase will reduce the number of magnetic swerving, or in other word, reduce the number of particle motion direction swerving times. Consequently, the alternating time has an optimum value. In this study 10s is better than 5s or 15s.

Conclusions

Inclusion particles agglomerates into clusters and migrated to the top of the melt under alternating CMF. By comparison, alternating CMF has a better removing effect than oriented CMF. With the increase of the frequency or current the particles are more obviously to migrate and agglomerate into clusters and the removing effect of inclusions become much finer. There has optimum alternating time for alternating RMF, in this study 10s is better than 5s or 15s. It is proposed that alternating CMF provides a highly effective approach for metal purification.

Fig. 1 :

 1 Fig.1: The distributions of primary silicon under different magnetic fields Fig.2shows the distributions of samples under alternating CMF with different currents and frequencies. It can be found that the size of the silicon-particle-free region enlarged and the silicon particles tend to migrate to the top of the samples with the increase of current and frequency of alternating RMF.

Fig. 2 :

 2 Fig.2: The distributions of primary silicon under different currents and frequencies of alternating magnetic fields

Fig. 4 Fig. 3 :Fig. 4 :

 434 Fig.4shows the macro distribution and micro distribution of primary silicon particles in samples under alternating RMF and oriented RMF. It is indicated that samples under alternating RMF has a lager silicon-particle-free area than the one under oriented RMF, while the fields have the same current and frequency, obtained from comparing Fig.4aand Fig.4c. However, as shown in Fig.4band Fig.4d, primary silicon particles distribute uniformly in the sample treated by oriented RMF, but those particles slightly tend to agglomerate into clusters in the sample treated by alternating RMF. Thus, alternating RMF has a better agglomeration effect than oriented RMF.

Fig. 5 :

 5 Fig.5: The diagram of the removal mechanism of combined magnetic field

Acknowledgment

Financial support from National Natural Science Foundation of China 50904042 is gratefully acknowledged.


E Rabot

I Cousin

C Hénault

A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space

Keywords: nitrous oxide emission modeling, water-filled pore space, gas diffusivity, soil

Nitrous oxide (N 2 O) fluxes can increase significantly following small increases in soil waterfilled pore space (WFPS). Thus, it is essential to improve our knowledge of this crucial relationship to better model N 2 O emissions by soils. We studied how much the addition of a gas transport and a gas-liquid equilibrium module to the model of N 2 O emissions NOE could improve simulation results. A sensitivity analysis of the modified model (NOE GTE : Gas Transport and Equilibrium) was first performed, and then the model was tested with published data of a wetting-drying experiment. Simulated N 2 O fluxes plotted against WFPS appeared to be bell-shaped during the 7 days simulated, combining the effects of the low N 2 O production for WFPS < 0.62, and the slow gas diffusion for WFPS > 0.95. The WFPS generating the maximum simulated N 2 O fluxes shifted with time, from 0.76 after 12 hours, to 0.79 after 168 hours, because of an increase over time of the gas concentration gradient between the soil surface and the atmosphere. NOE GTE appeared able to capture the pattern of N 2 O emissions monitored in the experimental data. In particular, N 2 O peaks during drying were well reproduced in terms of timing, but their magnitudes were often overestimated. They were attributed to the increasing gas diffusivity and N 2 O exchanges from the liquid phase to the gaseous phase.

Introduction

Nitrous oxide (N 2 O) is the third largest gas contributing to global warming, as its global warming potential is 300 times higher than that of carbon dioxide over a 100-year time scale (UNEP 2013). Soils under natural vegetation are estimated to account for 60% of natural N 2 O F W functionis a reduction function used to modify the potential denitrification of soils and/or the N 2 O/N 2 ratio. It is combined with other reduction functions related to soil nitrate content or soil temperature, which are used together to estimate N 2 O fluxes. For example, the DenNit [START_REF] Reth | DenNit -Experimental analysis and modelling of soil N 2 O efflux in response on changes of soil water content, soil temperature, soil pH, nutrient availability and the time after rain event[END_REF], ECOSSE [START_REF] Smith | Estimating changes in Scottish soil carbon stocks using ECOSSE. I. Model description and uncertainties[END_REF], and NOE [START_REF] Hénault | Predicting in situ soil N 2 O emission using NOE algorithm and soil database[END_REF] models used such functions. The F W function can be described as: a continuous exponential curve starting at a WFPS value of 0.62 in the NOE and ECOSSE models, an arctangent function with a level off for WFPS > 0.7-0.9 in DAYCENT (Del Grosso et al. 2000), a sigmoid curve with half maximum N 2 O emissions at 60% of the field capacity in DenNit, or a linear growing function starting at the drained upper limit in APSIM [START_REF] Keating | An overview of APSIM, a model designed for farming systems simulation[END_REF]. A comparison of the F W functions used in denitrification models is given in Heinen (2006b).

Several experiments have been designed to build F W functions, with different levels of soil disturbance and control on other variables. For example, experiments of [START_REF] Weier | Denitrification and the dinitrogen/nitrous oxide ratio as affected by soil water, available carbon, and nitrate[END_REF] on sieved and repacked soil samples of various textures were included in the NGAS model [START_REF] Parton | Generalized model for N 2 and N 2 O production from nitrification and denitrification[END_REF]. This denitrification sub-module has subsequently been integrated into DAYCENT, with supplementary results of Del Grosso et al. (2000) on undisturbed soil cores.

To derive appropriate F W equations, Del Grosso et al. (2000) eliminated data points subjected to strong limitations due to other variables (e.g., nitrate content, temperature). To build the F W function in the NOE model, [START_REF] Hénault | Predicting in situ soil N 2 O emission using NOE algorithm and soil database[END_REF] performed laboratory experiments where temperature and nitrate concentrations were favorable for N 2 O emissions. Results were closed enough to the field experiment of Grundmann and Rolston (1987) so that the equation of Comment citer ce document : Rabot, E., Cousin, I., Hénault, C. (2015). A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space. Biogeochemistry, 122 (2-3), 395-408. DOI : 10.1007/s10533-014-0048-1 Grundmann and Rolston (1987) was reused. For the DenNit model, results were derived by fitting the sigmoid function of [START_REF] Davidson | Fluxes of nitrous oxide and nitric oxide from terrestrial ecosystems[END_REF] on new field and laboratory experiments.

Models often assume that N 2 O emissions change immediately when an environmental variable does [START_REF] Xing | Modelling nitrous oxide and carbon dioxide emission from soil in an incubation experiment[END_REF]. This can lead to mismatches between the predicted fluxes and fluxes observed in the field, which themselves are highly variable over time, even at hourly scales. The purpose of this study was to improve NOE simulations by incorporating a gas transport and a gas-liquid equilibrium module to the original NOE model. The modified model (NOE GTE : Gas Transport and Equilibrium) was subjected to a sensitivity analysis to observe its response to the WFPS parameter. Then the model was tested with experimental published data in order to check the relevance of the new version of NOE and to further discuss the N 2 O emission processes in response to varying WFPS.

Material and methods

Model description

Nitrous oxide production module

Nitrous oxide production was estimated by using the NOE model [START_REF] Hénault | Predicting in situ soil N 2 O emission using NOE algorithm and soil database[END_REF], modified to be used in a 1-D configuration, i.e., to give an estimation on each vertical location within a soil horizon, instead of using an integrative value for the whole soil horizon. The NOE model was chosen because it requires few and accessible input data, and because it is frequently used in research studies (Heinen 2006a). The N 2 O flux produced by denitrification (N 2 O denit ) is a combination of the potential denitrification (D P ) and response functions to several environmental factors [START_REF] Hénault | Predicting in situ soil N 2 O emission using NOE algorithm and soil database[END_REF]:

N 2 O denit = D P .F W .F N .F T .r max [1]
where F W is the denitrification response factor to soil WFPS (dimensionless), F N is the denitrification response factor to soil nitrate content (dimensionless), F T is the denitrification response factor to soil temperature (dimensionless), and r max is the maximum ratio of N 2 O to denitrified nitrate under anaerobic incubations. Techniques used to determine D P and r max experimentally are described in [START_REF] Hénault | Predicting in situ soil N 2 O emission using NOE algorithm and soil database[END_REF]. F N and F T were taken from the original NOE model [START_REF] Hénault | Predicting in situ soil N 2 O emission using NOE algorithm and soil database[END_REF], where F N was built by [START_REF] Hénault | NEMIS, a predictive model of denitrification on the field scale[END_REF] from laboratory experiments and F T was originally designed by [START_REF] Stanford | Effect of temperature on denitrification rate in soils[END_REF]. The F W response function is defined by eq. [2] (Grundmann and Rolston 1987; Hénault and Germon

Comment citer ce document : Rabot, E., Cousin, I., Hénault, C. (2015). A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space.

, 62 . 0 WFPS If            F F [2]
We made the assumption that N 2 O denit in conditions of high WFPS estimates the total N 2 O production, which must then be partitioned between the gaseous and liquid phases.

Nitrous oxide transport module

Transport by diffusion is the major process allowing gas movement within soils (Heincke and Kaupenjohann 1999;[START_REF] Yoh | Diffusion analysis of N 2 O cycling in a fertilized soil[END_REF]. It was modeled by using the 1-D diffusion equation of Fick (eq. [3]), solved by the finite difference method with a central difference scheme:

             x C D x t C S [3]
where C is the N 2 O concentration (mol N 2 O m -3 gas), t is the time (s), D S is the gas diffusion coefficient in soil (m 3 gas m -1 soil s -1 ), and x is the vertical coordinate (m).

Fluxes inside a closed-chamber located above the soil horizon were also modeled because the closed-chamber technique, frequently used to measure N 2 O fluxes in the field, is known to influence the N 2 O fluxes [START_REF] Conen | An explanation of linear increases in gas concentration under closed chambers used to measure gas exchange between soil and the atmosphere[END_REF][START_REF] Venterea | Accuracy and precision analysis of chamberbased nitrous oxide gas flux estimates[END_REF]). Transport into the chamber was modeled by the same Fick's equation (eq. [3]), parameterized with D 0 , the gas diffusion coefficient in free-air.

Four models, chosen for their wide use, were tested for the estimation of the Ds parameter (Table 1). Soil-type effects are introduced through the soil total porosity P, which is related to the soil structure. Moreover, in the M model, additional soil-type effects are taken into account by using the soil water retention curve. Two families of gas diffusion models were thus used as the M and D models have been developed with undisturbed soils to represent complex and multiscaled soil systems. On the contrary, the B and MQ models have been developed with a model porous medium, the B model being experimental whereas the MQ model is theoretical.

Comment citer ce document : Rabot, E., Cousin, I., Hénault, C. (2015). A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space.

Hp C  aq [4]
where C aq is the N 2 O concentration in the aqueous phase (mol L -1 ), H is the Henry's constant of N 2 O in a given electrolyte solution at a given temperature (mol L -1 atm -1 ), and p is the partial pressure of N 2 O in the gaseous phase (atm). The effect of the presence of ions in the solution on the N 2 O solubility was taken into account with the Sechenov equation [START_REF] Schumpe | Temporal response of soil denitrification rates to rainfall and irrigation[END_REF], together with the temperature dependence of H. The gas-liquid equilibrium was applied only if the N 2 O concentration in the aqueous phase was lower than the saturation concentration of N 2 O in water. The simulation allowed for any dissolved N 2 O lost with the water outflow to be removed from the budget. Transport by diffusion in the aqueous phase is analogous to the transport in the gaseous phase and is also modeled with Fick's law (eq. [3]), with the N 2 O diffusion coefficient in water being equal to 1.80 × 10 -9 m 2 s -1 (Weast and Astle 1979).

Model parameterization

The model was used in two types of simulations. Its sensitivity to WFPS was first tested by using randomly chosen values of WFPS and BD. Secondly, the model was applied to the experimental data set of [START_REF] Rabot | Temporal variability of nitrous oxide emissions by soils as affected by hydric history[END_REF], who highlighted N 2 O peaks during drying, probably due to N 2 O entrapment during the wetting phase and fast release during the drying phase. The hypotheses regarding the functioning of N 2 O emissions during the drying phase were evaluated with our modeling approach. In the two cases, the modeling support was the same. Coding was done in FORTRAN 2003 within the INRA VSoil platform. The platform provides an easy way to use and couple numerical modules representing processes occurring in soils [START_REF] Lafolie | The VSoil platform: A tool to integrate physico-bio-geo-chemical models in soils at the local scale[END_REF]). Information about how to use and contribute to the platform can be found in the dedicated web site: http://www.inra.fr/sol_virtuel/.

The modeling domain

The soil horizon was represented as a 7-cm height 1-D space, with 8 discrete nodes. The closed-chamber was simulated with the same vertical spacing between simulation nodes as the soil horizon. Calculations were performed on each node with a time increment of 3 seconds and results were stored every 3600 seconds. No-flux boundary conditions were Comment citer ce document : Rabot, E., Cousin, I., Hénault, C. (2015). A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space.

Evaluating hypotheses on nitrous oxide emission processes

We used experimental data presented in [START_REF] Rabot | Temporal variability of nitrous oxide emissions by soils as affected by hydric history[END_REF] to parameterize and evaluate hypotheses on the N 2 O emission processes. Briefly, in this study, 12 undisturbed soil cores (15 cm inner diameter, 7 cm height) were subjected to two wetting-drying cycles. Nitrous oxide fluxes were measured by infrared correlation spectroscopy by using the closed-chamber method, soil matric potential was recorded by three tensiometers inserted at 3, 4, and 5 cm

Comment citer ce document : Rabot, E., Cousin, I., Hénault, C. (2015). A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space. Biogeochemistry, 122 (2-3) beginning with a -7 cm pressure head step. Three treatments of soil drying were applied depending on the number of steps required to reach -100 cm pressure head, and are hereafter referred as the Fast, Medium, and Slow treatment.

For each sample, the volumetric water content data were first smoothed to remove noise, by using the functional data analysis package "fda" [START_REF] Ramsay | Functional data analysis with R and MATLAB[END_REF]) built on R (R Development Core Team 2012). It was realized by using a B-spline basis system and a roughness penalty on the second derivative. The smoothing parameters were chosen by examining the quality of the resulting fit [START_REF] Ramsay | Functional data analysis with R and MATLAB[END_REF]). Four gas diffusivity models were tested (Table 1). The Campbell pore size distribution index (b) used in the M model was determined by fitting the [START_REF] Campbell | A simple method for determining unsaturated conductivity from moisture retention data[END_REF]

for               b [5]
where θ is the soil water content (cm 3 cm -3 ), θ s is the saturated water content (cm 3 cm -3 ), Ψ is the soil matric potential (m), and Ψ b is the air-entry potential (m). (10 cm inner diameter, 20 cm height) with a nitrate solution for 24 hours, then allowing the sample to drain freely for a further 24 hours, before measuring the N 2 O flux over a 3-hour period [START_REF] Hénault | Predicting in situ soil N 2 O emission using NOE algorithm and soil database[END_REF]. The wetting phase was four times longer in the experiment of [START_REF] Rabot | Temporal variability of nitrous oxide emissions by soils as affected by hydric history[END_REF], but the nitrate concentration of the wetting solution and the soil temperature were the same as for the experiments enabling the estimation of the D P parameter. We therefore approximated D P in the 12 soil samples by dividing the flux value at the end of the -7 cm pressure head step by four. During this step, the pressure head was lowered to the bottom of the soil sample, allowing the macropores to drain for 24 hours. D P was estimated for the two wetting-drying cycles. The r max parameter was fixed to 0.9, because at high nitrate availability, the N 2 O/N 2 ratio is known to be high [START_REF] Letey | Effect of air-filled porosity, nitrate concentration, and time on the ratio of N 2 O/N 2 evolution during denitrification[END_REF][START_REF] Ruser | Emission of N 2 O, N 2 and CO 2 from soil fertilized with nitrate: Effect of compaction, soil moisture and rewetting[END_REF][START_REF] Weier | Denitrification and the dinitrogen/nitrous oxide ratio as affected by soil water, available carbon, and nitrate[END_REF].

Data analyses

Cumulative N 2 O fluxes were calculated by linearly interpolating the N 2 O flux values that were frequently recorded or simulated with time, and then integrating the area under the curve [START_REF] Castellano | Hydrological and biogeochemical controls on the timing and magnitude of nitrous oxide flux across an agricultural landscape[END_REF]Dobbie et al. 1999). To compare the effect of the different D S /D 0 estimations in the model, we used the root-mean-square error (RMSE):

      n i i i O P n 1 2 1 RMSE [6]
where P i and O i are predicted and observed values and n is the number of observations. The mean error (ME) was used to evaluate over-or underestimations of the model:

      n i i i O P n 1 1 ME [7]
The effect of the hydric period or treatment on RMSE and ME were assessed by a Mann-Whitney U test or a Kruskal-Wallis test at the 5% level. Correlations were assessed by the calculation of Pearson correlation coefficients.

Results and discussion

Evaluating the model sensitivity to the water-filled pore space Some factors are known to modify the N 2 O/N 2 ratio: the N 2 O-reductase is inhibited by oxygen [START_REF] Ruser | Emission of N 2 O, N 2 and CO 2 from soil fertilized with nitrate: Effect of compaction, soil moisture and rewetting[END_REF], high nitrate contents [START_REF] Weier | Denitrification and the dinitrogen/nitrous oxide ratio as affected by soil water, available carbon, and nitrate[END_REF], low pH [START_REF] Knowles | Denitrification[END_REF], or high temperatures [START_REF] Keeney | Effect of temperature on the gaseous nitrogen products of denitrification in a silt loam soil[END_REF]. High carbon contents increase denitrification, so an increase in N 2 O fluxes has already been observed (e.g., Harrison-Kirk et al. 2013), or on the contrary, a decrease of the N 2 O/N 2 ratio (e.g., [START_REF] Khalil | Nitrous oxide production from an ultisol of the humid tropics treated with different nitrogen sources and moisture regimes[END_REF]. Even if the reduction of N 2 O into N 2 has been demonstrated [START_REF] Ciarlo | The effect of moisture on nitrous oxide emissions from soil and the N 2 O/(N 2 O+N 2 ) ratio under laboratory conditions[END_REF][START_REF] Letey | Effect of air-filled porosity, nitrate concentration, and time on the ratio of N 2 O/N 2 evolution during denitrification[END_REF][START_REF] Weier | Denitrification and the dinitrogen/nitrous oxide ratio as affected by soil water, available carbon, and nitrate[END_REF]), the Comment citer ce document : Rabot, E., Cousin, I., Hénault, C. (2015). A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space. In addition, the VARBD simulations showed a N 2 O flux increase with time at a given WFPS, when anoxic conditions were favorable. Indeed, as the N 2 O accumulated in the soil because of the slow gas diffusion and a constant production, the gas concentration gradient between the soil surface and the chamber headspace increased with time, and the flux increased. This phenomenon led to the shift of the peak to higher WFPS with time: maximum N 2 O fluxes occurred near WFPS = 0.76 after 12 hours and this value increased with time to reach WFPS = 0.79 after 168 hours (Fig. 2). Moreover, for high WFPS and for the latest times of simulation, N 2 O produced at deeper nodes diffused enough to contribute to emissions at the soil surface. By highly increasing the simulation time, the transport length of N 2 O molecules would increase and the right side of the bell would tend to disappear. Thus, the hydric history could explain the different WFPS values recorded in the literature for the maximum N 2 O fluxes, in addition to other variables linked to N 2 O production or N 2 O/N 2 ratio, such as texture, structure or carbon and nitrogen contents. It is also noteworthy that that in published experimental data, the F W relationship was often noisy compared to laboratory experiments or our modeling approach, because some other factors (e.g., nitrate content, temperature) were limiting [START_REF] Laville | Effect of management, climate and soil conditions on N 2 O and NO emissions from an arable crop rotation using high temporal resolution measurements[END_REF]. Using a boundary line method such as proposed by [START_REF] Schmidt | Using a boundary line approach to analyze N 2 O flux data from agricultural soils[END_REF] generally allows highlighting the bell-shaped relationship of field data.

Results

In the FIXEDBD simulations, by comparing the WFPS corresponding to the maximum simulated N 2 O flux at different times (Table 2), we observed that the effect of BD was low (difference in the WFPS of 0.007 after 168 hours between BD = 1.20 and 1.40 g cm -3 ), and that a soil with a high BD tended to produce the maximum N 2 O flux at lower WFPS compared to a soil with low BD. This low effect of BD was also seen in the cumulative N 2 O fluxes: they were in the same order of magnitude for the three BD, from 10.63 mg N m -2 d -1 at BD = 1.40 g cm -3 , to 10.74 mg N m -2 d -1 at BD = 1.20 g cm -3 . Dense soils are known to cause higher N 2 O fluxes than loose soils (e.g., [START_REF] Balaine | Changes in relative gas diffusivity explain soil nitrous oxide flux dynamics[END_REF][START_REF] Beare | Compaction effects on CO 2 and N 2 O production during drying and rewetting of soil[END_REF]Hansen et al. 1993;[START_REF] Ruser | Emission of N 2 O, N 2 and CO 2 from soil fertilized with nitrate: Effect of compaction, soil moisture and rewetting[END_REF][START_REF] Yamulki | Short-term effects of tillage and compaction on nitrous oxide, nitric oxide, nitrogen dioxide, methane and carbon dioxide fluxes from grassland[END_REF]. These high fluxes were often explained in field experiments by a reduction of the air-filled porosity (Hansen et al. 1993;[START_REF] Ruser | Emission of N 2 O, N 2 and CO 2 from soil fertilized with nitrate: Effect of compaction, soil moisture and rewetting[END_REF]). In our model, BD is a component of the gas diffusion coefficient calculation, and the amount of water involved in the gas-liquid equilibrium. Because there was a difference in the water content at a given WFPS between the three BD, contribution of the N 2 O dissolution in the liquid phase was different: the amount of N 2 O was higher in the soil solution for the low BD. Moreover, the gas diffusivity estimated with the MQ model as function of the WFPS is a very flat curve at high WFPS (Fig. 3). Thus, in the range of WFPS

Evaluating hypotheses on nitrous oxide emission processes

Comparison between measured and simulated nitrous oxide fluxes 3), because of the overestimated peaks during drying.

By comparing the N 2 O flux estimations from the four gas diffusivity models used (Fig. 6), we observed that they were very similar between B and M models on the one hand, and between MQ and D models on the other hand. Indeed, in the range of WFPS of the experiment (WFPS > 0.6), the B and M models in the one hand, and the MQ and D models in the other hand give similar D S /D 0 estimations, especially at high WFPS (Fig. 3). The B and M models tended to overestimate N 2 O fluxes, whereas the MQ and D models were closer to experimental data (Table 3). In particular, fluxes were generally underestimated during the wetting phase for the four models, and fluxes were overestimated for the B and M models and were generally better for the MQ and D models during the drying phase (Table 3). No trend in the ME or RMSE values was observed between the three treatments of decreasing pressure head (p > 0.05). The confidence interval was often modeled to be higher for the first wetting phase than for the Comment citer ce document : Rabot, E., Cousin, I., Hénault, C. (2015). A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space. Biogeochemistry, 122 (2-3) second wetting phase (Fig. 5). For high WFPS, the D S /D 0 was very similar for the four gas diffusivity models (Fig. 3). We attributed thus the lower variability in the simulation results during the second cycle to a lower N 2 O production during the second wetting cycle, linked to the lower WFPS and lower D P .

Whereas we obtained very different results depending on the gas diffusivity model used, [START_REF] Böttcher | Emission of groundwater-derived nitrous oxide into the atmosphere: model simulations based on a 15 N field experiment[END_REF] in their sensitivity analysis found few effects of D S /D 0 on the simulated hourly time steps have occurred (e.g., [START_REF] Bessou | Modelling soil compaction impacts on nitrous oxide emissions in arable fields[END_REF][START_REF] Hergoualc'h K | The utility of process-based models for simulating N 2 O emissions from soils: A case study based on Costa Rican coffee plantations[END_REF][START_REF] Metay | Simulating N 2 O fluxes from a Brazilian cropped soil with contrasted tillage practices[END_REF] and by numerically re-building fine water content chronicles, they provided moderately good simulation results. [START_REF] Cannavo | Modeling seasonal variations in carbon dioxide and nitrous oxide in the vadose zone[END_REF] combined NOE and simulated soil water content with gas transport equations. We assumed that introducing processes occurring at a fine temporal resolution, such as gas transport and gas-liquid equilibrium, would allow

Comment citer ce document : Rabot, E., Cousin, I., Hénault, C. (2015). A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space. Biogeochemistry, 122 (2-3) This phenomenon, highly pronounced in some of the experiments at the first wetting-drying cycle, may be linked to denitrifying microorganisms which adapted gradually to anaerobic conditions [START_REF] Laville | Effect of management, climate and soil conditions on N 2 O and NO emissions from an arable crop rotation using high temporal resolution measurements[END_REF]. Indeed, N 2 O emissions have already been observed to begin quickly after rewetting whereas the N 2 O reduction into N 2 has been observed to occur after 2 to 4 days of wetting (e.g., [START_REF] Letey | Effect of air-filled porosity, nitrate concentration, and time on the ratio of N 2 O/N 2 evolution during denitrification[END_REF], Hansen et al. 2014). Errors in the flux estimation during the wetting phase propagated then to the end of the simulation period.

Conclusion

The modeling approach performed in this study was intended to refine the NOE model in Pritchard and Curie (1982)), WFPS is the water-filled pore space, P is the soil total porosity (cm 3 cm -3 ), and b is the Campbell pore size distribution index [START_REF] Millington | Permeability of porous solids[END_REF] 12.30 0.00 5.30 -1.80 14.90 1.00 [START_REF] Moldrup | Modeling diffusion and reaction in soils: IX. The Buckingham-Burdine-Campbell equation for gas diffusivity in undisturbed soil[END_REF] 27.20 6.50 5.30 -0.10 33.60 10.10

  Evaluating the model sensitivity to the water-filled pore spaceTo test the NOE GTE sensitivity to the WFPS parameter, we built a quasi-random data set consisting of a combination of hydric conditions (WFPS in the range [0-1]) and bulk density (BD in the range [1.2-1.4], needed to estimate D S /D 0 ; the BD values were typical for the surface horizon of cultivated soils, and corresponded to P in the range [0.47-0.55]). These simulations are hereafter referred to as VARBD. To test the effect of BD on the simulation results, the model was also run for fixed BD values of 1.20, 1.30, and 1.40 g cm -3 , and WFPS in the range [0-1]. This second test of the model sensitivity to the WFPS parameter is hereafter referred to as FIXEDBD simulations. We used a Sobol' sequence in order to reduce the computational cost of the analysis, and generated thus 200 realizations from a uniform distribution. The values of the other parameters were fixed to be in agreement with the experimental data set of[START_REF] Rabot | Temporal variability of nitrous oxide emissions by soils as affected by hydric history[END_REF]: D P = 15 g N ha -1 d -1 , r max = 0.9, F N = 1, and F T = 1. WFPS was a uniform value in the entire column and was set to be constant with time. The gas diffusivity was estimated with the MQ model. The total simulation time was 168 hours (7 days).

  model to the soil water retention curve (eq. [5]), based on the measured soil water contents and soil matric potentials. The b parameter was estimated by curve fitting for the two wetting-drying cycles of each soil sample, to take into account the effect of the hysteresis in the soil water retention curve.

  For the N 2 O production module, we made the following assumptions: (1) N 2 O production occurred over the whole horizon depth, because the 12 soil samples were extracted from surface horizon, where C and N are available for microorganisms[START_REF] Jobbagy | The distribution of soil nutrients with depth: Global patterns and the imprint of plants[END_REF], (2) N 2 O was mainly produced by denitrification because water content was high throughout the experiment (WFPS always > 0.6), and (3) because the experimental setup begins with a quick rewetting to saturation, the N 2 O production increased so much that the initial N 2 O concentration in the soil appeared negligible in comparison. To focus on the effect of the F W function on N 2 O emissions, the experiment of[START_REF] Rabot | Temporal variability of nitrous oxide emissions by soils as affected by hydric history[END_REF] was conducted under laboratory conditions with the room temperature ranging between 20 and 21°C and the nitrate concentration of the wetting solution being equal to 200 mg N kg -1 , thus giving F T = 1 and F N = 1. Moreover, in the NOE model, D P is usually estimated by wetting a soil core Comment citer ce document : Rabot, E., Cousin, I.,Hénault, C. (2015). A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space.Biogeochemistry, 122 (2-3), 395-408. DOI : 10.1007/s10533-014-0048-1 Version définitive du manuscrit publié dans / Final version of the manuscript published in : Biogeochemistry, 2015, http://dx.doi.org/10.1007/s10533-014-0048-1 Manuscrit d'auteur / Author Manuscript Manuscrit d'auteur / Author Manuscript Manuscrit d'auteur / Author Manuscript 8

  of the VARBD simulations are given in Fig. 1. It shows the evolution of the N 2 O fluxes with time for the 200 simulated soil samples. No flux was observed for WFPS < 0.62Comment citer ce document : Rabot, E., Cousin, I.,Hénault, C. (2015). A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space. Biogeochemistry, 122 (2-3), 395-408. DOI : 10.1007/s10533-014-0048-1 Version définitive du manuscrit publié dans / Final version of the manuscript published in : Biogeochemistry, 2015, http://dx.doi.org/10.1007/s10533-014-0048-1 Manuscrit d'auteur / Author Manuscript Manuscrit d'auteur / Author Manuscript Manuscrit d'auteur / Author Manuscript 9 for the overall simulation period, because the source term was set to zero by the N 2 O production module. For WFPS between 0.62 and ~0.95, fluxes increased to the end of the simulation period. The maximum N 2 O fluxes were reached at a WFPS of approximately 0.8. Conversely, very low fluxes were simulated for WFPS > 0.95 because of the slow gas diffusion in the water-saturated soil. Considering only gas diffusion, at WFPS = 0.62, a N 2 Omolecule covers approximately 37 cm during the 7 days simulated, whereas at WFPS = 0.8 it covers 13 cm, and only 1.3 cm at WFPS = 0.95 (according to the MQ model, with BD = 1.30 g cm -3 ). Thus, the whole soil profile is expected to participate to the surface flux at WFPS = 0.8, where maximum fluxes were simulated. The three-dimensional representation of Fig.1is projected onto the plane formed by the N 2 O flux and WFPS axes in Fig.2for four simulation times. Fluxes were bell-shaped during the 7 days simulated, combining the effects of the low N 2 O production for low WFPS, and the slow gas diffusion for the highest WFPS. This shape was in agreement with other data collected in the field (e.g.,[START_REF] Laville | Effect of management, climate and soil conditions on N 2 O and NO emissions from an arable crop rotation using high temporal resolution measurements[END_REF][START_REF] Rafique | Nitrous oxide emission from grazed grassland under different management systems[END_REF][START_REF] Schmidt | Using a boundary line approach to analyze N 2 O flux data from agricultural soils[END_REF] and laboratory experiments (e.g.,[START_REF] Balaine | Changes in relative gas diffusivity explain soil nitrous oxide flux dynamics[END_REF][START_REF] Castellano | Hydrological and biogeochemical controls on the timing and magnitude of nitrous oxide flux across an agricultural landscape[END_REF][START_REF] Ciarlo | The effect of moisture on nitrous oxide emissions from soil and the N 2 O/(N 2 O+N 2 ) ratio under laboratory conditions[END_REF]. In these studies, maximum N 2 O fluxes occurred at a WFPS ranging between 0.6 and 0.8, and the decrease in N 2 O fluxes at high WFPS was attributed both to the slow gas diffusion and to a high reduction of N 2 O into N 2 at high water content, because the N 2 O-reductase is inhibited by oxygen[START_REF] Ruser | Emission of N 2 O, N 2 and CO 2 from soil fertilized with nitrate: Effect of compaction, soil moisture and rewetting[END_REF]). In the N 2 O production module used, the reduction of N 2 O into N 2 is represented by a fixed value measured experimentally, which integrates thus several soil parameters affecting the N 2 O/N 2 ratio.

  slow gas diffusion appeared to be enough to explain the decrease of N 2 O fluxes at high WFPS in our simulations. However, a major improvement of the model would be to include the N 2 O reduction as a function of the WFPS. It would lead to a shift of the simulated peak to lower WFPS. Moreover, some low N 2 O fluxes have already been measured in the field or in laboratory experiments for WFPS < 0.62, and were attributed to denitrification occurring in anaerobic zones inside water saturated aggregates, or to nitrification[START_REF] Bateman | Contributions of nitrification and denitrification to N 2 O emissions from soils at different water-filled pore space[END_REF].

  Measured and simulated cumulative N 2 O fluxes are presented in Fig.4. Correlation coefficients calculated for each gas diffusivity model were high, in the range 0.85 to 0.89, which demonstrates that the NOE GTE model provided satisfactory results for the cumulative N 2 O fluxes regardless of which model was used to calculate D S /D 0 . However, for a given soil sample, the simulated flux dynamics were still highly variable and depended on the gas diffusivity model used. Since estimation of the soil gas diffusivity is still a challenge, we integrated the four simulation results with the four gas diffusivity coefficients in the form of a 95% confidence interval for each sample. Measured and simulated flux dynamics are presented in Fig.5. For the 12 soil samples, the measured and simulated fluxes were in the same order of magnitude. NOE GTE appeared able to capture the pattern of N 2 O emissions monitored in the experiment of[START_REF] Rabot | Temporal variability of nitrous oxide emissions by soils as affected by hydric history[END_REF]. The use of a diffusion transport module in addition to the NOE model allowed the transient N 2 O peaks during the drying phase to be reproduced, but they were sometimes overestimated. Conversely, N 2 O dynamics were less well modeled for the wetting phase: an increase in N 2 O fluxes was modeled at the beginning of the wetting phase, instead of a peak occurring 2 or 3 days after rewetting. Nevertheless, RMSE and ME were lower for the wetting phase than for the drying phase (p < 0.05; Table

N 2 O

 2 fluxes. The soils were well-aerated, contrary to the current experiment, with water contents in the near-saturated range.[START_REF] Böttcher | Emission of groundwater-derived nitrous oxide into the atmosphere: model simulations based on a 15 N field experiment[END_REF] recommended, however, the use of measured rather than estimated D S /D 0 . Using an efficient gas diffusivity model is essential as[START_REF] Balaine | Changes in relative gas diffusivity explain soil nitrous oxide flux dynamics[END_REF] suggested that N 2 O emissions can be more efficiently predicted by D S /D 0 than by the WFPS. Indeed, they concluded that the maximum N 2 O emissions occurred at a D S /D 0 of 0.006 and that this value was independent of the soil BD. For lower D S /D 0 , they hypothesized that N 2 O was entrapped in the soil and that the reduction of N 2 O into N 2 was high. In our study, the D S /D 0 allowing the maximum simulated N 2 O fluxes varied depending on the simulated time, ranging from 0.002 to 0.004 (corresponding to the WFPS given inTable 2). Emissions may have been simulated to occur for D S /D 0 < 0.006 because N 2 O reduction into N 2 was not encoded in the model as a function of the WFPS, but as a fixed value. Other factors can influence the D S /D 0 value where maximum fluxes are observed. The study of Petersen et al. (2013) demonstrated that high soil carbon contents may increase the oxygen demand and lead to suboxic conditions, increasing thus the D S /D 0 where N 2 O emissions are observed. Our results support the observation of Balaine et al. (2013) that D S /D 0 is an efficient parameter to predict N 2 O emissions, because at a given BD, it can be seen as a proxy of the WFPS to trigger the N 2 O production, and because it controls the N 2 O transport by combining information about the solid-induced tortuosity and the water-induced disconnectivity. Description of the nitrous oxide emission processes Rabot et al. (2014) observed in their laboratory experiment that N 2 O flux peaks could occur during the wetting of a soil, as frequently observed in previous studies (e.g., Groffman and Tiedje 1988; Sanchez-Martin et al. 2010; Sexstone et al. 1985), but also during the drying phase, with a higher or similar intensity. Conversely, the N 2 O flux peak during drying has not previously been documented, probably because of its brevity. The maximum N 2 O flux occurred just after the decrease of the pressure head, at the end of the steep decline of the soil Comment citer ce document : Rabot, E., Cousin, I., Hénault, C. (2015). A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space. Biogeochemistry, 122 (2-3), 395-408. DOI : 10.1007/s10533-014-0048-1 Version définitive du manuscrit publié dans / Final version of the manuscript published in : Biogeochemistry, 2015, http://dx.doi.org/10.1007/s10533-014-0048-1 Manuscrit d'auteur / Author Manuscript Manuscrit d'auteur / Author Manuscript Manuscrit d'auteur / Author Manuscript 13 matric potential or water content. The flux decreased then drastically. To explain peaks during soil drying, Rabot et al. (2014) made the following hypothesis: N 2 O was produced and entrapped during the wetting phase and was emitted both by rapid gas displacement from the gaseous phase and released from the soil solution during the soil drying. After applying our modeling approach, we were able to decompose the N 2 O flux dynamics during drying in two parts: i) the rapid rise of the N 2 O flux can be attributed to the increasing D S /D 0 due to the increase of free-air porosity, and N 2 O exchanges from the liquid to the gaseous phase, ii) the decline of the N 2 O flux occurring approximately 1.6 hours after the beginning of the soil drying can be attributed to the removal of the N 2 O entrapped in the gaseous phase, the removal from the budget by drainage of a part of the N 2 O entrapped in the soil solution, and the declining water content and nitrate content leading to lower N 2 O production. The remaining question about the origin of the N 2 O released during the drying phase, i.e., from the gaseous or from the liquid phase, in the Rabot et al. (2014) experiment can also be answered by the model: the best simulation results were achieved by using both Fick's and Henry's laws, favoring the hypothesis that N 2 O was entrapped and released from the two phases. The behavior of N 2 O in the aqueous phase, i.e., its high solubility and its possible transport out of a soil system with the water flow is an important aspect to consider for the study of indirect N 2 O emissions. Our analysis underscores the importance of transient dynamics in N 2 O fluxes and identifies the need to use shorter time steps. A lot of models, e.g., APSIM (Thorburn et al. 2010), DAYCENT (Parton et al. 2001), DNDC (Deng et al. 2013), ECOSSE (Bell et al. 2012), were designed to be run at daily time steps. Although most of them succeeded in capturing cumulative N 2 O fluxes at monthly or seasonal time steps, they often failed to simulate precisely the magnitude of N 2 O fluxes. Indeed, even if the main controlling factors were understood, modeling emissions of a gas which is soluble and reacts to form other compounds with high temporal resolution is complex (Shcherbak and Robertson 2014). Estimating N 2 O fluxes at hourly time steps thus remains a challenge. Like the previously cited models, the NOE model was initially developed to be run at daily time steps. Attempts to use NOE at

  order to demonstrate the role of the physical processes relating water and N 2 O emissions and the importance of these in N 2 O modeling. A sensitivity analysis of the WFPS parameter was performed using the new NOE GTE model. The results showed that simulated N 2 O fluxes plotted against WFPS were bell-shaped during the 7 days simulated, combining the effects of the low N 2 O production for WFPS < 0.62, and the slow gas diffusion for WFPS > 0.95. It was in agreement with previous studies based on data collected in field or laboratory experiments. The WFPS generating the maximum simulated N 2 O fluxes shifted with time because of an increase over time of the gas concentration gradient between the soil surface and the atmosphere, and because the participation of the deeply produced N 2 O to the surface flux increased with time. By increasing the simulation time, the right side of the bell would tend to disappear. The hydric history is thus an additional explanation of the different WFPS values recorded in the literature for the maximum N 2 O fluxes, in addition to other variables linked to the N 2 O production or to the N 2 O/N 2 ratio. Moreover, the model appeared able to capture the pattern of N 2 O emissions monitored during wetting and drying experiments. Nitrous oxide peaks observed during soil drying were indeed well reproduced in terms of timing, but their magnitudes were often overestimated. We were able to validate the hypothesis that the rapid rise of the N 2 O flux during soil drying was attributed to the increasing D S /D 0 , and N 2 O exchanges from the liquid to the gaseous phase. The decline occurring a few hours later was attributed to a decrease of the N 2 O entrapped in the gaseous phase, the removal from the budget by drainage of a part of the N 2 O entrapped in the soil solution, and the declining water content and nitrate content leading to lower N 2 O production. The next improvement for N 2 O emission models at high temporal resolution would be then to finely describe N 2 O stocks in Comment citer ce document : Rabot, E., Cousin, I., Hénault, C. (2015). A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space. Biogeochemistry, 122 (2-3), 395-408. DOI : 10.1007/s10533-014-0048-1

FiguresFig. 1 Fig. 3 Fig. 4 Fig. 5 Fig. 6

 13456 Figures

  the gas diffusion coefficient in free air (D 0 = 1.42 × 10 -5 m 2 s -1 at 20°C and 1 atm,

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	Manuscrit d'auteur / Author Manuscript	2000), and assumes that the WFPS parameter is a proxy of the oxygen availability for microorganisms. 74 . 1 W 38 . 0 62 . 0 WFPS , 62 . 0 WFPS If W 0
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	Manuscrit d'auteur / Author Manuscript	Dissolved nitrous oxide Because N 2 O is highly soluble in water (Heincke and Kaupenjohann 1999), we introduced a gas-liquid equilibrium according to Henry's law (eq. [4]):
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Biogeochemistry, 122 (2-3), 395-408. DOI : 10.1007/s10533-014-0048-1

  chamber was set equal to 319 ppb, to simulate the regular chamber removal done before each N 2 O flux measurement in the study of[START_REF] Rabot | Temporal variability of nitrous oxide emissions by soils as affected by hydric history[END_REF].

		Version définitive du manuscrit publié dans / Final version of the manuscript published in :
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	Manuscrit d'auteur / Author Manuscript	imposed at either the upper (i.e., top of the closed-chamber) or lower (i.e., bottom of the soil horizon) boundaries. Input parameters for NOE GTE were the volumetric water content, soil total porosity, soil and air temperature, soil nitrate content, potential denitrification (D P ), and the ratio of N 2 O to denitrified nitrate (r max ). The values of all these parameters were assigned to each node of the soil horizon. At time t = 0 hour, initial N 2 O concentration in the gaseous phase, in both the soil and the chamber, was set to the atmospheric concentration (319 ppb), and the N 2 O concentration in the aqueous phase was initialized to be at equilibrium with the atmospheric concentration of N 2 O at 20°C. Then, every 30 minutes, the N 2 O gas concentration inside the
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		395-408. DOI : 10.1007/s10533-014-0048-1

  soil water content was recorded by a soil moisture probe installed vertically at the soil surface to record an integrated value of the soil moisture. The soil was first saturated for four days with a nitrate solution. The soil drying was then performed stepwise in a tension table, by applying a decreasing pressure head level once a day across the range 0 to -100 cm,

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Biogeochemistry, 122 (2-3), 395-408. DOI : 10.1007/s10533-014-0048-1

  Version définitive du manuscrit publié dans / Final version of the manuscript published in : productivity, the sensitivity of the MQ model to BD is low. It resulted in very similar D S /D 0 values for the three BD values.

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	Manuscrit d'auteur / Author Manuscript	which allows gas
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Comment citer ce document : Rabot, E., Cousin, I.,

Hénault, C. (2015)

. A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space. Biogeochemistry, 122 (2-3), 395-408. DOI : 10.1007/s10533-014-0048-1

  Version définitive du manuscrit publié dans / Final version of the manuscript published in :

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	Manuscrit d'auteur / Author Manuscript
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, 395-408. DOI : 10.1007/s10533-014-0048-1

  In our case, a constant rise in N 2 O fluxes was modeled at the beginning of the wetting phase, instead of a peak occurring 2 or 3 days after rewetting.

		Version définitive du manuscrit publié dans / Final version of the manuscript published in :
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	Manuscrit d'auteur / Author Manuscript	refining of NOE simulation results.
	Manuscrit d'auteur / Author Manuscript
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			,
		395-408. DOI : 10.1007/s10533-014-0048-1

  Version définitive du manuscrit publié dans / Final version of the manuscript published in : ) taking into account N 2 O production and consumption by microorganisms as a function of time and soil moisture, and ii) considering that equilibrium between the gaseous and aqueous phases is probably not direct[START_REF] Stolk | Modelling the effect of aggregates on N 2 O emission from denitrification in an agricultural peat soil[END_REF].Del Grosso SJ, Parton WJ, Mosier AR, Ojima DS, Kulmala AE, Phongpan S (2000) General model for N 2 O and N 2 gas emissions from soils due to denitrification. Glob

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	Manuscrit d'auteur / Author Manuscript	the soil by: iBiogeochem Cycle 14:1045-1060 doi:10.1029/1999GB001225 Deng J, Zhou ZX, Zheng XH, Li CS (2013) Modeling impacts of fertilization alternatives on nitrous oxide and nitric oxide emissions from conventional vegetable fields in southeastern China. Atmos Environ 81:642-650 doi:10.1016/j.atmosenv.2013.09.046 Dobbie KE, McTaggart IP, Smith KA (1999) Nitrous oxide emissions from intensive agricultural systems: Variations between crops and seasons, key driving variables, and mean emission factors. J Geophys Res-Atmos 104:26891-26899 doi:10.1029/1999jd900378
		Groffman PM, Tiedje JM (1988) Denitrification hysteresis during wetting and drying cycles
	Manuscrit d'auteur / Author Manuscript	in soil. Soil Sci Soc Am J 52:1626-1629 Grundmann GL, Rolston DE (1987) A water function approximation to degree of anaerobiosis associated with denitrification. Soil Sci 144:437-441 doi:10.1097/00010694-198712000-00008 Hansen M, Clough TJ, Elberling B (2014) Flooding-induced N 2 O emission bursts controlled by pH and nitrate in agricultural soils. Soil Biol Biochem 69:17-24 doi:http://dx.doi.org/10.1016/j.soilbio.2013.10.031 Hansen S, Maehlum JE, Bakken LR (1993) N 2 O and CH 4 fluxes in soil influenced by fertilization and tractor traffic. Soil Biol Biochem 25:621-630
		doi:http://dx.doi.org/10.1016/0038-0717(93)90202-M
	Manuscrit d'auteur / Author Manuscript	Harrison-Kirk T, Beare MH, Meenken ED, Condron LM (2013) Soil organic matter and texture affect responses to dry/wet cycles: Effects on carbon dioxide and nitrous oxide emissions. Soil Biol Biochem 57:43-55 doi:http://dx.doi.org/10.1016/j.soilbio.2012.10.008 Heincke M, Kaupenjohann M (1999) Effects of soil solution on the dynamics of N 2 O emissions: A review. Nutr Cycl Agroecosyst 55:133-157 doi:10.1023/A:1009842011599
			15

Heinen M (2006a) Application of a widely used denitrification model to Dutch data sets. Geoderma 133:464-473 doi:10.1016/j.geoderma.2005.08.011

Table 1

 1 Models of soil gas diffusivity used in the study

	Tables
	Abbreviation	Model	Formula a
	B	Buckingham (1904) model

Table 2

 2 Water-filled pore space corresponding to the maximum simulated nitrous oxide flux, after 12, 24, 72, and 168 hours, for three bulk densities (BD)

	BD	12 h	24 h	72 h	168 h
	1.20	0.762	0.770	0.783	0.798
	1.30	0.760	0.767	0.780	0.794
	1.40	0.757	0.764	0.777	0.791

Table 3

 3 Root-mean-square error (RMSE) and mean error (ME) of the predicted nitrous oxide fluxes, depending on the soil gas diffusivity model used

		Total		Wetting phase	Drying phase
		RMSE	ME	RMSE	ME	RMSE	ME
	Buckingham (1904)	33.30	8.90	5.70	0.20	41.20	13.60
	Deepagoda et al. (2011)	11.50	0.10	4.90	-1.30	13.80	0.80

Acknowledgements

We are grateful to F. Lafolie for his help with the VSoil Platform functioning. This work was supported by a Conseil Général du Loiret grant, and by the Labex VOLTAIRE (ANR-10-LABX-100-01).

Comment citer ce document : Rabot, E., Cousin, I., Hénault, C. (2015). A modeling approach of the relationship between nitrous oxide fluxes from soils and the water-filled pore space. Biogeochemistry, 122 (2-3)