Yanyan Yuan
email: yanyan.yuan@upmc.fr

Karine Le Guen

Jean-Michel André

Zhanshan Wang

Haochuan Li

Jingtao Zhu

Christian Mény

Angelo Giglia

Stefano Nannarone

Philippe Jonnard

Co/Mo2C multilayer as x-ray mirror: optical and thermal performances

Keywords: Co/Mo 2 C multilayer, x-ray mirror, standing wave

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Introduction

Periodic multilayer mirrors systems play an important role as optical components in the x-ray and extreme ultraviolet (EUV) spectral ranges for applications such as space telescopes, x-ray microscopes, EUV photolithography and synchrotron radiation beamlines [1][2][3][4]. Among them, Co-based multilayer mirrors could achieve high reflectivity, for example the Co/Mg multilayer has reflectivity higher than 50% at 25 nm wavelength at the angle of 45° [5,6]. In order to meet the needs of light sources working in the soft x-ray range, the Co/Mo 2 C multilayer is proposed. Its theoretical reflectivity is 45% at 778 eV close to the Co L3 absorption edge.

In addition, it has been reported that Mo 2 C layer was inserted into the Mo/Si multiyear as barrier layer to improve its thermal stability up to 600°C [7]. Recently the optical properties of the B 4 C/Mo 2 C multilayer have been studied [8] and have given evidence of abrupt interfaces with respect to the B 4 C/Mo multilayer where interlayers were detected. The standard enthalpies of formation of α-Mo 2 C compound was found to be ΔHf o (298.15 K) = -(6.37 ± 0.73) kcal.mol -1 [9]. This indicates that Mo 2 C possesses a good thermal stability and is a good barrier candidate in the multilayer stacks.

We characterize the optical performance of Co/Mo 2 C multilayer with the combination of three methods: (1) grazing incidence x-ray reflectometry (GIXR) at 0.154 nm to determine the structural parameters of multilayer; (2) soft x-ray reflectometry (SXR) at 1.59 nm and 1.33 nm, i.e. close to and far from the Co L3 absorption edge, to investigate the optical performance; (3) enhanced fluorescence by x-ray standing wave (EFXSW) to confirm the usefulness of the stack model. The value of the EUV optical index of nano-films in the vicinity of the absorption edges of the components is well known to have a large uncertainty. In fact, its accurate determination is required in order to calculate the optical performance of various optical films such as the proposed Co/Mo 2 C one. Thus, in addition to studying the optical performance of Co/Mo 2 C multilayers in both hard and soft x-ray regions, we show in the present work that it is possible to determine the optical index (n-ik) of a Co nanofilm in the Co/Mo 2 C multilayer system near the Co L3 edge by combining these three methods. While x-ray reflectometry is a well-established technique to determine the characteristics (thickness, density, optical index) of thin films [6], EFXSW in the soft-x-ray range is only at its early stages compared to hard-x-ray SW [10].

Recently some of us have developed a model based on the emission of a radiating dipole embedded in a multilayer structure to describe the EFXSW [11]. This model will be used in this work.

Sample fabrication and preparation

The Co/Mo 2 C multilayers were prepared by direct-current magnetron sputtering method. The substrates were sliced and polished Si (100) wafers, with surface roughness of 0.4 nm rms. The based pressure was 10 -5 Pa before deposition. The sputtering gas was argon (99.999% purity) at a constant working pressure 0.1 Pa. The powers applied to sputtering target were 40 W and 60 W for Co and Mo 2 C, respectively. The aimed period was equal to 4.1 nm and ratio of the Mo 2 C thickness to the period, known as a Γ ratio, was 0.36, resulting in Co and Mo 2 C thickness of 2.6 nm and 1.5 nm, respectively. Six samples with an area of 20 x 20 mm 2 were deposited separately on the Si wafer in the same conditions.

From one sample to another a small variation of the period can exist. The bi-layer number for each sample was 30. A 3.5 nm thick B 4 C capping layer was deposited onto the top to prevent oxidation. To evaluate the thermal behaviour of Co/Mo 2 C multilayer, five samples were annealed at the temperature of 200°C, 300°C, 400°C, 500°C and 600°C for 1 h in a furnace with a base pressure of 3.0×10 -4 Pa, respectively. After annealing, the samples were cooled down to the room temperature naturally.

Results and discussion

X-ray reflectivity measurements

Reflectivity measurements were carried out in both hard and soft x-ray regions. GIXR was performed using the Cu Kα emission line (0.154 nm, 8048 eV) while reflectivity curves at the Cu Lα emission line (1.33 nm, 930 eV), close to the application energy but far enough from the Co L3 edge, were measured with the MONOX apparatus [12]. The fitting procedure of the GIXR curves were performed with Bede Refs software (genetic algorithm). The multilayer structure model is substrate/[Co/Mo 2 C] 30 /B 4 C with layer thicknesses and their interface roughness variable in the fitting procedure [13]. The fit can provide the value of the structural parameters (thickness and roughness) of the layers while measurements at 1.33 nm allow checking and refining these values. SXR measurements in the Co L3 region (1.59 nm, around 778 eV) were performed at the BEAR beamline [START_REF] Nannarone | AIP Conf. Proc[END_REF] at the Elettra synchrotron radiation centre using s-polarized light. The photon energy was calibrated by x-ray photoemission spectroscopy using as a reference the Au 4f 5/2 binding energy of 87.6 eV. Since in the vicinity of Co L3 absorption edge the refractive index of the Co nanofilm may be strongly modified with respect to the tabulated bulk value, the real and imaginary parts of the Co refraction index have been considered as variables in the SXR fitting.

GIXR curves of as-deposited and annealed from 200 to 500°C are presented in Fig. 1. Four well-defined Bragg peaks are observed in the probed range. There is no significant change of the Bragg peaks between room temperature and 400°C, which indicates that the Co/Mo 2 C multilayer is stable up to 400°C. The intensity of the 4 th Bragg peak is low and varies, especially in the high annealing temperature range. At 500°C there is no more 4 th Bragg peak. Structural parameters such as the period and interfacial roughness, deduced from the fitting of the GIXR curves, are listed in Table 1. These fits were done using the bi-layer model, by considering only Co and Mo 2 C layers in the stack.

The measured periods are in good agreement with the aimed value of 4.10 nm but vary slightly from one sample to another (see the column before annealing) because the samples have been prepared separately. The roughness of Mo 2 C layers is small, around 0.25 nm, and independent of the annealing temperature. The fitted value of the roughness of Co layer fluctuates largely with the annealing temperature between 0.3 and 0.8 nm, which is considered to be large with respect to the thickness of the Co layer 2.60 nm. This means that Co-on-Mo 2 C and Mo 2 C-on-Co interfaces are asymmetrical. This asymmetry has also been reported in Co/Mg and Mo/Si systems [START_REF] Le Guen | [END_REF][16][17][18].

To confirm the description of each layer (thickness and roughness), reflectivity measurements around the first Bragg peak for samples annealed from 200 to 600°C temperatures were performed at 1.33 nm and are presented in Fig. 2. It can be noticed that the maximum position varies to some extent with the annealing temperatures, as has already been observed in the hard x-ray range, Fig. 1. Within the experimental uncertainty, the values of period and roughness deduced from the fit of the curves obtained at 1.33 nm are in agreement with those from the curves measured at 0.154 nm.

Fig. 3 shows the SXR curves measured at 1.59 nm for all the samples up to the fourth Bragg peak. The photon energies are chosen according to the maximum of the photon energy scan measured at 11°, see reference [START_REF] Yuan | Proc, SPIE[END_REF], and change slightly from one sample to another. The thermal stability of the multilayer is good because the reflectance at the first Bragg peak goes from about to 0.25 for the as-deposited sample to about 0.20 for the sample annealed at 600°C. In Fig. 3, the reflectivity curves are presented on a logarithmic scale. It can be seen that the difference between samples in terms of Bragg peak reflectivity and position increases with the grazing angle. Reflectivity of the fourth Bragg peak for all samples is less than 0.1%. In addition, except for the first peak, the others three Bragg peaks are surrounded by shoulders. This phenomenon is due to some contribution of the diffuse scattering. This was checked on one sample: in the same experimental condition, we used a detector with a smaller angular acceptance than the one to measure the sample annealed at 200°C and obtained the reflectivity curve without shoulders (not shown).

The structural parameters of the stacks are taken from the fits of the reflectivity curves (both at 0.154 and 1.33 nm). The The corresponding reflectivity curves and fit results are presented in Fig. 4 for the as-deposited and 600°C-annealed samples. The variations of optical indices n and k of Co with respect to the CXRO database [20] are listed in Table 2.

As can be seen, the imaginary part k for both samples has to be modified significantly to obtain a good agreement, while the real part n is almost equal to the value from the CXRO database and needs only to be adjusted slightly. The same has been done for the reflectivity curve of the 200°C-annealed sample. This leads to a 33% reduction of the imaginary part of the Co index, see Table 2. This means that the absorption in Co layers is much smaller than expected from the tables. Indeed it can be seen in Fig. 5 that the database value does not take into account the fine structure of the absorption coefficient in the vicinity of the Co L2,3 edge; in the database the absorption profile is represented by a single jump and the L2 edge does not exist. It is surprising to see that the imaginary part of the index deduced from the absorption experiment [21] should be higher than that from the database while in our analysis it is the contrary. However, the experimental curve in Fig. 5 is obtained for bulk Co and is probably not fully representative of Co nanofilm owing to some possible change of density or of chemical state if some intermixing exists with the Mo 2 C layers. Let us note also, that a slight error in the photon energy calibration can lead to very a different imaginary part of the Co index. 2).

Enhanced Fluorescence by XSW

EFXSW is based on the system of standing waves obtained within a periodic multilayer structure in the regime of Bragg diffraction. The peaks of electric field intensity can be localized in the regions of interest of the multilayer structure by adjusting the grazing angle of the incident excitation radiation. This radiation can give rise to fluorescence radiation coming mainly from the regions of the intensity peaks of the excitation radiation. This kind of experiment can be carried out with different geometries. In the present work we have adopted the so-called de Boer configuration [START_REF] De Boer | [END_REF] where only the incident excitation radiation undergoes Bragg diffraction. In our experiment the excitation radiation is By means of the model given in Ref. [11], we have fitted the EFXSW curves using a bi-layer model as for the reflectivity fitting. Fig. 7 shows the results: for the 200°C-annealed sample, Fig. 7a, using the tabulated value of the Co refractive index, does not allow us to fit the experimental curve while using the tabulated value of the real part of the refractive index and 25% of the tabulated value of the imaginary part allows us to obtain an agreement provided one smoothes the theoretical results to take into account the aperture of the detector. This analysis is in agreement with the results of the reflectivity measurements. The same fitting procedure was performed with the 600°C-annealed sample, Fig. 7b, and once again the best fit, in agreement with the results of the reflectivity measurements, is obtained when 40% of the tabulated value of the imaginary part of the Co optical index is used. Let us note that the simulation for the 600°C annealed sample seems better than the one for the 200°C annealed sample. This is probably due to the fact the simulations are made by considering the bi-layer model without interfacial mixing as also suggested in section 3.1. Actually, formation of an interfacial compound could be considered as one reason for the variation of the imaginary part of Co upon annealing (see Table 2).

Conclusion

The optical properties of Co/Mo 2 C multilayers are studied by the combination of hard and soft x-ray techniques, x-ray reflectivity measurements in the hard and soft x-ray ranges, and enhanced fluorescence by x-ray standing waves. The optical performance of the system depends a little on the annealing temperature up to 600°C showing the good thermal stability of the Co/Mo 2 C multilayer: the reflectivity value in the soft x-ray range at a grazing angle of 11° is 25% for the as-deposited sample and is still 20% after 600°C annealing temperature. The values of the structural parameters of the stack derived from the fit of the XRR curves (both at 0.154 and 1.33 nm) show a good agreement between experimental and aimed periods, and a limited variation of period and interfacial roughness after annealing. The convergence between the analysis by reflectivity and by fluorescence, requiring the use of the same modified optical indices of the Co layers, confirms the description of stack. Let us note that the thermal stability of the first layers, including the B 4 C capping layer, of the structure was confirmed by XPS induced by XSW [START_REF] Giglia | Proc SPIE[END_REF].

Figure 1

 1 Figure 1 Reflectivity curves measured at 0.154 nm of Co/Mo 2 C multilayers annealed at different temperatures. Data of the samples annealed at 200, 300, 400 and 500°C are shifted vertically for the sake of clarity.

Figure 2

 2 Figure 2 Reflectivity curves measured at 1.33 nm (Cu Lα emission) of Co/Mo 2 C multilayer annealed from 200 to 600°C.

Figure 3

 3 Figure 3 Reflectivity curves at 1.59 nm as a function of the annealing temperature.

  SXR curves are fitted by adjusting the optical indices, real and imaginary parts, of cobalt considering only a bi-layer system, i.e. Co and Mo 2 C, without interlayers. The optical constants of the other materials Mo 2 C and B 4 C are kept fixed to their tabulated values [20] since these materials have no absorption edge in this spectral region.

Figure 4

 4 Figure 4Comparison between soft x-ray reflectivity curves (black line) and fit (red line) using the parameters from XRR fit for asdeposited and 600°C annealed sample.

Figure 5 .

 5 Photon energy (eV)

  around 778.3 eV for the 200°C annealed sample and 777.6 eV for the 600°C annealed sample. With a SDD detector [23], we record the intensity of the Co Lα emission line at 776.4 eV versus the grazing angle in the range 8-13° around the first Bragg peak (11°). The results are displayed in Fig.6. Curves of the samples annealed at 200 and 600°C are obtained at different incident photon energies and thus show different intensities. Indeed for the sample annealed at 600°C the absorption coefficient is low, as indicated by the vertical bars in Fig.5, thus leading to a low generation of Co L3 ionizations and consequently a lower number of Co Lα transitions. Another effect is the small angular shift of the first Bragg peak, as indicated by the vertical bars in Fig.6, leading to a small angular shift of the XSW curves.

Figure 6

 6 Figure 6 EFXWS curve of the samples annealed at 200 and 600°C versus the grazing angle; the recorded radiation is the Co Lα line. Full red circles: sample annealed at 200°C; open blue squares: sample annealed at 600°C. The vertical bars indicate the position of the first Bragg peak. Red bar: sample annealed at 200°C; blue bar: sample annealed at 600°C.

Figure 7

 7 Figure 7 Comparison of the experimental (points) and simulated EFXSW curves (lines) for the samples annealed at 200°C (a) and 600°C (b); simulation with tabulated optical index of Co (blue dotted line); simulations with the imaginary part deduced from reflectivity measurements, without smoothing (black dashed line) and smoothing (black solid line).

Table 1 .

 1 Structural parameters extracted from the fit of the GIXR curves measured at 0.154 nm.

		Period d (nm)	Period d (nm)	Thickness (nm)		Roughness (nm)
	Sample
		before annealing	afetr annealing	B 4 C	B 4 C	Co	Mo 2 C
	As-deposited	4.20	-	3.60	0.56	0.32	0.26
	200°C	4.08	4.08	3.62	0.55	0.40	0.25
	300°C	4.17	4.18	3.31	0.56	0.82	0.26
	400°C	4.15	4.12	3.92	0.81	0.33	0.21
	500°C	4.12	4.09	3.36	0.62	0.71	0.22
	600°C	4.17	4.13	2.89	0.54	0.38	0.22

Table 2 .

 2 Variations of the optical complex index n-ik of Co, with respect to the CXRO database required in order to fit the soft x-ray reflectivity curves obtained around 778 eV.

	Sample	n (% of tabulated value)	k (% of tabulated value)
	As-deposited	99.96	24.0
	200°C	99.98	33.0
	600°C	100.0	40.0

Acknowledgments

This work was performed in the framework of the international ANR-NSFC COBMUL project (ANR #10-INTB-902-01 and NSFC #11061130549). Dr. F. Bridou from Institut d'Optique in Palaiseau is thanked for fruitful discussions regarding XSW.


Enrico Marchetto
email: enrico.marchetto@ircam.fr

Geoffroy Peeters
email: geoffroy.peeters@ircam.fr

A SET OF AUDIO FEATURES FOR THE MORPHOLOGICAL DESCRIPTION OF VOCAL IMITATIONS

In our current project, vocal signal has to be used to drive sound synthesis. In order to study the mapping between voice and synthesis parameters, the inverse problem is first studied. A set of reference synthesizer sounds have been created and each sound has been imitated by a large number of people. Each reference synthesizer sound belongs to one of the six following morphological categories: "up", "down", "up/down", "impulse", "repetition", "stable". The goal of this paper is to study the automatic estimation of these morphological categories from the vocal imitations. We propose three approaches for this. A base-line system is first introduced. It uses standard audio descriptors as inputs for a continuous Hidden Markov Model (HMM) and provides an accuracy of 55.1%. To improve this, we propose a set of slope descriptors which, converted into symbols, are used as input for a discrete HMM. This system reaches 70.8% accuracy. The recognition performance has been further increased by developing specific compact audio descriptors that directly highlight the morphological aspects of sounds instead of relying on HMM. This system allows reaching the highest accuracy: 83.6%.

INTRODUCTION 1.Using vocal imitations as sketches

In typical design approaches (whether in architecture, products, etc.), the very first step is often a "sketch", that is a simple graphical representation of the target. This initial sketch is a useful tool to enhance communications between designers and stakeholders. In the case of sound design, professionals often use vocal imitations to add more detail to the sound description [START_REF] Lemaitre | On the effectiveness of vocal imitations and verbal descriptions of sounds[END_REF], trying to transmit to their interlocutor the main cues of their sound idea [START_REF] Lemaitre | Do vocal imitations enable the identification of the imitated sounds?[END_REF]. "Vocal imitations" can therefore be considered as the sound design "sketches".

The goal of our current project, the SkAT-VG project, is to expand this vocal imitation idea toward a better sound design tool [START_REF] Lemaitre | Vocal imitations and the identification of sound events[END_REF][START_REF] Cartwright | VocalSketch: Vocally imitating audio concepts[END_REF]. The resulting device should be able to translate a vocal (and gestural) cue into a novel and pertinent synthetic sound. The interactive sound design begins with a phase in which the user produces an imitation and the system provides some draft sounds; in a second phase the latter are then interactively refined, again using voice and gestures. This paper addresses the task of automatic recognition of imitation, presenting different strategies to do that.

The recognition task and imitation dataset

In order to study the mapping between voice and synthesis parameters, the inverse problem is first studied. A set of reference synthesizer sounds (stimuli) have been created and each sound has been imitated by a large number of people. Each reference synthesizer sound belongs to one of the six following morphological categories: up, down, up/down, stable, impulse, repetition. Each of the categories is represented by two reference sounds, and each reference sound is imitated by 50 subjects.

The six categories are abstract and are defined as:

Up: Sounds which have an increasing profile in terms of spectral content and/or loudness, thus expressing a kind of rising;

Down: Opposite of the previous one, these stimuli present a downward profile;

Up/down: Sounds with non-monotonic profiles: can be described as combination of the previous two, the stimuli profile moves upward and then downward;

Impulse: This class contains sounds with very short duration and sharp attach and decay;

Repetition: Sounds which are composed by the repetition, with varied rhythmic patterns, of short and almost impulsive ones;

Stable: Longer sounds, with almost flat pitch and loudness profiles.

The goal of this paper is to study the automatic estimation of these six morphological categories from the vocal imitations of their reference sounds.

The study of the perception of vocal imitations (how do people choose their strategy to imitate a sound, how consistent are the imitations and how these imitations are recognized) have already been the subject of the paper [START_REF] Lemaitre | On the effectiveness of vocal imitations and verbal descriptions of sounds[END_REF] and will be the subject of further papers in the framework of the SkAT-VG project.

Related works

A well-known approach to allow time series recognition is the extraction of low level signal descriptors, which are then modeled using Hidden Markov Models (HMM) [START_REF] Rabiner | A tutorial on hidden Markov models and selected applications in speech recognition[END_REF][START_REF] Furui | Digital Speech Processing, Synthesis, and Recognition[END_REF]. This approach will be used to create our base-line system. In speech recognition [START_REF] Rabiner | Fundamentals of speech recognition[END_REF][START_REF] Juang | Automatic speech recognition-a brief history of the technology development[END_REF][START_REF] Benzeghiba | Automatic speech recognition and speech variability: A review[END_REF], the best results are obtained combing language models (based on grammars) and acoustical models [START_REF] Saon | Large-vocabulary continuous speech recognition systems: A look at some recent advances[END_REF]. Unfortunately, abstract sounds are not bound to any grammar and a language model cannot be used in our case.

Another closely related topic is the recognition of "words for sounds", such as onomatopoeias. Proposed approaches to this problem, linked to speech recognition, still rely on phonemes [START_REF] Ishihara | Automatic sound-imitation word recognition from environmental sounds focusing on ambiguity problem in determining phonemes[END_REF] or lexical cues [START_REF] Sundaram | Vector-based representation and clustering of audio using onomatopoeia words[END_REF]. There are also examples of features clustering and modeling [START_REF] Sundaram | Classification of sound clips by two schemes: Using onomatopoeia and semantic labels[END_REF], which are related to our base-line system and to the first methodology that we propose. Description of sounds in terms of morphological profiles has been initially proposed by P. Schaeffer works [START_REF] Schaeffer | Trait des objets musicaux[END_REF]. The automatic estimation of these profiles for abstract sounds has been previously studied by [START_REF] Ricard | Morphological sound description: Computational model and usability evaluation[END_REF] and [START_REF] Peeters | Sound indexing using morphological description[END_REF] which also propose dedicated descriptors.

AUTOMATIC RECOGNITION OF VOCAL IMITATIONS

In this section, we propose three methods to automatically recognize the six morphological categories indicated in sec. 1.2.

• The first method relies on the extraction of a set of instantaneous audio features di(k), i ∈ [1, ..., I] over time k. Each category is modeled by its own hidden Markov model.

• The second method uses the same instantaneous audio features di(k), which are quantified into symbols to be used as input for discrete hidden Markov models.

• The third method does not rely at all on hidden Markov models, but models the time evolution directly in the audio features. We therefore denote them by "morphological audio descriptors" as in Peeters et al., 2010 [17].

Before applying one of these methods, we first detect the non-silent regions (named "active regions" in the following) using standard methods such as [START_REF] Huijbregts | Robust speech/non-speech classification in heterogeneous multimedia content[END_REF][START_REF] Ito | Zero-crossing measurements for analysis and recognition of speech sounds[END_REF][START_REF] Ramırez | Efficient voice activity detection algorithms using long-term speech information[END_REF]. This leads to a set of N Active Region(s) A = {[br, fr] : r ∈ [1, ..., N ]} where br and fr are their starting and ending time.

Base-line system using Local Trend descriptors

We extract 6 instantaneous audio features di(k), i ∈ [1, ..., 6] where k denotes the time frame number. In order to smooth the variation of di(k) over time, a low-pass filter is applied (zerophase filter). The first 4 are standard audio features: the spectral centroid, spectral spread, sprectral rolloff and the pitch. They are computed using standard techniques [START_REF] Peeters | A large set of audio features for sound description (similarity and classification) in the Cuidado project[END_REF] and using the Swipep algorithm [START_REF] Camacho | A sawtooth waveform inspired pitch estimator for speech and music[END_REF] for the pitch 1 .

Given that one of the important specificities of the morphological categories relates to the temporal evolution of the spectrum content, we also propose two new audio features: "LPC-min" and "Spectral-peak-min". The novel features are defined as follows:

LPC-min: A one-pole preemphasis filter is applied. Low-order LPC is used to estimate the position of the single most prominent formant 2 . The prediction coefficients are converted into formant frequencies Fρ, where ρ is the formant index [START_REF] Mccandless | An algorithm for automatic formant extraction using linear prediction spectra[END_REF][START_REF] Markel | Linear Prediction of Speech[END_REF]. Only the frequencies Fρ > 20Hz are kept. The LPC-min value is measured in Hz, and is defined as the minimum Fρ.

Spectral-peak-min: From the energy spectrum (computed as the square DFT) we select the 5 most important frequency bins. The Spectral-peak-min is defined as the lowest frequency among these 5 frequencies; it is thus measured in Hz. Comparison between LPC-min (bold line), spectral centroid (dashed bold line) and Spectral-peak-min (thin line); pitch is not reported because perfectly matches LPC-min. This vocal imitation is harmonic but presents also noise in higher frequencies. LPC-min is clearly detecting the pitch; Spectral-peak-min is following the energy of noise, with better accuracy than centroid.

It should be pointed out that these descriptors could have overlapping meanings, and are used together to reinforce the information. Spectral centroid and LPC-min could be similar on noisy sounds, but when a strong formant is present the centroid may loose meaning compared to LPC-min (Fig. 1). Spectral centroid and Spectral-peak-min could also be similar on noisy signal, but when a strong partial exists at the pitch the Spectral-peak-min is better at measuring it (Fig. 2).

The six categories to be recognized relate to evolution of values over time, hence we compute the derivative of each di(k). The derivative d i (k) is found by linear regression on the local values (5 points on the left and 5 points on the right of k). We finally normalize their range to [-1, 1] using arctangent mapping: Gaussians and diagonal covariance matrix. The HMMs are created in a supervised way. To understand this, let's consider the case of the up/down category. This one can be represented as the transition from a state "silent" to state "up" to state "down" and back to state "silence". In the same spirit the up category can be represented as the succession of states "silence", "up", "silence". We therefore define 4 states: "silence", "up", "down", "stable".

d i (k) = 2/π arctan(d i (k)).
The training of the six HMMs is done in two stages:

• We first train the observation probabilities. This is done independently of Mc. Indeed, given that a state (such as "up" in the above example) can be shared by different Mc, we train the emission probabilities using descriptors from the up, down and stable classes, plus an added silent class.

• The transition probabilities are trained for each category.

Considering that the number of self-transition s(t + 1) = s(t) is much larger than the non-self ones s(t+1) = s(t), we found the training of the last difficult. In order to circumvent this, we decided to decimate over time the descriptors time series by a factor of 3. This allowed to increase the performances. Also, rather counterintuitively, better results were obtained by forcing the HMM training to not update the emission probabilities mixtures (thus only updating the transition matrix).

Global Trend descriptors

The same 6 audio features of sec. 2.1 are used as underlying time series for the Global Trend descriptors: spectral centroid, spectral spread, spectral rolloff, pitch, LPC-min and Spectral-peak-min. Instead of using them directly as input to a continuous HMM, we convert them to symbols.

For each descriptor di(k) and each active region r we apply the following procedure: • We compute the linear regression over the region r. We denote by α r i its angular coefficient and by r i its prediction error.

• If r i is larger than a specific threshold K13 , r is split into two regions at the position of the maximum value of di(k) and a two-piece minimum least-square linear regression is computed. We denote by α r1 i and α r2 i the corresponding angular coefficients. This process will allow us to discriminate between monotonic classes (such as up or down) and up/down.

• The quantized time serie ei(k) corresponding to di(k) is then built. It has the value ei(k) = 0 for k corresponding to silent part, ei(k) = α r i for k corresponding to region r (or α r1 i for region r1 and α r2 i for region r2). We then convert the values of ei(k) to symbols using the following rules:

e i (k) = 8 > > < > > : 1 if |ei(k)| ≤ 10 -7 ; 2 if 10 -7 < |ei(k)| ≤ 0.1; 3 if ei(k) > 0.1; 4 if ei(k) < -0.1. (1)
The four symbols {1,2,3,4} express the overall condition of the time serie, respectively: silence, stable (small angular coefficient), upward (large positive angular coefficient), downward (large negative angular coefficient).

As a final step, the descriptors series e i (k) are decimated over time by taking one value every 10 frames. It should be noted that we have chosen to not apply any antialiasing process, since we have found by experiment that active regions shorter than 10 samples usually correspond to errors. In Fig. 4 we illustrate the Global Trend descriptors.

Training. Since the time series e i (k) are symbols (unordered values) we model them using discrete hidden Markov models. Each descriptor i is modeled by its own HMM Mc,i.

For a given class c and a given descriptor i we denote by Ec,i its emission matrix (with size S × O, where S is the number of hidden states and O the number of symbols), by Tc,i the transition matrix (with sizes S × S) and by Sc,i(k) the decoded states at frame k.

In order to train the emission matrix for class c and descriptor i, we concatenate all descriptors of the sounds belonging to c into a matrix Dc. Each row of Dc corresponds to a given descriptor i.

We define a function F that normalizes an input matrix such that its rows elements sum up to 1.

The training algorithm is the following:

1. Set the initial value for the emission matrix to Ec,i = F(I + 0.05), where I is the diagonal identity matrix. This almost associates each state to a single symbol, but does not exclude the possibility for each state to emit each possible symbol.

2. Exploiting the previous association, estimate Tc,i by accumulating all the emissions transitions found in row i of Dc into the matrix T . Obtain the transition matrix for i as Tc,i = F(T ).

Use

Tc,i and Ec,i to estimate the hidden states Sc,i(k) by Viterbi decoding.

4. Re-estimate Ec,i by counting the number of times each state generates each emission, and again normalizing by F.

In principle, the re-estimation procedure (points 2.-4.) can be iterated, but early experiments showed little performance improvements.

Classification. In order to classify an unknown sound represented by its time series matrix D * , we decode each row i of D * using a specific class model Mc,i and the Viterbi decoding algorithm. Each model Mc,i provides a likelihood lc,i. The final class label is found as x = argmax c∈ [START_REF] Lemaitre | On the effectiveness of vocal imitations and verbal descriptions of sounds[END_REF][START_REF] Rabiner | A tutorial on hidden Markov models and selected applications in speech recognition[END_REF] P i lc,i.

Morphological descriptors

We introduce here a new set of morphological descriptors. These are crafted to compactly describe the structure of the signals present in the dataset. Each audio file is represented by these descriptors using a vector with 8 components:

• Ψ1, Ψ2 and Ψ3 measure repetitions or patterns in the serie;

• Ψ4, Ψ5 and Ψ6 describe the active region(s);

• Ψ7 and Ψ8 are related to the global signal trend.

The descriptors embed directly the time evolution of the signal. Because of this they can be used for classification without requiring the use of HMM for temporal modeling. Moreover the Ψi For two consecutive active regions, r and r + 1, we define the duty-cycle of r as ur = (fr -br)/(b (r+1) -br) (see Fig. 6). In this, we assume that every active region is followed by a silent one. When adjacent regions are in the same state (silent or nonsilent) we simply merge them, thus enforcing the active/non-active alternance. The first two pattern descriptors Ψ1 and Ψ2 are defined as the mean and the standard deviation of non-silent regions dutycycles ur, r ∈ [1, N ]. impulse and repetition classes are expected to have small values of Ψ1. In the opposite, the other classes (stable, up, down, up/down) will have a single long active region with a large value of Ψ1. Ψ2 measures the regularity of the repeated patterns. In the case of a single active region, Ψ2 = 0.

We define the "importance" ir of an active region as the product between its length lr and its mean loudness mr (over the active region duration). Both lr and mr are normalized in the range [0, 1] for each signal (the value of 1 is assigned to the longest and the loudest regions respectively).

The third descriptor Ψ3 is the number of active regions which have Importance ir above a threshold K2. A value of K2 = 0.25 is chosen in order to correspond to the product of half-range normalized values of lr and mr. Ψ3 is computed as:

Ψ3 = arctan (card ({ir such that ir > K2}) -1) (π/2) (2)
The threshold on ir allows the rejection of very short active regions, or with very low loudness level. For single-region signals Φ3 is equal to 0, while for signals with three or more regions (typical of repetition category) Ψ3 is above 0.7.

Descriptors Ψ4 and Ψ5 focus on the main region R only, that is the non-silent region with highest importance iR.

The Ψ4 descriptor is the duty cycle of the main region defined on the whole signal: Ψ4 = (fR -bR)/N , where bR and fR are the start and the end of R and N is the total signal length. Ψ4 is expected to discriminate impulse and stable classes.

The descriptor Ψ5 is computed on the loudness time serie in the main region dL(k), k ∈ [bR, fR], which has length lR. The original serie and its half-length circularly-shifted copy are used:

Ψ5 = l R X k=1 » dL(k) -dL " (k + lR 2 ) mod lR «-2 (3)
Ψ5 is thus the energy of the difference between dL(k) and its shifted copy. The descriptor is then normalized in the [0, 1] range using arctan, as for Ψ3. Ψ5 improves the discrimination between classes which have flat or non-flat evolution, such as up/down vs stable. The descriptor Ψ6 is defined as the sum of the active regions lengths lr, minus a constant γ. Ψ6 is then normalized by arctangent, such as in ( 2), and γ is optimized to have the "shift" of the arctangent function improving the discrimination between impulse and stable (or repetition) classes.

The Ψ7 and Ψ8 morphological descriptors have been developed to measure the slope of the signal. The aim is to evaluate the slope between the beginning and the middle, and between the middle and the end, of a given time serie.

Spectral-peak-min is taken as an underlying descriptor: only its values in the main region R are considered, deleting those below 40Hz as they are unreliable. To overcome boundary effects, Spectral-peak-min is observed within three windows of 11 samples taken at the beginning, the middle and the end of the region (see Fig. 7). In each window, the Spectral-peak-min is weighted by a triangular window function and then the average is computed. This leads to three mean values: V = [v1, v2, v3]. The trend descriptors Ψ7 and Ψ8 are found as:

Ψ7 = v2 -v1 v1 Ψ8 = v3 -v2 v2 (4)
and normalized using again the arctan function. Local windows are used in order to smooth the signal, possibly generated by noisy time series, and the triangular functions give more importance to the central part of the window. Ψ7 and Ψ8 measure the evolution in time of the signal: they discriminate between up, down and up/down.

EVALUATION

Description of the train and test sets

The dataset used in this paper comes from a perceptual experiment. In this experiment, 50 French subjects were asked to imitate sounds. For each of the 6 classes described in Sec. 1.2, two reference sounds have been selected. After listening to one of the reference sounds (without knowing its class), subjects were asked to imitate it using only voice (VO) or using voice and gesture (VG).

In each case, the subject could do several trials. In theory, each class is therefore represented by 1000 audio examples: 2 (reference sounds) times 50 (number of subjects) times 2 (VO and VG) times the number of trials of each subject (ranging from 1 to 5). In practice, considering the variability of the number of trials of each subject, the number of audio examples is lower. We represent the number of audio examples per class in Fig. 8. The average number of imitations provided by each subject is about 40, with large variations as showed in Fig. 9. On average, every subject provided 1.6 trials per stimulus (instead of 5).

The total size of our test-set is 1941 audio files, rather equally distributed among the six categories (except stable, see Fig. 8). In the following experiments all the available data is exploited.

Comparison of the recognition methods

We have described three recognition methods in this paper:

Local Trend: the descriptors rely on local variations of the signal, and are modeled using continuous HMMs;

Global Trend: the main evolutions of the signal are measured by discretized descriptors, modeled using discrete HMMs;

Morphological: the descriptors directly represent both the signal shape and its time evolution; the recognition of classes by the Morphological descriptors relies on the k-Nearest Neighbor algorithm (see sec. 2.3).

The results are presented in Table 1. All the figures have been obtained using 5-folds crossvalidation, selecting train and test set in order to not have the same subject in both. Recall and precision values are given for each of the three methods and for each class. The mean recall and precision, and the overall accuracy, are given at the bottom of Table 1.

The Global Trend descriptors obtain an accuracy of 70.8%, a 28.5% improvement compared to the base-line system (Local Trend, 55.1%). The Morphological descriptors give the best performances, with 83.6% accuracy (51.7% improvement over baseline). Fig. 10 shows the values of accuracy obtained by the system when using different values for k. The best value of k = 5 has been selected for the presented results.

It is interesting to look at the results class-by-class. up and down classes are well recognized by all methods. There are instead classes for which Morphological descriptors are better, such as repetition. The opposite case also happens, as the recall for stable is better using Global Trend; for down the best recall is given by Local Trend, but with poor precision.

The overall conclusion which can be drawn is that Morphological descriptors have a better performance because they work rather well on all classes, giving comparable recall/precision. This is not the case for Local and Global Trend, which have instead one or more classes with particularly bad results.

Discussion of the results

The Local Trend method has good performances on the up, down and stable classes, but not on the remaining ones. It has been verified that up/down recordings are often recognized as down (which has in fact a low precision). A possible explanation for the confusion arises by observing the spectrograms of the recordings: it has been found that many subjects prepare the downward slope in down by first producing a rising profile (see Fig. 11). Moreover, while up/down is recognized as down, the confusion with up is less frequent: in up/down the downward phase is usually stronger, thus justifying the observations.

The global shapes of up, down and stable are well modeled. Classes impulse and repetition are instead problematic: the transition matrices of the HMMs do not succeed to capture the temporal cues of the signals, and this has a bad influence on classes which are defined relying on that.

The purpose of Global Trend methodology is to provide better modeling of the overall temporal evolution of the signal, hence avoiding these shortcomings. The quantization of the descriptors in four symbols has the effect of keeping only the most relevant information, and the decimation enforces the transition matrices to describe the temporal cues of the signals. Despite having still poor results on up/down, Global Trend outperforms Local exactly because it improves the recognition of impulse and repetition.

The Morphological descriptors have been designed to embed the main characteristics of the classes into a compact and effec- tive representation. Among their good performances, it should be pointed out the improved discrimination between down and up/down compared to the previous methods. However, the confusion matrix in Table 2 shows that the issue is still present. Similarly there is confusion between up and down. repetition is well recognized, thanks to the presence of the specific Ψ3 descriptor. Both impulse and stable are confused, even if not to a large extent, with up, down and up/down. This could be explained by the fact that the system identifies rising or falling cues even in the impulse and stable imitations, and provides a classification according to this. The following two panels are imitations of the stimulus: both begin with a rising pitch, followed by the expected lowering; these imitations are likely to be recognized as class up/down.

Discussion on the dataset

The dataset classes have already been introduced in Sec. 1.2. In the following we give details about the dataset definition which may have an impact on the recognition. The classes up, down, up/down and stable are all defined by their evolution in time; this is not the case for impulse and repetition, which are instead defined by their duration and rhythm, respectively. In other words, the stimuli are labeled according to different domains. Moreover up and down are semantically portions of up/down: it is thus likely to have confusion between these three classes.

There are several factors which lead to a strong intra-class variability. Each class is defined by 2 different reference sounds, and each of the 50 subjects provides many recordings. The imitations are done by non-experts: the same stimuli is thus imitated using different strategies, and sometimes the imitations contents can be conflicting.

There are, finally, some issues related to the content of the dataset, that is to the vocal imitations. The definition of the classes, although very clear, can not be translated straightforwardly into acoustic cues: there are examples in which the subject imitates a complex stimulus by rising the pitch and lowering the first formant (thus decreasing the spectral centroid). The imitation has thus ambiguous meaning because its descriptors will have opposite evolutions. Many recordings suffer from boundary effects: the imitator could begin to produce sounds during the preparation phase of the articulation, introducing spurious effects at the begin of the recording. Similar artifacts can also be spotted at the end of some sounds.

The recognition system therefore has to cope with all the exposed issues of the dataset. The descriptors have to provide the main cues of the signal even in case of noisy or unreliable underlying time series (loudness, spectral centroid, etc.). This situation motivates the use of different descriptors with similar meanings, in order to reinforce the extracted information.

CONCLUSION

A dataset has been compiled, in the context of the SkAT-VG project, in which a large number of subjects have imitated sounds which belong to six morphological categories.

We have presented three methodologies to automatically recognize these morphological categories.

Our base-line system uses Local Trend descriptors, which are designed to measure the local behavior of the time serie. The descriptors are then modeled by continuous hidden Markov models with 4 states. The system reached an accuracy of 55.1%. An improved approach is based on Global Trend descriptors, which express the evolution of the signal along its whole duration. This second set of descriptors is modeled by discrete hidden Markov models, using 4 states and 4 emitted symbols. The obtained accuracy is 70.8%. Our third approach for the automatic recognition is based on the Morphological descriptors, which are designed to give a compact representation of the time series evolution. These descriptors do not need temporal modeling, such as HMM, and have low dimensionality. The classification is thus done using the k-Nearest Neighbor algorithm. This system has provided the best recognition accuracy of 83.6%.

The automatic classification on the given dataset proved to be a non-trivial task, despite the apparently clear definition of the classes. The manual check of many recordings within the dataset has confirmed a degree of confusion between certain classes, due to objective spectrograms similarities. A notable example is the pair down and up/down. Moreover the dataset is made by imitations of reference sounds, and imitators use different strategies to render the same stimulus: this rises the intra-class variability.

The non-optimal recognitions results are in part justified by these findings.

The presented set of Morphological descriptors goes toward the characterization of sounds by their acoustic shape. Future work will involve the organization of the descriptors in a systematic topology, similarly to [START_REF] Schaeffer | Trait des objets musicaux[END_REF]; this may point out shortcomings of the proposed set. Adding new descriptors could hence encompass a broader set of signal categories.

The proposed Morphological descriptors could be applied to other datasets, with classes defined in different ways. The integration of the Morphological descriptors with other, more traditional, ones is another topic of future studies, fostering recognition accuracy in many contexts.

Figure 1 :

 1 Figure1: Comparison between LPC-min (dashed bold line), Spectral-peak-min (bold line), spectral centroid (dashed line) and pitch by Swipep (thin line). This vocal imitation is noisy with a stable formant around 2kHz. Swipep does not detect any pitch, giving unreliable information, and the spectral centroid is moved toward higher frequencies. Both LPC-min and Spectral-peak-min are instead detecting and following the formant.

Figure 2 :

 2 Figure 2:Comparison between LPC-min (bold line), spectral centroid (dashed bold line) and Spectral-peak-min (thin line); pitch is not reported because perfectly matches LPC-min. This vocal imitation is harmonic but presents also noise in higher frequencies. LPC-min is clearly detecting the pitch; Spectral-peak-min is following the energy of noise, with better accuracy than centroid.

  This completes the computation of the Local Trend descriptors, exemplified in Fig. 3. For each of the six categories c, we define a continuous hidden Markov model Mc. Each Mc represents the transition between

Figure 3 :

 3 Figure 3: Example of Local Trend descriptors on up/down imitation. Topmost panel is the signal spectrogram with spectral centroid (thin line) and Spectral-peak-min (bold line). The bottom panel shows the same two descriptors after Local Trend computation (scale is shifted for Spectral-peak-min for clarity).

Figure 4 :

 4 Figure 4: Example of Global Trend descriptors on up/down imitation. Topmost panel is the signal spectrogram with spectral centroid (thin line) and Spectral-peak-min (bold line). Middle panel shows the same two descriptors after Global Trend computation (scale is shifted for Spectral-peak-min for clarity). In the bottom panel the two descriptors are quantized into symbols and downsampled (once more Spectral-peak-min has been shifted).

Figure 5 :

 5 Figure 5: Computation of morphological descriptors.

Figure 6 :

 6 Figure6: Computation of descriptors Ψ1, Ψ2 and Ψ3 on a repetition imitation. The loudness profile is showed (bold line), along with threshold T (dashed line) and active region detection (thin line); mean loudness value mr (dashed bold line) is used to compute importance ir.

Figure 7 :Figure 8 :

 78 Figure 7: Computation of descriptors Ψ7 and Ψ8 on an up/down imitation. Spectral-peak-min is showed (thin line), with 3 windows centered at 1/5, 1/2 and 4/5 of its total length. Mean values vj (bold line) are used to find Ψ7 and Ψ8, which are proportional to the slopes (dashed bold line).

Figure 9 :

 9 Figure 9: Number of recordings per subject.

Figure 10 :

 10 Figure 10: Recognition accuracy in % (line and circles) as function of k value in k-NN. Results are averaged by 5 folds, and the ±1 standard deviation intervals are marked by ×.

Figure 11 :

 11 Figure 11: Example of imitations labeled as class down. Topmost panel is one of the two reference stimuli for down. The following two panels are imitations of the stimulus: both begin with a rising pitch, followed by the expected lowering; these imitations are likely to be recognized as class up/down.

Table 1 :

 1 Recognition results by different methods, averaged over the 5 crossvalidation folds.

	Methods	Local Trend Global Trend	Morphol.
	Measures	Rec. Prec. Rec. Prec. Rec. Prec.
	up	80.8 83.9 83.2	81.8	87.7 79.6
	down	88.5 43.9 76.2	76.3	71.5 73.7
	up/down	38.2 53.0 39.1	57.2	76.3 76.2
	impulse	25.3 54.1 60.3	79.1	91.5 91.9
	repetition 29.5 35.5 78.0	62.4	90.3 93.2
	stable	72.9 99.2 97.2	70.0	85.8 92.4
	Average	55.9 61.6 72.3	71.1	83.9 84.5
	Avg. Accuracy	55.1	70.8	83.6

Table 2 :

 2 Confusion matrix for the morphological descriptors.

	Classes	1	2	3	4	5	6
	up -1 292	20	13	2	2	4
	down -2	32	244	49	9	6	1
	up/down -3	15	47	273	11	6	6
	impulse -4	4	11	8	301	3	2
	repetition -5	9	7	6	5	300	5
	stable -6	16	3	11	0	5	213

We used the Swipep algorithm since it has state-of-the-art performances and is readily available on-line. Spectral centroid, spread and rolloff are computed using well-known

formulas.[START_REF] Lemaitre | Do vocal imitations enable the identification of the imitated sounds?[END_REF] Here the objective is not a full-fledged formants tracking, but a robust analysis of the energy location among frequencies, complementary to spectral centroid.

K 1 has been optimized by grid-search. We use a value of 3 • 10 3 .

ACKNOWLEDGMENTS

This work was supported by the 7th Framework Programme of the European Union (FP7-ICT-2013-C FET-Future Emerging Technologies) under grant agreement 618067. The audio dataset as well as the choice of the categories and the annotations used in this paper have been created by the Perception and Sound Design team of IRCAM. We are grateful to the reviewers and to S. Perry for their valuable contributions and corrections.


Aline Migné
email: migne@sb-roscoff.fr

Dominique Davoult
email: davoult@sb-roscoff.fr

Nicolas Spilmont
email: nicolas.spilmont@univ-lille1.fr

Vincent Ouisse
email: vincent.ouisse@ifremer.fr

Guy Boucher
email: boucher@mnhn.fr

Spatial and temporal variability of CO 2 fluxes at the sediment-air interface in a tidal flat of a temperate lagoon (Arcachon Bay, France)

Keywords: Intertidal sediment, Benthic metabolism, Primary production, Respiration, French Atlantic coast, Arcachon lagoon

teaching and research institutions in France or abroad, or from public or private research centers.

Spatial and temporal variability of CO2 fluxes at the sediment-air interface in a tidal flat of a temperate lagoon (arcachon bay, France)

Introduction

The metabolic balance of the coastal ocean appears to be a key part of the global carbon budget [START_REF] Muller-Karger | The importance of continental margins in the global carbon cycle[END_REF]. Within coastal areas, intertidal sediments inhabited by microalgae and seagrasses play an important role in both the production and the remineralization of organic matter [START_REF] Cahoon | The role of benthic microalgae in neritic ecosystems[END_REF][START_REF] Duarte | Major role of marine vegetation on the oceanic carbon cycle[END_REF]. The definition of the status of these intertidal ecosystems as source or sink of CO 2 for the atmosphere requires evaluating the balance between primary production and respiration at relevant spatial and temporal scales.

Factors affecting the biomass of primary producers in intertidal sediments, and thereafter the associated metabolic processes, are numerous. Exposure to hydrodynamic energy (as indicated by sediment type) and tidal level have been recognized as significant factors affecting spatial variations of microphytobenthic biomass in intertidal flats. The biomass of microalgae is considered to be lower in sandy sediments than in muddy sediments [START_REF] Intyre | Microphytobenthos: the ecological role of the "secret garden" of unvegetated, shallow-water marine habitats. I. Distribution, abundance and primary production[END_REF], to peak between mid-tide level and mean high water neap tide level [START_REF] Underwood | Primary production by phytoplankton and microphytobenthos in estuaries[END_REF] and to show a high degree of heterogeneity at small spatial scale with a patchy distribution (Spilmont et al. 2011 and references therein). Seagrasses, such as Zostera, occur from the mid-intertidal to the immediate sublittoral on various sediments, and primary production has long been shown to be higher in sediment covered by seagrass than in unvegetated sediment (e.g. [START_REF] Asmus | The importance of grazing food chain for energy flow and production in three intertidal sand bottom communities of the northern Wadden Sea[END_REF]. Seasonality in light availability and temperature is well recognized as exerting an important influence on primary production in temperate areas (e.g. [START_REF] Migné | In situ measurements of benthic primary production during emersion: seasonal variations and annual production in the Bay of Somme (eastern English Channel, France)[END_REF]). Temporal variability of microphytobenthic biomass is however also dependent on local environmental changes at other temporal scales such as erosion and deposit events in muddy shores [START_REF] Underwood | Primary production by phytoplankton and microphytobenthos in estuaries[END_REF]. In microalgae community (e.g. [START_REF] Migné | In situ measurements of benthic primary production during emersion: seasonal variations and annual production in the Bay of Somme (eastern English Channel, France)[END_REF]) and seagrass meadows (e.g. [START_REF] Ouisse | Community-level carbon flux variability over a tidal cycle in Zostera marina and Z. noltii beds[END_REF], gross primary production has been shown to vary over the emersion period, in response to natural light variations. Variation in community gross primary production is also expected to occur during the course of emersion due to vertical migrations of the microphytobenthos in the surface sediment (e.g. [START_REF] Spilmont | Short-term variability of intertidal benthic community production during emersion and the implication in annual budget calculation[END_REF].

Factors controlling intertidal sediment respiration have been less studied than the ones controlling primary production and no general relationship with the sediment type has been evidenced [START_REF] Middelburg | Respiration in coastal benthic communities[END_REF]. Bacterial respiration is however suspected to be the highest contributor to benthic community respiration and granulometry could control the distribution of benthic compartments and thus the benthic respiration at an intertidal bay scale [START_REF] Hubas | Factors controlling benthic metabolism during low tide along a granulometric gradient in a intertidal bay (Roscoff Aber Bay, France)[END_REF].

Sediment respiration is also known to be enhanced in seagrass meadows due to the stimulation of the bacterial activity around roots [START_REF] Middelburg | Respiration in coastal benthic communities[END_REF]. Temporal variations in sediment respiration are expected to be mainly controlled by temperature both at seasonal and daily scales [START_REF] Van Es | Community metabolism of intertidal flats in the Ems-Dollard Estuary[END_REF][START_REF] Hancke | Temperature effects on respiration and photosynthesis in three diatomdominated benthic communities[END_REF].

The aim of this study was to explore the spatial and temporal variability of benthic primary production and benthic respiration in a temperate mesotidal lagoon. Sample sites varied according to their tidal level, their sediment type and the presence/absence of the seagrass Zostera noltei.

Primary production and respiration were measured in situ as CO 2 -exchange rates between the sediment and the atmosphere at low tide, using static benthic chambers under both light and dark conditions. Small spatial scale variability was considered at each site using three benthic chambers simultaneously. Measurements were performed at three seasons and the small temporal scale variability was considered performing successive incubations over the emersion period. The Arcachon Bay is a mesotidal shallow lagoon on the French Atlantic coast with a semidiurnal tide.

Materials and Methods

Study site

The studied tidal flat is located in the eastern part of the lagoon, near Cassy harbour (44°43′ N, 1°03′ W, figure 1). Three sites were investigated; site S1 was in the upper beach sandy area (covered with water 1 to 2 hours per tide, grain size ≈ 250 μm, porosity ≈ 0.4) and sites S2 and S3 were in the mid muddy area (covered with water 3 to 4 hours per tide, grain size ≈ 15-40 μm, porosity ≈ 0.8). Sites S1 and S2 were free of macrophytes while S3 was covered by the seagrass Zostera noltei, which biomass varied seasonally, from 23 to 377 g DW m -2 in March and September 2006 respectively (Deborde et al. 2008a).

CO 2 flux measurements

Fluxes of CO 2 were measured at the sediment-air interface at low tide using the closed-chamber method described in [START_REF] Migné | A closedchamber CO 2 -flux method for estimating intertidal primary production and respiration under emersed conditions[END_REF]. A sediment area of 0.071 m 2 was enclosed down to a 10-cm depth. Changes in air CO 2 concentration (ppm) in the benthic chamber (10.5 L) were measured with an infrared gas analyser (LiCor Li-800) for 10-20 min. CO 2 concentrations were recorded in a data logger (LiCor Li-1400) with a 15 s frequency. CO 2 flux was calculated as the slope of the linear regression of CO 2 concentration (μmol mol -1 ) against time (min) and expressed in mmolC m -2 h -1 assuming a molar volume of 22.4 L at standard temperature and pressure.

Transparent chambers were used to estimate the net benthic community production (NCP, the balance between the community gross primary production and the community respiration). Opaque chambers were used to estimate the community respiration (CR). During light incubations, incident photosynthetically available radiation (PAR 400-700 nm) was monitored with a LiCor SA-190 quantum sensor. During dark incubations, the temperature of the top layer of the sediment was measured using a digital pen thermometer (0.1°C accuracy).

Sampling strategy

Measurements were performed during spring tides, at the end of winter (March 2005), in spring (May 2006) and beginning of autumn (September 2007). Three benthic chambers were positioned about 10 m apart to take into account the small spatial scale variability at each site. Successive triplicate incubations were performed to take into account the small temporal scale variability at each occasion.

The number of successive triplicate incubations varied according to the date, the site and the light or dark condition, from 3 to 7 (but only one under darkness at S2 in March). In May 2006, a fourth chamber was used for monitoring dark fluxes over the low tide period at S1 (15 incubations from about 3 h after high tide to about 10 h after high tide).

After CO 2 flux measurements, three sediment cores (16-mm diameter, 10-mm depth) were collected inside each chamber to determine the Chlorophyll-a content (spectrophotometry method, Jeffrey and Humphrey 1975).

Benthic trophic state index

The benthic trophic state index (BTSI) proposed by [START_REF] Rizzo | A metabolism-based trophic index for comparing the ecological values of shallow-water sediments habitats[END_REF] was calculated at each site at each season. The BTSI was assigned to sediments based on the relative magnitude of maximum hourly rates of net community production (NCP) and community respiration (CR). The classification given by [START_REF] Cook | Carbon and nitrogen cycling on intertidal mudflats of a temperate Australian estuary. I. Benthic metabolism[END_REF] for CO 2 fluxes was applied on the NCP versus CR values (NCP:CR < 0, BTSI 1, net heterotrophic; 0 < NCP:CR < 1, BTSI 2, net autotrophic; NCP:CR > 1, BTSI 3, highly autotrophic).

Statistical analyses

ANOVA (or its non-parametric equivalent if necessary) was used to test the effect of site, season and their interaction on the sediment chlorophyll-a content. The normality of data was checked using the Shapiro test (P > 0.05) and the homogeneity of variances was checked using the Bartlett test (P > 0.05). Pairwise comparisons were made using t-tests with the Bonferroni correction.

Results

The sediment chlorophyll-a content ranged from 61 to 283 mg.m -2 (Figure 2). The Scheirer-Ray-Hare H-test (non-parametric 2-way ANOVA) showed significant effects of season (H = 21.169, P < 0.001), site (H = 9.205, P = 0.010) and their interaction (H = 28.217, P < 0.001). The sediment chlorophyll-a content increased in May at site 1 (ANOVA, F2,23 = 504.17, P < 0.001) while it did not vary significantly between the three months at S2 (ANOVA, F2,24 = 2.553, P = 0.099) and S3 (ANOVA, F2,14.02 = 1.950, P = 0.179). Light incubations were performed under incident photosynthetically available radiation varying from 185 to 1650 μmol m -2 s -1 (Figure 3). Mean light CO 2 -fluxes ranged from -9.89 to +0.41 mmol m -2 h -1 (Figure 3). Except for the first incubation performed at S3 in May, the light fluxes always corresponded to a sediment CO 2 -uptake. The sediment CO 2 -uptake increased with the time of exposure at each site and season, independently of light variations. . CO2 fluxes (mmol m -2 h -1 , left axis) x PAR (μmol m -2 s -1 , right axis) The benthic trophic state index, based on the relative magnitude of maximum hourly rates under light (NCPmax) and darkness (CRmax) measured at each site at each season, indicated that sediments were net autotrophic (BTSI 2) in spring at S1 and S3 and highly autotrophic (BTSI 3) in other cases (Figure 5). , mean ± se, n = 3) under light (NCPmax) versus under darkness (CRmax) at the upper sandy (S1, circles), at the mid muddy (S2, diamonds) and at the seagrass (S3, triangles) sites in March 2005 (dark), May 2006 (grey) and September 2007 (white) and corresponding benthic trophic state index according to [START_REF] Rizzo | A metabolism-based trophic index for comparing the ecological values of shallow-water sediments habitats[END_REF] (BTSI 2: net autotrophic, BTSI 3: highly autotrophic)

Discussion

The sediment chlorophyll-a contents measured during this survey indicated that the microphytobenthic biomass was seasonally influenced, with a peak in spring at the sandy site but not at the muddy sites. This is consistent with previous surveys of annual variations of sediment chlorophyll-a content in sands [START_REF] Migné | In situ measurements of benthic primary production during emersion: seasonal variations and annual production in the Bay of Somme (eastern English Channel, France)[END_REF][START_REF] Migné | Freshwater seepages and ephemeral macroalgae proliferation in an intertidal bay: II. Effect on benthic biomass and metabolism[END_REF]) and muds [START_REF] Spilmont | Benthic primary production during emersion: in situ measurements and potential primary production in the Seine Estuary (English Channel, France)[END_REF][START_REF] Davoult | Spatio-temporal variability of intertidal benthic primary production and respiration in the western part of the Mont Saint-Michel Bay (Western English Channel, France)[END_REF]) of various intertidal flats of the French coast of the English Channel. Temporal variations of microphytobenthic biomass are not only regulated by light and temperature at seasonal scale but are also dependent on local environmental changes at other temporal scales. In muddy shores, erosion and deposit due to particular weather events can lead to sudden decrease in microphytobenthos biomass compensated by rapid growth during favorable conditions (Underwood and Kromkamp 1999). Nevertheless, our samplings were performed during three seasons of three consecutive years and the present observation might also result from an inter-annual variability of microphytobenthos development. Indeed, monthly monitoring of tidal flats over a four to five year period allowed to highlight an inter-annual variability in the peaks of microphytobenthos biomass in the Dutch Wadden Sea [START_REF] Cadée | Primary production of the benthic microflora living on tidal flats in the Dutch Wadden Sea[END_REF] and in the Seto Inland Sea of South West Japan [START_REF] Montani | Seasonal and interannual patterns of intertidal microphytobenthos in combination with laboratory and areal production estimates[END_REF].

Both light and dark CO 2 -fluxes tended to increase over the emersion period whatever the season, the sediment type and the presence or not of seagrasses. These increases, not related to light nor temperature variations, should result from non-biological processes occurring in the sediment during emersion. Discrepancies between instantaneous soil respiration and CO 2 efflux have been shown and attributed to a temporary storage of CO 2 in the soil pore water after rainfalls [START_REF] Maier | Soil CO 2 efflux vs. soil respiration: Implications for flux models[END_REF]). In intertidal sediments, photosynthesis and respiration gradually change the amount of dissolved inorganic carbon in pore water, slowly changing the partial pressure of CO 2 and then the flux of CO 2 between the sediment and the atmosphere. This uncoupling between metabolism and CO 2 flux should result in an only slight delay of CO 2 uptake or emission relative to photosynthesis or respiration [START_REF] Middelburg | Organic matter mineralization in intertidal sediments along an estuarine gradient[END_REF]. During exposure, however, changes in the amount of pore water could occur, due to advection and evaporation, and drive variations of CO 2 exchanges at the sediment-air interface. Variations of CO 2 exchanges at the sediment-air interface during exposure could also be driven by changes in the chemistry of pore water. In the sandy sediments of the Kurose River Estuary (Japan), [START_REF] Sasaki | Tidal effects on the organic carbon mineralization rate under aerobic conditions in sediments of an intertidal estuary[END_REF] measured a rapid increase in the rates of CO 2 emission in the first hour of ebbing tide and thereafter fairly stable rates until the end of the period of emersion.

The initial phase of rapid increase in the CO 2 emission rates was supposed to correspond to the time when seawater drained rapidly in surface sediments. In a muddy tidal flat of the Wadden Sea, [START_REF] Klaassen | Inter-annual variability of CO 2 exchanges between an emersed tidal flat and the atmosphere[END_REF] observed negligible light and dark CO 2 fluxes at the start of the emersion, followed by slow increases until maximum values were reached after 3 hours of emersion.

Fluxes did not show any sign of change near the end of the period of emersion and maximum values were supposed to be reached and maintained after the pore water has been evaporated in the surface sediment. In the tidal flat of the Arcachon bay, the permeability of upper sands allows the advective transport of pore waters and the vertical distribution of reduced species (Mn, Fe, S) has been shown to vary during ebbing and rising tide [START_REF] Delgard | In situ study of short-term variations of redox species chemistry in intertidal permeable sediments of the Arcachon lagoon[END_REF]. Lower cohesive muds remain saturated with seawater at low tide, evaporation occurs however, and annelids and bivalves burrows act as ducts for pore water seeping (Deborde et al. 2008b). Furthermore, strong anaerobic organic matter mineralization has been evidenced in both vegetated and unvegetated muds (Deborde et al. 2008a;Deborde et al. 2008b;[START_REF] Deborde | Methane sources, sinks and fluxes in a temperate tidal Lagoon: The Arcachon lagoon (SW France)[END_REF], which should generate alkalinity changes leading to shifts in the equilibrium between the forms of dissolved inorganic carbon in pore water and hence in gaseous CO 2 flux [START_REF] Faber | The role of alkalinity generation in controlling the fluxes of CO 2 during exposure and inundation on tidal flats[END_REF].

A seasonal trend appeared in dark CO 2 fluxes at each site, with highest rates measured in spring when sediment temperature was the highest. Pooling data, but excluding the particularly high value measured in the Zostera site in May, there was a significant exponential relationship between maximum dark CO 2 fluxes and sediment temperature (R 2 = 0.920, n = 8, P < 0.001). This confirms the control of sediment respiration by temperature variations at a seasonal scale. The particularly high dark CO 2 fluxes measured in the Zostera site in May could result from the increase of anoxic respiration processes at the periphery of the rhizosphere which has been suggested to occur during the growth phase of seagrasses in the Arcachon bay (Deborde et al. 2008a).

Contrary to what was expected, higher net community production rates were measured in the unvegetated mud than in the seagrass meadow. Adding maximum dark and light fluxes led to estimate gross community production (GCP) to be 3, 12 and 11 mmolC m -2 h -1 , in March, May and September respectively, in the unvegetated mud and 4, 8 and 6 mmolC m -2 h -1 in the Zostera meadow. This is in accordance with results of [START_REF] Polsenaere | Spatial and temporal CO 2 exchanges measured by Eddy Covariance over a temperate intertidal flat and their relationships to net ecosystem production[END_REF] in the same bay. Based on the micrometeorological Eddy Covariance technique, autumn GCP was estimated to be 16 and 4 mmolC m -2 h -1 in muds with 20 and 90 % cover of Zostera respectively. This underlines the importance of microphytobenthic communities in the carbon cycle in the Arcachon flat.

The benthic trophic state index (BTSI) proposed by [START_REF] Rizzo | A metabolism-based trophic index for comparing the ecological values of shallow-water sediments habitats[END_REF] gives an indication of the balance between production and respiration using hourly rates. Applying this index to maximum CO 2 fluxes measured here indicated that sediments were net autotrophic in spring at the sandy site and at the muddy site with seagrass and highly autotrophic at the other occasions. The lowest ratio of net community production to community respiration was obtained in the Zostera site in May, when the particularly high rate of respiration was measured. The most autotrophic sediments were the midlevel unvegetated muds, with maximum net community production more than 4 times higher than community respiration whatever the season. A previous study, based on oxygen fluxes measured at the sediment/water interface in laboratory incubations, already showed a persistent autotrophy in the Zostera noltei meadow of the Arcachon Bay (de [START_REF] De Wit | ROBUST: The ROle of BUffering capacities in STabilising coastal lagoon ecosystems[END_REF]. The present study reinforced and completed this result. Based on in situ measurements of CO 2 fluxes at the sediment/air interface, it showed persistent autotrophy not only in seagrass meadow but also in bare mud and sand.

Benthic trophic state indices were also calculated using rates obtained in various tidal sedimentary flats along the French coast of the English Channel with the same method as the one presented here (Table 1). Net heterotrophy was observed only once, in the upper exposed sandy beach of Wimereux in winter. Net autotrophy was observed in the mid-level muddy sand flat of the Bay of Somme and high autotrophy in all the other cases. The investigation of [START_REF] Rizzo | A metabolism-based trophic index for comparing the ecological values of shallow-water sediments habitats[END_REF] of the variability of this index across a number of spatial and temporal scales showed a reduced autotrophy or enhanced heterotrophy associated with finer-grain sediment and a decline of autotrophy from winter to spring, particularly at sandy sites. In the study of [START_REF] Cook | Carbon and nitrogen cycling on intertidal mudflats of a temperate Australian estuary. I. Benthic metabolism[END_REF], however, the most autotrophic sediments were the finest ones in early spring. In the present investigation, no trend appeared according to the sediment type or to the tidal level but the ratio of net production to respiration was maximal in winter except in the upper sandy beaches of Wimereux and Roscoff Aber bay. No generalization can then be made about the effect of tidal-level, sediment type and season on the trophic status of the sediments assigned according to the BTSI. The benthic trophic state index does not take into account the trophic status over a diurnal cycle which is considered in the more traditional and ecologically relevant ratio of gross primary production to respiration. In intertidal unvegetated sedimentary flats where turbidity is likely to limit photosynthesis during immersion, the net primary production might be maximal during emersion but respiration might be enhanced during immersion. For example, [START_REF] Cook | Carbon and nitrogen cycling on intertidal mudflats of a temperate Australian estuary. I. Benthic metabolism[END_REF] measured inundated dark fluxes of dissolved inorganic carbon (TCO 2 ) 3 to 5 times higher than exposed fluxes of CO 2 in mudflats of a temperate Australian estuary. Net autotrophy assigned according to the BTSI means that the system is net autotrophic at saturating light during emersion but might present a net heterotrophy on a daily basis integrating the low/high tide cycle. The BTSI calculated on exposed CO 2 fluxes indicated that the muddy site of Cancale surveyed in the Bay of Mont St Michel was highly autotrophic at the 3 investigated seasons. This site was shown, however, to be net heterotrophic based on an annual budget taking into account the variability of fluxes with tidal, daily and seasonal cycles [START_REF] Migné | Annual budget of benthic production in Mont Saint-Michel Bay considering cloudiness, microphytobenthos migration, and variability of respiration rates with tidal conditions[END_REF]. This example highlights the need to incorporate the alternate periods of

Fig. 1 :

 1 Fig. 1: Detailed map of the study site and sampling stations in the Arcachon Bay (SW France). S1: upper tidal level, sand; S2: mid tidal level, bare mud; S3: mid tidal level, mud + Z. noltei. © Ortho littorale 2008

Fig. 2 :

 2 Fig. 2: Sediment chlorophyll-a content (Chla in mg m -2 ) in upper sandy site (S1) and mid muddy (S2) and seagrass (S3) sites in March 2005, May 2006 and September 2007 (mean ± se, n = 9, except for S1 in March n = 8)

Fig. 3 :

 3 Fig. 3: Sediment-air CO 2 fluxes (mean ± se, n = 3) measured under ambient light (PAR) at different moments after high tide (HT) at the upper sandy site (S1) and after mid tide (MT) at the mid muddy (S2) and seagrass (S3) sites in March 2005, May 2006 and September 2007During dark incubations, the temperature of the top layer of the sediment varied from 8.4 to 29.0 °C (Figure4). Mean dark CO 2 -fluxes ranged from +0.06 to +6.97 mmol m -2 h -1 (Figure4). The sediment CO 2 -release increased with the time of exposure at each site and season, independently of temperature variations. At S1 in May, fluxes measured in the supplementary chamber reached a plateau about 8 hours after high tide.

  Fig. 5: Maximum CO 2 -fluxes (in mmol m -2 h -1

  submersion and air exposure to determine the metabolic balance of intertidal sediments. The micrometeorological Eddy Covariance technique used by[START_REF] Polsenaere | Spatial and temporal CO 2 exchanges measured by Eddy Covariance over a temperate intertidal flat and their relationships to net ecosystem production[END_REF] over the intertidal mudflat of the Arcachon bay, provided net ecosystem exchange (NEE) at the air/sediment interface during emersion and at the air/water interface during immersion in the early autumn 2007. Strong CO 2 uptake was observed at low tide during the day but CO 2 degassing in all other cases. This suggests that the flat was autotrophic at low tide during the day but heterotrophic during the night and during the immersion. Nevertheless, NEE can differ from net ecosystem production due to the slow water-air diffusion. To determine the metabolic balance of the tidal sediments of the Arcachon bay, dissolved inorganic carbon fluxes measured at the sediment/water interface at high tide should also be considered.

Acknowledgements

This study was funded by the French programs PNEC Chantier Littoral Atlantique and EC2CO Bentidal.

The authors acknowledge P. Anschutz and the UMR-CNRS-5805-EPOC team for providing logistical support for the field work (so far from home). Thanks are also due to C. Rolet for drawing the map of the study site.