Simone Anzellini
email: simone2.anzellini@uv.es

Silvia Boccato

Samuel R Baty

Leonid Burakovsky

Daniele Antonangeli

Daniel Errandonea

Raffaella Torchio

Melting line and thermal equation of state of fcc-cobalt: a combined experimental and computational approach

Keywords: transition metals, melting curve, extreme condition, laser-heating, diamond anvil cell

The melting line of cobalt has been investigated both experimentally, using synchrotron X-ray diffraction coupled with laser-heated diamond anvil cells, and theoretically, using ab initio simulations. Over the investigated pressure and temperature range -between 30 and 100 GPa and from ambient temperature up to 4000 K -the hexagonal close-packed structure, stable at ambient conditions, is replaced at high temperature by the facecentred cubic structure, observed stable till melting. The melting temperatures obtained by the two methods are in remarkable agreement and the melting line can be well described by a Simon-Glatzel equation of the form T m =1768(K)(P(GPa)/35.62+1) 0.64 . Finally, from the obtained results it was possible to determine a thermal equation of state for the cubic face-centred phase of Co.

Introduction

Transition metals are characterized by a partially filled d-band and the consequent de-localization of their d-orbitals. This produces a strong metallic bonding responsible for a series of very interesting properties observed both in the pure transition metals and in their alloys. In particular, they are generally characterized by a high resistance to corrosion and wear, a good ductility and high yield strength, paramagnetism as well as high melting points and molar enthalpies of fusion. Concerning chemical reactivity, they can easily form alloys and metallic glasses. Due to all these properties, the technological applications and the economic importance of these elements, and their alloys, is immense (1; 2; 3; 4). As such, transition metals are among the most intensively studied family of elements, and in the past decades a big effort has been devoted to map and interpret systematic trends in their properties. Important examples include: the parabolic dependence of cohesive energy and bulk modulus on d-band filling [START_REF] Friedel | The Physics of Metals[END_REF], the sequence of most stable crystal structures associated with increasing band filling at ambient pressure [START_REF] Pettifor | Theory of the crystal structures of transition metals[END_REF], the pressure-induced increase of the d-band width going roughly as the fifth inverse power of the atomic volume [START_REF] Heine | s-d interaction in transition metals*[END_REF] and the consequent pressure-induced suppression of ferromagnetism [START_REF] Torchio | XAS and XMCD spectroscopies to study matter at high pressure: Probing the correlation between structure and magnetism in the 3d metals[END_REF]. From a purely physical point of view, several studies have focused their attention to predict and understand the phase diagram of transition metals, shedding lights on the role of the pressure (P )-temperature (T )-induced filling of the d-shells into the observed structural and magnetic phase transitions. Several studies tried to unveil the thermodynamics and the microscopic processes of melting under pressure, given rise to many controversies among the different experimental and theoretical studies (9; 10; 11; 12). Moreover, the study of transition metals under high pressure (HP ) and high temperature (HT ) is extremely relevant in geophysics and planetary science, as iron is the main constituent of terrestrial planetary cores [START_REF] Poirier | Introduction to the Physics of the Earth's Interior[END_REF]. In particular, the characterization of the phase diagram and melting lines of iron (14; 15; 16; 17; 18; 19), iron-alloys (20; 21) and transition metals more in general (10; 22; 23) is of fundamental importance for understanding the composition, structure and dynamics of planetary cores (13; 24; 25; 26).

Among the transition metals, cobalt (Co), which is adjacent to iron (Fe) in the periodic table, has been suggested as analogue to iron when addressing Earth's core elastic anisotropy (27; 28). Furthermore, understanding the HP -HT -induced structural behavior of Co, can also shed light on the phase diagram of Fe in general. This includes the stability field of the γ phase of Fe with respect to the ϵ one and, the existence of cubic Fe-alloys under Earth's inner-core conditions (29; 30; 31). Therefore, several studies have focused their attention in characterizing Co structure, magnetism and elastic properties under extreme conditions (32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42). At ambient conditions, cobalt is ferromagnetic and presents a hexagonal close-packed (hcp) structure. Upon compression, Co transforms to a facecentred cubic (f cc) phase in a P range between 70 and 150 GPa. This phase transition and the possible coexistence region of the two phases, has been shown to be strongly affected by the hydrostatic conditions of the experiments (30; 43). There is no measurable change of volume at the hcp-f cc transition but thereafter, the slope of the compression curve is reduced, in-dicating a net increase of its elastic stiffness as a function of P [START_REF] Goncharov | Elastic and vibrational properties of cobalt to 120 GPa[END_REF]. A structurally similar phase transition is observed when increasing T up to 700 K at ambient P and this boundary has been measured to P above 70 GPa (44; 30). Within the f cc stability field, there is a T -induced-secondorder phase transition from a ferromagnetic to a paramagnetic configuration. The thermal equation of state (EoS) of the f cc-Co was measured in a recent work by Armentout and Kavner [START_REF] Armentrout | A new high pressure and temperature equation of state of fcc cobalt[END_REF] up to 57 GPa and 2400 K using a combination of laser-heated diamond anvil cell (LH-DAC) and X-ray diffraction (XRD). As for other transition metals (e.g. Fe, Ta, Ni, etc..), the melting curve of Co reported in literature presents several discrepancies between the various studies. Early experiments performed by both Errandonea et al. [START_REF] Errandonea | Systematics of transition-metal melting[END_REF] and Lazor [START_REF] Lazor | Phase diagrams, elasticity and thermodynamics of ni, co and fe under high pressure[END_REF] in LH-DAC, using the direct observation of movements on the sample surface as melting criterion (speckle technique), resulted in melting curves that differ by 400 K at 60 GPa. A more recent experiment was performed by Wang et al. [START_REF] Wang | The melting curve of cobalt under high pressure[END_REF], but only up to 12 GPa, in a high volume cubic press using as melting criterion both the plateaus in the T vs. laser power dependence and ex situ scanning electron microscope (SEM) analysis of the texture of the recovered sample. When extrapolated to higher P , the obtained results seem to be more in agreement with the melting line reported by Lazor [START_REF] Lazor | Phase diagrams, elasticity and thermodynamics of ni, co and fe under high pressure[END_REF]. In contrast, previous resistivity measurements performed by Ezenwa and Secco [START_REF] Ezenwa | Invariant electrical resistivity of co along the melting boundary[END_REF] are more in line with the results obtained by Errandonea et al. [START_REF] Errandonea | Systematics of transition-metal melting[END_REF]. Noteworthy, in situ investigation by synchrotron techniques have not been performed yet.

From a computational point of view, the melting line of Co was calculated by Zhang et al. [START_REF] Zhang | Molecular dynamics study of melting curve, entropy of fusion and solid-liquid interfacial energy of cobalt under pressure[END_REF] using molecular dynamics (MD) simulations with the two embedded atoms method (EAM) potentials. However, the melting line obtained with these simulations plots significantly higher than the experimental determinations.

Since the early melting experiment of Errandonea et al. [START_REF] Errandonea | Systematics of transition-metal melting[END_REF], LH-DAC technology has considerably progressed, as in situ melting diagnostics. In particular, LH-DAC combined with synchrotron XRD, it has now become a challenging but routinely used technique for in situ characterizations of phase diagrams and melting lines of samples at P up to 3 Mbar and T in excess of 5000 K (48; 49). Indeed, it allows reliable analysis of the P -T -induced chemical, textural and structural evolution of both the sample and the insulating material, to be performed in a relatively short time (few seconds) compatible with confinement of liquid within the experimental chamber. In addition, XRD technique provides an objective melting criterion, i.e. the appearance of a diffuse signal in the diffraction pattern due to the scattering from the liquid sample (unlike crystalline materials, liquids and amorphous materials do not have a long range order, resulting in the absence of relatively sharp diffraction peaks, replaced by a diffuse signal). Thanks to the advances in this technique (metrology included) several discrepancies previously observed on the melting curves of other transition metals have been solved [START_REF] Parisiades | A Review of the Melting Curves of Transition Metals at High Pressures Using Static Compression Techniques[END_REF]. For these reasons, we decided to study the phase diagram and melting curve of Co both experimentally, using LH-DAC combined with XRD, and theoretically, using ab initio calculations based on the density functional theory (DFT).

Methods

Experiments

Three membrane DACs with culet sizes ranging from 300 µm down to 150 µm were equipped with pre-indented and laser-drilled rhenium gaskets. The sample was cut from a 4 µm thick 99.95 % Co policrystalline deposition prepared by Eric Monsifrot from the SARL DEPHIS in Etupes (FR). The obtained samples were sandwiched between two KCl disks previously-prepared by fs laser micro-machining and loaded in the high pressure chamber of the DAC. The KCl disks were used as insulating material as well as pressure transmitting medium (PTM) and gauge. In order to minimize any chemical reaction, the KCl disks were oven dried at 150 • C (above the KCl dehydration T ) for four hours before being used for the loading. For the same reason, the loaded cells were placed (slightly opened), back in the oven while waiting to be used on the beamline. The experiment was performed at the extreme conditions beamline I15 at Diamond Light Source [START_REF] Anzellini | Laser-heating system for high-pressure x-ray diffraction at the extreme condition beamline i15 at diamond light source[END_REF]. The beamline's polychromatic beam was tuned to 29.5 keV and focused down to 9×6 µm (Full Width at Half Maximum -FWHM) using two pairs of KB-mirrors. A Si Pilatus 2M detector was used to rapidly collect diffraction data from the sample while keeping a good signal-to-noise ratio. The sample-to-detector distance was determined from the diffraction rings of a CeO 2 standard using the calibration routine of the DIOPTAS software suite [START_REF] Prescher | Dioptas: a program for reduction of twodimensional x-ray diffraction data and data exploration[END_REF]. The HP -HT experiment was performed using the laser-heating system mounted on the beamline and following the procedure described in Anzellini and Boccato [START_REF] Anzellini | A practical review of the laser-heated diamond anvil cell for university laboratories and synchrotron applications[END_REF]. Before each heating ramp, the sample was brought to the target P evaluated according to the KCl equation of state following the calibration of Dewaele et al. [START_REF] Dewaele | High-pressure-high-temperature equation of state of KCl and KBr[END_REF]. Two 100 W Nd:YAG lasers were used to heat the sample from each side minimizing the axial thermal gradients. Both lasers were individually focused on the sample until clear hot spots of similar temperatures were obtained. The lasers were then intentionally unfocused and spatially coupled in order to maximize the surface at constant T on both sample sides (∼ 40 µm in diameter, much larger than the X-ray beam size). T was measured from each side simultaneously via spectral radiometry (Planck fitting in the range between 450 nm and 950 nm) and the final T was assumed as the average of the two determinations. The maximum difference in T measured on the two sides of the sample and the standard deviation of the histograms obtained from their two-colours pyrometry (Benedetti and Loubeyre ( 54)) was used as the error in the measurement. The corresponding thermal P was obtained from the thermal EoS of Dewaele et al. [START_REF] Dewaele | High-pressure-high-temperature equation of state of KCl and KBr[END_REF] under the assumption that both Co and KCl were experiencing the same T . Considering the present sample geometry and the corresponding axial thermal gradient, the maximum error in P was calculated as half the difference between the pressure obtained from the KCl at the measured T (surface of contact with the Co) and the one from the KCl at ambient T (when in contact with the diamond). Before and after each heating ramp, the alignment between the X-rays, the lasers and the T reading spot was checked following the procedure described in Anzellini et al. [START_REF] Anzellini | Laser-heating system for high-pressure x-ray diffraction at the extreme condition beamline i15 at diamond light source[END_REF].

The heating ramps were performed in "trigger mode": both lasers were set to a target power; after 0.3 s a diffraction pattern and a T measurement were simultaneously collected; 0.3 s after the XRD collection, the power of both lasers was set back to zero. This procedure, while assuring T stabilization and sample equilibration, allowed us to minimize the interaction time between the laser and the sample, so reducing the risk of possible chemical reactions, and to perform any adjustment in the optics when needed. During each heating ramp, the lasers powers were increased until a diffuse signal was detected in the diffraction pattern or it was not possible to further increase T (changes in the insulating conditions of the sample). Several heating ramps were performed on the same samples at different P -T conditions, each time on a different region, and suitability of the measurements (unreacted sample, good ratio in the sample vs. KCl signal etc.) were assessed by collecting XRD patterns before the actual ramp.

During the data analysis, great care was taken to investigate the different aspects of the experiment. The reliability of T measurements was double checked following the procedure described in Benedetti and Loubeyre [START_REF] Benedetti | Temperature gradients, wavelengthdependent emissivity, and accuracy of high and very-high temperatures measured in the laser-heated diamond cell[END_REF]. An accurate analysis of the diffraction patterns was performed to detect the onset of melting and to obtain structural and textural information about the sample and the insulating material. Masks were applied on a per-image basis and the images azimuthally integrated using the DIOPTAS suite [START_REF] Prescher | Dioptas: a program for reduction of twodimensional x-ray diffraction data and data exploration[END_REF]. Both Co and KCl data were treated as powder data and a Pawley analysis was performed with the TOPAS suite (55) using previously reported parameters as starting values. Finally, the outcome of the analysis of the in situ XRD measurements were associated to the corresponding T , so to obtain a precise structural evolution of the sample as a function of P and T .

Calculations

Theoretical calculations were performed based on a DFT approach, with the projector-augmented-wave (PAW) [START_REF] Blöchl | Projector augmented-wave method[END_REF] implementation and the generalized gradient approximation (GGA) for exchange-correlation energy, in the form known as Perdew-Burke-Ernzerhof (PBE) [START_REF] Perdew | Generalized gradient approximation made simple[END_REF]. For these calculations the Vienna Ab initio Simulation Package (VASP) was used. GGA was preferred to local density approximation (LDA), because, in spite of the case of hcp-Co, where LDA calculations yields to single crystalline elastic moduli in closer agreement with experimental results than GGA calculations [START_REF] Antonangeli | Elasticity of cobalt at high pressure studied by inelastic x-ray scattering[END_REF], GGA well account for the compressibility curve [START_REF] Antonangeli | Anomalous pressure evolution of the axial ratio ca in hcp cobalt: Interplay between structure, magnetism, and lattice dynamics[END_REF]. Furthermore, it is known that LDA does not accurately describe the properties of other 3d transition metals e.g. chromium for which its predictions are in drastic disagreement with experiment (58; 59), and iron for which it produces a wrong ground state (60; 61; 62; 63). LDA also fails in assessing the strength of the magnetovolume effect. On the other hand, GGA correctly predicts the structural and magnetic phase diagrams [START_REF] Hobbs | Fully unconstrained noncollinear magnetism within the projector augmented-wave method[END_REF].

Co was modeled using the core-valence representation [ 12 Mg]3p 6 3d 7 4s 2 , i.e., the 15 outermost electrons were assigned to the valence. The valence electrons were represented with a plane-wave basis set with a cutoff energy of 340 eV, while the core electrons were represented by PAW pseudopotential. The present ab initio Quantum Molecular Dynamics (QMD) simulations of the melting curves of both the non magnetic (NM) f cc-Co and the paramagnetic (PM) f cc-Co were carried out using the Z method implemented within VASP [START_REF] Burakovsky | Ab initio melting curve of osmium[END_REF]. The simulations were carried out with a single Γ-point; with such a large supercell, full energy convergence, to ∼ 10 meV/atom was achieved in every case considered, which is equivalent to an error of ∼ 100 K in the value of the melting temperature (T m ), within the accuracy of the Z method itself.

For the calculations on PM f cc-Co, the GGA+U scheme with spin-orbit coupling developed for the calculation of the properties of paramagnetic materials (66) was applied. Specifically, the Dudarev approach (67), in which only the difference U -J is meaningful rather than the values of the two parameters separately, was used. An U -J=5.0 eV was chosen following Aryasetiawan et al. [START_REF] Aryasetiawan | Calculation of hubbard u from first-principles[END_REF]. Note that the melting curve of PM f cc-Co does not seem to depend on the choice of the numerical value of U -J. Several melting points of PM f cc-Co were calculated using U -J in the 2.5-7.5 eV range. Although the corresponding values of P and T are slightly different from those of PM f cc-Co with U -J=5.0 eV having the same densities, all of the computed melting points lie on the melting curve of PM f cc-Co with U -J=5.0 eV. Thus, the melting curve of PM f cc-Co is essentially unique. Note that U -J=0 corresponds to the case of NM f cc-Co; even in this case the two melting curves are virtually identical in a very wide P range; their difference starts manifesting itself at ρ ∼ 14.5 g/cm 3 (a pressure of ∼ 500 GPa) and T m ∼ 9000 K.

Results and discussion

Phase diagram

Ten HT ramps were performed at selected P following the procedure described in the method section. The data were collected in a P -T range between 15 GPa and 98 GPa and from ambient T up to 4200 K. In this investigated range it was possible to index Co hcp and f cc solid phases and the B2 phase of KCl (used as PTM and standard). Only the ramp performed around 40 GPa showed some formation of CoO(69) above 2600 K, therefore the data obtained in this run above this T were discarded. The analysis of XRD patterns also excludes the formation of cobalt carbide and dicobalt carbide [START_REF] Nagakura | Study of metallic carbides by electron diffraction part iv. cobalt carbides[END_REF], thus if any reaction occurred, the amount of unwanted phases is below the detection limits of the XRD technique.

An overall similar T -induced textural evolution was observed in each of the performed ramps (Fig. 1). At ambient T (Fig. 1a) Co shows a f cc -hcp coexistence 1 , with both phases presenting the texture of a highly oriented 1 The observed f cc-hcp coexistence is a consequence of the alignment of the two lasers powder. Conversely, KCl in the B2 phase shows a nice powder signal. Upon T increase, the signal from the KCl PTM does not change considerably. On the other hand, it is possible to follow the progressive grain growth of Co, starting right after its complete transformation to the f cc structure as evidenced by the evolution from a powder-like (characterized by the presence of rings) to a single-crystal-like (spots) XRD pattern. Similarly to the case of other transition metals (14; 22; 71), above a certain T it was possible to observe the phenomenon referred to as "fast re-crystallization" i.e. for each measurement, single crystal spots belonging to the same crystallographic planes, disappear and appear at different azimuthal angles on the image plate (Fig. 1d and Fig. 1e) due to grain growth and re-orientation. Finally, under further T -increase, in eight of the performed ramps, it was possible to observe the appearance of a diffuse halo, characteristic of a liquid sample (Fig. 2a). The coexistence of liquid and solid phases for a single component system is a direct consequence of the presence of thermal gradients. Specifically, axial thermal gradients lead to XRD patterns simultaneously showing the liquid signal from the hotter portion of the sample at the surfaces and solid signal from the colder inner-most part of the sample. With further increase of T above melting, the relative intensity of the diffuse signal vs. the solid diffraction peaks increases as inner parts of the sample melt.

Changes in T vs. laser power plot, such as T plateau or sudden drops are often used as additional melting criterion. However, similar to the results obtained for Fe with an identical technique [START_REF] Anzellini | Melting of iron at Earth's inner core boundary based on fast X-ray diffraction[END_REF], only few of the experimental ramps of the present experiment evidenced such a behavior in the T evolution. On the other hand, as shown in Fig. 2b, it was possible to observe a plateau in the volumetric thermal expansion of f cc-Co at T corresponding to the estimated melting. Such phenomenon, arising from the inevitable thermal gradient within the sample can be interpreted as an additional confirmation of its melting. Indeed, f cc-Co volume expands with increasing T as commonly expected for solids up to a threshold value, corresponding to melting. The solid signal observed at higher temperatures is coming from un-melted portions of the samples that, due to thermal gradients, are still below melting T , with a volume effectively pinned at that of the hottest solid on the opposite surfaces of the samples and the successive rapid quench performed before the beginning of the actual heating ramp before melting [START_REF] Anzellini | Phase diagram of iron under extreme conditions measured with time-resolved methods[END_REF].

Due to the observed thermal gradients and the sensitivity of the XRD technique to the signal from liquid sample, the melting T was assumed as the average between the T of the last pattern corresponding to a completely solid sample and the first one showing diffuse scattering from a liquid.

The Co phase diagram constructed on the basis of the present experiments is reported in Fig. 3 and compared with results from our calculations and from literature. The ambient T data are those obtained before each heating ramps and do not necessarily represent the thermodynamic equilibrium (as some point are obtained from cold compression and others from the sample quenched from HT ). We note however that the observed f cc-hcp transition pressure at 300 K is in agreement with those obtained from nonhydrostatic compression [START_REF] Torchio | Probing the local, electronic and magnetic structure of matter under extreme conditions of temperature and pressure[END_REF], and lower than what expected on the basis of quasi-hydrostatic data (30; 37). We also note a good agreement between the HP -HT stability of the f cc phase observed in this study and the f cc-hcp phase boundary reported in previous studies [START_REF] Yoo | New b ( fcc ) -Cobalt to 210 GPa[END_REF]. However, because of the minimal temperatures that can be generated and measured in LH-DAC experiments it was only possible to obtain an in situ characterization of the HP -HT f cc-hcp phase boundary of Co for the ramp around 47 GPa.

The melting curve established on the basis of the here-obtained melting points can be well described by a Simon-Glatzel equation with the following parameters:

T m = 1768.15(K)(P (GP a)/35.62 + 1) 0.64

(1)

Extrapolation of the present experimental melting curve to lower pressure, down to ambient P is in remarkable agreement with the data recently obtained in large volume press by Wang et al. [START_REF] Wang | The melting curve of cobalt under high pressure[END_REF]. On the contrary, the present melting curve is higher than early determination by direct observation of movement on the sample surface(45; 10). In particular, at 60 GPa the differences are of the order of 800 K and 400 K with respect to the melting line of Errandonea [START_REF] Errandonea | Systematics of transition-metal melting[END_REF] and Lazor [START_REF] Lazor | Phase diagrams, elasticity and thermodynamics of ni, co and fe under high pressure[END_REF], respectively. A discrepancy between the melting line obtained using these two different melting criterion is not surprising as, with only few exceptions (74; 75; 71), similar situations were observed in most of the melting studies reported in the literature (14; 22; 76; 11; 77). However, it is interesting to note that the melting line reported by Errandonea [START_REF] Errandonea | Systematics of transition-metal melting[END_REF] corresponds to the onset of fast recrystallization (Fig. 3) as already the case for Fe, for which the melting curve determined by the speckle method [START_REF] Boehler | Temperatures in the Earth's core from melting-point measurements of iron at high static pressures[END_REF] plots very close to the onset of fast crystallization [START_REF] Anzellini | Melting of iron at Earth's inner core boundary based on fast X-ray diffraction[END_REF]. Such a correlation is not accidental, and is likely inherent to technical aspects of the LH-DAC and speckle techniques. In fact, grain reorientation and grain growth can facilitate grain migration under thermal gradients, which can be perceived by the speckle technique as movements on the sample surfaces and mis-interpreted as formation of liquid. On the other hand, it is more difficult to explain the discrepancy observed with respect to the data obtained by Lazor (45) that have been obtained using the same speckle technique as in Errandonea [START_REF] Errandonea | Systematics of transition-metal melting[END_REF]. Possibly these differences should be ascribed to differences in the adopted P -T metrology.

Concerning the comparison with calculations, our experimental and computational results are in good agreement. Computed melting curve is also in good agreement with the results of Zhang et al. (29) obtained using MD with a Zhou´s potential, whereas it is much lower than the one obtained by the same group using MD with a Pun potential [START_REF] Zhang | Molecular dynamics study of melting curve, entropy of fusion and solid-liquid interfacial energy of cobalt under pressure[END_REF], with a difference as large as 1900 K at 100 GPa.

Thermal equation of state

Fig. 4 shows the volumes measured for f cc-Co at HP -HT and the resulting compression curves along different isotherms. Starting from the presented data it was possible to establish the P -V -T equation of state (EoS) for f cc-Co using the EOSfit software suite [START_REF] Angel | EosFit7c and a Fortran module (library) for equation of state calculations[END_REF]. According to the formalism described in Angel et al. (78) P at HT can be described as the sum of P at a reference T condition (typically 300 K) and the thermal P with increasing T evaluated along isochors, and hence it can be expressed as:

P (V, T ) = P (V, 300K) + P T h (T ) (2)
where the P (V , 300 K) is the isothermal EoS of the material at ambient T and P T h (T ) the thermal pressure. In the present work, P (V , 300 K) was calculated from the data reported by Armentrout and Kavner (41), while (P T h ) was modelled fallowing Holland and Powell: Where Θ E is the Einstein T of the material (299 K for Co), K 0 is the bulk modulus obtained from the isothermal EoS at ambient T , α 0 is the thermal expansion coefficient at 300 K and ζ 0 is expressed as:

P T h (T ) = α 0 K 0 Θ E ζ 0 ( 1 exp(Θ E /T ) -1 - 1 exp(Θ E /300) -1 ) (3)
ζ 0 = (Θ E /300) 2 exp(Θ E /300) (exp(Θ E /300) -1) 2 (4)
As shown in Fig. 4 data grouped considering T ranges of ± 100 K are well described by a 3 rd order Birch-Murnaghan EoS at ambient T and a thermal pressure modelled according Holland and Powell expression with the following parameters: V 0 =44.88 [START_REF] Friedel | The Physics of Metals[END_REF] Å3 ; K 0 =194(2) GPa; K I 0 =3.75(3) and α 0 =2.897(8)×10 -5 K -1 .

Calculations

The results of the present QMD melting simulations obtained using VASP are summarized in Tables 1 and2 and compared to experimental results and work in literature in Fig. 3. The errors in the obtained melting points (T m ) are half of the increment of the initial T for a series of computer runs at the corresponding density [START_REF] Burakovsky | Ab initio melting curve of osmium[END_REF]. Increment of 250 K were chosen for the first two points, and increased at higher pressures (500 K for the 3rd, 4th and 5th pressure point, 750 K for the 6th and 7th pressure point, and 1000 K for the last (8th) pressure point. The corresponding T m errors are listed in the two tables as ∆T m . The errors in melting P (P m ) are negligibly small, of order 1-2 GPa for each case.

The best fits to the corresponding six data points to a Simon-Glatzel

Data are very little dispersed, with fits yielding to χ 2 of ≈ 1.5 if T m at ambient P is fixed to the experimentally determined value of 1768 K. Otherwise χ 2 values are around 1, if T m at ambient P is left as a free parameter. In this latter case best fit values for T m are 1762.4 K for PM f cc-Co and 1768.1 K for NM f cc-Co, this second in closer agreement with experiments at ambient pressure.

The initial slopes (dT m (P )/dP | P =0 ) of the two melting curves are 36.9 K/GPa (PM) and 37.5 K/GPa (NM). Either value is consistent with (37.1±1.1) K/GPa given by the Clausius-Clapeyron relation dT m /dP = T m ∆V m /∆H m , where ∆V m and ∆H m are the volume and enthalpy changes at melt, respectively, with the literature values of ∆V m = 0.35 cm 3 /mole and ∆H m = 16.7 ± 0.5 kJ/mole. The present experimental and simulated Simon-Glatzel melting curves (represented in Fig. 3 with blue, cyan and pink continuous lines, respectively) are in mutual agreement. A closer look indicates that melting of the simulated PM phase of Co is in sightly better agreement with experimental determination up to about 110 GPa, while, at higher pressures, NM calculations yields to a better agreement with the extrapolation of the measured melting curve.

Conclusions

The P -T phase diagram of cobalt was determined up to 100 GPa and 4000 K by LH-DAC and synchrotron-based XRD measurements. QMD simulation for both non magnetic and paramagnetic phases of fcc-Co were also performed up to 1 TPa and 14000 K to characterize its melting curve. The agreement between the experiment and the calculation is excellent in the P -T range experimentally explored, with the computed melting for the paramagnetic phase in slightly better agreement with the experimental data. Unit-cell volumes of the f cc phase measured at high pressures and high temperatures were used to obtain the thermal equation of state of f cc-Co. Data can be well fit by a combination of a 3rd order Birch-Murnaghan EoS describing the P -V compression curve at ambient T with a Holland and Powell expression for the thermal pressure with the following parameters: V 0 =44.88(5) Å3 ; K 0 =194(2) GPa; K I 0 =3.75(3) and α 0 =2.897(8)×10 -5 K -1 . Finally, the value of 37.5 K/GPa of the slope of Co melting line at 0 GPa obtained from the calculations performed for NM-f cc Co can be compare to the values reported for Fe (30.5 K/GPa, ( 14)) and Ni (38 K/GPa, [START_REF] Lord | The melting curve of Ni to 1 Mbar[END_REF]). Although, we note an increase in the values of the melting slope as a function of the d electron occupation, this increase is relatively small and can be considered within the experimental error. Therefore, the obtained results do not necessarily support the hypothesis that the behavior of the melting curve of 3d transition metals depends on the d-electron occupation as proposed in Japel et al. [START_REF] Japel | Melting of copper and nickel at high pressure: The role of d electrons[END_REF]. programme (Grant agreement No. 724690). This work was supported by the Generalitat Valenciana under grants PROMETEO CIPROM/2021/075-GREENMAT and MFA/2022/007, and by the Spanish Ministerio de Ciencia e Innovación, Agencia Estatal de Investigación, and the European Union (MCIN/AEI/10.13039/501100011033) under grants PID2019-106383GB-41 and RED2018-102612-T (MALTA Consolider Team).This study forms part of the Advanced Materials program and is supported by MCIN with funding from European Union Next Generation EU (PRTR-C17.I1) and by the Generalitat Valenciana. S.A. thanks the Generalitat Valenciana for the CIDE-GENT grant no. CIDEXG/2022/6.

Disclosure statement

The authors declare no conflict of interest

Data Availability

The datasets generated during and/or analysed during the current study are available from the corresponding author upon request. Figure 2: a) Integrated XRD patterns for increasing T around 47 GPa. The onset of melting, characterized by the first appearance of the diffuse signal, is observed at 2951 K (blue pattern). The diffuse scattering increases with the rising T , showing its maximum at 3256 K (red pattern). b) Evolution of T (black points) and sample's volume (green empty points) during the heating ramp performed at 47 GPa. It is possible to observe a plateau in the volumetric expansion starting between the measurement at 2860 K and 2951 K, independently confirming the onset of melting. Concerning the T evolution, it is possible to observe a first plateau after 2500 K ascribed for this particular ramp to the onset of fast re-crystallization. A sudden drop is observed after 3200 K, once the sample is already molten. [START_REF] Yoo | New b ( fcc ) -Cobalt to 210 GPa[END_REF] and used here as reference. Experimentally observed solid phases are reported as solid points: in green the hcp phase(or hcp-f cc coexistence), in blue the f cc phase. The empty blue symbols correspond to the experimentally observed liquid points. Black solid diamonds are used to evidence where fast re-crystallization was detected. The melting points calculated in a P -range up to 200 GPa (and their corresponding Simon-Glatzel curves) are reported for both PM and NM f cc-Co for comparison with the present experimental points. For reference, the melting line of KCl is also reported as a dashed orange line.

Figure 1 :

 1 Figure 1: 2D XRD signal collected on the image plate of the Pilatus 2M detector showing snapshots of the T -induced textural evolution of the sample and the insulating material during a heating ramp performed around 57 GPa at 300 K, 1950 K, 2627 K, 3262 K, and 3398 K.

  Notes on contributor(s) S.B. and R.T. conceived the experiment. S.A., S.B and R.T. conducted the HP-HT experiment. S.A. analyzed the results. L.B. and S.R.B. performed the calculations. D.E. and D.A contributed to the discussion and provided funding. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Figure 3 :

 3 Figure 3: Phase diagram of Co as obtained in the present work compared to literature studies. The solid-solid phase boundary reported as black dashed lines are after Yoo et al.[START_REF] Yoo | New b ( fcc ) -Cobalt to 210 GPa[END_REF] and used here as reference. Experimentally observed solid phases are reported as solid points: in green the hcp phase(or hcp-f cc coexistence), in blue the f cc phase. The empty blue symbols correspond to the experimentally observed liquid points. Black solid diamonds are used to evidence where fast re-crystallization was detected. The melting points calculated in a P -range up to 200 GPa (and their corresponding Simon-Glatzel curves) are reported for both PM and NM f cc-Co for comparison with the present experimental points. For reference, the melting line of KCl is also reported as a dashed orange line.

Table 1 :

 1 The eight ab initio melting points of PM f cc-Co, (P m , T m ± ∆T m ), obtained from the Z method implemented with VASP.

	lattice constant ( Å) density (g/cm 3 ) P m (GPa) T m (K) ∆T m (K)
	3.6	8.3901	4.96	1900	125.0
	3.4	9.9595	60.5	3270	125.0
	3.3	10.893	99.9	4150	250.0
	3.2	11.946	183.4	5430	250.0
	3.1	13.140	290.6	6850	250.0
	3.0	14.498	448.4	8570	375.0
	2.9	16.050	681.7	10610	375.0
	2.8	17.832	1030	13040	500.0

Table 2 :

 2 The eight ab initio melting points of NM f cc-Co, (P m , T m ± ∆T m ), obtained from the Z method implemented with VASP.

	lattice constant ( Å) density (g/cm 3 ) P m (GPa) T m (K) ∆T m (K)
	3.6	8.3901	5.60	1970	125.0
	3.4	9.9595	60.6	3450	125.0
	3.3	10.893	100.0	4250	250.0
	3.2	11.946	184.2	5650	250.0
	3.1	13.140	294.9	7170	250.0
	3.0	14.498	460.8	9050	375.0
	2.9	16.050	710.3	11400	375.0
	2.8	17.832	1088	14380	500.0
	equation provide, respectively for paramagnetic and non magnetic calcula-
	tions, the following melting curves:
		T PM fcc-Co m	(P ) = 1768 1 +	P 25.9	0.54 ,

Acknowledgement(s)

The authors acknowledge the DLS synchrotron facility for provision of beamtime at the beamlines I15 (exp. CY21943). The authors are also grateful to Francesca Miozzi, Ruggero Giampaoli, Annette Kleppe and Allan Ross for their support in the experimental preparation. Femtosecond laser micro-machining at IMPMC has been developed and realized by the "Cellule Project" with the financial support of ANR 2010-JCJC-604-01. D.A. and S.B. have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation


Georg Lackner

Florent Domine
email: florent.domine@gmail.com

Denis Sarrazin

Daniel F Nadeau

Maria Belke-Brea

Meteorological, snow and soil data, CO 2 , water and energy fluxes, from a low-Arctic valley in the forest-tundra ecotone of Northern Quebec

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The forest-tundra ecotone (FTE) marks a transition zone where the open-canopy forest of the boreal biome merges with the treeless Arctic tundra biome. According to [START_REF] Callaghan | The dynamics of the Tundra-Taiga Boundary: An overview and suggested coordinated and integrated approach to research[END_REF], the FTE spans more than 13 400 km across the northern parts of North America, Asia, and Europe, with a width of up to several hundred kilometers. This makes it the world's largest vegetation transition zone. A trend towards increased vegetation has been observed in the FTE. In fact, the above-ground biomass is on the rise for all Arctic environments [START_REF] Meredith | Polar Regions[END_REF]. Future projections indicate that the areal extent of tundra vegetation will decrease by at least 50% by 2050 (Pearson et al., 2013), while woody shrubs and trees will expand to 24-52% of the current tundra region, or 12-33% if tree dispersal is restricted [START_REF] Meredith | Polar Regions[END_REF]. This change will have major repercussions, such as large reductions in the soil carbon content due to more frequent wildfires (Mack et al., 2011) and widespread permafrost degradation occurring at increased rates compared to when only the changing environmental conditions are considered (Jones, 2015).

To understand, quantify, and project changes in the FTE, satellite monitoring and surface modeling are essential. However, both require in situ measurements. Although satellites cover large parts of the Earth's surface and are able to estimate a variety of surface-related variables (e.g., surface temperature (Qu et al., 2019), turbulent heat fluxes [START_REF] Jiménez | Applying multiple land surface temperature prod-ucts to derive heat fluxes over a grassland site[END_REF], vegetation cover [START_REF] Guo | Delineation of the forest-tundra ecotone using texture-based classification of satellite imagery[END_REF]), most must be calibrated and/or validated using point measurements (e.g., Boisvert et al. (2015); [START_REF] Riihelä | An intercomparison and validation of satellite-based surface radiative energy flux estimates over the Arctic[END_REF]; [START_REF] Martin | Comprehensive in situ validation of five satellite land surface temperature data sets over multiple stations and years[END_REF]). Surface schemes for climate models also require validation using in situ data (Krinner et al., 2018). Despite this need for data, few stations in Arctic regions are equipped to measure large sets of variables over long periods of time.

The Tasiapik Valley in northern Quebec, Canada is located within the FTE (Latifovic et al., 2017). This is an ideal location for conducting research because the lower valley is covered in open boreal forest while the upper valley consists of shrub and lichen tundra. Arctic and boreal biomes, as well as mixtures of both, are therefore present in close proximity to each other. Meteorological, snow, and soil data were collected starting in September 2012, and annual field surveys were conducted to study snow and soil characteristics (Domine et al., 2015). Turbulent heat fluxes were measured between 2017 and 2020 using the eddy covariance technique.

Detailed annual snowpit data are extremely valuable, as studies have shown that current snow models struggle to accurately simulate vertical profiles of density and thermal conductivity (Domine et al., 2016;Barrere et al., 2017;Gouttevin et al., 2018;[START_REF] Royer | New northern snowpack classification linked to vegetation cover on a latitudinal mega-transect across northeastern Canada[END_REF]Lackner et al., 2022a). Although new models are being developed to account for this deficiency [START_REF] Jafari | The impact of diffusive water vapor transport on snow profiles in deep and shallow snow covers and on sea ice[END_REF]Simson et al., 2021), critical validation data for snow density profiles remain very rare in the Arctic. In this paper, we present information on two research sites while fully documenting all the available data and providing a detailed analysis of the soil properties at the sites. We provide a comprehensive data set with meteorological, snow, soil, and turbulent flux data from 2012 to 2021.

Site Description

The study site is located in the Tasiapik Valley (Fig. 1) close to the village of Umiujaq,Quebec,Canada (56.55861°N,76.48222°W). The valley forms a small catchment 4.5 km long and 1.3 km wide, and borders Tasiujaq Lake at an elevation of 0 m. The climate is subarctic with a mean annual temperature of -4.0°C. No long-term precipitation records exist, but our recent data indicate a rather high mean annual precipitation compared to typical subarctic climates, at between 800 and 1000 mm. Around 50% of the precipitation occurs as snow. There is usually continuous snow cover from late October to early June.

Hudson Bay to the west of the valley (4 km distance) strongly influences the weather pattern. There is frequent fog throughout the year [START_REF] Robichaud | The Weather of Atlantic Canada and Eastern Quebec[END_REF]. Advection fog often forms in July and August when warmer air moves over the cold Hudson Bay. The precipitation pattern is influenced by the extent of the ice cover in Hudson Bay. After freeze-up, the precipitation rate drops and remains rather low until spring. Precipitation then increases in summer and peaks in late summer and fall. The heat storage of Hudson Bay in summer and the subsequent release in fall also affects air temperatures, resulting in relatively cold summer temperatures and warmer fall temperatures.

In Tasiapik Valley, vegetation is fairly spatially heterogeneous. In the upper valley, a mixture of lichen (Cladonia sp., mostly C. stellaris and C. rangiferina), and shrubs with dwarf birch (Betula glandulosa), and other shrub species (Vaccinium sp., Alnus viridis subsp. crispa and Salix sp. including S. planifolia) with heights between 0.2 and 2 m dominate. Live lichen are present not only on lichen tundra, but also in the understory of birches less than 80 cm tall. Live lichen can form in layers that are 5 to 20 cm thick over a 2 to 4 cm layer of dead lichen, progressively transitioning to a thin organic litter layer (Gagnon et al., 2019). The litter layer is only about 2 cm thick under lichen tundra and up to 5 cm thick under 80 cm tall birch. Taller birches such as those found in water tracks have a mossy understory with a 10 cm thick organic layer (Gagnon et al., 2019).

Towards the bottom of the valley, vegetation turns into a forest-tundra with black spruce (Picea mariana) covering about 20% of the surface. Below the open canopy, numerous birches are present. In areas not covered by woody vegetation, a variety of grasses and mosses cover the surface.

There is discontinuous to sporadic permafrost in the valley (Lemieux et al., 2020) due to the presence of permafrost mounds (lithalsas). At the exact location of the experimental setup, no permafrost was present. However, lithalsas were found within 30 m of the upper valley site. The soil composition is detailed in Sect. 7.

On 28 September 2012, a comprehensive meteorological station called TUNDRA (56.55877°N, 76.48234°W; elevation: 132 m) was deployed (Figure 1). Instruments were placed on a tripod. On 15 February 2013, snow temperature and thermal conductivity sensors were installed on a vertical post a few m from the tripod, in dwarf birch 30 cm tall. Soil temperature and humidity were measured starting on 19 September, 2015. One set of instruments was located under lichen, and one under low birch near the post holding the snow sensors.

The FOREST station (56.55308°N, 76.47258°W, elevation: 82 m) was set up on 21 September 2015 with the same instruments as those at the TUNDRA station. A fast-response gas analyzer with a sonic anemometer (model IRGASON, Campbell Scientific, USA) was mounted at a 10 m tower about 15 m north of the TUNDRA station on 10 June 2017 and was operational with no shrubs, about 15 m northwest of the tripod at TUNDRA. Multiple Reconyx time lapse cameras took several pictures per day and were installed in order to monitor the instrumentation and their surroundings. A complete list of all instruments deployed at TUNDRA and FOREST, as well as when each instrument was installed and at what precise position, is provided in Tables 1 and2, respectively. The data obtained are available in Lackner et al. (2022b). 95 Air temperature and relative humidity (RH) were measured at TUNDRA with a HC2-S3-XT sensor installed at a height of 2.3 m. No large data gaps were present. Small data gaps were filled using information from another sensor mounted close by on the 10-m tower. As the RH measurements never reached ice saturation in winter, we corrected the raw values using linear 105 equations based on air temperature in order to reach ice saturation. The method has been detailed in [START_REF] Royer | New northern snowpack classification linked to vegetation cover on a latitudinal mega-transect across northeastern Canada[END_REF]. 2, 2.5, 5, 7, 9.5, 12, 17, 21, 27, 32, 37, 42, 44.5, 47, 49.5, 52, 57, 62, 67, 72, 77, 82 (https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5). However, as the ERA5 data do not correspond with the same elevation, we corrected for a ≈10 hPa offset between the ERA5 data and the observations that was detected for times when both sets of data were available. Except for two long power outages (see Sect. 5), there were no other significant gaps in the time series for pressure. The gaps from the power outages were filled using the corrected ERA5 data.

Wind speed data were collected with a cup anemometer at a height of 2.3 m at TUNDRA. In winter, the instrument was sometimes stalled due to frost during stable, low-wind conditions. To fill those gaps, we used data from a Young anemometer affixed at a height of 10 m on the nearby tower (CEN,1997(CEN, -2020)). At times, the Young anemometer became covered in ice at the same time as the cup anemometer. During those times, we used the data from the FOREST station, where the instrument was installed at the same height as at TUNDRA. During one period in January 2021, all available instruments in the valley were stalled. We therefore used an instrument from the UMIROCA station (CEN, 1997(CEN, -2020)), a station located on the shore of Hudson Bay. All data used to fill the gaps were corrected using a linear regression. This was done to account for different installation heights and environments (vegetation, elevations, topography). Figure 2 shows the time series of all the variables mentioned above.

FOREST

At the FOREST site, air temperature and wind speed were recorded with the same instruments as at TUNDRA (see Fig. 3).

The temperature time series had no large gaps (> 3 h), and small gaps (≤ 3 h) were filled by interpolation. We used values from TUNDRA to gap fill data for FOREST when the cup anemometer was ice-covered in winter, and applied a linear regression to adjust wind speeds. There was also an RH sensor at FOREST, but due to malfunctions, the recorded data could not be used. 140

Compared to TUNDRA, temperatures at FOREST were slightly higher throughout the year, except in November and December.

From January 2016 to December 2020, the mean difference was ≈1°C. Since the surface roughness is greater at FOREST than at TUNDRA, wind speeds were lower for specific heights. Indeed, the mean wind speed from January 2016 to December 2020 was about ≈1 m s -1 lower at FOREST than at TUNDRA.

Radiation

TUNDRA

The surface radiation terms were measured using a 4-component radiometer (model CNR4, Kipp & Zonen, The Netherlands) mounted at 2.3 m above ground. It was equipped with a CNF4 heating/ventilation unit (Kipp & Zonen, The Netherlands), which mostly prevented snow accumulation and the build-up of frost and dew on the measuring lenses. The CNF4 was programmed to be active for 5 min every hour, just before radiation measurements were collected.

From 10 October 2018 to 27 September 2020, no temperatures were recorded in the CNR4, which were otherwise used to correct the longwave radiation. During this period, we estimated CNR4 temperatures using a gradient boosting regressor from scikit-learn [START_REF] Pedregosa | Scikit-learn: Machine Learning in Python[END_REF] with the following input variables: air temperature, radiation, humidity, and wind speed.

We trained the decision tree using data from periods when the CNR4 temperatures were recorded and found a good agreement between the observed and estimated values. Using the estimated temperatures, we calculated the longwave radiation (LW) using:

𝐿𝐿𝐿𝐿 = (5.67 × 10 -8 ) 𝑉𝑉 𝐶𝐶 𝑇𝑇 4 , ( 1
)
where V is the measured output voltage, C is the calibration constant and T is the temperature of the instrument in K.

In October 2018, the entire CNR4 unit was replaced and recalibrated. As the calibration constants changed, we applied a correction to account for the drift. We assumed that the calibration constants varied linearly over time between both calibrations. Between October 2018 and September 2021, no recalibration took place. We therefore used the constants of the instrument deployed in October 2018 without time variations.

Small, mostly negative values were observed at night for up-and downwelling shortwave radiation, although both these values are typically expected to be zero. To compensate for this discrepancy, we calculated the mean offset for both components and subtracted them from the respective upwelling and downwelling radiation.

Despite the CNF4 heating unit, the accumulation of frost and snow sometimes interfered with the incident radiation measurements (long and shortwave). The exact periods when the CNR4 sensors were impacted by frost and snow could only be determined visually. Since a detailed visual inspection could only be performed at the site, we applied several quality control criteria to the downwelling radiation (both long and shortwave) to exclude the affected periods. Therefore, all values at times when the wind speed was < 0.5 m s -1 or the uncorrected longwave downwelling radiation was > -5 W m -2 were discarded if the air temperature was < 0°C. Subsequently, gaps of up to 3 hours were interpolated, while longer gaps were filled using corrected ERA5 data. The correlation between ERA5 data and observations was established using the remaining data that passed our quality control measures. The 9-year time series for the 4 radiation components at TUNDRA are shown in Fig. 4.

FOREST

The FOREST station setup was similar to that at TUNDRA, with a CNR4 radiometer at a height of 2.3 m combined with a CNF4 heating/ventilation unit. The CNR4 at FOREST was recalibrated in October 2021. The raw values were corrected for the drift of the calibration constants. No power outages or instrumental failures occurred at this site and the complete time series from 28 September 2015 is shown in Fig. 5. At FOREST, we also observed small, non-zero values at night for the shortwave radiation. To account for these offsets, we applied the same procedure as for TUNDRA. The same problems with frost and snow build-up were observed at FOREST. We applied the same criteria as for TUNDRA. The linear equations for the ERA5 data are also shown in the Supplementary Material.

Small differences became apparent when we compared the radiation observations at both sites. The downwelling shortwave radiation was smaller at FOREST, which can be attributed to greater topographic shading. Between January 2016 and December 2020, when data from both stations were available, the mean difference was 4.15 W m -2 . For the longwave counterpart, there was very little difference in summer, but a small deviation was detected in winter when the longwave downwelling radiation was slightly higher at FOREST. This might be an effect of the higher vegetation levels at FOREST. Radiation from the steep ridges surrounding the valley may also contribute to the longwave downwelling radiation. However, for the same 4-year period, the difference was only 1.5 W m -2 . Differences in upwelling radiation were slightly higher (TUNDRA-FOREST: 4.6 W m -2

for shortwave radiation and -2.15 W m -2 for longwave radiation). However, these values heavily depend on the radiative and thermal properties of the surface and soil, as well as on the duration of the snow-free period.

Precipitation

In May 2016, a T200B precipitation gauge (Geonor, USA) equipped with a single Alter shield was installed to measure solid and liquid precipitation close to the TUNDRA station. The gauge recorded hourly cumulative precipitation (PRtot) in kg m -2

h -1 , equivalent to mm h -1 . The standard deviation (σi) of each hourly measurement was also recorded. The gauge has an inlet with a diameter of 16 cm and the rain/snow is collected in a cylinder with a capacity of 1000 mm. An anti-freeze agent was added in the cylinder to melt snow and keep the stored water from freezing. The use of an anti-freeze agent is preferable to a heating system, as heat increases water loss due to evaporation, particularly in summer. Evaporation is further reduced by adding a thin layer of oil to the water surface. Three vibrating wire load sensors weigh the entire cylinder and provide three independent measures for mass. First, the raw cumulative values from the three vibrating wire load sensors were transformed into hourly mass variations. Occasional erratic fluctuations occurred, induced by perturbations of the wire load sensors by the wind and other factors. Data that were obviously inconsistent given the latitude, for instance those beyond ± 30 mm h -1 , were eliminated and the three independent precipitation rates (PRi with i = 1, 2, 3) were combined using a weighted mean. Each hour, the wire load sensor with the highest standard deviation (σi) was removed and the weighted mean was computed using the remaining two values, with the inverse of the standard deviation defining the weights as wi = 1/σi, such that

𝑃𝑃𝑃𝑃 𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑤𝑤 1 𝑃𝑃𝑃𝑃 1 +𝑤𝑤 2 𝑃𝑃𝑃𝑃 2 𝑤𝑤 1 +𝑤𝑤 2 .
(2).

Subsequently, the precipitation was partitioned into snow and rain using a single threshold of 0.5°C, determined through visual observations at the airport weather station, located only 3.2 km away. In addition, a correction for the underestimation of solid precipitation in the presence of wind (undercatch) was applied following Kochendorfer et al. (2018),

𝑃𝑃𝑃𝑃 𝑐𝑐𝑡𝑡𝑐𝑐 = 𝑃𝑃𝑃𝑃 𝑢𝑢𝑢𝑢𝑐𝑐𝑡𝑡𝑐𝑐 1 0.742exp(-0.181𝑈𝑈+0.332) (3),
where PRcor is the corrected precipitation rate in mm, PRuncor is the uncorrected precipitation (in mm), and U (in m s -1 ) is the wind speed at the height of the gauge orifice, provided by the nearby weather station. Prior to installing the precipitation gauge with the single alter shield and three independent wire load sensors, a simpler version with a home-made alter shield and only one wire load sensor was present at the site. However, this setup did not produce reasonable data and therefore the data were discarded. For the period between 2012 and 2016, we used only ERA5 data, as it proved to be closer to our observations than data from the two closest meteorological stations from Environment and Climate Change Canada (Kuujjuarapik, 160 km south and Inukjuak, 230 km north). When comparing summer and winter monthly precipitation observations with ERA5 data, we observed no biases for the summer values. However, we detected an underestimation of ERA5 for the winter months, with cumulative precipitation exceeding 50 mm. To correct for this bias, the values for November to April were multiplied by 1.3822 for months with a cumulative precipitation greater than 50 mm. Otherwise, no correction was applied to the ERA5 precipitation data.

In the lower panel in Fig. 6, the daily precipitation at TUNDRA is shown from 2016 to 2021, as well as the ERA5 precipitation data before 2016. The upper panel in Fig. 6 depicts the seasonal cumulative precipitation for each summer and winter period, respectively. The dates associated with the onset of snow and meltout are shown in Table 3, and were determined using snow gauge data and time lapse cameras.

Spectral and Broadband Albedo

The surface albedo for various types of vegetation cover was measured between 12 and 18 September 2015 for wavelengths between 346.5 and 2513 nm with a portable field spectrometer (HR-1024 portable spectroradiometer, Spectra Vista Corporation). The radiation signal over this spectral range was monitored with a Si photodiode (346.5 to 982 nm) and two

InGaAs photodiodes over the 982-1882 and 1882-2513 nm ranges. For wavelengths greater than 2340 nm, upwelling irradiance was very low, resulting in a mostly unusable signal. We therefore present only the results for the 346.5-2340 nm range. The radiation signal was collected by an integrating sphere placed at the end of a 3 m rod to minimize interference from the person taking the measurements. The horizontal position of the sphere was ensured by an electronic inclinometer next to the sphere. The downwelling signal was collected first. Then, the sphere was rotated 180° to record the upwelling signal. A photodiode monitored the solar radiation to ensure that it remained constant (within 1%) during both measurements. Spectra were smoothed over 10 nm intervals for wavelengths shorter than 1780 nm, and over 60 nm intervals for longer wavelengths.

Five spectra were recorded over areas with lichen cover in the vicinity of the TUNDRA site. Five spectra were also recorded over short birch shrubs with lichen understories in the same area. We visually estimated that > 90% of the leaves were still green. The FOREST site consisted of a mixture of spruce that reached up to 3 m high, birch and grass. As such, it was not possible to obtain a representative spectrum of the entire FOREST area, as this would have required measurements from a height of at least 10 m. We therefore measured eight spectra of dense, short spruce within a few km of the FOREST station (Fig. 7).

Lastly, we measured the spectra of grassy surfaces with little to no erect vegetation and with little to no lichen. Although these spectra were not necessarily recorded at the FOREST site, the grassy vegetation was fairly similar at both locations. The average spectra for all four types of vegetation are shown in Fig. 7. The broadband (BB) albedo (346.5-2340 nm) of each spectrum was calculated from the ratio of the integrated upwelling radiation to downwelling radiation. The average BB albedos were 0.203 for lichen, 0.155 for birch, 0.174 for spruce and 0.180 for low grassy vegetation. Variations in the spectral albedo were observed for the measurements at the different sites, as detailed in Table 4. Variations between sites were smallest for lichen, increased for birch and spruce, and were highest for low grassy vegetation, Variations in birch and spruce are probably mostly due to differences in the leaf area index and in the amount of woody vegetation present.

Differences in low grassy vegetation are due to variations in species and the occasional presence of short shrubs, such as

Vaccinuim sp. and Betula glandulosa. These data allowed for the estimation of the BB albedo of the FOREST site. We estimated that the vegetation coverage is 25% spruce, 40% low grassy vegetation, and 35% birch, leading to a BB albedo of 0.170. We estimated the TUNDRA site to be 60% lichen and 40% birch, with a BB albedo of 0.184.

Turbulent Flux Data

Turbulent heat fluxes were measured at TUNDRA using a fast-response sonic anemometer and a CO2/H2O infrared gas analyzer (IRGASON, Campbell Scientific, USA) installed 4.2 m above ground on the 10-m tower. The three components for wind speed and concentrations of H2O and CO2 were recorded with a CR3000 datalogger (Campbell Scientific) at a frequency of 10 Hz. The 10-Hz data were processed with the EddyPro® (version 7.0.3; Li-COR Biosciences, USA) software package.

This software calculates 30-min averages of the turbulent heat and carbon fluxes and a set of corrections. These corrections are the detrending of turbulent fluctuations based on a running mean, covariance maximization, density fluctuation compensation [START_REF] Webb | Correction of flux measurements for density effects due to heat and water vapour transfer[END_REF], and analytic correction of high-pass and low-pass filtering effects [START_REF] Moncrieff | A system to measure surface fluxes of momentum, sensible heat, water vapour and carbon dioxide[END_REF]. To align the coordinate system with the surface, we have chosen to apply a double rotation. The planar fit method from [START_REF] Wilczak | Sonic anemometer tilt correction algorithms[END_REF] was also tested, but it was unsuccessful due to the presence of snow. In order to assess data quality, a random uncertainty quantification was used following [START_REF] Finkelstein | Sampling error in eddy correlation flux measurements[END_REF], which identified outliers, spikes, and artifacts. Finally, the 0-1-2 quality scheme from [START_REF] Mauder | A strategy for qual-ity and uncertainty assessment of long-term eddy-covariance measurements[END_REF] was applied to flag the data, and segments that were flagged as 2 (poor quality)

were removed from the data set.

To sort out the remaining outliers and to fill the gaps according to the EddyPro® procedure, post-processing was necessary.

This was done using the PyFluxPro program (Isaac et al., 2017), which comprises six processing levels and uses EddyPro output files as inputs and produces a continuous time series for all fluxes. For the first three processing levels, data were read, quality controlled, and finally, auxiliary measurements were merged when gaps were present. The quality control includes (i) range checks based on user-defined limits, (ii) spike detection, (iii) manual removal for specific dates, and (iv) data rejection based on other variables. Erroneous flux data were rejected based on CO 2 and H2O signal strengths from the infrared gas analyzer (IRGA) and internal error codes from both the sonic anemometer and the IRGA. For the fourth processing level, meteorological variables were gap-filled with ERA5 data. Each variable was bias-corrected using a linear fit between ERA5

and flux tower observations during periods when both were available.

Finally, the fluxes were gap-filled using interpolation and a self-organizing linear output map (SOLO) -a type of artificial neural network (ANN) (see [START_REF] Hsu | Self-organizing linear output map (SOLO): An artificial neural network suitable for hydrologic modeling and analysis[END_REF] and [START_REF] Abramowitz | Towards a benchmark for land surface models[END_REF]). Interpolation was only applied for gaps of up to 3 hours, while SOLO was used for longer gaps. SOLO requires a set of environmental drivers such as air temperature, radiation, and humidity, as well as the fluxes themselves as inputs. SOLO first constructs relationships between the environmental drivers by applying an ANN-equivalent of a principal component analysis. It then uses an ANN-equivalent of a multiple linear regression to make connections between the drivers and the fluxes. ANN together with marginal distribution sampling (MDS, Reichstein et al. (2005)) was shown to be the best choice for gap-filling flux data [START_REF] Moffat | Comprehen-sive comparison of gap-filling techniques for eddy covariance net carbon fluxes[END_REF]. The resulting series for the sensible 6 Snow Data

Snow Height

Two SR50 sonic distance sensors provided continuous snow height measurements near TUNDRA. One was installed exactly at the TUNDRA site and the other was mounted on the nearby 10-m tower. A snow height value of zero was assigned for the snow-free period in summer. Unfortunately, the snow height data were incomplete. We therefore decided to merge both data sets. The gaps that remained despite the merge were filled with estimates from time-lapse images of the snow poles. A similar SR50 sonic sensor was installed at FOREST. The snow height data at FOREST for winters 2016-17 and 2017-18 were also incomplete and thus, no data are shown for these periods. In spring, the snow height at FOREST almost reached the sensor.

We observed during our field visits that the wind formed a depression on the snow surface just below the sensor. We thus estimate that snow height was underestimated by about 20% by the sensor in late March-early April. The time series for both stations are depicted in Fig. 9. Snow height values at FOREST are consistently larger than at TUNDRA due to the presence of taller vegetation, which more effectively traps blowing snow. (SNOW2) from TUNDRA. They were equipped with Pt1000 thermistors (which are part of the TP08 needles) and collected temperature measurements every two days. SNOW1 was set up in 2015 in a patch of shrubs about 30 cm tall with a lichen understory. The Pt1000 thermistors were installed at 4, 14, 29, 44 and 64 cm above the lichen. However, because lichen height is somewhat arbitrarily determined, and given that the lichen might also be compacted by the snow, the indicated height data contain some uncertainty. SNOW2 was installed in 2018 on a patch of lichen. Four Pt1000 thermistors were placed at 7, 27, 47, and 67 cm above ground. Again, there is some uncertainty associated with these heights, as the there is no consistent line between the soil and lichen, making the zero reference slightly arbitrary. SNOW1 data are shown in Fig. 10.

For both stations, data associated with a positive snow temperature were deleted as they implied that the sensor was not buried in the snow or that the sensor was heated by the sun through a thin snow layer. Using time-lapse images, we were able to identify times when the thermocouples/thermistors were not covered with snow. However, as the camera was 10 to 15 m away from the stations, we cannot rule out that some data from times with no snow were included. Note that different snow heights and internal snow properties were observed at the two stations, and as such, the respective snow temperatures do not necessarily match for a similar measurement level.

FOREST

At FOREST, another snow pole (SNOW3) was installed and equipped with four Pt1000 thermistors (at 4, 14, 29, and 64 cm).

SNOW3 was placed in a patch of grass and moss. The heights associated with SNOW3 are reliable within 2 cm. No time-lapse camera was available at FOREST, and as seen in Fig. 9, the snow height time series was less complete. Thus, only positive temperatures were removed and no further data cleaning was performed. Figure 11 shows the snow temperature at the four measurement levels. Snow temperatures were substantially higher at FOREST due to the deeper snowpack.

FOREST

The soil temperature and water content were measured at FOREST using the same instruments as the TUNDRA site (Fig. 17).

The sensors were placed about 80 cm from the SNOW3 pole. The soil water content and temperatures at FOREST were very distinct from those measured at the TUNDRA site. During summer, the soil temperatures were slightly cooler than those under the low-shrub surface. However, in winter, the soil freezes late and the minimum temperatures were only slightly below 0°C due to the thick snow cover. The soil water content is substantially higher at FOREST than at TUNDRA because the soil contains less sand compared to TUNDRA and because more snow accumulates in winter at FOREST and melts in spring.

Soil Properties

The Tasiapik Valley consists of former beaches that have been uplifted by isostatic rebound after the Laurentide Ice Sheet melted a few millennia ago. According to Bhiry et al. (2011), land at an elevation of around 130 m, such as the TUNDRA site, emerged 6500 to 7000 years ago. The FOREST site, at an elevation 82 m, emerged about 5000 years ago. Because they were formerly beaches, the soil at both TUNDRA and FOREST sites is mostly sandy. Gagnon et al. (2019) conducted granulometric analyses at TUNDRA and reported a unimodal particle size distribution of around 500 µm (pure sand), with an occasional, small, secondary peak at around 80 µm (loamy sand). Based on two soil pits, we estimate the sand fraction of the soil at FOREST to be lower than at TUNDRA, but no granulometric analyses were performed there.

The organic carbon content of the soil at TUNDRA is among the lowest in the Arctic and subarctic (Gagnon et al., 2019), with about 1.5 kg m -2 of organic C in lichen tundra, and 4.2 kg m -2 in low birch shrubs (< 80 cm). No detailed soil analyses were performed at FOREST, but two soil pits were dug and revealed an organic litter layer 6 to 10 cm thick. The organic carbon content of the soil at FOREST was not measured, but given the thick litter layer, it is probably greater than at TUNDRA.

Soil thermal conductivity and density profiles are shown in Fig. 18. On 7 and 8 October 2014, short-distance spatial variation tests were performed, revealing changes within a range of 25% over a horizontal distance of 30 cm, and at a depth of 20 cm.

Overall, there was a clear trend for an increase in thermal conductivity with depth. The thermal conductivity of lichen was also measured and it was essentially the same as that of air, forming an efficient insulating layer in summer. In winter, snow crystals blend into the lichen. Therefore, we determined that assuming only a depth hoar snow layer while ignoring the lichen is likely adequate. We recommend using thermal conductivities of 0.12 W m -1 K -1 for the top 5 cm of the soil (starting at the base of the live lichen), 0.5 W m -1 K -1 for depths between 5 and 10 cm, 0.9 W m -1 K -1 between 10 and 20 cm, and 1.1 W m -1 K -1 for depths below 20 cm. We only measured three density profiles, which showed an increase in density down to 10 cm in depth,

and then remained at an almost constant value of around 1500 kg m -3 . Between depths of 0 and 10 cm, the density is approximately of 1000 kg m -3 . Sand has a specific heat of about 796 J kg -1 K -1 [START_REF] Carvill | 3 -Thermodynamics and heat transfer[END_REF].

Conclusions

The increasing temperatures in Arctic regions are causing substantial environmental changes, such as the thawing of permafrost and the greening of the Arctic landscapes. Both effects are more pronounced along the southern border of the Arctic, where the land is transitioning into a boreal forest. In this study, we present two data sets, a 9-year data set for TUNDRA and a 6-year data set for FOREST that include numerous measurements in soil, snow and above the ground at two sites along the treeline in eastern Canada. These data provide information that can be used to calibrate and improve earth system models, particularly snow schemes, which showed poor performance when simulating Arctic snowpack properties. Our data can help advance the understanding of the relationships between potential meteorological drivers, permafrost degradation and Arctic greening.

Figure 1 :

 1 Figure 1: (a) Location of the two sites in the Tasiapik Valley. (b) Location of the valley along the eastern shore of Hudson Bay in Northern Quebec. (c) Photo of the instrumentation at TUNDRA and (d) the instrumentation at FOREST. Source (a and b): ESRI.

Figure 2 :

 2 Figure 2: Time series of hourly air temperature, relative humidity, wind speed, and atmospheric pressure at TUNDRA. The red section of the atmospheric pressure curve represents local observations, while the grey sections represent ERA5 reanalysis data.

Figure 3 :

 3 Figure 3: Time series of hourly air temperature and wind speed at FOREST.

Figure 4 :

 4 Figure 4: Time series of hourly downwelling and upwelling shortwave and longwave radiation at TUNDRA.

Figure 5 :

 5 Figure 5: Time series of hourly downwelling and upwelling shortwave and longwave radiation at FOREST.

Figure 6 :

 6 Figure 6: Time series of cumulative precipitation and daily rain and snow. Before 28 May 2016, ERA5 data were used.

Figure 7 :

 7 Figure 7: Average spectral albedo for the four types of vegetation cover.

  and latent heat fluxes, as well as the CO2 fluxes, are shown in Fig. 8. Since the IRGASON is an open-path sensor that is sensitive to external disturbances such as precipitation particles, gaps are frequently present in the data set for the turbulent and CO2 fluxes. The fraction of gaps subsequently increased with each processing step in EddyPro® and PyFluxPro. Overall, 27% of the sensible heat flux, 43% of the latent heat flux, and 44% of the CO2 flux data were gap-filled using the SOLO. These values include two longer outages of IRGASON in March 2018 and from January to March 2019. The interpolated data and data gap-filled with SOLO are specifically flagged.

Figure 8 :

 8 Figure 8: Time series of hourly sensible and latent heat fluxes and the CO2 flux. The grey shaded areas indicate power outages at the station during which no flux data were recorded.

Figure 9 :

 9 Figure 9: Evolution of snow height from the automatic gauges at TUNDRA and FOREST.

Figure 10 :

 10 Figure 10: Bi-daily time series of the Pt1000 thermistors from the SNOW1 station at TUNDRA at heights of 4, 14, 29, 44 and 64 cm.

Figure 11 :

 11 Figure 11: Hourly time series of the Pt1000 thermistors from the SNOW3 station at heights of 4, 14, 29, and 64 cm.

Figure 16 :

 16 Figure 16: Time series of the daily soil temperature and the soil water content (SWC) volume under a patch of low shrubs 410 at depths of 9 cm, 15 cm, 27 cm, 39 cm, and 50 cm at TUNDRA.

Figure 17 :

 17 Figure 17: Time series of the daily soil temperature and the soil volume water content (SWC) below grass and moss at depths of 5 cm, 10 cm, 20 cm, 30 cm and 50 cm at FOREST.

Figure 18 :

 18 Figure 18: Thermal properties of soils. (a) Thermal conductivity; (b) density. Depths were measured from the base of the live lichen.

Table 1 : Instrumentation at the TUNDRA study site.

 1

	Variable	Instrument	Manufacturer	Height/Depth	Years available	Comment
		HC2-S3-XT sensor,
	Air temperature	inside white PVC	Rotronic	2.3 m	2012-2021
		tubing, ventilated
	Atmospheric pressure	IRGASON	Campbell Scientific	4.2 m	2017-2020	Before 2017 and after 2020 corrected ERA5 data
	Wind speed	A100 Cup anemometer	Vector instruments	2.3 m	2012-2021
		CNR4 with CNF4
	Radiation	heater/ventilator Kipp & Zonen	2.3 m	2012-2021
						Data before 2016
	Precipitation	T-200 BM	Geonor	2.3 m	2016-2021	from uncorrected
						ERA5
	Snow depth	SR50 acoustic gauge	Campbell Scientific		2012-2021
	Snow temperature	Pt1000 themistor	Hukseflux	4, 14, 29, 44 and 64 cm	2015-2021	Near TUNDRA (SNOW1)
	Snow	Pt1000 and
	temperature	thermcouples	Hukseflux

Table 2 : Instrumentation at the FOREST study site.

 2 The atmospheric pressure for SH was measured from June 2017 onward with the IRGASON analyzer. Before that date and after dismantling the instrument in April 2020, ERA5 data were used. ERA5 is a reanalysis product from the European Centre for Medium-Range Weather Forecast that provides hourly estimates for various

	2018-2021	Near TUNDRA
	cm	(SNOW2)

this instrument is susceptible to measurement errors caused by rain, snow, dew, or any other particles within the pathway of the gas analyzer. Complications with the IRGASON analyzer are detailed in Sect. 5. Gaps in the SH time series were filled using converted RH measurements.

Table 3 : Snow onset and meltout dates at the TUNDRA site, used to determine seasonal cumulative precipitation.

 3

	Snow year Snow onset	Meltout
	2012-13	9 November 2012 31 May 2013
	2013-14	26 October 2013	22 May 2014
	2014-15	31 October 2014	28 May 2015
	2015-16	18 October 2015	28 May 2016
	2016-17	12 October 2016	24 May 2017
	2017-18	29 October 2017	15 June 2018
	2018-19	6 October 2018	4 June 2019
	2019-20	29 October 2019	11 June 2020
	2020-21	17 October 2020	24 May 2021

Table 4 : Variation in albedo within each vegetation class, at 550 and 1100 nm.

 4

		550 nm	550 nm % variation 1100 nm	1100 nm % variation
	Lichen	0.116 to 0.131	11.5%	0.359 to 0.393	8.6%
	Low birch	0.051 to 0.067	23.9%	0.305 to 0.387	21.2%
	Spruce	0.058 to 0.107	45.8%	0.355 to 0.559	36.5%
	Low grassy 0.053 to 0.080	33.7%	0.370 to 0.523	29.3%

Acknowledgements.

This work was funded by the French Polar Institute (IPEV), the Natural Sciences and Engineering Research Council of Canada (Discovery Grant and Northern Research supplement programs), the BNP-Paribas foundation (APT project), and the European Union's Horizon 2020 research and innovation program under grant agreement No. 101003536 (ESM2025 -Earth System Models for the Future) and grant agreement No. 727890 (INTAROS). We thank the community of Umiujaq for welcoming us and allowing this research to be conducted. We benefited from facilities from the Centre d'Études Nordiques during the entire duration of this study. Compute Canada assisted with data storage and handling. This work is a contribution to the IASC project Terrestrial Multidisciplinary distributed Observatories for the Study of Arctic Connections (T-MOSAiC).

Data availability

The data are available on the PANGAEA repository, https://doi.org/10.1594/PANGAEA.946538 (Lackner et al., 2022b).

[For review, a perhaps easier data access is https://www.dropbox.com/sh/4j828hj4h2oee68/AACZS3yqD-_35r1K5_30B-S2a?dl=0]

thermal conductivity from the TP08 heated needle probes is provided in Domine et al. (2015). Figure 12 shows the observations from SNOW1 at five heights over 6 years.

FOREST

The thermal conductivity at FOREST was also recorded with the TP08 heated needles at SNOW3. These were also installed at the same heights as the Pt1000 temperature sensors. Because the sensors at 4 and 14 cm did not work properly, the corresponding values were not included. The recorded values at 29 and 64 cm are shown in Fig. 13.

Manual Snow Measurements

Field trips were conducted for most years to measure snow density and snow specific surface area (SSA). Snow density was measured with a 100 cm 3 box cutter [START_REF] Conger | Instruments and methods comparison of density cutters for snow profile observations[END_REF]) and a field scale, while SSA was measured using infrared reflectance in an integrating sphere as described in Gallet et al. (2009). In 2014 and 2016, we visited the site in January, while in 2013, 2014 and 2015, we conducted field trips in February. The site was visited in late March in 2015, 2016, 2017 and 2019, while in 2018, it was visited in early April. The available snow data therefore provide an overview of the snow properties in mid-winter and early spring. Visits in 2020 and 2021 were impossible because of the COVID pandemic. The profiles of snow density and SSA are illustrated in Fig. 14. Note that the representativity of the measured profiles is limited, as the physical snow properties are highly spatially variable due to vegetation, micro-topography, and wind erosion and redeposition. Soil temperatures at TUNDRA and FOREST were recorded using 5TM soil temperature and water content sensors. According to 5TM specifications, the resolution is 0.1°C for the soil temperature and 0.0008 m 3 m -3 for the soil water content. The accuracy is 1°C for the temperature and 0.03 m 3 m -3 for the soil water content. At all the stations, we observed offsets during the zero-curtain period, when T = 0°C. The temperatures were corrected for these offsets, ranging between 0.2°C and 0.6°C.

TUNDRA

The soil temperature and soil water content were measured at two sites near TUNDRA, each with a different type of vegetation.

Multiple Decagon 5TM probes were used for these measurements. Figure 15 shows these values for a lichen-covered surface, while Fig. 16 shows values for low-shrub vegetation. The soil temperature at the lichen-covered site is warmer during the Author contributions.

FD, GL and DN designed the research. FD and DN obtained funding. DS, FD, GL, and DN deployed and maintained the instruments. GL and FD analyzed the data and prepared the data files. FD, GL, and MBB performed the fieldwork. GL and FD wrote the paper with comments from MBB, DS and DN.

Competing interests

The authors declare that they have no conflict of interest.


Rodrigue Bravard

Laurent Demany

Inter-individual differences in the perception of frequency shifts

Titre :

Inter-individual differences in the perception of frequency shifts

Auteurs :

Rodrigue Bravard 1 , Laurent Demany 2 , Daniel Pressnitzer 1

Affiliations :

1 : Laboratoire des systèmes perceptifs, Département d'études cognitives, École normale supérieure, PSL University, CNRS, Paris, France.

2 : CNRS and Université de Bordeaux, Bordeaux, France.

Résumé :

Supra-threshold inter-individual differences have previously been reported in the auditory perception of ambiguous stimuli, in apparently unrelated situations such as pitch-shift judgments or word reports. Here, we investigate the possibility that listeners assign idiosyncratic perceptual weights to different frequency regions when they resolve the ambiguity of complex sounds. On a given trial, pairs of "random chords" (RCs) were played, one after the other, and participants had to report whether they heard an upward or downward pitch shift across the pair. The RCs were superpositions of several pure tones. For the first RC, the pure tone frequencies were randomly drawn from different frequency regions spanning the audible range. For the second RC, the frequency components of the first RC were randomly perturbed, by adding a log-frequency shift drawn from a Gaussian distribution. The pitch of the second RC was thus neither objectively lower of higher than the first one, but participants nevertheless reported the dominant pitch shift they heard. A reverse correlation method was then applied to derive the weights attributed to each frequency regions by individual listeners to perform the task. The weights are discussed in terms of their consistency over listeners, their stability over time, and the added information they provide to characterize individual hearing profiles compared to simple audibility thresholds.