V L Kovalenko

V A Kotok

A Sykchin

B A Ananchenko

A V Chernyad'ev

A A Burkov

S Deabate

A Mehdi

F Henn

J.-L Bantignies

K L Bychkov

V V Verbitskiy

K M Sukhyy

Al 3+ Additive in the Nickel Hydroxide Obtained by High-Temperature Two-Step Synthesis: Activator or Poisoner for Chemical Power Source Application?

    Al 3+ Additive in the Nickel Hydroxide Obtained by High-Temperature Two-Step Synthesis: Activator or Poisoner for Chemical Power Source Application?

Ni(OH) 2 , owing to its high electrochemical activity, is widely used in various electrochemical devices. 1,2 Nickel hydroxide and nickel-based LDHs are an active substance of nickel-oxide electrode in Ni-Fe, Ni-Cd, Ni-MH secondary cells. 3,4 Nickel hydroxides are also used in the Faradic electrode of hybrid supercapacitors. [5][6][7][8][9][10][11][12][13][14] For thin layer supercapacitors, a nickel hydroxide film can be formed on the conductive substrate. 15 Because oxidized form (NiOOH) of this compound has dark-brown color, while reduced form (Ni(OH) 2 ) in a thin layer is transparent, nickel hydroxide is used as electrochromic material. [16][17][18][19] Nickel hydroxide has high electrocatalytic activity and is used for electrooxidation of various organic compounds, 20,21 and in sensors. 22 Two polymorphs of nickel hydroxides are known 23 : β-hydroxide with formula Ni(OH) 2 and brucite-type structure and α-hydroxide with formula 3Ni(OH) 2 •2H 2 O and hydrotalcite-type structure. However, paper 22 describes the formation of nickel hydroxide structure that is in-between α-form and β-form. Papers [24][START_REF] Kovalenko | Influence of the carbonate ion on characteristics of electrochemically synthesized layered (α+β) nickel hydroxide[END_REF][26] describe the formation of hydroxide with layered (α + β) structure.

α-Ni(OH) 2 has a high electrochemical activity. However, α-form has low stability and in concentrated alkali and at elevated temperatures it transforms into less active β-form, 27,28 results in a decrease of specific capacity. To stabilize α-form, special additives are introduced to nickel hydroxide with the formation of LDH, 29,30 which consists of the host crystal lattice with part of host hydroxide cations (Ni 2+ ) substituted by guest cations 31,32 such as Al 3+ . 33 The extra positive charge is compensated by the incorporation of various anions that intercalated into interlayer space. 34,35 Various methods are used for α-Ni(OH) 2 and nickel-based LDHs preparation. [36][37][38][39][40][START_REF] Bora | Retrospective Theses and Dissertations[END_REF] The electrochemical activity of β-Ni(OH) 2 is lower than α-Ni(OH) 2 activity, and, it possesses higher storage and cycling stability. As such, this form is preferably used in alkaline batteries and hybrid supercapacitors. [START_REF] Kovalenko | [END_REF][43][44][45] For β-Ni(OH) 2 synthesis different chemical and electrochemical methods can be used. [46][47][48] Because of high charge and discharge currents in the operation of the Faradic electrode of hybrid supercapacitors, the electrochemical process takes place in a particles thin surface layer. As such, special requirements for supercapacitor applicable Ni(OH) 2 powders include small particle size, high specific surface area, optimal crystal structure, high electrochemical activity, and cycling stability. [49][50][51][52] Requirements of high electrochemical activity and cycling stability are rather contradictory. One way to solve this contradiction is could be a synthesis of β-Ni(OH) 2 with special morphology increasing its activity. Such types of nickel hydroxide have simple 53,54 and =pseudo-simple? particles. 55 In previous work, we proposed an indirect two-step high-temperature synthesis. On the first stage (synthesis) sodium nickelate is formed under t = 140 °С. On the second stage, sodium nickelate is hydrolyzed under t = 170 °С. As a result, the nickel hydroxide particles with =pseudo-single? morphology, fractal geometry and the increasing specific surface have been obtained. Such type of Ni(OH) 2 is a promising material for supercapacitor applications. We also proposed 55 synthesis of nickel hydroxide via cold (25 °С) and hot (170 °С) hydrolysis and found that both methods result in electrochemically active nickel hydroxide samples. However, the current task is to improve the activity of these nickel hydroxide samples.

Al 3+ is the most commonly used for the activation of nickel hydroxide. In many cases, the aluminum cation is used for stabilizing of α-Ni(OH) 2 with the formation of Ni-Al LDH. 35,[56][57][58][59][60][61][62][63][64] An aluminum cation is electrochemically inert and its low atomic mass is a significant advantage. The lower molecular mass of the inert activator results in a higher content of the electrochemically active component. It is worth to note, that Al 3+ not only stabilizes α-Ni(OH) 2 but also improves electrochemical activity, which means the higher specific capacity of nickel hydroxide. However, despite the introduction of Al 3+ , the stability of α-Ni(OH) 2 -based LDH is z E-mail: vadimchem@gmail.com insufficient, especially during cycling at high very high current densities (8С and higher). During cycling and storage, degradation of LDH can occur, leading to the release of aluminum cation into solution followed by absorption of onto nickel hydroxide. Absorbed aluminum poisons Ni(OH) 2 , significantly reducing its electrochemical activity. As such, the activation of β-Ni(OH) 2 with aluminum cation is promising. 35 However, this problem has not been studied in detail.

Thus the aim of this investigation is to determine the possibility of Al 3+ activation of β-Ni(OH) 2 prepared via two-step hightemperature synthesis. For this purpose, the influence of Al 3+ on structural, morphological and electrochemical properties of β-Ni(OH) 2 samples have been studied.

Experimental

Samples preparation.-For experiments, commercial chemicals with analytical grade were used. The basic scheme of the synthesis 55 :

Primary stage-nickel perchlorate obtaining.-The nickel perchlorate solution was prepared according to follows: (a) addition of sodium carbonate to nickel sulfate solution under vigorous stirring with basic nickel carbonate preparation. The obtained precipitate was rinsed from sodium sulfate. The absence of sulfate ions is controlled with the negative reaction with barium nitrate; (b) an extra quantity of basic nickel carbonate reacted with 45% perchloric acid to obtain рН 6.0 (HClO 4 amount was calculated based on reaction stoichiometry and required mass of nickel perchlorate). The prepared solution was filtered from an extra amount of basic nickel carbonate and was evaporated to obtain the needed nickel perchlorate to water ratio. 55 High-temperature two-step synthesis. First stage-precursor synthesis.-Required NaOH and H 2 O amounts (mass ratio NaOH:H 2 O was 5.5:1) were put into Teflon beaker (500 ml) with a hermetically sealed lid. Beaker was heated under vigorous stirring with a magnetic Teflon stirrer to temperature170 °С. For water loss prevention, the condenser with water flowing cooling was taking place in the hole in the beaker lid. After temperature 170 °С obtaining, prepared on the previous stage nickel perchlorate solution was drop-by drop added trough condenser. After that, the temperature was decreased to 140 °С. The first stage duration was 24 h. As a result, a sodium nickelate sediment, consists of olive-green microscale non-porous hexagonal plates, has been formed 65 according to the following reaction:

( ) [ ] +  + + Ni ClO 4NaOH Na NiO 2NaClO 2H O 1 4 2 2 2 4 2
High-temperature two-step synthesis. Second stage-precursor hydrolysis.-Ni(OH) 2 as a product has been obtained during hydrolysis according to the following reaction:

( Н) [ ] +  + O Na NiO 2H O Ni 2NaOH 2 2 2 2 2
Hydrolysis with different temperatures was carried out 55 :

• Hot hydrolysis. After the sodium nickelate synthesis, mother liquor (150 ml) was recovered from the beaker, and the same water volume was added into the beaker. Then the beaker was aged 24 h under vigorous stirring with constant temperature (170 °С).

• Cold hydrolysis. Reaction mixture with sodium nickelate was transferred from the beaker into a big volume (5 l) of distilled water under room temperature and was aged during 24 h with stirring vigorously.

Alteration of basis scheme.-In order to study the influence of Al 3+ , nickel hydroxide samples were synthesized with the addition of aluminum perchlorate to the solution of initial compounds (nickel perchlorate) in amounts of 3%, 5% and 10% (molar) Al 3+ to Ni 2+ . The samples were labeled as follows: NiAl 3% cold or NiAl 5% hot. 3%-molar content of aluminum, hot or cold-hydrolysis type.

For the synthesis of the samples with Al 3+ addition, solutions of nickel perchlorate and aluminum perchlorate with required Ni 2+ :Al 3+ molar ratio, have been prepared. For this, aluminum perchlorate solution was obtained by the method, similar for pure nickel perchlorate solution: a) addition of sodium carbonate to aluminum sulfate solution under vigorous stirring with precipitate formation. The obtained precipitate was rinsed from sodium sulfate. The absence of sulfate ions is controlled with the negative reaction with barium nitrate; b) an extra quantity of aluminum base carbonate reacted with 45% perchloric acid to obtain рН 6.0 (HClO 4 amount was calculated based on reaction stoichiometry and required mass of aluminum perchlorate). The prepared solution was filtered from an extra amount of aluminum base carbonate. After preparation, aluminum and nickel perchlorate solutions were mixed and mixed solution was evaporated to obtain the required nickel perchlorate to water ratio.

After the hydrolysis stage, Ni(OH) 2 sample has been filtered from the mother liquor, dried under 90 °С during 24 h, washed from soluble salts and re-dried at the same conditions.

In order to study the possible mechanism of aluminum influences, for sample NiAl 10% the synthesis procedure was interrupted on the precursor synthesis stage. The obtained precursor was vacuum filtered using a pre-heated glass frit filter, washed with isopropyl alcohol from an excess of alkali and dried at 90 °С. The sample was labeled as NiAl 10% precursor.

Samples characterization.-The crystal structure has been investigated by PXRD method with using DRON-3 diffractometer (Co-Kα radiation (wavelength 1.7903000 Å), 2θ range 10°-90°, scan rate 0.1°s -1 ). Samples of Ni hydroxide, obtained by hightemperature two-step synthesis without Al 3+ additive (labeled as Ni Pure Cold and Ni-Pure Hot), have been used as the referent samples for PXRD investigation. For phases detection Match! software was used. Crystallinity was calculated by Sherrer's formula. The morphology of the particles has been characterized by SEM (using microscope JEOL JSM-6510LV, Japan) and TEM (using microscope JEOL JEM-2100, Japan). The chemical composition of samples was investigated by EDX analysis with a microscope Hitachi S4500, Japan.

TG analysis has been carried out with DTG-60 ("Shimadzu," Japan) and DSC has been carried out with DSC-60 ("Shimadzu," Japan). Analysis conditions: an air atmosphere, the heating rate of 5 °Cmin -1 .

Electrochemical properties have been characterized by cycling voltammetry (CVA) and galvanostatic charge-discharge cycling (CDC), using SEC-2 special cell and electronic potentiostat-galvanostat Ellins P-8. For both investigations, electrodes for these electrochemical measurements were prepared by pasting of active mass on the working electrode, made from nickel foam base 82 and Ni foil current collector. 66,67 The active mass consists of a mixture of 82.5% (wt.) Ni(OH) 2 sample, 16%(wt.) graphite and 1.5% (wt.) PTFE. 66 The electrolyte -6 M KOH solution. As the counter electrode a nickel grid was used and as the reference electrode -saturated SCE.CVs were recorded at potential range 0-500 mV in the two regimes: 1) single-speed mode-at 1 mVs -1 ; 2) multispeed mode-at 1, 2, 5, 10 and 50 mVs -1 . Potentials in CV curves have been recalculated from SCE to NHE. Charge-discharge cycling in the supercapacitor mode has been carried out at 5, 10, 20, 40, 80 and 120 mAcm -2 . Al 3+ has a strong and fast effect on electrochemical properties of nickel hydroxide. 59,68 Thereby, GCD during 10 cycles per each current density was enough for Al 3+ impact estimation. Specific capacities C spec (Fg -1 ) and Q spec (mAhg -1 ) have been calculated based on CDC results. Specific capacities have been calculated taking into account the loading of nickel hydroxide samples in the working electrode.

Results and Discussion

Aluminum content of samples and discussion on the possible mechanism of its incorporation.-During the direct synthesis of nickel hydroxide with aluminum additive, 29,30,[33][34][35] Al 3+ is incorporated into hydroxide crystal lattice a guest. This results in the formation of monophase LDH, a singular compound with increased electrochemical properties. As such the aluminum plays the role of structural activator. However, the role of aluminum absorbed onto the nickel hydroxide surface is not entirely clear. According to Ezhov, 68 Al 3+ on the surface of nickel hydroxide decreases the polarization of O 2 evolution. This prevents nickel hydroxide from charging completely, which lowers its specific capacity. During the hot hydrolysis stage of the two-step, high-temperature synthesis 55 nickel hydroxide particle is formed on the nickelate particle surface. The mechanism of this reaction is not clear, but the assumption is this is a =Solid-state-Liquid-state? mechanism. This mechanism assumes the dissolution of nickel-containing forms and transfer of ions, most likely as absorbed ions, to the location of crystal growth. In this work, high-temperature two-step synthesis of nickel hydroxide with the introduction of aluminum perchlorate to initial solution was attempted. Properties of the final product (nickel hydroxide), including Al 3+ content, are primarily governed by the state of aluminum in reaction vessel after the first stage (precursor synthesis). This would further affect the process that occurs during the second strange (hydrolysis stage). Synthesis of precursor (sodium nickelate) for sample NiAl 10% was conducted to determine precursor composition and mechanism of aluminum incorporation into final hydroxide. Three possible mechanisms were proposed:

"Solid-Liquid-Solid" mechanism.-Aluminum and nickel cations form precursor precipitate and transform into nickel hydroxide during hydrolysis. There are two possible cases: (a) "Joint-Solid-Liquid-Solid" mechanism (JS-L-S). Aluminum cations are incorporated into precursor as a result of cocrystallization, forming a single phase with sodium nickelate. In this case, the aluminum content in the precursor should be about the same as it was in the initial solution. The formed phase has a single set of properties and acts as a single compound during hydrolysis. Aluminum is incorporated into nickel hydroxide via a liquid-phase mechanism, but simultaneously with nickel cation. In these cases, the probability for aluminum incorporation into the crystal lattice of forming Ni(OH) 2 is the highest. The hydroxide formed this way should be most active due to the activating role of aluminum in structure. (b) "Separate-Solid-Liquid-Solid" mechanism (SS-L-S). Aluminum forms a separate phase of sodium aluminate in precursor precipitate. In this case, the aluminum could be incorporated during hydrolysis through the liquid-phase mechanism, however, the separate aluminum-containing phase would possess properties different from sodium nickelate. In this case, the aluminum content (% mol.) would be different in different parts of the precipitate. This would mean that partial absorption of the aluminum onto the surface of nickel hydroxide is possible.

"Liquid-Liquid-Solid" mechanism (L-L-S).-During the first synthesis stage, the majority of aluminum would be in basic mother liquid. During hydrolysis would be incorporated into nickel hydroxide as a surface additive.

It should be noted, that under real conditions and different aluminum content, it possible that few mechanisms would realize simultaneously.

To study if the SS-L-S mechanism occurs, structural features of sodium nickelate and sodium aluminate were analyzed. Generally, nickelates and aluminates of sodium have a hexagonal and orthorhombic lattice structure. The attention was mainly focused on nickelates and aluminates with a hexagonal lattice. Nickelates and aluminates with the same space groups were found, but lattice parameters were rather different. Thus it was concluded that there was no isostructural sodium aluminates and nickelates. The most likely scenario is that sodium aluminate is incorporated into precursor precipitate as a separate phase, indicating the realization of SS-L-S mechanism. EDX results for sample NiAl 10% precursor (Fig. 1g) shows significant variability in aluminum content (0% to 9.3%). This indicates the realization of SS-L-S mechanism. Hot and cold hydrolysis samples show a significant difference in aluminum content compared to the initial solution. It should be noted that the difference in ionic radii of Ni 2+ and Al 3+ is more than 20%, which indicates that the direct substitution of Ni 2+ with Al 3+ in the crystal lattice is impossible, but the formation of interstitial solid solution is possible. However, charge difference possess an obstacle for such solution formation. Substitution of nickel with aluminum is known occurrence in LDH, however there the excessive charge is compensated by anions intercalated into interlayer space. Such α-like (or high defected β bc -structure) is characteristics for samples of cold hydrolysis. Aluminum content in cold hydrolysis samples is significantly higher than that for hot hydrolysis samples. For samples, NiAl 3% cold (Fig. 1f) and NiAl 5% cold (Fig. 1d) aluminum content is close to that in the initial solution. However, for sample NiAl 10% cold (Fig. 1b) aluminum contentment is significantly lower-4.6%-6.7% compared to 10% that was initially added. It is possible, that 7% (mol.) is the maximum aluminum content for β bc -Ni(OH) 2 and α-Ni(OH) 2 . It should be noted that the difference in ionic radii of Ni 2+ and Al 3+ is more than 20%, which indicated that the incorporation of aluminum should be possible only with the formation of the interstitial solid solution with some deformations of the crystal lattice. However, compensation of excessive charge requires the incorporation of additional anions, which is difficult for highly crystalline β-Ni(OH) 2 . As such doping of highly crystalline β-Ni(OH) 2 with small amounts of aluminum should be possible. This conclusion is supported by the results of EDX and chemical analysis (Table II) for samples NiAl 10% hot (Fig. 1a), NiAl 5% hot (Fig. 1c) and NiAl 3% hot (Fig. 1e), for which aluminum content doesn't exceed 1.8% (mol.).

Influences of Al 3+ additive on crystal structure and morphology of nickel hydroxide particles.-As previously described, 55 both cold and hot hydrolysis result β-Ni(OH) 2 , but with different crystallinity. It was detected, that the structure of reference samples (Ni Pure Hot and No Pure Cold) corresponds to standard #00-073-1520 Ni(OH) 2 (hexagonal crystal system, space group P-3m1, cell parameters a = 3.114 Å, c = 4.617 Å), which is β-Ni(OH) 2 . For comparison α-Ni(OH) 2 standard #00-022-0444 3Ni(OH) 2 ·2H 2 O (hexagonal crystal system, space group P-31m, cell parameters a = 5.34 Å, c = 7.5 Å) was used. The principal difference between β-Ni(OH) 2 (#00-073-1520 Ni(OH) 2 ) and α-Ni(OH) 2 (#00-022-0444 3Ni(OH) 2 ·2H 2 O), which have similar crystal hexagonal structure, is cell parameter "c" -4.617 Å, plate (001) and 7.5 Å, plate (100) respectively. For Co Kα radiation, peaks for these plates are situated at 2Θ = 22.4°for β-Ni(OH) 2 and 2Θ = 13.5°for α-Ni(OH) 2 . Ni Pure Cold sample has a more defective structure, which in literature is referred to as β bc -Ni(OH) 2 . 22,23 Based on PXRD results (Fig. 2a), it was found that the addition of aluminum results in sample crystallinity sharp decreasing in series NiAl 3% cold-NiAl 5% cold-NiAl 10% cold. Sample NiAl 10% cold is practically X-ray amorphous. The same tendency is observed for hot hydrolysis samples (Fig. 2b). All hot hydrolysis samples (Al-added and Pure), have the characteristic clear peak of β-Ni(OH) 2 at 2Θ = 22.2°-22.5°. But in the diffractogram of samples with Al-addition, a poorly defined, extra-wide peak of another phase at 2Θ = 16.1°-18.3°was detected. It was suggested that the detected phase is a nickel hydroxide hexagonal phase, which is intermediate between β-Ni(OH) 2 (2Θ = 22.4°) and α-Ni(OH) 2 (2Θ = 13.5°). Based on a suggestion, the value of parameter "c" has been estimated in 5.6-6.3 Å. It should be noted that β-Ni(OH) 2 is anhydrous Ni(OH) 2 , α-Ni(OH) 2 is 3Ni(OH) 2 ·2H 2 O, crystalline hydrate. Therefore, this phase also is α-like Ni(OH) 2 with less amount of water, than in α-Ni(OH) 2 . Increasing of aluminum content leads to increasing of the amounts of this α-like Ni(OH) 2 phase. The evidence of this is the increasing of intensity of the extra-wide peak. At the same time, crystallinity of this phase in the all samples is low. Peaks of main, β-Ni(OH) 2 phase, get broader and their intensity decreases. This indicates the presence of some amount of the alpha-phase domains or stacking faults. 69 Calculation of cell parameters and crystallinity was not successful by the reason for an extra high level of sample texturing. An increase in a number of structural defects is further supported by SEM and TEM images. For samples NiAl 3% hot (Figs. 3a,3b) and NiAl 3% cold (Figs. 3e, 3f), particle morphology doesn't differ significantly from that of nickel hydroxide prepared by two-step high-temperature synthesis at cold or hot hydrolysis without aluminum additive. 55 Sample NiAl 3% hot has =pseudosingle? particles, composed of hexagonal primal nanoparticles with a thickness of 30-40 nm. Sample NiAl 3% cold is composed of larger hexagonal particles stacked together. It is possible, that the addition of 3% Al results in doping of nickel hydroxide with the incorporation of aluminum into the crystal lattice, without significant changes in particle morphology. Increasing aluminum content to 10% leads to particle deformation for both cold and hot hydrolysis. Hot hydrolysis sample NiAl 10% hot is also composed of =pseudosingle? particles, however, the hexagonal shape of primal particles is strongly deformed (Fig. 4c). ТЕМ images (Fig. 4d) show that primal particles are coated with layers with a total thickness of 15-20 nm, which appears to be a core-shell structure. It is likely, that surface layer is defective, amorphous β bc -Ni(OH) 2 (which is seen as X-ray amorphous component on PXRD patterns), that contains aluminum cations. Cold hydrolysis sample NiAl 10% cold (Fig. 4g) is composed of spherical particles 80-190 nm in diameters. During cold hydrolysis, the aluminum cations are absorbed onto the surface of forming the hydroxide, altering particle growth rate in different directions, which results in spherical particles.

Results of DTG and DSC analyses support PXRD data. TG curves of NiAl 10% hot (Fig. 4a), NiAl 5% hot (Fig. 4b) and NiAl 3% hot (Fig. 4c), are characterized the hot hydrolysis samples as a high crystalline β-Ni(OH) 2 . 53,65 In this case, there is only one weight loss step (16%-19.3%) at the temperature around 300 °C, corresponded to nickel hydroxide decomposition with nickel oxide obtaining:

( Н) [ ]  + O Ni NiO H O 3 2 2
This is confirmed by the DSC curves showing a single endothermic peak at the t = 297 °C-312 °C. The cold hydrolysis sample NiAl 10% cold (Fig. 4d), NiAl 5% cold (Fig. 4e) and NiAl 3% cold (Fig. 4f) exhibit a two-weight loss step TG curve: a first step at the temperature range 60 °C-100 °C range and a second step with weight loss (6.22%) at the temperature 240 °C-340 °C. The first weight loss does not correspond with sharp calorimetric peaks and can thus be attributed to water, containing in the defect sites which are typical for badly crystallized β-phases. 69 The second weight loss associated with the sharp endothermic peak, related to the hydroxide degradation to NiO. These parameters are similar to thermal characteristics of pure Ni(OH) 2 , prepared by high-temperature two-step synthesis. 55 The addition of aluminum has no significant effect on the thermal behavior of hot hydrolysis samples. For cold hydrolysis samples, the first endothermic peak is split into few 55 broad peaks. First endothermic peaks characterize the thermal removal of crystalline and defect water and depend on water quantity and bond energy. According to the proposed mechanism, Al 3+ incorporation occurs in the surface layer. Therefore there are few broad peaks in the first endothermic peak, which correspond to water removal from different deepness layers. According to XRD results, increasing of Al 3+ additive to cold hydrolysis samples give the decreasing of the samples crystallinity, and as a result-decreasing the water quantity in the crystal lattice defects.

Influence of Al 3+ additive on electrochemical properties of nickel hydroxide.-The electrochemical activity (mass utility) of nickel hydroxide in the positive electrode of the alkaline Ni-Co, Ni-Fe, Ni-MeH secondary cell is strong determined by specific surface, proton diffusion rate in the particle and overpotentials of two electrochemical reactions under charge process: nickel hydroxide oxidation to oxyhydroxide and oxygen evolution. The two last parameters are based on polymorph type of nickel hydroxide (α, β, or α + β [START_REF] Kovalenko | Influence of the carbonate ion on characteristics of electrochemically synthesized layered (α+β) nickel hydroxide[END_REF]26,81 ) and it crystallinity. 2,3,[START_REF] Kovalenko | [END_REF] The electrochemical activity of Ni(OH) 2 used in supercapacitors is governed by a number of factors. In 51 is described that main parameters are: (1) type of nickel hydroxide (α, β, or α + β), which determines own electrochemical activity; (2) crystallinity, which determines the depth of electrochemical process; (3) particle size, specific surface area. Electrochemical properties of pure nickel hydroxide prepared by high-temperature two-step synthesis with cold and hot hydrolysis were studied previously. 55 In general, without additives, the different crystallinity and particle morphology of hot and cold hydrolysis samples give different electrochemical activities. The hot hydrolysis sample has higher cycling stability and reversibility but has decreased capacity. These data based on the increased surface area, probably resulting from the hexagonal "pseudo-single" morphology, but decreased proton diffusion rate, usually observed for high crystallized structures. 55 Influence of Al 3+ has been investigated by cyclic voltammetry and galvanostatic charge-discharge cycling.

Cyclic voltammetry at a scan rate of 1 mVs -1 , is approximately equal to alkaline secondary cells mode with low charge-discharge rate, revealed that cold hydrolysis samples (NiAl 10% cold-Fig. 5b, NiAl 5% cold-Fig. 5d, NiAl 3% cold-Fig. 5f) have higher peak current in comparison to hot hydrolysis samples (NiAl 10% hot-Fig. 5a, NiAl 5% hot-Fig. 5c, NiAl 3% hot-Fig. 5е). This indicates that cold hydrolysis samples possess higher electrochemical activity than hot hydrolysis samples, which is in agreement with data for pure nickel hydroxide prepared by high-temperature solid-state synthesis. 55 Increasing aluminum content in the initial solution from 3% (mol.) to 10% (mol.) has no significant effect on the electrochemical characteristics of samples. It can be noted, that at a low scan rate (in the secondary cell mode) no activating or poisoning effect of aluminum additive is observed.

To study electrochemical behavior at a higher rate of the electrochemical process (supercapacitor mode), the cyclic voltammetry was conducted at different scan rates (1, 2, 5, 10 and 50 mVs -1 ). Such method is widely used for the characterization of Ni(OH) 2 , NiO and Ni-LDH specially as an active substance of hybrid supercapacitor. CVA curves are shown in Fig. 6. The scan rate of 50 mVs -1 corresponds to high rates of charge and discharge of samples. At this scan rates, curves of almost all samples show two charge peaks, one at 490-500 mV, and second at 570-630 mV. In the general case, two charge peaks in the CV curves are characterized by the same reaction:

( ) [ ] -  + - + Ni OH 1e NiOOH H 4 2
But different forms of nickel hydroxide (β-Ni(OH) 2 , β bc -Ni(OH) 2 and α-Ni(OH) 2 ) are characterized by different charge potentials, according to their electrochemical activity. Electrochemical activity and the charge potential decreases among the line "α-Ni(OH) 2 -β bc -Ni(OH) 2 -β-Ni(OH) 2 ." Crystallinity increasing gives a similar result. [76][77][78][79] The presence of two peaks in CV curves describes the double-phase structure of both samples, included different types of nickel hydroxide. Cold hydrolysis samples consist of β-Ni(OH) 2 and β bc -Ni(OH) 2 . But during cycling meta-stable β bc -hydroxide transforms into stable β-hydroxide, and specific current of the first peak (corresponding to meta-stable β bc -Ni(OH) 2 ) is decreased, and specific current of the second peak (corresponding to β-Ni(OH) 2 ) is increased. There is an apparent contradiction for the hot hydrolysis sample. According to PXRD results (Fig. 2), the hot hydrolysis sample is high crystalline β-Ni(OH) 2 , but with the presence of few amounts of X-ray amorphous phase. In the 55 this behavior explained by double-phase of hot hydrolysis sample, which consists of nanosized particles with some amount of larger particles. Nanoparticles are characterized by a high percentage of surface nickel atoms. Therefore nanosized β-Ni(OH) 2 particles with high crystallinity have α-like electrochemical properties. At the same time, the X-ray amorphous component, formed under Al 3+ influencing, also have α-like electrochemical behavior. As such, the first peak for hot hydrolysis samples (NiAl 3% hot-Fig. 6a; NiAl 5% hot-Fig. 6c; NiAl 10% hot-Fig. 6e) can correspond to nanosized particles of high crystalline β-Ni(OH) 2 , and X-ray amorphous particles. Analysis of CVA curves at 50 mVs -1 for all samples was conducted, lists potentials and specific peak currents are shown in Table I. Analysis of Table I reveals that for all samples higher Al 3+ content results in lower specific currents of both charge and discharge peaks. It is worth highlighting the influence of aluminum additive on the first charge peak of cold hydrolysis samples (NiAl 3% cold, NiAl 5% cold and NiAl 10% cold), which characterizes electrochemical activity the most. Decrease of the specific current of first charge peak with an increasing amount of introduced Al 3+ , and real Al 3+ content is significant and for sample NiAl 10% cold the first charge peaks disappear. This clearly indicates the poisonous effect of aluminum additive introduced in large amounts. Upon realization of the SS-L-S mechanism, a significant part of the aluminum compound resided on the surface of nickel hydroxide. This supports previous findings of Ezhov, 68 regarding the poisonous effect of surface Al compounds. For hot hydrolysis samples (NiAl 3% hot, NiAl 5% hot and NiAl 10% hot) decrease in specific peak currents is also observed, but to a lesser degree. An interesting fact was discovered. As in previous study, 55 results of the present study (Table I) also show that electrochemical activity during discharge (expressed as the specific peak of discharge) of cold hydrolysis samples is higher than that of hot hydrolysis samples. This is explained by the lower crystallinity of β-Ni(OH) 2 and the presence of significant amounts of β bc -Ni(OH) 2 . However, it was found that under scan rate of 50 mV c -1 (Table I) sample NiAl 3% hot has a specific peak current of 5.77 Ag -1 , which is 19% higher than this value of NiAl 3% cold (4.85 Ag -1 ). This reveals the activating of the effect of small amounts of Al 3+ . This indicated that under these conditions Al 3+ is incorporated into the structure of surface layers of nickel hydroxide, and possibly partially replacing Ni 2+ in the crystal lattice of hydroxide. In this case, aluminum cations play the role of structural activator. 4,5,30,33,34 This can be indicative of partial ). Comparative analysis revealed a significant change in the ratio of specific characteristics of samples of cold and hot hydrolysis for samples with the addition of aluminum and pure nickel hydroxide. For all aluminum contents, specific capacities (Fg -1 and mAhg -1 ) for hot hydrolysis samples are higher than those of cold hydrolysis samples. This clearly shows the poisonous effect of Al 3+ compounds on nickel hydroxide of cold hydrolysis. Addition of 3% (mol.) Al 3+ for cold hydrolysis decreases specific capacity by 3.86 times (from 1057 Fg -1 Ni pure cold to 275 Fg -1 NiAl 3% cold). Further increase of added Al 3+ , results in a higher content of aluminum in the sample, which further decreases specific capacity. However, it should be detected, that the effect of Al 3+ on Ni(OH) 2 prepared by cold hydrolysis is not limited by poisoning. Increasing cycling current dense in series =10-20-40--80-120 mAcm -2 ? does not result in lower capacity, but results in some capacity aging =275-274-280-291-323 Fg -1 ?. This indicates the known stabilizing effect of Al 3+ on α-Ni(OH) 2 . [56][57][58][59]64,80 It can be concluded, that Al 3+ also has a stabilizing effect on β bc -Ni(OH) 2 , which primarily responsible for the electrochemical activity of cold hydrolysis samples, similar to what's been described in Ref. 66. The stabilizing effect comes from aluminum cations that were incorporated into the crystal lattice of nickel hydroxide. As such it can be concluded, that during cold hydrolysis part of aluminum cations is incorporated into hydroxide lattice. However, a further increase of aluminum content in the synthesis solution (and real content), the poisonous effect of aluminum outweighs its stabilizing effect. For hot hydrolysis samples, the increase of aluminum content also results in a capacity loss, but to a lesser degree. Additionally, despite increasing aluminum content in the synthesis solution, the final content in resulted samples was roughly the same. It is possible, that redistribution between Al 3+ present in the crystal lattice and Al 3+ on the surface occurs. This results in an increase of surface aluminum. This is supported by specific characteristics of sample NiAl 3% hot, the specific capacity of which (1112 Fg -1 ) exceeds the capacity of reference sample Ni pure hot (pure nickel hydroxide hot hydrolysis 55 ) by 1.95 times and sample NiAl 3% cold by 4.04 time. This indicates the significant activating effect of small amounts of aluminum. Increasing cycling current density leads to lower specific capacity and less pronounced activating effect. The realization of the proposed mechanism on the first stage is confirmed by theoretical analysis of nickelates and aluminates of sodium, which revealed the absence of isostructural forms, and significant variance in aluminum content in a different part of precursor, determined by EDX. The study of hydroxide samples by means of PXRD, SEM, TEM, and EDX revealed the realization of both ways of aluminum incorporation.

Conclusions

PXRD revealed that the addition of Al 3+ results in lower crystallinity of samples prepared by cold hydrolysis. For hot hydrolysis samples, the introduction of Al 3+ in crystal lattice decreases of highlycrystalline component (β-Ni(OH) 2 ) and form of X-ray amorphous component, which is highly defective β bc -Ni(OH) 2 .

By means of SEM and TEM it was found that at low amounts of Al 3+ (3% mol.) morphology and particle size don't differ much from pure nickel hydroxide: hot hydrolysis results in the formation of nanostructured =pseudo-single? particles, and cold hydrolysis-large hexagonal submicron particles stacked together. This indicated the doping of Ni(OH) 2 by the aluminum cation. An increasing amount of added Al 3+ to 10% (mol.) results in the significant defection of primal nanosized particles of hot hydrolysis sample; for cold hydrolysis, this results in the formation of spherical particles. This indicated the formation of a surface layer of Al 3+ compounds, which is supported by the appearance of "core-shell" type particles on TEM images.

By means of EDX analysis, it was found that aluminum content in hot hydrolysis samples is significantly lower in comparison to cold hydrolysis samples. It was also found that hot hydrolysis samples contained significantly less Al 3+ than what was in the initial solution. Upon introduction of 3% (mol.) Al 3+ to an initial solution, the aluminum content in nickel hydroxide was 0.792-1.04% (mol.).

(1) By means of cycling voltammetry at the low scan rate of 1 mVs -1 , the influence of Al 3+ additive on electrochemical properties of samples as a secondary cell active substance has been investigated. No activating or poisoning effect of aluminum additive is detected.

(1) By means of cycling voltammetry and galvanostatic chargedischarge cycling at different current densities, the influence of Al 3+ additive on electrochemical properties of samples has been investigated. It was found that Al 3+ can acts as a poison, activator or stabilizer. Under conditions for the formation of aluminum compounds (cold hydrolysis samples and high amounts of introduced Al 3+ for both hydrolysis types) electrochemical activity and specific characteristics of samples decrease significantly as a result of poisoning. It was found that when doped with aluminum cation, Al 3+ plays the role of activator and stabilizer of activity. Addition of 3% (mol) Al 3+ leads to improved capacity of hot hydrolysis sample by 1.95, in comparison to pure nickel hydroxide reference sample (1112 Fg -1 and 569 Fg -1 respectively). Also, upon addition of 3% (mol.), the stabilizing effect of Al 3+ was discovered, which manifested in stable (and even increasing) specific capacity of about 275-323 Fg -1 with an increase of cycling current density from 10 mA·cm -2 to 120 mA cm -2 .

Figure 1 .

 1 Figure 1. Al:Ni molar ratio (%) of different Ni(OH) 2 samples with Al additive (calculated from results of EDX): (a) NiAl 10% hot; (b) NiAl 10% cold; (c) NiAl 5% hot; (d) NiAl 5% cold; (e) NiAl 3% hot; (f) NiAl 3% cold; (g) NiAl 10% precursor.

Figure 2 .

 2 Figure 2. PXRDpatterns of Ni(OH) 2 samples with aluminium additive obtained by two-step high-temperature synthesis: (a) cold hydrolysis; (b) hot hydrolysis.

Figure 3 .

 3 Figure 3. SEM and TEM images of Ni(OH) 2 samples with aluminium additive obtained by two-step high-temperature synthesis:(a), (c), (e), (g) SEM images; (b), (d), (f), (h) TEM images; (a), (b) NiAl 3% hot; (c),(d) NiAl 10% hot; (e), (f) NiAl 3% cold; (g), (h) NiAl 10% cold.

Figure 4 .

 4 Figure 4. TG and DSC curves of Ni(OH) 2 samples with aluminum additive obtained by two-step high-temperature synthesis: (a) NiAl 3% hot; (b) NiAl 5% hot; (c) NiAl 10% hot; (d) NiAl 3% cold; (e) NiAl 5% cold; (f) NiAl 10% cold.

Figure 5 .

 5 Figure 5. Cyclic voltammograms (scan rate 1 mVs -1 ) of Ni(OH) 2 samples with aluminium addition obtained by two-step high-temperature synthesis: (a) NiAl 3% hot; (b) NiAl 3% cold; (c) NiAl 5% hot; (d) NiAl 5% cold; (e) NiAl 10% hot; (f) NiAl 10% cold.

Figure 6 .

 6 Figure 6. Cyclicvoltammograms (scan rate 1-50 mVs -1 ) of Ni(OH) 2 samples with aluminium addition obtained by two-step high-temperature synthesis: (a) NiAl 3% hot; (b) NiAl 3% cold; (c) NiAl 5% hot; (d) NiAl 5% cold; (e) NiAl 10% hot; (f) NiAl 10% cold (line captures-scan rate, mVs -1 ).

  (a) by incorporating into the structure; (b) by forming aluminum compounds on the surface of particles.

Figure 7 .

 7 Figure 7. Specific characteristics of Ni(OH) 2 samples with aluminum additive obtained by two-step high-temperature synthesis with (a), (b) hot hydrolysis; (c), (d) cold hydrolysis, calculated from galvanostatic CDC: (a), (c) С spec full , Fg -1 ; (b), (d) Q spec full , mAhg -1 .

Table I .

 I Potentials and specific currents of anodic and cathodic peaks for nickel hydroxide samples with different Al 3+ content.

				Anodic (charge) curve		Cathodic (discharge) curve
	Sample	Real Al 3+ content (% mol)	1st peak I spec , Ag -1 ,	2nd peak Ea, mV		I spec , Ag -1 , I spec , Ag -1 ,	Ec, mV Ea, mV
	NiAl 10% hot	0.38-1.83	0.59	495	1.5	603	1.72	439
	NiAl 10% cold	4.69-6.40	-	-	3.72	590	3.44	426
	NiAl 5% hot	0.76-1.66	3.03	496	1.75	583	3.00	434
	NiAl 5% cold	3.93-5.05	1.99	492	5.23	569	4.65	438
	NiAl 3% hot	0.92-1.04	3.53	489	3.41	569	5.77	429
	NiAl 3% cold	2.04-3.18	2.44	500	5.77	634	4.85	430

Table II .

 II Comparison of theoretical and experimental νAl: νNi (molar %) for nickel hydroxide samples with different Al 3+ addition.

					νAl: νNi, %
	Sample	Theoretical	Chemical method			EDX
	NiAl 10% Precursor	10	-	0	9.63	8.94	4.07
	NiAl 10% Hot	10	1.35	1.83	1.17	0.38	1.25	1.12	1.38
	NiAl 5% Hot	5	1.12	1.41	1.06	0.76	1.05	1.66	1.36
	NiAl 3% Hot	3	0.99	1.04	0.92	0.93	-	-	-
	NiAl 10% Cold	10	6.02	4.69	6.40	6.20	-	-	-
	NiAl 5% Cold	5	4.70	5.05	4.64	3.93	4.12	-	-
	NiAl 3% Cold	3	2.89	3.18	2.04	2.94	-	-	-

( 1 )

 1 Influence of Al 3+ additive on characteristics of nickel hydroxide prepared by two-step high-temperature synthesis with the use of hot (170 °С, 24 h) and cold (20 °С, 24 h) hydrolysis has been studied. A series of Ni(OH) 2 samples have been prepared with the addition of aluminum perchlorate to the solution of initial compounds (nickel perchlorate) in ratios 3%, 5% and 10% (mol.) Al 3+ to Ni 2+ . Physical, structural and electrochemical properties of obtained samples have been investigated. A precursor sample-sodium nickelate with the introduction of the maximum amount of Al 3+ (10% mol.) by stopping the synthesis procedure after the first stage has been synthesized.(2) It was proposed the mechanism, that describes the formation of nickel hydroxide during two-step high-temperature synthesis with Al 3+ additive to initial solution, which we call "Separate-Solid-Liquid-Solid." On the first stage, aluminum forms a separate phase of sodium or nickel aluminates. During hydrolysis aluminum through liquid phase mechanism can be incorporated into forming hydroxide powder in two ways:

Acknowledgments

This study was carried out according to an International collaboration agreement #130585 from 07.07.2014 between University Montpellier (Montpellier, France), Ukrainian State University of Chemical Technology (Dnipropetrovsk, Ukraine), Vyatka State University (Kirov, Russian Federation). ORCID V. L. Kovalenko https://orcid.org/0000-0002-8012-6732


Gilles Boulet
email: gilles.boulet@cesbio.cnes.fr

Bernard Mougenot

Tarik Ben

Tarik Ben Abdelouahab

An evaporation test based on Thermal Infra Red Remote-Sensing to select appropriate soil hydraulic properties

Keywords: Soil hydraulic properties, pedotransfer functions, infiltration test, evaporation, water stress, TIR remote-sensing, SVAT model

    An evaporation test based on Thermal Infra Red Remote-Sensing to select appropriate soil hydraulic properties

Introduction

Most water balance models, from the simplest ones (the FAO56 method, [START_REF] Allen | Crop evapotranspiration: guidelines for computing crop water requirements[END_REF] to the most complicated ones (complex SVAT schemes, hydrological models based on the Richards equation …) require an a priori knowledge of the soil hydraulic properties. Soil hydraulic properties can be classified in two types: textural properties, that describe the statistical distribution of the size of the pores, and structural properties, that describe the spatial organization and connectivity of the pores.

Both property groups are linked since the biggest pore sizes induce the largest connectivity and therefore the highest conductivity. Texture maps are the most largely, and sometimes the only available information on soil properties at regional scale. Therefore, for most agronomical or hydrological applications, pedotransfer functions are applied to textural classes to derive soil hydraulic properties [START_REF] Bouma | Using soil survey data for quantitative land evaluation[END_REF]. Pedotransfer functions are usually obtained from selected laboratory soil sample databases. Multivariate regression analyses are carried out to produce polynomial functions that link common retention and hydraulic conductivity curves (like the Brooks and Corey or the van Genuchten equations) to extended textural properties, at minimum clay and sand contents. Since these regressions are obtained from a limited number of samples, either stemming from a single region or from several laboratories (e.g. the Grizzly database, [START_REF] Haverkamp | Grenoble Soil Catalogue: Soil survey of field data and description of particle size, soil water retention and hydraulic conductivity functions[END_REF], their generality is rather questionable. Moreover, given the wide range of published pedotransfer functions (See [START_REF] Wagner | Evaluation of pedo-transfer functions for unsaturated soil hydraulic conductivity using an independent data set[END_REF], for a review) and the poor statistical link between structural and textural properties of a given soil, it is advisable to test the relevance of each of them before considering using one for a particular region/site of interest.

One possible way to check if one particular pedotransfer function can be applied locally is to perform lab analysis, but it is costly, both in time and money. A second approach is to carry out simple infiltration tests such as the Beerkan tests [START_REF] Braud | Use of scaled forms of the infiltration equation for the estimation of unsaturated soil hydraulic properties (the Beerkan method)[END_REF]. Interpreting infiltration tests consists in matching cumulative infiltration curves for ponding (well permeameter, Beerkan and double-ring tests) or non-ponding (disc infiltrometer) conditions with simple analytical functions or more complex mathematical expressions such as the Richards equation [START_REF] Zou | Estimation of depth averaged unsaturated soil hydraulic properties from infiltration experiments[END_REF][START_REF] Ritter | Analysis of alternative measurement strategies for the inverse optimization of the hydraulic properties of a volcanic soil[END_REF]Mynasni et al., 2005) that depend on the local hydraulic properties. Since these tests rarely provide a single set of valid soil hydraulic parameters, alternative methods must be carried out to reduce the space of acceptable solutions. At the same (local) scale, evaporation tests have been carried out using vapour flux measurements (at the laboratory: [START_REF] Schneider | Novel evaporation experiment to determine soil hydraulic properties[END_REF]. The physics of the extraction of vapour from the soil porous medium is strongly dependent on the movement of the liquid water below the evaporation front [START_REF] Boulet | Study of the mechanisms of evaporation under arid conditions using a detailed model of the soil-atmosphere continuum. Application to the EFEDA I experiment[END_REF] and, in turn, on the hydraulic properties. By minimizing the difference between the simulated and the observed vapour fluxes one can evaluate the hydraulic properties if an extra measurement of matric head and/or water content with time is available. Given the size of the ring or the evaporation chamber used in these methods, these tests provide point estimates of soil properties, whereas a global estimate at the scale of interest (usually the field) is required. There is therefore no direct means to access field-scale hydraulic data without a costly and time consuming lab or field study with multiple samples. Alternatively, eddy-correlation measurements of latent heat fluxes are usually based on a much larger footprint and can be considered as representative of the field; inverse methods consisting in minimizing the difference between the observed and the measured latent heat flux have been proposed, from synthetic [START_REF] Jhorar | Inversely estimating hydraulic functions using evapotranspiration fluxes[END_REF] or observed [START_REF] Gutmann | A comparison of land surface model soil hydraulic properties estimated by inverse modeling and pedotransfer functions[END_REF] evaporation data. But eddy-correlation systems are expensive and need well-trained staff to operate and maintain them. Furthermore, it is not possible to cover a large region in a short period except with a costly set-up.

Information on the water balance at the regional scale can be obtained routinely through the use of remote-sensing data. Several experiments have been carried out to test the assimilation of surface soil moisture inferred from active [START_REF] Santanello | Using remotely-sensed estimates of soil moisture to infer soil texture and hydraulic properties across a semi-arid watershed[END_REF] or passive [START_REF] Burke | Using a modeling approach to predict soil hydraulic properties from passive microwave measurements[END_REF] microwave remote-sensing data to constrain soil hydraulic properties. But soil moisture is not easy to observe through remote-sensing at an adequate resolution (for example the SMOS satellite mission will provide data on 0-5 cm soil moisture at ~50*50 km resolution) or with sufficient precision (radar data for instance is very sensitive to roughness and is usually acquired with a very sparse revisit period that is incompatible with most hydrological applications).

Amongst recent methods based on remote-sensing data, several papers have proposed to assimilate Thermal Infra Red (TIR) data into Soil Vegetation Atmosphere Transfer (SVAT) models (e.g. [START_REF] Demarty | Using a multiobjective approach to retrieve information on surface properties used in a SVAT model[END_REF]). In the near future, we expect that TIR remote-sensing data will be acquired every day or so at a resolution of less than 100m, which is consistent with the size of most agricultural fields. Remote Sensing data in the TIR part of the spectrum provides indirect estimates of water stress -defined as a function of the ratio between actual and potential evaporation rates -at the earth surface. During the first stage of evaporation ("energy limited" evaporation) of an interstorm period, water availability is large enough to sustain evaporation at a potential rate and the ratio between actual and potential evapotranspiration is close to one: evapotranspiration depends only on the available energy at the surface. During the second stage of evaporation ("soil controlled" evaporation), the water content has dropped below a critical value and the diffusion processes within the soil are considerably reduced. This critical value depends on the hydraulic properties of the soil. Since the amount of soil water that can be easily extracted by roots is entirely controlled by the diffusion within the soil, transpiration decreases with diffusion, and stress occurs; as a result the ratio drops below one. During water stress, stomatal resistance is increasing and the available energy (mostly net radiation) is no longer converted into evaporation but in sensible heat. The latter is less efficient in dissipating energy and the surface of the leaves warms up. Surface temperature is thus strongly related to water stress. Since surface temperature can be deduced from TIR remote sensing data, stress and no-stress conditions can be observed from space. Data assimilation readjusts dynamically the soil water content and/or the soil parameters to minimize the difference between the simulated and the observed surface temperatures. Again, these methods are difficult to put into practice, and are meant to be applied over a long period of time. Indeed, potential differences in surface temperature are not always explained by inaccurate soil moisture content, but often as well by large errors in estimating the water and energy balance parameters. SVAT models have indeed a large number of unknown parameters, and the resulting observing system based on TIR data and SVAT models is usually underdetermined. Here, we propose a simpler procedure based on the same idea: can one relate water stress observed by TIR remote sensing for a given sensor resolution to the underlying soil physical properties at the same spatial resolution ? For that purpose, a simple yet robust evaporation equation [START_REF] Boulet | A simple water and energy balance model designed for spatialisation and remote sensing data utilization[END_REF][START_REF] Boulet | Evaluation of a two-stage evaporation approximation for contrasting vegetation cover[END_REF] for the second stage evaporation is used as a tool to check what soil parameter values are computing the same date for the onset of stress as what is observed under given conditions of uncertainty in the system. By restricting our study to water stress periods, i.e. periods for which second stage evaporation exists, and by using a simple but robust model, we ensure that the information extracted from TIR data is tightly linked to the diffusion processes within the soil and therefore to the prevailing soil hydraulic properties. The duration of the first-stage drying, or time-to-stress, is so closely related to the hydraulic properties of the soil that it has been used as a surrogate to soil hydraulic properties by [START_REF] Salvucci | Soil and moisture independent estimation of stage-two evaporation from potential evaporation and albedo or surface temperature[END_REF] for short vegetation. [START_REF] Levine | Characteristic rate scale and timescale of supply-limited transpiration under a Richards-Cowan framework[END_REF] have later on extended the approach to all vegetation types but this method requires time-to-stress observations for all interstorm periods, which gives little predictive value to the method. In order to get a comprehensive and predictive estimate of the whole water balance, one must have access to the soil hydraulic properties themselves. Contrarily to those approaches, that model evaporation by replacing the hydraulic properties with a function of an observed time-to-stress, [START_REF] Boulet | Evaluation of a two-stage evaporation approximation for contrasting vegetation cover[END_REF] provide an analytical expression linking the time-to-stress to an average potential evapotranspiration rate, an average initial condition, and given soil hydraulic properties. Time-to-stress can thus be used to infer the latter if the two other inputs (potential evapotranspiration and initial soil moisture) are known. This paper builds on this hypothesis and presents an evaporation test designed to refine the range of acceptable soil hydraulic properties for use in a variety of water balance models. This test is based on the evaluation of the time-to-stress from TIR remote-sensing data and an analytical expression relating the time-to-stress to the hydraulic properties, the initial water content and a mean potential evaporation rate. The latter is derived from a simple energy balance equation driven by routinely available meteorological and ancillary remotesensing data. In the second part of the paper, the performance of various methods to constrain soil hydraulic properties is analysed for data acquired during two international field experiments. These methods are (i) the proposed evaporation test, (ii) fitting the daily evaporation simulated by the SVATsimple model on the observed one, (iii) Beerkan infiltration tests and (iv) three commonly used pedotransfer functions.

Theoretical basis of the "evaporation test"

Concept

The principle of the evaporation test has been briefly outlined above and is relatively simple: the time-to-stress of a given surface is closely related to the amount of water that has been extracted at a potential rate from the beginning of the interstorm period (say, after a heavy rainfall or an irrigation event); since this amount depends in turn on the hydraulic properties and the initial water content, it is possible to infer some information on those properties from an estimate of the time-to-stress if the latter is observable with TIR remote sensing data. The evaporation test consists in two successive modelling steps: First, a simple energy balance equation is solved to derive an average potential evapotranspiration rate and a related unstressed equilibrium surface temperature during each interstorm period for a given site. The difference between the unstressed and the observed surface temperature is then computed for all interstorm periods as a baseline to detect water stress (section 2.2). Second, a modelled time-to-stress (section 2.3) is calculated for all interstorm periods for which a reduction in evaporation due to water shortage is observed, using a range of realistic hydraulic parameter values. The parameter values that provide the smallest differences between the observed and the modelled time-to-stress are then kept as "appropriate".

Detecting water stress using information in the Thermal Infra Red Spectrum

Water stress is classically related to a sharp increase in the difference between the surface temperature and the air temperature. However, it was shown in [START_REF] Boulet | Monitoring water stress using time series of observed to unstressed surface temperature difference[END_REF] that using solely the difference between the actual and a theoretical unstressed surface temperature is more efficient than using the classical index as a baseline to monitor water stress. To illustrate this, Figure 1 shows two dry-down periods selected for the B123 wheat field during the SudMed experiment [START_REF] Chehbouni | An integrated modelling and remote sensing approach for hydrological study in arid and semi-arid regions: the SUDMED programme[END_REF] in 2003, one when the field is a bare soil (top), the other at the end of the growing season of winter wheat (bottom). On the left hand side, evaporation time series in potential and real conditions are displayed; potential evaporation rates are simulated with a simple energy balance equation [START_REF] Boulet | A simple water and energy balance model designed for spatialisation and remote sensing data utilization[END_REF], and the divergence between both evaporation curves corresponds to the time-to-stress.

On the right hand side, time series of unstressed to observed surface temperature difference show a significant increase around the time-to-stress, while the difference between the surface temperature and the air temperature does not show a clear trend around that time.

In general, the simple energy balance model used to compute both the unstressed temperature T sp and potential evaporation rate e p is a simple "big-leaf" model with a single "bulk" source of energy. This description is consistent with the remote sensing data that do not discriminate between the different elements within a pixel. The interesting feature is that since the "evaporation test" will be performed at the scale of the remote-sensing data, it provides an integrated or "effective" estimate of the hydraulic properties. An example of a simple "big leaf" model is provided in [START_REF] Boulet | Monitoring water stress using time series of observed to unstressed surface temperature difference[END_REF] and is given in Appendix. Following this approach, the data requirement to compute T sp and e p is then: (i) Meteorological forcing data and (ii) time series of Leaf Area Index (LAI), usually derived from time series of Normalised Differential Vegetation Index (NDVI) obtained from a combination of remotely sensed reflectances, and a given LAI/NDVI relationship [START_REF] Duchemin | Monitoring wheat phenology and irrigation in Center of Morocco: on the use of relationship between evapotranspiration, crops coefficients, leaf area index and remotely-sensed vegetation indices[END_REF].

An analytical expression of the "time-to-stress"

This section presents the analytical expression relating the time-to-stress to the amount of water that can be extracted by diffusion through the soil. For most models, the components of the water budget are obtained from a solution of the [START_REF] Richards | Capillary conduction of liquids through porous media[END_REF] equation under given initial and boundary conditions. During interstorm periods, those boundary conditions are made of an imposed flux (e p ) during the first stage of evaporation and an imposed (negative) pressure head during the second stage. Analytical simplifications of the Richards equation can be derived if the initial soil moisture profile is homogeneous. In that case, the transition from one stage to the other is solved by the Time Compression Approximation [START_REF] Salvucci | Equivalent steady soil moisture profile and the time compression approximation in water balance modeling[END_REF]. Let one use the following nondimensional expressions of time t [T], readily available water in the root zone A [L] and evaporation rate e [LT -1 ] (respectively):

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = 2 0 2 ~d S K A A (1) 2 0 2 ~⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = d S K t t (2) 0 / ~K e e =
(3) A is the amount of water in the root zone that can be easily extracted by roots, i.e. the difference between the actual and the wilting point soil moisture multiplied by the effective root zone depth. This effective root zone depth corresponds to the soil volume that contains the largest percentage of the roots. K 0 [LT -1 ] is the hydraulic conductivity and S d [LT -1/2 ] the desorptivity, both at initial water content. K 0 and S d depend on (i) the initial water content θ 0 [-] at the beginning of the dry-down period, (ii) the normalization parameters of the retention (saturated water content θ sat [-] and air entry pressure h g [L]) and conductivity (saturated hydraulic conductivity K sat [LT -1 ]) curves, that depend on the soil structure (Haverkamp et al., 1998) and are largely unknown and spatially variable and (iii) the shape factor of these two curves, that depend mostly on the soil textural properties and can be inferred from soil texture maps [START_REF] Haverkamp | Property-transfer models[END_REF].

In this study the van Genuchten retention curve [START_REF] Van Genuchten | A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[END_REF] relating water tension h [L] to soil volumetric moisture θ [-] under the Burdine assumption [START_REF] Burdine | Relative permeability calculation from size distribution data[END_REF] and the Brooks and Corey conductivity curve [START_REF] Brooks | Hydraulic properties of porous media[END_REF] relating hydraulic conductivity K [LT -1 ] to soil volumetric moisture θ were used:

m sat sat K K 1 2+ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = θ θ and m m g sat h h - - ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = 1 2 1 θ θ (4)
Where m [-] is a shape factor. In that case (see [START_REF] Boulet | Evaluation of a two-stage evaporation approximation for contrasting vegetation cover[END_REF] for details):

( ) ( ) m c m h K S sat p g sat d , , 3 1 4 0 2 θ θ - = and m sat sat K K 1 2 0 0 + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = θ θ (5) ( ) ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ - + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Β - ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ - + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Β = 2 1 , 2 1 7 , 2 1 , 2 1 5 , , , 1 0 , , 1 0 , , 0 0 m m m m m c m sat b a x sat m sat b a ( ) ( ) du u u b a x b x a b a x 1 0 1 , , 1 , , - - ∫ - = Β (7)
is the product of the Incomplete Beta function I x (a,b) and its corresponding Beta function B(a,b) (Press et al., 1992, p. 219).

It has been shown (see [START_REF] Boulet | Evaluation of a two-stage evaporation approximation for contrasting vegetation cover[END_REF] for details) that the instantaneous evaporation can then be expressed as:

( ) ( ) ( ) ⎪ ⎩ ⎪ ⎨ ⎧ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + - + - + - = > ∀ = ≤ ∀ t e A
It follows from Equation 2:

stress d stress t K S t 2 1 2 0 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = (10)
Equations 1-10 are used together with the simple energy balance described in Appendix to build the simple yet physically-based single source/single bucket SVATsimple model. Time-to-stress t stress is thus derived from Equations 9 and 10 from an estimate of e p , hydraulic properties, root depth and average initial water content. Again, only the shape factor of the retention and conductivity curves (m) is related dominantly to soil texture, while the three normalization parameters (θ sat and, to a larger extent, K sat , and h g ) depend mainly on soil structure. It is therefore difficult to estimate them from textural properties alone, as it is done traditionally with the pedotransfer functions. Consequently, the evaporation test consists in minimizing the difference between the observed and the simulated time-to-stress by adjusting the two main normalization parameters, K sat and h g .

Application and comparison with Beerkan tests and Pedotransfer functions

3.1. Field data Two interstorm periods have been selected for both the B123 (Figure 1) and the SALSA (Semi Arid Land Surface Atmosphere, [START_REF] Goodrich | Preface paper to the Semi-Arid Land-Surface-Atmosphere (SALSA) Program special issue[END_REF] experiments (see [START_REF] Boulet | Monitoring water stress using time series of observed to unstressed surface temperature difference[END_REF] for details on both datasets). For B123, soil moisture limits the evaporation of the wheat field at two classical stages in the agricultural calendar: one after the first irrigation following sowing, and one after the last irrigation when wheat is mature. For the SALSA experiment, the vegetation is a sparse grassland, and both water stress events are located at the end of the growing period during the summer monsoon, with slightly wetter conditions for the first interstorm. B123 is a clay loam (clay fraction is 35% clay and sand fraction is 23%), while SALSA Zapata site is a sandy loam (clay fraction is 8% and sand fraction is 67%). Saturated water content is derived from bulk density measurements as a fixed proportion (90%) of the porosity, following [START_REF] Rogowski | Watershed physics: Model of soil moisture characteristics[END_REF].

In both cases, time series of actual evapotranspiration measured by eddycorrelation systems are available but no hydraulic property has been measured in the laboratory, except for one disturbed sample taken at the surface (a few cm) of the B123 site, for which PF 4.2, PF 3, PF 2.5 and PF 2 soil moisture values have been measured. In both experiments, surface temperature is observed by in-situ thermoradiometers. The measurement footprint ranges from a few square meters for the radiometers to a few hectares for the eddy-correlation system that estimates the latent heat flux. As mentioned before, evapotranspiration is difficult to measure and needs a well-trained staff to operate the system whereas an in-situ thermoradiometer is easy to install. Moreover, even though current satellite platforms cannot provide any data at a satisfactory spatial (<100m) and temporal (1 acquisition per day) resolutions, one hopes that high resolution TIR images will be routinely acquired in the near future. In that case the proposed evaporation test could be applied more operationally. It is thus important to keep in mind that even though a performance criterion using the evaporation data will be developed in the next section to evaluate the method, the proposed methodology (the "evaporation test") relies on the minimization between the "observed" and simulated time-to-stress inferred from remote-sensing.

Hydraulic properties for the B123 site have been estimated through infiltration tests. Those tests provide an independent evaluation of the performance of the "evaporation test". Infiltration tests are based on fitting an analytical approximation of the [START_REF] Richards | Capillary conduction of liquids through porous media[END_REF] equation to an observed infiltration rate. The approximation is usually obtained for homogeneous initial conditions and under constant positive head and assumes that a pseudo-constant water depth is applied at the soil surface.

Here we implemented the Beerkan method [START_REF] Braud | Use of scaled forms of the infiltration equation for the estimation of unsaturated soil hydraulic properties (the Beerkan method)[END_REF], which fits this analytical approximation on an experimentally derived cumulative infiltration curve. The latter is obtained by pouring a given amount of water in a ring sitting on the soil surface, waiting for it to disappear in the ground, noting the corresponding time with a stopwatch and repeating this operation until the steady-

Diagnostic variables and inversion methods

Improving model parameterization during no stress periods

One expects that the usefulness of the "evaporation test" will largely depend on the accuracy of the numerous input data, including the potential evapotranspiration rate e p . Given the uncertainty on e p estimates derived from any "big leaf" model, it is advisable to use TIR data also to reduce the bias between the observed and the simulated latent heat flux in potential conditions, i.e. before the onset of stress. Indeed, even if with current satellite retrieval capabilities one can expect in the near future an overall measurement error of the order of 1°K, this error is generally small compared to the typical model error one obtains when the most sensitive parameters of the energy balance model are not known a priori. Comparing the observed and the computed surface temperature during no stress periods can help optimize the model parameterization. By choosing a-priori ranges of values for the most sensitive parameters (see Table 1), namely the minimum surface resistance, the soil heat flux to net radiation ratio under bare soil conditions and the parameter governing the difference between the aerodynamic and the surface temperature, an ensemble of potential evapotranspiration values can be generated with the simple "big leaf" model. From this ensemble one can compute a standard deviation of e p . which will be used as an error estimate in the uncertainty framework presented below for the second step of the evaporation test. For the second (full cover conditions) stress period of the B123 site, the temperature simulated by the simple energy balance using the middle of the ranges of values given in Table 1 is already close to the observed surface temperature (Figure 1). By selecting the parameter values that produce an average absolute bias between the simulated and the observed surface temperature before the time-to-stress that is lower than 1°C, the standard deviation of the latent heat flux is considerably reduced: It drops from 0.46 mm/day to 0.27 mm/day (Figure 3). It is noticeable that the difference between the observed and the simulated evapotranspiration during this no stress period is also reduced (from 0.13 mm/day to 0.07 mm/day). For bare soil conditions, observations are very far from the range of simulated temperature values (Figure 1) and this distance cannot be reduced by fitting the parameters within the ranges given in Table 1. The average standard deviation is not reduced by TIR data assimilation and the expected error without TIR data assimilation (also of the order of 0.27 mm/day) is kept in the second step of the evaporation test.

Diagnostic variables of the model performance for evaporation and time-to-stress

In order to evaluate the amount of information contained in the sole time-to-stress observation compared to a complete evaporation time series, two separate criteria will be computed to select the appropriate hydraulic properties [h g , K sat ]. The first criterion is only used to evaluate the method. It is based on the mean distance between the simulated (Eq. 8) instantaneous evaporation and the observed evaporation time series. A Nash efficiency is computed for all possible combinations of realistic hydraulic property values. We identify the overall maximum efficiency, and then select arbitrarily all solutions that lead to a Nash efficiency greater than 90% of the overall maximum as "acceptable". Nash efficiency E is given as: Where e sim and e obs are the simulated and observed daily evaporation rates, and stands for "average value over the calibration window", respectively.

The second criterion is meant to be used routinely in the "evaporation test". It is based on the difference between the observed (Eq. 10) and the simulated time-to-stress. Since the observed timeto-stress is likely to be derived from trend analysis with daily TIR observations, its precision is larger than a day. We therefore select all possible hydraulic property values that lead to a difference between the observed and the simulated time-to-stress of less than 1 day.

In order to produce maps of the two criteria (Nash efficiency for evaporation and difference in time-tostress) in the [h g , K sat ] parameter space, simulations were carried out for both interstorm periods of each site. The uncertainty framework takes into account errors in initial water content, potential evapotranspiration (as obtained from section 3.2.1), and shape factors of the retention and conductivity curves. K sat and h g values are chosen from within the realistic predefined ranges given in Table 1. Initial water content and root zone depth are evaluated locally at three locations within each field from gravimetric and bulk density measurements and an allometric survey (respectively). The root zone depth is different from the maximum root extent but coincides with the zone of maximum root density (around 20 cm in the case of the wheat). It can increase as LAI increases but in our case it is kept constant since all dry-down periods are located either at the end of the growing season or when vegetation is absent (A=0). Due to the difficulty to evaluate the extent of the root zone depth, it is important to use the same value for the evaporation test and the model for which an estimate of the hydraulic parameters is required. The shape factors of the retention and conductivity curves are deduced from the particle size distribution with Fractal Similarity following the method given by [START_REF] Braud | Use of scaled forms of the infiltration equation for the estimation of unsaturated soil hydraulic properties (the Beerkan method)[END_REF]. The search algorithm scans systematically the possible range of values by incrementing each parameter from the minimum to the maximum defined in Table 1 and investigating all combinations of the seven following quantities: h g , K sat , the shape factor of the Van Genuchten retention curve, the initial water content and the mean potential evaporation rate before the the onset of stress for both drydowns. Figure 4 shows a superposition of the contour plots for both criteria in the value corresponds to the highest Nash for the evaporation criterion and the lowest difference in time for the "evaporation test" criterion.

Diagnostic variables for the Beerkan tests

Because of the limited time available to perform each infiltration test, the number of points on each cumulative infiltration curve is rather small (4 to 9 volumes of 200 ml). Consequently, special care must be taken to select the appropriate [hg, Ksat] solutions when interpreting the tests. Two criteria were chosen for assessing the accuracy of the retrieved parameters:

(i) The number of solutions in the predefined parameter-space (same range as in Table 1) and (ii) the Root-Mean-Square-Error (RMSE) between the simulated and the observed cumulative infiltration curves. These two criteria are used for evaluation only, not the selection of the appropriate hydraulic parameters. Therefore, all solutions are shown in what follows and the criteria allow assigning a quality tag to each test.

Results

For B123, the best-fit [h g , K sat ] values are organized along a crest of Nash efficiency in the [h g , K sat ]

parameter space, making impossible to select one particular solution. This is consistent with findings by [START_REF] Zou | Estimation of depth averaged unsaturated soil hydraulic properties from infiltration experiments[END_REF] on soil properties retrieval from soil moisture observations. It is also consistent with the expression of the desorptivity (Equation 5) since the amount of water that can be extracted by diffusion is proportional to both h g and K sat . Due to the expected errors in field average initial water content and potential evapotranspiration, the segment of "acceptable" h g and K sat values occupies a much larger proportion of the parameter space than if those quantities were known with absolute precision.

The space defined by the contour lines with a time-to-stress difference of less than one day is consistent with the space between the contour lines of positive Nash efficiency values. Time-to-stress difference increases sharply from less than a day to values much larger than 5 days. Figure 5 shows the pattern of [h g , K sat ] values selected as "acceptable solutions" according to both criteria and following the increment used in the search algorithm. It also shows the solutions of the Beerkan infiltration tests (crosses) and the values given by the traditionally used [START_REF] Clapp | Empirical equations for some soil hydraulic properties[END_REF] pedotransfer function (stars). These solutions will be intercompared in the next section. As expected, the number of possible parameter values is much more limited with the first (efficiency, open squares) rather than with the second (time difference, filled dots) criterion: the evaporation time-series, including the amplitude and time-scale of the evaporation reduction after the onset of stress, contain more information on the second stage of evaporation than the sole time-to-stress.

For the SALSA data set (Figures 6 and7), there is again a much smaller zone with acceptable solutions for the first criterion (Nash efficiency) than for the second one (difference in time to stress).

Indeed, for all h g and K sat values above a certain threshold (around -0.1 m and 10 -5 m/s respectively), the large water loss by gravitational drainage implies that stress occurs in the early days of the drying cycle. In that case, the decline in daily evaporation over time during the second stage contains a large amount of information on the moisture diffusion processes within the soil, compared to the sole timeto-stress, and the first criterion enables to reduce at least the space of acceptable air entry pressure values to the [-0.2,-2] range. On the other hand, even if stress occurs on the very first day, as is the case for the second SALSA drying down period, the time-to-stress and the Nash efficiency on evaporation lead one to accept all K sat values above 10 -5 m/s, which means that the abrupt decrease in evaporation during Stage Two does not result in extra information compared to the time-to-stress.

Comparison with Beerkan tests and pedotransfer functions

Results for the 12 tests performed at the B123 site are shown as plusses on Figure 5; all solutions of the tests are shown, but, following the criteria presented above, the best Beerkan results are obtained for the isolated groups of plusses which mostly correspond to the lowest RMSE, while for the lowest hg and K sat values the fit is poor and there are many solutions along a straight line in the [h g , K sat ] loglog space. Again, this is consistent with the expression of the sorptivity (see [START_REF] Braud | Use of scaled forms of the infiltration equation for the estimation of unsaturated soil hydraulic properties (the Beerkan method)[END_REF] since the amount of water that can infiltrate by diffusion, a dominant process for low h g and K sat values, is proportional to both h g and K sat . The solutions of the Beerkan tests are also organized along a powershape curve in the [h g , K sat ] log-log space. This curve crosses the line of the solutions given by the evaporation test for medium [h g , K sat ] values corresponding to the [START_REF] Clapp | Empirical equations for some soil hydraulic properties[END_REF] estimates for a clay loam and a silty clay loam (stars). One must note that also the hydraulic parameters always correlate to some extend it is notable that here hg and K sat were derived for the Clapp and Hornberger models that are different from the van Genuchten and Burdine models.

Altogether, there is a good agreement between the three estimates since all solutions intersect at approximately K sat = 2 10 -6 m/s and h g = -0.4 m . This means that if one single method does not provide a narrow range of values, estimates can be combined to significantly reduce the overall range of parameters by keeping all values that show consistency with all three methods. One can assume that the alignment of all solutions along a curve either concave-up or concave-down in the [h g , K sat ]

space is linked to the mathematical form of either the evaporation or the infiltration curve. Finally, all estimates of the resulting wilting point and field capacity are compared (Table 2) with additional pedotransfer functions proposed by [START_REF] Rawls | Prediction of soil water properties for hydrologic modelling[END_REF] and [START_REF] Saxton | Soil water characteristic estimates by texture and organic matter for hydrologic solutions[END_REF] which are based on other mathematical expressions of the retention curve than the van Genuchten equation.

The mean, minimum and maximum values given by each method are very different, but there is always a substantial overlap between all estimates. Note that the single retention curve measured in the laboratory from an undisturbed sample taken from the first 10 cm of the soil surface provides values in the lower part of all ranges of values, with a field capacity of 0.35 m 3 /m 3 and a wilting point of 0.20 m 3 /m 3 . By fitting the Van Genuchten model to this experimental retention curve, a value of h g of -0.41 m is obtained, which is consistent with the intersection of all estimation methods. However, the retrieved m value (0.07) is larger than the one obtained by Fractal Similarity (0.05).

For the SALSA dataset, the [START_REF] Clapp | Empirical equations for some soil hydraulic properties[END_REF] pedotransfer function [h g , K sat ] values for sandy loam (star in Figure 6) are within the range of acceptable solutions given by the evaporation test (filled dots), but the air entry pressure is less negative than that provided by the evaporation criterion (open squares).

Conclusion

The principles of an "evaporation test" using remotely sensed TIR data have been presented in this paper. The "evaporation test" consists of two parts:

(i) detecting water stress as a sharp divergence between the observed and the unstressed surface temperature time series and inverting the unknown parameters of the energy budget by minimizing the difference between both temperatures before the onset of stress (information used :

TIR and Normalized Differential Vegetation Index NDVI data at representative scale; NDVI/Leaf Area Index relationship; meteorological data) and

(ii) selecting the hydraulic parameters [h g , K sat ] that give a simulated time-to-stress consistent with the observed time-to-stress (information used: difference between the date of last irrigation or rainfall and the time-to-stress derived in the previous step; water content at the beginning of the interstorm period; particle size distribution; estimate of the root zone depth).

This method allows for refining the range of valid hydraulic properties at the scale of the remotesensing measurements. The obtained range of values has been compared to i) the amount of information one can retrieve from observed evaporation time series and ii) local estimates of the hydraulic properties deduced from infiltration tests. It has been shown that deriving a rough estimate of the time-to-stress from remote-sensing yields significant information on the appropriate hydraulic properties compared to the evaporation time series measured by an eddy-correlation device.

Moreover, the soil hydraulic properties inferred from this estimate, although spanning a wide range of values in the hydraulic conductivity / retention curve parameter space, are consistent with the estimates obtained by other means (pedotransfer functions and infiltration tests). The main advantage of this method is that the information retrieved from TIR data is representative of the pixel size of the TIR imagery. The main limitation of this method is that a field average initial soil moisture is difficult to assess, especially with remote-sensing; a possible way to bypass this for irrigated agriculture is to assume that initial water content is close to field capacity, but this remains a very crude estimate.

Moreover, if several land uses or irrigation practices are present in the pixel, the results of the method are representative of an average water stress, even if such a stress occurs only on part of the pixel.

Further work should therefore address the scaling relationship between the evaporation time series simulated using these average parameters and the sum of the weighted individual flux estimates for each homogeneous unit of an heterogeneous pixel. Finally, it is expected that this method will be more easily implemented in arid and semi-arid climates rather than in temperate regions where dry periods are not very long and where water stress is seldom reached.

Appendix: the Simple "big leaf" energy balance model [START_REF] Boulet | A simple water and energy balance model designed for spatialisation and remote sensing data utilization[END_REF] T sp is the solution of the following energy balance equation: is the saturation vapour pressure at a given temperature, e a is the current air vapour pressure, ( )

( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ] ( ) ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + - + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - = - - + - L r T
⎩ ⎨ ⎧ ≥ < = 1 1 min min L if L r L if L r L r c c s
is the surface resistance and r cmin the minimum stomatal resistance.

One can note that with the above notations 1 See Appendix for the explanation of the symbol;

2 Root zone depth was fixed a priori in order to downsize the number of acceptable solutions;

  state flow is reached. 115 Beerkan tests have been carried out in the Haouz plain over selected fields in the irrigation district where the B123 site is located. Amongst those 115 tests, 12 Beerkan tests have been performed in the B123 field itself. The resulting h g and K sat values for the 115 tests and the whole range of textural properties present in the irrigation district are shown on Figure 2, alongside with those derived from the widely used pedotransfer function of Clapp and Hornberger (1978). All solutions of the Beerkan tests for each textural class are kept and shown on Figure 2 as a mean value and an error bar. Despite the decrasing trend in both hydraulic parameter values across the range of clay percentages, as documented by the parabolic regression, the large error bars and the large scatter of points show the large variability of parameter values within each textural class. This variability cannot be represented by the pedotransfer function and we describe below how both infiltration and evaporation tests can complete this information.

[

  h g , K sat ] parameter space. Each criterion is made of a composite of the two criteria values for the two dry-downs, weighted by the number of days in each dry-down. In order to produce this contour plot in a 7D optimization problem, only the optimal values of each criterion with respect to the five remaining parameters are shown in this Figure.The optimal set of the last five parameters for each [h g , K sat ]

  ρ is the air density, c p is the specific heat of air at constant pressure, a s is the surface albedo, Rs the incoming solar radiation, ε s the surface emissivity, ε a the air emissivity, σ the Stefan-Boltzman constant, T a the air temperature, soil heat flux G is a fraction ( ) radiation Rn depending on the Leaf Area Index (L) and an empirical parameter ξ s , T 0p is the aerodynamic temperature, to the surface temperature T sp according to L and an empirical parameter μ, relating the aerodynamic resistance without stability correction r a0 to the Richardson number Ri which is a function of the T sp -T a difference, η = 0.75 in unstable conditions and η = 2 in stable conditions, e *

  Figure and Table captions

Figure 1 .

 1 Figure 1. Evaporation and temperature time series for two dry-down periods of the 2003 B123 wheat growing season: bare soil (top) and full cover (bottom); the vertical bar indicates the onset of stress.

Figure 2 .

 2 Figure 2. Saturated hydraulic conductivity and air entry pressure values obtained for the 115 Beerkan tests in the Haouz plain, along with the interpolated Clapp and Hornberger (1978) pedotransfer function, plotted against clay fraction.

Figure 3 .

 3 Figure 3. Daily evaporation time series for the second dry-down period of the 2003 B123 wheat growing season: simulation results before (a) and after (b) the minimization on the observed surface temperature time series in potential conditions.

Figure 4 .

 4 Figure 4. Nash efficiency between the observed and the simulated daily evaporation time series (contour filled) and difference between the observed and the simulated time-to-stress (contour lines) in the saturated hydraulic conductivity K sat /air entry pressure h g parameter space for the B123 site.

Figure 5 .

 5 Figure 5. Selected saturated hydraulic conductivity K sat /air entry pressure h g parameter values deemed "acceptable" for the B123 site: according the Nash criteria for evaporation (empty squares) and the difference in time-to-stress (filled dots); stars show the value given by the Clapp and Hornberger (1978) pedotransfer function for a clay loam and a silty clay loam; crosses show the results of the 12 Beerkan tests performed in the B123 field.

Figure 6 .

 6 Figure 6. same as Figure 4. for the SALSA grassland site (Zapata).

Figure 7 .

 7 Figure7. same as Figure5. for the SALSA grassland site (Zapata); the star shows the value given by the[START_REF] Clapp | Empirical equations for some soil hydraulic properties[END_REF] pedotransfer function for a sandy loam.

  [m] Shape factor of the retention curve m [-] Initial water content θ 0 [-] Minimum surface resistance r cmin [s/m] 1 Albedo a s [-] 1 Soil heat flux to net radiation fraction ξ s [-

  Figure 2

Table 1 .

 1 Parameter range used in this study.

Table 2 .

 2 Field capacity and wilting point values obtained with different methods for the B123 site.

	Table 1
	parameter	range
	Saturated hydraulic conductivity K sat [m/s]
	Air entry pressure h g

Table 2

 2

					Beerkan	Evaporation	Clapp and	Rawls and	Saxton and	GRIZZLY	Surface soil
					tests	tests	Hornberger	Brakensiek	Rawls	database	sample
							(1978)	(1985)	(2006)	(laboratory)
	Field	Min	0.25	0.31	0.36	0.25
	capacity	Mean	0.36			0.34	0.35	0.38	0.35
	[m	3 /m	3 ]	Max	0.40	0.41	0.39	0.42
	Wilting	Min	0.17	0.22	0.22	0.14
	point	Mean	0.25			0.22	0.20	0.25	0.20
	[m	3 /m	3 ]	Max	0.33	0.35	0.25	0.31

Acknowledgments

This study was conducted within the framework of the IRD/Sud-Med project, with support from the European Union 5th Framework through the INCO-MED Program IRRIMED (http://www.irrimed.org/) and the integrated action French-Morocco PAI n°MA/06/148. Additional funding was provided through EU Pleiades project as well as CNES/TOSCA program. The authors would like to acknowledge the Sud-Med technical partners, and especially ORMVAH (Office Regional de Mise en Valeur Agricole du Haouz). All reviewers are thanked for their constructive comments that greatly improved the paper.