Iännis Roland

Domitille Schanne

Alexandra Bogicevic

Aloyse Degiron

Enhancement and tuning of the defectinduced electroluminescence of ZnO mesoporous layers in the visible range (preprint version)

We show a way to pattern the visible electroluminescence of solution-processed mesoporous ZnO layers. Our approach consists in locally changing the nanoscale morphology of the coated ZnO layers by patterning the underlying surface with thin metallic patches. Above the metal, the ZnO film is organized in clusters that enhance its defect-induced electroluminescence. The resulting emission occurs over a large continuum of wavelengths in the visible and near-infrared range. This broad emission continuum is filtered by thin-film interferences that develop within the device, making it possible to fabricate LEDs with different colours by adjusting the thickness of their transparent electrode. When the metallic patterns used to change the morphology of the ZnO layer reach sub-micron dimensions, additional plasmonic effects arise, providing extra degrees of freedom to tune the colour and polarization of the emitted photons.

Introduction

Zinc Oxide (ZnO) is a choice material in optoelectronic research. An inherently n-doped semiconductor with a direct bandgap in the ultraviolet (UV) at 375 nm, ZnO has become the standard electron transport layer in quantum dot LEDs operating in the visible and infrared range [START_REF] Stouwdam | Red, green, and blue quantum dot LEDs with solution processable ZnO nanocrystal electron injection layers[END_REF][START_REF] Sun | Bright infrared quantum-dot light-emitting diodes through inter-dot spacing control[END_REF][START_REF] Kirkwood | Enhancing Quantum Dot LED Efficiency by Tuning Electron Mobility in the ZnO Electron Transport Layer[END_REF]. Moreover, ZnO has also attractive luminescent properties by itself thanks to its large exciton binding energy that allows UV lasing at room temperature [START_REF] Özgür | A comprehensive review of ZnO materials and devices[END_REF]. In particular, powders and polycrystalline layers of ZnO have been used to demonstrate random UV lasing [START_REF] Cao | Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films[END_REF][START_REF] Cao | Random Laser Action in Semiconductor Powder[END_REF][START_REF] Leong | UV Random Lasing Action in p-SiC(4H)/i-ZnO-SiO2 Nanocomposite/n-ZnO:Al Heterojunction Diodes[END_REF]. ZnO under various forms (polycrystalline ZnO, nanowires, nanocrystals…) has also attracted considerable interest as an active material for UV LEDs, mostly in the form of n-doped regions of heterojunctions [START_REF] Könenkamp | Ultraviolet Electroluminescence from ZnO/Polymer Heterojunction Light-Emitting Diodes[END_REF][START_REF] Chen | Fairly pure ultraviolet electroluminescence from ZnO-based light-emitting devices[END_REF][START_REF] Ning | Hugely enhanced electroluminescence from mesoporous ZnO particles[END_REF][START_REF] Lupan | Low-Voltage UV-Electroluminescence from ZnO-Nanowire Array/p-GaN Light-Emitting Diodes[END_REF][START_REF] Toyama | Top-Emission Ultraviolet-Light-Emitting Diodes Containing Solution-Processed ZnO Nanocrystals[END_REF][START_REF] Chan | Enhanced ultraviolet electroluminescence from ZnO nanoparticles via decoration of partially oxidized Al layer Opt[END_REF], but also in pure ZnO homojunctions thanks to progresses in p-type doping of this material [START_REF] Lim | UV Electroluminescence Emission from ZnO Light-Emitting Diodes Grown by High-Temperature Radiofrequency Sputtering[END_REF].

Interestingly, ZnO also exhibit rich emission properties in the visible. The origin of this sub-bandgap emission is related to a variety of vacancy and interstitial defects that create a broad continuum spanning the whole visible range [START_REF] Crapanzano | Morphology Related Defectiveness in ZnO Luminescence: From Bulk to Nano-Size Nanomaterials[END_REF]. A potential application of this defect-induced emission is the development of white light emitting diodes, as suggested by studies in which ZnO nanocrystals (NCs) have been exploited as phosphors to convert UV or blue electroluminescence (EL) into a visible continuum [START_REF] Liu | Large-scale synthesis of ZnO nanoparticles and their application as phosphors in light-emitting devices[END_REF][START_REF] Rao | Effect of ZnO nanostructures on the optical properties of white light-emitting diodes[END_REF]. In parallel, direct visible electroluminescence of vacancy and interstitial defects in ZnO has also been demonstrated by many teams [START_REF] Du | Room temperature defect related electroluminescence from ZnO homojunctions grown by ultrasonic spray pyrolysis[END_REF][START_REF] Lima | Electroluminescence of zinc oxide thin-films prepared via polymeric precursor and via sol-gel methods[END_REF][START_REF] Lee | White Light Electroluminescence from Zinc Oxide Nanowire Composites[END_REF][START_REF] Lee | White-light electroluminescence from ZnO nanorods/polyfluorene by solution-based growth[END_REF][START_REF] Jha | ZnO nanorod based low turn-on voltage LEDs with wide electroluminescence spectra[END_REF][START_REF] Bano | Enhancement of external quantum efficiency and quality of heterojunction white LEDs by varying the size of ZnO nanorods[END_REF][START_REF] Son | White light-emitting diodes fabricated utilizing hybrid polymer-colloidal ZnO quantum dots[END_REF][START_REF] Oliva | Tunable white light from photo-and electroluminescence of ZnO nanoparticles[END_REF][START_REF] Li | Toward near-white-light electroluminescence from n-ZnO nanocrystals/n-Si isotype heterojunctions via an AZO spectral scissor[END_REF]. As is the case for ZnO-based LEDs in the UV, most of these developments have been achieved by pairing an n-doped ZnO region (e.g. a polycrystalline or powderbased layer [START_REF] Lima | Electroluminescence of zinc oxide thin-films prepared via polymeric precursor and via sol-gel methods[END_REF], a nanowire array [START_REF] Lee | White Light Electroluminescence from Zinc Oxide Nanowire Composites[END_REF][START_REF] Lee | White-light electroluminescence from ZnO nanorods/polyfluorene by solution-based growth[END_REF][START_REF] Jha | ZnO nanorod based low turn-on voltage LEDs with wide electroluminescence spectra[END_REF][START_REF] Bano | Enhancement of external quantum efficiency and quality of heterojunction white LEDs by varying the size of ZnO nanorods[END_REF], or a dense ensemble of ZnO colloidal NCs [START_REF] Son | White light-emitting diodes fabricated utilizing hybrid polymer-colloidal ZnO quantum dots[END_REF][START_REF] Oliva | Tunable white light from photo-and electroluminescence of ZnO nanoparticles[END_REF][START_REF] Li | Toward near-white-light electroluminescence from n-ZnO nanocrystals/n-Si isotype heterojunctions via an AZO spectral scissor[END_REF]) with a p-doped inorganic or organic layer, although it should be mentioned that ZnO homojunctions have also been demonstrated [START_REF] Du | Room temperature defect related electroluminescence from ZnO homojunctions grown by ultrasonic spray pyrolysis[END_REF]. In these studies, the turn-on voltage is around 3-5 V and the EL spectra are typically measured at 8-10 V. It is noteworthy that external quantum efficiencies (EQE) are usually not reported although a recent study reports EQE of 4% at 6V [START_REF] Bano | Enhancement of external quantum efficiency and quality of heterojunction white LEDs by varying the size of ZnO nanorods[END_REF]. In other words, the field of ZnO-based LEDs in the visible is not currently driven by performances but is a topic of academic interest. This fact is perhaps not surprising given that the origin of visible light emission in these devices comes from defects. Contrarily to band-to-band radiative recombination, which occurs within the whole medium, the visible light emission from ZnO is intrinsically limited by the density of defects. Moreover, such uncontrolled defects may also act as trap states that contribute to quench the radiative emission. In this context, there is an interest to develop strategies that maximize the defect density and their emissivity. A known avenue to enhance the defect-induced luminescence is to favor nano-composites (ZnO nanocrystals and nanowires…) over microstructured or bulk ZnO layers due to the higher surface-tovolume ratio [START_REF] Crapanzano | Morphology Related Defectiveness in ZnO Luminescence: From Bulk to Nano-Size Nanomaterials[END_REF] and most ZnO-based visible LEDs reported so far employ nanowires or nanocrystals [START_REF] Lee | White Light Electroluminescence from Zinc Oxide Nanowire Composites[END_REF][START_REF] Lee | White-light electroluminescence from ZnO nanorods/polyfluorene by solution-based growth[END_REF][START_REF] Jha | ZnO nanorod based low turn-on voltage LEDs with wide electroluminescence spectra[END_REF][START_REF] Bano | Enhancement of external quantum efficiency and quality of heterojunction white LEDs by varying the size of ZnO nanorods[END_REF][START_REF] Son | White light-emitting diodes fabricated utilizing hybrid polymer-colloidal ZnO quantum dots[END_REF][START_REF] Oliva | Tunable white light from photo-and electroluminescence of ZnO nanoparticles[END_REF][START_REF] Li | Toward near-white-light electroluminescence from n-ZnO nanocrystals/n-Si isotype heterojunctions via an AZO spectral scissor[END_REF].

In this study, we fabricate top-emitting LEDs operating with colloidal n-doped ZnO NCs in contact with p-doped polyvinylcarbazole (PVK), with indium tin oxide (ITO) as a transparent electrode. We show that the visible electroluminescence can be selectively enhanced by burying thin metallic patches under the surface of the ZnO NC assembly, increasing the granularity of the layer and thus the density of light-emitting defects. Several other levers, such as the ITO thickness and the geometry and metal of the underlying patches can be used to tune the colour emission and polarization in a controlled way.

Fabrication

Figure 1 shows the stack of the top-emitting LEDs investigated in this study. The substrate is a Si wafer covered with a 500 nm thick SiO2 insulating layer. The fabrication begins with the deposition of 80 nm thick and 500 µm wide aluminum cathodes using a combination of photolithography on S1818 resist, metal evaporation and lift-off. Then, a solution of ZnO colloidal NCs from Avantama is coated onto the sample. The ZnO NCs have a diameter of 12 nm, their concentration is 25 g/l in isopropanol and they are spun at 3000 rpm to form a mesoporous layer with a thickness of about 50 nm. This layer is partially sintered on a hot plate bake at 200°C during 5 minutes to prevent erosion during further steps. The next step is the fabrication of 30 nm thick Au metallic patterns. In this study, various sizes are considered ranging from large patches covering hundreds of micron squares to sub-micron antennas. While the largest patterns can be defined by photolithography, we have relied most of the times on electron beam lithography (using a Raith Pioneer Two System and the CSAR 62 resist) so as to define in a single step all the features regardless of their size. The Au patterns are subsequently buried in ZnO by covering them with a monolayer (~12 nm) of ZnO NCs from Avantama. To obtain this thickness, the ZnO solution is diluted at 3 g/l in isopropanol and spin cast at 3000 rpm onto the sample. After a new bake at 100°C for 5 minutes, the hole injection layer in PVK is added to the stack. A thickness of about 50 nm is obtained by spinning a solution of PVK from Sigma Aldrich at 8 g/L in chlorobenzene at 3000 rpm, which is then baked at 100°C during 5 minutes. The fabrication workflow ends with the deposition by radio-frequency sputtering of transparent ITO anodes through a shadow mask. As specified below, the thickness of the ITO anodes is set between 75 nm and 150 nm depending on the targeted emission colour. Because ITO is the last material deposited on the sample, we were not able to anneal it to improve its conductivity because it would have degraded the soft PVK layer underneath.

Observations

We start our study by examining a LED with a 50 × 50 µm 2 Au patch near its center. An optical image of the structure is given in Fig. 2(a). The horizontal stripe is the bottom aluminum cathode and the vertical stripe is the top ITO anode (with a thickness of 150 nm in this particular instance). The Au patch, which is slightly buried within the ZnO layer as described previously, is clearly visible near the middle of the junction. Figure 2(b) shows an image of the EL when a 9 V forward bias voltage is applied to the junction. We can see that EL mainly occurs above the gold patch while it is negligible everywhere else.

This behaviour is largely independent from the lateral dimensions of the Au features, as can be appreciated on Fig. 2(c) where Au patches of various sizes have been embedded in a single junction. In this case also, EL preferentially occurs above the Au patterns, with the same intensity and the same reddish hue as in Fig. 2(b). The EL spectrum of these samples, shown in Fig. 2(d) is centered on red wavelengths (660 nm). This EL peak is quite broad, covering most of the visible range and extending up to 800 nm (the UV emission from ZnO bandgap is not visible because it is outside of the sensibility range of our Flame spectrometer from Ocean Insight).

Origin of the enhancement

The behaviour evidenced on Fig. 2 only occurs when the Au patches are slightly buried under the ZnO surface. This result indicates that the source of EL is not Au itself: in particular, no EL enhancement has been observed when the Au patch was inserted at the interface between the n-doped ZnO and the pdoped PVK layers, which would have been in principle the best position for injecting electrons and holes within the Au region. In addition, photoluminescence experiments performed on half-finished samples with and without PVK reveal that the latter material does not contribute to the enhancement (results not shown here). These observations imply that the EL signal originates from the ZnO layer and that the brightness is considerably improved in the presence of the Au patches. However, we can rule out a contribution from the optical (plasmon) resonances of the Au patches because optical resonances are inherently geometry-dependent while we have seen that the EL colour and intensity do not depend on the size of the Au patches [Fig. 2(c)]. Likewise, it is also unlikely that Fermi pinning effects and band bending at the interface between ZnO and Au play a key role in the process: if such were the case, the preferential EL enhancement would be largely independent from the depth in which the Au patches are buried within ZnO. Besides, the results presented in Fig. 2 do not depend on the work function of the metal and the same results can also be reproduced with Ag, as will be shown in section 6.

To understand the origin of the EL enhancement, it is useful to inspect the surface of the second ZnO layer coated on the sample to bury the Au patterns. To this end, we have probed the samples with atomic force microscopy (AFM) before covering them with PVK and ITO. Figure 3(a) shows the topology of the ZnO surface on an area without Au patterns. A uniform granularity with feature sizes of approximately 10-15 nm is observed, which is consistent with the nominal diameter (12 nm) of the individual NCs forming this mesoporous layer. In contrast, Fig. 3(b) reveals that the surface morphology of the ZnO layer changes significantly above the Au patterns: while the image also features a clustering aspect, the size of the grains revealed by the AFM is about 50 nm in the plane of the sample and 30 nm in the direction normal to the surface. In other words, the organization of the ZnO NCs outside and above the Au patterns is quite different. This result is not surprising given that this second ZnO layer is very thin, implying that it is very sensitive to the morphology of the underlying material. In particular, the larger features seen on Fig. 3(b) are most likely related to the grains of the Au pattern underneath. In addition, a complementary inspection of the surface with a scanning electron microscope (SEM) suggests that this thin ZnO layer is not necessarily continuous above the Au patterns, as shown on Fig. 3(c). These surface changes are most likely responsible for the EL enhancement: since ZnO can only emit visible light via defects, which are themselves strongly dependent on the morphology of the layer, it is fully expected from the literature [START_REF] Crapanzano | Morphology Related Defectiveness in ZnO Luminescence: From Bulk to Nano-Size Nanomaterials[END_REF] that different NC organizations result in different emission yields. In addition, and as stated earlier, the results observed on Fig. 2 critically depend on the position of the Au patterns within the stack of the LED-meaning in particular that no EL enhancement occurs if the ZnO layer covering the Au patterns increases to the point of forming a continuous mesoporous film. As a last evidence that the behaviour of the LEDs is dominated by the defect states in ZnO, we show the current-voltage (I-V) curve of a representative device in a log-log plot on Fig. 3(d) (only the forward characteristic is shown because our junctions fail when biased with negative voltages). The I-V curve cannot be fitted with the usual exponential function typical of a P-N junction, but rather with a succession of power laws with different exponents. This observation is indicative of a space-chargelimited current (SCLC), a regime already observed in several transport studies on ZnO [START_REF] Aydoğan | Electrical characterization of Au/n-ZnO Schottky contacts on n[END_REF][START_REF] Dhananjay | Investigations on magnetron sputtered ZnO thin films and Au/ZnO Schottky diodes[END_REF][START_REF] Caglar | Thermally stimulated current and space charge limited current mechanism in film of the gold/zinc oxide/gold type[END_REF][START_REF] Bubel | Trap states and space charge limited current in dispersion processed zinc oxide thin films[END_REF][START_REF] Tyagi | Trap assisted space charge conduction in p-NiO/n-ZnO heterojunction diode[END_REF]. In some instances, the value of the exponents used to fit the different parts of the curve, as well as the voltage ranges at which each power law occurs can be used to extract quantitative information on the nature and the density of the defect states [START_REF] Nana | Effect of deep-level states on current-voltage characteristics and electroluminescence of blue and UV light-emitting diodes[END_REF]. However, such an analysis can only be performed for continuous layers where quantities such as the permittivity, length, and intrinsic semiconducting parameters can be defined, which is impossible with our samples due to the discontinuous nature of the ZnO film above the Au patterns.

Tuning the colour of the LEDs

So far, we have only considered LED stacks with 150 nm thick ITO anodes. The optical microscope images of Fig. 4(a) show that modifying the thickness of this transparent electrode by a few tens of nm has a strong impact on the colour of the emitted light, which can be tuned from the red to the green (the blue hue of the first image is an incorrect interpolation of the CCD camera used to capture the images). The corresponding EL spectra are plotted on Fig. 4(b).

We ascribe this colour tunability to a filtering effect, as schematized on Fig. 4(c): because ITO has a high index of refraction, thin film interferences can develop within the stack even though the total thickness of the LED is small compared to the emission wavelengths. This hypothesis is confirmed by the reflectivity spectra of the samples plotted on Fig. 4(d): each curve exhibits an interference dip that shifts to the blue as the ITO thickness decreases from 150 nm to 75 nm, modulating the broadband defect-induced emission of the ZnO layer. The exact wavelengths of the reflectance dips do not strictly follow the EL peaks of Fig. 4(b). In particular, for the two thinnest samples, the reflectance dips are more shifted to the blue than the EL. This observation indicates that little light is emitted at these wavelengths even in the absence of thin film interferences. It also explains why almost no light is emitted by the thinnest sample: the latter filters most wavelengths of the visible range, except in the blue where the ZnO-induced emission is negligible.

From micro-patches to nano-antennas

So far, we have worked with non-resonant metallic micron-sized patches. In this last section, we briefly examine the case of resonant plasmonic inclusions. Because Au is not a good plasmonic material for wavelengths below 600 nm, our starting point is the same geometry as before, except that Au is replaced by Ag. Fig. 5(a) displays the EL produced by LEDs with 50 × 50 µm 2 and 10 × 10 µm 2 patches. We observe the same effects as those previously reported for Au, namely, a preferential emission above the metallic features, with a colour and intensity that do not depend on the size of the metallic patches.

We have then repeated the experiments with Ag inclusions of sub-micron dimensions that sustain plasmonic resonances in the visible range. The dimensions of the Ag particles can be appreciated on the SEM image of Fig. 5(b): they have an elongated shape with a length of 100 nm, a width of 40 nm, a thickness of 30 nm and they are arranged in a regular array with a periodicity of 200 nm. The reflectivity measurements plotted on Fig. 5(b) show that the sample sustain plasmon resonances at two different wavelengths in the visible range: one resonance polarized along the short axis at 520 nm, and another one polarized along the long axis at 700 nm. The EL of such a device, visualized on Fig. 5(c) through a linear polarizer successively aligned along the short and long axes of the Ag particles, is markedly different from the emission above the micropatches of Fig. 5(a). The emission is polarized, with a bluish hue for the horizontal polarization along the short axis of the particles and pink-red tones for the polarization perpendicular to it. As was the case for Fig. 4(a), these colours are somewhat misleading because the colour rendition of our camera favors the blue. The EL spectra, displayed on Fig. 5(d), show that the emission is actually green for the horizontal polarization and red for the vertical polarization. This polarization-dependent EL can be attributed to the coupling of the emitted light to the plasmon resonances of the Ag inclusions, which thus play the role of optical nano-antennas. As was the case with the thin-film interference effects of Fig. 4, the EL peaks do not strictly coincide with the maxima of the plasmon resonances evidenced on the reflectivity spectra of Fig. 5(b) because the EL spectra result from a convolution of the resonances and the bandwidth of the ZnO defect-induced emission.

Conclusion

In conclusion, we have created electroluminescent patterns within LEDs that emit visible light via the vacancy and interstitial defects of ZnO NC assemblies. These patterns were obtained by burying thin metallic shapes within the ZnO layer, locally enhancing the luminescence by modifying the organization of the ZnO NCs coated above them. Additional control of the light emission (colour and polarization) has been demonstrated using thin film interferences and by making the metallic features resonant. These results contribute to the emerging toolbox aiming at rendering ZnO-based LEDs competitive for visible and white light applications.

Figure 1 .

 1 Figure 1. (a) SEM cross section view of the LED stack. (b) Schematic of a LED stack.

Figure 2 .

 2 Figure 2. (a) Image of a junction seen through an optical microscope (magnification: 5X). (b) EL at 9 V captured by the same microscope. The dashed white square on both panels represents the limits of the LED, corresponding to the overlap between the horizontal Al cathode and the vertical ITO anode. (c) EL at 8 V from Au patches with various sizes. Although we display a composite image, all these patches are actually embedded within the same junction and the scale bar applies to all images. Upper left: array of 1024 Au squares with a side of 2 µm, period 3 µm (the individual squares are not visible at this magnification). Upper right: 16 squares with a side of 10 µm. Lower left: 4 squares with a side of 20 µm. Lower right: single square with a side of 50 µm. (d) EL spectrum at 8 V of the square Au patch with a 50 µm side observed on panel (c).

Figure 3 .

 3 Figure 3. (a) Surface topography map of the second layer of ZnO NCs deposited onto the sample. This measurement was taken with a Core AFM from Nanosurf in a region of the sample without Au pattern. (b) Same measurement for the ZnO NCs above a Au patch. (c) SEM micrograph of the second ZnO layer coated onto the sample. The boundary between the two shades of grey corresponds to the left edge of a Au patch. (d) Current voltage characteristic of the device investigated on Figs. 2(c) and 2(d).

Figure 4 .

 4 Figure 4. (a) Preferential EL above single Au squares with a side of 50 µm, for samples with 75 nm, 100 nm, 125 nm and 150 nm thick ITO anodes, respectively. Images taken with a 5X microscope objective. (b) EL spectra at 8 V from the same series. (c) Schematic of the thin film interferences creating the different colours (d) Reflectivity of the four samples measured above the Au patches.

Figure 5 .

 5 Figure 5. (a) EL of samples with micron-sized Ag patches. Left: single Ag square with a side of 50 µm. Right: matrix of 16 Ag squares with a side of 10 µm. (b) Reflectance spectra of a sample with 40 × 100 nm 2 Ag nanoantennas for two different polarizations (blue curve: polarization parallel to the short axis, red curve: polarization parallel to the long axis). The total size of the array is 100 × 100 µm 2 . Inset: SEM image of the sample before coating the antennas with the second layer of ZnO NCs. (c) EL produced by the sample (left image: polarization parallel to the short axis, right image: polarization parallel to the long axis). (d) EL spectra for the same array and the same two polarizations.


It was with some surprise that I read Engelen's 'Why Liberals Can Favor Compulsory Attendance'. [START_REF] Engelen | Why Liberals Can Favor Compulsory Attendance[END_REF] According to Engelen, I claim that compulsory voting conflicts with 'free thought, free speech and privacy'. My article did not mention any of these, although I argued that compulsory voting is likely to fall foul of liberal commitments to respect reasonable disagreement over fundamental values when justifying public policy and state coercion. (Lever 2008) I made it clear that most proponents of compulsory voting, including Lacroix, [START_REF] Lacroix | A Liberal Defence of Compulsory Voting[END_REF]) believe that some legal exemptions would be justified on conscientious grounds and would allow -as current Australian law apparently would not -that the legal compulsion would be to 'turnout', rather than to cast a legally valid ballot. (Hill 2007, 9, 12) I also argued that proponents of compulsory voting would have to consider the justification for sending people to prison for not paying the fines for not-voting, (as has happened in Australia) but I never implied that liberal accounts of compulsion could be expected to justify imprisonment simply for failure to vote. Consequently, I find it hard to recognise my arguments against Lacroix in Engelen's defence of compulsory voting/turnout. (CV/T) But rather than clarifying my critique of Lacroix, it may be more helpful to clarify my reasons for thinking that compulsory voting is generally at odds with democratic government. My views are the result of prior research on the secret ballot, which first made me realise how complicated the ethics of voting are -far more complex, in fact, than I had assumed. (Lever 2007a) My research on judicial review, on feminism, and on privacy and democracy suggests that we often exaggerate the important of national elections to democratic theory and practice. [START_REF] Lever | Feminism, Democracy and the Right to Privacy', Minerva 9[END_REF][START_REF] Lever | Feminism, Democracy and the Right to Privacy', Minerva 9[END_REF](Lever , 2007b(Lever , 2009a, b, c), b, c).

Consequently, I believe that efforts to justify compulsory voting -whether in liberal egalitarian terms, as with Lacroix, or more social democratic ones, as in [START_REF] Lijphart | Unequal Participation: Democracy's Unresolved Dilemma[END_REF] or [START_REF] Keaney | A Citizens' Duty: Voter Inequality and the Case for Compulsory Turnout[END_REF] -overstate the importance of electoral participation to democratic conceptions of politics, and understate the complexity of democratic morality.

Some background clarifications may be helpful. Proponents of compulsory voting generally believe that people are morally obliged to vote unless they have conscientious objections to voting. No one thinks that there is a moral duty simply to turn out and tick your name off a list at election time unless people have a duty to vote.

So, such justification as there is for compulsory turnout is parasitic on the justification of compulsory voting. It is therefore wrong to suppose that it is easier to justify compulsory turnout than compulsory voting. How compulsory voting is supposed to fix the problems of low and unequal turnout at elections is reasonably clear. [START_REF] Lijphart | Unequal Participation: Democracy's Unresolved Dilemma[END_REF]Lever 2009a) By contrast, it is unclear how compulsory turnout is going to solve these problems. Consequently, it is harder, not easier, to justify compulsory turnout than compulsory voting once we have allowed that people with conscientious objections to voting should be exempt from moral and legal duties to vote.

Secondly, I assume that people sometimes have moral duties to vote. (Lever 2008, 2009a and[START_REF] Ballinger | Compulsory Turnout; A Solution to Disengagement?[END_REF]. However, proponents of compulsion require more than that: they need to show that we are obliged to vote at every election (although characteristically they never explain which elections trigger the case for compulsion and why). So, while I am happy to say that political participation can be intrinsically, as well as instrumentally valuable, and that sometimes voting is morally required, we need far stronger assumptions about the duty to vote before treating it as compulsory -not least because such a duty implies informed not random voting.

Arguments for compulsory voting typically come in two parts. The first is a claim about political morality, the second is a claim about morality more generally. The first holds that citizens have a moral duty to vote-whether because this is necessary to democratic legitimacy, or because the duty to vote is implicit in the justification for voting rights themselves. The second, more general, claim is that fairness or reciprocity supports compulsion, in order to stop non-voters from free-riding on, or exploiting voters. Let's take these in turn.

Modern views of democracy assume that competition for political power and opposition to the government of the day can both be justified. Failure to vote, or to vote for the winning candidate, may threaten us with serious losses. So the costs of democratic politics can be real, predictable and painful. But to suppose that we have a duty to prevent those costs is problematic. This is partly because these are risks to our interests that other people are entitled to impose on us via the exercise of their rights; but they are, as well, risks that we are entitled to impose on ourselves, by altruistic voting. This is likely to be true for most voters. Hence, democratic citizens will often have no duty to vote on either self-interested or altruistic grounds.

If compulsory voting is justified, then, we must suppose that one of the main political parties is so inconsistent with democratic values, or with basic human rights, that they could not constitute a legitimate government, however many people voted for them. I think that this is true of racist parties like the British National Party, (the BNP) and explains why most people have a duty to defeat and marginalise their candidates. 1 But in democracies, this should be the exception, not the rule. In short, because democratic legitimacy means that parties we think seriously mistaken are entitled to govern, the differences between the main candidates for political office will generally not justify moral duties to vote, let alone legal ones.

1 I say 'most people' have such a duty, because I am not convinced that the BNP, despite its racist platform, can never be the legitimate receptacle of protest votes aimed at established parties. If some people are morally entitled to vote BNP, however, this means that those of us, (the vast majority of people), who have no such justification may have quite stringent duties to vote against the BNP-duties which include voting strategically rather than sincerely in some cases.

The ethics of voting has received little attention from philosophers and political

scientists. Yet it is plain that they are no more self-evident than other ethical matters, on which attention is lavished. Reasonable people can have the same qualms about voting as they can about marrying, having children, joining a political party or a union. Such qualms can be moral as well as prudential: reflecting doubts about the extent and reliability of their knowledge or judgement; doubts about the consequences of their actions for other people; and doubts about how to reconcile their different duties. We have little control over the circumstances of our vote, and the ways in which it will be interpreted and used by others. So, the ethics of voting is by no means as simple as proponents of compulsion suppose.

Democracy means that we are entitled to participate in politics freely and as equals. However, this does not mean that we must exercise our political rights, however important it is that we should have them; nor does it require us to consider electoral politics more important than other endeavours. In established democracies, our political rights help to protect our interests in political participation whether or not we actually exercise them. Likewise, we need not refuse, accept, or offer to marry someone in order for our right to marry to be valuable and valued.

Rights can protect our interests, then, even if we do not use them. For example, they make certain practical possibilities unthinkable. Most of the time we never consider killing others in order to get our way. Nor do they consider killing us. So, while it is true that democracy requires people to be willing and able to vote, the empirics of legitimacy, as well as its theory, make turnout a poor proxy for legitimacy or for faith in democratic government. (Lever 2009 a, b) These, in brief, are my reasons for doubting that democratic norms support compulsory voting. But what about norms of fairness or reciprocity? We have duties of fairness and reciprocity whether or not we are citizens. If these imply that people who are entitled to vote should vote, we would have a remarkably robust justification for compulsory voting: one largely independent of our assumptions about political morality.

But is non-voting the equivalent of free-riding, or of unfairly seeking to benefit from the efforts and sacrifices of others? Political realism suggests that it is not.

Whatever is wrong with not-voting, it cannot be that non-voters are selfishly exploiting the idealism, energy and public-spirited efforts of the BNP and their ilk. This is not because the latter are evidently more self-interested than other voters. Whether they are or not is an empirical question. The problem, rather, is that we are entitled to refuse, and actively to oppose, the benefits that the BNP seeks to promote.

Non-voters, then, are not exploiting the BNP. Nor are they exploiting selfinterested voters, however respectable and democratic the parties for which they voted.

It is not obvious, either, that they are exploiting altruistic voters simply because they are not helping them. So, reflection on how and why people vote casts doubt on the idea that non-voters are selfishly preying on the public-spirited efforts of voters. (Lever 2009 a,b) When abstention is morally wrong, therefore, this seems to be because of its consequences for those who are incapable of voting -whether because they are too old, too young, because they are foreign, not yet born and so on-rather than because it is unfair to compatriots who voted.

We can put the point more sharply. The idea that non-voters are free-riders, assumes that voting is a collective good -whether because high levels of turnout are necessary to democratic legitimacy or for some other reason. But this begs the question, whether high levels of turnout are a collective good. Turnout has partisan effects. So even if some level of turnout is a public good, voting is not a pure public good as long as it has some bearing on who wins or loses an election. To suppose that people are morally wrong to abstain, therefore, requires us to assume that the cooperative aspect of voting is more important than the competitive. This is not a conceptual truth about elections, and may be false empirically. (Lever 2009 a,b) We cannot evade the complexity of democratic politics and morality, then, by insisting that democratic elections are a public good. Indeed they are. But this no more requires us to vote than it requires us to join a political party or to stand for election ourselves. A sufficient range and quality of parties and leaders is a prerequisite for democratic legitimacy and, off-hand, seems at least as important as ensuring a sufficient quantity and quality of voter participation. 2 Moreover, morality sometimes requires people to assume positions of leadership and responsibility that they would otherwise choose to forego. Nonetheless, it is incredibly difficult to get from the idea that we may sometimes have such duties to the conclusion that we actually do have such duties. The evidence suggests that CV does nothing for the quality of voting. Because it increases random voting, it seems to have no predictable effect on electoral outcomes, either. [START_REF] Ballinger | Compulsory Turnout; A Solution to Disengagement?[END_REF]Selb and Lachat, 2007) 3 My hunch is that people's sense of duty in such cases, even when justified, has more to do with their moral response to particular circumstances than it does from deducing the consequences of very general claims about democratic rights and duties.

  What we are morally required to do in politics depends importantly on what other people do, what they are likely to do, and what they are entitled to do. 3 Hence the complexities of democratic politics and morality. Political scientists, historians, novelists, playwrights and politicians have done an enormous amount to clarify that complexity. Political philosophers have much to learn from them. . (1,894 words) Bibliography 2


Research of new carbides:

More stable than TaC:

To limit the carbides ↘ and fragmentation [2] To limit the ↘ of the thermo-mechanical properties of superalloys [START_REF] Donachie | Superalloys -A technical guide[END_REF][START_REF] Berthod | proc. of "Matériaux 2006[END_REF] Study of hafnium carbides (HfC):

Crystallize as pro-eutectic compact HfC [START_REF] Berthod | [END_REF] and script-like carbides too [START_REF] Berthod | [END_REF] Better stability than TaC at very high temperature [START_REF] Berthod | [END_REF]8] Hf known to be good for resistance to high T oxidation

  Surface states of refractory alloys rich in chromium and strengthened by different types of MC carbides after oxidation at high temperature Elodie Conrath, Patrice Berthod Institut Jean Lamour, Faculty of Sciences and Technologies, University of Lorraine, BP 70239, Bd des Aiguillettes, 54506 Vandoeuvre-lès-Nancy, France elodie.conrath@univ-lorraine.fr How reinforcing equiaxed cast Co-based superalloys: With carbides: Generally eutectics and interdendritics Thermally very stable (applications at very high temperature (T)) More stable than chromium carbides (Cr is necessarily present in such superalloys) The most stable : tantalum carbides (TaC) Often used in Co-based superalloys [1]



  [9, 10] But, in so high quantities: risks of becoming detrimental for the resistance against the high T oxidation → point to verify In a parallel work [11]: 3 Co-based quaternary alloys with Hf (Co-25Cr-0.25C-3.72Hf ; Co-25Cr-0.5C-3.72Hf and Co-25Cr-0.5C-7.44Hf) and 2 Co-based ternary alloys (Co-25Cr-0.25C and Co-25Cr-0.5C): Cast by High Frequency induction melting Tested in oxidation in thermo-balance (50h, 1200°C): oTo characterize the oxidation kinetic The purpose of this work: Post-mortem characterization after high T oxidation Better understanding of the differences of kinetic between the HfC-containing alloys and the ternary ones: Comparison with similar Ni-based alloys All the Co-based alloys: Affected by catastrophic oxidation: Confirmed by the metallographic characterizations Contrarily to the Ni-based corresponding alloys (chromia-forming behavior conserved) Catastrophic oxidation: Appears early for the quaternary alloys: Fast parabolic kinetics Very high final mass gain Problems with the {m.(dm/dt) = Kp -Kv.m} method: oTo extract correct Kp and Kv values oBecause not only Cr 2 O 3 in the oxide scale Behavior in high T oxidation:  Not good at 1200°C: no great resistance against oxidation at high T  Worse for the quaternary alloys than for the ternary ones  Several solutions:  ↗ the Cr content: Up to 30 wt.%Cr  In order to have more than 15 wt.% on extreme surface  Adding more Hf:  To form not only HfC carbides and to have free Hf atoms in the matrix o Hf maybe able to diffuse to the oxidation front: • Improve the oxidation behavior • Better adherence of the oxide scales Faculté des Sciences et Technologies


Laurent Porot

Emmanuel Chailleux

Panos Apostolidis

Jiqing Zhu

Alexandros Margaritis

Lucia Tsantilis

Complex bituminous binders, are current test methods suitable for?

Keywords: Bitumen, Polymer modified Bitumen, asphalt additive, BBR, Rheology, Chemistry, Test protocol

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

Introduction

The worldwide demand for long-lasting pavement is leading the asphalt industry to incorporate various chemical substances, such as polymers or additives, in order to enhance the sustainability of pavement materials. Thus, performance-based binders need, together with the implementation of new modification technologies in bitumen, accurate standardised characterisation protocols and in-depth understanding of phase and interphase phenomena of these binders. Within this framework, RILEM initiated the Technical Committee 272-PIM 'Phase and Interphase behaviour of innovative bituminous Materials' on assessing the performance of complex binders. It aims to provide recommendations for the experimental tools and protocols used by the asphalt research and engineering community on bituminous binders. For this purpose, the Task Group 1 (TG1) of RILEM 272-PIM is specifically focusing on binders, while TG2 is looking at asphalt mix and TG3 on pavement structure. Herein, some preliminary results of TG1 activities are presented.

The current characterisation protocols have been initially developed for conventional binders and applied for modified bitumen. Penetration value and softening point temperature, amongst others, are empirical properties used in specifications [START_REF] Bitval | Analysis of Available Data for Validation of Bitumen Tests[END_REF]; while, since the initiation of the Strategic Highway Research Program (SHRP) Superpave program, more fundamental properties using Dynamic Shear Rheometer (DSR) were introduced [START_REF] Anderson | Binder characterization and evaluation Volume 3: Physical characterization[END_REF]. There was already some fundamental work, within the RILEM, on characterising the physico-chemical properties of bituminous binders [3] [4]. Furthermore, the activities of TG1 are extending to complex binders.

In this research, focus was given on elucidating the low temperature performance of fresh and aged complex binders formulated with polymers and liquid additives by using amongst others, Fraass breaking point, Bending Beam Rheometer (BBR), 4-mm plate DSR, Differential Scanning Calorimetry (DSC). A complementary testing program focuses on intermediate and high temperature domains as well. A total of 17 laboratories expressed interest in this experiment, 13 from Europe and 4 from the US. The experiment started earlier in 2019 and about 50% of the results have been delivered by the end of 2019. Examples of preliminary analyses are presented in this paper.

Experimental plan

The way to consider complex binders is wide and includes various materials, liquid or viscous additives either bio-based or hydrocarbon-based, polymers, solid particles. The amount used can vary between dopes from 0.1 to 1.5 %, or additives from 2 to 7-10 %, or extender from 20 to 40 %, or replacement above 50 %, all per weight of bitumen. In order to restrain the scope, only two groups of complex binders were considered, polymer modified binders and additive blends, and compared with neat bitumen. Group 1 is for assessing Polymer modified Bitumen with:  Bit1, a standard 35/50 pen grade bitumen used as a reference  PmB1, a standard commercial Polymer modified Bitumen  PmB2, a highly polymer modification with 7.5 % of high vinyl SBS in Bit2 Group 2 is to assess liquid additives in bitumen with:  Bit2, a standard 70/100 pen grade bitumen used as a reference  Blend1, 4% of commercial bio-based recycling additive in Bit1  Blend2, 8% of Refined Engine Oil Bottom (REOB) in Bit1  Blend3, 4% of paraffinic oil typically not used as paving additive in Bit1 For Group 1, the reference bitumen and PmBs were selected having the same consistency at intermediate temperature; PmB1 was industry produced and composition is proprietary information; PmB2 was lab produced. For Group 2, the dosage per blend was determined with the aim at resulting in properties as close as possible to the properties of the reference bitumen, Bit2; all blends being lab produced.

As the goal of the TG was not to run a round robin on testing, the experimental program was agreed and defined as a toolbox, where each laboratory could select the most appropriate way to assess the binders and depending on the available equipment of each laboratory. Table 1 shows the experimental matrix with, for each binder and test, the number of laboratories, and, in brackets, the numbers of results provided by end of 2019.

Results

As shown in Table 1, the experiment is still ongoing, with 50 % of data available, therefore, only partial analysis is presented here. As a first attempt, the different binders, from Group 1 or Group 2, were analysed towards current specifications. With pen grade system, depending on the binder, the analysed data set was from one to maximum three laboratories. The Group 1 binders, Bit1, PmB1 and PmB2 were displaying similar penetration value at 25 °C, while the softening point temperatures were much more discriminant. For the Group 2, Bit2, Blend 1 to 3 were all in the 70/100 pen box and, considering the error bars, there was no significant difference among them. For all binders, the variability between labs was relatively low except for the PmBs with high value of softening point temperature showing variation between 2 and 3 °C. However, the number of data points is still limited. Depending on the binder, the PG grading data set analysed was from one (Bit1, PmB1) to maximum four laboratories (Bit2). With Group 1, as compared to the neat bitumen, the temperature span for PmB was extended, especially at high temperatures. The PmB2, using Bit2 as base bitumen, maintained the low and intermediate temperatures and increased significantly the high temperature. For Group 2, all blends used the Bit1 as base bitumen and displayed similar shift to the left either for low, intermediate and high temperatures. Overall, the properties were not significantly different from the reference bitumen Bit2. The variability between labs, as shown with error bars, was relatively low except for PmB2. However, more data is needed here. Between the pen and PG grade system, the binders from the different groups disclosed the same grading. However, considering penetration value at 25 °C and PG intermediate critical temperature, addressing similar temperature domain, there were interesting differences. The pen values for Group 1 binders were similar and lower than Group 2, while for the PG intermediate T, PmB2 value was lower by almost 5 °C than PmB1 and Bit1 and in the same magnitude of range as the Group 2 binders. The PG grading system helps to better distinguish between complex bituminous binders.

Further analysis is ongoing including ductility, DSR data analysis with broader parameters and low temperature properties. Herein, a preliminary analysis of low temperature testing results is provided as an example. Fig 3 displays, in a bar chart, the Fraass breaking point temperature with the BBR temperatures when the creep stiffness S ≤ 300 MPa and the relaxation m-value ≥ 0.300, including the delta between them, known as Tc. Depending on the binder, the sets of data were from between two and four laboratories. As expected, the trend was similar at least, the lower the Fraass temperature, the lower the BBR critical temperatures were, although for the Blend1, the Fraass seems to underestimate the low temperature performance as indicated by BBR. the Fraass breaking point and the BBR continuous (as the max of TS and Tm-value) temperatures; the diagonal line is for equi-temperature. For the BBR, considering variability within the labs, there is a good balance between both criteria except for PmB1. At comparing the Fraass and BBR temperatures, for the Group 2, the Fraass is significantly higher than the BBR and all ranking in the same magnitude of range. The BBR continuous temperature seems to better discriminate among them, within the variability of the set of data. With more data including 4 mm plate DSR and DSC, further analysis will be presented in a future study.

Conclusion

The RILEM 272-PIM has set up a specific Task Group, TG1, looking at phase and interphase of complex bitumen. Two groups of binders, Polymer modified Bitumen and liquid additive blends, are included in an exhaustive experimental program encompassing physical and chemical properties. Seventeen laboratories are involved, providing a unique data set and characterisation approach on complex binders. The activities are still ongoing, and some preliminary results are presented in this paper, as example.

In terms of standard specifications, PmB binders clearly display very different properties, and the additive group shows all binders within a similar grading, in either pen grade or PG grade systems. Thanks to the PG system and by recording properties at low, intermediate and high temperature, some binders were already distinguished more efficiently at intermediate temperatures as compared with pen grade system.

Low temperature properties were further analysed based on empirical testing with Fraass breaking point and more fundamental rheology characterisation with BBR testing. While Fraass can distinguish between the two groups, within each group such as between additive blends, it does not enable to differentiate binders. By combining both creep stiffness and m-value critical temperatures, BBR provides a more efficient diagnosis of different complex bituminous binders.

  Fig 1 displays them in the pen grade system, as used in Europe (EN 12591, EN 14023), with penetration value at 25 °C and softening point temperature. Fig 2 displays them in the Performance Grade (PG) system, as used in the US (AASHTO M320) with the exact low, medium and high temperature criteria. For each figure, the points are for the mean value and the error bars representing the maximum and minimum values.

Fig 1 .

 1 Fig 1. The seven binders in the pen grading system

Fig 2 .

 2 Fig 2. The seven binders in the PG grading system

Fig 3 .

 3 Fig 3. Low temperature Fraass and BBR for the seven binders A comparison by pair is made in Fig 4 between (a) the two BBR temperatures and (b)the Fraass breaking point and the BBR continuous (as the max of TS and Tm-value) temperatures; the diagonal line is for equi-temperature. For the BBR, considering variability within the labs, there is a good balance between both criteria except for PmB1. At comparing the Fraass and BBR temperatures, for the Group 2, the Fraass is significantly higher than the BBR and all ranking in the same magnitude of range. The BBR continuous temperature seems to better discriminate among them, within the variability of the set of data. With more data including 4 mm plate DSR and DSC, further analysis will be presented in a future study.

Fig 4 .

 4 Fig 4. Comparison of (a) BBR S and m-value critical temperatures, (b) Fraass and critical BBR

Table 1 .

 1 Rilem PIM TG1 -Experimental matrix

Accepted author manuscript

Acknowledgements

This work has been conducted under the framework of the RILEM Technical Committee TC 272-PIM on "Phase and Interphase behaviour of innovative bituminous Materials" with the great contribution of Kraton (NL), Western Research Institute (US), University of New Hampshire (US), IFSTTAR (FR), TU Delft (NL), Institute of Transportation TU Wien (AU), FHWA (US), CEREMA mediterranee (FR), Colas CST (FR), Strukton (NL), Politecnico di Torino (IT), Belgium Road Research Centre (BE), Swedish National Road and Transport Research Institute (SE), Nynas and University of Antwerp (BE), Nebraska DoT (US), Aalto University (FI), Institut für Straßenwesen, Technische Universität Braunschweig (DE).


published or not. The documents may come


Laurane Charrier

Yajing Yan

Elise Colin Koeniguer

Jeremie Mouginot

Romain Millan

Emmanuel Trouvé

FUSION OF MULTI-TEMPORAL AND MULTI-SENSOR ICE VELOCITY OBSERVATIONS

Keywords: velocity time series, multi-sensors, multi-temporal, fusion, glacier displacements

Ice velocity observations available on-line or on-demand at intra-annual resolutions still contain gaps, noise, and artifacts, especially in mountain areas. There is a need to fuse the available multi-temporal and multi-sensor velocity observations to be able to study intra-annual glacier dynamics. The proposed approach includes an inversion based on the temporal closure of displacement observation networks and a temporal interpolation. It reconstructs velocity time series between consecutive dates at a regular temporal sampling (called Regular Leap Frog (RLF) time series) inferred from all the velocity observations without a prori knowledge on the displacement behavior. The RLF time series can be reconstructed for different temporal sampling. Root Mean Square Error (RMSE) over stable areas and Velocity Vector Coherence (VVC) over fast moving areas are proposed to select a temporal sampling allowing a compromise between uncertainty and temporal resolution. This study focuses on the Fox glacier, in the Southern Alps of New Zealand. It shows that RMSE over stable areas is decreased from 78% for a temporal sampling of 5 days to 40% for a temporal sampling of 60 days. Thus, using this approach, we obtain a velocity time series with complete temporal coverage and reduced uncertainty for a regular and optimal temporal sampling. The results highlight the large seasonal variability of the flow of Fox Glacier that fluctuates by more than 30% between spring and autumn.

INTRODUCTION

The increasing amount of remote sensing images enables the estimation of glacier velocities with a temporal resolution up to 2 days and a sampling resolution up to 50 m all over the world [START_REF] Millan | Mapping Surface Flow Velocity of Glaciers at Regional Scale Using a Multiple Sensors Approach[END_REF]. While many ice velocity observations are available on-line [START_REF] Gardner | Increased West Antarctic and unchanged East Antarctic ice discharge over the last 7 years[END_REF][START_REF] Fahnestock | Rapid large-area mapping of ice flow using Landsat 8[END_REF][START_REF] Millan | Mapping Surface Flow Velocity of Glaciers at Regional Scale Using a Multiple Sensors Approach[END_REF][START_REF] Friedl | Recent dynamic changes on Fleming glacier after the disintegration of Wordie ice shelf, Antarctic peninsula[END_REF], this large amount of data is still difficult to analyze, since velocity observations span different temporal baselines, have variable sampling resolution and are derived from different sensors. Velocities obtained from a small temporal baseline are close to the derivative of the displacement but are more likely to be contaminated by noise uncorrelated in time. Velocities obtained from a long temporal baseline approximate the mean velocity between two dates but can be affected by large errors due to temporal decorrelation. Despite of filtering steps, ice velocity observations produced by automated processing chains contain gaps, noise, and artifacts, especially in mountain areas where image-matching algorithms are more likely to fail because of surface locking, shadow casting, feature-less regions or strong surface changes (Dehecq et al., 2019, Altena and[START_REF] Altena | Ensemble matching of repeat satellite images applied to measure fast-changing ice flow, verified with mountain climber trajectories on Khumbu icefall, Mount Everest[END_REF]. In order to take advantage of the available dense velocity observations for the study of intraannual glacier dynamics, there is a need to develop advanced post-processing methods to fuse the available multi-temporal and multi-sensor velocity observations.

To carry out a regression on displacement observations from different temporal baselines, [START_REF] Greene | Detecting seasonal ice dynamics in satellite images[END_REF] propose to integrate over the time a parametric regression function. However, it requires a priori knowledge of the displacement behavior. Another approach to fuse velocities with different tem-poral baselines and to reduce the uncertainty is the temporal closure of the displacement observation network. This approach was originally developed for Interferometric Synthetic-Aperture Radar (InSAR) time series and called Small BAseline Subset (SBAS) approach [START_REF] Berardino | A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms[END_REF][START_REF] Lanari | An overview of the small baseline subset algorithm: A dinsar technique for surface deformation analysis[END_REF][START_REF] López-Quiroz | Time series analysis of Mexico City subsidence constrained by radar interferometry[END_REF]. The SBAS approach uses interferograms produced by image pairs spanning small temporal and geometrical baselines to minimize temporal and geometrical decorrelation. Later, this approach has been applied to offset-tracking displacement measurement of SAR images [START_REF] Casu | Deformation time-series generation in areas characterized by large displacement dynamics: The SAR amplitude pixel-offset SBAS technique[END_REF][START_REF] Euillades | Detection of glaciers displacement time-series using SAR[END_REF][START_REF] Guo | The Surge of the Hispar Glacier, Central Karakoram: SAR 3-D Flow Velocity Time Series and Thickness Changes[END_REF], Charrier et al., 2021a, Charrier et al., 2021b) and optical images [START_REF] Bontemps | Inversion of deformation fields time-series from optical images, and application to the long term kinematics of slow-moving landslides in Peru[END_REF][START_REF] Lacroix | Self-Entrainment Motion of a Slow-Moving Landslide Inferred From Landsat-8 Time Series[END_REF][START_REF] Ding | Quantifying the spatio-temporal patterns of dune migration near Minqin Oasis in northwestern China with time series of Landsat-8 and Sentinel-2 observations[END_REF].

However, most of the authors who use the temporal closure approach consider only one sensor [START_REF] Altena | Extracting recent short-term glacier velocity evolution over southern Alaska and the Yukon from a large collection of Landsat data[END_REF][START_REF] López-Quiroz | Time series analysis of Mexico City subsidence constrained by radar interferometry[END_REF][START_REF] Casu | Deformation time-series generation in areas characterized by large displacement dynamics: The SAR amplitude pixel-offset SBAS technique[END_REF][START_REF] Berardino | A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms[END_REF][START_REF] López-Quiroz | Time series analysis of Mexico City subsidence constrained by radar interferometry[END_REF][START_REF] Euillades | Detection of glaciers displacement time-series using SAR[END_REF], Charrier et al., 2021a, Charrier et al., 2021b) or invert a time series from each sensor apart [START_REF] Kim | Ground subsidence in Tucson, Arizona, monitored by time-series analysis using multi-sensor InSAR datasets from 1993 to 2011[END_REF][START_REF] Ding | Quantifying the spatio-temporal patterns of dune migration near Minqin Oasis in northwestern China with time series of Landsat-8 and Sentinel-2 observations[END_REF]. Only a few studies choose to include datasets from different sensors in one inversion. [START_REF] Pepe | The use of C-/X-band time-gapped SAR data and geotechnical models for the study of Shanghai's ocean-reclaimed lands through the SBAS-DInSAR technique[END_REF] proposes to invert displacement time series from ASAR/ENVISAT and CSK velocity observations. Since the two datasets are not overlapping in time, they add a constrain based on a displacement model to solve the system. Besides, [START_REF] Bontemps | Inversion of deformation fields time-series from optical images, and application to the long term kinematics of slow-moving landslides in Peru[END_REF] include displacements from different Spot and Pléiade images to invert displacements between consecutive observed dates.

Both previous studies open perspectives to take advantage of multi-sensors datasets. However, methodological or pratical is-sues still exist, for example, the use of a model-based constrain in [START_REF] Pepe | The use of C-/X-band time-gapped SAR data and geotechnical models for the study of Shanghai's ocean-reclaimed lands through the SBAS-DInSAR technique[END_REF] requires a priori knowledge of the displacement behavior. In addition, the inversion of displacements between consecutive observed dates as done in [START_REF] Bontemps | Inversion of deformation fields time-series from optical images, and application to the long term kinematics of slow-moving landslides in Peru[END_REF] is problematic for fast moving target such as glaciers since it produces irregular time series, i.e., the displacements are inverted between dates which are not equally distributed over the period. Indeed, [START_REF] Bontemps | Inversion of deformation fields time-series from optical images, and application to the long term kinematics of slow-moving landslides in Peru[END_REF] are interested in cumulative displacement (CD) time series, i.e. displacements between each date and a reference date, to study slow moving landslide whereas velocities between consecutive dates, named Leap Frog (LF) velocity time series in [START_REF] Hadhri | Timelapse optical flow regularization for geophysical complex phenomena monitoring[END_REF], Charrier et al., 2021b), are more appropriate to analyze intra-annual variations of fast moving targets such as glaciers [START_REF] Greene | Detecting seasonal ice dynamics in satellite images[END_REF][START_REF] Derkacheva | Data Reduction Using Statistical and Regression Approaches for Ice Velocity Derived by Landsat-8, Sentinel-1 and Sentinel-2[END_REF]. The analysis of an irregular LF time series can raise issues because: 1) The resulted velocities does not have the same temporal sampling. Since velocities measured on different temporal samplings are representative of the average displacement on different time intervals, LF displacements are not truly comparable if the temporal sampling of the LF time series is irregular. 2) displacements with very short temporal sampling are inverted if the images from the different sensors are acquired a few days apart (for example up to 1 day apart between Venµs and Sentinel-2 satellites). However, very short temporal sampling velocities are likely to be more noisy [START_REF] Casu | Deformation time-series generation in areas characterized by large displacement dynamics: The SAR amplitude pixel-offset SBAS technique[END_REF][START_REF] Millan | Mapping Surface Flow Velocity of Glaciers at Regional Scale Using a Multiple Sensors Approach[END_REF], Charrier et al., 2021b). 3) the dates between which the displacements are inverted can be different from one pixel to another because of different data quality since outliers are rejected in most of the available datasets [START_REF] Millan | Mapping Surface Flow Velocity of Glaciers at Regional Scale Using a Multiple Sensors Approach[END_REF][START_REF] Gardner | Increased West Antarctic and unchanged East Antarctic ice discharge over the last 7 years[END_REF][START_REF] Fahnestock | Rapid large-area mapping of ice flow using Landsat 8[END_REF].

Therefore, this paper aims at fusing velocity observations from different temporal baselines and sensors to obtain a LF time series with a regular and optimal temporal sampling to study intra-annual variations of ice velocity. For that, an Irregular LF (ILF) time series is first inverted. Then, a temporal interpolation is performed on a CD time series built by summing the ILF displacements. From the discrete derivative of this interpolated CD time series, a Regular LF (RLF) time series with an optimal temporal sampling is obtained. This temporal sampling is selected based on a compromise between uncertainty and temporal resolution. This approach is applied to Sentinel-2 and Venµs velocity observations covering the Fox glacier, in the Southern Alps of New Zealand.

DATA AND STUDY AREA

The study area is the Fox glacier which is situated in the Southern Alps of New Zealand. It is a fast-flowing, temporal maritime glacier [START_REF] Purdie | Seasonal variation in ablation and surface velocity on a temperate maritime glacier: Fox Glacier, New Zealand[END_REF][START_REF] Kääb | Glacier remote sensing using Sentinel-2. part I: Radiometric and geometric performance, and application to ice velocity[END_REF].

The considered dataset is from [START_REF] Millan | Mapping Surface Flow Velocity of Glaciers at Regional Scale Using a Multiple Sensors Approach[END_REF]. It contains velocity observations based on images acquired by two different optical sensors: Sentinel-2 and Venµs. The repeat cycles of the two satellites are 5 days and 2 days respectively and the spatial sampling of the images are 10 m and 5 m respectively. The radiometric resolution of the sensors are of 12 and 10 bit. Displacement offsets are computed using a modified version of the cross-correlation algorithm Ampcor from NASA [START_REF] Michel | Flow of Glaciar Moreno, Argentina, from repeat-pass Shuttle Imaging Radar images: comparison of the phase correlation method with radar interferometry[END_REF]. Post-processing have already been carried out to remove outliers: pixel offsets that deviate more than three pixels from a 9×9 pixels spatial median have been removed [START_REF] Millan | Mapping Surface Flow Velocity of Glaciers at Regional Scale Using a Multiple Sensors Approach[END_REF][START_REF] Mouginot | Mapping of ice motion in Antarctica using synthetic-aperture radar data[END_REF]. The temporal baselines of the velocity observations are ranging from 5 to 100 days and from

Confidence values

In order to quantify the quality of velocity observations, a confidence value is computed for each velocity vector (2 compon-ents in x and y directions) as a combination of the following criteria:

1) the cosinus of the angle between each vector and the spatiotemporal median vector [START_REF] Burgess | Surge dynamics on Bering Glacier, Alaska, in 2008-2011[END_REF][START_REF] Nguyen | A Pattern-Based Method For Handling Confidence Measures While Mining Satellite Displacement Field Time Series: Application to Greenland Ice Sheet and Alpine Glaciers[END_REF] called Median Angle (MA) here and defined as:

cos(⃗ ui,j,t, ⃗ v w i,j ) = ⃗ ui,j,t • ⃗ v w i,j ∥⃗ ui,j,t∥∥∥⃗ v w i,j ∥ (1)
where ui,j,t is the displacement vector at the pixel (i, j) and time t and v w i,j is the median vector over the time on a spatial window w, here set to 3 × 3 pixels. If the two vectors are colinear, as expected, this criterion will have a value of 1. The negative values are set to 0 to penalize vectors which have a direction from 90 • to 180 • away from the median direction.

2) the modified z-score which is a standardized and robust score that measures outlier strength [START_REF] Maronna | Robust statistics: theory and methods (with R)[END_REF]. The modified z-score is computed for the x and y component of the velocity vector as:

MZscore = xi,j,t -xw i,j 1.483 MAD (2)
where xi,j,t stands for the x or y component of the velocity at the pixel (i, j) and time t, xw i,j is the median of the x or y component of the velocity over the time on a spatial window w, here set to 3×3 pixels. MAD is the Median Absolute Deviation defined as: median|xi,j,t -xw i,j |.

The final confidence value of two velocity components is the same for a given pixel and time stamp. It corresponds to the multiplication of the three criterion scaled between 0 and 1: the scaled modified z-score for x components of the velocity, the scaled modified z-score for y components of the velocity and the MA. To fuse multi-temporal and multi-sensor ice velocity observations, a temporal inversion based on the temporal closure of the displacement observation network is used. The key principle relies on making use of the redundancy of the displacement observation network to build a LF displacement time series that respects the temporal closure constraint. The temporal closure is formulated on a pixel-by-pixel basis on the set of n displacement observations dt i ,t j with a temporal baseline tj -ti contained in the vector Y . The temporal closure formulation is Y = AX where X represents the vector of p output displacements dtn,tm with a temporal sampling tm -tn, and A is a design matrix of dimension n × p linking X with Y .

METHOD

Temporal inversion

The proposed method is an extension of (Charrier et al., 2021a) and (Charrier et al., 2021b). In (Charrier et al., 2021b), the mono-sensor dataset had enough redundancy to obtain directly a regular time series at user-defined temporal sampling using an improved temporal closure formulation. However, in the case of a multi-sensor data set with numerous gaps, the problem is more complex.

As shown in Figure 3 a), if X is a time series with the same temporal sampling as the satellite 2, the displacements from the satellite 1 could not be included in the system AX = Y because it is not possible to write dt 2 ,t 4 , dt 4 ,t 6 , dt 6 ,t 1 0 and dt 2 ,t 1 0 as a linear combination of dt 0 ,t 5 and dt 5 ,t 10 . Hence, the design matrix A contains four rows of zero, the system is ill posed and some information is lost.

Therefore, a solution can be to invert an irregular time series of displacements between each date of the displacement observations Y , as illustrated in Figure 3 b) to include all the observations in the system.

The system AX = Y is then solved using an Iterative Reweighted Least Square inversion with a regularization term on the discrete derivative of the leap frog velocities, as described in (Charrier et al., 2021b, Charrier et al., 2021a). The a priori weight corresponds to the confidence values presented in section 2.1. The result of the inversion gives an Irregular LF (ILF) time series.

Interpolation

In the ILF time series, each velocity vtm,tn corresponds to a given temporal sampling tm -tn. The velocities are not truly comparable if the temporal sampling is different because velocities measured on a small time interval are close to the derivative of the displacement whereas velocities measured on long time interval approximate the mean velocity between two dates. Therefore, an interpolation of this time series would not be rigorous. Hence, the interpolation should be done on Cumulative Displacement time series. The latest is built by summation of the ILF displacements obtained after inversion as:

dt 0 ,t k = k-∆τ k 0 dtm,t m+∆τm (3)
with dt 0 ,t k a CD displacement between dates t0 and t k , dtm,t m+∆τm a LF displacement between dates tm and tm+∆τ m , ∆τm the temporal sampling of the LF displacement m.

Then, the CD time series is interpolated using a cubic interpolation. Finally, a Regular LF time series is recovered by using a discrete derivative of the interpolated CD time series: where dtr,t r+∆τr is a LF displacement between dates tr and tr+∆τ r . ∆τr is the temporal sampling, which is identical for all the displacements in the time-series.

dtr,t r+∆τr = dt 0 ,t r+∆τr -dt 0 ,tr (4)
This discrete derivative can be computed at different temporal samplings. The choice of the temporal sampling will be discussed in section 4.2.

REGULAR LEAP FROG TIME SERIES WITH AN OPTIMAL TEMPORAL BASELINE

Irregular LF time series

The temporal inversion of multi-sensor velocities results in an Irregular LF time series. An example is shown on Figure 4 for the point of coordinates (-43.532,170.134), corresponding to the the blue point on Figure 1. The ILF displacements are coherent with the velocity observations trend. However, the results look noisy especially after January 2018 where Sentinel-2 and Venµs observations are overlapping. Because of this overlap, the time interval between two observations is small, i.e. up to 1 day. Therefore, the temporal samplings of the ILF time series are also small. Velocity is obtained by dividing displacement by the time, hence if each displacement has a constant white noise due to image correlation errors [START_REF] Millan | Mapping Surface Flow Velocity of Glaciers at Regional Scale Using a Multiple Sensors Approach[END_REF][START_REF] Mouginot | Mapping of ice motion in Antarctica using synthetic-aperture radar data[END_REF], the noise of small temporal baseline velocities could be larger than the velocity magnitude.

Figure 5 shows the distribution of temporal samplings according to their central date over the area represented in orange on Figure 1. It reveals the heterogeneity of temporal baselines which ranges from 1 to 90 days with a median value of 8 days. The smallest temporal baselines are recorded after January 2018 where Sentinel-2 and Venµs observations are overlapped. Moreover, the ILF displacements are inverted between the dates of the available observations for each pixel. Because of the previous outlier removal, these dates differ from one pixel to another. This implies that the velocity values of a given central date and temporal baselines are not reconstructed for every pixel. The percentage of non-masked value is 52% in average. This highlights the necessity to homogenize the temporal sampling of the ILF time series to facilitate the interpretation of the results.

Regular LF time series with different temporal sampling

After interpolation of the CD time series, a Regular LF time series can be reconstructed with any temporal sampling. A question arises: how to choose the optimal temporal sampling to study the short-term variation of ice velocity with an optimal signal-to-noise ratio?

It can be seen on Figure 6 that the larger the temporal sampling is, the smoother is the RLF time series. There is less noise but also a smaller temporal resolution.

To characterize the uncertainty of the RLF time series according to their temporal sampling, two criterion are defined:

1) the Root Mean Square Error (RMSE) over stable areas which relies on the assumption that the velocity magnitude is null on the stable areas. It is defined as:

RMSE = mean (i,j)∈ω 1 1 N + 1 N t=0 ∥⃗ v(i, j, t)∥ 2 (5)
where ⃗ v(i, j, t) stands for the velocity vector at time t and pixel (i, j), N + 1 is the number of velocity data at pixel (i, j) over the considered period, ω1 corresponds to ice-free areas defined according to the Randolph Glacier Inventory (RGI) V6.0 (RGI-Consortium et al., 2017).

2) the Velocity Vector Coherence (VVC) metric [START_REF] Dehecq | Deriving largescale glacier velocities from a complete satellite archive: Application to the Pamir-Karakoram-Himalaya[END_REF][START_REF] Nguyen | A Pattern-Based Method For Handling Confidence Measures While Mining Satellite Displacement Field Time Series: Application to Greenland Ice Sheet and Alpine Glaciers[END_REF] over fast moving areas which relies on the assumption that the flow direction on a point is roughly stable in time. It is a defined as:

VVC = mean (i,j)∈ω 2 N t=0 ⃗ V (i, j, t) ∥ ⃗ V (i, j, t)∥ (6)
where ω2 corresponds to the glacier parts where the mean of velocity observation magnitude is higher than 400 m/y.

These two criterion are computed for several temporal baselines on the area symbolized in orange on Figure 1.

Figure 7 shows that whatever is the temporal baseline/sampling, the RMSE over stable areas is always lower for the RLF time series than for the velocity observations: from 78% lower for a temporal baseline of 5 days to 40% lower for a temporal baseline of 60 days. In addition, Figure 8 highlights that VVC is lower for the velocity observations than for the RLF time series than for every temporal baselines: from 94% higher for a temporal baseline of 30 days to 42% higher for a temporal baseline of 5 days.

Moreover, the largest is the temporal baseline, the lowest is the RMSE and the highest is the VVC, i.e., the lowest is the uncertainty. The RMSE and VVC values reach a plateau at a temporal baseline of 40 days corresponding to a RMSE of 31 m/y for the velocity observations, and at temporal baseline of 30 days corresponding to a RMSE of 20 m/y for the RLF time series. This analysis provides a way to select an optimal temporal baseline/sampling which allows a compromise between temporal resolution and uncertainty. Since the RMSE and VVC of the RLF time series are roughly stable after a temporal sampling of 30 days, 30-days can be selected as an optimal temporal sampling. The RMSE and VVC of the velocity observations are stable after 40 days, the optimal temporal baselines would be 40 days. Hence, the optimal temporal sampling and the associated uncertainty is smaller for RLF time series than for the velocity observations.

SPATIO-TEMPORAL ANALYSIS OF THE RESULTS

Figure 9 b) shows the temporal evolution of the RLF time series at a temporal sampling of 30 days along a longitudinal profile represented on Figure 1. These results are compared with the initial velocity observations. To have a fair comparison, a moving average is performed using a temporal window of 30 days on the velocity observations. That is to say, for each period of 30 days, the average of all the velocities which overlap this period is computed. This post-processed dataset does not correspond to rough dataset and it is already a way to fuse data from different sensors and temporal baselines.

Figure 9 a) reveals that there is no velocity observations available in the center of the tongue between May and October 2017, between February and April 2018 and between October and November 2019. There are gaps in the dataset which make difficult the analysis of intra-annual variations of velocity. Using the proposed approach helps to fill in the gaps and decrease the uncertainty by using the temporal closure of the observation network and a temporal interpolation. Even if the method is pixel-based, the RLF time series seems to be spatially coherent: there is a smooth trend between pixels through the period. A seasonal signal is visible since ice velocity magnitude peaks between September and November and reaches a minimum between April and June. Along the longitudinal profile in Figure 9, the median increase between the minimum of velocity recorded in September to November 2017 and the maximum of velocity recorded from April to June 2018 is 40%. The median increase from April/June 2018 to September/November 2017 is 30%. Moreover, the RLF time series is coherent with the moving averaged velocity observations. However, some discrepancies can be noticed: for instance, the velocity magnitudes at 2.6 km in 2018 range between 200 and 800 m/y whereas the surrounding pixels show velocity magnitudes between 800 and 1200 m/y. This may be due to a discrepancy in the velocity observations which is also visible in Figure 9 a) at 2.6 km. This does not have a glaciological meaning and looks like an artefact. These kinds of remaining artefacts could be removed using a spatio-temporal interpolation or a spatial smoothing. It opens the discussion for further improvement of the current approach.

CONCLUSIONS

This article presents a new approach to fuse ice velocity observations from different temporal baselines and sensors in order to study short-term variations of glacier flow without any a priori on the displacement behavior. The proposed method relies on an inversion based on the temporal closure of the displacement observation network similar to the SBAS approach.

SBAS-like approaches usually retrieve Cumulative Displacement time series (displacements between each date and a reference date) whereas for fast-moving targets with a strong seasonality such as temperate glaciers, Leap Frog velocities (velocities between consecutive dates) are more adequate. To obtain an easily interpretable time series, the LF time series should have a regular temporal sampling, i.e., all the inverted velocities should span the same time interval. However, if the dataset is based on different sensors, it is not possible to obtain directly the same Regular LF time series for each pixel, especially if outliers are removed beforehand. Moreover, the length of the RLF temporal sampling is a crucial parameter but rarely discussed in the literature.

Therefore, the proposed approach firstly built an Irregular Leap Frog time series and then interpolate it to obtain a Regular Leap Frog time series. It enables the user to obtain a RLF time series on a unique temporal basis for each pixel while decreasing the uncertainty of the observations. The application of this method to the Fox glacier in the Southern Alps of New Zealand reveals that the Root Mean Square Error over stable areas is decreased from 78% lower for a temporal baseline of 5 days to 40% lower for a temporal baseline of 60 days. The RMSE over stable areas and VVC over fast moving areas are proposed to select a temporal sampling allowing a compromise between signal-to-noise ratio and temporal resolution. Finally, the 30-days RLF time series reveal a strong seasonal variation of ice velocity: velocities differ by more than 30% from spring to autumn. This was not clearly visible in the observations. It highlights the interest of the method to obtain a velocity time series with a complete temporal coverage and a reduced uncertainty at an optimal temporal sampling by taking advantage of all multi-sensor and multi-temporal velocity observations. This approach is not dataset dependent and could be applied to all kinds of available velocity observations.

Figure 1 .

 1 Figure 1. Studied area over the Fox glacier in the Southern Alps of New Zealand. The blue point is used for analysis in section 4.The orange rectangle corresponds to the considered area in section 4. The red longitudinal profile is considered for the spatio-temporal analysis in section 5. The red dotes are spaced 1 km apart. The background image is an optical image from the Google Earth collection.330 to 400 days. The resulting velocity maps have a 50 m spatial sampling. The measurements cover a period from August 2016 to May 2019.

Figure 2

 2 Figure2shows that Sentinel-2 velocities range from August 2016 to September 2018 whereas Venµs velocities range from January 2018 to May 2019. The percentage of non-masked velocities is on average 27% for Sentinel-2 and 14% for Venµs per central date and temporal baseline. This is due to outliers removal during post-processing. It highlights the difficulty to compute displacements on this narrow and fast glacier tongue and the need for a data fusion.

Figure 2 .

 2 Figure 2. Temporal baselines of the velocity observations according to their central date for Sentinel-2 velocities in blue and Venµs velocities in orange. The colormap which ranges from light to dark blue or orange indicates the percentage of non masked data for each temporal baseline and central date.

Figure 3 .

 3 Figure 3. Illustration of the temporal closure of the displacement observation network used to obtain a) a regular LF time series. The temporal sampling corresponds to the Satellite 1 repeat cycle b) an Irregular LF time series. The vector Y corresponds to the displacement observations. The vector X stands for the LF displacement time series. A is the design matrix linked X and Y in the temporal closure.

Figure 4 .

 4 Figure 4. Velocity observations in gold overlayed with the Irregular Leap Frog time series obtained after temporal inversion in red for the point of coordinates (-43.532,170.134) labeled as the blue point in Figure 1.

Figure 5 .

 5 Figure 5. Temporal baselines of the Irregular Leap Frog time series according to their central date. The colormap indicates the percentage of non masked data for each temporal baseline and central date.

Figure 6 .

 6 Figure 6. Velocity observations (in gold) overlayed with the RLF time series in blue for the point of coordinates (-43.532,170.134) labeled as the blue point in Figure 1. The RLF time series have a temporal sampling of a) 5 days b) 20 days c) 30 days and d) 90 days.

Figure 7 .

 7 Figure 7. Comparison of RMSE over stable areas for different temporal samplings. RMSE is performed over ice-free areas according to the Randolph Glacier Inventory V6.0.

Figure 8 .

 8 Figure 8. Comparison of VVC over fast moving ice for different temporal samplings. VVC is computed on glaciers areas according to the Randolph Glacier Inventory V6.0 where the mean velocity magnitude observation is higher than 400 m/y.

ACKNOWLEDGEMENTS

We acknowledge CNES (French Spatial Agency) and ISA (Israel Space Agency) for the VENµs observations acquired through the VENµs Scientific Mission, and ESA (European Space Agency) for the Sentinel-2 observations acquired though the EU Copernicus program. JM and RM acknowledge support from the CNES.