Aurélien Stcherbinine
email: aurelien.stcherbinine@ias.u-psud.fr

M Vincendon

Franck Montmessin

M J Wolff

Oleg Korablev

A Fedorova

Alexander Trokhimovskiy

A Patrakeev

Gaetan Lacombe

Lucio Baggio

A Shakun

global dust storm as observed by the ACS-MIR channel onboard the Trace Gas Orbiter

published or not. The documents may come

Martian water ice clouds during the 2018

Introduction

Since the first spectroscopic detection by Mariner 9 [START_REF] Hanel | Investigation of the Martian environment by infrared spectroscopy on Mariner 9[END_REF], water ice clouds have been extensively studied because of their connection to the Martian water cycle [START_REF] Clancy | Water Vapor Saturation at Low Altitudes around Mars Aphelion: A Key to Mars Climate?[END_REF][START_REF] Madeleine | Aphelion water-ice cloud mapping and property retrieval using the OMEGA imaging spectrometer onboard Mars Express: OMEGA ANALYSIS OF MARS WATER ICE CLOUDS[END_REF][START_REF] Smith | Vertical distribution of dust and water ice aerosols from CRISM limb-geometry observations[END_REF][START_REF] Clancy | The Distribution of Mars Water Vapor Versus Altitude, Season, and Latitude as Derived from Global Comparisons of CRISM Retrieved and LMD GCM Simulated O 2(ˆ1 g) Dayglow Profiles[END_REF]Guzewich & Smith, 2019). Clouds scatter and absorb incoming solar radiation, thus impacting atmospheric structure and temperature. As a result, water ice cloud particles can modify the global circulation of the Martian atmosphere [START_REF] Wilson | Influence of water ice clouds on Martian tropical atmospheric temperatures[END_REF]. Clouds are also a major actor in the inter-hemispheric water exchange [START_REF] Clancy | Water Vapor Saturation at Low Altitudes around Mars Aphelion: A Key to Mars Climate?[END_REF]. As the evolution of our understanding of the martian climate shows an increasing role of water ice clouds, there is a growing need to better characterize the properties of water ice aerosols in order to better understand and model Mars climate and weather [START_REF] Richardson | Water ice clouds in the Martian atmosphere: General circulation model experiments with a simple cloud scheme[END_REF][START_REF] Montmessin | Origin and role of water ice clouds in the Martian water cycle as inferred from a general circulation model[END_REF][START_REF] Navarro | Detection of detached dust layers in the Martian atmosphere from their thermal signature using assimilation[END_REF]. Recent studies have notably reveal how more precise vertical representation of water-related atmospheric phenomena may impact water cycle modeling [START_REF] Vals | Impact of the refinement of the vertical resolution on the simulation of the water cycle by the martian LMD Global Climate Model[END_REF]. Precise observational constraints about the actual microphysiccal properties of clouds as a function of altitude, notably particle size, are thus of interest to better characterize the whole water cycle.

Planetary-scale storms, characterized by widespread lifting and transport of dust particles, modify the thermodynamics and circulation of the Martian atmosphere on a global scale, and subsequently affect the water cycle. While regional dust storms are recurrent phenomena on Mars, few of them evolve into events that encircle the whole planet to become global dust storms (hereafter "GDS"). Such events are erratic, with an average of one occurrence every three to four Martian years [START_REF] Zurek | Interannual variability of planetencircling dust storms on Mars[END_REF][START_REF] Clancy | An intercomparison of ground-based millimeter, MGS TES, and Viking atmospheric temperature measurements: Seasonal and interannual variability of temperatures and dust loading in the global Mars atmosphere[END_REF][START_REF] Kass | Interannual similarity in the Martian atmosphere during the dust storm season[END_REF]. The first two GDSs of the 21 th century occurred 6 Earth years apart, in 2001 and 2007, corresponding to Martian Years (hereafter "MY") 25 and 28 (e.g. [START_REF] Wang | The origin, evolution, and trajectory of large dust storms on Mars during Mars years 2430[END_REF]. Two large (regional) dust storms developed in 2018 (MY 34): one in the Northern hemisphere starting at L s = 181 • , and the other in the Southern hemisphere at L s = 188 • . They subsequently merged to become a GDS at L s = 193 • , lasting until L s = 250 • (Guzewich et al., 2019;[START_REF] Sánchez-Lavega | The Onset and Growth of the 2018 Martian Global Dust Storm[END_REF][START_REF] Smith | THEMIS observations of the 2018 Mars global dust storm[END_REF]. This GDS occured near the Northern fall equinox, however, it should be noted that there is no unique timing for the onset and development of GDSs on Mars. For instance, the MY 28 GDS, occured significantly later, at the end of the so-called storm season (from L s = 260 • to L s = 310 • ) [START_REF] Wang | The origin, evolution, and trajectory of large dust storms on Mars during Mars years 2430[END_REF]. This variability implies that a variety of scenarios dictate the formation of GDSs, requiring individual assessments of GDS's.

The MY 28 dust storm has been shown to have profoundly influenced the water vapor atmospheric distribution, elevating water well above the troposphere (>60 km) [START_REF] Fedorova | Water vapor in the middle atmosphere of Mars during the 2007 global dust storm[END_REF] while pushing up the hygropause altitude [START_REF] Heavens | Hydrogen escape from Mars enhanced by deep convection in dust storms[END_REF]. A rapid increase of the H 2 O and HDO abundances at altitudes between 40 and 80 km [START_REF] Vandaele | Martian dust storm impact on atmospheric H 2 O and D/H observed by ExoMars Trace Gas Orbiter[END_REF] was observed during MY 34 storm, and recently reproduced in a GCM simulation [START_REF] Neary | Explanation for the increase in high altitude water on Mars observed by NOMAD during the 2018 global dust storm[END_REF]. This large augmentation of the high altitude water content is believed to boost hydrogen, or nearly equivalently, water escape from Mars [START_REF] Chaffin | Elevated atmospheric escape of atomic hydrogen from Mars induced by highaltitude water[END_REF][START_REF] Heavens | Hydrogen escape from Mars enhanced by deep convection in dust storms[END_REF][START_REF] Fedorova | Stormy water on Mars: The distribution and saturation of atmospheric water during the dusty season[END_REF]. However, the formation of clouds impacts the ability of water (or hydrogen) to escape as it confines (in theory) a significant fraction of water below the cloud level. Thus, understanding the extent to which high altitude water vapor condenses to form clouds during GDSs is important in assessing the possible propagation pathways of water vapor up to the exobase [START_REF] Neary | Explanation for the increase in high altitude water on Mars observed by NOMAD during the 2018 global dust storm[END_REF]. Because water vapor can exist in a supersaturated state in the Martian atmosphere [START_REF] Maltagliati | Evidence of Water Vapor in Excess of Saturation in the Atmosphere of Mars[END_REF] and has been observed in a large amount during the MY 34 GDS [START_REF] Fedorova | Stormy water on Mars: The distribution and saturation of atmospheric water during the dusty season[END_REF], simply supposing that the freezing point can be used to set the limits where water is free to be mobilized is likely to be problematic. The availability of condensation nuclei, supplied by the ubiquitous atmospheric dust particles, and possibly by interplanetary dust particles and micrometeoric smoke that aggregates as entering the Martian atmosphere [START_REF] Crismani | Detection of a persistent meteoric metal layer in the Martian atmosphere[END_REF][START_REF] Plane | Meteoric Metal Chemistry in the Martian Atmosphere[END_REF][START_REF] Hartwick | High-altitude water ice cloud formation on Mars controlled by interplanetary dust particles[END_REF], is another key factor controlling the potential for water ice clouds. It has for example been shown by a number of studies [START_REF] Michelangeli | Numerical Simulations of the Formation and Evolution of Water Ice Clouds in the Martian Atmosphere[END_REF] that the occurrence of supersaturation is anti-correlated to the availability of condensation nuclei. The condensation nuclei themselves are expected to be much more abundant during GDS, including with larger sizes (e.g. [START_REF] Wolff | Constraints on the size of Martian aerosols from Thermal Emission Spectrometer observations[END_REF][START_REF] Clancy | Extension of atmospheric dust loading to high altitudes during the 2001 Mars dust storm: MGS TES limb observations[END_REF][START_REF] Lemmon | Large Dust Aerosol Sizes Seen During the 2018 Martian Global Dust Event by the Curiosity Rover[END_REF], which may impact how and when water ice clouds form. It is however difficult to predict the distribution and properties of condensation nuclei at high altitude during GDS, which additionally modify the thermal structure of the atmosphere. In this complex situation, accumulating observational constraints about the actual behavior of water ice at high altitude during GDS is required to provide further constraints on the fate of high altitude water vapor during these events.

The ExoMars Trace Gas Orbiter (TGO), ESA-Roscosmos Atmospheric Chemistry Suite (ACS) and Nadir and Occultation for MArs Discovery (NOMAD) instruments started their science operation phase in March 2018 [START_REF] Korablev | The Atmospheric Chemistry Suite (ACS) of Three Spectrometers for the ExoMars 2016 Trace Gas Orbiter[END_REF][START_REF] Vandaele | NOMAD, an Integrated Suite of Three Spectrometers for the ExoMars Trace Gas Mission: Technical Description, Science Objectives and Expected Performance[END_REF][START_REF] Korablev | No detection of methane on Mars from early ExoMars Trace Gas Orbiter observations[END_REF][START_REF] Vandaele | Martian dust storm impact on atmospheric H 2 O and D/H observed by ExoMars Trace Gas Orbiter[END_REF], before the MY 34 GDS. The ACS middle-infrared (MIR) channel is a crossed-dispersion echelle spec-trometer dedicated to solar occultation (hereafter, "SO"): each observation covers a ∼300 nm wide spectral interval selected between 2.3 and 4.2 µm. This interval is set by rotating the spectrometer secondary grating (i.e., the diffraction order separation) to align the interval of interest with the detector. The cross-dispersion aspect provides from 10 to 21 diffraction orders (spectral segments) stacked on top of each other. The separation between consecutive orders is only dependent on the number of orders displayed at once and thus on the secondary grating position. Thirteen different positions can be employed to completely sample the full accessible spectral range of the instrument. With the two hours orbital period of TGO and the performing of SO in the mid-infrared, ACS and NOMAD provides a totally new and huge dataset of vertical profiles of the atmospheric extinction [START_REF] Korablev | The Atmospheric Chemistry Suite (ACS) of Three Spectrometers for the ExoMars 2016 Trace Gas Orbiter[END_REF][START_REF] Vandaele | NOMAD, an Integrated Suite of Three Spectrometers for the ExoMars Trace Gas Mission: Technical Description, Science Objectives and Expected Performance[END_REF]. We are using the ACS-MIR channel to study the extinction properties of the Martian airborne particles in the 3 µm spectral region, which possesses a distinct diagnostic capability to identify the O-H stretching signature; whether it is due to water ice absorption or bound water in dust. In the case of water ice, the depth and shape of the feature depend on both the abundance and the particle size of water ice [START_REF] Vincendon | New near-IR observations of mesospheric CO 2 and H 2 O clouds on Mars[END_REF][START_REF] Guzewich | The vertical distribution of Martian aerosol particle size: Vertical Profile of Mars Aerosol Size[END_REF]Clancy et al., 2019). The ACS-MIR occultation data in this spectral range gives us complementary information to those derived from previous limb and nadir scattered light observations by OMEGA [START_REF] Bibring | OMEGA: Observatoire pour la Minéralogie, l'Eau, les Glaces et l'Activité[END_REF][START_REF] Vincendon | New near-IR observations of mesospheric CO 2 and H 2 O clouds on Mars[END_REF] and CRISM [START_REF] Murchie | Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) on Mars Reconnaissance Orbiter (MRO)[END_REF]Clancy et al., 2019;[START_REF] Guzewich | The vertical distribution of Martian aerosol particle size: Vertical Profile of Mars Aerosol Size[END_REF]. We focus here on the use of the water ice absorption feature during the MY 34 GDS that offer a relevant framework for a further characterization of the interactions between water and dust during extreme dust events.

Data analysis

In order to study the 3 µm water ice absorption band, we use the instrument configuration centered on the 3.1 -3.4 µm spectral range corresponding to the 12th secondary grating position. Figure 1

Continuum extraction

Every ACS-MIR observation is composed of ∼20 spectral segments individually exhibiting broad instrumental shapes that generally prevents contiguous segments from matching precisely in their overlapping wavelength intervals (cf. figure 2) due to instrumental effects [START_REF] Korablev | The Atmospheric Chemistry Suite (ACS) of Three Spectrometers for the ExoMars 2016 Trace Gas Orbiter[END_REF][START_REF] Trokhimovskiy | Middle-infrared echelle cross-dispersion spectrometer ACS-MIR for the ExoMars Trace Gas Orbiter[END_REF]. As the aerosol property derivation is intrinsically dependent of the continuum behavior, we have adopted a method to extract the continuum across all displayed fraction orders, taking into account this spectral shape of each order. This allows us to derive the continuum shape across the 3 to 3.4 µm range.

In order to do this, we have chosen to fit the 200 centered spectral points of each diffraction order with a 2 nd degree polynomial, and use an iterative method to remove the gas absorption bands that tend to bias the continuum values represented by the fitted polynomial. After the first iteration, for each diffraction order we determine the standard deviation of the transmission values of the considered spectral points σ, and we consider that all the points with transmission lower than the polynomial fit by at least σ (i.e. Tr(λ) < (fit(λ) -σ)) are affected by some gas absorption. So we remove these points as they tend to underestimate the actual continuum. In a second step, we perform the same filtering method from a polynomial fit on each diffraction order for the remaining wavelengths (i.e. the 200 centered points without the ones with transmission values lower than (fit -σ)). Finally, we perform a third fit to the continuum and then only retain the fitted transmission value at the center point of each fitted order (cf. figure 2.b). As a result, the complete spectrum has an effective spectral resolution of one point per diffraction order, which corresponds to a spectral resolution of ∼ 1 -2 nm. This is a much smaller number of points than the ACS-MIR native sampling, but is sufficient to capture the general shape of the continuum used in the next sections for solid particles characterisation. Next, we estimate the uncertainties of the data as the sum of the standard deviation of the difference between the data and the polynomial fit for each order (random uncertainties), and the maximal gap between the polynomial fit of the order and the extracted continuum (1 point per order), linearly interpolated between each diffraction order (systematic uncertainties due to the curvature of the diffraction orders, see figure 2.c). Additionally, in the following we do not consider the outer regions of the spectra in order to avoid detector edge effects, i.e. the spectels corresponding to 3.10, 3.12 and 3.44 µm.

Haze top determination

Using this extracted continuum at each observed tangent point, we can determine the haze top altitude for each observation. We define haze top as the highest altitude at which aerosols can be sensed along the line of sight. We calculate haze top by finding the first altitude for which the transmission is greater than a defined threshold (1 -ε). ε introduces the consideration of the artificial non-steady nature of the measured transmission as it approaches unity at high altitude. We observe empirically that this transition occurs above transmissions around 0.99. We have thus selected a conservative value of ε = 0.02 for this threshold. An example is provided in the figure 3.

3 µm band monitoring

The 3 µm absorption feature corresponds to the OH/H 2 O absorption. We quantify the depth of this feature as a function of altitude using an Integrated Band Depth (IBD) method [START_REF] Jouglet | Hydration state of the Martian surface as seen by Mars Express OMEGA: 1. Analysis of the 3 m hydration feature[END_REF][START_REF] Calvin | Variation of the 3-µm absorption feature on Mars: Observations over eastern Valles Marineris by the Mariner 6 infrared spectrometer[END_REF]. This approach computes the mean depth of transmission between two selected wavelengths (see eq. 1 and figure 4). order proxy for the presence of some water ice clouds. In blue, we show an example of ACS-MIR position 12 spectra, showing a strong 3 µm absorption band. In green is shown the measurement of the 3 µm absorption using the IBD method (cf. equation ( 1)) with λ1 = 3.15 µm and λ2 = 3.4 µm). This spectrum is compared to the theoretical transmission of 0.5 µm spherical water ice particles in red (see section 3.1) and in black, another example of ACS-MIR spectra with a low 3 µm band, and presumably no water ice.

IBD(Tr

, λ 1 , λ 2 ) = 1 λ 2 -λ 1 λ2 λ1 [Tr(λ 2 ) -Tr(λ)] dλ (

Extinction coefficient determination

In order to retrieve the extinction profile and properties of the aerosols, we employ a vertical inversion algorithm based on the onion-peeling method [START_REF] Goldman | Analysis of atmospheric infrared spectra for altitude distribution of atmospheric trace constituentsI. Method of analysis[END_REF], from the total optical depth τ (i.e., as integrated along the line of sight). The result is the the extinction coefficient k ext as a function of altitude. Then, we can compute the opacity of a cloud by integrating the extinction coefficient along a vertical line between the boundary altitudes detected for the cloud (see the following sections for a description of the water ice clouds identification).

For each altitude level i, the optical depth is given by:

τ i (λ) = N j=i 2 × R 2 j+1 -R 2 i -R 2 j -R 2 i Ai,j k ext,j (λ) (2)
That we can rewrite in a matrix manner:

τ = A k ext (3)
The transfer matrix A is upper triangular so it is invertable and we can write :

k ext = A -1 τ (4)
I.e.

k ext,i = N j=i A -1 i,j τ j (5)
Then, according to [START_REF] Bimp | JCGM 100: Evaluation of Measurement Data -Guide to the Expression of Uncertainty in Measurement[END_REF], as τ = -log(Tr) and k ext given as a function of τ in (5), we have the uncertainties on the optical depth values (6) and their propagation to the extinction coefficient k ext throughout the vertical inversion given by (7).

∆τ (λ) = ∆Tr(λ) Tr(λ) (6) ∆ (k ext,i ) = N j=i (A -1 ) 2 i,j (∆τ j ) 2 (7)
Notation N The number of atmospheric layers.

Tr i The measured transmission value at the i th altitude. τ i The optical depth observed at the i th altitude (integrated along the line of sight). k ext,i The extinction coefficient of the i th atmospheric layer. R i The radius of the sphere corresponding to the bottom altitude of the i th atmospheric layer, i.e. the altitude of the bottom of the layer added to the Martian radius.

Figure 5 presents several examples of retrieved vertical profiles of the extinction coefficient k ext from ACS-MIR observations before and during the MY 34 GDS. We can already notice the presence of one or several detached layers in some profiles, which are located at various altitudes. We also observe strong spectral variability between observations, with some layers having a distinctive signature when comparing the transmissions at 3.2 and 3.4 µm (compare e.g. blue and red profiles in panels a and d of figure 5). We will discuss in the next section how this spectral behavior can be modeled to derive information about the presence and properties of water ice clouds.

3 Water ice cloud modeling

Model and hypothesis

In order to identify water ice clouds, and constrain their particle sizes, we have computed the wavelength dependence of the extinction coefficient of pure water ice and dust layers of various particle sizes (figure 6). These extinction coefficients are calculated using a public domain Mie code [START_REF] Toon | Algorithms for the calculation of scattering by stratified spheres[END_REF] and assuming a gamma size distribution [START_REF] Hansen | Light scattering in planetary atmospheres[END_REF] with an effective variance of 0.1 (e.g. [START_REF] Wolff | Radiative Process: Techniques and Applications[END_REF], and references contained within).

We can see in the figure 6 that the spectral properties of water ice and dust differ significantly in most cases, and that there is a strong dependence of the spectral shape on particle size for water ice. This is not true when water ice particles sizes become greater than about 3 µm: for such sizes the absorption become quite flat in the 3.1 -3.5 µm range whatever the particle size and it is even not possible to differentiate water ice from dust. Particles size lower than 0.1 µm have similar k ext spectra corresponding to the Rayleigh diffusion regime. As a consequence, we do not make any distinction between water ice particles with radii of 0.1 µm and lower.

In the following, we fit our retrieved extinction coefficient from ACS data to these models for pure water ice or dust layers in order to identify and characterize water ice rich layers composed of particles lower than ∼ 2 µm, as results suggesting larger water e

L s = 170° | lat = -38°0 .000 0.005 0.010 kext [km 1 ] f L s = 180° | lat = -24°0 .000 0.005 0.010 kext [km 1 ] g L s = 200° | lat = -74°0 .000 0.005 0.010 kext [km 1 ] h L s = 219° | lat = -74°F
igure 5. Typical extinction coefficient vertical profiles retrieved from different ACS-MIR observations. In blue the extinction coefficient at 3.2 µm, which provides a proxy for the overall particle (dust and ice) profile. In red the difference between the extinction coefficient at 3.2 µm and 3.4 µm, which provides a proxy for the presence of band depth associated with small-grained water ice We can see layers with various behavior, some typical of the presence of small-grained water ice (e.g., e at about 50 km) and some interpreted as resulting from either large-grained water ice, or dust (e.g., d at 20 km). See section 4 for discussion. The shadows regions show the uncertainties on the kext values.

ice particles are eliminated in the filtering process due to possible confusion with dust (see section 3.3). Layers not identified as such can correspond to either dust-dominated or large-grained water ice layers.

Water ice particle size retrieving method

As the extinction opacity C ext is proportional to k ext , we try to fit our ACS-MIR k ext data with the modeled C ext spectra. To do this, we consider the extinction coefficient as a function of the wavelength λ, the effective radius r eff and a scalar factor α > 0 (cf. equation ( 8)), where α is related to the number of particles that have scattered the light and C interp ext is interpolated from the input models, using a bivariate spline approximation. The distinction between k ext and C ext is just a matter of normalization Cext(λ,r eff )

Cext(λ0,r eff ) = kext(λ,r eff ) kext(λ0,r eff ) . However, we decide to leave α as a free parameter to get rid of the choice of normalization wavelength λ 0 .

k ext (λ, r eff , α) = α C interp ext (λ, r eff ) (8)
Then, in order to avoid the problem of the presence of local minima for r eff in the least-square fitting algorithm, we generate models on a grid of radii of 0.01 µm between 0.1 µm and 8 µm, and for each one we retrieve the optimal value of α using the Trust Region Reflective algorithm implemented in the scipy.optimize.curve fit() Python function [START_REF] Virtanen | SciPy 1.0-Fundamental Algorithms for Scientific Computing in Python[END_REF]. Thus, we obtain the best fit for each particle size, that we compare in a second time, by computing a χ 2 from the data and the model, as defined in the equation ( 9) [START_REF] Bevington | Data reduction and error analysis for the physical sciences -Second edition[END_REF]. This allows us to find the global minimum of χ 2 as a function of the particle size, and derive the associated r eff with this "best fit".

χ 2 (r eff ) = N i=1 (data i -model r eff , i ) 2 σ 2 i (9)
Finally, we use the reduced chi-square χ 2 ν defined in the equation ( 10), as a measure of the goodness of the fit [START_REF] Bevington | Data reduction and error analysis for the physical sciences -Second edition[END_REF]. In theory, a model is considered to be a good approximation of the data when χ 2 ν ≤ 1.

χ 2 ν (r eff ) = 1 N -2 N i=1 (data i -model r eff , i ) 2 σ 2 i = χ 2 ν ( 10
)
Notation data i The i th spectel of the k ext spectra from the ACS-MIR observation. model reff , i The i th spectel of the model extinction spectra for a particle size of r eff . σ i The uncertainty on the value of data i .

N The number of spectral points in the considered spectrum.

ν The number of degrees of freedom (ν = N -p).

p The number of fitting parameters (here p = 2).

Then, in order to quantify the uncertainties for the retrieved particles size, we search for the r eff of all the models that will pass our filtering criteria (cf section 3.3) during the fitting process of an ACS-MIR spectrum and verify χ 2 ν, ice ≤ 2χ 2 ν, ice, min + 1 , where χ 2 ν, ice, min is the minimal value of χ 2 ν, ice (i.e. associated with the optimal r eff value). This last criteria that essentially affects low χ 2 ν, ice values was add to take into account the goodness of the optimal fit in the uncertainties estimation As all these models can be considered as acceptable, they will define the uncertainties range of the fit. In other words, the optimal r eff corresponds to the model with the lower χ 2 ν, ice value, and the lower (respectively upper) bounds for the particle size uncertainties corresponds to the minimal (respectively maximal) value of r eff in the set of models that prove equation ( 11) along with χ 2 ν, ice ≤ 2χ 2 ν, ice, min + 1 .

Filtering of dust/ice ambiguous cases

We identify water ice clouds by correlating extinction coefficient spectral behavior compatible with water ice, and incompatible with dust. To do that, we experimentally determined χ 2 thresholds that we present in the following. Thus, to be classified unambiguously as a water ice cloud detection, a layer needs to have a χ 2 ν ≤ 9 for water ice, but also a lower quality fit to dust. We then apply the previously described fitting algorithm also for dust and not only for water ice. We eliminate all those observations that the water ice models don't improve the χ 2 ν by at least a factor 4, as well as the ones that it is possible to fit a dust spectra with a χ 2 ν ≤ 1. That is to say, we only consider the fits which verify the condition (11). This last criteria was added as a safeguard and is relevant in the case of a fit associated to a low χ 2 ν value, where even if χ 2 ν dust ≥ 4χ 2 ν ice , the dust model still provide a good fit of the data that we cannot ignore.

χ 2 ν, ice ≤ 9 & χ 2 ν, ice ≤ χ 2 ν, dust 4 & χ 2 ν, dust > 1 (11)
In addition, we also remove the fits whose error bars exceed a pre-defined threshold of 0.35 µm. An example of such a fit is found in figure 7.j. However, in most cases, such poorly constrained fits were already eliminated through the dust-fitting test (figure 7.k).

After this multi-step filtering process, we note that retrieved particle sizes never exceed 2 µm; in essence the fits indicating sizes between 2 µm and 8 µm have been removed, which was expected as the extinction coefficient is not diagnostic of water ice in that size range, as discussed previously. As a consequence, it is appropriate to consider that our method makes it possible to identify and characterize water ice rich layers with mean particle size of ∼ 2 µm maximum. Other layers can correspond to either dust-dominated or large-grained water ice layers.

Results and discussion

The 3 µm atmospheric absorption

The atmospheric 3 µm integrated band depth can be used to obtain a quick look at water ice clouds in our dataset. It is also of interest in itself as orbital observations of Mars surface have to account for atmospheric 3 µm contribution to deliver information We observe that even if all the presented spectra can be reproduced by our water ice model, the fourth case (j) remains ambiguous as the dust model is also able to provide a acceptable fit (k).

Thus, we will accept the three first fits a, d & g while the fit j will be rejected by the filtering process.

about surface hydration [START_REF] Jouglet | Hydration state of the Martian surface as seen by Mars Express OMEGA: 1. Analysis of the 3 m hydration feature[END_REF][START_REF] Audouard | Water in the Martian regolith from OMEGA/Mars Express[END_REF]. As illustrated in figure 8, the 3 µm IBD matches at first order the more elaborated water ice detection scheme presented in section 3. Actually, the 3 µm IBD captures only small-grained (r eff ≤ 1 µm) water ice clouds according to modeling results presented in figure 6, but this corresponds to typically 90% of detected clouds here (see figures 13 & 15). In addition, the IBD does not capture thin clouds that produce a tenuous absorption, whatever their grain size. Thus, thin layers (normal integrated layer optical depth lower than 0.01) that can be observed at very high altitudes (≥ 90 km) are not always discernible with IBD figures. Beside these slight differences, the IBD criteria thus illustrates the overall water ice pattern and provide a proxy for the optical thickness of clouds. We have illustrated the overall behavior of water ice clouds using figure 9 where the 3 µm IBD variations are represented from L s = 165 • to L s = 243 • in the Northern (a) and Southern (c) hemispheres.

We observe in figure 9 that some vertical profiles corresponding to observations acquired at close L s and are so overlapping in the figure can manifest notable differences in the 3 µm IBD criterion. This probably reflects actual variations between profiles, associated with longitudinal variations of the water ice clouds [START_REF] Smith | Interannual variability in TES atmospheric observations of Mars during 1999-2003[END_REF][START_REF] Wolff | Mapping water ice clouds on Mars with MRO/MARCI[END_REF], as illustrated in table 1. Local time differences [START_REF] Szantai | Martian cloud climatology and life cycle extracted from Mars Express OMEGA spectral images[END_REF] may also contribute to the variability (Table 1), although the dataset is not yet extensive enough to properly delineate local time effects.

Clouds monitoring

Using the method presented in section 3, we can both detect the presence of water ice clouds layers in the Martian atmosphere and retrieve their particle size (see discussion in section 4.5). Figure 10 presents the resulting vertical profiles of water ice particles from L s = 165 • to L s = 243 • in the Northern and Southern hemispheres. This overview reveals two main trends in our dataset. First, we detect water ice clouds in most observations. In more detail, in our dataset of 65 ACS-MIR grating position-12 observations, 11 of them have no water ice cloud detection, i.e., 83% of our profiles show at least one detection of water ice. Non-detections are localized in time and places: 45% of our non-detections are located at the onset of the GDS (193 • ≤ L s ≤ 198 • , 5 observations), and the other 55% are located during the GDS (219 • ≤ L s ≤ 231 • , 6 observations) but corresponds to low haze top altitude beyond the northern limit of the GDS (see detailed discussion in section 4.4). Second, we observe the presence of two distinct types of vertical profiles that correspond to the two periods separated by the sudden onset of the GDS at L s ∼ 195 • -200 • (Guzewich et al., 2019). Two main cloud characteristics differ between these two periods: the vertical extent, and the water ice cloud opacity. Most of the detected clouds are between 10 km and 70 km before the onset of the GDS, while clouds altitudes typically extend higher between 60 km and about 90 km afterward. Figure 12 shows the vertical profiles of k ext at 3.4 µm (i.e. the opacity per km). As 3.4 µm is on the edge of the 3 µm water ice band [START_REF] Vincendon | New near-IR observations of mesospheric CO 2 and H 2 O clouds on Mars[END_REF] it provides an estimator of the global atmospheric opacity, whereas the opacity at 3.2 µm is strongly increased by the presence of water ice clouds. We observe that the water ice clouds opacity at 3.2 µm (vertically integrated along the cloud) typically goes from 0.01 to 0.05 before the GDS, but falls to a few 10 -3 for the mesospheric clouds during the GDS, with k ext (λ = 3.2 µm) ∼ 10 -4 km -1 around 90 km (and k ext (λ = 3.4 µm) ∼ 10 -5 km -1 ). We discuss in more details the distribution and properties of clouds during these two periods in the next two sections.

Before the GDS (L

s < 195 • )
Before the dust storm, we observe the presence of water ice clouds in most profiles, with altitudes ranging from 11 to 44 km in the Northern hemisphere, and between 17 and 69 km in the Southern hemisphere, which is consistent with previous observations [START_REF] Smith | Vertical distribution of dust and water ice aerosols from CRISM limb-geometry observations[END_REF]. Thus, clouds are found below the mesosphere for most of the cases. However, the latitude coverage of available observations in the North and in the South are not equivalent (cf. figure 10): Northern observations prior to the GDS are restricted to polar latitudes ≥ 68 • .

During this period, we indeed observe a latitude-dependence of the haze top altitude that increases closer to the equator (up to ∼70 km at 24 • S) and decreases when moving towards polar latitudes (down to ∼40 km at 80 • N, or 60 • S), see also figure 11.a. This trend is consistent with the expected haze top behavior [START_REF] Jaquin | The vertical structure of limb hazes in the Martian atmosphere[END_REF][START_REF] Forget | Improved general circulation models of the Martian atmosphere from the surface to above 80 km[END_REF][START_REF] Montmessin | Stellar occultations at UV wavelengths by the SPICAM instrument: Retrieval and analysis of Martian haze profiles[END_REF][START_REF] Heavens | The vertical distribution of dust in the Martian atmosphere during northern spring and summer: Observations by the Mars Climate Sounder and analysis of zonal average vertical dust profiles[END_REF][START_REF] Smith | Vertical distribution of dust and water ice aerosols from CRISM limb-geometry observations[END_REF]. However, the lack of data around the equatorial latitudes before the GDS (no observations between 20 • S and 60 • N, see figure 11.a) prevents us to get access to the latitude of the maximum haze top altitude.

Water ice clouds are detected in the upper parts of most profiles, but some profiles also include lower detached layers (e.g. figure 5.f at 30 km) that are not detected either by the fitting process or the IBD (as the k ext at 3.2 µm and 3.4 µm are similar). Thus, these layers are likely be either composed primarily of dust or by > 2 µm water ice particles (cf. section 3.3). This suggests that water ice appears to frequently cap the dust layer in our solar longitude range [START_REF] Smith | Vertical distribution of dust and water ice aerosols from CRISM limb-geometry observations[END_REF]. Note however that larger- grained water ice clouds can also be present at lower altitude [START_REF] Wolff | Constraints on the size of Martian aerosols from Thermal Emission Spectrometer observations[END_REF], but remain undetected here due to a lack of a clear signature in our spectral range (as discussed previously). Nevertheless, the altitude distribution of the detected water ice clouds follows a similar latitudinal trend as the haze top itself: the average altitude Around L s = 200 • , there is a sudden increase in the altitudes of both the haze top (up to 100 km) and the water ice clouds (≥ 90 km), while geographical coordinates remain essentially the same (83 • S and 58 • N at L s = 196 • , and 74 • S and 39 • N at L s = 200 • ). These behaviors are combined with a decrease of the measured IBD values (cf. figure 9). We note that the above behavior appears to be relatively uniform around the planet (i.e., both zonally and meridionally). Specifically, in the Southern hemisphere, even though the observed latitude varies from 74 • S to 5 • S between L s = 219 • and L s = 241 • , one does not see a change in both the haze top altitude and the maximal altitude of the water ice clouds; in agreement with the simulations presented in Neary et al. (2019, Figure 3). We nonetheless identify a temporal trend likely related to the progressive decay of the dust storm (Guzewich 10) and the main 3 µm atmospheric absorption (i.e. the maximum of IBD for a given profile) decrease from 75 km to 58 km (cf. figure 9). Regardless that the haze top altitude remains at ∼ 85 -90 km, and the latitude goes successively towards and from the equator. Nevertheless, we note a slight North/South asymmetry during the dust storm that is represented by the smaller number of high-altitude water ice clouds in the Northern hemisphere (see figure 11.c&d).

Ice clouds are detected at very high altitudes in the mesosphere during this period, up to ≥ 80 km at the beginning of the GDS. A few profiles show robust water detections at altitudes above 90 km, up to 100 km maximum at L s ∼ 200 • (cf. figure 14.c). These high altitude water ice clouds are observed only at the beginning of the GDS. High altitude water ice clouds can also be seen during non-dust GDS years, when they occur during the storm season [START_REF] Vincendon | New near-IR observations of mesospheric CO 2 and H 2 O clouds on Mars[END_REF]Clancy et al., 2019). However, high cloud altitudes are nearly systematic in our observations during the peak phase of the GDS (cf. figure 10), while such altitudes are less typical during non-GDS years (Clancy et al., 2019). Moreover, peak cloud altitudes are slightly higher during the onset of the GDS than reported in non-GDS years. Indeed, models [START_REF] Neary | Explanation for the increase in high altitude water on Mars observed by NOMAD during the 2018 global dust storm[END_REF] showed that GDS are expected to slightly increase the average and maximum altitude of water ice clouds, which is consistent with our observations. The sharp increase in water ice cloud altitude observed during the GDS indeed confirms that this water ice cloud increase is directly connected to dust storm activity. The large-scale dust storm probably facilitates the formation of high altitude water ice clouds through increase in the altitude of both water vapor and condensation nuclei. This increase of water ice altitude during the GDS is indeed consistent with the recently reported increase of water vapor at higher altitudes [START_REF] Fedorova | Water vapor in the middle atmosphere of Mars during the 2007 global dust storm[END_REF][START_REF] Neary | Explanation for the increase in high altitude water on Mars observed by NOMAD during the 2018 global dust storm[END_REF].

We still observe a North/South latitudinal asymmetry during the GDS. In the Northern hemisphere, seven observations in the figure 11.c exhibit low haze top altitudes during the GDS. The haze top is between 26 km and 36 km, i.e. ∼ 50 km below the altitudes measured during the dust storm for most of the other profiles. Actually, these profiles were taken at high Northern latitude (60 • N -66 • N) during the decay of the dust storm (L s = 221 • -231 • ) at longitudes of ∼ 25 • W (Acidalia Planitia) and ∼ 155 • E (Utopia Planitia), see table 2: this suggests that 60 • N represents the Northern extent of the dust storm activity in these regions from L s ∼ 220 • , which is in agreement with MCS measurements (D. [START_REF] Kass | Mars Climate Sounder observation of Mars' 2018 global dust storm[END_REF]. The scheme is different for the Southern hemisphere, with high haze top altitudes (> 80 km) observed during the GDS up to the polar regions (73 during the same period, these observations can no longer be considered as part of the GDS.

These low haze top observations are located at latitudes greater than 60 • with some longitudinal variability. This latitude thus correspond to the Northern maximum extent of the GDS at that time, in agreement with MCS measurements (D. [START_REF] Kass | Mars Climate Sounder observation of Mars' 2018 global dust storm[END_REF].

Particle size

We observe that the particle size decreases on average with increasing altitude (cf. figure 13), as previously reported by Clancy et al. (2019). This global trend is also apparent in the majority of individual profiles: particle size is observed to decrease with altitude within a given cloud as we can see in figure 14. This is true regardless of the average altitude of the considered cloud (cf. figure 14). The distribution of particle size as a function of altitude is globally shifted to higher altitudes during the GDS (cf. figure 13), i.e., a given size of particles can go higher in the atmosphere during the GDS. Clancy et al. (2019) also observe a similar trend during non-GDS years, with a given class of particle size that increases in altitude during the perihelion season (L s = 180 -340 • ).

While trends can be identified on a global scale, some variability is also evident, as seen in figure 15. As the main clouds altitude increases, water ice particles become distinctly smaller in the storm, with a median effective radius of 0.28 µm before the dust storm and ≤ 0.1 µm during it. This narrower range of smaller particles, with a strong peak for r eff ≤0.2 µm, is typical of the mesospheric clouds (Clancy et al., 2019, figure 12).

Additionally, we also observe the appearance of a small population of larger water ice particles, with r eff ≥ 1.5 µm, at surprisingly high altitude (between 55 km and 64 km) in view of previous observations and studies (e.g. below 40 -50 km for Guzewich & Smith, 2019). Their identification as water ice particles is robust, i.e., attempts to fit using dust properties are unable to reproduce the observed wavelength dependence of the derived k ext (cf. figure 16). However, we have to keep in mind that our understanding of the spectral behaviour of the martian dust still needs to be improved, in particular about the hydration properties. Nevertheless, even updated dust optical properties are not expected to be able to reproduce the spectral bump observed in figure 16, as large water ice particles can do (cf. figure 6). These detections are found below smaller water ice particles (cf. figure 16, 3rd column). Although turbulence during dust storms is expected to enable the lifting of larger particles, the exact mechanism by which these large-grained water ice clouds form or are bring at high altitude remains to be investigated. In addition to turbulence, condensation nuclei properties could also play a role [START_REF] Gooding | Martian dust particles as condensation nuclei: A preliminary assessment of mineralogical factors[END_REF][START_REF] Michelangeli | Numerical Simulations of the Formation and Evolution of Water Ice Clouds in the Martian Atmosphere[END_REF][START_REF] Montmessin | Origin and role of water ice clouds in the Martian water cycle as inferred from a general circulation model[END_REF][START_REF] Hartwick | High-altitude water ice cloud formation on Mars controlled by interplanetary dust particles[END_REF]. One possibility is that these particles are not primarily composed of water ice but could host a relatively large dusty core. Incidentally, large dust particles have been reported from the surface during this GDS, [START_REF] Lemmon | Large Dust Aerosol Sizes Seen During the 2018 Martian Global Dust Event by the Curiosity Rover[END_REF], which could play a role as condensation nuclei for the water ice. [START_REF] Clancy | Extension of atmospheric dust loading to high altitudes during the 2001 Mars dust storm: MGS TES limb observations[END_REF] indeed observed during a previous GDS (2001) that large dust particles can propagate to high altitude (sizes between 1 µm and 2 µm above 70 km).

Conclusion

In this paper, we present our analyses of the Martian water ice clouds in the period before and during the MY 34 GDS using ACS infrared SO observations. This novel observational geometry in the mid-infrared allows us to monitor the 3 µm water ice absorption band, and subsequently constrain the sizes of the detected water ice particles. Indeed, the shape of the wavelength profile of the 3 µm absorption band is a sensitive function of the particle size. The sensitivity of this feature combined with the high resolution of ACS-MIR allows us to derive useful constraints on the particle size distribution of the clouds between r eff ≤ 0.1 µm and 2 µm. Moreover, the temporal range of this dataset, from L s = 165 • to L s = 243 • , offers an unique opportunity to observe the impact of such a dust storm on the distribution and composition of the water ice clouds in the Martian atmosphere. The main results are summarized below:

1. Using the ACS MIR dataset, we have developed of a method to identify water ice clouds, measure their opacity, and estimate their particle size. The method makes it possible to identify cloud for particle size smaller than 2 µm. 2. We have derived vertical profiles of water ice clouds opacity and average particle size before and during the MY 34 GDS (from L s = 165 • to L s = 243 • ). 3. We detect water ice clouds in most of the observations across the planet except during the onset of the GDS (4/5 of our profiles show at least one detection of water ice, and half of the non-detections are located within the onset of the GDS). 4. We retrieve very high haze top altitudes during the GDS, notably at solar longitudes close to the onset with evidence for mesospheric clouds at altitudes ≥ 90 km, and even up to 100 km for the maximum haze top altitude. This suggests that GDS may elevates peak haze altitudes by 10 to 20 km compared to the typical perihelion storm season values. 5. We observe that there is a general trend of decreasing particle size with altitude for the whole dataset, and more specifically that the particle size within a given cloud/profile also decreases with altitude, typically from 1 to 2 µm at the bottom of the cloud down to less than 0.2 µm at the top. 6. We note a decrease in the mean water ice particle size during the GDS, with a median r eff of 0.3 µm for water ice particles before the storm that become ≤ 0.1 µm during the dust storm. This is related to an increase of the average altitude of clouds during the GDS, with a higher proportion of mesospheric, small-grained water ice clouds. 7. Finally, we observe evidence for large water ice particles (r eff ∼ 1.5 -2 µm) at unexpectedly high altitudes during the GDS (between 50 km and 70 km). To conclude, this study shows that the MY 34 GDS has impacted the water ice clouds distribution, with more frequent clouds detections at very high altitudes up to above 90 km, along with evidence of unexpected particles with radii ≥ 1.5 µm up to 70 km. the MY 34 GDS. The yellow lines represent the median size for each distribution, respectively 0.28 µm (a) and 0.1 µm (b). We observe that during the dust storm we detect a fewer proportion of particle with a size between 0.5 µm and 1 µm, as most of our detection suggest sizes lower than 0.5 µm, with a strong peak at 0.1 µm. However, because we do not derive particles sizes lower than 0.1 µm, the median r eff value during the GDS must be consider as ≤ 0.1 µm as more than half of our retrievals indicates sizes on the lower bounds of the models.

Figure 1 .

 1 Figure 1. Spatial and time distribution of the 65 ACS-MIR observations used in this study.

Figure 2 .Figure 3 .

 23 Figure 2. Extraction of the spectral continuum. a. Reduced calibrated image of the ACS-MIR detector containing 20 diffraction orders along the y-axis. For each order, the wavelength varies along the x-axis. Each blue line corresponds to the detector pixels used to obtain the spectrum of one diffraction order. b. Corrections steps for the extraction of the spectral continuum. In blue the initial data, in yellow the polynomial fit of the 200 points from the center of each order (after the third iteration), and in red the extracted continuum (with the associated uncertainties in the red shadowed region). c. Zoom on two diffraction orders.

Figure 4 .

 4 Figure 4. Calculation of the 3 µm Integrated Band Depth (IBD) which can be used as a first

  170° | lat = 77°b L s = 181° | lat = 82°c L s = 200° | lat = 39°d L s = 240° | lat =

  Figure 6. Water ice and dust models. a. Simulated extinction opacity spectra Cext(λ) for water ice spherical particles of different sizes, normalized at λ0 = 3.1 µm. b. Same plot for dust spherical particles. For particles with r eff > 3 µm, we cannot distinguish between water ice and dust signature in this spectral window.

Figure 7 .

 7 Figure 7. Water ice cloud identification and particle size retrievals from ACS-MIR kext spectra. The two first columns shows the results of the fitting algorithm using the water ice model (left column) or the dust model (center column). The blue area represents the ACS-MIR spectra, while the red and yellow lines represent respectively the best fit using the water ice and dust models. The right column shows for each observation (line) the associated kext vertical profile (in blue the extinction coefficient at 3.2 µm, and in red the difference between the extinction coefficient at 3.2 µm and 3.4 µm). The black arrows indicate the altitude of the extracted spectrum.

Figure 8 .

 8 Figure 8. Vertical profile of a water ice cloud (Ls = 169.8 • , lat = 77 • N, lon = 152 • W),showing the vertical variations of the IBD (a), particle size (b) and the extinction coefficient (c, with in blue the extinction coefficient at 3.2 µm, and in red the difference between the extinction coefficient at 3.2 µm and 3.4 µm). We observe that the IBD criterion detects the same water ice cloud as the fitting methodology, and that the size of the water ice particles of the cloud decrease as the altitude increases (b): from 1.2 µm at 18 km to 0.2 µm at 31 km.

Figure 9 .

 9 Figure 9. 3 µm water ice absorption band (IBD) monitoring from the ACS MIR channel in Martian Northern (a) and Southern (c) hemisphere, before and during the 2018 GDS (MY 34). Latitude and local time of observations are indicated in panels b & d

.

Figure 10 .

 10 Figure 10. Vertical profiles of the retrieved size of the water ice particles in the Martian Northern (a) and Southern (c) hemispheres, before and during the MY 34 GDS. In grey the observations without water ice detection. Latitude and local time of the observations are indicated in panels b & d.

Figure 11

 11 Figure 11. a. The altitude of the haze top as a function of latitude for the observations before the MY 34 GDS (163 • ≤ Ls ≤ 195 • ). We observe a latitude dependence of the haze top which increases equatorwards in the Southern hemisphere. Unfortunately, all the observations of the Northern hemisphere during these period are concentrated at high latitudes. b. The vertical profiles of r eff as a function of latitude for the same observations. In the Southern hemisphere, we observe that the water ice clouds altitude seems to follow the same latitudinal trend of the haze top in the equatorial region. c. & d. Same as a. & b. but during the MY 34 GDS (199 • ≤ Ls ≤ 244 • ).

4. 4

 4 During the GDS (L s > 200 • )

Figure

  Figure Vertical profiles of the measured opacity (kext = dτ /dz) at 3.4 µm in the Martian Northern (a) and Southern (c) hemispheres, before and during the MY 34 GDS. Latitude and local time of the observations are indicated in panels b & d.

Figure 13 .

 13 Figure 13. Distribution of the water ice particles size, as a function of the observed altitude and the Solar longitude. During the dust storm (Ls ≥ 200 • ) the altitude of the water ice clouds increase, and they are mostly composed by smaller particles than before the dust storm (see also figure 15).

Figure 14 .

 14 Figure 14. Typical vertical profiles of water ice clouds particle size before (a & b) and during (c & d) the GDS. Each panel represents the same profile in two manners: first the vertical lineon the left where r eff is represented using a color scale (same as figure10); and second the green lines with r eff on the x-axis and the uncertainties shown by the shadowed regions. We observe that the size of the water ice particles of the cloud decreases as the altitude increases, regardless of the mean altitude of the cloud. The GDS is characterized by a shift in altitude of the particle size distribution (∼ 30 km higher, see profile c compared to a and b), along with a decrease of particles with size between 0.5 µm and 1 µm (cf. figure15). But some GDS profiles show evidence of larger-grained layers (> 1 µm) as we can see at 60 km in the profile d.

  Distribution of the retrieved water ice particles sizes, before (a) and during (b)

Figure 16 .

 16 Figure 16. Big water ice particles (r eff ≥ 1.5 µm) during the GDS. The two first columns shows the results of the fitting algorithm using the water ice model (left column) or the dust model (center column). The blue area represents the ACS-MIR spectra, while the red and yellow lines represent respectively the best fit using the water ice and dust models. The right column shows for each observation (line) the associated kext vertical profile (in blue the extinction coefficient at 3.2 µm, and in red the difference between the extinction coefficient at 3.2 µm and 3.4 µm). The black arrows indicate the altitude of the big particle observation. We can see in this figure that the detection of these large water ice particles is robust, as the full-dust model is not able to reproduce the observed spectra, especially the bump of extinction coefficient with the

Table 1 .

 1 Identification of consecutive observations with and without 3 µm atmospheric absorption using the IBD, showing the local aspect of our observed clouds (see the vertical IBD profiles in figure 9). The first three examples are associated with significant variations in longitude, while the last example also show strong local time variations.

	L s	Latitude Longitude Local time Observation
	168.1 •	51 • S	163 • W	17h39	No IBD
	168.2 •	50 • S	139 • E	17h40	IBD ∼ 0.25 at 40 km
	192.6 •	68 • N	28 • E	17h09	IBD ∼ 0.26 at 20 km
	192.7 •	68 • N	3 • E	17h09	No IBD
	229.4 •	38 • S	136 • E	18h53	IBD ∼ 0.18 at 65 km
	229.6 •	37 • S	50 • E	18h52	No IBD
	243.1 •	54 • N	70 • E	07h50	IBD ∼ 0.22 at 60 km
	243.3 •	55 • N	45 • W	22h10	No IBD

Table 2 .

 2 Properties of profiles located outside the GDS beyond its Northern limit at

	Ls	∼	225 • . With a mean haze top altitude of 30 km, i.e. 50 km lower other measurements

Acknowledgments ExoMars is a space mission of ESA and Roscosmos. The ACS experiment is led by IKI Space Research Institute in Moscow. The project acknowledges funding by Roscosmos and CNES. Science operations of ACS are funded by Roscosmos and ESA. Science support in IKI is funded by Federal agency of science organization (FANO). MJW acknowledge the support of the D'Alembert Fellowship program. Raw ACS data are available on the ESA PSA at https://archives.esac.esa.int/psa/#!Table% 20View/ACS=instrument. Derived opacity and particles sizes can be foud at http:// dx.doi.org/10.17632/w7yff8r97s.1. wavelength.

Clancy, R. T., Wolff, M. J., Smith, M. D., Kleinböhl, A., Cantor, B. A., Murchie, S. L., . . . Sandor, B. J. (2019, August). The distribution, composition, and particle properties of Mars mesospheric aerosols: An analysis of CRISM -24-manuscript submitted to JGR: Planets


Vassa Kontouma

VENETIAN CRETE IN THE 16th CENTURY THE PERSPECTIVE OF RELIGIOUS SCIENCES * Paper presented at the workshop "Ecclesiastical Chant in Venetian

I would like to express my very warm thanks to Professor Flora Kritikou for having me associated since the beginning to this challenging project, and Professor Tassos Anastassiadis for his friendly and rigorous support. The project is huge; it is also extremely exciting for a non-musicologist of my kind. In fact, in Byzantine and Post-Byzantine culture, and especially religious culture, music holds a prominent place. However, scholars dealing with Religious Sciences very rarely have to opportunity to deal with its technical, but even historical sides. For them -for us -Byzantine and Postbyzantine music remains an unexplored continent, a terra incognita. Being myself a specialist of John of Damascus, I experienced very close this reality, or let's rather say this serious problem, witch of course has now to be overcome by collective work, and by teams like ours.

Concerning Venetian Crete in the 16 th Century, where both main European religious cultures meet and develop in peculiar ways, the challenge seems even overwhelming and could mobilize a lifetime. Fortunately, and by contrast with other regions and periods, important archives have been preserved, and many studies have already been conducted in the last century. I shall not dwell to much on that point, a complete bibliography being prepared by some of us by now. Let me only mention the most significant contributions of G. Gerola, M. Manoussakas, Z. Tsirpanlès. However, we also notice that this abundant literature is sometimes confessionally-oriented, not only because of the opacity of the exchanges between Orthodox and Catholic communities in Venetian Crete, but also because of the permeability between them, a permeability that many scholars preferred to ignore, being themselves the advocates of one confession or another. As a first step, we will thus have to examine and understand these historiographic trends and try to interpret them in order to deliver a comprehensive assessment. In my view, analysis should be conducted on following topics: -Roman hierarchies and Greek prelates united to Rome (esp. protopapades); clergy of the Patriarchate of Constantinople travelling or dwelling in Crete.

-Ecclesiastical and religious politics; exchanges with central administrations.

-Cultural life related to religious trends. But where to start? From the point of view of Religious sciences, two high priority fields could be defined: prosopography; comparative analysis of primary theological documentation.

A renewed prosopography

The prosopography of the 16 th Century Latin clergy has been sufficiently studied, even if more information could be provided on several aspects. On the contrary, the prosopography of the Orthodox clergy dwelling in Crete is much less studied, and the same goes for the Greek rite clergy united to the Roman Church. Worse, the staff constituting the hierarchy of cantors in Cretan major places of worship has been largely ignored. In that sense, I believe that examining information provided by the musical manuscripts themselves, as proposed in our project, will be quite rewarding. However, archive material, or information provided by other compositions used during the cult (homiletical texts, prefaces of printed liturgical books, etc.), as well as by lists of subscribers, shall also contribute to prosopography. Regarding archive material, it is important to bear in mind that many documents already published or studied are not necessarily exploited from the point of view that interests us -music. It will have to be reconsidered.

Comparative analysis of theological sources

Here, we are in the heart of the field of Religious sciences. Let us recall that in the 16th C., theological and controversial literature experiences interesting developments. The decisions of the Council of Florence (1439), which have never been canceled by the Latins, remain a reference, although Venetians know that they have to deal with caution with the Greek population on Crete, especially after the fall of Constantinople and the refugee's arrival. Moreover, the Catholic Church is fully engaged in the Counter-Reformation of the Council of Trent (1542/45-1563). For the Orthodox theology, one of the main centers of production is Venice, where the influence of Latin theology is strong, but not imposing as in Rome.

It is understandable that the reality of the exchanges becomes particularly complex. Thankfully, the period sees also the outstanding development of Greek typography: a good portion of the works that will carry weight in the exchanges are available in print. Though, as I will show it today, important problems remain and shall be solved, if we wish to understand what really happened. Ideally, one aim of our project would be to build up a corpus of theological works originating from or responding to the concerns of the Cretan communities of that period, but also to explore on the basis of this corpus a certain number of original themes, related of course to the world of ecclesiastical music:

-sacramental theology, -liturgical commentaries -homiletics and other theoretical texts used in a liturgical context.

Of course, the name of Ioannes-Ioseph Plousiadenos is well known. He reflects the approach of the Union. From the Greek "Orthodox" side, some theologians of Cretan origin who shall primarily hold our attention are Zacharias Skordylios, Meletios Pegas, Maximos Margounios or Ioannes Nathanael. Although not a Cretan, Gabriel Severos shall also be considered: as an archbishop of Philadelphia with headquarters in Venice, he had a major influence on 16 th C. Greek theology.

Today, I will take a single example involving, among others, the personalities of the theologian and Patriarch of Alexandria Meletios Pegas -an Orthodox of Cretan origin (ca 1551-1601)and the protopsaltes of Chandax Dèmètrios Tamias (fl. 1610-ca 1661), in order to illustrate the entanglement of problems involving historiography, manuscript and book studies, prosopography, and of course some theology. These are questions that we shall face in the context of our project. Our Simontas has nothing to do with Crete. At the time where Pegas prepared for him the copy of his homilies, he was himself in Constantinople. However, two facts shall be considered: first, the Paris gr. 1254 has many features of a text prepared for print. It is possible that the dedication letter included -which is not signed -is not designed to reach its addressee in a manuscript form, but in printed form. In that case, the laudatio in latin verses could also be part of the printing project. Second, as in the case of the first printing operation, the shipper of the manuscript is Kyrillos Loukaris. And we know that Loukaris, a Cretan himself, travelled many times in Crete. So, the 24 th of December 1598, he was preaching in honor of Saint Catherine [Chrysostomos 1939, p. 72]. In that case, the manuscript Paris gr. 1256, which in fact never reached the printing press, could have been arrived in Crete as soon as the year 1598.

The case of the

Between the very end of the 16 th century and 1666, it seems that the manuscript circulated in the circle of the protopsaltes Demetrius Tamias. I say circle, because nothing proves that Tamias had it in hand: the writing of this piece is not its own, as it can be noticed through a comparison with the original letter of support of the catholic bishop Marc Antonio Sebastiano Quirino written in 1624. One might wonder, however, why the small composition of Tamias was copied on a prominent place, on the blank page following the index and preceding the text of the homilies. Is it sheer coincidence, or is there a meaning that we have to discover? In fact, many hypotheses could be made. It has also to be reminded that Pegas himself wrote several letters to Cretans. What remains however as a fact, is the link operated between an official text of the Orthodox Pegas -a text to be used in a liturgical context, homilies -and a composition of the protopsaltes of Chandax Tamias, a man fully integrated in the Greek-Venetian Church establishment.

Meletius Pegas on music

Searching

  Paris gr. 1254 had not yet been connected to the Library of the Sultan. In my opinion, this is though a highly probable hypothesis. Manoussakas, who dedicated a very interesting and informative paper to this manuscript, located its origins in Crete -even if it was impossible for him to prove that it had been copied there. For him, three clues or evidences connected it to the island: -a possessor's note of a certain Joseph Metropolitan of Seteia, dated 1666; -a laudatio of Pegas in latin verses, indicating the existence of two printed books of the patriarch; -a composition of the protopsaltes Demetrios Tamias, copied on a blank page of the manuscript. don't wish to dwell further on the description of the codex, even it's very interesting from many points of view. Let's note that the second clue, the latin verses, is not an evidence. There is also another point, that has been elucidated by Vranousses, and later by Litsas: the ms. contains also a dedication letter to a certain Ioannes Simontas. Manoussakas could not identify this person. But through Vranousses work, we now know that he was a rich merchant from Epirus, who dwelled in the Romanian Principalities, but also in the Polnish-Lituanian Commonwealth, especially in Lv'ov and Vilnius. He was well acquainted with Kyrillos Loukaris, a disciple of Meletios Pegas, and though him, to Pegas himself. It also appears that he funded the edition of a book of Pegas, printed in Vilna in 1596 [seeLegrand, n°218].

Ms. Paris gr. 1254 So, let us begin with a Parisian manuscript, which has already much drawn the attention of scholars, the BnF Paris gr. 1254 of the 16 th -17 th Century [olim Bibliothèque royale 2418/2, quoted by error by Fabricius and Renaudot under the number 4218 1 ]. This manuscript is available through an open access digitization, so it is easy to consult it at any time. It is a very nice copy of 20 Homilies of Meletios Pegas, all being preached in Constantinople in the years 1587 and 1588. It has to be underlined that the manuscript arrived in Paris exactly a century later, in 1687 or 1688, in the context of the second mission of Antoine Galland in the East, and the Embassy of Pierre de Girardin who, in a letter written in Constantinople and dated March 10, 1687, announced to have gained access -with the help of a livournese renagade -to more than two hundred Greek and oriental manuscripts of the Library of Sultan Mustapha I st . A list of some 53 manuscripts sent than to Paris has been conserved in the ms. BnF NAF 1328. [photo > non ligatus] / bound in Paris, at that time. Through found in this list by Manoussakas, our ms. [more precisely: the hymn Πάντα τὰ ἔθνη κροτήσατε χεῖρας, ἀλαλάξατε τῷ Θεῷ ἐν φωνῇ ἀγαλλιάσεως, ἦχος α´ -preserved in two mss : Sinai 1440 ; Paris gr. 1254].

I

  sacramental theology, there are few pages dedicated on prayer. They seemed quite interesting to me, and I wish to read them with you. But before considering this text, some exterior indications: -as said, the text is little known; however, it has been quoted by Nicodemos Hagioreites, in his Pedalion, ed. Leipzig 1800, in a footnote related to the canon 75 of the Council in Trullo. ΝΒ. Nicodemos was close to Neophytos Kausokalybites.-there is another point that could be discussed: in the ms. Marcianus gr. II 156, f. 83a-96b, the anonymous theoretical writing Διάλεξις ὁποῦ κάµνει ο Διδάσκαλος µὲ τὸν µαθητὴν περὶ τῶν σηµαδίων τῆς µουσικῆς (published by Giannopoulos) is also a dialogue between a master and his pupil (though the style is quite different of that of Pegas). But let us now read and comment Pegas' text. Ὅσα γὰρ φωνᾶς, τόσα καὶ σιγᾶς, ἀΐεις νοερᾶς 2 . Ἀλλ᾽ἡµεῖς χρήζοµεν φωνῆς ὑποµιµνησκούσης, ἅπερ τῷ νοῒ προσήκει προσεύχεσθαι πρὸς Θεόν. Μ. Καὶ ὥστε εἶναι αἴσια ἃ αἰτούµεθα, ὡς δὴ µηδαµῶς µήδ᾽ἀνθρωπείαν ἀκοὴν δεδιέναι. Τοῦτο γὰρ ἔφασαν τῶν ἔξω τινές. [in marg. : διατὶ ἡ προσευχὴ δεῖται φωνῆς] Δ. Πνεύµατι δὲ προσευχόµεθα, καὶ σιγῶντες, ἐπειδήπερ πνεύµατι ὄντι τῷ Θεῷ, οὐ δυνάµεθα προσοµιλῆσαι αὐτῷ, ὅτι µὴ πνεύµατι. Πέφυκε γὰρ τὸ ὅµοιον τῷ ὁµοίῳ προσπελάζειν. Ἔχοµεν δὲ καὶ αὐτὸν τὸν Δεσπότην, µεγάλην χρησάµενον φωνῇ προσευχόµενον ἐπὶ τοῦ πάθους [see Lk 23, 46]. Μωσῆς δὲ ὁ µέγας, καὶ σιγῶν [f. 93 v ] ἀκήκοεν, ὡς µεγαλοφωνότατα προσευχόµενος• Τὶ βοᾶς πρός µε; [Ex 14, 15] Προσηύξατο καὶ ὁ Σωτήρ, τοὺς ὀφθαλµοὺς ἀράµενος, φωνὴν µὴ ἀφείς [see Lk 22, 44]. [in marg. : πῶς καὶ διατὶ ἡ προσευχόµεθα πνεύµατι] Μ. Τὴν ψαλµῳδίαν ποῦ τάττοµεν; Δ. Προσευχὴ καὶ ἡ ψαλµωδία ἔµµελος, µέλους δὲ χρῆσις ἐν τοῖς θείοις οὐκ ὀλίγη, ὁ λόγος µετὰ µέλους, τουτέστιν ἐναρµόνιος θελξίνοος πέφυκε. Καὶ γοῦν εὐχερέστερον καταµαλάττει τὴν καρδίαν, καὶ κινεῖ ὅποι ἂν βούληται, παντὸς ἀν διατιθέµενος. Ἔστι γὰρ ὅτε καὶ κατανύγει, ἔστιν ὅπου καὶ παρακαλεῖ, καὶ οἷον εὐέλπιδα τίθησι, καὶ γεραρώτερον δὲ πρὸς αἶνον τοῦ τῶν ὅλου Θεοῦ τὸ ἔµµελον. Δι᾽ὃ καὶ οὐ µόνον εἰς εὐθυµίαν κελεύει τὴν ψαλµῳδίαν παραλαµβάνει τὸ λόγιονεὐθυµεῖ γὰρ τίς φησι, ψαλλέτω [Jc 5, 13] -, ἀλλὰ καὶ εἰς δοξολογίαν τοῦ Παντοκράτορος. Ψάλλατε τῷ Θεῷ φησι, ψάλλατε. [in marg. : µουσικῆς περί•] Συνετῶς δὲ γ᾽ὅµως. Μὴ γὰρ παντοίας ψαλµῳδίας, καὶ µουσικῆς εἶδος νοµίσῃς χρήσιµον. Πέφυκε γὰρ τὸν τόνον τῆς ψυχῆς ἐκλύειν 3 µουσική, τὸ σεµνὸν ἀποβαλλοῦσα, καὶ ψιλὴν ἀναλαβοῦσα τέρψιν, τὴν µαιεύτριαν τῶν ἡδονῶν. Ὥσπερ οὖν τὸ σεµνὸν, καὶ σύµµετρον τῆς µουσικῆς εὐπρόσιτον, διὰ τὸ ἀκµαιοτέρας καὶ νεωτέρας κατασκευάζειν τὰς καρδίας, καὶ δὴ καὶ εὐτονωτέρας, εἰς ὑµνῳδίαν τῷ ποιητῇ καὶ Θεῷ, οἷον ἀνασπῶσα τὴν ψυχὴν τοῦ σώµατος (ἁρµονία γὰρ τῷ πνεύµατι οἰκειότατον, µέσην ἔχουσα φύσιν σώµατος καὶ παχύτητος, καὶ πνεύµατος ἀϋλότητος), οὕτω πάλιν ὑπέρµετρος µουσική, καὶ τῷ ἡδεῖ παρὰ τὸ µέτρον ἐνασχολουµένη, οὐχ ἡδύνει, ἀλλ᾽ἐκλύει, καὶ νεανιεύεσθαι ἐπάγει τὴν καρδίαν. Μέχρις ἑαυτῆς ἱστῶσα τὴν φοράν, καὶ µὴ ἀνεχοµένη προσαναβαίνειν ἀνώτερον τὴν διάνοιαν, ἀλλὰ κατασχοῦσα καὶ ἀνακόπτουσα, καὶ τὸ χαλεπόν, ὅτι τοῦτο λανθάνει ποιοῦσα [f. 94], ἐκθηλύνοντος τὴν καρδίαν τοῦ ἡδέως, καὶ µεθύσκοντος τῇ θέλξει τὸν νοῦν. Ἐπεὶ καὶ φωνὰς τὰς ἀνθρώποις φύσει ἐνυπαρχούσας ἀποδεχόµενοι ἐν ἐκκλησίᾳ, ὡς περιεργῳδέστερα τὰ δι᾽ὀργάνων κρούσµατά τε καὶ ἐµπνεύµατα, οἱ πατέρες ἀποδιοποµπούσι. Μ. Θαυµαστὸν οὐδὲν, εἰ ῥυθµῷ, καὶ µέτρῳ, καὶ ἁρµονίᾳ συγκραθεὶς λόγος, πολὺ δύναται. Ἐξανίστησι γὰρ ἐπὶ τὰ ὅπλα καὶ ἁρµονία, ὡς ποτ᾽Ἀλέξανδρον Τιµόθεος τὸ φρύγιον ᾄδων µέλος.Σωφρονεῖν πείθει, ὡς Πυθαγόρας µεθύοντας εἰς σωφρονισµὸν ἀνακαλέσατο, ᾄδειν κελεύσας τὸν αὐλητὴν τὸ δώριον. Καὶ δὴ καὶ καθ᾽ἑαυτὸν λόγος ἰσχυρός. Ἐπειδὴ δὲ προσευχῆς µέρος, αἴτησις, εὐχαριστία, δοξολογία, ἐξοµολόγησις, ψαλµός, αἴνεσις, καὶ αἶνος. Φέρ᾽εἴδωµεν εἰ ἐπ᾽ἀδείας κεῖται τοῖς βουλοµένοις προσεύχεσθαι ὅπως ἂν καὶ δόξῃ, ἦ κᾂν ταῦτα, πῶς τοῦτο, καὶ τίσι ῥήµασι, ἢ ποίοις ἐπὶ πράγµασι, ποιητέον προσδιωρίσθη. Δ. Ὁ Σωτὴρ ἡµῶν ὁ διδάξας ἡµᾶς, καὶ τὰ κινήµατα τῆς καρδίας προαναστέλλειν, καὶ προανακόπτειν αὐτῶν τὴν πρόοδον, αὐταῖς φαύλαις πράξεσιν, ὁ καὶ τὴν γλῶσσαν παιδαγωγήσας τῆς πρὸς ἀνθρώπους ὁµιλίας, αὐτὸς ἐξεπαίδευσε, καὶ τίσι ῥήµασι, καὶ περὶ τίνων, καὶ πῶς δεῖ προσεύχεσθαι, καὶ οἷον ἐντυγχάνειν Θεῷ. [in marg. : ὅτι ὁ Σωτὴρ ἐδίδαξεν ἡµᾶς πῶς δεῖ προσεύχεσθαι] Ὡς ἔστιν ἐπικίνδυνον ἐν ταῖς πρὸς τὸ θεῖον ἐντεύξεσι καὶ ῥηµάτων ἀµελεῖν. Ἐχρῆν οὖν, τὸν παραθαῤῥήσαντα ἡµᾶς εἰς προσευχήν, ἐπιβεβαίαις ταῖς ὑποσχέσεσιν, ὅτι ὅσα ἂν αἰτήσωµεν ἐν τῷ ὀνόµατι αὐτοῦ, ληψόµεθα παρὰ Πατρός, αὐτὸν καὶ διδάξαι τίνα ἦν, ἃ εἰκὸς αἰτεῖν, εἰ µὴ µέλλοιµεν τῶν αἰτήσεων ἀποτυγχάνειν, ἵνα µὴ, ἢ ἀνωφελῆ αἰτούµενοι παρὰ Θεοῦ Σωτῆρος, ἢ µάταια παρὰ τῆς ὄντος σοφίας, ἢ παρὰ τοῦ Παντοκράτορος µικρά, ἢ ἐπιβλαβῆ παρὰ τοῦ παναγάθου, ἢ τὰ λοιπὰ [f. 94v] τῆς ἡµετέρας ἐµπαθείας, καὶ προσπαθείας, καὶ ἀσθενείας ἀπὸ τοῦ ἀπαθοῦς, καὶ ἀπροσωπολήπτου, καὶ παντοδυνάµου, καὶ µακροθύµου, καὶ πανοικτίρµονος Θεοῦ, ἐξεγείροµεν καθ᾽ἡµῶν τὴν ἐκείνου ἀγανάκτησιν, καὶ γένηται ἡµῖν εἰς ἁµαρτίαν κατὰ Δαβὶδ ἡ προσευχὴ ἡµῶν. Μ. Πῶς οὖν ἐδίδαξεν προσεύχεσθαι ὁ Σωτήρ; Δ. Πάτερ ἡµῶν ὁ ἐν τοῖς οὐρανοῖς καὶ τὸ ἑξῆς, ἕως τοῦ ὅτι σοῦ ἐστιν ἡ βασιλεία, καὶ ἡ δύναµις, καὶ ἡ δόξα, εἰς τοὺς αἰῶνας ἀµήν. Αὕτη δὲ ἡ προσευχὴ ἣν ἐδίδαξεν ὁ Σωτὴρ, καὶ προσευχῶν ἰδία.[in marg. : τίς ἡ προσευχὴ ἣν παρέδωκεν ἡµῖν ὁ Σωτήρ] Μ. Καὶ πῶς καὶ προφῆται, καὶ ἀπόστολοι, καὶ διδάσκαλοι ἄλλοις ῥήµασιν ἐσθ᾽ὅτε τυγχάνουσι προσευξάµενοι, ἐσθ᾽ὅπου δὲ καὶ καταρώµενοι τισίν; Δ. Πᾶσα προσευχῆς δύναµις, εἰς ταῦτην ἀναφέρεται δυνάµει. [in marg. : ὅτι πᾶσα ἄλλη προσευχὴ ταύτη περιέχει δυνάµει] Εἰ γὰρ καὶ ῥήµασιν ἄλλοις δοκεῖ γίγνεσθαι, ἀλλὰ πρὸς τὸν αὐτὸν φέρεται σκοπὸν, ὅν συλλέξας ἐνταῦθα ἐξέθηκεν ὁ Σωτὴρ. Ἤ γὰρ δόξαν Θεοῦ, ἢ βοήθειαν τῆς ἡµῶν ἀσθενείας κατὰ τε παθῶν, καὶ ἐχθρῶν, καὶ τοῦ πονηροῦ, ἢ αἴτησιν περιέχει ἀγαθῶν, ἐν οἷς ἐστιν ἰδεῖν τινὰς ἐκφαντικώτερον διηγουµένους, ἢ τὰς τῆς δυνάµεως καὶ ἀγαθότητος τοῦ Θεοῦ, καὶ οἷον ἐξοµολογουµένους τὴν µεγαλοπρέπειαν αὐτοῦ εἰς δοξολογίαν τοῦ Παντοκράτορος, ἢ τὰς τῆς ἡµετέρας ἀσθενείας ἀνάγκας, τὰς τῶν παθῶν ὁρµὰς τῶν ἐχθρῶν, τὰς ἐπιβουλὰς τῶν πονηρῶν δαιµόνων, τὰς ἐπιφορὰς πρὸς τὸ ἐµποιῆσαι οἶκτόν τινα τῷ θείῳ, καὶ τρόπους τῆς βοηθείας ὑποτυποῦσιν. Ἀνάστηθι γὰρ Κύριε φησὶν εἰς τὴν βοήθειάν µου, ἔκχεον ῥοµφαίαν, καὶ σύγκλεισον ἐξ ἐναντίας τῶν καταδιωκόντων µε. Ἀναµιµνήσκουσι γὰρ καὶ Θεῷ τῶν προτέρων οἰκτιρµῶν, Ποῦ εἰσι τὰ ἐλέη σου τὰ ἀρχαῖα Κύριε φάσκοντες. Ἔστι δ᾽ὅπου καὶ δικαιολογίας ἐπιπλέκουσιν, Ἡµεῖς γὰρ λαός σου, [f. 95] καὶ πρόβατα νοµῆς σου, ἃ καὶ τὴν ἰδίαν εὐγνωµοσύνην παρίστησιν. Εἰ δὲ σοι καὶ ἀρὰς ἐπαρᾶσθαι φαίνεταί τις, τῷ τοῦ λόγου εἴδει ἐχρήσατο εἰς µελλόντων πρόῤῥησιν, τουτέστι προσευξάµενος, ἢ εἰπεῖν οἰκειότερον δοκῶν προσεύχεσθαι, προεφήτευσεν, ὡς Δαβὶδ πολλαχοῦ, καὶ Παῦλος ἐπὶ τοῦ ἀρχιερέως, ἢλεγξε γὰρ ὡς τοῖχον κεκονιαµένον, καὶ προεφήτευσεν ὅτι τύπτειν αὐτὸν ὁ Θεὸς ἔµµελλεν, καὶ καταρώµενος δὲ οὐ κατὰ τοῦ πλάσµατος φέρονται τοῦ Θεοῦ, ἀλλὰ κατὰ τῆς ἐµφολευούσης τῷ πλάσµατι κακίας, καὶ κατ᾽αὐτοῦ τοῦ ἀρχεκάκου πονηροῦ, τοῦ καθοπλίζοντος εἰς κακίαν. Λέγουσι δὲ ταῦτα ἐπιποθοῦντες, µὴ τὸν ἄνθρωπον, ἀλλὰ τὴν κακίαν ἀπολέσθαι, ἵνα ἐκποδῶν γενοµένης, τὸ τοῦ Θεοῦ θέληµα γένηται, καὶ ἔλθη ἐφ᾽ἡµᾶς ἡ βασιλεία αὐτοῦ, ἃ πάντα τὴν τοῦ Θεοῦ δόξαν ἀποβλέπει.

	Text -Meletios Pegas, 'On Prayer'
	for this link -but having not yet elucidate the problem, as I must confess -I found
	an interesting element which I shall present to you by now.
	It has to do with another work of Pegas, namely his Ὀρθόδοξος διδασκαλία published in 1769
	under the supervision of Neophytos Kausokalybites (1713-1784). This is a very rich, but also
	little known work, since the edition is very rare. In fact, by now, it's easier to have access to a

ms. of it, namely the BL Add 10074, which is digitized and online. Fortunately, a copy of the book is preserved in the Library of the Parliament, in Athens, and I consulted it few days ago. The work of Pegas is a dialogue between a master (διδάσκαλος) and his pupil (µαθητής) on various issues of Orthodox faith. In the third part of the book, which deals mainly with Christian practice and • BL Add. 10074, ff. 93-95 [http://www.bl.uk/manuscripts/FullDisplay.aspx?ref=Add_MS_10074] • Ed. Ὀρθόδοξος διδασκαλία, συγγραφεῖσα µὲν παρὰ τοῦ µακαριωτάτου καὶ σοφωτάτου Πατριάρχου τῆς µεγάλης Πόλεως Ἀλεξανδρείας κυρίου Μελετίου τοῦ Πηγᾶ… νῦν δὲ τὸ δεύτερον τύποις ἐκδοθεῖσα ἐπὶ τῆς θεοφρουρήτου ἡγεµονίας… Γρηγορίου Ἀλεξάνδρου Γκίκα Βοεβόδα, ἐπιµελείᾳ καὶ δαπάνῃ τοῦ … Ἱεροσολύµων Πατριάρχου κυρίου Ἐφραὶµ ἐν τῇ Τυπογραφίᾳ τοῦ … Μητροπολίτου κυρίου Γρηγορίου … δι᾽ἐπιδιορθώσεως τοῦ … Πρωτοσυγκέλλου Καισαρίου, ˛αψξθ´ παρὰ Γρηγορίῳ ἱεροµονάχῳ τυπ., p. σκθ´-σλδ´. [= Βουλή ΣΒΕ 1769 ΟΡΘ] • Cit. Nicodemos Hagioreites, Πηδάλιον τῆς νοητῆς νηός ..., Athènes 1841 2 , p. 164; Zante 1864 3 , p. 286. • Original materials: https://drive.google.com/drive/folders/1VwDl0Wk_HW085D5VIu_T42N2ZVdNcSxJ?usp=sharing Μ. Περὶ προσευχῆς νῦν λέγωµεν. Δ. Ἔστι δὲ καὶ ἡ προσευχὴ ἔντευξις νοῦ πρὸς Θεὸν τῶν ἐπιγείων ὑπεραρθέντος, εἴτε σιγῶσα, εἴτε καὶ διὰ φωνῆς αἰτοῦσά τι, ἢ εὐχαριστοῦσα ἐπὶ τοῖς λη[φ]θεῖσιν, ἢ γεραίρουσα καὶ ὑµνοῦσα τὸν εὐεργέτην, ἢ τὰ µεγαλεῖα τοῦ Θεοῦ, ἢ καὶ τὰ ἑαυτῆς ὑστερήµατα ἐξοµολογουµένη. Μ. Τὶ δεῖ φωνῆς, εἰ αὐτάρκης σιγή; Δ. Θεὸς οὐ δεῖται φωνῆς.

Renaudot, Gennadii, p. 91.

Synesius, Hymn IV : Ὑµνῶ σε, µάκαρ, καὶ διὰ φωνᾶς, ὑµνῶ σε, µάκαρ, καὶ διὰ σιγᾶς. Ὅσα γὰρ φωνᾶς, τόσα καὶ σιγᾶς, ἀΐεις νοερᾶς. [ed. Synesii, De dono, Bâle 1563, p. 144].

John Chrysostom, Theophrastos, etc.


Zakariya Ghalmane

Chantal Cherifi

Hocine Cherifi

Mohammed El Hassouni

Searching for Influential Nodes in Modular Networks

Introduction

Ranking nodes according to their importance is a fundamental issue in the research on complex networks. While many centrality measures have been proposed over the years based on local or global topological properties of the networks, few studies have considered the influence of the community structure. Despite the fact that many realworld networks exhibit a modular organization, this property is almost always ignored in the design of the ranking strategies. In a modular network, we can distinguish two types of influences for a node [START_REF] Ghalmane | Centrality in modular networks[END_REF]: A local influence on the nodes belonging to its own community through the intra-community links, and a global influence on the nodes of the others communities through the inter-community links. Therefore, centrality measures should not be represented by a simple scalar value but rather by a two-dimensional vector. Its first component measures the local influence of the node, while the second component measures its global influence. Based on this assumption, we propose to extend all the classical centrality measures to modular networks [START_REF] Ghalmane | Centrality in complex networks with overlapping community structure[END_REF]. We need to consider two cases corresponding to the nature of the communities (with overlapping nodes or not). Thus, in the following, "Modular Centrality" stands for centrality in modular networks with non-overlapping communities, while "Overlapping Modular Centrality" refers to centrality in modular networks with overlapping communities. We conducted a series of experiments in order to test the relevancy of the Modular centrality and the Overlapping Modular centrality as compared to their classical counterpart. Considering the most influential centrality measures (Degree, Betweenness, Eigenvector, Closeness), the local and global components have been evaluated separately. Additionally, a straightforward combination of both components (modulus of the two-dimensional vector) has been tested. Experiments have been conducted on synthetic networks with controlled community structure, and on real-world networks in an epidemic spreading scenario using the SIR model. Results show that the spreaders identified by the proposed approach are more influential than those targeted by the standard centrality measures.

Proposed approach

The global component of the vector is defined in the same way for both type of community structure (overlapping and non-overlapping). It is computed on the global network obtained by removing all the intra-community links from the original network. Remaining isolated nodes are also removed. The local component computation depends on the type of the network. In networks with non-overlapping community structure, it is computed on the local graph obtained by removing all the inter-community links from the original network. In networks with overlapping communities, the local component of a node is computed according to its nature. For a non-overlapping node, as previously, only members of its community are considered. For an overlapping node, all the communities that the node belongs to are merged in a single community.

Due to the lack of space, we only present the algorithm used to compute the Modular centrality.

Step 1. Choose a standard centrality measure β .

Step 2. Remove all the inter-community edges from the original network G to obtain the set of communities C forming the local network G l .

Step 3. Compute the local measure β L for each node in its own community.

Step 4. Remove all the intra-community edges from the original network to reveal the set of connected components S formed by the inter-community links.

Step 5. Form the global network G g based on the union of all the connected component. Isolated nodes are removed from this network and their global centrality value is set to 0.

Step 6. Compute the global measure β G of the nodes linking the communities based on each component of the global network.

Step 7. Add β L and β G to the Modular centrality vector B M . where the number of overlapping nodes on is fixed to 5% of the size of the network, and the community membership parameter om is equal to 5% of the total number of communities.

We report the results of the Degree centrality in Figure 1. The ∆ r values between the various measures (Local component, Global component, and the modulus of either the Modular Degree centrality or the Overlapping Modular Degree centrality) and the classical Degree centrality have been computed while varying both the fraction of initial spreaders and the mixing proportion parameter µ. For low values of µ, the communities are well separated (few intercommunity links), while high values of µ indicates a weak community structure. Results for networks with strong community structure are illustrated in the left panel of Figure 1. We notice that in both type of networks, ∆ r is always positive for the local component , while it is always negative for the global component. Indeed, in networks with strong community structure the local influence predominates. The same type of results are shown in the right panel of Figure 1 for networks with weak community structure strength. This time, one can notice that ∆ r is always positive for the global component, while it is negative for the local component. Indeed, in this situation, the global influence takes over the local influence. Furthermore, we notice that the measure that combines both components is always the most efficient in any case.

To summarize, in order to evaluate efficiently the centrality of nodes in networks with community structure (overlapping communities and non-overlapping communities), we cannot rely on the traditional centrality measures that do not take into account this topological property. It is necessary to consider and combine properly the two types of influence (local, global) occurring in such networks.

Fig. 1 :

 1 Fig.1: Relative difference of the outbreak size ∆ r as a function of the portion of the initial spreaders f 0 . Where ∆ r = (R c -R s /R s ), R c and R s are the final number of recovered nodes for the centrality measure under test and the standard Degree centrality. Each value is the average of 100 SIR simulations per method and fraction of initially infected nodes. Positive value of ∆ r means that the centrality under test is more efficient than the standard centrality. Synthetic networks generated with the LFR algorithm are used with various community structure strength µ. (a) is for networks with non-overlapping community structure. (b) is for networks with overlapping community structure, where the number of overlapping nodes on is fixed to 5% of the size of the network, and the community membership parameter om is equal to 5% of the total number of communities.


Zakariya Ghalmane
email: zakaria.ghalmane@gmail.com

Chantal Cherifi

Hocine Cherifi

Mohammed El Hassouni

A backbone extraction method for complex weighted networks

Introduction

Network science provides effective tools to model and analyze complex systems. However, the increasing size of real-world networks becomes a major obstacle in order to understand their structure and topological features. Therefore, reducing the original network into a smaller one while preserving its information is an important issue. Extracting the so-called backbone of a network is a very challenging problem that is generally solved either by coarse-graining or filter-based methods. Coarse-graining methods reduce the network size by grouping similar nodes, while filter-based methods map the network by discarding nodes or edges based on a statistical property. In this work, we propose and investigate one filter-based method exploiting the overlapping community structure in order to extract the backbone in weighted networks. In the proposed method, called "overlapping nodes ego backbone", the backbone is formed simply from the set of overlapping nodes and their neighbors. It is based on the results of a previous study [START_REF] Ghalmane | Exploring Hubs and Overlapping Nodes Interactions in Modular Complex Networks[END_REF] showing that the overlapping nodes are neighbors of the highly connected nodes (hubs) of the network. Indeed, hubs and overlapping nodes are located at the heart of the network. In this method, the links with low weights are removed from the network as long as a backbone with a single connected component is preserved. Experiments have been performed on real-world weighted networks originating from various domains (social, co-appearance, collaboration, biological, and technological) and different sizes. Results of the comparison with the disparity filter method [START_REF] Serrano | Extracting the multiscale backbone of complex weighted networks[END_REF], which is considered as one of the most influential alternative filtering methods demonstrate the greater ability of the proposed backbone extraction method to uncover the most relevant parts of the network.

Methods

In this study, the backbone of weighted networks is extracted using a filter-based algorithm. It is called the "overlapping nodes ego backbone" which consists of defining the set of overlapping nodes and their neighbors as the network backbone. Let's consider a network G(V, E), where

V = {v 1 , v 2 , ...., v n } and E = {(v i , v j ) \ v i , v j ∈ V } denotes Table 1.
N is the size of the network. on is the fraction of overlapping nodes. A n represents the estimated values the proportion of common nodes of two backbones. A t is the proportion of the 10% of the most highly ranked nodes belonging to the backbone. < β > is the average node betweenness. OE stands for the overlapping nodes ego backbone, while DF stands for the disparity filter backbone. Each value is the average of 10 SLPA simulation runs. The standard deviation is excluded from this table due to its very small value (it is around 10 -3 ). the set of nodes and edges respectively. The algorithm of the model used to extract the backbone is detailed as follows:

Network N A n (%) A t (%) < β > OE-
Step 1: If not known, the community structure of the network using a given overlapping community detection algorithm is uncovered.

Step 2: Form the overlapping nodes ego sub-network. It is made of the union of the set of overlapping nodes and the set of their neighbors. It is obtained by removing all nodes that do not belong to one of the two sets.

Step 3: Remove the edges with low weights from the overlapping ego sub-network. To do so, edges are sorted in decreasing order according to their weights. Then, edges with low weights are removed as long as the sub-network component is not split into two components. This ensures that the backbone is formed with a single component.

Step 4: Control the size of the overlapping ego backbone with a parameter s. This parameter allows to preserve only the top-ranked nodes of this backbone. To this end, all the nodes of the overlapping nodes ego backbone are sorted in decreasing order according to the weighted degree centrality [START_REF] Opsahl | Node centrality in weighted networks: Generalizing degree and shortest paths[END_REF]. After that, according to the value of this threshold parameter, the nodes with low degrees are removed from the network.

Results

A set of experiments is performed to compare the overlapping nodes ego backbone with the disparity filter which is one of the most effective alternative backbones. Results of the comparative evaluation of the backbone extraction methods are presented and analyzed. Samples of various real-world networks (social, co-appearance, biological, technological and collaboration networks) have been used in order to cover a wide range of situations. The Speaker-Listener Label Propagation Algorithm (SLPA) [START_REF] Xie | Slpa: Uncovering overlapping communities in social networks via a speaker-listener interaction dynamic process[END_REF] is used to uncover the overlapping community structure of the networks. Note that in all the experiments, the size of the backbone is limited to 30% of the size of the original network by setting the parameter s to 0.3. Accordingly, the parameter α is tuned in order to obtain a disparity filter backbone of the same size. At first, the proportion of common nodes extracted by the two backbone extraction methods is computed. It is defined as the fraction of the size of the intersection between the two sets divided by their size. Our goal is to check if they extract the same set of nodes or not. Table 1 reports the proportion of common nodes computed between the proposed backbone and the disparity filter backbone. Its values exhibit usually medium values while it has high values in some networks. The main difference lies in the fact that the disparity filter concentrates on links while the proposed method is based on nodes in its extraction process. This can be visualized in Les Miserables network illustrated in Figure 1. In this figure, the overlapping nodes ego backbone is represented in (a), while the disparity filter backbone is reported in (b). The color of nodes refers to the communities to which they belong. The overlapping nodes are colored in grey. The size of the nodes is proportional to their weighted degree and the thickness of the links is proportional to their weights. One can notice from this figure that the disparity filter backbone misses some very important nodes such as "Marius" and "Cosette" that are considered as one of the main characters in the Victor Hugo's novel. Thus, the backbone obtained by the proposed approach preserves almost all high-connectivity nodes and essential connections.

(a) (b)

Furthermore, we also check if the top-ranked nodes of the original network are preserved in the backbones. The set of the 10% top-ranked nodes according to their weighted degree is computed in the original network. It is compared to the set of topranked nodes of the same size extracted from the backbones. Results reported in Table 1 show that both sets are identical most of the time for the proposed backbone. This remark is not valid for the disparity filter backbone which preserves a smaller proportion of the top-ranked nodes. It focuses on links rather than on nodes. That is the main difference between the proposed backbone and the disparity filter backbone that explain its lower ability to preserve hubs.

In the second part of the experiments, the performance of the two backbone extraction methods is compared by measuring the average betweenness. Table 1 reports the results for all networks under test. The average betweenness indicates how much information can pass through the nodes of the backbone. The values of the average betweenness of the proposed backbone are higher than the ones computed in the disparity filter backbone. This implies that the nodes extracted by the overlapping nodes ego backbone act as a better information gateway of the original network as compared to the disparity filter backbone. Its performance is higher than the disparity filter backbone for all the tested empirical networks. This confirms its ability to preserve nodes playing a major role in the network.

Fig. 1 .

 1 Fig. 1. The backbone extraction of different methods for Les Miserables network. (a) overlapping nodes ego backbone, (b) disparity filter backbone. Nodes are highlighted in different colors according to the community they belong to.Nodes with the same color belong to the same community while those in gray represent the overlapping nodes. The size of the nodes is proportional to their weighted degree, while the size of links is proportional to their weights. The community structure is revealed using the SLPA detection algorithm.