Sébastien Rodriguez
email: rodriguez@obs.u-bordeaux1.fr

P Paillou

M Dobrijevic

G Ruffié

P Coll

J M Bernard

P Encrenaz

Impact of aerosols present in Titan's atmosphere on the CASSINI radar experiment

Keywords: Titan, satellites, atmospheres, surfaces, satellite, radar

Simulations of Titan's atmospheric transmission and surface reflectivity have been developed in order to estimate how Titan's atmosphere and surface properties could affect performances of the Cassini radar experiment. In this paper we present a selection of models for Titan's haze, vertical rain distribution, and surface composition implemented in our simulations. We collected dielectric constant values for the Cassini radar wavelength (∼ 2.2 cm) for materials of interest for Titan: liquid methane, liquid mixture of methane-ethane, water ice and light hydrocarbon ices. Due to the lack of permittivity values for Titan's haze particles in the microwave range, we performed dielectric constant (ε r ) measurements around 2.2 cm on tholins synthesized in laboratory.

We obtained a real part of ε r in the range of 2-2.5 and a loss tangent between 10 -3 and 5.10 -2 . By combining aerosol distribution models (with hypothetical condensation at low altitudes) to surface models, we find the following results: (1) Aerosol-only atmospheres should cause no loss and are essentially transparent for Cassini radar, as expected by former analysis. (2) However, if clouds are present, some atmospheric models generate significant attenuation that can reach -50 dB, well below the sensitivity threshold of the receiver. In such cases, a 13.78 GHz radar would not be able to measure echoes coming from the surface. We thus warn about possible risks of misinterpretation if a "wet atmosphere" is not taken into account. (3) Rough surface scattering leads to a typical response of ∼ -17 dB. These results will have important implications on future Cassini radar data analysis.

Introduction

Titan is the second largest satellite in the solar system. It is the only one known to possess an extended and dense atmosphere, hiding its surface. Primarily composed of N 2 with less than 10% CH 4 and 1% H 2 , Titan's thick atmosphere is subject to an active chemistry induced by solar insolation, solar wind and charged particles from the saturnian magnetosphere. This chemistry results in the production of a great diversity of hydrocarbons and nitriles in the stratosphere with increasing complexity and molecular weight [START_REF] Yung | Photochemistry of the atmosphere of Titan: Comparison between model and observations[END_REF][START_REF] Toublanc | Photochemical modeling of Titan's atmosphere[END_REF][START_REF] Lara | Vertical distribution of Titan's atmospheric neutral constituents[END_REF]1998).

Settling in the atmosphere, chemistry end products form an extensive system of organic aerosol haze responsible for Titan's characteristic orange color and hiding the lower atmosphere and the surface at UV-visible-NIR wavelengths. It is also possible that lighter hydrocarbons or nitriles diffuse downwards and condense as liquids or solids on aerosols below altitudes of 85 km.

Ground-based observations, as well as Pioneer and Voyager missions, have brought a great number of constraints on the haze properties but revealed the difficulty to precisely determine not only its horizontal and vertical structure but also its chemical composition. Concerning the surface, radar observations and microwave radiometry or near-infrared studies only reveal the presence of a heterogeneous surface plausibly composed of randomly distributed patches of water ice and organic compounds, solid or liquid [START_REF] Muhleman | Radar reflectivity of Titan[END_REF][START_REF] Coustenis | Titan surface: Composition and variability from its near-infrared albedo[END_REF][START_REF] Ishimaru | Scattering and absorption of a wave by a single particle[END_REF]2001). The precise nature of Titan's surface is still completely unknown. With the hope of disclosing the remaining questions about its composition, the CASSINI-HUYGENS spacecraft -a joint NASA/ESA/ASI mission -was launched in 1997 and will reach Saturn in 2004. The spacecraft, composed of an orbiter and a probe, will favour the exploration of Titan. A multipurpose radar was included in the scientific payload of the Cassini orbiter. Three active modes (SAR -for Synthetic Aperture Radar -, altimeter and scatterometer) and one passive mode (radiometer) will be used within the Radar experiment. Thanks to its active modes, the Radar instrument is expected to be able to observe Titan's surface through its dense atmosphere and thus determine whether oceans are present and map the geology and the topography of the solid surface of Titan.

These scientific goals rely on analysis of the received radar echoes and the analysis depends on models describing microwave transmission in the atmosphere and on surface reflectivity. In this paper, we present a quantitative study of the possible impact of particles present in Titan's atmosphere on the Cassini Radar experiment and some results about surface reflectivity. We first present the models of Titan's surface and atmosphere we selected as a basis for our computations. Then, in section 3 we show results of experiments designed to determine the electromagnetic properties of titanian aerosol analogs -called tholins. We finally discuss in section 4 the possible behaviour of the Cassini Radar in presence of atmospheric haze and rain on the basis of simple simulation of radar wave propagation for various models for aerosol and rain particles formation. We also show some simulations of the backscattered power by smooth and rough surfaces covered with tholins.

2 Distribution of condensates in Titan's atmosphere and on its surface 2.1 Meso-and stratosphere: vertical distribution of aerosol haze

Since 1973, there is observational evidence for the existence of an aerosol component in Titan's upper atmosphere. Particles with size greater than molecules were invoked to reconcile models of Titan's upper atmosphere and polarimetric and photometric observations [START_REF] Veverka | Titan: Polarimetric evidence for an optically thick atmosphere[END_REF][START_REF] Zellner | The polarization of Titan[END_REF][START_REF] Rages | Titan aerosols: Optical properties and vertical distribution[END_REF]. Several radiative transfer models incorporating aerosols were published, considering the shape and optical properties of these aerosols as free parameters, as well as their vertical distribution in terms of size and number density. These models were regularly adjusted to be consistent with the growing number of observational data of increasing resolution. First generation models [START_REF] Danielson | An inversion in the atmosphere of Titan[END_REF][START_REF] Podolak | Axel dust on Saturn and Titan[END_REF]) assumed a homogeneous atmosphere where dust particles and gas were uniformly mixed above the surface of Titan. [START_REF] Podolak | An inhomogeneous scattering model of Titan's atmosphere[END_REF], [START_REF] Rages | Titan aerosols: Optical properties and vertical distribution[END_REF], [START_REF] Tomasko | Preliminary results of polarimetry and photometry of Titan at large phase angles from Pioneer 11[END_REF], and [START_REF] Rages | Vertical distribution of scattering hazes in Titan's upper atmosphere[END_REF] used in their calculations multi-layer models and [START_REF] Tomasko | Photometry and polarimetry of Titan: Pioneer 11 observations and their implications for aerosol properties[END_REF] used the first totally inhomogeneous models with a gradient in particle size with the optical depth. They constrained the aerosol mean radius to between 0.1 µm and 0.5 µm, but always failed to simultaneously fit the polarimetric and photometric data acquired by Pioneer and Voyager missions when considering spherical particles of single size mode.

Further studies greatly improved the model fit to data with the use of more com- (1989), [START_REF] Frère | Microphysical modeling of Titan's aerosols: application to the in situ analysis[END_REF][START_REF] Cabane | Formation and growth of photochemical aerosols in Titan's atmosphere[END_REF] are quite similar. The recent microphysical modeling taking into account aerosol growth into fractal aggregates [START_REF] Rannou | Growth of aerosols in Titan's atmosphere and related time scales: a stochastic approach[END_REF][START_REF] Cabane | Fractal aggregates in Titan's atmosphere[END_REF][START_REF] Rannou | Titan's geometric albedo: role of the fractal structure of the aerosols[END_REF] gives concentrations and effective profiles (Fig. 1 and 3 in [START_REF] Cabane | Fractal aggregates in Titan's atmosphere[END_REF]) close to those given by classical microphysics dealing with spherical particles (close enough for the precision in radius and concentration we need), so we will not consider this model here.

Besides in the wavelengths range we consider, fractal nature of micron-sized scatter-ers would not have significant effect on scattering and absorption calculations. Figure 1-(a) shows profiles of aerosol radius and concentration versus altitude resulting from computation by [START_REF] Mckay | The thermal structure of Titan's atmosphere[END_REF], [START_REF] Frère | Microphysical modeling of Titan's aerosols: application to the in situ analysis[END_REF] and [START_REF] Cabane | Formation and growth of photochemical aerosols in Titan's atmosphere[END_REF].

2.2 Low stratosphere and troposphere: models for clouds and rain

After a rapid lapse rate below 120 km altitude, the thermal profile of Titan reaches a minimum of 74 K at the tropopause (42 km). This thermodynamical cold trap region certainly induces saturation (even supersaturation for the dominant and more volatile species) and probably gas/liquid or solid phase transitions. These transitions should occur for most of the organics and nitriles present in gas phase if seed nuclei are present [START_REF] Sagan | Production and condensation of organic gases in the atmosphere of Titan[END_REF][START_REF] Frère | Microphysical modeling of Titan's aerosols: application to the in situ analysis[END_REF]). If nucleation can be activated, the most relevant scenario is that individual aerosol particles may act as condensation nuclei, accrete hydrocarbons and nitriles with more or less efficiency depending on solubility properties of the aerosols, and rain out when they pass through saturated regions of the troposphere (Lorenz 1993a;[START_REF] Mckay | Physical properties of the organic aerosols and clouds on Titan[END_REF]. However, observational evidence for a dense, persistent and ubiquitous cloud coverage in the supersaturated regions

is not yet conclusive. [START_REF] Griffith | Transient clouds in Titan's lower stratosphere[END_REF][START_REF] Griffith | Detection of daily clouds on Titan[END_REF] hemispheric integrated observations of Titan suggested a cloud cover. Titan's large cloud system that might have been observed in September 1995 [START_REF] Griffith | Transient clouds in Titan's lower stratosphere[END_REF] displayed cloud tops at an altitude of z ∼ 15 ± 10 km, covering about 10% of Titan's disk, and seemed to live for more than 2 days. Analysis of more recent spectra [START_REF] Griffith | Detection of daily clouds on Titan[END_REF] suggested another identification of tropospheric clouds. It revealed that clouds should reside at the altitude of z ∼ 27 km. These clouds covered ∼ 0.5 ± 1% of the moon's disk, and dissipated in only 2 hours. Thus, if clouds exist, they seem to be patchy, occupying only a fraction of Titan's disc. It may also be an intense but transient and fickle phenomena, making them even more difficult to observe and firmly identify.

Several models treating condensation in Titan's saturation region have been developed [START_REF] Toon | Methane rain on Titan[END_REF][START_REF] Frère | Microphysical modeling of Titan's aerosols: application to the in situ analysis[END_REF][START_REF] Courtin | Titan's thermal emission spectrum: reanalysis of the Voyager infrared measurements[END_REF][START_REF] Samuelson | Steady-state model for methane condensation in Titan's troposphere[END_REF], aiming at the determination of cloud properties. [START_REF] Toon | Methane rain on Titan[END_REF] and [START_REF] Courtin | Titan's thermal emission spectrum: reanalysis of the Voyager infrared measurements[END_REF] studied the characteristics of hypothetical pure methane clouds, considering atmospheric radiative properties. In particular, [START_REF] Toon | Methane rain on Titan[END_REF] assumed that if the mixing ratio of methane exceedzd 2% by volume near and below the tropopause, it would reach (and even exceed) saturation level, triggering its probable condensation.

Re-examining the Voyager IRIS infrared spectra of Titan, [START_REF] Toon | Methane rain on Titan[END_REF] obtained an optimal fit when adding a methane cloud composed of droplets with a radius between 50 µm and 3 mm and a density between 1 and 3500 m -3 . This cloud cover, that can be considered as an ubiquitous homogeneous layer in addition to the aerosol haze, should extend from 10 km to 30 km. The new re-interpretation of IRIS spectra led [START_REF] Courtin | Titan's thermal emission spectrum: reanalysis of the Voyager infrared measurements[END_REF] to quite different conclusions. Their results, in best agreement with the data, did not contain a cloud layer. They found however that if a condensed CH 4 cloud is added, it must have a mean particles radius of about 50 -60 µm and be located near the tropopause (about 40 km in altitude), though they could not put constraints on its vertical extent. A combination of cloud characteristics inferred from [START_REF] Toon | Methane rain on Titan[END_REF] and [START_REF] Courtin | Titan's thermal emission spectrum: reanalysis of the Voyager infrared measurements[END_REF] are summarized in Table 1.

[ Lorenz (1993a)). Variations of the droplet density follow those of the radius but in the opposite way due to collection processes. More recent studies of rain occurence in Titan's lower atmosphere [START_REF] Samuelson | Steady-state model for methane condensation in Titan's troposphere[END_REF] led to similar conclusions as those of [START_REF] Frère | Microphysical modeling of Titan's aerosols: application to the in situ analysis[END_REF]. They obtained the same altitude for the maximum particle size (z ∼ 11 -12 km) and roughly the same size profiles versus altitude. The experimental work of [START_REF] Mckay | Elemental composition, solubility, and optical properties of Titan's organic haze[END_REF] and recently Coll et al. (1999a) argued in favour of droplet chemical structure and size proposed by [START_REF] Frère | Microphysical modeling of Titan's aerosols: application to the in situ analysis[END_REF] (Fig.

1-(b))

. [START_REF] Mckay | Elemental composition, solubility, and optical properties of Titan's organic haze[END_REF] and Coll et al. (1999a) [Figure 1]

Surface

Very little is known about the surface of Titan, which is hidden from view by the organic haze. Voyager 1 and 2 flybys allowed some progress in the knowledge of the puzzling nature of the satellite's surface, though they failed to directly reveal surface details.

Surface properties were only indirectly inferred from the atmosphere characterization performed by the spacecrafts. Voyager 1 and 2 flybys allowed the determination of the atmospheric properties with an accuracy such that it was possible to propose some new and more relevant models for Titan's surface nature and to postulate the existence of a deep, global ocean of hydrocarbon [START_REF] Lunine | Ethane ocean on Titan[END_REF]. The fact that methane is likely to be depleted in the stratosphere within barely 10 million years due to a photolytical sink, coupled with the fact that Titan's surface temperature is close to the triple point of methane, supports the idea that Titan should possess a liquid hydrocarbon reservoir at its surface or at least in its subsurface [START_REF] Eshleman | Is Titan wet or dry?[END_REF].

Observations have become available which suggest that Titan is not covered by an ubiquitous ocean. Subsequent ground-based radar observations, passive microwave radiometry and near-infrared observations give us today a new insight in the current understanding of Titan's surface. Direct radar sensing of Titan's surface at a wavelength of 3.5 cm [START_REF] Muhleman | Radar reflectivity of Titan[END_REF]) revealed a surprisingly high reflectivity (much higher than the reflectivity of a global methane-ethane ocean) but still lower than that of the icy Galilean satellites. Radar reflectivity was also extremely variable from one night to the other, suggesting a heterogeneous surface. Passive radiometry undertaken at the same time by [START_REF] Muhleman | Radar reflectivity of Titan[END_REF] suggested an emissivity of about 0.9 at similar wavelengths (higher than those of Europa and Ganymede, but similar to that of Callisto). The only way they found to reconcile high emissivity and high reflectivity was to consider a surface covered with "dirty" ice (ice contaminated by organic compounds). This hypothesis was recently confirmed with the help of near-infrared observations from HST (Hubble Space Telescope), CFH (Canada-France-Hawaii) and, AEOS (Advanced Electro Optical System) telescopes in the methane-window regions (0.94, 1.08, 1.28, 1.58, 2 and 5 µm), where it may be possible to probe the surface between methane absorption bands. These observations are consistent with dirty ice, including areas of hydrocarbon seas (Lorenz 1993b;[START_REF] Lorenz | Titan's surface reviewed: the nature of bright and dark terrain[END_REF]. [START_REF] Coustenis | Images of Titan at 1.3 and 1.6 µm with adaptative optics at the CFHT[END_REF] have investigated the nature of ice present at the surface of Titan.

They took images (albedo maps) of Titan's surface at 1.3 and 1.6 µm with a resolution high enough to resolve Titan's disk with 20 pixels. They observed the same bright feature at the equator that was previously observed by the HST [START_REF] Smith | Titan's surface, revealed by HST imaging[END_REF] and the Keck I telescope [START_REF] Gibbard | Titan: high resolution speckle images from the Keck telescope[END_REF]. That allowed them to propose some candidates spectrally relevant for the icy composition of the different (bright/dark) regions observed. By comparison to other surface spectra [START_REF] Coustenis | Titan surface: Composition and variability from its near-infrared albedo[END_REF][START_REF] Ishimaru | Scattering and absorption of a wave by a single particle[END_REF], they suggested the presence of methane (or ethane) frost, ammonia ice, and water ice on Titan's surface, probably covered by sediments of organics, as foreseen by photochemical atmospheric models. [START_REF] Toon | A physical model of Titan's clouds[END_REF] predicted indeed that the aerosols produced in the upper stratosphere should settle and deposit on the ground at the rate of 0.1 µm each year, to form a layer of about 400 m over geological times. The hydrocarbon and nitrile liquids they drag towards the surface are expected to stream down the relief and fill lakes or seas, whereas solid organic cores of the droplets should form sedimentary layers. It is nevertheless impossible to discriminate whether aerosols are intimately mixed with ice or whether they constitute a dark organic layer over an icy surface with some bright regions of exposed ice. The aerosols falling over a lake or a sea do not sink and create an organic layer, due to their poor solubility into hydrocarbon liquids.

3 Electromagnetic characterization of titanian materials

Electromagnetic characterization of tholins

Electric properties of titanian aerosol analogs were often measured in visible-UV range, but are poorly known in the microwave range. The only published value for dielectric constant at GHz frequencies is the one taken from [START_REF] Khare | Optical constants of organic tholins produced in a simulated atmosphere: From soft X-ray to microwave frequencies[END_REF] measurements.

They found a permittivity of 4.71 -j0.013 at f ∼ 300 GHz. Considering that tholins are major compounds of Titan's atmosphere susceptible to interact with Cassini radar electromagnetic wave, we performed a set of measurements of aerosols' analogs permittivity in the GHz frequency range.

Synthesis of tholins

Since the early work of [START_REF] Khare | Red clouds in reducing atmospheres[END_REF], many laboratory simulations of Titan's atmosphere have been achieved. Such experiments were conducted by irradiation with UV light, electrical discharge, or energetic electrons, of a gas mixture close to the Titan's atmosphere composition, isolated from contamination in a glass recipient -the reactor. Without any exceptions, these simulations produced a solid organic material -termed tholin -which has optical properties similar to those needed to match the geometric albedo of Titan [START_REF] Rages | Titan aerosols: Optical properties and vertical distribution[END_REF][START_REF] Mckay | The thermal structure of Titan's atmosphere[END_REF].

In order to get tholin samples for further dielectric measurements, we conducted experiments in the LISA laboratory where a reactor essentially dedicated to the study of the titanian atmospheric chemistry was designed. A detailed description of the experimental devices can be found in Coll et al. (1999a) and Coll et al. (1999b). According to [START_REF] Mckay | Physical properties of the organic aerosols and clouds on Titan[END_REF], this experiment promises to give the most accurate simulation of Titan's haze formation, as the dinitrile C 4 N 2 (detected in solid phase on Titan), has been identified for the first time as a product of the simulation, this clearly constitutes a validation of the experiment (Coll et al. 1999b).

In our case, we performed three titanian atmosphere simulations with a low pressure flux (∼ 1 -4 mbar of total pressure) of a N 2 /CH 4 mixture (in a 98:2 proportion).

A glass tablet or a silica cylinder was inserted into the reactor where tholins are deposited to form a film. In order to collect tholin samples, the reactor was installed inside a glove box filled with nitrogen to avoid contamination of the sample by the atmosphere in the room, in particular oxygen atoms, before electromagnetic characterization. Finally, the volume of deposited tholins -an essential parameter for future permittivity measurements -is determined using scanning electron microscopy to measure the thickness of the sample. Table 2 summarizes synthesis conditions and volume estimations for each set of experiments.

[Table 2]

Dielectric constant measurements

Tholin samples produced in the LISA reactor were characterized at the PIOM laboratory in order to measure their dielectric properties in the GHz range. Permittivity measurements were performed using a rectangular resonant cavity pierced on its top with a hole used to insert the sample. For the purpose of these experiments, we used two different kind of cavities : one at 10 GHz (i.e. λ = 3 cm) and a second one at 2.45 GHz (i.e. λ = 12.2 cm). As the change in the dielectric constant value should be small in the range 1-10 GHz, the choice of a cavity was made only because of the sample holder shape : the 10 GHz cavity is too small to allow a large rectangular hole on its top center and only a cylindrical sample holder can be used. Each cavity is composed of a wave-guide short-circuited at each end. Excitation and detection of resonance inside the cavity are done by co-axial transitions mounted on connectors linked to a network analyzer (ANRITSU 37325A).

The resonance modes that can be established in a cavity are deduced from the theory of wave propagation along a wave-guide. These modes are characterized by three integer indices m, n and p. In the case of a rectangular cavity, T E01p resonance modes are usually used (m = 0 and n = 1 as dominant mode, p representing the number of maxima of the electric field along the wave-guide length). In particular, the index p is chosen odd (p = 3) in order to ensure the position of a maximum in the center of the cavity, where we insert the sample. The sample holder symmetry axes are set in a way that they are parallel to the electric field established in the cavity, in order to minimize perturbations due to depolarization effects.

Once the cavity is connected to the network analyzer, we first introduce an empty sample holder into the cavity to measure the resonance frequency F 0 , and the quality coefficient Q 0 of the cavity as blank references. Then, we insert an identical sample holder -same glass/silica volume -but covered with a tholin film. The introduction of a tholin sample triggers a deviation from the resonance frequency, ∆F , and an additional attenuation conducting to a new quality factor Q 1 . As it is well established for resonant cavity experiments, the measurement of ∆F , Q 0 , and Q 1 allows to directly obtain the dielectric constant ε ′ -jε ′′ of the sample thanks to the relations [START_REF] Boudouris | Cavité électromagnétique[END_REF]:

∆F F 0 = -α(ε ′ -1) (1) ∆( 1 Q 1 - 1 Q 0 ) = 2αε ′′ (2)
with α = α 0 × V sample , V sample being the volume of the tholin sample and α 0 being the cavity filling coefficient (ratio between the tholin sample + sample holder volume and the cavity volume).

For each set of tholin samples (see Table 2), we obtained a value for the tholin dielectric constant. Results of our measurements are shown in Table 3. While real part of the dielectric constant shows a very little variation (∼ 10%), the imaginary part varies by a factor of 50. This variation is due to the poor estimation of factor Q, which is highly sensitive to the volume of material introduced in the cavity. An accurate value for this volume is very hard to obtain.

[Table 3] 3.2 Electromagnetic characterization of other titanian materials in liquid and solid states

Apart from tholin characterization, we also searched in the literature for values of permittivities of materials of interest for radar sounding of Titan's atmosphere and surface, in the microwave range.

Pure liquid methane

The dielectric properties of pure liquid methane and their implications for Titan's study were investigated by [START_REF] Thompson | Titan and other icy satellites: Dielectric properties of constituent materials and implications for radar sounding[END_REF]. They published a rough estimate of ε r for liquid CH 4 around 94 K: ε ′ ∼ 1.7 and ε ′′ ∼ 1.5 × 10 -2 . This is fully consistent with the value found in Handbook of Chemistry andPhysics (1988-1989) (1990) indicate that the real part of the dielectric constant for liquid hydrocarbons is well known to be in the range of 1.6 to 2 and that loss tangents are of the order of 10 -3 -10 -4 in the GHz range. [START_REF] Singh | Compressed-liquid dielectric constants and derived excess volumes for binary and ternary mixtures of N 2 , Ar, CH 4 and C 2 H 6[END_REF] found a real part of permittivity between 1.77 and 1.9 for methane-ethane mixtures at low temperature (typically around 100 K) and [START_REF] Ulamec | Dielectric constant measurements in simulated Titan ocean liquids[END_REF] obtained values between 1.71 and 1.95 around 94 K. The values from [START_REF] Singh | Compressed-liquid dielectric constants and derived excess volumes for binary and ternary mixtures of N 2 , Ar, CH 4 and C 2 H 6[END_REF] were obtained using a fit to an equation derived from the Clausius-Mossotti function, on the basis of liquid compressibility considerations, and those coming from [START_REF] Ulamec | Dielectric constant measurements in simulated Titan ocean liquids[END_REF] were inferred from capacity measurements. We have no indications about what could be frequency range they considered. However, such values are consistent with dielectric constant measurements of [START_REF] Sen | Dielectric constant of liquid alkanes and hydrocarbon mixtures[END_REF] for liquid alkanes and hydrocarbon mixtures at 1.2 GHz and 298 K.

Titan's surface: hydrocarbons and water ice

Titan's surface is supposed to be composed of various icy materials (H 2 O ice, hydrocarbons in solid state) due to its low 94 K temperature [START_REF] Lellouch | Titan's thermospheric profile[END_REF] All the dielectric constants of interest for radar sounding of Titan are summarized in Table 4.

[Table 4]

4 Simulation of the CASSINI radar behaviour 4.1 Testing the radar penetration through the atmosphere

In this part, we present simulations of the CASSINI Radar experiment in active modes.

This section mainly deals with the dielectric models we have developed to quantify the impact of condensates in Titan's atmosphere.

We used in our calculations the complex dielectric constant we measured for tholin material. Uncertainties on the permittivity of tholins have repercussions on the attenuation we calculate: concerning atmospheric transmission simulations, the attenuation does not vary linearly with the dielectric constant. The minimum value for attenuation was obtained with ε ′ = 2.1 and ε ′′ = 0, and the maximum attenuation corresponds to ε ′ = 2.1 and ε ′′ = 0.1. For the preliminary results on homogeneous atmosphere models, we considered the mean value measured for the dielectric constant of tholins: ε r = 2.2 -j0.05.

Description of the Rayleigh-Mie scattering model

We consider the propagation of a radar wave through Titan's atmosphere. The simple model we developed enables us to determine the attenuation an incident radar wave (emitted power P inc ) will undergo while crossing the dense atmosphere of Titan. The attenuation in decibels is given by Att total (dB) = Att gases + Att particles = 10 log 10 (

P ground P inc ) (3)
with P ground being the radar wave power reaching the surface of Titan.

The gaseous component is considered with no ambiguity as totally transparent for the radar and its permittivity is set equal to one. Thus, Att gases (dB) = 0 (4)

Only the condensate -aerosols, hail and rain particles -component could have sufficient size, density and permittivity to interfere with the radar wave. In this case, we can reasonably simulate the medium that the wave will encounter before reaching the surface by a diluted medium composed of dielectric spheres in suspension in vacuum.

Only single scattering and absorption of the incident wave are considered here and we can then write for an homogeneous atmosphere:

P ground P inc = e -[C(σscat+σ abs ) h cos θ )]
(5) with, C, particle density, h, thickness of the atmosphere, θ, incidence angle of radar wave (set to 0 o for the altimetric mode), σ scat , single scattering cross section, σ abs , absorption cross section.

Cross sections for spherical scatterers are taken from Rayleigh and Mie theories.

Transition between the Rayleigh and Mie regimes occurs when the particle radius is greater than r lim = 0.05. Rayleigh formalism is valid only for small particles in comparison to the wavelength. In the case of the Cassini Radar, the upper limit to the radius r lim of the scatterer is set to 1.08 mm.

Rayleigh scattering and absorption cross sections can be analytically solved and are given by [START_REF] Ishimaru | Scattering and absorption of a wave by a single particle[END_REF]:

σ scat = 128π 5 r 6 3λ 4 | ε r -1 ε r + 2 | 2 (6) σ abs = 8π 2 r 3 ε ′′ 3λ | 3 ε r + 2 | 2 (7)
Mie scattering cross sections are numerically computed by means of a classic BHMIE code taken from [START_REF] Bohren | Absorption and Scattering of Light by Small Particles[END_REF]. The complex parameter ε r = ε ′jε ′′ represents the dielectric constant of the spheres of radius r. It should be frequencydependent and was experimentally measured around the Cassini Radar experiment frequency (cf. section 3).

[Figure 2]

In our model (for heterogeneous atmosphere cases), the atmosphere of Titan is vertically cut off into homogeneous layers containing particles of fixed size and density (Fig. 2). We then compute the ratio between outgoing and incident flux P out i /P inc i for each layer i of thickness h i . The resulting final attenuation is the sum of attenuations induced by each layer i. It is given by :

Att total (dB) = i Att i = i 10 log 10 ( P out i P inc i ) (8)
Equation ( 5

Homogeneous atmospheres

We computed the attenuation of the centimetric signal emitted by the Cassini Radar instrument induced by the presence of particles in a ideal Titan-like homogeneous atmosphere. In this simple case, we considered single crossing of the wave through a totally homogeneous atmosphere, made of a unique layer with a single mode of particle size, density and dielectric properties.

The thickness H of the homogeneous layer was constrained by the aerosol haze extension within Titan's atmosphere and was fixed to h = 500 km. We fixed ε r to its experimental mean value of 2.2 -j0.05. The only free parameters in our simulation were particle radius and density. We decided to put a constraint on these parameters from extreme values found in literature: density ranges between unity and a maximum around 10000 cm -3 , and radius ranges between a few nanometers and a high value of 20 µm. Attenuations induced by such particles over a 500 km thick layer are shown in Fig. 3-(a). Each point of the figure represents the attenuation calculated for a unique atmospheric scenario, i.e a unique pair of particle radius and density over a homogeneous Titan atmosphere.

[Figure 3]

The detection threshold (noise equivalent σ 0 ) of the Cassini Radar instrument is limited to about -25 dB [START_REF] Elachi | Cassini Titan radar mapper[END_REF]. It means that, with the hypothesis that all the power reaching the surface of Titan is backscattered to the radar, a signal attenuation greater than 12.5 dB for the first crossing of the atmosphere would lead to no signal detection by the instrument. Figure 3-(b) is a 2-D representation of the variation of the attenuation versus particle radius and density. It shows the position of the 12.5 dB attenuation limit, and attenuation greater than 12.5 dB for only one atmosphere crossing is represented in gray on the Fig. 3-(b)). Some radius/density combinations are then prejudicial to the Radar experiment and its main objective of surface imaging. The model we considered here is very simple but shows that it is worthwhile to study the possible impact of atmospheric particles (aerosols, hail particles, drizzle and rain droplets) on the radar experiment. It allows also to define some first order ranges of radius and density for which the radar could encounter difficulties to see the surface of Titan. It would be the case with, for example, a 500 km thick atmosphere constituted of particles of 6 µm radius with a 1000 cm -3 density, which is not completely unexpected or unrealistic at first order when we refer to distributions retrieved from observations or microphysical calculations including rain occurrence (particles are then concentrated in a thinner layer, but are much bigger than ten microns [START_REF] Toon | Methane rain on Titan[END_REF][START_REF] Frère | Microphysical modeling of Titan's aerosols: application to the in situ analysis[END_REF])). The scattering cross section increases with the sixth power of the radius of the scatterers and constitutes the more sensitive parameter. These first results lead us to the conclusion that Titan's atmosphere might not be as transparent to Cassini radar frequencies as it was expected. Radar pulses could at least be affected and distorted, even if they encounter smaller particles than those we considered in this section.

Heterogeneous atmospheres and cloud layers

In this section, we take into account as a modeling refinement the possible heterogeneity of aerosol properties with altitude. We do not treat the atmosphere as an ideal homogeneous layer anymore but as a more complex medium as predicted by numerous published models.

We used the heterogeneous distribution of particles discussed in section 2 in order to simulate a more realistic Titan's atmosphere (see Fig. 1-(a)). We also included as a reference two semi-homogeneous models for Titan's atmosphere inferred from Pioneer and Voyager image analysis [START_REF] Smith | Encounter with Saturn: Voyager 1 imaging science results[END_REF][START_REF] Smith | A new look at the Saturn system: The Voyager 2 images[END_REF][START_REF] Tomasko | Photometry and polarimetry of Titan: Pioneer 11 observations and their implications for aerosol properties[END_REF]. Highresolution views of the limb at high-phase angles revealed the presence of several layers of aerosols: an optically thin layer of haze ∼ 50 km thick roughly 100 km above a main aerosol layer. The aerosol particle average size in the main haze layer was found to be between 0.1 and 0.5 µm for a real part of refractive index n r chosen between 1.7 and 2 at visible wavelengths. For the upper haze layer, a mean value for the particle radius was taken to 0.3 µm. Particle densities were calculated by [START_REF] Toon | A physical model of Titan's clouds[END_REF]. They found 10 4 cm -3 for the first tenth of the visible optical depth in Titan's atmosphere and 10 3 cm -3 at an optical depth of 1. In addition to the detached haze layer, and above it, [START_REF] Rages | Vertical distribution of scattering hazes in Titan's upper atmosphere[END_REF] discovered a small but persistent feature in the Voyager 2 extinction profiles, characteristic of another haze layer with the following physical properties: roughly 50 km thick, composed of 3 µm-particles with a density of ∼ 0.2 cm -3 (cf. Table 5). We considered a mean aerosol permittivity ε r = 2.2 -j0.05.

Errorbars on attenuation come from uncertainties on tholin permittivity (the minimum value for attenuation was calculated with ε ′ = 2.1 and ε ′′ = 0, and the value maximum with ε ′ = 2.1 and ε ′′ = 0.1).

We considered also the probable occurrence of hydrocarbon rain at low altitudes.

It was treated differently according to two scenarios: (1) We simulate the rain as another independent layer in addition to aerosols [START_REF] Toon | Methane rain on Titan[END_REF] and Courtin et al. (1995) approach) and, (2) we consider rain as the result of continuous growing of aerosols [START_REF] Frère | Microphysical modeling of Titan's aerosols: application to the in situ analysis[END_REF] approach). In case (1), we construct the cloud cover by substituting the "dry" particle distribution (two homogeneous multi-layer models as defined earlier and models presented on Fig. 1-(a)) by a homogeneous layer containing methane droplets inspired by [START_REF] Toon | Methane rain on Titan[END_REF] (cf. Table 1). The vertical extension of the cloud is supposed to range between altitudes of 30 and 10 km. We fixed an average methane droplet radius to 2 mm and their permittivity to ε r = 1.7 -j0.015, based on the hypothesis that the raindrops are only composed of pure liquid methane and that the tholin nuclei can be neglected (the liquid phase hugely dominates the composition of the droplet). The way we control the density of the cloud was inspired by recent work of [START_REF] Samuelson | Steady-state model for methane condensation in Titan's troposphere[END_REF] and [START_REF] Guez | Importance of phase changes in Titan's lower atmosphere. Tools for the study of nucleation[END_REF]. They suggested that liquid hydrocarbons may condense only from a limited subset of the aerosols falling through the saturated layer, in particular for kinetic reasons. [START_REF] Guez | Importance of phase changes in Titan's lower atmosphere. Tools for the study of nucleation[END_REF] introduced the concept of nucleation rate. Indeed, the condensation process efficiency is highly dependent on the contact angle of condensed materials on the nucleus. This is an essential parameter to estimate the compatibility between nucleus and the condensed phase. As contact angles are very unconstrained parameters, we treated the problem in a simple way thanks to a condensation efficiency factor f that can be free to vary between 0 and 100%. Using this coefficient, we simulate the fact that only a fraction of aerosols can supply the cloud in droplets at the condensation level: for an atmosphere sampled every kilometer, cloud concentration is then given by C droplets (z = 30 km) = f ×C aerosols (z = 31km). We checked that densities obtained for the top of the methane cloud (z = 30km) never exceed the limits imposed by [START_REF] Toon | Methane rain on Titan[END_REF], whatever higher aerosol distribution can be. The f parameter was fixed equal to 10 -4 %, giving particle concentrations at the cloud top of 1000, 1000, 8, and 250 m -3 respectively for the atmospheric models A, B, C and D (cf. Table 5). The cloud's particle radius and concentration are then constant with respect to the altitude from the cloud top (30 km)

to its base (10 km). Aerosols which don't participate in the condensation process are neglected, and Titan's atmosphere is then only constituted of a homogeneous cloud of methane rain droplets between 30 and 10 km. Below 10 km, as Lorenz (1993a) showed, pure methane droplets should evaporate and resupply aerosol layers, forming a "ghost" mist of aerosols close to the surface. In order to simulate rain sublimation in the last kilometers of Titan's troposphere, we stop the rain layer below 10 km and replace it by the "dry" scenario we used to describe the atmosphere above 30 km.

In case (2), we simply used the heterogeneous distribution computed by [START_REF] Frère | Microphysical modeling of Titan's aerosols: application to the in situ analysis[END_REF] (Fig. 1-(a)) as the complete description of the fate of particles over the full extent of Titan's atmosphere, even at low altitudes where condensation should occur. As they treated the differential condensation of a great number of hydrocarbons and nitriles, we chose an averaged permittivity for the raindrops inferred from those measured for a homogeneously mixed hydrocarbon-nitrile liquid: ε r = 1.8 -j0.002

(as for case (1), electrical properties of the condensation nuclei were neglected). In this case, the artificial factor f has no sense anymore. All aerosols participate in the condensation process. The density and the size of the rain droplets below 100 km are thus self-determined by the calculations of [START_REF] Frère | Microphysical modeling of Titan's aerosols: application to the in situ analysis[END_REF] thanks to modeling of collisional and sticking processes.

All the models used in our calculations are summarized in Table 5.

[Table 5]

[Figure 4]

Figure 4 shows the results obtained for the nine models described in Table 5.

Cases A, B, C and D correspond to attenuations induced by a dry atmosphere, only constituted of aerosol hazes. The attenuation never exceeds -0.02 dB, even for the least favorable scenario B (containing the highest particle size and density over the greatest part of the atmosphere), and are globally negligible (≤ -10 -3 dB). We can conclude that, without rain occurrence in the troposphere, Titan's atmosphere should be totally transparent for the 13.78 GHz radar of the Cassini orbiter. When we consider cases A♯, B♯, C♯, D♯ and E, the conclusions are quite different. The addition of a rain layer in the middle troposphere increases the signal attenuation by at least four orders of magnitude. For D♯, A♯-B♯ (rain attenuation overflows the attenuation induced by aerosols and the difference between scenario A♯ and B♯ is then small; thus A♯ and B♯ can be considered as one unique scenario), and E models, attenuation reaches respectively -5 dB, -20 dB and -25 dB. On the other hand, the value of attenuation is still low for scenario C♯ (-0.17 dB), due to the fact that the rain cloud modeled for this case presents a very low density. This parameter is controlled by the factor f , fixed to 10 -4 %, and the density of aerosols just above 30 km. For scenario C♯, the cloud has a density of only 8 m -3 , in comparison to models A♯ and D♯ which have a raincloud density of respectively 1000 m -3 and 250 m -3 . We have to keep in mind that the titanian [Figure 5]

The rain layer we used in addition to models A, B, C, and D in order to simulate the condensation process in Titan's low atmosphere is intrinsically artificial in its construction. We explored the way the attenuation may vary if we free some badly constrained parameters of this layer: radius of droplets and condensation efficiency f.

The radius can vary between 0 mm (no rain) and 4.5 mm (limit imposed by aerodynamics (Lorenz 1993a)). For the parameter f , even if there are no means at the present time to physically impose a constraint on it, we can consider that the value we chose (f = 10 -4 %, i.e. one aerosol per million acts as a condensation nucleus) in order to match the cloud densities predicted by [START_REF] Toon | Methane rain on Titan[END_REF] is very low. Higher values (up to 0.1%) cannot be totally excluded and should cause much more attenuation. We present in Fig. 5 the results of this parametric study: the attenuation as a function of rain droplet radius (Fig. 5-(a)) and condensation efficiency (Fig. 5-(b)) for models A♯-B♯, C♯ and D♯. The increase of r and f induces a drastic rise of attenuation for all the cases considered. Attenuations are much greater than unity as soon as r reaches 2 mm, and f reaches 0.001%. Figure 5 demonstrates the high sensitivity of the attenuation to r and f , which are unfortunately weakly constrained.

Surface reflectivity

As aerosols are supposed to deposit on Titan's surface and form a "dirty ice" mixture, we tried to simulate the radar response of a surface covered with tholins. It allows us to refine the first hypothesis we made in the previous section of a perfectly reflecting surface (i.e. all the energy reaching Titan's surface is backscattered to the instrument).

Since the Cassini Radar experiment will operate in the Ku-band (f = 13.8 GHz, λ = 2.17 cm, HH polarization [START_REF] Elachi | Cassini Titan radar mapper[END_REF], most of Titan's surface is likely to appear as rather rough for the radar [START_REF] Dierking | Quantitative roughness characterisation of geological surfaces and implications for radar signature analysis[END_REF]. We shall then consider surface scattering models developed for medium rough to very rough surfaces, i.e.

the Physical Optics (PO) model and the Geometric Optics (GO) model, which were derived from the Kirchhoff model under the scalar approximation and the stationaryphase approximation respectively. These models are relevant to evaluate performances of a side-looking imaging radar. We shall consider here a single homogeneous layer covered by tholins (characterized by its averaged dielectric constant ε = 2.2 -0.05j), water ice or liquid methane, and characterized by its surface roughness. The latter is defined by the surface correlation function ρ(x) (a Gaussian function is assumed here), the height standard deviation σ, and the correlation length L (cf. Fig. 6).

[Figure 6]

The PO model validity range is defined by the following conditions:

√ 2σ L < 0.25, kL > 6 and L 2 > 2.76σλ (9)
where k is the wave number of the incident plane wave (k = 2π/λ). The HH noncoherent scattering coefficient is then given as a function of the incidence angle θ by [START_REF] Ulaby | Microwave Remote Sensing: Active and Passive[END_REF]:

σ 0 HH (θ) = 2k 2 cos 2 θΓ H (θ)e -(2kσ cos θ) 2 • ∞ n=1 (4k 2 σ 2 cos 2 θ) n /n! ∞ 0 ρ n (x)J 0 (2kx sin θ)xdx (10)
where J 0 is the zeroth-order Bessel function of the first kind, Γ H (θ) =| R H (θ) | 2 is the Fresnel reflectivity, and ρ(x) = exp(-x 2 /L 2 ) is the Gaussian surface correlation function.

The GO model validity range is expressed by: (2kσ cos θ) 2 > 10, kL > 6 and L 2 > 2.76σλ (11) and the HH (or VV) noncoherent scattering coefficient is given as a function of the angle of incidence θ by [START_REF] Fung | Multiple scattering and depolarization by a randomly rough Kirchhoff surface[END_REF]:

σ 0 HH (θ) = Γ(0)e -tan 2 (θ)/2m 2 2m 2 cos 4 θ ( 12
)
where m = √ 2σ

L is the rms slope for a Gaussian surface and Γ(0) is the Fresnel reflectivity evaluated at normal incidence:

Γ(0) = | 1 -ε/µ 1 + ε/µ | 2 (13)
(we consider here a magnetic permeability µ = 1).

[Figure 7] Results obtained here should be of course considered as indicative, since very little is known about Titan's surface composition and roughness. In particular, due to the low loss tangent of tholins (tan δ = ε ′′ /ε ′ = 0.02) and other surface materials such as water ice, the penetration depth D P of the incident Ku-band wave given by:

D P = λ 4π { µε ′ 2 [ 1 + ( ε ′′ ε ′ ) 2 -1]} -1/2 (14)
is about 10 cm. This could give rise to some attenuation and volume scattering effects that could change the radar backscattered power computed from Eq. ( 10) and ( 12). A mixture between silicate and tholins should also lead to higher values of ε, and then to a higher reflectivity of the surface.

If we make the link between the results we obtained for atmospheric attenuation and the surface backscattered power, it leads to more realistic conclusions for the attenuating role of the atmosphere. The surface should not be perfectly reflective for the radar wave as we hypothesized in the previous section. In the favorable case of a rough surface, the reflected signal could still lose 17 dB, and the limit of the acceptable atmospheric attenuation should then be reduced to -4 dB instead of -12.5 dB if considering a radar sensitivity limit of -25 dB. This dramatically increases the impact of an attenuating atmosphere on the Radar experiment (see Fig. 4 and 5 with the attenuation limit fixed at -4 dB).

Conclusion and perspectives

The Cassini mission has been designed to send a spacecraft to the planet Saturn, and deploy an instrument probe, Huygens, that will descend to the surface of Saturn's moon Titan. The radar instrument onboard the orbiter is expected to bring the scientific community new information to characterize the surface of Titan. We are convinced that correct interpretation of the measurements made with the Cassini Radar instrument requires simulations and laboratory measurements to anticipate possible atmospheric effects and then better invert and interpret radar data.

In this paper we presented a study of the behaviour of a 13.78GHz plane wave going through Titan's atmosphere and backscattered by its surface. Titan's atmosphere was modeled by a diluted medium filled with spherical particles of size, density and permittivity estimated from what could be found in the literature and laboratory experiments. We considered one homogeneous atmosphere model and five heterogeneous models including or not condensation that could occur in the lowest part of titanian atmosphere. In order to fix some parameters of our models, we conducted a series of experiments in order to derive the dielectric properties around 13.78 GHz of Titan's aerosol analogs produced in laboratory.

The results we obtained in terms of radar power attenuation after crossing the simulated Titan's atmosphere are of two kinds:

• the "dry" heterogeneous atmospheric models, only taking into account the aerosol component, do not cause any attenuation and the radar wave will reach the surface of Titan without any losses. The particle radius never exceeds 1 µm (far from the critical limit around 10 µm we estimated from the ideal homogeneous case) and the corresponding attenuation never exceeds -0.01 dB. In such cases, Titan's atmosphere is totally transparent to microwaves and its effect should be totally neglected in the future processing of Cassini radar data.

• on the contrary, when we add in our simulation a rain layer in the last few kilometers, the attenuation reaches and rapidly exceeds the instrument sensitivity limit, due to the enhancement in size of the particles encountered (that could reach a few millimeters). A wave emerging from such a cloud layer could be so attenuated that the radar antenna wouldn't be able to detect a returned echo from Titan's surface. This could be a problem for the retrieval of Titan's surface images, as well as for altimetry measurements, and it should be taken into account when interpreting future data of the Cassini Radar experiment.

Simulation of the backscattered signal by Titan's surface covered by tholins also shows that a rather low return could be expected, even for rough surfaces. This could dramatically increase the possible attenuation role of Titan's atmosphere.

There is also a non-negligible risk for the Cassini radar instrument to detect a false signal coming from a reflective atmospheric layer, screening and flooding the surface signal, that could cause false interpretation of "surface" images. As the Cassini radar is a multipurpose instrument, a way to discriminate between possible atmospheric and surface echoes would be to combine altimetric and SAR data. It could then be possible to avoid false interpretation of "non-surfacic" signal, if both altimetric and SAR acquisition can be performed in the same short time period. The altimetry pulse shape could also be analyzed in order to detect an atmospheric effect and get unexpected information about Titan's lower atmosphere (rain occurrence and extension of cloud systems, size, density and velocity of the particles). In a flyby strategy which would maximize the coverage of Titan's surface, the radar will certainly not map the same region twice. In this case, using the altimetry data would be the only way to discriminate possible cloud layers from surface features. On the other hand, two flybys over the same area could give the opportunity to distinguish persistent features related to the surface from transient ones, which are likely to be due to atmospheric phenomena.

The new analysis scheme we propose for the Cassini radar measurements will be subject to further investigations. For this purpose, we shall improve our present simulation of the Cassini Radar instrument in order to model the behaviour of the pulse it will send towards Titan's surface (not only power attenuation, but also shape distortion). We shall also take into account the doppler shift in frequency of the signal sent and received by the orbiter, as could be produced by the relative motion of the atmospheric scatterers. In order to properly prepare for the analysis of future

Cassini radar data, we also need for more accurate measurements of haze and rain properties (size, density and dielectric constant) as we showed the sensitivity of our calculations to these parameters. Rain droplet radius and condensation efficiency in the low atmosphere are in particular crucial parameters. Such information could also be retrieved from the combined interpretation of independent observations of Titan's atmosphere coming from the other instruments onboard the Cassini orbiter or Huygens probe, as well as results of future rain modeling.

Table 1: Methane rain properties retrieved from modeling by [START_REF] Toon | Methane rain on Titan[END_REF] and [START_REF] Courtin | Titan's thermal emission spectrum: reanalysis of the Voyager infrared measurements[END_REF].

Physical property Value

Cloud

  plex haze distribution models. Inspired by the pioneer work of[START_REF] Toon | A physical model of Titan's clouds[END_REF],[START_REF] Mckay | The thermal structure of Titan's atmosphere[END_REF] considered Titan's aerosols properties in the new light of microphysical modeling, with the aim of integrating these results in a radiative-convective model of the thermal structure of Titan's atmosphere. They assumed that all particles at a fixed altitude had the same radius and that only thermal coagulation, sedimentation, and electrostatic forces are responsible for variations in particle size and concentration with altitude. They predicted a size of ∼ 0.4 µm for the aerosols around an altitude of 85 km, in good agreement with previous values obtained from observational fits. In the same way,[START_REF] Cabane | Formation and growth of photochemical aerosols in Titan's atmosphere[END_REF] developed a model including sedimentation and eddy diffusion accounting for transport processes, gravitational (coalescence) and thermal coagulation for collection processes. Their calculations focused on the prediction of the distribution and radius of aerosol particles throughout the atmosphere between the higher formation region and the lower stratosphere (above 85 km), before condensation of hydrocarbons and nitriles on the aerosols could occur. The final particle radius obtained in the low stratosphere is about 0.2 µm. In the meantime,[START_REF] Frère | Microphysical modeling of Titan's aerosols: application to the in situ analysis[END_REF] pursued the development of a complete microphysical modeling of Titan's aerosols, including for the first time condensation processes of organics and nitriles present in the gas phase in the low stratosphere. Above 100 km, the profiles computed byMcKay et al.

  1999) that could constitute a 10 µm-hail around the altitude of 90 km). Aerosols might need a first nitrile layer to activate hydrocarbon condensation, as predicted by Frère et al. (1990) (Fig. 1-(b)).

  , probably fractionally covered or mixed with tholin material. It then should present a high and contrasted reflectivity in the radar wavelength range. Dielectric constants of such materials were experimentally measured. We had access to precise values for the real part of their permittivity, but only to rough estimations for the imaginary part: H 2 O ice corresponds to ε ′ ∼ 3.1, measured around 10 GHz and valid within the temperature range from -1 to -185 o C (Ulabyet al. (1982), vol. 3, appendix E, p. 2028), and aCH 4 -C 2 H 6 ice mixture has ε ′ ∼ 2 -2.4 in the same wavelength range[START_REF] Thompson | Titan and other icy satellites: Dielectric properties of constituent materials and implications for radar sounding[END_REF]).

  ) indicates that the part of the flux scattered or absorbed by the particles is lost. It reproduces well what could happen to a wave in single scattering regime along the radar line-of-sight.

  aerosol modeling of[START_REF] Mckay | The thermal structure of Titan's atmosphere[END_REF] (scenario C and C♯) was rather simple, and the aerosol density it predicts around 30 km is certainly less accurate than the one obtained from[START_REF] Frère | Microphysical modeling of Titan's aerosols: application to the in situ analysis[END_REF] (scenario E) and[START_REF] Cabane | Formation and growth of photochemical aerosols in Titan's atmosphere[END_REF] (scenario D and D♯). We are convinced that, even if clouds in Titan's atmosphere are transient and rare phenomena, they could surely affect the radar signal. For two of the scenario we studied (A♯ and E), clouds should totally attenuate the radar pulse before it reaches Titan's surface. For model D♯, it should also cause sufficient attenuation to possibly blur surface images by diminishing the contrast between distinct surface echoes.

Figure 7

 7 Figure7presents the radar backscattered power for two types of surfaces: a relatively smooth surface with σ = 0.5 cm and L = 25 cm described by the PO model, and a rough surface with σ = 7 cm and L = 10 cm described by the GO model.Calculations were performed for surfaces covered by tholins, water ices and liquid methane. Uncertainties on experimental tholin dielectric constant were considered, but the resulting imprecision on backscattered power actually stays between the values obtained for water ice and liquid methane. For the mean look angle foreseen for the imaging mode of the Cassini radar (θ L ∼ 11 o[START_REF] Elachi | Cassini Titan radar mapper[END_REF])), we can see that the backscattered power for a smooth flat surface is very low (about -80 dB), much lower than the noise equivalent σ 0 of the instrument announced to be around -25 dB[START_REF] Elachi | Cassini Titan radar mapper[END_REF]). On the contrary, a rough and flat surface should present a much higher return, about -17 dB. As a first approximation, the Cassini imaging radar should only see very rough regions covered by tholins (land surfaces ?) whereas smooth and flat surfaces (seas and lakes ?) should appear as dark zones. Nevertheless, for non-flat smooth regions, Fig.7shows that slopes facing the radar with an incidence angle θ less than 7 o would produce a backscattered power higher than -25 dB. Considering the mean look angle θ L , it corresponds to a slope ranging between 4 o and 28 o , which represent a large fraction of slope values that can be observed on planetary surfaces.

  FIGURE CAPTIONS

Figure 2 .

 2 Figure 2. Geometry and description of the multi-layer model we used for atmospheric transmission computation.

Figure 3 .

 3 Figure 3. (a): Attenuation versus particle radius and density for a 500 km thick homogeneous atmosphere with ε r = 2.2 -j0.05; (b): 12.5 dB-threshold versus radius and density of dielectric spheres (ε r = 2.2 -j0.05) for a 500 km thick homogeneous medium. The grayed region represents atmosphere models for which the radar is unable to see the surface of Titan.

Figure 4 .

 4 Figure 4. Attenuation caused by heterogeneous models (aerosol only and aerosol+condensation

Figure 5 .

 5 Figure5. (a): Attenuation for heterogeneous models A♯, B♯, C♯, and D♯ with increasing droplet radius from no rain (0 mm) to the limit of 4.5 mm imposed byLorenz (1993); (b): Attenuation for models A♯, B♯, C♯, and D♯ with increasing condensation efficiency on aerosols (factor f ) varying between our nominal case (10 -4 %), in agreement with[START_REF] Toon | Methane rain on Titan[END_REF], and 0.1%. Errorbars on attenuation values due to uncertainties in the dielectric constant of tholin become insignificant beyond a certain value of r (2 mm) and are totally hidden by attenuation due to rain as soon as f is higher than 10 -4 %. For (a) and (b), the dielectric constant of tholins was taken from the value we experimentally measured: ε r = 2.2 ± 0.1 -j0.05 ± 0.05. The solid horizontal line shows the -12.5 dB sensitivity threshold and the dotted line the -4 dB threshold.

Figure 6 .

 6 Figure 6. Geometry of the single layer scattering problem.

Figure 7 .Figure 3 :Figure 4 :Figure 5 :

 7345 Figure 7. Compared radar backscattered power for a relatively smooth surface (σ = 0.5 cm and L = 25 cm, PO model) and a rough surface (σ = 7 cm and L = 10 cm, GO model) covered by tholins (ε r = 2.2 -j0.05), water ice (ε r = 3.1 -j0.001) or liquid methane (ε r = 1.7 -j0.015). The solid horizontal line shows the sensitivity threshold at -25 dB.

Table 1 ]

 1

	Frère et al. (1990) was the first to present a microphysical approach for conden-

  demonstrated the insolubility of aerosol material in hydrocarbons and their relative solubility in nitriles. It is also consistent with the identification of nitriles in solid phase in Voyager IRIS spectra (C 4 N 2[START_REF] Khanna | Vibrational infrared and Raman spectra of dicyanoacetylene[END_REF][START_REF] Coustenis | Plausible condensates in Titan's stratosphere from Voyager infrared spectra[END_REF]) and HCN, HC 3 N, CH 3 CH 2 CN(Coustenis et al.

  around 100 K in the hundreds of MHz range.3.2.2 Titan's raindrops and hypothetical surface oceans: liquid hydrocarbon and nitrile mixtures According to Frère et al. (1990), Titan's raindrops are primarily made of light hydrocarbon liquids instead of pure methane, progressively accreted in concentric layers around aerosols. During the fall of the raindrops, internal dynamics stirs the liquid CH 4 and C 2 H 6 into a homogeneous mixture. Such a mixture was the subject of a few experimental studies aiming at determining its dielectric properties. Muhleman et al.

ACKNOWLEDGMENTS

We sincerely thank PIOM's director, Jean-Paul Parneix, and LISA's director, François Raulin, who welcomed us in their laboratories and gave us the opportunity to instructively collaborate with some of their team members. We are also very grateful to Jonathan Braine who patiently checked the English language of the paper. This work was supported by the French Programme National de Planétologie of the Institut 35 National des Sciences de l'Univers, CNRS.


Sarah Zribi

Fre ´de ´ric Be ´naben

Amira Ben Hamida

Jean-Pierre Lorre Ábstract

Towards a Service and Choreography Governance Framework for Future Internet

The Service Oriented Architecture (SOA) Governance refers to all measures, rules, descision-making, information and evaluation that ensure the proper functioning and control of services whithin an organization. In the Future Internet vision of services and in a choreography context, many heteregenous services from several organizations need to collaborate together to achieve a common goal. In order to improve the interoperability, reuse, the good behavior, the control and the efficiency of a choreography, it is necessary to define a governance framework for services and choreographies. This paper addresses the raised issues by providing a governance framework vision. EasierGov deals with both services and choreographies.

Introduction

Since its inception, SOA was revealed as being the de facto paradigm for future systems. It combines best practices inspired from previous application models. Modularity, encapsulation, fine-grained, publication, and discovery help SOA to S. Zribi (*) Industrial Engineering Center, Universite ´ de Toulouse Mines d'Albi Carmaux, Route de Teillet, 81013 Albi Cedex 9, France Petals Link (former EBM WebSourcing), 4 rue Ame ´lie, 31000 Toulouse, France e mail: sarah.zribi@petalslink.com F. Be ´naben Industrial Engineering Center, Universite ´ de Toulouse Mines d'Albi Carmaux, Route de Teillet, 81013 Albi Cedex 9, France A.B. Hamida • J. P. Lorre Ṕetals Link (former EBM WebSourcing), 4 rue Ame ´lie, 31000 Toulouse, France be widely used by developers and users. As a consequence, enterprise information systems are migrating to this new trend.

As systems are moving from classical IT to innovative SOA, essential functions need also to be exported and adapted. SOA Governance is a first and foremost function in IT systems. It ensures the best practices and the success of an SOA within an organization. To achieve an objective and respond to consumer requirements, services may need to collaborate with several services coming from other business entities. This is the first vision about what is service choreography.

This work is based on an ongoing work supported by the CHOReOS project funded by the European program. Petals Link1 involvement in this project is focusing on governance of ultra large scale choreographies of services for the Future Internet.

The remainder of this paper is structured as follows. In section 2, we survey the state-of-the-art of both SOA Governance and Service Choreography. We introduce definitions of both concepts and study solutions from both the literature and the industrial worlds. In section 4, we describe our contribution: EasierGov: a Governance framework for services and choreographies for the Future Internet. Finally, section 5 concludes this paper and gives the future perspectives.

SOA Governance

What is SOA Governance?

In [START_REF] Bennett | SOA Governance Governing Shared Services On Promise and in the cloud[END_REF], the authors define SOA Governance as an act of governing or administrating something. By far the most common form of governance is that of an organization. More recently, IT Governance appears as an unavoidable issue for the management of modern organizations. SOA Governance extends IT Governance for the purpose of ensuring the SOA success. It ensures the best interests of an organization to be met through corporate decisions from strategy to execution [START_REF] Marks | Service oriented architecture governance for the services driven enterprise[END_REF]. Lack of governance can be a serious impediment to success and the most common reason for the failure of SOA projects [START_REF] Afshar | SOA Governance Framework and Best Practices[END_REF]. The authors in [START_REF] Papazoglou | Service oriented computing: State of the art and research challenges[END_REF] identify SOA governance as a major research area in the field of SOA design and development. Nevertheless, SOA Governance is not clearly defined in the literature. We rely on the following definitions to identify key topics in SOA Governance. First, in [START_REF] Brown | SOA Governance IBM's Approach. Application Innovation IBM Global Services Effective governance through the IBM SOA Governance Management Method approach[END_REF], IBM researchers assume SOA Governance to be an extension of IT Governance specifically focused on the lifecycle of services, metadata and composite applications in an organization's SOA. SOA Governance extends IT Governance by assigning decision rights, policies and measures around the services, processes, and life cycle of SOA to address such concerns as: service registration, versioning, funding, monitoring, publishing, discovery, etc. Second, sun [START_REF] Wheaton | Decorating your soa services with governance enforcement contracts[END_REF] states SOA Governance as the ability to organize, enforce, and reconfigure service interactions within an SOA. Third, in [START_REF] Marks | Service oriented architecture governance for the services driven enterprise[END_REF], the author aggregates several definitions to give his own: SOA Governance is the definition, implementation and ongoing execution of a SOA stakeholder decision model, and accountability framework that ensures an organization is pursuing an appropriate SOA strategy aligned with business goals, and is executing that strategy in accordance with guidelines and constraints defined by a body of SOA principles and policies. SOA policies are enforced via a policy enforcement model, which is realized in the forms of various policy enforcement mechanisms such as governance boards and committees. To sum up, SOA Governance is revealed in the trilogy (decision, process and policy): doing the right SOA Things the right way for the stakeholders (decision makers).

SOA Governance Tools

SOA Governance needs to be achieved at several levels, from strategy to execution. Governance tools provide the functionality required to support the governance processes associated with a specific SOA initiative including: Policy management, Interoperability, Registry/Repository and metadata management, Service life cycle management, Statistical and Key Performance Indicators data collection and Monitoring. The following surveys approaches to SOA Governance.

First, authors of [START_REF] Derler | Models and tools for SOA governance[END_REF] address SOA Governance by proposing a generic model and two governance tools. Services are described according to their life cycle, activities and roles. The authors propose two tools: a Service Repository Console and a Service Browser. The Service Repository is used for creating service proposals and service descriptions, for specifying service relationships, and for defining service installations. The Service Browser is used for searching and browsing the service repository and for investigating service details, service relationships and service status. Second, the IBM approach to SOA Governance is presented in [START_REF] Brown | SOA Governance IBM's Approach. Application Innovation IBM Global Services Effective governance through the IBM SOA Governance Management Method approach[END_REF] as a four-step life cycle. It consists on a planning phase, a definition phase, an enabling phase, and finally a measurement phase. IBM proposes the IBM Web Sphere Service Registry and Repository [START_REF] Schepers | A lifecycle approach to SOA governance[END_REF], which offers a governance solution in IBM SOA; it supports service discovery and access. Besides, it offers features for service metadata management. Third, Mule Galaxy [START_REF] Mulesoft | [END_REF] is an open source SOA Governance platform. It provides a SOA Registry/ Repository. Galaxy helps in the management of SOA by supporting features such as life cycle, dependency and artifact management, service discovery and reporting, and application deployment management. Finally, there are some other available tools, such as Petals Master SOA Governance Solution [START_REF]Petals Master SOA Governance Solution[END_REF], WS02 [START_REF]WSO2 Governance Registry[END_REF], Progress's SOA tool Actional [START_REF]CentraSite A little structure goes a long way Software[END_REF], Interoperability Framework [START_REF]HP SOA Governance Interoperability Framework (GIF)[END_REF], etc. They typically provide service discovery, dependency management, policy management and federation with other repositories.

Service Choreography

What is a Service Choreography?

A Service Choreography describes a collection of services that collaborate together in order to achieve a common purpose. According to the World Wide Web Consortium (W3C) Glossary [START_REF]W3C Glossary[END_REF], it concerns the interactions of services with their users. Any user of a Web Service, automated or otherwise, is a client of that service. These users may, in turn, be other Web Services, applications or human. A choreography gives a more distributed and scalable envision of service composition. A Service Choreography allows several processes of service composition to collaborate involving multiple services (potentially from differents partners) and put a special emphasis on their interactions seen from a global perspective.

Service Choreography Approaches

While service composition languages are numerous, there are few languages for describing service choreography. In [START_REF] Barros | Standards for Web Service Choreography and Orchestration: Status and Perspectives, Business Process Management Workshops[END_REF], the authors classify the choreography languages into two-abstraction level: Implementation-independent or specific.

Implementation-independent: on this level, the fundamental decisions about interactions are made. We can quote the newly OMG Specification Business Process Model and Notations (BPMN) version 2.02 which has been released fully in 2011. It integrates in this latest version the choreography graphical annotations. This later is interesting since it is an independent platform and it allows an easy representation of high-level Service Choreography; Implementation-specific: on this level, the concrete message formats and communication protocol as well as security issues need to be addressed. On this level, we can find both W3C standards for describing choreographies: Web Service Business Process Execution Language (WS-BPEL or BPEL for short) 3 and the Web Service Choreography Description Language (WS-CDL). 4The authors in [START_REF] Yildiz | Towards decentralized service orchestrations[END_REF] address this issue by proposing a framework for process transformation technique. Their approach converts a centralized BPEL process into a set of nested processes able to be deployed on dynamically bound services. The authors consider a graph-like representation of the process and a transformation algorithm. In [START_REF] Viroli | Engineering a BPEL orchestration engine as a multi agent system[END_REF], the authors consider a multi-agent system where BPEL activities are autonomously executed by agents and the mediation is supported via a coordination model. Moreover, the authors in [START_REF] Chen | Developing a Concurrent Service Orchestration Engine Based on Event Driven Architecture. On the Move to Meaningful Internet Systems[END_REF] develop a concurrent service orchestration engine called OnceBPEL2.0 and based on Event-Driven Architecture (EDA). They target the improvement of performance under massive concurrency and design a scalable BPEL engine.

To summarize, the SOA Governance is a concept used for activities related to exercising controls over services and to achieve service integration within an organization. The approaches presented previously define a standard way and a solid model to consider SOA Governance and Service Choreography. Nevertheless, they are limitative and they do not address governing practices when multiple services coming from heterogeneous organizations or platforms need to collaborate together -such in a Service choreography-to respond to the client requirements. In order to ensure the effective interoperability between these multiple organizations, and the compliance between these different services, it is necessary to define and implement an SOA Governance framework for both services and Choreographies.

EasierGov: A Vision of Governance Framework for Services and Choreography

EasierGov is a vision of an SOA Governance Framework for both services and choreographies. In the following, we present its architecture and its main components.

Architecture

Future Internet environments challenge the SOA Governance by providing a set of policies and rules. SOA Governance activities ensure the adoption of the right way of doing things, at the right time and by the right persons. EasierGov is a framework that underlines, at design time and run-time, the whole service and choreography lifecycle, the IT system and at the borderline of three concerns: SOA Discovery, SOA Management and Governance Policies as illustrated in the Fig. 1.

The SOA Discovery covers the services registries and repositories which provide service discovery capabilities. They serve not only to inventory, catalogue service data, but also serve as a place to store metadata about services, necessary to governance (such as the Web Service Description Language, 5 documents, capabilities, locations of their service contracts, etc). In EasierGov, we intend to provide registry/repository functionality both for services and choreographies.

The provider of the service as well as the designer of the choreography will publish services and choreographies on such registries/repositories. Then, consumers looking for services and choreographies can refine their search according to nonfunctional concerns, for instance: performance, usage frequency, rating, etc. Section 4.2 addresses these concerns.

The SOA Management covers the management of the service, choreographies and agreements lifecycles from design until run time phase. It includes the definition of the several stages of the corresponding lifecycles and the definition of the right policies to apply. Moreover, SOA Management includes the run time evaluation of the non-functional requirements of services and choreographies. We describe our contribution concerning SOA Management in section 4.3.

The Governance Policies are the cornerstone of the governance paradigm. Through the adoption and enforcement of a set of policies and standards, SOA governance makes the exposed services compliant with other services coming from different organizations. Both SOA Discovery and SOA Management are concerned with Governance Policies as they define each step of the lifecycle. Each stakeholder involved in the governance process has a clearly identified role and responsibility. We detail the selected governance policies in section 4.4.

Registry Repository

Life Cycle

Non Functional Requirements

Service Service Choreography

Users and organizations Policies

SOA Discovery

Governance Policies

SOA Management

Fig. 1 Overview of the SOA Governance Framework "EasierGov"

EasierGov, Governance Registry and Repository

Having a robust service discovery mechanism promotes the services publication, discovery, and reusability. Governance capabilities, such as looking for a service or a choreography, retrieving it, or managing its lifecycle, are needed. EasierGov answers these requirements by providing an innovative registry dedicated for both services and choreographies. Indeed, it will enable the discovery of business services and choreographies at both design and run times. This functionality is essential for dealing with a large number of heterogeneous services coming from different sources.. In order to tackle this heterogeneity of business services and to facilitate the SOA Discovery adoption, it is important to coalesce around a uniform and common service description language. For this purpose, we adopt a unified description language.

The Unified Service Description Language (USDL 6 ) enables the expression of the common business services descriptions in a unique agreed way. According to its specification, it is a generic language for service description. The W3C USDL Incubator Group is working on the standardization of this language to make services tradable and consumable. USDL provides a way to model services from a business and operational views and align this with a technical perspective. This approach is useful and efficient for EasierGov where we intend to cover the main important concepts to design services, describe what a service is offering and how consumers are able to access it. On a whole, USDL is made up of a set of modules: Service, Foundation, Participants, Technical, Pricing, Functional, Legal, Service Level, and Interaction. These modules are inter-dependent and cover the main SOA Governance aspects related to services, policies, metadata management, processes and control and management of the lifecycle. Moreover, it is worth mentioning that the USDL is extensible and enables to model new concepts and explore new possibilities that are needed to implement the EasierGov framework. Besides, the discovery functionality, our framework provides capabilities dedicated to the management of services, contracts, and choreographies. In the following section, we address these concerns.

EasierGov: Governance Management

Governance Management covers the definition of the several stages of the life cycle of the business services, choreographies and service level agreements (SLA). To ensure its good behavior, it is essential to apply the appropriate policies at each phase of the lifecycle. In Fig 2, we define the lifecycle steps for both services and choreographies. We assume that for each of these steps we apply adequate governance policies. We distinguish between design time policies and run time ones.

Concerning services, EasierGov provides capabilities for managing services for their design, development, testing and validation, publication in the registry (presented in section 4.2), deployment on top of a middleware, monitoring at runtime and finally versioning and retirement. Moreover, EasierGov enables the creation, negotiation and assessment of service level agreements. By analogy the choreographies are also managed using EasierGov, as described in the previous figure.

Generally, Web Services can run based only upon their functional requirements. However, for an efficient participation in a corporate environment, a service should also provide some guarantees about its availability, dependability, efficiency, in short about its Quality of Services (QoS). The QoS parameters for a service are very important to maintain its trust. They are defined in the Service Level Agreements (SLA). The SLA is a commonly used way for designing non-functional objectives to be reached by the business service. In a choreography context where a large number of services interoperate, EasierGov needs to provide a governance solution that considers a choreography level agreement between this collection of services. Indeed, it is a form of policy that the choreography must respect in order to satisfy the user requirements. The conformance of these policies to the specific service, choreography or non-functional agreements is evaluated. Services and choreographies must respect all the policies defined at the design time and must fulfill the non-functional requirements as defined in the SLA and the choreography global agreement that were agreed. In order to set up the governance system, an important step resides in defining which, when and where to use policies and standards in order to insure compliance between them. In the following section we survey our selection of standards and policies.

EasierGov: Governance Policies Standards

In order to ease the EasierGov interoperability, it is necessary to adopt common agreed technological standards for both design and development phases. In choreography context where several heteregenous services collaborate together, adopting standards and rules is a good way to provide governance on top of such scalable systems. The Fig. 3, presents a classification of some SOA policies and protocols according to the scope to which they can be related.

These policies are commonly used by SOA community and are the ones that we are likely to manage in the EasierGov governance framework. We classify the level of policies adoption into three classes: services, choreography and transaction. Service policies are dedicated to the service level. For instance, a service would abide policies concerning its description as WSDL. Besides, the contract between the service consumer and the service provider would be defined in accordance with the Web Service Agreement (WS-Agreement) specification. Process policies concern the process and collaboration between several services. It includes the Service Choreography. Moreover, a choreography would abide the BPMN 2.0 and BPEL specifications for the representation of the business and technical processes. Finally, the transaction level refers to the policies that can be evaluated at the level of the messages transmitted between services within a process. For instance, the messages within transactions have to follow Web Service Security and Simple Object Access Protocol (SOAP 7 ) protocols specification to guarantee the software interoperability.

Conclusion and Perspectives

SOA Governance can be defined as a set of processes, rules, policies, mechanisms of control, enforcement policies, and best practices put in place throughout the life cycle of services to ensure the successful achievement of the SOA implementation. In this paper, we survey approaches deling with SOA Governance and Service Choreography. Then, we propose an initial framework, namely EasierGov, for governance of services and choreographies. EasierGov is presented according to three main concepts, SOA Management, SOA Discovery and Governance Policies.

We intend, as perspectives to this work, first to make stronger this conceptual approach of EasierGov, in particular by aligning the specifying design of the Governance Framework with the several components of the theory of Gregor and Jones [START_REF] Gregor | The anatomy of a design theory[END_REF].

Moreover, in order to concretize our approach we started the implementation of EasierGov prototype basing on the USDL service model. Further, we need to define the right policies and rules. Meanwhile, by considering the deployment of services and choreographies on top of run time middleware, we will be able to check and validate the policies compliance and the respect of non-functional agreements.

Fig. 2

 2 Fig. 2 Service and Choreography Lifecycles in "EasierGov"

Petals Link http://www.petalslink.com/

http://www.omg.org/spec/BPMN/2.0/

http://docs.oasis open.org/wsbpel/2.0/wsbpel v2.0.html

http://www.w3.org/TR/2004/WD ws cdl 10 20041217/

http://www.w3.org/TR/wsdl20/

USDL, http://www.internet of services.com/index.php?id 264&L 0&tx ttnews

SOAP, http://www.w3.org/TR/soap/

Acknowledgement This paper is based on an ongoing work supported by the European Community's FP7 (FP7 ICT 2009 5 Objective1.2/2010 2013) through the Project CHOReOS: Large Scale Choreographies for the Future Internet (IP) under grant agreement number 257178.