Radar-bright channels on Titan

Icarus 207 (2010) 948–958

Contents lists available at ScienceDirect

Icarus journal homepage: www.elsevier.com/locate/icarus

Radar-bright channels on Titan A. Le Gall a,*, M.A. Janssen a, P. Paillou b, R.D. Lorenz c, S.D. Wall a, the Cassini Radar Team a

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, United States Observatoire Aquitain des Sciences de l’Univers, University of Bordeaux I, 33271 Floirac, France c Space Department, Planetary Exploration Group, Johns Hopkins University Applied Physics Lab, Laurel, MD 20723, United States b

a r t i c l e

i n f o

Article history: Received 25 June 2009 Revised 19 October 2009 Accepted 22 December 2009 Available online 4 January 2010 Keywords: Titan Radar observations Radio observations Satellites, Surfaces Geological processes

a b s t r a c t During Cassini’s T44 flyby of Titan (May 28, 2008), the Cassini SAR (synthetic aperture radar) revealed sinuous channels in the Southwest of Xanadu. These channels feature very large radar cross-sections, up to 5 dB, whereas the angle of incidence was relatively high, 20°. This backscatter is larger than allowed by the coherent backscatter model considered to explain the unusual reflective and polarization properties of the icy satellites and only a few radar scattering mechanisms can be responsible for such high radar returns. The presence of rounded (icy) pebbles with size larger than the radar wavelength (2.18 cm) is proposed to explain the large radar cross-sections measured in these units. The radar-bright channels are thus interpreted as riverbeds, where debris, likely shaped and transported by fluvial activity, have been deposited. Similar debris were observed in the landing site of the Huygens probe. This work may point the way to an explanation for the enhanced brightness of other fluvial regions of Titan. Ó 2009 Elsevier Inc. All rights reserved.

1. Introduction The Radar onboard the Cassini spacecraft is a multi-mode microwave sensor designed to explore the surface of Titan through its optically opaque atmosphere. It operates at 13.78 GHz, either as a high-resolution synthetic aperture radar (SAR) imager, a profiling altimeter or a scatterometer. It also includes a passive mode (radiometer) able to acquire data with, or separately from, the active measurements (Elachi et al., 2004). During the Cassini 4-years prime mission (July 2004–July 2008), the Cassini Radar mapped 28% of the surface of Titan in the SAR mode of operation, i.e. with a resolution ranging from 350 m to 1.7 km. Its major discoveries include vast dune fields, lakes and seas of liquid hydrocarbons, evidence for possible cryovolcanism, meteor impacts, plate tectonics and fluvial features (Lopes et al. (2009), for a review). Features indicating fluvial erosion cover the surface of Titan. Though possibly speculative, we use the terms ‘valleys’ and ‘channels’ to refer to fluvial features that appear morphologically similar to valleys and channels on Earth. Cassini Radar images have revealed a variety of fluvial valleys on Titan either in the form of meandering or branching single channels or networks of channels (Elachi et al., 2006; Barnes et al., 2007; Lunine et al., 2008; Lorenz et al., 2008; Jaumann et al., 2008). Fluvial features seem to be present at all latitudes but are generally absent from dune fields. Channels were also observed at optical wavelengths by the Huygens probe (Tomasko et al., 2005) at a higher resolution, which suggests * Corresponding author. Fax: +1 818 354 8895. E-mail address: [email protected] (A. Le Gall). 0019-1035/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2009.12.027

that many fluvial features might exist though they are not resolved by the SAR. Most of Titan’s channels were presumably carved by liquid hydrocarbons as a result of atmospheric precipitation (Perron et al., 2006; Lorenz et al., 2008; Jaumann et al., 2008). It is unclear whether it is still an ongoing process; however, variations in the brightness of the channels observed so far suggests different ages. The brightest ones seem to dominate in the equatorial region of Xanadu, whereas the darkest are located in the North, at higher latitudes. The two channels imaged during the T44 flyby (May 2008) are the largest radar-bright channels yet observed on Titan and also among the brightest units unveiled by the Cassini Radar anywhere on the satellite. Their radar cross-sections (the effective area that intercepts the transmitted power and scatters that power isotropically back to the receiver) exceed 4 dB even though they were observed at oblique incidence (20°). Together with Xanadu and other sparse hummocky terrains they are ones of the areas of Titan identified as anomalously bright at the wavelength of 2.2 cm (Janssen and Le Gall, 2009). This paper proposes an explanation for the enhanced radar backscatter measured in the two channels Southwest of Xanadu and by inference to contribute to understanding Titan’s bright terrains. We discuss the possible presence of icy rounded rocks in the channels that would act as efficient natural retro-reflectors. The channels are described in Section 2. Section 3 is devoted to our interpretation of their peculiar radar properties. Section 4 investigates the possible analogy between the channels and the Huygens landing site. The implications in terms of Titan geology are addressed in Section 5.

A. Le Gall et al. / Icarus 207 (2010) 948–958

2. Radar observations of the radar-bright channels of Titan Two radar-bright channels were observed by the Cassini SAR in May 2008, during the last swath of the Cassini prime mission. They are located southwest of the 2500 km continental-scale feature Xanadu (see Figs. 1 and 2) at a latitude of 17°. They are, respectively, 185 km and 140 km long, a few kilometers wide (1–8 km) and seem somewhat larger upstream than downstream. They appear to originate from Xanadu rugged terrains consisting of overlapping mountain ranges and drain to the southern darker lowlands. They are possibly the terminus of the developed dendritic fluvial networks observed in the Northwest of Xanadu during T 13 and described by Barnes et al. (2007) and Lorenz et al. (2008). Their sinuous morphology, where we calculate sinuosity ratios close to 1.5, suggests a low regional gradient. A further (and maybe stronger) argument to this assertion is that the topographic observations of Titan to date (Zebker et al., 2009; Stiles et al., 2009) show a maximum elevation spread of 2 km which makes a slope higher than 1° very unlikely (a more formal slope survey is in preparation). The channels flow away from the margins of Xanadu in the very location of the sharp linear boundary identified both in the RADAR and radiometry observations (see Figs. 1 and 2). This abrupt transition from a radar-bright (radiometrically cold) to a radar-dark (radiometrically warm) terrain also appears in the effective dielectric constant map of Titan’s surface (Janssen et al., 2009) and must correlate with change in the physical and/or chemical properties of

949

the surface. It has recently been interpreted as a tectonic fault responsible for a regional subsidence of the bedrock (Radebaugh et al., 2009). Rivers might have been carved after this event by methane rainfall or, if they were preexistent, might have had to adjust their width and sinuosity to the new local slope. Fig. 1C and D depicts the measured backscatter values, in dB, of the channels area. These values are averaged down to 1.4 km by 1.4 km in order to remove the speckle noise. They are absolutely calibrated to about 1.3 dB per pixel (West et al., 2009). The highest radar cross-sections are close to 5 dB. Since parts of these channels probably have widths smaller than the pixelization of the radar reflectivity, their radar cross-sections may be underestimated. The channels were also observed by the Cassini Radiometer. As expected, they are radiometrically colder than their surroundings (the exception being Xanadu) but the resolution of the data is not high enough to estimate their actual brightness temperature or emissivity at 2.2 cm (see Fig. 2).

3. Interpretation high backscattering of Titan’s channels On Titan, the effective average dielectric constant determined from radiometric polarimetry is low (1.7) (Paillou et al., 2008; Janssen et al., 2009); likely surface materials are hydrocarbons, tholins and, in some places, water ice, possibly with ammonia. In such conditions it is difficult to explain the measurements of radar

Fig. 1. (A) Combination of the Cassini Radar images of the 2500-km continental-scale radar-bright feature Xanadu observed in the SAR and HiSAR (additional technique developed to use the SAR processor at larger distances) modes of operation. The region of the bright channels is outlined in black (cylindrical projection). The resolution is 500 m. (B) Radar-bright channels observed during the T44 radar swath (C and D). Normalized radar cross-sections in dB of the channels area.

950

A. Le Gall et al. / Icarus 207 (2010) 948–958

Fig. 2. Calibrated mosaic of equivalent brightness temperature Tb (in K) at normal incidence in the region of the channels observed during the T44 flyby. The absolute calibration is about 2 K or better, while the relative calibration is about 1 K across the map (Janssen et al., 2009). The radiometer resolution is at best 6 km. It is constrained by the real-aperture footprint of the beam and thus coarser than the resolution of the SAR. The two radar-bright channels are outlined in black.

cross-sections higher than 3 dB at relatively high incidence angles (20°).

3.1. How to obtain naturally enhanced radar cross-sections? Naturally occurring mechanisms that can be responsible for very large backscatter are few. As far as the channels are concerned, the hypothesis of a slope effect (i.e. that the entire surface imaged is substantially tilted towards the radar) can be excluded since high backscatters are measured over several tens of kilometers despite the meanders of the channels. Besides, as already pointed out, the regional slope is necessary much lower than incidence angle (20°). Apart from the specular (or quasi-specular) reflection from smooth surface facets normal to the viewing angle, strongest radar returns are obtained either by double or triple reflection of the incident wave on a dihedral or trihedral corner-reflector (Ruck et al., 1970; Ulaby et al., 1982). Double bounce effect on the wall of the rivers will be thus a very efficient scattering mechanism but it is unlikely to occur in many places. Besides, dihedral corner-reflectors have the disadvantage that they provide a large cross-section only in the plane perpendicular to the corner walls. An array of trihedral corner-reflectors (either circular, squared or triangular) would ensure a huge enhancement of the radar crosssection over a substantially wider angular coverage but is implausible. We might also think of Titan’s bright surfaces as similar to the highly reflecting surfaces of the ice-rich Saturn’s and Galilean satellites. Refraction scattering from dielectric inclusions (Hagfors et al., 1985, 1997) or interface cracks (Goldstein and Green, 1980) has been argued to explain their high reflectivities and polarization properties but the generally accepted explanation is coherent backscattering which consists in high-order volume scattering caused by subsurface inhomogeneities (Hapke, 1990; Black et al., 2001). Such mechanism is expected, for instance, in presence of wavelength-sized scatterers (voids, rocks) embedded in a weakly absorbing regolith. However, the coherent backscattering effect produces backscatter that is enhanced by a factor of only 2 and can therefore

not easily account for radar cross-sections in excess of 3 dB. Paillou et al. (2006) advance a two-layer model to explain the bright flows observed during the Ta SAR swath but this mechanism cannot explain the measured backscatter enhancement. A more likely explanation would be that the high backscatter is due to the presence of low-loss rounded scatterers in the river channels that act as efficient natural retro-reflectors. This is the possibility explored in this paper. Indeed, it has long been known that transparent spheres with diameter larger than the wavelength backscatter significantly more (of about an order of magnitude) than metal spheres of the same size (Herman and Battan, 1961; Glover and Atlas, 1963; Pettengill and Hagfors, 1974). This results from the internal reflection of the waves on the rear surface of the sphere that focuses the power in the backscattering direction as illustrated by Fig. 3. Despite the intensity reduction produced at the three dielectric discontinuities, this mechanism can lead to an extreme enhancement of the backscatter when the sphere is transparent enough to preclude significant attenuation on the

Fig. 3. Schematic diagram of backscattering by a low-loss sphere. For poorly absorbing spheres, the back-surface internal reflection governs r0. e0 and e0 0 are, respectively, the real and imaginary parts of the complex dielectric constant of the sphere.

A. Le Gall et al. / Icarus 207 (2010) 948–958

round-trip between the front and back surfaces. On Earth, water droplets of a particular size produce the optical phenomenon known as ‘‘the glory” which appears like a bright halo surrounding the shadow of an airplane on clouds. For that matter this property of transparent spheres is commonly exploited in the manufacture of reflective paints and tape. The profound enhancement of optical reflectivity in the backscatter direction in these materials is readily demonstrated by flash photography. Radar glory, not from spheres but from buried craters, has also been invoked to explain the strong echoes observed on the icy moons of Jupiter (Eshleman, 1986). 3.2. Radar backscattering from ice spheres The scattering properties of dielectric spheres of arbitrary size are well described by the Mie theory. This model has been extensively used to predict scattering by hailstones or raindrops. In planetary science, the Mie theory can be taken as a reasonable approximation to estimate like-polarized backscatter from rockstrewn fields, i.e. surfaces covered by debris of impact cratering, fluvial activity or landslides (Campbell, 2001). A number of applications can also be found in the study of Saturn’s rings (Pettengill and Hagfors, 1974; Cuzzi and Pollack, 1978). The Mie theory has been advanced to explain the Opposition Effect of the Moon (sharp increase of brightness of the lunar surface when the phase angle approaches 0°) (Akimov, 1980), at least as an additional mechanism to coherent backscattering and/or shadow-hiding effects (Shkuratov, 1983). The Mie solution of Maxwell equation consists of a slowly converging series. The normalized backscattering cross-section for a sphere with a radius a is given by:



r

0 Mie

2

 1 rMie 1 X  ¼ ¼ 2  ð2n þ 1Þð1Þn ðan  bn Þ 2   pa a n¼1

ð1Þ

where a ¼ 2pa=k is the size parameter and an and bn are the scattering amplitude coefficients given by Bohren and Huffman (1983).

951

r0Mie is a dimensionless quantity. As expressed by the relationship (1), it strongly depends on the ratio of its circumference to the incident wavelength a. It also varies with respect to the dielectric properties of the sphere (e0 and e00 the real and imaginary parts of the relative dielectric constant of the sphere). The magnetic permeability of the sphere is here assumed to be equal to the permeability of the ambient medium (void in this study). Notably because of the bulk density of Titan (1.88 g/cm3), its crust is thought to be mainly composed of low-pressure phase water ice I (Lewis, 1971; Grasset et al., 2000; Tobie et al., 2006). Potential enrichment in ammonia is also expected as a by-product of cryovolcanism (Mitri et al., 2008). Other more complex compounds might be present in small proportion. At cryogenic temperature (Titan’s surface temperature is 92–94 K), water ice at is a low-loss material; its dielectric loss tangent (e00 /e0 ) at the Cassini Radar frequency of operation is less than 103 (Lorenz et al., 2003; Paillou et al., 2008). Doped with a concentration of 28% of ammonia, water ice is lossier than pure water ice but remains relatively transparent to microwaves (Paillou et al., 2008). Fig. 4 shows the theoretical Mie radar cross-section of an icy sphere as a function of its radius (for values ranging from 0.1 cm to 150 cm) and its composition (pure water ice, pure water ice with enhanced loss tangent, water ice containing 28% ammonia). The radar cross-section of the sphere is normalized with respect to its geometric cross-section pa2. Three regimes can be distinguished: the Rayleigh, Mie and optical regimes. They occur as the size of the sphere increases with respect to the incident wavelength (here 2.18 cm). For pure water ice, the normalized radar cross-section goes readily beyond 20 dB. When the loss tangent is multiplied by a factor of 5, it reaches a maximum of 16 dB for a sphere radius of 18 cm. Even when the loss tangent is increased tenfold or when the water ice is doped with a significant concentration of ammonia (28%), the normalized radar cross-section is substantially larger than 5 dB in the range of radii 2–10 cm. As sphere grows larger, its normalized cross-section converges to the reflection coefficient of a plane surface and thus its geometric optics limj2 (McDonald, 1962). In the Mie regime, oscillations appear. it j N1 Nþ1 They result from the internal resonant effects that arise within the

Fig. 4. Theoretical smoothed Mie normalized radar cross-section rMie/pa2 in dB as a function of the radius a of the spheres at the wavelength of 2.18 cm. The dielectric properties of the spheres vary from those of pure water ice to those of water ice containing 28% of ammonia at cryogenic temperatures (Paillou et al., 2008). The Mie theory is also shown for pure water ice with its loss tangent multiplied by 5 and 10. The range of radii of the pebbles observed on the Huygens landing site is indicated.

952

A. Le Gall et al. / Icarus 207 (2010) 948–958

sphere from constructive and destructive interferences. These oscillations grow as the loss tangent of the dielectric sphere decreases. When the loss tangent is significant, oscillations are damped rapidly as the radius increases. The values of the loss tangents we used are among the largest available in literature, so that the Mie cross-sections presented here are likely underestimated. Besides, we assumed that water ice, potentially doped with ammonia, was the most likely candidate material for the rocks, whereas some authors postulate that the bedrock of Titan might rather be made of clathrate hydrates (Tobie et al., 2009). This would not affect significantly the backscattering properties of the spheres since clathrate hydrates must have also a low loss tangent (clathrate hydrates are crystalline compounds in which the solid water substance serves as a host lattice for one or more molecules of another substance; to first-order their dielectric properties are likely to be analogous to that of porous water ice). The same conclusion can be drawn if Titan rocks are in fact aggregated tholins or other hydrocarbons or nitriles produced photochemically. 3.3. Radar backscattering from ice oblate spheroids DISR (Descent Imager and Spectral Radiometer) images acquired after Huygens probe landing suggest that icy rocks present on Titan surface might be better described as oblate spheroids than as true spheres. Significant research effort has been undertaken to examine electromagnetic scattering by non-spherical particles. It showed that scattering from spheroids is still well described by the Mie theory when their size is on the order of the wavelength (Bohren and Huffman, 1983) (as long as the radius is consistent with a sphere of equal volume or surface area) but generally departs from this theory when they are much larger. Relative to spheres, several additional physical parameters are involved in the scattering of a spheroid; its size but also its shape (or sphericity) and the geometry of observation (incidence angle) matter. Latimer (1980) proposed an approximate solution for the scattering coefficient in terms of the incident field and of the scattering object physical characteristics but this solution is valid for dielectric spheroidal objects with size parameter a inferior to 15 (radius of 5 cm at the Cassini Radar frequency of operation). Only a few authors investigate an exact solution (Asano and Yamamoto, 1975; Barber and Yeh, 1975; Holt et al., 1978; Asano, 1979; Asano and Sato, 1980) and these have often a restricted domain of validity and/or are difficult to implement. We investigated the scattering behavior of spheroids using the 3D simulator TEMSI-FD, developed by the XLIM laboratory, in Limoges, France. This code is based on the finite difference time domain (FDTD) method that solves the set of Maxwell equations in a rigorous manner. It relies on the discretization of the Maxwell equations following the algorithm proposed by Yee (1966) and their resolution using a time stepping procedure. A detailed description of this code can be found in Besse (2004) and Le Gall (2007). In order to compute the scattered field, TEMSI-FD applies the equivalence theorem that takes the scattered field to be due to a set of surface currents located coincident with the surface of the scattering object. In practice, we modeled a computational box with the same dimension in the three orthogonal directions (360  360  360). The mesh size was set equal to 1 mm in all axes, which is small enough to prevent numerical dispersion. For smaller objects (a < 5 cm), the mesh size was even taken smaller (0.5 mm) to limit the numerical roughness. In order to respect the Courant–Friedrichs–Levy stability criterion, the time step Dt was forced to be smaller than Dtc, the delay minimum required for a wave to propagate into an elementary cell: Dt = 0.95Dtc. In addition, 10 CPML (Convoluted Perfectly Matched Layers) (Roden and Gedney, 2000) were implemented on the boundaries to avoid wave reflections

on the walls of the computational box. A closed surface S (a Huygens surface) was then defined around the scattering spheroid and an incident wave plane injected within the region bounded by S. The region outside S is, by definition, source-free and the equivalence theorem states that the fields in this region could be produced by a distribution of electric and magnetic currents on the surface. TEMSI-FD computes these equivalent surfaces currents and converts them into scattered fields using the near-field/farfield transformation theory. The radar cross-section can then be deduced from the scattered electrical field as follows:



rðhinc ; /inc jhs ; /s Þ ¼ r!1 lim 4pr 2 ¼ 4p

Ps ðr; hinc ; /inc jhs ; /s Þ Pinc ðhinc ; /inc Þ

jF s ðhinc ; /inc jhs ; /s Þj2 jEinc ðhinc ; /inc Þj2



ð2Þ

Fs is the far-field vector amplitude of the scattered electrical field in the direction (hs, /s) created by an incident plane wave propagating in the direction (hinc, /inc). Pinc and Ps are the powers of the incident and scattered fields. Einc is the incident electrical field. Fig. 5 illustrates the geometry of the problem. The code was first tested on spherical objects made of pure water ice. Fig. 6 demonstrates its ability to retrieve the Mie theory (dark blue squares). In order to investigate the scattering cross-section of spheroids, a scattering angle n is usually introduced as follows: cos n = cos hinc cos hs + sin hinc sin hs cos(/s  /inc). In the backscattering direction: hs = hinc and /s = p + /inc, i.e. n = p (n = 0 in the forward scattering direction). The sphericity of an oblate spheroid is defined as the ratio between the minor and major axis diameters b/a. Simulations were performed for an incidence angle of 20°, sphericities of 0.75 and 0.5 and major semi-axis a ranging from 1 to 14 cm. The backscattering radar cross-section is ultimately normalized to the area pr 2v of a sphere of the equal volume: r3v ¼ a2 b. Fig. 6 gathers the results of the numerical simulations. It shows that the backscatter of the icy spheroids decreases as they get more oblate. However, even for a sphericity of 0.5, the normalized crosssection can exceed 5 dB at an incidence angle of 20°. Other simulations (not shown here) suggest that for higher incidence angles it is no longer possible to draft a clear trend in the results. 4. A Titan analog for the radar-bright channels: the Huygens landing site? Rounded rocks exist on Titan; they were observed on the Huygens landing site, the only location on the surface for which such

Fig. 5. Scattering geometry. The spherical coordinate system is adopted to represent the incident and scattered electrical fields in the far-field zone, respectively, Einc and Es.

A. Le Gall et al. / Icarus 207 (2010) 948–958

953

Fig. 6. Numerically computed radar cross-sections (in dB) for oblate spheroids with sphericity of 1 (sphere), 0.75 and 0.5. Spheroids are made of pure water ice and the incidence angle is 20°. The radar cross-sections are normalized by the area of a sphere of equal volume (r 3v ¼ a2 b). The theoretical smoothed Mie normalized radar crosssection of a sphere made of pure water ice is also plotted to demonstrate the ability of the FDTD code to retrieve the Mie theory.

ground truth is available. This section addresses the question: if the channels are indeed filled with large spheroidal and transparent objects, to what extent would their streambeds resemble to the Huygens landing site? 4.1. Description of the Huygens landing site The images acquired by the DISR instrument after Huygens probe landing (see Fig. 7) show rounded and smooth rocks-like objects lying above a darker, finer-grained substrate in a variable spatial distribution. The pebbles, most likely composed of hydrocarbon-coated water ice (Tomasko et al., 2005), appear moderately oblate. Their sizes range between 3 mm (limit of detectability of the instruments) and 20 cm (Keller et al., 2008), somewhat larger than first estimated by Tomasko et al. (2005). No boulder larger than 20 cm was observed. The Huygens landing site has been interpreted as a dry lakebed or a collection basin downhill from several channel networks (Tomasko et al., 2005; Lebreton et al., 2005; Keller et al., 2008). The rounded shape of the icy rocks and evidence of erosion at their base, indeed, point to fluvial activity (Perron et al., 2006). Coarse-sediments would have been deposited there by floods coming from the Northern highlands. Perron et al. (2006) constrain the minimum precipitation rate required to mobilize such sediments to 0.5–15 mm/h. Keller et al. (2008) estimate that the flow velocity likely to have transported the pebbles to their current location should be in the order of 1 m/s. No liquid was detected but several observations suggest that the ground was damp with methane liquid (Niemann et al., 2005; Lorenz et al., 2006). The darker underlying material is probably organic compound precipitated from the atmosphere. The observation of the Huygens landing site points to the mobility and processing of sediments on the surface of Titan. As the dune fields indicate the existence of sand-sized particles on Titan, the images provided by the DISR camera establish the presence centimeter-sized pebbles, i.e. objects with size of the order

Fig. 7. Merged Huygens DISR images acquired after the Huygens probe soft landing. The horizontal diameters of the pebbles covering Titan’s surface have been estimated by Keller et al. (2008) by visual inspection. Distance from the probe is indicated as well as possible flow features (red arrows). This figure is extracted from Keller et al. (2008). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

or larger that the Cassini wavelength of operation. This prompts the idea that the T44 channels might also be areas of erosion and collection of debris.

954

A. Le Gall et al. / Icarus 207 (2010) 948–958

4.2. Density of the pebbles in the Huygens landing site versus density of the pebbles in the T44 channels The Huygens landing site has been observed three times by the Cassini SAR: during the T 8 (October 2005) and T 41 (February 2008) flybys of Titan in conventional SAR mode, plus a longrange ‘HiSAR’ observation made on T 13 (May 2006). In spite of the degraded resolution (1 km), the location of Huygens landing site was successfully identified on the T 8 SAR swath. It appears quite bright (Lunine et al., 2008) with a backscattered radar cross-section of 2.5 dB for an angle of incidence close to 16° (Paganelli et al., 2007). T 41 observations were performed at a shorter range hence with a higher spatial resolution. The radar cross-section of the landing site was then 2 dB for an incidence angle of 9.5°. During the T 13 ‘HiSAR’ swath, a backscatter coefficient of 4 dB was recorded for an incidence angle of 18°. In this section, our goal is not to compare these measurements to model predictions (especially since the surface observed by the lander’s view may not be representative of the full extent of the area illuminated by the Cassini SAR) but rather to provide the theoretical upper limit of the backscattering crosssection of the Huygens landing site and to compare it with the T44 channels radar cross-section in order to infer the density of the pebbles in their streambed. The upper limit of the normalized backscatter cross-section of a rock-strewn field can be estimated by integrating the Mie solution over the range of rock radii as follows (Harmon and Ostro, 1985; Campbell, 2001):

r0Surface ¼

Z

r0 pa2 nðaÞda ðunitlessÞ

ð3Þ

where n is the number of objects with radii between a and a + da per unit of area. This model assumes that the rocks are relatively sparsely distributed so that they do not shield each other. It also neglects multiple scattering between the rocks and the surface. Fig. 4 shows that the Mie theory predicts high radar returns for spheres with size comparable to the size of the pebbles revealed by the DISR camera. We used the formula (3) to estimate Mie backscatter crosssection of the Huygens landing site. As mentioned earlier, the pebble population of the Huygens landing site was investigated by Tomasko et al. (2005) and more recently by Keller et al. (2008). We use the rock count derived from the DISR Side Looking Imager (SLI) images labeled SLI < 2.27 m by Keller et al. (2008). Forty rocks were identified on this image that covers a surface area of 12,515 cm2 (Küppers, private communication). Fig. 8 illustrates the size distribution of the discrete pebbles seen by the instrument SLI < 2.27 m. It was derived from Fig. 27 of Keller et al. (2008) that provides the number of pebbles with a size ranging between 23/4a and 25/4a as a function of their diameter 2a (Küppers, private communication). As is often the case on the Earth and on Mars (Golombek and Rapp, 1997), their density n is well described by an exponential function of the radius a (in cm):

nðaÞ ¼ Ceba in cm

3

ð4Þ

The best-fit parameters (in least-squares sense) are: C = 0.000878713 ± 0.0003 cm3 and b = 0.380722 ± 0.04 cm.

Fig. 8. Differential pebbles-radius distribution (in cm3) for the Huygens landing site observed by the Side Looking Imager. The best-fit exponential function (dotted line) is n(a) = 0.000878713e0.380722a, where a is the radius in centimeters. Error bars are indicated.

A. Le Gall et al. / Icarus 207 (2010) 948–958

The Mie theory yields an upper limit of the normalized radar cross-section of 3 dB (for spheres of pure water ice). As expected, this is far beyond the measured values. Yet, it is important to note that this value is lower than the highest radar cross-section measured in the T44 channels. This suggests that, if the channels are also areas of collection of sediments, the density of the pebbles in their streambed has to be larger than the density of the pebbles in the Huygens landing site in order to account for the measured high backscatter. Their rock abundance and distribution are difficult to constrain but we expect the sediments to be closely spaced, possibly closely packed and maybe also larger in the channels. 5. Geological implications under discussion The fluvial nature of the channels, our analysis of their peculiar backscattering properties and the analogy with the Huygens landing site argue for the presence of fluvial deposits. These icy ‘river rocks’ would have been carried down and rounded by stream flow or flood of liquid hydrocarbons. 5.1. Weathering, fluvial erosion and transport of sediments on Titan: state of knowledge Cassini Radar and VIMS images attest that fluvial processes have played an important role in modeling Titan surface. The efficiency of fluvial activity in processing Titan crust and sediments strongly depends on the solubility and the mechanical strength of its bedrock in hydrocarbon liquids. Lorenz and Lunine (1996) explored the theory of dissolution as an erosional process on Titan. They show that chemical weathering of pure water ice by liquid methane or ethane should be minimal, whereas ammonia–rich water ice is somewhat soluble in these fluids as are hydrocarbons and nitriles. Solution erosion has been suggested (Mitchell et al., 2009) as a mechanism for the formation of some north polar lakes on Titan, which may resemble karst-like terrain on Earth. Solution erosion could form rounded clasts; since dissolution will tend to remove material more quickly at corners than at facets. The primary mechanism that formed fluvial valleys on Titan is likely to be streambed erosion by saltating bedload (Perron et al., 2006; Collins et al., 2008) and this mechanical process may be a more likely candidate for rock-rounding than solution. Coarse-sediments that are transported along riverbeds (bedload) tend to become smaller and more rounded as they are carried downstream (Mill, 1979; Richards, 1982). The downstream fining can result from differential transport as well as from mechanical breakdown. The rates of downstream rounding and fining differ with lithology. Relying on the saltation-abrasion bedrock incision model developed by Sklar and Dietrich (2004) and Collins et al. (2008) identified three parameters that control the erosion rate of Titan’s icy crust: the tensile strength (stress at which a material breaks or permanently deforms), the elastic modulus (ability of a substance to be deformed elastically when a force is applied to it) and the abrasion susceptibility coefficient. The first two parameters can be derived from the strain–stress curve, which is not yet well known for water ice at cryogenic temperatures. However, it has been established that tensile strength continuously increases as the temperature drops (Polito et al., 2008). The abrasion coefficient is determined experimentally by impact tests (an ice clast is repeatedly dropped onto an ice disk target). The most recent laboratory measurements show that water ice at 110 K may be 2 or 3 times more erodible than rocks of equal tensile strength (Polito et al., 2008), which is much less than first reported by Collins (2005). But, this finding might change again since the role of fracture toughness (ability of a material containing

955

a crack to resist fracture) has not been investigated yet. Moreover, the actual composition of Titan’s bedrock remains unknown. Thus, to date, the lack of information on geotechnical properties of crustal ice at the conditions that prevail on Titan precludes any definitive and quantitative conclusion on the erodability of Titan’s crust. However, it seems broadly speaking, that fluvial erosion on Titan should not differ dramatically from fluvial erosion on the Earth. We are unaware at present of any systematic study that compares the relative rates of fining and rounding of sediments in terrestrial rivers, and relates them to rock properties. However, it seems reasonable the channel brightness on Titan implies particles are easily rounded but not easily broken by fracture. This in turn might imply smoothing and rounding by some fine-grained abrasive suspended in the liquid (as with the polishing action of grit in a gem-tumbler), or perhaps that the material is ductile, deforming plastically during collisions into a rounder shape, rather than fracturing into smaller pieces. As far as fluvial transport is concerned (once the sediments have been generated from bedrock), the lower gravity on Titan’s surface implies that sediments are transported more slowly in rivers than on the Earth. Together with the greater buoyancy of water ice sediments, this would slow the rate of erosion if it was not partially balanced by the lower viscosity of liquid methane compared to water (Collins, 2005). Burr et al. (2006) conclude that, for a given stream velocity, Titan channels should be able to transport 2 times larger sediments than Earth rivers, even larger if the fluid display a high concentration of fine-grained sediments. 5.2. Implication for the radar-bright channels observed during T44 On the Earth, fluvial erosion produces specific landscapes. In particular, as the meanders migrate and exaggerate, they may create an entirely new course for the river, abandoning the old one. The morphologically similar but darker curving patterns next to bright channels are likely to be remnants of old rivers (see Fig. 1). Several mechanisms can account for the obscuration of the channels with age. It could be due to the burial of the icy rocks by the deposition of fine particles precipitating out from the atmosphere. A mechanical weathering process (Aeolian weathering or rainfall) might also be responsible for the in situ fining of the icy sediments over the time thus reducing the efficiency of their backscatter (see Fig. 4). Another feature commonly associated with rivers on Earth is the point bar. When the liquid flows around a bend, material can be swept laterally across the stream and accumulate on the bank. These areas of deposition are on the convex side of the river, where the velocity of the flow is the greatest. The T44 channels are not uniformly radar-bright but the resolution is not high enough to distinguish point bars. However, the channels appear brighter upstream, at their exit from the mountains, than downstream. This could be due to selective sorting that leaves behind larger sediments as the slope drops and the flow becomes less confined. On the other hand, the non-uniform brightness of the channels can be partially ascribed to the variation of the viewing angle (20° upstream, 25° downstream). The T44 channels presumably developed as a result of precipitation of hydrocarbons on the more elevated terrains of Xanadu that should be more subject to rainfall (Lorenz, 1993). On the Earth, the mountainous fringes of desert areas experience strongly episodic river flows. Rain falls in sudden and heavy downpours so that gullies that are usually dry may rapidly become full with liquid flowing fast enough to roll even large boulders along in the bedload. Episodes of violent storms might also be possible on Titan equatorial regions (Lorenz et al., 2005). For Keller et al. (2008), the pronounced size sorting of pebbles observed in the Huygens landing suggests that their deposition is due to a single flash flood

956

A. Le Gall et al. / Icarus 207 (2010) 948–958

event. The dampness of the Huygens landing site (Lorenz et al., 2006) argues in favor of a geologically recent event. The apparent fresh erosion surface that can be distinguished at the base of the pebbles (see Fig. 7) is a further argument for this assumption. The broad spatial extent and gentle slope of the T44 fluvial features point also to catastrophic floods, possibly intermittent and reinforced by hyperconcentrated flows (Burr et al., 2006), as the most likely processes capable of having progressively filled the channels with successive layers of imbricated boulders and pebbles. Until recently, Xanadu was tough to consist of a rugged raised terrain. But SARTopo (Stiles et al., 2009; see also Zebker et al., 2009) recently established that Xanadu is actually lower than most of its surrounds and that the Northwest of Xanadu is topographically higher than its South. As a consequence, all the channels of Xanadu are draining south. Thus, the location of the T44 channels suggests that they could be the mouth of the developed narrow stream channels networks observed in the Northern part of Xanadu (during T 13). If so, the sediments transported during episodic floods have hundreds of kilometers to be eroded and rounded. Besides, the regional topographic gradient might be the result of subsidence along tectonic faults (Radebaugh et al., 2009). The formation of the T44 channels most likely postdate to the loss of elevation of Xanadu but their landform evolution may still be tectonically controlled. The channels, as a matter of fact, traverse a sharp linear boundary that has been identified as a fault (Radebaugh et al., 2009). Their large width (1–8 km) might be the result of the drainage adjustment to the fault migration. The dendritic pattern that developed North of Xanadu seems also to be affected by an East–West fault motion.

5.3. Implications for other radar-bright regions of Titan Constraining the T44 channels environment might help understand other radar-bright areas of Titan. In particular, wide triangular radar-bright regions have been identified at the end of some channels and interpreted as alluvial fans (Lebreton et al., 2005; Elachi et al., 2006; Paillou et al., 2006; Lorenz et al., 2008). We postulate that they are zone of deposition covered with sediments transported by rivers. In particular, Leilah Fluctus, in the vicinity of Ganesa Macula, appears on the 3-D flyover of the digital topographic model (DTM) of the stereo overlap area between Ta and T 23 as an alluvial fan associated with bright channels coming out from the surrounding mountains (see Fig. 9) (Kirk et al., 2009). On the Earth, outwash fans are often associated with rockstrewn surfaces (Farr and Chadwick, 1996). As a general matter, the presence of sedimentary deposits consisting of large transparent rounded rocks provides a plausible explanation for bright fluvial features on Titan. Moreover, the correlation between SAR and VIMS (Visual and Infrared Mapping Spectrometer) data shows that the spectral units represented as dark blue in the VIMS analyses are present in the margin of the bright fluvial channels observed during the T 13 flyby (April, 2006) within the equatorial region of Xanadu (Barnes et al., 2007; Jaumann et al., 2008). In VIMS analyses, the blue spectral unit is believed to correspond to an enrichment in water ice relative to the rest of Titan (Rodriguez et al., 2006). It is thought to be associated with sedimentary deposits deriving from channel outwash (Barnes et al., 2007), consistent with our interpretation. Langhans et al. (2009) recently conducted a global investigation of Titan’s fluvial valleys and their spatial arrangement. They conclude that 60% of them are lying next to a blue spectral unit, which strengthens the hypothesis of fluvial debris. Moreover, the Huygens probe landed in a dark blue spectral unit (Soderblom et al., 2007). To date, neither Leilah Fluctus nor the channels observed during T44 have been imaged by VIMS.

Fig. 9. Leilah Fluctus observed during the Ta SAR swath, 100 km to the east of Ganesa Macula. The two triangular radar-bright channels and the associated bright area are interpreted as alluvial units where were collected icy coarse-sediments.

As noted previously, the sources of the T44 channels are likely to be found in the elevated Northern terrains of Xanadu and both of these units display an anomalously enhanced backscatter (Wye et al., 2007; Zebker et al., 2008; Janssen and Le Gall, 2009). It is thus tempting to apply our interpretation of the channels’ peculiar radar properties to Xanadu. Xanadu is also characterized by very low brightness temperature (70–80 K) and an effective dielectric constant approaching the unity (Janssen et al., 2009). Volume scattering has been invoked to explain these observations (Janssen et al., 2009). To date, the most satisfying model of Xanadu’s near surface describes a graded-density layer consisting of organics material covering or mixed with an extensively fractured water ice bedrock (Radebaugh et al., 2009). Single-bounce backscattering into a monolayer of large and poorly absorbing spheres would not produce the observed depolarization. In contrast, multiple layers of transparent spheres would both reduce the brightness temperature and randomize the polarization of emitted radiation. A companion paper (Janssen and Le Gall, 2009) shows that random scattering processes cannot explain the puzzling radar properties of Xanadu. It concludes that some new mechanism, putatively due to ordered structures on the surface, must be in play. Yet, the presence of layers of spherical icy rocks would be hard to explain in terms of geology for the full extent of Xanadu and other processes must be explored. It is pertinent to recall that strong echoes from small regions (tens of kilometers) on Titan were detected in groundbased 12 cm radar observations with the 300 m Arecibo radio telescope (Campbell et al., 2003) prior to Cassini’s arrival. At the time, these were interpreted as possible specular reflection from lakes of liquid hydrocarbons, although it was puzzling that many of these echoes seemed to correspond to optically-bright longitudes on Titan (Campbell et al., 2003; Roe et al., 2004), whereas lakes of liquid hydrocarbons would be expected to be optically dark. The strong echoes must have come from low latitudes (in fact if they were specular glints, they had to come from the sub-telescope latitude of 26°S), whereas it is now known that Titan’s tropics appear rather dry and lakes are found instead near the polar regions. We

A. Le Gall et al. / Icarus 207 (2010) 948–958

close this section with the observation that a geologically-plausible explanation (lakes) for these remarkable and unusual radar signatures was offered, and no other simple scenario suggested itself. Yet that explanation now seems difficult to reconcile with Cassini observations, which do not show lakes in these areas. This experience suggests that while we have similarly offered what we consider to be a geologically-plausible scenario for a different (but remarkable and unusual) radar signature, namely the bright channels, caution is appropriate. Titan remains complex and mysterious. 6. Conclusion On Titan, unlike on the Earth, on Mars or on the Moon, the rocks are transparent to microwaves. We postulate that such a difference explains, at least partially, the enhanced backscatters measured in many regions of Titan and, in particular, in the channels observed in the Southwest of Xanadu. This paper discusses the possible presence, in these channels, of ice rounded pebbles that would act as lenses that focus the waves in the backwards direction following the glory phenomenon. We indeed find the other mechanisms proposed either implausible or difficult to accept as an explanation for the strong backscatter measured. If our interpretation is correct, the high backscatter radar crosssections recorded in the T44 channels and the analogy with the Huygens landing site strongly suggest that the density of the pebbles in the channels is much higher that the density of rounded cobbles observed in the landing site of the probe. Icy rocks are likely to be closely spaced and potentially closely packed in their streambed, whereas they are strewn on the Huygens landing site. Modeling of the surface would then have to take into account multiple scattering and interference effects. Our preliminary simulations have shown that scattering in successive layers of imbricated large and transparent spheroids can indeed yield high backscatter. Though there is a variety of ways to form spheroids in nature (sap from pine trees, eggs, cannonball concretions, hailstones, meteorite ejecta that melt and harden in glassy quasi-spherical particles, etc.), the origin of the pebbles in the Huygens landing site is most probably fluvial, the equivalent of our polished river rocks. Our interpretation of the radar brightness of the channels is actually a further argument for this assumption. Rocks were transported and rounded by flowing liquid hydrocarbons, most likely during episodes of large floods. This raises the question of the rate of fluvial erosion on Titan. But in order to address it properly, we are somewhat hampered by a lack of knowledge about the geotechnical properties of materials relevant to Titan starting with water ice at 92 K. Other regions of Titan display a backscatter enhancement. In particular, radar brightness of some fluvial (or pluvial) features of Titan could be geologically explained by the presence of icy sedimentary deposits. Acknowledgments We gratefully acknowledge those who designed, developed and operate the Cassini/Huygens mission, which is a joint endeavor of NASA, the European Space Agency (ESA), and the Italian Space Agency (ASI) and is managed by JPL/Caltech under a contract with NASA. The research described in this publication was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The authors wish to thank H.U. Keller and M. Küppers for sharing their size statistic analysis of the pebbles of the Huygens landing site. Fig. 7 is extracted from Keller et al. (2008). They are

957

also grateful to Alain Reineix and Christophe Guiffaut from XLIM, Limoges, France who designed the TEMSI-FD code and whish to thank two anonymous reviewers for their insightful and thorough reviews. A. Le Gall is supported by the NASA Postdoctoral Program, administrated by Oak Ridge Associated Universities.

References Akimov, L.A., 1980. On the nature of the opposition effect. Vestn. Kharkovskogo Univ. 204 (15), 3–12. Asano, S., 1979. Light scattering properties of spheroidal particles. Appl. Opt. 18 (5), 712–723. Asano, Sato, 1980. Light scattering by randomly oriented spheroidal particles. Appl. Opt. 19, 962–974. Asano, S., Yamamoto, G., 1975. Light scattering by a spheroidal particle. Appl. Opt. 14 (1), 29–49. Barber, P., Yeh, C., 1975. Scattering of electromagnetic waves by arbitrary shaped dielectric bodies. Appl. Opt. 14 (12), 2864–2872. Barnes, J.W., 18 colleagues, and the Cassini Radar Team, 2007. Near-infrared spectral mapping of Titan’s Mountains and channels. J. Geophys. Res. 112, E11006. Besse, S., 2004. Etude Théorique de Radars Géologiques: Analyses de Sols, d’antennes et Interprétation des Signaux. Ph.D. dissertation, Univ. de Limoges, Limoges, France. Black, G.J., Campbell, D.B., Nicholson, P.D., 2001. Icy Galilean satellites: Modeling radar reflectivities as a coherent backscatter effect. Icarus 151, 167–180. Bohren, C.F., Huffman, D.R., 1983. Absorption and Scattering of Light by Small Particles. Wiley-Interscience Ed., New York, pp. 100–101. Burr, D.M., Emery, J.P., Lorenz, R.D., Collins, G.C., Carling, P.A., 2006. Sediment transport by liquid surficial flow: Application to Titan. Icarus 181, 235–242. Campbell, B.A., 2001. Radar backscatter from Mars: Properties of rock-strewn surfaces. Icarus 150 (1), 38–47. Campbell, D.B., Black, G.J., Carter, L.M., Ostro, S.J., 2003. Radar evidence for liquid surfaces on Titan. Science 302, 431–434. Collins, G.C., 2005. Relative rates of fluvial bedrock incision on Titan and Earth. Geophys. Res. Lett. 32, L2202. doi:10.1029/2005GL024551. Collins, G.C., Sklar, L.S., Zygielbaum, B., Polito, P., 2008. Laboratory investigation relevant to the erosion of ice on Titan. American Geophysical Union, Fall Meeting 2008, San Francisco, CA. Cuzzi, J.N., Pollack, J.B., 1978. Saturn’s rings: Particle composition and size distribution as constrained by microwave observations: I. Radar observations. Icarus 33 (2), 233–262. Elachi, C., and 21 colleagues, 2004. RADAR: The Cassini Titan radar mapper. Space Sci. Rev. 115, 71–110. Elachi, C., and 34 colleagues, 2006. Titan Radar Mapper observations from Cassini’s T 3 fly-by. Nature 441, 709–713. Eshleman, V.R., 1986. Radar glory from buried craters on icy moons. Science 234 (4776), 587–590. Farr, T.G., Chadwick, O.A., 1996. Geomorphic processes and remote sensing signatures of alluvial fans in the Kun Lun Mountains, China. J. Geophys. Res. 10 (E10), 23091–23100. Glover, K.M., Atlas, D., 1963. On the back-scatter cross-section of ice spheres. J. Appl. Math. Phys. 14, 563–573. Goldstein, R.M., Green, R.R., 1980. Ganymede: Radar surface characteristics. Science 207, 179–180. Golombek, M., Rapp, D., 1997. Size–frequency distributions of rock on Mars and Earth analog sites: Implications for future landed missions. J. Geophys. Res. 102, 4117–4129. Grasset, O., Sotin, C., Deschamps, F., 2000. On the internal structure and dynamics of Titan. Planet. Space Sci. 48, 617–636. Hagfors, T., Gold, T., Ierkic, H.M., 1985. Refraction scattering as origin of the anomalous radar returns of Jupiter’s satellites. Nature 315, 637–640. Hagfors, T., Dahlstrom, I., Gold, T., Hamran, S.-E., Hansen, R., 1997. Refraction scattering in the anomalous reflections from icy surfaces. Icarus 130, 313–322. Hapke, B.W., 1990. Coherent backscatter and the radar characteristics of outer planet satellites. Icarus 88, 407–417. Harmon, J.K., Ostro, S.J., 1985. Mars: Dual-polarization radar observations with extended coverage. Icarus 62, 110–128. Herman, B.M., Battan, L.J., 1961. Calculations of Mie back-scattering of microwaves from ice spheres. Q. J. R. Meteorol. Soc. 87, 223–230. Holt, A.R., Uzunoglu, N.K., Evans, B.G., 1978. An integral equation solution to the scattering of electromagnetic radiation by dielectric spheroids and ellipsoids. IEEE Trans. Antennas Propag. 26, 706–712. Janssen, M.A., Le Gall, A., 2009. Anomalous radar backscatter from Titan’s surface. Icarus, submitted for publication. Janssen, M.A., 15 colleagues, and the Cassini Radar Team, 2009. Titan’s surface at 2.2-cm wavelength imaged by the Cassini Radar radiometer: Calibration and first results. Icarus 200, 222–239. Jaumann, R., and 18 colleagues, 2008. Fluvial erosion and post-erosional processes on Titan. Icarus 197, 526–538. Keller, H.U., Grieger, B., Kuppers, M., Schroder, S.E., Skorov, Y.V., Tomasko, M.G., 2008. The properties of Titan’s surface at the Huygens landing site from DISR observations. Planet. Space Sci. 56, 728–752.

958

A. Le Gall et al. / Icarus 207 (2010) 948–958

Kirk, R.L., 16 colleagues, and the Cassini Radar Team, 2009. High resolution topographic models of Titan’s surface derived by radar stereogrammetry with a rigorous sensor model. Icarus, submitted for publication. Langhans, M., Jaumann, R., Stephan, K., Brown, R.H., Buratti, B.J., Clark, R., Baines, K.H., Nicholson, P.D., Lorenz, R.D., 2009. Fluvial valleys on Titan – A global perspective. In: 40th Annual Lunar and Planetary Science Conference, March 23–27, 2009, The Woodlands, TX, USA, 1681 (abstract). Latimer, P., 1980. Predicted scattering by spheroids: Comparison of approximate and exact methods. Appl. Opt. 19 (18), 3039–3041. Le Gall, A., 2007. Sondage des sous-sols planétaires par radar à pénétration de sol – Etude et modélisation des performances de l’instrument TAPIR. Universite Pierre et Marie Curie (Paris VI), France, November 2007. Lebreton, J.P., and 11 colleagues, 2005. An overview of the descent and landing of the Huygens probe on Titan. Nature 438, 758–764. Lewis, J.S., 1971. Satellites of outer planets – Their physical and chemical nature. Icarus 15 (2), 174–185. Lopes, R.M.C., 24 colleagues, and the Cassini RADAR Team, 2009. Distribution and interplay of geologic processes on Titan from Cassini RADAR. Icarus 205, 540– 558. Lorenz, R.D., 1993. The life, death and afterlife of a raindrop on Titan. Planet. Space Sci. 41, 647–655. Lorenz, R.D., Griffith, C.A., Lunine, J.I., McKay, C.P., Renno, N.O., 2005. Convective plumes and the scarcity of clouds on Titan. Geophys. Rev. Lett. 32, L01201. Lorenz, R.D., Lunine, J.I., 1996. Erosion on Titan: Past and present. Icarus 122, 79–91. Lorenz, R.D., Builloz, G., Encrenaz, P., Janssen, M.A., West, R.D., Muhleman, D.O., 2003. Cassini Radar: Prospects for Titan surface investigations using the microwave radiometer. Planet. Space Sci. 51, 353–364. Lorenz, R.D., Niemann, H., Harpold, D., Zarnecki, J., 2006. Titan’s damp ground: Constraints on Titan surface thermal properties from the temperature evolution of the Huygens GCMS inlet. Meteorit. Planet. Sci. 41, 1405–1414. Lorenz, R.D., Lopes, R., Paganelli, F., Lunine, J.I., Kirk, R.L., 2008. Fluvial channels on Titan: Initial Cassini Radar observations. Planet. Space Sci. 56, 1132–1144. Lunine, J.L., and 43 colleagues, 2008. Titan’s diverse landscapes as evidenced by Cassini Radar’s third and fourth looks at Titan. Icarus 195, 415–433. McDonald, J.E., 1962. Large sphere limit of the radar back-scattering coefficient. Q. J. R. Meteorol. Soc. 88, 183–186. Mill, H.H., 1979. Downstream rounding of pebbles – A quantitative review. J. Sediment. Petrol. 49 (1), 295–302. Mitchell, K.L., and 16 colleagues, 2009. Titan’s north polar lake district: Insights from the Cassini Titan Radar Mapper. Icarus, submitted for publication. Mitri, G., Showman, A.P., Lunine, J.I., Lopes, R.M.C., 2008. Resurfacing of Titan by ammonia–water cryomagma. Icarus 196, 216–224. Niemann, H.B., and 17 colleagues, 2005. Huygens probe gas chromatograph mass spectrometer: The atmosphere and surface of Titan. Nature 438, 779–784. Paganelli, F., 13 colleagues, and the Cassini Radar Team, 2007. Titan’s surface from the Cassini Radar SAR and high resolution radiometry data of the first five flybys. Icarus 191, 211–222. Paillou, P., Crapeau, M., Elachi, C., Wall, S.D., Encrenaz, P., 2006. Models of synthetic aperture radar backscattering for bright flows and dark spots on Titan. J. Geophys. Res. 111. doi:10.1029/2006JE002724. E11011. Paillou, P., Lunine, J.I., Ruffié, G., Encrenaz, P., Wall, S.D., Lorenz, R.D., Janssen, M.A., 2008. Microwave dielectric constant of Titan-relevant materials. Geophys. Res. Lett. 35, L18202, doi:10.1029/2008GL035216. Perron, J.T., Lamb, M.P., Koven, C.D., Fung, I.Y., Yager, E., Ádámkovics, M., 2006. Valley formation and methane precipitation rates on Titan. J. Geophys. Res. 111. doi:10.1029/2005JE002602. E11001.

Pettengill, G.H., Hagfors, T., 1974. Comment on radar scattering from Saturn’s rings. Icarus 21, 188–190. Polito, P.J., Zygielbaum, B.R., Sklar, L.S., Collins, G., 2008. Experimental investigation of fluvial incision on Titan by low-velocity sediment impacts. American Geophysical Union, Fall Meeting 2008, San Francisco, CA. Radebaugh, J., 17 colleagues, and the Cassini Radar Team, 2009. Regional geomorphology and history of Titan’s Xanadu province. Icarus, submitted for publication. Richards, K., 1982. Rivers: Form and Process in Alluvial Channels. Routledge Ed.. Roden, J.A., Gedney, S.D., 2000. Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media. Microwave Opt. Technol. Lett. 27 (5), 334–339. Rodriguez, S., Le Mouelic, S., Sotin, C., Clénet, H., Clark, R., Buratti, B.J., Brown, R.H., Mc Cord, T.B., Nicholson, P.D., Baines, K.H., 2006. Cassini/VIMS hyperspectral observations of the Huygens landing site on Titan. Planet. Space Sci. 54, 1510– 1523. Roe, H.G., de Pater, I., Gibbard, S.G., Macintosh, B.A., Max, C.E., Young, E.F., Brown, M.E., Bouchez, A.H., 2004. A new 1.6 micron map of Titan’s surface. Geophys. Res. Lett. 31. L17S03. Ruck, G.T., Barrick, D.E., Stuart, W.D., Krichbaum, C.K., 1970. Radar Cross Section Handbook, vols. 1 and 2. Plenun Press, New York, London. Shkuratov, Yu.G., 1983. A model of the opposition effect in the brightness of airless cosmic bodies. Soviet Astron. 27, 581–583. Sklar, L., Dietrich, W.E., 2004. A mechanistic model for river incision into bedrock by saltating bedload. Water Resour. Res. 40. doi:10.1029/2003WR002496. W06301. Soderblom, L.A., and 26 colleagues, 2007. Correlations between Cassini VIMS spectra and RADAR SAR images: Implications for Titan’s surface composition and the character of the Huygens Probe Landing Site. Planet. Space Sci. 55 (13), 2025–2036. Stiles, B.W., 18 colleagues, and the Cassini Radar Team, 2009. Determining Titan surface topography from Cassini SAR data. Icarus, 5. doi:10.1016/ j.icarus.2009.03.032. Tobie, G., Lunine, J.I., Sotin, C., 2006. Episodic outgassing as the origin of atmospheric methane on Titan. Nature 440, 61–64. Tomasko, M.G., and 39 colleagues, 2005. Rain, winds and haze during the Huygens probe’s descent to Titan’s surface. Nature 438, 765–778. Ulaby, F.T., Moore, R.K., Fung, A.K., 1982. Microwave Remote Sensing – Active and Passive, vol. II: Radar Response and Surface Scattering and Emission. AddisonWesley Publishing Company. West, R., and 19 colleagues and the Cassini RADAR Team, 2009. Sequence planning and instrument performance. IEEE Trans. Geosci. Remote Sensing 47(6), 1777– 1795. Wye, L.C., Zebker, H.A., Ostro, S.J., West, R.D., Gim, Y., Lorenz, R.D., the Cassini Radar Team, 2007. Electrical properties of Titan’s surface from Cassini Radar scatterometer measurements. Icarus 188, 367–385. Yee, K.S., 1966. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propagat. 44, 302–307. Zebker, H.A., Wye, L.C., Janssen, M.A., the Cassini Radar Team, 2008. Titan’s surface from reconciled Cassini microwave reflectivity and emissivity observations. Icarus 194, 704–710. Zebker, H.A., Stiles, B., Hensley, S., Lorenz, R., Kirk, R.L., Lunine, J., 2009. Size and shape of Saturn’s moon Titan from Cassini Radar altimeter and SAR monopulse observations. Science 324, 921–923.