Precipitation-induced surface brightenings seen on Titan by Cassini VIMS and ISS
- Jason W Barnes1Email author,
- Bonnie J Buratti2,
- Elizabeth P Turtle13,
- Jacob Bow1,
- Paul A Dalba2, 3,
- Jason Perry5,
- Robert H Brown5,
- Sebastien Rodriguez10,
- Stéphane Le Mouélic8,
- Kevin H Baines15,
- Christophe Sotin2,
- Ralph D Lorenz13,
- Michael J Malaska2,
- Thomas B McCord4,
- Roger N Clark6,
- Ralf Jaumann12,
- Paul O Hayne7,
- Philip D Nicholson9,
- Jason M Soderblom14 and
- Laurence A Soderblom11
© Barnes et al.; licensee Springer. 2013
Received: 17 March 2012
Accepted: 29 October 2012
Published: 14 January 2013
Observations from Cassini VIMS and ISS show localized but extensive surface brightenings in the wake of the 2010 September cloudburst. Four separate areas, all at similar latitude, show similar changes: Yalaing Terra, Hetpet Regio, Concordia Regio, and Adiri. Our analysis shows a general pattern to the time-sequence of surface changes: after the cloudburst the areas darken for months, then brighten for a year before reverting to their original spectrum. From the rapid reversion timescale we infer that the process driving the brightening owes to a fine-grained solidified surface layer. The specific chemical composition of such solid layer remains unknown. Evaporative cooling of wetted terrain may play a role in the generation of the layer, or it may result from a physical grain-sorting process.
KeywordsTitan Atmosphere Titan Hydrology
Dendritic networks of channels seen by Huygens revealed that rainfall drives surface erosion on Titan . Subsequent Cassini observations showed that similar channels are seen globally on all types of Titan terrain [2–7]. While some channels terminate in broad alluvial fans, like those at the spot of Huygens’ touchdown, others lead to polar seas [8, 9] or dry lakebeds [10, 11].
The timing of channel formation remains largely unknown. As yet there is no evidence for any of Titan’s channels being presently filled with downhill-streaming liquid. Titan’s atmospheric methane is being irreversibly destroyed [12, 13], meaning that the channels could be vestigial – left over from a subsequently altered paleoclimatic regime. Global circulation models imply a relative paucity of rainfall at equatorial latitudes [14, 15]. And the presence of sand dunes at low latitudes [16, 17] is certainly consistent with Titan’s equator being a desert in the present day. However soil moisture present at the equatorial Huygens landing site [18–20], along with the ubiquity of channels in Earth’s deserts, are a reminder that rainfall-driven (pluvial) processes affect deserts despite infrequent rain events.
Heavier cloud cover, and presumably higher rainfall, occurs at the poles and at 40° latitude in the summer hemisphere [21–24]. However the correlation between clouds and surface rainfall is not obvious. Early theoretical models indicated that rain could not reach the surface of Titan owing to evaporation during its fall . A more complete calculation including the effects of latent heat more recently established that rain is possible at Titan’s surface .
Recent Cassini Imaging Science Subsystem (ISS) data dramatically confirmed that rain occurs on Titan through observation of regional darkenings southwest of Adiri associated with large cloud outbursts . Turtle et al. (2011)  interpret these darkenings as pluvially derived liquid wetting of the surface. Subsequent to the rainfall event, some of the affected areas have brightened again. Interestingly, Turtle et al. (2011)  report that some locations within Adiri brightened to albedos higher than the values prior to their wetting.
In this paper, we use new observations from the Cassini Visual and Infrared Mapping Spectrometer (VIMS) and ISS instruments to further examine the brightenings in Adiri and newly recognized brightening in three other tropical locations on Titan’s surface. Section “Observation” describes the Cassini VIMS and ISS observations that we use and the state of the surface prior to the wetting event. In Section “Variation” we describe the time-evolution of the albedo of the wetted areas over the past year, with particular concentration on the brightening of the surface that occurs after the wetting-induced darkening. VIMS observations of the area allow us to evaluate the nature of the change in the spectral character of the surface, which we do in Section “Coloration”. We describe possible physical processes that could be creating the brightening in Section “Discussion”, and present our conclusions in Section “Conclusion”.
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The changes that we will describe in Section “Variation” occurred near 36°E 18°S. This area is part of Yalaing Terra, inside the Equatorial Bright unit. Two mountain ranges, inferred from subtle blue deviations from the equatorial bright spectrum of the sort discovered empirically by Barnes et al. 2007 , cross the area. The eastern mountain range (labelled ‘E’ in Figure 2) is linear, with a north-south orientation. The western range (labelled ’W’ in Figure 2) has a roughly circular shape, and thus could be the remnant of an ancient impact crater wall. The eastern range is more prominent than the western range; hence it is probably either higher, rougher, or larger in total extent.
Northeast of the eastern mountain range, between it and the dunes, lies an instance of 5- μ m-bright terrain. 5- μ m-bright terrain was first identified early in the Cassini mission [36–38], and its spectrum is consistent with either very low or zero water-ice content. Its specific nature as dry lakebeds of evaporite, however, was only recently proposed . We interpret that this area, too, represents an evaporitic dry-lake deposit.
Even in the Cassini Equinox mission (2008 July through 2010 October), VIMS views of Hetpet Regio are of relatively coarse spatial resolution and have high emission angles (see Table 1). The map in Figure 3 is a best guess based on this limited information. Cassini RADAR from T21 covers the western portion of this study area.
The area is mostly free of high mountains. The dunes end at the northern edge of the change area, and cross it in one case. This area is bordered on the west, and possibly on the east as well, by the rarest of Titan surface spectral units: bright blue terrain (as from ). The bright blue spectral unit shows a higher signature of water ice than other areas on Titan , a characteristic that it shares with the dark blue unit (outwash plains, like at the Huygens Landing Site ). Presumably the bright blue differs from the dark blue in that it has a thinner or less extensive coating of dark organic material on it, but little else is known about bright blue terrain. The central portion of the Hetpet Regio change site consists of Equatorial Bright material.
In the north of this image is the Belet sand sea. Concordia Regio extends into the dunes from the south as an instance of Equatorial Bright  terrain. Several areas show slight enhancements in water ice. VIMS’ spatial resolution and signal-to-noise here are insufficient to break the degeneracy between those icy areas being mountains or channels. Future observations could shed more light on the geology of this area. Concordia Regio is of particular interest given the changes seen by Turtle et al. 2011  and those that we describe herein.
The bright albedo feature Adiri itself represents an instance of the VIMS Equatorial Bright spectral unit typical of those parts of Titan’s tropics that are not covered in dunes. Adiri is surrounded by sand seas, with Belet to the west and Shangri-La to the east. Unusually for large Equatorial Bright regions, Adiri also has sand dunes within its extent. The four central dunefields have been assigned the names Eurus Undae, Boreas Undae, Kajsa Undae, and Notus Undae after the Greek gods of the eastern, northern, western, and southern winds respectively (Figure 5, lower-left panel).
We identify mountains in the SAR data using the techniques outlined in  – primarily via bright-dark line pairings indicative of layover of topography in delay-Doppler space. Adiri is highly mountainous . The mountains here are primarily linear or curvilinear. Their orientations are broadly east-west. The mountains interact with the interspersed dunefields in a complex pattern, sometimes delineating the margins of dunefields and sometimes intruding into them. The identification of mountains in the unit map in Figure 5 is the most certain of any of the areas due to the presence of RADAR data and VIMS coverage with both high signal-to-noise and moderate spatial sampling (14 km/pixel). For ease of reference, six of Adiri’s mountain ranges in our study area have been named as we indicate in Figure 5 (lower-left panel).
All of our study areas show roughly the same pattern of brightness changes, centered on the 2010 September cloudburst, but occurring with slightly different timescales. Here we examine the time-evolution of each area in individual detail, before inferring general trends.
On T76 (2011 May 8), VIMS sees several large regions that have brightened beyond their original Equatorial Bright albedo spectrum. The areas are tens to hundreds of kilometers across, with at least seven distinct, separated areas having brightened. VIMS’ only intervening view between T67 and T76 was on T74 (2011 February 18). The T74 observations were of rather coarse spatial resolution, and hence are inconclusive, but appear to show that the brightening had already occurred by the time of that flyby.
ISS observes Titan more frequently than just on the close flybys. The finer angular resolution of the ISS Narrow Angle Camera (NAC) allows moderate-spatial-resolution, full-disk Titan imaging from distances over 3 million kilometers. During both the Equinox and Solstice extended missions, Cassini ISS observes Titan every few weeks in the Titan Meteorological Campaign (TMC) in order to monitor cloud activity. In so doing, ISS resolves the recent surface changes in Yalaing Terra in time, complementing the ability of VIMS to resolve them in wavelength (spectrum). Because TMC observations occur between numbered close Titan flybys, they do not have a T-number associated with them.
The first image in the sequence, from 2010 December 20, shows both brightening and darkening in Yalaing Terra, both changes from the original, pre-cloudburst albedo spectrum. Darkening occurs both in the eastern end of Yalaing Terra and in the north-central area that we interpret as evaporite in Figure 2, consistent with ephemeral ponding in a local basin. A larger area centered 300 km west of the evaporite shows more modest but still significant surface darkening as well, perhaps from surface wetting as seen elsewhere .
Brightened areas exist directly contiguous with darkened areas. ISS sees that the surface has brightened immediately surrounding the larger moderately darkened area to the west, south, east, and northeast. These brightenings appear only in VIMS spectral units identified as Equatorial Bright terrain. The brightenings avoid the areas richer in water ice that could be mountains or icy plains.
By 2011 April 25, the large, moderately darkened area has disappeared. Instead, much of that area is now brightened instead, beyond its original albedo. Most of those previously brightened areas are still brightened, but some on the periphery have reverted to their original (‘Equatorial Bright’) state.
Later observations show brightened areas with similar extent to those identified by VIMS on T76 (2011 May 8). The brightest areas seen by VIMS on T76 occur in the same area that ISS identified as moderately darkened on 2010 December 20. The brightened areas appear to be drawing inward to smaller and smaller spatial extents over the course of many months, with the areas first identified as moderately dark and those that were brightest persisting for longest. The instance of the evaporitic spectral unit seen by VIMS prior to the cloudburst of 2010 September is no longer evident on T76.
Our most recent observation from VIMS, on T80 (2012 January 2), though of modest resolution, shows the least areal extent of brightening since T67. Despite the modest quality of the observation, the evaporite deposit is again visible on T80, implying that whatever process prevented it from being visible on T76 no longer does so.
where V represents the measured brightness value of each respective area in the processed ISS image, and R represents the relative reflectivity as defined. The resulting curve matches the qualitative description of albedo changes as described previously.
Our second study area, Hetpet Regio (centered near 72°E 22°S), is 1600 km east of Yalaing Terra. Like Yalaing Terra, historical VIMS observations acquired over the full Cassini mission confirm that the area was static until sometime between T67 (2010 April 5) and T74 (2011 February 18). We show before and after views in Figure 10 for comparison. In Hetpet Regio, a swath of Titan’s surface also brightened as seen by VIMS. This change was approximately 3.5 times more extensive in surface area than the Yalaing Terra changes.
Over the ensuing months many of the darkened areas become brightened areas – not just reverting, but brightening beyond their original reflectivity significantly. By T80 (2012 January 2), the total contrast that the Hetpet Regio brightening shows relative to its surroundings decreased as seen by VIMS. The coarse spatial resolution coverage makes analysis of the extent of the brightenings ambiguous from VIMS T80.
Turtle et al. (2011)  first saw brightening in the southeast portion of the area that was rain-wetted on 2010 October 29 (see  supplemental online material). Multiple observations separated by 15 hours showed that the brightening was surficial, and not atmospheric in nature. Given the other cotemporal brightenings in Yalaing Terra, Hetpet Regio, and Adiri (see next subsection, “Adiri”) over the ensuing months, the initial brightening in the wake of the 2010 October 29 darkening is evidently part of a larger geographic event.
Our best opportunity to place the changes that we see into local context are within Adiri. There, high-quality imaging from VIMS (T70, T77, T79), ISS, and RADAR (T8 and T61) all coincide, giving us the best opportunity to constrain the processes driving surface change.
By 2011 January 15 most of the altered areas had brightened, but with one moderate-sized darkened area still southeast of Notus Undae. That darkened area is flanked to both the ENE and WSW by similarly sized brightened areas. The previously darkened zones in south Adiri adjacent to Belet became brightened areas. The previously darkened region between Dolmed Montes and Notus Undae had by then also become brightened relative to its original, pre-cloudburst state. A larger brightened area west of Dolmed Montes extends for 250 km to the south of the Angmar Montes range and parallel to it. Along the eastern part of this study area there is a large brightened region located between Echoriath Montes and Gram Montes, east of the eastern lobe of Notus Undae. And some smaller brightened surfaces exist either in or adjacent to the eastern end of Merlock Montes.
The ISS observations for this area are of sufficient quality to measure relative reflectivity as a function of time, shown in Figure 9. The overall evolution in surface reflectivity for Adiri tracks well with that in Yalaing Terra. Adiri seems to evolve faster, though, brightening before Yalaing Terra and beginning to revert to normal at +9 months.
In addition to brightness and morphological information, the VIMS observations of our four change areas contain spectral information. Here we use that spectral information to constrain the altitude and composition of the changed regions.
The frequent ISS observations of the four areas (Section “Variation”) show consistency in the geographic locations of the changes, along with slow changes in the brightness of each area following the same pattern. The geographic stability of the areas over time implies that the changes are surficial and not atmospheric.
VIMS spectra of the changed regions agree that they are inconsistent with clouds. At the top of Figure 20, we show spectra of the changed and unchanged parts of Hetpet Regio and compare them to the spectrum of a cloud from the T33 flyby (2007 June 29). As is evident from the figure, the brightening in Hetpet Regio occurred exclusively within the atmospheric windows to the surface. In particular, at the spectral wings of the atmospheric windows, where clouds in the upper troposphere show distinctive and significant brightening over surface features (arrows in Figure 20), the changed region is static, as would be expected if it were purely a surface phenomenon. Griffith  and others have used similar altitude discriminators, particularly at the longward end of the 2-micron window.
The relative I/F of each of the brightened areas within the spectral windows is also inconsistent with clouds. Figure 21 shows the integrated I/F for the Yalaing Terra brightened pixels from T76 compared against Equatorial Bright terrain, dark brown terrain (dunes), and clouds, all with the same viewing geometry. The T76 brightenings plot outside the bounds of normal Equatorial Bright terrain, but also fall well outside the region associated with clouds. Because this in-window test depends more highly on the target’s spectrum and less on its altitude, it allows us to rule out near-surface ground fogs as well as high clouds. The longevity and temporal consistency of the changed features is likewise inconsistent with fog. Viewing geometry significantly affects Titan spectra. To maximize the interpretability of intercomparison we therefore use observations with as nearly identical observing geometry as possible. In particular, we elect to use the cloud on T33 as a comparison, based on the incidence and emission angles from the T76 Hetpet Regio geometry (i=31°, e=47°), having searched the entire VIMS dataset for points on each flyby that had identical geometry. In general, there is at least one such point for each flyby (though their phase angles will differ depending on the illumination geometry of the flyby). We then correlated that ‘best match’ pixel on each flyby with its corresponding cylindrical map to find the best geometric matches to any given category of spectral unit (in this case, cloud). The T33 cloud at 40.1°S 142.9°E compares most favorably and is shown in Figure 20.
Although our temporal coverage is incomplete, in at least some places the changed areas darken first, remain dark for a period of weeks to months, become brightened beyond their original equatorial bright state, and then the extents of the brightened areas slowly decrease over timescales of months to a year.
Brightening only occurs on Equatorial Bright terrains, never in dunes, mountains, or the VIMS dark blue unit despite the geographic proximity of those terrains to the brightened areas.
The brightenings are surficial features, inconsistent with both high altitude clouds and low-lying fog.
I/F increases at all wavelengths in brightened areas.
The spectra of brightened areas all match each other to within the uncertainty of measured surface reflectance, at least at wavelengths where such comparisons are valid.
One instance of evaporite in Yalaing Terra disappeared temporarily as a result of the event.
Early on, brightened areas exist contiguously with darkened areas.
The similarities in brightened spectra (constraint 5) along with the similarities of brightness histories (constraint 1) together imply that we are looking at multiple instances of the same physical process. Moreover, the similarity in latitude, relative contiguity in longitude, cotemporal occurrence, and correlation with the 2010 cloudburst event identified by Turtle et al. 2011  are all consistent with the process originating with some sort of precipitation.
A potential problem with wetting by pure liquid methane comes from the evaporation rate. Mitri  estimates evaporation rates for 100% methane at 94 K exposed to a 1 m/s wind to be ∼15 meters per year, while for 35% methane, 60% ethane, 5% nitrogen it was estimated to be ∼6 meters per year. These translate to 2-5 mm/day. More detailed calculations [15, 50] show that the Mitri calculation most likely represents an upper limit, and that evaporation rates on the order of ∼1 m per Titan year are more likely. The most trustworthy observations of continuous surface darkening are from Concordia Regio (Figure 14), where the darkening lasted for at least 80 days. An exposed solution would evaporate 1.6 meters of liquid in that time. However, that number would be decreased by the liquid’s surface activity, given wetting, and reduced further by evaporative cooling of the liquid and solid surface . Further numerical studies and/or experiments are needed characterize the process of a hydrocarbon-wetted icy surface drying due to evaporation on Titan.
The geologic context for the ensuing brightening – not in dunes or mountains, but rather in valleys (sometimes) adjacent to mountains – might relate to the nature of the surface. Rain on mountains might be expected to easily run off, whereas rain onto a porous regolith could penetrate in and wet the surface layer. Rain into dunes might then very easily percolate down far enough so as to be inaccessible from the surface.
The brightening lasted many months (over a year in Yalaing Terra and Hetpet Regio) before fading back to the original spectrum. That duration is inconsistent with chemical alterations to the surface. A chemical change to the surface associated with precipitation – say by rain washing the surface clean (as proposed for the origin of Xanadu ), physical overturn of the surface layer exposing fresh regolith, chemical weathering, or sediment deposition – would likely not return to the original spectrum so closely or so quickly. Deposition timescales for atmospheric haze [53, 54] are estimated to be 0.1 μ m per Titan year – too low to bury and overprint chemically altered surfaces.
Thus we conclude that the surface brightening that follows the precipitation-wetted and -darkened surface is probably the result of the presence of a transient layer of material – potentially a volatile. A volatile can both be emplaced and removed over the timescales shown by the observations. Any solid with small grain size would appear bright at all wavelengths to VIMS, and thus be consistent with the observed spectrum.
The composition and nature of such a volatile remains an open question. The Huygens-measured surface temperature in Titan’s tropics was 93.65±0.25 K  – well above the freezing point of both methane (90.7 K) and ethane (90.4 K). Hence, even if hail survived passage through Titan’s lower atmosphere as a solid to land on the surface , the warm surface might eventually melt it. If that timescale is sufficiently short, less than a few weeks, then both solid and liquid precipitation might be expected to leave a darkened wetted surface like that seen by ISS. Given that we see the time progression of dark, then brightened, a simple hail or snow scenario is not consistent with the observations.
Some process then needs to occur that leaves a thin layer of solid on the surface.
One possible option would be dissolution, wicking upward, and subsequent reprecipitation of heavier hydrocarbons like acetylene or hydrogen cyanide on the surface. This process would be related to evaporite formation , but is sufficiently distinct as to the chemicals involved that it might reasonably be expected to lead to different surface spectra from the lake-bottom evaporites. The crystals of such precipitates could sinter together over time to increase the grain size and revert the surface to its previous state. Initial calculations using a model that assumes ice grain growth by vapor exchange (after ) indicate that propane (for example) would take weeks to months to coalesce, and is therefore a credible candidate. Here we assume that evaporative cooling keeps propane as ice (its melting point is 85.5 K). Solids with melting points signficantly above ambient Titan temperatures, like acetylene and butane, would take several years and a thousand years respectively for grain growth – inconsistent with the observed reversion time that is on the order of months to a year.
Scenarios involving subsurface percolation of liquid might be expected to not be possible in rocky areas without surficial regolith, or in extremely porous media like sand. Hence this could explain the geographical confinement of brightening to Equatorial Bright terrain.
The evaporative cooling scenario would necessarily involve surface temperatures ≲90 K. A thermal signature of the resulting surface cold spots might then be visible to the Cassini InfraRed Spectrometer (CIRS) instrument, which has measured Titan surface temperatures previously [57, 58]. Unfortunately no CIRS observations exist that are sufficient to constrain surface temperatures of the changed areas in the relevant timeframe (2010 September to 2011 December; V. Cottini, personal communication).
Another possibility is that the precipitated liquid itself freezes on the surface due to evaporative cooling. In this scenario, evaporation subsequent to the initial wetting continually cools the surface, with a cooling thermal wave propagating into the surface via conduction. Evaporative cooling can be tremendously efficient, as any swimmer leaving a swimming pool on a windy day in the desert will experience. After some or most of the near-surface liquid is evaporated away, the surface temperature could drop below the freezing point, resulting in a thin frost that then sublimes away over the course of the ensuing months. Alternately, if the structures left on the surface are sufficiently fragile then wind might be able to erode them away by wind entrainment over time.
The chemical identity of such evaporatively cooled frost would probably be methane, ethane, or a solution of methane and ethane. Graves  suggested two possible composition models for Titan’s rain, which wetted the surface in the first place: 40% methane, 40% ethane, 20% dissolved nitrogen (assuming 50% relative humidity for ethane); and 77% methane, 23% nitrogen (with 0% ethane relative humidity). Graves  predicted that ethane-rich drops would be warm when they reached the ground (93.5 K), but methane-nitrogen drops would be cold due to evaporative cooling (90.0 K). Hence a surface wetted by methane-nitrogen drops would evaporate methane and cool off and might continue to do so until the surface temperature becomes cold enough to freeze the liquid as its composition evolves. In the context of lakes, modeling has shown that a pure-methane lake would freeze due to evaporative cooling under polar conditions [49, 51].
Alternatively, the nearly pure methane hail that Graves  suggests might be able to both cool the surface significantly on its initial melting, and to increase the freezing point of the liquid due to exsolution of nitrogen from the hailstone on freezing.
This evaporative-cooling/frost hypothesis is consistent with the observational data. Clearly, however, additional thinking, modeling, and experimentation would be needed to verify whether or not it is indeed plausible under Titan conditions. More comprehensive work might also be able to constrain possible compositions for the resulting frost. If surface temperature measurements were sufficiently precise, they might also be able to test the model by directly determining temperatures in affected areas before, during, and after a rainfall event.
An alternate scenario for the origin and disappearance of the thin, brightened surface layer involves purely physical processes. On Earth, some types of terrain will typically develop a very thin deposit of bright, fine-grained material in the wake of rain storms. This deposit is composed of local materials that were remobilized by the presence of liquid. On Titan, such a layer could develop rapidly upon drying, and then disappear as the fine-grained material blows away due to aeolian erosion.
We analyze the surface reflectivity history of four study areas on Titan in the wake of the 2010 September cloudburst storm: Yalaing Terra, Hetpet Regio, Concordia Regio, and Adiri. Cassini ISS shows that these areas darkened in the wake of the storm due to wetting of the surface regolith by rainfall . Weeks to months later, each of these areas showed patches of significant and extensive surface brightening that persisted for up to a year before reverting to their previous spectrum.
Each of these areas had been completely static for the entirety of the mission up until the 2010 September cloudburst. Their temporal co-association along with the narrow latitude range and large longitude range (120°) indicates that the surface changes, both darkening and brightening, are associated with precipitation.
Near-infrared spectral mapping from VIMS observations of the affected areas shows that the brightening occurred at all wavelengths and was uniform across the four study areas. The cloud wings and the in-window I/F measured rule out an atmospheric source for the brightening. The spectrally uniform (‘white’) brightening is consistent with either full or patchy deposition of a fine-grained solid.
The physical process that led to the brightening might be deposition of a thin layer of volatile frost. Multiple pathways for generating such a layer are possible. One is that cooling via methane evaporation might freeze either a component of the liquid itself or condense atmospheric gases out on to the surface. The volatile layer then sublimates over the ensuing year.
Alternatively, fine remobilized grains could generate the brighened surface layer. In this scenario, the fine grains would blow away over time in order to allow the surface to revert to its original spectrum.
Analysis of RADAR overlap with the Adiri study area shows that the brightenings do not occur within mountain or dune units, but rather only occur in VIMS Equatorial Bright terrain between mountains. This geologic correlation could result from differences in regolith properties or the local liquid (hydrocarbon) table.
Future work needs to be done to either constrain or rule out various brightening mechanisms. Computer models and/or laboratory work could significantly contribute to our understanding of the brightening’s origin. Furthermore, continued monitoring by Cassini’s instruments will be able to identify future instances of surface changes and, by using comparison with the events described here, to further constrain the deposition process and Titan’s volatile cycle.
The authors acknowledge support from the NASA/ESA Cassini Project. JWB acknowledges support from NASA Outer Planets Research Program grant NNX10AQ10G.
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