Fluvial features on Titan: Insights from morphology and modeling

Devon M. Burr1,†, J. Taylor Perron2, Michael P. Lamb3, Rossman P. Irwin III4, Geoffrey C. Collins5, Alan D. Howard6, Leonard S. Sklar7, Jeffrey M. Moore8, Máté Ádámkovics9, Victor R. Baker10, Sarah A. Drummond1, and Benjamin A. Black2 1Earth and Planetary Sciences Department, University of Tennessee–Knoxville, 1412 Circle Drive, Knoxville, Tennessee 37996-1410, USA 2Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA 3Geological and Planetary Sciences, California Institute of Technology, 1200 E California Boulevard, MC 170-25, Pasadena, California 91125, USA 4Center for Earth and Planetary Studies, National Air and Space Museum, Smithsonian Institution, MRC 315, 6th Street at Independence Avenue SW, Washington, District of Columbia 20013, USA 5Physics and Astronomy Department, Wheaton College, 26 E. Main Street, Norton, Massachusetts 02766, USA 6Department of Environmental Sciences, University of Virginia, P.O. Box 400123, Charlottesville, Virginia 22904-4123, USA 7Department of Geosciences, San Francisco State University, 1600 Holloway Avenue, San Francisco, California 94132, USA 8Space Sciences Division, National Aeronautics and Space Administration Ames Research Center, MS 245-3, Moffett Field, California 94035, USA 9Astronomy Department, University of California, 601 Campbell Hall, Berkeley, California 94720-3411, USA 10Department of Hydrology and Water Resources, The University of Arizona, J.W. Harshbarger Building, Room 246, 1133 E. James E. Rogers Way, Tucson, Arizona 85721-0011, USA

ABSTRACT leys rather than channels, and that uplands INTRODUCTION elsewhere on Titan may also have fi ne-scale Fluvial features on Titan have been iden- fl uvial dissection that is not resolved in SAR Observations of Titan from the Cassini- tified in synthetic aperture radar (SAR) data. Radar-bright terrain with crenulated Huygens mission to the Saturn system (Kerridge data taken during spacecraft fl ybys by the bright and dark bands is hypothesized here et al., 1992; Matson et al., 2002) revealed an Cassini Titan Radar Mapper (RADAR) and to be a signature of fi ne-scale fl uvial dissec- extraterrestrial world with an active volatile in Descent Imager/Spectral Radiometer tion. Fluvial deposition is inferred to occur cycle and resultant fl uvial landforms. Analysis (DISR) images taken during descent of the in braided channels, in (paleo)lake basins, of fl uvial landforms on Earth by the founders Huygens probe to the surface. Interpreta- and on SAR-dark plains, and DISR images of modern geology (e.g., Lyell, 1830) laid the tions using terrestrial analogs and process at the surface indicate the presence of fl uvial groundwork for a better understanding of terres- mechanics extend our perspective on fl uvial sediment. Flow suffi cient to move sediment is trial landscape evolution. The discovery of relict geomorphology to another world and offer inferred from observations and modeling of valley networks and outfl ow channels on Mars insight into their formative processes. At the atmospheric processes, which support the in- (Mars Channel Working Group, 1983) funda- landscape scale, the varied morphologies ference from surface morphology of precipi- mentally revised our view of that planet’s evolu- of Titan’s fl uvial networks imply a variety tation-fed fl uvial processes . With material tion and early history. Likewise, the revelation of mechanical controls, including structural properties appropriate for Titan, terrestrial of fl uvial features on Titan provides a powerful infl uence, on channelized fl ows. At the reach hydraulic equations are applicable to fl ow tool to better understand the geologic history of scale, the various morphologies of individual on Titan for fully turbulent fl ow and rough this largest satellite of Saturn. fl uvial features, implying a broad range of boundaries. For low-Reynolds-number fl ow On both Mars and Titan, fl uvial features have fl uvial processes, suggest that (paleo-)fl ows over smooth boundaries, however, knowl- been inferred through their planform similarity did not occupy the entire observed width edge of fl uid kinematic viscosity is necessary. to terrestrial fl uvial networks, a type of ana- of the features. DISR images provide a spa- Sediment movement and bed form develop- logical reasoning common in planetary geology tially limited view of uplands dissected by ment should occur at lower bed shear stress (Mutch, 1979) and all sciences (Hess, 1966). valley networks, also likely formed by over- on Titan than on Earth. Scaling bedrock ero- One pitfall with analogical reasoning is equi- land fl ows, which are not visible in lower- sion, however, is hampered by uncertainties fi nality, in which different causative processes resolution SAR data. This high-resolution regarding Titan material properties. Overall, yield similar effects (Mutch, 1979; Schumm, snapshot suggests that some fl uvial features observations of Titan point to a world per- 1991). An illustration from planetary science is observed in SAR data may be river val- vasively infl uenced by fl uvial processes, for the past debate over the volcanic or impact ori- which appropriate terrestrial analogs and gin of lunar craters. This directionality, whereby †E-mail: [email protected] formulations may provide insight. landscapes are fi rst encountered remotely at low

GSA Bulletin; March/April 2013; v. 125; no. 3/4; p. 299–321; doi: 10.1130/B30612.1; 7 fi gures; 1 table.

For permission to copy, contact [email protected] 299 © 2013 Geological Society of America Burr et al. resolution and only later (if at all) at outcrop 2007a), and the Cassini Titan Radar Mapper in SAR data are equally consistent with inter- scale, is the inverse of the traditional direction- (RADAR; Elachi et al., 2004, 2005) (Fig. 1). Of pretations as river valleys as they are with the ality for terrestrial geology. It makes planetary these three data sets, fl uvial features have been more commonly published interpretation as geology particularly susceptible to the effects most extensively observed in synthetic aperture channels. We discuss interpretations of individ- of equifi nality because the low resolution limits radar (SAR) data (examples in Fig. 2) from the ual fl uvial landforms in the section Individual discernment of key characteristics. As corrob- RADAR instrument. These images have the best Fluvial Landforms Observed in SAR Data. orative input to geologic analogs, mathematical combination of map resolution (best map reso- The fi ne-scale fl uvial networks observed in models are strong analogs in which attributes lution ~300 m/pixel) and coverage (~40% of the the DISR image mosaic (Fig. 3) are not dis- and physical laws are expressed in a simplifi ed surface to date) for observing fl uvial networks, cernible in SAR data (Soderblom et al., 2007b; formulation that can be compared to the land- and they were collected at a wavelength simi- Jaumann et al., 2009), raising a second question scape under study. Models also provide versatil- lar to the size of fl uvial cobbles observed on the as to the extent of fi ne-scale fl uvial dissection on ity in attribute parameters, which is critical for surface (Tomasko et al., 2005). Although fl uvial Titan. Based on mapping using SAR data, ~1% extraterrestrial investigations. features were inferred from early VIMS data of Titan’s surface was inferred to be covered by The largest contribution of the Mars Channel (Barnes et al., 2007b; Jaumann et al., 2008), fl uvial landforms (Lorenz et al., 2008a; Lopes Working Group (1983) to understanding Mars more recent work has not shown a strong global et al., 2010) with endogenic and other exogenic developed a decade after the fi rst Mariner 9 correlation between fl uvial features mapped processes shaping the remaining surface. How- images were returned from that planet, where from SAR and from VIMS data (Langhans ever, an alternative interpretation of Titan’s fl uvial features were formed by fl owing water et al., 2012). Fluvial networks have also been global landscape is formation entirely by exo- eroding and transporting silicate rock and sedi- mapped in higher-resolution visible light im- genic processes (Moore and Pappalardo, 2011). ment, as on Earth. Almost a decade has now ages (~20–90 m/pixel) taken by the Descent Some regions on Titan show a distinctive tex- passed since the Cassini-Huygens mission fi rst Imager/Spectral Radiometer (DISR; Tomasko ture in SAR images of alternating brighter and returned images from Titan, where fl uvial fea- et al., 2005) (Fig. 3) on the Huygens probe dur- darker kinked, wrinkled, or crenulated banding tures are formed by fl owing liquid alkanes (pri- ing its descent to the Titan surface. Jaumann (e.g., Figs. 2A, 2B, 2F, and 2G). Although fl u- marily methane) acting on materials derived et al. (2009) provide a detailed overview of the vial networks are typically not discernible in this from an icy crust and organic-rich atmosphere. characteristics of the Cassini-Huygens surface- crenulated terrain, they are often adjacent to or As with Mars, understanding of fl uvial features sensing data sets for Titan. connected with it, suggesting a possible genetic on Titan is advanced through analogy to ter- Because of the difference in data set resolu- relationship. We discuss our hypothesis that the restrial features and application of mechanical tions, the mapped fl uvial features give contrast- crenulated terrain on Titan is fl uvial dissected principles. The distinct materials and very dif- ing impressions regarding formation as river in the section Crenulated Terrain: Evidence of ferent conditions on Titan highlight the need channels versus river valleys. The individual Fine-Scale Fluvial Dissection. for morphologic analogies to be supported by features observed in the SAR data are of order These discussions are presented by decreas- physical theory. 0.5–1 km in width, with maximum reported ing scale, beginning with networks observed in This paper presents an analysis of fl uvial widths of ~3 km to ~10 km (Lorenz et al., SAR data, followed by individual features ob- processes on Titan through both qualitative inter- 2008a). Based on their curvilinear appearance, served in SAR data, then the networks observed pretation of spacecraft images and quantitative networked morphology, and radar shadowing, in DISR data, and fi nally the crenulated terrain. theory. In the fi rst part of the paper, we review which implies negative relief, these features have and analyze the morphology of fl uvial features been generally referred to as channels (Porco Fluvial Networks Observed in SAR Data observed in Cassini-Huygens data. In the second et al., 2005; Elachi et al., 2006; Barnes et al., part, we present an overview and discussion of 2007b; Lorenz et al., 2008a). In contrast, the in- Fluvial network morphology or drainage pat- Titan’s “alkanology” (dynamics and cycling of dividual features in DISR images, with roughly tern provides geologic information at the land- hydrocarbons), including precipitation and run- an order of magnitude better resolution, show scape scale, including substrate lithology and off production. In the third part, we articulate widths of ~30 m (Tomasko et al., 2005; Perron permeability, structural features, and landscape the theoretical underpinnings of both hydraulic et al., 2006). Terrestrial rivers may carve and be topography (e.g., Howard, 1967; Twidale , and sedimentologic processes likely to occur inset within much wider valleys or canyons, such 2004). Classes of drainage patterns have per- on Titan. The concluding summary includes as the Colorado River within the Grand Canyon, vasive characteristics that distinguish them suggestions of high-priority areas for future and similar fl uvial morphologies have been ob- from other basic patterns, although modifi ed or investigations. served in high-resolution images of Mars (e.g., transitional patterns may have spatially vary- Irwin et al., 2005). By analogy, these Huygens ing characteristics of multiple patterns. Howard TITAN’S FLUVIAL LANDFORMS DISR features have been inferred to be river val- (1967) and Ichoku and Chorowicz (1994) pre- leys that contain channels (Perron et al., 2006). sented examples of both basic and modifi ed Questions of Formation Mechanism Distinguishing channels from valleys is vi- patterns. and Extent tal for correct estimates of fl uvial processes Network drainage pattern analysis has proven and effects, including the correct estimation of to be valuable in planetary studies for multiple Fluvial features have been mapped in data liquid and sediment discharge. At SAR resolu- reasons. It is applicable to networks composed from the three Cassini surface-imaging instru- tion, diagnostic channel features such as stream of either river channels or river valleys, which is ments, namely, the Imaging Science Subsystem banks and bed forms are not resolved, and shad- helpful for low-resolution data, where the exact (ISS; best map resolution ~1–2 km/pixel; Porco ing by valley walls and differences in refl ectiv- nature of the fl uvial features cannot be discerned et al., 2004, 2005), the Visual and Infrared Map- ity of surface materials contribute to diffi culty in (cf. Pieri, 1979). Drainage pattern analysis is ping Spectrometer (VIMS; best map resolution direct interpretation of fl uvial features. In many valid at a range of map resolutions, so even in ~1 km/pixel; Brown et al., 2004; Barnes et al., cases, the appearances of Titan fl uvial features the likely event that low-order (distal or “fi nger-

300 Geological Society of America Bulletin, March/April 2013 Fluvial features on Titan

Figure 1. Global mosaic using Cassini Imaging Science Subsystem (ISS) data (lower layer) and Cassini Titan Radar Mapper (RADAR) synthetic aperture radar (SAR) data up through T71 (upper layer), with fl uvial features mapped on SAR data shown in blue. White boxes show locations of subsequent fi gures as identifi ed by adjacent lettering. (A) Fluvial features from 60°N to 60°S. (B) Fluvial features in the north polar region, 60°N to 90°N. (C) Fluvial features in the south polar region, 60°S to 90°S. Scale varies across image, 10° longitude or 10° at the equator is equal to ~450 km. tip”) tributaries are not discernible, the approach existing terrestrial drainage pattern terminology gests control by tectonic structures and associ- still provides accurate information (e.g., Ichoku may be usefully applied to Titan fl uvial net- ated topography. Analysis of the shape of some and Chorowicz, 1994). Such analysis provides works, in order to more precisely identify and well-resolved north polar networks indicates information over the region covered by the dis- suggest impli ca tions for each network class. that these networks have produced only minor cernible network, whereas information from Application to Titan networks of a quantitative erosional modifi cation of the surface, suggest- channel patterns (e.g., straight, meandering, terrestrial classifi cation algorithm (Ichoku and ing either recent resurfacing or slow fl uvial inci- braided, anastomosing, anabranching) is com- Chorowicz, 1994) yields rectangular, dendritic, sion (Black et al., 2012). monly more restricted in area. and parallel network morphologies (Burr et al., The range of terminology applied to drain- 2009b). Rectangular networks constitute the Individual Fluvial Landforms Observed age patterns on Titan hints at a range of hydro- majority of Titan’s networks (Drummond et al., in SAR Data logic controls on channelized runoff (Baugh, 2012), including networks adjacent to Kraken 2008; Lorenz et al., 2008a; Langhans et al., and Ligeia Maria (Cartwright et al., 2011) (e.g., Individual fl uvial features in SAR data from 2012). Given the surprisingly Earth-like nature Figs. 2A and 2B). While each network mor- Titan may be grouped into six morphological of Titan’s surface (e.g., Coustenis and Taylor, phology carries important geologic implications classes using the basic qualitative parameters 2008) and calculations suggesting similar fl u- (e.g., Howard, 1967; Twidale, 2004; for a sum- of radar backscatter (bright or dark), relative vial erosion and transport processes on Earth mary, see Drummond, 2012), the rectangularity width (narrow or wide), and relative length and Titan (Collins, 2005; Burr et al., 2006), the characterizing the majority of networks sug- (stubby or long). This classifi cation scheme,

Geological Society of America Bulletin, March/April 2013 301 Burr et al. based on readily observable plan-view attri- ously for Titan networks observed in SAR data Interpretations: The morphology of networks butes, yields a limited number of classes for (Lorenz et al., 2008a; Langhans et al., 2012), of narrow radar-dark features indicates tributary which specifi c hypotheses may be proposed. due to the inherent differences in use of stream fl ow, with moderate to high tributary junction The following discussion describes those six order versus link magnitude and possibly to the angles suggesting low-terrain slopes and/or classes and offers some interpretations (sum- “segmented storage of valleys in the database” structural infl uence (Drummond et al., 2012). marized in Table 1). Type examples of the six of previous work. The dark tone may result from deposition of classes are shown in Figure 2, with their loca- 1. Narrow, long, radar-dark features can be fi ne-grained material (Lorenz et al., 2008a). A tions indicated on Figure 1. found either as individual sinuous landforms or drape of fi ne grains implies either consistently We include Shreve magnitudes (i.e., the as well-developed networks, such as those ob- low-energy fl ow, possibly due to low slopes, or number of headwater links upstream of a given served in the north polar vicinity of Ligeia Mare a hydrograph with a low-fl ow tail, which may link) in these class descriptions, rather than in (Fig. 2A). Apparent Shreve magnitudes of the result from an extended or irregularly shaped the previous network discussion, because we prominent networks in this area range from ~20 drainage basin area (Knighton, 1998). Alter- fi nd that the magnitudes vary by the class of to ~70, and the most extensive of these networks natively, the dark tone may indicate a smooth the individual links comprising the network. is ~340 km in length. Junction angles are mod- bed of sand-sized particles, the availability of In comparison to the Horton-Strahler stream- erate to high (up to 90°). Although width varies which is inferred from the presence of extensive ordering technique, Shreve magnitudes pro- considerably with location in the network, the tropical dunes (e.g., Radebaugh et al., 2007b). vide a measure of topology that gives a better main (trunk) links are ~0.5 km wide. A general Available coverage indicates that radar-dark indication of discharge from runoff (Knighton, lack of radar shadowing, observable as light- fl uvial features may be concentrated at higher 1998). Because of SAR image speckle and reso- dark pairing, suggests fairly shallow depths latitudes, although the degree and signifi cance lution limits, the apparent Shreve magnitudes and/or shallowly sloping walls, although shad- of this concentration have not yet been quanti- reported here almost certainly underestimate the owing may be obscured by the radar-dark tone. fi ed. If substantiated, this concentration may true values. Nonetheless, these values are pro- Many of these features terminate at dark areal indicate a greater supply of fi ne-grained organic vided as a measure of relative network integra- features interpreted as hydrocarbon lakes sediment poleward, contrary to what might be tion. The magnitudes reported here are several (Stofan et al., 2007), as seen near 74°N, 246°W expected from the concentration of organic-rich times higher than stream orders reported previ- (Fig. 2A; other locations indicated in Fig. 1). dunes in the tropics (Radebaugh et al., 2007b;

Figure 2 (on following page). Examples of the six morphological classes for individual fl uvial features. On all fi gures, solid small black arrows indicate Cassini Titan Radar Mapper (RADAR) illumination directions. (A) Examples of narrow, long, radar-dark features near 74°N, 246°W. The dark tone of these features is interpreted here as a deposit of fi ne-grained material. The dark area to the north (right) is Ligeia Mare. Filled white arrows point to inferred drowned valleys (Stofan et al., 2007), with the width of the submerged region narrow- ing headward. The hollow white arrow points to a partially drowned river valley system. Area of crenulated terrain is visible immediately south (left) of the mare. The rectangular drainage pattern suggests formation on landscapes affected by tectonic structures (Drummond et al., 2012). (B) Examples of narrow, long, radar-bright features near 10°S, 137°W, in western Xanadu. The bright tone in the fl uvial fea- tures is interpreted as resulting from internal refl ections from debris with diameters larger than the RADAR wavelength (2.17 cm) (LeGall et al., 2010). This region illustrates the interspersion of darker units within lighter, inferred rougher terrain, suggesting embayment of the rougher terrain by fi ne-grained deposits. The visible fl uvial network is an example of a rectangular drainage pattern (Burr et al., 2009b; Drummond et al., 2012). Crenulated terrain, hypothesized to be fi nely fl uvially dissected, is visible at the upper-left portion of the image. (C) An example of a wide, long, radar-dark feature near 74°S, 27°W. The dark tone may be due in some locations to inherently radar-dark material (e.g., the fl oor of the main trunk) and elsewhere to radar shadowing (e.g., the western side of main trunk valley), although the dis- tinction between these two causes is not clear everywhere. Based on the radar shadowing, this feature is hypothesized here to be an incised bedrock channel or confi ned meandering river set within a river valley formed by erosion. (D) A second example of a wide, long, radar-dark feature near 59°S, 5°W, proposed to be a distributary channel (Lorenz et al., 2008a) and hypothesized here to be a braided or an anabranch- ing network. (E) Examples of wide, long, radar-bright features near 20°N, 80°W, named Elivagar Flumina. Narrower ends originate on a dark surface, inferred to be smooth plains material, and wider ends terminate at smooth, radar-bright terrain, inferred to be sedimentary deposits with debris on the scale of or larger than the RADAR wavelength (2.17 cm). In accordance with previous work (Lorenz et al., 2008a), we hypothe size these features to be gravel-bed, braided, ephemeral rivers that terminate in alluvial deposits. (F) Examples of wide, long, radar-bright features near 18°S, 122°W, northeastern Tui Regio. These features are proposed to have roughness elements on the same scale as or larger than the 2.17 cm wavelength of the RADAR (Le Gall et al., 2010). The wider ends originate from crenulated terrain (upper right), inferred to be rough upland, and the narrow ends disappear on a dark surface (lower left), inferred to be smooth plains. The origination of this fl uvial feature at maximum width from the crenulated terrain indicates that the crenulated terrain has contributing fl uvial features below the image resolution. A few of these tributaries are visible as connected zigzag traces at upper left and center right. (G) Examples of stubby, radar-dark features (in white ovals) near 69°N, 298°W, around the southern margin of Kraken Mare (dark area at upper right). Shorelines having “sinuous extensions” are described as being similar in appearance to drowned river valleys on Earth (Stofan et al., 2007). Portions of the radar-bright terrain with the brightest return have crenulated texture. (H) Examples of stubby, radar- bright features (white oval) on the eastern rim and wall of Menrva crater near 20°N, 83°W. The black box marks the location of the inset image at upper right, showing an individual feature with bright and dark regions (white and black arrows), which are located distal from and proximal to the radar illumination direction (from upper left), indicating radar illumination and shadowing, respectively. Between the dark and bright regions, there is a region of intermediate brightness (gray arrow), inferred to be a rough fl oor.

302 Geological Society of America Bulletin, March/April 2013 Fluvial features on Titan

A B

D E

C

G H F

Figure 2.

Geological Society of America Bulletin, March/April 2013 303 Burr et al. AB

C

D

Figure 3. Huygens Descent Imager/Spectral Radiometer (DISR) mosaics of features around the Huygens probe landing site, at ~10°S, 168°E. Background: stereographic projection of the view from 6 km above the surface, centered on the landing site, marked with a star. North is up. Scale varies across image. White boxes show the approximate extents of insets A–C. Insets: (A) Western drainage networks. Image width is ~8 km. (B) Northern drainage networks. Image width is ~6 km. (C) Stereographic projection of the landing site from 600 m above the surface. Image width is ~2 km. (D) View from the landing site, looking toward the horizon. Diameter of the largest clasts in middle distance is ~15 cm. Dark zones stretching to the right from clasts in the middle distance suggest scour tails. All images are courtesy of National Aeronautics and Space Administration (NASA)/Jet Propulsion Laboratory (JPL)/European Space Agency (ESA)/U. Arizona.

Barnes et al., 2008), and it would indicate com- ered to be icy rounded rocks larger in size than 3. Wide, long, radar-dark features are similar plex global sediment supply and/or transport. the radar wavelength (2.17 cm) acting as natu- in tone and length to their narrow counterparts, 2. Narrow, long, radar-bright features have ral radar retro-refl ectors (Le Gall et al., 2010). but they are several times wider (~2.5–5 km). dimensions similar to the radar-dark features Grains (pebbles and cobbles) of this size were They may be subdivided by morphology and discussed in point 1. They often form well-devel- observed at the Huygens landing site (Tomasko geographic location into two groups. In polar oped networks with apparent Shreve magnitudes et al., 2005), demonstrating the production and regions, they occur as branching networks with up to ~40. Bright networks in western Xanadu transport of such material. Thus, radar-bright enlarged main trunks, which often show radar observed in the overlapping T13 (Lorenz et al., fl uvial features are hypothesized to be river val- shadowing and illumination patterns (e.g., Fig. 2008a) and T44 swaths (Fig. 2B) range from leys with debris a few centimeters or larger in 2C). As seen in this example, smaller tribu- ~250 km to 400 km in total length, and the indi- size (Lorenz et al., 2008a). Relative radar bright- taries may likewise show evidence of shadow- vidual features are ~0.75 km and ~1.5 km wide. ness on the sides of fl uvial features that face the ing and be radar-dark, though not universally Interpretations: The bright appearance indi- illumination direction (e.g., smallest tributaries so. These networks of wide radar-dark features, cates signifi cant radar backscatter, for which in Fig. 2C) may result from radar illumination like those composed of narrow radar-dark links, the most likely explanation at present is consid- of the valley walls. commonly terminate in inferred lakes or other

304 Geological Society of America Bulletin, March/April 2013 Fluvial features on Titan

TABLE 1. SUMMARY OF THE SIX PROPOSED MORPHOLOGICAL CATEGORIES, POSSIBLE INTERPRETATIONS, AND EXAMPLE FIGURES* Morphological class Hypothesized interpretations Example fi gures Narrow, long, radar-dark • River valleys, the dark tone of which is due to deposition of fi ner-grained particles from low-energy fl ow, resulting from Figure 2A low slopes and/or extended or irregularly shaped drainage basin; possibly some shadowing of steep-sided valley walls

Narrow, long, radar-bright • River valleys, the bright tone of which is due to internal refl ections by debris larger than the RADAR wavelength Figure 2B (2.17 cm); possibly some illumination of steep-sided valley walls

Wide, long, radar-dark 1. Sinuous features with radar shadowing hypothesized to be incised bedrock channels or confi ned meandering stream Figures 2C and 2D valleys (e.g., Fig. 2C) 2. Straighter features lacking radar shadowing and conjoined in braided networks hypothesized as anabranching channels with possible terminal splays where features widen (e.g., Fig. 2D)

Wide, long, radar-bright 1. Features originating on dark plains and terminating in radar-bright, homogeneous terrain hypothesized to be gravel-bed, Figures 2E and 2F braided, ephemeral rivers terminating at fl uvial deposits (e.g., Fig. 2E) 2. Features originating in radar-bright, crenulated terrain and terminating in dark plains hypothesized to be braided rivers draining mountainous, dissected landscapes (e.g., Fig. 2F)

Stubby, radar-dark • River valleys formed by a headward retreat mechanism Figure 2G • Dark tone due to fi ll by dark tholins and/or drowning by liquid, possibly shadowing of steep-sided slopes

Stubby, radar-bright • River valleys formed by a headward retreat mechanism Figure 2H • Bright tone due to illumination of valley walls; intermediate-toned pixels due to rough material on valley fl oor *See “Titan’s Fluvial Landforms” section for further details.

depositional basins. At lower latitudes, observed with plants (Davies and Gibling, 2010a, 2010b). We hypothesize the radar-bright features wide, radar-dark features may lack radar shad- As on Mars (Burr et al., 2009b, 2010), putative that terminate at homogeneous bright terrain owing, have less-well-defi ned edges, tend to meandering channels on Titan would require a (Fig. 2E) to be gravel-bed, braided, ephemeral be straighter, and form networks with an inter- nonbiological cohesion mechanism. This cohe- rivers (e.g., Bridge and Lunt, 2006) and their twined appearance, having multiple conjoined sion mechanism may be common; data from the terminal gravelly deposits. Terrestrial braided features and faint lineations within the features Huygens Surface Science Package (SSP) show streams have weak banks, an abundant supply (e.g., Fig. 2D). For these networks, boundaries that the material at the Huygens landing site of bed load, highly variable discharge, and high are poorly defi ned, and apparent Shreve magni- may have been cohesive at the time of landing stream power (Knighton, 1998), which together tudes are low. (Lorenz et al., 2009; Atkinson et al., 2010). can create irregular widening and narrowing, Interpretations: The wide, radar-dark fea- 4. Wide, long, radar-bright features have di- as observed in Figure 2E. This interpretation tures shown in Figure 2D were speculated to mensions similar to their darker counterparts implies commonly sub-bankfull fl ow in these be channels with fi ne-grained deposits (Lorenz (~200–300 km in length, ~4.5–6 km in width), multithread channels with a low discharge per et al., 2008a). Lack of apparent radar shad- and they can have a similar intertwined or multi- unit channel width. Terrestrial braided channels owing, indicative of shallowly sloping sides, thread appearance with diffuse boundaries. are typically straighter in overall planform than along with individual link and networked These features appear to form only poorly de- streams formed in cohesive alluvium, which morphologies, suggests a braided or possibly veloped networks (apparent Shreve magnitudes may meander or anabranch, so low sinuosity in anabranching network of low width-to-depth, <10) or individual landforms. Widths often vary these instances does not necessarily imply either multithread channels. The multiple subparal- noticeably along the features. The narrower structural control or strong banks. lel features, if they connote a distributary net- ends terminate in radar-dark terrain, inferred to We hypothesize that the radar-bright features work, would suggest depositional processes be smooth plains material, and the wider ends that terminate at crenulated bright terrain (e.g., within and adjacent to these channels. For commonly abut radar-bright terrain. This radar- Fig. 2F) are likewise braided channels, based on example, sites where the dark features widen bright terrain, where homogeneous in tone, has similar morphological observation, but with the might be indicative of terminal splays, deposits been interpreted as either cryovolcanic or allu- inverse fl ow direction relative to the adjacent that form in dryland fl uvial-lacustrine systems vial (e.g., Fig. 2E; see Lopes et al., 2007). In bright terrain. The bright, crenulated terrain, in- where a river debouches into a playa lake or other cases, the radar-bright terrain may have a terpreted as mountainous (Lopes et al., 2010), is onto its fl oodplain (Graf, 1988). crenulated appearance (Fig. 2F), which has been inferred to be the source region for these braided For the other group of wide, radar-dark fea- interpreted as mountainous (Lopes et al., 2010; channels. In these cases of bright features drain- tures, which are commonly found near the Radebaugh et al., 2011). ing crenulated terrain, the decrease in width and poles (e.g., Fig. 2C), shadowing and illumina- Interpretations: The lack of radar shadow- tone with distance may be due to a decrease in tion indicative of steep side slopes and a sinu- ing, suggesting only shallow incision into the discharge due to evaporation and/or infi ltration ous planform pattern support an interpretation plains, along with their intertwined planform over the dark plains material. Alternatively, the as incised bedrock channels or confi ned mean- appearance and variable width (Lorenz et al., change in appearance may result from com- dering rivers set within river valleys formed by 2008a; Lopes et al., 2010), suggests anabranch- minution of sediment to sizes smaller than the erosion. Incised channels may have point bar ing, anastomosing, or braided channels. Thus, radar wavelength. or other deposits of fi ner-grained alluvial fi ll, wide, long, radar-bright networks may include Thus, the wide, long, radar-bright features, suggested by radar-dark material distributed the most likely river channels seen in SAR data. like their radar-dark counterparts, may be sub- at various locations (bends) within the feature. In such multithread channels, the fl owing liquid divided into two groups (Table 1). For these Meandering channels require some cohesion of would be unlikely to simultaneously occupy the features, however, the basis for the division is the bank material, which on Earth is associated full width of the feature as resolved in SAR data. the appearance—homogeneous or crenulated—

Geological Society of America Bulletin, March/April 2013 305 Burr et al. of the adjacent radar-bright terrain. These two tributed to different types of sedimentary fi ll strate in that area has substantially different me- subgroups of radar-bright features are less dis- (rounded icy cobbles or fi ner-grained particles, chanical properties than the substrate underlying tinctive in appearance than the radar-dark sub- respectively). The wide, long, dark features the northern networks. No independent evidence groups, and both are found at low latitudes. with shadowing may be confi ned meandering to suggest such a contrast in subsurface materials 5. Stubby, radar-dark features range from streams or incised bedrock channels, for which is observed. ~1.5 km to 3 km in length. These features are fl ow widths again would be less than observed With a water-ice crust that is far below its found individually or as poorly developed net- widths. The straighter, shallower features in this melting temperature and minimally soluble works (apparent Shreve magnitudes of 2–5). class are interpreted as braided or anabranch- in hydrocarbons (Lorenz and Lunine, 1996), Stubby, radar-dark features are found, for ex- ing multichannel systems. The wide, long, Titan’s fl uvial valleys are unlikely to be the ample, near 69°N, 298°W around the perimeter bright features are hypothesized to be either product of thermal erosion or dissolution of Kraken Mare (Fig. 2G). ephemeral braided rivers terminating at bright (Perron et al., 2006). If the surface is composed Interpretations: The stubby shape of these deposits, or braided multichannel rivers fed partly of organic compounds with very different features suggests formation by some mecha- from dissected mountainous terrain and termi- physical properties, then melting or karst may nism of headward retreat of the inferred chan- nating on dark plains. For none of these various have played a part in shaping the surface topog- nel. Such retreat occurs by waterfall erosion multichannel systems would the fl ow be likely raphy, as has been suggested for the polar lakes where a strong capping layer overlies a weak to occupy all the channels. Stubby features are (Stofan et al., 2007; Bourgeois et al., 2008), but substrate or where rocks have pervasive verti- inferred to be valleys produced by headward no such compounds have yet been identifi ed. cal joints, or by groundwater seepage erosion erosion, for which fl ow would occupy only a In view of the erosive capability of overland in loose or weakly cemented sediment (Lamb fraction of the width. fl ow and the abundant independent evidence of et al., 2006, 2008a; Lamb and Dietrich, 2009). atmospheric precipitation, we consider erosion The dark tone may indicate fi ll by dark tholins Fluvial Landforms Observed in DISR Data by precipitation-fed runoff to be the more likely or organic hydrocarbons (Soderblom et al., formation mechanism for both the northern and 2007a; Barnes et al., 2008) or possibly shadow- At considerably smaller scale, valley net- western networks. ing in steep-sided valleys (for discussion of how works observed in DISR images have two dis- The straighter valleys and more orthogonal to test for shadowing effects, see Soder blom tinct morphologies. The networks to the north tributary junction angles of the western net- et al., 2007b). In cases where the radar-dark fea- of the Huygens landing site (Fig. 3B) are more work have also been interpreted as the result of tures debouch into basins or plains, the conti- sinuous, originate close to topographic divides, structural or tectonic control of valley incision nuity between radar-dark basin material and the and show downstream increases in valley width. (Tomasko et al., 2005; Soderblom et al., 2007b; dark stubby features suggests tholin deposition In contrast, the networks to the west of the Jaumann et al., 2009). This interpretation is by backwater in or drowning of the contributing Huygens landing site (Fig. 3A) have straighter plausible, especially in view of the identifi cation valleys (Stofan et al., 2007). main-stem valleys, larger tributary junction from SAR data of rectangular fl uvial networks 6. Stubby, radar-bright features tend to be angles, shorter tributaries, and possibly more elsewhere on Titan (Burr et al., 2009b; Drum- larger than stubby, radar-dark features (~20 km enlarged dark areas around the valley heads mond et al., 2012). Such morphologic correla- in length) and have poorly developed branching (Tomasko et al., 2005; Perron et al., 2006). This tions are not unique, however. Straight valleys (apparent Shreve magnitudes also of 2–5), as morphological contrast has been interpreted as on Earth may form where fl ow directions are seen on the eastern rim of Menrva crater near evidence for disparate formation processes, with enforced by preexisting topography (which may 20°N, 83°W (Fig. 2H). Although mostly radar- the more northern networks interpreted as hav- be tectonic in origin), and orthogonal tributary bright, these features also show sub parallel ing a distributed atmospheric source for the fl ow junctions are frequently observed where a trunk radar-dark regions, with some intermediate- (Perron et al., 2006), and the western networks stream incises rapidly or channel longitudinal toned pixels in between. These bands of dif- having formed through groundwater sapping profi les are strongly concave-up (Horton, 1945; ferent radar tone trend roughly orthogonal to due to subsurface fl ow of methane (Tomasko Schumm, 1956; Howard, 1971). illumination direction (Fig. 2H). et al., 2005; Soderblom et al., 2007b). The valley networks near the Huygens land- Interpretations: The stubby appearance again Inferences about groundwater sapping based ing site terminate at a boundary between the suggests formation by some mechanism of head- solely on valley network morphology are prob- bright, elevated, fl uvially dissected area, and the ward retreat. The orientation and bands of bright lematic. On Earth, fi eld studies of putative dark, low-lying area in which the probe landed and dark tone are inferred to be areas of radar groundwater sapping networks incised into com- (Fig. 3). The boundary resembles a shoreline, illumination and radar shadowing, respectively. petent bedrock have revealed no clear evidence but the dark area contained no pooled liquid The interspersed pixels of intermediate tone that spring discharge can form valleys without at the time of landing (Zarnecki et al., 2005; suggest a region of rough material on the fea- overland fl ow, and they indicate that surface Keller et al., 2008). In north polar lakes, the in- ture fl oor, such as debris loosened from the runoff has contributed substantially to network ferred drowned fl uvial networks (e.g., Fig. 2G) surrounding wall rock by weathering and/or in- formation (Lamb et al., 2007, 2008a). If thick (Stofan et al., 2007) appear to record changes cision during overland fl ow. deposits of unconsolidated, permeable material in lake levels, and paleolake clusters have been Our interpretations of the different classes mantle Titan’s surface, (e.g., Soderblom et al., hypothesized for low-latitude sites (Moore and of fl uvial features visible in SAR data (see also 2009; Waite et al., 2009), then groundwater Howard, 2010). This evidence of substantial Table 1) have implications for the likely rela- sapping might play a role in forming valley net- changes in the volume of liquid surface reser- tionships between observed feature width and works, as it can on Earth in such settings (Dunne voirs elsewhere on Titan supports the hypoth- the actual (paleo-)fl ow width. We interpret the and Black, 1980; Howard, 1988; Schumm et al., esis that the boundary at the Huygens landing narrow, long features as river valleys, for which 1995; Perron and Hamon, 2012). However, site was once a shoreline or some transitional valley widths likely exceed fl ow widths. The if sapping formed the western networks in the zone between an erosional surface and a depo- different SAR albedos (bright or dark) are at- DISR mosaic, then it would imply that the sub- sitional one.

306 Geological Society of America Bulletin, March/April 2013 Fluvial features on Titan

It is not known whether the observed fl u- the Himalayas, this crenulated banding was (cf. Lopes et al., 2010), as shown in Figure 2F. vial features near the Huygens landing site are suggested to be a possible expression of fl uvial These few examples substantiate the possibility typical of Titan’s surface. However, the greater dissection (Radebaugh et al., 2007a). In some that many additional tributaries exist within the abundance of lakes (Hayes et al., 2008), fl uvial locations, obvious fl uvial networks are embed- crenulated terrain. networks (Drummond et al., 2012; Langhans ded in the crenulated terrain. These fl uvial fea- et al., 2012), and cloud activity (Porco et al., tures may debouch onto dark plains (Fig. 2F) Terrestrial Analogs 2005) at the poles suggests that the probe land- or into lakes (Fig. 2A), but they become indis- A comparison of SAR images and topography ing site in the tropics could have sparse fl uvial cernible with distance headward (i.e., into the for two variously dissected terrestrial landscapes dissection relative to polar regions. Jaumann et al. crenulated terrain). However, multiple lines of illustrates the diffi culty of identifying fi ne-scale (2009) summarized observations of the land- reasoning support the inference that crenulated drainage networks even in high-resolution SAR ing site in coarser-resolution Cassini images, terrain is a heavily dissected landscape of chan- data (e.g., Farr et al., 2007). Topography of a showing how diffi cult it is to discern the fl u- nels and adjacent valley slopes. fi nely dissected region of the Allegheny Plateau, vial features in the SAR data, even when those shown in a shaded relief image (Fig. 4A), exhib- features are known to exist. This comparison Comparison of SAR and DISR Images its obvious hierarchical drainage networks. The under scores the value of Huygens observations, As noted already, SAR data do not resolve the main valleys of these networks are also easily showing that the apparent scarcity of fi ne-scale Huygens landing site networks that are visible in visible in a SAR image, but even in this highly fl uvial features in Cassini images should not be the DISR images (Fig. 3) (Jaumann et al., 2009), dissected landscape with high-relief valleys, the construed as evidence of their absence. Hence, highlighting the possibility of unresolved fi ne- low-order tributaries are somewhat obscured we turn to a discussion of landscapes in SAR scale fl uvial dissection elsewhere on Titan. (Fig. 4B). In a landscape that may be more com- images that might be signatures of fi ne-scale, parable to some locations on Titan, a region of fl uvially dissected landscapes, even if drainage Tributary Nature of Networks Michigan’s Upper Peninsula, which was heavily networks are not resolved. The dendritic, parallel, and rectangular drain- modifi ed by the Laurentide ice sheet, shows age patterns identifi ed on Titan (Burr et al., partial dissection by low-relief fl uvial networks Crenulated Terrain: Evidence of Fine-Scale 2009b; Drummond et al., 2012) are tributary, that empty into Lake Superior. This geographic Fluvial Dissection implying that the observable links must have relationship between the fl uvial networks and lower-order tributaries feeding into them. terminal lake basins is similar to that of the fl u- In Cassini SAR images, much of the bright vial features that terminate at Titan’s north polar highlands (e.g., Xanadu) has repeated bright and Visibility of Some Tributaries lakes (e.g., Fig. 2A). The terrestrial fl uvial topog- dark crenulated bands with apparent widths A few lower-order tributaries are visible raphy is again identifi able in a shaded relief im- of ~2–6 km (e.g., Figs. 2A, 2B, 2F, and 2G). within the crenulated terrain, feeding into broad age (Fig. 4C). However, only a few of these Through visual similarity to a SAR image of fl uvial features that stretch onto dark plains features are visible as faint lineations or crenula-

Figure 4. Comparison of synthetic aperture radar (SAR) images and topography for terrestrial A B drainage networks. (A) Topog- raphy shown as a shaded relief image and (B) SAR image of the region southwest of L’Anse Bay, Lake Superior, on Michigan’s Upper Peninsula, centered at 46.57°N, 88.67°W. (C) Topog- raphy shown as a shaded relief image and (D) SAR image of a section of the Allegheny Plateau east of the Ohio River in north- ern West Virginia and south- D west Pennsylvania, centered at C 39.67°N, 80.70°W. SAR images are from the C-band antenna on board the Shuttle RADAR Topography Mission (Farr et al., 2007). Topography is from the U.S. Geological Survey National Elevation Data Set. Map pro- jections are transverse Merca- tor, with a pixel size of ~30 m. Figure is modifi ed from Black et al. (2012).

Geological Society of America Bulletin, March/April 2013 307 Burr et al. tions in a SAR image with comparable spatial 2006; see also Figs. 6 and 7A). Images collected darker, smooth-textured areas that may connect resolution (Fig. 4D). Thus, in both of these ex- just before landing resolved meter-size boulders to adjacent fl uvial links (e.g., Fig. 2B). In other amples, fl uvial networks that are readily appar- near the landing site, although none was visible regions, similar radar-dark terrain, with fl uvial ent in topographic data are underrepresented in from the surface (Tomasko et al., 2005). Grains features terminating within it, appears to embay SAR images. That terrestrial SAR images with at the surface have been rounded, perhaps by the brighter terrain (e.g., Fig. 2F). Some of this much higher resolution than Cassini SAR data mechanical abrasion during energetic fl uvial radar-dark terrain, parts of which belong to the can obscure fl uvial features suggests that fl uvial transport consistent with possible scour tails plains units of Lopes et al. (2010), is likely to be dissection on Titan may be much more extensive (Fig. 2D) or by in situ chemical weathering of deposits from the fl uvial features that are adja- than is apparent in SAR images. the water-ice and soluble organic compounds as cent to or terminate within it. Not all SAR images of crenulated terrain show indicated by spectra of the site (Tomasko et al., obvious valley networks, and not all bright high- 2005; Jacquemart et al., 2008; Schröder and Lacustrine Deposits lands exhibit obvious crenulations. However, the Keller, 2008). Multiple Cassini instruments have identi- inability of SAR images to resolve the intricate fi ed alkane lakes and inferred paleolakes (e.g., drainage network imaged by DISR suggests that Regional Sedimentary Landforms Stofan et al., 2007; Brown et al., 2008; Turtle many or most of these bright highlands, whether SAR images reveal probable fl uvial sedimen- et al., 2009) into which fl uvial features terminate. obviously crenulated or not, are fl uvially dis- tary depositional environments that appear to The lake boundaries exhibit a variety of mor- sected at a scale too fi ne to be resolved in SAR be analogous to terrestrial braid plains, alluvial phologies, from highly irregular shorelines ad- data. The radar-bright “hummocky and moun- fans, and depositional basins. Several valley jacent to crenulated terrain (“terrestrial fl ooded tainous terrain” unit is inferred to cover ~12% systems terminate in fan-like forms with fl uvial river valleys”; Stofan et al., 2007) to smoother of Titan’s surface as mapped up to T30 (Lopes features that broaden, split, and appear to braid shorelines for lakes within plains units. Where et al., 2010). If this percentage can be accurately (e.g., Figs. 2D–2F). In some cases, topographic valley systems enter lakes with smooth shore- extrapolated to the entire body, then greater data demonstrate that these fan-like forms occur lines, they sometimes terminate at or adjacent than a tenth of the surface of Titan—an order in regional lows, supporting their identifi cation to broad platforms (e.g., Fig. 5). Because the al- of magnitude higher than the previous estimates as alluvial fans (e.g., Moore and Howard, 2010). kane lakes are only partially transparent to radar (Lorenz et al., 2008a; Lopes et al., 2010)—may In general, neither the mechanism(s) of em- illumination (e.g., Hayes et al., 2008, 2010, be dissected by fl uvial features. placement of sedimentary deposits—whether 2011), these inferred fl uvial features gradually from rivers or debris fl ows (cf. Blair and fade with distance lakeward. On the basis of Depositional Environments McPherson, 1994)—nor the grain-size char- plan-view morphology and variation (fading) acteristics of the deposits are known, although in tone, these features are hypothesized to be Evidence of fl uvial sediment transport and high radar backscatter for some fl uvial features fl uvial fans or deltaic deposits (e.g., Moore and deposition on Titan appears at a variety of scales (i.e., those shown in Fig. 2F) suggests the pres- Howard, 2010; Wall et al., 2010). as observed in both Huygens and SAR data. ence of grains larger than the radar wavelength Potential sources of sediment, including tools of 2.17 cm (Le Gall et al., 2010). Many of the TITAN ALKANOLOGY for incision, are discussed under “Bedrock Ero- depositional landforms are radar-bright, sug- sion” later herein. gesting an abundance of particles greater in size To the extent that the terrestrial analogs for than the RADAR wavelength. the fl uvial features on Titan are valid, they re- Local Sedimentary Deposits In some regions, radar-bright fl uvial networks quire atmospheric and near-surface processes Huygens data offer hints about the processes in crenulated uplands are interspersed with to create the channelized surface flow. Here, operating on the Titan landscape. Stereo-topog- raphy indicates that the valley walls north of the landing site approach the angle of repose for cohesionless material (Tomasko et al., 2005; Soderblom et al., 2007b), suggesting that the Figure 5. Ontario Lacus in the landscape is being actively dissected, and that south polar region of Titan, mass wasting may be an important hillslope centered near ~72°S, 183°W. sediment production and transport mechanism. Outlined arrow within the lake DISR images of the landing site show a ground shows a smooth shoreline. White surface completely mantled with sediment (Fig. arrows point to inferred fl uvial 3D; Tomasko et al., 2005). The Huygens SSP deposits at the mouth of valleys penetrometer measurements indicate a soft, debouching into the lake. Sub- solid surface with a stronger upper layer and lake topography is suggested a weaker subsurface, consistent with either a in some portions of the lake, crust or a layer of coarse sediment over fi ner- including shallowly submerged grained sediment (Zarnecki et al., 2005; Keller topography in the western and et al., 2008; Atkinson et al., 2010). The observed southern areas. Solid black surface grain-size distribution includes particle arrow indicates Cassini Titan sizes ranging from roughly 3 mm, the small- Radar Mapper (RADAR) illu- est diameter resolvable by the camera, up to mination direction. 15 cm (Tomasko et al., 2005), i.e., grain sizes that could be moved by fl uvial fl ow (Burr et al.,

308 Geological Society of America Bulletin, March/April 2013 Fluvial features on Titan we consider relevant atmospheric processes lized by the absorption of methane gas, such that Frequency of Fluvially Signifi cant Events and possible near-surface pathways by which 1 μm droplets would have lifetimes of hours to The frequency of precipitation events that liquid may be supplied to the surface. We days before freezing (Wang et al., 2010). lead to surface modifi cation can be constrained group these processes and pathways under the by modeling and observations. Simple thermo- term “alkanol ogy,” defi ned here as the occur- Rainfall Rate dynamic modeling suggested rainstorms on rence, circulation, distribution, and properties of Rainfall rates on Titan have been estimated Titan may occur only every millennium (Lorenz alkanes on Titan and in its atmosphere, includ- through various approaches. Simple models et al., 2005). However, observations of surface ing precipitation and runoff production. equating an assumed energy available for con- changes in ISS data over Titan’s equatorial re- vection to either latent heat or to work done in gion are attributed to methane storm precipita- Precipitation Characteristics dissipating the drag on falling raindrops yield tion, inferred to occur seasonally (Turtle et al., maximum mean annual rainfall of 0.6 cm to 2011). From DISR data, the calculated rainfall Volatile Sources ~2 cm (Lorenz, 2000; Lorenz and Rennó, 2002). rates of 0.05–1.5 cm/h, in conjunction with an Although the photochemical dissociation of More advanced models tend to give lower esti- assumed 2 h storm duration and modeled yearly methane in Titan’s atmosphere leads to irrevers- mates: a one-dimensional (1-D) cloud micro- rainfall rates (Tokano et al., 2001; Barth and ible methane loss over ~10–100 m.y. (Flasar physics model predicts a precipitation rate of Toon, 2006), yield estimated recurrence inter- et al., 1981; Yung et al., 1984), the lack of strong ~0.2 cm/yr (Barth and Toon, 2006), and a two- vals for erosive runoff events ranging from once carbon isotopic fractionation in methane (Nie- dimensional (2-D) global circulation model per Titan season (~6 Earth yr) to once per Earth mann et al., 2005) indicates that the atmospheric with a deep reservoir of surface methane gives day (Perron et al., 2006). Observations demon- methane is continually resupplied. As on Earth, a mean annual precipitation rate of ~0.5 cm/yr strate spatially and temporally uneven rainfall the resupply of atmospheric volatiles is complex. (Mitchell, 2008). Conversely, the general circu- on Titan, where it is likely seasonally controlled Some evidence is consistent with a subsurface lation model (GCM) of Tokano et al. (2001) pre- (e.g., Schneider et al., 2012), so similar data on source of methane: The surface was measured dicts globally averaged rates of up to 10 cm/yr, sediment size, topography, and channel geom- to be “damp” by the Huygens probe (Lorenz and although rainfall at particular times and places etry would be required to make similar esti- Lunine, 2006), and some surface features suggest would be affected by temporal and elevation mates elsewhere on Titan. geologically recent cryovolcanic activity (Sotin effects (Barth, 2010), precipitation-evaporation et al., 2005; Nelson et al., 2009a, 2009b; Wall balances, putative cryovolcanic outgassing of Precipitation Patterns et al., 2009; Lopes et al., 2010). Other evidence methane, and other factors. Recent three-dimen- suggests surface sources: Models of atmospheric sional (3-D) simulations show that signifi cant Modeled circulation and weather patterns require a surface precipitation of several millimeters per day can In general, model precipitation occurs in source (e.g., Mitchell, 2008), and evaporation occur near the equator at equinox (Mitchell areas of methane reservoirs and large-scale from polar lakes (see Mitri et al., 2007; Lopes et al., 2011; Schneider et al., 2012), consistent updrafts associated with surface-level conver- et al., 2010) is implied by the detection of south with observations (Turtle et al., 2011). gence, where adiabatic cooling tends to result polar fog (Brown et al., 2009) and changes in lake Rainfall rate information can also be derived in condensation (Mitchell et al., 2006). Assum- shorelines (Turtle et al., 2009; Hayes et al., 2011). for particular locations from the observed effects ing an infi nite surface reservoir, various models on the surface. DISR data provide constraints on have reproduced observed cloud formation as Droplet Size fl ow width, sediment grain size, drainage area, resulting from upwelling following transport From these sources, Titan’s atmosphere is and slope for the fl uvial networks northwest of of moisture toward the summer pole (Tokano estimated to hold several meters of precipitable the Huygens landing site (Fig. 3B). Using these et al., 2001; Mitchell et al., 2006; Rannou et al., methane (e.g., Tokano et al., 2006), relative to data as constraints in a model of runoff, chan- 2006). Idealized 2-D and 3-D GCMs with shal- only a few centimeters of precipitable water nel fl ow, and grain entrainment, Perron et al. low (7 m) global surface reservoirs make predic- at Earth (Gao et al., 2004), so optically thick (2006) calculated rainfall rates of 0.05–1.5 cm/h tions that are consistent with most observations, clouds at Titan are expected. Voyager infra red to move the observed sediment sizes. This range including some seasonal variability (Mitchell, (IR) spectra suggest cloud drop sizes in excess of values for this specifi c location fi ts within the 2008; Mitchell et al., 2011). Including (sub) of 50 μm, therefore classifi able as rain (Toon two-order-of-magnitude range of global values surface methane transport in such models ex- et al., 1988). Later telescopic spectroscopy given by numerical models. plains the north polar clustering of (paleo)lakes, (Griffi th, 2000) and direct imaging (Brown Storm rainfall in mass per area can be con- low-latitude storm intensities at equinox, and et al., 2002; Roe et al., 2002) both show clouds. verted into rainfall rates using the density of the observed distribution of southern clouds Early raindrop models predicted evaporation liquid methane (taken as 450 kg/m3) and storm (Schneider et al., 2012). of the droplets in the atmosphere, i.e., virga duration. Complex 3-D mesoscale microphysi- (Lorenz, 1993), but suggestions of “raindrop cal models of Titan storms predict maximum Observed splashes” (Karkoschka et al., 2007), although methane rainfall of 110 kg/m2 (“equivalent Earth-based near-infrared (IR) spectra later discounted (Karkoschka and Tomasko, to fl ash fl oods”; Hueso and Sánchez-Lavega, showed enhanced opacity, attributed to con- 2009), provide motivation for revisiting this 2006), which equates to ~6–8 cm/h for a 3–4 h densed methane clouds near ~30 km altitude conclusion. Modeling of ternary mixtures of storm. Application of a modifi ed terrestrial cloud and methane drizzle at lower altitudes, local- methane-ethane-nitrogen (Graves et al., 2008) model with additional microphysics shows sig- ized near Xanadu (Ádámkovics et al., 2007, and modeling of cloud micro physics (Barth and nifi cant rain accumulation (20–30 kg/m2) over a 2009). In the north polar region, nondetection Rafkin, 2007; Barth and Rafkin, 2010) both pre- 5 h period, with peak accumulations in excess of clouds in Cassini radar observations rules dict that rainfall droplets grow large enough to of 100 kg/m2 (Barth and Rafkin, 2007), yielding out storms at the time of the observation (dur- reach the surface. Laboratory experiments show an average rainfall rate of ~1 cm/h or a peak rate ing the winter) and limits persistent drizzle that supercooled ethane droplets may be stabi- of ~5 cm/h. to less than ~10 cm/yr (Lorenz et al., 2008b).

Geological Society of America Bulletin, March/April 2013 309 Burr et al.

Large cloud outbursts observed both in ISS and subsurface storm fl ow can be signifi cant in high- These results, though imprecise, are similar to telescopic data have occurred at the southern permeability zones near streams. theoretical precipitation rates in individual storms summer pole near solstice (Porco et al., 2005; Base fl ow, which also has a groundwater (see previous section, Precipitation Characteris- Schaller et al., 2006), with equa torial storms source, fl uctuates over longer periods and has tics). However, the Cassini radar data often cover near equinox (Schaller et al., 2006; Turtle et al., little dependence on individual precipitation only part of a watershed, and the sparseness of 2011). The evolution of a large midlatitude events (e.g., Dingman, 2002). topographic data complicates mapping of drain- storm was recorded by both ground-based and age divides, so measurements of contributing spacecraft observations (Ádámkovics et al., Application to Titan area are often uncertain and may be low. Surface 2010). Surveys of cloud coverage during the The infi ltration capacity and depth to the attenuation can be negligible in small drainage Cassini-Huygens prime mission are broadly fl uid table are uncertain for Titan, so the relative basins (see examples in Perron et al., 2006), but it consistent with circulation models (Rodriguez importance of channel precipitation, overland can also be signifi cant, especially at larger scales. et al., 2009, 2011; Brown et al., 2010). fl ow, and subsurface fl ow is unknown. The event Thus, runoff estimates should be interpreted as fl oods that dominate river channel morphometry maxima. Surface and Near-Surface Flow Paths are also a function of climate, recent precipita- Rarity of precipitation appears to be the most tion history, and storm intensity, which may direct cause of aridity at Titan’s equator, per- Lakes cover only a few percent of Titan’s be highly variable on Titan. In observations to haps due to interpolar migration of the ITCZ surface (e.g., Stofan et al., 2007), so most pre- date (over approximately one-quarter of a Titan (Tokano, 2011), but high evaporation rates for cipitation would fall on land. As on Earth, rain- year), the largest cloud bursts have occurred at methane (Mitri et al., 2007; Tokano, 2009) fall could evaporate from, infi ltrate into, or fl ow the southern (summer) pole (Porco et al., 2005; may also remove fl uid from the (near-)surface, across the surface to a fl uvial network. Runoff Schaller et al., 2006), consistent with models affect ing the hydrologic response during the in networks can arrive via channel precipitation, showing migration of the intertropical conver- next event. Some terrestrial landscapes are arid saturation overland fl ow, Hortonian overland gence zone (ITCZ) between the summer poles because evaporation is high more than because fl ow, shallow subsurface fl ow, and base fl ow. (Tokano, 2011). Particularly if antecedent con- precipitation is low. In northern Australia, the Stream channels comprise a few percent ditions are dry, intense storms offer the greatest summer monsoon delivers 0.5–1.5 m/yr of rain, or less of a watershed’s area, but precipitation potential for precipitation to exceed infi ltra- but annual potential evaporation is 2.0–2.6 m. into the channels and adjacent fl ooded areas tion and generate Hortonian overland fl ow. As The potential moisture defi cit averaged across can contribute up to ~30% of a fl ood event’s the south (summer) polar convection migrates the continent is considerably higher, with annual peak discharge, because the supply is not de- northward, short-term surface changes due to rainfall of 0.47 m and potential evaporation of layed (Dingman, 1970; Beven and Wood, 1993; precipitation have been documented near Titan’s 3.25 m (Nanson et al., 2002). Crayosky et al., 1999). In a terrestrial study, the equator (Turtle et al., 2011), where the rapid On Titan, despite the much lower solar radia- largest percentages of channel precipitation as a changes might have been produced by Horto- tion, annual evaporation rates for methane are fraction of peak discharge occurred during dry- nian overland fl ow over low-permeability sedi- similar to evaporation of water from terrestrial season fl ood events (Crayosky et al., 1999). ments, e.g., tholins. The distribution of saturated lakes. Calculated methane evaporation rates of Rainfall onto saturated areas with emerging areas near channels is unknown, but the occur- 0.3–10 m/yr are consistent with its relative hu- groundwater generates saturation overland fl ow, rence of high-latitude lakes suggests the poten- midity in Titan’s atmosphere and the fractional which can also enter the channel quickly due to tial for saturated areas and saturation overland surface area covered by lakes (Mitri et al., 2007) the commonly low position of saturated areas in fl ow in the polar regions. and with observed changes in lake levels (Hayes the watershed (Dunne and Black, 1970). Satura- et al., 2008). The fraction of rainfall that is shed tion overland fl ow is common in humid regions Runoff Production as runoff varies widely in terrestrial dryland on Earth where water tables are maintained watersheds, but evaporation from the surface near the land surface. Concave hillslope pro- Runoff production is equal to the stream dis- or soil can be more signifi cant than runoff as a fi les, wide valley fl oors, convergent topography charge divided by the contributing area. Event water loss mechanism. In the Colorado River on hillslopes, and perched saturated layers are runoff (above base fl ow, if any) represents pre- drainage basin, for example, only 3.3 cm of the important sources of saturation overland fl ow cipitation minus infi ltration, evaporation, and at- total 36 cm annual average precipitation is lost (Ward, 1984). tenuation of fl ow over the contributing surface, as runoff (Graf, 1988). By analogy, evaporation Hortonian overland fl ow occurs when the all of which may vary during an individual storm. from watershed surfaces on Titan may be a more precipitation rate exceeds the surface infi ltration Assuming losses by these three mechanisms to signifi cant fl uid-loss mechanism than runoff. capacity (Horton, 1933, 1945), and it develops be negligible, Perron et al. (2006) calculated a during intense storms on fi ne-grained soils or minimum precipitation rate of 0.05–1.5 cm/h Discharge impermeable surfaces. It contributes signifi - in the watershed shown in their fi gure 2 (our cantly to streamfl ow in dryland areas, where Fig. 3B), in order to generate their estimated Once runoff becomes channelized, it is char- precipitation commonly occurs as storms, soil discharge. Lorenz et al. (2008a) used a 10-km- acterized by the discharge, estimated as the may be compacted, and low water tables do not wavelength bend, assumed to be a meander, in product of fl ow width, fl ow depth, and depth- favor saturation overland or groundwater contri- inferring a discharge of ~5000 m3/s from a con- averaged fl ow velocity, which is a function of butions (Yair and Lavee, 1985). tributing area of roughly 80 by 30 km, deriving channel slope, gravity, and the friction exerted Precipitation may also infi ltrate and move as ~1 cm/h of runoff. Jaumann et al. (2008) calcu- by the channel on the liquid (see Eq. 2 in the shallow subsurface fl ow. Typically, infi ltrated lated that measured “channel” (possibly valley ) next section). Order-of-magnitude estimates water moves too slowly to contribute signifi - widths and discharge estimates from scaled of discharge on Titan have been derived from cantly to the intermittent fl ood discharges that empirical relationships imply 0.06–6 cm/h of measured dimensions of fl uvial features or dominate river channel morphometry. However, precipitation and therefore runoff from storms. the likely size of transported sediment (Perron

310 Geological Society of America Bulletin, March/April 2013 Fluvial features on Titan et al., 2006; Jaumann et al., 2008; Lorenz et al., tems. In a transport-limited river, the sediment Thus, assuming that fl uid fi lls a channel of 2008a). However, the fl ow depth, channel slope, fl ux is determined by the capacity of the fl ow to given dimensions (i.e., bankfull fl ow), the fl uid or friction factor values are poorly constrained transport the material (i.e., qs = qsc). Thus, sedi- discharge can be calculated from Equation 2 for Titan (with the exception of the topography ment fl ux can be estimated from fl ow hydraulics from topographic measurements of channel of the fl uvial networks imaged by the DISR, dis- alone. These riverbeds tend to be fully alluvi- depth, width, and slope alone, with an appropri- cussed previously). In addition, the fl ow width ated (i.e., no exposed bedrock) and can be net ate estimate of the coeffi cient of friction. is imprecise because the nature of the fl uvial depositional, bypass, or erosional, depending on The friction coeffi cient has been found to be a features—whether channels or valleys—is un- the time scale of interest. function of the fl ow Reynolds number (i.e., Re = certain. For these reasons, the usual approach is We begin the discussion with the better-stud- Uh/ν, where ν is the kinematic viscosity of the not straightforward to apply. ied and constrained transport-limited systems fl uid) for laminar fl ows (Re < 500) and is inde- An alternative approach uses empirical re- carrying a predominantly undissolved (solid) pendent of the fl uid viscosity and Re for turbu- lationships between width or meander wave- load. In this regime, the sediment transport lent fl ows with hydraulically rough beds (i.e., length and dominant discharge from studies of is highly dependent on the stresses within the uk∗ s Re > 103 and Re > 100, where Re = is the terrestrial channels (see summary by Knighton, fl owing fl uid, and we consider the dynamics of ks ks ν

1998). This approach is valid only for the range fl uid fl ow fi rst. bed roughness Reynolds number, u∗ ≡τρb of variables from which the empirical function is the shear velocity, and ks is a characteristic was derived (Williams, 1988) and requires mea- Flow Characteristics bed roughness length scale; Nikuradse, 1933; surement of channel (not valley) dimensions. Schlichting, 1979; Garcia, 2007). On Earth, The nature of the features might be constrained The effects of fl ow of a Newtonian fl uid in fl ow is predominantly turbulent, and this condi- by comparison with wavelength/width ratios for a channel can be modeled through conserva- tion likely holds true on Titan as well (Perron alluvial channels, which typically fall within a tion equations for fl uid mass and momentum et al., 2006), especially for meter-plus–scale narrow range for Earth (~10–14; Leopold and and a parameterization for bed friction in turbu- channel widths. For example, given that liquid Wolman, 1960). However, this range of values lent fl ow (i.e., a drag law). In their most simple methane has a kinematic viscosity (ν) of 4 × may not pertain to sinuous bedrock valleys with forms for depth-averaged, Reynolds-averaged, 10–7 m2 s–1 for Titan’s surface conditions (http:// inset channels (Dury, 1964, 1985), as the bed- steady and uniform condition, these equations webbook.nist.gov), fl ows with a discharge per rock valley dimensions may refl ect much larger, for bed friction are unit width (Uh) greater than 4 × 10–4 m2 s–1 (i.e., rarer fl oods (Baker, 1977; Kochel, 1988; Wohl, depths of centimeters and velocities of centi-

2000). For resistant bedrock valleys, the bank τρbd= gh R S, (1A) meters per second) will be turbulent. Fur- erodibility is low and the recovery time may be thermore, hydraulically rough conditions are very large, so the most geomorphically effective and expected in river channels that transport sedi- fl ood may have a long recurrence interval, even ment of diameter D > 1 mm over a fl at bed. Hy- 2 by Titan’s standards (Lorenz et al., 2005). τρbf= CU , (1B) draulically rough conditions may exist for fi ner sediment if bed forms (e.g., ripples or dunes) or τ MODELING HYDRAULICS, where bd is the driving stress acting on the fl uid other larger roughness elements are present. For τ FLUVIAL EROSION, AND due to gravitational acceleration, b is the shear turbulent, hydraulically rough fl ow conditions, SEDIMENT TRANSPORT stress on the bed due to friction, ρ is the fl uid many empirical parameterizations have been

density, g is gravitational acceleration, hR is the proposed for Cf, which depend on the ratio of

On Earth, fl uvial morphology results from hydraulic radius of the fl ow, S is bed slope, Cf is the fl ow depth to the bed-roughness length scale. feedbacks among fl uid fl ow, sediment supply a friction coeffi cient (e.g., Chow, 1959), and U is For example, one formula for Cf for gravel-bed 1/6 –1/2 and transport, and topography. The existence the depth-averaged fl ow velocity. For the case of rivers is Cf = (8.1[h/ks] ) , where ks = 2D or τ τ of fl uvial features on Titan and the terrestrial steady and uniform fl ow, b = bd, which is an ap- 3D (Parker, 1991). Because Cf is independent of analogs discussed herein suggest that simi- proximation appropriate for many river systems fl uid density, viscosity, and gravity for turbulent, lar processes are at work there. Sediment fl ux (e.g., Parker et al., 2007). However, in regions hydraulically rough fl ow conditions, it should in terrestrial rivers may be supply-limited or where fl ow is dynamic in time (e.g., fl oods) or be applicable to similar conditions, e.g., gravel- transport-limited (e.g., Howard et al., 1994). space (e.g., lateral spreading or confi nement), bed rivers, on Titan. τ ≠ τ In a supply-limited river, the sediment fl ux is a b bd, and spatial and temporal accelerations function of erosion of bedrock in the riverbed, (excluding turbulent fl uctuations) need to be Application to Titan delivery of sediment from neighboring hill- taken into account (e.g., Chow, 1959). Another Formulae like Equation 2 have been used to slopes or upstream reaches, and atmospheric common assumption is that hR = h, where h is calculate bankfull fl ow discharge for putative deposition. Thus, the sediment fl ux qs is lim- the fl ow depth, which introduces only a small fl uvial channels on Titan (Perron et al., 2006; ited by the amount of material supplied to the error (<10%) for channels that are much wider Jaumann et al., 2008; Lorenz et al., 2008a).

fl ow, i.e., qs < qsc, where qsc is the volumetric than they are deep (w > 10h), a common con- Perhaps the biggest limitation in these calcula- sediment transport capacity of the river per unit fi guration for most terrestrial alluvial channels. tions is the assumption of fl ow width, because channel width. Under these conditions, river- With these assumptions, the hydraulic conserva- the nature of the fl uvial features—whether beds contain partial or full exposure of bedrock, tion equations for steady fl ow can be combined river channels or river valleys—is uncertain. and river channels tend to be net erosional. Al- into a single expression for the volumetric fl ux If this parameter could be determined, how- though some progress has been made to under- of fl uid in a channel Q, ever, then we expect these hydraulic formulae stand the mechanics of supply-limited rivers to be valid for Titan. In particular, if the fl ow is ⎛ ⎞ 12 (for a review, see Whipple, 2004), knowledge is ghS fully turbulent and the boundary is rough, then Qwh= ⎜ ⎟ . (2) limited in comparison to transport-limited sys- ⎝ Cf ⎠ the hydraulics are insensitive to fl uid viscosity ,

Geological Society of America Bulletin, March/April 2013 311 Burr et al. making hydraulics equations developed for In low-gradient rivers, the increased par- work assumes spherical particles, which again Earth directly applicable to Titan conditions ticle exposure and lower friction angles of requires evaluation for Titan. when the difference in gravity and fl uid den- larger particles tend to offset the effects of their The transitions between sediment transport sity are accounted for in Equations 1A and 2. If greater weight, rendering mixtures of different modes can be described using the Rouse num- the boundaries are hydraulically smooth or the sizes nearly equally mobile (Parker et al., 1982; ber, P, which is a ratio of grain settling velocity fl ow Reynolds number is suffi ciently low, then Wiberg and Smith, 1987; Parker, 1990). Thus, to turbulence acting to suspend grains and equal κ the kinematic viscosity of the fl uid will need to a prediction of incipient motion of the median to ws/ u*, where u* is the shear velocity, and be known to make quantitative predictions of particle size often is representative of the entire κ = 0.407 is the von Karman constant. The tran- fl ow rates. bed. This assumption breaks down, however, sition from bed load to suspended load is P ~ 2.5 τ in bimodal mixtures, where ∗c can decrease and for suspension to wash load is P ~ 0.8. The Sediment Transport by ~2-fold (Wilcock and Crowe, 2003), and on threshold of bed-load motion has been treated τ steep slopes (S > 1%), where ∗c can increase separately, above. Fluvial networks transport the products of by up to an order of magnitude due to par- weathering from hillslopes and upstream chan- ticle emergence (reducing the cross-sectional Application to Titan nels in both the solid and dissolved state. The area exposed to fl ow) and changes to turbulent To apply terrestrial sediment transport equa- total sediment fl ux (or “load”) per unit width mixing in very rough conditions (Lamb et al., tions to Titan, a limited number of parameters shown in Equation 1 can be divided into bed 2008c). Expressions that partition bed-load fl ux need to be adjusted, including gravitational ac- load (qb) and suspended load (qsus), such that among discrete grain-size classes have been de- celeration, the densities of fl uid and sediment, qs = qb + qsus. The dissolved load (qd) is a volu- veloped (e.g., Parker, 1990) and should be used and the fl uid viscosity. These calculations indi- metric fl ux and affects the land surface, but it is for the cases of bimodal sediment mixtures cate that both water-ice and organic particles fall not part of the sediment fl ux unless or until it (Wilcock and Crowe, 2003), which DISR im- through liquid methane on Titan more slowly precipitates. In terrestrial landscapes, suspended ages (Tomasko et al., 2005) suggest may exist than do silicate clasts in water on Earth, primar- transport is often the dominant mode, although on Titan. ily because of the lower gravity, although this bed load can dominate in steep, rapidly eroding gravitational effect is partly offset by the greater terrain, and dissolved load may be dominant Suspension submerged specifi c gravity (r) of the grain and in karst terrains. Even where bed-load fl ux is a At larger fl ow velocities or (for a given chan- the lower viscosity (ν) of the liquid (Burr et al., minor fraction of the total load, bed material dy- nel confi guration) lower gravity, sediment mo- 2006). As a result, for a given grain size, a lower namics can be important in controlling channel tion in suspension, whereby the stream sediment shear velocity is required to drive grain mo- morphology and roughness and in modulating rarely contacts the bed, is enhanced (Komar , tion across thresholds between transport modes the rate of incision into underlying bedrock. 1980). The suspended load is composed both (Fig. 6). A key unknown in estimating sediment of material entrained from and exchanged with transport modes and rates on Titan is the spatial Incipient Motion the bed, termed “suspended bed material load,” distribution of grain sizes, which depends on the As the motion of fl uid in a river imparts a and of the fi ner particles supplied from upstream size distribution supplied to the channel network critical shear stress to the riverbed, available that settle too slowly to exchange with the bed, and the rate of particle breakdown in transport. sediment typically begins to move as bed load termed “wash load.” Analysis of the backscatter from radar-bright by rolling and bouncing. For a range of sedi- Suspension occurs where the fallout under fl uvial features, which implies a cover of ment sizes and fl ow conditions, the criterion gravity is balanced by entrainment due to tur- rounded ice cobbles (Le Gall et al., 2010), as for entrainment can be calculated from the non- bulence. The conditions for suspended sediment well as the rounded cobbles at the Huygens dimen sional bed shear stress, also known as the transport can be determined from the bed stress landing site (Tomasko et al., 2005), suggests Shields stress, defi ned as necessary to initiate particle suspension, which that, although rounding during transport may be be found from effi cient, breakdown may be limited. τ τ ≡ b . (3) The density of sediment particles in Titan ∗ ρρ− 2 ()s gD τρbs= w , (4) riverbeds may be variable because multiple candidate surface materials could dominate the

Shields (1936) showed that the critical value where ws is the particle settling velocity (Bagnold, local supply of sediment particles. Near-surface τ of this stress, ∗c, for incipient motion, varies with 1966). Settling velocities may be determined spectra from the Huygens probe are consistent 12 ()rgD D experimentally. Dietrich (1982), for example, with the presence of water-ice and organic tholin the particle Reynolds number, Rep = , ν explicitly accounted for particle and fl uid densi- compounds along with an unknown IR-blue ma- where r is the submerged specifi c gravity of the ties, fl uid viscosity, and the acceleration due to terial (Schröder and Keller, 2008). Microwave ρ ρ ρ ρ ρ sediment (r = [ s – ]/ , where s and are the gravity, making those formulations directly ap- scattering from Titan’s surface is also consistent densities of sediment and fl uid, respectively) plicable to Titan conditions. For this approach, with a mix of fractured or disaggregated water- τ for small Rep and is roughly constant (i.e., ∗c particle shape and roundness are required, ice particles and “fl uffy” deposits of organic ma- ≈ 0.045; Miller et al., 1977; Wilcock, 1993) for which are not well known for Titan, but which terials (Janssen et al., 2009). The bulk of Titan’s 2 Rep > 10 . The condition for constant critical might be approximated for at least one location crust is likely predominantly composed of Shields stress is met for D > ~1 mm for condi- from data at the Huygens landing site. Empirical water-ice, with a relative density to liquid meth- tions on both Earth and Titan, taking values for data for non-Newtonian fl ow (Turton and Clark, ane of ~2.1, and this ice may make up a signifi - Titan of r = 1.18, g = 1.35 m/s2, and ν = 4 × 1987; Kelessidis, 2004) have been converted cant fraction of the sediments. The gravel- and 10–7 m2/s for transport of water-ice sediment by into settling velocities for silicate sediment on cobble-strewn surface at the Huygens landing fl owing methane (e.g., Burr et al., 2006; Perron Earth and for hypothesized organic and water- site appears to be more enriched with water-ice et al., 2006). ice sediments on Titan (Burr et al., 2006). This particles than the surrounding areas (Keller et al.,

312 Geological Society of America Bulletin, March/April 2013 Fluvial features on Titan

τ bed shear stress ( b) or stream power per unit bed area (ω). The empirical coeffi cients in these relationships are complex parameters into which many variables are lumped, including the Figure 6. Sediment transport rock resistance to erosion, channel roughness diagram showing the bed shear and geometry, the effi ciency of the dominant stress required for each sedi- erosional processes, and the inherent tradeoffs ment transport mode. For a between the magnitude and frequency of dis- given grain diameter, lower charges capable of eroding bedrock (Howard stress is required for both types and Kerby, 1983; Whipple and Tucker, 1999). of Titan materials than for ter- This scaling approach is appealing because of restrial conditions (modifi ed its simplicity, and it is readily incorporated into from Burr et al., 2006). landscape evolution models. Using hydraulic conservation equations (e.g., Eq. 2), and assum- ing that fl ow depth and discharge (for a given fl ood recurrence interval) can be expressed as functions of drainage area (A), the incision rate can be written as

2008). The atmosphere is also a source of fi ne hydration-fracturing in clay-rich shales, and EkAS= mn, (5) sediment in the form of micron-sized organic cavitation on surfaces that protrude into high- aerosol particles (Waite et al., 2009). Dunes velocity fl ow (Whipple et al., 2000). where the parameters k, m, and n are model- on Titan are likely made of sand-sized organic specific parameters empirically calibrated particles (Barnes et al., 2008) that may have ag- Sediment (Tools) Production using river longitudinal profi les that are as- glomerated over time from these smaller aerosol On Earth, fl uvial sediment production gener- sumed to be in topographic steady state or particles. The density of the organic sediments ally requires physical and/or chemical weather- where initial and boundary conditions are on Titan is relatively unconstrained—if they are ing to reduce coherent bedrock to transportable known (Whipple, 2004). solid, they could be signifi cantly denser than sizes—typically less than meter-scale. On Titan, This stream power approach is of limited util- water-ice (e.g., Khare et al., 1994), but if they some sediment may be organic particulates from ity for simulating rates of channel incision on are porous, they could be less dense than ice. A atmospheric sources (such as the sediment form- Titan because of the lack of physical constraints lack of knowledge regarding the exact types and ing the tropical dunes), but this sediment should on the model parameters under Titan conditions. proportions of the fl uvial liquid hydrocarbons on be fi ne grained and probably could not facilitate Process-specifi c models, ideally with physically Titan also adds some uncertainty to these results. widespread valley incision and formation of steep explicit parameters, are better suited to explor- Our discussion of sediment transport thresh- slopes, as observed in DISR data (Tomasko et al., ing controls on rates and patterns of landscape olds assumes that the sediment particles are not 2005; Soderblom et al., 2007b). The Titan crust evolution. However, without information about cohesive. This assumption may be reasonable is primarily water-ice with some mixture of other hydraulic geometry and the frequency and for water-ice particles, but for sediments com- compounds. Recent experimental work, showing magnitude of fl ows, even erosion models with posed of, or covered by solid tholins (Barnes the diffi culty of eroding coherent icy bedrock, physically explicit parameters will be of limited et al., 2008), it may not be correct. The morphol- suggests that the bedrock on Titan must be per- utility for modeling absolute rates of landscape ogy of some terrestrial longitudinal dunes is hy- vasively fractured prior to fl uvial erosion (Collins evolution. pothesized to be the result of the sand particles et al., 2011). However, no relevant chemical or Brief discussion of specifi c erosion processes being slightly cohesive (Rubin and Hesp, 2009). physical weathering processes that would per- shows the present extent of applicability of these If this hypothesis is correct and applicable to vasively break down coherent ice bedrock have process-specifi c models to Titan. Plucking is the Titan , then organic sediment particles may be been identifi ed. Meteor impact can reduce rock removal of material from a channel bed “by less prone to saltate than water-ice particles, and to transportable sizes, but Titan’s observed crater lifting or sliding of blocks defi ned by an exist- the sediment transport threshold stresses derived population is sparse (Wood et al., 2008). How- ing set of discontinuities in the rock” (Hancock for Titan would represent lower limits. ever, if, Titan did not develop a thick, volatile- et al., 1998), and it results from pressure fl uctua- cycle–sustaining atmosphere until relatively late tions in highly turbulent fl ows. It can be mod- τ Bedrock Erosion in Solar System history (e.g., McKay et al., 1993; eled as a power function of bed shear stress ( b) τ Lorenz et al., 1997), then the initial surface could in excess of the threshold stress ( c) required to Under supply-limited conditions, when sedi- have had a substantial impact-generated regolith initiate detachment (e.g., Whipple et al., 2000): ment transport capacity (qsc) exceeds sediment layer generated prior to the onset of fl uvial activ- =−()ττn supplied to the river (qs), bedrock may be ex- ity. Such a starting icy regolith could have pro- Ekbc, (6) posed in some or all of the channel bed and vided ample tools for incision and/or sediment subject to erosion. Erosion of terrestrial bedrock for transport once the rains began. where k and n are model-specifi c parameters. occurs primarily through abrasion by bed load More physically explicit models are available and suspended load particles (“tools”) and by Incision Rates and Mechanisms for bedrock wear by abrasion by saltating bed plucking (or “quarrying”) of fracture-bounded The rate of fl uvial incision is convention- load (Sklar and Dietrich, 2004) and by bed load blocks (Whipple, 2004). Less-common mecha- ally assumed to follow power-law scaling with and suspended load particle impacts (Lamb nisms include dissolution in carbonate rocks, some metric of fl ow intensity, such as average et al., 2008b). These models are based on the

Geological Society of America Bulletin, March/April 2013 313 Burr et al. notion that sediment provides abrasive tools, but to the weak physical basis for most terrestrial conceptual models and rough empirical cor- at high supply rates, transient sediment deposits model formulations. Abrasion by ice clasts relations are available for steeper, gravel- and can cover and protect underlying bedrock from (Collins, 2005) moving as bed load and/or sus- coarser-bedded terrestrial channels (Montgomery all erosive mechanisms except dissolution. A pended load (Burr et al., 2006) is a reasonable and Buffi ngton, 1997). general expression that encompasses tools and candidate mechanism, given the rounded grains cover, as well as most other published incision observed at the Huygens landing site (Tomasko Low-Gradient Terrestrial Channels model formulations (Sklar and Dietrich, 2006), et al., 2005). This process can be modeled with In relatively low-gradient channels on Earth, can be written as physically explicit sediment-abrasion models a predictable sequence of bed morphologies de- (Sklar and Dietrich, 2004; Lamb et al., 2008b). velops with increasing bed shear stress, includ- ⎛ ⎞ c a b qs Parameters that need to be adjusted for Titan ing ripples, upper plane bed, and antidunes for Ek=−()γγcs q⎜1− ⎟ , (7) ⎝ qsc ⎠ conditions include gravity, the buoyant density beds of silt and fi ne sand, and lower plane bed, of sediments, and possibly the fl uid viscosity dunes, upper plane bed, and antidunes for beds where k is model specifi c, γ is a generic fl ow in- for modeling wear by fi ner-grained suspended of coarse sand and gravel (e.g., Southard, 1991). tensity variable (e.g., shear stress, Shields stress, particles, depending on the particle Reynolds In steady, uniform, open-channel fl ow of a γ γ stream power, etc.), c is the value of at the on- number. Incision rates predicted by the salta- Newtonian fl uid, dimensional analysis indicates set of sediment motion or bedrock detachment tion-abrasion model, for fi xed channel geometry that at least three key dimensionless variables depending on model assumptions, qs and qsc and sediment conditions, are remarkably similar are needed to describe stable bed-form states are the sediment supply (fl ux) and transport ca- for Earth and Titan (Collins, 2005), as Titan’s (Vanoni, 1974; van Rijn, 1984; Southard, 1991; pacity per unit width, respectively, and the em- lower gravity and higher sediment buoyancy van den Berg and van Gelder, 1993). These pirical exponents b and c control the tools and are partially offset by lower resistance to impact dimensionless variables provide a set of scale- cover effects, respectively. For wear by particle wear for water-ice compared to rock of similar modeling parameters that can take into account impacts, rock resistance varies with the square tensile strength (Polito et al., 2009). a wide range of sedimentologically interesting of tensile strength (Sklar and Dietrich, 2001). The material properties of ice bedrock and behaviors such as the effects of changing grain However, for other incision mechanisms, little is regolith on Titan are fi rst-order controls on the size, current velocity, fl ow depth, fl uid viscos- known about the ways in which wear rates scale occurrence and effi ciency of the various pos- ity, grain density, and the acceleration of gravity. with rock material properties (Whipple, 2004). sible incision mechanisms. The tensile strength Herein, we describe bed states by representing To apply a tools-and-cover model as shown in and erosion resistance of polycrystalline water- the fl ow strength (or intensity of sediment trans- Equation 7, predictive relations are needed for ice increases with decreasing temperature port) through the dimensionless Shields stress, the spatial variation in grain size and supply rate (Polito et al., 2009; Litwin et al., 2012), and the τ∗ (Eq. 3), and the effective sediment size using of sediment delivered to channel networks by strength is sensitive to ice grain size and poros- the particle Reynolds number, Rep, along with hillslopes. In terrestrial models, sediment sup- ity (Schulson and Duval, 2009). Moreover, ice U the Froude Number, Fr = , as the fi nal ply is often estimated as the product of drainage erodibility may be infl uenced by impurities gh area and long-term mean denudation rate, and such as atmospherically derived tholins (e.g., dimensionless number needed to describe bed- partitioned arbitrarily between coarse bed load Soderblom et al., 2007a) and cryovolcanically form stability in this framework. Numerous and fi ner suspended load (e.g., Sklar and Diet- derived ammonium sulfate compounds (Fortes fl ume experiments have shown that for Fr >~1, rich, 2006). At present, little is known about the et al., 2007), although evidence for cryo vol- fl ows are considered supercritical, and anti- controls on grain-size distribution of sediments canism on Titan has been challenged (Moore and dunes form rather than ripples, dunes, or plane supplied to channels on Earth (Attal and Lavé, Pappalardo, 2011). The extent and characteristic beds (Vanoni, 1974; van Rijn, 1984; Southard 2006) or on Titan. scale of fracturing in ice bedrock will infl uence and Boguchwal, 1990a). For Fr <1, bed-form Another set of bedrock incision mechanisms the grain size supplied to channels, as well as stability is independent of Fr and therefore can is associated with migrating knickpoints and the potential role of plucking and knickpoint be neglected as a variable for the analysis of waterfalls, including plunge pool scour, under- retreat in channel incision. Whether landslides ripple bed forms of concern here (van den Berg cutting, seepage, and block toppling (Lamb and debris fl ows occur on Titan depends in part and van Gelder, 1993). et al., 2006; Lamb and Dietrich, 2009), as well on the extent of disaggregation of hillslope bed- We have compiled results from fi ve sediment as effects on upstream channels due to fl ow ac- rock and on the dynamics of methane rainfall transport and bed-form studies to build a com- celeration approaching free fall (Haviv et al., infi ltration and runoff. prehensive bed-form stability diagram for Fr < 1

2006). Debris fl ows can also be important agents that spans a large range in Rep (Fig. 7A) (Chabert of channel incision in headwater channels (Stock Bed Morphology and Chauvin, 1963; White, 1970; Brownlie, and Dietrich, 2006), where steep slopes tend to 1983; Southard and Boguchwal, 1990b; van generate sediment fl ows. However, global relief Channel bed morphology is important for den Berg and van Gelder, 1993). Each study on Titan is lower than on Earth (Perron and de fl uvial processes and landscape evolution be- contains many data points (in cases thousands) Pater, 2004; Jaumann et al., 2009; Lorenz et al., cause of its infl uence on hydraulic roughness, that each represent a single fl ume experiment 2011), which may serve to reduce the geomor- sediment transport and erosion rates, and the or fi eld observation, and these data points are phic effectiveness of debris fl ows, if all other fac- dominant bedrock incision mechanisms (Wohl, not reproduced here. Instead, the dividing lines tors are assumed to be equal. 2000). Bed morphology varies systematically were found empirically to bound the bed-form through terrestrial river networks and is strongly stability fi elds from each study, with solid lines Application to Titan infl uenced by bed material grain size. The in- where the stability fi elds have been explored Scaling terrestrial bedrock incision models fl uence of fl ow hydraulics on bed confi guration experimentally or with fi eld data, and dashed to Titan is diffi cult due to the uncertainty as to is better understood mechanistically for low- lines where data represent power-law extrapo- which erosional processes are dominant and gradient, sand-bedded channels on Earth. Only lations (Fig. 7A). For the case of Southard and

314 Geological Society of America Bulletin, March/April 2013 Fluvial features on Titan

Boguchwal (1990b), we recast their dimensional diagram (their fi g. 11) into the dimensionless A τ variables ∗ and Rep. The compilation shows a lower boundary separating no motion from the fi elds of sediment transport, i.e., the Shields curve (Shields, 1936). In the regimes of mobile

sediment, ripples form at low Rep and moder- ate values of τ∗, and ripples begin to wash out to τ upper plane bed at ∗ >~1. For large Rep, a stable regime of lower plane bed is followed with in- creasing Shields parameter by dunes and upper plane bed. The results are robust even though the databases contain fi eld data, fl ume data, and measurements made by different authors, and even though they span a wide range of fl ow veloci ties, fl ow depths, particle sizes, particle densities, fl uid densities, and fl uid viscosities.

Application to Titan The bed-form stability diagram reveals that stable bed-form states depend on fl uid and par- ticle density, viscosity, and gravity, all of which are different for fl ows on Titan as compared to Earth. To illustrate this effect, we replot the stability fi elds in terms of the fl ow stress on the τ bed ( b) versus particle diameter (D) (Fig. 7B). This replotting requires values for the physical B properties of the fl ows and sediment on Titan, approximated as r = 1.18, ν = 4 × 10–7 m2/s, and g = 1.35 m/s2 for transport of water-ice sediment by fl owing methane. A reference case for fresh- water fl ows on Earth is also shown with r = 1.65, ν = 10–6 m2/s, and g = 9.81 m/s2. This dimensional plot shows a signifi cant shift in bed-form stability for conditions on Titan as compared to Earth (Fig. 7B), primarily due to the 10-fold reduction in the submerged specifi c weight of the sediment (i.e., rg). For example, sediment of size D = 0.1 mm on Titan is predicted to have an upper plane bed confi gu- ration, the highest energy state, for the same bed stresses at which the same size sediment is at the threshold of motion on Earth. Despite the drastic change in fl uid stresses for Titan con- ditions, the equivalent bed forms are expected to form in the same sediment sizes on Titan as on Earth. For example, ripples are expected for D < ~0.1 mm and dunes for D > ~2 mm, with both bed forms possible for intermediate sizes, whether on Earth or Titan. This similar- ity of bed forms with sediment size is because the lower fl uid viscosity on Titan by a factor of Figure 7. Bed-form stability diagrams for low-gradient rivers. (A) Nondimensional represen- 2.5 is compensated for by the decrease in sub- tation of stable bed forms. Solid lines are boundaries between bed states that have been ex- merged specifi c weight of the sediment in the plored based on fi ve previous studies and compilations (Chabert and Chauvin, 1963; White, calculation of Rep. 1970; Brownlie, 1983; Southard and Boguchwal, 1990b; van den Berg and van Gelder, 1993). (B) Dimen sional representation of stable bed states for methane fl ows transporting water-ice High-Gradient Terrestrial Channels particles on Titan (thick lines), and freshwater fl ows transporting siliceous material on Earth Upstream of the gravel-sand transition, ter- (thin lines). Dashed lines are power-law extrapolations of stability boundaries from part A. restrial riverbeds display a predictable sequence “Upper plane bed” and “lower plane bed” apply to both Titan and Earth conditions. of channel types correlated strongly with slope

Geological Society of America Bulletin, March/April 2013 315 Burr et al.

(S), progressing downstream from cascade to (Knighton , 1998). However, terrestrial relations, porosity and permeability, stratifi cation, and step-pool to alternating bar-pool morphology, being empirical, may scale differently on Titan. solubility, would contribute to inferences about as drainage area, channel width, sediment sup- (3) If some features are inferred to be chan- the locations, timing, and effi ciency of each fl ow ply, discharge, and mean fl ow velocity all in- nels, then questions may be raised pertaining to path. Estimations of the amount of runoff and crease and grain size systematically decreases meandering (e.g., Fig. 2C). Meandering chan- the recurrence interval of the channel-forming (Montgomery and Buffi ngton, 1997; Knighton, nels require some bank material cohesion, which (dominant) discharge require additional infor- 1998). These characteristic trends result from on Earth is associated with plants (Davies and mation on precipitation patterns and mechanical downstream shifts in the dominant processes Gibling, 2010a; Davies and Gibling, 2010b). properties of the surface. delivering sediments (e.g., debris fl ows to bank However, meandering paleochannels are also (8) Channelized fl ow may be modeled using erosion), and the scale and type of hydraulic inferred for Mars (Malin and Edgett, 2003; terrestrial hydraulic formulae with appropriate roughness elements (e.g., boulders to bars), as Moore et al., 2003; Burr et al., 2009a, 2010). If modifi cations. If the fl ow is fully turbulent and well as the increase in width-depth ratio and the some sinuous fl uvial features on Titan are deter- the boundary is rough, then hydraulic equations shift from confi ned to fl oodplain valley bottoms mined to be meandering river channels (as op- developed for Earth are directly applicable to (Montgomery and Buffi ngton, 1997). Hillslope posed to river valleys), then they would imply Titan conditions with changes in gravity and sediment production and delivery processes a second example of a nonbiological cohesion fl uid density. If the boundaries are hydraulically and valley-bottom morphology largely con- mechanism. Cohesion has been suggested for smooth or the fl ow Reynolds number is suffi - trol coarse-bedded channel morphologies, but the material at the Huygens landing site (Atkin- ciently low, then knowledge of the kinematic because we currently lack a nondimensional son et al., 2010). Laboratory investigation of the viscosity of the fl uid is necessary, which requires framework for these processes, they cannot yet properties of Titan sediments would contribute knowing the behavior of particles of appropriate be scaled to Titan. to addressing this question. size and composition in liquid hydrocarbons. (4) The morphology of valley networks ob- (9) Sediment transport on Titan may be de- SUMMARY AND AREAS FOR served near the Huygens landing site is most fi ned using stability fi elds. For model sediment FUTURE INVESTIGATION consistent with mechanical erosion by chan- densities and equivalent fl ow conditions, trans- nelized fl ows fed by atmospheric precipitation, port requires less shear stress on Titan than on Here, we summarize our main fi ndings, and though sapping erosion is a possibility if the sur- Earth for equivalent grain size. However, the we suggest some areas for future investigations. face material is cohesionless. Laboratory inves- geomorphic effect of this lower shear stress (1) At the landscape scale, Titan fl uvial net- tigations into cohesion, permeability, and other depends on the alkanology, including the fre- works imaged in SAR data include rectangular, properties of Titan analog sediments would con- quency of fl ows that exceed the transport thresh- dendritic, and parallel morphologies (Burr et al., tribute to addressing this issue. old. Rainfall and infi ltration rates and locations 2009b; Drummond et al., 2012). In this analy- (5) Comparison of DISR and SAR images are fundamental inputs into the rates, locations, sis to date, rectangular networks are inferred to suggests that highlands elsewhere on Titan are and types of overland and near-surface fl ow, predominate, although current SAR resolution dissected by fl uvial features at scales fi ner than which in turn control the river fl ow regimes, limits our ability to distinguish rectangular from the resolution of SAR data. We hypothesize sediment transport, and incision that shape the trellis networks (Drummond, 2012). Higher- that extensive fi ne-scale dissection exists within landscape. Sediment production rate, the fl ux of resolution data, as from an airplane (Barnes crenulated terrain (e.g., Fig. 2F), in which case sediment from hillslopes into stream channels, et al., 2012), would improve our network clas- dissection of Titan’s surface may be much more and the sorting and breakdown effects of fl uvial sifi cation. Either rectangular networks or trellis extensive than can be inferred from resolved processes on sediment would provide impor- networks imply structural control on runoff, and networks. This hypothesis may be tested by tant information for interpreting the fl uvial and analysis of the predominant azimuths would textural analysis of Titan SAR images for com- global sediment cycle on Titan. One distinctive provide information on the hypothesized con- parison with SAR images of fl uvially and non- aspect of fl uvial processes on Titan is the con- trolling structures. fl uvially dissected terrain on Earth. tinuous deposition of aerosols onto the surface (2) At the reach scale, varied morphologies (6) The incised appearance of some fl uvial and their apparent removal from higher-relief (Table 1) imply a range of fl uvial processes features implies the existence of sediment that surfaces. Constraining this rate of aerosol depo- (Table 1). In general, data do not support in- acts as erosive tools. In addition, sites of fl uvial sition and removal is vital for accurate fl uvial terpretation of these features as single-thread sediment deposition are inferred from SAR data sediment transport modeling. channels, but as river valleys, braid plains, to include braid plains, fan-shaped deposits, and (10) Under supply-limited conditions, bed- anabranching channels, or other features for lake basins, and DISR images at the surface show rock may be exposed in the channel. Bedrock which direct discharge estimation based on rounded sediment of sizes that could reasonably incision rates under Titan conditions could be morphology (feature width) is invalid. These be moved by channelized fl ow. However, the derived with knowledge of model parameters interpretations can be tested by global mapping mechanism for generating such fl uvial sediment for specifi c processes (e.g., plucking, abrasion, of fl uvial feature morphology in comparison on Titan is uncertain. Additional laboratory ex- knickpoint retreat), but this knowledge is cur- with geologic context, terrain type, local and periments would contribute to understanding rently unavailable. Ongoing investigations into regional relief, composition, and other param- incision into Titan bedrock, and more refi ned icy bedrock tensile strength indicate that pre- eters. Comparison of morphometric data from mapping of Titan’s surface may indicate (a) conditioning of water-ice is important for cre- Titan and terrestrial fl uvial landscapes would source(s) for the erosive sediments. ation of icy fl uvial sediment on Titan (Collins provide another test. For example, channel (7) Observations and modeling show that fl u- et al., 2011; Litwin et al., 2012). However, widths implied by the interpretation of either vial runoff on Titan can be supplied by precipi- mechanisms for pervasive breakdown of bed- the Huygens or Cassini features as channels tation, which may follow a variety of fl ow paths rock remain uncertain. may be signifi cantly out of proportion to typical to the fl uvial networks. Additional information (11) Scaling the mechanics of low-gradient channel width–drainage area relations on Earth about surface material properties on Titan, e.g., sand beds to Titan shows that bed morpholo-

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