This study focuses on the formation and physical properties of the gullies observed over large Martian dunes, especially those of the Russell crater (54°S, 347°W). Geomorphic features like sinuosities and connections of the channels show that gullies over dunes involve flows with a significant proportion of liquid. The occurrence of levees implies that these flows are debris flows with a yield strength characteristics of Bingham plastic materials. We apply terrestrial methods to estimate viscosity and velocity of these flows from levee size and sinuosities. We obtain average velocities in the range of 1 to 7 m s−1 and apparent viscosities of 2.8 to 46,000 Pa s, with an average at 740 Pa s, compared with the 0.001 Pa s of pure water. These viscosities and velocities are in the range of terrestrial debris flows with a proportion of 10 to 40% of H2O. These properties are typical of water-holding debris flows but not of pure water surface runoff or CO2 driven flows. The debris flows over dunes are oriented on south-facing slopes like other recent gullies. Meltwater from ground ice formed during a recent period of high obliquity is the more likely explanation for the formation of such flows over dunes.
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 The discovery of young gullies on Mars has modified the conception that Mars has been a pure dry planet in the recent past [Malin and Edgett, 2000]. These authors propose that recent gullies are formed by debris flows helped by liquid water and that this water has a subsurface origin. Other hypotheses assuming subsurface origin also involve other fluids like CO2-driven flows [Musselwhite et al., 2001] or salt-saturated sources [Andersen et al., 2002]. On the other hand, Costard et al.  showed that the solar heating in recent periods of high obliquity was sufficient to trigger these debris flows. Such a hypothesis is consistent with the distribution and poleward orientation of the observed gullies. Among all evidence proposed for an external origin, the discovery of potential debris flows over dunes is an unexpected but crucial observation. In this study we focus on the formation of these gullies over dunes, especially one group of gullies over a 500 m high megadune in Russell crater. We present geomorphic evidence for their formation by debris flows triggered by a liquid. From the determination of physical properties such as viscosity and velocity, we show that these flows may be due to a mixture of solid grains and liquid water and likely no other kind of liquids. These flows are likely similar to most debris flows on hillslopes or crater interior flanks. We therefore agree with Malin and Edgett  about the nature of the fluid involved in the flows, but we argue for an external origin.
2. Geomorphological and Mechanical Properties of Gullies Over Dunes in Russell Crater
2.1. General Description
 Russell crater is a 200 km large crater located in Noachis quadrangle at 55°S and 347°W. The crater is a part of the Noachian highlands in the southern hemisphere of Mars. In the interior of the crater lays a dune field with a curved megadune which limits the field to the East (Figure 1). With 500 m high and 40 km long (Figure 1b), this megadune is the biggest of the area compared to the other dune with elevation of 150–200 m [Mangold et al., 2002]. These dunes display a very dark albedo which should be the signature of volcanic sands. A mosaic of several MOC images shows that the dunes appear mainly in two directions, NE and NW (Figure 2). Long and narrow gullies are observed on the western flanks of several dunes (Figures 1c, 1d, and 2). A total of about 300 narrow gullies are observed on the SW flank of the megadune over a total area of 20 km large (Table 1). Gullies also exist on seven other dunes in the same area. Notice that numerous slides forming small aprons are also observed on several dunes. However, they are morphologically different from gullies because of the lack of channels (Figure 1e). Their shape is similar to the dark streaks of equatorial regions [Sullivan et al., 2001].
Table 1. Coordinates and Properties of Dunes Affected by Narrow Gullies
 Narrow gullies on the megadune are strongly parallel over 2.5 km (Figure 1c). They all follow the direction of the slope, as expected for gravity-driven processes. The source areas of the gullies correspond to small alcoves under the crest of the dune, thus at the steepest part of the dune. Indeed, the shadow under the crest on Figure 1c implies the existence of a sharp rise under the crest with a slope significantly higher than the average of 10° measured on the flank. Gullies are especially well developed where the dune displays such sharp rise. This is the case, for example, on the left on Figure 1c where the alcoves are up to 100 m large and the channels larger and more than 100 m spaced. On the contrary, on the right of Figure 2 and in most locations along the crest the alcoves are smaller than 50 m and the spacing of the channels also lower than 50 m. It seems therefore that the size of the sharp rise under the crest is a parameter in the development of the size of gullies as in many terrestrial landslides.
2.2. Geomorphic Evidence for a Liquid Involved in the Flows
 Gullies correspond to channels with an apparent erosive capacity unusual for dry slides. The length of about 2.5 km and the slope of 10° in average do not favor dry granular flows. Indeed, dry flows would only occur over slopes larger than 30° due to the friction angle of sand grains [e.g., Allen, 1997]. Only the sharp rise under the crest could present a slope larger than 25°, but it would be difficult for small dry flows to slide over more than 2 km on the flanks. Furthermore, two characteristics are very typical of liquid flows (Figure 3). First, some channels are connected with branching tracks as in terrestrial channel networks over hillslopes. Such connections can only be explained by flows involving a liquid. The connections are very visible especially in the upper part of dunes (Figures 1d and 3a). In the lower part, most channels are not connected together (Figures 1c, 1d, and 3c). The second line of evidence typical of liquid flows are sinuosities. The wavelengths of these sinuosities (10 to 100 m) are in the same range for the gullies on the megadune (Figures 3a and 3c) than the ones on other dunes when present (Figure 3d). No dry granular flows can explain such sinuosity because pure dry gravity-driven flows produce only linear trajectories. The simple slides (Figure 1e) which show no sinuosity or channeling could correspond to dry slides in contrast to the connected and sinuous channels.
2.3. Geomorphic Evidences for Debris Flows
 A close-up over parts of the flow (Figures 1d, 3b, and 3e) shows that all the channels are bordered by symmetric lateral deposits, usually called levees in terrestrial debris flows. These levees are especially visible in the terminal part of the gullies. Levees on each side of the channels are typical of a particular kind of flows with a yield strength [Johnson, 1970; Allen, 1997]. The yield strength corresponds to the minimal shear strength the material needs to reach before flow. For example, the debris flows found in the Southern Alps are 100 to 500 m long, their width is of 3 to 10 m, with levees in the order of 1 m high [Van Steijn, 1988]. These debris flows usually occur on talus with slopes 10 to 30° (Figure 4). Their range of size is similar to that of gullies observed on the dunes.
 Debris flow is a term often used to describe any flow, flood, or slump over a slope involving a substantial amount of liquid. In the following, we use the term debris flow according to its mechanical definition which corresponds especially to materials in which the proportion of solid is of 50% to 90% in volume [e.g., Coussot and Meunier, 1996]. Floods and flows with less than 50% solid correspond to concentrated or hyper-concentrated fluids in which solid particles are transported and deposited by the flow. Particles have no interactions except collisions due to turbulence. In contrast, solid particles of debris flows are all in contact and the fluid acts macroscopically as a single-phase plastic fluid [Pierson, 1995]. Turbulence is therefore rare in debris flows which are usually laminar. The transition from hyper-concentrated flows to debris flow is marked by a rapid increase in yield strength and features indicative of plastic-fluid flow like lateral levees [Pierson, 1995]. Thus debris flow is a gravity-induced mass movement somewhere between landsliding and waterflooding, although with mechanical characteristics very different from either of these processes [Johnson, 1970; Coussot and Meunier, 1996]. Debris flows are therefore different from pure surface runoff, where the flow is liquid without any yield strength and subsequent levees. Features typical of liquid flows like sinuosities and connections also exist for terrestrial debris flows [e.g., Johnson and Rodine, 1984].
 Most debris flows on Earth produce a terminal lobe when the flow suddenly stops. Indeed, sediments incorporated into the flow can not be selectively deposited, so the end of the flow corresponds to the “freezing” of the entire mass when the shear stress drops below the yield strength [e.g., Pierson, 1995]. On the gullies over the Martian dunes, the end is usually very short without major terminal deposits (Figures 2d and 3a). Only a few channels show genuine terminal deposits (Figure 3e), and most show only terminal levees, not much larger than lateral ones. However, terminal levees could be a form of terminal deposit if the amount of material transported is not large. This question will be discussed in more detail in a following section. With the exception of the apparent lack of terminal deposits, these channels are very similar to terrestrial debris flows (1) because they form on the steepest part of the slope like landslides, (2) because geometric characteristics, like the sinuosity, need the occurrence of a liquid, and (3) because the occurrence of levees implies a plastic behavior typical of debris flows.
2.4. Bingham Plastic Model for Debris Flows
 The Bingham model, first proposed by Johnson , is the simplest and the most often used viscoplastic model to simulate debris flows. It combines the simple plastic behavior with a Newtonian flow [e.g., Allen, 1997]:
where τ is the shear stress, K is the yield strength, dγ/dt is the shear rate, and μ is the viscosity. If τ < K, there is no strain so no internal deformation [Allen, 1997]. This model is relevant for debris flow because the existence of a yield strength K is confirmed by the occurrence of levees. In cross-section, debris of the upper part of the flow are submitted to a shear stress lower than the yield strength (Figure 5). They do not flow and form a rigid plug over the flowing part of debris. This rigid part of the debris corresponds to the thickness of the lateral and final deposits at a given slope. Lateral levees are thus at their critical thickness at the time they form. So by measuring their thickness, we can compute the yield strength K of the debris, which corresponds to the shear stress without flow [e.g., Johnson, 1970]:
where α is the slope of the hill, h is the thickness of levees, g is the gravity (g = 3.72 m s−2 on Mars), and ρ is the density. The thickness of levees can also be expressed by
The yield strength does not vary during the flow if the material does not show changes of composition [Coussot and Meunier, 1996]. Thus at a given yield strength the levee thickness is inversely proportional to the slope. The lower the slope, the higher and larger the levees (Figure 6a). Several gullies show the behavior predicted by that Bingham law (Figure 6b). Variations in the topography are visible from the difference in brightness at the left of the image. Slopes from S1 to S4 are organized similarly than on Figure 5a; slopes S1 and S3 are larger than the nearly flat S2 and S4. We observe, at left, that four channels stop at the first step S2. Other channels, like channel C, have large levees when crossing S2 and smaller levees inside S3. They finally stop with large final levees on S4. In the right part of the figure, the slope S2 is attenuated and the levees have a regular size before arriving on the flat S4 where levees are larger. This variation of levee size with slopes may fit the prediction of the Bingham model on Figure 6a. The increase of levee size with progressive decrease of the slope can also be observed on Figure 2d where the slope decrease progressively. There is thus a consistency between the levees observed and those predicted by Bingham law. Levees are likely the result of debris deposits and not of other processes like the erosion tracks of any resistant boulder or ice block that could have been detached from the dune crest. Because the flows follow the Bingham model it is possible to quantify some properties of the flow like the yield strength, the velocity and the viscosity.
2.5. Calculation of the Debris Flow Yield Strength
 The measurement of the levee heights in the relation in equation (2) is the major uncertainty to calculate the yield strength. There is no direct topographic data from which this parameter can be determined. We propose to estimate a range of possible values for the levee thickness by two methods measuring a minimum and a maximum value. First, photoclinometry can be used to extract topographic data from an image. Photoclinometry is difficult to use in terrains of various albedo like many of MOC images, but the dark dunes consist of homogeneous materials where photoclinometry may be used successfully. Photoclinometric models are developed using the method described by Davis and Soderblom . Models were calibrated using MOLA profiles as an envelope for the topography, but at the scale of gullies, MOLA data cannot be used directly. Cross sections were then chosen orthogonal to the flow. Assuming that the flow is in the direction of the slope, orthogonal profiles should have the same elevation on both sides of the gullies. This permits us to fix the base of the profile. Unfortunately, the method is not applicable to the gullies of Figure 6 because the resolution of the MOC image is not sufficient and the quality not optimal. We applied this method to several other gullies (Figure 7). Through profiles A, B, and C (Figure 7), the levees are clearly distinguishable, with tens of centimeters high and several meters large. We see that the levees increase in size close to the end of the flow and become larger than the channel (profile C). Levees have sharp edges because the resolution of the image of 2.8 m/pixel gives only few points through the 20 m wide channels. Indeed, this method extracts the slope from the radiometry, but over 2.8 m/pixel it gives only an average of the slope. Thus the gray level of the channel bottom is not as black as it would be actually inside the shadow. The levees could also have been brighter if the image was at a higher resolution. For this reason, the integration of all slopes minimizes the total elevation difference. The photoclinometry therefore gives a minimum estimate of the levee height.
 In order to estimate a maximum height, we can assume that the height of a levee is strictly less than its width. Indeed, it is unrealistic to imagine a levee of 10 m high but 1 m wide because of the mechanical properties of the material. Thus in the case of a sand pile the internal friction angle of dry sand is of about 30° leading to a sand pile two times less elevated than wide. The levees being approximately 2 pixels wide, we use 7 meters as a maximum, which is probably a large estimate, a levee height of 1 meter being more realistic. It is now possible to estimate minimum and maximum values of the yield strength. The density ρ is taken as 2000 kg/m3, which is a usual value for porous material mixed with any liquid [Johnson and Rodine, 1984]. It is not necessary to know this parameter precisely because realistic variations from 1500 or 2500 kg/m3 would only give minor modifications to the results. The slope α can be deduced from MOLA data to about 8° in the region of these debris flows. The yield strength, calculated from the relation in equation (2), would thus be of 100 Pa with a 10 cm high levee, 7000 Pa with a 7 meters high levee, and an average of 1000 Pa with a 1 m high levee.
2.6. Calculation of the Flow Velocity From Sinuosity
 The velocity is usually difficult to determine without in situ measurements during the flow. Nevertheless, several studies have noted that debris flow levees are commonly higher on outsides of bends than on insides. This characteristic allows the determination of the velocities of debris flows [Johnson and Rodine, 1984]. Indeed, the surface of the flow tilts toward the center of curvature of the bend as a result of the radial acceleration of the debris (Figure 8). The consequence of this tilt after the flow is the presence of larger and broader deposits on the outsides of channel bends. The levees are much narrower on the insides of channels bends. According to Johnson and Rodine , the mean angular velocity of the flow inside the bends can be deduced from the radial acceleration a:
where V is the velocity and R is the radius of curvature. This radial acceleration is also equal, according to Figure 8, to:
with β the tilt estimated from the difference of elevation of levees (g and α as in previous paragraph). So, from equations (4) and (5):
 This method is used over the two small sinuosities observed on Figure 7. This flow takes place in the terminal part of a channel. The tilt of the flow, given by the difference of elevation of levees on each side of the channel, is difficult to measure precisely. Nevertheless, we can first maximize the tilt angle with the width of the levees. The outside deposits has a width of 4 pixels, therefore about 15 m, which can represent a higher limit for the levee height. Assuming no deposit on the internal side, we obtain a maximum height of 15 m over only 26 m laterally. The corresponding angle is β = 30° which is probably a very large estimate of the tilt angle. A minimum value can be estimated using photoclinometric profiles. Profiles D and E (Figure 7) show a strong outside deposits (left) and a low internal one (right). On these profiles the difference of elevation is low, and probably underestimated (for the reasons explained in the previous paragraph about the resolution of the image) with about 40 cm at minimum on E. Taking these values we calculate a minimum tilt angle of about β = 1°. On the other hand, the image allows us to measure the radius of curvature R to 25 m approximately. According to the relation in equation (6), we thus obtain minimum and maximum velocities of respectively 1.3 m s−1 and 7.3 m s−1. An average of 2.8 m s−1 for this flow is also calculated taking β = 5° which corresponds to 2 m high outside levee. The variation in velocities at a factor 7 is small in comparison to the large variations in tilt angle β from 1 to 30°. Indeed, the radius of curvature R is a much stronger parameter in the determination of velocities. The observation of other sinuosities on the megadunes shows that many other channels have radius of curvature of some tens of meters, in the same order of magnitude of that measured (Figures 3a, 3c, and 3d). The origin of the sinuosity is also questionable. It is possibly a consequence of the slow motion of the flow. In this case the flow meanders to find the line of steepest slope while faster flows just go straight down the slope. However, a beginning of turbulence in an especially water-rich flow could also have an effect on the sinuosity.
2.7. Calculation of the Flow Velocity From Channel Connections
 Another method to estimate the velocity uses the existence, or absence, of connections between gullies. This method is based on the fact that most flows are not enough energetic to cut levees and connect to nearby channels, suggesting that the energy of the flow is not sufficient to pass over the levee of the gully next to it. Channels on Figure 9 are located in the middle part of the dune. Two channels oriented in the direction of another channel with one crossing the levee and connecting to the channel on its way. The other one remains parallel without crossing any levees. Thus flows of the same order of size can sometimes cross the obstacle and sometimes not. If not crossing the obstacle, the flow remains parallel to the channel next to it. Physically, this means that the kinetic energy Ec of the flow is of the same order of magnitude than the potential energy Ep necessary to pass over the levee. If the kinetic energy was strongly higher than the potential energy, all flows would be connected. On the contrary, if the potential energy due to the levees was strongly higher than the kinetic energy, no channels would be connected. We can then estimate the velocity using the relation:
with ρ the density of the debris flow. The effect of the slope of the dune on the potential energy is neglected because the slope is low. Channels and levees being approximately of the same width than channels of Figure 7, thicknesses of levees are chosen as estimated previously from 0.1 to 7 m with an average at 1 m. We obtain respective velocities from 0.85 to 7.2 m s−1 with an average at 2.7 m s−1, closed to the velocities found by the method of sinuosity. On the other hand, the geometry described on Figure 7 is also observed on other images like Figures 3b and 3c. These flows may have equivalent velocities because the size of the channel and the width of the levee are similar to the example taken on Figure 7. The fact that velocities measured in the middle part of the dune are similar to those measured in the terminal part and also similar by two different methods argues that these values are good estimates for the flows over this dune in general. Nevertheless, channels on the steepest part of the dunes have smaller levees and likely velocities slightly larger than in the middle and terminal part because the slope is steeper. Smaller levees and larger velocities may explain why connections between channels can occur more frequently in the upper parts of the flows (Figures 1d and 3a) than in the lower parts (Figures 1c, 3b, and 7).
2.8. Calculation of the Flow Viscosity
 The viscosity μ is the most used parameter to characterize debris flows. The apparent viscosity can be determined by the relation [Allen, 1997]:
All parameters are known except the channel thickness T. On Earth the channel thickness is always lower than its width, so we can constrain the maximum of this parameter by 10 m corresponding to the channel width on Figure 6 on cross section A. If the channel is slightly larger than the levees at the position we estimated the velocity, it should be slightly thicker than the levees. We assume a minimum of 0.2 m for the channel thickness T, knowing the minimal levees heights of 0.1 m. A realistic average between 0.2 and 10 would be about 2 m for T. We use values of velocities of 1.1, 2.8, and 7.3 m s−1 to calculate the maximum, average, and minimum viscosity, respectively. Values calculated from equation (8) are thus 2.8 Pa s at minimum and 46,000 Pa s at maximum with an average of 740 Pa s. We thus have estimated the viscosity of Martian debris flows over dunes to the range of viscosity of 1 to 105 Pa s compared to the viscosity of pure water of 0.001 Pa s.
2.9. Comparison of Mechanical Properties With Terrestrial Data
 All the values found can be compared with values of these parameters for terrestrial debris flows. Gravity is different on Mars, but this parameter may have low effects in the comparison of velocity and viscosity. Indeed, the debris flow is a competition between the potential energy and the resisting force of the flow which both depend on gravity [Iverson, 1997]. With a lower gravity, the velocity should be lower due to lower potential energy, but friction forces are also lower and this effect would increase the velocity. In the case of a simple debris flow, the two effects cancel [Iverson, 1997]. Nevertheless, friction inside mixture like debris flows is not well understood and could modify slightly the behavior. These effects can nevertheless be assumed to be low because a factor of only 3 for Mars in comparison with Earth would not change the order of magnitude of these parameters.
 The yield strengths of debris flows are of the order of hundreds to thousands of Pa on Earth [Allen, 1997], in the same range that we have determined of 100 to 7000 Pa. For example, the method of the levees heights give values in the order of 1,000 to 10,000 Pa in Alpine debris flows [Van Steijn, 1988]. Laboratory measurements on samples of the Moscardo debris flows (Italy) give yield strengths from respectively 100 Pa to 3000 Pa with volume water fraction decreasing from 50% to 15% [Coussot et al., 1998]. In Lainbach glacial deposits, while the water content decreases from 20 to 10% in weight, the measured yield strength increases exponentially from 1000 to 20,000 Pa [Bonte et al., 2000]. Such yield strengths are typical of a mixture of a liquid in solid granular material in which the liquid is water.
 The velocities of terrestrial debris flows are typically between 0.5 and 10 m s−1. Larger values of 30 m s−1 have been measured occasionally on huge catastrophic debris flows which are not considered here [Johnson and Rodine, 1984]. For example, velocities of 2 to 4.5 m s−1 have been measured on Alpine debris flows [Van Steijn, 1988]. In a compilation of debris flows velocities, Phillips and Davies  plotted velocities of 20 groups of hillslope debris flows versus the channel thickness. Terrestrial debris flows fall in the range of velocities of 1 to 12 m s−1 with channel thicknesses of 10 cm to 4 m. These values are in the same range with those measured on the Martian gullies. Such velocities are typical of water + solid grains mixture but not CO2 triggered flows. Indeed, such flows are very energetic due to the high volatility of CO2 at atmospheric pressure and should produce pyroclastic flows and nuees ardentes like on Earth [Musselwhite et al., 2001; Hoffman, 2001]. Thermodynamical properties of CO2 liquids would imply velocities of 20 to 100 m s−1 on Mars [Stewart and Nimmo, 2002] which are not consistent with our measurements.
 The viscosity calculated for Martian gullies fits also terrestrial data about debris flows. For example, a viscosity of 2,780 Pa s has been determined at Dragon Creek [Pierson, 1981]. We can plot the solid fraction (in volume) of any liquid-solid mixture versus the viscosity (Figure 10). Pure liquid water is plotted at the origin with no solid fraction and a viscosity of 0.001 Pa s. Hyperconcentrated flows with solid fraction of less than 50% have viscosities one or two ranges of magnitude higher than liquid water. Terrestrial debris flows have typically solid fraction from 50 to 90% in volume and viscosities of 1 to 10,000 Pa s [e.g., Corominas et al., 1996]. Circles and triangles correspond to experimental data on fine-grained slurries (clay + sand + water) in various proportions with total solid fractions of 50 to 60% [Major and Pierson, 1992]. These slurries are likely similar to the material over the dune which incorporates a major part of sand grains and probably a proportion of fine dust deposed in periods of low winds. These values of 1 to 10 Pa s are in the lower bound of the measurements over Martian flows. So, this implies that a minimal solid fraction of 60% is likely for Martian debris flows. A much higher proportion of 80 or 90% still fits the estimation of viscosity. Thus viscosities estimated for the Martian debris flows fall in the range of terrestrial debris flows with proportion of water of 10 to 40%.
 The Bingham model seems to be appropriate to the debris flows observed. However, the composition of the studied debris flows over dunes imply finer particles than usual terrestrial debris flows. The behavior would be similar if the sand is coarse (>0.1 mm), but some differences of behavior may exist if it contains a significant proportion of fine particles (<10 μm). The Herschel-Bulkley model has been proposed to simulate the mechanical behavior of more muddy debris flows [Major and Pierson, 1992; Coussot and Meunier, 1996]. This model is more sophisticated than Bingham law but it also includes the occurrence of a yield strength [Major and Pierson, 1992]. Nevertheless, while Bingham is a strict linear Newtonian model, Herschel-Bulkley allows non-Newtonian power laws which are especially adapted to take into account the shear-thinning behavior of muddy materials laws [Coussot and Meunier, 1996]. In this case the apparent Newtonian viscosity decreases when the shear rate increases. Experimental data show that the Bingham law is valid even for mud flows if the shear rate is higher than 5 s−1 [Major and Pierson, 1992]. The shear rate is the ratio of the velocity with the channel thickness. The shear rate of Martian debris flows is estimated in the range of 0.7 s−1 to 10 s−1 (taking minimum estimate for channel thickness of 10 cm and its corresponding velocity of 1 m s−1 and maximum estimate of 10 m large with its corresponding velocity of 7 m s−1). Either Newtonian or non-Newtonian flows are thus possible. The consequence of non-Newtonian flows would be that the viscosity was slightly overestimated by applying the relation in equation (8) available for Bingham fluid. Nevertheless, error bars are large, and terrestrial works on such material do not show magnitude change in the measurements of apparent viscosity [Major and Pierson, 1992]. This discussion is limited by the lack of field data about the proportion of fine particles on the sand dunes.
 Some explanations can be given for the apparent lack of terminal deposits. The levees are much higher in the final part of the debris flow tracks. This is observed on Figures 1d, 3b, 3e, and 5, as well on photoclinometric cross sections (Figure 7, profile C). The channel becomes progressively narrower than the levees. This could mean that the debris are progressively accommodated by the levees as it occurs sometimes on Earth (Figure 4). The end of the flow is thus very gradual without terminal deposits other than levees. The presence of a gradual stop could be related to the progressive decrease of the slope. Moreover, the low velocity implies that little energy is available for the dry debris to slide far away after the flow stopped, especially if the amount of debris is small. Nevertheless, other properties of liquid-solid suspensions could explain the flow's end without any decrease of the slope. The yield strength of the material varies if its composition changes. Thus the decrease of the water/rock proportion creates an increase of the yield strength. Progressive modifications of the composition of debris flows are observed on Earth [Johnson and Rodine, 1984]. This mechanism is possible on Mars either by incorporating more solid fraction (like dry sand) during the flow or by downward percolation of water or even by loosing a part of the liquid water by evaporation. This last process could have a strong effect on Mars due to the low atmospheric pressure. All the calculations made are also limited by the knowledge we have of the proportion of water, clay, and sand in the mixture and by the resolution of MOC images to determine levees heights. The Bingham model used is a first-order model for the calculations done but it is justified by the observation of levees.
 Finally, we find from that quantitative analysis that the liquid inside Martian debris flows is likely liquid H2O because of the correspondence of the physical properties calculated, like yield strength, velocity, and viscosity, with terrestrial properties of water holding debris flows. This does not exclude the possibility of an amount of brines (1–10%) inside the water-solid mixture because brines would not modify the viscosity significantly if remaining in low proportion. However, one would need to explain how a significant amount of brines could have been deposited over these dunes. On the other hand, CO2-triggered flows are unlikely because such flows would give very different physical properties like high velocities. The viscosity of exotic materials in such context, like mixture of CO2 and H2O ices for example, are poorly known to be compared with our estimations. However, one would explain why such viscosity would fall in the same range of magnitude than water holding debris flows and we strongly support the fact that the consistency of the viscosity found on Mars with terrestrial debris flows is not a coincidence.
3. Origin of Liquid Water and Debris Flow Formation
 Current seasonal defrosting has been proposed to explain gullies on hillslopes [Bridges et al., 2001] or over dunes [Reiss and Jaumann, 2002]. Images taken during defrosting (Figure 11) show a blanketing of CO2 frost covering the South flank of dunes while the North face is frost-free. Dark spots are observed at the top of the dune and on the flank of nearby dunes. These spots can be attributed to the sublimation of CO2 [e.g., Bridges et al., 2001] in locations where the heating is sufficient. The dark albedo corresponds to the surface of the underlying dune. We especially see levees in the lower parts of dunes which are defrosted while the center of the channel is still frost covered. This can be explained because parts of the levees were more heated whereas the channel remained in the shade. No relation between dark spots and gullies are observed. Nevertheless, it has also been proposed that the late defrosting of CO2 permits a more rapid heating of the underlying surface [Costard et al., 2002]. Current temperature changes in springtime may permit to the temperatures to climb up to the melting point and could locally melt the surface water frost [Reiss and Jaumann, 2002]. However, this heating has only a duration of few hours around midday when the Sun is at maximum elevation and the temperature drops again well below zero during the night. Consequently, the thermal wave penetrates only a few millimeters inside the ground [e.g., Mellon and Jakosky, 1993]. Assuming that water frost can melt on the surface, this would imply very superficial and thin runoff. However, we showed that pure runoff cannot explain the formation of debris flows, especially because of the existence of levees which imply a significant thickness of material to initiate debris flows. On the other hand, no new gully has been detected on images taken at defrosting, though more than one year of survey should be done to definitively conclude if there is current activity.
 In order to explain the formation of gullies on dunes and their relations with gullies on hillslopes [Malin and Edgett, 2000], we looked at the global distribution of similar gullies on dunes on the whole planet. Only long and narrow gullies similar to those of Russell crater have been considered (Figure 12a). Large slides, different from the small slides of Figure 1e because they are erosive, have not been taken into account though they could also involve liquid water (Figure 12b). All the gullies attributed to debris flows are located in four dunes fields inside large craters, including Russell, at latitude from 45 to 55° south (Table 1). This is consistent with the latitudes poleward of 28° found for the distribution of recent gullies [Malin and Edgett, 2000]. Nevertheless, the meaning of this distribution is limited by the low number of large dune fields on the planet.
 On the other hand, the orientation of all of these gullies shows a preferential poleward facing orientation (Table 1) like recent gullies [Malin and Edgett, 2000; Costard et al., 2002]. The statistical meaning of these orientations is valid because dunes are oriented in various directions. The megadune shows a curvature in direction and the dunes below these megadunes are oriented in two main directions NE and SW that provides all possible orientations of flows on each side of their flanks (Figure 13). Nevertheless, gullies of the eight dune flanks of Russell crater are all oriented SW, from N180 to N275 (Table 1), but none are oriented to the SE. In parallel, all of the postulated dry slides (Figure 2e) are oriented NW and none NE (Figure 13). All kind of slides, gullies included, are thus oriented west like the sharp rise under the dune crest. The westward orientation of such sharp rise, especially on the megadune, shows that the wind, or at least the latest dominant wind, was coming from the east. Indeed, such steep slopes are the result of avalanches formed on a slipface on the lee of the dune. Therefore the restriction of the channels orientation to the SW and small slides to the NW may be explained by the combination of an east-west asymmetry due to the presence of steeper slopes on the west side and a north-south asymmetry due to dry-wet flows.
 These two characteristics, middle or high latitude and poleward facing slopes, are consistent with recent gullies over hillslopes. The existence of debris flows over sand dunes implies that they are triggered by external processes involving meltwater because no subsurface seepage and aquifers would exist near the crest of dunes. These debris flows are thus consistent with the melting of near-surface ground ice produced by solar heating and predicted at high obliquity [Costard et al., 2002]. The recent discovery of proportions of interstitial ice up to 50% in volume by the Mars Odyssey probe favors such a hypothesis [Boynton et al., 2002]. The possibility of snowmelt is not excluded [Lee et al., 2001]. According to models of Costard et al. , the formation of debris flows at 55° of latitude is possible with obliquity of only 35°. An increase of obliquity up to 35° is predicted to exist about one half million years ago [Laskar et al., 2002]. On Earth, megadunes of 500 m high exist in the Badain Jaran desert in China and their formation has a duration of tens of thousands of years [Zhu, 1980]. Such duration is probably a minimum on Mars under the thin Martian atmosphere. On the other hand, the slide scar at the dune crest is sometimes so sharp that dunes could have been partially indurated (Figure 12b). MOC images show that some Martian dunes may be significantly indurated for tens of thousands of years and that dunes are inactive in many locations [e.g., Edgett and Malin, 2000]. Thus small slides previously interpreted as avalanching resulting from the current activity of dunes caused by the wind [Malin and Edgett, 2001] could also result from past dune activity [Edgett and Malin, 2000] or from the sublimation of interstitial CO2 or H2O ice. So, the studied dunes could be more or less inactive for several hundreds of thousand years, but no impact craters give us the possibility to estimate this duration.
 Finally, debris flows over dunes could have formed by the melting of frost and near-surface ground ice by the process proposed by Costard et al. . Debris flows would form from the failure of the material due to pore saturation by water and the subsequent increase of fluid pressure. Such process would be very efficient on the slipfaces of the dunes, with typical slopes of 30° on which the stress is already near the critical threshold before incorporation of water. This may explain why debris flows begin near the summit of the dune and not in other places on the slope. However, in sand dunes, liquid water would percolate downward due to the gravity. On Earth, debris flows over dunes are not frequent because dunes are in dry areas usually not submitted to conditions favoring such processes. Nevertheless, past mass wasting over dunes has been described in sandstone layers in Mongolia [Loope et al., 1999]. In this example, water is supposed to come from heavy showers. This water was stopped by a cemented layer of calcite dust 1 m below the dune surface [Loope et al., 1999]. The same kind of dust-cemented layers could also exist on Martian dunes as deposition of dust is a common process. It is also possible that the frozen medium underlying the thawed layer stops the percolation of water, the exact process of formation remaining speculative.
 The study of the gullies over the megadune of Russell crater shows:
 1. Geomorphic features like sinuosities and connections show that long and narrow gullies involve flows with a significant proportion of liquid.
 2. The occurrence of the alcoves at crest of the dunes and levees of increasing size to the end of the flow show that these gullies are formed by debris flows and that these flows have yield strength characteristics of Bingham materials.
 3. By measuring velocities using both sinuosity and connections, we obtain velocities in the range of 1 to 7 m s−1 similar to terrestrial water holding debris flows but lower than pyroclastic flows and CO2 driven flows.
 4. Using the Bingham model, we obtain apparent viscosities of 2.8 to 46,000 Pa s, with an average at 740 Pa s, which fall in the range of terrestrial debris flows with a proportion of 10 to 40% of liquid H2O. This conclusion quantitatively supports prior interpretations of the involvement of liquid water in producing recent gullies [Malin and Edgett, 2000].
 5. Debris flows over dunes involve water formation from external processes rather than subsurface aquifers. Flows are all oriented on poleward facing slopes and distributed in regions poleward of 45° like other recent gullies. These flows may formed by the melting of interstitial ice and frost during a recent period of high obliquity as explained by Costard et al. .
 More accurate estimation of flow properties could be done with better topographical data. Such data could be provided in the future by the Mars Express stereo camera HRSC in 2003 or the very high-resolution imager of Mars Reconnaissance Orbiter mission in 2005.
 The authors thank P. Allemand and an anonymous reviewer for detailed remarks and D. Baratoux, C. Delacour, V. Jomelli, and J.-P. Peulvast for helpful discussions. The authors acknowledge the use of Mars Orbiter Camera images processed by Malin Space Science Systems that are available at http://www.msss.com/moc_gallery/. This work was supported by the Projet National de Planétologie (PNP) of the Institut National de Sciences de l'Univers (INSU), France.