Ancient melting of mid-latitude snowpacks on Mars as a water source for gullies

Transcription

1 Accepted Manuscript Ancient melting of mid-latitude snowpacks on Mars as a water source for gullies K.E. Williams, O.B. Toon, J.L. Heldmann, M.T. Mellon PII: S (08) DOI: /j.icarus Reference: YICAR 8849 To appear in: Icarus Received date: 9 July 2008 Revised date: 17 October 2008 Accepted date: 11 December 2008 Please cite this article as: K.E. Williams, O.B. Toon, J.L. Heldmann, M.T. Mellon, Ancient melting of mid-latitude snowpacks on Mars as a water source for gullies, Icarus (2009), doi: /j.icarus This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

2 Ancient melting of mid-latitude snowpacks on Mars as a water source for gullies. K. E. Williams 1, O. B. Toon 1, J. L. Heldmann 2, M.T. Mellon 3 1 Dept of Atmospheric and Oceanic Sciences & Laboratory for Atmospheric and Space Physics (LASP UCB 392, University of Colorado, Boulder, CO kaj.williams@colorado.edu ) 2 NASA Ames Research Center, Division of Space Sciences and Astrobiology, Moffett Field, CA Laboratory for Atmospheric and Space Physics,UCB 392, University of Colorado, Boulder, CO Pages 12 Figures 1 Table 1

3 Proposed running head: Ancient Snowmelt and Gullies On Mars Direct editorial correspondence to: Kaj Williams NASA Ames Mail Stop 245 Moffett Field, CA

4 Abstract We hypothesize that during past epochs of high obliquity seasonal snowfields at mid-latitudes melted to produce springtime sediment-rich surface flows resulting in gully formation. Significant seasonal mid-latitude snowfall does not occur on Mars today. General Circulation Model (GCM) results, however, suggest that under past climate conditions there may have been centimeters of seasonal mid-latitude snowfall (Mischna et al. 2003). Gully locations have been tabulated by several researchers (e.g. Heldmann and Mellon, 2004; Heldmann et al. 2007; Malin and Edgett 2000) and found to correspond to mid-latitude bands. A natural question is whether the latitudinal bands where the gullies are located correspond to areas where the ancient snowfalls may have melted, producing runoff which may have incised gullies. In this study we model thin snowpacks with thicknesses similar to those predicted by Mischna et al. (2003). We model these snowpacks under past climate regimes in order to determine whether snowmelt runoff could have occurred, and whether significant amounts of warm soil (T>273K) existed on both poleward and equatorward slopes in the regions where gullies exist. Both warm soil and water amounts are modeled because soil and water may have mixed to form a sediment-rich flow. We begin by applying the snowpack model of Williams et al. (2008) to past climate regimes characterized by obliquities of 35 (600 ka before present) and 45 (5.5 ma before present), and to all latitudes between 70 N and 70 S. We find that the regions containing significant snowmelt runoff correspond to the regions identified by Heldmann and Mellon (2004), Heldmann et al. (2007) and Malin and Edgett (2000) as containing large numbers of gullies. We find that the snowmelt runoff (>1 mm, with equivalent rainfall rates of 0.25 mm/hr ) and warm soil ( >1 cm 3

5 depth) would have occurred on slopes within the gullied latitudinal bands. The snowfall amounts modeled are predicted to be seasonal (Mischna et al. 2003), and our modeling finds that under the previous climate regimes there would have been meltwater present on the slopes in question for brief periods of time, on the order of days, each year. Our model provides a simple explanation for the latitudinal distribution of the gullies, and also suggests that the gullies date to times when water migrated away from the present poles to the mid-latitudes. Keywords: Ices, Mars, surface 4

6 Introduction and background Gully-like landforms exist in both the northern and southern hemispheres of Mars (Heldmann et al. 2007; Heldmann and Mellon, 2004; Malin and Edgett, 2000; Balme et al. 2006; Dickson et al. 2007). The characteristics of the gully forms vary considerably (Malin and Edgett, 2000; Treiman, 2003). One type of gully includes a well-defined alcove, an incised channel and a debris apron (Malin and Edgett, 2000), as shown in Fig. 1. In this study, we look for correspondence between gully occurrence and predicted localities where surface liquid water could be explained by snowmelt. (Figure 1 here) Christensen (2003) hypothesized that after equatorward movement of ice occurred during past high obliquity periods, surface ice or snow remained stable long enough to begin melting and producing meltwater runoff under the subsequent lower obliquity periods. The meltwater runoff was then suggested as a source for gullies. Williams et al. (2008) have shown that snowsheets at midlatitudes on present-day Mars will melt or sublimate quickly, often in only a few seasons depending on snowpack thickness and slope geometry. These results indicate that exposed layers of snow are not preserved from previous epochs of high obliquity, when extensive movement of ice away from the permanent polar caps may have occurred (e.g. Jakosky et al. 1993). Midlatitude snowsheets are expected to have been present in the past on Mars when the obliquity was higher than now (Mischna et al. 2003; Levrard et al. 2004). We propose that such snow sheets melted during the spring and summer season to form the gullies. Other researchers have proposed a link between ancient snowfall and valley 5

7 channels (Clow, 1987; Fassett and Head, 2006; Fassett and Head, 2007; Gulick, 2001; Gulick et al. 1997). Our idea, proposed in this paper, focuses on gullies and unites multiple concepts, including the concept of Christensen (2003) that snowsheets will melt, the work of Mischna et al. (2003) showing that significant snowfall will occur at midlatitudes under higher obliquity conditions, the observations that gullies are relatively young (Malin and Edgett, 2000; Heldmann et al. 2007) and the polar caps are relatively young (~ 4 ma) with predictions that the obliquity of Mars was high ( 35 ) about 4.5 million years ago (e.g. Laskar, 2004; Milkovich et al. 2008). In addition, our theory provides a natural explanation for the latitudes in which gullies are found. There has been disagreement in the scientific literature over the characteristics of the fluid responsible for Martian gully formation. While a CO 2 gaseous flow has been posited by Hoffman (2002) in order to explain polar gullies, the thermodynamic difficulties of getting CO 2 to form on mid-latitude slopes of arbitrary orientation prevents the explanation of Hoffman (2002) from being applied to low and mid-latitude gullies. Alternative erosive agents for Mars that have been suggested have included debris flows (Malin and Edgett, 2000), liquid CO2 (Musselwhite et al. 2001; later refuted by Stewart and Nimmo, 2002), dry material (Treiman, 2003), salty brines (Knauth and Burt, 2002) or mostly pure water (Heldmann et al. 2007). Our work suggests that erosional flows may occur in environments on Mars, charged by the modest amounts of water supplied by seasonal deposition of snow. Martian gullies are relatively common between 30 to 70 in both the northern and southern hemispheres (c.f. Heldmann et al. 2007; Heldmann and Mellon, 2004; Balme et al. 2006; Dickson et al. 2007). The orientation and inclination of gully-bearing 6

8 slopes for both hemispheres has been studied and appear to encompass all aspect orientations (Heldmann and Mellon, 2004; Heldmann et al. 2007), though in some locations such as the southern mid-latitudes there appears to be a poleward preference (Dickson et al. 2007; Balme et al. 2006). The majority of gully-bearing slopes appear to have slope inclination angles between 12 and 38 for the northern hemisphere and 5 to 40 for the southern hemisphere (Heldmann et al. 2007; Heldmann and Mellon, 2004; Dickson et al. 2007). In this paper we have elected to model 20 slopes facing toward and away from the equator. (Figure 2 here) The climate of Mars is believed to have undergone extensive fluctuations (c.f. Milkovich et al. 2008) driven primarily by fluctuations of orbital parameters (e.g. Ward, 1974). The planetary obliquity (axial tilt) and the orbital eccentricity are commonly analyzed in this context. Dynamical calculations by Laskar (2004) have determined the variations of obliquity and eccentricity for the past several million years (Fig. 2). A noteworthy feature of Fig. 2 is that prior to about 4.5 million years ago the mean obliquity was above 35, with excursions to 45. More recently there have been periods of time with high obliquity. According to GCM studies of Mars, there were considerable amounts of seasonal snowfall and atmospheric water vapor present when the obliquity was > 35 (Mischna et al. 2003). According to the calculations by Laskar (2004) (and in Fig. 2) the obliquity was most recently 35 approximately 600 ka before present (bp). The obliquity was 45 approximately 5.5 ma bp. In this study we attempt to explain a subset of the observed gullies on Mars, namely those with features suggestive of fluvial activity (Malin and Edgett 2000; 7

9 Heldmann and Mellon, 2004; Heldmann et al. 2005). To do so we assume that various snowfall amounts occurred over latitudes suggested by Mischna et al. (2003), and then run the snow melt model of Williams et al. (2008) under two past climate regimes (characterized by 35 and 45 obliquities). We wish to investigate the question of whether snowmelt runoff and warmed soil occurred in sufficient quantities to provide enough material for surface flows. Unfortunately other Martian paleo- GCM simulations, such as the Levrard et al. (2004) study, provide insufficient data regarding latitudinal distribution of seasonal snowfall for high obliquity cases, and thus we were unable to use their data for this study. We do not explore longitudinal distributions of gullies in this paper because the existing Martian paleo-general Circulation Model (GCM) simulations disagree with regard to residual ice cap placement and the longitudinal occurrences of stable ice. Levrard et al. (2004) found that while the transport of polar ice to midlatitudes does occur under high obliquity (>30 ) conditions, they were unable to obtain a stable (residual) ice cap at mid-latitudes for high obliquities. On the other hand, the Mischna et al. (2003) simulations produced stable surface ice at mid-latitudes for similar high obliquities. In addition, in order to study the longitudinal occurrences of gullies it would also be necessary to minutely examine each geological setting for gullies to determine the topographic features that might control local snowfall. Hence the correlation of longitudinal location of gullies with paleo -GCM simulations is an open research question that we do not address. Model Description 8

10 For this study we use the snowpack model of Williams et al. (2008). No salts or brines are included in the modeling process. A general overview of the snowpack model follows. The model utilizes a finite-volume solver in order to compute the energy and mass transport within the snowpack. Mass loss is permitted to occur from the top of the snowpack (as sublimation) or runoff from the bottom of the snowpack. Meltwater percolation and refreezing is also permitted within the snowpack. The model itself is solved on a mass grid, rather than a spatial grid, in order to make mass and energy conservation tractable. The snowpack layers are permitted to grow and shrink, but are initially set to 1 mm thickness since we are interested in modeling relatively thin snowpacks (< 10 cm). (Figure 3 here) The surface energy balance in our model consists of the following components (Fig. 3): latent heat flux due to mass loss/gain, atmospheric infrared emission to the snow, sensible heat flux, infrared emission from the snow, solar absorption by the snow and infrared emission from an adjacent surface to the snow. The energy for the surface layer is evolved by the following expression: U = k(t) T εσt 4 + (F 1/2 F +1/2 ) + A H + S H + Fir L M t z bottom t Here it is understood that the right-hand side terms are each averaged over a time interval (1) greater than or equal to the integration timestep. The integration timestep for Eq. 1 was set at 0.25 seconds. The choices of various parameters in Eq. 1 are summarized in 9

11 Williams et al. (2008), but with several exceptions for past climate regimes (outlined below). The quantity U = mcpt is the area-normalized energy of the surface layer of ice/dust/liquid mixture of mass m. Again the equations are solved on a mass grid; when required, layer thickness Δz is determined from the layer mass since the relative mass contributions of liquid water, dust and ice are tracked for each layer. The k(t) T z bottom term is the heat conducted out of the bottom face of the top layer. The εσt 4 term is the infrared radiation emitted by the surface. The F 1 / 2 F+ 1/ 2 term is the average net solar flux absorbed by the surface layer (direct and scattered radiation) for the timestep. The A H term is the downwelling atmospheric infrared heat flux density, and S H is the atmospheric sensible heat flux density. The F ir term is the infrared heat flux density contribution from a planar surface at the foot of the slope and L M t heat loss. Each of these terms is described in detail by Williams et al. (2008). is the latent Aside from the capability of being run at different latitudes, the snowpack model is run for a given slope inclination and aspect. We have used the equivalent slope concept (as outlined in Dingman, 2002) to account for slope geometry (Williams et al. 2008). This concept accurately represents the solar flux on a plane parallel semi-infinite slope, and makes no approximations other than ignoring shadowing and other threedimensional issues. These limitations are discussed in Williams et al Our model uses the two-stream shortwave radiative transfer code of McKay et al. (1994) to simulate energy deposition within the snow. The two-stream radiative transfer code simulates solar energy distribution in a snow column with a non-homogeneous dust 10

12 distribution. The dust is initially homogeneously mixed into the snow, but the model permits a concentrated dust layer (lag) to form on the surface as the snow ablates. The snowpack model computes the temperature profile within the soil underlying the snowpack (i.e. the soil substrate). In addition, the temperature profile is computed in an adjacent soil column, which is not covered by snow. The adjacent soil column temperature profile is used to infer the air temperature above the snow. The adjacent soil column temperature profile is solved with a simple finite-difference model, and is solved over a uniform grid of 1 cm layers. The soil temperature model has been described in Williams et al. (2008). The adjacent soil column model is also used for another purpose. As a snowpack gradually ablates on a slope, we presume that bare patches of soil are present on the slope as well. The temperature of the topmost soil layer is of interest because the soil may provide mobile sediment to be incorporated in a flow. Soil cohesion, as well as other physical properties related to the potential of a soil to be mobilized in a flow, are largely unknown for the Martian slopes. As a rough estimate of the potential for a layer of soil to be mobilized, we have elected to use the temperature of the soil layer; if the soil temperature is > 273K we assume it may be easily mobilized in a flow, whereas otherwise the meltwater runoff might simply freeze upon contact with cold (< 273K) soil. We have therefore modeled the temperatures of a bare soil column colocated with the snowpacks on slopes in order to determine how much warm soil (soil with temperatures > 273K) is available for transport. Hence, by our definition, warm soil has units of depth, and is defined to be soil with temperature greater than 273K. The instant that runoff is produced from a given snowpack, we check the adjacent soil model 11

13 on the slope and determine how much warm soil exists at the soil surface. The melting and runoff occurs only over a few days, and occur during late spring. Hence the depth of warm soil will not change significantly during melting and runoff, other than diurnal variations in the soil temperature during those several days. The soil column is much darker than the snow, and warms up much more quickly than the snow. According to our model, by the early afternoon (at which time the snow is melting), the soil is as warm as it ever will be for that day. We also compute the temperature of the soil substrate beneath the snowpack. The model parameter settings have been described in Williams et al. (2008), with several exceptions. Since in the present study we are modeling freshly fallen snow that begins melting after settling and aging for >100 Mars days, we have elected to follow Clow (1987) and set the snow density to 400 kg/m 3 and the snow grain radius to 1 mm. A snow density of 400 kg/m 3 corresponds to terrestrial wind-packed snow (Paterson, 1994). The dust mixture is initially set to 10 parts per million by weight (ppmw). The amount of atmospheric dust which would have been deposited in seasonal snowfalls under past climate regimes is unknown, but it seems reasonable that there would have been at least small amounts of dust present. Given Viking Lander estimates of atmospheric dust optical depth to be between ~0.1 and 3.0 (Toigo et al. 2002), we estimate the amounts of dust swept out of the lower atmosphere and incorporated within the snow to be between 10 and 500 ppmw. For sensitivity tests, discussed below, we varied the amount of dust in the snow between 10 and 500 ppmw. We have set the ground thermal inertia to 250 J m -2 K -1 s -1/2 which corresponds to the median of the thermal inertia values observed in regions where gullies occur 12

14 (Heldmann et al. 2007; Heldmann and Mellon, 2004). Our soil albedo is set to 0.13, which falls within the range of values observed around the gully sites (Heldmann et al. 2007; Heldmann and Mellon, 2004). The orbital parameters in this study include the present-day longitude of perihelion ( ), eccentricity values of (for 35 obliquity) to (45 obliquity), and obliquities of 35 and 45. For sensitivity tests, the longitude of perihelion was varied by 360 in 90 increments. The seasonal snowfall was presumed to have occurred at midwinter (Ls=90 for the southern hemisphere and Ls=270 for the northern hemisphere), and in a single episode. No additional precipitation is allowed to occur during the springtime. It is of course likely that ancient snowfalls may have occurred differently, including multiple snowfalls per season. It is the aim of this study, however, to determine the thermodynamic feasibility of melting and runoff, as well as potential for flows and not to address the infinite number of meteorological scenarios that were possible at all latitudes. The model parameter settings relevant to the present study are summarized in Table 1. The snowfall amounts modeled include 1 5 cm depths. Mischna et al. (2003) predicted that the snowfall amounts for 35 obliquity were approximately 1.0 cm for midlatitudes, and approximately 2.0 cm for 45 obliquity at midlatitudes. However, Erickson et al. (2005) suggest that winds can cause considerable snow depth variations to occur on terrestrial slopes, with depth variations between 0x and >5x. Therefore we feel the 1-5 cm snowfall depths modeled are in accordance with the snowdrift depth variation suggested by Erickson et al. (2005). It is also possible that snowdrifts may have occurred on Martian hillslopes in a manner similar to terrestrial nivation hollows. In terrestrial 13

15 situations, nivation hollows can develop on hillslopes when seasonal snowpatches erode the underlying soil (Christiansen 1998). Subsequent seasonal snow deposits tend to accumulate in such hollows, providing regions where snow can form deeper drifts (Christiansen 1998). It is possible a similar process would have occurred on Mars, creating regions where snowdrifts preferentially form (in this case, the nivation hollow would correspond to the gully alcove). The nivation concept is discussed again below. Model Results We have run the snowpack model of Williams et al. (2008) under two past climate regimes (characterized by 35 and 45 obliquities) in order to determine whether seasonal melts of small amounts of snow could have yielded meltwater runoff on slopes. In general, all of our modeled snowpacks lasted less than one Mars year, eventually disappearing by late spring. Sublimation was the dominant mass loss process. Melting, if it occurred, only was present during the last several days of the snowpack lifetime, when then snow was very thin and dusty. (Figure 4 here) Many gully images indicate episodic gully activity, since superposed fans, crosscutting channels and superposed alcoves are relatively common. A cartoon of one possible process is depicted in Fig. 4. It should be noted that even if only a few mm of runoff are produced (a few liters / m 2 ), that the total meltwater volumes could still be significant when taken over the extent of the gully alcoves as discussed below. Therefore it is possible that the gully erosion and sediment deposition could occur due to 14

16 meltwater alone, without need for the example in Figure 4. Nevertheless it seems extremely unlikely that the meltwater in the channel would be devoid of sediment since clearly sediment transport is required for gully incision. It is also possible that the meltwater flowed in pre-existing gully channels. We do not know the extent to which the meltwater runoff might infiltrate the soil on Martian slopes. For terrestrial cases, Dingman (2002) suggests that infiltration rates for grass-covered standard soil and moderate slopes (16 ) can be close to 50% of the water input rate, however other work suggests that infiltration rates are negligible for terrestrial Arctic slopes (Heldmann et al. 2005). Nevertheless, even if infiltration was extensive there could likely still be significant meltwater volumes remaining. For example, if a given gully alcove containing snow has an area of 300 x 300 m = 9x10 4 m 2, and if there was 1 mm of meltwater runoff produced, the total volume of meltwater produced within the alcove would be 90 m 3. Even if the majority of the meltwater was consumed via infiltration, there could potentially still be 10s of cubic meters of meltwater runoff left. According to our simulations, the snow sublimated over ~150 days but the meltwater runoff is produced over only 1 2 days, and only in the afternoon. The actual meltwater production occurs only after the majority of snow has sublimated. Restricting our attention to the latitudinal bands where gullies appear to be common (30-70 ), GCM model estimates by Mischna et al. (2003) for 35 obliquity indicate that the amounts of zonally averaged atmospheric water vapor could have been greater than 200 prμm (precipitable microns) during summer and the seasonal extent of surface ice extended as far south as 10 N in northern winter and as far north as 20 N in the southern winter. As will be discussed below, the ice extents are not hemispherically 15

17 symmetric due to the longitude of perihelion occurring during southern hemisphere summertime in the simulations. The seasonal snow depths at mid-latitudes given by the model of Mischna et al. (2003) ranged from 0.5 cm under 35 obliquity to 1 cm under 45 obliquity, though it should be stressed that these numbers are only rough estimates. Note that given our modeled snow density of 400 kg/m 3, the Liquid water Equivalent Depth (LED) of a 1 cm snowpack is 0.4 cm. (Figures 5 and 6 here) Figs. 5 and 6 show the amounts of runoff produced for various amounts of snowfall as a function of latitude on 20 slopes facing toward and away from the equator, for an obliquity of 35. The data have been smoothed via cubic polynomial regression. Note that in our columnar model meltwater runoff amounts (mm) convert immediately to liters/m 2. According to Figs. 5 and 6, most of the slopes in the latitudes considered are warm enough to produce runoff, with the exception of the N and 70 S polar slope locations. The model results suggest that a 5 cm snowpack would produce a maximum of approximately 2.5 mm (2.5 liters / m 2 ) of runoff at 60 S latitude for an equatorward slope, and that for poleward slopes a similar (maximum) runoff amount occurred at 10 S latitude. As expected, in general the equatorward slopes were warmest, and hence produced slightly larger amounts of runoff for a given latitude than poleward slopes. The mesh area indicates the region covered by a perennial cap (where runoff is not expected), and the hatched area covers the area where significant seasonal snowfalls are not expected to occur, based on the results of Mischna et al. (2003). (Figures 7 and 8 here) 16

18 We also model the thermal structure of the soil substrate (beneath the snow column). In all of the cases where snowpack melting occurred, the topmost 1 mm of the soil substrate under the snow column was above 273K, whereas the remainder of the soil substrate column was below 273K. We believe that the topmost 1 mm of the soil substrate being warm makes it unlikely that the meltwater runoff would simply refreeze at the base of the snow column. According to Figs. 7 and 8, the amount of warm soil available on the same slope as the snowpack ranges from 1-2 cm for the obliquities of 35. The 70 N location for poleward slopes is slightly cooler than the equatorward slope, and hence neither runoff nor warmed soil was present at that location. It should be noted, however, that the models and parameters used here are imperfect (as are all models and parameter estimates), and hence the 70 N region should not be considered a hard limit. (Figures 9 12 here) As can be seen in Fig. 9-12, the 45 obliquity cases are similar to the 35 obliquity cases in that there is a maximum runoff of ~ 2.1 mm on equatorward slopes for 60 S and ~2.0 mm on poleward slopes for 20 S. Depending on the initial snowfall amounts, in the southern hemisphere on both slope azimuths we find that 1 cm warm soil amounts are fairly common but less so in the northern hemisphere. For deeper snowpacks (5 cm snow, or 2 cm LED), however, we find 2 3 cm warm soil amounts are common in the latitudinal ranges in question. The greater amounts of warm soil present on slopes when a 5 cm (2 cm LED) snowpack is melting is a consequence of the fact that 5 cm snowpacks melt later in the springtime, by which time the soil surface has become warmer. 17

19 Fig. 10 shows that for equatorward slopes under 45 obliquity, and excluding areas of insufficient snowfall or a permanent cap, the runoff amounts from a 5 cm snowpack (2 cm LED) are less than the runoff amounts produced by thinner snowpacks. Thicker snowpacks have a longer lifetime than thinner snowpacks, however the amount of runoff produced can vary depending on factors such as the snow dust content, remaining snow thickness and season (insolation) when the melting occurs. The reason the 5 cm snowpack produces less meltwater runoff than a thinner snowpack is that the thicker snowpack is able to survive long enough that insolation begins to decline (for this particular slope and latitude), whereas the thinner snowpack expires when insolation is still relatively intense. For both obliquities, and again restricting our attention to the latitudinal bands in question, it is apparent from the model results that the thinnest snowpacks (< 3 cm) do not consistently yield meltwater runoff at all latitudes. Nevertheless the deeper snowpacks (3-5 cm) do melt and produce runoff at all latitudes considered, yielding between mm of runoff depending on the slope geometry and latitude. We have conducted extensive sensitivity tests of our snowpack model, which are summarized elsewhere (Williams et al. 2008), where we concluded the most sensitive parameters were slope geometry, orbital characteristics and dust content. Under current Mars conditions (obliquity 25.19, eccentricity ~0.09 and longitude of perihelion ~250 ) the snowpack is most sensitive to slope geometry and dust content. Poleward slopes generally greater than 40 were found to be sufficiently steep (at least at mid-latitudes) that no melting could occur. The dust sensitivities were more pronounced when initial snowpack dust amounts exceeded 100 ppmw. We have also varied the slope inclination 18

20 between 10 and 30 in order to measure the effect on the amount of meltwater produced. The effect on the lifespan of the snowpack was somewhat significant (as Williams et al also showed), however in this case the effect on meltwater amounts produced were negligible. We conducted three new sensitivity tests on the snowpack model under the 35 climate regime. Specifically, we varied the atmospheric water amounts between precipitable microns, the snow dust content between 10 and 500 ppmw and the longitude of perihelion from The result of varying the atmospheric water was very small; assuming a base case of a 3 cm snowfall on an equatorward slope at 50 S, we found that varying the atmospheric water in the range specified produced only a small change (0.017 mm) in the amount of runoff, which corresponds to approximately 15% by volume of the total runoff. The effect of increasing the snow dust content was to both shorten the snowpack lifetime and to reduce the amount of meltwater runoff. At 10 ppmw (our base case) the snow surface was relatively cool in springtime, inhibiting sublimation and therefore extending the snowpack lifetime to early summer. In the 500 ppmw case, however, the snow surface was relatively warm in the spring season, and thus sublimated vigorously. By summertime the 500 ppmw snowpack was almost gone, and hence only a tiny amount of meltwater was produced when the more intense summer heating began. The effect of varying the longitude of perihelion was significant; varying the longitude of perihelion by +/- 45, 90, 180 affected the runoff amounts by as much as 100 % (increases of as much as +/- 0.5 mm). The sensitivity tests indicate that the runoff 19

21 amounts are sensitive to our parameter choices, but not enough to affect the conclusions of this study that runoff will occur. Note that a comparison of Figs 10 and 11 with Figs. 5 and 6 show that, according the modeling by Mischna et al. (2003), obliquity dramatically affects the availability of snowfall in the southern hemisphere for the longitude of perihelion being considered. As with any complex model, GCM predictions are not infallible. It is difficult to know even what degree of confidence to attach to a variable such as snowfall depth. Nevertheless we feel that the amounts predicted by Mischna et al. are plausible. Discussion and Conclusion We have found that the modest snowfalls similar to those predicted by Mischna et al. (2003) for obliquities of 35 and 45 o, can melt over a few day time period and release mm of runoff each year. We have also found that exposed soil, on the same slope as the snow, will have temperatures > 273K to depths of 1-2 cm each spring. We suggest this combination of snowmelt runoff and warm soil provide material which may be mobilized each spring, and that this admixture may have incised gullies. We have chosen not to posit a more specific erosional or depositional flow mechanism for gully incision in this study. Possible types of flow that may be relevant include debris flows, mudflows, hyperconcentrated streamflows, or open channel flows. The rheologies and other characteristics of these types of flows are vast and complicated subjects. As one possible example however, we consider terrestrial snowmelt-induced debris flows. 20

22 The amounts of water required to form the initial slope failure for terrestrial snowmelt-induced debris flows are presently poorly constrained and depend greatly on the properties of the material. However some Mars researchers have suggested that Martian debris flows could form with water concentrations as small as 10% by volume (Malin and Edgett, 2000). Several debris flows in the Swiss Alps during 1987 were analyzed by Roesli and Schindler (1990), who found that the soils were remarkably sensitive to water content in the sense that the addition of 3-4% (weight) of water was enough to change the slope material from the plastic to the liquid regime. Our study suggests that similar liquid/sediment ratios may be possible on the Martian slopes, given that our model indicates mm of liquid runoff and cm of warm soil occur on the slopes. The question remains of how, given initially thin (e.g cm) snowfalls, a sufficiently thick (e.g. 5 cm) snow patch might develop that could produce significant meltwater runoff. One possible mechanism is that they may have developed in a manner similar to that of terrestrial nivation hollows. As mentioned previously, snowdrifts may develop, often several times thicker than the initial snowfall (Erickson et al. 2005). In terrestrial research, it has been noted that nivation often begins with the formation of snowdrifts on the leeward side of ridges (Cain 1995; Christiansen 1998). Once the snowdrifts begin seasonally melting, erosion at the edges begin to excavate a hollow, often producing backwall erosion and alluvial fan deposition (Christiansen 1998). Once even a very shallow hollow develops, positive feedbacks can occur whereby the nivation hollow accumulates greater amounts of snow in subsequent seasons, producing even more melting and subsequent hollowing (Mark Williams, private comm., Christiansen 1998). An interesting observation related to nivation is that the locations of nivation 21

23 hollows are often controlled more by prevailing winds and snowfall amounts, and less by slope aspect (Christiansen 1998). Hence the locations of the Martian gully alcoves may not be controlled solely by slope insolation amounts as others have suggested (c.f. Dickson et al. 2007), but rather by wind direction. Similarly, Erickson et al (2005) found that of the several modeled parameters (elevation, slope, radiation, wind sheltering and wind drifting), that wind sheltering had the greatest effect on predicted snow depth. The results in Fig. 5 and 6 show a marked asymmetry in that both the runoff amounts and the available warm soil amounts are generally greater in the southern hemisphere than in the north. The asymmetry is due to the generally greater solar irradiation amounts in the southern hemisphere in our simulation, leading to generally higher surface temperatures. Higher surface temperatures are due to the fact that the longitude of perihelion falls at approximately Ls=250, and therefore the periapse occurs during the southern summer. Given that the longitude of perihelion is expected to vary with the 50 ka precession cycles, which is of shorter duration than obliquity variations, we expect that the hemispherical asymmetry in runoff to be temporary. By varying the longitude of perihelion in our model, we are able to reverse the hemispheric asymmetry in slope runoff amounts, favoring the northern hemisphere. Some research, such as that of Heldman et al. (2007), suggest that there is roughly the same number of gullies in both hemispheres. Our modeling results in this case provide a natural explanation for this hemispheric parity, as long as the gully formation mechanism would have occurred over equal or greater timescales than a precession cycle. Combining the work of Milkovich et al. (2008) and Mischna et al. (2003), as well as the meltwater runoff potential from our snowpack model, leads us to suggest that some 22

24 of the mid-latitude gullies were formed (or resurfaced) by flows under previous climate epochs with high obliquity. One implication of this hypothesized mechanism is that some of the gullies should have about the same age as the top of present polar ice sheets, because once the ice sheets started to re-form in the polar areas the obliquity must have been near its present value, ending the gully formation period. It is possible that the last gullies formed (or the last erosion occurred) as the ice sheets (residual caps) returned to present locations within the last 100 ka. Recent work by Milkovich et al. (2008), however, suggest that the top 300 m of the polar layered deposits may be less than 100 ka old, overlying older ice. If true, one possible inference would be that the 300 m of ice of the top part of the Polar Layered Deposits could have also been redistributed to lower latitudes in the form of atmospheric water (snowfall) since the last obliquity cycle, along with the overlying ice sheet. From the model results, there appears to be availability of > 1 mm of runoff, as well as the availability of > 1 cm of warm soil on both equatorward and poleward slopes between 60 and 30 S, as well as approximately 20 and 60 N. Assuming an adequate seasonal supply of snow (2-5 cm), we argue that the meltwater runoff could have incised the gullies, as well as contributed material to debris aprons during both of the past climate regimes studied (35 and 45 obliquity). It should be emphasized that the modeled process is capable of large amounts of erosion and deposition, given that it is both a seasonal and cumulative process. Such repetitive erosive and depositional events would almost certainly leave direct geologic evidence for us to observe in current and future spacecraft missions. 23

25 Acknowledgements The authors wish to thank Mark W. Williams for helpful discussions regarding terrestrial nivation, and to thank Trinity Allen for assistance with the gully images. Ginny Gulick and an anonymous reviewer provided very helpful suggestions as well. 24

26 Table 1. A summary of the model parameters which were relevant to the present study. Atmospheric water and longitude of perihelion parameters were varied for sensitivity testing over the stated range. For other parameters, see Williams et al. (2008). Parameter Value Snowpack density 400 Kg/m 3 Snow grain radius Snowpack depths Snowpack dust content 1 mm 1 5 cm Dust and soil albedo ppmw Soil thermal inertia 250 J m -2 K -1 s -1/2 Obliquity 35, 45 Eccentricity Longitude of perihelion Season of Snowfall deposition Slope inclination 10, 20, 30 Slope aspect (measured clockwise from N) 0, 180 Atmospheric water content prμ m (35 obl.), (45 obl.) Ls = 90 for southern hemisphere Ls = 270 for northern hemisphere 25

27 Fig. 1. An example of gully morphology. This HiRISE image is located at 49.0 S latitude and E longitude. The photo was taken at Ls=164.4 (southern winter) at 3:51 pm local Mars time. The gully slope faces approximately equatorward. HiRISE image credit: NASA/JPL/University of Arizona. Fig. 2. Eccentricity and Obliquity for Mars for the last 6 million years. (data from Laskar, private comm.) Fig. 3. The energy terms used in our snowpack model. Fig. 4 A possible mechanism for sediment movement and deposition. Arrows indicate the flow of meltwater. Fig. 5 The meltwater runoff amounts computed for poleward slopes and 35 obliquity. The hatched region indicates latitudes where insufficient snowfall is expected to allow runoff and the meshed area indicates latitudes where a perennial cap is expected to occur which will prevent melt. The data have been smoothed by polynomial regression. Note that in our columnar model meltwater runoff amounts (mm) convert immediately to liters/m 2. Fig. 6. The meltwater runoff amounts computed for equatorward slopes and 35 obliquity. The hatched region indicates latitudes where insufficient snowfall is expected for runoff to occur and the meshed area indicates latitudes where a perennial cap is expected to occur. The data have been smoothed by polynomial regression. 26

28 Fig. 7. Depth of soil with temperatures > 273K at start of melt season, for poleward 20 slope inclination and 35 obliquity. The grid spacing of the soil model is 1 cm. Fig. 8. Depth of soil with temperatures > 273K at start of melt season, for equatorward 20 slope inclination and 35 obliquity. Fig. 9 The water runoff amounts computed for poleward slopes and 45 obliquity. The hatched region indicates latitudes where insufficient snowfall is expected to allow runoff and the meshed area indicates latitudes where a perennial cap is expected to occur preventing melting. The data have been smoothed. Fig. 10 The water runoff amounts computed for equatorward slopes,and 45 obliquity. The hatched region indicates latitudes where insufficient snowfall is expected to allow runoff and the meshed area indicates latitudes where a perennial cap is expected to occur preventing melting. The data have been smoothed. Fig. 11. Depth of soil with temperatures > 273K at start of melt season, for poleward 20 slope inclination and 45 obliquity. Fig. 12. Depth of soil with temperatures > 273K at start of melt season, for equatorward 20 slope inclination and 45 obliquity. 27

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