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Keywords:

  • CO2;
  • Mars;
  • gully;
  • polar

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model
  5. 3. Conclusion
  6. Acknowledgments
  7. References
  8. Supporting Information

[1] Martian gully landforms, indicative of rapid flow of sediment down steep slopes, have been cited as evidence of the action of near-surface liquid water in Mars' recent past. Gullies in polar regions cannot involve pure liquid water because ambient temperatures are too low. Here, we show that polar gullies could be initiated by fluidization of sediment over a subliming seasonal deposit of CO2 frost, as has been proposed previously. For gullies in sand, the gas speed and CO2 sublimation rate required for fluidization is calculated with the semi-empirical Ergun relation (as validated in industrial applications). For gullies in dust, the gas speed and sublimation rate required for fluidization are estimated from laboratory experiments with comparable materials. To determine if those rates can be achieved, we compute diurnal and seasonal surface (and subsurface) temperatures through a Martian year (including CO2 condensation and sublimation) using the MARSTHERM one-dimensional finite difference thermal model. Models were run without sediment, and with layers of sand or dust 10−4–10−1 m thick deposited over a seasonal layer of CO2 frost. The simulations show that, in the spring, sufficient heat reaches the CO2 frost, underlying the surface sediment layer, to fluidize them. This result confirms that Martian gullies may have diverse origins – and that polar and mid-latitude gullies can be initiated on steep slopes by the fluidization of loose sediment on a sublimating seasonal deposit of CO2 gas.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model
  5. 3. Conclusion
  6. Acknowledgments
  7. References
  8. Supporting Information

[2] Martian gullies (Figure S1 in the auxiliary material), landforms produced by the flow of granular material from high slopes, flow across intermediate slopes, and forming deposition fans below, have been interpreted as evidence for the action of liquid H2O as groundwater or snowmelt [Malin and Edgett, 2000; Costard et al., 2002]. However, gullies are also present in polar regions [Balme et al., 2006; Hansen et al., 2011] where surface and subsurface temperatures are too low for the stable presence of pure liquid water (although concentrated brines might remain liquid [Knauth and Burt, 2002; Chevrier et al., 2009]). It has been suggested that polar gullies might be initiated and grow as sediment is fluidized by gas generated from sublimating CO2 frost or ground ice [e.g., Hoffman, 2002; Ishii and Sasaki, 2004; Hugenholtz, 2008; Diniega et al., 2010; Dundas et al., 2010]. Here we consider only the potential role of subliming CO2 surface frosts, as the formation of CO2 ground ice (where CO2 migrates into and condenses within the regolith pores) appears thermodynamically precluded by the latent heat released by condensing atmospheric CO2 – which will prevent the propagation of the CO2 frost point (and, thus, the condensation of CO2) beneath the surface.

[3] CO2 sublimation can be an important geological process in Mars' polar regions, and has been proposed as an explanation for the origin of the south-polar ‘spider’ structures [Piqueux et al., 2003]. Thus, we consider the formation and sublimation of polar CO2 frosts in detail, to determine whether sublimation can occur at a rate sufficiently high to fluidize eolian sediment and affect the formation of polar gullies [Cedillo-Flores et al. 2008].

[4] Several mechanisms have been invoked to explain how the sublimation of subsurface CO2 frost could enable gully formation. Hoffman [2002] proposed that gully-forming avalanches were initiated by basal heating of massive CO2 ice, similar to the process invoked for formation of south-polar spiders [Piqueux et al., 2003]. Cedillo-Flores et al. [2008] showed, in fact, that gas flow from beneath loose sediment could initiate formation of gullies. Hugenholtz [2008] emphasized the importance of CO2 frost coating to solid particles, and that the heat generated during an avalanche could make that frost sublimate and lubricate the flow. Russell et al. [2008] reported avalanches of CO2 frosts, which carried some dust. However, these avalanches did not produce gullies.

[5] Here, we investigate whether CO2 gas fluidization is a viable mechanism for the initiation of Martian polar gullies [Cedillo-Flores et al., 2008]. To test this hypothesis, we apply criteria for the fluidization of granular materials with a thermal model of the Martian surface and sub-surface. We test whether enough heat can reach a buried CO2 frost layer to induce sublimation rates sufficient to fluidize an overlying layer of sediment.

2. The Model

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model
  5. 3. Conclusion
  6. Acknowledgments
  7. References
  8. Supporting Information

[6] For polar gully landforms to be initiated by fluidization of CO2, slopes mantled in annual CO2 frosts must be covered by sediment, sand or dust. This constraint can be met only under restricted conditions – where a pole-facing slope (e.g., of a crater or dune) develops a seasonal cover of CO2 frost, while nearby equator-facing slopes remain bare (Figure S1a). Surface winds could then cause sediment (sand, dust, or aggregates of dust) to saltate from the equator-facing slopes and be deposited on the frosted pole-facing slopes, thus burying the CO2 frost beneath the sediment. This scenario could involve pole-ward or equator-ward winds, with sediments being moved from one side of a dune or crater (or pit) to the other, or transported further downwind to cover some other pole-facing frosted slope. As the sun comes to shine on the slopes, incident solar heat is then absorbed by the lower albedo sediment and conducted into the underlying CO2 frost, which sublimates in response. If gas velocities during sublimation are high enough, the overlying sediment can be fluidized and a gully initiated.

[7] Here we assume a pole-facing slope angle θ = 25°; an initial thickness of the CO2 on the frosted slopes equal to the maximum annual thickness of the local seasonal deposit; and thicknesses of eolian sediment ranging from 3 × 10−4 to 10−1 m (Figure S2). The gas velocity of the subliming CO2 is then calculated from the sublimation rate.

[8] The problem can be divided into two parts: (1) calculating the gas speed required for fluidization, and (2) modeling the thermal response of the system to the variation in incident heat.

2.1. Fluidization Gas Speed

2.1.1. Sand

[9] A bed of loose particles becomes fluidized when the weight of the particles (minus buoyancy from the surrounding fluid) is exceeded by the upward forces on the particles exerted by fluid flowing among them. In this case, viscous forces dominate because the flow Reynolds number Re is small, ≈0.002 (data shown in Table 1). The density ρf and viscosity μ of CO2 gas at Mars polar conditions (T = 150 K and P = 500 Pa) are taken as 0.018 kg · m−3 (ideal gas law) and ∼1 · 10−5 Pascal · sec (zero-density viscosity, extrapolated from 200K [Vesovic et al., 1990]) respectively.

Table 1. Physical Properties of Solid Materialsa
PropertySymbolUnitsSandDustCO2 Frost
Equivalent DiameterbDpm1 × 10−43 × 10−6
Bond AlbedoA0.10.250.65
Porosityϕ0.40.55
Thermal ConductivityckJ · m−1 · K−1 · sec−10.250.01
Densityρpkg · m−330002000

[10] The upward viscous force exerted on the grains is calculated via the semi-empirical Ergun equation [Ergun, 1952], which has been validated for industrial fluidized bed systems [e.g., Fogler, 2005]. At low Re (low inertial forces), one has

  • equation image

where vmf is the superficial gas velocity (volume flux of gas per unit area, not gas speed among grains) at which a bed of particles becomes fluidized, g is the acceleration of gravity (3.71 m · sec−2 for Mars), θ is the surface slope angle, ϕ is the porosity of the sediment, ρs is the density of a sediment particle [Fogler, 2005], and the number ‘150’ is an empirical geometric factor reflecting permeability and tortuosity of a bed of grains. The effect of slope angle θ is negligible, as cos(25°) = 0.91. Using the properties of Martian sand (Table 1), equation (1) gives a minimum gas speed for fluidization vmf = ∼8 × 10−3 m · sec−1, consistent with experiment and theoretical values [Roche et al., 2004; Bentley et al., 2011], and with the inferred low Re.

2.1.2. Dust

[11] Calculation of vmf via equation (1) implicitly assumes that inter-particle forces are negligible compared to gravitation and viscous drag. This assumption is not valid for dust-sized particles, <∼20 μm diameter [Geldart, 1973], which clump together easily from inter-particle electrostatic forces. For example, equation (1) would suggest that dust particles of Dp ∼ 3 × 10−6 meters effective radius, at 298 K could be fluidized by flow of Earth air at ∼1 × 10−5 m · sec−1. Beds of such particles are actually fluidized at air flow rates orders of magnitude larger – ∼2 × 10−3–2 × 10−2 m · sec−1 [Wang et al., 1998; Zhu et al., 2005; Saleh et al., 2006], depending on their shapes and electrostatic properties.

[12] Equation (1) would imply that Martian dust particles of Dp = 1.7 × 10−6 meters could be fluidized by CO2 flow of ∼7 × 10−6 m · sec−1. The properties of Martian dust are poorly known, but it is reasonable to think that their electrostatic properties and propensity to clump are within the range of terrestrial particles described above. So, to estimate vmf for Mars dust, we can scale its calculated vmf (including Mars gravity, and atmospheric viscosity and density) by the ratio of calculated and measured vmf for such particles on Earth (as above), which translates to a correcting factor of 200–2000. Using this scaling and including the difference in gravitational acceleration, we estimate that vmf for aggregated Martian dust grains is in the range of ∼3 × 10−3–3 × 10−2 m · sec−1. These estimated vmf are smaller than the vmf calculated for Martian sand.

2.2. Sublimation Rate and Heat Input

[13] For gas produced by the sublimation of CO2 ice, we calculate the ice sublimation rate required to produce a gas flow of vmf. From the ideal gas law [e.g., Smith et al., 1999], molar and mass fluxes at vmf are calculated as 3.1 × 10−3 mole · m−2 · sec−1 or 1.3 × 10−4 kg · m−2 · sec−1 for sand, and 2.7 × 10−4–2.7 × 10−3 moles · m−2 · sec−1 or 1.2 × 10−5–1.2 × 10−4 kg · m−2 · sec−1 for dust. The heat required to produce this much CO2 gas is calculated via the enthalpy of sublimation of CO2sublequation image(CO2) = 26.1 kJ · mole−1 near 150 K [Stephenson and Malanowski, 1987]), yielding minimum heat fluxes for fluidization of ∼84 and 7–70 J · m−2 · sec−1 for sand and dust respectively.

2.3. Thermal Model

[14] To compute diurnal and seasonal surface (and subsurface) temperature variations (including the condensation and sublimation of CO2) throughout the Martian year we used the one-dimensional finite difference thermal model MARSTHERM [Clifford and Bartels, 1986], see auxiliary material. MARSTHERM considers heat transfer only by conduction, assumes that the CO2 frost and sediment layers are homogeneous, and that the latter are optically opaque to visible and thermal radiation. For these reasons, and those of computation time, our MARSTHERM models are restricted to layers of 300 μm and thicker.

[15] Using MARSTHERM, we modeled the geological circumstances described above for climate conditions representative of the current epoch. In winter, slopes accumulate CO2 frost; a layer of sediment (if present) is emplaced instantaneously onto a winter's thickest accumulation of CO2 frost (Figure S3); sublimation of that CO2 frost is tracked through spring and summer until the frost vanishes (Figure S3). The tested models, Figure 1, are for pole-facing slopes of 25° at latitudes of 75°N and S, with no sediment mantle and with mantles of 300 μm to 10 cm thicknesses of sand or dust (results for 300μm, not shown, are nearly identical to those for 1 mm). Figures 1a and 1b show maximum daily sublimation rates as functions of season; Figures 1b and 1c show hourly rates during the day of maximum sublimation.

image

Figure 1. Results of MARSTHERM calculations of sublimation rates on pole-facing slopes of 25° for (a and c) 75°N latitude and (b and d) 75°S latitude for a range of thicknesses of eolian sand and dust. Calculations for thicknesses of 300 μm are essentially coincident with those for 1 mm, and are not shown for clarity. Figures 1a and 1b show daily average sublimation rates over a Martian year (Ls 0° to 360°). The curves terminate when CO2 frost equivalent to an annual winter deposit has sublimated away. Figures 1a and 1b also show the threshold sublimation rates to fluidize dark sand (solid line) and light-tone dust (gray field). Figures 1c and 1d show sublimation rates during the single day of maximum sublimation. For Figure 1c, the days of maximum sublimation rates are at Ls =: 98.3° for 10 cm of dust; 95.6° 1 cm of dust; 75.2° for 1 mm of dust; 83.3° for 10 cm of sand; 72.6° for 1 cm of sand; 68.5° for 1 mm of sand; and 95.4° when no sediment is present. For Figure 1d, the days of maximum sublimation rates are at Ls =: 268° for 10 cm of dust; 268° 1 cm of dust; 258° for 1 mm of dust; 268° for 10 cm of sand; 257° for 1 cm of sand; 250° for 1 mm of sand; and 268° when no sediment is present.

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[16] The low albedo of the overlying sediment causes the CO2 frost to sublimate rapidly, because of its greater absorption of solar heat. This creates conditions that are conducive to the fluidization of the sediment by the sublimation of underlying CO2 frost. For all cases, sublimation begins in early spring (Ls ∼ 40° for northern hemisphere, Figures 1a, S3a, and S3b), and is greatest at local ‘midnight’ when pole-facing slopes receive the most direct solar illumination (Figures 1c, 1d, and S3c).

[17] For frost mantled by sand, sublimation is rapid because the sand absorbs ∼90% of the solar heat and conducts it efficiently to the frost (Table 1). Sublimation rates rapidly exceed the critical value for sand fluidization, vmf (horizontal black line in Figures 1a and 1b). At these times, CO2 gas flow through the sand will be sufficient to fluidize it, initiating avalanches and possibly producing gullies (Figure S1). The sublimation rate curves in Figure 1 assume that the sand layer remains immobile, even though sublimation rates rise to more than an order of magnitude larger than those necessary for fluidization. Once a packet of sediment is fluidized, it will flow downhill under the influence of gravity, destabilize all nearby sediment above sublimating frost, and thus initiate the massive flow of a gully. These events are beyond the constraints of our model.

[18] For CO2 frost mantled by light-tone dust, sublimation is later and sublimation rates are slower than for sand mantles (Figure 1). This difference between dust and sand represents the dust's lower albedo and lower thermal conductivity (Table 1). The thickest layer of dust, 10 cm, acts as a good thermal insulator and prevents an annual frost layer from sublimating completely (Figures 1a and 1b). Thinner dust layers concentrate and conduct enough heat to the CO2 frost to permit fluidization.

3. Conclusion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model
  5. 3. Conclusion
  6. Acknowledgments
  7. References
  8. Supporting Information

[19] These results (Figure 1) show that thin layers of eolian sediment deposited over a seasonal accumulation of CO2 frost could be fluidized by sublimation of that frost. Once fluidized, the sediment will flow and could potentially produce the massive flows represented now by polar gullies [Hoffman, 2002; Cedillo-Flores et al., 2008; Hansen et al., 2011]. Fluidization is predicted to occur in the early spring, coinciding with the observed occurrences of seasonal gully activity [Diniega et al., 2010; Dundas et al., 2010; Hansen et al., 2011]. Because CO2 frosts can be deposited locally at intermediate to low latitudes [Schorghofer and Edgett, 2006], fluidization from sublimation of those frosts could thus initiate gully formation across most of Mars. Gullies in polar and temperate latitudes show similar ranges of sizes and morphologies [Malin and Edgett, 2000; Hoffman, 2002], which is consistent with formation by a common mechanism (i.e., gas fluidization. However, similar gully morphologies can also arise in liquid-rich flows [e.g., Hartmann et al., 2003; Coleman et al. 2009; Kolb et al., 2010] which suggests that gullies can be initiated by multiple processes – and that, once begun, flow processes in gully-forming avalanches are independent of the initiation mechanism.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model
  5. 3. Conclusion
  6. Acknowledgments
  7. References
  8. Supporting Information

[20] This work was done at the Lunar and Planetary Institute, under a fellowship to the first author from the Secretaría de Educación Pública, Republica de Mexico, under the “Programa de Apoyo al Posgrado Beca Bicentenario de Alta Competencia para Posgrado e Investigación en el Extranjero, Ciclo 2010.” We are grateful for assistance from J. Gross, for constructive reviews from S. Byrne and an anonymous expert, and editorial handling by P. D'Odorico. Lunar and Planetary Institute contribution 1638.

[21] The Editor thanks the two anonymous reviewers.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model
  5. 3. Conclusion
  6. Acknowledgments
  7. References
  8. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Model
  5. 3. Conclusion
  6. Acknowledgments
  7. References
  8. Supporting Information

Auxiliary material for this article contains a text file and three figures.

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FilenameFormatSizeDescription
grl28605-sup-0001-readme.txtplain text document1Kreadme.txt
grl28605-sup-0002-txts01.docWord document38KText S1. Captions for auxiliary figures and explanatory text on Reynolds number for gas flow, calculation of mass fluxes of gas, and description of the MARSTHERM program.
grl28605-sup-0003-fs01.tifTIFF image1563KFigure S1. Images of Martian gullies and a similar structure produced in the laboratory by gas fluidization.
grl28605-sup-0004-fs02.pdfPDF document1217KFigure S2. Diagram of the physical setting modeled here.
grl28605-sup-0005-fs03.pdfPDF document520KFigure S3. MARSTHERM results for CO2 ice deposition and sublimation on slopes without sediment cover.
grl28605-sup-0006-t01.txtplain text document0KTab-delimited Table 1.

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