A mechanism for bringing ice and brines to the near surface of Mars

Authors


Corresponding author: B. J. Travis, Computational Earth Science Group, Los Alamos National Laboratory, EES-16/MS-J535, Los Alamos, NM 87545, USA. (bjtravis@lanl.gov)

Abstract

[1] Recent discovery of transient ice deposits uncovered by five small craters between 40 and 55°N latitude, reinterpretation of MONS neutron data that indicate the wide-spread presence of ice within 1 m of the surface at midlatitudes (down to 30°N) of Mars, and evidence of recent periglacial activity within 10°N of the equator, all suggest ice may be or recently was present at latitudes where it is not expected and at unexplained abundance. As ice may be unstable under present Mars climatic conditions, a mechanism may be needed to explain the presence of ice in the near surface at these latitudes. Water release history, chemical composition, and heat fluxes are variable over the surface of Mars, and there could be more than one mechanism responsible for near-surface ice. The purpose of this study is to show that hydrothermal circulation of brines in the subsurface of Mars is a possible mechanism that can deposit ice and brine, close to, or even at, the surface of Mars. Furthermore, the action of brine convection can be related to some of the surface features associated with subsurface water during previous or even present epochs, such as polygonal ground and sorted stone circles.

1 Introduction

[2] There is abundant evidence for ice and water in the subsurface of Mars at a range of length and time scales. Martian surface topography retains incontrovertible evidence for the occurrence of several massive floods during Mars' early history that originated at low latitudes, producing enormous channels before emptying into the northern lowlands [e.g., Carr, 1996]. A detailed study of the MOLA topographical data revealed evidence for a temporary ocean covering much of the Vastitas Borealis formation [Baker et al., 1991; Parker et al., 1993; Clifford and Parker, 2001], although Head et al. [2002] argue that volcanic resurfacing was a significant contributor to northern lowland infilling. The total water released during these flood events is estimated to amount to a global equivalent water layer of at least 500 m covering the surface of Mars. Some of that water may have been lost to space, but most estimates indicate that, in addition to the water ice locked in the polar caps and associated layered deposits, significant amounts of water must reside as water ice filling a cryosphere beneath the Martian surface, and some liquid water may be present in an aquifer that sits beneath the cryosphere [Clifford, 1993; Clifford and Parker, 2001; Clifford et al., 2010]. The northern plains, because of their lower elevation, are the most likely areas to have a cryosphere in contact with underlying groundwater.

[3] There are several indicators of water in the Martian subsurface. Correct classification of several kinds of features (pingos, rootless cones, rings) is frequently problematic on Mars, but whether of periglacial or volcanic origin, water and ice are involved. Pingo-like structures are a common feature in some areas, and if they are indeed pingos, they must have required a significant thickness of water and/or permafrost [Cabrol et al., 2000; Soare et al., 2005; Burr et al., 2005; Page and Murray, 2006; dePablo and Komatsu, 2009; Dundas and McEwen, 2010]. Pingos are typically about a hundred meters in diameter; studies suggest a roughly 200 m deep water system below them [e.g., Mackay, 1998]. They also imply a heat source or significant change in climate to produce thawing. Most pingo-like fields are in the Northern Hemisphere [see, e.g., Burr et al., 2009], with the Utopia basin being the locus for most, but not all, of them. The Utopia basin has experienced extensive sediment infilling; pingos on Earth are associated primarily with unconsolidated sediments. The Utopia basin was also subjected to repeated aqueous inflows, providing the needed groundwater/near-surface ice for pingo formation. Studies of terrestrial pingos, in a very cold, high-altitude region of China [Burr et al., 2009; Yoshikawa et al., 2006], show that many of the associated groundwater systems are briny. The presence of permafrost and a freezing surface provide a mechanism for pressurizing groundwater and focusing water flow during pingo formation. De Pablo and Komatsu [2009] studied pingo-like stuctures in the midlatitude northern lowlands of Mars and concluded that they are most likely due to the action of an extensive heat source under Utopia Planitia, possibly related to nearby volcanic features, or remnant heat from the impact that formed the basin, allowing the melting of ground ice periodically in response to climate changes. Lakes or even an ocean may have overlain Utopia basin [Baker et al., 1991; Parker et al., 1993; Clifford and Parker, 2001; Carr, 1996]; much of that water may still reside as ice in the pores of the Utopia soils.

[4] Other signs of subsurface ice include polygonal ground, which is widespread [Mangold et al., 2004; Mangold, 2005; Levy et al., 2009]—seen generally at high northern latitudes [Mellon et al., 2008, 2009], in Athabasca Valles, Elysium basin, Marte Vallis, western Amazonis Planitia, as well as the Cerberus Fossae region [Page and Murray, 2006; Gallagher and Balme, 2011]. Indeed, Balme and Gallagher [2009] have interpreted HiRISE images of the Athabasca Vallis of Mars to support the situation of a landscape modified by thawing of significant amounts of ground ice and subsequent fluid flow, similar to degrading permafrost regions on Earth that form retrogressive thaw slumps. Balme et al. [2009] report nonsorted, patterned ground at mid- to high-latitude occurrences, as well as sorted stone circles, indicative of periglacial activity, even at low latitudes. Some in Athabasca Vallis can be dated and appear to be [see, e.g., McEwen et al., 2012] only a few Myrs old. Their diameters range roughly from 10 to 20 m, in agreement with sizes that have been shown to result from thermal contraction in ice-rich permafrost [Mellon, 1997; Mellon et al., 2008]. Polygons are also frequently observed nearby, some with positive, some with negative relief margins, more often domed, with similar diameters, although some are as large as 40 m. Sorted patterned ground on Earth results from freeze-thaw cycling and cryoturbation. Martian sorted stone circles are similar to corresponding structures on Earth, which range in size from 5–10 m to 20 m or even larger. Balme et al. [2009] take stone circles to mean a warmer climate in the recent past. In addition to pingos and circles and polygonal ground, there are other examples of water-driven features; Schulze-Makuch et al. [2007] found evidence for many endogenic hydrothermal sites on Mars. Apparent water-carved gullies down to 30° latitude and below, observed by Malin and Edgett [2000], have been interpreted as recent water flows, yet permanent ground ice, and especially water, is expected only poleward of 30°– 40° [Mellon and Jakosky, 1993, 1995; Mellon and Phillips, 2001]. Additionally, McEwen et al. [2011] review observations of southern, midlatitude recurring slope lineae and conclude that a likely explanation is that they are fed by near-surface sources of brine.

[5] On a smaller scale, there are the recent observations by Byrne et al. [2009] of small impact craters between 40°N and 56°N latitude using HiRISE images. These observations clearly revealed the presence of a layer or lenses of nearly pure water ice within about 1–2 m of the surface. Renno et al. [2009] interpret data from the Phoenix Lander site as indicating the presence of both ice and liquid brines at very shallow depths.

[6] In light of the Byrne et al. [2009] observations, Feldman et al. [2011] carried out a reinterpretation of MONS thermal and epithermal neutron data from low to midlatitudes, using a new combined analysis of fast and epithermal neutron fluxes and the crater observations to eliminate the nonuniqueness in the original analysis. Their new results are consistent with ice-rich soil lying up to 0.5 m below a soil layer having ~4%–5% water equivalent. Several extensive locations, as close to the equator as about 30°N, were identified that displayed the same behavior as that found for the five small craters that are the subject of the Byrne et al. [2009] study.

[7] Significant deposits of near-surface water-equivalent hydrogen [Feldman et al., 2002; Boynton et al., 2002; Mitrofanov et al., 2002; Prettyman et al., 2004] have also been seen at latitudes higher than about ±60° [Diez et al., 2008; Feldman et al., 2008], in agreement with latitudinal contours of equilibrium ground-ice stability [Paige, 1992; Mellon et al., 2004; Schorghofer and Aharanson, 2005].

[8] There is ice at high latitudes where it would be expected, but also evidence of near-surface ice at mid and even low latitudes where it would not be expected. Since ice within 1 m of the surface at latitudes equatorward of about 45° should be unstable under the existing climatic conditions [Mellon and Jakosky, 1993, 1995; Mellon and Phillips, 2001; Schorghofer and Aharonson, 2005], the question arises as to the source of the ice. Given that thermal and chemical conditions vary significantly over the surface of Mars, more than one mechanism, either acting alone or in combination with others, could be responsible for observations of near-surface ice. One likely source of H2O in the very shallow subsurface is by vapor diffusion from the atmosphere [e.g., see Vincendon et al., 2010]. Levy et al. [2012] report on a related possibility, deliquescence of salts, that is, direct vapor sorption into soil pore brine. A third possibility, given the evidence for the presence of H2O below the northern plains and the flanks of volcanic terrain [e.g., Clifford and Parker, 2001, 2005] is that ice and brine are brought up to the near surface by the action of hydrothermal convection, driven by geothermal or compositional gradients. That is the mechanism examined in this report.

2 Brine Transport Under Freezing Conditions

2.1 Previous Experimental and Numerical Work

[9] For freezing systems, convection has been observed in laboratory experiments on briny solutions [e.g., McGraw et al., 2006]. There are few, if any, field studies of convection in freezing soils, and only limited studies in briny, nonfreezing systems [e.g., van Dam et al., 2009] present evidence of free convection in a field-brine system. Field observations of convection in freezing, briny systems have focused mainly on sea ice. Typically a mushy, partially frozen layer develops, and “chimneys” form. Chimneys are narrow, cylindrical, ice-free channels that form within the mushy region. Fowler [1985] developed a criterion for chimney formation; they can form when (uV)*∇T > 0, where u is fluid flow rate and V is solidification rate. So when u > V, as in our case, and u and ∇T < 0, chimneys can form. Worster [1997] reviewed a variety of experiments and theoretical studies on dynamics of mushy layers and chimney formation due to Darcy flow convection in cold, briny systems. Worster and Wettlaufer [1997] described experiments and numerical simulations of salt water freezing and mushy layer formation with chimney development with application to growth and evolution of sea ice, finding that brine remains trapped in sea ice, draining out only after the ice layer exceeds a critical thickness. Wells et al. [2011] recently examined, in a theoretical model with 2-D numerical simulations (for very high permeability) and by comparison to experimental data, the spacing of brine chimney conduits and flux of salt in permeable, growing sea ice. Schulze and Worster [1999] performed numerical simulations of convection and solidification of metallic alloys with chimney formation. In all of these studies, flow in the mushy layer is approximated by Darcy's law.

[10] The situation for Mars contains an extra factor—the soil is assumed to be a fixed matrix, and brine and ice form within the porosity of the soil, but the dynamics described below appear to be very similar to the observations and analyses of two-component ice-water porous systems. The above-referenced studies provide a means of validating numerical models in limiting situations. Furthermore, the numerical study here adds to this body of research on mushy layer chimney conduits by presenting a limited parameter study of fully nonlinear simulations of freezing and chimney formation in a porous medium in 2-D and 3-D. For a heat flux bottom boundary condition, a thermal/chemical Rayleigh number, combining thermal and chemical buoyancy, can be defined as

display math(1)

where ρ is fluid density, α is fluid thermal expansion coefficient, g is gravity, Q is bottom heat flux, k is permeability, H is aquifer depth, κ is thermal diffusivity, μ is maximum fluid viscosity, KT is average thermal conductivity, ΔC is maximum concentration difference in the system, and β = ∂ρf/∂C is the dependency of fluid density on salt concentration. Worster [1997] found that at low Ra number, hexagons are the preferred convection pattern, while at higher Ra numbers, rolls are the dominant pattern. The numerical results presented here include a mix of both patterns, producing a variety of polygon sizes. In this study, Ra number ranges from 10 (near the critical value) to over 200.

[11] A few studies of hydrothermal convection in the Martian subsurface have been reported. For example, numerical models of hydrothermal circulation (without ice) [Harrison and Grimm, 2002; Gulick, 1998] and a boundary layer model (with ice) [Craft and Lowell, 2012] showed that reasonably sized magmatic intrusions within ground formations having reasonable permeability can drive groundwater outflows sufficiently large to form observed fluvial valleys at mid to low latitudes and outflow channel systems, such as Athabasca Valles, on Mars. Grimm and Painter [2009] modeled three-phase subsurface permeable Darcy flow in a whole planet model of Mars over geologic time. Their model tracked the evolution of subsurface water and ice and vapor but lacked salts. Horizontal resolution is coarse at 5°. They showed that a global multiphase model of subsurface H2O transport on Mars supports geomorphological observations interpreted to indicate subsurface hydrothermal circulation to produce past H2O surface outflows and that surface water may have been abundant in the past, but not the present. Additionally, Lane and Christensen [2000] carried out an analysis of pore fluid convection (assuming pure water) as a reasonable mechanism for formation of Martian scalloped and large polygonal features and related polygon size to aquifer depth. However, they neglected freezing and salt transport and considered different boundary conditions from the present study, all of which can change the temperature range over which convection is possible and also can change relationships between surface features and aquifer properties. Brines will allow convection at much colder temperatures, so rapid emplacement, e.g., is not necessary, and climate would not have to be warm. Ogawa et al. [2003] applied a model of hydrothermal convection with phase change to the melting of ice in the near surface due to heating from a magma intrusion as a mechanism to supply outflow channels. Impact craters have also been a focus of other numerical hydrothermal convection studies, including Abramov and Kring [2005] and recently Barnhart et al. [2010], who included freezing and thawing of soil ice. These last two studies do not consider the impact of brines on convective behavior and involve strong heat sources.

2.2 Our Model

[12] Our previous simulation study of aquifer dynamics in the Martian subsurface considered only pure water aquifers [Travis et al., 2003]. It found that hydrothermal convection develops for a range of geothermal gradients, for reasonable soil properties, but that pure water convecting systems cannot exist very close to the cold Martian surface. Subsequent experimental and numerical studies [McGraw et al., 2006; Travis and Feldman, 2009] considered both pure water and salty aquifer dynamics in response to a thermal gradient. Salt not only depresses the freezing point but can add an unsteady characteristic to convection. Those studies and this one use the MAGHNUM code. MAGHNUM solves the time-dependent governing equations for water and vapor flow, and heat and salt transport in porous, permeable media in 2-D or 3-D geometries. It employs mass and energy conserving integrated finite volume algorithms in its numerical solution. It allows changes between liquid, vapor, and ice phases, depending on local thermodynamics. Thermal conductivity and specific heat are recomputed on each time step in each computational cell by a volume fraction-weighted average [McKenzie et al., 2007] of the thermal conductivities and specific heats of soil, water, ice, and air, each of which can be temperature dependent. Chemical, as well as thermal buoyancy, is an important factor in driving flow. Part of the driver of brine convection is the increase in density of brines near the cold surface as ice precipitates out of solution. Fluid density ρf is a function of temperature T and salt content C:

display math(2)

where ρw is pure water density. Fluid viscosity μ depends on temperature and salt content. A relationship of the form

display math(3)

provides an excellent fit to experimental data [McGraw et al., 2006] from the eutectic temperature to about +70°C. At the eutectic, fluid viscosity is more than an order of magnitude greater than for pure water above freezing. Salt precipitation and dissolution are computed by partitioning salt between fluid and solid phases according to the binary phase graph for CaCl2 and H2O. Descriptions of the full model equations and numerics are given in Travis et al. [2012]. Our numerical simulations are conducted in a 200 m × 200 m domain (200 m × 200 m × 200 m for the 3-D simulations). The size of the domain is large enough to encompass the expected convective dynamics without interference from boundaries. Computational grid cells are 2 m on a side. A few simulations were repeated at higher resolution (1 m grid cells) to confirm results of the larger study. Time step size is variable and is updated by the MAGHNUM code after each time step. Circulation of fluids through the Martian subsurface depends on several properties, primarily, the soil permeability, the presence of H2O and salts, the surface temperature, and a driving force, either heat or a compositional gradient, or both.

2.3 Permeability

[13] Permeability models of the Martian subsurface have been developed in previous studies. The Clifford [1993] model, based on various theoretical and experimental data, has high surface permeability and porosity, with exponential decay with depth. Hanna and Phillips [2005] revisited permeability models for the Martian regolith. Their megaregolith model permeability also decays with depth, but more slowly than the Clifford model, ranging from about 10−11 m2 (10 darcies) at the surface to about 10−15 m2 (1 millidarcy) at 10 km depth. They argue that asperities and compressibility of fractured rock will keep fractures open to some minimum aperture (around 10 µm) even at considerable depth. Porosity similarly varies from around 16% to 20% at the surface to about 4% at depth. The northern terrains are likely to be composed of basaltic lava flows and sediments. Terrestrial basaltic aquifers have high porosity and high permeability, and there is no reason to believe that Martian basalts would be different from terrestrial basalts. Sedimentary sandstones exhibit a decrease in permeability with depth, but they tend to be less sensitive to their stress state. Permeability versus depth for sediments is similar for the Clifford [1993] and Hanna and Phillips [2005] models down to about 2 km depth, while porosities predicted by the various models versus depth track more closely to greater depths. A mixture model of basaltic and sedimentary layers overlying a fractured megaregolith will yield overall permeabilities and porosities versus depth that are similar to the Clifford model. Our simulations in this study are based on that model. All the models, however, indicate that soil permeability will not decrease significantly over 200 m depth, the aquifer thickness we consider here.

[14] In the model, permeability and porosity are reduced locally by the presence of ice. Permeability has a power law dependence on the water-filled fraction of porosity [see, e.g., Newman and Wilson, 1997; McKenzie et al., 2007; Frampton et al., 2011], similar to relative permeability relationships in unfrozen, partially saturated soils. Permeability and porosity are recomputed each time step for each computational cell, depending on ice content.

2.4 Salts

[15] Subsurface water on Mars is likely to be salty rather than pure water. Salts are important because they can depress the freezing point of solutions, dramatically in some cases. Our understanding of the possible salts in Martian waters has evolved over time. Clark and van Hart [1981], based on analyses of Viking data and geochemical and thermodynamic considerations, considered several candidates for Martian salts: MgSO4·nH2O, NaCl, CaCl2, and double salts of the form MgSO4·Na2SO4·nH2O. More recently, Knauth and Burt [2002] argue that the early Martian hydrosphere evolved first into a NaCl brine, and then, after exposure to basaltic or komatiitic rock, into a Ca-Mg-Na-Cl brine mixture, and that CaCl2 brines may be most likely near the surface. A recent study [Osterloo et al., 2008], using THEMIS data, has found evidence of chloride salt deposits associated with a number of features on the surface of Mars, primarily in the southern hemisphere. Based on their interpretation of the data, precipitation from briny aquifers and surface ponds is a likely source of those salts. Fairen et al. [2009] carried out numerical geochemical simulations of thermodynamic evolution of solutions based on weathered basalts, starting with the chemical compositions found at Martian landing sites (Viking 1 – Chryse Planitia, Pathfinder – Ares Vallis, Opportunity – Meridiani Planum, and Spirit – Gusev crater). Their model yielded mineral assemblages similar to those observed on the surface of Mars, and their simulations indicated a highly saline solution develops, which could remain fluid at temperatures comparable to low- to midlatitude average surface temperatures on Mars. Wang and Ling [2011] found that hydrated ferric sulfate salts were exposed by trenching operations by Spirit in Gusev crater soils, along with Mg and Ca sulfates, just a few centimeters to tens of centimeters below the Martian surface. Yellowish salty soil, apparently not in equilibrium with the atmosphere, changed over time to whitish soil, presumably after losing water of hydration. Ca, Mg, and Fe sulfates are fairly common in MER observations, while Fe sulfates are apparently difficult to observe from satellites. Eutectic freezing points of brines span a range nearly 70°C wide, e.g., a NaCl brine has a eutectic of −22°C, CaCl2 brine has a eutectic point of about −52°C and a mixture of CaCl2 and MgCl2 has a −55°C eutectic point. Ferric sulfates have a eutectic of 205 K (−68°C) at 48 wt.% concentration [Chevrier and Altheide, 2008]. Some perchlorates have even lower eutectic points; for example, Mg(ClO4)2 has a −70°C eutectic temperature and is highly soluble. Perchlorates have been observed at the Phoenix lander site [Hecht et al., 2009] (but at unknown concentrations).

2.5 Boundary Conditions

[16] Side boundary conditions are reflective, impermeable, and insulated. The bottom boundary is impermeable to advective and diffusive mass flow; thermal conditions are either a specified temperature or specified heat flux. At the top boundary, temperature is fixed, and the surface is open to advective and diffusive mass transport. However, very little mass flow occurs through the surface. At the surface, much of the pore space is filled with ice, greatly reducing effective permeability. At places where liquid brine is present, the strongest flow is horizontal or downward in return flow regions. A small amount of brine flows onto the surface in some of the cases considered herein. Because of the saturated conditions, vapor transport is also cut off and relative humidity is not a factor; this is the most important approximation for surface fluxes. We are assuming that our model is particularly relevant in locations where floods occurred or where significant up-flow occurs or occurred, producing a saturated condition, at least for a time, which could happen, for example, where aquifers are or were pressurized from plutonic intrusions or tectonic stresses. At the surface, much of the H2O is frozen and much of the salt immediately below the surface will have precipitated (a process our simulations bear out), contributing to creation of a vapor diffusion barrier. Hudson and Aharonson [2008] carried out diffusion experiments on media approximating Mars' surface conditions; they determined that a heavily salt-encrusted soil would reduce diffusion coefficients by a factor of about 10. Hudson and Aharonson [2008] and Hudson et al. [2009] conducted laboratory experiments on vapor diffusion into permeable media under Mars-like temperature and pressure conditions. One of their findings is that vapor diffusivity is diminished further by a factor that varies roughly as the square of the fraction of the pore space not occupied by ice. That result is essentially the same as found in the Millington [1959] relationship for reduction of diffusivity of gases in a partially saturated soil. The convective systems modeled in our study develop rapidly and are near steady state in less than a thousand years. Given the very low density of water vapor at the surface temperatures assigned in our simulations and a reduced diffusion coefficient, the amount of water lost as vapor in that time interval is not much, on the order of a meter. Furthermore, as long as the brine convection continues, hydrodynamic forces will tend to fill in pore space opened by vaporization. For example, an unsaturated condition caused by vapor outflow would increase capillary tension, tending to pull brine from deeper in the system upward to fill in for the mass lost by vapor diffusion. A simple balance has ratio of capillary suction flux to vapor flux at the surface

display math(4)

where k is permeability, μ is viscosity, Pc is capillary pressure, σ is liquid saturation, Δσ is saturation difference, “a” is fraction of pore space not occupied by brine or ice, Dv is vapor diffusivity, Δρv is vapor density difference between soil and atmosphere, and fh-a ~ 0.1 is the reduction in diffusivity found by Hudson and Aharonson [2008] in a salt-encrusted soil. For a ~ Δσ ~ 0.1, k ~ 100 darcies, Rcv ~ 10−3/10−11 = 108. Capillary flow appears much stronger than vapor diffusion at very cold temperatures, and our assumption of a saturated subsurface is a reasonable simplification. If the convective system dies out (for example, due to colder surface conditions), vapor diffusion would not be counteracted, and eventually the ice stability profile as determined by Schorghofer and Aharonson [2005] and Schorghofer [2007] could establish itself.

2.6 Parameters and Ranges

[17] To demonstrate the ability of hydrothermal convection driven by even modest geothermal gradients to deliver brines very close to the Martian surface, we present results of a limited parameter study. Sensitivity factors include soil permeability, surface temperature, initial pore water salt content, and geothermal heat flux. Soil permeability values of 10, 100, and 1000 darcies are considered, covering the range of most soils. Soil porosity is fixed at 35%, typical of many soils [Arvidson et al., 1989]. Surface temperature Tsurf is an important controlling factor. If Tsurf is warmer than the eutectic temperature, the subsurface does not completely freeze. If Tsurf is colder than the eutectic, the system will be frozen down to a depth at which the eutectic occurs. The most interesting situation, then, appears to be a surface temperature that is at or close to the eutectic temperature. We use CaCl2 to represent the soil pore water salt; its low eutectic, −52°C, is close to Mars' average surface temperature at low latitudes, there is reason to believe it could be a major constituent of near-surface chemistry [Knauth and Burt, 2002], and further, its properties at low temperatures are available. Surface temperatures are allowed to range between −50°C and −54°C. Initial model pore water salt concentrations from 5% to 29% mass fraction cover the range from low to high salt content. Geothermal heat flux likely varies considerably over the surface of Mars, from lows of 15–20 mW/m2 in thick crustal areas to 60 mW/m2 or more in regions associated with recent volcanic activity, and more widely in the past [Schubert et al., 1992]. Parameter combinations considered in our simulations are summarized in Table 1. We note that without the presence of salts, the domain considered would be completely frozen.

Table 1. Parameter Values for the Various Simulations
Case No.Permeability (darcies)Q (mW/m2)Tsurf (°C)Ci (wt.%)Dimension
110040−52292
21040−52292
3100040−52292,3
410040−52252
510040−52202
610030−52292
710060−52292
810040−50202
910040−54292
1010040−50292
1110040−52102
1210040−5252,3

2.7 Simulation Results

[18] Using the parameter values indicated above, the system convects for almost every combination of parameters. The thermal gradient drives a broad, upward flow of brine through the soil pores. Compositional changes also help drive convection; as ice precipitates out of solution near the cold surface, the remaining brine solution becomes more dense, significantly enhancing the thermally unstable density profile. In the model, convection initiates through a random perturbation to the initial conductive temperature profile.

2.8 2-D Simulations

[19] The impact of each of the four primary parameters—soil permeability, geothermal heat flux, surface temperature, and initial pore water salt concentration—on subsurface ice distribution are considered in turn. Figures 1-5 display soil pore ice fraction distributions after the flow patterns have reached a steady state, which occurs generally after about 1000–2000 years after start-up.

Figure 1.

Dependence of ice precipitation (as fraction of pore volume) in the mushy layer on permeability for (a) 10 darcies, (b) 100 darcies, (c) 1000 darcies (cases 2, 1, and 3, Table 1).

Figure 2.

Dependence of ice precipitation (as fraction of pore volume) in the mushy layer on basal heat flux for (a) 30 mW/m2, (b) 40 mW/m2, and (c) 60 mW/m2 (cases 6, 1 and 7, Table 1).

Figure 3.

Dependence of ice precipitation (as fraction of pore volume) in the mushy layer on surface temperature Tsurf versus eutectic temperature Teu, for TsurfTeu = (a) −2°C, (b) 0°C, (c) +2°C, (d) +2 and Ci = 20wt.% (cases 9, 1, 10, and 8 in Table 1).

Figure 4.

Dependence of ice precipitation (as fraction of pore volume) and mushy layer thickness on initial pore water salt concentrations (mass fractions) of (a) 5%, (b) 10%, (c) 20%, (d) 25%, (e) 29% (cases in 12, 11, 5, 4 and 1, Table 1).

Figure 5.

(a–f) Profiles of horizontally averaged temperature T, aqueous salt concentration C, precipitated salt concentration S, and ice pore fraction, versus depth, after steady state conditions are established, for selected 2-D simulation cases as listed in Table 1, cases 1, 3, 5, 6, 7 and 11, respectively.

[20] Figures 1a–1c summarize the effect of soil permeability on ice distribution (cases 2, 1, and 3, Table 1, respectively). For the lowest permeability, 10 darcies, convection does not occur (Figure 1a). The subsurface pore fluid is completely liquid up to within 10 m of the surface. The brine is partially frozen in the top few meters, but there is no variation in near-surface ice. For an intermediate permeability value, 100 darcies, the other parameters unchanged, convection does occur (Figure 1b). Near the cold surface, some water ice precipitates out of the brine, creating a mushy, partially frozen region. “Mushy” here means that soil pores contain a mixture of liquid brine and water ice. Flow in the mushy region is upward, turning horizontal close to the surface. A downward return flow occurs in channels, “drainage pipes,” also called chimneys, that are essentially at the eutectic concentration and are completely ice-free liquid. This contrasting structure of a mushy upwelling layer penetrated by ice-free downwelling channels is the distinctive feature of brine convection under freezing conditions. In Figure 1b, the mushy region is about 50 m deep. The pore ice in the mushy layer precipitates out to about the 25% pore volume level. Near surface ice shows little variation. Convective cells are roughly 40–60 m wide. Down-welling (ice-free) regions are relatively wide. For the high permeability case, 1000 darcies (other parameters unchanged), convection is much more vigorous. As seen in Figure 1c, the mushy layer is less than 20 m thick, and narrow downwelling ice-free chimneys occur at about 20 m intervals. Peak soil ice fractions reach up to about 60% of pore volume in mushy upwelling regions. Ice lenses, then, are present within a few meters of the surface and are roughly 15–20 m wide. Permeability controls the thickness of the mushy layer and the width of convective cells, as well as peak ice concentrations. Permeability values given in Table 1 correspond to fully water-saturated, ice-free conditions; effective permeabilities can be considerably less.

[21] Worster and Wettlaufer [1997] carried out a linear stability analysis of “mushy convection” and found that a simple scaling analysis matched much of their experimental data:

display math(5)

where hc is the mushy layer thickness, ΔC is salt concentration difference in the system, fi is the ice fraction in the mushy region, and k(fi) is effective permeability of the mushy layer. As permeability k increases, mushy layer thickness will decrease. Further, as ΔC decreases, hc will increase. However, in our simulations of very cold soil, when steady state is reached, ΔC is small and similar for almost all cases—salt concentrations have to be close to eutectic for brines to remain liquid. In effect, then, mushy layer thickness is controlled primarily by the effective mushy layer permeability. These behaviors are seen in our simulations—the mushy layer in Figure 1c, the high permeability case, is much thinner than in Figure 1b, in agreement with equation ((5)). Furthermore, the analysis presented in Wells et al. [2011] finds that mushy layer convective cell width is closely related to mushy layer depth, ranging from 1 to 1.5 times depth, as salt concentration increases. Our simulations agree with that result.

[22] Figures 2a–2c summarize the effect of varying geothermal heat flux (cases 6, 1, and 7, Table 1). (Comparison of horizontally averaged profiles versus depth for these cases as seen in Figures 5d, 5a, 5e, respectively, is helpful to understand the differences in Figures 2a–2c.) Three flux values are considered—30, 40, and 60 mW/m2. Convection occurs in each case. For a relatively low basal heat flux of 30 mW/m2 (Figure 1a), convective cells in the mushy layer are roughly 30 m wide, the mushy layer extends to almost 100 m deep, and peak ice fraction in the mushy layer is about 22% (although ice fraction in the surface boundary layer reaches about 45%). For the 40 mW/m2 case, the mushy layer extends down to about 90 m, downwellings are broad and spaced at roughly 60 m, peak ice saturation away from the surface is about 18%. For the 60 mW/m2 case, the mushy layer is about 60 m thick, downwellings are narrower and about 30 m apart. Peak ice saturation reaches 45% at the surface and about 23% in the interior of the mushy layer. In all of the cases, ice variations are buried 10 m or more below the surface; at the surface, ice content is essentially uniform. The dependence on heat flux is not strong across these simulations. For this range of basal heat fluxes, the mushy layer average temperature increases and its thickness decreases as one would expect with increasing heat flux (easier to see in Figure 5), but the distribution of ice is somewhat different from case to case, perhaps reflecting the variable evolution of a nonlinear system from random initial conditions. There are competing effects; as heat flux increases, average temperature of the mushy layer increases, total ice may decrease, but salt concentration difference across the layer can increase, increasing average fluid viscosity.

[23] Surface temperature vis a vis the salt's eutectic temperature is an important parameter. If average surface temperature is colder than the eutectic, the near surface will be frozen, and the liquid region and convection will be restricted to depths below the point at which soil temperature reaches the eutectic, as seen in Figure 3a (from case 9, Table 1). When the average surface temperature equals the eutectic temperature, the typical pattern of a mushy layer near the surface forms (Figure 3b—from case 1, Table 1). When surface temperature exceeds the eutectic, a mushy layer still forms (Figure 3c—from case 10, Table 1) near the surface, with ice lenses, and chimneys, but it is thinner as expected because the average temperature of the mushy layer is higher. Furthermore, there is no surface boundary layer of elevated ice formation. Brine remains liquid even at the surface. In our simulations, surface temperature is maintained at an average value. Seasonal and daily oscillations in surface temperature should allow a brine system to be liquid at the surface for part of the year or part of a day if the average Tsurf is at or above the salt eutectic temperature. The amount of salt in soil pore water is uncertain. In all of the simulations up to this point, initial pore water salt concentration has been assumed to be near the eutectic value. If it is reduced, as in Figure 3d (from case 8, Table 1), the ice distribution can change markedly. Much higher ice contents can develop in the mushy layer near the surface.

[24] Dramatic changes in patterns in soil pore ice fraction distribution occur when the initial pore water salt concentration is varied from a low of 5 to 29 wt.%. When the initial salt concentration is high, the mushy layer is characterized by broad upwellings, narrower ice-free downwellings, low peak ice content, and wide convective cells—about 60 m wide, 60 m deep, and little variation at the surface (Figure 4e—from case 1, Table 1). As initial salt concentration drops, more ice must precipitate in the mushy layer to achieve a eutectic concentration in downwellings, and downwellings constrict to narrow chimneys. Initial salt concentration of 25% (Figure 4d—from case 4, Table 1) already results in a thicker mushy layer (75 m), and a spacing between downwelling chimneys of about 50 m, and peak ice concentrations up to 80%, although ice content is roughly 40%–60% throughout most of the mushy layer. As initial salt content decreases to 20 wt.% (case 5, Table 1), the mushy layer thickness increases to about 125 m, peak ice content reaches over 90%, and shorter chimneys are beginning to appear near the surface in addition to the deeply penetrating chimneys (Figure 4c). At 10 wt.% initial salt concentration (case 11, Table 1), the mushy layer reaches all the way to the bottom of the domain. Ice content is about 80%–90% of pore volume throughout the domain, and about 80% in the shallowest few meters. A couple of deeply penetrating down-flow chimneys are seen in Figure 4b. These chimneys can take tortuous paths. Near the surface, in the shallowest few meters, more closely spaced, short chimneys form; a multiscale structure is developing. Finally, at the lowest initial salt concentration considered, 5 wt.% (case 12, Table 1), a cascade of down-flow chimneys develop (Figure 4a), shorter near the surface, feeding into longer chimneys as depth increases. Chimney spacing is irregular, but roughly 20 m near the surface, increasing to about 100 m in the lowest part of the domain. These results, although complex in structure, still follow the scaling relation in eqn. ((5)). As initial salt concentration drops, more ice must precipitate out to achieve the near-eutectic salt concentrations needed to keep brines from freezing. Higher ice concentrations mean lower effective permeability and thicker mushy layers, according to equation ((5)); this effect is what all the panels in Figure 4 show.

[25] The “drain pipes”—chimneys—range from a few meters to 10s of meters in diameter and are spaced at intervals ranging anywhere from 10 to 60 m or more, depending on the parameter set. The depth of the mushy zone down from the surface varies from as little as 15 m to over 100 m, depending on the choice of parameter values. The temperature difference between the surface and the bottom of the brine aquifer, at 200 m depth, is generally only 1 to 5°C; the brine systems are very cold, averaging around −48°C to −50°C, nonetheless, they can convect. The “drainage pipes” reflect a nonuniform pattern of ice in the top few meters below the surface; there are icy lenses embedded in the mushy brine zone. There are also salt precipitate inclusions in the water ice. Because of the salt concentration, the lower part of the system remains liquid. In the partially frozen region, the pore ice saturation can range from about 20% of pore volume, to over 90%, in a patchy spatial pattern, depending on the parameter set. These ice pore saturations correspond to roughly 3% to as high as 14% H2O content of bulk soil. Our simulations use a single salt; inclusion of several salts should result in a vertical stratification of salt precipitates due to their different eutectic points. The details of the very near surface partitioning between ice and brines will depend on the eutectic temperature of the dominant salts compared to the average surface temperature, but as noted earlier, there are salts on Mars that have very low eutectic points. In our simulations, considerable salt can precipitate out in the surface ice layer. If the lens ice evaporates over time, significant high-porosity salt deposits will be left behind. This effect has been seen in neutron data at latitudes between 60° and 75° in both hemispheres [Feldman et al., 2008].

[26] Figures 5a–5f contain profiles of horizontally averaged temperature, pore ice fraction, salt concentration in pore liquid and precipitated salt versus depth after steady state has developed for a few selected 2-D cases. Temperature is close to linear in most of the cases, dropping from −47°C to −50°C at the base, depending on the parameter set used, to the surface temperature. Salt precipitates out invariably in the shallowest 5 to 10 m, and the average precipitated salt concentration is very roughly 0.1 kg/m3 of soil. Peak precipitated salt ranges from 0.05 to 0.4 kg/m3 at the surface, depending on the parameter case. A few cases have no precipitated salt. Liquid salt concentration is virtually at the eutectic in all cases, regardless of the initial concentration. Ice content varies greatly from case to case but is present up to the surface in almost all cases.

2.9 3-D Simulations

[27] Two 3-D geometry simulations have also been made. One case (I-3D-A = case 3, Table 1) includes high initial pore water salt concentration, 29 wt.%, close to the eutectic value, heat flux is 40 mW/m2, and soil permeability is 1000 darcies. The second case (I-3D-B = case 12, Table 1) starts with much lower pore water salt concentration, only 5 wt.%, and has a lower soil permeability, 100 darcies. The briny upwellings and downwellings in I-3D-A take on polygonal patterns (Figure 6) that are very roughly 30–50 m in diameter for a 200 m deep aquifer. Downward flow occurs along the edges of the polygons, with down-flow pinching out into chimneys frequently. Figure 6 plots ice fraction isosurfaces for 20% and 50% fractions of soil pore space occupied by ice. The 50% isosurfaces are in the upwelling regions and lie in the top 20 m of soil, just as in the corresponding 2-D case (see Figure 4a). The 20% isosurface is restricted to and defines the down-flow, along the polygon margins. There is a distribution of polygon sizes and more variability in polygon size in the 3-D case versus the 2-D case.

Figure 6.

Distribution of subsurface ice as percentage of pore volume from the 3-D simulation of case 3. Shown are isosurfaces of pore ice at 20% and 50% of pore volume. Near-surface ice lenses are clearly seen. The mushy layer is about 20 m thick. Domain is 200 m × 200 m × 200 m. Note: Surface of domain is at 200 m on vertical scale; base of aquifer at 0 m.

[28] The second case, I-3D-B, shows a very different ice distribution. Figure 7 plots isosurfaces of pore ice fraction for 40%, 60%, and 94%. The ice distribution is characterized by many narrow, ice-free, down-flow chimneys. The initial pore water salt concentration is only 5%, spread uniformly. A dilute 5 wt.%. brine would be frozen if no flow occurred. As seen in Figure 7, flow can occur, and the flow ends up concentrating salt up to the eutectic in the narrow down-flow chimneys. Even though the ice fraction is over 90% for most of the depth of the domain in the mushy region outside the chimneys, there is still flow.

Figure 7.

Distribution of subsurface ice as percentage of pore volume from the 3-D simulation having an initially low pore water salt concentration of 5 wt.%, with q = 40 mW/m2, permeability k = 100 darcies, Tsurf = −52°C, at 2500 years (case 12, Table 1). Isosurfaces correspond to ice at 40%, 60%, and 94% of pore volume. Domain is 200 m × 200 m × 200 m. Note: Surface of domain is at 200 m on vertical scale; base of aquifer at 0 m.

2.10 Surface Deformation

[29] Freezing of water results in a volume change, which in turn, leads to either heaving of soil (upon freezing) or slumping (due to melting of ice). We have estimated the surface deformation, that is, spatial distribution of elevation change, due to the spatial pattern of subsurface ice formation in our model simulations, by integrating volume change over depth, that is,

display math(6)

where Δz is the local surface elevation (compared to an unfrozen soil), i(x, z) is the local ice fraction, ε(x, z) is local porosity, ρi and ρw are ice and water densities. Figures 8a–8d display plots of surface elevation change (relative to the average elevation change) versus horizontal location for selected 2-D cases, and Figures 9 and 10 are plots of surface elevation versus horizontal location for the two 3-D simulations. In some cases, substantial average uplift of the soil occurs on freezing, as much as 6 m in one case. Generally, the average uplift is in the 0.5–2 m range, with variations in topography superimposed. A general result is that margins and troughs are typically deeper than mounds are high. Mounds overlie ice lenses in the upwelling regions, while troughs overlie downwellings that are ice-poor. The elevation difference between mound height and the surrounding trench depression ranges from roughly 0.35 to 1.50 m. The size of polygons at the surface is roughly 20 m, but some cases show wider spacing, up to 50–60 m, as well as a few smaller ones. The two 3-D simulations exhibit a strong contrast in surface deformation. Figure 9, the case of high initial pore water salt concentration (29wt.%.), shows a polygonal pattern of mounds and trenches, while the initially low pore water salt concentration (5wt.%.) case is very different (Figure 10), yielding a field of surface pits that are a few meters in diameter, with depths that vary from fractions of a meter, to several meters. The polygonal patterns seen in Figure 9 are similar to (but larger than) those shown for example in Figure 1a of Smith et al. [2009].

Figure 8.

(a–d) Surface displacement, relative to average displacement, for selected 2-D simulations (cases 1, 3, 7, and 11, respectively, in Table 1), due to variations in subsurface ice distribution.

Figure 9.

Surface displacement (SrfDis), relative to average displacement, due to subsurface freezing for the 3-D simulation (case 3, Table 1), having a high initial aqueous salt concentration, after 2500 years. Troughs are deeper than mounds are high with maximum elevation difference between high and low of about 0.5 m.

Figure 10.

Surface displacement (SrfDis) relative to average displacement, due to subsurface freezing, for the 3-D simulation having low initial aqueous salt (case 12, Table 1), after 2500 years. The small, deep pits overlie downwelling chimneys.

3 Conclusion

[30] Given the likely highly permeable nature of the Martian regolith, the presence of salts that can strongly depress freezing points and form a compositional gradient, and sufficient heating of geothermal or magmatic origin, the possibility exists for convective fluid transport in the Martian soils. Our limited parameter study indicates that brine convection is robust over a wide range of conditions, and could bring ice and salt to the Martian surface. We have shown through numerical simulations that ice lenses and briny fluids can be sustained in the very near surface of Mars due to hydrothermal/compositional convection of brines. Our model uses reasonable values of the primary variables—soil permeability, pore water salt concentration, surface temperature, and heat flux. Upwelling brine plumes in a cold aquifer precipitate their water as ice near the surface, forming deposits of nearly pure lenses of water ice along with eutectic brine fluid. The remainder of the brine returns within ice-free drainage channels to the subsurface water table. Even initially low salt concentration in soil can end up supporting a briny convection. If the system dies out due to a colder climate, the remnant remains would be patterned (perhaps somewhat irregularly patterned) ice (and salt precipitate) deposits near the surface. The H2O content for the various cases ranges from 3 to about 14 wt.%, covering the range of values seen in MONS data analyses [Maurice et al., 2011; Feldman et al., 2011] at low to midlatitudes. Electrical conductivity of briny fluid is much higher than that of dry rock; presence of brines should consequently be detectable in the Martian subsurface, even to depths of several hundred meters [Grimm, 2002]. Volume changes associated with freezing out of ice from the brines translate to heaving or slumping of the surface, producing microtopography reflecting the up-welling and downwelling convective patterns, likely leading to displacement of surface rocks and small boulders toward the low points, generally over the downwellings. Local elevation differences on the order of a meter or more could be expected. Repeated cycles of climatic warming and cooling would lead to cycles of convection and surface heaving, contributing to cryoturbation and possibly formation of features such as stone circles that involve movement of surface rocks and small boulders.

Acknowledgments

[31] This work was supported in part by LANL, NASA, and the CESR of France and conducted under the auspices of the Los Alamos National Laboratory, and the Planetary Science Institute. One of us (WCF) also wishes to thank the Los Alamos National Laboratory for providing office space and access to their library and the Internet while spending summers in Los Alamos.

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