Journal of Geophysical Research: Earth Surface

Sublimation and ice condensation in hyperarid soils: Modeling results using field data from Victoria Valley, Antarctica

Authors


Abstract

[1] Most soils of the Dry Valleys of Antarctica are ice-cemented within a few decimeters of the ground surface despite the hyperarid conditions. This fact brings into question current sublimation models since they indicate that water vapor in soils is being lost at rates that would rid them of ice to at least several meters in less than a few thousand years, and yet most ice-rich soils in the Dry Valleys are much older. In this paper, we explore mechanisms that slow or may reverse ice loss from the soil to the atmosphere and incorporate them into a sublimation model that uses high-resolution climate and soil temperature data from 2002 to 2005 in Victoria Valley, where the surface is ∼10 ka old and the soil is ice-cemented 0.22 m below the surface. According to this model, ice currently sublimates 0.22 mm a−1, which corresponds to a descent of the ice cement boundary of ∼1.2 mm a−1. Water vapor condenses in the upper dry soil during the winter but is lost completely to the atmosphere during the austral summer. Some water vapor diffuses downward into the frozen soil, condensing at rates of 0.02–0.09 mm a−1. Snow cover in the summer temporarily reverses the vapor transport and reduces the annual ice loss. Hence while snow slows long-term sublimation, the dearth of data on the duration and timing of snow cover prevent us from quantifying this effect and from assessing the potential of snowmelt to offset water loss from the soil.

1. Introduction

[2] Subsurface ice is pervasive in the extremely cold and hyperarid Dry Valleys, Antarctica. Ice-rich permafrost is found to depths of at least 320 m in cores from Taylor Valley collected during the Dry Valley Drilling Project (DVDP) [Stuiver et al., 1981]. In a compilation of soil characteristics from 473 sites in the Dry Valleys, Bockheim [2002] noted that 36% of the soils contain ice, predominantly at coastal sites and in the proximity of the ice cap. Pore ice contents range between 5 and 35 wt% down to at least 9.5 m for Sirius Group sediments on Table Mountain [Dickinson and Rosen, 2003]. Subsurface ice is paramount in controlling the geomorphologic development of the region, for example, the development of contraction cracks that leads to polygonal patterned ground and to analogous features on Mars [e.g., Sletten et al., 2003]. The longevity of ground ice is also relevant to efforts to determine the age of buried glacial ice, which remains elusive. In Beacon Valley, Antarctica, for example, suggested ages range from several hundred ka based on cosmogenic nuclide data of the overburden [Ng et al., 2005] to 8 Ma based on a superimposed ash deposit [Sugden et al., 1995]. Factors controlling the long-term stability of subsurface ice are of interest not only to terrestrial but also to planetary scientists. Notably, the longevity of subsurface ice on Mars bears directly on the broad question of whether much of the planet was inundated; the frozen remnant of such an event may long persist below the Martian surface [Baker, 2001; Seibert and Kargel, 2001].

[3] Models of ice sublimation and vapor transport in Dry Valley soils suggest that over seasonal cycles H2O is lost from the soils to the atmosphere. Computed sublimation rates through a 0.2- to 0.4-m-thick dry soil layer are of the order of 1 mm a−1 for massive buried ice in Beacon Valley (1250 m elevation) [van der Wateren and Hindmarsh, 1995; Hindmarsh et al., 1998; Schorghofer, 2005] and for ground ice in Linnaeus Terrace (1550–1700 m elevation) [McKay et al., 1998]. Thus, according to sublimation models, no shallow ground ice should be present even under a young surface in the Dry Valleys. For example, taking an age of 10 ka (e.g., Victoria Valley; Kelly et al. [2002]), ice content of ∼10%, and sublimation rate of ∼1 mm a−1, the top tens of meters of the soil should be free of ice. Contrary to this, ice is often 5 to 40 cm beneath the surface. This shallow depth of ice is more consistent with data on cosmogenically-produced 10Be measured in ice and quartz grains from a 7-m core of buried glacial ice taken in Beacon Valley that imply a sublimation rate of 3.7 × 10−2 mm a−1 [Stone et al., 2000]. In view of the existing controversy about age and stability of ground ice [Hindmarsh et al., 1998; Ng et al., 2005] and its implication for past and modern climate conditions both on Earth and Mars, it is important to understand more completely the persistence of ground ice in cold, dry areas. Such improved understanding bears on two major research areas: (1) the age and stability of ground ice and its implication for past and modern climate conditions on Earth, and (2) the age of ice occurring directly below much of the Martian surfaces and its implications for water in its history [Boynton et al., 2002; Mellon et al., 2004].

[4] The near ubiquity of ground ice close to the surface suggests that current models of sublimation are incomplete. Notably, they lack mechanisms to recharge the ground ice or greatly slow the net loss of ice from the subsurface to the atmosphere. Schorghofer [2005] modeled ice sublimation for Beacon Valley constrained by climate data and found rates comparable to those McKay et al. [1998] modeled for Linnaeus Terrace. He suggests that a decrease in annual air temperature by 5°C would halt sublimation, this amount of cooling would also lead to an increase of relative humidity (RH) of ∼20%. According to the climate record found in the Vostok ice core, cooling of this magnitude last occurred ∼15 ka ago [Petit et al., 1999]; therefore, this climate scenario is unlikely to have affected the current state of ice cement in Victoria Valley soils. Furthermore, all models indicate that ground ice would have sublimated to several meters depth since this time. Other plausible mechanisms to reduce net sublimation include recharging of ice by infiltration of snowmelt, slowing sublimation by covering the ground with snow, or lowering the chemical activity of water with salts, which are abundant in Dry Valley soils. Hindmarsh et al. [1998] evaluated the effect on sublimation when vapor pressure in the glacial till overlying the Beacon ice is saturated and pointed out that such a situation could be caused by snow cover. He found that snow cover leads to slow icing of soil pores, forming pore ice above the buried glacial ice. Unfortunately, explicit incorporation of these processes in mass balance models of subsurface ice is not currently possible because of the lack of information about the timing and amount of snowfall and snowmelt water and the challenge of adequately modeling the effect of salt on H2O transport in soils at sub-zero temperatures. Herein, we report progress toward a realistic mass balance model through a case study of ice-cemented soils in the McMurdo Dry Valleys, Antarctica. The study site in Victoria Valley is at an elevation of 450 m, lower and closer to the sea than previous sublimation study sites in the region. We measured hourly climate parameters (relative humidity, air temperature, wind speed, and wind direction) along with soil temperature at 11 depths to 1.1 m below the ground surface to model vapor diffusion and sublimation rates. Our model accounts for water vapor transport and condensation in both the upper ice-free soil and the underlying porous ice-cemented soil. In addition, we explore the effects of winter and summer snow cover on the mass balance of ground ice, and we discuss the effects of infiltrating snowmelt water and changes in local microclimate on ground ice stability.

2. Site Description and Methods

2.1. Site Description and Soil Characteristics

[5] Victoria Valley is one of the Dry Valleys, Antarctica, at approximately 450 m elevation. Based on sedimentologic and geomorphic evidence and on 14C-dates of lake-algae, Kelly et al. [2002] suggested that the former Lake Victoria covered the entire valley 10–12 ka ago. The study site is characterized by distinct polygonal patterned ground [Sletten et al., 2003]. The smooth, gently sloping surface, stratification, and well-sorted sands (d50: 357–510 μm) suggest that the sediments are alluvial deposits. The soils have a desert pavement and are slightly salt-cemented in the upper 5–10 cm. The upper boundary of ice cement in the soil ranges from 0.20 to 0.40 m. At the study site, the boundary between dry soil and ice-cemented soil is at 0.22 m with ice content of 6 wt% at the ice boundary increasing to 13.5 wt% at 1.6 m depth.

2.2. Sample Collection and Methods

[6] Soil samples were collected incrementally to a depth of 1.6 m during the austral summer of 2001–2002 using a gas-powered auger drill. Samples were stored in tightly sealed plastic bags below −20°C until they were processed. Equivalent water contents of soils were determined gravimetrically after drying at 60°C for 72 hours. Grain size distribution was measured on 1-g samples of dry soils using a laser diffraction particle size analyzer (Beckman–Coulter LS 13-320). The bulk and intrinsic densities were determined, respectively, by weight of dry soil that was gently packed into a 10-cm3 volume and by the pycnometer method with water as the fluid. The field climate data were recorded using a Campbell CR10X data logger. The air temperature and relative humidity (RH) were measured every 10 s (Vaisala HMP45C probe) and were averaged hourly. Since the HMP45C does not measure temperatures below −40°C, the internal logger temperature is reported under colder conditions. The HMP45C probe reports humidity relative to liquid water; therefore, RH values recorded at sub-zero temperatures have been converted to RH values with respect to ice using Lowe's [1977] equations for saturated vapor pressure, which are given in Appendix A. The published error for the HMP45C temperature is ±0.2°C at 20°C and increases linearly to ±0.4°C at −40°C. The accuracy of RH probe at 20°C is ±2% RH between 0% and 90% relative humidity and ±3% between 90% and 100% relative humidity. In addition, the temperature dependence of relative humidity accuracy is ±0.05% RH/°C.

3. Results and Discussion

3.1. Climate Records and Soil Temperature

[7] Figure 1 summarizes the climate record from January 2002 to January 2005. The air temperature averaged −24.4°C; it reached a maximum of 10°C on 12 January 2002 and minimum of −51°C on 12 August 2002. The wind speed in Victoria Valley averaged 5 m s−1 and reached a maximum on 17 September 2003 of 64 m s−1. The prevailing wind direction is WSW (260°). In addition to the prominent seasonal temperature variations, on multiple occasions during the winter the air suddenly warms several tens of degrees Celsius, the relative humidity drops, and wind speeds increase with the prevailing wind direction being WSW (240°). These events are due to warm katabatic winds (föhn) and are characteristic for the Dry Valleys [Schwertfeger, 1984] and elsewhere in Antarctica [Breckenbridge et al., 1994; Bromwich et al., 1994; Carrasco and Bromwich, 1994; Wendler et al., 1994; Doran et al., 2002; Nylen et al., 2004]. The average wind speed during these periods is 40 m s−1; the fastest winds are recorded during such events. Compared with climate recorded between 1995 and 2000 at nearby Lake Vida, ∼8 km down valley and ∼150 m lower elevation, the average annual air temperature at the study site is several degrees higher, and the average and maximum wind speeds are higher while relative humidity is lower, presumably due to more frequent katabatic winds [Doran et al., 2002]. Nylen et al. [2004] estimated that the frequency of katabatic winds increased by 14% every 10 km up valley toward the ice sheet, which is consistent with the differences in air temperature and wind speed between the study site and Lake Vida. In addition, Doran et al. [2002] suggested that the frequency of katabatic winds at Lake Vida is relatively low due to the formation of a cold air cell that prevents katabatic winds from reaching the valley floor at this location.

Figure 1.

Hourly record of (a) relative humidity (blue line) and air temperature (red line), (b) wind speed, (c) wind direction, and (d) soil temperature at various depths from January 2002 to January 2005. Sudden warming events (katabatics or föhns) punctuate the dark winter months and warm the soil to a depth of 1.06 m. From October to February, the soil temperature decreases with depth; during the rest of the year, the upper soil is colder than lower soil. The horizontal dashed white line marks the boundary between dry and ice-cemented soil; the solid white line delineates the 0°C isotherm during the summer.

[8] The soil at the study site is dry to a depth of 0.22 m; below this depth it is ice-cemented with the fraction of pore space occupied by ice increasing with depth. The average soil temperature from 2002 to 2005 was −23°C down to 1.1 m depth, about 1–1.6°C higher than the average air temperature (Table 1). The soil averages 0.6°C above zero during the summer months to the depth of the ice-cemented boundary, which is near the base of the active layer, the maximum depth to which the temperature rises above 0°C (Figure 1). The soil temperature gradient is one important parameter that defines the direction of vapor flux. The soil cools with depth during the summer, and when solar radiation is absent during winter, the soil is colder at the surface and the temperature gradient reverses (Figure 1). However, föhn during the winter can warm the soil considerably to a depth of 1.1 m and temporarily invert the temperature gradient. These large soil temperature fluctuations in the winter dwarf those noted in the Arctic due to thick snow cover there [Roth and Boike, 2001].

Table 1. Annual Average, Minimum, and Maximum Values of Relative Humidity (RH), Air Temperature (T-Air), Soil Temperatures, and Frost Points (Tf) From Hourly Data From 2002 to 2005
 2002200320042002–2005
AveMaxMinAveMaxMinAveMaxMinAveTf air
RH%67.11007.764.410023.562.01006.764.9 
T-Air°C−26.710.1−51.3−23.28.2−49.9−24.47.0−50.2−24.7−23.4
Soil probeDepth mSoil temperature (°C)Tf soil
MRC-10.0−25.524.9−58.0−21.327.3−55.8−22.831.5−61.4−23.1
MRC-2−0.08−25.512.9−52.6−22.113.0−50.7−23.413.9−55.3−23.6
MRC-3−0.15−25.25.6−47.6−22.24.9−45.9−23.25.8−48.9−23.5
MRC-4−0.23−24.70.4−42.8−22.2−0.6−41.4−22.90.6−43.7−23.3−16.5
MRC-5−0.31−24.5−2.9−39.3−22.3−5.1−38.2−22.8−3.4−40.0−23.2−17.9
MRC-6−0.38−24.4−4.1−38.4−22.3−6.2−37.2−22.8−4.7−39.0−23.1−18.3
MRC-7−0.46−24.4−5.0−37.6−22.4−7.1−36.7−22.9−5.6−38.3−23.2−18.7
MRC-8−0.61−24.2−5.7−36.8−22.4−7.9−35.8−22.8−6.3−37.5−23.1−18.9
MRC-9−0.76−24.2−6.5−36.3−22.5−8.8−35.4−22.8−7.0−36.9−23.1−19.3
MRC-10−0.91−24.1−7.2−35.8−22.6−9.5−34.9−22.8−7.6−36.4−23.2−19.6
MRC-11−1.07−24.0−7.9−35.2−22.6−9.9−34.4−22.8−8.1−35.7−23.1−19.7

3.2. Vapor Transport and Annual Sublimation Rate

[9] To determine the ice mass balance in ice-cemented soil under current atmospheric conditions, we modified the vapor diffusion model described by McKay et al. [1998]. In this model, diffusion of water vapor in the atmosphere–soil–ice system is driven by water vapor density gradients (molecules m−3); water vapor diffuses toward regions of lower vapor density. The water vapor density is calculated from the water vapor pressure using the ideal gas law (see Appendix A). According to the Clausius–Clapeyron equation, the vapor pressure in equilibrium with water/ice (the saturated vapor pressure) increases exponentially with temperature. The temperature that water vapor condenses to water or ice at a given vapor density is the dew or frost point, respectively. It follows that the frost/dew point decreases with increasing vapor density. Based on the measured average annual relative humidity of air in the observed system, the atmosphere has an annual average frost point of −23.4°C, which is close to average annual soil temperature (Table 1). The frost point at the ice boundary calculated from the annual average saturated vapor density over ice is −16.5°C. The frost point in the air is lower than at the ice cement boundary because of the low annual average humidity in air (65%), suggesting that the overall annual vapor flux will be toward the atmosphere. These frost points for the ice-cemented soil boundary and air are warmer as those found by McKay et al. [1998] at Linnaeus Terrace (−21.7°C and −27.1°C, respectively) even though the annual average soil and air temperatures are similar. The warmer frost point at the ice cement soil boundary reflects the larger annual soil temperature amplitude (−43.7°C to 0.6°C) and a different seasonal temperature distribution in Victoria Valley compared to Linnaeus Terrace (−38.0°C to −6.8°C), thereby affecting the average saturated vapor density and frost point. The lower atmospheric frost point at Linnaeus Terrace is consistent with a lower moisture content (RH 50%) and air temperature amplitude (−42.6°C to −3.8°C) compared with Victoria Valley (−51.3°C to 10.1°C). Ground ice should be stable at the depth where the average annual frost point converges to the average annual soil temperature (−23.2°C; Table 1); extrapolating the decreasing seasonal amplitude in soil temperature with depth and neglecting geothermal gradient, this soil temperature would be reached at ∼35 m.

[10] Vapor transport can be described by an advection diffusion model (ADM) or a dusty-gas model (DGM). The ADM combines advective flow driven by gradients in air pressure calculated using Darcy's law and Fickian diffusion due to density gradients of water vapor.

[11] Darcy's law gives the flux ν (m s−1) of air by

equation image

where k is the gas permeability (m2), μ is the air viscosity (Pa s−1), p is the pressure (Pa), and z is the depth (m). Diffusive transport can be described by Fick's first law:

equation image

where F is the flux of vapor, nv is the water vapor density (molecules m−3 air), and Dv is the diffusion coefficient of water vapor in free air (m2 s−1) multiplied by ɛ/τ to account for the cross-sectional area of diffusion (ɛ = porosity) and for the length of the diffusion pathway (τ = tortuosity). The porosity is calculated from intrinsic density of the soil particles and bulk density of the soil (see Table 2). Several theoretical and experimental models exist to estimate tortuosity from gas content or porosity [Penman, 1940a, 1940b; Millington and Quirk, 1961; Abu-El-Sha'r and Abriola, 1997] and they give an average value of 3 for the observed soil porosity of 0.37. The diffusion coefficient for water vapor in free air at the given soil temperatures is calculated from an empirical relation [Geiger and Poirer, 1973]:

equation image

Here Tav is the spatial average temperature (K) for each soil layer; Dv ranges between 1.5 × 10−5 and 2.3 × 10−5 m2 s−1. Combining Darcy's flux with Fickian diffusion yields the mass flux of vapor through soil:

equation image

The dusty-gas model (DGM), which is based on the full Chapman Enskog kinetic theory of gases, considers soil particles as large stationary molecules. Compared to the ADM, the DGM incorporates ordinary (Fickian) diffusion, Knudsen diffusion, and advective flow as presented in detail by Cunningham and Williams [1980] and Mason and Malinauskas [1983]. Knudsen diffusion is dominated by molecule–wall interactions and therefore depends on pore size. When the pore radius is at least ∼10 times the mean free path of molecules, molecule–molecule interactions dominate and diffusion is described well by Fick's first law. If pore radius is less than a tenth of the mean free path of molecules, Knudsen diffusion dominates. Webb and Pruess [2003] compared the ADM and the DGM and found that using only Fick's law overpredicts gas diffusion negligibly (<10%) at atmospheric pressure and gas permeability >10−13 m2. Applying empirical equations given by Hazen [1911] and Massmann [1989] to the observed grain size distribution yields gas permeability between 10−8 and 10−11 m2 for soils at the study site (Table 3), suggesting that the ADM describes adequately vapor transport in these soils. Schorghofer [2005] found that vapor advection is negligible in Dry Valley soils; therefore, in this paper, vapor transport is calculated only by Fickian diffusion using equation (2).

Table 2. Characteristic Soil Parameters Used in This Paper. The Average Soil Particle Density Reflects Weathering of the Regolith
ParameterValueUnitNote
Sediment average density (ρi)2450kg m−3Measured
Soil bulk density (ρb)1730kg m−3Measured
Porosity (ε)0.37(ρi − ρb) / ρi
Tortuosity (τ)3Assumed
Specific surface area3100m2 kg−1Measured
Table 3. Soil Characteristics: Grain Size Distribution, Water Content, and Total Salt Content of Investigated Soil Profile, Victoria Valley. The Soil is Dry to 0.22 m and is Ice-Cemented Below This Depth. S, Skewness; K, Kurtosis; D10, 10% of the Sample Have Grain Diameters Less Than the Given Values
SampleDepth (m)>2 mm (%)D10 (μm)D50 (μm)<2 mm D90 (μm)SKH2O (wt%)Salt (g kgsoil−1)
Dry soil
# 10–833.883908970.57−0.3504.3
# 20.8–0.386.41913577101.523.0802.1
 
Ice-cemented soil
Vic 10.22–0.4212.51684309701.422.426.00.93
Vic 20.42–0.6224.215447210791.201.556.11.3
Vic 30.62–0.8213.912351012871.010.557.01.3
Vic 40.82–1.0213.154.740310071.261.7011.70.79
Vic 51.02–1.2218.758.14219871.322.109.50.85
Vic 61.22–1.428.469.93718571.462.8913.50.60
Vic 71.42–1.6216.11153757771.242.4213.00.75

[12] In the soil under study, water is present as ice, water adsorbed on particle surfaces, water vapor, and transient pore water in summer. The vapor density at depth changes as a function of the divergence in the water vapor flux; following mass conservation the change can be expressed as [Mellon and Jakosky, 1993; Hindmarsh et al., 1998; Schorghofer and Aharonson, 2005]:

equation image

where θ is the amount of condensed water (molecules msoil−3) and σ is the amount of adsorbed water (molecules msoil−3).

[13] A finite difference approach is used to solve equations (2) and (5) to determine vapor flux between ice-cemented soil and atmosphere. The initial conditions assume a uniform vapor density gradient between the ice cement boundary and the air above the soil. For this, vapor density at the ice boundary is calculated from soil temperatures, assuming saturated vapor densities, and at the ground surface the vapor density in the air is calculated from the air temperature and relative humidity. The boundary values are given by the measured vapor density in atmosphere and saturated vapor density in ice-cemented soil. In dry soil, condensation of water vapor occurs when temperature drops to the frost point at the calculated water vapor density (nv > nv,saturation). It is assumed that water density equals the saturated vapor density for the measured soil temperature as long as the condensate is present. In such situations, vapor density depends on soil temperature and divergence of flux can lead to formation of ice in dry soil [Hindmarsh et al., 1998]. If ice is present in soil, the porosity (ɛice) is calculated as the difference between the intrinsic porosity of the soil (Table 3) and volumetric ice content:

equation image

where Av is the Avogadro number, mw is the mass of water molecule, and ρice is the density of ice (917 and 920 kg m−3 at 0°C and −20°C, respectively).

[14] The amount of adsorbed water is usually much larger than the amount of water vapor and can have a large effect on the mass balance in the soil over the short term. The adsorbed water may change vapor density gradients in dry soil, which can influence the seasonal pattern of vapor fluxes [Schorghofer and Aharonson, 2005]. Over the long term, however, adsorption would not affect the mass balance because the amount of water stored in the adsorbed phase is not expected to change from year to year for periods with similar temperature and humidity, whereas the annual net flux of water to the atmosphere is larger [Schorghofer and Aharonson, 2005]. A widely used empirical equation to calculate water adsorption as a function of temperature and vapor pressure is based on the data of water adsorption on basalt powder from Fanale and Cannon [1971, 1974] and used by Zent et al. [1986] to calculate water adsorption in Martian soils:

equation image

Here Asoil is the specific surface area of soil (m2 kg−1), measured from water adsorption isotherms, γ is the 2.0847 × 10−15 (g m−2 Pa−1), Pv is the vapor pressure (Pa), δ is −2679.8 (K), and T is the soil temperature (K). However, as shown by Zent and Quinn [1997], this equation overestimates H2O adsorption under Mars-like conditions by several orders of magnitude, highlighting the necessity to determine adsorption equations for the material and environmental conditions under consideration. No such relationships have been developed for Dry Valley soils and hence instantaneous vapor transport was calculated without considering adsorption; however, the effect of adsorption based on equation (7) is discussed qualitatively.

[15] The calculated hourly vapor flux for 2002–2004 is displayed in Figure 2. Herein, we define flux as positive when vapor diffuses into the soil (gain) and negative when transport is toward the atmosphere. Vapor is lost from the upper ice boundary during most of the year and the rate of loss is highest during the austral summer from December to February. A small gain at the ice boundary is observed in October and November when the air temperature and vapor content in the air rise but the soil is still cold. During the winter, minute amounts of ice accumulate at depths of 0.15 and 0.076 m but it disappears completely when air temperature approaches 0°C. The amount of condensed vapor (ice) in the dry soil reaches a maximum of 1.4 × 10−3 mmice (Figure 2), which fills about 0.07% of pore space (ɛsoil = 0.37) in a 0.08-m-thick layer of soil, therefore having little effect on vapor diffusivity through the soil. Föhn events temporarily reduce ice formation to 0.076 m depth and increase ice formation slightly at the ice boundary. In addition, vapor diffuses from the ice boundary into the ice-cemented soil where it accumulates at rates between 0.04 and 0.07 mmice a−1 down to 0.30 m depth (Figure 2). Vapor transport is fastest from the ice boundary to 0.30 m while it is extremely slow below 0.6 m. Extrapolating the findings from the years 2002 to 2005, such rates of ice accumulation between 0.22 and 0.3 m depth would completely fill the remaining pore space (ɛice ∼0.19) within ∼50 years. This time to fill the pores is likely to be an underestimate because the gradual closure of pores and an increase in tortuosity would impede vapor transport. The water vapor transport measured over the 3 years indicates a net loss of 0.22 mm a−1 of solid ice and is accordant with the frost point distribution in the atmosphere–soil–ice system.

Figure 2.

Results of the diffusion model for 3 years starting 12 January 2002. (a) Air temperature and vapor concentration in air and at the ice boundary. (b and c) Divergence in vapor flux in dry soil and ice-cemented soil, respectively, expressed as millimeters of ice per day. Positive/negative flux indicates vapor transport directed in/out of the soil. (d) Condensation of vapor due to excess vapor accumulation expressed as mm ice. (e) Total change in ice content of ice-cemented soil over the period of this study. All calculations are made using a tortuosity of 3 and dry-soil porosity of 0.37. Note that water vapor is transported downward into ice-cemented soil thereby increasing the ice content, particularly at a depth of 0.3 m (e).

[16] Adsorption is not expected to affect the net annual sublimation, but it would impact short-term variation in the sublimation rate considerably. According to equation (7), the amount of adsorbed water exceeds the water vapor in the pore space by ∼2 orders of magnitude, thereby strongly buffering the system and reducing the formation of transient ice in dry soil during the winter.

[17] The 0.22 mm a−1 ablation rate corresponds to a recession (descent) of the ice boundary of about 0.59 mm a−1, given the porosity of 0.37 if soil was initially saturated with ice; however, it would be 1.2 mm a−1 assuming an average ice content of 10 wt% as measured in the soil. The 0.22 mm a−1 ablation rate corresponds to ice recession rates calculated for Linnaeus Terrace (0.44–0.59 mm a−1) by McKay et al. [1998] using the same diffusion model but assuming a uniform vapor pressure gradient between the ice boundary and the atmosphere at each time step. If we assume that the present depth of the ice boundary is due to sublimation only, that the climate has been stable for the recent centuries and that the soil was initially ice-saturated, this sublimation rate would imply that the Victoria Valley study site has been exposed to atmosphere for less than 400 years. This would be an upper estimate since sublimation would be faster when ice is closer to the soil surface. On the other hand, geologic evidence indicates that this site was flooded ∼10 ka ago [Kelly et al., 2002] and then froze. If the soil was ice-saturated initially, this would imply that the ice front has receded on average 0.02 mm a−1, which corresponds to an average sublimation rate of only 8 × 10−3 mmice a−1. To reduce sublimation rates by a factor of thirty as demanded to adjust the depth of ice cement to the geological age would require a tortuosity of ∼30, which has never been reported for vapor diffusion modeling in soil [Hindmarsh et al., 1998]. Therefore as McKay et al. [1998] noted, the difference between theoretical and apparent rates suggests that the vapor diffusion models are incomplete; perhaps other important processes occur that slow, offset, or even reverse the progressive loss of vapor from the soil.

[18] The summer (January, February, and December), winter (June, July, and August), and annual average air temperature, relative humidity, and soil temperature at the ice boundary are shown in Table 4, along with calculated annual sublimation rates from January 2002 to January 2005. The sublimation rate increased from 0.20 mm a−1 in 2002 to 0.22 mm a−1 in 2003 and to 0.26 mm a−1 in 2004 (Figure 2), generally following a trend of increasing summer temperature at the soil–ice boundary. Moisture concentration increases with winter air temperature but is not sufficient to offset the accompanying increase in sublimation rate due to the summer soil warming. Nylen et al. [2004] studied the effect of katabatic winds on Dry Valley climate and found that these warm winds increase winter and summer temperature by 0.8–4.2°C and 0.1–0.4°C, respectively. Furthermore, they found that a warming of +4.2°C is associated with an 8.5% decrease in relative humidity; both these factors would increase sublimation. The absolute vapor pressure in the ice-cemented soil would still be greater than the atmospheric vapor pressure assuming that the soil temperature increases as much as the air temperature. Applying the observed changes in temperature and relative humidity due to katabatic winds to the 2003 data, doubling the frequency of katabatic events would increase the sublimation rate by 10%. A lowering of air and soil temperature by 5°C without changing the absolute moisture content in the air, as modeled by Schorghofer [2005] in the case of Beacon Valley ice, would slow sublimation in Victoria Valley by 90%; however, assuming vapor concentration is constant increases the relative humidity from the current annual average of 65% to 80%.

Table 4. Annual, Summer (January, February, December), and Winter (June, July, August) Sublimation Rates, Water Contents, and Temperatures of the Air and Soil at the Ice Cement Boundary for Years Modeled in This Paper
YearAnnualSummer (JFD)Winter (JJA)
Sublimation (mm a−1)Moisture (g m−3)Tair (°C)Tice (°C)Moisture (g m−3)Tair (°C)Tice (°C)Moisture (g m−3)Tair (°C)Tice (°C)
2002−0.200.59−26.7−24.71.47−3.4−5.70.07−41.6−36.4
2003−0.220.66−23.2−22.21.66−2.9−5.20.10−39.4−34.8
2004−0.260.60−24.4−22.91.57−3.6−4.20.12−37.1−35.9

3.3. The Effect of Snow Cover on Ice Sublimation Rates

[19] To assess the potential effect of snow cover throughout the year, the vapor transport was modeled assuming an extreme scenario: continuous annual snow cover. Assuming that the air below the snow layer is saturated, the vapor density gradient in the dry soil and hence the vapor flux out of the soil is reduced. Since snow cover temperatures are not available for Victoria Valley, the saturated vapor pressure was calculated at 0°C for the periods when air and soil surface were above 0°C and at the air temperature otherwise.

[20] The saturated vapor pressure in the snow layer exceeds the vapor pressure at the ice boundary from October through the end of January and during the winter föhn events (Figure 3). This leads to a gain of ice in the soil of 0.14 mm a−1 (Figure 2). Most of this vapor is transported into the ice-cemented soil and accumulates at depths between 0.2 and 0.6 m. The small amount of vapor transported into the soil during winter föhn events is enhanced by snow cover, while during other times in the winter the presence of a snow cover has a minimal effect on vapor transport. Adsorption in the model calculation may change the results considerably because most of the water vapor supplied from snow cover would first be adsorbed by the soil and have minimal effects on the water vapor density gradient. Therefore the effect of snow cover strongly depends on the amount of adsorbed water in the soil especially if snow cover is transient.

Figure 3.

Sublimation model results assuming year-round thin isothermal snow cover with saturated water vapor pressure. (a) Air temperature and vapor concentration in snow layer and ice boundary. (b–d) The same as in Figure 2. Total gain of ice is 0.13 mm a−1, most of which accumulates below the ice cement boundary.

[21] Snowfall has not been recorded in detail for Victoria Valley; however, according to Schwertfeger [1984] the total annual snowfall in the lower Dry Valleys is between 100 and 200 mm water equivalent (weq.), and values as low as 7 mm have been reported from direct observations [Bromley, 1986]. Although the timing of snowfall is uncertain, McKay et al. [1994] observed more snow events during the summer at Battleship Promontory, Convoy Range Dry Valleys. Snow cover is likely to occur during katabatic events since strong winds transport substantial amounts of wind-blown snow [Breckenbridge et al., 1994; Carrasco and Bromwich, 1994] that can be deposited in areas of diminishing wind speed. Snow cover during both the summer and the periods of katabatic winds would enhance vapor transport into the soil; hence, incorporating snow cover in the process-based models may reduce sublimation rates substantially.

[22] Gooseff et al. [2003] investigated the effect of snow patches persisting into early summer on soil temperature and moisture regimes in Taylor Valley, Antarctica. Snow cover reduces thermal variations and increases moisture in soils. Such changes in the thermal regime of soil would also affect the saturated vapor pressure at and below the ice boundary but is not incorporated in the present calculation. If the snow cover is thick enough it could cause an overall warming of the soil beyond the times when snow is present. This would increase the saturated vapor pressure at the ice boundary and enhance sublimation. More detailed data on the amount, timing, duration, and physical characteristics of snow (e.g., temperature, density) are required to assess quantitatively the impact of episodic snow cover on the mass balance of ground ice.

3.4. Potential of Ice Recharge by Infiltrating Snowmelt Water

[23] Another mechanism to reduce or reverse the net loss of ice from the soil is recharge by snowmelt water as has been noted by McKay et al. [1998]. Friedman [1978] and McKay et al. [1994] measured meltwater events beneath rocks as a water source for cryptoendolithic microbes during the summer at Battleship Promontory. Summer solar radiation on barren ground and rocks warms the surface above 0°C and causes snow to melt. On a longer timescale, the presence of salt horizons and salt crystallization beneath stones attest to a significant amount of moisture infiltrating into the soil [Gibson, 1962]. In 2001, we observed active recharge in the form of a wetting front in Victoria Valley soils after a January snowfall. Furthermore, soil moisture (Vitel) probes installed at 0.03, 0.10, and 0.33 m below the surface adjacent to the study site documented water infiltration down to 0.10 m. Infiltration events occurred consistently about once a year between 1 December and 31 January through the study period (1998–2005). Maximum infiltration of 0.11 and 0.08 v/v water at depths of 0.03 and 0.10 m, respectively, was observed on 8 December 2002. The probe at 0.33 m depth is within the ice-cemented permafrost and did not record any liquid water. Since only approximately 0.2% of the annual snowfall is needed to balance the observed sublimation rates, rare infiltration events might be sufficient to recharge the ground ice. The high salt content lowers the freezing point of bulk water well below 0°C and may enable water percolation even if soil temperature is below 0°C. Shallow groundwater and unsaturated flow have been observed in Taylor Valley and Wright Valley, reflecting the presence of liquid water at sub-zero temperatures [Cartwright and Harris, 1981]. A thorough discussion of meltwater recharge of ice cement is beyond this paper but will be quantitatively addressed in a forthcoming paper (B. Hagedorn et al., manuscript in preparation, 2007) based on the stable isotopes of water in pore ice from this site.

4. Summary and Conclusions

[24] Water vapor transport in a soil with porous ice cement below a 0.22-m depth is calculated with an enhanced diffusion model using climate and soil temperatures recorded from 12 January 2002 to 31 December 2004. The climate data show a consistent seasonal pattern with frequent warm katabatic winds (föhn) entering Victoria Valley during the dark winter months. The calculated annual ice loss from the soil averages 0.22 mm with most sublimation occurring during the summer. Extension of the diffusion model to the ice-cemented soil reveals that water vapor diffuses downward from the ice cement boundary. Over the 3-year study period, the sublimation rate increased from 0.20 mm a−1 in 2002 to 0.26 mm a−1 in 2004, paralleling warming of the air during winter and warming at the ice-soil boundary during summer. The frost point in the atmosphere of −23.4°C is close to the average soil temperature. This suggests that ice could be stable at a depth of ∼35 m under current climate conditions if vapor diffusion is the only mechanism that controls the occurrence of ice cement.

[25] The data were collected in Victoria Valley where the soil surface age is 10 ka and the soil was likely initially flooded and ice saturated when exposed to the atmosphere; however, the modeled sublimation rate is too rapid for the pore ice to persist close to the surface after 10 ka. Hence the model appears to be incomplete. Incorporating a snow cover into the diffusion model reduces this discrepancy as snow during the summer reverses vapor transport thereby decreasing the annual sublimation rate and potentially helps account for the shallow depth of ice cement. In addition, in situ measurements of liquid soil water and direct observations of wetting fronts reveal the potential role of snowmelt in recharge. This snowmelt infiltration, together with slowing of sublimation due to snow cover, would reduce greatly the total amount of ice sublimated. A better assessment of frequency, duration, and seasonality of snow events is required to quantify the impact of snow on subsurface ice stability. It is interesting to note that analogous to the effect of snow in the Dry Valleys, frostings on Mars [Dollfus et al., 1996; Feldman et al., 2004; Bibring et al., 2005] may similarly help form or preserve ground ice there.

Appendix A

[26] I. Polynomial for calculation of saturated water pressure (es) over water/ice as a function of temperature (T, °C) [Lowe, 1977]

equation image

Water IceA6.1077999616.109177956B0.4436518520.503469897C1.428945805 × 10−21.886013408 × 10−2D2.650648471 × 10−44.176223716 × 10−4E3.031240396 × 10−65.824720280 × 10−6F2.034080948 × 10−84.838803174 × 10−8G6.136820929 × 10−111.838826904 × 10−10H0.0099980.009998

[27] II. Calculation of water vapor pressure from relative humidity

equation image

RH: relative humidity (%)

[28] III. Calculation of frost point temperature

[29] The frost point is calculated from annual average vapor density <nv(T)> by iterating temperature in Lowe's formula until <nv(T)> is reached:

equation image

[30] IV. Calculation of specific surface area from water adsorption

[31] (a) Gravimetric water content for monolayer Xm (gH2O kgsoil−1)

equation image

X is the gravimetric water content (g kgsoil−1) and h is the relative humidity (RH/100).

[32] (b) Specific surface area of soil Asoil (m2 kgsoil−1):

equation image

where mw is the mass of water molecule, Av is the Avogadro number, and AH2O is the cross-sectional area of a water molecule (10.5 × 10−20 m2).

Acknowledgments

[33] This study was supported by the National Science Foundation Grants OPP-9726139 and OPP-0124824, the German Research Foundation (DFG) Grant HA 2942/2-1, and the NASA Grant NNX06AC10G. We thank Christopher McKay for informative discussions that improved the manuscript, Ron Paetzold and Don Huffman for assistance in collecting the meteorological and soil moisture data, and Jackie Aislabie and Megan Balks for assistance in field sampling. We are grateful to Richard Hindmarsh and Norbert Schorghofer for their comprehensive and insightful reviews and to David McTigue for assistance in presenting the diffusion model.

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