PERMAFROST AND PERIGLACIAL PROCESSES
Permafrost and Periglac. Process., 23: 1 –14 (2012)
Published online 11 November 2011 in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/ppp.731
A 2D Model for Characterising First-order Variability in Sublimation of Buried
Glacier Ice, Antarctica: Assessing the Influence of Polygon Troughs, Desert
Pavements and Shallow Subsurface Salts
Douglas E. Kowalewski,1*,† David R. Marchant,1 James W. Head III2 and David W. Jackson1
1
2
Department of Earth Sciences, Boston University, Boston, MA, USA
Department of Geological Sciences, Brown University, Providence, RI, USA
ABSTRACT
To assess the role of thermal contraction-crack polygons (sublimation polygons) in modulating sublimation of
buried glacier ice in Antarctica, we applied a 2D numerical model using COMSOL Multiphysics that calculates
the rate and spatial variability of vapour diffusion through porous media. Specifically, we examined vapour
transport through Granite drift, a dry supraglacial till marked with thermal contraction-crack polygons that rests
on glacier ice reportedly ≥8-million years in age. The model results show that sublimation varies with drift
texture and surface topography. Initially, the rates are highest beneath relatively coarse-grained sand-wedge
deposits at polygon margins, creating deep, surface troughs. As troughs approach ~1-m depth, the cooler atmospheric and soil temperatures that arise from solar shielding reduce the rates of ice sublimation to levels below that
at polygon centres, preventing runaway ice loss at polygon margins. Including the effects of a salt-cemented horizon
at 10 15-cm depth (porosity 20%) and a rocky surface pavement (75% ground coverage), our modelled ice loss at
polygon centres, for example, is 0.022 mm a1, an order of magnitude lower than previous estimates (0.14 mm a1).
This finding highlights the importance of including field-based data for drift texture, topography and microclimate
variation in modelling ice sublimation. The results also suggest that stable conditions (no ice loss) at polygon centres
are possible with either a 1.9 C decrease in mean annual atmospheric temperature or a 12 per cent increase in mean
annual relative humidity. These results indicate that the preservation of buried, multi-million-year-old ice is plausible in the coldest and driest regions of Antarctica. Copyright © 2011 John Wiley & Sons, Ltd.
Supporting information may be found in the online version of this paper.
KEY WORDS:
Antarctica; Beacon Valley; ancient ice; sublimation; thermal contraction-crack polygons; numerical modelling
INTRODUCTION
Recent findings of shallow, buried glacier ice beneath dry
tills <1 m thick in Antarctica have prompted numerous
inquiries regarding the physical and environmental factors
that modulate vapour diffusion through porous media
(Hindmarsh et al., 1998; McKay et al., 1998; Marchant
et al., 2002; Pringle et al., 2003; Schorghofer, 2005;
Kowalewski et al., 2006; Hagedorn et al., 2007, 2009;
* Correspondence to: Douglas E. Kowalewski, Department of Earth
Sciences, Boston University, 675 Commonwealth Avenue, Boston,
MA 02215, USA. E-mail: dkowal@geo.umass.edu
†
Climate System Research Center, Department of Geosciences, University of Massachusetts, 233 Morrill Science Center, Amherst, MA
01003, USA
Copyright © 2011 John Wiley & Sons, Ltd.
McKay, 2009; Lacelle et al., 2011; Morgan et al., 2011).
Some of the oldest buried ice deposits in Antarctica are reportedly up to 8.1-million-years old (Sugden et al., 1995).
Although the age is debated (Hindmarsh et al., 1998), the
possibility of Miocene-aged buried ice has led to much discussion regarding long-term climate variability (or lack
thereof) within high-elevation regions (>1200 m) of the
Transantarctic Mountains (Lewis et al., 2007, 2008; Naish
et al., 2009). In addition, results from the analyses of such
buried ice deposits have helped frame discussions on the origin of similar appearing, postulated ice-rich deposits on
Mars (Head and Marchant, 2003; Marchant and Head,
2007; Holt et al., 2008; Plaut et al., 2009; Smith et al.,
2009; Head et al., 2010). It is within this framework that
we modelled sublimation of ancient buried glacier ice in
the McMurdo Dry Valleys, Antarctica.
Received 3 August 2010
Revised 17 June 2011
Accepted 17 July 2011
2
D. E. Kowalewski et al.
GEOLOGIC SETTING
Ancient Ice
Ancient buried glacier ice occurs in the central Beacon
Valley (Figure 1) (Sugden et al., 1995). The ice is derived
from Taylor Glacier, which advanced southwards into
Beacon Valley during Miocene time (>8.1 Ma; Sugden
et al., 1995) (Figure 2). The remnant ice is not physically
connected with the modern Taylor Glacier, but instead
appears as a detached, stagnant block ~5 km from the margin
of Taylor Glacier at the valley mouth (Figure 2). The buried
ice surface lies beneath ~50 to 100 cm of dry supraglacial
till, informally termed Granite drift (Sugden et al., 1995).
Ice thicknesses beneath Granite drift are unknown, but geophysical measurements of nearby buried glaciers in the upper Beacon Valley (Figure 2) suggest values of at least
~150 m are plausible (Shean and Marchant, 2010).
Sublimation Polygons
The surface of Granite drift displays well-developed ‘sublimation polygons’ (Figure 3). The term sublimation polygon
is used for a subset of thermal contraction-crack polygons
that form over buried glacier ice (or excess ice) and in
regions lacking saturated active layers (Marchant et al.,
2002; Marchant and Head, 2007; Levy et al., 2008). These
conditions are met in the highest and driest regions of the
McMurdo Dry Valleys, for example, Beacon Valley and
the stable upland zone of Marchant and Head (2007). Sublimation polygons are essentially sand-wedge polygons that
form over buried ice. As is the case for all contraction-crack
polygons, abrupt cooling induces tensile stresses that, in
competent debris, result in near-vertical cracks; in this case,
the cracks truncate the buried surface of glacier ice beneath
the Granite drift. Persistent subsurface temperatures well
below 0 C ensure that ice loss is via sublimation. The
absence of freezing and thawing restricts cryoturbation,
and the dominance of ice sublimation generates a relatively
simple, three-fold internal stratigraphy common to all
examined sublimation polygons:
(1) a fresh (pristine) facies that rests directly above buried ice (this forms as sublimation concentrates englacial debris at the top of downwasting ice, for
example, a lag deposit that forms as dirty ice sublimes (Schaefer et al., 2000));
(2) a weathered facies that forms at, and near, the
ground surface via physical disintegration of rocks
from aeolian deflation, oxidation of iron-bearing
minerals and salt formation via minor snowmelt on
solar-heated rocks; and
(3) a sand-wedge facies that forms at polygon margins
via episodic infill of thermal cracks (the sand wedges
are identical to those that form in classic sand-wedge
polygons (Murton et al., 2000; Marchant et al.,
2002; Marchant and Head, 2007)). Gravitational
sliding at the margin of steep polygon troughs
Figure 1 The McMurdo Dry Valleys (MDV). The MDV lie between the McMurdo Sound sector of the Ross Sea and the East Antarctic Ice Sheet (EAIS). Black
outline in the Quartermain Mountains shows Beacon Valley and the region depicted in Figure 2. Upper left inset: location of MDV plotted on map of Antarctica.
Copyright © 2011 John Wiley & Sons, Ltd.
Permafrost and Periglac. Process., 23: 1 –14 (2012)
A 2D Model for Characterising Variability in Sublimation of Buried Ice
3
Figure 2 Sketch map of Beacon Valley showing the distribution of buried-ice deposits and overlying drifts. Granite drift (tan) was deposited from a Mioceneage (>8.1 Ma) advance of Taylor Glacier southward into Beacon Valley (Sugden et al., 1995; mapped drift limit from Potter et al., 2003). Remnant glacier
ice from this advance occurs on the floor of central Beacon Valley, <1 m below the surface of Granite drift (brown). Similar-aged ice may also occur on the
valley floor north of this location, but if so it lies >1 m below the surface and beyond the reach of our hand-dug soil excavations. The blue colors on the
map show locations of drift and buried ice associated with alpine glaciers sourced from ice accumulation at the valley headwall (e.g., Shean and Marchant,
2010; Kowalewski et al., 2011). The mapped contacts among the different buried-ice deposits in central Beacon Valley are diffuse; neither moraines nor icemarginal features are present. Differentiation is made possible only on the basis of mapping lithological characteristics of supraglacial deposits and englacial
debris. In this regard, Granite drift, and underlying remnant ice from Taylor Glacier both contain granite and metamorphic erratics from outside Beacon Valley
(Sugden et al., 1995; Marchant et al., 2002), whereas drifts and underlying ice sourced from upper Beacon Valley (blue colors) lack erratics and contain only
locally derived debris (Kowalewski et al., 2011). Base map adapted from Marchant et al. (2002).
admixes the fresh and weathered facies (Figure 4).
Because the location of thermal contraction shifts
over time (Berg and Black, 1966), relict sand-wedge
deposits (i.e. those no longer associated with active
thermal contraction) truncate this three-fold stratigraphy (see also Kowalewski et al., 2011).
As initially hypothesised in Marchant et al. (2002), textural variations among these three facies impart first-order
control on vapour diffusion and loss of subsurface ice. Of
particular interest (and modelled here) are the sand-wedge
deposits, which, if coarser grained than pristine lags (which
Copyright © 2011 John Wiley & Sons, Ltd.
is the case for Granite drift, see below), would increase vapour diffusion and ice loss at polygon margins. Ultimately,
this process would lead to elevated polygon centres surrounded by deep, marginal troughs (Marchant et al.,
2002). We emphasise that although sublimation polygons
may appear morphologically similar to the well-known,
high-centred polygons of the Arctic, they differ in origin:
the elevated centres of sublimation polygons arise from enhanced ice loss at polygon margins, whereas high-centred
polygons of the Arctic typically arise from widespread
active-layer cryoturbation, including diapirism at polygon
centres (Mackay, 2000; Singleton et al., 2010).
Permafrost and Periglac. Process., 23: 1 –14 (2012)
4
D. E. Kowalewski et al.
Figure 3 Oblique aerial view of Granite drift in central Beacon Valley. “Sublimation polygons” (e.g., Marchant et al., 2002) mark the drift surface; the average
polygon diameter in this image is ~18 m (see also Supplemental Table 3). Inset: the surface of buried-glacier ice beneath Granite drift; tape is 1 m long. Although
sublimation polygons are morphologically similar to classic high-centered polygons of the Arctic, they differ in origin: elevated centers of sublimation polygons
arise from enhanced ice loss at polygon margins, rather than from saturated active layer processes, including diapirism at polygon centers.
Figure 4 COMSOL Multiphysics model geometry. (a) Basic geometry for instrumented polygon showing polygon plateau, polygon trough, and the array of
HOBO™ Smart Sensors. (b) The same instrumented polygon as shown in (a) but with alterations for the following tests: Test 1, snow in the polygon trough;
Test 2, relict sand-wedge deposits at polygon centers; Test 3, shallow subsurface salts; and Test 4, rocky surface pavements. The weathered facies is represented
by the rocky pavement and subsurface salt horizon; the fresh facies in noted simply as Granite drift; the sand-wedge facies occurs at the base of the polygon
trough and continues for an unknown depth in glacier ice (not shown); and, the admixture of the fresh and weathered facies at trough walls is noted as slumped
Granite drift (see text for details). Standard porosity values used in our baseline model run (section 4.1) are 30% for Granite drift, 45% for sand-wedges, and
40% for slumped Granite drift (see also Supplemental Documents).
Copyright © 2011 John Wiley & Sons, Ltd.
Permafrost and Periglac. Process., 23: 1 –14 (2012)
A 2D Model for Characterising Variability in Sublimation of Buried Ice
5
Table 1 Monthly and annual meteorological data, polygon centers versus polygon troughs, Beacon Valley.
Centre
Difference (trough-centre)
Mean
January
February
March
April
May
June
July
August
September
October
November
December
Annual
Atm T
6.1
13.3
25.5
34.6
34.7
33.4
39.6
29.8
29.8
24.2
12.7
4.6
24.1
Atm RH
35.8
44.1
55.3
62.8
51.4
63.6
54.2
57.1
60.3
47.3
44.0
44.2
51.7
Soil 0 cm T
2.1
10.6
24.6
34.9
36.1
34.5
40.8
31.2
31.1
23.8
9.8
0.2
23.4
Soil 30 cm T
5.3
10.8
20.8
30.2
32.6
31.7
37.5
30.8
31.0
25.7
15.5
6.4
23.2
Atm T
0.4
0.3
0.4
0.6
0.3
0.4
0.6
0.4
0.1
0.5
0.1
0.5
0.3
Atm RH
2.2
1.5
1.3
0.8
1.3
2.5
0.0
0.1
1.7
0.5
0.5
3.1
0.3
Soil 0 cm T
0.9
1.1
0.2
1.0
0.7
0.8
1.0
0.1
0.1
1.7
2.0
1.4
0.3
Soil 30 cm T
1.4
0.9
0.5
1.8
1.5
1.3
1.8
0.6
0.6
0.7
1.6
1.7
0.1
Minimum
January
February
March
April
May
June
July
August
September
October
November
December
13.5
27.1
39.6
47.7
47.7
50.4
50.4
41.3
47.7
38.0
27.1
10.6
8.3
11.3
13.8
42.3
9.8
29.8
15.8
18.3
30.8
14.3
15.8
5.8
12.6
23.6
36.8
46.4
46.7
48.4
48.4
41.2
43.3
37.6
26.7
11.6
8.7
14.8
26.5
36.2
38.5
39.5
40.7
35.2
36.5
31.0
22.0
9.6
0.6
1.9
1.6
0.0
0.0
0.0
2.7
0.0
2.3
1.6
1.0
1.1
0.5
1.5
4.5
7.0
1.0
16.5
3.5
2.5
2.0
2.5
1.0
0.0
0.3
2.8
1.2
2.2
2.4
1.9
1.9
1.5
1.2
0.8
0.7
0.5
0.8
0.2
1.7
2.8
2.6
2.4
2.3
1.5
1.3
0.4
0.9
1.3
Maximum
January
February
March
April
May
June
July
August
September
October
November
December
2.5
4.8
7.9
18.8
13.5
14.7
20.2
15.4
14.1
11.1
2.0
4.2
90.8
86.8
77.8
78.8
80.3
85.3
77.8
78.3
79.8
75.3
88.8
91.8
13.1
5.4
6.0
21.7
17.6
19.8
23.9
19.0
16.0
4.0
7.9
13.9
2.5
7.5
14.5
26.4
24.6
25.8
31.8
25.8
24.3
20.3
8.4
2.7
2.5
1.9
0.0
0.0
0.6
0.0
0.8
0.0
0.0
2.2
1.8
0.4
3.5
0.0
5.0
0.0
1.0
1.5
3.5
0.5
2.0
0.0
3.5
3.0
2.0
2.2
5.9
0.8
1.9
0.2
1.3
1.2
2.5
4.7
2.9
2.6
1.8
1.2
0.2
1.6
0.1
0.3
0.7
0.1
0.4
1.8
1.8
2.0
Climate data were recorded from 8 December 2005 to 8 December 2006.
Temperatures recorded in C
T = Temperature; RH = relative humidity.
Local Climate Conditions
Table 1 and Figure 5 show details regarding local microclimate conditions at the study site (77.84939E, 160.59826S,
~1300-m elevation). The mean annual atmospheric temperature (MAAT), as recorded over the 12-month study
interval (8 December 2005 to 8 December 2006) is
24.1 C; summertime air temperatures rarely rise above
0 C (Table 1; Figure 5) and precipitation is <50-mm water
Copyright © 2011 John Wiley & Sons, Ltd.
equivalent per year (Fountain et al., 2010). Atmospheric
absolute humidity typically ranges from 0.0148 103 to
0.0036 kg m3. Given these conditions, Granite drift is
exceptionally dry and lacks the typical freeze-thaw cryoturbation associated with nearly all other supraglacial
deposits worldwide (Paul and Eyles, 1990). The buried
ice surface beneath Granite drift is smooth, dry and
≪0 C (Figure 3). See also supplementary documents for
additional microclimate information.
Permafrost and Periglac. Process., 23: 1 –14 (2012)
6
D. E. Kowalewski et al.
Figure 5 A subset of measured meteorological conditions for central Beacon Valley. (a) Relative humidity (RH); black line shows the RH at the polygon
center; gray line shows the difference in RH between the polygon center and the base of the polygon trough. (b) Atmospheric temperature; black line
shows the atmospheric temperature at the polygon center; gray line shows the difference in atmospheric temperature between the polygon center and
the base of the trough. All RH and temperature data were collected from a height of 10 cm above the ground surface. See supplementary document
for sensor specifications.
Table 2 COMSOL simulation output for polygon centres and troughs in the Beacon Valley
Model
run
GD-01
GD-02
GD-03
GD-04
GD-05
GD-06
GD-07
GD-08
GD-09
GD-10
GD-11
GD-12
GD-13
GD-14
GD-15
GD-16
GD-17
GD-18
GD-19
GD-20
Snow
pack
✓
Vertical relict
sand wedge
45% porosity
delta Temperature
Salt lens
20% porosity
✓b
Salt lens
10% porosity
Rocky
2 C
4 C
6 C
2 C
pavement Existing T Annual Annual Annual Summer
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Model does not include latent heat; negative modelled values predict a net downward vapour flux.
Ice loss is reported for a relict sand wedge in the centre of a polygon (see Test 2 in text).
RH = Relative humidity.
a
b
Copyright © 2011 John Wiley & Sons, Ltd.
Permafrost and Periglac. Process., 23: 1 –14 (2012)
A 2D Model for Characterising Variability in Sublimation of Buried Ice
where r represents water vapour density, t the time, D the
diffusivity of water vapour (0.16 cm2 s1) and z is equal to
depth. Introducing a porous medium into Equation 1, we assign
values for porosity (f) as deduced from thin-section analyses
(Kowalewski et al., 2011; Supplemental Table 2), and we assume a constant tortuosity (b) of 2, consistent with earlier studies
(Hindmarsh et al., 1998; Schorghofer, 2005; Kowalewski et al.,
2006). Vapour flux through the medium is thus expressed as:
MODELLING STUDY
Model Overview
Our model simulates vapour transport via Fickian diffusion
across a 2D domain as noted in Figure 4. Measured values
for temperature and relative humidity (RH) are explicitly incorporated into the model to establish: (a) initial conditions
at t = 0 throughout the domain, and (b) boundary conditions
for the ice surface and the till surface at each model time
step. Model output includes calculated vapour densities
within the domain at each time step.
@r
¼
@t
Our model for vapour diffusion through Granite drift assumes
ice loss is accommodated solely by sublimation and that vapour
transport is dominated by non-steady state Fickian diffusion
(Schorghofer, 2005; Kowalewski et al., 2006). We follow
Albert and Perron (2000) and Schorghofer and Aharonson
(2005) in noting that the effects of advection and/or Knudsen
diffusion are minor for relatively coarse-grained deposits like
Granite drift, and therefore these are not included. We thus express vapour diffusion as:
Existing
RH
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
+10%
Annual
(1)
✓
✓
✓
✓
✓
✓
Copyright © 2011 John Wiley & Sons, Ltd.
+20%
Annual
✓
+30%
Annual
(2)
where eo and To are constant parameters equal to 0.611 kPa
and 273 K, respectively. L/ℜv is equal to the latent heat of
deposition divided by the gas constant of water vapour
(6139 K). T is the measured temperature. The relationship
between vapour pressure and vapour density can be
delta RH
4 C
Summer
2
fD @ r
2:
b
@z
Our model does not consider vapour density exceeding saturation, as would be required for studies of relatively wet supraglacial deposits (Hagedorn et al., 2007, 2009; Hunt et al.,
2010; Swanger et al., 2010).
The vapour density for initial and boundary conditions is
calculated from the water vapour pressure (e), which can be
derived using the Clausius-Clapeyron equation:
L
1
1
RH
e ¼ e0 exp
(3)
Rv T0 T
100
Model Detail
@r
@2r
¼D 2
@t
@z
7
Annual ice loss (mm)
+10%
Summer
+20%
Summer
+30%
Summer
✓
✓
✓
✓
Polygon
centre
0.059
0.059
0.085
0.055
0.047
0.023
0.035
0.015
0.002
0.041
0.023
0.000
0.040
0.023
0.009
0.043
0.027
0.012
0.022
0.022
Base of
polygon trough
0.039
0.012
0.039
0.039
0.039
0.039
0.019
0.003
0.011
0.022
0.005
0.010
0.020
0.004
0.009
0.024
0.010
0.004
0.039
0.012
a
Permafrost and Periglac. Process., 23: 1 –14 (2012)
8
D. E. Kowalewski et al.
calculated using the ideal gas law for any given temperature
as follows:
e ¼ ρRv T
(4)
where the equation is solved for the vapour density, r. We
assume the recorded till temperature is a strong approximation for the temperature of the air in pores within the Granite
drift.
COMSOL Multiphysics was used to solve Equation 2
with the finite element method run in 2D non-steady state
diffusion-only mode for the initial model geometry as noted
in Figure 4a (see also Supplemental Table 3). Boundary and
initial vapour densities were established from field data. For
initial conditions, we assume that pores within Granite drift
just above the buried ice surface are saturated with water
vapour. Therefore the initial ice surface RH is set to 100 per
cent and interpolated linearly to the measured RH at the
ground surface. The initial conditions for temperature are derived from interpolation between measured soil temperature
data points (Figures 4a and 5; Table 1). Boundary conditions
for RH at the till surface are taken from measured data; absolute humidity at the till surface above the polygon centre
ranged from 0.0223 103 to 0.0036 kg m3, absolute
humidity ranged from 0.0148 103 to 0.0027 kg m3 at
the till surface above the trough. We assume that RH at the
ice surface is 100 per cent at all time steps. The boundary conditions for temperature are taken from measured data at the till
surface and buried ice surface.
Figure 6 Spatial variation in mean annual vapor fluxes predicted by our
COMSOL 2D model (polygon geometry as depicted in Figure 4). For
textural input, we used a porosity for Granite drift of ~30% (e.g., Marchant
et al., 2002); a porosity of ~45% for sand-wedges; (e.g., Marchant et al.,
2002) and, a porosity of 40% for slumped Granite drift at trough walls;
see online supplement for additional details regarding porosity values.
Results for this baseline model run (see also Section 4.1) exclude the effects
of snowfall, near-surface salts, relict sand-wedge deposits, and rocky pavements. The changes in vapor fluxes are due to variations in topography and
porosity. Negative values for vapor represent an outward flux to the
atmosphere (net ice loss). The minimum net outward vapor flux (and hence
minimum ice loss) occurs at the base of the polygon trough (from 5.3 m to
7.0 m; trough is deepest at position 6.15 m along the x-axis).
Copyright © 2011 John Wiley & Sons, Ltd.
Figure 7 Details for incoming solar radiation measured for the polygon
center and polygon trough. Values for the polygon center are shown in black
and the dotted line represents solar radiance at the base of the polygon
trough. The sinuous pattern observed for polygon center (as especially seen
on the right side of the figure) represents a period of cloudless days. The
sharp decrease/increase in solar radiance at the base of polygon troughs is
a product of localized shielding from adjacent polygon-trough walls. Spikes
within the data are caused from increased diffuse radiation or sunlight
passing through the periphery of clouds that may cause a short-lived intense
focusing of incoming solar radiance.
Model Rationale
The strength of our modelling study stems from the robust
boundary conditions derived from our meteorological dataset. The dataset enables us to capture diurnal variations in
vapour flux as a result of the non-linear relationship between temperature and vapour density. Ignoring latent heat
is one limitation of our model and its absence prevents us
from calculating true ice gain as vapour moves downward
though the till (at times). However, this limitation does not
influence our first-order results regarding net ice loss on seasonal and/or annual timescales. An additional limitation is
that our model does not apply different thermal conductivities with depth; for example, it ignores variations that might
be associated with variable lithologies for rocks at the
ground surface and for salts at depth. Finally, our measured
internal temperatures are not used explicitly to validate
model results; however, they do help determine conditions
where and when supersaturation in the till is likely to occur,
and whether pore ice could likely form. Notwithstanding
these limitations, our 2D model provides the first semiquantitative assessment of sublimation of shallow, buried
glacier ice in the Dry Valleys as a function of surface topography, rocky pavements, snow cover and near-surface salts.
In all, over 60 different solutions were generated for six different model configurations (Table 2).
RESULTS
We first describe model results for our baseline geometry, and then compare these with more advanced simulations that take into consideration variable snow cover,
till porosity, the presence of near-surface salts and rocky
desert pavements, and the aspect of polygon trough walls
Permafrost and Periglac. Process., 23: 1 –14 (2012)
A 2D Model for Characterising Variability in Sublimation of Buried Ice
9
Figure 8 Results from Test 1: Addition of 26 cm of snow in the polygon trough located from approximately 5.3 to 7.0 m along the x-axis. Simulations also
show the results that arise from additionally varying the porosities for Granite drift at the polygon center and trough wall, as well as for sand wedges at the base
of polygon troughs. The different values of porosity (P) reflect the percentage increase above the “standard” porosity employed in the baseline model (Figure 6,
section 4.1). For example, NC (no change) indicates a model run with the same porosity as used in Figure 6. A P value of +5% reflects a porosity of 35% for
Granite drift at the polygon center, 45% at the polygon-trough wall, and 50% for the sand wedge at the center of the polygon trough (positioned at 6.15 m along
the x-axis); likewise a value of +10% reflects porosity of 40% for Granite drift at the polygon center, 50% at the polygon-trough wall, and 55% for the sand
wedge at the center of the polygon trough. Negative values represent outward fluxes to the atmosphere. The panels show the mean flux (a), the minimum flux
(b), and the maximum flux (d). (c) shows the mean flux as in (a) but plotted on the same scale as (b) and (d).
(north facing, south facing, etc.). None of these additional parameters has been incorporated in previous
modelling studies (Hindmarsh et al., 1998; Kowalewski
et al., 2006; Schorghofer, 2005).
feedback to runaway ice loss at polygon troughs related
to self-shadowing (solar shielding) alongside elevated
polygon centres (Figure 7; see also temperature data in
Table 1; Supplemental Table 4; and the Discussion).
Baseline Model
Test 1: Snow in Polygon Troughs
For the baseline model run, we calculated ice loss as a
function of the simple polygon geometry and facies distribution as noted in Figure 4a. (In this run, we start with
an established polygon trough; for model results on initial trough development, see Test 2 below). Results show
that sublimation varies considerably with topography.
Maximum ice loss occurred along polygon trough walls
(0.098 mm for the 12-month study interval), followed
by diminished losses at the polygon plateau
(0.059 mm); the lowest rates were recorded at the base
of the polygon trough (0.039 mm) (the latter being a
34% reduction from the sublimation rate at the polygon
centre) (Figure 6). The very low rate of ice sublimation
at the base of deep polygon troughs arises from local
cooling at the till and buried ice surfaces – a negative
To simulate the effects of trapped snowfall on subsurface
ice loss (Figure 4b), we adjusted the saturation vapour density at the base of the modelled polygon trough to reach 100
per cent (while maintaining consistency with measured atmospheric temperatures). We retained all other variables
as noted in the baseline model. Field observations show that
snow typically collects in polygon troughs; polygon centres
are windswept and snowfall there rarely remains for more
than a few hours/days.
Results of our snowfall test predict a net downward flux
of water vapour (for the 12-month period) at the top of buried glacier ice in the polygon trough. The volume of water,
if deposited as secondary ice (ignoring the local influence of
latent heat), would be equivalent to a lens of ice ~0.012 mm
thick. Also predicted is a slight reduction in ice loss along
Copyright © 2011 John Wiley & Sons, Ltd.
Permafrost and Periglac. Process., 23: 1 –14 (2012)
10
D. E. Kowalewski et al.
Figure 9 Results from Test 2: Relict sand-wedge deposits at polygon centers; colored lines show the effect of varying sand-wedge porosity; the porosity for
Granite drift is held at 30%. The panels show the mean flux (a), minimum flux (b), and maximum flux (d). (c) shows the mean flux as in (a) but plotted on the
same scale as (b) and (d). Sand wedge on left is 10 cm wide and on the right it is 50 cm wide. For reference, the polygon trough is located from ~5.3 to 7.0 m
along the x-axis.
adjacent polygon trough walls by 0.020 mm (i.e. reduced by
20%). As expected, the addition of snow in the polygon
trough had a negligible effect on ice loss at the polygon centre (Figure 8).
Test 2: Sand Wedges and Relict Sand-wedge Deposits at
Polygon Centres
To understand better the changes in vapour flux and ice
loss near sand-wedge deposits (Marchant et al., 2002;
Kowalewski et al., 2011; Figure 4b), we adjusted the
modelled porosity at polygon centres to include two relict
sand wedges: one 10 cm wide and a second 50 cm wide.
These widths span measured values for relict sand-wedge
deposits observed in Granite drift. All other variables
remained identical to those of the baseline model run.
Results show that sublimation is enhanced beneath sandwedge deposits, though deposit width has a negligible impact on ice loss. For sand-wedge deposits of 40 per cent,
45 per cent, 50 per cent and 60 per cent porosity (i.e. the
maximum range of reported values in the region; Marchant
et al., 2002; Kowalewski et al., 2011), the model predicts an
annual increase in ice loss of 0.016 mm (27% increase),
0.026 mm (44% increase), 0.035 mm (59% increase) and
0.051 mm (86% increase), respectively (Figure 9).
Copyright © 2011 John Wiley & Sons, Ltd.
Test 3: Salt-cemented Horizons
To simulate the physical effect of shallow, salt-cemented
horizons within the Granite drift (Bockheim, 2002;
Bockheim et al., 2009; Bao and Marchant, 2006), we reduced model porosity between 10- and 15-cm depths at
the centre of our modelled polygon (Figure 4b).
Results show that the addition of a 5-cm thick, saltcemented layer with a porosity of 20 per cent (i.e. reduced
from 30%) decreases annual ice loss by 7 per cent (by
0.004 mm a1); likewise, lowering the porosity of the salt
lens to 10 per cent decreases sublimation losses by 20 per
cent (by 0.012 mm a1).
Test 4: Rocky Pavements
To simulate the effect of a rocky pavement on subsurface ice
sublimation, we ran a model simulation with 75 per cent of
the ground surface capped with dolerite clasts. Visually, this
translates to a uniform spacing of clasts, with each clast being
15 cm long and spaced 5 cm from adjacent clasts (Figure 4b);
this approximates conditions observed in the field (Marchant
et al., 2002). We assigned a value of 0 per cent porosity for
the clasts, with 30 per cent porosity (unchanged from the baseline model) for intervening regions. Results show a ~60 per cent
Permafrost and Periglac. Process., 23: 1 –14 (2012)
A 2D Model for Characterising Variability in Sublimation of Buried Ice
11
Figure 10 Results from Test 4: Rocky surface pavements. The addition of a rocky pavement at polygon centers has minimal affect on ice loss at polygon troughs
(~5.3 to 7.0 along the x-axis), but can decrease sublimation rates at polygon centers by as much as 60%. The panels show the mean flux (a), minimum flux (b), and
maximum flux (d). (c) shows the mean flux as in (a) but plotted on the same scale as (b) and (d). Porosity values (P) are as defined in Fig. 8.
reduction in ice loss over the 12-month study period, with
ice loss decreasing from 0.059 mm to 0.023 mm (Figure 10).
Test 5: Varying the Aspect of Polygon Trough Walls
To simulate the effect of enhanced solar insolation on northfacing polygon trough walls, we artificially increased soil
and underlying ice surface temperatures on the north-facing
side of our modelled polygon trough for the month of January
by 4 C. The choice of 4 C comes from direct temperature
measurements on a similar north-facing polygon trough wall
<1 km from the study site. Temperatures were measured just
below polygon rims (i.e. high enough to avoid complications
associated with self-shielding from polygon geometry). Given
this change, our model results show that ice loss along the
warmed polygon trough wall increased by ~275 per cent during the month of January (see also Levy et al., 2008).
DISCUSSION
The Role of Textural Variation and Surface Morphology
on Subsurface Ice Loss
Our 2D model results suggest a complex, though predictable, dynamic among subsurface ice loss, ground-surface
morphology and textural variation within Granite drift. In
Copyright © 2011 John Wiley & Sons, Ltd.
general, the results provide a physical mechanism that
yields high-centred polygons (Marchant et al., 2002) in
the absence of saturated, active-layer cryoturbation as described by Hallet and Waddington (1991). Taken together,
our results show that during the initial stages of polygon formation, locally enhanced sublimation beneath immature
sand wedges leads to the development of marginal sublimation troughs (this conclusion arises from Test 2, in which
isolated sand wedges result in enhanced subsurface ice
loss). Continued ice loss, however, generates deeper
troughs, and basal portions of such troughs are ultimately
shielded from direct solar insolation, providing a negative
feedback for enhanced ice loss (Table 1). Indeed, at the base
of deep polygon troughs, which at >1-m depth typically remain largely in shadow and experience colder-than-average
microclimate conditions (Table 1), sublimation is reduced to
levels below that modelled for polygon centres (Figures 6
and 8). If windblown snow becomes trapped in such
troughs, ice loss is further reduced (Table 2). Moreover,
windblown snow in polygon troughs may actually result
in ice accretion at depth (from downward movement of vapour). Given our model limitations, we cannot quantify potential ice accretion. However, we note that lenses of
secondary ice have been observed at the base of polygon
troughs in Beacon Valley (Marchant et al., 2002), and that
dD and d18O analyses corroborate an origin via downward vapour transport from the surface snow (Marchant et al., 2002;
Permafrost and Periglac. Process., 23: 1 –14 (2012)
12
D. E. Kowalewski et al.
see also Hagedorn et al., 2007, 2009; McKay, 2009). Collectively, these processes describe a self-organising mechanism
that controls the maximum depth of polygon troughs.
trough walls with slumped debris (Marchant et al., 2002) varies considerably, suggesting that slumping locally thickens
and thins Granite drift.
The Role of Rocky Pavements and Salt-cemented
Horizons in Subsurface Ice Loss
The Potential for Long-Term Preservation of Buried
Glacier Ice
Most modelling studies that have examined sublimation of
buried ice in Antarctica have ignored the effects of rocky surface pavements and/or shallow, salt-cemented horizons in
modulating ice loss (Hindmarsh et al., 1998; Schorghofer,
2005; Kowalewski et al., 2006). Here, we modelled pavements and salts as distinct horizons with reduced porosity
(Tests 3 and 4). Results show that by adding a realistic pavement with subsurface salts, the levels of ice sublimation are reduced by as much as 60 per cent. Even greater declines in net
annual ice sublimation are probable if secondary factors
beyond simple reductions in porosity are considered. For
example, the addition of rocky pavements would tend to
increase surface roughness, resulting in the deposition of
windblown snow in the lee of the largest clasts. Episodic
snowmelt along the margin of solar-heated clasts (especially
along low-albedo Ferrar Dolerite) would create a moist,
near-surface horizon that would tend to elevate near-surface
soil vapour pressures and suppress subsurface ice loss (see
also Kowalewski et al., 2006; McKay, 2009; Schorghofer,
2009). In addition, the snow and minor meltwater thus
established would add salts to the shallow subsurface
(Claridge and Campbell, 1977; Campbell et al., 1997;
Bockheim, 2002; Bao and Marchant, 2006; Campbell and
Claridge, 2006), facilitating the movement of brines at
subfreezing temperatures. Finally, episodic hydration of soil
salts could also lead to further reductions in soil porosity
and tortuosity, thereby further diminishing sublimation of
buried glacier ice.
Results from our 2D modelling exercises suggest that
under current environmental forcing, ice loss beneath
Granite drift at polygon centres (modelled with the addition of a rocky surface pavement and shallow subsurface
salts) approaches 0.022 mm a1 (Table 2). We have
shown that ice loss is extremely sensitive to minor
changes in MAAT and RH. Consider the modelled scenario in which Granite drift at a polygon centre is
capped by a rocky pavement (75% coverage) and contains a salt-cemented horizon at 10 15-cm depth (20%
porosity). In such a situation, a stable ice surface (zero
net annual ice loss) is achieved with either a 1.9 C decrease in MAAT (from present conditions) or a 12 per
cent increase in mean annual RH. If we assume that wintertime conditions remain unchanged, then a stable ice
surface could be achieved by decreasing summertime
temperatures (October-March) by 2.3 C or by increasing
summertime RH by 14 per cent. Both of these conditions
could occur with a modest increase in summertime cloud
cover (Kowalewski et al., 2006). In addition, the greater
surface snowmelt expected under such conditions would
tend to elevate soil moisture and further retard sublimation of underlying ice (McKay, 2009; Schorghofer,
2009). Collectively, the results demonstrate complex,
but quantifiable, relations among ice loss, polygon formation, and subtle changes in atmospheric temperature
and RH. Although these results do not prove the
hypothesised great antiquity of buried glacier ice in the
central Beacon Valley (Sugden et al., 1995), they do
suggest that the preservation of multi-million-year-old
ice is plausible in the coldest and driest regions of the
Transantarctic Mountains (Schorghofer, 2005; Kowalewski
et al., 2006; Marchant and Head, 2007; Swanger et al.,
2010; Morgan et al., 2011).
The Role of Polygon Trough Wall Aspect on Sublimation
of Buried Ice
Results from Test 5 show that ice loss along a north-facing
polygon trough wall (i.e. oriented favourably to solar radiation) can increase by as much as ~275 per cent relative to
that along a south- facing polygon trough wall. Field inspection, however, shows no obvious and consistent trends in
the slope of polygon trough walls with respect to aspect in
the central Beacon Valley. Levy et al. (2008) report a subtle
variation in polygon trough wall geometry with aspect (by a
few degrees), but the magnitude of this slope change is not
in keeping with the expected variations that would arise
from enhanced ice sublimation on the north-facing trough
wall. As one hypothesis to test, we suggest that secondary
processes, such as marginal slumping along trough walls,
likely counteract the potential for dramatic solar-induced
trough asymmetry. In this regard, episodic mass wasting via
gravitational sliding and slumping would tend to maintain
slope angles at the angle of repose (~30 ), as noted in the field.
We also note that the depth to buried ice observed on polygon
Copyright © 2011 John Wiley & Sons, Ltd.
SUMMARY AND CONCLUSIONS
(1) We applied a relatively simplistic 2D model for vapour diffusion through porous media to calculate
the sublimation rates for buried glacier ice in the
central Beacon Valley, Antarctica. The results show
that the development of thermal contraction-crack
polygons modulates subsurface ice loss. During the
initial stages of polygon formation, locally enhanced
sublimation beneath immature sand wedges leads to
the development of deep, marginal troughs (and high
polygon centres). Continued ice loss, however, deepens troughs so that basal portions are shielded from
direct solar insolation. This shielding results in local
Permafrost and Periglac. Process., 23: 1 –14 (2012)
A 2D Model for Characterising Variability in Sublimation of Buried Ice
cooling, which in turn acts to suppress sublimation
and provides a negative feedback for runaway ice
loss at polygon margins. Windblown snow, which
is trapped preferentially in deep polygon troughs,
reduces sublimation even further, and may lead to
ice accretion at depth. At polygon shoulders (i.e.
high enough on trough walls to avoid the consequences of self-shielding) solar warming on northfacing trough walls can elevate rates of sublimation
by up to 275 per cent relative to south-facing trough
walls. Field data from the central Beacon Valley,
however, show no obvious slope asymmetry for
opposing north- and south-facing trough walls. One
explanation is episodic mass wasting from gravitational sliding and slumping, which would tend to
maintain slope angles at the angle of repose (~30 ),
as noted in the field. Taken together, the results point
toward self-organisation as a mechanism that
controls the geometry of polygon troughs.
(2) Results from our 2D model show that the surface of
remnant glacier ice beneath Granite drift at polygon
centres lowers by 0.022 mm a1. This rate is significantly lower than that first modelled by Hindmarsh
et al. (1998) (~1 mm a1) and Kowalewski et al.
(2006) (0.14 mm a1), who used either generic temperatures and/or assumed homogeneous till textures
in model domains. Our results, however, are consistent with recent estimates of ice loss based on the
abundance of cosmogenic nuclides in Granite drift
in the central Beacon Valley (e.g. 0.005 to
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