JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B10, 2474, doi:10.1029/2002JB002364, 2003
Depth and seasonal variations in the thermal properties
of Antarctic Dry Valley permafrost from temperature
time series analysis
D. J. Pringle,1 W. W. Dickinson,2 H. J. Trodahl,1 and A. R. Pyne2
Received 23 December 2002; revised 8 May 2003; accepted 7 June 2003; published 16 October 2003.
[1] We present the first dedicated study of the thermal properties of perennially frozen,
ice-cemented, subsurface Dry Valley permafrost. From time series analysis of 14 months’
temperature measurements, we resolve depth and seasonal variations in the thermal
properties at two nearby sites at Table Mountain with different origin, composition, and
polygonal ground patterning. We determine apparent thermal diffusivity (ATD) profiles
directly from thermistor array measurements at 13.5-cm-depth intervals and 4-hour time
intervals in the top 2 m. We treat the system as purely conductive year round due to
the cold temperatures and compare the performance of several common analysis schemes
with a graphical finite difference method that we present in detail. This comparison is
facilitated by one site showing strong depth variations including an abrupt twofold
increase in ATD across a sharp compositional boundary. We characterize the composition
of the inhomogeneous ground from recovered cores and estimate an ice-fractiondependent heat capacity in the range C = 1.7 ± 0.1 to 1.8 ± 0.1 MJ m3 C1. We calculate
apparent thermal conductivity profiles that correlate very well with the core compositions. The conductivity generally lies in the range 2.5 ± 0.5 W m1 C1 but is as high as
4.1 ± 0.4 W m1 C1 for a quartose Sirius sandstone unit at one site. The seasonal
variation in the ATD is consistent with its expected temperature dependence.
INDEX
TERMS: 3299 Mathematical Geophysics: General or miscellaneous; 5134 Physical Properties of Rocks:
Thermal properties; 5194 Physical Properties of Rocks: Instruments and techniques; KEYWORDS: Dry Valleys,
Antarctica, thermal properties of frozen ground, permafrost
Citation: Pringle, D. J., W. W. Dickinson, H. J. Trodahl, and A. R. Pyne, Depth and seasonal variations in the thermal properties of
Antarctic Dry Valley permafrost from temperature time series analysis, J. Geophys. Res., 108(B10), 2474, doi:10.1029/2002JB002364,
2003.
1. Introduction
[2] Recent years have seen an increased scientific interest
in the McMurdo Dry Valleys, which represent a littlestudied end-member of terrestrial permafrost environments,
being both very cold and very dry [Putkonen et al., 2003].
This interest is largely due to the region representing the
best terrestrial analogue of the Martian polar regions, in
which patterned ground is observed and ground ice is likely
to exist [Mellon, 1997; Malin and Edgett, 2000], and a
debate surrounding the age and stability of Beacon Valley
ground ice [e.g., Sugden et al., 1995; Hindmarsh et al.,
1998; Marchant et al., 2002; J. O. Stone et al., Age and
sublimation rate of ancient ice, Beacon Valley, Antarctica,
submitted to Journal of Geophysical Research, 2002,
hereinafter referred to as Stone et al., submitted manuscript,
2002]. The extreme climate of the Dry Valleys is charac1
School of Chemical and Physical Sciences, Victoria University of
Wellington, Wellington, New Zealand.
2
Antarctic Research Centre, Victoria University of Wellington, Wellington, New Zealand.
Copyright 2003 by the American Geophysical Union.
0148-0227/03/2002JB002364$09.00
ECV
terized by very low precipitation (<10 cm yr1 in the form
of fine ‘‘diamond dust’’ snow), low annual mean temperatures (<20C), large annual temperature amplitude
(15C), and strong, katabatic winds [e.g., Thomson et
al., 1971; McKay et al., 1998]. The valleys are not ice
covered primarily because the Trans-Antarctic Mountains
block ice from the polar plateau flowing into and through
the valleys [McKay et al., 1998]. The ground surface is
typically an ice-free, rock debris mineral soil, up to 1 m
deep, overlying a perennially frozen ice/mineral soil matrix,
referred to here as ‘‘ice-cement.’’
[3] Attention has also been focused on polygonal-patterned ground features, which are found extensively
throughout the greater Dry Valley region, ranging in diameter from 1 to 20 m [Péwé, 1959; Marchant et al., 2002;
Putkonen et al., 2003; Sletten et al., 2003]. This widespread
occurrence of sand-wedge polygons reflects contraction
crack networks within the underlying ice cement (buried
ice in the case of Beacon Valley).
[4] Our focus is the thermal regime and properties of two
sites separated by 100 m at Table Mountain in the Dry
Valleys (Figure 1). These sites show different scale surface
patternings, and furthermore, one of the sites lies in a debris
flow of unknown age or flow mechanism, discussed below.
3-1
ECV
3-2
PRINGLE ET AL.: THERMAL PROPERTIES OF ANTARCTIC PERMAFROST
Figure 1. Locations, surface features, and core log of sites TM1 and TM2 on Table Mountain. The
aerial photo (top right) shows the different scale polygons, demarcated by snow, and the debris flow
(left). The middle figure shows the contact between the intrusive dolerite flow and Sirius. The core
stratigraphy and photos from central sections of the cores illustrate the very different compositions at the
two sites (detailed in text).
In this paper we characterize the depth and seasonal
variations in the thermal properties and present the lithographic profile in the top 2 m of these sites. In particular, we
seek to identify any differences in thermal properties that
might contribute to the factor-of-three difference in polygon
diameters between the nearby sites. Although previous
temperature measurements have been made in the nearsurface layers in Antarctic permafrost [Matsuoka et al.,
1990; McKay et al., 1998], we present the first in-depth
study of the thermal properties of the subsurface.
PRINGLE ET AL.: THERMAL PROPERTIES OF ANTARCTIC PERMAFROST
[5] In December 2000 identical, 2-m-long thermal arrays
were installed in two core holes in two polygonal ground
sites, 100 m apart, on the northwest flank of Table Mountain
(Figure 1). Although there is the potential for low-level
vapor transport, with a resulting transfer of latent heat, in
most soils, such transport is expected to be exceedingly
small in the ice-rich ground; and due to the very low yearround temperatures, there is no expectation of latent heat
effects or heat flow other than by conduction. We proceed
by this assumption and resolve the depth and seasonal
dependence of the apparent thermal diffusivity (ATD).
One site shows a weakly and smoothly varying ATD
profiles, whereas the other shows an abrupt twofold increase
over a sharp compositional boundary. We present the results
of several established ‘‘time series’’ methods for computing
the mean ATD profile. In particular, we are interested in the
performance of these methods at this abrupt boundary. We
calculate the heat capacity at the sites, and from it and the
ATD profiles we calculate the apparent thermal conductivity
profiles which we correlate with core compositions.
2. Site Details
[6] The experimental sites TM1 (775703600S; 1615701500E,
1840 m above mean sea level) and TM2 (775703900S;
1615702500E, 1852 m) are on the northwest flank of Table
Mountain, which is on the south side of the Ferrar Glacier
near the eastern margin of the Dry Valleys (Figure 1). Table
Mountain is made up of sandstones of the Beacon Supergroup, which have been intruded by Ferrar Dolerite (Jurassic). These formations are mantled by a linear band (2 5 km) of Sirius Group, a glacial till [Passchier et al., 1998]
with a probable, but controversial, mid-Miocene age [Miller
and Mabin, 1998]. Sirius Group sediments crop out in a
series of low (<3 m) ridges and have a hardness of dried
mud, but those below depths of 50 cm are generally
ice-cemented.
[7] The northwestern flank of Table Mountain also has
several debris flows that appear to originate from weathered dolerite dikes. Although the age and mechanism by
which these debris flows formed are unknown, they are
clearly defined by large-scale polygonal ground (Figure 1).
The debris flow in our study area truncates the Sirius
Group, which is marked by small-scale polygons (Figure 1).
Regardless of the sediment composition and soil horizonation, loose, dry, ice-free permafrost in the vicinity of these
sites is 10– 50 cm thick and lies on top of the ice-cemented
permafrost. The contact between the dry and ice-cemented
permafrost is not flat but undulates depending on the aspect
of the ground surface and overlying materials. The depths
quoted in this paper are referenced to the level surface at each
installation site. Note that the dry permafrost overlying the
ice-cemented permafrost is not an ‘‘active layer.’’ Aside from
direct solar heating of surface rocks during the summer, this
layer is below freezing year round but is simply ice free. The
sublimation and evaporation rates of the subsurface ice
through such layers is currently under investigation [Sugden
et al., 1995; Hindmarsh et al., 1998; Marchant et al., 2002;
Putkonen et al., 2003; Stone et al., submitted manuscript,
2002]. A desert pavement of ventifacted dolerite pebbles and
cobbles covers the surface at both sites.
ECV
3-3
Figure 2. Ice content of recovered cores: TM1 (closed
circles) and TM2 (open circles); lines, running three-point
averages. The left-hand axis is measured mass fractions and
right-hand axis the volume fractions calculated using rice =
0.91 g cm3, rmineral phase = 2.65 g cm3.
[8] At site TM1 the polygons on the surface have an
average diameter of 16 m and are demarcated by snow
accumulation in the peripheral trenches, which are about
0.5 m below the polygon centers. Sediment at this site
originates as a debris flow, which contains mostly dolerite
as both clasts and matrix. At the installation hole, the dry
permafrost is loose to a depth of 0.45 m and consists of very
poorly sorted sediment with about 20% gravel, and 70%
sand, silt, and clay. The ice cement from 0.45 to 0.66 m
consists of essentially the same material as in the dry
permafrost zone, but the dolerite clasts are more weathered
(Figure 1). Below 0.66 m the sediment comprises about 30%
ice, 20% clasts (scattered pebbles and cobbles 3 –10 cm
diameter), and 50% sand, silt, and clay. Clasts in this lower
zone are mostly unweathered and fresh looking.
[9] Polygons at site TM2 have an average diameter of
5 m, and although smaller, they have a similar morphology
to those at site TM1. The dry surface permafrost is light tan
in color and loose to a depth of 0.14 m. It consists of about
40% small dolerite pebbles and 60% sand, silt, and clay,
which derive mostly from Sirius group facies. From a depth
of 0.14 – 0.92 m the sediment is a moderately sorted,
medium to coarse quartz-rich sand with several zones of
weathered dolerite clasts (5 cm diameter) and segregation
ice. The overall composition in this unit is about 23% ice,
10% dolerite clasts, and 67% quartz-rich, medium grain
sand. Several 0.01-m-thick ice lenses occur between 0.7
and 0.9 m. From 0.92 to 1.86 m is a massive, well-sorted,
medium to coarse-grained, quartose sandstone of the Sirius
group, cemented by pore ice and fine clays [Dickinson and
Grapes, 1997]. See photo (Figure 1). The sandstone contains about 15% ice, mostly in pore space. Below this, and
extending to the bottom of the thermistor array, is a zone of
about 30% dolerite clasts (10 –15 cm diameter) 50% quartzrich sand, and 20% ice, both in pore spaces and as ice
lenses.
[10] The ice mass-fraction profiles for both sites are
shown in Figure 2. These were determined from approximately 50-mm-long, 60-mm-diameter sections from the
ECV
3-4
PRINGLE ET AL.: THERMAL PROPERTIES OF ANTARCTIC PERMAFROST
frozen and dehydrated weights. Within the ice cement, ice is
present as both lenses (see Figure 1) and as pore ice. The
length scale of features in the ice cement, for example, ice
lenses and pebbles, is comparable with the core-section
dimensions (50 mm), so the ±10% variability in ice
content over these length scales is not surprising.
to ice horizon. The top three thermistors at TM1 were in the
ice-free debris, whereas at site TM2 the top thermistor was
just above the ice horizon. To smooth out the random
measurement noise, sTnoise 0.005C, we filtered the data
with a time domain Gaussian filter of full, truncated width 1
day and standard deviation, s = 1/2 day [Kanasewich, 1981].
3. Instrumentation and Temperature
Measurements
4. Analysis Methods
[11] The thermistor arrays are adapted from units custom-built for measuring heat flow in first-year sea ice
[McGuinness et al., 1998; Trodahl et al., 2000, 2001]. The
body of the array is a 2-m-long, 0.25-inch (6.35 mm)
diameter, thin-walled (0.2 mm) stainless steel tube. This
houses a thin Teflon string along which 15 high-precision
YSI 55031 thermistors are spaced 13.5 cm apart. The tube is
filled with an oil, which is poured in at room temperature,
but at field temperatures it freezes to a viscous gel providing
good thermal contact without convection. Thermistor resistance measurements were made with a Campbell CR10X
data logger. The thermistors have an accuracy (interchangeability) of 0.1C at 20C but a precision better than
0.01C. We stress that for all the analytical methods we
use, it is the precision that is important, not the absolute
accuracy. The thermistor chain was read every 4 hours.
[12] Sites TM1 and TM2 were core-drilled using compressed air and diamond bits [Dickinson et al., 1999].
Because core recovery was only possible from the icecemented sediments, the dry permafrost was excavated from
around the hole before drilling. The cores were described,
photographed, and analyzed for particle size and ice chemistry in New Zealand. A small v-shaped notch was cut into
2-m-long, 75-mm-diameter polyurethane pipe insulation.
The thermistor probe was placed in the notch, and both
were gently pushed into the 63-mm-diameter hole so that
the pipe insulation held the probe against the side of the
hole to optimize thermal contact. To minimize the disturbance to the natural heat flow, there must be either a
matching of thermal properties across the interface or no
heat flow; we approximate the latter case. Once the array
was installed, the excavated area above the ice cement was
refilled and leveled to its original condition.
[13] Figure 3 shows the measured temperatures. The raw
temperature series for sites TM1 and TM2 are shown in
Figures 3a and 3e where only every second thermistor is
shown for clarity. False color reconstructions of the temperature field are shown in Figures 3d and 3f. Due to a
power regulator failure, TM1 did not record between
August and December 2001. Figures 3b and 3c show the
characteristic temperature response in summer and winter at
site TM2. In the summer months, the surface driving is
principally solar cycling superimposed on the annual variation, and the solar cycling is seen to penetrate more than
50 cm at both sites. In the Austral night of the winter
months, large-amplitude surface events occur about every
3 weeks with a duration of approximately 3 days due to
winter storm activity [e.g., Matsuoka et al., 1990]. Surface
temperature events are clearly coincident at both sites in
Figures 3a and 3e and in Figures 3d and 3f. Differences in
the traces of the uppermost thermistors between the sites are
due to the natural variation in the surface layer and the depth
[14] A variety of general approaches have been used to
calculate thermal properties from temperature measurements, including direct time series analysis, through to more
sophisticated inverse problem methods. Several authors
have compared subsets of these approaches, including
Persaud and Chang [1985], Hinkel [1997], and Fuhrer
[2000]. When the thermal diffusivity is calculated from real
data, assuming 1-D conductive heat flow, it is commonly
termed the ATD to acknowledge that it may include contributions from mechanisms other than 1-D conduction. We
anticipate a system that is well described by 1-D conductive
heat flow with no latent heat effects and seek to resolve the
ATD depth profile at both sites with direct time series
analysis methods.
[15] The heat equation for conductive, linear heat flow
with no latent heat effects, or other heat generation, is
CV
@T ð z; t Þ
¼ rk rT þ kr2 T ;
@t
ð1Þ
where CV is the volumetric heat capacity and k is the thermal
conductivity. As the vertical temperature gradient of
approximately 1– 10C m1 exceeds the lateral gradient
between the two sites by more than two orders of magnitude
we reduce equation (1) to 1-D:
CV
@T ð z; t Þ @k @T
@2T
¼
þk 2 :
@t
@z @z
@z
ð2Þ
Equation (2) is more readily solvable if the first term on the
right is neglected by assuming, at least locally, constant
thermal properties. It becomes
@T ð z; t Þ
@2T
¼D 2;
@t
@z
ð3Þ
where D = k/CV is the thermal diffusivity. Most Fourierderived methods based on the attenuation and phase lag of
temperature waves derive from equation (3) and rely on this
assumption of globally constant thermal properties [e.g.,
DeVries, 1963; Carson, 1963; Nassar and Horton, 1990]. In
real situations, thermal properties invariably do vary with
depth. A common way to account for this is to calculate a
mean, local ATD by assuming constant thermal properties
between the depths of the temperature sensors used in the
calculation. However, ‘‘perturbed Fourier’’ methods have
been developed to accommodate nonconstant thermal
properties [e.g., Lettau, 1954, 1962; Stearns, 1969; Hurley
and Wiltshire, 1993]. We consider three analysis methods
that require only measurements of the temperature field, and
not also the heat flux, which some methods require [Lettau,
1954, 1962; Stearns, 1969]. As we address a simple thermal
regime, we limit ourselves to time series analysis and do not
PRINGLE ET AL.: THERMAL PROPERTIES OF ANTARCTIC PERMAFROST
ECV
Figure 3. Temperature data. In all time series the bottom thermistor (z = 1.98 m) is the dashed line and the
top thermistor (z = 0.09 m) has the largest amplitude. (a) TM2 time series showing every second thermistor
for clarity. (b and c) Characteristic summer and winter variations from TM2 (see text). (d) False
color reconstruction of TM2 temperature field; isotherm increments are 2C. (e) TM1 time series.
(f ) Reconstructed TM1 temperature field. Missing data due to power regulator failure. See color version of
this figure at back of this issue.
3-5
ECV
3-6
PRINGLE ET AL.: THERMAL PROPERTIES OF ANTARCTIC PERMAFROST
consider more sophisticated inverse problem schemes; we
seek a simple but accurate method for resolving variations
in the ATD.
4.1. Method I, Simple Fourier Methods of Carson
[16] When the first term on the RHS in equation (2) is
omitted, it admits a Fourier decomposition solution:
T ð z; t Þ ¼ T ð zÞ þ
X
An ez=dn eiðwn tz=dn þf0;n Þ ;
ð4Þ
n
where T(z)is the mean temperature at depth z, and n indexes
the frequency components of magnitude An, frequency wn,
penetration depth dn = (2D/wn)1/2 and phase fn(z) = f0,n z/dn.
In this case the mean local ATD can be estimated from
the amplitude attenuation and phase lag of a given frequency component between two or more depths [Carson,
1963]:
Damp ¼
Dphase
w ðz2 z1 Þ2
;
2 ½lnðA1 =A2 Þ2
w ðz2 z1 Þ2
¼
:
2 ðf1 f2 Þ2
ð5aÞ
ð5bÞ
4.2. Method II, Perturbed Fourier Method
[17] Hurley and Wiltshire [1993] applied a perturbation
approach to enable a Fourier decomposition approach while
still retaining the @k/@z term in equation (2). We adopt
their approach and slightly modify the mathematics. We
expand the temperature in a generalized form similar to
equation (4):
X
ern ðzÞ ei½wn tþfn ðzÞ ;
T ð z; t Þ ¼ T ð zÞ þ
ð6Þ
n
where An ð zÞ ¼ ern ðzÞ and fn(z) are now unknown functions
of z. By inserting equation (6) into equation (2) and solving
for the real and imaginary parts, an expression for D is
obtained:
1
0
f0
2f
Dn ð zÞ ¼ wn r0 f0 þ ðf0 Þ 0 þ f00 r00 0
;
r
r
ð7Þ
where the primes denote depth derivatives, and the subscript
n has been dropped from all terms in the square brackets.
The relevant derivatives are determined by calculating the
parameters An and fn at the depth of each thermistor and
fitting polynomials to plots of ln(An(z)) and fn(z), see
Figure 4, discussed in section 5.
4.3. Method III, Graphical Finite Difference Method
[18] Several different finite difference methods for calculating the ATD have been presented and critiqued [e.g.,
McGaw et al., 1978; Persaud and Chang, 1985; Zhang and
Osterkamp, 1995; Hinkel, 1997]. The most direct approach
is to use finite difference estimates of the derivatives in
equation (3) and to calculate the mean ATD by their ratio on
a point-by-point basis [McGaw et al., 1978; Zhang and
Osterkamp, 1995; Hinkel, 1997; Westin and Zuidhoff,
Figure 4. Depth dependence of the natural logarithm of
the amplitude (left axis, circles), and phase (right axis,
diamonds) of the 1 yr1 component at site TM2. The curves
are the sixth-order polynomials used in equation (7).
2001]. The mean ATD is then given by the time average
of these ratio values. This method suffers systematic difficulties when the temperature curvature, @ 2T/@z2, passes
through zero [Zhang and Osterkamp, 1995]; and furthermore, it requires temperature measurements with an accuracy comparable to their precision. Hinkel [1997], provides
a method for calculating the ATD using equation (5a)
specifically for diurnal forcing whereby the temperature
amplitudes A1 and A2 are calculated from a finite difference
estimate of the average time rate of change of temperatures.
[19] We use a graphical finite difference scheme, which
we have previously applied to sea ice measurements
[McGuinness et al., 1998; Trodahl et al., 2000, 2001], that
does not require harmonic forcing and is insensitive to
interthermistor calibration offsets. As for the other finite
difference methods discussed in the preceding paragraph,
we make the assumption of locally constant thermal properties for the space between adjacent thermistors. We graph
a scatterplot of the finite difference estimates of the derivatives in equation (3): @T(z, t)/@t [T(z, t + t) T(z, t t)]/2t and @ 2T(z, t)/@z2 [T(z + z, t) 2T(z, t) +
T(z z, t)]/(z)2, see Figure 5. The best fit slope of the
graph is then the mean ATD for this depth interval and for
the time interval for which data is plotted. Note that any
calibration offsets for each thermistor, ai, will not affect @T/
@t and will provide a constant shift in @ 2T/@z2 of (ai+1 2ai + ai1)/(z)2 This systematic shift in the @ 2T/@z2
values means that the best fit line will not generally pass
through (0, 0) but its slope will be unaffected. The measurement noise in T results in scatter in both @T/@t and @ 2T/
@z2. In this case, and for small relative errors, an unbiased
estimate of the slope is given by the geometric mean of
regressing @T/@t on @ 2T/@z2, (D1), and @ 2T/@z2 on @T/@t,
(D21), i.e., D = (D1D2)1/2 (see Appendix A for details).
5. ATD Results
[20] In this section we show the ATD profiles resulting
from the application of the above methods to our temperature measurements. We compare the different profiles and
PRINGLE ET AL.: THERMAL PROPERTIES OF ANTARCTIC PERMAFROST
Figure 5. Finite Difference method scatterplot of @T/@t
versus @ 2T/@z2, for site TM2, thermistor 4 (z = 0.50 m), in
the summer: 20 November 2001 to 20 January 2002. The
solid line is the least squares regression of @T/dt versus @ 2T/
@z2, and the dashed line the least squares regression of @ 2T/
@z2 versus @T/dt, see text and Appendix A.
comment on the performance of the different methods,
starting with the simple Fourier method I.
[21] The temperature variations are dominated by the
yearly cycle, so we have truncated the record to include
one complete yearly cycle and fitted Fourier components
at different depths within this record. The two lowestfrequency components that can be estimated are then 1 and
2 yr1, and indeed, these are very strong components given
the approximately periodic nature of the dominant variations. We have used the fitted amplitudes and phases of
these components in applying the Fourier methods I and II.
The initially small amplitudes of the higher-frequency
components rapidly attenuate to the limits of our resolution.
[22] Figure 4 shows r(z) = ln[A(z)], and f(z) for the 1 yr1
component at site TM2, from which it can be seen that they
are clearly not linear with depth. Both curves have a similar
trajectory, indicating a depth variation in the ATD. The ATD
profiles obtained directly from the local slopes of r(z) =
ln[A(z)], and f(z) using equations (5a) and (5b) of Method I
are shown in Figure 6 together with the results of the other
methods. We have used the strongest well-constrained
component at each site: 1 yr1 at site TM2 and, due to
the missing data, 2 yr1 at site TM1. Only the amplitude
data are shown for TM1 as the phase was poorly constrained by the data.
[23] The smooth curves through the r(z) and f(z) data
points in Figure 4 are sixth-order polynomials fitted to
obtain the derivatives needed in equation (7) for Method
II. The ATD profile thus obtained from equation (7) for
TM2 is shown by the thick dashed line in Figure 6 and
clearly resolves a central region of enhanced diffusivity. As
the phase of the 2 yr1 component was poorly constrained,
this method could not be used for either of the two dominant
components at TM1. Fortunately, site TM2 shows the
strongest ATD depth variation and so provides better data
for a comparison of methods and is also the geophysically
ECV
3-7
more interesting system as is discussed in section 5.1. For
the long periods considered, this perturbed Fourier method
is insensitive to measurement noise but has no time resolution. Its spatial resolution is limited by the order of the
derivatives of the fitted polynomial, in turn limited by the
number of depths recorded. A general rule is that the order
of fitted polynomial, n, should be less than half the number
of thermistors used [Hurley and Wiltshire, 1993]. In our
case n = 6, so the first and the second derivatives are
quintics and quartics, as reflected in the shape of the ATD
profile. This method necessarily smooths out sharp variations and limits depth resolution to about 2 m/(n 2) =
50 cm.
[24] The ATD profiles resolved from our graphical finite
difference method, Method III, are shown in Figure 6. Note
that the first depth at which these profiles can be calculated
is the second thermistor frozen into the ice-cemented
ground; this depth is 0.63 m at TM1 and 0.36 m at TM2.
This is only one of our methods capable of identifying a
seasonal variation, and indeed, the data of Figure 7 show a
thermal diffusivity, which is higher in winter (1 April to
1 August) than in summer (20 November to 20 January).
Below, we show how the site-to-site variation reflects the
compositional difference revealed by the cores, and the
seasonal variation reflects the temperature dependence of
the thermal properties.
[25] Figure 6 shows very clear differences in the thermal
diffusivity profiles returned by the three methods, especially noticeable at site TM2, the site in which there is a
strong depth dependence in that parameter. It is further
clear that even at that site Methods II and III are consistent
(within the limited spatial resolution of Method II) but
Method I returns an ATD up to 50– 70% higher. While a
direct comparison of such methods is hindered by not
Figure 6. ATD profiles D(z) at sites (a) TM1 and (b) TM2
from all methods: solid symbols and line, graphical finite
difference method (III), with uncertainties from determining
the best fit gradient at each depth; heavy dashed curve,
perturbed Fourier method (II); dot-dashed curve, Carson
method (I) amplitude; dotted curve, Carson method (I)
phase.
ECV
3-8
PRINGLE ET AL.: THERMAL PROPERTIES OF ANTARCTIC PERMAFROST
their volume fractions, but the effective thermal conductivity is a function of the geometric configurations of the
components as well as their volume fractions:
keff ðki ; vi Þ
Deff ¼ P
:
vi Ci
Figure 7. Seasonal variation in ATD profiles: (a) TM1 and
(b) TM2. Solid line: winter; dashed line: summer. Profiles
start from the second thermistor embedded in the ice
cement.
knowing a priori the diffusivity structure [Persaud and
Chang, 1985], we show below that Methods II and III are
consistent with the core composition and stratigraphy but
that Method I gives unphysically high values. The failure
of Method I lies in the assumption of a globally constant
thermal properties, invoked to obtain equation (4). This
solution considers the downward propagation of surface
disturbances and is unable to accommodate thermal waves
reflected upwards from diffusivity variations. The solution
is thus inappropriate even to determine a local diffusivity
that is piecewise constant. In contrast, Methods II and III
make no such assumptions so that they can be expected to
return realistic depth-dependent diffusivities limited only
by the depth resolution imposed by the thermistor spacings. Figure 6b shows that within this reduced resolution,
the mathematically robust Methods II and III resolve
consistent ATD profiles, in particular, the magnitude in
the region of enhanced diffusivity at site TM2: 0.9 m <
z < 1.4 m.
5.1. Interpreting the ATD Profiles
[26] The range of ATD values in Figure 6 values are, in
general, not greatly different from the diffusivity of ice and
typical mineral components, D(20C) ice = 1.15 106 m2 s1, Dmins (0C) 1.5 106 m2 s1, and
they lie below the value of quartz, which displays the
highest diffusivity of soil minerals, Dquartz (0C) 4.3 106 m2 s1 [Farouki, 1981]. We now turn to a quantitative
examination of the depth-, site-, and seasonal-ATD variations resolved by Methods II and III in terms of the core
composition and temperature dependence of the local heat
capacity and thermal conductivity. We first note that the
effective thermal diffusivity of a composite material is the
ratio of the effective thermal conductivity to its volumetric
heat capacity. The heat capacity is a simple average of the
volumetric heat capacities of the constituents, weighted by
ð8Þ
There are many models for the effective thermal conductivities, keff(ki, vi), of such composites [Farouki, 1981], but one
common feature is that they all contain only terms which are
first order in the thermal conductivities of the constituents, a
feature to which we refer below.
5.1.1. Temperature Dependence and Seasonal
Variation
[27] The difference in winter-to-summer diffusivity is
found to be 15% ± 5 at site TM1, 20% ± 10 at site TM2,
and 18% ± 9 overall. No seasonal change was observed in a
high-precision reference resistor at a depth of 2 m in either
array, eliminating data logger performance as the source of
the variation. From summer to winter the average ground
temperature in the top 2 m decreases from 12C (261 K)
to 27C (246 K), a 6% relative change, and we will now
demonstrate that the observed diffusivity variation is consistent with its expected temperature dependence.
[28] The thermal conductivity of electrically insulating
crystals is expected to vary approximately as k / T1,
where T is the absolute temperature [Ashcroft and Mermin,
1976; Roy et al., 1981], and this relationship has been
recognized for rocks, minerals, and ice at moderate temperatures [Clauser and Huenges, 1995; Anderson and Suga,
2002]. Thus the numerator of equation (8) will show a
similar dependence, raising the thermal diffusivity by
approximately 6% during the winter months. Furthermore,
the heat capacity of such materials decreases with temperature, so the diffusivity increases even faster than T 1 with
falling temperatures. Over our temperature range the heat
capacity of ice increases by 6% [Weast, 1971]. Data on the
temperature dependence of the heat capacity of materials
suitable for comparison with the mineral components of our
cores in our temperature range are scarce. However, we note
that the thermal diffusivity of Berea sandstones suggests a
11% decrease from winter to summer temperatures [Roy et
al., 1981], equivalent to a 5% increase in the heat capacity.
The numerator and denominator of equation (8) are first
order in the thermal conductivities and heat capacities,
respectively, of ice and minerals. Consequently, they will
show the same relative variations as found in the materialspecific parameters and lead to a thermal diffusivity increase
of approximately 11 – 12% from winter to summer. Accounting for a seasonal temperature variation decreasing
with depth, this figure becomes 11% ± 3 which lies within
the measured uncertainties at both sites. Although the
thermal conductivity of rocks and soils depends greatly on
physical and diagenic factors [Clauser and Huenges, 1995],
the above comparison suggests that it is not unreasonable
that the observed seasonal variation reflects the underlying
temperature dependence.
5.1.2. Composition Dependence: Depth and Site
Variations
[29] The depths at which the diffusivity profiles in
Figure 6 show features correlate well with the stratification
PRINGLE ET AL.: THERMAL PROPERTIES OF ANTARCTIC PERMAFROST
and composition profiles shown in Figures 1 and 2
and described in detail in section 3. Turning first to
site TM1, the core shows little stratification consistent
with the weak depth dependence shown in the diffusivity.
Below 60 cm, the core shows a mixture of dolerite
pebbles and fragments frozen into an ice matrix. The
ice-content profile shows a low ice fraction nearer the ice
horizon, increasing to a roughly constant value of 30% ± 10
by mass (55% ± 10 by volume) at lower depths. The highest
diffusivity (2 106 m2 s1) is resolved, where the ice
content is lowest, ice lenses are less prevalent, and the soil
phase most consolidated. In the bottom 1 m, the diffusivity
approaches the value of pure ice (1.15 106 m2 s1 at
20C).
[30] Site TM2 shows substantially more structure in both
the stratification and the diffusivity profiles, as described in
section 3. For 0.14 m < z < 0.9 m, the core is a Sirius till/ice
matrix with prominent ice lenses. There is a sharp transition
at z = 0.9 m to the quartose Sirius sandstone and little sign
of segregation ice down to z = 1.45 m except a few lenses
near z = 1.2 m. Below 1.45 m, ice lenses become increasingly prevalent followed by a return to a disordered regolith/
ice matrix for z > 1.7 m. Each of these features is clearly
represented in the diffusivity profile which shows a sharp
transition at z 0.9 m, a region of enhanced diffusivity
0.9 m < z < 1.45 m and a smoother transition to lower
diffusivity at depth. The high ATD values in the middle of
the core, 2.5 ± 0.5 106 m2 s1, can only be consistent
with a well-consolidated, high quartz-content mineral phase,
as seen in the core. The stratigraphy of this site is representative of the local ground composition. In particular, this
quartose sandstone unit is not an isolated sandstone boulder
but rather, an extended feature, with several downslope
outcrops.
5.2. Heat Capacity and Thermal Conductivity
[31] The most uncertain of the thermal parameters of
relevance to our study is the effective thermal conductivity
of the composite; we have a direct measure of the diffusivity
and can obtain a rigorously justified estimate of the heat
capacity from a volume-fraction-weighted average of the
heat capacities of the constituent materials. For this reason
we have used the two known parameters to determine an
implied depth profile of the thermal conductivity.
[32] We start by estimating the volumetric heat capacity
of the ice-mineral mixture. The parameters required for the
purpose are the densities {rice, rmin soil} = {0.91, 2.65 ±
0.05} g cm 3 and specific heats {c ice (20C), c min
1
C1 [Weast,
soil(20C)} = {1790, 700 ± 50} J kg
1971; Farouki, 1981; Roy et al., 1981]. The ice massfractions vary approximately between 0.1 and 0.35,
corresponding to volume fractions 0.25– 0.6 (see Figure 2)
and Csoil = 1.8 ± 0.1 1.7 ± 0.1 MJ C1 m3.
[33] The points and dashed line in Figure 8 shows the
thermal conductivity profile k(z) = D(z)C(z) for site TM2
(left axis). C(z) has been calculated for the ice volumefraction at the site as described above and D(z) is the
arithmetic average of the summer- and winter-time diffusivity profiles. As expected, the conductivity near the
surface, and below the high-ATD zone, is consistent with
ice, kice(20C) = 2.4 W m1 C1 and typical soil
ECV
3-9
Figure 8. Thermal conductivity at site TM2. Circles and
dashed line: k(z) = D(z)C(z) (left-hand axis); series of lines:
j@T/@zj1 profiles for the days best satisfying quasi-static
conditions 26– 29 December 2001 (right-hand axis).
minerals, kmins(20C) 3.1 W m1 C1 (temperatureadjusted as k / T 1 from Farouki [1981]).
[34] The apparent thermal conductivity of the quartose
sandstone unit is 4.1 ± 0.4 W m1 C1. As this region
includes approximately 10– 15% ice by mass (25 – 35% ice
by volume), the conductivity of the mineral phase must
have an even higher value. By inverting the ‘‘Maxwell’’
model for the thermal conductivity of two-phase mixtures
[e.g., Farouki, 1981; Roy et al., 1981], which treats all
the ice simplistically as spherical inclusions, we estimate
the apparent conductivity of the soil phase to be 5.2 ±
0.5 W m1 C1. Such a high value is physically reasonable
only for very quartz-rich materials [Clauser and Huenges,
1995], as seen in this unit. Quartz is less prevalent in the
non-Sirius units of the core (and at site TM1), which are
characterized mainly by lower-conductivity dolerite debris.
[35] Figure 8 also shows the thermal conductivity, up to a
scale factor, determined directly from the temperature data
with another method. In steady state linear heat flow, the
temperature profile is by definition static: @T/@t = 0, and the
heat flux JQ(z) = k(z)rT(z) is constant, so k(z) / rT(z)1.
Due to surface driving, this situation does not apply near the
surface in our case, but at greater depths where the annual
variation dominates, temperatures do vary slowly over
several measurement time intervals. Quasi-static conditions
are best approximated in our data at site TM2 for 26–
29 December 2000. Each thin curve in Figure 8 is a profile
of the inverse of the daily-averaged gradient, jrT(z)j1 for
this period (right-hand axis). Below z = 0.6 m, where the
short-period surface disturbances are damped, this approximation is most robust, and the curves closely match the shape
of the diffusivity-derived conductivity profile. Because we
cannot independently determine the magnitude of the heat
flow, jJQj, these curves give the form of the conductivity
structure k(z) / jrT(z)j1 but not its magnitude.
[36] The form of k(z) calculated in this way provides
direct and independent evidence for a region of enhanced
apparent thermal conductivity at site TM2, and its excellent
agreement with the diffusivity-derived conductivity profile
ECV
3 - 10
PRINGLE ET AL.: THERMAL PROPERTIES OF ANTARCTIC PERMAFROST
confirms the depth resolution of the finite difference method.
We present this analysis for site TM2 to illustrate the
consistency of the methods, in particular, their resolution
of region of enhanced diffusivity; the TM1 profiles are also
consistent. Our results are consistent with the only other
conductivity measurement we are aware of in the greater Dry
Valley area. McKay et al. [1998] determined an ice-cement
thermal conductivity 2.5 ± 0.5 W m1 C1 just below the
ice horizon at Linnaeus Terrace. However, our profiles show
that due to the inhomogeneous composition, the thermal
properties can vary strongly over small distances. For icecemented permafrost sites in the Dry Valleys with a low
proportion of Sirius facies, we predict a thermal conductivity
in the range 2.5 ± 0.5 W m1 C1. However, the conductivity could be as much as twice as large for quartose facies
of the Sirius group.
6. Application of Results to Patterned Ground
[37] A detailed discussion of the important factors in
establishing polygon size is beyond the scope of this paper,
but we can relate a few field observations on the polygonal
ground to our results. The buildup of thermal stresses
depends on the rate of temperature change, dT(z)/dt, which
depends on how the variations in surface heat flux are
propagated to depth as measured by the thermal inertia,
I = (krc)1/2 = D1/2rc. Our results show that within the
permafrost, the conductivity can vary by as much as a factor
of 2 but that the p
heat capacity is roughly constant giving a
factor of about 2 variation in the thermal inertia. It is
unlikely that this maximal variation is a critical factor in the
observed threefold change in polygon diameter between
sites.
[38] We find little difference, and certainly no order of
magnitude difference in the distribution of dT/dt values
calculated at the nearest thermistors to the ice horizon at
the two sites. Furthermore, the age and origin of the debris
flow, and the history of the depth to ice horizon from the
time of initial crack formation until now are all unknown at
both sites. We believe that the ice-rich and heavily disordered debris flow was weaker than the surrounding, wellconsolidated ground during the development of the polygon
networks, which lead to deeper cracks and stress relief
over larger distances, resulting in a larger-scale network
[Lachenbruch, 1962].
7. Summary and Conclusions
[39] We have applied three time series analysis methods
to 14 months’ high-precision temperature measurements
from two nearby sites at Table Mountain. The system is
physically simple, with only 1-D conductive heat flow
expected. This has enabled a comparison of the reliability
of several analysis methods and a resolution of depth and
seasonal variations in the ATD. The simplified Fourier
method of Carson, using the phase lag and attenuation of
the 1 yr1 and 2 yr1 temperature components, has overestimated the ATD at site TM2 by 50– 70% due to not
accommodating reflected thermal waves. The perturbed
Fourier method of Hurley and Wiltshire is mathematically
robust in the presence of diffusivity variations but has a
depth resolution limited by the number and spacing of
thermistors used and gives only a time-averaged value over
the period examined. The graphical finite difference scheme
described here is simple to implement, has depth and time
resolution, and does not require harmonic temperature
variations. It gives a mean local ATD profile, which is
consistent with the perturbed Fourier method and an independent quasi-static analysis. These profiles quantitatively
correlate very well with the composition of recovered cores,
including a sharp twofold increase in ATD across an abrupt
compositional boundary at one site. This method resolves a
seasonal variation, where wintertime ATD values are on
average 18% ± 9 higher than summertime values, overlapping the estimated underlying temperature dependence
of 11% ± 3.
[40] The calculated heat capacity depends weakly on ice
fraction and falls in the range, CV (20C) = {1.7 ± 0.1 1.8 ± 0.1} MJ m3 C1. The apparent thermal conductivity, calculated as k(z) = D(z)C(z), correlates very well with
the cores. The conductivity generally lies in the range 2.5 ±
0.5 W m1 C1, but is as high as 4.1 ± 0.4 W m1 C1 for
the quartose Sirius sandstone unit at site TM2. The conductivity of the mineral component of this quartose unit is
estimated to be 5.2 ± 0.5 W m1 C1.
[41] We do not believe that the variations in thermal
properties have played a critical role in the threefold
difference in polygon size at these two sites. The surface
cover and material strength at the times of debris flow
creation and polygon network development are considered
to have been more critical factors.
Appendix A: Details of Graphical Finite
Difference Method
A1. Effect of Measurement Noise
[42] From equation (3), the physical diffusivity (D) will
be given by the gradient of a scatterplot of @T/@t versus @ 2T/
@z2. However, some care must be taken in determining the
best fit gradient. Random errors in the variable considered
independent leads to a least squares slope being underestimated by the factor [1 + (dx)2]1, where dx = sx noise/sx
signal is a measure of the relative error in X. It is the
uncertainty-related variance divided by the natural range
of the data [Fuller, 1987]. This effect applies to both of our
variables. We identify X with @ 2T/@z2 and Y with @T/@t and
determine two estimates of the thermal diffusivity, as the
gradient of Y versus X, (D1), and as the inverse of the
gradient of X versus Y, (D2) (see Figure 5.) We then estimate
the slope as the geometric mean Dgm = (D1D2)1/2, which to
second order in d gives
1
Dgm ¼ D 1 þ d2Y d2X :
2
ðA1Þ
[43] If the relative uncertainties, dY and dX, are equal,
equation (A1) gives an unbiased estimate of the slope,
despite the measurement errors. The random measurement
noise in our case is dx 2.5 dy. (Note that both uncertainties
have their source in temperature-measurement uncertainties,
so that sx and sy are related.) For the winter months both are
less than 20%, so that the geometric mean gives an error
less than 2%. In the present work, the natural range of @T/@t
PRINGLE ET AL.: THERMAL PROPERTIES OF ANTARCTIC PERMAFROST
and @ 2T/@z2 values is reduced during the summer months,
resulting in higher relative errors, corrected for up to 4% by
using equation (A1).
A2. Effect of Finite Sampling Intervals
[44] The accuracy of the finite difference approximations
ð@t T Þij ¼ Tjiþ1 Tji =t;
ðA2bÞ
depends on the sampling intervals z and t. The ratios
(z/d) and (t/T) must be sufficiently small, where d is the
characteristic penetration depth d = (2D/w)1/2 and T is a
characteristic period of the driving temperature forcing.
[45] In reality, there will be nonharmonic forcing and
measurement noise. As an example to illustrate potential
pitfalls in applying the method, we consider here the case of
harmonic forcing: q(0, t) = T0 exp(iwt). It is mathematically
convenient to use complex exponentials, where it is understood that the physical temperature is given by the real part
of this expression: q(0, t) = Re(q(0, t)) = T0 cos(wt). The
solution to the semi-infinite homogeneous problem is then
T ð z; t Þ ¼ T0 exp½ð1 þ iÞz=d expðiwt Þ:
ðA3Þ
Using equations (A3) and (A2), and expanding the resulting
expressions to third order in (t/T) and fourth order in
(z/d ), and taking the real part gives
!
2p2 t 2
wT0 expðz=d Þ sinðwt z=d Þ;
@t Tji ¼ 1 FD
3
T
ðA4aÞ
!
1 z 4 2T0
i
@zz Tj
¼ 1þ
expðz=d Þ
FD
d2
72 d
!#
1 z 2
sin½ðwt z=d Þþ tan1
:
36 d
ðA4bÞ
[46] Analytically, both @ tT and @ zzT are sine functions,
and for t = z = 0, the analytical forms are recovered.
Due to the phase shift in @ zzT, the two expressions are no
longer in phase, and the ratio of their magnitudes is
decreased. When plotted as @ tT versus @ zzT, the locus of
points will not describe a straight line of slope D, but rather,
a Lissajous figure (ellipse) with average gradient (principleaxis direction) given not by D but by
1 þ ð1=72Þðz=d Þ4
uted previously to physical hysteresis effects in sea ice
measurements [Trodahl et al., 2000].
[49] Acknowledgments. This work was funded by the New Zealand
Public Good Science Fund (PGSF) with logistics support from Antarctica
New Zealand. We are very grateful to Tim Kerr (Scott Base Science
Technician), Alan Rennie and Eric Broughton for design and instrumentation, Mark McGuinness and Juila Boike for helpful discussions, and
Webster’s Drilling Co.
References
1 ð2p2 =3Þðt=T Þ2
3 - 11
ðA2aÞ
i
i
ð@zz T Þij ¼ Tjþ1
=ðzÞ2 ;
2Tji Tj1
gradient ¼ D
ECV
:
ðA5Þ
[47] In practice, the (1/72)(z/d)4 term will usually be
entirely negligible, though some attention must be paid to
the (t/T)2 term when short-period forcing is present. We
stress that for the present work this effect was not important.
[48] Any such ellipses will be traced out in a counterclockwise fashion and may be the origin of features attrib-
Anderson, O., and H. Suga, Thermal conductivity of amorphous ices, Phys.
Rev. B, 65, 140201(R), 1 – 4, 2002.
Ashcroft, N. W., and N. D. Mermin, Solid State Physics, Holt, Rinehart, and
Winston, Fort Worth, Tex., 1976.
Carson, J. E., Analysis of soil and air temperatures by Fourier techniques,
J. Geophys. Res., 68, 2217 – 2232, 1963.
Clauser, C., and E. Huenges, Thermal conductivity of rocks and minerals,
in A Handbook of Physical Constants: Rock Physics and Phase Relations, AGU Ref. Shelf, vol. 3, edited by T. Ahrens, pp. 105 – 126, AGU,
Washington, D. C., 1995.
DeVries, D. A., Thermal properties of soils, in Physics of Plant Environment, edited by W. R. Van Wijk, pp. 210 – 235, North-Holland, New
York, 1963.
Dickinson, W. W., and R. H. Grapes, Authigenic chabazite and implications
for weathering in Sirius Group diamictite, Table Mountain, Dry Valleys,
Antarctica, J. Sediment. Res., 67, 815 – 820, 1997.
Dickinson, W. W., P. Cooper, B. Webster, and J. Ashby, A portable drilling
rig for coring permafrosted sediments, J. Sediment. Res., 69, 518 – 521,
1999.
Farouki, O. T., Thermal Properties of Soils, CRREL Monogr., vol. 81 – 1,
U.S. Army Cold Reg. Res. and Eng. Lab., Hanover, N.H., 1981.
Fuhrer, O., Inverse heat conduction in soils: A new approach to recovering
soil moisture from temperature records, Diploma thesis, Swiss Fed. Inst.
of Technol., Zürich, 2000.
Fuller, W. A., Measurement Error Models, John Wiley, Hoboken, N. J.,
1987.
Hindmarsh, R. C. A., F. M. van der Wateren, and A. L. L. M. Verbers,
Sublimation of ice through sediment as a constraint on ice age in Beacon
Valley, East Antarctica, Geogr. Ann., 80A, 209 – 219, 1998.
Hinkel, K. M., Estimating seasonal values of thermal diffusivity in thawed
and frozen soils using temperature time series, Cold Reg. Sci. Technol.,
26, 1 – 15, 1997.
Hurley, S., and R. J. Wiltshire, Computing thermal diffusivity from soil
temperature measurements, Comput. Geosci., 19, 475 – 477, 1993.
Kanasewich, E. R., Time Sequence Analysis in Geophysics, Univ. of Alberta
Press, Edmonton, Alberta, Canada, 1981.
Lachenbruch, A. H., Mechanics of thermal contraction cracks and icewedge polygons in permafrost, Spec. Pap. Geol. Soc. Am., 70, 1962.
Lettau, H. H., Improved models of thermal diffusion in the soil, Trans.
AGU, 35, 121 – 132, 1954.
Lettau, H. H., A theoretical model of thermal diffusion in nonhomogeneous
conductors, Gerlands Beitr. Geophys., 71, 257 – 271, 1962.
Malin, M. C., and K. S. Edgett, Evidence for recent groundwater seepage
and surface runoff on Mars, Science, 288, 2330 – 2335, 2000.
Marchant, D. R., A. R. Lewis, W. M. Phillips, E. J. Moore, R. A. Souchez,
G. H. Denton, D. E. Sugden, N. J. Potter, and G. P. Landis, Formation of
patterned ground and sublimination till over Miocene glacier ice in Beacon Valley, southern Victoria Land, Antarctica, Geol. Soc. Am. Bull., 114,
718 – 730, 2002.
Matsuoka, N., K. Moriwaki, S. Iwata, and K. Hirakawa, Ground temperature regimes and their relation to periglacial processes in the Sør Rondane
Mountains, East Antarctica, Proc. NIPR Symp. Antarct. Geosci., 4, 55 –
65, 1990.
McGaw, R. W., S. I. Outcalt, and E. Ng, Thermal properties of wet tundra
soils at Barrow, Alaska, Proceedings of 3rd International Conference on
Permafrost, vol. 1, pp. 47 – 53, Nat. Res. Counc. of Can., Ottawa,
Canada, 1978.
McGuinness, M. J., K. Collins, H. J. Trodahl, and T. G. Haskell, Nonlinear
thermal transport and brine convection in first year sea ice, Ann. Glaciol.,
27, 471 – 476, 1998.
McKay, C. P., M. T. Mellon, and E. I. Friedmann, Soil temperatures and
stability of ice-cemented ground in the McMurdo Dry Valleys, Antarctica, Antarct. Sci., 10, 31 – 38, 1998.
Mellon, M. T., Small-scale polygonal features on Mars: Seasonal thermal
contraction cracks in permafrost, J. Geophys. Res., 102, 25,617 – 25,628,
1997.
Miller, M. F., and M. C. G. Mabin, Antarctic Neogene landscapes: In the
refrigerator or in the deep freeze?, GSA Today, 8, 1 – 3, 1998.
ECV
3 - 12
PRINGLE ET AL.: THERMAL PROPERTIES OF ANTARCTIC PERMAFROST
Nassar, I. N., and R. Horton, Determination of soil apparent thermal diffusivity from multiharmonic temperature analysis for nonuniform soils, Soil
Sci., 149, 125 – 130, 1990.
Passchier, S., A. L. L. M. Verbers, F. M. van der Wateren, and F. J. M.
Vermeulen, Provenence, geochemistry, and grain-sizes of glacigene sediments, including the Sirius Group, and Late Cenozoic glacial history of
the southern Prince Albert Mountains, Victoria Land, Antarctica, Ann.
Glaciol., 27, 270 – 276, 1998.
Persaud, N., and A. C. Chang, Computing mean apparent soil diffusivity
from daily observations of soil temperatures at two depths, Soil Sci., 139,
297 – 304, 1985.
Péwé, T. L., Sand-wedge polygons (tessellations) in the McMurdo Sounds
region, Antarctica-A progress report, Am. J. Sci., 257, 545 – 551, 1959.
Putkonen, J., R. S. Sletten, and B. Hallet, Atmosphere/ice energy exchange
through thin debris cover in Beacon Valley, Antarctica, paper presented
at the 8th International Permafrost Conference, Int. Permafrost Assoc.,
Zurich, Switzerland, in press, 2003.
Roy, R. F., A. E. Beck, and Y. S. Touloukian, Physical properties of rocks
and minerals, in McGraw-Hill/CINDAS Data Series on Material Properties, vol. II-2, edited by Y. S. Touloukian and C. Y. Ho, pp. 408 – 481,
McGraw-Hill, New York, 1981.
Sletten, R. S., B. Hallet, and R. C. Fletcher, Resurfacing time of terrestrial
surfaces by the formation and maturation of polygonal patterned ground,
J. Geophys. Res., 108(E4), 8044, doi:10.1029/2002JE001914, 2003.
Stearns, C. R., Application of Lettau’s theoretical model of thermal diffusion in soil particles of temperature and heat flux, J. Geophys. Res., 74,
532 – 541, 1969.
Sugden, D. E., D. R. Marchant, N. J. Potter, R. A. Souchez, G. H. Denton,
C. C. Swisher, and J.-L. Tison, Preservation of Miocene glacier ice in
East Antarctica, Nature, 376, 412 – 414, 1995.
Thomson, D. C., R. M. F. Craig, and A. M. Bromley, Climate and surface
heat balance in an Antarctic Dry Valley, N. Z. J. Sci., 14, 245 – 251, 1971.
Trodahl, H. J., M. J. McGuinness, P. J. Langhorne, K. Collins, A. E.
Pantoja, I. J. Smith, and T. G. Haskell, Heat transport in McMurdo Sound
first-year fast ice, J. Geophys. Res., 105, 11,347 – 11,358, 2000.
Trodahl, H. J., S. O. F. Wilkinson, M. J. McGuinness, and T. G. Haskell,
Thermal Conductivity of sea ice: Dependence on temperature and depth,
Geophys. Res. Lett., 28, 1279 – 1282, 2001.
Weast, R. C., (Ed.), Handbook of Chemistry and Physics, 52nd ed., Chem.
Rubber Co., Cleveland, Ohio, 1971.
Westin, B., and F. S. Zuidhoff, Ground thermal conditions in discontinuous
permafrost, Permafrost Periglacial Process., 12, 325 – 335, 2001.
Zhang, T., and T. E. Osterkamp, Considerations in determining the thermal
diffusivity from temperature time series using finite difference methods,
Cold Reg. Sci. Technol., 23, 333 – 341, 1995.
W. W. Dickinson and A. R. Pyne, Antarctic Research Centre, Victoria
University of Wellington, P.O. Box 600, Wellington, New Zealand.
(warren.dickinson@vuw.ac.nz)
D. J. Pringle (corresponding author) and H. J. Trodahl, School of
Chemical and Physical Sciences, Victoria University of Wellington, P.O.
Box 600, Wellington, New Zealand. (pringldani@student.vuw.ac.nz)
PRINGLE ET AL.: THERMAL PROPERTIES OF ANTARCTIC PERMAFROST
Figure 3. Temperature data. In all time series the bottom thermistor (z = 1.98 m) is the dashed line and
the top thermistor (z = 0.09 m) has the largest amplitude. (a) TM2 time series showing every second
thermistor for clarity. (b and c) Characteristic summer and winter variations from TM2 (see text). (d) False
color reconstruction of TM2 temperature field; isotherm increments are 2C. (e) TM1 time series.
(f ) Reconstructed TM1 temperature field. Missing data due to power regulator failure.
ECV
3-5