Annals of Glaciology 51(55) 20109

Dielectric permittivity of snow measured along the route traversedin the Japanese–Swedish Antarctic Expedition 2007/08
Shin SUGIYAMA,1 Hiroyuki ENOMOTO,2 Shuji FUJITA,3 Kotaro FUKUI,4Fumio NAKAZAWA,3 Per HOLMLUND5
1

Institute of Low Temperature Science, Hokkaido University, Sapporo 060-0819, Japan
E-mail: sugishin@lowtem.hokudai.ac.jp
2
Department of Civil and Environmental Engineering, Kitami Institute of Technology, Koen-cho 165, Kitami 090-8507, Japan
3
National Institute of Polar Research, 10-3 Midori-cho, Tachikawa, Tokyo 190-8518, Japan
4
Tateyama Caldera Sabo Museum, 68 Bunazaka, Tateyama-cho, Toyama 930-1405, Japan
5
Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91 Stockholm, Sweden
ABSTRACT. As a joint contribution of Japan and Sweden to the International Polar Year 2007–09, a field
expedition between Syowa and Wasa stations in East Antarctica was carried out in the 2007/08 australsummer season. Along the 2800 km long expedition route, the dielectric permittivity of the upper 1 msnow layer was measured at intervals of approximately 50 km using a snow fork, a parallel-wiretransmission-line resonator. More than 2000 measurements were performed under carefully calibrated
conditions, mostly in the interior of Antarctica. The permittivity "0 was a function of snow density as inprevious studies on dry snow, but the values were significantly smaller than those reported before. In thelight of the dielectric mixture theory, the relatively smaller "0 obtained in this study can be attributed tothe snow structures characteristic in the studied region. Our data suggest that the permittivity of snow
in the Antarctic interior is significantly affected by weak bonding between snow grains, which is due todepth-hoar formation in the extremely low-temperature conditions.

1. INTRODUCTION
It is essential to determine the dielectric properties of snow
to carry out glaciological research in polar regions. The
velocity of electromagnetic waves, which must be known
for radio-echo soundings in glaciers, ice sheets and snow
cover, can be determined from these properties. Satellite
remote sensing also requires knowledge of dielectric
properties since these control the reflection, scattering,emission and penetration of the waves in a snow layer.
Despite its importance, the dielectric nature of snow has
not yet been well understood; it is difficult to understandbecause of the complexity of snow structure and its spatiotemporal variability. For example, in the case of dry snow,
the real part of the relative complex permittivity "0 (referred
to as the permittivity in this paper) is mostly dependent on
the volume fraction of ice and air. However, the influenceof snow structure on the permittivity is not clearly understood, although the influence has been predicted intheoretical studies.
The dielectric properties of snow have been measured in
the field and laboratories using various instruments. For
example, Tiuri and others (1984) used cylindrical cavity
resonators to measure the permittivity of snow in Finland.
They proposed an empirical relationship between "0 andsnow density in microwave frequencies. Similar relationships have been reported in many studies (e.g. Cumming,
1952; Ambach and Denoth, 1980; Hallikainen and others,
1986; Denoth, 1989; Kovacs and others, 1995; Mätzler,
1996). These studies indicate that "0 is mostly controlled by
the density, and observed density dependence is consistent
with dielectric mixture theory (e.g. Polder and Van Santen,
1946; Taylor, 1965; Tinga and others, 1973). Colbeck (1982)
discussed the influence of snow structure on the permittivity
using experimental data. This effect is believed to beimportant for interpreting dielectric properties obtained for

different snow conditions. For example, Lytle and Jezek(1994) found that the permittivity of firn from Greenland wasdependent on the direction of the electric field. They
attributed the observed dielectric anisotropy to the snow
grains that were elongated in the vertical direction under the
influence of thermal gradient near the surface.
In Antarctica, radio-echo soundings and satellite remotesensing are crucial methods for studying the ice sheet.
However, very few ground measurements of dielectric
properties have been made, especially for surface snow
layers in the interior of the continent. Shiraiwa and others(1996) measured the permittivity and density in the upper
1 m at six locations between the Mizuho and Dome F
stations in East Antarctica (70.5–748 S, 43–458 E; 2250–
3350 m a.s.l.). The measured "0 was not very well correlatedwith the snow density. Kärkäs and others (2005) conducted
dielectric measurements in 1–2 m deep snow pits in western
Dronning Maud Land (72.5–758 S, 10–16.58 W; 2250–
3350 m a.s.l.). From data obtained using two different
instruments, they found relationships between the permittivity and density, but the correlation coefficients wererelatively low (r = 0.48 and 0.59). These studies indicate thecomplexity of dielectric properties of snow and the difficulties in performing these measurements in the field.
To better understand the physical properties of snow in
Antarctica, we carried out 1 m deep snow-pit measurements during the Japanese–Swedish Antarctic Expedition(JASE) 2007/08. In this paper, we present the results ofdielectric measurements conducted in the microwave
frequency range. The relationship between the permittivity
and snow density was determined using more than 2000
data points collected along the traversed 2800 km inland
route. Our data serve as the basis for snow and ice radarmeasurements and as a reference for satellite remotesensing in Antarctica.

10

Sugiyama and others: Dielectric permittivity of snow measured by the JASE

Fig. 1. Map of the studied region of Antarctica along with the route traversed in the JASE 2007/08. Open circles denote the location of thesnow-pit measurements. Contour lines represent the surface elevation at intervals of 200 m based on Bamber and Bindschadler (1997).

2. METHOD
2.1. Study site
During the 2007/08 austral summer season, a traverse
expedition was carried out by Japanese and Swedish teams
in East Antarctica between Japanese inland base S16 (30 km
from Syowa station, 698030 S, 408040 E) and Swedish Wasa
station (738040 S, 138410 W) (Fig. 1; Table 1) (Holmlund andFujita, 2009). The two teams departed from their homestations in snow vehicles in November 2007 and met at the
point 758890 S, 258830 E on 27 December 2007. The distanceof the meeting point from each of the starting points wasapproximately 1400 km. The teams exchanged some of the
expedition members and scientific instruments before they
began their return trips, so that various research activities
could be carried out along the entire stretch from S16 to
Wasa (approximately 2800 km).
The permittivity and density were measured in the upper
1 m snow layer at 35 locations along the route (Fig. 1;
Table 1). The first measurement was made 671 km inlandfrom S16 (MD408) on 2 December 2007. We repeated themeasurements along the rest of the expedition route atintervals of approximately 20–100 km until the final measurement at Wasa station was completed on 28 January 2008.

Table 1. Sites along the expedition route referred to in the text
Site

S16
MD408
Dome F
DK120
Meeting point
91B
C0107
KohnenMalins Mac
Wasa

Long.

408030 E
428420 E
398370 E
348650 E
258830 E
228280 E
128530 E
008040 E
108000 W
138410 W

Lat.

698020 S
748240 S
778220 S
768900 S
758890 S
768040 S
748580 S
758000 S
758000 S
738040 S

Elevation

Distance from
S16

m

km

591
3485
3807
3757
3661
3566
3420
2892
2532
414

0
671
1005
1122
1381
1474
1795
2168
2457
2764

The elevation of the measurement site increased from3485 m (MD408) to 3807 m (Dome F), and then gradually
decreased to 2500 m at a point 290 km west of Kohnen
station. From this point, the route descended steeply fromthe high inland plateau to the coastal region. Annual snow
layer thicknesses near the surface are 50–200 mm for thesection between MD408 and Dome F (Furukawa and others,
1996), 140–250 mm in the vicinity of Kohnen (Oerter andothers, 1999) and 550  110 mm for the coastal region near
Wasa (Kärkäs and others, 2005). Thus, the uppermost 1 m ofsnow cover consists of several to more than ten annual
layers.

2.2. Permittivity measurements
The permittivity was measured using Snow Fork model
LJ 9902, a microwave resonator probe manufactured by
Toikka Engineering Ltd in Finland (Sihvola and Tiuri, 1986).
This device measures the resonance spectrum using aparallel-wire transmission-line resonator to determine thecomplex permittivity in the frequency range 500–900 MHz.
Its performance was tested and compared with other
instruments using Alpine snow (Denoth and others, 1984).
The imaginary part of the permittivity can be neglected when
the snow is dry, as it is expected to be in the studied region.
Thus, we consider only the real part of the permittivity, "0 , inthis study. The permittivity was calculated from the resonant
frequencies measured in air, fa, and snow, fs:
 2
fa
"0 ¼
:
ð1Þ
fs
The snow-fork measurement was carried out using a 1 m
deep snow-pit wall (Fig. 2). Parallel wires of the resonator,
60 mm long and separated by an 18 mm distance, were
pushed into the snow wall at intervals of 30 mm from thesurface to 1 m depth. We measured the resonant frequency
twice at a fixed depth by positioning the parallel wires of theresonator in horizontal and vertical alignment. In these two
measurements, the directions of the electric field induced by
the resonator are both in the horizontal plane. Reference
measurements were made in air before and after a series ofthe measurements were completed, and the mean value wasused for the calculation of "0 . The total mean of fa wasSugiyama and others: Dielectric permittivity of snow measured by the JASE

11densification due to the insertion of the parallel-wireresonator is +(1.5–3.0)% (Sihvola and Tiuri, 1986).

2.3. Density measurements

Fig. 2. Schematic diagram showing the permittivity and density
measurements. Intervals of the measurements in the verticaldirection are 30 mm.

The snow density was measured by sampling a 30 mm thickblock using a box-type stainless density cutter (30 mm 
60 mm  56 mm, Climate Engineering Co.). A digital benchscale (CS200, OHAUS Co.) with a resolution of 0.1 g wasused for weighing the snow block. The accuracy of thedensity measured using similar devices is reported as 4%(Conger and McClung, 2009). The sampling was performed
from the surface to 1 m depth at intervals of 30 mm (Fig. 2).
The central sampling depth corresponded to the points of thesnow-fork measurement, so the density can be comparedwith the permittivity at the same level. The horizontal
distance between the density and snow-fork measurements
was within 1 m. Stratigraphical information (snow structureand grain size) was also recorded following the guidelines
given by Colbeck and others (1990).

3. RESULTS
891.7 MHz with a standard deviation of 4.0 MHz, which
compares with the ideal value of this instrument (887–888 MHz) within the accuracy of the resonant frequency(5 MHz). The accuracy of "0 by the snow-fork measurement
is reported as 1.5%, and the possible effect of snow

As typical examples of the measurement data, the verticalprofiles of the permittivity and density are shown along withsnow stratigraphy (Fig. 3). The structure of the snow in theupper 1 m snow layer was dominated by faceted crystals(solid-type depth hoar) and depth hoar consisting of medium(0.5–1.0 mm) to coarse (1.0–2.0) grains (Fig. 4a). For

Fig. 3. Permittivity (, 4), density (grey line) and stratigraphy measured at (a) DK120 (768900 S, 348650 E), (b) 91B (768040 S, 228280 E), (c)C0107 (748580 S, 128530 E) and (d) Malins Mac (758000 S, 108000 W) (Fig. 1; Table 1). The permittivity was measured when the resonator was
horizontally () and vertically (4) positioned. The snow structures are classified as faceted crystals and depth hoar (^), compacted snow (grey)
and a crust layer (solid line).

12Sugiyama and others: Dielectric permittivity of snow measured by the JASE

Fig. 4. Photographs of snow samples used for the density measurement: (a) depth hoar and (b) very hard compacted snow.

simplicity, we refer to both these structures as depth hoar in
the remainder of this paper. A very hard compacted snow
layer with a thickness of 10–100 mm was also observed.
Fine snow grains (0.2–0.5 mm) were bonded tightly, forminga very hard and relatively dense layer (Fig. 4b). Crust layerswith a thickness of several millimeters were also commonly
observed.
The vertical profiles show that the permittivity is correlated with the density. The high-density compacted snow
layers coincide with the permittivity peaks, as observed for
0.4 m in Figure 3a. The difference between the measurements obtained when the snow fork is horizontally
positioned and those obtained when it is vertically
positioned is not clear. Discrepancies between the two
methods are observed at the sharp peaks for the high-density
layers, but the deviations are not consistent with each other.
For example, at 0.4 m in Figure 3b the permittivity is greater
when the resonator is horizontally positioned, whereas at
0.35 m in Figure 3d it is greater when the resonator isvertically positioned.
Figure 5 shows the permittivity measurements at the 35
sites; for clarity, only the results from the horizontal
positioning of the resonator are shown. The permittivity
varies within the range 1.361–2.001, with a total mean of
1.644 and a standard deviation  ¼ 0:102. The mean value
at each sampling site ranges from 1.567 to 1.781, with ¼ 0:058.
The correlation of the permittivity "0 with the density (kg m–3) measured at the same depth was investigated using

Fig. 6. Plots of all the data on the permittivity vs snow density: thepermittivity was measured when the resonator was positioned
horizontally (+) and vertically (). The lines correspond to the linear
regression of the two datasets (solid and bold grey lines) and theequation proposed by Tiuri and others (1984) (dashed line). The
error bars indicate 1.5% and 4% errors expected in thepermittivity and density measurements, respectively.

all the data obtained in this study (Fig. 6). Least-squares
linear regression gives the coefficients of the relationship"0 ¼ a þ b

ð2Þ

as a ¼ 0:00178 kg–1 m3 (95% confidence interval (0.00169,
0.00186)) and b ¼ 0:997 (0.965, 1.029) with correlation
coefficient r ¼ 0:76 for the horizontal resonator setting, anda ¼ 0:00176 (0.00168, 0.00184) and b ¼ 1:010 (0.979,
1.040) with r ¼ 0:77 for the vertical setting. Tiuri and others(1984) proposed an empirical relationship with a ¼ 0:002
and b ¼ 1. This equation is plotted in Figure 6 forcomparison, as it is based on the measurements of various
types of snow. Our relationships give a smaller permittivity
than Tiuri’s equation, and the discrepancy is 0.04–0.1(3–5%) in the density range 200–500 kg m–3.
Regression was also performed for non-linear equations
used in previous studies (Table 2). Fitting a second-orderpolynomial to the data (e.g. Denoth, 1989) gives a relationship very similar to the linear regression, and the error
increases in the cases of refraction-type (e.g. Kovacs andothers, 1995) and Looyenga-type equations (Glen and Paren,1975).

Table 2. Least-squares regression coefficients and root-mean-squareerrors (RMSE) determined for the permittivity measured with theresonator positioned horizontally and verticallyEquationFig. 5. Permittivity measured along the expedition route. The
permittivity was measured with the resonator positioned horizontally. The individual measurements and the mean value for eachsite are denoted by () and (), respectively.

"0 ¼ a þ b"0 ¼ a2 þ b þ 1"0 ¼ ð1 þ aÞ2
"0 ¼ ð1 þ aÞ3

Coefficients

RMSE

a ¼ 0:00177, b ¼ 1:003
a ¼ 8:22  109 , b = 0.00177
a ¼ 7:75  104a ¼ 4:94  1040.06500.06500.0657
0.0664

Sugiyama and others: Dielectric permittivity of snow measured by the JASE

13

Table 3. Empirical relationships between permittivity "0 and density  (kg m–3) proposed for dry snow. The relationship in this study was
obtained for the permittivity measured with the resonator positioned horizontally and verticallyEquation

Snow type

Frequency

Densitykg m"0 ¼ 0:0022 þ 1"0 ¼ 0:002 þ 1"0 ¼ 0:00191 þ 1"0 ¼ 4:4  107 2 þ 0:0019 þ 1"0 ¼ 0:0026 þ 0:8"0 ¼ ð8:45  104  þ 1Þ2"0 ¼ 0:0017 þ 0:9597"0 ¼ 0:002 þ 0:9904"0 ¼ 0:00177 þ 1:003

Coarse old snow
Coarse, fine, new, aged and prepared snow
Natural snow from various depths
New and old snow, multi-year firn
Greenland firn
Combination of reported data
Compacted snow
Antarctic firn
Antarctic firn

4. DISCUSSION
The permittivity of snow measured in this study wascorrelated with the density, and the relationship "0 () could
be approximated by a linear function, as reported inprevious studies. The regression lines are essentially
identical when the resonator is horizontally and vertically
positioned. Thus, we conclude that there is no influence ofthe measurement method on the relationship between "0 and when the number of measurements is sufficiently large.
The measurement was dependent on the resonator positionin the vicinity of the high-density layers. This was probably
because the permittivity is measured at an exact depth by
the horizontally positioned resonator, whereas the mean of
an 18 mm thick layer is measured in the vertical position.
In an interesting observation, the "0 values along the
expedition route were smaller than those reported previously for the same density. Previously obtained relationships for dry snow are summarized in Table 3. Except for thatobtained by Shiraiwa and others (1996) for dry compacted
snow in Japan, the "0 given by these equations is greater thanthat given by the relationship determined by this study.
The permittivity of dry snow is virtually independent of
the microwave frequency in a range that extends up to atleast 10 GHz (e.g. Mätzler, 1996). The temperature dependence of "0 for polycrystalline ice is very small (5  104 8C–1;
e.g. Fujita and others, 1992), and the influence of a quasiliquid layer occurring at the snow particle surface attemperatures above –108C (Petrenko, 1994) is negligible
under the temperature conditions in this study. The effect ofdielectric anisotropy of ice crystals (e.g. Matsuoka andothers, 1997) under the consideration of dielectric mixture
theory (e.g. Polder and Van Santen, 1946) is <1%. Thus, it islikely that "0 was dependent on the volume fraction of ice
and the snow structure. The structural dependence of "0 has
been discussed in many studies (e.g. Colbeck, 1982;
Denoth, 1982; Sihvola and others, 1985; Kovacs and others,
1995), but little observational evidence has been reported
thus far. The structural dependence is hard to prove, as
accurate measurements of "0 and  in the field are difficult toobtain, and expected difference in "0 is small. Moreover, it ishard to acquire sufficient data for different types of snow
structures. By using the large number of data obtained for
relatively simple snow structures, we discuss the possible
influence of snow structure on the relationship between "0and .

MHz range
0.85–12.6 GHz
3–37 GHz
10 MHz26.5–40 GHz
20 MHz (UHF)
500–900 MHz
500–900 MHz
500–900 MHz

Source–3

100–500
100–450
100–650
350–400
100–900
200–450
200–450
250–500

Ambach and Denoth (1980)
Tiuri and others (1984)
Hallikainen and others (1986)
Denoth (1989)
Lytle and Jezek (1994)
Kovacs and others (1995)
Shiraiwa and others (1996)
Kärkäs and others (2005)
This study

Dry snow can be regarded as a dielectric mixture of ice
and air. Applying multiphase dielectric mixture theory, Tinga
and others (1973) derived the permittivity of a two-phasemixture with spherical inclusions as follows:
"0 ¼

ð2 "0

3ðV2 =V1 Þ"01 ð"0 2  "0 1 Þþ "0 1 ,000
1 þ " 2 Þ  ðV2 =V1 Þð" 2  " 1 Þð3Þwhere "1 and "2 are the permittivity of the host and guest(spherical inclusions) materials, respectively, and V2 =V1 isthe volume fraction of the two materials. By assuming thepermittivity of ice to be 3.15 (e.g. Cumming, 1952; Koh,
1992; Fujita and others, 2000), Equation (3) gives therelationships between "0 and  for two extreme cases:
spherical ice particles surrounded by air and ice containing
spherical air bubbles (dashed and solid lines in Fig. 7a). A
linear correlation is expected when ice plates are aligned
along an electric field (dash-dotted line in Fig. 7a). The
bubbly ice has a greater "0 than the spherical ice particles("0 ¼ 0:136 at  ¼ 400 kg m–3), and the majority of our data
points lie between the two lines that show these relationships(Fig. 7b). The two structures can be distinguished by thebonding of ice particles. The mixture theory suggests that "0 islarger when the bonding between the snow grains is greater.
In our study, the dominant snow structure was the depth hoar,
which is characterized by weak bonding of the grains.
Therefore, the smaller "0 obtained in our study is possibly due
to the snow structure that is characteristic of interior
Antarctica. This hypothesis can be understood by considering
an analogy with a sintered material. The highly compressed
powder has a lower permittivity than the material obtained
after a sintering process (Polder and Van Santen, 1946).
Among the data obtained when the resonator was
horizontally positioned, those measured in the depth hoar
and in the firmly compacted snow are plotted in Figure 8.
The linear regression of the two datasets shows that the "0 ()obtained for depth hoar is smaller than that obtained forcompacted snow for the same density. The common
regression performed for all data (model 1) was comparedwith the regression performed separately for depth hoar andcompacted snow (model 2); the comparison was made byusing the F test, a standard statistical method (Weisberg,1985). F test of model 1 against model 2 gave a significancelevel much lower than 0.01, which supports the effectiveness of model 2. The compacted snow layer was very hard,indicating that the grains were tightly bonded. Thus, the14Sugiyama and others: Dielectric permittivity of snow measured by the JASE

Fig. 8. Plots of the permittivity measured in depth hoar () andcompacted snow () vs snow density. The lines correspond to thelinear regression of the two datasets (grey bold and solid lines) andthe equation proposed by Tiuri and others (1984) (dash-dotted line).
The permittivity was measured with the resonator positioned
horizontally.

Fig. 7. (a) Plots of the permittivity vs snow density: the dashed, solidand dash-dotted lines represent the relationship given by Equation (3) for the snow structures illustrated by the insets, where ice
and air are indicated by grey and white, respectively. The
permittivity was measured with the resonator positioned horizontally. (b) Same plot as (a) for the region indicated by the greybox. The contour lines show the data-point density.

regression of the two different snow structures agrees withthe hypothesis that the smaller "0 obtained in this study wasdue to the weak bonding of depth hoar.
Our data also imply structural anisotropy of the snow.
Polar firn tends to have weaker grain bonding in thehorizontal direction than in the vertical, i.e. the grains areelongated in the vertical direction, as a result of crystal
growth in the extremely low-temperature condition. In such
structures, the permittivity is expected to be greatest whenthe electric field is in the vertical direction. Dielectricanisotropy reported for firn in Greenland (Lytle and Jezek,
1994) and in Antarctica (Fujita and others, 2009) is
consistent with this assumption. Since the snow-forkmeasurements in this study used the electric field directed
parallel to the horizon, our data imply that the bonding ofsnow grains in the horizontal direction is very weak in theinland of Antarctica.

5. CONCLUSION
The real part of the complex permittivity "0 was measured forthe upper 1 m snow layer along the route traversed in the
JASE 2007/08. The result was compared with the snow
density  to find a relationship between "0 and . The

relationship was determined as "0 ¼ 0:00177 þ 1:003 on
the basis of more than 2000 data points obtained for 35
locations. This result is independent of the horizontal andvertical positions of a parallel-wire resonator of themeasurement device. The values of "0 given by this equation
are 3–5% smaller than those reported previously in thedensity range 200–500 kg m–3. The smaller permittivity
suggests the effect of snow structure on the dielectric
properties. A majority of the measurements were made in
the depth hoar that is characterized by the weak bonding ofsnow grains. According to the dielectric mixture theory, thepermittivity of such structures is smaller than that of snow
consisting of tightly bonded grains.

ACKNOWLEDGEMENTS
We thank the members of the JASE 2007/08 for their help in
the field. The field activity was a part of the 48th and 49th
Japanese Antarctic Research Expedition and supported by
the National Institute of Polar Research, Tokyo, and theSwedish Polar Research Secretariat. The snow fork was
kindly loaned by K. Fujita of Nagoya University. The surface
elevation data used for the map were provided by the US
National Snow and Ice Data Center. We thank two anonymous referees for providing careful reviews, and thescientific editor A.M. Smith for handling the paper. This
study was funded by the Japanese Ministry of Education,
Science, Sports and Culture, Grant-in-Aid for Scientific
Research (A), 20241007, 2008–2010.

REFERENCES
Ambach, W. and A. Denoth. 1980. The dielectric behaviour ofsnow: a study versus liquid water content. In Rango, A., ed.
Microwave remote sensing of snowpack properties. Washington, DC, National Aeronautics and Space Administration,
69–91. (NASA CP-2153.)

Sugiyama and others: Dielectric permittivity of snow measured by the JASE

Bamber, J.L. and R.A. Bindschadler. 1997. An improved elevation
dataset for climate and ice-sheet modelling: validation withsatellite imagery. Ann. Glaciol., 25, 439–444.
Colbeck, S.C. 1982. The geometry and permittivity of snow at highfrequencies. J. Appl. Phys., 53(6), 4495–4500.
Colbeck, S.C. and 7 others. 1990. The international classification
for seasonal snow on the ground. Wallingford, Oxon, International Association of Scientific Hydrology. International
Commission on Snow and Ice.
Conger, S.M. and D.M. McClung. 2009. Comparison of density
cutters for snow profile observations. J. Glaciol., 55(189),
163–169.
Cumming, W.A. 1952. The dielectric properties of ice and snow at
3.2 centimeters. J. Appl. Phys., 23(7), 768–773.
Denoth, A. 1982. Effect of grain geometry on electrical properties ofsnow at frequency up to 100 MHz. J. Appl. Phys., 53(11),7496–7501.
Denoth, A. 1989. Snow dielectric measurements. Adv. Space Res.,
9(1), 233–243.
Denoth, A. and 6 others. 1984. A comparative study of instruments
for measuring the liquid water content of snow. J. Appl. Phys.,
56(7), 2154–2160.
Fujita, S., M. Shiraishi and S. Mae. 1992. Measurement on the
microwave dielectric constant of ice by the standing wave
method. In Maeno, N. and T. Hondoh, eds. Proceedings of theInternational Symposium on the Physics and Chemistry of Ice.
Sapporo, Hokkaido University Press, 415–421.
Fujita, S., T. Matsuoka, T. Ishida, K. Matsuoka and S. Mae. 2000. A
summary of the complex dielectric permittivity of ice in themegahertz range and its applications for radar sounding of polar
ice sheets. In Hondoh, T., ed. Physics of ice core records.
Sapporo, Hokkaido University Press, 185–212.
Fujita, S., J. Okuyama, A. Hori and T. Hondoh. 2009. Metamorphism of stratified firn at Dome Fuji, Antarctica: a mechanism for local insolation modulation of gas transport conditions
during bubble close off. J. Geophys. Res., 114(F3), F03023.
(10.1029/2008JF001143.)
Furukawa, T., K. Kamiyama and H. Maeno. 1996. Snow surface
features along the traverse route from the coast to Dome Fuji
Station, Queen Maud Land, Antarctica. Proc. NIPR Symp. Polar
Meteorol. Glaciol., 10, 13–24.
Glen, J.W. and J.G. Paren. 1975. The electrical properties of snow
and ice. J. Glaciol., 15(73), 15–38.
Hallikainen, M.T., F.T. Ulaby and M. Abdelrazik. 1986. Dielectric
properties of snow in the 3 to 37 GHz range. IEEE Trans.
Antennas Propag., 34(11), 1329–1340.
Holmlund, P. and S. Fujita. 2009. Japanese–Swedish Antarctic
Expedition, JASE. In Thorén, A., ed. Swedish Polar Secretariat

15

Year Book 2008. Stockholm, Swedish Polar Research Secretariat,
18–21.
Kärkäs, E., T. Martma and E. Sonninen. 2005. Physical properties
and stratigraphy of surface snow in western Dronning Maud
Land, Antarctica. Polar Res., 24(1–2), 55–67.
Koh, G. 1992. Dielectric constant of ice at 26.5–40 GHz. J. Appl.
Phys., 71(10), 5119–5122.
Kovacs, A., A.J. Gow and R.M. Morey. 1995. The in-situ dielectric
constant of polar firn revisited. Cold Reg. Sci. Technol., 23(3),245–256.
Lytle, V.I. and K.C. Jezek. 1994. Dielectric permittivity andscattering measurements of Greenland firn at 26.5–40 GHz.
IEEE Trans. Geosci. Remote Sens., 32(2), 290–295.
Matsuoka, T., S. Fujita, S. Morishima and S. Mae. 1997. Precise
measurement of dielectric anisotropy in ice Ih at 39 GHz.
J. Appl. Phys., 81(5), 2344–2348.
Mätzler, C. 1996. Microwave permittivity of dry snow. IEEE Trans.
Geosci. Remote Sens., 34(2), 573–581.
Oerter, H., W. Graf, F. Wilhelms, A. Minikin and H. Miller. 1999.
Accumulation studies on Amundsenisen, Dronning Maud Land,by means of tritium, dielectric profiling and stable-isotope
measurements: first results from the 1995–96 and 1996–97 fieldseasons. Ann. Glaciol., 29, 1–9.
Petrenko, V.F. 1994. The surface of ice. CRREL Spec. Rep.
94-22.
Polder, D. and J.H. van Santen. 1946. The effective permeability of
mixtures of solids. Physica, 12(5), 257–271.
Shiraiwa, T., H. Shoji, T. Saito, K. Yokoyama and O. Watanabe.
1996. Structure and dielectric properties of surface snow along
the traverse route from coast to Dome Fuji Station, Queen Maud
Land, Antarctica. Proc. NIPR Symp. Polar Meteorol. Glaciol.,
10, 1–12.
Sihvola, A. and M. Tiuri. 1986. Snow fork for field determination of
the density and wetness profiles of a snow pack. IEEE Trans.
Geosci. Remote Sens., 24(5), 717–721.
Sihvola, A., E. Nyfors and M. Tiuri. 1985. Mixing formulae andexperimental results for the dielectric constant of snow.
J. Glaciol., 31(108), 163–170.
Taylor, L. 1965. Dielectric properties of mixtures. IEEE Trans.
Antennas Propag., 13(6), 943–947.
Tinga, W.R., W.A.G. Voss and D.F. Blossey. 1973. Generalized
approach to multiphase dielectric mixture theory. J. Appl. Phys.,44(9), 3897–3902.
Tiuri, M.T., A.H. Sihvola, E.G. Nyfors and M.T. Hallikainen. 1984.
The complex dielectric constant of snow at microwave
frequencies. IEEE J. Ocean. Eng., 9(5), 377–382.
Weisberg, S. 1985. Applied linear regression. Second edition. New
York, etc., John Wiley and Sons.