Geology Reference
In-Depth Information
3.5.2. Thermal Conductivity of Snow
grain characteristics, and hence thermal properties. These
layers, however, evolve and change continually through-
out the winter due to ice growth and deformation.
The wide range of snow conditions and layering contrib-
utes to an equally wide range of thermal conductivity
K
s
(between 0.03 and 0.80 W/m · K). Lower values are expected
from dry fresh snow and higher values from wet, metamor-
phozed or compacted snow. The variability of thermal
conductivity of snow is greater than that of sea ice, which
varies around 2.1 W/m · K as mentioned before. Accurate
measurements of
K
s
that capture the spatial, temporal, and
stratigraphic variations is difficult, but simple models
(mostly empirical equations) have been suggested to esti-
mate this parameter in terms of snow density, wetness, and
geometrical forms of the inclusions. Measurements of
thermal conductivity of snow over land have been pre-
sented in the literature since 1886. A few expressions for
K
s
as a function of snow density
ρ
s
were suggested by a few
authors. Although most of these expressions were not
developed for snow on sea ice, they can practically be
applied to it.
Bader
[1962] presented a few expressions
developed in studies conducted before 1945. Among them
is the first equation developed in 1893, called Abel's equa-
tion (the original paper by the same author is in German):
Snow is a composite material consisting of fresh snow
flakes, ice grains, air, and possibly water when it is wet.
Therefore, heat transfer inside the snow pack takes one or
more of the following three forms: by conduction between
interconnected grains of snow ice, by convection through
water contents if existing within the snow pack, and by
radiation across the air inside the snow. These simultane-
ous mixed processes render the measurements of thermal
conductivity difficult. The measured values are com-
monly referred to as effective conductivity [
Weeks,
2010].
To further complicate the issue, the spatial variability of
snow composition and properties is also high within
short distances due to snow drifting and local weather
conditions. The vertical profile of snow may reveal layer-
ing of different structural types and therefore properties.
Sturm et al.
[2002] monitored the evolution of the snow
during the Surface Heat Budget of the Arctic Ocean
expedition (SHEBA) in the Arctic from October 1997 to
October 1998. For synopsis of the expedition see
Perovich
et al.
[1999]. At the peak of the snow depth in April
Sturm
et al.
[2002] measured the stratigraphy of the snow along
with profiles of a few physical parameters (density, tem-
perature, salinity, and thermal conductivity and salinity).
They identified many structurally different layers that are
associated with different thermal properties. Figure 3.21
shows the different layers, which can be grouped into
three major categories: recent snow, wind slab, and depth
hoar. Each layer existed with a different thickness range
and tended to be homogeneous with recognizable density,
2
K
s
0 0068
.
(3.52)
s
In this equation,
ρ
s
is in g/cm
3
and the resulting
K
s
is in
cal/s · cm · C. Note that 1 W = 0.239 cal/s. This equation is
most frequently cited and used to predict conductivity of
the snow.
Ye n
[1981] developed the following expression, which
was used later in thermodynamic model studies such as
Ebert and Curry
[1993]:
May 7 (Drifting)
New & recent
recent
Apr. 11
1000
1 885
.
K
s
2 2236
.
/
(3.53)
Apr. 7-9
s
Jan 29 (Snowfall)
Feb. 2 (Drifting)
Fine-grained
Sturm et al.
[1997] suggested other expressions:
K
s
0 023 0 234
.
.
0 156
.
(3.54)
Wind slab
Dec. 2-8
s
s
K
s
2
(3.55)
0 138 101 233
.
.
.
0 156
.
06
.
Depth hoar
Dec. 2
s
s
s
Wind slab to
depth hoar
Nov. 11-13
The same reference contains another logarithmic
expression valid for
d
s
≤ 0.6:
Nov. 6
Chains of
depth hoar
Oct. 29-30
10
0 00265
.
1 652
.
K
s
s
(3.56)
Snow ice
Snow ice
In equations (3.54)-(3.56)
ρ
s
is in g/cm
3
and
K
s
in W/m · K.
Many methods have been developed to calculate thermal
conductivity of the snow from temperature measurements.
Different approaches include using steady state heat flow
Figure 3.21
Stratigraphy of snow on Arctic sea ice obtained
in April 1998 during the SHEBA program. Snow depth was
between 0.28 and 0.65 m [
Sturm et al.,
2002; Figure 3, with
permission from AGU].
