Geology Reference
In-Depth Information
across snow blocks, transient heat flow in the snow pack
or its samples, and Fourier analysis of temperature cycle
in the snow. The methods are discussed and assessed in
Pratt
[1969] in terms of their merit to predict thermal
conductivity of low‐conductivity materials.
Sturm et al.
[1997] compiled conductivity values from 27
studies conducted on snow over land before 1993. They
presented the results in a table that includes the author
name(s), location of measurements, and methods of cal-
culating the conductivity. Figure 3.22 includes data com-
piled from 23 studies. Different symbols denote different
data sources. References to the data sources can be found
in the original figure (Figure 4 in
Sturm et al.
[1997]). The
purpose of presenting the graph here is to show how
sparse the measurements of snow thermal conductivity
are. At any given density between 0.2 and 0.4 g/cm
3
the
snow conductivity varies largely by more than an order
of magnitude. The authors attributed the scattering of
the data to the inaccuracy of some measurements as well
as the influence of other factors such as snow wetness,
grain size, and ice layering. The snow temperature deter-
mines the water vapor contents within the snowpack and
this affects the thermal conductivity. The temperature
dependence of the conductivity must be taken into con-
sideration when explaining the scattering of the data. The
snow temperature from which the data in the figure were
obtained varied over a wide range, between 0° and −60 °C.
Nevertheless, even with the significant scattering, there is an
obvious trend of conductivity increase with snow density.
Abel's regression equation [equation (3.52)] is fitted to the
data in Figure 3.22 for comparison. The equation confirms
the visible trend. The center of mass of the data points is
at
K
s
= 0.251 and
ρ
s
= 0.273 g/cm
3
.
Figure 3.22 includes an inset showing two plots
obtained from equation (3.53) [
Yen,
1981] and equation
(3.55) [
Sturm et al.,
1997]. This inset is a modified version
of a plot presented in
Lecomte et al.
[2013]. The density
varies over the range between 200 and 450 kg/m
3
, i.e., part
of the wider range shown in the main plot. It can be seen
that the two equations, which depict the same trend of
conductivity increase with density, do not coincide with
Abel's equation. The typical value of snow conductivity
used in sea ice thermodynamic coarse resolution ice‐
ocean models (0.31 W/m · K) is based on Abel's equation
at density 330 kg/m
3
. This value is greater than the ther-
mal conductivity produced by the other two equations.
The above discussions point out the importance of an
accurate estimate of the thermal conductivity of snow to
be used in thermodynamic ice growth models because
of its much wider range compared to that of sea ice. In
general, the lower thermal conductivity of the snow
protects the ice underneath it against sharp variations of
atmospheric temperature (as seen in Figures 3.3 and 3.4).
Consequently, the heat flux through ice is reduced and
the ice growth slows down.
Satyawali and Singh
[2008] studied the effects of a few
idealized shapes of solid ice inclusions in the snowpack
on its thermal conductivity using a one‐dimensional heat
transfer model. Solid particles were represented as aggre-
gations of three geometrical shapes: spherical, cylindrical,
or cubical arranged in cubic packing. They concluded
that the spherical shape is associated with a higher con-
ductivity than the cubical shape. Conductivity from using
all shapes depends on characteristic ratios that combine
the particle size and spacing, denoted “particle contact
ratio.” Figure 3.23 shows results from their model for
the three particle shapes and two contact ratios. It also
includes comparison with the expression developed by
Sturm et al.
[1997] [equation (3.56)]. Once again, the results
confirm the increase of snow thermal conductivity with
the snow density. Equation (3.56) returns higher values
than the model of
Satyawali and Singh
[2008] for cubical
and cylindrical grains with
ρ
s
> 350 kg/m
3
. Note the
sharper increase of conductivity near the packing ice
density for all three shapes.
In a more recent study,
Sturm et al.
[2002] compiled
measurements of
K
s
from 89 points of snow on sea ice in
the Beaufort Sea during the SHEBA program. Average
values ranged from 0.078 W/m · K for dry fresh snow to
1
9
Center of data
6
5
4
3
2
0.1
9
0.5
0.45
6
5
0.35
0.31 W/m
.
K
4
3
0.25
Yen
[1981]
2
0.15
Sturm et al.
[1997]
0.05
200
250 300
Snow density (kg/m
-
3
)
350
400
450
0.01
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Snow density (g/m
3
)
Figure 3.22
Effective thermal conductivity measurements of
snow versus density from 23 studies (listed in
Sturm et al.,
1997) and the regression equation from equation (3.52). The
inset shows plots of equations (3.53) and (3.55). The main plot
and the inset are adapted from
Sturm et al.
[1997]
and Lacomte
et al
. [2013], respectively.
