Geology Reference
In-Depth Information
temperature inversion within the ice cover. Moreover, the
simultaneous effect of the latent heat required to precipi-
tating solid salts inside brine pockets in the temperature
range between −8.2 °C and −22.8 °C requires careful
consideration. A methodology of measurements of ther-
mal conductivity of sea ice using this approach is
described in
McGuinness et al.
[1998] and
Pringel et al.
[2006]. It assumes 1D heat conduction and measures the
temperature gradient in the direction of heat conduction
z
using an array of thermistors. It then uses a form of con-
servation of energy equation (
T
is the local temperature):
and
2
T
z
2
Tz z TzTzz z
2
/
(3.50)
2
The last term in equation (3.48) can be expanded as
follows in order to facilitate its estimation:
K
z
T
z
K
T
T
z
K
S
S
z
K
T
z
(3.51)
si
si
si
si
si
si
z
si
si
D
U
t
2
T
z
K
z
T
z
The spatial derivatives ∂
T
/∂
z
, (∂
S
si
)/∂
z
, and (∂
ρ
si
)/∂
z
can be determined from measurements of temperature,
salinity, and density profiles, while the derivatives of
K
si
are determined from equation (3.47); and
K
si
can be
determined using the temperature, salinity, and density
measurements along with equation (3.48) as the best fit
to the scatter plot of [
ρ
si
(∂
U
/∂
t
) − (∂
K
si
/∂
z
) (∂
T
/∂
z
)] versus
∂
2
T
/∂
z
2
.
Pringle et al.
[2007] used this method to estimate the
conductivity of land-fast FY ice in the Arctic (Chukchi
Sea near Barrow, Alaska) and Antarctic (McMurdo
Sound). They compared the measurements with their
model [equation (3.47)] and the
Maykut and Untersteiner
[1971] model [equation (3.46)]. Figure 3.20 shows the
measured and the modeled data. The bubbly‐brine
model prediction provides a better comparison with the
measurements.
si
K
(3.48)
si
2
where
U
(
S
si
,
T
) is the sea ice internal energy per unit mass
found by integrating the specific heat equation [equation
(3.58)]. Three thermistors are required to estimate the
second derivative on the right‐hand side (RHS) in the
above equation. Since the conductivity may not be con-
stant over the depths of the three thermistors, the second
term on the RHS is introduced to represent the deriva-
tives of the conductivity. The omission of this term does
not affect estimates of conductivity near the surface
[
Pringle et al.,
2006]. The derivatives in equation (3.48)
are determined by finite differences. For example,
U
t
/2
(3.49)
Ut tUt
t
t
2.6
FY McMurdo arrays
FY Chukchi arrays
Pringle et al.
[2006]
Nazintsev
[1959]
Nazintsev
[1964]
2.4
Schwerdtfeger
[1963]
Lewis
[1967] heat flow
Lewis
[1967] ice growth
2.2
Bubbly brine
S
=4.8 ppt
M&U (1971)
S
=4.8 ppt
2.0
1. 8
-
25
-
20
-
15
-
10
-
5
0
Temperature (°C)
Figure 3.20
Measured and modeled conductivity of sea ice. Measurements were obtained from FY fast ice in the
McMurdo Sound, Antarctic, and the Chukchi Sea (Arctic). Open symbols represent historical measurements as
indicated in the legend. Solid squares (with and without the white center) are measurements presented in
Pringle
et al.
[2007]. Model calculations are obtained from equation (3.47) (bubbly‐brine model) and equation (3.46)
(M&U model). The upper and lower curves of the models' calculations are for ice salinity 8‰ and 4‰, respec-
tively [
Pringle et al.,
2007, Figure 7, with permission from AGU].
