Geology Reference
In-Depth Information
profiles in ice and snow as well as the snow‐ice interface
temperature using these three parameters was developed
by the author (
N. Sinha
, unpublished). This utterly simple
method was verified and used by the Canadian Ice Services
(CIS) operators, on board the CCG icebreakers, in the
early 1980's for Arctic sea ice and coined the name, “Sinha
Rule”. It is based on the assumption that ice is 10 times
more thermally conductive than snow and freezing tem-
perature of fresh water is 0 °C (−1.8 °C for sea water).
Since snow acts like a blanket it is expected that the tem-
peratures within the ice and at the snow‐ice interface will
be significantly higher than the air temperature. By equat-
ing the two expressions for
G
i
from equations (3.1) and
(3.5), the resulting equation takes the form
50
Mean air
temperature
Water
temperature
Top snow
surface
0
Snow-ice
interface
Theoretical
(Feb. 16)
50
Theoretical
(April 6)
100
125 cm
150
TTh
/10
h
h
(3.7)
175 cm
si
ai
s
i
Equation (3.7) can be put into practice as described below.
Using a stick, one can scratch the snow surface and draw
the composite of ice and snow based on the measured
snow and ice depths (Figure 3.2a). A second picture can
be drawn, as shown in Figure 3.2b, where thickness of the
ice is kept the same but the snow depth is multiplied 10
times. This would represent the “equivalent” ice cover
(i.e., snow is thermally converted to its equivalent ice
thickness). A line perpendicular to the surface is then
drawn to represent the reference of the water temperature
at the ice‐water interface. A point is marked on the top
surface representing the measured air temperature
T
a
. A
straight line is connected between this point and the refer-
ence temperature at the bottom of the ice. The slope of
the line gives the temperature gradient of the “equivalent
ice cover”, and the point of intersection at the snow‐ice
surface gives the snow/ice interface temperature
T
s
/
i
. The
last step (Figure 3.2c) is to connect
T
s
/
i
to
T
a
while using
the actual snow depth (i.e., shrink back to the actual snow
depth). That gives the real temperature gradient in the
snow pack. Suppose, as an example, that the ice thickness
is 1 m with a snow cover depth of 0.1 m. If the air tem-
perature is −10 °C and the water temperature is 0 °C, then
the snow‐ice interface temperature will be −5 °C. This
shows that even thin snow covers can have profound
influence on the ice surface temperature, and ice could be
significantly warmer than the snow and air temperature.
In an unpublished study conducted by M. Shokr on
FY ice in Mould Bay, Banks Island, in the Canadian
western Arctic, temperature profiles in the ice and the
overlaid snow were sampled every 30 min during most of
the ice growth season from 5 December, 1996 until the
end of May 1997. A temperature probe of 140 cm in
length was inserted into the snow and ice with the top
part remaining in the air. The probe had 24 thermistors,
the top 16 were spaced at 4 cm and the bottom 8 at 10 cm.
Only the bottom 8 thermistors were under the ice surface
200
-
30
-
20
-
10
0
Temperature (°C)
Figure 3.1
Comparison between measured and theoretical
temperature distributions in an ice sheet for two days in 1978.
Theoretical calculations are based on mean air temperatures
for days shown [
Sinha and Nakawo,
1981].
Two temperature profiles in sea ice obtained on 16
February and 6 April, 1978, from fully grown FY ice in
Eclipse Sound [
Sinha and Nakawo,
1981] are shown in
Figure 3.1. The ice grew from 125 cm on 16 February to
170 cm on 6 April. Note the almost perfect linear trend
shown in 6 April data and the deviation from linearity
near the top of the ice surface in 16 February data because
of the warm week prior to that date. The figure shows
also comparison of measured data against temperature
calculations using the simple model described above. In
the model, the authors used
T
w
= −1.8 °C,
k
i
=5 × 10
−3
cal/
cm · s · C [
Schwerdtfeger,
1963],
k
s
=6 × 10
−4
cal/cm · s · C
[
Mellor,
1977], and
T
a
was selected to be equal to the mean
air temperature. Although the results from the above sim-
ple model are verified for the date of 6 April, the deviation
of the profile of 16 February from the model (following a
week of relatively warm air temperature) indicates that
the model underestimates the temperature and produced
a higher temperature gradient. The authors suggested
that this simple model should be improved by taking into
consideration three factors: (1) the thermal history in pre-
vious days, (2) the effects of wind and cloud cover on the
heat transfer conditions at the exposed snow surface, and
(3) the uncertainty of the thermal conductivities of snow
when it acquires salinity from the ice surface.
Often in the ice field experiments people usually meas-
ure air temperature, ice thickness, and snow depth. A sim-
ple practical rule to determine roughly the temperature
