Geology Reference
In-Depth Information
layer. As the salinity of the layer and therefore its density
increases, it sinks deeper into the ocean, starting a verti-
cal convection current. As a rule of thumb, the faster the
rate of sea ice growth the more salt is entrapped within
the ice. Considerable salt is usually entrapped in the sub-
surface layer of thin ice and that affects the radiometric
emission and scattering from the surface. As ice grows,
the salinity varies with time at any point, but it eventually
stabilizes at what is known as “stable salinity.” This term
is defined and described in details in Section 3.2. It
suffices here to mention that
Nakawo and Sinha
[1981]
related stable salinity of a section of ice at a given depth
with its corresponding growth rate. Finally, ice growth
rate is important for marine navigation because it facili-
tates at least an approximate estimation of ice thickness
distributions in areas of limited ice dynamics.
Many studies have been conducted and a few methods
have been developed to estimate ice growth rate using
direct field measurements and/or simple models with
input from meteorological and climatic data. Early stud-
ies on ice thickness prediction include
Lebedev
[1938],
Zubov
[1938]
, Tabata
[1958]
,
and
Billelo
[1961]. A quick
but rough empirical equation to estimate ice thickness
(
h
) in centimeters from thermodynamic growth was pre-
sented by
Lebedev
[1938]:
where
k
is the thermal conductivity of ice,
T
s
and
T
w
are the ice and water surface temperatures, respectively.
A more accurate estimate of
Q
* can be achieved by esti-
mating its four components:
(2.4)
*
4
QQTQTQTQ
Es Hs
(
)
(
)
(
)
LW s
SW
where
Q
E
Q
H
,
Q
LW
, and
Q
SW
are latent, sensible, long‐wave
and short‐wave fluxes, respectively.
The growth rate of ice can be inferred using a simple
model of heat balance at the ice‐water interface and
energy balance at the upper surface. The latter is more
important during the early growth period. Figure 2.13 is
an idealized schematic diagram showing a section of
floating sea ice of thickness
h
i
with snow cover of depth
h
s
. Ice is formed, primarily under two heat transferring
influences: (1) the oceanic heat flux
F
w
from the warm
ocean to the colder ice interface and (2) the conductive
heat flux
F
c
through the bulk of the ice and snow, created
by the difference between the colder air temperature and
the warmer ocean temperature. These two influences are
balanced by the quantity of heat released during freezing,
which is determined as the multiplication of the latent
heat of water for freezing
L
i
, the ice density
ρ
i
, and the
rate of increase in ice thickness.
The energy balance at the ice‐water interface deter-
mines the rate of ice growth. Following the convention
of positive fluxes in the upward direction, this can be
formulated as:
058
.
(2.1)
h
132
.
(FDD)
where FDD is the accumulated freezing degree‐days (or
AFFD used some times), defined as the sum of the average
daily subfreezing degrees (below 0°C for freshwater and
about −1.8°C for sea water) for a specific period. For exam-
ple, if the total number of days with air temperature below
freezing is 3 and the average daily temperature is −2.8°C,
−3.8°C and −5.8°C, then for sea water with freezing point
of −1.8°C, the FDD becomes the sum of the daily tem-
peratures after subtracting the freezing temperature; i.e.,
1 + 2 + 4 = 7°C. This method is used in the operational sea
ice monitoring environment to roughly estimate ice thick-
ness for the early growth period. Equation 2.1, however,
does not take into consideration any environmental factors
such as ice motion, snow accumulation, ice thickness, sur-
face radiation budget, and surface physical conditions.
Under calm ocean conditions and stable weather, the
growth rate of thin ice can be determined using a simple
heat flux equation:
dh
dt
0
(2.5)
FF L
i
w
c
i
i
The ice thickness can be determined by integrating
this equation provided that expressions for
F
c
and
F
w
(as a function of time) are provided. The continuity of
heat flux throughout the ice and snow layers and into
the atmosphere (as illustrated in Figure 2.13) leads to the
following net conductive heat flux equation:
1
h
k
h
k
FTT
(
)
i
s
(2.6)
c
a
w
k
i
s
T
a
Air
h
s
Snow
T
b
Q
L
*
g
(2.2)
F
c
Ice
h
i
where
Q
* is heat flux from ocean to the atmosphere,
L
is
the latent heat of fusion for water, and
ρ
is the density of
ice. Under thermal equilibrium
Q
* can be determined
using the following equation:
Water
T
w
F
w
Figure 2.13
Idealized heat fluxes in a snow‐covered floating
ice sheet.
*
(2.3)
QTTk
s w
(
)
/
