Geology Reference
In-Depth Information
where
k
0
is the conductivity of pure ice (=2.034 W/m · K)
and
β
= 0.13 W/m · kg and
T
s
is, as usual, the surface
temperature (more accurate results can be obtained if
the bulk ice temperature is considered). The sea ice salin-
ity, measured in parts per thousands, is modeled by the
empirical relationship developed by
Cox and Weeks
[1974]
F
dn
T
4
(10.70)
l
a
a
where
σ
is the Stefan‐Boltzmann constant (= 5.6704 ×
10
−8
W/m
2
·K
4
). According to
Yu and Rothrock
[1996], the
ice emissivity
i
can be taken as 0.97 and emissivity of
the atmosphere
a
= 0.7855(1 + 0.2232
C
2.75
), where
C
is
the cloud fraction. The ice surface temperature
T
s
can be
obtained from any TIR sensor such as MODIS. The air
temperature
T
a
at 2 m level can be obtained through
either one of the following two approaches. The first is
the average surface temperature from a TIR sensor (e.g.,
AVHRR or MODIS) over a 50 × 50 km
2
area plus a bias
of 0.4 °C.
Lindsay and Rothrock
[1995] adopted a similar
approach where the bias was a monthly varying climato-
logical air/surface temperature difference. The second
approach entails using reanalysis of meteorological
parameters from any weather model such as the Global
Environmental Multiscale (GEM) model of the Canadian
Meteorological Center.
The turbulent and latent heat fluxes,
F
s
and
F
e
, which
can be neglected as a first approximation, are estimated
from the equations
S
14 24 19 39
.
.
H
for
H
40
cm
(10.75)
S
788159
.
.
H
for
H
40
cm
Snow depth is a crucial parameter especially over thin
ice because it changes the thermal fluxes and sur-
face temperature significantly. Unfortunately, it cannot
be determined accurately from an appropriate sensor
(usually passive microwave as explained in section 10.6)
and concurrently with the TIR sensor passes. Therefore
an empirical relationship between snow depth
h
and ice
thickness can be used [
Yu and Rothrock
, 1996]:
h
0
for
H
cm
for m
5
h
005
.
.
h
5
H
20
cm
(10.76)
h
01
h
for
H
20
cm
Fc CuTT
s
(10.71)
a ps a
s
Values from equations (10.64)-(10.76) can be substi-
tuted in equation (10.63), which can then be solved for
the unknown ice thickness
H
[this parameter appears in
equation (10.73)]. As mentioned before, the application
of this approach requires a cloud masking module to
flag out cloudy areas. Various algorithms have been
developed to screen clouds [e.g.,
Stowe et al.
, 1999],
though
Yu and Lindsay
[2003] reported that no algo-
rithm was developed to detect clouds during the dark
seasons in the polar regions. The technique requires also
a “thick ice filter” to identify areas of thin ice that are
suitable for the application.
Rudjord et al.
[2011] used
passive microwave spectral profiles of OW and ice types
to identify an appropriate parameter for such a filter.
They recommended using the inequality (
T
b
,89
V
/
T
b
,19
V
> 1)
to keep only pixels of thin ice.
The above approach has been used in a few studies.
Drucker et al.
[2003] used it to estimate thin ice thickness
in a coastal polynya adjacent to the St. Lawrence Island
in the Bering Sea. They used gridded AVHRR data at
1 km resolution and co‐located measured meteorological
data (air temperature and wind speed). Figure 10.29 is a
composite image of the polynya region constructed from
a near‐coincident Radarsat‐1 image (the gray area) and
AVHRR‐derived thin ice thickness (colored areas). The
boundary of the polynya can be identified in the ice thick-
ness map. Most of the thickness values under 20 mm were
located in an active frazil region within the polynya. A set
of upward‐looking sonar (ULS) sensors were placed in
F Cu fe e
e
(10.72)
a
e
sa
s
0
where
ρ
a
is the air density,
c
p
is the specific heat of air,
L
is the latent heat of vaporization, and
C
s
and
C
e
are the
bulk transfer coefficients for heat and evaporation.
Yu
and Rothrock
[1996] chose
C
s
=
C
e
= 0.003 for very thin ice
and =0.00175 for thicker ice. The term
e
s
0
in equation
(10.72) is the saturation vapor pressure at the surface.
The surface wind speed
u
at 2 m level above the surface
can be obtained from the output of any weather model.
Finally, the conductive heat flux is estimated assum-
ing linear temperature gradients through the snow and
ice cover:
kk TT
kh kH
is f
s
F
(10.73)
c
i
s
where
k
i
and
k
s
are the thermal conductivity of sea ice
and snow, respectively,
h
is the snow depth,
H
is the ice
thickness,
T
f
is the freezing temperature of the seawater
and is derived from a simplified relationship, and
T
f
= − 0.055
S
w
where
S
w
is the seawater salinity. The snow
conductivity
K
s
can be set to 0.31, while the ice conduc-
tivity can be calculated from
kk ST
i
/
273 15
.
(10.74)
0
s
