Geology Reference
In-Depth Information
Recent attempts to estimate ice thickness from the
microwave Soil Moisture and Ocean Salinity (SMOS)
satellite have been presented in
Kaleschke et al
. [2010,
2012]. SMOS was launched in November 2009 and
has been providing data since the summer of 2010
[
Mecklenburg et al
., 2012]. It carries a radiometer called
Microwave Imaging Radiometer with Aperture Synthesis
(MIRAS), which features a multiangular, dual‐polariza-
tion (H and V) channels operating in the L‐band (1.4 GHz
and 21 cm wavelength). The spatial resolution is around
50 km. It is suitable for ice thickness retrieval because of
the deeper penetration of the L‐band signal [
Kerr et al
.,
2010]. The coarse footprint also makes it suitable for
synoptic‐scale observations.
The approach that has been adopted for retrieval of ice
thickness is different from the above‐described empirical
approach using the traditional microwave channels. Here,
ice thickness is calculated inversely from a model of
brightness temperature as a function of sea ice and water
emissivity. The model starts with the familiar equation
that decomposes an observed brightness temperature
T
b
from a heterogeneous footprint that includes ice and OW
into its two components, weighted by the ice concentra-
tion
C
and the emissivity :
where
T
b
,ice
is the brightness temperature of the infi-
nitely thick sea ice. Both
T
b
,ice
and
T
b
,
w
are functions of
the surface temperature and salinity. These parameters
can be determined using satellite observations from ice‐
free and thick‐ice‐covered footprints. The coefficient
γ
in
equation (10.85) can be determined from a least‐squares
curve‐fitting brightness temperature versus ice thickness.
The resulting brightness temperature variation with ice
thickness from the above method is presented in Figure 10.33.
The data points are determined for different bulk sea ice
temperatures with a constant low salinity of 0.65‰ (typical
of the ice in the Baltic Sea) and surface roughness equivalent
to one‐tenth of the ice thickness. The figure includes plots of
equation (10.85) with appropriate coefficients that lead to
an almost perfect fit to the model's data points. A striking
observation from the calculations is the sensitivity of
brightness temperature to ice thickness up to 40 cm at ice
temperature −5 °C and around 150 cm when the tempera-
ture drops to −20 °C. Recall that the polarization ratios
from the 37 and 85 GHz channels are sensitive to ice thick-
ness up to about 10-20 cm (Figure 10.30). This demon-
strates the advantage of using the L‐band data for mapping
thicker ice although the output is produced at a coarse reso-
lution of 50 km.
Kaleschke et al
. [2010] stated that for typical
polar sea ice with bulk ice temperature of −5 °C and salinity
and 8‰, the resulting
T
b
from the L‐band would resemble
that of sea ice in the Baltic Sea at a temperature of −0.5 °C.
The ice thickness can be derived from equation (10.85):
(10.84)
TCTCT
b
(
1
)
i
i
w w
where subscripts
i
and
w
stand for ice and water, respec-
tively, and
T
is the physical temperature. The large
contrast between the typical brightness temperatures of
ice and water in the L‐band (150 and 90 K, respectively)
justifies the use of this equation. Although this simple
equation does not account for the atmospheric and
ionospheric effects, these effects are truly insignificant in
the case of the L‐band [
Reul et al
., 2008]. From this
point, the model proceeds by introducing expressions for
i
and
w
as well as the sea ice and water permittivities,
which are required to calculate the emissivities [
Kaleschke
et al
., 2010]. The emissivity of the ice is a function of its
thickness
H
. It is derived in terms of the brine volume
fraction as presented in section 3.4.1. All terms are
derived with respect to the nadir view. A semiempirical
approximation for the incoherent solution of equation
(10.84) is given by:
TT
TT
1
ln
bm
,
b
H
(10.87)
bm
,
bw
,
This equation has been used by
Kaleschke et al
. [2012] to
derive ice thickness up to 50 cm from the SMOS observa-
tions when surface temperature is below −10 °C. The
authors define the maximum ice thickness
H
max
that can
be retrieved for a given observational error
δ
as
1
H
max
ln
(10.88)
where Δ = (
T
b
,
m
−
T
b
,
w
), and
δ
is the uncertainty of the tie
point
T
b
,ice
.
The accuracy of this retrieval has been estimated by
same authors. They reported that an uncertainty in the
radiometric accuracy of ±1 °C leads to a thickness
uncertainty of ± 2 cm for
H
= 40 cm, and ±5 cm for
H
= 70 cm. However, due to its coarser resolution small
polynyas and refrozen ice in leads and other openings
may not be detected by the SMOS MIRAS. Therefore, a
combination of the L‐band microwave with other tradi-
tional bands may satisfy operational ice monitoring and
TT TT H
b
exp
(10.85)
b m
,
bmb w
,
,
where
T
b
,
w
and
T
b
,
m
and are the brightness temperatures
of seawater and the mixture of the heterogeneous foot-
print (ice and water), respectively. The latter is given by
T T
1
C T
(10.86)
bm
,
b
,
ice
b w
,
