Geology Reference
In-Depth Information
addresses the retrieval of sea ice emissivity from AMSR‐E
at various frequencies. The retrieval is conducted using a
new method that employs a form of radiative transfer
equation similar to equation (7.57) after neglecting the
term of the reflected space radiation:
results from different sources. Among the factors that
influence the emissivity and the dielectric constant of the
snow‐covered sea ice in ways that have not been fully
understood are the snow depth, wetness, and grain size.
Authors usually refer to these factors as “causes of error
in emissivity calculations” without providing definite
trends about their impacts on the emissivity. A less men-
tioned factor but perhaps not less important pertains
to brine pockets; their intensity and geometry within the
crystallographic structure of the ice. These are the prime
absorbers of energy. The only way to understand the com-
bined effects of these parameters on the variability of
the emissivity is through forward modeling. It is not pos-
sible to achieve this task by linking estimated emissivity
from remote sensing observations to field measurements
because point sampling does not represent the condi-
tions within the footprint of the sensor. Sea ice emissivity
modeling, however, has not advanced to match the level
of maturity of the radiative transfer models.
In a study presented by Mills and Heygster [2011] the
authors examined three models, all constrained by the
condition of spectral reflection at the interfaces. The
models, which are described in detail Mills and Heygster
[2011], employ a few concepts: a single three‐layer plane‐
parallel RT process, an ensemble of plane‐parallel RT
calculations, and a ridged ray‐tracing Monte Carlo model
that accounted for the topography of both the top and
bottom surfaces of the ice using geometric optics. The
study focused on emissivity for the L‐band (1.4 GHz) fre-
quency to facilitate retrieval of ice thickness from the Soil
Moisture and Ocean Salinity (SMOS) satellite that car-
ries a radiometer operating at that frequency. Mills and
Heygster [2011] present results of brightness temperature
from the three models. Maps of brightness temperature
as  a function of the complex permittivity of sea ice are
shown. Model results compared well with airborne meas-
urements obtained during a field campaign in the north-
ern Baltic Sea in March 2007. One interesting finding from
the study is the effect of ice ridging on brightness tempera-
ture. In general, emissivity models can be useful if input
parameters of ice and snow are specified accurately.
The rest of this section gives a summary of results
of  emissivity of ice types using the above‐mentioned
approaches (in situ measurements of T b , remote sensing
measurements of T b , and modeling the emissivity). Data
are given for a few ice types under different surface and
snow conditions.
A summary of emissivity of sea ice types is presented
in  an early study by Eppler et al . [1992]. This reference
includes a comprehensive table of emissivity of a few ice
types with different conditions at microwave frequencies
4.9, 6.7, 10, 18.7, 21, 37, 90, and 94 GHz in both horizon-
tal and vertical polarizations. In addition to OW, the ice
types and surface conditions include new ice, Nilas (dark,
T
(
,
)
(
,
)
T e
sec
T
(
,
)
b
s
up
se
c
1
(
,
)
T
(
,
)
e
(8.20)
down
where T s is physical temperature of the ice surface, T up is
the up‐welling radiation from the atmosphere, and ϑ and
θ are the observing frequency and incidence angle,
respectively. This equation is valid for a specular reflect-
ing surface. Mätzler [2005] has shown that this assump-
tion is valid if the viewing angle of a passive microwave
radiometer is around 55°, which is close to the viewing
angle of AMSR‐E. Equation (8.20) can be solved for the
emissivity:
sec
TTTe
Te Te
b
up
down
(8.21)
sec
sec
i
down
For  =0 and  =1 the corresponding T b can be obtained
from equation (8.20):
sec
T
b  0
T
,
T
,
e
(8.22)
up
down
sec
T
 1
T
,
Te
(8.23)
b
up
s
Using equations. (8.22) and (8.23) into equations. (8.21),
the equation for emissivity can be written as
TT
0
bb
(8.24)
T
1
T
0
b
b
Here, T b is the brightness temperature observed by the
satellite while T b ( = 0) and T b ( = 1) are simulated values
that can be obtained using a radiative transfer model
such as the Microwave Model (MWMOD). This model
is designed to compute brightness temperatures between
1 and 300 GHz, assuming a specular reflection surface
and nonscattering atmosphere [ Fuhrhop, et al . 1998]. The
inputs to MWMOD are vertical profiles of temperature,
pressure, and humidity. These parameters can be obtained
from a weather model.
Modeling emissivity from sea ice is very crucial for
improving our understanding about the complex inter-
actions between ice and snow properties that affect the
emissivity and the unexplainable discrepancy of the
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