Geology Reference
In-Depth Information
10.2.2.1. Description of Selected Algorithms
therefore deviates from the given tie point. This behavior
was confirmed in previous laboratory and theoretical
studies. From a study on laboratory‐grown sea ice,
Grenfell and Comiso [1986] show that significant changes
in ice surface emissivity and polarization ratio occur as
ice grows up to 5 cm thick. Subsequent changes were
associated with changes in surface characteristics, inclu-
ding roughness and brine distribution. Grenfell et  al .
[1992] show trajectories of undisturbed young ice in the
PR 19 /GR 37 v 19 v parameter space. They stated that changes
in both parameters occur fast during the early phase of
ice growth but slow down later. Deviation of an actual
observation from the tie point of certain ice type may
lead to erroneous results of ice concentration. This was
particularly noticeable in results from NT in the presence
of new and young ice types. To overcome this shortcom-
ing another version, called NT thin ice, was developed by
Cavalieri [1994]. It should be noted that the simple
approach of solving the algebraic equations described
above does not have a provision to avert solutions above
100% or below 0%. In these cases of unrealistic results
the output concentration is truncated at 100% if it exceeds
this value or at 0% if it becomes negative.
A . The NASA Team Algorithm (NT) The original ver-
sion of this algorithm was developed by Cavalieri et  al .
[1984] to retrieve total ice concentration in addition to
partial ice concentrations of FY and MY ice. It was origi-
nally applied to SMMR and later adopted to calculate
the same parameters from SSM/I observations [ Cavalieri
et al ., 1991]. Another version of the algorithm was devel-
oped to calculate concentrations of thin ice and FY ice
[ Cavalieri , 1994]. The algorithm solves a set of linear
equations that take the form
TCTCTCT
MY MY
(10.15)
b
,
obs
ow
b
,
ow
FY
b
,
FY
b
,
where T b , obs is the observed brightness temperature, T b ,ow ,
T b , FY , and T b , MY are the typical T b from OW, FY, and MY
ice, respectively. The subscripts i and j denote the fre-
quency and the polarization of the observation. Here C ow ,
C FY and C MY are the concentration of the three surfaces.
The summation of the fractional concentration from n
surfaces should add up to 1:
n
c
1
(10.16)
B . The Enhanced NASA Team Algorithm (NT2) The
enhanced NASA Team sea ice algorithm (NT2) is
presented in Markus and Cavalieri [2000]. The algorithm
has the same functional form as the NT algorithm but
with a different approach designed mainly to account
for the “surface effects” that cause underestimation of ice
concentration by NT. The surface effects include snow
glaze and layering within the snow cover, which have
proven to be problematic in estimating ice concentration
[ Comiso et  al ., 1997]. These effects are grouped in what
Markus and Cavalieri [2000] referred to as the C‐type ice.
In addition to the total ice concentration, NT2 outputs
the concentrations of a couple of ice types from one of
the following two pairs: (1) thick ice (including FY ice and
MY ice combined) and thin ice or (2) thick ice and C‐type
ice. As mentioned before, the NT2 approach is based on a
search in a parameter space for a solution that satisfies the
closest distance with a given observation vector. In this
manner it is different than the NT algorithm, which seeks
a deterministic solution of linear algebraic equations.
The algorithm utilizes the same radiometric ratios that
are used in the original NT algorithm; namely PR 19 and
GR 37 V 19 V (from SSM/I). In addition, it makes use of three
more ratios, PR 85 , GR 85 H 19 H , and GR 85 V 19 V . From these five
ratios, the algorithm uses three derived parameters defined
as follows:
i
1
In principle, the left hand side of equation (10.15) can
be an observation (from a given frequency and polari-
zation channel)/or a calculated parameter. The NT
algorithm uses the polarization ratio PR 18 and the
gradient ratio GR 37 V 18 V in equation (10.15) instead of
brightness temperature. The general expressions of
these ratios are presented in equations. (8.10) and
(8.11). The specific expressions for SMMR parameters
that are used in the NT algorithm take the form
TT
TT
bV bH
,
18
,
18
PR 18
(10.17)
bV bH
,
18
,
18
TT
TT
bV bV
,
37
,
18
GR 37 18
(10.18)
VV
bV bV
,
37
,
18
Using these two parameters in equation (10.15) results in
two equations that can be solved simultaneously along
with equation (10.16) for the three unknowns C ow , C FY ,
and C MY . The use of the polarization ratio is necessary
because of its significantly higher value for water com-
pared to ice. The justification for using the gradient ratio
is that it varies markedly in magnitude and sign between
the three surfaces of OW, FYI, and MYI.
This simple method does not account for surface con-
ditions that cause significant deviation of the emitted
radiation from the tie points. For example, the emitted
radiation from YI types may vary over a wide range and
PR
19
GR
sin
PR
cos
(10.19)
R
37 19
V V
19
19
19
PR
85
GR
sin
PR
cos
(10.20)
R
37 19
V V
85
85
85
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