Geology Reference
In-Depth Information
as a search domain to find the point of closest distance to
a measured emissivity spectrum. The required answer is
the ice concentration vector associated with that point.
The measured emissivity spectrum is obtained, along
with a suite of geophysical parameters including skin
temperature and atmospheric profiles of tempera-
ture, humidity, and cloud liquid water, from a one‐
dimensional variational assimilation scheme (1‐DVAR),
called the Microwave Integrated Retrieval System
(MISR) [
Boukabara et al.,
2007]. The scheme finds a
vector of the geophysical parameters
X
given a vector
of satellite observations
Y
m
(in this case data from the
AMSU and SSMIS sounding instruments) that mini-
mizes the following cost function:
result from solving a set of deterministic equations as
the one presented in equation (10.15) or (10.32)
Environment Canada's Ice Concentration Extractor
(ECICE) algorithm was developed to avoid these two
difficulties. Two new concepts are employed. The first is
using a large number of tie points (instead of a single tie
point) to represent each ice type. These are called char-
acteristic radiometric values (CRV). They are generated
from the probability distribution of each radiometric
parameter for each ice type (the algorithm uses a num-
ber of radiometric parameters specified by the user).
The probability distributions are input to the algorithm
and the algorithm generates a number of CRV sets
(specified by the user but typically 1000) using a random
number generator. The distribution of the CRV for each
parameter mimics the given probability distribution of
that parameter for each surface. The second concept
entails inclusion of a set of inequality constraints in
the formulation. This guarantees that the concentra-
tion solution will always be within the feasible domain
between 0% and 100%.
ECICE is a generic algorithm in that it can be applied
to determine the concentration of any number of ice
types in a heterogeneous footprint using a number of
observations equal or larger than the given number of ice
types. The algorithm can combine observations from any
type of sensors (VIS, TIR, passive microwave, and radar)
provided that a special module is incorporated to address
the peculiarities of the sensor (e.g., atmospheric and
cloud influences in the case of the VIS or TIR data or
wind effect on backscatter from OW in the case of radar
backscatter). In addition to the concentration output,
the algorithm outputs a confidence level attached with
the concentration value. The algorithm is presented
briefly in
Shokr et al.
[2008] but more details about the
concepts and the formulation are presented here.
ECICE is based on an optimal criterion to find the ice
concentration solution that minimizes a cost function.
The latter represents the summation of the error between
the observed and the expected value of each parameter
employed in the formulation at each pixel. The expected
value of a radiometric observation
j
is
R
ej
, which is calcu-
lated from a set of linear equations similar to equation
(10.15). The linear model can be written in the form
JX XXBXX
YFXEYFX
m
() .( (
.( ( )
05
05
)
T
1
)
0
0
(10.34)
T
1
(
( )
m
where
X
0
is the mean background vector (a priori
information),
B
is the background error covariance
matrix,
E
is the observation error covariance matrix, and
F
(
X
) is the forward operator that relates the geophysical
parameters to the observations. This operator is based on
the Community Radiative Transfer Model (CRTM)
[
Weng
, 2007]. The 1‐DVAR assumes independence of
background and observation errors. As usual, the solution
that minimizes the cost function is found by solving a
linear system produced by equating the first derivative of
equation (10.34) to zero.
The measured emissivity spectrum is used to determine
the ice concentration by searching for the point of the
closest distance in the emissivity spectrum database to the
given point. The distance is expressed as the root mean
square of the residuals (RMSE) of the two emissivity
spectra;
1
N
2
RMSE
(
º
)
(10.35)
i
il
N
i
1
where
N
is the number of frequency channels,
i
indicates
a specific frequency channel, and
l
indicates a specific
emissivity spectrum from the database.
E
. The Environment Canada's Ice Concentration
Extractor (ECICE) Algorithm
Estimation of ice type
concentration from remote sensing data is hampered by
two factors: (1) the difficulty of representing each ice
type by a single tie point, especially young ice types,
which are exposed to significant temporal and spatial
changes in response to weather conditions, and (2) the
possibility of obtaining ice concentration values outside
the feasible domain between 0% and 100%. This may
n
RcT
ej
(10.36)
,
iij
,
i
1
where
c
i
is the concentration of the surface type
i
(
i
= 1, …,
n
) and
n
is the number of surfaces including OW
(so if concentration of young (YI), FY, and MY ice are
required, then
n
= 4).
T
i
,
j
is the typical value of the obser-
vation
j
from surface
i
. This is the tie point. The number
