Geology Reference
In-Depth Information
where
α
k
are the weights whose summation is equal to 1.
This step is performed iteratively where
M
is incremented
until the coefficient of determination between the actual
distribution and the mixture of
M
Gaussians exceeds a
given threshold. Based on the Bayes rule,
10.3. sea Ice exTenT and area
Ice extent is defined as the area that has an ice concen-
tration exceeding a certain threshold. The threshold set
by the National Snow and Ice Data Center (NSIDC), one
of NASA's Distributed Active Archive Centers (DAAC),
is 15%. Therefore, ice extent calculated from any ice con-
centration retrieval algorithm is simply the summation of
the area of pixels that have their ice concentration > 15%.
Ice area, on the other hand, is defined as the multiplica-
tion of the ice concentration percentage by the pixel area,
summed over all qualified pixels in an ice concentration
map. In some calculations all pixels are qualified. Other
calculations, which are more commonly used, use pixels
that have ice concentration > 15%. Since the ice area cal-
culation takes into account the actual concentration at
each pixel, it is usually lower than the ice extent, which
considers any pixel with concentration > 15% as fully
covered with ice. Obviously, ice area is a more accurate
estimate. However, NSDIC uses ice extent in order to
compensate for the underestimation of ice concentra-
tion in the summer using passive microwave observations
when the ice surface is melting. Ice extent and ice area are
derived from the total ice concentration estimates from
any retrieval algorithm (mostly from passive microwave
data, although VIS and IR data algorithms are also
used). Different algorithms produce different estimates as
shown in Figure 10.25.
The most important application of ice extent is in mon-
itoring the annual variation of the Arctic ice; an impor-
tant indicator of global warming. Several centers produce
maps of ice concentration and extent regularly. Japan
Aerospace Exploration Agency (JAXA) produces daily
maps. The data are based on a passive microwave sea ice
concentration algorithms developed at NASA (NT, NT2,
and BS) using a suite of sensors depending on the date
of the data acquisition (SMMR, SSM/I, AMSR‐E,
WindSAT, and AMSR2). A graph showing the extent of
Arctic sea ice, generated from daily ice concentration
maps, is presented in Figure 10.27. This graph is updated
daily by JAXA and can be accessed from the website
The Arctic ice reaches its maximum in March and its
minimum in September. The figure shows that the maxi-
mum extent in the past few years is remarkably lower
than the average maximum extent in the 1980s, 1990s,
and 2000s. The trend of the decrease is obvious. In March
2014 the ice extent reached a maximum of 14 million
km
2
, which is considerably below the averages from the
previous three decades. The lowest ice extent on record,
3.41 million km
2
, was observed in September 2012. This
was considerably lower than second lowest extent of
4.1 km
2
, which occurred in September 2011. The minimum
in 2013 (not shown in Figure 10.27) was 5.1 km
2
. The
gx
|
mm i m
gmx
| ,
(10.58)
i
m
gx
|
j
j
i
j
j
1
where
m
= 1, ..
M
,
Θ
'
and
j
refer to the estimated param-
eters from the previous iteration for the
j
th Gaussian. The
iterative updates for the Gaussian mixture in equations
(10.56) and (10.57) are given by
N
1
gmx
| ,
(10.59)
m
i
N
i
1
N
xg mx
| ,
i
i
i
1
(10.60)
m
N
gmx
| ,
i
i
1
N
2
x
g mx
| ,
i m i
2
i
1
(10.61)
m
N
gmx
| ,
i
i
1
If the mean
μ
1
of the mixture Gaussian with the lowest
mean is less than a given threshold (the only adjustable
parameter in the algorithm), this Gaussian is interpreted
to present open water. The concentration is then estimated
to be
C
= 1.0 −
α
1
, otherwise
C
= 1.0. Results from the algo-
rithm were verified using the ice concentration maps gen-
erated at the Finnish Ice Service (FIS) and the operational
ASI sea ice concentration products from the University of
Bremen. An example is presented in Figure 10.26. It is
obvious that the SAR algorithm underestimates the con-
centration in the core area of the image with respect to the
other two sources. However, this could be the true estima-
tion because it is produced at a significantly finer resolu-
tion compared to the operational analysis charts and the
ASI concentration map. The ice concentration estimates
from operational analysis tends to be more conservative,
and the concentration from using passive microwave data
is produced at a coarse resolution (although ASI uses data
from the finest resolution channel). Ice concentration
maps at SAR resolution has long been a goal of the remote
sensing sea ice community. This is where the promise of
this method resides.
