Geology Reference
In-Depth Information
cross‐polarization images also enhance the appearance of
ridges (Figure 8.15)
The second approach that has been used routinely to
identify surface deformation (particularly pressure
ridges) in SAR images relies on estimating the ice
motion field from pairs of Radarsat images. From
the motion field the rates of ice shear and divergence
can be calculated. These two invariants characterize ice
deformation. This approach has been used operation-
ally in the RGPS at the ASF of the University of Alaska
[
Kwok
, 1998]. It has been described in a few papers [e.g.,
Li et al
., 1995;
Lindsay and Stern
, 2003;
Herman and
Glowacki
, 2012]. The estimation of the ice motion (or
displacement) vector from a pair of Radarsat images,
along with a few details about the RGPS, are addressed
in section 10.7. Derivation of the surface deformation is
presented here.
To identify the evolving deformation of the ice cover
using a series of satellite images, a Lagrangian ice motion
field should be generated. In a Lagrangian representation
a grid should be established in the first image, and the
velocity at the grid corners are tracked between sequen-
tial pairs of images (details are provided in section 10.7.2
and illustrated in Figure 10.48). By tracking the displace-
ment of grid points between successive images, a defor-
mation field at a spatial scale less than the grid spacing
can be obtained. The Lagrangian ice motion algorithm
from the RGPS tracks 10 km × 10 km cells typically at
3 day intervals during an entire ice growth season. An
example of a deformation representation produced by
the RGPS is presented in Figure 9.4, which includes
selected frames from an animation provided by Ron
Kwok of JPL. The dates and locations are not shown
since the figure aims at showing the concept of distorted
cells from one date to the next. As mentioned, the distor-
tion of each cell is obtained from the displacement vec-
tors of the four corner points. Area changes of the cells
can be used as an indicator of the creation or transforma-
tion of young ice.
Rothrock
[1986] stated that sea ice deformation can be
characterized by three invariants: the divergence/
convergence rate
E
d
, the shear rate
E
s
, and the vorticity
vrt defined as
where
u
and
v
denote the velocity components along the
x
and
y
axes of the grid points, respectively. In equation
(9.1), a positive value of
E
d
indicates a divergent motion
(that generates openings in the ice cover) and a negative
value indicates a convergent motion (that generates pres-
sure ridges). In the differential operators,
u
and
v
can be
regarded as the displacement assuming a unit interval
between the times of acquisition of the image pairs, there-
fore, ∂
u
and ∂
v
are calculated by comparisons of the
displacements at the two ends of the
x
and
y
sides. Also,
∂
x
and ∂
y
are the size of the grid cell. The total defor-
mation (strain) rate
E
t
is defined as
1
2
(9.4)
2
2
EEE
t
(
)
d
s
and the azimuth of the strain rate as
E
E
tan
1
s
(9.5)
t
Values of
θ
= 0,
π
/2, and
π
correspond to pure divergence,
pure shear, and pure convergence, respectively [
Feltham,
2008].
The strain rate components are computed from approx-
imations of the line integral around the boundary of each
cell [
Lindsay and Stern
, 2003]:
u
xA
udy
1
1
2
n
A
uuyy
i
(
)(
)
(9.6)
i
1
i
i
1
i
1
where
n
and
A
are the number of vertices of the cell and
its area; respectively. The area is computed as
1
2
1
n
A
(
xy x
)
(9.7)
ii
1
ii
1
i
Yu et al
. [2009] calculated the total strain rate
[Equation 9.4] from the motion field generated from two
consecutive SAR images acquired on 11 and 14 December
2001 of the marginal ice zone of the Bering Sea. An
example from their results is presented in Figure 9.5. The
averaged azimuth
θ
over the scene shown in the figure is
79.2°, which is close to the value of 90° for the case of
pure shear. The mean shear
E
s
[equation 9.2] was found
to be 13.2% per day, which was significantly higher than
values in neighboring areas. More details on shear and
convergence rates in different areas and their relation
to the wind and ocean current fields can be found in
Yu et al
., [2009]. Wind forcing is generally considered to
be the main stimulus of sea ice deformation.
A main advantage of the Lagrangian motion represen-
tation is the ability to detect what is known as linear kin-
ematics features (LKF) and their temporal evolution
[
Kwok
, 2003]. These are apparents long, narrow features
u
x
v
y
E
(9.1)
d
u
y
v
x
E
(9.2)
s
1
2
2
2
u
x
v
y
u
y
v
x
vrt
(9.3)
