4 Extraction of Intermediate Scale Sea Ice Deformation Parameters from SAR Ice Motion Products
73
Although the centers of the cells are uniformly spaced on the initial source image,
they become somewhat irregularly positioned on the target image because of the differential motion of different portions of the pack ice. The results are displayed on the
Geophysical Processor System (GPS) (Kwok and Cunningham 1993) as an array of vectors that are scaled such that their magnitude is less than the grid spacing. In the
schematic representation of this process, shown in Figure lA, the ice is drifting toward
the NNE. Here the dashed lines, which are not part of the computer display, represent
the boundaries of the 5 x 5 km grid cells on the source image. Because this fixed size of
the grid cells was adopted in the production of the ASF ice motion products, and our
purpose for developing the algorithm discussed here is to avoid or at least minimize
the use of the SAR images in deformation studies, we presently only consider sea ice
deformation problems addressable at a 5 x 5 km grid resolution which is suitable for
the study of intermediate-scale sea ice deformation.
4.2.2
Derivation of Ice Deformation
lce deformation can be defined in terms of ice motion by two invariants (Thorndike et
al.1975; Rothrock 1986; Fily and Rothrock 1990):
E[ = ou + ov
ox oy
1
E[ =((OU + OV)2 +(OU + OV)2]2
ox oy
oy ox
Here the first invariant quantifies the divergence or convergence of the ice field with a
positive value indicating a divergent motion field, and a negative value indicating a convergent field. The second invariant quantifies the magnitude of the shearing. They
depict different aspects of deformation and are invariant with translation and rotation.
In a grid configuration, differential operations can be approximated by division, the
quantities ox and oy can be represented by the size of the grid cell in the x and y directions, while U and v can be regarded as the displacement, assuming a unit interval
between the times of acquisition of the image pairs. Calculations of OU and OV then
involve comparisons of the displacements at the two ends of the x or y side.
By making a slight rearrangement in the grid configuration by changing the boundary of each grid cell, the geometric meanings of the ice deformation parameters
become clearer. In the original configuration, the cell boundaries consist of bisects
between the center of the cell and those of the four neighboring cells (Fig. 1A). In the
modified configuration, the boundaries of cells are defined by four neighboring tie
points indicated directly by the ASF ice motion products (Fig. 1B). Figure 1B is an
enlarged version of Fig. 1A on which the initial cell boundaries are indicated by dashed
lines and the modified cell boundaries by continuous lines. In the modified representation (Fig. 1B), the motion vectors are drawn to scale and, therefore, are commonly
longer than 5 km (typical ice drifts in this portion of the polar basin are 2-3 km/day).
In the modified representation, ice deformation can be regarded simply as the change
73
Although the centers of the cells are uniformly spaced on the initial source image,
they become somewhat irregularly positioned on the target image because of the differential motion of different portions of the pack ice. The results are displayed on the
Geophysical Processor System (GPS) (Kwok and Cunningham 1993) as an array of vectors that are scaled such that their magnitude is less than the grid spacing. In the
schematic representation of this process, shown in Figure lA, the ice is drifting toward
the NNE. Here the dashed lines, which are not part of the computer display, represent
the boundaries of the 5 x 5 km grid cells on the source image. Because this fixed size of
the grid cells was adopted in the production of the ASF ice motion products, and our
purpose for developing the algorithm discussed here is to avoid or at least minimize
the use of the SAR images in deformation studies, we presently only consider sea ice
deformation problems addressable at a 5 x 5 km grid resolution which is suitable for
the study of intermediate-scale sea ice deformation.
4.2.2
Derivation of Ice Deformation
lce deformation can be defined in terms of ice motion by two invariants (Thorndike et
al.1975; Rothrock 1986; Fily and Rothrock 1990):
E[ = ou + ov
ox oy
1
E[ =((OU + OV)2 +(OU + OV)2]2
ox oy
oy ox
Here the first invariant quantifies the divergence or convergence of the ice field with a
positive value indicating a divergent motion field, and a negative value indicating a convergent field. The second invariant quantifies the magnitude of the shearing. They
depict different aspects of deformation and are invariant with translation and rotation.
In a grid configuration, differential operations can be approximated by division, the
quantities ox and oy can be represented by the size of the grid cell in the x and y directions, while U and v can be regarded as the displacement, assuming a unit interval
between the times of acquisition of the image pairs. Calculations of OU and OV then
involve comparisons of the displacements at the two ends of the x or y side.
By making a slight rearrangement in the grid configuration by changing the boundary of each grid cell, the geometric meanings of the ice deformation parameters
become clearer. In the original configuration, the cell boundaries consist of bisects
between the center of the cell and those of the four neighboring cells (Fig. 1A). In the
modified configuration, the boundaries of cells are defined by four neighboring tie
points indicated directly by the ASF ice motion products (Fig. 1B). Figure 1B is an
enlarged version of Fig. 1A on which the initial cell boundaries are indicated by dashed
lines and the modified cell boundaries by continuous lines. In the modified representation (Fig. 1B), the motion vectors are drawn to scale and, therefore, are commonly
longer than 5 km (typical ice drifts in this portion of the polar basin are 2-3 km/day).
In the modified representation, ice deformation can be regarded simply as the change