80
S. LI, Z. CHENG, AND W.E WEEKS
the algorithm also produces a summary file that records the most critical deformation
results. This facilitates the fast screening and extraction of significant ice deformation
events from a series of ice motion files.
The grid files are in byte format consisting of integer values ranging from 0 to 250.
In the Er file, the number 125 is taken as a neutral value, with 250 representing divergence of 31.25% or more and zero representing convergence of 31.25% or more. The larger the deviation from neutral, the larger the deformation. The other basic grid file is
the shear file, in which zero represents non-shearing and 250 indicates an amount of
0.625 or larger in shear. The grid files can be easily displayed by most image processing and graphics software packages.
The ASCII file is a line-oriented text file that provides the deformation values for all
the individual grid cells traceable by the algorithm. Also, some intermediate results are
printed out for the user's information. The summary file is also a text file. It lists the
number of ice motion records, the number of rows and columns of tie points, and the
total and average divergence and convergence derived from each input ice motion file.
4.5
Accuracy in Estimation of Deformation Parameters
According to Fily and Rothrock (1990), the error sources in deformation calculations
made on a grid basis consist of (1) mislocation of the tie points, and (2) nonlinearity of
the boundaries of the deformed grids. The mislocation of tie points can be minor or
severe depending on the situation. In this section we will discuss the impact of these
errors in calculation of the net divergence, which is the difference of divergence and
convergence, and for the separately aggregated divergence and convergence values for
a set of grid cells.
The magnitude of errors caused by minor mislocation of tie points is our primary
concern because of the pervasiveness in errors of this type. Fortunately, the magnitude
of this type of errors can be quantified. According to a previous study (Li et al. 1995), it
is safe to state that the random error in the corner locations of a deformed grid caused
by minor mislocation due to the limitation of the resolution of images used in the
motion tracking is within ±50 m. In the extreme case, for a cell with sides of 5 km, the
size error caused by this random mismatch error can have a maximum value of ±4%
if the random errors of the four corners of the cell happen to act additively. For a large
number of cells, the standard deviation of the errors in deformation caused by minor mismatch of tie points is 0.82%. For features such as leads and large ice floes that are composed of m cells, this type of error in deformation is further reduced by a factor of rm.
Separate aggregation of the divergence and convergence values for a set of cells introduces errors if there are errors in the individual cells. Those errors cannot cancel each
other if the deformation is small. Suppose there is a uniform deformed area with a divergence value of EJ and minor mislocations in the tie points which produce normally distributed errors in the values for individual cells. In such cases the separate aggregation
of divergence and convergence values will result in an error in the averaged value which
can be determined by the formula
(5)
S. LI, Z. CHENG, AND W.E WEEKS
the algorithm also produces a summary file that records the most critical deformation
results. This facilitates the fast screening and extraction of significant ice deformation
events from a series of ice motion files.
The grid files are in byte format consisting of integer values ranging from 0 to 250.
In the Er file, the number 125 is taken as a neutral value, with 250 representing divergence of 31.25% or more and zero representing convergence of 31.25% or more. The larger the deviation from neutral, the larger the deformation. The other basic grid file is
the shear file, in which zero represents non-shearing and 250 indicates an amount of
0.625 or larger in shear. The grid files can be easily displayed by most image processing and graphics software packages.
The ASCII file is a line-oriented text file that provides the deformation values for all
the individual grid cells traceable by the algorithm. Also, some intermediate results are
printed out for the user's information. The summary file is also a text file. It lists the
number of ice motion records, the number of rows and columns of tie points, and the
total and average divergence and convergence derived from each input ice motion file.
4.5
Accuracy in Estimation of Deformation Parameters
According to Fily and Rothrock (1990), the error sources in deformation calculations
made on a grid basis consist of (1) mislocation of the tie points, and (2) nonlinearity of
the boundaries of the deformed grids. The mislocation of tie points can be minor or
severe depending on the situation. In this section we will discuss the impact of these
errors in calculation of the net divergence, which is the difference of divergence and
convergence, and for the separately aggregated divergence and convergence values for
a set of grid cells.
The magnitude of errors caused by minor mislocation of tie points is our primary
concern because of the pervasiveness in errors of this type. Fortunately, the magnitude
of this type of errors can be quantified. According to a previous study (Li et al. 1995), it
is safe to state that the random error in the corner locations of a deformed grid caused
by minor mislocation due to the limitation of the resolution of images used in the
motion tracking is within ±50 m. In the extreme case, for a cell with sides of 5 km, the
size error caused by this random mismatch error can have a maximum value of ±4%
if the random errors of the four corners of the cell happen to act additively. For a large
number of cells, the standard deviation of the errors in deformation caused by minor mismatch of tie points is 0.82%. For features such as leads and large ice floes that are composed of m cells, this type of error in deformation is further reduced by a factor of rm.
Separate aggregation of the divergence and convergence values for a set of cells introduces errors if there are errors in the individual cells. Those errors cannot cancel each
other if the deformation is small. Suppose there is a uniform deformed area with a divergence value of EJ and minor mislocations in the tie points which produce normally distributed errors in the values for individual cells. In such cases the separate aggregation
of divergence and convergence values will result in an error in the averaged value which
can be determined by the formula
(5)