S.G. BEAVEN AND S.P. GOGINENI
assumption results in a maximum error of about 10 m for SAR frames of 100 x 100 km.
Image coordinates along each side of the image frame are first computed by interpolation from the end points using a bilinear interpolation in Cartesian coordinates. The
corner points must first be converted to three-dimensional Cartesian coordinates,
using the local Earth radius. This radius is computed based on an elliptical model of
the Earth and the center latitude and longitude coordinates of the image. Once the corner points are converted to Cartesian coordinates, the coordinates along any line are
computed using the bilinear interpolation,
X'-X ~ x-.!L
-
1
+ z
(1)
d 1 +d z
d 1 +d z
for each of the coordinates, where X' is any point between the end points X, and X2 and the
distance from X' to the end points is given by d, and d2• Equations for the other two coordinates, Y' andZ',are similar to Eq. (1). In practice, the interpolation is first performed along
two opposite sides of the image. Then each row or column uses the interpolated edges as
end points. The final step involves transforming from Cartesian coordinates into spherical coordinates to obtain the latitude and longitude for each pixel within the SAR image.
The SSM/I data, obtained from the US National Snow and Ice Data Center (NSIDC),
are mapped to polar stereographic coordinates and the brightness temperature data
are stored on a rectangular grid. Latitude and longitude coordinates for each pixel of
the SSM/I data were obtained with a conversion program supplied by NSIDC. The
reported accuracy of these location programs is less than 1 km, which is approximately the same accuracy as the SSM/I sensor data record geographic location values
(NSIDC 1992). The conversion from latitude/longitude values to image pixel locations
was performed in two steps. First, we transformed the latitude/longitude into polar
stereographic coordinates for the polar regions. Then we used these to find the row and
column values for the particular pixel in which the latitude/longitude point was located. The algorithm is described in detail in the NSIDC report (1992).
Using the two-step process for obtaining the SSM/I grid locations for each SAR image
pixel we generated SSM/I -gridded brightness temperature images that were mapped to
the coordinates of each SAR image frame used in this study. We then used these pixel
values to find the brightness temperature that corresponded to each ERS-I SAR pixel
and a resampled SSM/I brightness temperature image was obtained. The brightness
temperatures from these resampled images were then used in the fusion algorithm with
the corresponding SAR-derived multiyear ice fraction estimate.
5.4.3
Relationship to Freeze-Up Detected with SAR
We used the co registered ERS-l SAR and SSM/I imagery to investigate the relationship
between passive microwave-based estimates of ice concentration and radar backscatter signature. We used the NT algorithm to compute sea ice type concentrations on the
resampled SSM/I image data using hemispheric tie points. The mean values over each
SAR frame area are plotted in Fig. 4 to demonstrate the changes in relative concentrations of first-year and multiyear ice estimated by the NT algorithm during this time
frame. The mean ice type concentrations for SSM/I pixels are located within the SAR
frame are listed in Table 1. The estimated changes in first-year and multiyear ice con-
assumption results in a maximum error of about 10 m for SAR frames of 100 x 100 km.
Image coordinates along each side of the image frame are first computed by interpolation from the end points using a bilinear interpolation in Cartesian coordinates. The
corner points must first be converted to three-dimensional Cartesian coordinates,
using the local Earth radius. This radius is computed based on an elliptical model of
the Earth and the center latitude and longitude coordinates of the image. Once the corner points are converted to Cartesian coordinates, the coordinates along any line are
computed using the bilinear interpolation,
X'-X ~ x-.!L
-
1
+ z
(1)
d 1 +d z
d 1 +d z
for each of the coordinates, where X' is any point between the end points X, and X2 and the
distance from X' to the end points is given by d, and d2• Equations for the other two coordinates, Y' andZ',are similar to Eq. (1). In practice, the interpolation is first performed along
two opposite sides of the image. Then each row or column uses the interpolated edges as
end points. The final step involves transforming from Cartesian coordinates into spherical coordinates to obtain the latitude and longitude for each pixel within the SAR image.
The SSM/I data, obtained from the US National Snow and Ice Data Center (NSIDC),
are mapped to polar stereographic coordinates and the brightness temperature data
are stored on a rectangular grid. Latitude and longitude coordinates for each pixel of
the SSM/I data were obtained with a conversion program supplied by NSIDC. The
reported accuracy of these location programs is less than 1 km, which is approximately the same accuracy as the SSM/I sensor data record geographic location values
(NSIDC 1992). The conversion from latitude/longitude values to image pixel locations
was performed in two steps. First, we transformed the latitude/longitude into polar
stereographic coordinates for the polar regions. Then we used these to find the row and
column values for the particular pixel in which the latitude/longitude point was located. The algorithm is described in detail in the NSIDC report (1992).
Using the two-step process for obtaining the SSM/I grid locations for each SAR image
pixel we generated SSM/I -gridded brightness temperature images that were mapped to
the coordinates of each SAR image frame used in this study. We then used these pixel
values to find the brightness temperature that corresponded to each ERS-I SAR pixel
and a resampled SSM/I brightness temperature image was obtained. The brightness
temperatures from these resampled images were then used in the fusion algorithm with
the corresponding SAR-derived multiyear ice fraction estimate.
5.4.3
Relationship to Freeze-Up Detected with SAR
We used the co registered ERS-l SAR and SSM/I imagery to investigate the relationship
between passive microwave-based estimates of ice concentration and radar backscatter signature. We used the NT algorithm to compute sea ice type concentrations on the
resampled SSM/I image data using hemispheric tie points. The mean values over each
SAR frame area are plotted in Fig. 4 to demonstrate the changes in relative concentrations of first-year and multiyear ice estimated by the NT algorithm during this time
frame. The mean ice type concentrations for SSM/I pixels are located within the SAR
frame are listed in Table 1. The estimated changes in first-year and multiyear ice con-