....
e
W
Combined Geosat and ERS-1 Inclinations
4~---'-----'----'----'-----'----r----. ____ ~
3.5
3
east slope
2.5
~ 2
~
Qi
ex:
1.5
north slope
I
~8~O~----6=O~----4~O~---~2~O-----OL-----2LO----~40~--~60-----8~O
Latitude (deg)
Fig. 4. Propagation of along-track slope errors from dense Geosat and ERS-l profiles
into north and east components of vertical deflection. At the equator" satellite tracks run
mainly N-S so the E-W component of VD is more poorly determined than the N-S
component. This covariance information is used in both the blending and filtering steps
of the iteration (Figure 3.).
transformation of the sum. If the grid pixels are equidimensional then the transformation
from vertical deflection to gravity largely avoids latitude-dependent length-scale problems
[Haxby and Hayes, 1991]. For example, the operator on the fourier transform of the east
component of vertical deflection is kx/lkl so the length scale largely cancels. Maximum
error induced by this approximation will correspond to the change in length scale that
occurs over a latitude range corresponding to about 400 Ian of distance. At the equator this
change is less than 0.2% while at 700N this change is 6%. We expect that the actual errors
are smaller than this because most of the contribution to the gravity anomaly will be due to
nearby vertical deflection signals. Note that this "flat earth" error can be reduced by first
removing a higher-degree spherical harmonic model [Haxby and Hayes, 1991]. Also note
that to safely avoid edge effects the dimensions of the vertical deflection grids must be
several times larger than the longest wavelength remaining in the residual data. In our case
we use overlapping grids that are 6000 km long and 3000 km tall. The final step in the
gravity computation is to restore the gravity anomaly corresponding to the spherical
harmonic model removed in step (2).
Over areas of permanent ice cover, the standard algorithm for identifing the leading edge
of the radar echo fails which results in a noisy profile (Figure 5, top). However, by
retracking the full waveform of the echo, Laxon and McAdoo [1994] have been able to
substantially reduce the noise (Figure 5, middle) and have shown agreement with tracks
collected during ice-free periods (Figure 5, bottom). The relatively flat surface of the ice
conforms to the marine geoid but with a small offset related to the ice freeboard. As over
the oceans, the along-track derivative of the re-tracked geoid profile is used to construct
vertical deflection grids which are then converted to gravity anomaly as described above.
The ERS-l altimeter provides coverage to 81.5° latitude so almost all ocean areas have been
mapped by satellite altimeters.
16
e
W
Combined Geosat and ERS-1 Inclinations
4~---'-----'----'----'-----'----r----. ____ ~
3.5
3
east slope
2.5
~ 2
~
Qi
ex:
1.5
north slope
I
~8~O~----6=O~----4~O~---~2~O-----OL-----2LO----~40~--~60-----8~O
Latitude (deg)
Fig. 4. Propagation of along-track slope errors from dense Geosat and ERS-l profiles
into north and east components of vertical deflection. At the equator" satellite tracks run
mainly N-S so the E-W component of VD is more poorly determined than the N-S
component. This covariance information is used in both the blending and filtering steps
of the iteration (Figure 3.).
transformation of the sum. If the grid pixels are equidimensional then the transformation
from vertical deflection to gravity largely avoids latitude-dependent length-scale problems
[Haxby and Hayes, 1991]. For example, the operator on the fourier transform of the east
component of vertical deflection is kx/lkl so the length scale largely cancels. Maximum
error induced by this approximation will correspond to the change in length scale that
occurs over a latitude range corresponding to about 400 Ian of distance. At the equator this
change is less than 0.2% while at 700N this change is 6%. We expect that the actual errors
are smaller than this because most of the contribution to the gravity anomaly will be due to
nearby vertical deflection signals. Note that this "flat earth" error can be reduced by first
removing a higher-degree spherical harmonic model [Haxby and Hayes, 1991]. Also note
that to safely avoid edge effects the dimensions of the vertical deflection grids must be
several times larger than the longest wavelength remaining in the residual data. In our case
we use overlapping grids that are 6000 km long and 3000 km tall. The final step in the
gravity computation is to restore the gravity anomaly corresponding to the spherical
harmonic model removed in step (2).
Over areas of permanent ice cover, the standard algorithm for identifing the leading edge
of the radar echo fails which results in a noisy profile (Figure 5, top). However, by
retracking the full waveform of the echo, Laxon and McAdoo [1994] have been able to
substantially reduce the noise (Figure 5, middle) and have shown agreement with tracks
collected during ice-free periods (Figure 5, bottom). The relatively flat surface of the ice
conforms to the marine geoid but with a small offset related to the ice freeboard. As over
the oceans, the along-track derivative of the re-tracked geoid profile is used to construct
vertical deflection grids which are then converted to gravity anomaly as described above.
The ERS-l altimeter provides coverage to 81.5° latitude so almost all ocean areas have been
mapped by satellite altimeters.
16