be found in Table 2.
Table 2. Empirical and anal)1ically computed covariances. The covariances are
shown as a function of spherical distance psi.
Sph.
Geoid and
Geoid and Gra\ity and Geoid and Gravity and DFV and
dist.
geoid
gravity
gravity
DFy l
DFY'
DFY'
(deg)
(m 2 )
(m*mgal)
(mgal 2 )
(m*arcsec) (mgal*arcsec) (arcsec 2 )
'¥ Emp. Anal b • Emp. Anal b • Emp. Anal b • Anal b •
Analb.
Analb.
0.00 0.095 0.109 3.004 3.106 167.6 173.0
0.000
0.00
3.85
0.05 0.083 0.107 3.160 2.996 157.7 161.1
0.100
-7.94
3.46
0.10 0.078 0.104 2 .
862 2.701 141.0 132.0
0 . 181
-13.41
2.52
0.15 0.070 0.098 2.356 2.300 99.1 97.2
0.235
-15.81.
1.44
0.20 0.058 0.091 1.729 1.869 66.2 64.6
0.260
-15.84
0.48
0.25 0.047 0.084 1.239 1.460 33.5 37.6
0.263
-14.36
-0.25
0.30 0.036 0.077 0.765 1.102 8.5 17.1
0.249
-12.09
0.75
0.35 0.026 0.071 0.403 0.811 -4.9 2.7
0.224
-9.51
-1.04
0.40 0.018 0.065 0.206 0.589 -11.6 -6.2
0.194
-6.98
-l.l6
0.45 0.011 0.060 0 . 108 0.432 -1104 -10.9
0.162
-4.69
-1.14
0.50 0.008 0.056 0.130 0.332 -5.2 -12.3
0.133
-2.78
-1.03
0.55 0.003 0.053 0.075 0.278 -2.2 -11.3
0.107
-1.30
-0.85
0.60 -0.000 0.050 0.098 0.258 8.6 -8.8
0.087
-0.25
-0.65
0.65 -0.003 0.048 0.101 0.260 8 .4 -5.5
0.072
0.38
-0.44
0.70 -0.008 0.0460.052 0.275 11.4 -2.1
0.062
0.66
-0.25
a DFV IS deflection of vertical.
b The analytically computed values are based on a fitting of the gravity covariance
function.
Subsequently,
the
covariance
function of the stacked altimeter data
from the 35-day repeat mission was g., 4~~~~~J..,llL-J...,.<~H4'~~74"1
fitted using the procedure above. The
result was a derived gravity variance of
357 mgal 2 , a depth to the Bjerhammar
sphere of 5.7 km and a weight factor
for the error degree variances of 0.15.
This covariance function was also used
in the experiments, but it gave results - T~~:t::75?T~~~~YJ.r/i1
than obtained using the covariance
function obtained from the gravity data
(Table 3).
The prediction using all altimeter
data or along-track deflections were
7.1$
LOO
Figure 5 ERS-I altimeter heights relative
to the OSU91A geoid. Units are in meters.
222
Table 2. Empirical and anal)1ically computed covariances. The covariances are
shown as a function of spherical distance psi.
Sph.
Geoid and
Geoid and Gra\ity and Geoid and Gravity and DFV and
dist.
geoid
gravity
gravity
DFy l
DFY'
DFY'
(deg)
(m 2 )
(m*mgal)
(mgal 2 )
(m*arcsec) (mgal*arcsec) (arcsec 2 )
'¥ Emp. Anal b • Emp. Anal b • Emp. Anal b • Anal b •
Analb.
Analb.
0.00 0.095 0.109 3.004 3.106 167.6 173.0
0.000
0.00
3.85
0.05 0.083 0.107 3.160 2.996 157.7 161.1
0.100
-7.94
3.46
0.10 0.078 0.104 2 .
862 2.701 141.0 132.0
0 . 181
-13.41
2.52
0.15 0.070 0.098 2.356 2.300 99.1 97.2
0.235
-15.81.
1.44
0.20 0.058 0.091 1.729 1.869 66.2 64.6
0.260
-15.84
0.48
0.25 0.047 0.084 1.239 1.460 33.5 37.6
0.263
-14.36
-0.25
0.30 0.036 0.077 0.765 1.102 8.5 17.1
0.249
-12.09
0.75
0.35 0.026 0.071 0.403 0.811 -4.9 2.7
0.224
-9.51
-1.04
0.40 0.018 0.065 0.206 0.589 -11.6 -6.2
0.194
-6.98
-l.l6
0.45 0.011 0.060 0 . 108 0.432 -1104 -10.9
0.162
-4.69
-1.14
0.50 0.008 0.056 0.130 0.332 -5.2 -12.3
0.133
-2.78
-1.03
0.55 0.003 0.053 0.075 0.278 -2.2 -11.3
0.107
-1.30
-0.85
0.60 -0.000 0.050 0.098 0.258 8.6 -8.8
0.087
-0.25
-0.65
0.65 -0.003 0.048 0.101 0.260 8 .4 -5.5
0.072
0.38
-0.44
0.70 -0.008 0.0460.052 0.275 11.4 -2.1
0.062
0.66
-0.25
a DFV IS deflection of vertical.
b The analytically computed values are based on a fitting of the gravity covariance
function.
Subsequently,
the
covariance
function of the stacked altimeter data
from the 35-day repeat mission was g., 4~~~~~J..,llL-J...,.<~H4'~~74"1
fitted using the procedure above. The
result was a derived gravity variance of
357 mgal 2 , a depth to the Bjerhammar
sphere of 5.7 km and a weight factor
for the error degree variances of 0.15.
This covariance function was also used
in the experiments, but it gave results - T~~:t::75?T~~~~YJ.r/i1
than obtained using the covariance
function obtained from the gravity data
(Table 3).
The prediction using all altimeter
data or along-track deflections were
7.1$
LOO
Figure 5 ERS-I altimeter heights relative
to the OSU91A geoid. Units are in meters.
222