Omission Errors. We expect the radial differences computed using equation (18) to
decrease asymptotically to zero as higher degree and order harmonics are used. When the
results converge to a number other than zero and we assume that omission errors are
negligible, the radial distortion is a combination of errors of comission from the model
and errors in the normal heights. If the radial distortion is greater than the error in the
measurement of the normal height, then we may conclude that the radial distortion is a
result of errors of comission from the model. Tables 6 and 7 contain a preliminary
examination of the convergence of the geopotential model at the GMT stations. In spite
of problematic heights, those SLR sites with large differences from JGM-3 were used for
a preliminary analysis of the errors of omission. Table 6 contains the 8Rp values
computed at the selected SLR sites based on the OSU91A geopotential model using
summations to various maximum degrees, N max. Table 7 contains the same data for the
38 GPS-leveling sites.
Table 6. Radial differences in meters with OSU91A at selected SLR sites.
Maximum harmonic degree
Station
36
50
70
90
120
150
180
210
240
280
320
360
7068
-1.08 -1.50 -1.45 -3.22 -2.78 -1.49 -0.38
0.21
0.24
0.14
-0.31 -0.67
7080 -1.55 -2.03 -2.07 -2.24 -2.10 -1.74 -1.48 -1.15 -0.90 -0.76 -0.70 -0.66
7084 -2.93 -2.17 -2.27 -1.25 -1.04 -0.37
0.13
0.13
-0.05 -0.05 -0.07 -0.13
7092 -3.31 -2.43 -2.82 -3.04 -2.68 -2.49 -2.21 -1.45 -1.06 -0.86 -0.65 -0.55
7096 -3.96 -4.22 -3.62 -2.50 -0.58 -0.42 -0.71 -0.84 -0.86 -0.52 -0.20 -0.13
7114 -2.93 -2.16 -2.26 -1.24 -1.03 -0.36 0.13
0.14 -0.05 -0.04 -0.07 -0.13
7307
-0.87 -2.70 -3.28 -3.51
-2.60 -1.89 -0.90 -1.02 -0.86 -0.68 -0.51 -0.50
7401
-7.83 -7.93 -6.67 -4.53 -2.45 -0.65
0.20
0.21
-0.10 -0.02 -0.40 -0.43
7541
-5.40 -4.01 -2.78 -1.54 -0.64 0.02 -0.32 -0.60 -0.76 -0.49 -0.20 -0.14
7545
-1.49 -2.91 -2.44 -2.15 -1.28 -1.23 -0.64 -0.58 -0.44 -0.39 -0.41 -0.44
7546
6.83
3.96
2.80
1.77
0.68
0.12 -0.10 -0.35 -0.39 -0.26 -0.45 -0.47
7575
4.32
2.37
2.27
1.63
0.47
0.57
1.01
0.42
0.47
0.72
0.51
0.55
7835
-3.71 -3.18 -2.35 -2.93 -1.12 -0.89 -0.73 -0.56 -0.48 -0.60 -0.60 -0.60
7844 -9.12 -8.72 -8.25 -7.38 -6.09 -4.57 -3.14 -2.21 -1.47 -0.81 -0.54 -0.43
7853
-2.92 -2.16 -2.26 -1.24 -1.03 -0.36 0.13
0.14 -0.05 -0.04 -0.07 -0.13
7885
-1.56 -2.04 -2.08 -2.25 -2.10 -1.74 -1.48 -1.16 -0.91
-0.76 -0.70 -0.66
7891
-2.52 -3.03 -2.16 -1.47 -1.33 -0.97 -1.13 -1.16 -1.01
-0.76 -0.79 -0.61
7907 -7.95 -6.73 -3.80 -5.08 -3.48 -1.46 -0.83 -1.61 -1.39 -0.84 -0.86 -0.70
7939 -5.40 -4.01 -2.79 -1.54 -0.64
0.02 -0.32 -0.60 -0.77 -0.49 -0.20 -0.14
7401
-7.83 -7.93 -6.67 -4.53 -2.45 -0.65
0.20
0.22 -0.10 -0.02 -0.40 -0.43
Table 7. Radial differences with OSU91A at GPS-leveling sites.
Maximum harmonic degree
Station
36
50
70
90
120
150
180
210
240
280
320
360
4N
-0.58 -0.71 -1.15 -0.62 -0.45 -0.56 -0.86 -0.69 -0.71 -0.74 -0.57 -0.54
17N
-0.99 -1.51 -1.01 -0.47 -0.25 -0.34 -0.57 -0.22 -0.38 -0.40 -0.36 -0.40
23N
-0.50
0.21
-0.41 -1.45 -0.78 -0.65 -0.31
0.02 -0.22 -0.13 -0.19 -0.11
30N
-0.20 -0.11 -0.09 -0.55
0.50
0.25
0.23
-0.20 -0.02 -0.26 -0.05
0.03
49N
-0.66 -1.19
0.15
0.84
-0.04 0.26
0.06
0.14
0.26
0.16
0.25
0.20
54N
-1.51 -2.04 -0.87
0.68
-0.30
0.28
0.29
0.43
0.34
0.17
0.24
0.18
63N
-0.23 -0.31
0.33
-0.88 -0.30 -0.34 -0.17 -0.17 -0.25 -0.07 -0.19 -0.16
71N -1.04 -1.38 0.00 -0.38 -0.48 -0.39 -0.20 -0.16 -0.07 -0.02 0.08 0.18
77N
-0.31 -0.50 0.98
1.40
0.30
0.53
0.18
0.21
0.15
0.35
0.33
0.34
98N
-0.70
0.09 -0.04 -0.15 -0.16 -0.05
0.13
0.53
0.41
0.32
0.26
0.21
57