computed based on hypotheses concerning the position of the geoid or the Earth's internal
mass distribution. Finally, the accuracy of the testing method should depend only on the
accuracy of the observations. This paper presents a Geopotential Model Testing (GMT)
methodology that satisfies the stated conditions.
THEORY OF THE GEOPOTENTIAL MODEL TESTING METHOD
The GMT methodology compares the gravity potential computed from a spherical
harmonic model to an "observed" value computed from measurements and fundamental
constants. This section describes a methodology for computing an "observed" gravity
potential at a point on the Earth's surface and interpreting the results of model
comparisons.
Fundamental Parameters
The GMT methodology first adopts parameters that define the level ellipsoid and the
normal gravity potential. For this study, the authors have elected to use the following
parameters:
1. Geocentric gravitational constant (Ries, et al., 1992):
GM = (398,6oo,441.8 ± 0.8) x 10 6 m 3 / S2
(1)
2. Mean angular velocity of the Earth's rotation (Report SC3flAG, 1995):
m = 7292115 x 10- 11 rad S-l
3. Geoidal gravity potential derived from TOPEXIPOSEIDON altimeter data (Ries,
1995):
Wo = (62636856. 5 ± 0.10) m 2 / S2
(2)
(3)
4. Second zonal geopotential coefficient in the zero-frequency tidal system (Report
SC3nAG, 1995):
J 2 = (1082635.9 ± 0.1) x 10- 9
(4)
Tidal System. Constants (1)-(4) provide an accuracy of approximately ±3 x 10-9 in the
zero-frequency tidal system. Defining J 2 in the zero-frequency tidal system results in
geopotential model defined in this tidal system. In the GMT method, the normal
potential is computed at the normal height of each GMT station. The best estimates for
the parameters of the level ellipsoid are defined in the mean tide system. The conversion
these parameters to the zero-frequency tidal system is based on the Earth's Love number.
Accurately determining the Love number is problematic. Therefore, the authors have
chosen to use the mean tide system. This requires the conversion of model geopotential
values to the mean tide system. The conversion factor is the second degree direct zerofrequency zonal tidal potential, 8~O), given by (Zadro and Marussi, 1973):
51
mass distribution. Finally, the accuracy of the testing method should depend only on the
accuracy of the observations. This paper presents a Geopotential Model Testing (GMT)
methodology that satisfies the stated conditions.
THEORY OF THE GEOPOTENTIAL MODEL TESTING METHOD
The GMT methodology compares the gravity potential computed from a spherical
harmonic model to an "observed" value computed from measurements and fundamental
constants. This section describes a methodology for computing an "observed" gravity
potential at a point on the Earth's surface and interpreting the results of model
comparisons.
Fundamental Parameters
The GMT methodology first adopts parameters that define the level ellipsoid and the
normal gravity potential. For this study, the authors have elected to use the following
parameters:
1. Geocentric gravitational constant (Ries, et al., 1992):
GM = (398,6oo,441.8 ± 0.8) x 10 6 m 3 / S2
(1)
2. Mean angular velocity of the Earth's rotation (Report SC3flAG, 1995):
m = 7292115 x 10- 11 rad S-l
3. Geoidal gravity potential derived from TOPEXIPOSEIDON altimeter data (Ries,
1995):
Wo = (62636856. 5 ± 0.10) m 2 / S2
(2)
(3)
4. Second zonal geopotential coefficient in the zero-frequency tidal system (Report
SC3nAG, 1995):
J 2 = (1082635.9 ± 0.1) x 10- 9
(4)
Tidal System. Constants (1)-(4) provide an accuracy of approximately ±3 x 10-9 in the
zero-frequency tidal system. Defining J 2 in the zero-frequency tidal system results in
geopotential model defined in this tidal system. In the GMT method, the normal
potential is computed at the normal height of each GMT station. The best estimates for
the parameters of the level ellipsoid are defined in the mean tide system. The conversion
these parameters to the zero-frequency tidal system is based on the Earth's Love number.
Accurately determining the Love number is problematic. Therefore, the authors have
chosen to use the mean tide system. This requires the conversion of model geopotential
values to the mean tide system. The conversion factor is the second degree direct zerofrequency zonal tidal potential, 8~O), given by (Zadro and Marussi, 1973):
51