by the French DORIS tracking system has provided notable improvements to the gravity
model due to the unprecedented precision of the Doppler data as well as the global coverage
provided by the tracking beacons.
Nerem et al. (1994b) summarize the satellites/tracking data which were employed in the
development of JGM-2. These data have served as a starting point for the satellite data
reiterative processing for this project. A number of new data sets have become available
since the completion of JGM-2, and these provide important improvements for this project.
The most important of these data sets are (1) SLR tracking of the ERS-l, Lageos 2, and
Stella satellites, and (2) GPS and TDRSS tracking of the TIP and EUVE satellites. The
GPS data are especially important as they provide essentially continuous tracking of a
satellite for the fIrst time. Tracking of additional satellites by SLR, DORIS, and GPS is
anticipated as the project continues, and these data will be included if they fIll a gap in the
current ensemble of data. In addition, NSWC has provided older Doppler tracking data
from their archives for fIlling inclination gaps in the current JGM-2 complement of
satellites. The gravity model resulting from this project contains the most comprehensive
set of satellite tracking data ever assembled for such a purpose. Table 1 summarizes the
satellite tracking data used in the preliminary gravity solutions discussed in this paper.
The satellite tracking data is used together with direct altimeter data and l O x 1 0 surface
gravity anomalies to formally determine a least squares estimate for a 70 x 70 gravity model
which forms the basis of the 360 x 360 model. The data processing for each satellite varies
considerably, but generally the data are processed in arcs that are between 1 week and 1
month in length, and parameters are estimated describing the position and velocity at the
beginning of the arc, solar radiation pressure, and atmospheric drag. This is accomplished
using GSFC's state-of-the-art orbit determination program GEODYN, which precisely
models the tracking measurements, Earth rotation, solid Earth and ocean tides, and a
variety of other phenomena that affect the satellite dynamics or the tracking measurements.
Sometimes empirical spacecraft accelerations are also estimated in order to account for
unmodeled non-conservative forces which can contaminate the observed gravitational
perturbations. These accelerations are often estimated at the expense of some of the
gravitational signal, but this is often necessary to avoid contaminating the entire model with
unmodeled non-gravitational effects. Once the satellite orbit for each arc has been
determined, a system of least squares normal equations are created for each of the estimated
parameters in the gravity solution including the geopotential coeffIcients (both mean and
time-varying), the tidal coeffIcients, polar motion, station coordinates, measurement model
parameters (troposphere/measurement biases), and satellite arc parameters (position,
velocity, drag scaling, etc.).
For the altimeter satellites such as Geos-3, Seasat, Geosat, ERS-l, and TIP, the altimeter
data are processed simultaneously with the satellite tracking data to determine the gravity
fIeld. The altimeter measures the range between the satellite and the ocean surface, which
closely corresponds to the geoid except for the effects of ocean dynamic topography.
Therefore, for long-wavelength "combination" models like JGM-2, the altimeter data are
processed in this "direct" manner (as opposed to processing it in the form of gravity
anomalies for example) by simultaneously estimating a spherical harmonic model of the
dynamic topography, usually complete to about degree 20. This technique of processing
the altimeter data in a "joint solution" for the satellite orbit, the gravity fIeld, and the
dynamic topography has been used with great success in the past (Marsh et aI., 1990;
Denker and Rapp, 1990; Nerem et al., 1990; Nerem et al., 1994b). While the benefit to the
longest wavelengths of the gravity fIeld is smaller, the shorter wavelengths of the model (>
degree 20) are significantly improved and uniform coverage over the oceans is obtained.
Normal equations for the altimeter data are created separately from the tracking data so that
each data set may be weighted independently.
Each of the satellite normal equations are added together, along with the surface gravity
and altimeter data, before a simultaneous solution for the estimated parameters is
96
model due to the unprecedented precision of the Doppler data as well as the global coverage
provided by the tracking beacons.
Nerem et al. (1994b) summarize the satellites/tracking data which were employed in the
development of JGM-2. These data have served as a starting point for the satellite data
reiterative processing for this project. A number of new data sets have become available
since the completion of JGM-2, and these provide important improvements for this project.
The most important of these data sets are (1) SLR tracking of the ERS-l, Lageos 2, and
Stella satellites, and (2) GPS and TDRSS tracking of the TIP and EUVE satellites. The
GPS data are especially important as they provide essentially continuous tracking of a
satellite for the fIrst time. Tracking of additional satellites by SLR, DORIS, and GPS is
anticipated as the project continues, and these data will be included if they fIll a gap in the
current ensemble of data. In addition, NSWC has provided older Doppler tracking data
from their archives for fIlling inclination gaps in the current JGM-2 complement of
satellites. The gravity model resulting from this project contains the most comprehensive
set of satellite tracking data ever assembled for such a purpose. Table 1 summarizes the
satellite tracking data used in the preliminary gravity solutions discussed in this paper.
The satellite tracking data is used together with direct altimeter data and l O x 1 0 surface
gravity anomalies to formally determine a least squares estimate for a 70 x 70 gravity model
which forms the basis of the 360 x 360 model. The data processing for each satellite varies
considerably, but generally the data are processed in arcs that are between 1 week and 1
month in length, and parameters are estimated describing the position and velocity at the
beginning of the arc, solar radiation pressure, and atmospheric drag. This is accomplished
using GSFC's state-of-the-art orbit determination program GEODYN, which precisely
models the tracking measurements, Earth rotation, solid Earth and ocean tides, and a
variety of other phenomena that affect the satellite dynamics or the tracking measurements.
Sometimes empirical spacecraft accelerations are also estimated in order to account for
unmodeled non-conservative forces which can contaminate the observed gravitational
perturbations. These accelerations are often estimated at the expense of some of the
gravitational signal, but this is often necessary to avoid contaminating the entire model with
unmodeled non-gravitational effects. Once the satellite orbit for each arc has been
determined, a system of least squares normal equations are created for each of the estimated
parameters in the gravity solution including the geopotential coeffIcients (both mean and
time-varying), the tidal coeffIcients, polar motion, station coordinates, measurement model
parameters (troposphere/measurement biases), and satellite arc parameters (position,
velocity, drag scaling, etc.).
For the altimeter satellites such as Geos-3, Seasat, Geosat, ERS-l, and TIP, the altimeter
data are processed simultaneously with the satellite tracking data to determine the gravity
fIeld. The altimeter measures the range between the satellite and the ocean surface, which
closely corresponds to the geoid except for the effects of ocean dynamic topography.
Therefore, for long-wavelength "combination" models like JGM-2, the altimeter data are
processed in this "direct" manner (as opposed to processing it in the form of gravity
anomalies for example) by simultaneously estimating a spherical harmonic model of the
dynamic topography, usually complete to about degree 20. This technique of processing
the altimeter data in a "joint solution" for the satellite orbit, the gravity fIeld, and the
dynamic topography has been used with great success in the past (Marsh et aI., 1990;
Denker and Rapp, 1990; Nerem et al., 1990; Nerem et al., 1994b). While the benefit to the
longest wavelengths of the gravity fIeld is smaller, the shorter wavelengths of the model (>
degree 20) are significantly improved and uniform coverage over the oceans is obtained.
Normal equations for the altimeter data are created separately from the tracking data so that
each data set may be weighted independently.
Each of the satellite normal equations are added together, along with the surface gravity
and altimeter data, before a simultaneous solution for the estimated parameters is
96