harmonic coefficients. The proper combination of these data, along with the desire to
acquire an accurate representation of the model errors, require application of complex
procedures for computing these solutions.
ADVANCES IN MODELING THE EARTH'S GRAVITY FIELD
Advances in satellite tracking techniques, satellite altimetry, and gravity solution
techniques along with the availability of surface gravity data in previously uncovered or
unavailable regions have led to significant improvements in models of the Earth's gravity
field during the last four years. While the 1980s saw the development of long
wavelength gravity models mainly from satellite tracking data, models developed in the
1990s have increasingly been based on a combination of satellite tracking, satellite
altimeter, and surface gravity data. This in turn has led to a marriage of techniques used
to compute long wavelength (spherical harmonic degree 50) gravity models and high
resolution (degree 360) gravity models (Rapp, 1993a) such that future models will
represent the best in each. The most recent of these models is Ohio State University
(OSU)-91A (Rapp et al., 1991) which is a comprehensive model complete to degree 360
in spherical harmonics. This will almost certainly change in the near future as will be
discussed later. The 1 sigma errors in the geoid defined by this model are described by
Rapp (1993b), and are estimated at ±28 cm over the oceans and ±46 cm over the
continents with significantly larger errors seen in regions lacking available
precise/modem surface gravimetry (Asia, polar regions). At this accuracy level, gravity
modeling can only support determination of the ocean dynamic topography at
wavelengths longer than about 2500 km; thus significant improvement in the ocean geoid
is sought for many oceanographic applications (Nerem and Koblinsky, 1993).
These global gravity models are often used as a reference for (:omputing detailed
regional gravity models (Wang, 1993b). Recent examples of this include the detailed
geoid model for the U.S. denoted GEOID93 (Milbert and Schult2:, 1993) which has
become popular for various GPS applications. Rapp and Wang (1994) and Rapp and
Smith (1994) have similarly developed a gravimetric geoid for the Gulf Stream region.
Refinements in data processing and solution techniques (Wang, 1993a; 1993b) have led
to improvements in the calculation of geoid undulations. These global models have also
been used for a number of statistical studies of the gravity field (Balmino, 1993; Kaula,
1993; Jekeli, 1991).
Whereas improvements in regional gravity modeling have not improved areas
previously deficient in surface gravity/altimetry coverage, geopote:ntial modeling for
geodetic satellite orbit determination has been revolutionized. Orbit modeling for
TOPEXIPOSEIDON (TIP) was a major goal, with mission requirements being vastly
exceeded. Currently, static geopotential and dynamic tidal modeling accuracies permit
radial orbit determination at the ±2 cm level, a remarkable accomplishment thought
unachievable as little as 5 years ago.
With this introduction to the current state of global gravity model determination, we
will now review the applications of these models in oceanographk, geophysical, and
geodetic studies of the Earth and the planets.
ORBIT DETERMINATION
Precision orbit determination has a variety of applications in positioning, altimetry,
SAR interferometry and Earth rotation studies. For high satellites such as LAGEOS and
the GPS constellation, orbit determination errors caused by gravity field mismodeling are
at the sub-cm level. However, for many lower satellites, especially satellite altimeter
missions, gravity model error can be one of the limiting error sources in the determination
of the orbit. For TIP, a comprehensive decade-long gravity model development effort
culminated in 1994 with the development of a series of gravity models whose radial
2
acquire an accurate representation of the model errors, require application of complex
procedures for computing these solutions.
ADVANCES IN MODELING THE EARTH'S GRAVITY FIELD
Advances in satellite tracking techniques, satellite altimetry, and gravity solution
techniques along with the availability of surface gravity data in previously uncovered or
unavailable regions have led to significant improvements in models of the Earth's gravity
field during the last four years. While the 1980s saw the development of long
wavelength gravity models mainly from satellite tracking data, models developed in the
1990s have increasingly been based on a combination of satellite tracking, satellite
altimeter, and surface gravity data. This in turn has led to a marriage of techniques used
to compute long wavelength (spherical harmonic degree 50) gravity models and high
resolution (degree 360) gravity models (Rapp, 1993a) such that future models will
represent the best in each. The most recent of these models is Ohio State University
(OSU)-91A (Rapp et al., 1991) which is a comprehensive model complete to degree 360
in spherical harmonics. This will almost certainly change in the near future as will be
discussed later. The 1 sigma errors in the geoid defined by this model are described by
Rapp (1993b), and are estimated at ±28 cm over the oceans and ±46 cm over the
continents with significantly larger errors seen in regions lacking available
precise/modem surface gravimetry (Asia, polar regions). At this accuracy level, gravity
modeling can only support determination of the ocean dynamic topography at
wavelengths longer than about 2500 km; thus significant improvement in the ocean geoid
is sought for many oceanographic applications (Nerem and Koblinsky, 1993).
These global gravity models are often used as a reference for (:omputing detailed
regional gravity models (Wang, 1993b). Recent examples of this include the detailed
geoid model for the U.S. denoted GEOID93 (Milbert and Schult2:, 1993) which has
become popular for various GPS applications. Rapp and Wang (1994) and Rapp and
Smith (1994) have similarly developed a gravimetric geoid for the Gulf Stream region.
Refinements in data processing and solution techniques (Wang, 1993a; 1993b) have led
to improvements in the calculation of geoid undulations. These global models have also
been used for a number of statistical studies of the gravity field (Balmino, 1993; Kaula,
1993; Jekeli, 1991).
Whereas improvements in regional gravity modeling have not improved areas
previously deficient in surface gravity/altimetry coverage, geopote:ntial modeling for
geodetic satellite orbit determination has been revolutionized. Orbit modeling for
TOPEXIPOSEIDON (TIP) was a major goal, with mission requirements being vastly
exceeded. Currently, static geopotential and dynamic tidal modeling accuracies permit
radial orbit determination at the ±2 cm level, a remarkable accomplishment thought
unachievable as little as 5 years ago.
With this introduction to the current state of global gravity model determination, we
will now review the applications of these models in oceanographk, geophysical, and
geodetic studies of the Earth and the planets.
ORBIT DETERMINATION
Precision orbit determination has a variety of applications in positioning, altimetry,
SAR interferometry and Earth rotation studies. For high satellites such as LAGEOS and
the GPS constellation, orbit determination errors caused by gravity field mismodeling are
at the sub-cm level. However, for many lower satellites, especially satellite altimeter
missions, gravity model error can be one of the limiting error sources in the determination
of the orbit. For TIP, a comprehensive decade-long gravity model development effort
culminated in 1994 with the development of a series of gravity models whose radial
2