The geostrophic component of the ocean circulation can be studied if geoid undulations are
accurately known, since the geostrophic current velocity is directly proportional to the slope
of the sea surface with respect to the geoid (Nerem and Koblinsky, 1993). Estimates of
ocean dynamic topography (the separation between the ocean surface and the geoid) have
recently been described using Geosat and TOPEXJPQSEIDON (TIP) data (e.g. Visser et
aI., 1993; Nerem et al., 1994c; Wang and Rapp, 1994). The specific evaluation of the
impact of geoid undulation errors on basin-wide circulation estimates is described by
Stammer and Wunsch (1994) and Tapley et al. (1994b). Other oceanographic studies
require more detailed knowledge of the geoid for more high frequency implications than
found in basin-scale studies. Some examples of recent studies using regional geoid
determinations are those of Knudsen (1994) and Rapp and Wang (1994). As before, the
potential coefficient model forms a base for the precision geoid determinations.
High degree gravity models also have applications in precision orbit determination.
While current applications do not require modeling the gravity field much past degree 70,
new satellites in low orbits designed explicitly for measuring the gravity field will require
modeling the gravity field at very high resolution. High degree gravity mqdels will be
useful for mission planning/simulations studies of these new missions, as well as serving
as a starting point for accomplishing their gravity improvement objectives.
The above discussion points out the need for an accurate potential coefficient model for a
variety of applications. In the next section, a new application will be discussed, which is
an important driver for the project being described here.
A World Vertical Reference System
The determination of height or elevation is a classical problem that requires a gravity
equipotential reference surface. Currently, this reference surface is defined differently from
region to region so that there is a large number of height systems or vertical datums in the
world today. The unification of these datums and the possible definition of a single world
height datum has been discussed for some time. Recent references in this area include Xu
and Rummel (1991), Rapp and Balasubramania (1992), and Balasubramania (1994). In
the past, this surface has been approximated by mean sea level, which today is an
unacceptable approximation. The proposed alternative is to accept the concept of the geoid
as the reference surface and to determine geoid undulations to a sufficient accuracy and
resolution for global applications. These needs can be met through the estimation of geoid
undulations from a degree 360 model. Although such a model will not provide the
resolution and accuracy for all requirements, it can be a base model for the determination of
high-resolution geoid undulations in areas where terrestrial gravity data are sufficiently
dense.
The undulations can be used to determine the orthometric height from the basic equation:
H=h-N
(2)
In such computations, it is desirable to adopt the most accurate ellipsoid parameters to
which h is referred. For example, a current estimate (Rapp et aI., 1994) of the equatorial
radius, based on TIP altimeter data, is 6378136.5m. The uncertainty of this estimate is
approximately ±10 cm. The world height system and the need for the geoid reference
surface is applicable for both land and ocean since reference to bathym(~tric depths requires
a specified surface. A variety of ways in which this is done today for nautical charts, and
could be done in the future, is discussed by Kumar (1994).
This section has briefly outlined one of the new applications that could be found for an
accurate representation of geoid undulations. More details of the world vertical datum
concept can be found in Rapp (1993).
94
accurately known, since the geostrophic current velocity is directly proportional to the slope
of the sea surface with respect to the geoid (Nerem and Koblinsky, 1993). Estimates of
ocean dynamic topography (the separation between the ocean surface and the geoid) have
recently been described using Geosat and TOPEXJPQSEIDON (TIP) data (e.g. Visser et
aI., 1993; Nerem et al., 1994c; Wang and Rapp, 1994). The specific evaluation of the
impact of geoid undulation errors on basin-wide circulation estimates is described by
Stammer and Wunsch (1994) and Tapley et al. (1994b). Other oceanographic studies
require more detailed knowledge of the geoid for more high frequency implications than
found in basin-scale studies. Some examples of recent studies using regional geoid
determinations are those of Knudsen (1994) and Rapp and Wang (1994). As before, the
potential coefficient model forms a base for the precision geoid determinations.
High degree gravity models also have applications in precision orbit determination.
While current applications do not require modeling the gravity field much past degree 70,
new satellites in low orbits designed explicitly for measuring the gravity field will require
modeling the gravity field at very high resolution. High degree gravity mqdels will be
useful for mission planning/simulations studies of these new missions, as well as serving
as a starting point for accomplishing their gravity improvement objectives.
The above discussion points out the need for an accurate potential coefficient model for a
variety of applications. In the next section, a new application will be discussed, which is
an important driver for the project being described here.
A World Vertical Reference System
The determination of height or elevation is a classical problem that requires a gravity
equipotential reference surface. Currently, this reference surface is defined differently from
region to region so that there is a large number of height systems or vertical datums in the
world today. The unification of these datums and the possible definition of a single world
height datum has been discussed for some time. Recent references in this area include Xu
and Rummel (1991), Rapp and Balasubramania (1992), and Balasubramania (1994). In
the past, this surface has been approximated by mean sea level, which today is an
unacceptable approximation. The proposed alternative is to accept the concept of the geoid
as the reference surface and to determine geoid undulations to a sufficient accuracy and
resolution for global applications. These needs can be met through the estimation of geoid
undulations from a degree 360 model. Although such a model will not provide the
resolution and accuracy for all requirements, it can be a base model for the determination of
high-resolution geoid undulations in areas where terrestrial gravity data are sufficiently
dense.
The undulations can be used to determine the orthometric height from the basic equation:
H=h-N
(2)
In such computations, it is desirable to adopt the most accurate ellipsoid parameters to
which h is referred. For example, a current estimate (Rapp et aI., 1994) of the equatorial
radius, based on TIP altimeter data, is 6378136.5m. The uncertainty of this estimate is
approximately ±10 cm. The world height system and the need for the geoid reference
surface is applicable for both land and ocean since reference to bathym(~tric depths requires
a specified surface. A variety of ways in which this is done today for nautical charts, and
could be done in the future, is discussed by Kumar (1994).
This section has briefly outlined one of the new applications that could be found for an
accurate representation of geoid undulations. More details of the world vertical datum
concept can be found in Rapp (1993).
94