variety of ways in which this is done today for nautical charts, and could be done in the
future, is discussed by Kumar (1994).
Orthometric heights, as opposed to ellipsoidal heights, are often needed when
comparing positions derived from GPS measurements with positions determined from
historical leveling data, which implicitly provide orthometric quantities. An example of
this is the recent work of Cohen et al., (1995) which compared GPS positioning across
the Kenai Pennisula in Alaska to leveling measurements taken following the 1964 Prince
William Sound earthquake. In order to measure the uplift that had occurred since 1964, a
new geoid model had to be developed; nevertheless, geoid errors remained one of the
limiting error sources in this study.
TEMPORAL GRAVITY VARIATIONS
Temporal variations of the Earth's gravity field are caused by a variety of complex
phenomena including lunar-solar tides, atmospheric and oceanic mass redistribution,
variations in groundwater storage and snow cover/ice thickness, earthquakes, post-glacial
rebound in the Earth's mantle, long-term mantle convection and core activities, and other
geophysical phenomena (Chao, 1993). It is important to understand these variations
because of the implications they have for understanding and monitoring global climatic
and geophysical processes, Earth rotation, and synoptic sea level changes. There have
been a number of geophysical studies of the response of the Earth to loading and the
secular changes this induces in the gravity field (Ivins et al., 1993; Trupin et al., 1992;
Trupin, 1993; Mitrovica et al., 1994a; 1994b; Peltier, 1994). These models would
provide important constraints on mantle viscosity and sea level if reliable independent
satellite estimates of the changes in the gravity field were available. Redistribution of the
Earth's mass will also cause changes in the location of its center of mass with respect to
the Earth's crust, which have been measured using Lageos by Watkins and Eanes (1993).
Temporal variations in gravity caused by ocean and solid Earth tides are relatively well
determined because they occur at well known astronomical frequencies, but non-tidal
variations in gravity are more difficult to detect. Recent progress has been made in both
measuring and modeling temporal gravity variations. Chao and Au (1991) provided
estimates of the temporal variations of the low degree zonal coefficients from an analysis
of surface atmospheric pressure fields. For 12, the degree 2 zonal spherical harmonic
coefficient, these results were corroborated by the measurement of similar variations
using SLR tracking data from Lageos by Nerem et al. (1993b), Gegout and Cazenave,
(1993), and Chao and Eanes (1995). These studies concluded that much of the observed
variation of 12 is forced by mass redistribution in the atmosphere, with substantial yearto-year variations. These studies also showed that the 13 variations measured using
Lageos SLR data did not compare favorably with the models of atmospheric mass
redistribution. This is partially caused by the contamination of the Lageos 13 results by
other unmodeled effects (whether these effects are gravitational or not is still unknown),
but there is also undoubtedly significant variations in 13 and many other individual
harmonics that are caused by phenomena other than the atmosphere. Undoubtedly, ocean
mass redistribution is a significant source of non-tidal temporal gravity variations
(Marshall and Pavlis, 1993).
PLANETARY APPLICATIONS
The determination of the gravity field, together with knowledge of the surface
topography, provides one of the primary means of inferring the density structure and
dynamics of planetary interiors (Phillips and Lambeck, 1980; Hager, 1985). After
removing the topographic gravity signal, the distribution of internal density anomalies
caused by thermal or compositional differences can be studied. Gravity field models can
5
future, is discussed by Kumar (1994).
Orthometric heights, as opposed to ellipsoidal heights, are often needed when
comparing positions derived from GPS measurements with positions determined from
historical leveling data, which implicitly provide orthometric quantities. An example of
this is the recent work of Cohen et al., (1995) which compared GPS positioning across
the Kenai Pennisula in Alaska to leveling measurements taken following the 1964 Prince
William Sound earthquake. In order to measure the uplift that had occurred since 1964, a
new geoid model had to be developed; nevertheless, geoid errors remained one of the
limiting error sources in this study.
TEMPORAL GRAVITY VARIATIONS
Temporal variations of the Earth's gravity field are caused by a variety of complex
phenomena including lunar-solar tides, atmospheric and oceanic mass redistribution,
variations in groundwater storage and snow cover/ice thickness, earthquakes, post-glacial
rebound in the Earth's mantle, long-term mantle convection and core activities, and other
geophysical phenomena (Chao, 1993). It is important to understand these variations
because of the implications they have for understanding and monitoring global climatic
and geophysical processes, Earth rotation, and synoptic sea level changes. There have
been a number of geophysical studies of the response of the Earth to loading and the
secular changes this induces in the gravity field (Ivins et al., 1993; Trupin et al., 1992;
Trupin, 1993; Mitrovica et al., 1994a; 1994b; Peltier, 1994). These models would
provide important constraints on mantle viscosity and sea level if reliable independent
satellite estimates of the changes in the gravity field were available. Redistribution of the
Earth's mass will also cause changes in the location of its center of mass with respect to
the Earth's crust, which have been measured using Lageos by Watkins and Eanes (1993).
Temporal variations in gravity caused by ocean and solid Earth tides are relatively well
determined because they occur at well known astronomical frequencies, but non-tidal
variations in gravity are more difficult to detect. Recent progress has been made in both
measuring and modeling temporal gravity variations. Chao and Au (1991) provided
estimates of the temporal variations of the low degree zonal coefficients from an analysis
of surface atmospheric pressure fields. For 12, the degree 2 zonal spherical harmonic
coefficient, these results were corroborated by the measurement of similar variations
using SLR tracking data from Lageos by Nerem et al. (1993b), Gegout and Cazenave,
(1993), and Chao and Eanes (1995). These studies concluded that much of the observed
variation of 12 is forced by mass redistribution in the atmosphere, with substantial yearto-year variations. These studies also showed that the 13 variations measured using
Lageos SLR data did not compare favorably with the models of atmospheric mass
redistribution. This is partially caused by the contamination of the Lageos 13 results by
other unmodeled effects (whether these effects are gravitational or not is still unknown),
but there is also undoubtedly significant variations in 13 and many other individual
harmonics that are caused by phenomena other than the atmosphere. Undoubtedly, ocean
mass redistribution is a significant source of non-tidal temporal gravity variations
(Marshall and Pavlis, 1993).
PLANETARY APPLICATIONS
The determination of the gravity field, together with knowledge of the surface
topography, provides one of the primary means of inferring the density structure and
dynamics of planetary interiors (Phillips and Lambeck, 1980; Hager, 1985). After
removing the topographic gravity signal, the distribution of internal density anomalies
caused by thermal or compositional differences can be studied. Gravity field models can
5