Altimeter Derived Gravity Anomalies
The major part of the altimetry derived anomaly file used in the joint project was
computed by DMA from their Geosat holdings. The Geosat satellite is a U.S. Navy satellite
launched in March 1985 to provide coverage of all ocean areas between 72 0 Nand 72 0 S
latitudes. The Geosat Geodetic Mission (GM) point data consists of 49 million
observations with a 4 kilometer spacing at the equator. The Geosat Exact Repeat Mission
(ERM), which commenced in November 1986, repeated its ground track every 17 days
producing a spacing at the equator of 160 kilometers. DMA adjusted the GM data to a
reference network derived from the ERM network. This procedure included area
adjustments of overlapping diamond shaped areas bounded by network arcs and automated
crossover point editing (van Hee, 1987). After the adjustment, over 5 million 5' x 5'
Geosat mean sea surface heights were computed. The next step in the altimetry work was
to utilize a ocean dynamic topography model, based on TIP and ERS-l altimeter data and
complete in spherical harmonics to degree 20 (Nerem, 1994, private communication), to
apply a dynamic topography correction to the sea surface height file and produce a global
set of geoid heights. The fmal step in the preparation of the altimetric data was to transform
all the 5' x 5' geoid heights from the WGS-84 Reference System to the International
Terrestrial Reference Frame 1991 (ITRF 91), which was chosen as the standard reference
frame for this project. The Geosat GM sea surface heights were transformed into the TIP
reference frame using three translation parameters and a bias parameter. This
transformation was developed by estimating the translation and bias between an OSU mean
sea surface (Basic and Rapp, 1992) and the Geosat GM surface. Knowing the relation
(Rapp et al., 1994) between the OSU mean sea surface and the TIP sea surface, the
conversion from the Geosat GM was carried out
The collocation procedure used at DMA to calculate 30' mean gravity anomalies from the
5' x 5' Geosat geoid heights uses the Forsberg logarithmic covariance model (Forsberg,
1987). This model features simple, closed formulas for covariances between all
gravimetric quantities based on a planar approximation and provides good fits to actual
gravity field characteristics. The estimation process to compute the 30' mean gravity
anomalies consisted of two main steps. First, accurate covariances must be developed
between gravity anomalies in lOx 1 0 (with 1 0 overlap) cells for all ocean areas. These
covariances were developed from a previous ocean-wide file of 5' x 5' gravity anomalies
produced by DMA in December 1992 from the Geosat 5' geoid heights that did not benefit
from a dynamic topography correction or more accurate covariance modeling being
performed for this project. The JGM-2 70 x 70 gravity model augmented with the
OSU91A 360 x 360 gravity model was used to reduce all the 5' x 5' altimetric gravity
anomalies before covariances were calculated. The empirical covariances from these 5'
gravity anomalies were fit to the Forsberg covariance parameters, Co (variance of the
gravity field), D (high frequency attenuation factor), and T (low frequency attenuation
factor). The fitting of the analytical Forsberg model to the empirical covariance model
ensures that the proper power spectrum of the gravity field is being represented.
The second step is to use the analytical Forsberg parameters with the Geosat 5' x 5' geoid
heights in least-squares collocation. Collocation is a linear minimum variance unbiased
estimator of gravity field quantities using the principles of least-squares adjustment and
covariance propagation to describe functional relationships between the disturbing potential
and other related quantities. DMA developed a collocation procedure that utilizes the
Forsberg covariance model and Cholesky decomposition to efficiently and accurately
calculate the 30' mean anomalies directly using the 5' Geosat anomalies and local
covariance parameters. Each l O x 1 0 cell with a 1 0 overlap was separat,ely computed based
on the local characteristics (Forsberg parameters) of the gravity field and Geosat 5' geoid
heights reduced by the JGM-2/0SU91A 360,360 spherical harmonic model. The mean of
the reduced altimetry for each 3 0 x 3 0 computational area was then removed from the
100
The major part of the altimetry derived anomaly file used in the joint project was
computed by DMA from their Geosat holdings. The Geosat satellite is a U.S. Navy satellite
launched in March 1985 to provide coverage of all ocean areas between 72 0 Nand 72 0 S
latitudes. The Geosat Geodetic Mission (GM) point data consists of 49 million
observations with a 4 kilometer spacing at the equator. The Geosat Exact Repeat Mission
(ERM), which commenced in November 1986, repeated its ground track every 17 days
producing a spacing at the equator of 160 kilometers. DMA adjusted the GM data to a
reference network derived from the ERM network. This procedure included area
adjustments of overlapping diamond shaped areas bounded by network arcs and automated
crossover point editing (van Hee, 1987). After the adjustment, over 5 million 5' x 5'
Geosat mean sea surface heights were computed. The next step in the altimetry work was
to utilize a ocean dynamic topography model, based on TIP and ERS-l altimeter data and
complete in spherical harmonics to degree 20 (Nerem, 1994, private communication), to
apply a dynamic topography correction to the sea surface height file and produce a global
set of geoid heights. The fmal step in the preparation of the altimetric data was to transform
all the 5' x 5' geoid heights from the WGS-84 Reference System to the International
Terrestrial Reference Frame 1991 (ITRF 91), which was chosen as the standard reference
frame for this project. The Geosat GM sea surface heights were transformed into the TIP
reference frame using three translation parameters and a bias parameter. This
transformation was developed by estimating the translation and bias between an OSU mean
sea surface (Basic and Rapp, 1992) and the Geosat GM surface. Knowing the relation
(Rapp et al., 1994) between the OSU mean sea surface and the TIP sea surface, the
conversion from the Geosat GM was carried out
The collocation procedure used at DMA to calculate 30' mean gravity anomalies from the
5' x 5' Geosat geoid heights uses the Forsberg logarithmic covariance model (Forsberg,
1987). This model features simple, closed formulas for covariances between all
gravimetric quantities based on a planar approximation and provides good fits to actual
gravity field characteristics. The estimation process to compute the 30' mean gravity
anomalies consisted of two main steps. First, accurate covariances must be developed
between gravity anomalies in lOx 1 0 (with 1 0 overlap) cells for all ocean areas. These
covariances were developed from a previous ocean-wide file of 5' x 5' gravity anomalies
produced by DMA in December 1992 from the Geosat 5' geoid heights that did not benefit
from a dynamic topography correction or more accurate covariance modeling being
performed for this project. The JGM-2 70 x 70 gravity model augmented with the
OSU91A 360 x 360 gravity model was used to reduce all the 5' x 5' altimetric gravity
anomalies before covariances were calculated. The empirical covariances from these 5'
gravity anomalies were fit to the Forsberg covariance parameters, Co (variance of the
gravity field), D (high frequency attenuation factor), and T (low frequency attenuation
factor). The fitting of the analytical Forsberg model to the empirical covariance model
ensures that the proper power spectrum of the gravity field is being represented.
The second step is to use the analytical Forsberg parameters with the Geosat 5' x 5' geoid
heights in least-squares collocation. Collocation is a linear minimum variance unbiased
estimator of gravity field quantities using the principles of least-squares adjustment and
covariance propagation to describe functional relationships between the disturbing potential
and other related quantities. DMA developed a collocation procedure that utilizes the
Forsberg covariance model and Cholesky decomposition to efficiently and accurately
calculate the 30' mean anomalies directly using the 5' Geosat anomalies and local
covariance parameters. Each l O x 1 0 cell with a 1 0 overlap was separat,ely computed based
on the local characteristics (Forsberg parameters) of the gravity field and Geosat 5' geoid
heights reduced by the JGM-2/0SU91A 360,360 spherical harmonic model. The mean of
the reduced altimetry for each 3 0 x 3 0 computational area was then removed from the
100