The Carmel Mountain Precise Geoid
by Dan Sharni & Haim B. Papo
Key words: Israel geoid, Stokes, gravity anomalies.
This paper presents the final results of a
pilot-project, for mapping an accurate geoid of the State of Israel.
The purpose of the project was to develop a feasible methodology,
assemble all necessary data, design and test field procedures and
finally to work out a suitable analysis algorithm, including the
respective computer programs. The project was funded and supported by
the Survey of Israel over a period of five years between 1994 and
1999. An area of about 600 sq. km. on and around the Carmel Mountain
served as a field laboratory and proving ground. The ultimate goal was
to render a geoid map of the pilot area with a one-sigma accuracy of 4
The geoid map was compiled from three complementary
- Measured geoid undulations (indirectly - by GPS and
trigonometric leveling) at a network of anchor points. The network
density was set high by a factor of three to four in order to
provide means for testing the quality of the map.
- A global gravity model of the highest order available. Over the
years 1994-1999 a succession of gravity models was used, beginning
with OSU91, then - EGM96 and finally - the 1800 order GPM98B
- A dense grid of free-air gravity anomalies (3') extending up to
a distance of 2o from the pilot area. Within the state boundaries
we used directly measured anomalies. At sea and beyond the state
boundaries we had to depend on free-air gravity anomalies,
reconstructed from a dense Bouguer anomalies grid and a DTM of
surface and sea-floor topography.
The computational procedure was based on the
"remove-restore" approach as follows:
- Transform the free-air-anomalies grid into a grid of residual
anomalies, by removing model (GPM98B) anomalies.
- At every anchor point compute model geoid undulations (including
a number of corrections such as "zero order" undulation,
the effect of global elevation, indirect effect, etc.) and add
Stokes's integration of the residual f.a. anomalies field.
- Subtract the above (b) "crude prediction" from the
"measured" undulations and create an anchor-point
correction field. Interpolate the correction field into a contour
map or - a grid. At any point within the grid boundaries, geoid
undulation can be predicted now by adding the interpolated
correction grid value to a "GPM98B plus Stokes" crude
Three factors dominate the accuracy of the final
- Density of the anchor points.
- Over-all fit of the gravity model to the geoid.
- Radius of Stokes's integration of the residual f.a. anomalies
With anchor points spaced 5-20 km apart; employing
the GPM98B model and finally extending Stokes's integration up to 2
degrees we obtained an accuracy (one-sigma) of 2 cm or better.
Although our accuracy estimates are based on sound analysis principles
they may seem a bit too optimistic. Analysis of additional test fields
should confirm our "optimistic" results or else - define
more realistic accuracy estimates.
Dr. Dan Sharni
Tel. + 972 4 829 2482
Fax + 972 4 823 4757
Haim B. Papo
Fax + 972 4 823 4757