The Carmel Mountain Precise Geoid
by Dan Sharni & Haim B. Papo
Key words: Israel geoid, Stokes, gravity anomalies.
Abstract
This paper presents the final results of a
pilotproject, 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 onesigma accuracy of 4
cm.
The geoid map was compiled from three complementary
data sources:
 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 19941999 a succession of gravity models was used, beginning
with OSU91, then  EGM96 and finally  the 1800 order GPM98B
model.
 A dense grid of freeair 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 freeair gravity anomalies,
reconstructed from a dense Bouguer anomalies grid and a DTM of
surface and seafloor topography.
The computational procedure was based on the
"removerestore" approach as follows:
 Transform the freeairanomalies 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 anchorpoint
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
prediction.
Three factors dominate the accuracy of the final
geoid map:
 Density of the anchor points.
 Overall fit of the gravity model to the geoid.
 Radius of Stokes's integration of the residual f.a. anomalies
field.
With anchor points spaced 520 km apart; employing
the GPM98B model and finally extending Stokes's integration up to 2
degrees we obtained an accuracy (onesigma) 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
Geodesy
Technion
32000 Haifa
ISRAEL
Tel. + 972 4 829 2482
Fax + 972 4 823 4757
Email: sharni@techunix.technion.ac.il
Haim B. Papo
Geodesy
Technion
32000 Haifa
ISRAEL
Fax + 972 4 823 4757
Email: haimp@tx.technion.ac.il
