Diapositiva 1

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An example of gravimetric geoid computation
The Iberian Gravimetric Geoid of 2005
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The figure of Earth in first approximation the
revolution ellipsoid
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Relationship between orthometric (H) and
ellipsoidal (h) height the undulation of the
geoid (N)
H h - N
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The figure of Earth in second approximation the
geoid undulation (N) measured over the ellipsoid
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The leveling with GPS computing height
differences requires the use of a geoid to
calculate DN
A
Earth surface
B
H
Geoid
h
C
NA
NB
Ellipsoid
HA hA - NA
DHBA DhBA - DNBA
HB hB - NB
DNBA NB NA 0
DHBA DhBA
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Calculating DN for two paths of 100 km, it can be
observed that the values of Dh - DH are related
to the topography
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DN calculated in plane zone path AB
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DN calculated in mountainous zone path CD
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• As conclusion, a geoid model is required to use
  GPS heights (h) for leveling.
• The geoid models available in the study area,
  have not enough precision to be used in the major
  part of the engineering problems.
• For this reason, it is necessary the computation
  of a new geoid for the Iberian area, which has
  the major precision possible.

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Problem the computation of an Iberian geoid
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• NECCESARY DATA
• Gravity data available from several
  international centers (usually, from internet
  links).
• Digital terrain models (DTM) that can be
  combined (and interpolated, if it is necessary)
  to get a high-resolution Iberian DTM.
• Validation data (GPS/leveling data) that can be
  supplied by several European centers.

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Land and Marine Gravity Data
http//www.ngdc.noaa.gov/seg/
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Land and Marine Gravity Data
http//bgi.cnes.fr8110/bgi_debut_a.html
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Land and Marine Gravity Data
http//www.usgs.gov/
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The gravity data needed for the computation
can be obtained from the above-mentioned centers
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http//www2.jpl.nasa.gov/srtm/
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http//www.ngdc.noaa.gov/mgg/gdas/gd_designagrid.h
tml
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The elevation data needed for the computation
can be obtained from the above-mentioned centers
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The short and long wavelength effects are removed
from the gravity data by means of
Thus, the interpolation of the gravity data
randomly distributed over the study area to a
regular grid, is facilitated (Corchete et al.,
2005)
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The term href corresponds to the elevations
filtered with a long wavelength filter of 60
arc-minutes
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The term DgGM is calculated using a geopotential
model
EIGEN-CG01C Gravity Anomalies (nmax 360)
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The short-wavelength contribution must be
recovered after the interpolation by means of
Obtained by interpolation
For it, the digital terrain model previously
computed will be used (Corchete et al., 2005)
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Obtained by interpolation
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Determination of a geoid model (N)
N NGM Nb NI
NGM contribution of the geopotential model
Nb contribution of the residual gravity
NI indirect effect
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NGM contribution of the geopotential model
http//www.gfz-potsdam.de/pb1/op/grace/results/ind
ex_RESULTS.html
EIGEN-CG01C Geoid (nmax 360)
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Nb contribution of the residual gravity
where
Dg Dgfree c dg ,, dg 0.3086 NI
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c terrain correction (only considering the
masses over the geoid)
f(x,y) and g are
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Nb contribution of the residual
gravity (obtained after integration with the FFT
1D)
where
F1 FFT 1D F1-1 FFT 1D backward
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NI indirect effect
f(x,y) and g are
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• MODEL VALIDATION
• The model validation is performed comparing its
  values with high-precision data.
• These data are the geoid undulations (N0)
  obtained by means of GPS/leveling.
• These data can be supplied by European centers
  for our study area the Iberian Peninsula.

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GPS/leveling process calculation of the observed
geoid undulations (N0)
GPS satellite receiver
N0 hGPS - Hlev
Leveling instrument
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Organisms that can supply validation data
           European Vertical Reference System (EVRS)          
http//crs.bkg.bund.de/evrs/
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Data of the European Vertical Network (EVRS) on
Iberia
http//crs.bkg.bund.de/evrs/tabelle_neu.html
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• COMPARISON WITH OTHERS MODELS
• The official geoid used in Spain (Sevilla,
  1997) the IBERian GEOid of 1995 (IBERGEO95).
• The European Geoid (Denker and Torge, 1998) the
  European Gravimetric Geoid 1997 (EGG97).
• The worldwide geoids EGM96 y EIGEN-CG01C.

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IBERian GEOid 1995 (IBERGEO95)
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European Gravimetric Geoid 1997 (EGG97)
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Worldwide geoid models
http//cddis.gsfc.nasa.gov/926/egm96/egm96.html
EGM96 geoid
EIGEN-CG01C Geoid
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CONCLUSIONS

• The IGG2005 geoid model improves all previous
  geoid, being much more precise.
• The IGG2005 is a first step towards a
  centimetric precision geoid for the Iberian area.
• The centimetric precision in the geoid
  computation will be achieved, if more and more
  precise gravity data are available for the
  Iberian area.

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REFERENCES
Corchete V., Chourak M. and Khattach D., 2005.
The high-resolution gravimetric geoid of Iberia
IGG2005. Geophys. J. Int., 162, 676684. Denker,
H., and W. Torge. The European Gravimetric
Quasigeoid EGG97. International Association of
Geodesy Syposia, Vol. 119, Geodesy on the Move.
Springer-Verlag, Berlin-Heidelberg-New York, S.
249-254, 1998. Sevilla, M. J. A new gravimetric
geoid in the Iberian Peninsula. BGI Bull. DInf.
Nº 77 (Toulouse) and IGeS Bull. Nº 4 (Milano),
163-180, 1995.
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CONTACT
Prof. Dr. Víctor Corchete Department of Applied
Physics Higher Polytechnic School - CITE
II(A) UNIVERSITY OF ALMERIA 04120-ALMERIA.
SPAIN FAX [phone] e-mail
corchete_at_ual.es