An example of gravimetric geoid computation: The Iberian Gravimetric Geoid of 2005

The figure of Earth in first approximation: the revolution ellipsoid

Relationship between orthometric (H) and ellipsoidal (h) height: the undulation of the geoid (N) H = h  N

The figure of Earth in second approximation: the geoid undulation (N) measured over the ellipsoid

Ellipsoid Geoid Earth surface H h NANA A B C H A = h A  N A H B = h B  N B  H BA =  h BA   N BA NBNB  N BA =  B – N A 0  H BA  h BA The leveling with GPS computing height differences requires the use of a geoid to calculate  N

Calculating  N for two paths of 100 km, it can be observed that the values of  h   H are related to the topography

 N calculated in plane zone: path AB

 N calculated in mountainous zone: path CD

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.

Problem: the computation of an Iberian geoid

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.

Land and Marine Gravity Data

Land and Marine Gravity Data

Land and Marine Gravity Data

The gravity data needed for the computation can be obtained from the above-mentioned centers

The elevation data needed for the computation can be obtained from the above-mentioned centers

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)(Corchete et al., 2005)

The term h ref corresponds to the elevations filtered with a long wavelength filter of 60 arc-minutes

EIGEN-CG01C Gravity Anomalies (n max = 360) The term  g GM is calculated using a geopotential model

The short-wavelength contribution must be recovered after the interpolation by means of: For it, the digital terrain model previously computed will be used (Corchete et al., 2005) Obtained by interpolation

Determination of a geoid model (N) N = N GM + N b + N I N GM : contribution of the geopotential model N b : contribution of the residual gravity N I : indirect effect

EIGEN-CG01C Geoid (n max = 360) N GM : contribution of the geopotential model

N b : contribution of the residual gravity  g =  g free + c +  g,,  g = N I where:

f(x,y) and g are: c: terrain correction (only considering the masses over the geoid)

N b : contribution of the residual gravity (obtained after integration with the FFT 1D) F 1 = FFT 1D F 1 -1 = FFT 1D backward where:

f(x,y) and g are: N I : indirect effect

MODEL VALIDATION The model validation is performed comparing its values with high-precision data. These data are the geoid undulations (N 0 ) obtained by means of GPS/leveling. These data can be supplied by European centers for our study area: the Iberian Peninsula.

GPS/leveling process: calculation of the observed geoid undulations (N 0 ) N 0 = h GPS - H lev GPS satellite receiver Leveling instrument

European Vertical Reference System(EVRS)European Vertical Reference System(EVRS) Organisms that can supply validation data

Data of the European Vertical Network (EVRS) on Iberia

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.

IBERian GEOid 1995 (IBERGEO95)

European Gravimetric Geoid 1997 (EGG97)

EGM96 geoidEIGEN-CG01C Geoid Worldwide geoid models

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.

REFERENCES Corchete V., Chourak M. and Khattach D., The high-resolution gravimetric geoid of Iberia: IGG2005. Geophys. J. Int., 162, 676–684.The high-resolution gravimetric geoid of Iberia: IGG2005 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 , Sevilla, M. J. A new gravimetric geoid in the Iberian Peninsula. BGI Bull. D’Inf. Nº 77 (Toulouse) and IGeS Bull. Nº 4 (Milano), , 1995.

CONTACT Prof. Dr. Víctor Corchete Department of Applied Physics Higher Polytechnic School - CITE II(A) UNIVERSITY OF ALMERIA ALMERIA. SPAIN FAX: