Ilias N. Tziavos

Aristotle University of Thessaloniki, Department of Geodesy and Surveying, Univ. Box 440,

54006 Thessaloniki, Greece, e-mail:



This report summarizes the main work and activities of the IAG Special Study Group (SSG) 3.167 "Regional Land and Marine Geoid Modelling" between August 1999 and April 2001. This SSG was established for the period 1999-2003 during the 1999 General Assembly of IUGG in Birmingham, the UK. It is a continuation of a previous SSG of IAG (1995-1999) under the same title and the same objectives, since IAG has recognized the importance of the geoid modelling on a regional scale in land and marine areas.

The primary objective of this SSG is the accurate regional-scale land and marine geoid determination mainly emphasizing on the following directions: (a) Investigation of modelling procedures for land and marine geoid, differences between methods and difficulties when working across the land/sea boundary; (b) new efficient ways of working with heterogeneous data for geoid determination; (c) the use of numerical techniques and the possibilities to prescribe or recommend the extent of a standard procedure; (d) revision of procedures for calculating the errors of geoid/quasi-geoids; (e) the impact of GPS - heights not only to validation procedures but also to common adjustments with geoid heights; (f) the contribution of high accuracy and resolution marine geoid to sea surface topography determination and other related oceanographic studies; (g) modelling of long-wavelength errors in regional geoid/quasi-geoid computations by the new satellite gravity missions CHAMP, GRACE and GOCE; (h) the contribution of airborne gravimetry to geoid modelling in combination procedures.

It is worth mentioning that the work and activities included in this report belong to those members of the SSG who sent me in time their contributions. These contributions are available via the SSG’s website at the following URL ( Due to space limitations I describe below that part of the work which mainly reflects the leading tasks and goals of SSG. Additionally, scientific work by other colleagues is also briefly presented and reference is given to several recent papers published in geodetic journals or in papers presented in geodetic symposia during the last two years. Some results reported in recent dissertations are also discussed. A more complete list of references can be found in the above mentioned web page.



SSG 3.167 had, primarily, thirty regular members, including the president and ten corresponding members. After the IAG GGG2000 meeting held in Banff (August 2001) eleven colleagues joined SSG as corresponding members. The geographical spread of the SSG members is quite satisfactory. The members expertise range from mathematical and physical geodesy to gravity field applications in different branches of geosciences. The names of the members of the SSG and countries are given below:

Full Members:
I.N. Tziavos  (Greece, chairman)  H. Abd-Elmotaal (Egypt) R. Barzaghi (Italy)
J. Catalao  (Portugal)  J.Y. Chen  (China) O.C. Dahl (Norway)
H. Denker (Germany) W. Featherstone  (Australia) R. Hipkin (United Kingdom)
R. Haagmans  (The Netherlands) Z. Jiang (France) J. Kaminskis  (Latvia)
N. Kuehtreiber  (Austria) Y. Kuroishi (Japan) U. Marti (Switzerland)
C. Merry (South Africa) D. Smith (USA)  J. Toth (Hungary)
G.C. Tsuei (Taiwan)  M. Veronneau (Canada)


Corresponding Members:
H. Duquenne (France)  J. Fernandes (Portugal) Y. Fukuda (Japan)
C. Hwang  (Taiwan) C. Jekeli (USA) W. Kearsley (Australia)
P. Knudsen (Denmark)  J. Krynski  (Poland) M. Kuhn (Germany)
D. Milbert (USA) G. Papp (Hungary) K. Prijanta  (Indonesia)
L. Sanchez (Colombia) K. Zhang  (Australia)


Corresponding Members (after the meeting in Banff):
V. Andritsanos (Greece)  M.E. Ayhan (Turkey) A. Bayoud (Canada)
L. Biagi  (Italy) J. Brozena (Canada) G. Fotopoulos  (Canada)
A. Kenyeres (Hungary) C. Kotsakis (Canada) M. Pearse (N. Zealand)
D.R. Roman  (USA) G.S. Vergos (Canada)



Different geoid or quasi-geoid determinations on a local or regional scale have been carried out by members of the SSG in different sea/land test areas using combinations of heterogeneous data sources referred to high degree and order geopotential solutions. The methods employed range from the classical numerical integration procedures, the spectral FFT techniques and the stochastic least-squares collocation algorithms to the input/output system theory algorithms in the frequency domain (Abd-Elmotaal 2000, Andritsanos and Tziavos 2000, Fotopoulos et al. 2000, Duquenne 2000, Rodriguez 1999, Toth et al. 2000, Tziavos 2000). The results obtained meet the today accuracy demands of a wide number of applications related to surveying, geodesy, geophysics and other disciplines of geosciences. The quality of the geoid heights produced in land areas was assessed by comparisons with corresponding heights at GPS benchmarks (see, e.g., Featherstone 2001, Marti et al. 2000, Toth et al. 2000). The use of GPS in combined adjustments with gravimetric geoid heights is discussed by Kotsakis and Sideris (2000). The estimated accuracy of the determined geoid/quasi-geoid heights reached in some cases the level of one decimeter and in pure marine geoid solutions found close to one centimeter (Fernandes et al. 2000, Rodriguez 2000, Vergos et al. 2001, Andritsanos 2000, Andritsanos et al. 2000). Gravimetric geoid solutions were also computed on a national scale by different authors and attempts were made to the direction of datum unification (see, e.g., Featherstone 2000, Marti et al. 2001, Fotopoulos et al. 2000, Toth et al. 2000).

Kotsakis (2000) discussed problems occurring in linear signal estimation from discrete gridded data and has drawn interesting conclusions related to modern operational geodesy and practical applications like local/regional geoid determination. Hwang and Lih-Shinn Hwang (2001) computed an improved geoid model for Taiwan with an accuracy ranging from 2 cm to 10 cm in order to assess the accuracy of orthometric heights and detect vertical rates of land motion. Toth et al. (2001) investigated the recovery of gravity and geoid in Hungary from torsion balance data using collocation and spectral techniques. A thorough comparative analysis on regional high-frequency geoid computations in Canada using a synthetic gravity field is given by Novak et al. (2000).

Several simulation studies were carried out in the frame of modelling the long wavelength part of the Earth’s gravity field taking advantage from the new satellite gravity missions of CHAMP, GRACE and GOCE. Tscherning (2001) has illustrated the advent of pure satellite gravity models by the new missions. These models will considerably improve our possibilities for computing precise quasi-geoidal differences. The expected accuracy could be better enough than that obtained by EGM96.

The effects of density variations on terrain corrections and the handling of topography in practical geoid determination were studied by several authors (see, e.g., Kuhn 2000, Omang and Forsberg 2000, Tziavos and Featherstone 2000, Biagi and Sanso 2000). The geophysical dimension of a regional quasi-geoid determination and its correlations with Moho depths and other geophysical parameters have been studied in several papers (see, e.g., Abd-Elmotaal 2000, Kuehtreiber and Abd-Elmotaal 2000, Toth et al. 2000). In the same frame and according to Molodensky theory efficient ways of computing the G1 term and the influence of the grid size of digital elevation models on quasi-geoid contribution has been also investigated (Merry 2001, Amod 2001). Tsoulis (2000) studied the spherical harmonic analysis of a global digital elevation model using the Airy/Heiskanen and Pratt/Hayford isostatic models.

The essential role of airborne gravimetry in combination solutions with marine gravity observations, satellite altimetry derived and land gravity for high resolution geoid computations is demonstrated in several studies (Bastos et al. 2000, Olesen et al. 2000). The increasing interest for new airborne gravity surveys during the last two years contributed to the better knowledge of the geoid and sea surface topography in different areas (Greenland, eastern Mediterranean and Crete island, Azores islands, Corsica). The geoid results reached the level of one decimeter or better in several cases in terms of standard deviation of the differences between the computed geoid heights and the corresponding heights derived from satellite altimetry (Andritsanos et al. 2000, Fernandes et al. 2000, Rodriguez 1999, Rodriguez and Sevilla 2000). Several authors discussed the role of satellite altimetry in gravity field modelling in self-seas and coastal areas and pointed out inherent problems when working across the land/sea boundary (see, e.g., Andersen and Knudsen 2000, Andritsanos 2000, Hipkin 2000, Vergos et al. 2001). Pure altimetric geoid solutions were carried out taking advantage from the most accurate mission of TOPEX/Poseidon and the high resolution geodetic missions of GEOSAT and ERS-1 (see, e.g., Fernandes et al. 2000, Vergos et al. 2000, Andritsanos et al. 2000). Moreover, marine geoid solutions were computed by combining altimetric data with shipborne gravity data in areas presenting geodynamic and oceanographic interest (see, e.g., Rodriguez 1999, Andritsanos 2000, Fernandez et al. 2000, Vergos et al. 2000).



The geographical distribution of the members of the SSG made difficult their close cooperation and common research. However there was a collaboration between different members on an individual basis. The research carried out by the members of SSG during the last two years was mainly addressed in its different targets, promising results were reported and important conclusions were drawn with respect to regional geoid modelling. However, additional work should be done within the next two years until the General Assembly of IUGG in Saporo, Japan, in 1993. Some suggestions for future work are summarized as follows:

       Refinement of the procedures used for the computation and evaluation of the regional geoid/quasi-geoid solutions and their errors.

       Investigation of the comparison and combination techniques between geoid heights and GPS/levelling heights.

       More systematic analysis on the contribution of the new satellite gravity missions to the improvement of the long-wavelength part of a geoid/quasi-geoid determination.

       High-resolution marine geoid solutions by combining satellite altimetry, airborne and sea gravimetry data for oceanographic applications.



Abd-Elmotaal, H.: A gravimetric geoid for Egypt derived by FFT techniques. Presented at Gravity, Geoid and Geodynamics 2000, Banff, Canada, July 31-August 4, 2000.

Abd-Elmotaal, H.: Vening Meinesz inverse isostatic problem with local and global Bouguer anomalies. Journal of Geodesy, 74/5, 390-398, 2000.

Amod, A.: The use of spectral methods in quasi-geoid determination. Ph.D. Thesis, Dept. of Geomatics, University of Cape Town, 2001.

Andersen, O.B. and P. Knudsen: The role of satellite altimetry in gravity field modelling in coastal areas. Phys. Chem. Earth (A), vol. 25, No. 1, 17-24, 2000.

Andritsanos, V.D., and I.N. Tziavos: Estimation of gravity field parameters by a multiple input/output system. Phys. Chem. Earth (A), vol. 25, No. 1, 39-46, 2000.

Andritsanos, V.D., G.S. Vergos, I.N. Tziavos, E.C. Pavlis and S.P. Mertikas: A high-resolution geoid for the establishment of the GAVDOS multi-satellite calibration site. Proceedings of Gravity, Geoid and Geodynamics 2000, Banff, Canada, July 31-August 4, 2000.

Andritsanos, V.D., M.G. Sideris and I.N. Tziavos: Quasi-stationary sea surface topography estimation using input/output method and error analysis of satellite altimetry. Accepted for publication in Journal of Geodesy.

Andritsanos, V.D.: Optimal combination of terrestrial and satellite data using spectral methods for applications to geodesy and oceanography. Ph.D. Thesis, Dept. of Geodesy and Surveying, Aristotle Univ. of Thessaloniki, 2000.

Bastos, L., C. Cunha, R. Forsberg, A. Olesen, A. Gidskehaug, L. Timmen and U. Meyer: On the use of airborne gravimetry in gravity field modelling: experiences from the AGMASCO project. Phys. Chem. Earth (A), vol. 25, No. 1, 1-8, 2000.

Biagi, L. and F. Sanso: A new algorithm for fast RTC computation. Presented at Gravity, Geoid and Geodynamics 2000, Banff, Canada, July 31-August 4, 2000.

Duquenne, H.: The geoid in New Caledonia. Private communication, 2001.

Featherstone W.E.: Towards unification of the Australian height datum between the mainland and Tasmania using GPS and the AUSgeoid98 geoid model. Geomatics Research Australasia, 73, 30-40, 2000.

Featherstone W.E.: Absolute and relative testing of gravimetric geoid models using GPS and orthometric height data. Accepted for publication in Computers and Geosciences, 2001.

Fernandes, M.J., L. Bastos, J. Catalao: The role of multi-mission ERS altimetry in the determination of the marine geoid in the Azores, Marine Geodesy, 23, 1-16, 2000.

Fotopoulos, G., C. Kotsakis and M.G. Sideris: A new Canadian geoid model in support of levelling by GPS. Geomatica, 54.1, 53-62, 2000.

Hipkin, R.: Modelling the geoid and sea-surface topography in coastal areas. Phys. Chem. Earth (A), vol. 25, No. 1, 9-16, 2000.

Hwang , C. and L.S. Hwang: Use of geoid for assessing trigonometric height accuracy and detecting vertical land motion. Draft, 2001.

Kotsakis, C.: Multiresolution aspects of linear approximation methods in Hilbert spaces using gridded data. Ph.D. Thesis, Dept. of Geomatics Eng., University of Calgary, UCGE Rep. Nr. 20138, 2000.

Kotsakis, C. and M.G. Sideris: On the adjustment of combined GPS/levelling/geoid networks. Journal of Geodesy, 73/8, 412-421, 1999.

Kuehtreiber, N. and H.A. Abd-Elmotaal: Gravimetric geoid computation for Austria using seismic Moho data. Presented at Gravity, Geoid and Geodynamics 2000, Banff, Canada, July 31-August 4, 2000.

Kuhn, M.: Geoidbestimmung unter Verwendung verschiedener Dichtehypothesen. Ph.D. Thesis, DGK, Reihe C, Heft Nr. 520, Munich 2000.

Marti, U., A. Schlatter and E. Brockmann: The possibilities of combining levelling with GPS measurements and geoid information. Presented at the EGS XXVI Gen. Assembly, Nice, France, 26-30 March, 2001.

Merry, C.L.: Personal communication, 2001.

Novak, P., P. Vanicek, M. Veronneau, S. Holmes, W.E. Featherstone: On the accuracy of modified Stokes’s integration in high-frequency gravimetric geoid determination. Journal of Geodesy, 74/9, 644-654, 2000.

Olesen, A.V., R. Forsberg, K. Keller, A. Gidskehaug: Airborne gravity survey of Linkoln Sea and Wandel Sea, north Greenland, Phys. Chem. Earth (A), vol. 25, No. 1, 25-30, 2000.

Omang, O.C.D. and R. Forsberg: How to handle topography in practical geoid determination: three examples. Journal of Geodesy, 74/6, 458-466, 2000.

Rodriguez, G., M.J. Sevilla, C. de Toro: Crossover analysis in the Canary-Azores region of ERS-1 altimetric data. Bollettino di Geofisica Teorica ed Applicata, 40, 3-4, 1999.

Rodriguez, G.: Geoid studies using terrestrial and marine gravity data (in Spanish). Ph.D. Thesis, Universitad Complutense de Madrid, 1999.

Toth, Gy., Sz. Rosza, V.D. Andritsanos, J. Adam and I.N. Tziavos: Towards a cm-geoid for Hungary: recent efforts and results. Phys. Chem. Earth (A), vol. 25, No. 1, 47-52, 2000.

Toth, Gy., Sz. Rosza, J. Adam and I.N. Tziavos: Gravity field recovery from torsion balance data using collocation and spectral methods. Presented at the EGS XXVI Gen. Assembly, Nice, France, 26-30 March, 2001.

Tscherning, C.C.: Geoid determination after the first satellite gravity missions (draft version). To appear in the Festschrift volume for Prof. Torge, 2001.

Tsoulis, D.: A comparison between the Airy/Heiskanen and the Pratt/Hayford isostatic models for the computation of potential harmonic coefficients. Journal of Geodesy, 74/9, 637-643, 2000.

Tziavos, I.N. and W. Featherstone: First results of using digital density data in gravimetric geoid computation in Australia. Proceedings of Geodynamic, Gravity and Geoid 2000, Banff, Canada, July 31-August 4, 2000.

Tziavos, I.N.: The geoid in the Mediterranean-Recent results and future plans. Invited paper, presented at the FIG Symposium “Mediterranean Surveyors in the new millennium”, Malta, Sept. 18-21, 2000.

Vergos, G.S., F.A. Bayoud, M.G. Sideris and I.N. Tziavos: High-resolution geoid computation by combining shipborne and multi-satellite altimetry data in the eastern Mediterranean sea. Presented at the EGS XXVI Gen. Assembly, Nice, France, 26-30 March, 2001.


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