Report of IAG Special Commission 1 for 1999-2003

Report of IAG Special Commission 1
MATHEMATICAL AND PHYSICAL FOUNDATIONS OF GEODESY
for the period 1999-2003
by
Petr Holota
Research Institute of Geodesy, Topography and Cartography
250 66 Zdiby 98, Praha-vychod, Czech Republic
e-mail: holota@pecny.asu.cas.cz

1. Introduction

The Special Commission on Mathematical and Physical Foundations of Geodesy (CMPFG) was established by the International Association of Geodesy on the occasion of the 20th General Assembly of the International Union of Geodesy and Geophysics in Vienna in 1991, as a consequence of the need for a permanent structure working on the foundations of geodesy. The establishment of the special commission is essentially associated with the preparatory work done by K.-P. Schwarz (the Section IV president of that time) and the Section IV Steering Committee of that time. It met with a considerable support. The main objectives of the special commission were the following:

to encourage and promote research on the foundations of geodesy in any way possible;
to publish, at least once every four years, comprehensive reviews of specific areas of active research in a form suitable for use in teaching as well as research reference;
to actively promote interaction with other sciences;
to closely cooperate with the special study groups in Section IV - General Theory and Methodology. (As an IAG structure the CMPFG belongs particularly to this section).

These formulations are short but in reality they represent a challenging program. It was published in the 2000 issue of The Geodesist's Handbook [Journal of Geodesy (2000), Vol. 74, No. 1]. In addition one can read about details concerning the CMPFG on the website of the commission at http://pecny.asu.cas.cz/IAG_SC1/ which contains also the bibliography of the CMPFG . (Note that there is an intention to keep this website working also after the 23rd General Assembly of the IUGG in Sapporo, 2003. )

In a sense, in the period 1999-2003 the research program of the CMPFG represented a continuation of the activities developed during two four-year terms (stating with 1991) when the commission was successfully chaired by E.W. Grafarend. In the research program of the CMPFG the main focus was on: statistical problems in geodesy, numerical and approximation methods, geodetic boundary value problems, on problems in geometry and differential geodesy, relativity, cartography, on equilibrium reference models and also on the theory of orbits and dynamics of systems.

In this field the CMPFG derived important driving impulses especially from the work of the IAG. As a minimum let us mention, e.g., two problems that were discussed at a special plenary session held in Birmingham on the occasion of the 22nd General Assembly of the International Union of Geodesy and Geophysics in 1999: 1) "Are our contemporary theoretical and computer models sufficient to handle the 1:10⁹ accuracy in frame realization, Earth rotation, positioning etc. consistently?"; - 2) "Can we be sure that sensor and/or model deficiencies do not enter into geophysical interpretation?". Of course, there are also other facts that stimulated the work of the CMPFG. The close tie between geodesy and mathematics is one of them. This tie is confirmed in the whole history of the development of these two disciplines, which is well-known, but it is worthwhile to mention that more than three decades already there exists an independent research program for a theory and methodology oriented body in the structure of the IAG.

2. Structure and Members

The broad spectrum of research objectives of the CMPFG led to a subdivision of its research program into specific tasks. In 1999, immediately upon its approval by the IAG, the following subcommissions were established:

Subcommission 1 "Statistic and Optimization"
Chair: P. Xu (Japan)

Working Group "Spatial statistics for geodetic science"
Chair: B. Schaffrin (USA)

Subcommission 2 "Numerical and Approximation Methods"
Chair: W. Freeden (Germany), http://www.mathematik.uni-kl.de/~wwwgeo

Subcommission 3 "Boundary Value Problems"
Chair: R. Lehmann (Germany)

Subcommission 4 "Geometry, Relativity, Cartography and GIS"
Chair: V. Schwarze (Germany, in the period 1999-2001)

Subcommission 5 "Hydrostatic/isostatic Earth's Reference Models"
Chair: A.N. Marchenko (Ukraine), http://people.polynet.lviv.ua/sc5/

The theory of orbits and dynamics of systems were an exception. In general problems that by nature have a tie to this topic are given a considerable attention in many branches of science. Here the topic was left within the framework of the special commission itself. The focus was on the interplay between mathematics (especially analysis) and applications that together with problems related to methods of integration, modelling, analysis of perturbations and qualitative aspects in the evolution of trajectories have an essential relation to space geodetic methods and inertial systems. Now, after four years the original intention broad visible achievements. The work of the CMPFG members resulted in a number of very valuable contributions. They concern, e.g., dynamic satellite geodesy on the torus; the relation between analytical and numerical integration in satellite geodesy; energy relations for the motion of satellites within the gravity field; the use of asymptotic series, celestial mechanics and physical geodesy; satellite geodesy on curved space-time manifolds; differential equations in inertial navigation systems etc. Considerable research activities of CMPFG members develop also in the field of dedicated satellite mission, independently as well as in a contact with IAG Special Commission 7 (Satellite Gravity Field Missions, http://www.geod.uni-bonn.de/SC7/index.html.)

The following distinguished scientists have been invited to work in the CMPFG:

Ex officio Members
B. Heck (Germany), President of Section IV;
C. Jekeli (USA), Secretary of Section IV, Chairman SSG 4.191: Theory of fundamental height systems
http://www-ceg.eng.ohio-state.edu/~cjekeli/ssg4-191.htm ;
Yuanxi Yang (China), Secretary of Section IV;
W. Keller (Germany), Chairman SSG 4.187: Wavelets in geodesy and geodynamics
http://www.uni-stuttgart.de/iag ;
G. Strykowski (Denmark), Chairman SSG 4.188: Mass density from integrated inverse gravity modelling
http://research.kms.dk/~ssg4188/study_group/index.html ;
D. Wolf (Germany), Chairman SSG 4.189: Dynamic theories of deformation and gravity field;
H. Kutterer (Germany), Chairman SSG 4.190: Non-probabilistic assessment in geodetic data analysis
http://www.dgfi.badw.de/ssg4.190/welcome.html ;
E.W. Grafarend (Germany), Chairman SSG 4.195: Fractal geometry in geodesy (The proposal for this SSG was adopted at the Executive Committee meeting in Budapest, September 4, 2001)
http://www.uni-stuttgart.de/gi/

Individuals
M. Bougeard (France), C. Cui (Germany), A. Dermanis (Greece), E.W. Grafarend (Germany),
http://www.uni-stuttgart.de/gi/ , E. Groten (Germany), K.H. Ilk (Germany),
http://www.geod.uni-bonn.de/SC7/index.html , J. Janak (Slovak Republic), R. Klees (The Netherlands), L. Kubacek (Czech Republic), Z. Martinec (Czech Republic), G. Moreaux (Denmark), J. Otero (Spain), M. Petrovskaya (Russia), R. Rummel (Germany), F. Sacerdote (Italy), K.-P. Schwarz (Canada), M. Sideris (Canada), N. Sneeuw (Canada), H. Sünkel (Austria), L. Svensson (Sweden), P. Teunissen (The Netherlands), C.C. Tscherning (Denmark), P. Vanicek (Canada), G. Venuti (Italy), M. Vermeer (Finland), R.J. You (Taiwan)

Maintenance of liaisons with related activities:
IUGG Committee on Mathematical Geophysics: M. Vermeer (Finland)

Additional Members invited to work in:

Subcommission 1: J.A.R. Blais (Canada), Y. Kagan (USA), M. Sambridge (Australia), Y.X. Yang (China), S.D. Pagiatakis (Canada)
Working Group: Shaofeng Bian (China), W. Caspary (Germany), K. Kraus (Austria), S. Meier (Germany)
Subcommission 2: C. Jekeli (USA), W. Keller (Germany), J. Mason (England), V. Michel (Germany), F.J. Narcowich (USA), Z. Nashed (USA), E. Schock (Germany), L. Schumaker (USA), J. Sloan (Austria), G. Steidl (Germany), L. Sjöberg (Sweden), L. Svensson (Sweden), C.C. Tscherning (Denmark), J. Ward (USA)
Subcommission 3: M. Günter (Germany), M. Kern (Canada), Yu.M. Neyman (Russia), Yu.A. Rozanov (Russia), N. Weck (Germany), W. Wendland (Germany), K.J. Witsch (Germany), A.I. Yanushauskas (Lithuania)
Subcommission 4: S.A. Klioner (Germany), D. Milbert (USA), M. Schmidt (Germany)
Subcommission 5: O.A. Abrikosov (Ukraine), V.K. Kholshevnikov (Russia), S. Kostyanev (Bulgaria), D. Lelgemann (Germany), H. Moritz (Austria), G. Papp (Hungary)

Corresponding Members invited to work in Subcommission 1: O. Abrikosov (Ukraine), M.Y. Markuze (Russia), C. Shi (China) and in the Working Group: N. Cressie (USA), J. Menz (Germany), J. Pilz (Austria), A. Stain (Netherlands)

3. Subcommissions

The subcommissions were very productive. It can be seen from the bibliography of the CMPFG which is accessible on the website of the special commission (at the address given above and also in the end of this report). It contains a rich list of entries that document the research done by the members of the special commission in the reported period. (Note that the bibliography on the website is an open material that is under a process of a permanent completion.) Some of the achievements reached by CMPFG members get a special IAG recognition, see Sect. 8. In the sequel, for page limit, we have to confine ourselves to some highlights only.

Subcommission 1. This subcommission placed emphasis on areas such as statistics and optimization for inverse problem theory, space techniques and informatics science. Since almost all realistic models are nonlinear, and especially because global optimization has been developing rapidly theoretically and practically, the title of the subcommission was changed from "Statistics" to "Statistics and Optimization" for 1999-2003. Also the goals for this Subcommission were clearly defined. The major new development was achieved in the following areas:
(1) Inverse Problem Theory. The major progress in this area has been related to the determination of geopotential fields from space geodetic observations. Xu investigated the L-curve method from the point of view of quality control. The Delft group (Kusche, Klees, and Ditmar) has been focused on comparing different regularization methods, development of techniques to deal with color noises, and stochastic models.
(2) Space Techniques. The achievements in this area are very significant, geodetically and mathematically, in particular, in multiplicative noise models and mixed integer linear models. In the case of multiplicative noise models, Xu (1999) developed bias-corrected least squares methods and a Bayesian method to deal with (In-) SAR-like multiplicative models. Geodetic applications of multiplicative noise models can be found in the dissertation of Hanssen and other reports from the Delft group. In the case of mixed integer linear models, The contributions are mainly in three aspects: GPS ambiguity decorrelation; statistics and Lower and upper probability bounds; and integer Bayesian estimation. The Delft group led by Teunissen has made a great contribution to this area, by developing and testing the so-called LAMBDA method and a number of lower and upper probability bounds for the integer estimators, in particular, the simple rounding method. Xu (1998) further investigated the integer programming and its applications to GPS. Hassibi and Byod (1998) and Grafarend (2000) developed the LLL algorithm for GPS decorrelation. Xu (2001) developed The inverse Cholesky integer decorrelation and showed that it outperformed the integer Gaussian decorrelation and the LLL algorithm, and thus indicates that the integer Gaussian decorrelation is not the best decorrelation technique and further improvement is possible; and (ii) no decorrelation techniques available up to the present can guarantee producing a smaller condition number in the case of high dimension. Recently, Xu (2003) first developed a method to construct Voronoi cells and systematically study the fitting of the Voronoi cell from inside and outside. He then derived a number of new lower and upper bounds for the probability with which the estimated integers are correct. And finally he gave the tests of two hypotheses on the integer mean. Bayesian integer estimation has been developed by Gundlich and Koch (2002), de Lacy et al (2002) and others.
(3) Informatics Science. In this regard, Xu (1999, 2002) developed some isotropic probabilistic models for use in geodesy. They have been used in quality control of strain/stress tensors. These models have also played a key role in numerically comparing the performances of different GPS decorrelation methods. The most significant advantage of the approach is that it does not depend on nor favour any particular satellite-receiver geometry and weighting system;
(4) Global optimization. In this regard, Xu (2002, 2003a,b) developed a new global optimization method for nonlinear nonconvex inversion by combining local optimization methods with feasible point finders. Local optimization algorithms have been proved to be robust, reliable and quickly convergent to a local optimal solution in the neighbourhood of a starting point. Feasible point finders serve as an engine, either for repelling or lifting the whole algorithm from trapping into a local optimal solution or for providing the warranty that the global optimal (earth model) solution has been found correctly. A number of examples of one- and multiple-dimensions will be used to demonstrate how the method works. The method has also recently been applied to determine stress state from fault-slip data (Xu 2003).
(5) in addition to the above mentioned areas, we have also seen some development on those traditional topics, such as linear and/or nonlinear model; robust estimation and its geodetic applications (Yang and others). In particular, Xu (2003) found that the nonlinear filtering theory of nonlinear continuous systems may have a fundamental defect in the foundation.

Working Group. The Working Group on "Spatial Statistics for Geodetic Science" was founded within Subcommission 1 in order to highlight this increasingly important area in view of novel applications that reach far beyond the classical case of gravity field interpolation. A variety of issues was investigated from a more fundamental point of view, including: - the interplay and equivalences among least-squares collocation, Kriging, spline interpolation, multiquadrics and (biharmonic) wavelets; - collocation/Kriging for data with skew probability density function; - non-probabilistic (e.g. fuzzy) methods in a spatial environment such as GIS; - spatial filtering of Kalman type with and without further constraints; - hierarchical Bayesian analysis, soft unbiasedness, reliability measures, missing values in spatial models, etc.

Members of the subcommission and the working group brought significant contributions to a number of meetings listed in Sect. 7, but in particular to the Workshop of IAG-SSG 4.190 "Non-probabilistic Assessment in Geodetic Data Analysis", Karlsruhe, 2000 and to the IAG 1st International Symposium on Robust Statistics and Fuzzy Techniques in Geodesy and GIS, Zurich, 2001.

Subcommission 2 ( http://www.mathematik.uni-kl.de/~wwwgeo ). An intensive mathematical research oriented to problems in the representation and approximation of the Earth's gravitational potential, to problems in physical geodesy and in the treatment of modern space geodetic data was in the focus of interest of this subcommission. The season is that one has to think of the geopotential as a "signal" in which the spectrum evolves over space in significant way. This space-evolution of the frequencies is not reflected in the Fourier transform in terms of non-space localizing spherical harmonics. Wavelet transforms are a counterpart. Therefore, aspects of constructive approximation, decorrelation, data compression etc. were treated within the wavelet theory. Moreover, an uncertainty principle was formulated and used as it gives appropriate bounds for the quantification of space and frequency properties of trial functions in geodesy. In the focus there were also combined models, where expansions in terms of spherical harmonics are combined with local methods, e.g. radial base function techniques as splines, wavelets, mass-points, finite elements etc. In the limited time span of the four years the subcommission also significantly progressed in the methodology of the treatment of spaceborn observations. In addition to a number of interesting papers presented at the meetings listed in Sect. 7 and entries in the CMPFG bibliography also an important contribution on "Multiscale modelling of GOCE data products" to the ESA International GOCE User Workshop held in Noordwijk, The Netherlands, 2001, resulted from the work of Subcommission 2.

Subcommission 3. This subcommission focused on boundary value problems (BVPs) in physical geodesy. These problems are essentially connected with the use of potential theory and the theory of partial differential equations in the determination of the gravity field and figure of the Earth. In the reported period the research carried out by the subcommission concentrated on the refinement of the solution of the standard problems and new mathematical models, on free-datum and multi-datum BVPs, as they arise from unknown height datums; on mixed BVPs and especially various types of altimetry-gravimetry problems with their capability to give a mathematical model for a combined use of different data on the boundary; on stochastic BVPs; overdetermined and constraint BVPs; BVPs on special surfaces and also on pseudo BVPs. The research covered also non-classical methods in the solution of BVPs, as variational methods with their close tie to the concept of the so-called weak solution. The application of boundary element techniques was investigated too, similarly as the use of various function bases. A considerable attention was given to the apparatus of ellipsoidal harmonics. A remarkable progress was achieved in its application for the solution of practical problems of geodetic relevance. Within traditional concepts the role of the BVPs is rather well-known in physical geodesy, but nowadays the work of the subcommission is strongly influenced by new striking impulses. Among others they reflect the progress in the data collection, data accuracy, higher requirements on the accuracy of the solution and also a need for mathematical modelling associated with the use of modern technologies, as e.g. airborn gravimetry and dedicated satellite missions (a spacewise approach, Slepian's problem etc.). The results of this subcommission were clearly visible and heard with interest at nearly all the meetings listed in Sect. 7.

Subcommission 4. Geometry oriented problems, relativity aspects, cartography and GIS defined the field of interest of this subcommission. Within the research carried out in this subcommission geometry means the Marussi-Hotine approach to differential geodesy, foundations of Gaussian differential geodesy, geometry of plumblines as geodesics in conformal 3-manifould, Fermi's coordinates etc. The main progress was achieved in the use of the theory of relativity, in particular in the reformulation of geodetic measurement processes within the framework of general relativity. Here the metric tensor plays an important role and it was represented with respect to a set of appropriate charts. Using the words of the subcommission chairman, we knew that almost every quantity of interest in geodetic and geophysical applications refers to a geocentric, Earth-fixed coordinate system (chart). Therefore, the space-time metric with respect to an Earth-fixed chart was derived at first post Newtonian order. The field equations determining the terrestrial gravitational field were derived and its explicit representation was outlined. On this basis the impact of the results on the modelling of geodetic measurement process including space-time positioning scenarios as well as the high-precision gravitational filed estimation was discussed. The subcommission took an active part in a number of international meetings. Its results achieved in cartography and GIS were presented at the IAG 1st International Symposium on Robust Statistics and Fuzzy Techniques in Geodesy and GIS, Zurich, 2001.

Subcommission 5 ( http://people.polynet.lviv.ua/sc5/ ). This subcommission was a new substructure of the CMPFG. Nevertheless it proved to be very active. The research carried out within the subcommission covered the construction of piecewise radial density models, stable determination of parameters of radial density models and variational problems. It also focused on the low-frequency Earth's gravity field and the evolution of the Earth's principal axes and moments of inertia completed with a canonical form of the solution. Corresponding changes of the 3D mass density model were also considered. Some research was oriented to incompressible fluid Earth, to the compressibility and vicoelestic perturbations. For the density recovery from seismic velocities the solution was based on three differential equations and the density function was separated into a hydrostatic (main) part and an additional small part due to chemical/phase inhomogenieties or superadiabatic temperatures. Some famous laws (Legendre-Laplace, Roche, Darwin, Gauss) were considered for radial density distribution in connection with the solution of the famous Clairaut, Poisson and Williamson-Adams differential equations. In the interpretation of reproducing kernels it was shown that the set of all suitable kernel functions may be interpreted as a finite sum of two point singularities (pole and dipole) and also straight line singularities. Moreover, an optimum point mass model of the global gravitational filed was compiled. In addition to some of the meetings listed in Sect. 7, e.g. the IAG 2001 Scientific Assembly in Budapest, the results achieved in the subcommission were also presented at the International Symposium on Modern Achievements of Geodetic Science and Industry, Lviv, Ukraine, 2002.

4. Business Meeting in Banff

The CMPFG proved to be an important discussion forum. This was evident from the business meeting of the commission organized in Banff on the occasion of the IAG International symposium "Gravity, Geoid and Geodynamics 2000". A circular letter distributed well before the meeting met with a good response. "What you think is the most urgent problem to be solved related to the foundations of geodesy" this was a key question formulated by C.C. Tscherning and circulated with the letter. The response was obvious and mirrored the impact of the future or up-coming satellite missions. In particular the following urgent problems were mentioned (in the formulations by R. Rummel):

How to deal in a proper way with the actual Earth boundary when bringing down the high resolution gravity information from GOCE from satellite altitude to the Earth's surface? Should one simply apply some kind of topographic correction or are there better and/or more correct ways?
A mission like GRACE drifts (in the course of the entire mission length) down from, say 500 km to 300 km. While going down the gravity field is sampled in a changing manner and at the same time it drifts through several regimes of resonance. At the same time one tries to recover the temporal variations of the gravity field. Thus one is faced with a very complicated sampling/aliasing problem, which to my best knowledge is not sorted out so far.
A similar problem in altimetry which certainly affects, for example, estimates of sea level change. Again the satellite samples time variable effects such as tides in a very complicated time and space pattern. What is the aliasing situation there, what could be done to improve it?
In real world satellite sensors such as accelerometers or gradiometers do not show a normally distributed noise behavior but drifts and a similar effects cause systematic distortions which result in e.g. 1/f (f = frequency) behavior. We have taken into account these things but in an ad hoc manner. Could one work on stochastic models on the sphere for processes with less favorable error behavior?
Currently several groups try to determine center-of-mass changes of the Earth from the analysis of global tracking data. What is the proper formulation of datum definition and S-transformation for a real deformable Earth with moving plates, how should a center-of-mass change determination be correctly formulated from the theoretical point of view?

K.-H. Ilk mentioned another view. He pointed out "three problem areas related to the satellite missions CHAMP, GRACE and COCE": - analysis of the observation system; - modelling and data analysis aspects; - applications in geosciences, oceanography, climate change studies and other interdisciplinary research topics. Finally, M. Vermeer suggested for discussion the term "best practices" and the use of "common sense" in connection with modern techniques in geodesy. He recalled that in traditional geodesy there were these common sense rules such as "working from the large to the small" and many many more. With new techniques, and the availability of fast computers and complex theories, sometimes it seems that common sense has been a bit forgotten.

The subsequent discussion at this business meeting concerned some reflections on the running process towards the new structure of the IAG. B. Heck, the president of IAG Section IV outlined the key aspects that motivate this initiative. His information were then amplified by F. Sanso, the IAG president who paid a considerable attention to the work of the CMPFG itself and than focused on a detailed explanation of principles and actions that are most frequently discussed within the IAG executive in preparing the concepts for the new IAG structure. The business meeting of the CMPFG was well attended, not only by the members, but also by a number of participants of the Banff symposium "Gravity, Geoid and Geodynamics 2000".

5. Business Meeting in Budapest

The meeting took place in the building of the Hungarian Academy of Sciences in 2001, concurrently with the IAG Scientific Assembly in Budapest. It was well attended and organized as a Joint business meeting of IAG Section IV and the CMPFG (IAG Special Commission 1). The meeting and its program were announced on the website of the CMPFG with a considerable advance. The main items of the agenda were: results achieved, new topics and trends, liaisons with related activities, the publication of the results and finally the position of Section IV and the commission within the process towards the new IAG structure. The meeting was attended by the IAG secretary general and also by the president of the IAG, who himself reviewed the work of Section IV and CMPFG and expressed a supporting standpoint of the IAG executive to future activities in this field of geodesy.

6. Hotine-Marussi Symposium and the Business Meeting in Matera

This business meeting was held in Centro di Geodesia Spaziale "C. Colombo" in Matera (Italy) on the occasion of the V Hotine-Marussi symposium on Mathematical Geodesy, which by tradition is an important forum to the discussion on theoretical problems in geodesy. For the business meeting the whole morning segment was reserved in the program of the symposium on 19 July 2002. This gave to the participants of the symposium an excellent opportunity to take part in the meeting. The meeting was open by the chairman of the CMPFG. He updated information concerning the structure of the commission and its work in the period passed. Thanks to local organizers it was possible to arrange a direct connection with the server of the CMPFG and in this way to support the introductory talk by an on-line presentation of the content of the CMPFG www-page. This gave all the information a great degree of authenticity and met with an explicit recognition of the participants and also the IAG secretary general and the president of the IAG who took part in the meeting. It was explicitly stated that the CMPFG website represents a very good source of information which, through the Internet, may be used especially by students of geodesy to get (without limits) useful knowledge on the program and work of the commission.

The discussion at the meting then focused on problems related to the reorganization process in the IAG and to the possibilities of mapping IAG research activities of theoretical and methodological nature into the new structure of the IAG. Information on this process were given by the president of Section IV with explanations concerning the aims and concepts followed by the IAG in the reorganization process. Details were also mentioned concerning the Planning Committee for the new Inter-Commission Committee on Theory (ICCT), the preparatory work done by the committee and the position and role of the ICCT within the IAG in the period after the Sapporo IUGG General Assembly in 2003.

7. Participation in International Scientific Meetings and Boards

In the reported period the CMPFG was well represented at a number of IAG sponsored meetings and also at important scientific occurrences organized by other IUGG bodies or by EGS (European Geophysical Society), EUG (European Union of Geosciences), ECGS (European Center for Geodymanics and Seismology), ESA, AGU and other international and local scientific organizations. In all these cases a stress on the mathematical and physical nature of geodetic problems, typical for the research done in the CMPFG, was clearly visible in the presented or invited contributions prepared by CMPFG members. For space limit let us highlight only the following events:

25th General Assembly of the European Geophysical Society, Nice, France, 2000;
Geostatistics Congress, Cape Town, South Africa, 2000;
Workshop of IAG-SSG 4.190 "Non-probabilistic Assessment in Geodetic Data Analysis", Karlsruhe, Germany, 2000;
4th International Symposium on Spatial Accuracy, Amsterdam, Netherlands, 2000;
XIX ISPRS Congress, Amsterdam, Netherlands, 2000;
IAG International Symposium "Gravity, Geoid, and Geodynamics 2000", Banff, Canada, 2000;
9th International Symposium on Spatial Data Handling, Beijing, China, 2000
9th International Symposium on Matrices and Statistics in Honor of C.R. Rao's 80th Birthday, Hyderabad, India, 2000;
IAG 1st International Symposium on Robust Statistics and Fuzzy Techniques in Geodesy and GIS, Zurich, 2001;
ESA International GOCE User Workshop held in Noordwijk, The Netherland, 2001.
26th General Assembly of the European Geophysical Society, Nice, France, 2001;
IAG 2001 Scientific Assembly, Budapest, 2001;
AROPA Workshop (Analytical Representation of Potential Field Anomalies for Europe), "Institute d’Europe", Castle of Münsbach, Luxembourg, 2001;
27th General Assembly of the European Geophysical Society, Nice, France, 2002;
V Hotine-Marussi Symposium on Mathematical Geodesy, Matera, Italy, 2002;
3rd Meeting of the IAG International Gravity and Geoid Commission, Thessaloniki, Greece, 2002;
Weikko A. Heiskanen Symposium in Geodesy, Celebrating 50 Years of Geodetic Science at The Ohio State University, A Look to the Future, Columbus, Ohio, 2002;
EGS-AGU-EUG Joint Assembly, Nice, France, 2003;

Frequently, the members and officers of the CMPFG took part in the work of scientific (program) and organizing committees or were entrusted to act as conveners of individual scientific sessions. The CMPFG was also involved in the work of the committee for selecting the Best Student Paper at the IAG Scientific Assembly in Budapest. In the period 1999-2003 members of the CMPFG worked also in the editorial board of the Journal of Geodesy.

8. Publications recognized by the IAG

In this report it is proper to make also an explicit mention that achievements reached by some of CMPFG members get a special IAG recognition in the period 1999-2003. At its meeting in Nice, 2000, the IAG Executive Committee decided to give Dr. Peiliang Xu (the chair of the Subcommission 1) the IAG young authors award for his paper "Biases and the accuracy of, and an alternative to, discrete nonlinear filters", published in the Journal of Geodesy, Vol. 73(2000), pp. 35-46. Also in 2001 the awarded publication originated from the work of one of CMPFG members. In Budapest the IAG Executive Committee decided to give the IAG young authors award to Dr. Rüdiger Lehmann (the chair of the Subcommission 3) for his paper "Altimetry-gravimetry problems with free vertical datum", published in Journal of Geodesy, Vol. 74(2000), pp. 327-334. [Note for the sake of completeness that on this occasion the award was given to two authors sharing the same (i.e. the first) place. The second was Christopher Kotsakis with his paper "The multiresolution character of collocation", published in the Journal of Geodesy, Vol. 74(2000), pp. 275-290.]

Acknowledgements. Concluding this brief report, I wish to thank all my colleagues from IAG Special Commission SC1 for excellent cooperation and the results achieved, which often meant months and years of a great endeavor and devoted work. Your help was very important for the commission in order that it accomplished its mission. Many thanks and much success in your further work!

References

The bibliography of the CMPFG may be found at http://pecny.asu.cas.cz/IAG_SC1/ , as already mentioned above. Also www-links inserted in the text of the report may be used for a similar purpose. Note again that there is an intention to keep the server with the CMPFG home page working also after the 23rd General Assembly of the IUGG in Sapporo, 2003.
In 2001 a Mid-term report of the CMPFG for the period 1999-2001 was prepared and submitted to the IAG Central Bureau before the IAG 2001 Scientific Assembly in Budapest. The report was then posted on the website of the CMPFG and also published in the IAG Travaux, Vol. 32 – General and technical reports 1999-2001, together with similar reports of other IAG structures. Subsequently, the volume (on CD-ROM) was distributed by the IAG Central Bureau at the IAG Scientific Assembly in Budapest, especially among national committees of IAG member countries. This editorial initiative helped to inform the international scientific community about the profile and activities of the IAG in connection with the organizational changes prepared within the IAG.