NATIONAL REPORT OF THE FEDERAL REPUBLIC OF ... - IAG Office

a boundary value formulation of the equations of motion.
The theoretical background on integrals of motion as well
as on the use of short-arc boundary value approaches has
recently been further developed by SCHNEIDER (2004, 2005,
2006), SCHNEIDER and CUI (2005) and LÖCHER and ILK
(2005).
A third in situ methodology is the kinematic approach in
which GPS-derived orbit ephemeris is numerically differenced
twice to provide 3D forces. Though elementary in
principle, this approach also requires delicate data handling
and corrections for nuisance force models. It was successfully
implemented at the GIS, Stuttgart University, cf.
REUBELT et al. (2003) or REUBELT et al. (2006).
GRACE’s very high KBR accuracy demands orbit accuracy
at a compatible level, which is hardly feasible considering
GPS positioning. Thus, also for GRACE it seems to make
sense to consider the KBR as in situ gravity field observable
with GPS only providing the geolocation. SHARIFI and
KELLER (2005) and SHARIFI (2006) convert the GRACE
observable into a in-line along-track gravity gradient. See
also NOVÁK et al. (2006).
Combined with semi-analytical techniques, leading to
block-diagonal normal equation structures, gravity field
recovery from in situ data becomes a highly efficient and
fast recovery tool. Despite the necessary approximations,
such a tool is used for CHAMP, GRACE and GOCE processing,
e.g. WERMUTH and FÖLDVARY (2003) FÖLDVARY
and WERMUTH (2005), often as quick-look tool, cf. WER-
MUTH et al. (2006).
Further advances
The sensors of such complicated systems as CHAMP,
GRACE and GOCE require deeper knowledge of the
appropriate stochastic models and associated estimation
techniques. Several contributions have been made in the
wider area of stochastic modelling, e.g. MARINKOVIC et al.
(2003). ALKHATIB and SCHUH (2007) apply Monte Carlo
covariance estimation to GOCE gravity recovery. Also
robust estimation techniques and outlier detection methods
have been thoroughly investigated to this end, e.g.
KARGOLL (2005) or GÖTZELMANN et al. (2006).
When modelled in a straight-forward fashion, the huge
numbers of observations and of unknowns lead to large
equation systems that can only be dealt with by highperformance
computing, also referred to as brute force.
Much of this work was pioneered by ITG at University
Bonn. More recent developments include improved stochastic
modelling ALKHATIB and SCHUH (2007). At GIS, University
Stuttgart, the LSQR method was topic of research.
It could be established as a viable alternative to conjugate
gradient and other methods, e.g. BAUR and GRAFAREND
(2006), BAUR and KUSCHE (2007).
Specific issues that arise in high performance computation
are treated by AUSTEN et al. (2006).
The methodology to calibrate space gravimeters and to
validate the results of gravity field satellite mission has also
been further advanced. In particular, the validation of
N. Sneeuw: Satellite Gravity Theory 71
GOCE observations by various techniques, e.g. cross-over
analysis or upward continuation of terrestrial data, has been
topic of research at IfE, University Hannover, e.g. JARECKI
and MÜLLER (2003).
Great advances have been made in the area of multi-resolution
gravity field modelling, much of which is due to the
activities at University of Kaiserslautern, e.g. (FREEDEN and
MICHEL, 2004). At the same time, in the past few years
multi-resolution analysis has made the transition from
mathematical research to a mainstream geodetic analysis
technique for spaceborne gravity recovery, e.g. FENGLER
et al. (2004), FREEDEN and SCHREINER (2005), FENGLER
et al. (2007), or SCHMIDT et al. (2005, 2007).
Working group on Satellite Gravity Theory
Under the new IAG structure a joint working group on
Satellite Gravity Theory was initiated between Commission
2 and the Intercommission Committee on Theory right after
the IUGG general assembly 2003, Sapporo. According to
its terms of reference the working group was dedicated to
monitoring and stimulating research in gravity field estimation
from satellite missions, merging, modelling timevariable
gravity field representation and satellite orbit
dynamics. Chaired by N. SNEEUW (Calgary, Stuttgart) this
international working group had a strong German participation:
MAYER-GÜRR (Bonn), KUSCHE (Delft, Potsdam),
GERLACH, PETERS (Munich), NOVÁK (Stuttgart, Prague),
WILD (Karlsruhe).
One of the working group’s achievements, in collaboration
with the IAG working group on Inverse Modelling (chair:
J. KUSCHE), was a special issue of the Journal of Geodesy
Vol. 81, Nr. 1, 2007, dedicated to the combined field of
satellite gravity theory and inverse theory. Significant
participation from German scientists documented the
activities in these areas. In FENGLER et al. (2007) spherical
wavelets as developed by the University of Kaiserslautern
group have been established as a tool for multiscale
modelling of the GRACE monthly gravity fields. In the
same vein, the contribution by SCHMIDT et al. (2007)
systematically reviews spherical wavelets with application
to regional analysis and interpretation of CHAMP and
GRACE gravity data. In the same issue ALKHATIB and
SCHUH (2007) deal with the Monte Carlo covariance
estimation and error propagation strategy. The authors focus
on the recovery of the Earth’s gravity field in spherical
harmonics from the GOCE mission, a challenging and
numerically huge task.
Activities in preparation of future missions
Despite the scientific successes and research activities
around the satellite missions CHAMP, GRACE and GOCE,
many groups have started to plan ahead. Most notably,
IAPG at Technical University Munich group has initiated
and organized several workshops and projects to this end.
The full spectrum of spaceborne gravimetry—from orbit
dynamics through geoscience applications to future concepts
– is covered in the proceedings of one such workshop
BEUTLER et al. (2003). A study on Future Satellite Gravi-