MASS TRANSPORT AND MASS DISTRIBUTION IN THE EARTH SYSTEM

MASS TRANSPORT AND MASS DISTRIBUTION IN THE EARTH SYSTEM
Jakob Flury(1) and Reiner Rummel(1)
(1) German GOCE Project Bureau
Institute for Astronomical and Physical Geodesy
Technische Universit¨at M¨unchen, D-80290 M¨unchen
flury@bv.tum.de, rummel@bv.tum.de
1 INTRODUCTION
In 2001 a German GOCE project bureau has been established, funded by the German Aerospace Center (Deutsches
Zentrum f¨ur Luft- und Raumfahrt DLR). Its main objectives are (1) to promote research on the scientific use of the
products to be delivered by GOCE, (2) to maintain close contact with industry and institutions involved in GOCE, (3) to
inform the public about the progress of the GOCE mission and (4) to organize regular workshops for the scientific user
community. For more details it is referred to [1] and http://www.goce-projektbuero.de. In this article we
focus on a very recent activity. In a joint effort, a group of German Earth scientists formulated and submitted a proposal
”Mass Transport and Mass Distribution in the Earth System” for a so-called German Priority Research Program to the
Deutsche Forschungsgemeinschaft (DFG), see [2].
2 SCIENTIFIC RATIONALE
GOCE has been selected as the first explorer mission of ESA’s ”Living Planet Programme” [3]. The program is based on
an Earth system approach. Its aim is to advance the quantitative knowledge of processes within the various Earth system
components and of their interrelations and to increase the overall understanding of the system in order to allow timely
responses. The missions are selected on the basis of the contribution that can be expected towards these goals. Before this
background, it is expected that GOCE, in particular, and satellite gravimetric missions, in general, can play an important
and a very unique role in Earth system research. Our basic hypothesis is the following: ”From a combination of surface
geometry and surface geometry changes with gravity it will be possible to quantify mass anomalies, mass transport, mass
exchange and ultimately mass balance in the Earth system”. It will be a very fundamental contribution to the establishment
of the energy budget inside the Earth system.
What is the role of the measurement of gravity and of the geoid with high spatial and temporal resolution in this? One
can distinguish three principal fields of application. The first one is the comparison of the measured gravity or geoid with
the corresponding quantity of an Earth model, e.g. a model co-rotating with the Earth and in hydrostatic equilibrium,
see e.g. [4]. The deviation is referred to as anomaly. It is a direct measure of the imperfection of the Earth model and
ultimately of unmodelled dynamics. This approach is as old as geodesy itself, already Huygens proposed to derive the
Earth’s flattening from pendulum measurements. Nowadays Earth models are very refined. An excellent example of a
forward modelling of the long-wavelength part of the geoid, up to spherical harmonic degree and order 15, with a 92%
agreement between measured and modelled geoid is given in [5]. Modern Earth models of crust and mantle are based on
a large variety of geophysical evidence, such as seismic tomography, topography, tectonic velocities or laboratory studies
of material properties. The future trend will be a joint modelling taking into account gravity and geoid as well as all
other geophysical sources. The second application is of much more recent date. The geoid is defined as the equipotential
surface of the gravity field at mean sea level. It is reference surface of all topographic heights, those of the topographic
terrain as well as those of ocean topography. In ocean areas, the geoid represents the surface of a hypothetical ocean at
rest. The ocean topography is very small, typically smaller than 1 m. Thus, its determination very much depends on the
precision with which the geoid and the ocean surface are known. With the geometric shape of the actual mean ocean
surface measured by satellite altimetry and the geometric shape of the geoid computed from the measured gravity field,
dynamic ocean topography can be determined. Under the assumption of geostrophic balance the latter translates directly
into ocean surface circulation. The spatial scales of interest range from several thousand kilometres to scales between 30
and 70 km. The principle of this method dates back to the comparison of geodetic and oceanic levelling along coast lines,

---

compare e.g. [6], [7]. With the advent of ocean altimetry and with the availability of more precise geoid models in the
eighties the method became applicable on a global scale. Dynamic ocean topography is a key quantity for ocean studies,
including the study of mass and heat transport in the oceans. The third field of application is the most evident albeit
most challenging one. Any redistribution of mass inside Earth system results in temporal variations of gravity and geoid.
This may be redistribution of mass inside of a component, such as solid Earth or the ocean, or mass exchange between
components, e.g. between atmosphere, ocean and ice. Dependent of the material and its physical state (gas, liquid or
solid) there exists a wide range of temporal and spatial scales. In general, temporal variations are very small and therefore
difficult to measure. However, their measurement should allow, for example, the distinction between thermal expansion
and mass surplus in sea level rise, see e.g. [8], or the transport of water through Earth system. Absolute gravimetry
or superconducting relative gravimetry are very precise and are easily capable of detecting temporal gravity changes.
However it is very difficult if not impossible to discern the various individual global, regional and local contributions in
the sum of the measured signal. The effect of vertical crustal movements of the stations poses an additional problem.
Gravimetric satellites, on the other hand, sense the effect of temporal variations integrated over large areas, so that even
very tiny signals, e.g. due to variations in snow cover, become detectable. Very successful is the measurement of temporal
variations in J2 and in a few additional low degree zonal coefficients, and currently a very exciting debate is going on
about their interpretation; see e.g. [9], [10], [11]. The separation of the individual contributions to the measured signal is
a great challenge.
In summary, there are three ways in which gravity and geoid information can be used. Gravity and geoid anomalies are
the difference between the measured gravity or geoid and the corresponding quantities of a model Earth. They reflect
unmodelled mass heterogeneities. Ocean topography is the difference between an altimetrically derived mean ocean
surface and the geoid. The geoid takes here the role of the model, i.e. the model of a hypothetical ocean at rest. Via the
geostrophic balance ocean topography can be translated in ocean surface circulation. Temporal variations of gravity and
geoid result from mass redistribution inside the Earth system.
3 MASS TRANSPORT IN THE EARTH SYSTEM
Based on the applications described above, a group of German Earth scientists has formulated a proposal for an inter-
disciplinary research program. Its title is ”Mass Transport and Mass Distribution in the Earth System – Contribution of
the New Generation of Satellite Gravity and Altimetry Missions to Geosciences”. The proposal has recently been sub-
mitted to the DFG in order to establish a German Priority Research Program. The implementation of the program is still
uncertain, because only about 20% of the submitted proposals are granted.
The objective of this project is the comprehensive study of mass anomalies, mass transport, mass exchange and mass
balance in the Earth system. In particular, the dynamics of the Earth’s crust and mantle, ice mass balance and sea level, the
hydrological cycle and ocean transport as well as their interactions will be investigated. Mass transport in the atmosphere
and mass exchange between atmosphere and hydrosphere are of importance, too, and will be taken into account employing
the best available atmospheric models. However, our expectation is that at this point an improved modeling of atmospheric
mass changes is not feasible based on gravity data. All mass phenomena are derived from the combination of geometric
and gravimetric satellite missions. We denote geometric satellite missions those which provide the shape and changes of
shape of ocean, ice and land surfaces as well as ice and tectonic velocities. The corresponding techniques are ocean and ice
altimetry, interferometric SAR of ice and land areas as well as point positioning by GNSS (GPS, GLONASS, GALILEO).
Their combination with the gravity and geoid data produced by gravimetric satellite mission yields the required mass
signals. The project takes advantage of a unique constellation of geometric and gravimetric satellite missions, partly
already in orbit now and partly to be launched in the near future. Only because of this unique constellation this research
project becomes feasible at all. An overview is given in Fig. 1.
Fig. 1 shows on the left hand side a selection of the satellite configuration on which this project is based. The new
generation of dedicated gravimetric missions CHAMP, GRACE and GOCE will provide, in their combination, the global
gravity field and geoid with unprecedented precision and spatial as well as temporal resolution. These three missions
are the key for the determination of gravity and geoid anomalies, ocean topography and temporal changes of gravity and
geoid with much higher detail and accuracy than ever before. As a selection the altimetric missions Envisat, Jason-1,
CryoSat and ICESat are shown, too. In addition, there are missions that deliver complementary data such as land and ice

---

gravity field missions
oceanic transport
oc
oc ea
e n ci
an ci rcul
rcul atio
ati n (q
on (q ua
ua si
si -st
-st a
a ttiic a
c n
an d time
d time va
va ria
ri t
at ion),
ion),
m
m a
a s
s s
s an
an d hea
d hea tt t
t rrans
ans p
p or
or tt,,
atmosphere
ed
ed die
die s
s ,,
se
se a
a le
le ve
ve l: ma
l: ma ss a
ss a n
n d
d vo
vo lu
lu me
me ch
ch an
an g
g e
e
CHAMP
GRACE
GOCE
hydrological cycle
altimetry missions
hydrological cy
continental water budget,
from satellite sensor data
continental water budget,
closur
closur e of
e of glo
gl b
ob al and
al an
d regio
regi n
on al wat
al wat e
e r ba
r ba lan
la ce,
nce,
to mass signals
wa
wa tte
e rr s
s ttor
or a
a ge
ge v
v a
a rriiat
at io
io n,
n,
consistent combination of missions,
ttr
r end
end s
s a
a n
n d c
d clliim
m at
at e c
e c h
h a
a nge
nge
reference systems, data preparation
for model assimilation,
Envisat
Jason-1
regional representations,
filtering, error models,
ice mass balance and sea level
separation of signal components,
iic
c e surface:
e surface: he
heiig
g ht
ht chan
chan ge,
ge, ve
vello
o c
ciittiies
es ,,
mass balance,
m
m a
a s
s s
s bu
bu dge
dge tt of
of ic
ic e s
e s h
h e
e e
e tts
s ,,
complementary data
se
se a le
a le ve
ve l rise
l rise from mel
from mel ttiin
n g
g ,,
CryoSat
ICESat
d
d y
y na
na mi
mi c i
c i c
c e
e mod
mod e
ells
s ,, sea
sea i
i c
c e
e :: co
co ve
ve rag
rag e
e ,, thi
thi ckn
ckn ess
ess
complementary remote sensing
TerraSAR,
dynamics of mantle and crust
topography, sea
mantle dynamics and geoid signal,
surface temperature,
mantle dynamics and geoid signal,
geoid time variation from glacial isostatic
winds, salinity, soil
geoid time variation from glacial isostatic
adjustment, plumes, slabs,
moisture (SMOS) etc.
adjustment, plumes, slabs,
gr
gr avi
av t
it y
y sig
si nal
gnal of
of crustal
crusta an
l an d lit
d lit ho
ho sp
s he
phe re
re structure
structure
Fig. 1: Structure and themes of the program ”Mass transport and mass distribution in the Earth system”.
shape and velocities, sea surface temperature, winds, salinity, soil moisture a.s.o.
Fig. 1 shows also the four research fields: dynamics of mantle and crust, ice mass balance and sea level, hydrological
cycle, ocean transport (mass and heat). The respective uses of the gravity and geoid information are indicated, too. The
link between the various satellite sensor data and their geophysical application is established by the research theme ”from
satellite sensor data to mass signals”.
As shown in Fig. 2, this interface theme is very challenging. Mass anomalies and mass transport signals are very small and
they have to be deduced from a combination of geometric and gravimetric sensor data. This is very difficult by definition.
It will only be feasible if all involved satellite sensor systems operate as one Earth encompassing global instrument. This
implies that all satellite systems have to be integrated into one terrestrial reference system, with a relative precision of
one part-per-billion, free of systematic distortions and stable over decades. The International Association of Geodesy
(IAG) has initiated the pilot project ”Integrated Global Geodetic Observing System” (IGGOS) with this goal. Here one
has to deal with its realisation for all used satellite systems. In a further step the geometric and gravimetric products
have to be prepared for data assimilation into Earth models. Thus, on the one hand, their mathematical representation has
to be compatible with the assimilation model; on the other hand, a complete stochastic model has to be developed that
takes into account the stochastic properties of the sensor data, their propagation to the assimilation model, an appropriate
sampling strategy in space and time as well as the size and character of omission errors. The third area of research, related
to this theme, is the separation of the measured mass signals into all individual effects. For this purpose a comprehensive
separation strategy has to be developed, see Fig. 2 (lower part).
The output of this interface theme are mass signal data, fully assessed and prepared for data assimilation. The theme
”dynamics of mantle and crust” will deal with modelling of the crustal and lithospheric structure, mantle dynamics,
mantle plumes, subducting slabs, and glacial isostatic adjustment. It will exchange information on postglacial rebound
with the theme ”ice mass balance and sea level”. Here the aim will be the improvement of dynamic ice models and
mass budget. For the first time it will be possible to determine the ice mass balance of the polar areas directly, based
on geometric information about changes of ice cover and ice velocity, crustal motion and gravimetrically measured mass
changes. This will, for example, give an answer to the open question, whether the Antarctic ice sheet is loosing mass
or not. A key challenge is the separation from vertical land movements. Sea level change is a link to the oceanographic

---

From satellite sensor data to mass signals:
consistent combination of missions,
reference systems,
data preparation for model assimilation,
regional representations,
filtering,
error models,
separation of signal components,
mass balance,
points along ground tracks
complementary data
Separation Toolbox
regional characteristics
special satellite configurations
time characteristics
complementary data
spectral characteristics
complementary missions
known parameters
exchange of mass model results
...
...
model grid
Fig. 2: Challenges for geodesy: consistent combination of missions, combination of different representations (e.g. points
along tracks with triangular mesh models, see the examples to the right), and separation strategies.
Table 1: Core team for the proposed priority program on mass transport and mass distribution in the Earth system
Prof. H. Schmeling
Univ. Frankfurt/M
mantle dynamics
Prof. D. Wolf
GFZ Potsdam
mantle dynamics
Prof. H. J. G¨otze
FU Berlin
crust dynamics
Prof. R. Dietrich
TU Dresden
ice mass balance
Prof. H. Miller
AWI Bremerhaven
ice mass balance
Dr. C. Haas
AWI Bremerhaven
ice mass balance
Dr. Ph. Huybrechts
AWI Bremerhaven
ice mass balance
Prof. D. Stammer
Univ. Hamburg
oceanic transport
Prof. W. Zahel
Univ. Hamburg
oceanic transport
Dr. J. Schr¨oter
AWI Bremerhaven
oceanic transport
Prof. A. Bardossy
Univ. Stuttgart
continental hydrology
Dr. J. Riegger
Univ. Stuttgart
continental hydrology
Dr. B. Merz
GFZ Potsdam
continental hydrology
Dr. A. G¨untner
GFZ Potsdam
continental hydrology
Prof. K. H. Ilk
Univ. Bonn
gravity field, coordination
Dr. P. Schwintzer
GFZ Potsdam
gravity field
Prof. Reigber
GFZ Potsdam
gravity field
Prof. R. Rummel
TU M¨unchen
gravity field
Dr. J. Flury
TU M¨unchen
gravity field, coordination
Dr. W. Bosch
DGFI M¨unchen
altimetry
part of the project where the separation of the steric and mass related component of sea level variations is addressed. The
theme ”hydrological cycle” is a first attempt to employ global mass movements as large scale constraints for continental
water budget and for global and regional water balance, for storage variation, trends in evapotranspiration and ultimately
climate change. As large parts of the continents are very sparsely covered by hydrological in-situ data, the satellite data
could enable considerable improvements for hydrological modelling, due to the global coverage. The ocean theme will
concentrate on ”ocean transport”. Here dynamic ocean topography as derived from altimetry and geoid will yield global
ocean surface circulation. Oceanographers are waiting in particular for the so-called barotropic component of circulation,
which could not be measured so far. On the other hand, gravity changes can be related to bottom pressure variations and to
deep ocean circulation. Thus, it is to be seen what the effect of these new types of global data will be on ocean modelling.
A detailed description of this research proposal is given in [2]. The list of core group members is given in Table 1.
Coordinators are Prof. K.-H. Ilk and Dr. J. Flury.

---

Fig. 3: Temporal and spatial scales of geoid signals associated to solid Earth (orange), ocean (green), ice (dark blue) and
continental hydrology (light blue) processes. The red lines show the spatial and temporal resolution limits of the
CHAMP, GRACE and GOCE missions. From [2].
4 THE FUTURE
It has been pointed out that the above research and similar research initiatives on an international level are based on this
unique and excellent constellation of geometric and gravimetric satellite missions. Thus, the question arises whether
these missions and the related research projects are able to answer all questions concerning mass transport in the Earth
system. Of course the answer is in the negative. For this reason, an assessment has recently been carried out about
the need of future gravimetric satellite missions. This investigation has been done in the context of a study to ESA
on ”Scientific Objectives for Future Geopotential Missions” [12]. Fig. 3 summarizes the state of affairs after CHAMP,
GRACE and GOCE. It can be seen that the emphasis of future missions has to be on the accurate and much more detailed
determination of temporal variations of gravity and geoid. The temporal resolution should aim at monthly variations, the
spatial resolution on typically half-wavelengths of 100 km or shorter. This is difficult to achieve. Only very sophisticated
low-low SST links in very low orbit and based on laser tracking or new concepts of satellite gravity gradiometry may be
able to meet these challenges. In a workshop at the International Space Science Institute in Bern, Switzerland, in 2002,
compare [13], a group of invited participants discussed future concepts of gravimetric satellite systems and their use in
Earth science. What is needed now is the formulation of a mission proposal for a next generation gravimetric satellite
mission as well as a comprehensive and conclusive scientific rationale.

---

REFERENCES
1. Flury, J. and Rummel, R., GOCE activities in Germany, poster at 2nd International GOCE User Workshop, ES-
TEC/ESRIN, 2004.
2. Ilk, K.H., Flury, J., Rummel, R., Schwintzer, P., Bosch, W., Haas, C., Schr¨oter, J., Stammer, D., Zahel, W., Miller,
H., Dietrich, R., Huybrechts, P., Schmeling, H., Wolf, D., Riegger, J., B´ardossy, A. and G¨untner, A., Mass Transport and
Mass Distribution in the Earth System, Contribution of the New Generation of Satellite Gravity and Altimetry Missions to
Geosciences, Technische Universit¨at M¨unchen and GeoForschungsZentrum Potsdam, 2004.
3. ESA, The Science and Research Elements of ESA’s Living Planet Programme, ESA SP-1227, 1998.
4. Chandrasekhar, S., Ellipsoidal Figures of Equilibrium, New Haven, CT, Yale University Press, 1969.
5. Lithgow-Bertelloni, C. and M. A. Richards, ”Dynamics of Cenozoic and Mesozoic plate motions”, Reviews of Geo-
physics 36, 1998
6. Sturges, W., ”Sea level slope along continental boundaries”, J. Geophys. Res. 79:825-830, 1974.
7. Fisher, I., ”Does sea level slope up or down towards north?”, Bulletin G´eod´esique 115:17-26, 1974.
8. Cabanes, C., A. Cazenave and C. Le Provost, ”Sea level changes from TOPEX/POSEIDON altimetry for 1993-1999,
and warming of the southern oceans”, Geophys. Res. Lett., 28:9-12, 2001.
9. Cox, C.M. and B.F. Chao, ”Detection of a large scale mass redistribution in the terrestrial system since 1998”, Science,
297:831-833, 2002.
10. Cazenave, A. and S. Nerem, ”Redistributing Earth’s Mass”, Science 297:783-784, 2002.
11. Dickey, J., S.L. Marcus, O. de Viron and I. Fukumori, ” Recent Earth oblateness variations: unraveling climate and
postglacial rebound effects”, Science 298:1975-1977, 2002
12. Rummel, R., J. Flury, R. Haagmans, C. Hughes, P. Le Grand, J. Riegger, E. Schrama, N. Sneeuw, B. Vermeersen,
P. Woodworth, Scientific Objectives for Future Geopotential Missions, Technical Note, ESA Contract 1/3962/01/NL/GS,
2004.
13. Beutler, G., R. Rummel, M.R. Drinkwater and R. von Steiger (eds.), Earth Gravity Field from Space - from Sensors
to Earth Sciences, Space Science Series of ISSI, Kluwer 2003.

---