ESA wishes a study of the refinement of the current observation requirements
of the GOCE Mission.
The aim is to study in some more detail than already done (cf. Ref A: ESA,
SP-1196, 1996) the relationship between the precision of a gravity
field model and the solution of different tasks, where the gravity field
plays a major role.
In the following it will be supposed that the
quality of the gravity field model is expressed through a variance-
covariance matrix of the spherical harmonic coefficients. From this matrix
the precision of derived quantities like geoid undulation differences and
gravity anomalies can be expressed. Due to the limited time of the project,
it may be necessary to work with only a diagonal matrix.
So, the observation requirements are expressible as a function of the
elements of this variance-covariance matrix through covariance propagation.
Information about the structure of such a matrix is available from earlier
spherical harmonic models and recent simulations.
Observation requirements are derived from applications of gravity field
information in three areas: oceanography, geodynamics (including
glaciology) and geodesy. Deliverables will be specified in each area.
Consequently the project includes experts in these three fields. The
following groups of experts have agreed to participate:
University of Copenhagen Goup (UCph):
C.C.Tscherning, UCph, Denmark, with D.Arabelos (AUT, Greece) and
F.Sanso' (POLIMI, Italy)
National Survey and Cadastre, (Denmark), (KMS).
O.Balt. Andersen, R.Forsberg, P.Knudsen (KMS, Denmark)
University of Milano Group (UM):
R.Sabadini, and 2 co-wokers (UM, Italy),
In the following each task and the associated deliverable will be described
and discuss the content of the proposed work-packages.
Task 1. Project Management. UCph.
Faculty of Science, International Secretariate and Department of
Geophysics.
Task 2. Creation of a Monte-Carlo type simulator of spherical harmonic
coefficient (SHC) errors as a function of a prescribed geoid or gravity
error and corresponding spatial resolution (see the table ref. A, p. 48).
WP 2.1 Monte-Carlo Simulator. Responsible UCph. WP manager: C.C.Tscherning.
The spherical harmonic field, EGM98 (Wenzel, 1998) completer to degree and
order 1800 will be used as the "true" gravity field, and the simulated
fields will be pertubations of this field. A random number generator will
generate pertubations with given standard deviation per spherical
harmonic degree. The models will be used to generate geoid and gravity
anomaly fields in geographical areas chosen in other workpackages.
Software partially developed in earlier CIGAR projects will be used.
Personel: C.C.Tscherning, D.Arabelos.
Output: Report and software with i/O examples.
Task 3. Refined observation requirements. Coordinator: C.C.Tscherning.
WP 3.1: Oceanography. A report of how geoid + altimetry can improve
estimates of dynamic ocean topography will be prepared. The improvement
depends on to which extend a level of no motion (the geoid) can be defined.
Responsible: KMS. WP Manager P.Knudsen.
WP 3.1.1. Study (through simulations) the relationship between the
improvements of the geoid as a function of wavelength (coefficient
variances) and the errors in current velocities obtained using the
geostrophic assumption. Three different senarios (areas) will be selected,
where the current velocities are high, medium and low. Responsible:
Ole Andersen.
WP 3.1.2. Improvement under non-geostrophic conditions. Extra information is
needed, e.g. from drifters, and an oceanographic model (with assumptions of
temperature, salinity and bottom topography included). Such a model
is available and will be used in 3 areas where large bathymetric, temperature
or salimity variations may cause non-geostrophic conditions.
In such a study we will show how geoid and altimetry knowledge together
with auxiliary data may reduce the uncertainty of the deep circulation.
This is a quite difficult task, at the edge of current research.
Responsible: P.Knudsen, Ole Andersen.
Task 3.2: Geodynamics. A report should here summarize how improved gravity
field information may improve estimates of the processes inside the Earth.
Task manager: R.Sabadini, UM.
WP. 3.2.1. Study of the influence of gravity field model errors on models
of the thermal structure. Different 5 deg. x 5 deg .areas with known rheology variations
are selected. Grids of gravity and geoid heights will be delivered from
WP 2.2. Corresponding topography will be calculated from SHC of topography
or equivalent rock-equivalent topography.
Personel: R.Sabadini & co-workers.
WP 3.2.2. Study of the influence of gravity field errors on post-glacial
rebound models.
The study of post-glacial rebound is also aided by improved gravity
information. The aid comes today from better viscosity estimates in areas
of post-glacial rebound. Like in WP 3.2.1 such estimates can be improved
from gravity
Isostacy and mass balance can be studied by determining transfer-functions
between gravity and topography. The precision of such transfer-functions
(related to depths of compensation) will depend on the quality of the gravity
field information. A study will be carried out using input from WP 2.1.
as well as from the rock-equivalent topography values. (Made available
by H-G. Wenzel, Karlsruhe).
The feasability of using the collocation method implemented by P.Knudsen
in "grcol" will be studied. This method delivers uncertainty estimates on
values of isostatic compensation depths and of deeper interfaces.
Personel: R.Sabadini & Co-wokers, aided by P.Knudsen & D.Arabelos.
Task 3.3: Geodesy. Manager R.Forsberg, KMS.
WP 3.3.1. The influence of the SHC on the establishment of
a world-wide height system can be studied as a function of supposed
error-variances of the coefficients. The geoid-height difference precision
can be calculated for various distances and in various senarious (high, medium
high and low gravity field variation). The basic input is again the variance
covariances of the coefficients, which we can vary by a scale-factor.
(Input from WP 2.1).
Personel: R.Forsberg, D.Arabelos.
WP 3.3.2. Study of the influence on levelling by GPS.
This is a very local process, which will be studied by seeing how local
gravity becomes more and more correlated with the geoid heights, when a
more precis egravity field model is used in a remove-restore procedure.
Personel: R.Forsberg, D.Arabelos, C.C.Tscherning.
WP 3.3.3. Study of the influence on inertial navigation.
It can be studied under various senaries. The error due to velocity errors
(which depend on the quality of the gravity field model) will be integrated
for various supposed tracks. Here some of the senarios used earlier will be
used again. Input from WP 2.1.
Results for low-speed applications (ships, airplanes), medium speed
(commercial aircrafts) and high speed applications (rockets, missiles)
will be given. The error of improment will be expressed in terms of
error-growth in nm/hr.
Personel: R.Forsberg, D.Arabelos.
WP 3.3.4. Study of separation of steric/non-steric sea-level changes.
It is proposed to study the influende on the separation of steric from
nonsteric sea-level fluctations. This will be done by integration of
longer-wavelength phenomena. (HERE STILL SOME UNCERTINTY)
Personal: R.Forsberg with input from R.Sabadini.
WP 3.3.5. Study the influence on ice-mass balance.
Gravity and geoid data will be simulated for one or several areas in
Greenland where topographic models are well known.
The influence of the error in the SHC on mass-balance values will be
studied.
Personel: R.Forsberg with input from R.Sabadini.
New WP defined after project start:
WP 3.3.6. Study the influence on Depth Estimation from gravity.
Staff: D.Arabelos.
Last update 1999-02-23 by cct.