Environmental Geodesy
Lecture 8 (March 22, 2011): Observing Earth's gravity field
-Introduction
-CHAMP
-GRACE
-GOCE
-Perspective
Introduction
Important quantity of the gravity field: the geoid
Relevance of the geoid:
- constitutes the surface known as 'sea level' in land surveying;
- topographic heights are related to the geoid (heights above 'sea level');
- for transformation of ellipsoidal heights to topographic heights, geoid
undulations have to be subtracted, i.e., geoid has to be known with the same
accuracy as ellipsoidal heights;
- dynamic sea surface topography is deviation of sea surface from geoid;
- time variations in geoid are related to mass relocation.
Introduction
Definition of geoid height above ellipsoid:
Determination of N from observations of gravity:
where
can be determined from gravity observations and leveling.
Introduction
Initially, gravity was measured in situ, airborne or shipborne and combined with
leveling (in situ) and tracking (ship, airplane)
Introduction
Problems:
- difficult to measure gravity and topographic height (leveling) on the whole
Earth surface;
- long wave length have large errors (due to leveling);
- theory is first order;
Advantage:
- high spatial resolution for short wave length.
Improvements:
- use of satellite orbit perturbations;
Satellite Orbit Perturbations
- Since 1975, global models of the gravity field at the surface of the Earth are
derived from observed satellite orbit perturbations.
- Due to insufficient data coverage and non-optimized orbit configurations,
tracking data from many satellites have to be merged together.
- Satellite-only models represent, due to the attenuation of the signal at orbit
altitude, the broad structure of the global field.
- Adding terrestrial gravity measurements and altimetry data over the oceans
allows to resolve smaller signatures of the Earth's gravity field.
Satellite Orbit Perturbations
EGM-96 geoid error from covariance matrix to degree and order 70.
Moore P et al. Phil. Trans. R. Soc. A 2006;364:1009-1026
©2006 by The Royal Society
Satellite Orbit Perturbations
GRIM Model
Year S/C Data
GRIM5-S1 1999 S
21 satellites
GRIM5-C1 2000 C
21 satellites, surface gravity, altimetry
Satellite Orbit Perturbations
CHAMP
CHAllenging Minisatellite Payload (CHAMP):
- German small satellite mission for geoscientific and atmospheric research
and applications, managed by GFZ, Potsdam
- payload elements: magnetometer, accelerometer, star sensor, GPS receiver,
laser retro reflector, ion drift meter
- orbit characteristic: near polar, low altitude, long duration (End of mission:
September 19, 2010, after ten years, two month and four days, after 58277
orbits).
CHAMP
CHAMP gravity:
- dedicated orbit design,
- an unpreceded low altitude in a near-polar orbit,
- continuous GPS satellite-to-satellite tracking capability;
- direct on-board measurement of the non-gravitational orbit perturbations
Result:
- an improvement of up to two orders of magnitude in accuracy of the broad to
mesoscale structures of the Earth gravity field.
CHAMP
EIGEN-2: Six months CHAMP only; gravity anomaly
European Improved Gravity model of the Earth by New techniques (EIGEN)
CHAMP
EIGEN-2: Six months CHAMP only; geoid height
CHAMP
EIGEN-CHAMP03S: 33 months CHAMP only; gravity anomaly
CHAMP
EIGEN-CHAMP03S: 33 months CHAMP only; geoid height
GRACE
GRAVITY Recovery And Climate Experiment (GRACE):
"The primary Science Objective of the GRACE mission is to provide with
unprecedented accuracy, global and high-resolution estimates of the constant
and time-variable part of the Earth's gravity field."
- USA-German joint mission;
- Launched in March 2002, expected life time already exceeded by far;
- Twin satellites, dedicated to the measurement of the time-variable gravity
field;
- maps the Earth's gravity field by making accurate measurements of the
distance between the two satellites, using GPS and a microwave ranging
system.
GRACE
Typical GRACE Science Applications are the improved knowledge of the mean
geoid, which will lead - in conjunction with altimetry and in-situ data - to
significant advances in oceanographic, geodetic or solid Earth science studies
such as
* oceanic heat flux,
* long term sea level change,
* upper oceanic heat content,
* absolute surface geostrophic ocean currents or
* precise positioning, orbit determination and leveling.
Estimates of time variable components of the gravity field will help for a better
understanding of time variable processes in oceanography, hydrology,
glaciology or solid Earth sciences like
* deep ocean current changes,
* large-scale evapotranspiration,
* soil moisture changes,
* mass balance of ice sheets and glaciers,
* changes in the storage of water and snow of the continents,
* mantle and lithospheric density variations,
* postglacial rebound or
* solid Earth's isostatic response.
GRACE
GRAVITY Recovery And Climate Experiment (GRACE)
Geoid, published in July 2003
(a) Gravity anomaly map derived from 39 days of
GRACE data (EIGEN-GRACE01S model).
(b) Gravity anomaly map derived from tracking
data of 30 Earth orbiting satellites over more
than 20 years (GRIM5-S1)
Moore P et al. Phil. Trans. R. Soc. A 2006;364:1009-1026
©2006 by The Royal Society
GRACE
Limiting factors for GRACE gravity field determination:
- sensor accuracy
- disturbances
- spatial-temporal sampling
- parameterization, modeling, representation
GRACE
GRACE
GRACE
GRACE
GRACE
GRACE
GRACE
GRACE
http://grace.jpl.nasa.gov/information/
Satellite Gravity Missions (GRACE)
GRACE Hydrology Products Versus University of Washington Hydrology Data
Rodell et al., 2010
Land Surface Water Storage
- Uncertainties from one to
several decimeters;
- Combination of GRACE and
satellite altimetry provide
information on groundwater
changes.
Examples from Calmant et al., 2011
GRACE
Daily solutions using Kalman smoothing
Left: RMS of the time variabilities of the daily Kalman solutions.
Right: Daily water storage variations in the Congo basin calculated from ITG-Grace2010.
From: http://www.igg.uni-bonn.de/apmg/index.php?id=itg-grace2010
GOCE
Gravity Field and Steady-State Ocean Circulation Explorer (GOCE):
- ESA satellite;
- launched on March 17, 2009;
- carries a highly sensitive gravity gradiometer;
- fly in an unusually low orbit (operational altitude 270 km);
- short mission lifetime: In November, 2010, it was decided to extend the
mission lifetime of 18 months, untill the end of 2012.
Mission objectives
* To determine gravity-field anomalies with an accuracy of 10−5 ms−2 (1 mGal).
* To determine the geoid with an accuracy of 1–2 cm.
* To achieve the above at a spatial resolution better than 100 km.
From: http://www.esa.int/SPECIALS/GOCE/index.html
GOCE
Main payload:
Electrostatic Gravity Gradiometer (EGG):
- Three pairs of ultra-sensitive accelerometers arranged in three dimensions;
- The different position in the gravitational field leads to slightly different
gravitational acceleration;
- The three axes of the gradiometer allow the simultaneous measurement of
the five independent components of the gravity gradient tensor.
Other payload:
- onboard GPS receiver used as a Satellite-to-Satellite Tracking Instrument
(SSTI);
- a compensation system for all non-gravitational forces acting on the
spacecraft.
- laser retroreflector to enable tracking by ground-based lasers.
GOCE
First global gravity model based on only two months of GOCE data, from
November and December 2009. From
http://www.esa.int/SPECIALS/GOCE/SEMQC9VTLKG_1.html.
GOCE
Mean dynamic topography of the world oceans (in metres) derived from an
altimetric sea-surface model combine with a model of the geoid based on just
two months of GOCE data. From
http://www.esa.int/esaLP/SEMCJOSRJHG_LPgoce_1.html
Perspective
Improvement of the Earth’s gravity field models. From top left to bottom right:
- GRIM-5S1: Best model prior to CHAMP and GRACE, SLR data only;
- EIGEN-CHAMP03S: Gravity field from CHAMP;
- EIGEN-GRACE03S: Gravity field from GRACE;
- EIGEN-CG03C: Gravity field from GRACE combined with terrestrial data.
Source Reigber et al. (2005).
Perspective