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Classically, vertical reference frames were realized as national or continent-wide networks of geopotential differences derived from geodetic leveling, i.e., from the combination of spirit leveling and gravimetry. Those networks are affected by systematic errors in leveling, leading to tilts in the order of decimeter to meter in larger networks. To...
Die genaue Bestimmung der Großform der Erde und die Errichtung eines weltweit einheitlichen Bezugssystems sind dank der im 20. Jahrhundert entwickelten Verfahren in greifbare Nähe gerückt.
Since Kepler, Newton and Huygens in the seventeenth century, geodesy has been concerned with determining the figure, orientation and gravitational field of the Earth. With the beginning of the space age in 1957, a new branch of geodesy was created, satellite geodesy. Only with satellites did geodesy become truly global. Oceans were no longer obstac...
Satellite gravimetry began with the launch of the satellites Sputnik 1 and 2 in 1957. During the following 43 years, more
and more details were discovered and the models of the Earth’s gravity could be refined. Methods improved and more and
more satellite orbits and ground stations were added in the analysis, employing more advanced and precise mea...
The effects of temporal changes in the marine geoid on estimates of the ocean dynamic topography are being investigated. Influences from mass redistribution due to changes of land hydrology, ice sheets, glacial isostatic adjustment (GIA), and ocean and atmospheric dynamics are considered, and the associated crustal deformation is included. The stro...
Satellite Gravitational Gradiometry (SGG) is an observational technique of globally establishing the fine structure and the characteristics of the external Earth’s gravitational field. The “Gravity field and steady-state Ocean Circulation Explorer” GOCE (2009–2013) was the first satellite of ESA’s satellite program intended to realize the principle...
Satellite gravimetry began with the launch of the satellites Sputnik 1 and 2 in 1957. During the following 43 years, more and more details were discovered and the models of the Earth’s gravity could be refined. Methods improved and more and more satellite orbits and ground stations were added in the analysis, employing more advanced and precise mea...
General ocean circulation models are not perfect. Forced with observed atmospheric fluxes they gradually drift away from measured distributions of temperature and salinity. We suggest data assimilation of absolute dynamical ocean topography (DOT) observed from space geodetic missions as an option to reduce these differences. Sea surface information...
Höhensysteme werden klassischerweise durch nationale oder regionale Nivellementnetze realisiert. Dem Verfahren des geometrischen Nivellements sind allerdings einige inhärente Nachteile zu eigen, die das Verfahren – gemessen an den heutigen Ansprüchen an Genauigkeit und Effizienz – für großräumige oder gar globale Anwendungen ungeeignet machen. Mode...
Comparisons between high-degree models of the Earth’s topographic and gravitational potential may give insight into the quality and resolution of the source data sets, provide feedback on the modelling techniques and help to better understand the gravity field composition. Degree correlations (cross-correlation coefficients) or reduction rates (qua...
Das Handbuch der Geodäsie ist ein hochwertiges, wissenschaftlich fundiertes Werk über die Geodäsie unserer Zeit und bietet anhand von in sechs Bänden zusammengestellten Einzelthemen ein repräsentatives Gesamtbild des Fachgebiets.
Die Herausgeber des Gesamtwerks
Professor Dr. Willi Freeden studierte Mathematik und Geographie an der RWTH Aachen. Dort...
Satellite-only gravity fields and surface gravity obtained from altimetric measurements now agree well at wavelengths greater than ~180 km. Satellite gravity fields can therefore be used to estimate the elastic thickness Te in regions where surface observations are sparse. They are used for this purpose in a number of continental regions, of India,...
describes and compares methods of geoid computation from spherical harmonics and terrestrial mean gravity anomalies
describes and compares methods of geoid computation from spherical harmonics and terrestrial mean gravity anomalies
Spring 2009 the satellite Gravity and steady-state Ocean Circulation Explorer (GOCE), equipped with a gravitational gradiometer, was launched by European Space Agency (ESA). Its purpose is the detailed determination of the spatial variations of the Earth's gravitational field, with applications in oceanography, geophysics, geodesy, glaciology, and...
Höhensysteme werden klassischerweise durch nationale oder regionale Nivellementnetze realisiert. Dem Verfahren des geometrischen Nivellements sind allerdings einige inhärente Nachteile zu eigen, die das Verfahren – gemessen an den heutige Ansprüche an Genauigkeit und Effizienz – für großräumige oder gar globale Anwendungen ungeeignet machen. Modern...
Detailed analyses of the original GOCE data have shown that specific improvements can be achieved by a Level 1b (L1b) processor update Stummer et al. (2011, 2012). In the first part of this work the four processor update steps are discussed, and the impact on GOCE gravity fields is shown. The largest improvements occur in the lower spherical harmon...
Spring 2009 the satellite Gravity and steady-state Ocean Circulation Explorer (GOCE), equipped with a gravitational gradiometer, was launched by European Space Agency (ESA). Its purpose is the detailed determination of the spatial variations of the Earth’s gravitational field, with applications in oceanography, geophysics, geodesy, glaciology, and...
The cold upper part of the lithosphere can support the elastic stresses that govern rigid plate movements and support the Earth's topography. In many regions the thickness Te of the layer involved can be estimated from the relationship between surface gravity measurements and topography. However, there are extensive regions of the continents where...
The ocean north of the Antarctic continent is one of the most dynamic ocean areas on our globe. It is also critical for the regulation of the global climate.We compute a high resolution mean dynamical ocean topography (MDT) using geodetic data and derive a detailed model of the global ocean circulation in this crucial area. The MDT is determined us...
The basis of geodetic science is its measurements. It is a geodetic trademark to present measured results always together with their estimates of accuracy and reliability. This diligence explains the geodesist's role as notary of our earth. Space age, automation and new measurement methods have opened fundamentally new opportunities. One could say:...
Four new gravity field models from GOCE, two of them combined with GRACE, are compared here with EGM2008. The objectives are to look into the differences in consecutive ranges of the spherical harmonic expansion globally as well as in selected geographical regions and in the regions of the various data sources used for EGM2008. In general, GOCE is...
“What’s up?” is a question that is answered by the gravity field. Gravity not only determines what is up and down but also reflects the Earth’s mass distribution and its changes with time. Since the launch of Sputnik in 1957, global models of the Earth’s gravity field of reasonable quality were determined from satellite
orbit tracking of irregularl...
New GOCE gravity field models based on about 2 years of completely
reprocessed gradiometer data have been recently released to the user
community. They were obtained based on different processing strategies
and reflect the state-of-the-art of GOCE gravity field models. With the
improved gravity gradients resulting from a number of updates
implement...
A gravity field model is computed from the four accurate gravitational gradient components of GOCE (Gravity field and steady-state Ocean Circulation Explorer), combined with the analysis of the kinematic orbits, and some moderate constraint (or stabilization) in the polar areas where no observation from GOCE is available due to the orbit geometry....
With the gravity field and steady-state ocean circulation explorer
(GOCE) (preferably combined with the gravity field and climate
experiment (GRACE)) a new generation of geoid models will become
available for use in height determination. These models will be globally
consistent, accurate ( < 3 cm) and with a
spatial resolution up to degree and orde...
The magnetic field mission Swarm, expected to be launched in 2012, comprises a constellation of three satellites. As all of them are equipped with GPS receivers and accelerometers, they can be used for gravity field recovery. We study the capability of a Swarm-like constellation for (time-variable) gravity field recovery and compare it with a gravi...
A mean dynamic ocean topography (MDT) has been computed using a high
resolution GOCE (Gravity field and steady-state Ocean Circulation
Explorer) gravity model and a new mean sea surface obtained from a
combination of satellite altimetry covering the period 1992 October till
2010 April. The considered gravity model is GO-CONS-GCF-2-TIM-R3, which
com...
Estimation of ocean circulation is investigated via assimilation of satellite measurements of the dynamic ocean topography (DOT) into the global finite-element ocean model (FEOM). The DOT was obtained by means of a geodetic approach from carefully cross-calibrated multi-mission altimeter data and GRACE gravity fields. The spectral consistency was a...
A number of global gravity field models based on GOCE data have been
produced by ESA's High Level Processing Facility (HPF) and by a few
other teams. The models mainly differ by the amount of GOCE data used
and by the a-priori information applied. ESA released two model series.
One is purely based on GOCE data showing the value of GOCE gravity
grad...
In this work we examine the impact of assimilation of multi-mission-altimeter data and the GRACE/GOCE gravity fields into the finite element ocean model (FEOM), with the focus on the Southern Ocean circulation. In order to do so, we use the geodetic approach for obtaining the dynamical ocean topography (DOT), that combines the multi-mission-altimet...
Die Geodäsie beschäftigt sich seit Kepler, Newton und Huygens im 17. Jahrhundert mit der Bestimmung von Figur, Orientierung und Gravitationsfeld der Erde. Mit dem Beginn des Raumfahrtzeitalters im Jahr 1957 entstand ein neuer Zweig der Geodäsie, die Satellitengeodäsie. Erst durch den Einsatz von Satelliten wurde die Geodäsie wirklich global, Ozeane...
A gravity field model is estimated from the four accurate components of
GOCE (Gravity field and steady-state Ocean Circulation Explorer)
gradiometer, combined with kinematic orbit measurements, and some
moderate constraint (or stabilization) in the polar areas where no
observation from GOCE is available due to the orbit geometry. The normal
matrix...
One of the main objectives of ESA’s Gravity Field and Steady-State Ocean Circulation mission GOCE (Gravity field and steady-state ocean circulation mission, 1999) is to allow global unification of height systems by directly providing potential differences between benchmarks in different height datum zones. In other words, GOCE provides a globally c...
The CHAMP satellite, equipped with a GPS receiver and an accelerometer, has yielded an enormous increase in accuracy of global satellite-only gravity field models and it has proved the concept of high-low satellite to satellite tracking (SST) for gravity field recovery. Therefore, we are interested whether the Swarm mission, consisting of three CHA...
Before addressing GGOS issues we briefly introduce the modern understanding of geodesy and we review the development of geodesy as a science. This background is required to understand the motivation behind the development the International Association of Geodesy’s Global Geodetic Observing System (GGOS).
The article then reviews the development of...
GOCE will allow the determination of geoid heights with an accuracy of
1-2cm and spatial resolution of about 100 km. An important application
that will benefit from this is the global unification of the (over 100)
existing height systems. GOCE will provide three important components of
height unification: highly accurate potential differences (geop...
One of the science objectives of the satellite gradiometry mission GOCE
is global unification of height systems. The aim is thereby to refer all
national and regional height systems to one common vertical datum. The
most obvious method of datum unification is the determination of gravity
potential values at the various datum points by solving the G...
In 2009 the European Space Agency satellite mission GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) was launched.
Its objectives are the precise and detailed determination of the Earth’s gravity field and geoid. Its core instrument, a three
axis gravitational gradiometer, measures the gravity gradient components V
xx
, V
yy
, V...
In this work we examine the impact of assimilation of multi-mission-altimeter data and the GRACE/GOCE gravity fields into the finite element ocean model (FEOM), with the focus on the Southern Ocean circulation. In order to do so, we use the geodetic approach for obtaining the dynamical ocean topography (DOT), that combines the multi-mission-altimet...
GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) is one of the four selected ESA Earth Explorer Missions (Phase A has started in summer 1998). The main objective of GOCE is the determination of the Earth’s gravity field with high spatial resolution and with high homogeneous accuracy. For this purpose, two observation concepts will b...
Gravity field modeling in the case of GOCE is based on a combination of
the SST contribution for the low wave- length part and on gravitational
gradiometry for the spatial details. The gradiomter part of the solution
is derived from a combination of the gradient components Vxx, Vyy , Vzz
. Variance components in the domain of spherical harmonics al...
Estimation of ocean circulation is investigated via assimilation of satellite measurements of dynamical ocean topography (DOT) into the global finite-element ocean model (FEOM). The DOT was obtained by means of geodetic approach from carefully cross-calibrated multi-mission- altimeter data and GRACE/GOCE gravity fields. The spectral consistency was...
The GRACE mission has been providing time-variable gravity field solutions for nearly a decade, which are widely used in hydrology, oceanography and solid earth research. As GRACE has already passed its designed life time and the follow-on missions are still in development, there will be likely a gap in between, following an eventual failure of GRA...
One of the most important and likewise most complex parts of the GOCE gradiometer processing is the determination of the angular velocities of the spacecraft about the gradiometer axes. In the nominal GOCE processing this step is called angular rate reconstruction. It is done by combining gradiometer and star sensor attitude information. The gradio...
With the GOCE satellite launched on March 17th 2009, a huge amount of measurements are collected and a gravity field of high accuracy and resolution can be recovered. In order to evaluate the quality of the gradiometer measurements, a small set of original GOCE data are compared with reference values from the EGM08 gravity field model up to a compa...
The GOCE mission provides gravity gradients as a new type of observation
of the Earth gravity field. The gradients are derived from acceleration
differences. The gradiometer consists of three orthogonal pairs of
accelerometers, each with a base length of half a meter. The orbits are
derived from GPS. Several processing steps are required for their...
GOCE has been launched on March 17, 2009. It is the first satellite of ESA’s Living Planet Programme. It is aiming at a better
understanding of the Earth system. The mission objective of GOCE is the determination of the Earth’s gravity field and geoid
with high accuracy and maximum spatial resolution. The geoid, combined with the actual mean ocean...
In 1988 the interdisciplinary role of space geodesy has been discussed by a prominent group of leaders in the fields of geodesy and geophysics at an international workshop in Erice (Mueller and Zerbini, 1989). The workshop may be viewed as the starting point of a new era of geodesy as a discipline of Earth sciences. Since then enormous progress has...
GOCE is the first gravitational gradiometry satellite mission. Gravitational gradiometry is the measurement of the second
derivatives of the gravitational potential. The nine derivatives form a 3 × 3 matrix, which in geodesy is referred to as Marussi
tensor. From the basic properties of the gravitational field, it follows that the matrix is symmetr...
The geoid models from GRACE and soon GOCE in combination with sea surface geometry data from satellite altimetry allow to
obtain a precise estimate of the absolute dynamic sea surface topography with rather high spatial resolution. However, this
requires the combination of data with fundamentally different characteristics and different spatial reso...
Estimation of ocean circulation via assimilation of satellite measurements of dynamical ocean topography (DOT) into the global finite-element ocean model (FEOM) is investigated. The DOT was obtained by means of geodetic approach from carefully cross-calibrated multi-mission-altimeter data and GRACE gravity fields. The spectral consistency was achie...
The Gravity field and steady-state Ocean Circulation Explorer (GOCE)
mission is the first Earth Explorer Core mission of the Living Planet
Programme of the European Space Agency (ESA). The primary objective of
the GOCE mission is to provide global and regional models of the Earth
gravity field and the geoid, its reference equi-potential surface, wi...
Geoid models from the new generation of satellite gravity missions, such as GRACE and GOCE, in combination with sea surface
from satellite altimetry allow to obtain absolute dynamic ocean topography with rather high spatial resolution and accuracy.
However, this implies combination of data with fundamentally different characteristics and different...
Before the background of more accurate and denser gravity data it is worthwhile to reassess geodetic isostasy. Currently,
in geodesy isostatic models are primarily applied to gravity reduction as needed by geoid and gravity modeling. The selection
of the isostatic model is based on four criteria: Isostatically reduced gravity anomalies should be (1...
The separation between the reference surfaces for orthometric heights and normal heights—the geoid and the quasigeoid—is typically
in the order of a few decimeters but can reach nearly 3m in extreme cases. The knowledge of the geoid–quasigeoid separation
with centimeter accuracy or better, is essential for the realization of national and internatio...
The complexity of the Earth system has been discussed in many fundamental documents in recent years. Trying to understand the Earth system and improve our forecast capability step by step are the great challenges of Earth system science. The opening sentence of the recent NRC report “Earth Science and Applications from Space: Urgent Needs and Oppor...
This chapter is concerned with the implementation of GGOS, addressing mainly the organizational aspects mentioned in Section.1.3 GGOS monitors and maintains the geometric and gravimetric reference frames, and provides the transformation between these systems with state-of-the-art observational tools. In doing so, GGOS provides the observational bas...
In this Chapter, we summarize the recommendations of the GGOS 2020 Writing Team. The recommendations are numbered, with the first number indicating the chapter from which a recommendation originates.
Ungenaue Atmosphärendaten (insbesondere der Bodendruck) haben Auswirkungen auf berechnete Schwerefelder der Erde.
A few months ago the GOCE mission went onto its science operation mode. Since then, the High level Processing Facility, which is responsible for the generation of the orbit and gravity field products from GOCE, is analyzing the data and thereby contributing to the optimization of the ground processing. Currently, systematic processing of GPS-tracki...
With GOCE we expect to observe the Earth gravity field with very high accuracy and spatial resolution by gravity gradiometry. Preparing gradiometric observations and processing GOCE data to global gravity field solutions is a great challenge to geodetic research. Further, the GOCE gravity data and models will enable a set of new applications in Ear...
Least-squares adjustment is a very common and effective tool for the calculation of global gravity field models in terms of spherical harmonic series. However, since the gravity field is a continuous field function its optimal representation by a finite series of spherical harmonics is connected with a set of fundamental problems. Particularly wort...
GOCE has been launched on March, 17, 2009. It is the first satellite of the Living Planet Programme, which is ESA's Earth science programme. It is aiming at a better understanding of the Earth system. The mission objective of GOCE is the determination of the Earth's gravity field and geoid with high accuracy and maximum spatial resolution. The geoi...
Research on global gravity field recovery from satellite missions such as CHAMP and GRACE was initiated at the Astronomical Institute of the University of Bern (AIUB, Switzerland) in the year 2006. Since September 2007, the activities were extended in the framework of the project Satellite Geodesy sponsored by the Institute for Advanced Study (IAS)...
By the time of the Fall Meeting the GOCE mission is expected to have been in orbit for a couple of months. This paper describes the initial in-orbit experience with the satellite and its instrumentation, focussing on the commissioning and calibration activities. Also described are the first data processing efforts, including a very preliminary esti...
“Geodesy” is a term coined by the Greeks in order to replace the original term “geometry”, which had meanwhile lost its original
meaning of “earth or land measuring” (surveying) and acquired the new meaning of an abstract “theory of shapes”. Aristotle
tells us in his “Metaphysics” that the two terms differ only in this respect: “Geodesy refers to t...
Geophysical and geodetic inverse problems are often ill posed. They are smoothed to guarantee stable solutions. Geophysical and geodetic applications of smoothness techniques like Tikhonov's regularization method seem to have been limited to one realization of sampling. However, smoothness (or ridge) parameters are data related but empirically chos...
The five independent components Γxz, Γyz, Γzz, Γxx - Γyy, and Γxy, of the gravity tensor are measurable by gradiometers. When grouped into {Γzz}, {Γxz, Γyz} and {Γxx - Γyy, 2Γxy} and expanded into an infinite series of pure-spin spherical harmonic tensors, simple eigenvalue connections can be derived between these three sets and the spherical harmo...
The science requirements on future gravity satellite missions, following from the previous contributions of this issue, are
summarized and visualized in terms of spatial scales, temporal behaviour and accuracy. This summary serves the identification
of four classes of future satellite mission of potential interest: high-altitude monitoring, satelli...
Purpose of this article is to demonstrate the effect of background geophysical corrections on a follow-on gravity mission.
We investigate the quality of two effects, tides and atmospheric pressure variations, which both act as a surface load on
the lithosphere. In both cases direct gravitational attraction of the mass variations and the secondary p...
After GRACE and GOCE there will still be need and room for improvement of the knowledge (1) of the static gravity field at
spatial scales between 40 km and 100 km, and (2) of the time varying gravity field at scales smaller than 500 km. This is
shown based on the analysis of spectral signal power of various gravity field components and on the compa...
GOCE is an ESA mission to be launched in summer 2007 and dedicated to
the precise mapping of the Earth's gravity field. Measuring the
quasi-static gravity field with an increased spatial detail resolution,
it is complementary to the GRACE mission. The integration of the GOCE
platform and instrumentation, and the preparations of the ground segment
a...
The mission objectives of GOCE in terms of geoid and gravity accuracy and spatial resolution are extremely high. This poses a great challenge for the development of the on-board sensor systems and spacecraft as well as for data analysis. Current research activities concentrate on the combination of satellite altimetry with the GOCE geoid for a dete...
The GOCE High-level Processing Facility (HPF) is in charge of the production of the following final level 2 products: Calibrated and corrected gravity gradients, precise science orbits and global gravity field models. These products represent the main input to all further applications of GOCE. In order to correctly apply these products the user has...
Within the national German geoscientific research and development programme "GEOTECHNOLOGIEN", funded by the Federal Ministry of Education and Research (BMBF) and the German Research Foundation (DFG), the research theme "Observation of the System Earth from Space" was selected as one of 13 key areas in this programme. During the first research phas...
GOCE will be the first satellite mission equipped with a gravity gradiometer. In order to achieve maximum precision and spatial resolution, the instrument is guided around the Earth in an extremely low orbit, employing active along track drag-free control and angular control by magnetic torquers. Furthermore, the orbit trajectory is determined very...
The International Association of Geodesy has decided to establish an Integrated Global Geodetic Observing System (IGGOS). The objective of IGGOS is to integrate in a well-defined global terrestrial reference frame the three fundamental pillars of geodesy, which are the determination of all variations of surface geometry of our planet (land, ice and...
This short note reviews our thinking on how IGGOS can best achieve a high status within the set of global monitoring programmes. If such a high status can be obtained, then the importance of geodetic networks and services will be recognized more widely, and their activities will consequently be better resourced in the long term. One particular aspe...
A full year of champ gravity field solutions has been calculated using the energy integral approach. The monthly solutions in the time frame 03.2002–02.2003
were based solely on kinematic orbits from champ gps orbit tracking and accelerometry. These kinematic orbits have not been contaminated by a priori gravity field information.
Recovery of medi...
In march 2002 the satellite mission GRACE was launched with the objective to map the Earth's gravity field with high spatial and temporal resolution. The mission is de-signed to detect temporal changes in the gravity field from a series of monthly global potential models. This requires highly accurate sensors and sophisticated data processing techn...
We have used one year of CHAMP data for deriving a gravity fleld model based on the energy balance approach. In order to avoid the use of any a priori gravity information, purely kinematic orbits have been computed from GPS measurements only. Subsequently velocities have been derived from these kine- matic positions by two difierent methods, namely...
