[1] The GRACE twin satellites reveal large inter-annual terrestrial water-storage variations between 2002 and 2003 for central Europe. GRACE observes a negative trend in regional water storage from 2002 to 2003 peaking at −7.8 cm in central Europe with an accuracy of 1 cm. The 2003 excess terrestrial water storage depletion observed from GRACE can be related to the record-breaking heat wave that occurred in central Europe in 2003. We validate the measurements from GRACE using two independent hydrological estimates and direct gravity observations from superconducting gravimeters in Europe. All datasets agree well with the GRACE measurements despite the disparity of the employed information; the difference between datasets tends to be within GRACE margin of error. The April-to-August terrestrial water storage depletion is found to be significantly larger in 2003 than in 2002 from both models and observations.

GRACE‐derived terrestrial water storage depletion associated with the 2003 European heat wave

This chapter is devoted to the superconducting gravimeter (SG) and its wide use in Earth sciences. The first part is merely instrumental: the history of the technical developments is first given followed by a precise description of the basic principles of operation. The instrument performances in terms of long-term drift, calibration stability, and precision are provided. Recent technical developments and user requirements for operating in an optimal way an SG station are reviewed. The second part deals with the SG data analysis. The various steps going from the raw observed gravity signal to the residual signal ready for geophysical investigation are described in detail: pre-processing (gaps, offsets), corrections for solid and ocean tides, atmospheric pressure effects. The importance of calibration issues (amplitude and phase) is emphasized. This second part ends with other corrections to the residual gravity due to polar motion, instrumental drift, and hydrology. The third part presents the scientific achievements using SGs. The Global Geodynamics Project (GGP) of the existing international network of SGs is first introduced and we point out the broad spectral range of geophysical phenomena (from 1s to several years) that can be investigated with SGs. We show how the extremely low noise in the long-period seismic band can be exploited to retrieve seismic normal modes. Special attention is paid to the search for the Slichter translational mode of the solid inner core in the subseismic band. The various approaches to model atmospheric loading in gravity are reviewed, as well as solid Earth tidal effects including the free core nutation resonance in the diurnal band. Ocean loading can also be investigated on a wide spectral range through the detection of nonlinear ocean tides (harmonics of the classical diurnal and semidiurnal tides) and the observation of long-period tides (fortnightly and monthly). The signature in SG data of nontidal ocean circulation, continental hydrology (soil moisture and groundwater), and Earth rotation effects all demonstrate the ability of these instruments to study seasonal and multiyear geodynamical processes. Some specific applications related to tectonics are shown. We also comment on the possibility of using surface gravity measurements with a regional network of SGs to validate satellite-derived gravity missions such as GRACE. A prospective of future possibilities using SGs in various fields ends this third part.

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Gravimetric Methods – Superconducting Gravity Meters

[1] In this paper we present results of a global gravity field recovery using half a year of CHAMP data. We use the energy integral of the motion of a satellite to transform satellite velocities into values of gravitational potential. The feasibility of this approach has already been demonstrated by several groups, using CHAMP reduced-dynamic orbits. We show, that the potential recovered from this kind of orbits depends on the a priori gravity field used for orbit determination. Thus, it cannot be excluded that errors present in the prior field propagate into the new CHAMP gravity model. It is the intention of this paper to avoid this dependency through the use of kinematic orbits, which are free from prior information. The derived potential model, TUM-1S, is validated by comparison to ground data and by satellite orbit residuals. It is shown to be comparable in quality to other state-of-the-art gravity field models.

A CHAMP-only gravity field model from kinematic orbits using the energy integral

A technique is proposed for Earth’s gravity field modeling on the basis of satellite accelerations that are derived from precise orbit data. The functional model rests on Newton’s second law. The computational procedure is based on the pre-conditioned conjugate-gradient (PCCG) method. The data are treated as weighted average accelerations rather than as point-wise ones. As a result, a simple three-point numerical differentiation scheme can be used to derive them. Noise in the orbit-derived accelerations is strongly dependent on frequency. Therefore, the key element of the proposed technique is frequency-dependent data weighting. Fast convergence of the PCCG procedure is ensured by a block-diagonal pre-conditioner (approximation of the normal matrix), which is derived under the so-called Colombo assumptions. Both uninterrupted data sets and data with gaps can be handled. The developed technique is compared with other approaches: (1) the energy balance approach (based on the energy conservation law) and (2) the traditional approach (based on the integration of variational equations). Theoretical considerations, supported by a numerical study, show that the proposed technique is more accurate than the energy balance approach and leads to approximately the same results as the traditional one. The former finding is explained by the fact that the energy balance approach is only sensitive to the along-track force component. Information about the cross-track and the radial component of the gravitational potential gradient is lost because the corresponding force components do no work and do not contribute to the energy balance. Furthermore, it is shown that the proposed technique is much (possibly, orders of magnitude) faster than the traditional one because it does not require the computation of the normal matrix. Hints are given on how the proposed technique can be adapted to the explicit assembling of the normal matrix if the latter is needed for the computation of the model covariance matrix.

A technique for modeling the Earth’s gravity field on the basis of satellite accelerations

Gravity recovery and climate experiment (GRACE)-derived temporal gravity variations can be resolved within the μgal (10−8 m/s2) range, if we restrict the spatial resolution to a half-wavelength of about 1,500 km and the temporal resolution to 1 month. For independent validations, a comparison with ground gravity measurements is of fundamental interest. For this purpose, data from selected superconducting gravimeter (SG) stations forming the Global Geodynamics Project (GGP) network are used. For comparison, GRACE and SG data sets are reduced for the same known gravity effects due to Earth and ocean tides, pole tide and atmosphere. In contrast to GRACE, the SG also measures gravity changes due to load-induced height variations, whereas the satellite-derived models do not contain this effect. For a solid spherical harmonic decomposition of the gravity field, this load effect can be modelled using degree-dependent load Love numbers, and this effect is added to the satellite-derived models. After reduction of the known gravity effects from both data sets, the remaining part can mainly be assumed to represent mass changes in terrestrial water storage. Therefore, gravity variations derived from global hydrological models are applied to verify the SG and GRACE results. Conversely, the hydrology models can be checked by gravity variations determined from GRACE and SG observations. Such a comparison shows quite a good agreement between gravity variation derived from SG, GRACE and hydrology models, which lie within their estimated error limits for most of the studied SG locations. It is shown that the SG gravity variations (point measurements) are representative for a large area within the accuracy, if local gravity effects are removed. The individual discrepancies between SG, GRACE and hydrology models may give hints for further investigations of each data series.

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Combination of temporal gravity variations resulting from superconducting gravimeter (SG) recordings, GRACE satellite observations and global hydrology models

. The energy conservation method is based on knowledge of the state vector and measurements of nonconservative forces. This is or will be provided by CHAMP, GRACE and GOCE. Here the analysis of one month of CHAMP state vector and accelerometer data is described. The energy conservation method is used to estimate the gravity potential at satellite altitude. When doing so we consider the tidal potential from the sun and the moon, the explicit time variation of the gravity potential in inertial space and loss of energy due to external forces. Fast Spherical Collocation have been used to estimate a gravity field model to degree and order 90, UCPH2002 04. This gravity field model is compared to EGM96 and EIGEN-2. The largest differences with respect to EGM96 are found at those places where the gravity data used to determine EGM96 had the largest uncertainty. EIGEN-2 and UCPH2002 04 are similar, though there are some differences in Antarctica and Central Asia.

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E Howe

Papers

Analysis of one month of CHAMP state vector and accelerometer data for the recovery of the gravity potential