Local gravity field continuation for the purpose of in-orbit calibration of GOCE SGG observations

The use of ground gravity data in wellsurveyed areas, continued upward to satellite altitude, is one of the most promising external absolute in-orbit calibration/ validation methods for GOCE satellite gravity gradient (SGG) observations. Based on a synthetic gravity test environment – providing in addition to statistical error information also absolute error estimates – several upward continuation methods, e.g. least squares collocation, equivalent source techniques using point masses or area density distributions defined on a spherical surface section, are described, assessed and compared. It turns out that all these strictly local approaches fail to work sufficiently accurate. Consequently, a combined adjustment strategy is proposed, supporting the high-quality gravity field information within the well-surveyed test area with a low-accuracy, but globally defined Earth model. Under quite realistic assumptions the upward continuation is performed with rms errors in the order of 1 mE. The most crucial limiting factor of this method is spectral leakage in the course of an adequate representation of the initial gravity information, which can be overcome by an enlargement of the parameter model in combination with <i>a priori</i> filtering of the initial gravity data.<br><br><b>Key words.</b> Satellite gravity gradiometry – GOCE – calibration – least squares adjustmen

GOCE SGG and SST quick-look gravity field analysis

International audienceThe purpose of quick-look analysis in the framework of the GOCE data processing architecture is to analyse partial data sets of satellite gravity gradiometry (SGG) and satellite-to-satellite tracking in high-low mode (hl-SST), in order to derive a diagnosis of the system performance. The semi-analytic (SA) method for gravity field recovery from GOCE observations, which is based on Fast Fourier Transform, is used. From a theoretical point of view, a number of requirements (circular, exact repeat orbit, uninterrupted measurement time series) have to be fulfilled. However, in the present paper it is demonstrated, that the SA approach can also be applied in the practical case of non-circular, nonrepeat orbits, and data gaps in the GOCE measurement time series. The performance of this approach is assessed in 5 case studies on the basis of a realistic closed-loop simulation.Key words. GOCE ? semi-analytic approach ? colored noise ? data gaps ? repeat orbi

Comparison of numerical solution strategies for gravity field recovery from GOCE SGG observations implemented on a parallel platform

International audienceThe recovery of a full set of gravity field parameters from satellite gravity gradiometry (SGG) is a huge numerical and computational task. In practice, parallel computing has to be applied to estimate the more than 90 000 harmonic coefficients parameterizing the Earth?s gravity field up to a maximum spherical harmonic degree of 300. Three independent solution strategies, i.e. two iterative methods (preconditioned conjugate gradient method, semi-analytic approach) and a strict solver (Distributed Non-approximative Adjustment), which are operational on a parallel platform (?Graz Beowulf Cluster?), are assessed and compared both theoretically and on the basis of a realistic-as-possible numerical simulation, regarding the accuracy of the results, as well as the computational effort. Special concern is given to the correct treatment of the coloured noise characteristics of the gradiometer. The numerical simulations show that there are no significant discrepancies among the solutions of the three methods. The newly proposed Distributed Nonapproximative Adjustment approach, which is the only one of the three methods that solves the inverse problem in a strict sense, also turns out to be a feasible method for practical applications.Key words. Spherical harmonics ? satellite gravity gradiometry ? GOCE ? parallel computing ? Beowulf cluste

Highly-reduced dynamic orbits and their use for global gravity field recovery: A simulation study for GOCE

The so-called highly reduced-dynamic (HRD) orbit determination strategy and its use for the determination of the Earth's gravitational field are analyzed. We discuss the functional model for the generation of HRD orbits, which are a compromise of the two extreme cases of dynamic and purely geometrically determined kinematic orbits. For gravity field recovery the energy integral approach is applied, which is based on the law of energy conservation in a closed system. The potential of HRD orbits for gravity field determination is studied in the frame of a simulated test environment based on a realistic GOCE orbit configuration. The results are analyzed, assessed, and compared with the respective reference solutions based on a kinematic orbit scenario. The main advantage of HRD orbits is the fact that they contain orbit velocity information, thus avoiding numerical differentiation on the orbit positions. The error characteristics are usually much smoother, and the computation of gravity field solutions is more efficient, because less densely sampled orbit information is sufficient. On the other hand, the main drawback of HRD orbits is that they contain external gravity field information, and thus yield the danger to obtain gravity field results which are biased towards this prior informatio

Study of the Earth’s short-scale gravity field using the ERTM2160 gravity model

This paper describes the computation and analysis of the Earth’s short-scale gravity field through high-resolution gravity forward modelling using the Shuttle Radar Topography Mission (SRTM) global topography model. We use the established residual terrain modelling technique along with advanced computational resources and massive parallelisation to convert the high-pass filtered SRTM topography – complemented with bathymetric information in coastal zones – to implied short-scale gravity effects. The result is the ERTM2160 model (Earth Residual Terrain Modelled-gravity field with the spatial scales equivalent to spherical-harmonic coefficients up to degree 2160 removed). ERTM2160, used successfully for the construction of the GGMplus gravity maps, approximates the short-scale (i.e., ~10 km down to ~250 m) gravity field in terms of gravity disturbances, quasi/geoid heights and vertical deflections at ~3 billion gridded points within ±60 latitude. ERTM2160 reaches maximum values for the quasi/geoid height of ~30 cm, gravity disturbance in excess of 100 mGal, and vertical deflections of ~30 arc-seconds over the Himalaya mountains.Analysis of the ERTM2160 field as a function of terrain roughness shows in good approximation a linear relationship between terrain roughness and gravity effects, with values of ~1.7 cm (quasi/geoid heights), ~11 mGal (gravity disturbances) and 1.5 arc-seconds (vertical deflections) signal strength per 100 m standard deviation of the terrain. These statistics can be used to assess the magnitude of omitted gravity signals over various types of terrain when using degree-2160 gravity models such as EGM2008. Applications for ERTM2160 are outlined including its use in gravity smoothing procedures, augmentation of EGM2008, fill-in for future ultra-high resolution gravity models in spherical harmonics, or calculation of localised or global power spectra of Earth’s short-scale gravity field. ERTM2160 is freely available via http://ddfe.curtin.edu.au/gravitymodels/ERTM2160

Altimetry, gravimetry, GPS and viscoelastic modeling data for the joint inversion for glacial isostatic adjustment in Antarctica (ESA STSE Project REGINA)

The poorly known correction for the ongoing deformation of the solid Earth caused by glacial isostatic adjustment (GIA) is a major uncertainty in determining the mass balance of the Antarctic ice sheet from measurements of satellite gravimetry and to a lesser extent satellite altimetry. In the past decade, much progress has been made in consistently modeling ice sheet and solid Earth interactions; however, forward-modeling solutions of GIA in Antarctica remain uncertain due to the sparsity of constraints on the ice sheet evolution, as well as the Earth's rheological properties. An alternative approach towards estimating GIA is the joint inversion of multiple satellite data – namely, satellite gravimetry, satellite altimetry and GPS, which reflect, with different sensitivities, trends in recent glacial changes and GIA. Crucial to the success of this approach is the accuracy of the space-geodetic data sets. Here, we present reprocessed rates of surface-ice elevation change (Envisat/Ice, Cloud,and land Elevation Satellite, ICESat; 2003–2009), gravity field change (Gravity Recovery and Climate Experiment, GRACE; 2003–2009) and bedrock uplift (GPS; 1995–2013). The data analysis is complemented by the forward modeling of viscoelastic response functions to disc load forcing, allowing us to relate GIA-induced surface displacements with gravity changes for different rheological parameters of the solid Earth. The data and modeling results presented here are available in the PANGAEA database (https://doi.org/10.1594/PANGAEA.875745). The data sets are the input streams for the joint inversion estimate of present-day ice-mass change and GIA, focusing on Antarctica. However, the methods, code and data provided in this paper can be used to solve other problems, such as volume balances of the Antarctic ice sheet, or can be applied to other geographical regions in the case of the viscoelastic response functions. This paper presents the first of two contributions summarizing the work carried out within a European Space Agency funded study: Regional glacial isostatic adjustment and CryoSat elevation rate corrections in Antarctica (REGINA)

Joint inversion estimate of regional glacial isostatic adjustment in Antarctica considering a lateral varying Earth structure (ESA STSE Project REGINA)

A major uncertainty in determining the mass balance of the Antarctic ice sheet from measurements of satellite gravimetry, and to a lesser extent satellite altimetry, is the poorly known correction for the ongoing deformation of the solid Earth caused by glacial isostatic adjustment (GIA). Although much progress has been made in consistently modelling the ice-sheet evolution throughout the last glacial cycle, as well as the induced bedrock deformation caused by these load changes, forward models of GIA remain ambiguous due to the lack of observational constraints on the ice sheet's past extent and thickness and mantle rheology beneath the continent. As an alternative to forward modelling GIA, we estimate GIA from multiple space-geodetic observations: GRACE, Envisat/ICESat and GPS. Making use of the different sensitivities of the respective satellite observations to current and past surface mass (ice mass) change and solid Earth processes, we estimate GIA based on viscoelastic response functions to disc load forcing. We calculate and distribute the viscoelastic response functions according to estimates of the variability of lithosphere thickness and mantle viscosity in Antarctica. We compare our GIA estimate with published GIA corrections and evaluate its impact in determining the ice mass balance in Antarctica from GRACE and satellite altimetry. Particular focus is applied to the Amundsen Sea Sector in West Antarctica, where uplift rates of several cm/yr have been measured by GPS. We show that most of this uplift is caused by the rapid viscoelastic response to recent ice-load changes, enabled by the presence of a low-viscosity upper mantle in West Antarctica. This paper presents the second and final contribution summarizing the work carried out within a European Space Agency funded study, REGINA, (www.regina-science.eu)

Consolidated science and user requirements for a next generation gravity field mission

In an internationally coordinated initiative among the main user communities of gravity field products the science and user requirements for a future gravity field mission constellation (beyond GRACE-FO) have been reviewed and defined. This activity was realized as a joint initiative of the IAG (International Association of Geodesy) Sub-Commissions 2.3 and 2.6, the GGOS (Global Geodetic Observing System) Working Group on Satellite Missions, and the IUGG (International Union of Geodesy and Geophysics). After about one year of preparation, in a user workshop that was held in September 2014 consensus among the user communities of hydrology, ocean, cryosphere, solid Earth and atmosphere on consolidated science requirements could be achieved. The consolidation of the user requirements became necessary, because several future gravity field studies have resulted in quite different performance numbers as a target for a future gravity mission (2025+). Based on limited number of mission scenarios which took also technical feasibility into account, a consolidated view on the science requirements among the international user communities was derived, research fields that could not be tackled by current gravity missions have been identified, and the added value (qualitatively and quantitatively) of these scenarios with respect to science return has been evaluated. The resulting document shall form the basis for further programmatic and technological developments. In this contribution, the main results of this initiative will be presented. An overview of the specific requirements of the individual user groups, the consensus on consolidated requirements as well as the new research fields that have been identified during this process will be discussed