scholarly journals An Improved Model of the Earth’s Static Gravity Field Solely Derived from Reprocessed GOCE Data

2021 ◽  
Author(s):  
Jan Martin Brockmann ◽  
Till Schubert ◽  
Wolf-Dieter Schuh
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Gravity Anomalies ◽  
Geoid Height ◽  
Gravity Gradients ◽  
Data Set ◽  
Gravity Field Recovery ◽  
Global Gravity ◽  
The Impact ◽  
Goce Satellite

AbstractAfter it was found that the gravity gradients observed by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite could be significantly improved by an advanced calibration, a reprocessing project for the entire mission data set was initiated by ESA and performed by the GOCE High-level processing facility (GOCE HPF). One part of the activity was delivering the gravity field solutions, where the improved level 1b and level 2 data serve as an input for global gravity field recovery. One well-established approach for the analysis of GOCE observations is the so-called time-wise approach. Basic characteristics of the GOCE time-wise solutions is that only GOCE observations are included to remain independent of any other gravity field observables and that emphasis is put on the stochastic modeling of the observations’ uncertainties. As a consequence, the time-wise solutions provide a GOCE-only model and a realistic uncertainty description of the model in terms of the full covariance matrix of the model coefficients. Within this contribution, we review the GOCE time-wise approach and discuss the impact of the improved data and modeling applied in the computation of the new GO_CONS_EGM_TIM_RL06 solution. The model reflects the Earth’s static gravity field as observed by the GOCE satellite during its operation. As nearly all global gravity field models, it is represented as a spherical harmonic expansion, with maximum degree 300. The characteristics of the model and the contributing data are presented, and the internal consistency is demonstrated. The updated solution nicely meets the official GOCE mission requirements with a global mean accuracy of about 2 cm in terms of geoid height and 0.6 mGal in terms of gravity anomalies at ESA’s target spatial resolution of 100 km. Compared to its RL05 predecessor, three kinds of improvements are shown, i.e., (1) the mean global accuracy increases by 10–25%, (2) a more realistic uncertainty description and (3) a local reduction of systematic errors in the order of centimeters.

The BRAT and GUT Couple: Broadview Radar Altimetry and GOCE User Toolboxes

2020 ◽  
Author(s):  
Américo Ambrózio ◽  
Marco Restano ◽  
Jérôme Benveniste
Keyword(s):  
Gravity Field ◽  
Ad Hoc ◽  
Gravity Anomalies ◽  
Geoid Height ◽  
Gravity Models ◽  
Gravity Gradient ◽  
Data Set ◽  
Radar Altimetry ◽  
Isostatic Gravity ◽  
L1 And L2

<p>The scope of this work is to showcase the BRAT (Broadview Radar Altimetry Toolbox) and GUT (GOCE User Toolbox) toolboxes.</p><p>The Broadview Radar Altimetry Toolbox (BRAT) is a collection of tools designed to facilitate the processing of radar altimetry data from all previous and current altimetry missions, including Sentinel-3A L1 and L2 products. A tutorial is included providing plenty of use cases on Geodesy & Geophysics, Oceanography, Coastal Zone, Atmosphere, Wind & Waves, Hydrology, Land, Ice and Climate, which can also be consulted in  http://www.altimetry.info/radar-altimetry-tutorial/.</p><p>BRAT's last version (4.2.1) was released in June 2018. Based on the community feedback, the front-end has been further improved and simplified whereas the capability to use BRAT in conjunction with MATLAB/IDL or C/C++/Python/Fortran, allowing users to obtain desired data bypassing the data-formatting hassle, remains unchanged. Several kinds of computations can be done within BRAT involving the combination of data fields, that can be saved for future uses, either by using embedded formulas including those from oceanographic altimetry, or by implementing ad-hoc Python modules created by users to meet their needs. BRAT can also be used to quickly visualise data, or to translate data into other formats, e.g. from NetCDF to raster images.</p><p>The GOCE User Toolbox (GUT) is a compilation of tools for the use and the analysis of GOCE gravity field models. It facilitates using, viewing and post-processing GOCE L2 data and allows gravity field data, in conjunction and consistently with any other auxiliary data set, to be pre-processed by beginners in gravity field processing, for oceanographic and hydrologic as well as for solid earth applications at both regional and global scales. Hence, GUT facilitates the extensive use of data acquired during GRACE and GOCE missions.</p><p>In the current version (3.2), GUT has been outfitted with a graphical user interface allowing users to visually program data processing workflows. Further enhancements aiming at facilitating the use of gradients, the anisotropic diffusive filtering, and the computation of Bouguer and isostatic gravity anomalies have been introduced. Packaged with GUT is also GUT's Variance/Covariance Matrix (VCM) tool, which enables non-experts to compute and study, with relative ease, the formal errors of quantities – such as geoid height, gravity anomaly/disturbance, radial gravity gradient, vertical deflections – that may be derived from the GOCE gravity models.</p><p>On our continuous endeavour to provide better and more useful tools, we intend to integrate BRAT into SNAP (Sentinel Application Platform). This will allow our users to easily explore the synergies between both toolboxes. During 2020 we will start going from separate toolboxes to a single one.</p><p>BRAT and GUT toolboxes can be freely downloaded, along with ancillary material, at https://earth.esa.int/brat and https://earth.esa.int/gut.</p>

scholarly journals Signal and error assessment of GOCE-based high resolution gravity field models

2019 ◽  
Vol 9 (1) ◽  
pp. 71-86 ◽  
Author(s):  
T. Gruber ◽  
M. Willberg
Keyword(s):  
High Resolution ◽  
Gravity Field ◽  
Gravity Data ◽  
Geoid Height ◽  
Harmonic Series ◽  
Regional Data ◽  
Data Set ◽  
Global Models ◽  
The Impact ◽  
Gravity Field Models

Abstract The signal content and error level of recent GOCE-based high resolution gravity field models is assessed by means of signal degree variances and comparisons to independent GNSS-levelling geoid heights. The signal of the spherical harmonic series of these models is compared to the pre-GOCE EGM2008 model in order to identify the impact of GOCE data, of improved surface and altimetric gravity data and of modelling approaches. Results of the signal analysis show that in a global average roughly 80% of the differences are due to the inclusion of GOCE satellite information, while the remaining 20% are contributed by improved surface data. Comparisons of the global models to GNSS-levelling derived geoid heights demonstrate that a 1 cm geoid from the global model is feasible, if there is a high quality terrestrial gravity data set available. For areas with less good coverage an accuracy of several centimetres to a decimetre is feasible taking into account that GOCE provides now the geoid with a centimetre accuracy at spatial scales of 80 to 100 km. Comparisons with GNSS-levelling geoid heights also are a good tool to investigate possible systematic errors in the global models, in the spirit levelling and in the GNSS height observations. By means of geoid height differences and geoid slope differences one can draw conclusions for each regional data set separately. These conclusions need to be considered for a refined analysis e.g. to eliminate suspicious GNSS-levelling data, to improve the global modelling by using full variance-covariance matrices and by consistently weighting the various data sources used for high resolution gravity field models. The paper describes the applied procedures, shows results for these geoid height and geoid slope differences for some regional data sets and draws conclusions about possible error sources and future work to be done in this context.

GRACE Follow-On Gravity Field Recovery from Combined Laser Ranging Interferometer and Microwave Ranging System Measurements

2021 ◽  
Author(s):  
Saniya Behzadpour ◽  
Andreas Kvas ◽  
Torsten Mayer-Gürr
Keyword(s):  
Gravity Field ◽  
Laser Ranging ◽  
Measurement Technology ◽  
Additional Measurement ◽  
Covariance Functions ◽  
Gravity Field Recovery ◽  
Global Gravity ◽  
Least Squares Adjustment ◽  
Noise Covariance ◽  
Component Estimation

<p>Besides a K-Band Ranging System (KBR), GRACE-FO carries a Laser Ranging Interferometer (LRI) as a technology demonstration to provide measurements of inter-satellite range changes. This additional measurement technology provides supplementary observations, which allow for cross-instrument diagnostics with the KBR system and, to some extent, the separation of ranging noise from other sources such as noise in the on-board accelerometer (ACC) measurements.</p><p>The aim of this study is to incorporate the two ranging systems (LRI and KBR) observations in ITSG-Grace2018 gravity field recovery. The two observation groups are combined in an iterative least-squares adjustment with variance component estimation used to determine the unknown noise covariance functions for KBR, LRI, and ACC measurements. We further compare the gravity field solutions obtained from the combined solutions to KBR-only results and discuss the differences with a focus on the global gravity field and LRI calibration parameters.</p>

The Impact of Temporal Gravity Variations on GOCE Gravity Field Recovery

2006 ◽  
pp. 255-269 ◽  
Author(s):  
Oleg Abrikosov ◽  
Focke Jarecki ◽  
Jürgen Müller ◽  
Svetozar Petrovic ◽  
Peter Schwintzer
Keyword(s):  
Gravity Field ◽  
Gravity Field Recovery ◽  
Gravity Variations ◽  
The Impact ◽  
Temporal Gravity

Towards an updated, enhanced regional gravity field solution for Antarctica

2021 ◽  
Author(s):  
Mirko Scheinert ◽  
Philipp Zingerle ◽  
Theresa Schaller ◽  
Roland Pail ◽  
Martin Willberg
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Data Set ◽  
Gravity Field Model ◽  
Terrestrial Gravity ◽  
Field Solution ◽  
Gravity Disturbances ◽  
Regional Gravity

<p>In the frame of the IAG Subcommission 2.4f “Gravity and Geoid in Antarctica” (AntGG) a first Antarctic-wide grid of ground-based gravity anomalies was released in 2016 (Scheinert et al. 2016). That data set was provided with a grid space of 10 km and covered about 73% of the Antarctic continent. Since then a considerably amount of new data has been made available, mainly collected by means of airborne gravimetry. Regions which were formerly void of any terrestrial gravity observations and have now been surveyed include especially the polar data gap originating from GOCE satellite gravimetry. Thus, it is timely to come up with an updated and enhanced regional gravity field solution for Antarctica. For this, we aim to improve further aspects in comparison to the AntGG 2016 solution: The grid spacing will be enhanced to 5 km. Instead of providing gravity anomalies only for parts of Antarctica, now the entire continent should be covered. In addition to the gravity anomaly also a regional geoid solution should be provided along with further desirable functionals (e.g. gravity anomaly vs. disturbance, different height levels).</p><p>We will discuss the expanded AntGG data base which now includes terrestrial gravity data from Antarctic surveys conducted over the past 40 years. The methodology applied in the analysis is based on the remove-compute-restore technique. Here we utilize the newly developed combined spherical-harmonic gravity field model SATOP1 (Zingerle et al. 2019) which is based on the global satellite-only model GOCO05s and the high-resolution topographic model EARTH2014. We will demonstrate the feasibility to adequately reduce the original gravity data and, thus, to also cross-validate and evaluate the accuracy of the data especially where different data set overlap. For the compute step the recently developed partition-enhanced least-squares collocation (PE-LSC) has been used (Zingerle et al. 2021, in review; cf. the contribution of Zingerle et al. in the same session). This method allows to treat all data available in Antarctica in one single computation step in an efficient and fast way. Thus, it becomes feasible to iterate the computations within short time once any input data or parameters are changed, and to easily predict the desirable functionals also in regions void of terrestrial measurements as well as at any height level (e.g. gravity anomalies at the surface or gravity disturbances at constant height).</p><p>We will discuss the results and give an outlook on the data products which shall be finally provided to present the new regional gravity field solution for Antarctica. Furthermore, implications for further applications will be discussed e.g. with respect to geophysical modelling of the Earth’s interior (cf. the contribution of Schaller et al. in session G4.3).</p>

scholarly journals Long Periodic Variation of Orbital Elements of A Satellite Perturbed by Discrete Gravity Anomalies

1978 ◽  
Vol 41 ◽  
pp. 240-240
Author(s):  
M.P. Ananda
Keyword(s):  
Gravity Field ◽  
Gravity Anomalies ◽  
Large Data ◽  
Periodic Variation ◽  
Static Case ◽  
Orbital Elements ◽  
Disturbing Potential ◽  
Data Set ◽  
Simple Matrix ◽  
Derivatives Of

AbstractA method for generating long periodic variations in satellite orbital elements when perturbed by discrete gravity anomalies is presented. The method consists of developing a disturbing potential as a function of orbital and gravity anomaly parameters, and generating partial derivatives of the potential with respect to the orbital elements. The partials are averaged over the period of the satellite to eliminate the short periodic variations. The averaged partials are substituted into the variation of parameter equations to give the mean orbital rates. Classically orbital elements are used in generating gravity field and thus the method is dynamic in nature. The problem is extremely cumbersome and complex when multi-state parameters have to be estimated from a considerably large data set. However, when mean orbital rates are used, the problem reduces to a simple linear static case, where only the gravity parameters have to be estimated, and it is a simple matrix inversion problem. Thus the method developed here was utilized in reducing Appolo 15 and 16 subsatellite radio tracking data to produce a lunar gravity field represented by point masses.

scholarly journals Effects of Interferometric Radar Altimeter Errors on Marine Gravity Field Inversion

Sensors ◽  
2020 ◽  
Vol 20 (9) ◽  
pp. 2465
Author(s):  
Xiaoyun Wan ◽  
Shuanggen Jin ◽  
Bo Liu ◽  
Song Tian ◽  
Weiya Kong ◽  
...  
Keyword(s):  
Gravity Field ◽  
Gravity Anomalies ◽  
Ocean Surface ◽  
Radar Altimeter ◽  
The North ◽  
Phase Errors ◽  
Marine Gravity ◽  
East Component ◽  
The Impact ◽  
Field Inversion

The traditional altimetry satellite, which is based on pulse-limited radar altimeter, only measures ocean surface heights along tracks; hence, leads to poorer accuracy in the east component of the vertical deflections compared to the north component, which in turn limits the final accuracy of the marine gravity field inversion. Wide-swath altimetry using radar interferometry can measure ocean surface heights in two dimensions and, thus, can be used to compute vertical deflections in an arbitrary direction with the same accuracy. This paper aims to investigate the impact of Interferometric Radar Altimeter (InRA) errors on gravity field inversion. The error propagation between gravity anomalies and InRA measurements is analyzed, and formulas of their relationship are given. By giving a group of possible InRA parameters, numerical simulations are conducted to analyze the accuracy of gravity anomaly inversion. The results show that the accuracy of the gravity anomalies is mainly influenced by the phase errors of InRA; and the errors of gravity anomalies have a linear approximation relationship with the phase errors. The results also show that the east component of the vertical deflections has almost the same accuracy as the north component.

scholarly journals Evaluation of Gravity Data Derived from Global Gravity Field Models Using Terrestrial Gravity Data in Enugu State, Nigeria

2018 ◽  
Vol 8 (1) ◽  
pp. 145-153 ◽  
Author(s):  
O.I. Apeh ◽  
E.C. Moka ◽  
V.N. Uzodinma
Keyword(s):  
Gravity Field ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Mean Square ◽  
Bouguer Gravity ◽  
Bouguer Anomalies ◽  
The Earth ◽  
Global Gravity ◽  
Enugu State ◽  
Gravity Field Models

Abstract Spherical harmonic expansion is a commonly applied mathematical representation of the earth’s gravity field. This representation is implied by the potential coeffcients determined by using elements/parameters of the field observed on the surface of the earth and/or in space outside the earth in the spherical harmonic expansion of the field. International Centre for Gravity Earth Models (ICGEM) publishes, from time to time, Global Gravity Field Models (GGMs) that have been developed. These GGMs need evaluation with terrestrial data of different locations to ascertain their accuracy for application in those locations. In this study, Bouguer gravity anomalies derived from a total of eleven (11) recent GGMs, using sixty sample points, were evaluated by means of Root-Mean-Square difference and correlation coeficient. The Root-Mean-Square differences of the computed Bouguer anomalies from ICGEMwebsite compared to their positionally corresponding terrestrial Bouguer anomalies range from 9.530mgal to 37.113mgal. Additionally, the correlation coe_cients of the structure of the signal of the terrestrial and GGM-derived Bouguer anomalies range from 0.480 to 0.879. It was observed that GECO derived Bouguer gravity anomalies have the best signal structure relationship with the terrestrial data than the other ten GGMs. We also discovered that EIGEN-6C4 and GECO derived Bouguer anomalies have enormous potential to be used as supplements to the terrestrial Bouguer anomalies for Enugu State, Nigeria.

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