scholarly journals Height unification using GOCE

2012 ◽  
Vol 2 (4) ◽  
pp. 355-362 ◽  
Author(s):  
R. Rummel
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
European Space Agency ◽  
Direct Determination ◽  
Gravity Anomalies ◽  
Satellite System ◽  
Future Trend ◽  
Reference Points ◽  
Gravity Models ◽  
Geoid Model

AbstractWith 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 order 200, when expressed in terms of a spherical harmonic expansion. GOCE is a mission of the European Space Agency (ESA). It is the first satellite equipped with a gravitational gradiometer, in the case of GOCE it measures the gradient components Vxx , Vyy, Vzzand Vxz. The GOCE gravitational sensor system comprises also a geodetic global positioning system (GPS)-receiver, three star sensors and ion-thrusters for drag compensation in flight direction. GOCE was launched in March 2009 and will fly till the end of 2013. Several gravity models have been derived from its data, their maximum degree is typically between 240 and 250. In summer 2012 a first re-processing of all level-1b data took place. One of the science objectives of GOCE is the unification of height systems. The existing height offsets among the datum zones can be determined by least-squares adjustment. This requires several precise geodetic reference points available in each height datum zone, physical heights from spirit levelling (plus gravimetry), the GOCE geoid and, in addition, short wavelength geoid refinement from terrestrial gravity anomalies. GOCE allows for important simplifications of the functional and stochastic part of the adjustment model. The future trend will be the direct determination of physical heights (orthometric as well as normal) from precise global navigation satellite system (GNSS)-positioning in combination with a next generation combined satellite-terrestrial high-resolution geoid model.

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

&lt;p&gt;The scope of this work is to showcase the BRAT (Broadview Radar Altimetry Toolbox) and GUT (GOCE User Toolbox) toolboxes.&lt;/p&gt;&lt;p&gt;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 &amp; Geophysics, Oceanography, Coastal Zone, Atmosphere, Wind &amp; Waves, Hydrology, Land, Ice and Climate, which can also be consulted in &amp;#160;http://www.altimetry.info/radar-altimetry-tutorial/.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;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 &amp;#8211; such as geoid height, gravity anomaly/disturbance, radial gravity gradient, vertical deflections &amp;#8211; that may be derived from the GOCE gravity models.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;BRAT and GUT toolboxes can be freely downloaded, along with ancillary material, at https://earth.esa.int/brat and https://earth.esa.int/gut.&lt;/p&gt;

scholarly journals GRAVITY ANOMALY ASSESSMENT USING GGMS AND AIRBORNE GRAVITY DATA TOWARDS BATHYMETRY ESTIMATION

2016 ◽  
Vol XLII-4/W1 ◽  
pp. 287-297
Author(s):  
A. Tugi ◽  
A. H. M. Din ◽  
K. M. Omar ◽  
A. S. Mardi ◽  
Z. A. M. Som ◽  
...  
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Ocean Circulation ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Airborne Gravity ◽  
Satellite Gravity ◽  
Earth’S Gravity Field ◽  
Explorer Mission ◽  
Satellite Gravity Missions

The Earth’s potential information is important for exploration of the Earth’s gravity field. The techniques of measuring the Earth’s gravity using the terrestrial and ship borne technique are time consuming and have limitation on the vast area. With the space-based measuring technique, these limitations can be overcome. The satellite gravity missions such as Challenging Mini-satellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), and Gravity-Field and Steady-State Ocean Circulation Explorer Mission (GOCE) has introduced a better way in providing the information on the Earth’s gravity field. From these satellite gravity missions, the Global Geopotential Models (GGMs) has been produced from the spherical harmonics coefficient data type. The information of the gravity anomaly can be used to predict the bathymetry because the gravity anomaly and bathymetry have relationships between each other. There are many GGMs that have been published and each of the models gives a different value of the Earth’s gravity field information. Therefore, this study is conducted to assess the most reliable GGM for the Malaysian Seas. This study covered the area of the marine area on the South China Sea at Sabah extent. Seven GGMs have been selected from the three satellite gravity missions. The gravity anomalies derived from the GGMs are compared with the airborne gravity anomaly, in order to figure out the correlation (R<sup>2</sup>) and the root mean square error (RMSE) of the data. From these assessments, the most suitable GGMs for the study area is GOCE model, GO_CONS_GCF_2_TIMR4 with the R<sup>2</sup> and RMSE value of 0.7899 and 9.886 mGal, respectively. This selected model will be used in the estimating the bathymetry for Malaysian Seas in future.

scholarly journals Regional Recovery of Gravity Anomaly from the Inversion of Diagonal Components of GOCE Gravitational Tensor: A Case Study in Ethiopia

2018 ◽  
Vol 53 (2) ◽  
pp. 55-74 ◽  
Author(s):  
Mehdi Eshagh ◽  
Andenet A. Gedamu ◽  
Tulu B. Bedada
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Ocean Circulation ◽  
Opposite Sign ◽  
Joint Inversion ◽  
Gravity Anomalies ◽  
The Earth ◽  
Tikhonov Regularisation ◽  
The Difference

Abstract The tensor of gravitation is traceless as the gravitational field of the Earth is harmonic outside the Earth’s surface. Therefore, summation of the 2nd-order horizontal derivatives on its diagonal components should be equal to the radial one but with the opposite sign. The gravity field can be recovered locally from either of them, or even their combination. Here, we use the in-orbit diagonal components of the gravitational tensor measured by the gravity field and steady state ocean circulation explorer (GOCE) mission for recovering gravity anomaly with a resolution of 1°×1° at sea level in Ethiopia. In order to solve the system of equations, derived after discretisation of integral equations, the Tikhonov regularisation is applied and the bias of this regularisation is estimated and removed from the estimated gravity anomalies. The errors of the anomalies are estimated and their significance of recovery from these diagonal components is investigated. Statistically, the difference between the recovered anomalies from each scenario is not significant comparing to their errors. However, their joint inversion of the diagonal components improved the solution by about 1 mGal. Furthermore, the inversion processes are better stabilised when using errors of the input data compared with its exclusion, but at the penalty of degradation in accuracy of the estimates.

scholarly journals An alternative method to improve gravity field models by incorporating GOCE gradient data

2018 ◽  
Vol 22 (3) ◽  
pp. 187-193 ◽  
Author(s):  
Xiaoyun Wan ◽  
Jiangjun Ran
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Field Model ◽  
Direct Method ◽  
European Space Agency ◽  
Gravity Field Model ◽  
Alternative Method ◽  
Space Agency ◽  
Gravitational Model ◽  
Gravity Field Models

The aim of this paper is to present an alternative method that can be used to improve existing gravity field models via the application of gradient data from Gravity field and Ocean Circulation Explorer (GOCE). First, the proposed algorithm used to construct the observation equation is presented. Then methods for noise processing in both time and space domains aimed at reducing noises are introduced. As an example, the European Improved Gravity model of the Earth by New techniques (EIGEN5C) is modified with gradient observations over the whole lifetime of the GOCE, leading to a new gravity field model named as EGMGOCE (Earth Gravitational Model of GOCE). The results show that the cumulative geoid difference between EGMGOCE and EGM08 is reduced by 4 centimeters compared with that between EIGEN5C and Earth Gravitational Model 2008 (EGM08) up to 200 degrees. The large geoid differences between EGMGOCE and EIGEN5C mainly exist in Africa, South America, Antarctica and Himalaya, which indicates the contribution from GOCE. Compared to the newest GOCE gravity field model resolved by direct method from European Space Agency (ESA), the cumulative geoid difference is reduced by 7 centimeters up to 200 degrees. 

scholarly journals Centimeter Precision Geoid Model for Jeddah Region (Saudi Arabia)

2020 ◽  
Vol 12 (12) ◽  
pp. 2066
Author(s):  
Alessandra Borghi ◽  
Riccardo Barzaghi ◽  
Omar Al-Bayari ◽  
Suhail Al Madani
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Gravity Data ◽  
Independent Set ◽  
Geoid Undulation ◽  
Height Anomaly ◽  
Geoid Model ◽  
Satellite Gravity ◽  
Earth’S Gravity Field ◽  
Long Wavelength

In 2014, the Jeddah Municipality made a call for an estimate of a centimetric precision geoid model to be used for engineering and surveying applications, because the regional geoid model available at that time did not reach a sufficient precision. A project was set up to this end and dedicated sets of gravity and Global Positioning System (GPS)/levelling data were acquired in the framework of this project. In this paper, a thorough analysis of these newly acquired data and of the last available Global Gravity Field Models (GGMs) has been done in order to obtain a geoid undulation estimate with the prescribed precision. In the framework of the Remove–Compute–Restore (RCR) approach, the collocation method was used to obtain the height anomaly estimation that was then converted to geoid undulation. The remove and restore steps of the RCR approach were based on GGMs, derived from the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and Gravity Recovery and Climate Experiment (GRACE) dedicated gravity satellite missions, which were used to improve the long wavelength components of the Earth’s gravity field. Furthermore, two different quasi-geoid collocation estimates were computed, based on gravity data only and on gravity plus GPS/levelling data (the so-called hybrid estimate). The best solutions were obtained with the hybrid geoid estimate. This was tested by comparison with an independent set of GPS/levelling geoid undulations that were not included in the computed solutions. By these tests, the precision of the hybrid geoid is estimated to be 3.7 cm. This precision proved to be better, by a factor of two, than the corresponding one estimated from the pure gravimetric geoid. This project has been also useful to verify the importance and reliability of GGMs developed from the last satellite gravity missions (GOCE and GRACE) that have significantly improved our knowledge of the long wavelength components of the Earth’s gravity field, especially in areas with poor coverage of terrestrial gravity data. In fact, the geoid models based on satellite-only GGMs proved to have a better performance, despite the lower spatial resolution with respect to high-resolution models (i.e., Earth Gravitational Model 2008 (EGM2008)).

scholarly journals Accuracy assessment of GOCE-based geopotential models and their use for modelling the gravimetric quasigeoid - A case study for Poland

2014 ◽  
Vol 63 (1) ◽  
pp. 3-24 ◽  
Author(s):  
Walyeldeen Godah ◽  
Malgorzata Szelachowska ◽  
Jan Krynski
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Accuracy Assessment ◽  
Gravity Anomalies ◽  
Geopotential Model ◽  
Satellite Gravity ◽  
Earth Gravity ◽  
Geopotential Models ◽  
Gravimetric Quasigeoid ◽  
Gravity Signal

Abstract The GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) has significantly upgraded the knowledge on the Earth gravity field. In this contribution the accuracy of height anomalies determined from Global Geopotential Models (GGMs) based on approximately 27 months GOCE satellite gravity gradiometry (SGG) data have been assessed over Poland using three sets of precise GNSS/levelling data. The fits of height anomalies obtained from 4th release GOCE-based GGMs to GNSS/levelling data were discussed and compared with the respective ones of 3rd release GOCE-based GGMs and the EGM08. Furthermore, two highly accurate gravimetric quasigeoid models were developed over the area of Poland using high resolution Faye gravity anomalies. In the first, the GOCE-based GGM was used as a reference geopotential model, and in the second - the EGM08. They were evaluated with GNSS/levelling data and their accuracy performance was assessed. The use of GOCE-based GGMs for recovering the long-wavelength gravity signal in gravimetric quasigeoid modelling was discussed.

scholarly journals A multilayer approach and its application to model a local gravimetric quasi-geoid model over the North Sea: QGNSea V1.0

2018 ◽  
Vol 11 (12) ◽  
pp. 4797-4815 ◽  
Author(s):  
Yihao Wu ◽  
Zhicai Luo ◽  
Bo Zhong ◽  
Chuang Xu
Keyword(s):  
Gravity Field ◽  
North Sea ◽  
Ocean Circulation ◽  
Goodness Of Fit ◽  
Gravity Data ◽  
Single Layer ◽  
Geoid Model ◽  
The North ◽  
Gravity Field Recovery ◽  
The North Sea

Abstract. A multilayer approach is set up for local gravity field recovery within the framework of multi-resolution representation, where the gravity field is parameterized as the superposition of multiple layers of Poisson wavelets located at different depths beneath the Earth's surface. The layers are designed to recover gravity signals at different scales, where the shallow and deep layers mainly capture the short- and long-wavelength signals, respectively. The depths of these layers are linked to the locations of different anomaly sources beneath the Earth's surface, which are estimated by wavelet decomposition and power spectrum analysis. For testing the performance of this approach, a gravimetric quasi-geoid model over the North Sea, QGNSea V1.0, is modeled and validated against independent control data. The results show that the multilayer approach fits the gravity data better than the traditional single-layer approach, particularly in regions with topographical variation. An Akaike information criterion (AIC) test shows that the multilayer model obtains a smaller AIC value and achieves a better balance between the goodness of fit of data and the simplicity of the model. Further, an evaluation using independent GPS/leveling data tests the ability of regional models computed from different approaches towards realistic extrapolation, which shows that the accuracies of the QGNSea V1.0 derived from the multilayer approach are better by 0.4, 0.9, and 1.1 cm in the Netherlands, Belgium, and parts of Germany, respectively, than that using the single-layer approach. Further validation with existing models shows that QGNSea V1.0 is superior with respect to performance and may be beneficial for studying ocean circulation between the North Sea and its neighboring waters.

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.

scholarly journals GOCE-Derived Coseismic Gravity Gradient Changes Caused by the 2011 Tohoku-Oki Earthquake

2019 ◽  
Vol 11 (11) ◽  
pp. 1295
Author(s):  
Xinyu Xu ◽  
Hao Ding ◽  
Yongqi Zhao ◽  
Jin Li ◽  
Minzhang Hu
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Spherical Harmonic ◽  
Least Squares Method ◽  
Time Variable ◽  
Gravity Models ◽  
Gravity Gradient ◽  
Gravity Field Recovery ◽  
Before And After ◽  
Gravity Field Models

In contrast to most of the coseismic gravity change studies, which are generally based on data from the Gravity field Recovery and Climate Experiment (GRACE) satellite mission, we use observations from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) Satellite Gravity Gradient (SGG) mission to estimate the coseismic gravity and gravity gradient changes caused by the 2011 Tohoku-Oki Mw 9.0 earthquake. We first construct two global gravity field models up to degree and order 220, before and after the earthquake, based on the least-squares method, with a bandpass Auto Regression Moving Average (ARMA) filter applied to the SGG data along the orbit. In addition, to reduce the influences of colored noise in the SGG data and the polar gap problem on the recovered model, we propose a tailored spherical harmonic (TSH) approach, which only uses the spherical harmonic (SH) coefficients with the degree range 30–95 to compute the coseismic gravity changes in the spatial domain. Then, both the results from the GOCE observations and the GRACE temporal gravity field models (with the same TSH degrees and orders) are simultaneously compared with the forward-modeled signals that are estimated based on the fault slip model of the earthquake event. Although there are considerable misfits between GOCE-derived and modeled gravity gradient changes (ΔVxx, ΔVyy, ΔVzz, and ΔVxz), we find analogous spatial patterns and a significant change (greater than 3σ) in gravity gradients before and after the earthquake. Moreover, we estimate the radial gravity gradient changes from the GOCE-derived monthly time-variable gravity field models before and after the earthquake, whose amplitudes are at a level over three times that of their corresponding uncertainties, and are thus significant. Additionally, the results show that the recovered coseismic gravity signals in the west-to-east direction from GOCE are closer to the modeled signals than those from GRACE in the TSH degree range 30–95. This indicates that the GOCE-derived gravity models might be used as additional observations to infer/explain some time-variable geophysical signals of interest.

scholarly journals On quality of NKG2015 geoid model over the Nordic countries

2019 ◽  
Vol 9 (1) ◽  
pp. 97-110
Author(s):  
Mehdi Eshagh ◽  
Jenny Berntsson
Keyword(s):  
Confidence Interval ◽  
Ocean Circulation ◽  
Statistical Tests ◽  
Satellite System ◽  
Average Error ◽  
Variance Estimator ◽  
Geoid Model ◽  
Local Variance ◽  
Baltic Countries ◽  
Global Navigation Satellite

Abstract The NKG2015 geoid model covers the Nordic and Baltic countries and has been computed based on the least-squares modification of Stokes’ formula with additive corrections method. New and precise terrestrial, airborne and shipborne gravimetric measurements, the recent global gravity model of the gravity field and steady-state ocean circulation explorer (GOCE) and detailed digital terrain models over each territory have been used for computing this new geoid model. Some estimates for the error of this model have been roughly presented by comparing it with the global navigation satellite system (GNSS) data over each country. In this paper, our goal is to have a closer look at the relative error of this model by performing some statistical tests and finding the proper corrective surface for absorbing the systematic errors over each country. Our main assumption is realisticity of the errors of GNSS/levelling data and we will investigate its consequences in estimating the error of the geoid model. Our results show that the 4-parameter corrective surface is suitable for modelling the systematic trends of the differences between the gravimetric and GNSS geoid heights in Sweden, Denmark and Finland, but a filtered discrepancies by a confidence interval of 95% should be used for Sweden. A 7-aparameter model is suitable for the filtered discrepancies with the confidence interval of 95% in Norway. Based on the selected corrective surface and our newly developed regional iterative variance estimator, the confidence interval for the error of NKG2015 geoid model in Sweden, Denmark and Norway yielded 0-6.5 mm, 1.8-5.2 mm, 14.8-17.7 mm, respectively with a confidence level of 95%. We could not estimate the geoid error in Finland because the given error of the GNSS/levelling heights is significantly larger than the size of residuals. Based on the selected corrective surfaces and our presented local variance estimator, the average error of geoid becomes 3.6, 2.4, 8.8 and 5.8 mm with a confidence interval of 68%, respectively, over Sweden, Denmark, Norway and Finland.

Sign in / Sign up

Export Citation Format

Share Document