PosterPDF Available

Computation and assessment of the fifth release of the GOCE-only space-wise solution

Authors:
Andrea Gatti
Andrea Gatti
Mirko Reguzzoni at Politecnico di Milano
Mirko Reguzzoni
Federica Migliaccio at Politecnico di Milano
Federica Migliaccio
Fernando Sansò at Politecnico di Milano
Fernando Sansò
Download file PDF
Read file
Download citation

Abstract

The fifth release of the space-wise approach, as well as the ones of the direct and time-wise approaches, is based on the processing of the whole GOCE dataset, from November 2009 to October 2013. It consists in global grids of gravity gradients at 0.2°x0.2° spatial resolution and in a spherical harmonic model derived from these grids by a discretized quadrature formula and by a proper global regularization. Output products will be distributed through the ESA website and the ICGEM service. The main difference between the space-wise approach and the other two official methods is that the GOCE data acquired along the orbit are compressed onto global grids by applying collocation on local data patches, each of them with its own locally adapted signal covariance. In this way the filtering level is locally controlled, differently from the other solutions where a global regularization on spherical harmonic coefficients is applied. The good quality of the space-wise products has been assessed by comparing them with other grid solutions (e.g. the ones computed in the framework of the STSE GOCE+ GeoExplore project) and with other spherical harmonic models (e.g. the ones by the direct and time-wise approaches). The latter comparison also indicates the weakness of the local collocation method to optimally estimate the low degrees of the gravity field spectrum but, at the same time, its better capability to recover the highest degrees where the regularization strategy plays an important role.
Content uploaded by Andrea Gatti
Author content
All content in this area was uploaded by Andrea Gatti on Apr 12, 2017
Content may be subject to copyright.
Gatti, A.; Reguzzoni, M.; Migliaccio, F.; Sansò, F. Politecnico di Milano,
Italy
Computation and assessment of the fifth
release of the GOCE-only space-wise solution
!The fifth release of the space-wise approach, as well as the ones of the direct and time-wise approaches, is based on the processing of the whole GOCE dataset, from
November 2009 to October 2013. It consists in global grids of gravity gradients at 0.2°x0.2° spatial resolution and in a spherical harmonic model derived from these grids by a
discretized quadrature formula and by a proper global regularization. Output products will be distributed through the ESA website and the ICGEM service
!The main difference between the space-wise approach and the other two official methods is that the GOCE data acquired along the orbit are compressed onto global grids by
applying collocation on local data patches, each of them with its own locally adapted signal covariance. In this way the filtering level is locally controlled, differently from the
other solutions where a global regularization on spherical harmonic coefficients is applied
!The good quality of the space-wise products has been assessed by comparing them with other grid solutions (e.g. the ones computed in the framework of the STSE GOCE+
GeoExplore project) and with other spherical harmonic models (e.g. the ones by the direct and time-wise approaches). The latter comparison also indicates the weakness of
the local collocation method to optimally estimate the low degrees of the gravity field spectrum but, at the same time, its better capability to recover the highest degrees where
the regularization strategy plays an important role
ABSTRACT
Space-wise products - release 5
Pre-Processing
GRIDSSH model
LS SST SST local
gridding
Wiener filter
+ local gridding
Whitening filter
+ local gridding
analysis and global regularization
The pre-processing is a fundamental step to be performed before using GOCE
data. Each dataset (positions,
accelerations, rotations and gradients)
used for the solution is checked,
outliers are removed, and whenever
possible filled with reasonable
interpolated data that help the filtering
step
PRE PROCESSING
09/2009
01/2010
04/2010
07/2010
10/2010
01/2011
04/2011
07/2011
10/2011
01/2012
04/2012
07/2012
10/2012
01/2013
05/2013
08/2013
0
10
20
30
XX
XZ
YY
ZZ
% of flagged data
per gradient
(map of XY not
shown here)
(below) % of flagged data per gradient per cycle
SST SOLUTION
The SST solution is computed in two steps, a Least Squares adjustment up to
degree 140 considering only error variances of the along orbit potential,
followed by a spherical gridding @229km based on local signal covariances
the SST gridding is masked to
provide corrections only where
the SNR is high enough
[m2/s2]
[m2/s2]
SGG FILTERING
The gradients are prepared for the gridding steps by removing a low frequency
systematic effect in ascending and descending orbits. Wiener and White filters
are almost complementary.
MF grid
weights
HF grid
weights
Collocation weights (from Trr to Trr)
for the two gridding steps:
Medium Frequencies and High Frequencies
Frequency
10-6 10-4 10-2
0
0.2
0.4
0.6
0.8
1Wiener filter on Trr
Whitening filter on Trr
Spectral response of the
Wiener and Whitening filter
[Hz]
SGG GRIDDINNG
In the first gridding step, applied to the Wiener filtered signal, grids of different
derivatives w.r.t. r and lambda are estimated. By analysing these grids we derive
different sets of spherical harmonic coefficients that are combined to produce a
correction to the SST solution. The combination is driven by Monte Carlo (MC)
samples that pass through the same processing of the data.
In the second gridding step, after the Whitening filtering, grids of the full tensor
are estimated
,
Here we show the differences of the solution
w.r.t. synthesized spherical grids of Trr having
the same radius of 6600 km (229 Km altitude).
As a comparison we show the results using
the DIR R5 and TIM R5 models too
Differences between the two GOCE-only models (TIM and SPW)
can be seen at low frequencies and at high frequencies in areas
where a strong signal is present
Empirical Difference Degree Variances reveal the good performance of the space-wise solution but
for the low degrees below 80. Coefficients directly coming from the grids (black) are regularised
according to MC samples to produce a set of regularised coefficients (green)
The power of the space-wise coefficients
derived from the GOCE grids, even when
regularised, is higher than the one of the other
official GOCE solutions, this is probably due to
the type of local covariance adaptation
implemented in the gridding
Synthesis of Trr grids of the differences between
the SPW coefficients and TIM release 5 solution
above degree 230 (right)
Space-wise and STSE GOCE+ solutions over an
ellipsoidal grid at 225 km are finally compared with
a grid computed from GOCO up to degree 1440,
thus including very high frequency information
(see below for results)
•Spherical grids of gravity gradients by the space-wise approach have been computed and will be distributed by ESA
•From the grids, a set of spherical harmonic coefficients is derived and compared with other models, showing good performance at high degrees. This model will be made
available through the ICGEM website after a final refinement/optimization
•In the future, besides optimizing the present solution, a new model based on GRACE prior information will be computed, to be compared e.g. with DIR and GOCO solutions.
Local grids will be also studied for the ISG service
Conclusion
degree
050 100 150 200
degree variances [unitless] Log scale
10-20
10-18
10-16
Error (Difference) Degree Variances
DV EIGEN 6C4
EDV LS SST
EDV LS gridding
estimated error
disregarding low
order coefficients
degree
050 100 150 200
degree variances [unitless] Log scale
10-20
10-18
10-16
Error (Difference) Degree Variances
DV EIGEN 6C4
EDV LS SST
EDV LS gridding
estimated error
considering low
order coefficients
[mE]
[mE]
[mE]
[mE]
[mE]
[mE]
[mE]
[mE]
... The quality of the satellite gravitational gradient grids has up to now been validated with respect to GGMs (Gatti et al. 2014(Gatti et al. , 2016Sebera et al. 2014;Bouman et al. 2016;Reguzzoni et al. 2019) but not with respect to available height anomalies computed at GNSS/levelling points. In this contribution, we present a validation method which is based on transformation of gravitational gradients to height anomalies and their comparison with independent reference height anomalies. ...
... • ; 179.9 • ]. The SST solution or the low-frequency part of the gravity field has been derived in two steps (Migliaccio et al. 2011;Gatti et al. 2014Gatti et al. , 2016. Firstly, the along-track gravitational potential has been estimated by applying the energy conservation approach (Jekeli 1999;Visser et al. 2003) from kinematic orbits. ...
... The variance-covariance matrix of spherical harmonics is estimated by the Monte Carlo simulation method. SPW GGM is derived from these grids by a discretized quadrature formula and by proper global regularization (Gatti et al. 2016). The main difference between the space-wise approach and the other two official approaches is that the GOCE along-orbit observables are interpolated onto global grids by collocation with the emphasis on local data patches and their own local signal covariances (Gatti et al. 2016). ...
Validation of Space-Wise GOCE Gravitational Gradient Grids Using the Spectral Combination Method and GNSS/Levelling Data
Article
Full-text available
  • Mar 2023
  • SURV GEOPHYS
The launch of gravity-dedicated satellite missions at the beginning of the new millennium led to an accuracy improvement of global Earth gravity field models (GGMs). One of these missions was the Gravity field and steady-state Ocean Circulation Explorer (GOCE) launched in 2009. As the first European Space Agency’s Earth Explorer Mission, the satellite carried a novel instrument, a 3-D gradiometer, which allowed measurement of the second-order directional derivatives of the gravitational potential (gravitational gradients) with a uniform quality and a near-global coverage. The main mission goal was to determine the static Earth’s gravity field with the ambitious precision of 1-2 cm in terms of geoid heights and 1 mGal in terms of gravity anomalies for spatial resolution of 100 km (half wavelength at the equator). More than three years of the outstanding measurements resulted in three levels of data products (Level 0, Level 1b and Level 2), six releases of GGMs, and several global grids of gravitational gradients. The grids, which represent a step between gravitational gradients measured directly along the GOCE orbit and those represented by GGMs, found their usage mainly in geophysical applications. In this contribution, we validate the official Level 2 product GRD_SPW_2 using height anomalies over two test areas located in central and northern Europe (Czechia/Slovakia and Norway). A mathematical model based on the least-squares spectral weighting is employed with corresponding spectral weights estimated for validation of gravitational gradient grids. This model continues gravitational gradients from the mean orbital altitude of GOCE down to the irregular Earth’s surface (not to a sphere) and transforms them to height anomalies in one computational step. Analytical downward continuation errors of the model are estimated using a closed-loop test. Prior to the comparison of height anomalies estimated from gravitational gradients with their reference values derived from Global Navigation Satellite Systems (GNSS)/levelling over the two test areas, the gravitational gradients and reference data are corrected for all systematic effects such as the tide system conversion. Moreover, the high-frequency part of the gravitational signal is estimated and subtracted from reference data as it is attenuated in the gravitational gradients measured by GOCE. A relative improvement between the release 6 and release 2 gradient grids reaches 48%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} in terms of height anomalies in Czechia/Slovakia. The relative improvement in Norway is even more significant and reaches 55%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}. The release 6 of the official Level 2 product GRD_SPW_2 gained the absolute accuracy with the standard deviation of 8.7 cm over Czechia/Slovakia and 9.3 cm over Norway.
View
... The high-altitude analysis also emphasizes the regional gravity effects of the dominant density contrasts in the terrain's air, water, ice, and rock components over the effects of its elevation and density errors (e.g., Leftwich et al., 2005;. Comparison at the 250 km approximate mean GOCE altitude of (left) the observed free-air gravity anomalies (FAGA; Gatti et al., 2016) to degree and order 280 and (right) their largely noncrustal regional components (rFAGA) to degree and order 8. These and the rest of the maps in this study were produced at a 0.5° grid interval. ...
... left) illustrates FAGA up to spherical harmonic degree and order 280 (half wavelength ≈ 70 km) used for this study from the GO_CONS_GCF_2_SPW_R5 model(Gatti et al., 2016). The white polar cap in this and subsequent maps corresponds to the region devoid of GOCE observations due to the 96.7° inclination of the satellite's polar orbits. ...
GOCE constraints on the Antarctic Moho and its potential isostatic adjustments
Article
Full-text available
We investigate the impact of combining Gravity Field and Steady-state Ocean Circulation Explorer (GOCE) satellite gravity anomaly and Bedmap2 terrain relief data to enhance Antarctic seismic Moho estimates over the satellite's coverage region south of latitude 60°S. The study considers improving the seismic surface wave-inferred AN1 Moho (An et al., 2015a, https:// doi.org/10.1002/2014JB011332) from misfits of the gravitational effects of the terrain and the seismic Moho computed at 250 km altitude. The updates also relate the GOCE gravity anomalies that correlate directly and inversely with the terrain's gravity effects as isostatic anomalies of the uncompensated mantle relief. These terrain-correlated effects infer potential isostatic adjustments of the Moho that may help constrain the crust's stress field, track the Gamburtsev Subglacial Mountains to the Kerguelen mantle hotspot, and further test the putative Wilkes Land impact basin for its crustal attributes. Analysis of the gravity-updated seismic AN1 Moho (sAMoho) estimates suggests that most are within the seismic errors of several kilometers or less. However, the gravity-updated estimates that are deeper than the sAMoho estimates tend to characterize anomalously hot upper mantle where the assumed mantle-to-crust density contrast may be too low. These Moho difference estimates discern elevated heat flow for the Maud Rise, Kerguelen Plateau, Pacific-Antarctic Ridge, and most of western Antarctica extending from the Pacific-Antarctic Ridge along the Transantarctic Mountains and across the Ross Sea through Marie Byrd Land and the western margin of the Antarctic Peninsula Microplate to the Scotia Ridge. The methodology of this study also is effective in updating any Moho model for improved gravity and terrain data.
View
... In this investigation, GGMs based on previous satellite-only gravity missions have been truncated to obtain the long wavelength spectrum up to d/o 120. These models are GRACE-based ITSG-GRACE2018s (Mayer-Gürr et al., 2018) and GOCE-based GO_CONS_GCF_2_SPW_R5 (SPW5) (Gatti et al., 2016), GO_CONS_GCF_2_DIR_R6 (DIR6) (Bruinsma et al., 2014) and GO_CONS_GCF_2_TIM_R6 (TIM6) (Brockmann et al., 2021) in addition to the XGM2019e (Zingerle et al., 2019) as a reference gravity model. Moreover, the simulated gravity models of four FGMs named after Bender; Cartwheel; Helix, and Pendulum as defined in Elsaka et al. (2014) will be used to get the long wavelength spectrum. ...
Assessment of changing satellite gravity mission architectures using terrestrial gravity and GNSS-leveling data in the Kingdom of Saudi Arabia
Article
Full-text available
  • Apr 2023
This research investigates the effect of the 'future' gravity mission (FGM) architectures i.e. Bender, Helix, Pendulum, and Cartwheel up to spherical harmonics (SH) degree/order (d/o) 120/120 to improve the estimation of the gravitational field in the Saudi Arabia. For this purpose, we evaluate ground-truth gravity anomalies and GNSS/Leveling data with the satellite-based gravity models of each aforementioned FGMs. The comparison with gravity anomalies given by the FGM provides refinements of about 57-61 lGal with respect to (w.r.t.) those of GRACE-and GOCE-based GGMs. The comparison with GNSS/Leveling indicates that the least differences in terms of standard deviations (STD) of geoid heights are provided by the Bender-type FGM that provides the overall least STD differences of about 62.58 cm w.r.t. the GRACE-and GOCE-based GGMs, that provide STD differences of about 62.88 cm and 62.62 cm, respectively. The outcome of this study shows that implementing additional gravity information in different flight directions of the proposed FGMs (i.e along-track, cross-track, and radial) showed slight improvement (sub of a millimeter).
View
... In the first part of the numerical tests, all releases of DIR [40][41][42], TIM [26,[43][44][45], SPW [46][47][48][49] and GOCO [39,[50][51][52][53] satellite-only models were included in the determination of the most suitable GOCE-based GGM for Turkey. The satellite data content and maximum degree of expansion of these models are given in Table 1. ...
Improvement of GOCE-Based Global Geopotential Models for Gravimetric Geoid Modeling in Turkey
Article
Full-text available
  • Nov 2022
This study investigates the contribution of global geopotential models which are calculated with GOCE satellite mission data to the improvement of gravimetric geoid models in Turkey. In this context, direct (DIR), time-wise (TIM), space-wise (SPW), and GOCO satellite-only model series were considered. The research was carried out in two parts. The first part includes the validation of models in each series at 100 homogeneously distributed GNSS/leveling stations over the country utilizing spectrally enhanced geoid heights to determine the best performing model and its optimal expansion degree. According to obtained statistics, the TIM-R6 model was selected as the best model with an optimal expansion degree of 204. In the second part, the TIM-R6 model up to 204 degree/order was linearly blended with EGM2008 to obtain an improved version up to 360 degree/order of expansion. To clarify the contribution of the linearly blended model to the improvement of the regional geoid model, the gravimetric geoid models were computed adopting TIM-R6 up to 204 degree/order and its improved version up to 360 degree/order as reference models. To further emphasize the contribution of the GOCE mission’s data, the gravimetric geoid computations were repeated relying on EGM2008 up to 204 and 360 degrees of expansions, since EGM2008 does not contain GOCE data. In addition, we computed gravimetric geoids based on another combined model that includes GOCE mission data, the EIGEN-6C4 model. The calculated regional geoids were compared to each other and validated using GNSS/leveling data set. The obtained results revealed a ∼23% improvement in regional geoid model accuracy when the blended GOCE-based geopotential model was used as a reference. In addition, the results of this study presented the significance of GOCE contribution to mapping the gravity field in Turkey. The best accuracy obtained from this study was 7.7 cm for the Turkey geoid.
View
... [53] GGMs have been investigated in Kuwait. According to their research, the EIGEN-6C4 and XGM2016 models at their highest degree, as well as the most suited Spherical Harmonics (SH) degree-and-order (d/o) for Kuwait, are the best combined GGMs models for application in Kuwait GOCE GGMs are 250 according to the Space Wise model (SPW_R5) [61] with EGM2008 [62] up to SH d/o 2190. (SPW R5) is included in this study. ...
Determination of local geometric geoid model for Kuwait
Article
  • Jul 2022
  • J Appl Geodes
Determining a precise local geoid is particularly important for converting the Global Navigation Satellite System (GNSS) heights to orthometric heights. The geometric method for computing the geoid has been extensively used for a comparatively small region, which, in some points, interpolates geoid heights based on GNSS-derived heights and levelling heights. Several considerations should be considered when using the geometric method to increase the accuracy of a local geoid. Kuwait is used as a test area in this paper to investigate several features of the geometric method. The achievable precision is one of these aspects, the role of the interpolation method, global geopotential models, and the influence of the topo-graphic effect. The accuracy of the local geoid can be substantially enhanced by integrating a geopotential model with a digital terrain model of the research region. It is possible to get a precision of 2-3 cm.
View
... All recent GGMs, such as GOCO05s (Mayer-Guerr, 2015), GOCE TIM-R5 (Brockmann et al., 2014) and GOCE SPW-R5 (Gatti et al., 2016), were tested in this study, in steps of 10 degrees, to determine the best GGM and its optimum maximum degree in combination with EGM2008. Figure 3.1 indicates the STD of the differences between the GOCE GGMs in combination with EGM2008 (up to d/o 2190) and the GNSS/levelling data, described in Section 3.1.4. It can be seen that thanks to the GOCE, STD of GGMs significantly improves (from 0.29 m down to 0.16 m). ...
Height system unification and estimation of the lithospheric structure beneath Vietnam through high-resolution gravity field and quasigeoid modeling
Thesis
Full-text available
  • Feb 2021
The goal of this work was twofold. The first part was devoted to the research of the size and physical shape of the Earth in Vietnam through the determination of a local gravimetric quasigeoid model. The second part was to better constrain the Earth's interior structure beneath Vietnam by determining the Moho and Lithosphere-Asthenosphere Boundary (LAB) depth models. For the first objective, a high-resolution gravimetric quasigeoid model for Vietnam and its surrounding areas was determined based on new land gravity data in combination with fill-in data where no gravity data existed. The resulting quasigeoid model was evaluated using 812 GNSS/levelling points in the study region. This comparison indicates that the quasigeoid model has a standard deviation of 9.7 cm and 50 cm in mean bias. This new local quasigeoid model for Vietnam represents a significant improvement over the global models EIGEN-6C4 and EGM2008, which have standard deviations of 19.2 and 29.1 cm, respectively, when compared to the GNSS/levelling data. An essential societal and engineering application of the gravimetric quasigeoid is in GNSS levelling, and a vertical offset model for Vietnam and its surrounding areas was determined based on the GNSS/levelling points and gravimetric-only quasigeoid model for this purpose. The offset model was evaluated using cross-validation technique by comparing with GNSS/levelling data. Results indicate that the offset model has a standard deviation of 5.9 cm in the absolute sense. Thanks to this offset model, GNSS levelling can be carried out over most of Vietnam's territory complying to third-order levelling requirements, while the accuracy requirements for fourth-order levelling networks is met for the entire country. To unify the height system towards the International Height Reference Frame (IHRF), the zero-height geopotential value for the Vietnam Local Vertical Datum W_0^LVD was determined based on two approaches: 1) Using high-quality GNSS/levelling data and the estimated gravimetric quasigeoid model, 2) Using the Geodetic Boundary Value Problem (GBVP) approach based on the GOCE global gravity field model enhanced with terrestrial gravity data. This geopotential value can be used to connect the height system of Vietnam with the neighboring countries. Moreover, the GBVP approach was also used for direct determination of the gravity potential on the surface at three GNSS Continuously Operating Reference Station (CORS) stations at epoch 2018.0 in Vietnam. Based on time series of the vertical component derived from these GNSS observations as well as InSAR data, temporal variations in the geopotential were also estimated on these permanent GNSS stations. This enables monitoring of the vertical datum and detect possible deformation. These stations may thus contribute to increase the density of reference points in the IHRF for this region. For the second objective, the local quasigeoid model was first converted to the geoid. Then, high-resolution Moho and LAB depth models were determined beneath Vietnam based on the local isostatic hypothesis using the geoid height derived from the estimated geoid, elevation data and thermal analysis. From new land gravity data, a complete grid and map of gravity anomalies i.e., Free-air, Bouguer and Isostatic was determined for the whole of Vietnam. The Moho depth was also computed based on the gravity inversion using the Bouguer gravity anomaly grid. All new models are computed at 1' resolution. The resulting Moho and LAB depth models were evaluated using available seismic data as well as global and local lithospheric models available in the study region. [...]
View
... In this contribution, different datasets are used in order to develop gravimetric geoid model for Egypt from different sources such as gravity anomalies determined from the GOCE-based global geopotential model GO_CONS_GCF_2_SPW_R5 (SPW-R5) ( Gatti et al., 2016), from the Earth Geopotential Model 2008 (EGM2008) (Pavlis et al., 2012) and from ground-based gravity measurements. In addition, geoid undulations obtained from 17 GPS/levelling stations will be used to adjust the gravimetric geoid model with the national local vertical datum for Egypt. ...
Determination of local gravimetric geoid model over Egypt using LSC and FFT estimation techniques based on different satellite- and ground-based datasets
Article
Full-text available
  • Jun 2021
In this contribution, two gravimetric geoid models for Egypt; EGY-LGM2019 and EGY-FGM2019 are developed using the least-squares collocation and the Fast-Fourier Transformation methods, applying Remove-Restore procedure. Different datasets are used in terms of gravity anomalies obtained from GOCE-based SPW-R5 and EGM2008 models, and from 1015 terrestrial gravity stations. Two gravimetric geoid models, EGY-FLGM2019 derived by the LSC method and EGY-FFGM2019 derived by 1D-FFT method are computed and fitted using the 17 GPS/levelling measurements to adjust the gravimetric geoid model with the national local vertical datum for Egypt. Our findings between the 6 GPS/levelling geoid undulations and the developed fitted geoid models EGY-FFGM2019 and EGY-FLGM2019 are about 7.57 and 18.46 cm, respectively. In addition, the former model improves the geoid heights of about 72-65% over Egypt w.r.t. the EGM2008 and GECO models, respectively. Therefore, the EGY-FFGM2019 model is recommended as a reliable model that improves the geoid heights over Egypt.
View
... This is used to reduce the satellite gravity gradiometry (SGG) observations, which are filtered along the orbit using a Wiener filter. From these filtered SGG observations, locally regularized patches are predicted and composed to a global grid (Gatti et al. 2016). These global grids can again be converted to spherical harmonics with a covariance matrix determined by Monte Carlo samples (Migliaccio et al. 2008). ...
An Improved Model of the Earth’s Static Gravity Field Solely Derived from Reprocessed GOCE Data
Article
Full-text available
  • Mar 2021
  • SURV GEOPHYS
After 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.
View
Regional evaluation of global geopotential models and three types of digital elevation models with ground-based gravity and GNSS/levelling data using several techniques over Sudan
Article
  • May 2024
  • J Appl Geodes
To evaluate the performance of the global geopotential models (GGMs) in a more unbiased way, ground-based gravity and GNSS/levelling datasets are highly required. In this study, the eight latest releases of the satellite-only and combined GGMs are evaluated on the regional scale using the available terrestrial gravity and GNSS/Levelling data over Sudan, considering the spectral consistency issue by applying the spectral enhancement method (SEM). The evaluation process consists of three stages: firstly, the eight GGMs are evaluated globally with each other by using different degree variances in terms of geoid heights, gravity anomalies, and signal-to-noise ratio (SNR); secondly, the GGMs are compared against the Earth Gravitational Model 2008 (EGM2008) on a regional scale over Sudan; thirdly, apply the SEM strategy by incorporating high (SEM_WITHOUT_RTM technique) and very-high (SEM technique) frequencies of the gravity field spectrum from the EGM2008 and high-resolution residual terrain model (RTM), respectively. For reliable robustness of the latter evaluation process, three different DEMs are used, namely, SRTM30, ASTER30, and GTOPO30. Our findings on the evaluation process using SEM_WITHOUT_RTM technique show improved gravity anomalies solutions regarding differences of standard deviations (STD) from 19–20.7 mGal to about 14 mGal. When applying the SEM technique, more improvements are achieved, providing STD differences in gravity anomalies and geoid heights of about 12 mGal and 45 cm, respectively. Among the three applied DEMs, it has been found that despite the slight refinements, the ASTER30 and GTOPO30 models show better performance than the SRTM30 model.
View
Improving Accuracy of Local Geoid Model using Machine Learning Approaches and Residuals of GPS/Levelling Geoid Height
Article
  • Sep 2021
  • SURV REV
This study aims to use GPS/Levelling data and machine learning techniques to model a high precision local geoid for Kuwait. To improve the accuracy of a local geoid the global geopotential model and local terrain effect should be incorporated. The geoid model was improved based on the modeling of geoid residuals using three machine learning algorithms (MLs). The geoid residuals were determined using geoid undulation of 78 GPS/Levelling points with considering the Global Geopotential Models (GGMs) and Residual Terrain Model (RTM) effects at these stations. Minimax Probability Machine Regression (MPMR), Gaussian Process Regression (GPR), and Multivariate Adaptive Regression Splines (MARS) MLs were developed and compared for modeling the calculated geoid residuals. The results show that the accuracy of the three MLs was improved compared to previous studies, and the accuracy of the GPR model was better than the other models. The standard deviations of Kuwait geoid undulation determined by GPS/Levelling, gravimetric, and developed GPR models were 1.377 m, 1.375 m, 1.375 m, respectively. Thus, the developed GPR model has successfully predicted an accurate geoid height of Kuwait with maximum variation approaches +0.02 m.
View
ResearchGate has not been able to resolve any references for this publication.