GOCE-based Global Geopotential Models Research Articles

Improvement of GOCE-Based Global Geopotential Models for Gravimetric Geoid Modeling in Turkey

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.

ASSESSMENT OF RECENT GOCE-BASED GLOBAL GEOPOTENTIAL MODELS AND EGM2008 IN NIGER REPUBLIC

In this study, we assessed recent GOCE-based Global Geopotential Models (GGMs) and EGM2008 in Niger. The combined GGMs EIGEN_6C4, GECO and EGM2008 were evaluated up to their maximum degree and order (d/o) 2,190 to select the one for gravity database densification. The following pure satellite GGMs were assessed for the modelling of the long and medium wavelengths in geoid computation: GGM05G, ITU_GGC16, EIGEN_6S4v2 and the fifth releases from direct (DIR5), space-wise (SPW5) and time-wise (TIM5) approaches. The GGMs are compared to terrestrial gravity data and geoid heights from GNSS/Levelling points before and after applying spectral enhancement method (SEM) by residual terrain model (RTM) for combined models and by RTM and the coefficients of selected combined GGM for pure satellite models. The agreements of combined GGMs with terrestrial gravity data and GNSS/Levelling points, in terms of root mean square (RMS) are about 4.88 to 5.02 mGal and 0.14 to 0.16 m, respectively. EIGEN_6C4 was selected as it showed the best performance in terms of geoid height differences and the probability of 3-sigma rule for gravity anomaly differences. At d/o 200, DIR5 showed a good agreement with terrestrial gravity data (5.04 mGal) and GNSS/Levelling points (0.15 m) after applying SEM, it was then retained. All GOCE-based models exhibited a good performance in long and medium wavelengths confirming the good recovery of the gravity field by the spatial gravity mission in these spectral bands.

Preliminary results of GOCE-based height system unification between Greece and Turkey over marine and land areas

The unification of local vertical datums (LVDs) at a country-wide scale has gained significant attention lately due to the availability of GOCE-based global geopotential models (GGMs) and the unprecedented geoid height accuracies offered. Within a single country, several LVDs may be used, especially in the case of islandic nations. Therefore, the unification of all of them to a single nation-wide LVD is of utmost importance. The same holds for neighboring countries, where the unification of their vertical datums is necessary as a tool of engineering, cross-border collaboration and environmental and risk management projects. The aforementioned set the main scope of the present study, which focuses on the use of GOCE and GOCE/GRACE GGMs in order to investigate the offsets between the Greek and Turkish LVDs. First an evaluation of the latest release 5 GOCE GGMs is carried out, either to their maximum degree or through spectral enhancement with EGM208 and topographic effects. Then, the geopotential value for the Greek and Turkish LVDs is performed, along with different estimates for the marine area of the Aegean Sea where several islands and isles exist with each one realizing its own LVD. The relative offset between the two LVDs was determined and used to provide a direct link between the Greek and Turkish LVDs with the IAG conventional value recently proposed as a global WHS. From the results achieved it was concluded that the spectrally enhanced GOCE GGMs reduce the standard deviation of the differences with GPS/levelling data by 2–4 cm over Turkey and 2 cm for mainland Greece. In terms of the zero-level geopotential determination, the LVD of the Greek mainland is 64.9 cm below the IAG conventional value, while that of Turkey is 9.6 cm above. Finally, it is concluded that in practice each Greek island realizes its own LVD with offsets between them as large as 35 cm. Despite that fact, the spectrally enhanced GOCE GGMs and in particular GOCO05s provides the overall smallest height residuals over the islands, hence the $$ \widehat{W}_{o}^{LVD} $$ based on that can be recommended as the best estimate. In that way, relative offsets with the LVD of mainland Greece can be computed for each island, ranging between −23.8 and 15.5 cm.

On High-Frequency Topography-Implied Gravity Signals for a Height System Unification Using GOCE-Based Global Geopotential Models

National height reference systems have conventionally been linked to the local mean sea level, observed at individual tide gauges. Due to variations in the sea surface topography, the reference levels of these systems are inconsistent, causing height datum offsets of up to ±1–2 m. For the unification of height systems, a satellite-based method is presented that utilizes global geopotential models (GGMs) derived from ESA’s satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE). In this context, height datum offsets are estimated within a least squares adjustment by comparing the GGM information with measured GNSS/leveling data. While the GNSS/leveling data comprises the full spectral information, GOCE GGMs are restricted to long wavelengths according to the maximum degree of their spherical harmonic representation. To provide accurate height datum offsets, it is indispensable to account for the remaining signal above this maximum degree, known as the omission error of the GGM. Therefore, a combination of the GOCE information with the high-resolution Earth Gravitational Model 2008 (EGM2008) is performed. The main contribution of this paper is to analyze the benefit, when high-frequency topography-implied gravity signals are additionally used to reduce the remaining omission error of EGM2008. In terms of a spectral extension, a new method is proposed that does not rely on an assumed spectral consistency of topographic heights and implied gravity as is the case for the residual terrain modeling (RTM) technique. In the first step of this new approach, gravity forward modeling based on tesseroid mass bodies is performed according to the Rock–Water–Ice (RWI) approach. In a second step, the resulting full spectral RWI-based topographic potential values are reduced by the effect of the topographic gravity field model RWI_TOPO_2015, thus, removing the long to medium wavelengths. By using the latest GOCE GGMs, the impact of topography-implied gravity signals on the estimation of height datum offsets is analyzed in detail for representative GNSS/leveling data sets in Germany, Austria, and Brazil. Besides considerable changes in the estimated offset of up to 3 cm, the conducted analyses show that significant improvements of 30–40% can be achieved in terms of a reduced standard deviation and range of the least squares adjusted residuals.

Gravity field anomalies from recent GOCE satellite-based geopotential models and terrestrial gravity data: a comparative study over Saudi Arabia

Global geopotential models (GGMs) provide important information about the Earth gravity field in terms of precise gravity anomaly, gravity disturbance, and geoid height on global and regional scales. The GGMs based on the Gravity Recovery and steady-state Ocean Circulation Explorer (GOCE) satellite gravity mission provided by the International Center for Global Earth Models (ICGEM) differ in their accuracy and spatial resolution. In this paper, we evaluate the free-air gravity anomalies and geoid heights determined from several recent GOCE-based GGMs using the corresponding gravity functions (i.e., gravity anomalies and geoid heights) obtained from the Earth Gravitational Model 2008 (EGM2008) over the Kingdom of Saudi Arabia (KSA). Moreover, free-air gravity anomalies determined from GOCE-based GGMs have also been compared with the corresponding ones obtained from ground-based “terrestrial” gravity measurements over the study area. The latter comparison, using the available 3500 terrestrial gravity observations, applies the spectral enhanced method (SEM). We use the SEM to compensate the missed high-frequency component of geoid heights in GOCE-based GGMs using EGM2008 and a high-resolution digital terrain model based on the Shuttle Radar Topography Mission (SRTM). The statistical comparisons of the computed results in terms of free-air gravity anomalies and geoid heights obtained from GOCE-based GGMs are in general agreement. The estimated standard deviations of differences are 5 mGal (20 cm), 6–7 mGal (22–24 cm), and 8 mGal (25.9 cm) at spherical harmonic (SH) degree/order (d/o) 200, 240, and 280, respectively. Free-air gravity anomalies computed from available terrestrial gravity data, using the SEM, have been compared with the corresponding ones estimated from GOCE-based GGMs, and the results indicate an improvement over EGM2008 in the medium wavelengths. Investigation of various releases of GOCE-based GGM, up to d/o 200, reveals that the fourth and fifth releases of GOCE-based GGMs developed with the use of time-wise solution strategies (TIM_R4 and TIM_R5) approximate the gravity field well over the KSA region, since they provide the least standard deviation differences at SH. Thus, the TIM_R5 and TIM_R4 are suggested as reference models for recovering the long wavelength up to SH d/o 200 and 240, respectively, when modeling the gravimetric quasi-geoid over the KSA area.

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

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.

North American height datums and their offsets: Evaluation of the GOCE-based global geopotential models in Canada and the USA

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission was launched on March 17, 2009. Three generations of global geopotential models have been computed and released based on the data collected by GOCE since then. The first generation of the models has been computed from the first two months of the data, and more observations, ranging from six to eight months, have been used in the computation of the second generation models. The third generation models are based on eighteen months of GOCE observations. The evaluation of these models is important in view of Canada’s and the USA’s decision to modernize and unify their vertical datums based on the geoid. In this paper, the released GOCE-based models are evaluated using 1315 and 18399 GNSS/levelling stations in Canada and the USA, respectively. In addition, three GRACE-based models and EGM2008 are included in the evaluation procedure as ’pre-GOCE era’ models to identify any improvements brought by the new GOCE-based models in the region. The results provide evidence that the third generation time-wise (go_cons_gcf_2_tim_r3) and direct approach (go_cons_gcf_2_dir_r3) GOCE models perform slightly better than the rest of the geopotential models in Canada and the USA

North American height datums and their offsets: Evaluation of the GOCE-based global geopotential models in Canada and the USA

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission was launched on March 17, 2009. Three generations of global geopotential models have been computed and released based on the data collected by GOCE since then. The first generation of the models has been computed from the first two months of the data, and more observations, ranging from six to eight months, have been used in the computation of the second generation models. The third generation models are based on eighteen months of GOCE observations. The evaluation of these models is important in view of Canada’s and the USA’s decision to modernize and unify their vertical datums based on the geoid. In this paper, the released GOCE-based models are evaluated using 1315 and 18399 GNSS/levelling stations in Canada and the USA, respectively. In addition, three GRACE-based models and EGM2008 are included in the evaluation procedure as ’pre-GOCE era’ models to identify any improvements brought by the new GOCE-based models in the region. The results provide evidence that the third generation time-wise (go−cons−gcf−2−tim−r3) and direct approach (go−cons−gcf−2−dir−r3) GOCE models perform slightly better than the rest of the geopotential models in Canada and the USA.