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The GOCE satellite was orbiting the Earth in a Sun-synchronous orbit at a very low altitude for more than 4 years. This low orbit and the availability of high-quality data make it worthwhile to assess the contribution of GOCE GPS data to the recovery of both the static and time-variable gravity fields. We use the kinematic positions of the official GOCE precise science orbit (PSO) product to perform gravity field determination using the Celestial Mechanics Approach. The generated gravity field solutions reveal severe systematic errors centered along the geomagnetic equator. Their size is significantly coupled with the ionospheric density and thus generally increasing over the mission period. The systematic errors may be traced back to the kinematic positions of the PSO product and eventually to the ionosphere-free GPS carrier phase observations used for orbit determination. As they cannot be explained by the current higher order ionospheric correction model recommended by the IERS Conventions 2010, an empirical approach is presented by discarding GPS data affected by large ionospheric changes. Such a measure yields a strong reduction of the systematic errors along the geomagnetic equator in the gravity field recovery, and only marginally reduces the set of useable kinematic positions by at maximum 6 % for severe ionosphere conditions. Eventually it is shown that GOCE gravity field solutions based on kinematic positions have a limited sensitivity to the largest annual signal related to land hydrology.

In a context of global change and increasing anthropic pressure on the environment, monitoring the Earth system and its evolution has become one of the key missions of geosciences. Geodesy is the geoscience that measures the geometric shape of the Earth, its orientation in space, and gravity field. Time-variable gravity, because of its high accuracy, can be used to build an enhanced picture and understanding of the changing Earth. Ground-based gravimetry can determine the change in gravity related to the Earth rotation fluctuation, to celestial body and Earth attractions, to the mass in the direct vicinity of the instruments, and to vertical displacement of the instrument itself on the ground. In this paper, we review the geophysical questions that can be addressed by ground gravimeters used to monitor time-variable gravity. This is done in relation to the instrumental characteristics, noise sources, and good practices. We also discuss the next challenges to be met by ground gravimetry, the place that terrestrial gravimetry should hold in the Earth observation system, and perspectives and recommendations about the future of ground gravity instrumentation. Plain Language Summary: In a context of global change and increased human vulnerability to terrestrial hazard, monitoring the Earth system is one of the key challenges of geoscience. In particular, terrestrial gravimetry, with its precision at the level of one part of a billion, allows the monitoring of many phenomena, from water resource availability to volcanic activity. This paper reviews the technique, its advantages and limitations, how it has been used in the Earth monitoring, and the next challenges to be met by ground gravimetry.

The GOCE gravity gradiometer measured highly accurate gravity gradients along the orbit during GOCE’s mission lifetime from March 17, 2009, to November 11, 2013. These measurements contain unique information on the gravity field at a spatial resolution of 80 km half wavelength, which is not provided to the same accuracy level by any other satellite mission now and in the foreseeable future. Unfortunately, the gravity gradient in cross-track direction is heavily perturbed in the regions around the geomagnetic poles. We show in this paper that the perturbing effect can be modeled accurately as a quadratic function of the non-gravitational acceleration of the satellite in cross-track direction. Most importantly, we can remove the perturbation from the cross-track gravity gradient to a great extent, which significantly improves the accuracy of the latter and offers opportunities for better scientific exploitation of the GOCE gravity gradient data set.

New-generation synthetic aperture radar altimetry, as implemented on CryoSat-2, observes sea surface heights in coastal areas that were previously not monitored by conventional altimetry. Therefore, CryoSat-2 is expected to improve the coastal mean dynamic topography (MDT). However, the MDT remains highly reliant on the geoid. Using new regional geoid models as well as CryoSat-2 data, we determine three geodetic coastal MDT models in Norway and validate them against independent tide-gauge observations and the operational coastal ocean model NorKyst800. The CryoSat-2 MDTs agree on the ∼3–5 cm level with both tide-gauge geodetic and ocean MDTs along the Norwegian coast. In addition, we compute geostrophic surface currents to help identifying errors in the geoid models. We find that even though the regional geoid models are all based on the latest satellite gravity data as provided by GOCE, the resulting circulation patterns differ. We demonstrate that some of these differences are due to erroneous or lack of marine gravity data. This suggests that there is significant MDT signal at spatial scales beyond GOCE, and that the geodetic approach to MDT determination benefits from the additional terrestrial gravity information provided by a regional geoid model. We also find that the border of the geographical mode mask of CryoSat-2 coincides with the Norwegian Coastal Current, making it challenging to distinguish between artifacts in the CryoSat-2 observations during mode switch and ocean signal.

Global gravity models are being developed according to new data sets available from satellite gravity missions and terrestrial/marine gravity data which are provided by different countries. Some countries do not provide all their available data and the global gravity models have many vague computational methods. Therefore, the models need to be evaluated locally before using. It is generally understood that the accuracy of global gravity models is enough for local (civil, mining, construction, etc.) projects, however, our results in Iran show that the differences between synthesized values and observation data reach up to ∼300 mGal for gravity anomalies and ∼2 m for geoid heights. Even by applying the residual topographical correction to synthetized gravity anomalies, the differences are still notable. The accuracy of global gravity models for predicting marine gravity anomalies is also investigated in Persian Gulf and the results show differences of ∼140 mGal in coastal areas. The results of evaluating selected global gravity models in Iran indicate that the EIGEN-6C4 achieves the lowest RMS for estimating the geoid heights. EGM08 predicts the closest results to terrestrial gravity anomalies. DIR-R5 GOCE satellite-only model estimates the low-frequency part of gravity field more accurately. The best prediction of marine gravity anomalies is also achieved by EGM08.

Geocentre motion between the centre-of-mass of the Earth system and the centre-of-figure of the solid Earth surface is a critical signature of degree-1 components of global surface mass transport process that includes sea level rise, ice mass imbalance and continental-scale hydrological change. To complement GRACE data for complete-spectrum mass transport monitoring, geocentre motion needs to be measured accurately. However, current methods of geodetic translational approach and global inversions of various combinations of geodetic deformation, simulated ocean bottom pressure and GRACE data contain substantial biases and systematic errors. Here, we demonstrate a new and more reliable unified approach to geocentre motion determination using a recently formed satellite laser ranging based geocentric displacement time-series of an expanded geodetic network of all four space geodetic techniques and GRACE gravity data. The unified approach exploits both translational and deformational signatures of the displacement data, while the addition of GRACE's near global coverage significantly reduces biases found in the translational approach and spectral aliasing errors in the inversion.

The results of the theoretical and experimental research on the technique for refining the global Earth geopotential models such as EGM2008 in the continental regions are presented. The discussed technique is based on the high-resolution satellite data for the Earth’s surface topography which enables the allowance for the fine structure of the Earth’s gravitational field without the additional gravimetry data. The experimental studies are conducted by the example of the new GGMplus global gravity model of the Earth with a resolution about 0.5 km, which is obtained by expanding the EGM2008 model to degree 2190 with the corrections for the topograohy calculated from the SRTM data. The GGMplus and EGM2008 models are compared with the regional geoid models in 21 regions of North America, Australia, Africa, and Europe. The obtained estimates largely support the possibility of refining the global geopotential models such as EGM2008 by the procedure implemented in GGMplus, particularly in the regions with relatively high elevation difference.

The circulation in the North Indian Ocean (NIO) is one of the most complex systems compared with other regions of global oceans, mostly due to its interactions with the monsoon winds. In recent yea...

Since 2010 several new satellite altimetry missions have commenced delivering altimetry-derived gravity data with a global offshore coverage and with a quality in many regions nearing that of ship-borne gravity observations. This is resulting in greatly improved global offshore high resolution gravity fields. The DTU13 and Sandwell and Smith’s v23.1 grids of altimetric gravity anomalies from offshore Western Australia are compared with ship-track gravity anomalies computed from the Geoscience Australia marine gravity database. The standard deviation of the difference between the ship-borne gravity data and the satellite altimetric gravity data is 3.1mGal for the DTU13 data and 3.3 mGal for Sandwell and Smith’s v23.1 grid. In water depths less than 20m we observed significant differences between ship-borne gravity and altimetric gravity. Over the sampled wavelengths, the DTU13 altimetric gravity data appears to have the best resemblance to the reference marine gravity data, exhibiting the overall least difference amplitude over most wavelengths.

The global geopotential models (GGMs) derived from the gravity field and steady-state ocean circulation explorer (GOCE) mission provide important information about Earth gravity functionals (e.g., geoid heights, gravity anomalies, and disturbances). Among gravity functionals, we utilize geoid heights which have been determined from several recent GOCE-based GGMs and validate them against 5187 collocated Global Navigation Satellite System (GNSS)/leveling observations over a network of dedicated benchmarks in Saudi Arabia. Our aim is to consider the spectral consistency between GOCE-based GGMs and ground-based data. Accordingly, we incorporate high/very high frequencies of gravity functionals, i.e., the gravity signal beyond the maximum d/o of GOCE-based GGMs, using EGM2008 and a high-resolution digital terrain model based on the Shuttle Radar Topography Mission (SRTM). This investigation indicates that completing the missing high-frequency component of geoid heights in GOCE-based GGMs, using EGM2008 and SRTM data, results in an improvement of about 16% in the reduction in the standard deviation (SD) of the differences. This is provided by DIR_R5 at SH d/o 230, which shows improvement from 37.5 cm, without applying the spectral enhancement method (SEM), compared to 31.4 cm when applying the SEM. Finally, three types of transformation models, namely four-, five-, and seven-parameter transformations, are examined to deal with the data biases and to provide a better fitting of geoid heights obtained from the studied GOCE-based GGMs to those from GNSS/leveling data. These models reveal that the SD of vertical datum over the region of Saudi Arabia is at the level of about 22 cm.

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 (R2) 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 R2 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.

Global geopotential models (GGMs) are vital in computing global geoid undulations heights. Based on the ellipsoidal height by Global Navigation Satellite System (GNSS) observations, the accurate orthometric height can be calculated by adding precise and accurate geoid undulations model information. However, GGMs also provide data from the satellite gravity missions such as GRACE, GOCE and CHAMP. Thus, this will assist to enhance the global geoid undulations data. A statistical assessment has been made between geoid undulations derived from 4 GGMs and the airborne gravity data provided by Department of Survey and Mapping Malaysia (DSMM). The goal of this study is the selection of the best possible GGM that best matches statistically with the geoid undulations of airborne gravity data under the Marine Geodetic Infrastructures in Malaysian Waters (MAGIC) Project over marine areas in Sabah. The correlation coefficients and the RMS value for the geoid undulations of GGM and airborne gravity data were computed. The correlation coefficients between EGM 2008 and airborne gravity data is 1 while RMS value is 0.1499.In this study, the RMS value of EGM 2008 is the lowest among the others. Regarding to the statistical analysis, it clearly represents that EGM 2008 is the best fit for marine geoid undulations throughout South China Sea.

The impact of GOCE Satellite Gravity Gradiometer data on gravity field models was tested. All models were constructed with the same Laser Geodynamics Satellite (LAGEOS) and Gravity Recovery and Climate Experiment (GRACE) data, which were combined with one or two of the diagonal gravity gradient components for the entire GOCE mission (November 2009 to October 2013). The Stokes coefficients were estimated by solving large normal equation (NE) systems (i.e., the direct numerical approach). The models were evaluated through comparisons with the European Space Agency's (ESA) gravity field model DIR-R5, by GPS/Leveling, GOCE orbit determination, and geostrophic current evaluations. Among the single gradient models, only the model constructed with the vertical ZZ gradients gave good results that were in agreement with the formal errors. The model based only on XX gradients is the least accurate. The orbit results for all models are very close and confirm this finding. All models constructed with two diag...

The Global Geopotential Models (GGMs) of GOCE (Gravity Recovery and steady- state Ocean Circulation Explorer) differ globally as well as regionally in their accuracy and resolution based on the maximum degree and order (d/o) of the fully normalized spherical harmonic (SH) coefficients, which express each GGM. The main idea of this study is to compare the free-air gravity anomalies and quasi geoid heights determined from several recent GOCE-based GGMs with the corresponding ones from the Earth Gravitational Model 2008 (EGM2008) over Egypt on the one hand and with ground-based measurements on the other hand. The results regarding to the comparison of GOCE-based GGMs with terrestrial gravity and GPS/levelling data provide better improvement with respect to EGM2008. The 4th release GOCE-based GGM developed with the use of space-wise solution strategy (SPW_R4) approximates the gravity field well over the Egyptian region. The SPW_R4 model is accordingly suggested as a reference model for recovering the long wavelength (up to SH d/o 200) components of quasi geoid heights when modelling the gravimetric quasi-geoid over the Egypt. Finally, three types of transformation models: Four-, Five- and Seven-parameter transformations have been applied to reduce the data biases and to provide a better fitting of quasi geoid heights obtained from the studied GOCE-based GGMs to those from GPS/levelling data. These models reveal that the standard deviation of vertical datum over Egypt is at the level of about 32 cm.

The summary of research activities concerning gravity field modelling and gravimetric works performed in Poland in the period of 2011-2014 is presented. It contains the results of research on geoid modelling in Poland and other countries, evaluation of global geopotential models, determination of temporal variations of the gravity field with the use of data from satellite gravity space missions, absolute gravity surveys for the maintenance and modernization of the gravity control in Poland and overseas, metrological aspects in gravimetry, maintenance of gravimetric calibration baselines, and investigations of the nontidal gravity changes. The bibliography of the related works is given in references.

Firstly, the Earth's gravitational field from the past Challenging Minisatellite Payload (CHAMP) mission is determined using the energy conservation principle, the combined error model of the cumulative geoid height influenced by three instrument errors from the current Gravity Recovery and Climate Experiment (GRACE) and future GRACE Follow-On missions is established based on the semi-analytical method, and the Earth's gravitational field from the executed Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission is recovered by the space-time-wise approach. Secondly, the cumulative geoid height errors are 1.727 × 10 −1 m, 1.839 × 10 −1 m and 9.025 × 10 −2 m at degrees 70,120 and 250 from the implemented three-stage satellite gravity missions consisting of CHAMP, GRACE and GOCE, which preferably accord with those from the existing earth gravity field models involving EIGEN-CHAMP03S, EIGEN-GRACE02S and GO_CONS_GCF_2_DIR_R1. The cumulative geoid height error is 6.847 × 10 −2 m at degree 250 from the future GRACE Follow-On mission. Finally, the complementarity among the four-stage satellite gravity missions including CHAMP, GRACE, GOCE and GRACE Follow-On is demonstrated contrastively.

Zero-length spring gravity sensors, such as the Micro-g LaCoste Turnkey Airborne Gravity System (TAGS), are widely used in airborne gravimetry applications due to their virtually drift-free characteristics. However, the quality of the final gravity product depends on the methods chosen to correct for several dynamic effects, including the Eötvös correction, the vertical acceleration correction of the moving aircraft, and the instrument platform tilt correction. For geodetic applications using regional gravity field mapping for geoid determination, the choices of correction method are extremely important because the flights are done uncommonly high and fast. For this reason, and in support of the Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project, the National Oceanic and Atmospheric Administration’s National Geodetic Survey (NGS), and Fugro Geospatial have independently developed airborne gravity processing software packages for TAGS data — called Newton and GravPRO, respectively. We have evaluated the airborne gravity data processing methods that are used in the two software packages. We processed a GRAV-D data set collected by NGS over Louisiana and the Gulf of Mexico in 2008 with both packages, we compared the results for each major data correction applied, and we evaluated unique add-on features and tools. The results determined that the two software packages were very comparable, both yielding an excellent crossover root-mean-square of 1.8 mGal without any crossover adjustment applied. For the worst 14% of survey lines, which had higher levels of aircraft dynamics during flight, GravPRO was able to retain more data due to advantages in its platform tilt correction method. Also, GravPRO’s instrument calibration function, which is based on crossover error analysis, found a 45% improvement in achievable survey precision from approximately 2 mGal to approximately 1 mGal when comparing the test data set to a global gravity model.

Spectral characteristics of modern models of the Earth’s gravity field obtained from the CHAMP, GRACE and GOCE space gravity missions are considered. The resolution is estimated for a specified accuracy.

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) is the European Space Agency's (ESA)satellite gravity mission to determine the Earth's mean gravity field. GOCE delivers gravity gradients, anew type of satellite data. We study how these data can improve modeling of the Earth's lithosphere. We discuss the use of the original GOCE gravity gradients versus the use of gravity gradients in grids at satellite altitude or close the Earth's surface and conclude that grids are easier to handle than the original data because one does not have to deal with very different error characteristics of the different gradients, given in a rotating frame at varying heights. The downward continuation to the surface enhances signaland better reflects the near-surface geology. But this does not outweigh the amplification of noise and omission errors, which is why we recommend using the field at mean satellite altitude for lithospheric modeling. The North-East Atlantic region is ideal to analyze the additional value of GOCE gravity gradients because it is a well-studied region in terms of regional geophysics. We calculated the gradient sensitivity for crustal depth slices using a 3D lithospheric model. This reveals that especially interfaces with large density contrasts have a distinct signal in the gravity gradients, but that they are quite insensitive to intra-crustal density sources, which can have quite a large effect on surface gravity data. We also show thatthe satellite gradients have a depth sensitivity well suited to study the upper mantle density structure, making them complementary to gravity and seismic tomography. In the underexplored Rub'al-Khaliarea the GOCE vertical gradient was used to invert for crustal thickness. The updated Moho model givesa good fit to four of the six gradients and independent depths from seismic stations. The Moho modelwas used to update the heat flow model and source rock maturity maps, which are generally consistent with known source rock maturity trends in the surrounding regions. GOCE gradients are therefore usefulto map crustal thickness and deep regional structures for frontier areas. In combination with other data, heat flow can be modeled which is essential for basin maturity evaluation. © 2013 Elsevier B.V.

At present, gravity field and steady-state ocean circulation explorer (GOCE) gravity data are always used to compute regional gravity anomaly and geoid height. In this study, the latest GOCE gravity field model data (from Oct. 2009 to Jul. 2010) are used to compute the gravity gradient of mainland China according to a rigorous recursion formula (in all the six directions). The results show that the numerical values of the gravity gradients are larger in the T rr direction than those in the other directions. They reflect the terrain characteristics in detail and correlate with the regional tectonics; however, in the T θλ and T rλ directions, the numerical values are relatively smaller and the gravity gradients in the T rλ direction do not reflect the terrain characteristics in detail.

The Gravity Recovery and Climate Experiment (GRACE) mission is able to observe the global large-scale mass and water cycle for the first time with unprecedented spatial and temporal resolution. However, no other time-varying gravity fields validate GRACE. Furthermore, the C20 of GRACE is poor, and no GRACE data are available before 2002 and there will likely be a gap between the GRACE and GRACE-FOLLOW-ON mission. To compensate for GRACE’s shortcomings, in this paper, we provide an alternative way to invert Earth’s time-varying gravity field, using a priori degree variance as a constraint on amplitudes of Stoke’s coefficients up to degree and order 60, by combining continuous GPS coordinate time series and satellite altimetry (SA) mean sea level anomaly data from January 2003 to December 2012. Analysis results show that our estimated zonal low-degree gravity coefficients agree well with those of GRACE, and large-scale mass distributions are also investigated and assessed. It was clear that our method effectively detected global large-scale mass changes, which is consistent with GRACE observations and the GLDAS model, revealing the minimums of annual water cycle in the Amazon in September and October. The global mean mass uncertainty of our solution is about two times larger than that of GRACE after applying a Gaussian spatial filter with a half wavelength at 500 km. The sensitivity analysis further shows that ground GPS observations dominate the lower-degree coefficients but fail to contribute to the higher-degree coefficients, while SA plays a complementary role at higher-degree coefficients. Consequently, a comparison in both the spherical harmonic and geographic domain confirms our global inversion for the time-varying gravity field from GPS and Satellite Altimetry.

The performance of Gravity field and steady-state Ocean Circulation Explorer (GOCE) global gravity field models (GGMs), at the end of GOCE mission covering 42 months, is evaluated using geoid undulations and free-air gravity anomalies over Japan, including six sub-regions (Hokkaido, north Honshu, central Honshu, west Honshu, Shikoku and Kyushu). Seventeen GOCE-based GGMs are evaluated and compared with EGM2008. The evaluations are carried out at 150, 180, 210, 240 and 270 spherical harmonics degrees. Results show that EGM2008 performs better than GOCE and related GGMs in Japan and three sub-regions (Hokkaido, central Honshu and Kyushu). However, GOCE and related GGMs perform better than EGM2008 in north Honshu, west Honshu and Shikoku up to degree 240. This means that GOCE data can improve geoid model over half of Japan. The improvement is only evident between degrees 150 and 240 beyond which EGM2008 performs better than GOCE GGMs in all the six regions. In general, the latest GOCE GGMs (releases 4 and 5) perform better than the earlier GOCE GGMs (releases 1, 2 and 3), indicating the contribution of data collected by GOCE in the last months before the mission ended on 11 November 2013. The results indicate that a more accurate geoid model over Japan is achievable, based on a combination of GOCE, EGM2008 and terrestrial gravity data sets. Graphical abstract Standard deviations of the differences between observed and GGMs implied (a) free-air gravity anomalies over Japan, (b) geoid undulations over Japan. n represents the spherical harmonic degrees

National geodetic reference system is basement for geodetic and geospatial data and information obtaining, maintenance and distribution in common reference system in country. It means, that it must be as accurate as possible and lockstep with time. Latvian national geodetic reference system (LNGRS) derives from Soviet Union geodetic reference system at beginning of 90-ties last century. Development of LNGRS was done as historical continuation of practice to use height, coordinates, Earth gravitational and geomagnetic systems and national networks. For coordinates was established new Latvian geodetical coordinate system using one week campaign data of GPS NAVSTAR. Heights were kept in Baltic normal height system epoch 1977. Earth gravitational system was established newly by absolute gravimetric measurements. Geomagnetic system was developed as repeat station system. Earth is constantly change system internally and outwardly More growing use of GIS and GNSS in agriculture, construction, logistic, military and everyday life put new challenge for LNGRS and it reliability to actual situation in top level.Main goal of publication is to analyze all aspects of LNGRS against nowadays criteria and requirements of dynamic national geodetic reference system. Results of analyses show feeble and powerful sides of LNGRS. DOI: https://doi.org/10.3846/enviro.2017.215

An improved hybrid gravimetric geoid model for Egypt, EGY-HGM2016, has been recently computed implementing the least-squares collocation (LSC) method through the remove-compute-restore (RCR) procedure. The computation of EGY-HGM2016 involves different datasets in terms of gravity anomalies determined from the GOCE (gravity field and steady-state ocean circulation explorer)-based global geopotential model (SPW-R4) up to d/o 200 and EGM2008 from d/o 201 to 720 combined with terrestrial gravity datasets in terms of 2140 gravity field anomalies and about 121,480 marine surface gravity anomalies. In addition, orthometric heights from 17 GPS/levelling measurements have been considered during the modelling process to improve the determination of the hybrid gravimetric geoid over the Egyptian region. The EGY-HGM2016 model estimated over Egypt provides geoid heights that are ranging from 7.677 to 21.095 m with a standard deviation (st. dev.) of about 2.534 m in the northwest of the country excluding the involvement of the orthometric heights from GPS/levelling measurements. When the later dataset is considered during the implementation of LSC process, hybrid residual height anomalies ranging from −1.5 to +0.9 m, with a mean of 0.22 m and a st. dev. of 0.17 m, are obtained. Comparison of the predicted hybrid gravimetric geoid with the corresponding ones obtained from EGM2008, GOCE-based SPW R4 model, and GPS/levelling reveals considerable improvements of our EGY-HGM2016 model over Egypt.

A definition of a Global geodetic observing space system design and space geodetic techniques are described. It is proposed that the Global geodetic observing space system shall consist of 1–2 MEO (Medium Earth Orbit) spacecraft(s), a LEO (Low Earth Orbit) spacecraft featuring on-board gravity gradiometer and/or 2 LEO spacecrafts featuring high-precision satellite-to-satellite tracking (SST) instruments, GNSS (GLONASS, GPS and Galileo) navigation spacecrafts (if needed), a passive satellite of Blitz-M type, launcher and launch facilities, ground control segment, a timing system, ground processing facilities. Geodetic technique includes a conventional dynamic method together with gravimetry and altimetry methods, a satellite gravity gradiometer and/or satellite-to-satellite tracking to measure relative position between two LEO spacecrafts.

After more than 4.5 years in orbit, the Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission ended with the reentry of the satellite on 11 November 2013. This publication serves as a reference for the fifth gravity field model based on the time-wise approach (EGM_TIM_RL05), a global model only determined from GOCE observations. Due to its independence of any other gravity data, a consistent and homogeneous set of spherical harmonic coefficients up to degree and order 280 (corresponding to spatial resolution of 71.5 km on ground) is provided including a full covariance matrix characterizing the uncertainties of the model. The associated covariance matrix realistically describes the model quality. It is the first model which is purely based on GOCE including all observations collected during the entire mission. The achieved mean global accuracy is 2.4 cm in terms of geoid heights and 0.7 mGal for gravity anomalies at a spatial resolution of 100 km.

Traditionally, the Earth’s gravity field model is computed from GRACE orbit and range rate measurements, e.g., in a short arc approach where both the position and the velocity vectors are integrated from a force model. In this contribution, we use the GRACE orbit and range measurements to recover the Earth’s gravity field model, thus we only need to integrate the position vectors. We use the range differences between two adjacent epochs to eliminate the range ambiguities. Using GRACE Level-1B RL02 data released by Jet Propulsion laboratory, the gravity field model TJGRACE02O complete to degree and order 90 is developed from 7 years of reduced dynamic orbits covering the period 2004–2010, and the gravity field model TJGRACE02K complete to degree and order 120 is computed from 1 month of kinematic orbits and K-band range data of January. Comparing the degree geoid errors of our new models with recent gravity field models such as the CHAMP-only models EIGEN-CHAMP05S, AIUB-CHAMP03S, ULUX-CHAMP2013S and the GRACE-only models GGM05S, Tongji-GRACE01 as well as a monthly model from the ITG-GRACE2010 time series, and validating these models with GPS-leveling data sets in the USA, we can conclude that the TJGRACE02O model is more accurate than all the CHAMP-only models and TJGRACE02K is comparable in quality to the corresponding GRACE monthly model from ITG-GRACE2010.

Multi-source gravity data including measurements on land, shipboard surveys, satellite altimetry, Bouguer gravity anomalies and EGM2008 global gravity model data were collected and analyzed for compiling the free-air gravity anomaly map on a scale of 1:5000000 in the land and seas of China and adjacent areas. The data merging and integration method was established based on analysis of the accuracy and resolution of different sources of gravity data. Evenly distributed land gravity data was gridded in flat land areas. A synthetic method using Bouguer gravity and high precision topographic data to calculate the free-air gravity data was proposed to fill the land areas where the gravity measurement is hardly or impossible to implement due to complex terrain. Data comparison between the synthetic free-air gravity data, measured data and EGM2008 data proves that using the synthetic data is a better choice for filling the areas lacking real data. This method was also applied to the continental and island areas outside mainland China where there are no real data collected. The STD analysis method was applied to the northern part of the South China Sea to compare the accuracy of three independent gravity data, the shipboard gravity data and two kinds of satellite altimetry derived gravity data, the SS series from Scripps, US and DNSC08GRA from DTU, Denmark. SSV18.1 and DNSC08GRA data, which show very good consistence in terms of accuracy and resolution. The standard deviation of the latest two satellite gravity data in the SCS is less than 2 mGal, which is a major improvement compared with the previous SS16.1. With the rectification of shipboard gravity data, the wide coverage of satellite gravity data could be used for small-scale free-air gravity mapping. In the coastal zone, the EGM2008 global potential model was used as a reference field providing a seamless gravity transition from land to ocean. Wavelet transform and multiscale analyses were applied to decompose the free-air gravity field in China and its adjacent areas to help gravity field interpretation. Eight anomaly areas were demarcated by three horizontal and four vertical first-order gravity gradient belts. Anomaly subareas and the second-order gravity gradient belts were delineated in the gravity field to provide evidence for establishing the tectonic framework in the block tectonic scheme.

With the advent of satellite altimetry in 1973, new scientific applications became available in oceanography, climatology, and marine geosciences. Moreover, satellite altimetry provides a significant source of information facilitated in the geoid determination with a high accuracy and spatial resolution. The information from this approach is a sufficient alternate for marine gravity data in the high-frequency modeling of the marine gravity field quantities. The gravity gradient tensor, consisting of the second-order partial derivatives of the gravity potential, provides more localized information than gravity measurements. Marine gravity observations always carry a high noise level due to environmental effects. Moreover, it is not possible to model the high frequencies of the Earth's gravity field in a global scale using these observations. In this article, we introduce a novel approach for a determination of the gravity gradient tensor at sea level using satellite altimetry. Two numerical techniques are ...

Results obtained as a solution to the geodetic boundary-value problem, where two different sources of input boundary data are combined together, are presented. On the upper part of the boundary defined by the Earth surface and separated from the Earth masses, the gravity anomalies are derived from GOCE gravity gradiometry data using a transformation and downward continuation procedure. On the bottom part of the boundary, the gravity anomalies derived from the terrestrial or marine gravity measurements are used. The boundary-value problem is then solved numerically by the finite element method. In some cases an independency of our solution from the highdegree global gravity models (e.g. EGM2008) can be considered as the advantage. The standard deviation of our model tested by GNSS/leveling method in Auvergne area is 10 cm.

Accurate knowledge of Antarctica's topography, bedrock, and ice sheet thickness is pivotal for climate change and geoscience research. Building on recent significant progress made in satellite gravity mapping with European Space Agency's Gravity field and Ocean Circulation Explorer (GOCE) mission, we here reverse the widely used approach of validating satellite gravity with topography and instead utilize the new GOCE gravity maps for novel evaluation of Bedmap1/2. Space-collected GOCE gravity reveals clear improvements in the Bedmap2 ice and bedrock data over Bedmap1 via forward modeled topographic mass and gravity effects at spatial scales of 400 to 80 km. Our study demonstrates GOCE's sensitivity for the subsurface mass distribution in the lithosphere and delivers independent evidence for Bedmap2's improved quality, reflecting new radar-derived ice thickness data. GOCE and Bedmap2 are combined to produce improved Bouguer gravity maps over Antarctica. We recommend incorporation of Bedmap2 in future high-resolution global topography and geopotential models and its use for detailed geoid modeling over Antarctica.

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.

GOCE satellite gravity data is often used to compute gravity anomaly and geoid height. In the paper, GOCE gravity data is used to inverse the crustal thickness of Chinese mainland (E70°~130°, N20°~50°) in this paper. In order to test the reliability of the result, the computing result is compared with previous studies. The comparative analysis shows that the inversion result by GOCE gravity data has higher resolution and has good consistence with the previous studies.

Because the twin GRACE Follow-On satellites are equivalent to the one-dimensional horizontal gravity gradiometer with a baseline length of the intersatellite range, the feasibility demonstrations on precisely and rapidly recovering the next-generation Earth's gravitational field by the GRACE Follow-On satellite gravity gradiometry method (GFO-SGGM) are carried out in this study. The research results are as follows: Firstly, based on the GRACE Follow-On satellite gravity gradiometry method, using the orbital parameters of the satellite (e.g. orbital altitude of 250 km, intersatellite range of 50 km, orbital inclination of 89° and orbital eccentricity of 0.001), the measurement precisions of key payloads (e.g. 10−6 m in intersatellite range, 10−7 m·s−1 in intersatellite range- rate and 10−10 m·s−2 in intersatellite range-acceleration by the interferometric laser ranging system, 10−3 m in orbital position and 10−6 m·s−1 in orbital velocity by the GPS receiver, and 10−11 m·s−2 in non-conservative force by the accelerometer), a 30-day observation time and a sampling interval of 10 s, the Earth's gravitational field complete up to degree and order 120 is accurately recovered, and the cumulative geoid height error is 9.331×10−4 m at degree 120. Secondly, in 120 degrees, the accuracy of the gravity recovery from the future twin GRACE Follow-On satellites is averagely improved by about 61 times than that from the current twin GRACE satellites. Therefore, the GRACE Follow-On satellite gravity gradiometry method promisingly becomes a preferred approach for further improving the determination accuracy of the next-generation Earth gravity field model. Finally, the advantages of the next-generation GRACE Follow-On mission as compared with the present GRACE mission principally consist of the lower orbital altitude of the satellite between 200 km and 300 km, the higher measurement accuracy of the space-borne instruments between 10−7 m·s−1 and 10−9 m·s−1 and the shorter intersatellite range between 50 km and 100 km.

The quality of mean dynamic topography (MDT) models derived from an altimetric mean sea surface and a gravity field model mainly depends on the spatial resolution and accuracy of the particular gravity field model. We use an integrated approach which allows for estimating the MDT and its (inverse) covariance matrix on a predefined grid which is one of the requirements for ocean data assimilation. The quality and accuracy of the MDT directly reflects the quality and accuracy of the used gravity field model. For the first time, MDT estimates along with its full error covariance matrix based on Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) data can be provided. We demonstrate the progress accomplished with GOCE processing and the valuable contribution of the GOCE gravity field models regarding the estimation of the MDT by showing results based on altimetric observations of Jason-1 and Envisat in combination with different GOCE gravity field models for the North Atlantic.

With the launch of the Gravity field and Ocean Circulation Explorer (GOCE) in 2009 the study of Earth's gravity field received another boost. After the time-dependent and long-wavelength information from the Gravity Recovery and Climate Experiment (GRACE) mission a new sensor with high accuracy and spatial resolution was available for determination of the Earth's gravity field and geoid. Equipped with a 6-component gradiometer and flying at an altitude of 260 km and less, GOCE provides the most detailed measurements of Earth's gravity from space to date. Additionally, GOCE provides gravity gradients, i.e., the three-dimensional second derivatives of the gravitational potential. This special issue provides a review of the results presented at the ‘GOCE solid Earth workshop’ at the University of Twente, The Netherlands (2012). The goal of this 2-day workshop was to provide training on the usage of GOCE data as well as to present the latest scientific results. The main workshop components were: to show the latest results on GOCE data in relation to solid Earth, provide new users with tips and tricks on which models and software to use, discuss quality and reliability of gravity data and models, and how to integrate GOCE data with own (local) gravity data. The workshop specifically focussed on where GOCE data has made a unique contribution and provides insights that would not have been possible without GOCE.

We construct 1′ × 1′ grids of free-air and Bouguer gravity anomalies around Taiwan with well-defined error estimates for quality assessment. The grids are compiled from land, airborne and shipborne gravity measurements, augmented with altimeter gravity at sea. Three sets of relative land gravity measurements are network-adjusted and outlier-edited, yielding accuracies of 0.03–0.09 mGal. Three airborne gravity sets are collected at altitudes 5156 and 1620 m with accuracies of 2.57–2.79 mGal. Seven offshore shipborne gravity campaigns around Taiwan and its offshore islands yield shallow-water gravity values with 0.88–2.35 mGal accuracies. All data points are registered with GPS-derived geodetic coordinates at cm–dm accuracies, allowing for precise gravity reductions and computing gravity disturbances. The various datasets are combined by the band-limited least-squares collocation in a one-step procedure. In the eastern mountainous (or offshore) region, Bouguer anomalies and density contrasts without considering the oceanic (or land) topographic contribution are underestimated. The new grids show unprecedented tectonic features that can revise earlier results, and can be used in a broad range of applications.

a b s t r a c t The interaction and coupling of the Earth system components that include the atmosphere, hydrosphere, cryosphere, lithosphere, and other fluids in Earth's interior, influence the Earth's shape, gravity field and its rotation (the three pillars of geodesy). The effects of global climate change, such as sea level rise, glacier melting, and geoharzards, also affect these observables. However, observations and models of Earth's system change have large uncertainties due to the lack of direct high temporal-spatial mea- surements. Nowadays, space geodetic techniques, particularly GNSS, VLBI, SLR, DORIS, InSAR, satellite gravimetry and altimetry provide a unique opportunity to monitor and, therefore, understand the pro- cesses and feedback mechanisms of the Earth system with high resolution and precision. In this paper, the status of current space geodetic techniques, some recent observations, and interpretations of those observations in terms of the Earth system are presented. These results include the role of space geo- detic techniques, atmospheric-ionospheric sounding, ocean monitoring, hydrologic sensing, cryosphere mapping, crustal deformation and loading displacements, gravity field, geocenter motion, Earth's oblate- ness variations, Earth rotation and atmospheric-solid earth coupling, etc. The remaining questions and challenges regarding observing and understanding the Earth system are discussed.

The availability of digital elevation databases representing the topographic and bathymetric relief with global homogeneous coverage and increasing resolution permits the computation of crust-related Earth gravity models, the so-called topographic/isostatic Earth gravity models (henceforth T/I models). Although expressing the spherical harmonic content of the topographic masses, the interpretation purpose of T/I models has not been given the attention it deserves, apart from the fact that they express some degree of compensation to the observed spectrum of the topographic heights, depending on the kind of the applied compensation mechanism. The present contribution attempts to improve the interpretation aspects of T/I Earth gravity models. To this end, a rigorous spectral assessment is performed to a standard Airy/Heiskanen T/I model against different CHAllenging Minisatellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), Gravity field and steadystate Ocean Circulation Explorer (GOCE) satellite-only, and combined gravity models. Different correlation bandwidths emerge for these four groups of satellite-based gravity models. The band-limited forward computation of the models using these bandwidths reproduces nicely the main features of the applied T/I model.

The dedicated satellite gravity missions have provided homogeneous and uniformly accurate information on the long and medium wavelengths of the Earth’s gravity field. Since the launch of GOCE satellite gravimetry mission by the European Space Agency (ESA) in 2009, several global geopotential models (GGMs) have been published. This study evaluates the recent GOCE-based GGMs over the area of Poland. The evaluation has been performed with the use of the EGM08 as well as high-precision GPS/levelling control traverse consisting of 184 stations. One GOCE-only GGM, four GOCE/GRACE satellite-only GGMs, and one GOCE/GRACE GGM combined with terrestrial gravity data have been selected for the evaluation. The results of inter-comparison of the models as well as their accuracy assessment have been discussed.

This paper gives brief information on existing metrological support for the Yavoriv of scientific of the geodetic of test field (SGTF) for testing of modern of surveying equipment (rangefinders, electronic total stations and GNSS receivers). Analyzed ways to improve the fundamental geodetic network and the standard linear of basis, as working standards for testing, in accordance, GNSS receivers and a rangefinders, as well as for study an accuracy technology of GNSS leveling.

9 10 Abstract 11 We provide an unprecedented ultra-high resolution picture of Earth's gravity over all continents 12 and numerous islands within ± 60 degree latitude. This is achieved through augmentation of new 13 satellite and terrestrial gravity with topography data, and use of massive parallel computation 14 techniques, delivering local detail at ~200 m spatial resolution. As such, our work is the first-of- 15 its-kind to model gravity at unprecedented fine scales yet with near-global coverage. The new 16 picture of Earth's gravity encompasses a suite of gridded estimates of gravity accelerations, 17 radial and horizontal field components and quasigeoid heights at over 3 billion points covering 18 80% of Earth's land masses. We identify new candidate locations of extreme gravity signals, 19 suggesting that the CODATA standard for peak-to-peak variations in free-fall gravity is too low 20 by about 40%. The new models are beneficial for a wide range of scientific and engineering 21 applications and freely available to the public. 22 23 Keywords 24

[1] Reprocessed Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) gravity gradient data were combined with data from Laser Geodynamics Satellite (LAGEOS) 1/2 and Gravity Recovery and Climate Experiment (GRACE) to generate a satellite-only gravity field model to degree 260 using the direct approach, named DIR-R4. When compared to Earth Gravitational Model 2008 (EGM2008), it is more accurate at low to medium resolution thanks to GOCE and GRACE data. When compared to earlier releases of ESA GOCE models, it is more accurate at high degrees owing to the larger amount of data ingested. It is also slightly more accurate than ESA's fourth release of the time-wise model (TIM-R4), as demonstrated by GPS/leveling, orbit determination tests, and an oceanographic evaluation. According to the formal, probably too optimistic by a factor of 2–2.5, cumulated geoid (1.3 cm) and gravity anomaly (0.4 mGal) errors at 100 km resolution, the GOCE mission objectives have been reached.

We present a global static model of the Earth’s gravity field entitled DGM-1S based on GRACE and GOCE data. The collection of used data sets includes nearly 7 years of GRACE KBR data and 10 months of GOCE gravity gradient data. The KBR data are transformed with a 3-point differentiation into quantities that are approximately inter-satellite accelerations. Gravity gradients are processed in the instrumental frame. Noise is handled with a frequency-dependent data weighting. DGM-1S is complete to spherical harmonic degree 250 with a Kaula regularization being applied above degree 179. Its performance is compared with a number of other satellite-only GRACE/GOCE models by confronting them with (i) an independent model of the oceanic mean dynamic topography, and (ii) independent KBR and gravity gradient data. The tests reveal a competitive quality for DGM-1S. Importantly, we study added value of GOCE data by comparing the performance of satellite-only GRACE/GOCE models with models produced without GOCE data: either ITG-Grace2010s or EGM2008 depending on which of the two performs better in a given region. The test executed based on independent gravity gradients quantifies this added value as 25–38 % in the continental areas poorly covered with terrestrial gravimetry data (Equatorial Africa, Himalayas, and South America), 7–17 % in those with a good coverage with these data (Australia, North America, and North Eurasia), and 14 % in the oceans. This added value is shown to be almost entirely related to coefficients below degree 200. It is shown that this gain must be entirely attributed to gravity gradients acquired by the mission. The test executed based on an independent model of the mean dynamic topography suggests that problems still seem to exist in satellite-only GRACE/GOCE models over the Pacific ocean, where noticeable deviations between these models and EGM2008 are detected, too.

In July 2003 the International Association of Geodesy (IAG) established the Global Geodetic Observing System (GGOS). The GGOS is integrating the three basic components: geometry, the earth rotation and gravity. The backbone of this integration is the existing global ground network, based on the geodetic space techniques: very long baseline interferometry, satellite laser ranging, global navigation satellite systems and Doppler orbitography and radiopositioning integrated by satellite. These techniques have to operate as one global entity and in one global reference frame. The global reference frame in the GGOS is a realization of the International Terrestrial Reference System (ITRS). The ITRS is a world spatial reference system co-rotating with the Earth in its diurnal motion in the space. The IAG Subcommision for the European Reference Frame (EUREF) in 1991 recommended that the terrestrial reference system for Europe should be coincident with ITRS at the epoch t 0 = 1989.0 and fixed to the stable part of the Eurasian Plate. It was named the European Terrestrial Reference System 89 (ETRS89). On the 2nd of June 2008, the Head Office of Geodesy and Cartography in Poland commenced operating the ASG-EUPOS multifunctional precise satellite positioning system. The ASG-EUPOS network defines the European Terrestrial Reference System ETRS89 in Poland. A close connection between the ASG-EUPOS stations and 15 out of 18 Polish EUREF permanent network stations controls the realization of the ETRS89 on Polish territory. This paper is a review of the global ITRS, as well as a regional and a national geodetic reference systems ETRS89.