Centimeter Precision Geoid Model for Jeddah Region (Saudi Arabia)

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 abstractStandard 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

A unified height datum is essential for global geographic information resource construction, ecological environment protection, and scientific research. The goal of this paper is to derive the geopotential value for the Chinese height datum (CNHD) in order to realize the height datum unification in China. The estimation of height datum geopotential value usually depends on high-precision global gravity field models (GFMs). The satellite gravity missions of the Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Exploration (GOCE) provide high-accuracy, medium–long-wavelength gravity field spectra, but satellite-only GFMs are limited to medium–long wavelengths, which will involve omission errors. To compensate for the omission errors in satellite-only GFMs, a spectral expansion approach is used to obtain the refined gravity field models using the EGM2008 (Earth Gravitational Model 2008) and residual terrain model (RTM) technique. The refined GFMs are evaluated by using high-quality GNSS/leveling data, the results show that the quasi-geoid accuracy of the refined DIR_R6_EGM2008_RTM model in China has optimal accuracy and, compared with the EGM2008 model and the DIR_R6 model, this refined model in China is improved by 9.6 cm and 21.8 cm, and the improvement ranges are 35.7% and 55.8%, respectively. Finally, the geopotential value of the Chinese height datum is estimated to be equal to 62,636,853.29 m2s−2 with respect to the global reference level defined by W0 = 62,636,853.4 m2s−2 by utilizing the refined DIR_R6_EGM2008_RTM model and 1908 high-quality GNSS/leveling datapoints.

Quantum optical technology provides an opportunity to develop new kinds of gravity sensors and to enable novel measurement concepts for gravimetry. Two candidates are considered in this study: the cold atom interferometry (CAI) gradiometer and optical clocks. Both sensors show a high sensitivity and long-term stability. They are assumed on board of a low-orbit satellite like gravity field and steady-state ocean circulation explorer (GOCE) and gravity recovery and climate experiment (GRACE) to determine the Earth’s gravity field. Their individual contributions were assessed through closed-loop simulations which rigorously mapped the sensors’ sensitivities to the gravity field coefficients. Clocks, which can directly obtain the gravity potential (differences) through frequency comparison, show a high sensitivity to the very long-wavelength gravity field. In the GRACE orbit, clocks with an uncertainty level of 1.0times 10^{-18} are capable to retrieve temporal gravity signals below degree 12, while 1.0times 10^{-17} clocks are useful for detecting the signals of degree 2 only. However, it poses challenges for clocks to achieve such uncertainties in a short time. In space, the CAI gradiometer is expected to have its ultimate sensitivity and a remarkable stability over a long time (measurements are precise down to very low frequencies). The three diagonal gravity gradients can properly be measured by CAI gradiometry with a same noise level of 5.0 {mathrm{mE}/sqrt{mathrm{Hz}}}. They can potentially lead to a 2–5 times better solution of the static gravity field than that of GOCE above degree and order 50, where the GOCE solution is mainly dominated by the gradient measurements. In the lower degree part, benefits from CAI gradiometry are still visible, but there, solutions from GRACE-like missions are superior.

The results of this study suggest that a traditional height network based on fundamental benchmarks can be used meaningfully to assess the quality of a satellite‐derived geoid model. We compare the pre‐ Gravity Recovery and Climate Experiment (GRACE) OSGM02 and the recent OSGM05 geoid models with the datum surface inferred by the UK fundamental benchmark network combined with network monument ellipsoidal heights derived from GPS data. OSGM05 incorporates long‐wavelength gravity field data from GRACE to degree/order 90. Switching from OSGM02 to OSGM05, the mean difference between the leveling datum and the geoid model reduces from −0.129 m to −0.004 m, and RMS differences reduce from 0.110 m to 0.048 m. The mean tilt between the height datum and the geoid model in the north‐south direction reduces from 34 mm to 12 mm per degree of latitude. Hence we demonstrate a systematic convergence between the geoid models and the leveling datum surface in terms of mean offset, RMS scatter and tilt without any fitting of one surface to the other. The implication is that the leveling datum surface represented a more accurate model of the geoidal geometry compared to OSGM02 in terms of form (in both short‐ and long‐wavelength features) and surprisingly also in terms of its offset from the GRS80 ellipsoid. While the latter point can be no more than a coincidence, the former indicates that the UK leveling network, based on its fundamental benchmark network, can be used to test the accuracy of geoid model improvements derived from missions such as GRACE, with implications for the forthcoming Gravity Field and Steady State Ocean Circulation Explorer (GOCE) mission.

ESA’s Gravity field and steady-state Ocean Circulation Explorer (GOCE) orbited the Earth between 2009 and 2013 for the determination of the static part of Earth’s gravity field. The GPS-derived precise science orbits (PSOs) were operationally generated by the Astronomical Institute of the University of Bern (AIUB). Due to a significantly improved understanding of remaining artifacts after the end of the GOCE mission (especially in the GOCE gradiometry data), ESA initiated a reprocessing of the entire GOCE Level 1b data in 2018. In this framework, AIUB was commissioned to recompute the GOCE reduced-dynamic and kinematic PSOs. In this paper, we report on the employed precise orbit determination methods, with a focus on measures undertaken to mitigate ionosphere-induced artifacts in the kinematic orbits and thereof derived gravity field models. With respect to the PSOs computed during the operational phase of GOCE, the reprocessed PSOs show in average a 8–9% better consistency with GPS data, 31% smaller 3-dimensional reduced-dynamic orbit overlaps, an 8% better 3-dimensional consistency between reduced-dynamic and kinematic orbits, and a 3–7% reduction of satellite laser ranging residuals. In the second part of the paper, we present results from GPS-based gravity field determinations that highlight the strong benefit of the GOCE reprocessed kinematic PSOs. Due to the applied data weighting strategy, a substantially improved quality of gravity field coefficients between degree 10 and 40 is achieved, corresponding to a remarkable reduction of ionosphere-induced artifacts along the geomagnetic equator. For a static gravity field solution covering the entire mission period, geoid height differences with respect to a superior inter-satellite ranging solution are markedly reduced (43% in terms of global RMS, compared to previous GOCE GPS-based gravity fields). Furthermore, we demonstrate that the reprocessed GOCE PSOs allow to recover long-wavelength time-variable gravity field signals (up to degree 10), comparable to information derived from GPS data of dedicated satellite missions. To this end, it is essential to take into account the GOCE common-mode accelerometer data in the gravity field recovery.

Nyamuragira volcano is an active volcano near the city of Goma in the Democratic Republic of the Congo, situated about 25 kilometers north of Lake Kivu. It has been described as Africa's most active volcano and has erupted over 40 times since 1885. on 2 January 2010 Nyamuragira began spewing out lava flows. Extensive lava flows from the 2010 eruption can be seen on satellite photographs reaching 25 kilometers south-west to Lake Kivu, about 22 kilometers north-west and 35 kilometers north-north-east. The volcano erupted again on 5 November 2011.That eruption produced a 400-meter-high column of lava, and it is said to have been its largest eruption in 100 years. Volcanic activity attributed to The Kivu rift resulted from a sub-equatorial extensional motion and normal faulting and accompanied with seismological activities.  It suggests a complicated lower and upper crust tectonic patten and old neo tectonic settings. It is a challenge to determine active tectonic and geologic structure attributed to magma eruption. Shallow and deep geologic structures around the volcanic area. Heterogeneities of the lithosphere and its impact on the volcanic activities. Old and neo tectonics responsible for volcanic and seismic activities. quantitatively predict the position and direction of dike intrusions and resulting eruptive fissures at volcanoes, because they are governed by the interplay between several factors, such as a heterogeneous regional stress field, preexisting discontinuities and heterogeneous and anisotropic properties of rocks.  Radar altimetry data has been used to derive gravity and its variations over the world's oceans and an excellent tool for mapping sea floor structures, including tectonics, sea mounts and rifts. On the other hand, the Gravity Recovery and Climate Experiment (GRACE) satellite mission has widely demonstrated its sensitivity to ongoing mass redistribution within the various sub-systems of the earth. Finally, GOCE (Gravity field and steady-state Ocean Circulation Explorer) satellite is the first satellite mission that observes gradient of the Earth gravity field from space.  Integrated satellite gravity data have been used to delineate the tectonic settings, magma referred pathway, magma reservoirs and vertical dikes.

Besides the Global Navigation Satellite Systems (GNSS), Satellite and Lunar Laser Ranging (SLR, LLR) and the Doppler distance measurement technique DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite), Very Long Baseline Interferometry (VLBI) is one of the space-geodetic techniques. In addition to the aforementioned, satellite missions such as radar and laser altimetry and geodetically used components of gravity field satellites in particular CHAMP (CHAllenging Mini satellite Payload), GRACE (Gravity Recovery And Climate Experiment), and GOCE (Gravity field and steady-state Ocean Circulation Explorer) can be counted to the space-geodetic techniques. In radio astronomy VLBI is a technique for astrophysics and astrometry. The later has many things in common with geodetic VLBI; only the schedule varies among terrestrial and celestial motivated observing sessions in terms of the number of observed radio sources as well as the number and sequence of observations to radio sources. Together with geodynamics, oceanography, glaciology, meteorology, and climatology, geodesy provides the metric basis for interdisciplinary research within the geosciences.

An ever increasing number of low Earth orbiting (LEO) satellites is, or will be, equipped with retro-reflectors for Satellite Laser Ranging (SLR) and on-board receivers to collect observations from Global Navigation Satellite Systems (GNSS) such as the Global Positioning Sys- tem (GPS) and the Russian GLONASS and the European Galileo systems in the future. At the Astronomical Insti- tute of the University of Bern (AIUB) LEO precise or- bit determination (POD) using either GPS or SLR data is performed for a wide range of applications for satellites at different altitudes. For this purpose the classical numeri- cal integration techniques, as also used for dynamic orbit determination of satellites at high altitudes, are extended by pseudo-stochastic orbit modeling techniques to effi- ciently cope with potential force model deficiencies for satellites at low altitudes. Accuracies of better than 2 cm may be achieved by pseudo-stochastic orbit modeling for satellites at very low altitudes such as for the GPS-based POD of the Gravity field and steady-state Ocean Circula- tion Explorer (GOCE).

“Gravity From Space” for Oceans, Land Ice, and Sea Level Rise; Hamburg, Germany, 29–30 September 2010; Twenty‐five scientists met at the University of Hamburg's KlimaCampus to discuss current analyses and future applications of spaceborne gravity measurements to studies of ocean circulation, cryospheric science, and sea level rise. The Challenging Minisatellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), and Gravity Field and Steady‐State Ocean Circulation Explorer (GOCE) satellites, complemented with radar and laser altimeters, provide the necessary data. Spaceborne gravity measurements provide two important quantities for ocean circulation studies: (1) the time‐averaged geoid, which when subtracted from a time mean sea surface from radar altimetry yields the absolute surface dynamic topography and absolute surface geostrophic currents, and (2) time changes in ocean bottom pressure and total ocean mass. For sea level rise, the difference between the globally averaged trend from altimetry and that from GRACE is used to infer the top‐to‐bottom steric component (the component of sea level rise resulting from expansion of seawater due to temperature and salt), which is observable with data from the Argo system, a network of drifting probes that measure temperature up to 2000 meters in depth, and from expendable bathythermographs (XBT), temperature sensors deployed by ships.

The satellite gravity gradiometry (SGG) data of the recent European satellite mission, the Gravity field and steady-state Ocean Circulation Explorer (GOCE), can be used as an external source for quality description of terrestrial gravity anomalies and the Earth’s gravity models (EGMs). In this study integral estimators are provided and modified in a least-squares sense to regenerate the SGG data of GOCE from terrestrial gravity anomalies and an existing EGM. Based on the differences between the generated and real GOCE SGG data, condition adjustment models are constructed and variance component estimation (VCE) is applied for balancing the a priori errors of data with these differences. Here, a 1-month orbit of GOCE is considered over Iran and the condition adjustment models and VCE process are used to calibrate the errors of the GOCE data, terrestrial gravity anomalies of the area and the EGM. Numerical studies over Iran show that the a priori errors of the GOCE data and the EGM were properly presented. Also the average error of the terrestrial gravity anomalies, with a resolution of 0.5° × 0.5°, after condition adjustment and VCE process using Tzz, Tx, Tyz and −Txx −Tyy is about 30 mGal.

The aim of the MOCAST+ (MOnitoring mass variations by Cold Atom Sensors and Time measures) project, which was carried out during the years 2020–2022, was the investigation of the performance of a gravity field mission based on the integration of atomic clocks and cold atom interferometers. The idea was that the combined observations of the two sensors would be beneficial for the detection and monitoring of geophysical phenomena which have an impact on the time-variable part of the Earth gravity field models. Several different mission scenarios were simulated, considering different satellite configurations such as a Gravity Recovery and Climate Experiment (GRACE)-class formation and a Bender-class formation with either two or three in-line satellites along each orbit. Moreover, different atomic species (rubidium and strontium), different inter-satellite distances, different noise power spectral densities, and different observation rates were taken into account. For the gravity field estimation from the simulated data, the space-wise approach was exploited. The results showed that, as it could be expected, the Bender configuration provides significantly better monthly gravity field solutions, as compared to a ‘nominal’ configuration with two or three satellites in a GRACE-class formation. In this way, and pushing the quantum sensors technology to its limits, it is in fact possible to obtain results which are comparable with those from GRACE at low harmonic degrees, and are better at higher degrees with positive effects in the detectability of localized time variable phenomena, as well as in the determination of the static gravity field at a higher maximum spherical harmonic degree than the one achieved by Gravity Field and Steady-State Ocean Circulation Explorer (of course considering an equivalent mission life-time).

Gravity Recovery and Climate Experiment (GRACE) satellite gravimetry can monitor surface mass variations with a spatial resolution of ~300km and a temporal resolution of 1 month. GRACE intersatellite geopotential difference (GPD) is a type of in-situ gravimetric observables with explicit geophysical interpretation, which can directly reflect surface mass variations. The intersatellite GPDs are estimated from GRACE Level-1B (RL03) data (including KBR range-rate measurements (KBR1B), satellite orbits (GNV1B), accelerometer measurements (ACC1B), and satellite attitude measurements (SCA1B)) based on an improved energy balance equation, and the orbit and background model errors are reduced using empirical parameters based on the remove-compute-restore (RCR) technique. Background models used for estimating GRACE intersatellite GPDs are consistent with GRACE Level-2 Processing Standards Document (for Level-2 Product RL06). GRACE intersatellite GPD data are processed over the period from April 2002 to July 2016 with a sampling rate of 5s along the satellite orbits (orbit height is ~450km), and stored on a monthly basis. There are total 155 months of data files over the period from April 2002 to July 2016, and the other 17 months of data are not available due to the instrument failure or other influencing factors. Each data file includes the positions of GRACE satellites A and B in Earth-centered Earth-fixed (ECEF) coordinate system, intersatellite geopotential differences after deducting the mean gravity field model GGM05C (i.e., the disturbance potential difference TAB=TB-TA), and the corresponding quality flags. GRACE intersatellite GPD data are validated through the estimation of monthly gravity field solutions and regional surface mass variations. The estimates inferred from GPD data are compared with GRACE official monthly solutions and mascon solutions, such as the products published by the Center for Space Research (CSR), Jet Propulsion Laboratory (JPL), German Research Center for Geosciences (GFZ), and Goddard Space Flight Center (GSFC). It is demonstrated that the differences between GPD-inferred results and the official released models are within the range of the differences among those official models.  GRACE intersatellite GPD dataset enriches the GRACE data products, and can be applied to directly invert the monthly gravity field models, global and regional surface mass variations, which is helpful to study the terrestrial water cycle, ice sheets and mountain glacier mass balance, sea level change, and ocean bottom pressure variations, etc.

Owing to the intense tectonic activity and significant seasonal surface mass change, Southwest China is characterized by noticeable vertical land movement. We determined the vertical movement of Southwest China using 10 years of data from 41 continuous global positioning system (GPS) stations, gravity recovery and climate experiment (GRACE), and surface loading model (SLM). The annual variation in hydrological loading is the main factor causing the seasonal oscillation of surface deformation in Southwest China. Seasonal deformations captured by GPS, GRACE, and SLM are consistent to a certain extent, and the correlation coefficients between GPS/GRACE, and GPS/SLM are 0.82 and 0.81, respectively. After deducting the results yielded by GRACE and SLM from the GPS time series, the average reductions in root mean square were 41.3% and 38.0%, respectively. However, some systematic differences were observed among the annual amplitudes and phases of the seasonal deformations among the three products. For example, the average amplitudes estimated by GRACE and SLM were 7.4 mm and 6.1 mm, respectively, which were smaller than the amplitude deduced from GPS (9.7 mm). Furthermore, mean phase delays of 16, 22, and 6 days were observed between GPS/GRACE, GPS/SLM, and GRACE/SLM. The data processing errors and local geophysical signals in GPS and the underestimation of land water storage in GRACE and SLM were jointly responsible for the systemic differences. The simulated data show that the misestimating of hydrological loading can explain approximately 50%, 64%, and 83% of the phase delays between GPS/GRACE, GPS/SLM, and GRACE/SLM, respectively. In addition, we obtained long-term vertical crustal motion rates by subtracting the loading deformation rates estimated by GRACE from the linear rates of the GPS. The vertical crustal motion in this region is block-dependent. The Central Yunnan block and its eastern boundary are uplifted; meanwhile, the Southwest Yunnan block, which features stretching in the horizontal direction, appears to be subsiding. The aforementioned results can provide data support for the study of water resource utilization and geodynamics in Southwest China.

Abstract. 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.

In this study we estimate the discrepancies between the Brazilian vertical network, realized in the system of normal-orthometric heights, and a global quasi-geoid model. We consider the GNSS-leveling and a global quasi-geoid model derived from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission enhanced by high degree components of the Earth Gravitational Model 2008 (EGM2008). The results indicate that the enhanced geopotential model fits the GNSS-leveling with a root mean square error of 20.2 cm. The estimated bias of − 0. 4 ± 0.6 cm (w.r.t. the centroid of the network) implies that any future changes to the geopotential value W0 (62636856.0 m2 s−2) should be minor for the Brazilian Height System (BHS). However, since the GNSS-leveling based “height anomalies” refer to the Brazilian Vertical Datum at Imbituba harbor (BVD-I), Southern Brazil, the results of the comparisons may be an indicator of the mean bias of the national leveling network due to the effect of Mean Dynamic Topography (MDT) at the BVD-I.