Gravity Field And Steady-state Ocean Circulation Explorer Mission Research Articles

Satellite gradiometry based on a new generation of accelerometers and its potential contribution to Earth gravity field determination

An accurate model of the Earth’s gravity field is beneficial for practical engineering and many applications in geosciences. European Space Agency (ESA) realized the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) gradiometry mission between 2009 and 2013. However, the low-frequency drift of the onboard electrostatic accelerometers (EA) limits the observation accuracy of the GOCE mission to some extent. Advances in electrostatic and quantum technology offer new measurement concepts for future gradiometry missions. In this study, we evaluate the contributions of several types of accelerometers through numerical closed-loop simulation which rigorously maps the accelerometers’ sensitivities to the gravity field coefficients. In comparison to the simulated results of the GRADIO gradiometer used in GOCE, it is demonstrated that the MicroSTAR-type gradiometer has superior precision within degree and order 100 and provides more signal information in the off-diagonal components of the gravity gradient tensor (GGT). The precision of the gravity field model recovery from a HybridACC-type gradiometer is significantly affected by the noise level of the cold atom interferometry (CAI) accelerometer. A HybridACC-type gradiometer with low CAI performance (1×10-9m·s-2/Hz) only favors the high degree component because of its higher accuracy in the measurement bandwidth (MBW) between 5 mHz and 100 mHz. While a better CAI performance up to 1×10-11m·s-2/Hz will increase retrieval performance remarkably. With an orbital rotation compensation mechanism, the CAI gradiometer performs with greater accuracy overall. Otherwise, the accuracy based on this sort of gradiometer is only superior up to degree 50.

Reprocessed precise science orbits and gravity field recovery for the entire 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.

The earth\u2019s gravity field recovery using the third invariant of the gravity gradient tensor from GOCE

Due to the independence of the gradiometer instrument’s orientation in space, the second invariant I_2 of gravity gradients in combination with individual gravity gradients are demonstrated to be valid for gravity field determination. In this contribution, we develop a novel gravity field model named I3GG, which is built mainly based on three novel elements: (1) proposing to utilize the third invariant I_3 of the gravity field and steady-state ocean circulation explorer (GOCE) gravity gradient tensor, instead of using the I_2, similar to the previous studies; (2) applying an alternative two-dimensional fast fourier transform (2D FFT) method; (3) showing the advantages of I_3 over I_2 in the effect of measurement noise from the theoretical and practical computations. For the purpose of implementing the linearization of the third invariant, this study employs the theory of boundary value problems with sphere approximation at an accuracy level of O(J_2^2cdot T_{ij}). In order to efficiently solve the boundary value problems, we proposed an alternative method of 2D FFT, which uses the coherent sampling theory to obtain the relationship between the 2D FFT and the third invariant measurements and uses the pseudo-inverse via QR factorization to transform the 2D Fourier coefficients to spherical harmonic ones. Based on the GOCE gravity gradient data of the nominal mission phase, a novel global gravity field model (I3GG) is derived up to maximum degree/order 240, corresponding to a spatial resolution of 83 km at the equator. Moreover, in order to investigate the differences of gravity field determination between I_3 with I_2, we applied the same processing strategy on the second invariant measurements of the GOCE mission and we obtained another gravity field model (I2GG) with a maximum degree of 220, which is 20 degrees lower than that of I3GG. The root-mean-square (RMS) values of geoid differences indicates that the effects of measurement noise of I3GG is about 20% lower than that on I2GG when compared to the gravity field model EGM2008 (Earth Gravitational Model 2008) or EIGEN-5C (EIGEN: European Improved Gravity model of the Earth by New techniques). Then the accuracy of I3GG is evaluated independently by comparison the RMS differences between Global Navigation Satellite System (GNSS)/leveling data and the model-derived geoid heights. Meanwhile, the re-calibrated GOCE data released in 2018 is also dealt with and the corresponding result also shows the similar characteristics.

From GOCE to NGGM: Automatic Control Breakthroughs for European future Gravity Missions

Abstract After the successful European gravity mission GOCE (Gravity field and steady-state Ocean Circulation Explorer), which provided an unprecedented high resolution static global map of the Earth’s gravity field, the European Space Agency has proposed several preparatory studies for a Next Generation Gravity Mission (NGGM). The NGGM mission objective aims at measuring the temporal variations of the Earth gravity field over a long time span with an unprecedented level of accuracy, both in spatial and temporal resolution. The GOCE technological heritage is leveraged as starting point while defining the NGGM future mission concept. Nonetheless, to accomplish its challenging scientific objective, the NGGM mission concept envisages a wide range of innovations, with respect to the past or flying missions, both on technological and automatic control side. Thus, this paper focuses on the guidance, navigation and control design evolution for the European gravity missions, from GOCE to NGGM. After recalling the GOCE GNC main design concepts, the paper will describe the most important innovation required by NGGM. Indeed, such a future concept will consist of a two-satellite long-distance loose formation, where each satellite is controlled independently to be drag-free, GOCE-like. The satellite-to-satellite distance variations, encoding gravity anomalies, will be then measured by laser heterodyne interferometry for inter-satellite ranging at 20 nm resolution, or better. Hence, an orbit and formation control is now required to counteract bias and drift of the residual drag-free accelerations, in order to reach a bounded orbit/formation long-term stability. Finally, GOCE control flight results as well as NGGM simulated results, via a high-fidelity simulator, will be provided. These results highlight the GOCE GNC in-flight achievements as well as the NGGM concept validity, showing that the expected control performances are in agreement with the consolidated mission requirements, all over the 10-year mission.

Towards sub-lithospheric stress determination from seismic Moho, topographic heights and GOCE data

Sub-lithospheric stresses can be estimated by analysis of gravity field measurements. Depending on the measured gravimetric quantity, different methods can be employed to estimate those sub-lithospheric stresses. Here, we further develop the Runcorn’s theory for estimation of mantle stresses (1967) such that a Moho model and full topographic information are used to recover the function from which the stress can be computed by taking derivatives northwards and eastwards. We develop new integral equations for such a purpose and recover this function by solving those integral equations locally over the Indo-Pak (India-Pakistan) region from (1) a gravimetric Moho model computed from the SRTM (Shuttle Radar Topography Mission) and the Earth gravity model EGM2008, (2) SRTM and the seismic Moho model of CRUST1.0 and (3) data and measurements of the GOCE (Gravity field and steady-state Ocean Circulation Explorer) mission. Finally, we perform a joint inversion of seismic and GOCE data for the same purpose. The numerical results show that the use of a seismic Moho model recovers information about the stress field which is not seen in the results derived from a gravimetric Moho model. A combination of the seismic Moho model, SRTM and GOCE yields a better stress field than that of either the seismic and/or gravimetric data alone. The magnitudes of the sub-lithospheric stress are computed from the shear stress components over the area and good agreement is seen between the recovered combined stress field, the regional tectonic boundaries and the seismicity of the World Stress Map 2008 database.

A regional background model for the Arabian Peninsula from modeling satellite gravity gradients and their invariants

Gravity gradients of the GOCE (Gravity field and steady state Ocean Circulation Explorer) mission are available and provide free available data with global homogeneous coverage. The spatial resolution is about 80km which makes it possible to construct regional models of large or remote areas. We study the benefit of using this data for compiling a 3D regional density model of the lithosphere with emphasis on the crustal structure for the Arabian Peninsula. We keep the data at satellite level to avoid noise amplification. The initial density model was set up with only a few seismic constraints and modified by forward modeling. Forward models benefits from the use of the full gravity gradient tensor and the invariants. The misfits between the measured and calculated field are more easily recognized in the gravity gradient tensor than in the gravity field alone. Different shape and location of anomalies are visible in the different components. Hence, modeling is better controlled as geometries which fit one component do not necessarily fit all other components. Regional models are important for a general understanding of any area and as a background for local interpretations. Here, we explain how to construct density models from satellite gravity gradients and show the advantage of such an approach by comparison to earlier studies based on either seismic or gravity data.

The European way to gravimetry: From GOCE to NGGM

The European gravity mission GOCE (Gravity field and steady-state Ocean Circulation Explorer), which flew between 2009 and 2013 with extraordinary success, was the result of more than 20years of system studies and technology developments directed by the European Space Agency (ESA). Already while GOCE was being developed, ESA started preparatory studies for a Next Generation Gravity Mission (NGGM). While GOCE aimed to provide a high resolution static map of the Earth’s gravity, the objective of NGGM is long-term monitoring of the time-variable gravity field with high temporal and spatial resolution, by satellite-to-satellite tracking, a technique flown with the US–German mission GRACE for the first time. With respect to GOCE, the new mission implies new measurement techniques and instrumentation, a new mission scenario and different spacecraft design drivers. Despite the differences, however, several achievements of GOCE (e.g. demonstration of long-duration wide-band drag compensation, ultra-sensitive accelerometers, stable non-cryogenic temperature control in low Earth orbit) stand as the basis upon which NGGM is being defined. Technologies and techniques specific of the new mission (laser metrology, multi-task control architectures, high performance propulsion) are undergoing parallel developments in anticipation of the NGGM implementation phase. The paper recalls the GOCE mission and heritage, and introduces the objectives, scenarios, concepts and challenges of the NGGM, highlighting commonalities and differences between the two missions.

Error analysis of a new planar electrostatic gravity gradiometer for airborne surveys

Moving-base gravity gradiometry has proven to be a convenient method to determine the Earth’s gravity field. The ESA mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) has enabled to map the Earth gravity field and its gradients with a resolution of 80 km, leading to significant advances in physical oceanography and solid Earth physics. At smaller scales, airborne gravity gradiometry has been increasingly used during the past decade in mineral and hydrocarbon exploration. In both cases the sensitivity of gradiometers to the short wavelengths of the gravity field is of crucial interest. Here, we quantify and characterize the error on the gravity gradients estimated from measurements performed with a new instrument concept, called GREMLIT, for typical airborne conditions. GREMLIT is an ultra-sensitive planar gravitational gradiometer which consists in a planar acceleration gradiometer together with 3 gyroscopes. To conduct this error analysis, a simulation of a realistic airborne survey with GREMLIT is carried out. We first simulate realistic GREMLIT synthetic data, taking into account the acceleration gradiometer and gyroscope noises and biases and the variation of orientation of the measurement reference frame. Then, we estimate the gravity gradients from these data. Special attention is paid to the processing of the gyroscopes measurements whose accuracy is not commensurate with the ultra-sensitive gradiometer. We propose a method to calibrate the gyroscopes biases with a precision of the order $$10^{-8}$$ rad/s. In order to transform the tensor from the measurement frame to the local geodetic frame, we estimate the error induced when replacing the non-measured elements of the gravity gradient tensor by an a priori model. With the appropriate smoothing, we show that it is possible to achieve a precision better than 2E for an along-track spatial resolution of 2 km.

EGM_TIM_RL05: An independent geoid with centimeter accuracy purely based on the GOCE mission

AbstractAfter 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.

Perturbing effects of sub-lithospheric mass anomalies in GOCE gravity gradient and other gravity data modelling: Application to the Atlantic-Mediterranean transition zone

The GOCE (Gravity field and steady-state Ocean Circulation Explorer) mission, launched on March 2009, included a new type of satellite instrument, an on-board three-axis gradiometer able to measure the Earth's gravity gradients at the satellite height (255km). The potential of this new type of measurement and its derived products (i.e., global gravity field models), together with other land-based geophysical observables (Bouguer and geoid anomalies), to image sub-lithospheric thermal and compositional anomalies is evaluated in this study. We focus on the Atlantic-Mediterranean Transition Region (AMTR), the diffuse, transpressive contact between the Iberian Peninsula and North Africa. The present-day lithospheric structure in the area is characterized by a wide band of active deformation, large lateral variations in the lithosphere and the presence of a positive seismic-velocity anomaly in the uppermost mantle beneath the Betics and the westernmost Alboran Basin-Gibraltar Arc. Here, the perturbing effects of deep, sub-lithospheric density anomalies in GOCE gravity gradients and other land-based geophysical data are assessed, and its impact in lithospheric-scale geophysical-petrological modeling within a thermodynamically consistent framework analyzed. Some of the gravity gradients computed at the satellite altitude are rather sensitive to the presence of even a relatively small sub-lithospheric cold slab, like the one observed in the AMTR, showing the potential of the new GOCE data to map upper mantle anomalies. Lithospheric models ignoring the AMTR sub-lithospheric heterogeneities could be significantly biased. In particular, extreme changes of 4–6km and 60–70km in the crustal and lithospheric thickness, respectively, are required to include sub-lithospheric mantle contributions to land-based and satellite gravity data.

Observing coseismic gravity change from the Japan Tohoku‐Oki 2011 earthquake with GOCE gravity gradiometry

AbstractThe Japan Tohoku‐Oki earthquake (9.0 Mw) of 11 March 2011 has left signatures in the Earth's gravity field that are detectable by data of the Gravity field Recovery and Climate Experiment (GRACE) mission. Because the European Space Agency's (ESA) satellite gravity mission Gravity field and steady‐state Ocean Circulation Explorer (GOCE)—launched in 2009—aims at high spatial resolution, its measurements could complement the GRACE information on coseismic gravity changes, although time‐variable gravity was not foreseen as goal of the GOCE mission. We modeled the coseismic earthquake geoid signal and converted this signal to vertical gravity gradients at GOCE satellite altitude. We combined the single gradient observations in a novel way reducing the noise level, required to detect the coseismic gravity change, subtracted a global gravity model, and applied tailored outlier detection to the resulting gradient residuals. Furthermore, the measured gradients were along‐track filtered using different gradient bandwidths where in the space domain Gaussian smoothing has been applied. One‐year periods before and after earthquake occurrence have been compared with the modeled gradients. The comparison reveals that the earthquake signal is well above the accuracy of the vertical gravity gradients at orbital height. Moreover, the obtained signal from GOCE shows a 1.3 times higher amplitude compared with the modeled signal. Besides the statistical significance of the obtained signal, it has a high spatial correlation of ~0.7 with the forward modeled signal. We conclude therefore that the coseismic gravity change of the Japan Tohoku‐Oki earthquake left a statistically significant signal in the GOCE measured gravity gradients.

The new ESA satellite‐only gravity field model via the direct approach

AbstractReprocessed 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.

Validation of static gravity field models using GRACE K-band ranging and GOCE gradiometry data

The ability of satellite gravimetry data to validate global static models of the Earth’s gravity field is studied. Two types of data are considered: K-band ranging (KBR) data from the Gravity Recovery and Climate Experiment (GRACE) mission and Satellite Gravity Gradiometry (SGG) data from the GOCE (Gravity field and steady-state Ocean Circulation Explorer) mission. The validation is based on analysis of misfits obtained as the differences between the data observed and those computed with a force model that includes, in particular, a static gravity field model to be assessed. To facilitate the model assessment on a region-by-region basis, we convert KBR data into so-called range combinations, which are approximately equivalent to the intersatellite accelerations.We only use the accurately measured components of SGG data, that is, xx, yy, zz and xz components with x, y and z being along-track, cross-track and radial axes.We perform the validation in spectral and spatial domain. The latter requires elimination of low-frequency noise in the misfit data with a subsequent averaging over pre-defined blocks. Only ‘independent’ data are used, that is, those that have not been used in the production of the models under consideration. The proposed methodology is applied to eight models: EGM2008 (truncated at degree 250), EIGEN-6C (truncated at degree 250), two GRACE-only models (ITG-Grace03 and ITGGrace2010s) and four (satellite-only) combined GRACE/GOCE models (GOCO01S, EIGEN- 6S, GOCO02S and DGM-1S). The latter is a novel model developed at Delft University of Technology in collaboration with GNSS Research Centre of Wuhan University. The GRACE KBR and GOCE SGG data demonstrate a pronounced sensitivity to inaccuracies of EGM2008 in 5–22 mHz (27–120 cycles-per-revolution, cpr) and 10–28 mHz (54–150 cpr) frequency ranges, respectively. The latter data also show a high sensitivity to inaccuracies of ITGGrace2010s in 25–37 mHz (135–200 cpr) frequency range. From the validation in the spatial domain, it is confirmed that independent data of both types allow a difference in performance of the models to be observed, despite the fact that the duration of these data is much shorter than that of data used to produce those models. It is shown that EGM2008 performs weaker than the combined GRACE/GOCE models (up to the highest spectral sensitivity of the validation data). Considering the root mean square misfits related to the zz gravity gradient component, the differences in performance are: 76–83 per cent in the continental areas poorly covered by terrestrial gravimetry measurements (Himalayas, South America and Equatorial Africa); 4–16 per cent in the continental areas well covered by these measurements (Australia, North Eurasia and North America); and 11 per cent in theworld’s oceans (65?S–65?N). The identified differences in the regions of the latter two categories are related to the added value of the GOCE mission. It is shown that ITG-Grace03 and ITG-Grace2010s are of a much lower accuracy than EGM2008 in the gravimetrically well-surveyed continental areas: by 62–70 and 19–35 per cent and in the world’s oceans: by 54 and 18 per cent, respectively. Nevertheless, the former models show a higher accuracy in the gravimetrically poorly surveyed continental areas: by 62–69 and 69–75 per cent, respectively. This difference is explained mostly by a loss of information content of ITG-Grace03 when it was combined with terrestrial gravimetry data to produce EGM2008. The KBR and SGG test data identify this loss of information content in 4–23 mHz (22–124 cpr) and 9–26 mHz (50–140 cpr) frequency ranges, respectively. It is shown that EIGEN-6C also suffers from a similar problem but in a much less pronounced manner. In South America, for instance, this model is found to perform somewhat poorer than its satellite-only counterpart, that is, EIGEN-6S, by about 12 per cent. The combined GRACE/GOCE models show in the poorly surveyed continental areas a higher accuracy than ITG-Grace2010s: by 23–36 per cent, which is attributed to the added value of the GOCE mission data. GOCO02S outperforms GOCO01S by not more than 2–5 per cent. DGM-1S and GOCO02S show an almost similar performance against SGG test data. However, the former model shows a slightly better agreement with KBR test data. Both models agree with test data better than EIGEN-6S.

Approximations of the GOCE error variance-covariance matrix for least-squares estimation of height datum offsets

AbstractOne main geodetic objective of the European Space Agency’s satellite mission GOCE (gravity field and steady-state ocean circulation explorer) is the contribution to global height system unification. This can be achieved by applying the Geodetic Boundary Value Problem (GBVP) approach. Thereby one estimates the unknown datum offsets between different height networks (datum zones) by comparing the physical (e.g. orthometric) height values H of benchmarks in different datum zones to the corresponding values derived from the difference between ellipsoidal heights h (e.g. determined by means of global navigation satellite systems) and geoid heights N. In the ideal case, i.e. neglecting data errors, the misfit between H and (h − N) is constant inside one datum zone and represents the datum offset. In practise, the accuracy of the offset estimation depends on the accuracy of the three quantitiesH, h andN, where the latter can be computed from the combination of a GOCE-derived Global Potential Model (GPM) for the long to medium wavelength and terrestrial data for the short wavelength content. Providing an optimum estimation of the datum offsets along with realistic error estimates, theoretically, requires propagation of the full error variance and covariance information of the GOCE spherical harmonic coefficients to geoid heights, respectively geoid height differences. From a numerical point of view, this is a very demanding task which cannot simply be run on a single PC. Therefore it is worthwhile to investigate on different levels of approximation of the full variance-covariance matrix (VCM) with the aim of minimizing the numerical effort. In this paper, we compare the estimation error based on three levels of approximation, namely (1) using the full VCM, (2) using only elements of the dominant m-block structure of the VCM and (3) using only the main diagonal of the VCM, i.e. neglecting all error covariances between the spherical harmonic coefficients. We show that the m-block approximation gives almost the same result as provided by the full VCM. The diagonal approximation however over- or underestimates the geoid height error, depending on the geographic location and therefore is not regarded to be a suitable approximation.

Performance of GOCE and GRACE-derived mean dynamic topographies in resolving Antarctic Circumpolar Current fronts

Presently, two satellite missions, Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE), are making detailed measurements of the Earth’s gravity field, from which the geoid can be obtained. The mean dynamic topography (MDT) is the difference between the time-averaged sea surface height and the geoid. The GOCE mission is aimed at determining the geoid with superior accuracy and spatial resolution, so that a more accurate MDT can be estimated. In this study, we determine the mean positions of the Antarctic Circumpolar Current fronts using the purely geodetic estimates of the MDT constructed from an altimetric mean sea surface and GOCE and GRACE geoids. Overall, the frontal positions obtained from the GOCE and GRACE MDTs are close to each other. This means that these independent estimates are robust and can potentially be used to validate frontal positions obtained from sparse and irregular in situ measurements. The geodetic frontal positions are compared to earlier estimates as well as to those derived from MDTs based on satellite and in situ measurements and those obtained from an ocean data synthesis product. The position of the Sub-Antarctic Front identified in the GOCE MDT is found to be in better agreement with the previous estimates than that identified in the GRACE MDT. The geostrophic velocities derived from the GOCE MDT are also closer to observations than those derived from the GRACE MDT. Our results thus show that the GOCE mission represents an improvement upon GRACE in terms of the time-averaged geoid.

GPS-derived orbits for the GOCE satellite

The first ESA (European Space Agency) Earth explorer core mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) was launched on 17 March 2009 into a sun-synchronous dusk–dawn orbit with an exceptionally low initial altitude of about 280 km. The onboard 12-channel dual-frequency GPS (Global Positioning System) receiver delivers 1 Hz data, which provides the basis for precise orbit determination (POD) for such a very low orbiting satellite. As part of the European GOCE Gravity Consortium the Astronomical Institute of the University of Bern and the Department of Earth Observation and Space Systems are responsible for the orbit determination of the GOCE satellite within the GOCE High-level Processing Facility. Both quick-look (rapid) and very precise orbit solutions are produced with typical latencies of 1 day and 2 weeks, respectively. This article summarizes the special characteristics of the GOCE GPS data, presents POD results for about 2 months of data, and shows that both latency and accuracy requirements are met. Satellite Laser Ranging validation shows that an accuracy of 4 and 7 cm is achieved for the reduced-dynamic and kinematic Rapid Science Orbit solutions, respectively. The validation of the reduced-dynamic and kinematic Precise Science Orbit solutions is at a level of about 2 cm.

GOCE, Satellite Gravimetry and Antarctic Mass Transports

In 2009 the European Space Agency satellite mission GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) was launched. Its objectives are the precise and detailed determination of the Earth’s gravity field and geoid. Its core instrument, a three axis gravitational gradiometer, measures the gravity gradient components V xx , V yy , V zz and V xz (second-order derivatives of the gravity potential V) with high precision and V xy , V yz with low precision, all in the instrument reference frame. The long wavelength gravity field is recovered from the orbit, measured by GPS (Global Positioning System). Characteristic elements of the mission are precise star tracking, a Sun-synchronous and very low (260 km) orbit, angular control by magnetic torquing and an extremely stiff and thermally stable instrument environment. GOCE is complementary to GRACE (Gravity Recovery and Climate Experiment), another satellite gravity mission, launched in 2002. While GRACE is designed to measure temporal gravity variations, albeit with limited spatial resolution, GOCE is aiming at maximum spatial resolution, at the expense of accuracy at large spatial scales. Thus, GOCE will not provide temporal variations but is tailored to the recovery of the fine scales of the stationary field. GRACE is very successful in delivering time series of large-scale mass changes of the Antarctic ice sheet, among other things. Currently, emphasis of respective GRACE analyses is on regional refinement and on changes of temporal trends. One of the challenges is the separation of ice mass changes from glacial isostatic adjustment. Already from a few months of GOCE data, detailed gravity gradients can be recovered. They are presented here for the area of Antarctica. As one application, GOCE gravity gradients are an important addition to the sparse gravity data of Antarctica. They will help studies of the crustal and lithospheric field. A second area of application is ocean circulation. The geoid surface from the gravity field model GOCO01S allows us now to generate rather detailed maps of the mean dynamic ocean topography and of geostrophic flow velocities in the region of the Antarctic Circumpolar Current.

Research Spotlight: Using satellite data to estimate the North Atlantic Ocean circulation

By redistributing heat and freshwater around the planet, ocean currents play a crucial role in regulating Earth's climate. Accurate knowledge of the subtle regional variations in Earth's gravity field is fundamental to the measurement of ocean currents, but the challenge of mapping Earth's gravity in sufficient detail has previously limited scientists' ability to reliably determine the ocean's time‐mean circulation. To address this problem, in October 2009 the European Space Agency launched the Gravity field and steady‐state Ocean Circulation Explorer (GOCE) satellite with the aim of mapping Earth's gravity field with unprecedented spatial resolution. Bingham et al. present an initial assessment of the performance of GOCE by using the first data from the satellite to estimate the time‐mean circulation of the North Atlantic Ocean. This basin is particularly interesting because it contains the Gulf Stream, the world's strongest current and a key component of the global overturning circulation, which carries heat from the equator to high northerly latitudes. The scientists show that with just 2 months of observations, the GOCE estimate of the North Atlantic circulation is superior to that obtained from 8 years of data from the Gravity Recovery and Climate Experiment (GRACE) satellite. In many places, the current speeds estimated from the GOCE data compare well with those obtained from in situ observations, providing strong validation of the GOCE mission design. Accumulation of data as the mission progresses could lead to a more accurate and detailed map of the ocean's currents. (Geophysical Research Letters, doi:10.1029/2010GL045633, 2011)

Impact of GPS antenna phase center variations on precise orbits of the GOCE satellite

The first European Space Agency Earth explorer core mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) has been launched on March 17, 2009. The 12-channel dual-frequency Global Positioning System receiver delivers 1 Hz data and provides the basis for precise orbit determination (POD) on the few cm-level for such a very low orbiting satellite (254.9 km). As a member of the European GOCE Gravity Consortium, which is responsible for the GOCE High-level Processing Facility (HPF), the Astronomical Institute of the University of Bern (AIUB) provides the Precise Science Orbit (PSO) product for the GOCE satellite. The mission requirement for 1-dimensional POD accuracy is 2 cm. The use of in-flight determined antenna phase center variations (PCVs) is necessary to meet this requirement. The PCVs are determined from 154 days of data and the magnitude is up to 3-4 cm. The impact of the PCVs on the orbit determination is significant. The cross-track direction benefits most of the PCVs. The improvement is clearly seen in the orbit overlap analysis and in the validation with independent Satellite Laser Ranging (SLR) measurements. It is the first time that SLR could validate the cross-track component of a LEO orbit.

The measurement of Earth’s gravity field after the GOCE mission

GOCE ( Gravity Field and Steady-State Ocean Circulation Explorer), the first Earth Explorer Core Mission in ESA’s Living Planet programme, has been launched on March 17th 2009. Employing an ultra-sensitive gradiometer on a very low altitude orbit in along-track drag-free condition, within about 2 years GOCE will provide a global model of the Earth’s gravity field and of the geoid to unprecedented spatial resolution and accuracy. Meanwhile, the requirement for monitoring the temporal variations of gravity with a spatial resolution similar to GOCE, but over much longer time periods than the lifetime of GOCE, is emerging. It is driven by the need to detect long-term periodicities and trends in geophysical phenomena that involve large mass redistributions (e.g. melting of the polar ice sheets, changes in continental water storage, etc.), which are extremely valuable for a better understanding of climate change. From a series of preparatory studies led by the European Space Agency (ESA) since 2003, it turned out that the most suitable technique for such a next-generation gravity mission is the so-called Low-Low Satellite-to-Satellite Tracking based on laser distance metrology. A first design of this mission and of its laser metrology system has been defined in the studies performed for ESA the team led by Thales Alenia Space Italia (TAS-I).