The limited achievable temporal resolution poses one of the main limitations of current satellite gravity field missions such as GRACE and GRACE-FO and is, eventually, responsible for temporal aliasing. Increasing the temporal resolution is thus one of the most important tasks for future satellite gravity field missions. This, however, can only be achieved by means of larger satellite constellations since the temporal resolution can basically be defined as the time needed to achieve a global observation coverage. This needed (retrieval) time scales linearly with the number of satellites: e.g., a two-pair mission such as the upcoming joint ESA/NASA MAGIC mission can easily achieve global coverage with sufficient spatial resolution within less than a week. For a hypothetical 6-pair mission, even an independent daily retrieval is feasible. Future missions will hence allow to sample the gravity field in much shorter intervals. However, up until now, the parametrization of the gravity field within these intervals usually only accounts for a static behavior, resembling a step function in the time domain. Obviously, such a behavior is unnatural and does not follow the actual progression of the gravity field. So, even if sufficient temporal resolution would be available, temporal aliasing will not be fully mitigated due to this mis-parametrization. In this contribution we will thus investigate the impact of a direct time-variable parametrization through continuous spline-functions. On the example of a fictive 6-pair mission, we show how such a spline parametrization with daily support points can be applied: firstly, we prove that the spline parametrization allows numerically stable and correct solution based on a closed loop scenario without residual (sub-daily) temporal aliasing. Secondly, based on a more realistic scenario with sub-daily temporal gravity signal, we also highlight the (theoretical) limitations of a 6-pair mission due to the still very dominant temporal aliasing (from sub-daily signal sources). This work is supported by the ESA QSG4EMT study in collaboration with Politecnico di Milano, Delft University of Technology, HafenCity University Hamburg, University of Bonn and University of Trieste.

Cold Atom Interferometry (CAI) stands poised as a groundbreaking technique in satellite gravimetry, offering unparalleled precision and unbiased measurements. Despite the numerous studies on CAI's conceptual measurement techniques, attitude reconstruction accuracy poses a critical challenge. This submission seeks to bridge this gap by conducting an analysis of state-of-the-art attitude sensors and their suitability for upcoming quantum low-low satellite-to-satellite and gravity gradiometry missions utilizing CAI instruments. Acknowledging the immense promise of Cold Atom Interferometry, we emphasise the need to put this conceptual potential in the context of the accuracy of attitude reconstruction, a factor that significantly influences the feasibility of Quantum Space Gravimetric (QSG) missions. We examine the specifications, strengths, and limitations of attitude, acceleration, position and inter-satellite distance sensors to combine them realistically in scenarios specific to quantum low-low satellite-to-satellite and gravity gradiometry missions relying on CAI instruments. We also analyse the classic counterparts, offering valuable insights into the conceptual mission configurations that benefit the most from CAI-based observations. Our findings contribute not only to the advancement of the use of CAI technology in future graviemtric missions but also to the broader understanding of the intricate interplay between cutting-edge measurement techniques and the supporting instrumentation required for their successful implementation. This work is supported by the European Space Agency, under the project Quantum Space Gravimetry for monitoring Earth’s Mass Transport Processes (QSG4EMT), which has the general objectives to analyse future QSG mission architectures with ultimate goal to optimally exploit the performance of quantum sensors for retrieving temporal variations of Earth’s gravity field, evaluate the impact of mission configurations on the quality of the retrieved gravity field models and support the evolution of user requirements for future QSG missions.

AbstractWe investigate the benefits of future quantum accelerometers based on cold atom interferometry (CAI) on current and upcoming satellite gravity mission concepts. These mission concepts include satellite‐to‐satellite tracking (SST) in a single‐pair (GRACE‐like) and double‐pair constellation as well as satellite gravity gradiometry (SGG, single satellite, GOCE‐like). Regarding instruments, four scenarios are considered: current‐generation electrostatic (GRACE‐, GOCE‐like), next‐generation electrostatic, conservative hybrid/CAI and optimistic hybrid/CAI. For SST, it is shown that temporal aliasing poses currently the dominating error source in simulated global gravity field solutions independent of the investigated instrument and constellation. To still quantify the advantages of CAI instruments on the gravity functional itself, additional simulations are performed where the impact of temporal aliasing is synthetically reduced. When neglecting temporal aliasing, future accelerometers in conjunction with future ranging instruments can substantially improve the retrieval performance of the Earth's gravity field (depending on instrument and constellation). These simulation results are further investigated regarding possible benefit for hydrological use cases where these improvements can also be observed (when omitting temporal aliasing). For SGG, it is demonstrated that, with realistic instrument assumptions, one is still mostly insensitive to time‐variable gravity and not competitive with the SST principle. However, due to the improved instrument sensitivity of quantum gradiometers compared to the GOCE mission, static gravity field solutions can be improved significantly.

Cold Atom Interferometry (CAI) accelerometers and gradiometers have emerged as promising candidates for future gravimetric satellite missions due to their potential for detecting gravitational forces and gradients with high precision and accuracy. Current satellite gravimetry missions have demonstrated the utility of gravity data in understanding global mass transport phenomena, climate dynamics, and geological processes. However, state-of-the-art measurement techniques face noise and long-term drift limitations, which might propagate on the recovery of Earth's time-varying gravity field. Quantum sensors, particularly atom interferometry-based devices, offer promise for improving the accuracy and stability of space-based gravity measurements. This study explores the sensitivity of CAI accelerometers and gradiometers. We explore the low-low satellite-to-satellite and gravity gradiometry measurements to build analytical models of measurements and associated errors. We selected an ambitious scenario for CAI parameters that illustrates a potential path for increasing instrument accuracies and capabilities for space gravimetry. Two operational modes, concurrent and sequential, are compared to mitigate the effects of inaccurately known attitude rates on Coriolis accelerations. The sequential mode shows the potential to reduce these effects since the atom cloud has initial zero velocity, otherwise the Corilis effects are dominant in the concurrent operational mode. The CAI configuration considered in this study allows for the time variable gravity signal to be observed for the case of low-low Satellite-to-Satellite Tracking missions, but is inadequate to gravity gradient missions because of the reduced signal amplitude.

Abstract Temporal aliasing is currently the largest error contributor to time-variable satellite gravity field models. Therefore, the evolution of sensor technologies has to be complemented by strategies to reduce temporal aliasing errors. The most straightforward way to improve temporal aliasing is through extended satellite constellations because they improve the observation geometry and increase the achievable temporal resolution. Therefore, strategies to optimize the design of larger satellite constellations are investigated in this contribution. A complete constellation modeling procedure is presented, starting from primary design variables (such as the required targeted resolutions) and concluding with concrete orbital elements for the individual satellites. In parallel, it is evaluated if improved instrument sensitivities based on quantum technologies (cold atom interferometry) can be fully exploited in the case of larger constellations. For this, future quantum satellite gravity missions adopting the gradiometry concept (similar to the GOCE mission) and the low-low satellite-to-satellite tracking concept (similar to GRACE/-FO) are simulated on optimized constellations with up to 6 satellites/pairs. The retrieval performance of a 6-pair mission in terms of the global equivalent water height RMS can be improved by a factor of roughly 3 compared to an inclined double-pair mission. 3D-gradiometry intrinsically has a better de-aliasing behavior but has extremely high accuracy requirements for the gradiometer (about 10 µEotvos) and the attitude reconstruction to be of any benefit. All simulations show that when incorporating improved sensor technologies, such as future quantum sensing instruments in extended constellations, temporal aliasing will remain the dominant error source by far, up to five orders of magnitude larger than the instrument errors. Therefore, improving sensor technologies has to go hand in hand with larger satellite constellations and improved space–time parameterization strategies to further reduce temporal aliasing effects. Graphical Abstract

<p>With the evolution of cold atom interferometry (CAI), an adaptation for spaceborne applications may become possible in the near future. One of the applications which may benefit from such CAI instruments are next-generation satellite gravity field missions (NGGMs), since they rely heavily on the accelerometer performance. Here, either future satellite-to-satellite tracking (SST) missions (such as GRACE/-FO) or satellite gravity gradiometry (SGG) missions (such as GOCE) are feasible. Until now, only electrostatic accelerometers have been used. However, all suffer from an increased long-term instability which affects the accuracy of the long wavelengths of the retrieved gravity field. In this contribution we investigate the impact of CAI sensors on various NGGM mission concepts (either SST or SGG variants) and quantify the instrument-only error separately from the full gravity field retrieval error (which is hampered by temporal aliasing). Knowing that temporal aliasing currently poses one of the main limiting factors, special attention is given to strategies which may help to minimize this error source. Therefore, in addition to investigating future instruments, also extended mission constellations containing several satellites/pairs and alternative satellite configurations are examined with respect to their time-variable gravity field retrieval performance. This work is supported by the ESA QSG4EMT study in collaboration with Politecnico di Milano, Delft University of Technology, HafenCity University Hamburg, University of Bonn and University of Trieste.</p>

In the frame of the IAG Subcommission 2.4f “Gravity and Geoid in Antarctica” (AntGG) a first Antarctic-wide grid of ground-based gravity anomalies was released in 2016 (Scheinert et al. 2016). That data set was provided with a grid space of 10 km and covered about 73% of the Antarctic continent. Since then a considerably amount of new data has been made available, mainly collected by means of airborne gravimetry. Regions which were formerly void of any terrestrial gravity observations and have now been surveyed include especially the polar data gap originating from GOCE satellite gravimetry. Thus, it is timely to come up with an updated and enhanced regional gravity field solution for Antarctica. For this, we aim to improve further aspects in comparison to the AntGG 2016 solution: The grid spacing will be enhanced to 5 km. Instead of providing gravity anomalies only for parts of Antarctica, now the entire continent should be covered. In addition to the gravity anomaly also a regional geoid solution should be provided along with further desirable functionals (e.g. gravity anomaly vs. disturbance, different height levels). We will discuss the expanded AntGG data base which now includes terrestrial gravity data from Antarctic surveys conducted over the past 40 years. The methodology applied in the analysis is based on the remove-compute-restore technique. Here we utilize the newly developed combined spherical-harmonic gravity field model SATOP1 (Zingerle et al. 2019) which is based on the global satellite-only model GOCO05s and the high-resolution topographic model EARTH2014. We will demonstrate the feasibility to adequately reduce the original gravity data and, thus, to also cross-validate and evaluate the accuracy of the data especially where different data set overlap. For the compute step the recently developed partition-enhanced least-squares collocation (PE-LSC) has been used (Zingerle et al. 2021, in review; cf. the contribution of Zingerle et al. in the same session). This method allows to treat all data available in Antarctica in one single computation step in an efficient and fast way. Thus, it becomes feasible to iterate the computations within short time once any input data or parameters are changed, and to easily predict the desirable functionals also in regions void of terrestrial measurements as well as at any height level (e.g. gravity anomalies at the surface or gravity disturbances at constant height). We will discuss the results and give an outlook on the data products which shall be finally provided to present the new regional gravity field solution for Antarctica. Furthermore, implications for further applications will be discussed e.g. with respect to geophysical modelling of the Earth’s interior (cf. the contribution of Schaller et al. in session G4.3).

The gravity field reflects mass inhomogeneities (mostly) inside the Earth. Therefore, gravity inversion and geophysical gravity field modelling are important tools to study the Earth's inner structure and tectonic evolution. In Antarctica, it is extremely challenging to carry out geoscientific studies due to its harsh environment and difficult logistics. Additionally, the continent is covered by an up to 5 km thick ice sheet. However, in the framework of IAG Subcommission 2.4f “Gravity and Geoid in Antarctica” (AntGG) a large database of airborne, shipborne and ground based gravity data has been compiled. Especially airborne data have been acquired during recent years, among others in the area of the polar gap of satellite gravity data. Now, in a joint project funded by the German Research Foundation (DFG) all existing and new gravity data were processed to infer an enhanced gravity field solution for Antarctica (see contribution by Scheinert et al., session G1.5). Processed data e.g. gravity disturbances on the ground or a constant height and other functionals will be provided on a regular grid with 5 km grid spacing. Subsequently, the new Antarctic gravity field solution can now be used for further geophysical and tectonic studies. We use the newly calculated gravity disturbances to study subglacial topography, sediment thickness and Moho depth and to improve respective existing models in Antarctica. For this, we apply 2D Parker-Oldenburg inversion in combination with results from other gravity based studies and further constraining data (e.g. seismic data and ice penetrating radar). We investigate how the higher resolution (5 km) of the new Antarctic gravity field solution facilitates the study of smaller regions in more detail, specifically parts of Wilkes Land, Dronning Maud Land and the Weddell Sea. Additionally, we will infer accuracy estimates for the resulting boundaries in terms of the used inversion parameters (density contrast, average density and filter wavelengths) and their respective gravity signal. Thus, the challenges of gravity field inversion in Antarctica will be discussed in detail and first results of the subsurface modelling will be presented.

The primary objective of the 1-cm geoid experiment in Colorado (USA) is to compare the numerous geoid computation methods used by different groups around the world. This is intended to lay the foundations for tuning computation methods to achieve the sought after 1-cm accuracy, and also evaluate how this accuracy may be robustly assessed. In this experiment, (quasi)geoid models were computed using the same input data provided by the US National Geodetic Survey (NGS), but using different methodologies. The rugged mountainous study area (730 km ×\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} 560 km) in Colorado was chosen so as to accentuate any differences between the methodologies, and to take advantage of newly collected GPS/leveling data of the Geoid Slope Validation Survey 2017 (GSVS17) which are now available to be used as an accurate and independent test dataset. Fourteen groups from fourteen countries submitted a gravimetric geoid and a quasigeoid model in a 1′×\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document}1′ grid for the study area, as well as geoid heights, height anomalies, and geopotential values at the 223 GSVS17 marks. This paper concentrates on the quasigeoid model comparison and evaluation, while the geopotential value investigations are presented as a separate paper (Sánchez et al. in J Geodesy 95(3):1. https://doi.org/10.1007/s00190-021-01481-0, 2021). Three comparisons are performed: the area comparison to show the model precision, the comparison with the GSVS17 data to estimate the relative accuracy of the models, and the differential quasigeoid (slope) comparison with GSVS17 to assess the relative accuracy of the height anomalies at different baseline lengths. The results show that the precision of the 1′ × 1′ models over the complete area is about 2 cm, while the accuracy estimates along the GSVS17 profile range from 1.2 cm to 3.4 cm. Considering that the GSVS17 does not pass the roughest terrain, we estimate that the quasigeoid can be computed with an accuracy of ~ 2 cm in Colorado. The slope comparisons show that RMS values of the differences vary from 2 to 8 cm in all baseline lengths. Although the 2-cm precision and 2-cm relative accuracy have been estimated in such a rugged region, the experiment has not reached the 1-cm accuracy goal. At this point, the different accuracy estimates are not a proof of the superiority of one methodology over another because the model precision and accuracy of the GSVS17-derived height anomalies are at a similar level. It appears that the differences are not primarily caused by differences in theory, but that they originate mostly from numerical computations and/or data processing techniques. Consequently, recommendations to improve the model precision toward the 1-cm accuracy are also given in this paper.

We present a partition-enhanced least-squares collocation (PE-LSC) which comprises several modifications to the classical LSC method. It is our goal to circumvent various problems of the practical application of LSC. While these investigations are focused on the modeling of the exterior gravity field the elaborated methods can also be used in other applications. One of the main drawbacks and current limitations of LSC is its high computational cost which grows cubically with the number of observation points. A common way to mitigate this problem is to tile the target area into sub-regions and solve each tile individually. This procedure assumes a certain locality of the LSC kernel functions which is generally not given and, therefore, results in fringe effects. To avoid this, it is proposed to localize the LSC kernels such that locality is preserved, and the estimated variances are not notably increased in comparison with the classical LSC method. Using global covariance models involves the calculation of a large number of Legendre polynomials which is usually a time-consuming task. Hence, to accelerate the creation of the covariance matrices, as an intermediate step we pre-calculate the covariance function on a two-dimensional grid of isotropic coordinates. Based on this grid, and under the assumption that the covariances are sufficiently smooth, the final covariance matrices are then obtained by a simple and fast interpolation algorithm. Applying the generalized multi-variate chain rule, also cross-covariance matrices among arbitrary linear spherical harmonic functionals can be obtained by this technique. Together with some further minor alterations these modifications are implemented in the PE-LSC method. The new PE-LSC is tested using selected data sets in Antarctica where altogether more than 800,000 observations are available for processing. In this case, PE-LSC yields a speed-up of computation time by a factor of about 55 (i.e., the computation needs only hours instead of weeks) in comparison with the classical unpartitioned LSC. Likewise, the memory requirement is reduced by a factor of about 360 (i.e., allocating memory in the order of GB instead of TB).

Within this contribution we present a method that allows a smooth integration of in-situ ground gravity observations into high-resolution global models up to d/o 5400 (2’ global resolution). The functionality is shown on the example of the airborne GRAV-D gravity dataset which is integrated into a global satellite-topographic spherical harmonic model. Conceptually, the method is divided into three steps: firstly, since the processing is based on residuals, a precursor model needs to be identified which is used for reducing the observations. In the actual example a combination between a satellite-only model (GOCO06s) and topographic model (EARTH2014) is chosen (named SATOP2) to ensure independency to the observations. Secondly, the previously reduced (GRAV-D) observations are gridded onto a regular geographic grid making use of the recently developed partition-enhanced least squares collocation approach (PE-LSC). PE-LSC allows an efficient collocation of virtually arbitrary large datasets using a partitioning technique that is optimized for computational performance and for minimizing fringe effects. As a third and last step, the obtained regular grid gets analyzed and combined with a satellite-only model (GOCO06s) on the normal equation level up to d/o 5400. This can be achieved efficiently by using a so-called kite-normal equation system which emerges when combining dense and block-diagonal normal equation systems (assuming equal accuracies for the ground gravity grid). The herby obtained global gravity field model, named SGDT, is dominated by the satellite information in the lower frequencies (up to d/o 200), by GRAV-D in the mid-frequencies (d/o 200-2000) and by the topographic information in the high frequencies (above d/o 2000). The main purpose of the SGDT model is to validate the method itself and to allow a comparison of GRAV-D observations to pre-existing ground-gravity data by synthesizing SGDT to actual observation sites.

Low-pass filters are commonly used for the processing of airborne gravity observations. In this paper, for the first time, we include the resulting correlations consistently in the functional and stochastic model of residual least-squares collocation. We demonstrate the necessity of removing high-frequency noise from airborne gravity observations, and derive corresponding parameters for a Gaussian low-pass filter. Thereby, we intend an optimal combination of terrestrial and airborne gravity observations in the mountainous area of Colorado. We validate the combination in the frame of our participation in ‘the 1 cm geoid experiment’. This regional geoid modeling inter-comparison exercise allows the calculation of a reference solution, which is defined as the mean value of 13 independent height anomaly results in this area. Our result performs among the best and with 7.5 mm shows the lowest standard deviation to the reference. From internal validation we furthermore conclude that the input from airborne and terrestrial gravity observations is consistent in large parts of the target area, but not necessarily in the highly mountainous areas. Therefore, the relative weighting between these two data sets turns out to be a main driver for the final result, and is an important factor in explaining the remaining differences between various height anomaly results in this experiment.

Within this contribution we present the new experimental combined global gravity field model XGM2020. Key feature of this model is the rigorous combination of the latest GOCO06s satellite-only model with global terrestrial gravity anomalies on normal equation level, up to d/o 2159, using individual observation weights. To provide a maximum resolution, the model is further extended to d/o 5400 by applying block diagonal techniques. To attain the high resolution, the incorporated terrestrial dataset is composed of three different data sources: Over land 15´ gravity anomalies (by courtesy of NGA) are augmented with topographic information, and over the oceans gravity anomalies derived from altimetry are used. Corresponding normal equations are computed from these data sets either as full or as block diagonal systems. Special emphasis is given to the novel processing techniques needed for very high-resolution gravity field modelling. As such the spheroidal harmonics play a central role, as well as the stable calculation of associated Legendre polynomials up to very high d/o. Also, a new technique for the optimal low-pass filtering of terrestrial gravity datasets is presented. On the computational side, solving dense normal equation systems up to d/o 2159 means dealing with matrices of the size of about 158TB. Handling with matrices of such a size is very demanding, even for today’s largest supercomputers. Thus, sophisticated parallelized algorithms with focus on load balancing are crucial for a successful and efficient calculation.

The Dynamic ocean Topography (DT) describes the deviation of the true ocean surface from a hypothetical equilibrium state ocean at rest forced by gravity alone. With the geostrophic surface currents obtained from its gradients the DT is an essential parameter for describing the ocean dynamics. Observation-based global temporal Mean geodetic DTs (MDTs) are obtained from the difference of altimetric Mean Sea Surface (MSS) and the geoid height, that equipotential surface of gravity closest to the ocean surface. The geoid is provided either as a satellite-only, or a combined model including in addition gravity anomalies derived from satellite altimetry and ground data. In recent years the focus was on satellite-only models, produced from new space-born observations obtained from the Gravity Recovery and Climate Experiment (GRACE) and Gravity field and Ocean Circulation Explorer (GOCE) satellite missions. Moreover, combined geoid models are only cautiously used for MDT calculation, since it is still in question to what extent the gravity information obtained from altimetry is distorted by the MDT information included therein and how this translates into errors of the MDT. Here we want to concentrate on MDT models based on recent combined geoid models. An assessment is provided based on comparisons to near-surface drifter data from the Global Drifter Program (GDP). Besides providing a general, global assessment, we focus on signal content on small scales, addressing mainly two questions: 1) Do MDTs obtained from combined geoid models contain signal for scales smaller than resolvable by the satellite-only models? 2) Is there a maximum resolution beyond which no signal is detectable? Until recently, these questions couldn't be answered since low resolution MDTs usually contained strong wavy-structured errors and thus needed a strong spatial filtering thereby killing the smallest scales resolved in the MDT. These errors, which worsen with lower resolution, are caused by Gibbs effects provoked by imperfections in bringing the high resolution ocean-only MSS models into spectral consistency with the much lower resolved global geoid model. A new methodology, however, improves the necessary globalization of the MSS. After subtraction of the geoid model, subsequent cutting-off the signal beyond a specific spherical harmonic degree and order (d/o) results in an MDT without any Gibbs effects, also for low resolution models. To answer the questions posed above applying the new methodology, the scale-dependent signal in MDTs for different geoid models is presented for a list of cut off d/os. To minimize the influence of noise on the results we concentrate on strong signal Western Boundary Currents like the Gulf Stream and the Kuroshio. For the Gulf Stream results of a high resolution hydrodynamic model are available and presented as an independent method to estimate the scale dependent signal.

Within this contribution we present the new experimental combined global gravity field model XGM2020. Key feature of this model is the rigorous combination of the latest GOCO06s satellite-only model with global terrestrial gravity anomalies on normal equation level, up to d/o 2159, using individual observation weights. To provide a maximum resolution, the model is further extended to d/o 5400 by applying block diagonal techniques. To attain the high resolution, the incorporated terrestrial dataset is composed of three different data sources: Over land 15´ gravity anomalies (by courtesy of NGA) are augmented with topographic information, and over the oceans gravity anomalies derived from altimetry are used. Corresponding normal equations are computed from these data sets either as full or as block diagonal systems. Special emphasis is given to the novel processing techniques needed for very high-resolution gravity field modelling. As such the spheroidal harmonics play a central role, as well as the stable calculation of associated Legendre polynomials up to very high d/o. Also, a new technique for the optimal low-pass filtering of terrestrial gravity datasets is presented. On the computational side, solving dense normal equation systems up to d/o 2159 means dealing with matrices of the size of about 158TB. Handling with matrices of such a size is very demanding, even for today’s largest supercomputers. Thus, sophisticated parallelized algorithms with focus on load balancing are crucial for a successful and efficient calculation.

XGM2019e is a combined global gravity field model represented by spheroidal harmonics up to degree and order (d/o) 5399, corresponding to a spatial resolution of 2′ (~ 4 km). As data sources, it includes the satellite model GOCO06s in the longer wavelength range up to d/o 300 combined with a ground gravity grid which also covers the shorter wavelengths. The ground data consist over land and ocean of gravity anomalies provided by courtesy of NGA (15′ resolution, identical to XGM2016) augmented with topographically derived gravity information over land (EARTH2014). Over the oceans, gravity anomalies derived from satellite altimetry are used (DTU13 with a resolution of 1′). The combination of the satellite data with the ground gravity observations is performed by using full normal equations up to d/o 719 (15′). Beyond d/o 719, a block-diagonal least squares solution is calculated for the high-resolution ground gravity data (from topography and altimetry). All calculations are performed in the spheroidal harmonic domain. In the spectral band up to d/o 719, the new model shows a slightly improved behaviour in the magnitude of a few mm RMS over land as compared to preceding models such as XGM2016, EIGEN6c4 or EGM2008 when validated with independent geoid information derived from GNSS/levelling. Over land and in the spectral range above d/o 719, the accuracy of XGM2019e marginally suffers from the sole use of topographic forward modelling, and geoid differences at GNSS/levelling stations are increased in the order of several mm RMS in well-surveyed areas, such as the US and Europe, compared to models containing real gravity data over their entire spectrum, e.g. EIGEN6c4 or EGM2008. However, GNSS/levelling validation also indicates that the performance of XGM2019e can be considered as globally more consistent and independent of existing high-resolution global models. Over the oceans, the model exhibits an enhanced performance (equal or better than preceding models), which is confirmed by comparison of the MDT’s computed from CNES/CLS 2015 mean sea surface and the high-resolution geoid models. The MDT based on XGM2019e shows fewer artefacts, particularly in the coastal regions, and fits globally better to DTU17MDT which is considered as an independent reference MDT.

The AntGrav project, funded by the German Research Foundation (DFG) has the main objective to homogenize and optimize Antarctic gravity field information. Within this project an evaluation procedure is needed to inspect all different kind of gravity field surveys available in Antarctica. In this paper a suitable methodology is proposed. We present an approach for fast 3D gravity point data reduction in different spectral bands. This is achieved through pre-calculating a fine 3D mesh of synthesized gravity functionals over the entirety of the Antarctic continent, for which two different global models are used: the combined satellite model GOCO05s for the long-wavelength part, and the topographic model Earth2014 for the shorter wavelengths. To maximize the applicability separate meshes are calculated for different spectral bands in order to specifically reduce a certain band or a selected combination. All meshes are calculated for gravity anomalies as well as gravity disturbances. Utilizing these meshes, synthesized gravity data at arbitrary positions is computed by conventional 3D interpolation methods (e.g. linear, cubic or spline). It is shown that the applied approach can reach a worstcase interpolation error of less than 1 mGal. Evaluation results are presented for the AntGG grid and exemplary for the in-situ measurements of the AGAP and BAS-LAND campaigns. While general properties, large-scale errors and systematic effectscan usually be detected, small-scale errors (e.g. of single points) are mostly untraceable due to the uncertainties within the topographic model.