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For decades, the residual terrain model (RTM) concept (Forsberg and Tscherning in J Geophys Res Solid Earth 86(B9):7843–7854, , 1981) has been widely used in regional quasigeoid modeling. In the commonly used remove-compute-restore (RCR) framework, RTM provides a topographic reduction commensurate with the spectral resolution of global geopotential models. This is usually achieved by utilizing a long-wavelength (smooth) topography model known as reference topography. For computation points in valleys this neccessitates a harmonic correction (HC) which has been treated in several publications, but mainly with focus on gravity. The HC for the height anomaly only recently attracted more attention, and so far its relevance has yet to be shown also empirically in a regional case study. In this paper, the residual spherical-harmonic topographic potential (RSHTP) approach is introduced as a new technique and compared with the classic RTM. Both techniques are applied to a test region in the central European Alps including validation of the quasigeoid solutions against ground-truthing data. Hence, the practical feasibility and benefits for quasigeoid computations with the RCR technique are demonstrated. Most notably, the RSHTP avoids explicit HC in the first place, and spectral consistency of the residual topographic potential with global geopotential models is inherently achieved. Although one could conclude that thereby the problem of the HC is finally solved, there remain practical reasons for the classic RTM reduction with HC. In this regard, both intra-method comparison and ground-truthing with GNSS/leveling data confirms that the classic RTM (Forsberg and Tscherning 1981; Forsberg in A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modeling. Report 355, Department of Geodetic Sciences and Surveying, Ohio State University, Columbus, Ohio, USA, , 1984) provides reasonable results also for a high-resolution (degree 2160) RTM, yet neglecting the HC for the height anomaly leads to a systematic bias in deep valleys of up to 10–20 cm. [ABSTRACT FROM AUTHOR]

In Gravity Recovery and Climate Experiment (GRACE) Follow‐on (GRACE‐FO) mission, similar to its predecessor GRACE, the twin satellites are equipped with three‐axis accelerometers, measuring the non‐gravitational forces. After 1 month in orbit, during the in‐orbit‐checkout phase, the noise on GRACE‐D accelerometer measurements elevated and resulted in systematical degradation of the data. For this reason, the GRACE‐D data need to be replaced by synthetic data, the so‐called transplant data, officially generated by the GRACE‐FO Science Data System (SDS). The SDS transplant data are derived from the GRACE‐C accelerometer measurements, by applying time and attitude corrections. Furthermore, model‐based residual accelerations due to thruster firings on GRACE‐D were added, proven to improve the data quality in gravity field recovery. However, preliminary studies of GRACE‐FO data during the single accelerometer months show that the low degree zonal harmonics, in particular C20 and C30, are sensitive to the current transplant approach. In this work, we present a novel approach to recover the GRACE‐D ACT1B data by incorporating non‐gravitational force models and analyze its impact on monthly gravity field solutions. The results show the improved ACT1B data not only contributed to a noise reduction but also improved the estimates of the C20 and C30 coefficients. The application of this new approach demonstrates that the offset between Satellite Laser Ranging (SLR) and GRACE‐FO derived C30 time series can be reduced by the use of the alternative accelerometer product. Key Points: Alternative processing is proposed for recovering GRACE‐D accelerometer dataThe recovered products improve overall accuracy of gravity field solutionsThe recovered products improve the estimates of low degree zonal coefficients [ABSTRACT FROM AUTHOR]

In this article, we present a computationally efficient method to incorporate background model uncertainties into the gravity field recovery process. While the geophysical models typically used during the processing of GRACE data, such as the atmosphere and ocean dealiasing product, have been greatly improved over the last years, they are still a limiting factor of the overall solution quality. Our idea is to use information about the uncertainty of these models to find a more appropriate stochastic model for the GRACE observations within the least squares adjustment, thus potentially improving the gravity field estimates. We used the ESA Earth System Model to derive uncertainty estimates for the atmosphere and ocean dealiasing product in the form of an autoregressive model. To assess our approach, we computed time series of monthly GRACE solutions from L1B data in the time span of 2005 to 2010 with and without the derived error model. Intercomparisons between these time series show that noise is reduced on all spatial scales, with up to 25% RMS reduction for Gaussian filter radii from 250 to 300 km, while preserving the monthly signal. We further observe a better agreement between formal and empirical errors, which supports our conclusion that used uncertainty information does improve the stochastic description of the GRACE observables. [ABSTRACT FROM AUTHOR]

For further improvements of gravity field models based on Gravity Recovery and Climate Experiment (GRACE) observations, it is necessary to identify the error sources within the recovery process. Observation residuals obtained during the gravity field recovery contain most of the measurement and modeling errors and thus can be considered a realization of actual errors. In this work, we investigate the ability of wavelets to help in identifying specific error sources in GRACE range-rate residuals. The multiresolution analysis (MRA) using discrete wavelet transform (DWT) is applied to decompose the residual signal into different scales with corresponding frequency bands. Temporal, spatial, and orbit-related features of each scale are then extracted for further investigations. The wavelet analysis has proven to be a practical tool to find the main error contributors. Besides the previously known sources such as K-band ranging (KBR) system noise and systematic attitude variations, this method clearly shows effects which the classic spectral analysis is hardly able or unable to represent. These effects include long-term signatures due to satellite eclipse crossings and dominant ocean tide errors. [ABSTRACT FROM AUTHOR]

This article describes the raw observation approach as implemented at Graz University of Technology to determine GNSS products like satellite orbits, clocks, and station positions. To assess the performance of the approach, 15 years (2003–2017) of observations from a network of 245 globally distributed IGS stations to the GPS constellation were processed on a daily basis using the IGS14 reference frame and antenna calibrations. The resulting products are evaluated against those determined by IGS analysis centers. Orbit fit quality relative to the IGS combination is comparable to the best-fitting solutions used for evaluation. Starting from early 2017, when the IGS switched to IGS14, the determined orbits fit better to the IGS combination than any other considered solution. Midnight discontinuities show good internal orbit consistency and no noticeable satellite block-dependency. Satellite clocks are comparable to the considered IGS analysis center solutions. Station positions differ from the IGS combination on a similar level to the solutions they were evaluated against. The temporal repeatability of station positions is slightly better than that of the IGS combination. The quality of resulting GNSS products confirms that the raw observation approach is well suited for the task of determining satellite orbits, clocks, and station positions. It provides an alternative to well-established approaches used by IGS analysis centers and simplifies the introduction of additional observables from new and modernized GNSS. [ABSTRACT FROM AUTHOR]

For further improvements of gravity field models based on Gravity Recovery and Climate Experiment (GRACE) observations, it is necessary to identify the error sources within the recovery process. Observation residuals obtained during the gravity field recovery contain most of the measurement and modeling errors and thus can be considered as a realization of actual errors. In this work, we investigate the ability of wavelets to help in identifying specific error sources in GRACE range rate residuals. The Multi-Resolution Analysis (MRA) using Discrete Wavelet Transform (DWT) is applied to decompose the residual signal into different scales with corresponding frequency bands. Temporal, spatial, and orbit-related features of each scale are then extracted for further investigations. The wavelet analysis has proved to be a practical tool to find the main error contributors. Beside the previously known sources such as K-Band Ranging (KBR) system noise and systematic attitude variations, this method clearly shows effects which the classic spectral analysis is hardly able or unable to represent. These effects include long-term signatures due to satellite eclipse crossings and dominant ocean tide errors. [ABSTRACT FROM AUTHOR]

Future gravity missions like GRACE Follow-on and beyond will deliver low-low satellite-to-satellite ranging measurements of a much increased precision on the order of nanometers. This necessitates a re-evaluation of the processes used in gravity field determination with an eye to numerical stability and computational precision. This study investigates the computation of dynamic orbits, which are used for multiple purposes in gravity recovery. They are, for example, used in computing linearized observations for the low-low satellite-to-satellite tracking instruments. The precision at which the dynamic orbits are determined thus must surpass the precision of the ranging observations. Dynamic orbits for GRACE were computed both in a simple simulation, where the force model was reduced to a static potential of degree and order 60, and for real observational data. Encke’s method was employed while using a novel reference trajectory determined through rigorous optimization. This reference trajectory was parametrized with equinoctial elements to minimize errors resulting from imprecision in the reference motion. The differences in coordinates between successive iterations of orbit determination were used as a benchmark for the quality of the orbit solution. Using Encke’s method with equinoctial elements, the coordinate difference between iterations was reduced from on the order of tens of micrometers to some nanometers in the spectral range relevant to GRACE satellite-to-satellite tracking observations. The resulting dynamic orbits are self-consistent to below the expected precision of the GRACE Follow-on ranging instruments. [ABSTRACT FROM AUTHOR]

For more than 14 years, the Gravity Recovery and Climate Experiment (GRACE) mission has provided information about Earth’s gravity field with unprecedented accuracy. The twin satellites GRACE-A and GRACE-B are both equipped with a three-axis electrostatic accelerometer, measuring the non-gravitational forces acting on the spacecraft. In order to make use of the uncalibrated Level-1B accelerometer (ACC1B) data during gravity field recovery, bias and scale parameters have to be estimated. The proposed calibration method is a two-step approach and makes use of modeled non-conservative accelerations. The simulated non-conservative accelerations serve as reference for the a priori accelerometer calibration, i.e. for the ACC1B data. During gravity field recovery the calibration parameters are re-estimated. Several calibration parameters for the GRACE accelerometers using different methods have already been published. The aim of our study was primarily to analyze the temperature-dependent behavior of the accelerometer scale factors and biases, and the impact of the parametrization of scale factors and biases on the recovered gravity field solutions; but not to obtain calibrated accelerometer data. Within the ITSG-Grace2016 release, the accelerometer biases are estimated daily using uniform cubic basis splines (UCBS), the scale factors are also estimated daily using a fully-populated scale factor matrix. Therefore, not only the scale factors in along-track, cross-track, and radial direction are estimated, but also the non-orthogonality of the accelerometer axes (cross-talk) and the misalignment between the Accelerometer Frame (AF) and Science Reference Frame (SRF) are taken into account. The time evolution of the estimated calibration parameters over the whole GRACE period (2002-04 to 2016-01) shows a clear temperature-dependency for both scale factors and biases. Using this new approach, the estimates of the C20 coefficient significantly improve, with results now comparable to Satellite Laser Ranging (SLR) solutions. Based on the achieved results, we suggest the presence of a clear temperature-dependent behavior and the presence of off-diagonal elements in the accelerometer scale factor matrix. [ABSTRACT FROM AUTHOR]

Precise orbit determination is an essential part of the most scientific satellite missions. Highly accurate knowledge of the satellite position is used to geolocate measurements of the onboard sensors. For applications in the field of gravity field research, the position itself can be used as observation. In this context, kinematic orbits of low earth orbiters (LEO) are widely used, because they do not include a priori information about the gravity field. The limiting factor for the achievable accuracy of the gravity field through LEO positions is the orbit accuracy. We make use of raw global positioning system (GPS) observations to estimate the kinematic satellite positions. The method is based on the principles of precise point positioning. Systematic influences are reduced by modeling and correcting for all known error sources. Remaining effects such as the ionospheric influence on the signal propagation are either unknown or not known to a sufficient level of accuracy. These effects are modeled as unknown parameters in the estimation process. The redundancy in the adjustment is reduced; however, an improvement in orbit accuracy leads to a better gravity field estimation. This paper describes our orbit determination approach and its mathematical background. Some examples of real data applications highlight the feasibility of the orbit determination method based on raw GPS measurements. Its suitability for gravity field estimation is presented in a second step. [ABSTRACT FROM AUTHOR]

Over the past decade, the Global Positioning System has released pre-flight calibrations for the transmit antennas of the Block IIR/IIR-M, Block IIF, and GPS III satellites that make up the current GPS constellation. Frequency-specific phase variations (PHVs) provided as part of these data sets are of key interest for an accurate and consistent modeling of GNSS carrier phase observations in precise point positioning applications as well as orbit and clock offset determination of the GPS satellites themselves. For proper utilization of the manufacturer calibrations, complementary information on the phase center offset (PCO) from the spacecraft center-of-mass is required. We describe necessary processing steps for converting the raw phase calibrations of Lockheed Martin and Boeing into a representation compatible with antenna models of the International GNSS Service (IGS), and provide a detailed discussion of inherent assumptions for combining PHVs and PCOs from different sources. Comparison with estimated antenna data from globally distributed monitoring stations shows good consistency of PHVs and suggests the use of manufacturer-calibrated, azimuth-dependent patterns in future releases of the IGS antenna model. In terms of PCOs, the new Block IIF calibrations exhibit a systematic bias of about 12 cm from PCOs estimates based on the IGS20 reference frame. This value closely matches the bias observed for manufacturer calibrations of GPS III and Galileo satellites, and suggests a careful review of the contribution that GNSS can make to the scale definition of the International Terrestrial Reference Frame (ITRF). [ABSTRACT FROM AUTHOR]

Electromagnetic signals commonly used in geodetical applications, such as the Global Navigation Satellite System (GNSS), undergo bending and delay in the neutral gas atmosphere of the Earth. The least-travel-time (LTT) concept is one of the approaches to model signal slant delays via a ray tracing (RT) procedure. In this study, we developed an LTT-based RT algorithm (LTT v2), where the 3-dimensional refractivity field of the atmosphere is based on the atmospheric model data. This representation is complete in a sense that the domain of the RT conforms to the native grid geometry of the atmospheric model. In addition, some physical and numerical approximations are improved compared to the previous version (LTT v1). The atmospheric states are generated using a global numerical weather prediction model, the Open Integrated Forecast System of the European Centre for Medium-Range Weather Forecasts. The slant delays of LTT v2 are compared with the products of the original least-travel-time GNSS delay model (LTT v1) and the products of the state-of-the-art VieVS Ray Tracer (RADIATE). The skill of slant delay estimation is assessed using metrics that are indicative of the quality of GNSS products derived using the GROOPS (Gravity Recovery Object Oriented Programming System) orbit solver software toolkit of the Graz University of Technology. Employment of slant delay products of the LTT RT algorithm shows radical improvement in GNSS processing. When using LTT v2 delay estimates, the GNSS orbit midnight discontinuities are reduced by more than 10 % compared to RADIATE, and more than 2 % compared to LTT v1. The residuals of ground station precise positioning are analysed with respect to the IGS14 reference positions. The RMS of residuals (accuracy) and standard deviation (precision) are substantialy reduced compared to RADIATE. [ABSTRACT FROM AUTHOR]

The Gravity Recovery Object Oriented Programming System (GROOPS) is a software toolkit written in C++ that enables the user to perform core geodetic tasks. Key features of the software include gravity field recovery from satellite and terrestrial data, the determination of satellite orbits from global navigation satellite system (GNSS) measurements, and the computation of GNSS constellations and ground station networks. Next to raw data processing, GROOPS is capable to operate on time series and spatial data to directly analyze and visualize the computed data sets. Most tasks and algorithms are (optionally) parallelized through the Message Passing Interface, thus the software enables a smooth transition from single-CPU desktop computers to large distributed computing environments for resource intensive tasks. For an easy and intuitive setup of complex workflows, GROOPS contains a graphical user interface to create and edit configuration files. The source code of the software is freely available on GitHub (https://github.com/groops-devs/groops) together with documentation, a cookbook with guided examples, and step-by-step installation instructions. • GROOPS is a software package for geodetic, geophysical, and environmental applications. • Global and regional gravity field recovery. • GNSS processing from single-station precise point positioning to large global networks. • Orbit determination of low-Earth-orbiting satellites [ABSTRACT FROM AUTHOR]

The satellite missions GRACE and GRACE Follow-On have undoubtedly been the most important sources to observe mass transport on global scales. Within the Combination Service for Time-Variable Gravity Fields (COST-G), gravity field solutions from various processing centers are being combined to improve the signal-to-noise ratio and further increase the spatial resolution. The time series of monthly gravity field solutions suffer from a data gap of about one year between the two missions GRACE and GRACE Follow-On among several smaller data gaps. We present an intermediate technique bridging the gap between the two missions allowing (1) for a continued and uninterrupted time series of mass observations and (2) to compare, cross-validate and link the two time series. We focus on the combination of high-low satellite-to-satellite tracking (HL-SST) of low-Earth orbiting satellites by GPS in combination with satellite laser ranging (SLR), where SLR contributes to the very low degrees and HL-SST is able to provide the higher spatial resolution at an lower overall precision compared to GRACE-like solutions. We present a complete series covering the period from 2003 to 2022 filling the gaps of GRACE and between the missions. The achieved spatial resolution is approximately 700 km at a monthly temporal resolutions throughout the time period of interest. For the purpose of demonstrating possible applications, we estimate the low degree glacial isostatic adjustment signal in Fennoscandia and North America. In both cases, the location, the signal strength and extend of the signal coincide well with GRACE/GRACE-FO solutions achieving 99.5% and 86.5% correlation, respectively. [ABSTRACT FROM AUTHOR]

The estimation of satellite orbits and clocks plays a central role in different Global Navigation Satellite System (GNSS) domains, e.g. precise positioning or time transfer. Such products can be computed in the process of Orbit Determination and Time Synchronization (ODTS), which relies on a network of ground-based stations, well distributed around the globe. The mm-level precision of carrier-phase measurements is exploited in this network estimation following a correct resolution of their ambiguities. For several stations, satellites and/or signals, thousands of ambiguities have to be processed, which means having to deal with high-dimensional ambiguity resolution (HDAR) problems. In this research work, we firstly account for the impact of ambiguity resolution in a varying network size, based on GPS-only, Galileo-only and GPS+Galileo configurations. Using 25 or more stations, the accuracy (1D RMS orbital errors) of fixed solutions reaches a plateau at 1–2 cm. Hence, we focus on a small global network of 14 stations, where the model strength decreases, so does the reliability of the ambiguity fixing process and advantages over a float solution might become less evident. In order to allow reliable HDAR, two implementations of the Vectorial Integer Bootstrapping estimator are presented and evaluated with respect to their scalar counterpart. Finally, it is shown how the proposed fixing processes are more robust, still very efficient, and on certain days they provide a large improvement to satellite products. The orbital results are ultimately validated by considering the satellite midnight discontinuity errors over a 3-month period in 2019. [ABSTRACT FROM AUTHOR]

With the modernization of GPS and GLONASS and the advent of Galileo, BeiDou, and regional satellite systems, there is now a multitude of signals available for ground station networks to observe. As a result, the complexity of deriving GNSS products like satellite orbits, clocks, station positions, and signal biases increases significantly when dealing with all these signals at once. The raw observation approach was developed to cope with this increased complexity in multi-GNSS processing. It is based on undifferenced and uncombined observations and therefore allows full exploitation of the information contained in each individual observable and preserves the original measurement accuracy. While the approach was developed with the aim of multi-GNSS processing, it was initially tested and evaluated using only the GPS constellation to limit the complexity of the software implementation. It is now being expanded to full multi-GNSS processing, the details of which will be the main topic of this submission. One focus lies on how inter-frequency and inter-system signal biases are handled during processing. The time-variability of those and related parameters and possible modeling strategies will be investigated, e.g. by modeling clocks and biases as stochastic processes. The resulting multi-GNSS products are compared with those of the IGS MGEX analysis centers to evaluate the performance of the raw observation approach. [ABSTRACT FROM AUTHOR]

The main objective of the GOCO ("Gravity Observation Combination") project is to compute high-accuracy and high-resolution static global gravity field models based on data of the dedicated satellite gravity missions CHAMP, GRACE, and GOCE, SLR data, and kinematic orbits from different Low Earth Orbiters. In this contribution we present the latest release GOCO06s. The motivation for this new release lies in various improvements within the processing chain as well as the availability of reprocessed observation data for GRACE and GOCE and updated background models. The main focus in the GOCO combination process is on the proper handling of the stochastic behaviour of the data. Therefore, the resulting accuracy information in terms of a full variance covariance matrix is quite realistic and also published with the solution. GOCO06s consists not only of a static gravity field, but the temporal variations are modelled as well. These are represented as regularized trend and annual signal. [ABSTRACT FROM AUTHOR]

In both GRACE (Gravity Recovery and Climate Experiment) and GFO (GRACE Follow-On) missions, the twin satellites are equipped with three-axis accelerometers, measuring the non-gravitational forces. Close to the end of the GRACE mission, the accelerometer onboard GRACE-B was switched off due to the reduced battery capacity and its measurements were replaced by synthetic accelerometer data, the so-called transplanted data. The transplanted data was derived from the GRACE-A accelerometer measurements, by applying time and attitude correction. Furthermore, the residual linear accelerations due to thruster firings on GRACE-B were added, proven to improve the data quality in gravity field recovery. Coincidentally, after one month in orbit, the GFO-B accelerometer data also degraded which raise demand for synthetic data in the current mission as well.In this work, we will present an approach to recover the transplanted data by (a) implementing the state-of-the-art non-gravitational force models and (b) applying additional corrections based on extracted features of the available measurement signals in a machine learning approach. The results will be validated with the GRACE Level-1b (RL03) accelerometer data transplant. [ABSTRACT FROM AUTHOR]

Temporal aliasing errors induced by high-frequency tidal and non-tidal mass variability in the Earth system are among the three most important error sources that limit the accuracy of present-day surface mass estimates from satellite gravimetry. By means of end-to-end simulations, we demonstrate that the Kalman Smoother approach developed by Kurtenbach et al. effectively captures non-tidal submonthly variability, and thereby reduces temporal aliasing errors way beyond the level of simply subtracting the standard dealiasing model AOD1B. Validation against in situ ocean bottom pressure observations confirms that the Kalman Smoother solutions published together with the ITSG-Grace2016 monthly gravity fields contain high-frequency signal over the oceans not predicted by AOD1B. The daily gravity fields therefore reduce aliasing artefacts in the monthly gravity fields, and at the same time provide observational evidence on submonthly bottom pressure variability presently not reflected in state-of-the-art numerical ocean circulation models. It is thus recommended to include a Kalman Smoother approach into any standard GRACE processing scheme. For a hypothetical double-pair configuration currently under consideration as a future mass change mission, we find that the benefit of the Kalman Smoother is much smaller thanks to the increased number of observations taken at different inclinations, which lead to generally reduced aliasing errors and much more isotropic spatial error correlations. We also reassess the idea of pre-eliminating low-resolution daily gravity fields and find large distortions in the monthly mean gravity solution at spatial wavelengths around the cut-off-degree of the daily fields. We thus recommend further study for any satellite gravity mission concept that critically relies on such pre-elimination schemes for reaching its science objectives. [ABSTRACT FROM AUTHOR]

Abstract The twin satellite mission Gravity Recovery and Interior Laboratory (GRAIL) aims to recover the lunar gravity field by means of Ka-band ranging observations. In order to exploit the potential of the inter-satellite range variations, absolute position information of the two probes is required. Hitherto, the Graz lunar gravity field models (GrazLGM) relied on the official science orbit products provided by NASA. In this contribution, we present for the first time a completely independent Graz Lunar Gravity Model based on Primary Mission data. The models are resolved up to spherical harmonic degree and order 420. The orbits of the two probes are determined using variational equations following a batch least squares differential adjustment process implemented in the in-house developed software package ORCA (Orbit Re-Construction Application). These orbits are based on S-band radiometric tracking data collected by the Deep Space Network (DSN) and are used for the independent GRAIL gravity field recovery. To reveal a highly accurate lunar gravity field, an integral equation approach using short orbital arcs is adopted to process the Ka-band data, where no regularization or Kaula constraint is applied. The correlation of gravity with lunar topography as well as the Bouguer spectrum of our solutions is comparable to the models officially released by the GRAIL Science Team. [ABSTRACT FROM AUTHOR]

Neutral gas atmosphere bends and delays propagation of microwave signals in satellite-based navigation. Weather prediction models can be used to estimate these effects by providing three-dimensional refraction fields to ray-trace the signal delays. In this study, a global numerical weather prediction model (Open Integrated Forecasting System (OpenIFS) licensed for Academic use by the European Centre for Medium-Range Weather Forecast) is used to generate the refraction fields. The ray-traced slant delays are supplied as such – in contrast to mapping – for an orbit solver (GROOPS (Gravity Recovery Object Oriented Programming System) software toolkit of Graz University of Technology) which applies the raw observation method. Here we show that such a close coupling is possible without need for major additional modifications in the solver codes. The main finding here is that the adopted approach provides a very good a priori model for the atmospheric effects on navigation signals. We suspect that removal of the intermediate mapping step allows us to take advantage of the local refraction field asymmetries in the GNSS signal processing. Moreover, the direct coupling helps in identifying deficiencies in the slant delay computation because the modeling errors are not convoluted in the mapping procedures. These conclusions appear robust, despite the relatively small data set of raw code and phase observations covering the core network of 66 ground-based stations of the International GNSS Service over 1-month periods in December 2016 and June 2017. More generally, the new configuration enhances our control of geodetic and meteorological aspects of the orbit problem. This is pleasant because we can, for instance, regulate at will the weather model output frequency and increase coverage of spatiotemporal aspects of weather variations. The direct coupling of a weather model in precise GNSS orbit determination presented in this paper provides a unique framework for benefiting even more widely than previously the apparent synergies in space geodesy and meteorology. [ABSTRACT FROM AUTHOR]

Neutral atmosphere bends and delays propagation of microwave signals in satellite-based navigation. Weather prediction models can be used to estimate these effects by providing 3-dimensional refraction fields to estimate signal delay in the zenith direction and determine a low-dimensional mapping of this delay to desired azimuth and elevation angles. In this study, a global numerical weather prediction model (OpenIFS licensed for Academic use by ECMWF) is used to generate the refraction fields. The ray-traced slant delays are supplied as such - in contrast to mapping - for an orbit solver (GROOPS software toolkit of TUG) which applies the raw observation method. Here we show that such a close coupling is possible without need for major additional modifications in the solver codes. The main finding here is that the adopted approach provides a very good a priori model for the atmospheric effects on navigation signals, as measured with the midnight discontinuity of GNSS satellite orbits. Our interpretation is that removal of the intermediate mapping step allows to take advantage of the local refraction field asymmetries in the GNSS signal processing. Moreover, the direct coupling helps in identifying deficiencies in the slant delay computation because the modelling errors are not convoluted in the precision-reducing mapping. These conclusions appear robust, despite the relatively small data set of raw code and phase observations covering the core network of 66 ground-based stations of the International GNSS Service over one-month periods in December 2016 and June 2017. More generally, the new configuration enhances our control of geodetic and meteorological aspects of the orbit problem. This is pleasant because we can, for instance, regulate at will the weather model output frequency and increase coverage of spatio-temporal aspects of weather variations. The direct coupling of a weather model in precise GNSS orbit determination presented in this paper provides a unique framework for benefiting even more widely than previously the apparent synergies in space geodesy and meteorology. [ABSTRACT FROM AUTHOR]

GOCO06s is the latest satellite-only global gravity field model computed by the GOCO (Gravity Observation Combination) project. It is based on over a billion observations acquired over 15 years from 19 satellites with different complementary observation principles. This combination of different measurement techniques is key in providing consistently high accuracy and best possible spatial resolution of the Earth's gravity field. The motivation for the new release was the availability of reprocessed observation data for the Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE), updated background models, and substantial improvements in the processing chains of the individual contributions. Due to the long observation period, the model consists not only of a static gravity field, but comprises additionally modeled temporal variations. These are represented by time-variable spherical harmonic coefficients, using a deterministic model for a regularized trend and annual oscillation. The main focus within the GOCO combination process is on the proper handling of the stochastic behavior of the input data. Appropriate noise modeling for the observations used results in realistic accuracy information for the derived gravity field solution. This accuracy information, represented by the full variance–covariance matrix, is extremely useful for further combination with, for example, terrestrial gravity data and is published together with the solution. The primary model data consisting of potential coefficients representing Earth's static gravity field, together with secular and annual variations, are available on the International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/ , last access: 11 June 2020). This data set is identified with the following DOI: 10.5880/ICGEM.2019.002. Supplementary material consisting of the full variance–covariance matrix of the static potential coefficients and estimated co-seismic mass changes is available at https://ifg.tugraz.at/GOCO (last access: 11 June 2020). [ABSTRACT FROM AUTHOR]

GOCO06s is the latest satellite-only global gravity field model computed by the GOCO (Gravity Observation Combination) project. It is based on over a billion observations acquired over 15 years from 19 satellites with different complementary observation principles. This combination of different measurement techniques is key in providing consistent high-accuracy and best possible spatial resolution of the Earth's gravity field. [ABSTRACT FROM AUTHOR]

The 2004 Sumatra, 2010 Maule, and 2011 Tohoku great earthquakes triggered tsunamis as large as a few decimeters over a few 100 km in the open ocean. The transient ocean mass redistribution propagating as tsunamis changed the Earth’s gravity field enough to perturb the GRACE satellites’ orbits at ~ 500 km above the surface. The on-board microwave ranging system detected inter-satellite acceleration anomalies of up to 1.0–4.0 nm/s2. There is good agreement between GRACE measurements and tsunami models for the three events. Complementarily to buoys, ocean bottom pressure sounders, and satellite altimeters, GRACE is sensitive to the long-wavelength spatial scale of tsunamis and provides an independent source of information for assessing alternate early earthquake and tsunami models. Our study demonstrates an innovative way of applying GRACE and GRACE Follow-On data to detect transient geophysical mass changes which cannot be observed by the conventional monthly Level-2 and mascon solutions. [ABSTRACT FROM AUTHOR]

Although the knowledge of the gravity of the Earth has improved considerably with CHAMP, GRACE, and GOCE (see appendices for a list of abbreviations) satellite missions, the geophysical community has identified the need for the continued monitoring of the time-variable component with the purpose of estimating the hydrological and glaciological yearly cycles and long-term trends. Currently, the GRACE-FO satellites are the sole dedicated provider of these data, while previously the GRACE mission fulfilled that role for 15 years. There is a data gap spanning from July 2017 to May 2018 between the end of the GRACE mission and start the of GRACE-FO, while the Swarm satellites have collected gravimetric data with their GPS receivers since December 2013. We present high-quality gravity field models (GFMs) from Swarm data that constitute an alternative and independent source of gravimetric data, which could help alleviate the consequences of the 10-month gap between GRACE and GRACE-FO, as well as the short gaps in the existing GRACE and GRACE-FO monthly time series. The geodetic community has realized that the combination of different gravity field solutions is superior to any individual model and set up the Combination Service of Time-variable Gravity Fields (COST-G) under the umbrella of the International Gravity Field Service (IGFS), part of the International Association of Geodesy (IAG). We exploit this fact and deliver the highest-quality monthly GFMs, resulting from the combination of four different gravity field estimation approaches. All solutions are unconstrained and estimated independently from month to month. We tested the added value of including kinematic baselines (KBs) in our estimation of GFMs and conclude that there is no significant improvement. The non-gravitational accelerations measured by the accelerometer on board Swarm C were also included in our processing to determine if this would improve the quality of the GFMs, but we observed that is only the case when the amplitude of the non-gravitational accelerations is higher than during the current quiet period in solar activity. Using GRACE data for comparison, we demonstrate that the geophysical signal in the Swarm GFMs is largely restricted to spherical harmonic degrees below 12. A 750 km smoothing radius is suitable to retrieve the temporal variations in Earth's gravity field over land areas since mid-2015 with roughly 4 cm equivalent water height (EWH) agreement with respect to GRACE. Over ocean areas, we illustrate that a more intense smoothing with 3000 km radius is necessary to resolve large-scale gravity variations, which agree with GRACE roughly at the level of 1 cm EWH, while at these spatial scales the GRACE observes variations with amplitudes between 0.3 and 1 cm EWH. The agreement with GRACE and GRACE-FO over nine selected large basins under analysis is 0.91 cm, 0.76 cm yr -1 , and 0.79 in terms of temporal mean, trend, and correlation coefficient, respectively. The Swarm monthly models are distributed on a quarterly basis at ESA's Earth Swarm Data Access (at https://swarm-diss.eo.esa.int/ , last access: 5 June 2020, follow Level2longterm and then EGF) and at the International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/series/02%5fCOST-G/Swarm , last access: 5 June 2020), as well as identified with the DOI 10.5880/ICGEM.2019.006 (Encarnacao et al., 2019). [ABSTRACT FROM AUTHOR]

Changes in terrestrial water storage as observed by the satellite gravity mission GRACE (Gravity Recovery and Climate Experiment) represent a new and completely independent way to constrain the net flux imbalance in atmospheric reanalyses. In this study daily GRACE gravity field changes are used for the first time to investigate high-frequency hydro-meteorological fluxes over the continents. Band-pass filtered water fluxes are derived from GRACE water storage time series by first applying a numerical differentiation filter and subsequent high-pass filtering to isolate fluxes at periods between 5 and 30 days corresponding to typical time-scales of weather system persistence at moderate latitudes. By comparison with the latest atmospheric reanalysis ERA5 of the European Centre for Medium-Range Weather Forecasts (ECWMF) we show that daily GRACE gravity field models contain realistic high-frequency water flux information. Furthermore, GRACE-derived water fluxes can clearly identify improvements realized within ERA5 over its direct predecessor ERA-Interim particularly in equatorial and temperate climate zones. The documented improvements are in good agreement with rain gauge validation, but GRACE also identifies three distinct regions (Sahel Zone, Okavango Catchment, Kimberley Plateau) with a slight degradation of net-fluxes in ERA5 with respect to ERA-Interim, thereby highlighting the potentially added value of non-standard daily GRACE gravity series for hydro-meteorological monitoring purposes. [ABSTRACT FROM AUTHOR]

ITSG‐Grace2018 is a new series of GRACE‐only gravity field solutions based on reprocessed GRACE observation data (L1B RL03) and the latest atmosphere and ocean dealiasing product (AOD1B RL06). It includes unconstrained monthly and constrained daily solutions, as well as a high‐resolution static gravity field. Compared to the previous ITSG release, we implemented a number of improvements within the processing chain and use updated background models. In an effort to better model all known error sources, we propagate synthetic orientation uncertainties of the star camera assembly to the antenna offset correction for intersatellite ranging observations. This enables the disentanglement of the stationary noise of the K‐Band system and the nonstationary noise of the antenna offset correction. We further incorporated uncertainties of the atmosphere and ocean dealiasing product to reduce temporal aliasing effects. To mitigate errors in the applied ocean tide model, we used constrained GRACE estimates of selected tidal constituents as an additional background model. Variability over quiet ocean areas suggests a 27% to 46% lower noise level compared to the current spherical harmonic solutions of the official processing centers (300 km Gaussian filter applied). To ensure that the low noise floor is not accompanied by signal loss, we examined drainage basin averages, which showed consistent amplitudes with the official GRACE time series. These evaluations lead to the conclusion that ITSG‐Grace2018 is a state‐of‐the‐art GRACE time series which exhibits an excellent signal‐to‐noise ratio. Key Points: Overview of the ITSG‐Grace2018 processing strategyDiscussion and evaluation of selected processing stepsIntercomparison of ITSG‐Grace2018 and official L2 products [ABSTRACT FROM AUTHOR]

GRACE satellites have detected regional‐scale preseismic, coseismic, and postseismic gravity changes associated with great earthquakes during the GRACE era (2002‐2017). Earthquakes also excite global‐scale transient gravity changes associated with free oscillations that may be discerned for a few days. In this study, we examine such global gravity changes due to Earth's free oscillations and quantify how they affect GRACE measurements. We employ the normal mode formalism to synthesize the global gravity changes after the 2004 Sumatra earthquake and simulate the (gravitational) free oscillation signals manifested in the GRACE K‐band ranging (KBR) measurements. Using the Kaula orbit perturbation theory, we show how GRACE inter‐satellite distances are perturbed through a complex coupling of eigenfrequencies of the normal modes with the Earth's rotation rate and the GRACE satellites' orbital frequency. It is found that a few gravest normal modes can generate range‐rate perturbations as large as 0.2 μm/s, which are comparable to actual errors of GRACE KBR ranging and accelerometer instruments. Wavelet time‐frequency analysis of the GRACE KBR residual data in December 2004 reveals the existence of a significant transient signal after the 2004 Sumatra earthquake. This transient signal is characterized by a frequency of ~0.022 mHz that could be potentially associated with the largest excitation due to the "football" mode of the Earth's free oscillation. However, the results are also affected by low‐frequency noise of the GRACE accelerometers. Improved space‐borne gravitational instrumentation may open new opportunities to study the Earth's interior and earthquakes independently from global seismological analysis. Key Points: Earth's free oscillations excited by great earthquakes cause transient global gravity changes that perturb the GRACE orbital trajectoryWe develop an analytic model of inter‐satellite range perturbation caused by the Earth's free oscillationsWavelet analysis of GRACE data reveals a candidate for football mode excited by 2004 Sumatra earthquake but obscured by accelerometer error [ABSTRACT FROM AUTHOR]

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) completed its science mission to observe the Earth's gravity field in 2013. From the collected observations, gravity gradients and tracking by the GPS constellation, global gravity field models were estimated in terms of spherical harmonic series. From the complete mission data set, the release 5 gravity field models were published in 2014. One of those models is EGM_TIM_RL05 which is computed with the time-wise approach. Within the computation of the time-wise models only GOCE observations are used. They remain independent of other available ground or satellite based gravity data sets. Thus, it represents the gravity field as seen by the GOCE mission. Within the estimation of the time-wise models, a lot of effort is spent on the stochastic modeling of the input observations to derive an uncertainty description in form of a covariance matrix. Recent studies have identified an imperfect calibration of the level 1B gravity gradients. Within a reprocessing campaign, the entire mission data set was reprocessed, such that the quality of the gravity gradients could be significantly improved. In addition, the orbits were reprocessed, reducing systematic artifacts. Within this contribution, the sixth release of the time-wise GOCE gravity field models is presented. Using the reprocessed input data, orbits as well as gravity gradients, and a robustified processing, the entire data set is used to estimate the updated gravity field model EGM_TIM_RL06. The processing used to generate the new solution is shown. It is validated and compared to the older releases. Three kinds of improvements are shown: i) a reduction of the mean error in the range of 15 to 25 %, ii) a reduction of systematic errors at centimeter level and iii) an even more realistic covariance description. The presented model will be made available as the ESA official GOCE time-wise gravity field model. [ABSTRACT FROM AUTHOR]

We develop a transfer function to determine in situ line‐of‐sight gravity difference (LGD) directly from Gravity Recovery and Climate Experiment (GRACE) range‐acceleration measurements. We first reduce GRACE data to form residual range‐acceleration referenced to dynamic orbit computed with a reference gravity field and nonconservative force data. Thus, the residuals and the corresponding LGD data reflect time‐variable gravity signals. A transfer function is designed based on correlation‐admittance spectral analysis. The correlation spectrum shows that residual range‐acceleration and LGD are near‐perfectly correlated for frequencies >5 cycles‐per‐revolution. The admittance spectrum quantifies that the LGD response to range‐acceleration is systematically larger at lower frequencies, due to the increased contribution of centrifugal acceleration. We find that the correlation and admittance spectra are stationary (i.e., are independent of time, satellite altitude, and gravity strength) and, therefore, can be determined a priori with high fidelity. We determine the spectral transfer function and the equivalent time domain filter. Using both synthetic and actual GRACE data, we demonstrate that in situ LGD can be estimated via the transfer function with an estimation error of 0.15 nm/s2, whereas the actual GRACE data error is around 1.0 nm/s2. We present an application of LGD data to surface water storage changes in large basins such as Amazon, Congo, Parana, and Mississippi by processing 11 years of GRACE data. Runoff routing models are calibrated directly using LGD data. Our technique demonstrates a new way of using GRACE data by forward modeling of various geophysical models and in‐orbit comparison with such GRACE in situ data. Key Points: In situ gravimetric observables can be computed from combination of GPS and KBR data of the GRACE satellite missionWe develop a transfer function for accurate estimation of LOS gravity difference directly from level‐1B residual KBR range‐acceleration dataThe in‐orbit comparison between in situ gravimetric data and models is a simple and powerful approach for hydrological model evaluations [ABSTRACT FROM AUTHOR]

We investigate the post-fit range-rate residuals after the gravity field parameter estimation from the inter-satellite ranging data of the g ravity r ecovery and c limate e xperiment ( grace ) satellite mission. Of particular interest is the high-frequency spectrum ( f > 20 m h z) which is dominated by the microwave ranging system noise. Such analysis is carried out to understand the yet unsolved discrepancy between the predicted baseline errors and the observed ones. The analysis consists of two parts. First, we present the effects in the signal-to-noise ratio ( snr s) of the k- band ranging system. The snr s are also affected by the m oon intrusions into the star cameras’ field of view and magnetic torquer rod currents in addition to the effects presented by Harvey et al. (2016). Second, we analyze the range-rate residuals to study the effects of the kbr system noise. The range-rate residuals are dominated by the non-stationary errors in the high-frequency observations. These high-frequency errors in the range-rate residuals are found to be dependent on the temperature and effects of s un intrusion into the star cameras’ field of view reflected in the snr s of the k- band phase observations. [ABSTRACT FROM AUTHOR]

It is of great interest to numerous geophysical studies that the time series of global gravity field models derived from Gravity Recovery and Climate Experiment (GRACE) data remains uninterrupted after the end of this mission. With this in mind, some institutes have been spending efforts to estimate gravity field models from alternative sources of gravimetric data. This study focuses on the gravity field solutions estimated from Swarm global positioning system (GPS) data, produced by the Astronomical Institute of the University of Bern, the Astronomical Institute (ASU, Czech Academy of Sciences) and Institute of Geodesy (IfG, Graz University of Technology). The three sets of solutions are based on different approaches, namely the celestial mechanics approach, the acceleration approach and the short-arc approach, respectively. We derive the maximum spatial resolution of the time-varying gravity signal in the Swarm gravity field models to be degree 12, in comparison with the more accurate models obtained from K-band ranging data of GRACE. We demonstrate that the combination of the GPS-driven models produced with the three different approaches improves the accuracy in all analysed monthly solutions, with respect to any of them. In other words, the combined gravity field model consistently benefits from the individual strengths of each separate solution. The improved accuracy of the combined model is expected to bring benefits to the geophysical studies during the period when no dedicated gravimetric mission is operational. [ABSTRACT FROM AUTHOR]

A realistically perturbed synthetic de-aliasing model consistent with the updated Earth System Model of the European Space Agency is now available over the period 1995-2006. The dataset contains realizations of (1) errors at large spatial scales assessed individually for periods 10-30, 3-10, and 1-3 days, the S1 atmospheric tide, and sub-diurnal periods; (2) errors at small spatial scales typically not covered by global models of atmosphere and ocean variability; and (3) errors due to physical processes not represented in currently available de-aliasing products. The model is provided in two separate sets of Stokes coefficients to allow for a flexible re-scaling of the overall error level to account for potential future improvements in atmosphere and ocean mass variability models. Error magnitudes for the different frequency bands are derived from a small ensemble of four atmospheric and oceanic models. For the largest spatial scales up to $$\hbox {d/o} = 40$$ and periods longer than 24 h, those error estimates are approximately confirmed from a variance component estimation based on GRACE daily normal equations. Future mission performance simulations based on the updated Earth System Model and the realistically perturbed de-aliasing model indicate that for GRACE-type missions only moderate reductions of de-aliasing errors can be expected from a second satellite pair in a shifted polar orbit. Substantially more accurate global gravity fields are obtained when a second pair of satellites in an moderately inclined orbit is added, which largely stabilizes the global gravity field solutions due to its rotated sampling sensitivity. [ABSTRACT FROM AUTHOR]

Temporal variations in the geographic distribution of surface mass cause surface displacements. Surface displacements derived from GRACE gravity field coefficient time series also should be observed in GPS coordinate time series, if both time series are sufficiently free of systematic errors. A successful validation can be an important contribution to climate change research, as the biggest contributors to mass variability in the system Earth include the movement of oceanic, atmospheric, and continental water and ice. In our analysis, we find that if the signals are larger than their precision, both geodetic sensor systems see common signals for almost all the 115 stations surveyed. Almost 80% of the stations have their signal WRMS decreased, when we subtract monthly GRACE surface displacements from those observed by GPS data. Almost all other stations are on ocean islands or small peninsulas, where the physically expected loading signals are very small. For a fair comparison, the data (79 months from September 2002 to April 2009) had to be treated appropriately: the GPS data were completely reprocessed with state-of-the-art models. We used an objective cluster analysis to identify and eliminate stations, where local effects or technical artifacts dominated the signals. In addition, it was necessary for both sets of results to be expressed in equivalent reference frames, meaning that net translations between the GPS and GRACE data sets had to be treated adequately. These data sets are then compared and statistically analyzed: we determine the stability (precision) of GRACE-derived, monthly vertical deformation data to be ~1.2 mm, using the data from three GRACE processing centers. We statistically analyze the mean annual signals, computed from the GPS and GRACE series. There is a detailed discussion of the results for five overall representative stations, in order to help the reader to link the displayed criteria of similarity to real data. A series of tests were performed with the goal of explaining the remaining GPS-GRACE residuals. [ABSTRACT FROM AUTHOR]

Improvements of a global state-of-the art ocean tide model are identified and quantified by applying three independent approaches, namely (i) empirical ocean tide analysis of multimission altimeter data, (ii) evaluation of GRACE data and gravity field models and (iii) high resolution hydrodynamic modelling. Although these approaches have different capabilities to sense ocean tides they obtain results which are basically consistent one with each other. The analysis of altimeter data clearly identifies significant residual amplitudes over shallow water for all major diurnal and semidiurnal constituents and the non-linear tide M4. GRACE data and the time-series of monthly gravity field models exhibit—on a larger scale—residual ocean tide signals over much the same areas. The analysis of dynamic residuals of hydrodynamic modelling with data assimilation proves the validity of linear dynamics in the deep ocean and shows correlation of dynamic residuals with energy dissipation in these areas. [ABSTRACT FROM AUTHOR]

In the frame of the European Gravity Service for Improved Emergency Management (EGSIEM), a prototype service was established to combine monthly gravity field solutions from the past US-German GRACE mission in order to deliver improved gravity field solutions for applications in Earth and environmental science research. This prototype now is in transition to the Combination Service for Time-variable Gravity Field Solutions (COST-G), a Product Center of the International Gravity Field Service (IGFS) of the International Association of Geodesy (IAG).We report on the achievements made so far and the transition of the prototype phase into regular operation. We present a comparison, validation and combination of the latest GRACE gravity field time-series of different GRACE processing centers, based on recent RL03 Level-1B GRACE observation data as well as updated background models and processing standards. A focus is laid on the effect of different background modeling strategies on the resulting gravity field models and the relative weights determined by Variance Component Estimation on solution level. [ABSTRACT FROM AUTHOR]