The Gravity Recovery and Climate Experiment (GRACE) and its Follow-On (GRACE-FO) missions have provided valuable insights in the fields of Hydrology, Oceanography, Cryosphere Sciences, Solid Earth etc. and improved our understanding of the changes in the Earth’s water cycle since 2002.

While the temporal resolution of the official GRACE/GRACE-FO products is 30 days, this study aims to push those boundaries. This study focuses on the 5-day global mascon solution produced from GRACE/GRACE-FO satellite tracking data. This paper discusses the techniques used and challenges encountered with production of such a global total water storage and ocean bottom pressure product with high temporal sampling. Analysis is performed over hydrological and ocean basins to validate the higher frequency signals captured in this product. An important goal for the production of this higher temporal resolution GRACE/GRACE-FO product is to be able to use these signals with a latency of a few days for ingestion into automated machine learning algorithms for early flood detection applications.

How to cite: Save, H., Tamisiea, M., Hasan, E., Sun, A., Rateb, A., and Scanlon, B.: Results from five-day GRACE/GRACE-FO mascon solutions from CSR, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-9787, https://doi.org/10.5194/egusphere-egu23-9787, 2023.

For GRACE-FO gravity field recovery synthetic accelerometer data is required to replace the GRACE-D measurements due to their high noise level. Official transplant products published by the Jet Propulsion Laboratory (JPL) are the calibrated acceleration product (ACT) and the updated hybrid accelerometer transplant (ACX). At TU Graz an alternative in-house transplant product is generated using a remove-restore method. Based on the work from Behzadpur, 2021 the transplant product was further optimized. 

Improvements in the force modeling comprise an adjusted satellite macro model and a self-shadowing model as well as the consideration of thermal re-radiation. To account for the different orientations of the satellites in relative pointing mode, an additional step was introduced in the transplant processing by determining the thermospheric density along the orbit. Investigations were carried out to further improve the accelerometer transplant by incorporating data from the GRACE-D accelerometer.   

How to cite: Öhlinger, F. and Mayer-Gürr, T.: Improved alternative GRACE-FO accelerometer transplant product computed at TU Graz, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-5584, https://doi.org/10.5194/egusphere-egu23-5584, 2023.

The onboard GRACE and GRACE-FO accelerometers measure the non-gravitational accelerations of the spacecraft that are indispensable for the modelling of the Earth’s gravity field since they are subtracted from the GPS POD total accelerations to isolate the pure gravitational accelerations. The accelerometers, like any other instrument, must be calibrated very accurately to serve their purpose but the calibration cannot be done as per standard metrological methods, in a laboratory environment due to the influence of the gravitational signal which is almost 10 orders of magnitude larger. Many researchers have proposed different approaches for the estimation of the bias and the scale factor of the accelerometers, most of which are based on the physical models of the non-gravitational accelerations The drawback of these methods is the dependency of the calibration on the theoretical models and specifically on the drag models that exhibit the highest uncertainty due to the complexity of the upper atmosphere. An alternative, on-orbit calibration of the accelerometers is proposed that is commensurate with standard metrological methods and thus it is based only on the satellite measurements. The idea behind this method lies in a time-reversal method widely used in radar applications for the detection and measurement of known but distorted pulses hidden in the scattered signal from the reflectors. By analogy to radar applications, the total accelerations estimated from GPS through numerical double POD differentiation, correspond to the ‘transmitted signal’ (calibrated) and the accelerometer measurements (uncalibrated) comprise the ‘return signal’ (scattered signal).  The key to this method is that the penumbra transitions are present in both signals and play the role of the known calibration pulse. Examples of 30 daily scale factors are calculated for different operational periods during lower and higher solar activity of GRACE and GRACE-FO and the accelerometer bias is computed by a daily polynomial fit. The results show a robust estimation of the scale factor and bias of the accelerometers. The thermal sensitivity of the accelerometer and its correlation with the β’ angle is investigated. 

How to cite: Tzamali, M. and Pagiatakis, S.: On-orbit Calibration of GRACE and GRACE-FO accelerometers, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-10422, https://doi.org/10.5194/egusphere-egu23-10422, 2023.

GRACE Follow On measures the Earth's gravitational field by recording distance variations between two satellites flying behind each other around the planet. The attitude and orbit  control system ensures that nominal attitude variations do not exceed a magnitude of a few 100 urad in yaw and pitch. Star cameras and fibre optic gyroscopes measure the inter-satellite pointing angles and indicate when an attitude correction needs to be performed.

The Laser Ranging Interferometer (LRI), which was designed as a technology demonstrator but will be implemented as the main science instrument in future missions, measures the distance changes in parallel to the microwave system. However, to maximize the interferometric contrast in the LRI, even when the satellite attitude jitters, a precise pointing between transmitted and received laser beam is necessary and achieved by a two-axes Fast Steering Mirror (FSM).  The FSM measurements provide essentially information about the satellite pointing angles pitch and yaw w.r.t. the line-of-sight connecting both satellites. That allows to compare the FSM to the different attitude sensors like star cameras.

We are particularly interested in the characterization of FSM at low-frequencies, i.e. long-term stability of the FSM readout under temperature changes induced for instance by the varying geometry of orbital plane and Sun. We will present recent results on how to model the differences between the star camera and the FSM pointing angles and show analysis results,  which of the instruments might cause the variations in the residuals.

Our results are of relevance for future missions, as these missions might employ the LRI FSM as an attitude sensors in order to control the satellite attitude.

How to cite: Müller, L., Müller, V., Misfeldt, M., and Heinzel, G.: Comparing LRI Steering Mirror and Star Camera Data at Low Frequencies, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-14334, https://doi.org/10.5194/egusphere-egu23-14334, 2023.

The Atmosphere and Ocean non-tidal De-aliasing Level-1B (AOD1B) product is widely used in satellite gravimetry to correct for transient effects of atmosphere-ocean mass variability that would otherwise alias into monthly-mean global gravity fields. The most recent release is based on the global ERA5 reanalysis and ECMWF operational data together with simulations from the general ocean circulation model MPIOM consistently forced with fields of the same atmospheric data-set.

To fully utilise the potential of geodetic data for climate applications, addressing long-term stability in background (or observation-reduction) models is critically important. Spurious trends, low-frequency signals or bias jumps in the background model data can be, if unaccounted for, be introduced into the final gravity solutions and erroneously interpreted in geophysical analyses. We here present the recently published new release RL07 of AOD1B, which is produced from 1975 onwards, and analyse its stability both on long time-scales through the study of trends as well as short-scale stability through the analysis of 3 hourly tendencies. Results are compared to other atmospheric reanalyses and the previous version of AOD1B. A special focus is placed on the transition from ERA5 to ECMWF operational atmospheric data and model changes in ECMWFs IFS.

How to cite: Shihora, L., Liu, Z., Balidakis, K., Dill, R., and Dobslaw, H.: Stability of AOD1B RL07, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-5115, https://doi.org/10.5194/egusphere-egu23-5115, 2023.

The problem of gravity estimation from satellite-satellite tracking measurements is fundamentally ill-posed due to upward continuation, which results in poor observability of the high-frequency components of the potential. Additionally, the ground track orientation and orbital resonance introduce poor observability along certain directions and spectral bands of the solution. Consequently, the gravity estimates obtained by direct inversion exhibit non-physical noise features. Regularization schemes are employed in the solution of ill-posed problems, wherein pseudo-information is added to the optimization cost function to stabilize the inversion. The preferred regularization scheme for spaceborne gravity estimation has been L2-Tikhonov regularization with a heuristic constraint matrix.

Regularization schemes based on the spatial gradient of the solution field, such as H1 and Total Variation (TV), produce a penalty that naturally increases with frequency. Thus, they are effective in countering the ill-posedness due to poor observability of higher frequencies. Additionally, the TV penalty has the unique feature of promoting sharp edges, which could limit signal leakage in the solution. We previously reported results from the application of gradient regularization schemes as post-processing to the GRACE/GRACE-FO problem, as well as preliminary results from the application of these techniques to the full problem.

Here, we present the time series of solutions obtained by the application of gradient regularization methods to the full GRACE/GRACE-FO gravity estimation problem. The edge-preserving nature of the TV penalty facilitates recovery of sharp edges and signal localization in the solution, without the need for explicit spatial constraints. Additionally, we present results from the application of higher order generalizations of the TV penalty (Total Generalized Variation), which allows for recovery of sharp edges while limiting the undesirable peak-flattening effect induced by the TV penalty.

How to cite: Jacob, G. and Bettadpur, S.: Gravity Estimation from Satellite-Satellite Tracking using Total Variation Regularization, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-3602, https://doi.org/10.5194/egusphere-egu23-3602, 2023.

Time-variable gravity field solutions from satellite missions prior to GRACE are of limited applicability in climate studies, due to their low spatial resolution. To overcome this disadvantage, we developed a novel parametrization in which the temporal changes of the gravity field are represented by a finite number of spatial patterns tailored to the expected signal power. These patterns are identified by an EOF analysis applied to the GRACE and GRACE Follow-On solutions. Using such tailored base functions does not break down the limits of the tracking technique, but allows to isolate large-scale mass variations with the full GRACE resolution, while the parameter space is kept extremely tight. 

In a previous publication, this approach has been successfully applied to compute a GRACE-like time series from five SLR satellites going back to 1992. To further enhance this solution, we now turned towards the DORIS constellation from which we processed data from ten satellites at altitudes up to 1000 km. It was found that our parametrization is highly suitable also for the DORIS system and results in a time series that agrees well with that from SLR. Such agreement is found even for the very first years when the DORIS solution is occasionally based on one single satellite. We note that we include the estimation of thermosphere model scaling parameters that can help in understanding neutral density change.

The contribution will provide details of our DORIS processing and present total water storage maps and mass balances for selected regions from DORIS, SLR and from the combination of both techniques. We believe our results will contribute to long-term mass studies concerned with sea-level change, ice mass loss at high latitudes or water storage changes in large river basins. In addition, it will be shown that the presented time series can improve the force models for precise orbit determination at higher altitude. For example, a dynamic reconstruction of Jason-3 orbits from kinematic positions reveals that the SLR/DORIS solution performs competitively in this task when compared to the frequently applied EIGEN-GRGS.RL04 model, with some advantage in the later years when the EIGEN model provides pure predictions. 

How to cite: Kusche, J. and Löcher, A.: High-resolution temporal gravity fields from SLR and DORIS using tailored base functions, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-8735, https://doi.org/10.5194/egusphere-egu23-8735, 2023.

Since its launch in early 2002, datasets from the Gravity Recovery and Climate Experiment (GRACE) and its 2018 follow-on mission (GRACE-FO) have become indispensable for monitoring terrestrial water storage. GRACE-derived terrestrial water storage anomalies (TWSA), especially when used in conjunction with other water budget datasets (i.e., precipitation, evapotranspiration, surface runoff), provide insight into groundwater and glacier mass fluctuations. With over 20 years of observations, long-term statistical analysis reveals water storage trends, however, the 11-month gap between the two missions must be filled. The goal of this presentation is to compare four gap filling methods over Canada, namely: extreme gradient boosting, artificial neural networks, an automated machine learning (ML) algorithm (AutoML), and projection onto convex sets (POCS). The GRACE mascon product (RL06M.MSCNv02) released by the Jet Propulsion Laboratory was used, and all data were bounded by GRACE availability (April 2002 - March 2022) at the time of the study. Reconstruction of TWSA data in Canada required consideration of glacier surface mass balance models derived from the GMAO Modern-Era Retrospective Analysis for Research and Applications, Version 2 reanalysis, and the Randolph Glacier Inventory. Nine sets of nation-wide hydrological and climatic parameters were used as predictors for the machine learning models: GRACE average seasonal signal, TWSA from the GLDAS Catchment Land Surface Model, precipitation, air temperature, glacier surface mass balance, ocean tides, the North Atlantic Oscillation, the Multivariate ENSO Index, and sea surface temperature. Results indicate that ML algorithms can fill the gap with mean normalized root mean square errors ranging from 6 – 13% and AutoML performs the best with 2.5 cm equivalent water height (EWH). The purely mathematical signal synthesis POCS method resulted in approximately 4.0 cm EWH for some basins. Filling the gap between missions allows for more comprehensive terrestrial water storage trend analysis, including basin-by-basin analysis, which is ongoing over Canada.

How to cite: Bringeland, S. and Fotopoulos, G.: Analysis of gap filling techniques for GRACE/GRACE-FO terrestrial water storage anomalies in Canada, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-516, https://doi.org/10.5194/egusphere-egu23-516, 2023.

The gravity anomalies over Nigeria range from -47.54 mgals to 70 mgals in the flat region and from 70 mgals to 157.26 mgals in regions of significant topography. In geodesy, combined global gravity field models (GGMs) are used for gravimetric geoid modelling. Due to the multitude of GGMs, evaluation against independent data is very important for the quality description of the different models and to establish their precision for application in those localities. It is pivotal that these gravity datasets be evaluated within the study area before they are used for gravimetric geoid modelling. This study aims to evaluate, for the first time, five combined GGMs (EGM2008, SGG-UGM-2, EIGEN-6C4, XGM2019e_2159 and GECO) over Nigeria using a new set of terrestrial gravity anomalies. There exist few evaluations of gravity anomalies based on state boundaries. However, this gravity dataset has not been used to evaluate the above five combined GGMs over the entire country of Nigeria. Our strategy is to compare GGM-derived gravity anomalies at a spectral resolution of d/o 300 in steps to d/o 2190 with terrestrial (free-air and Bouguer) anomalies in terms of standard deviation (SD) and root mean square (RMS) for determining the best fit global model in the study area. The gravity datasets cover the study area, Nigeria within longitudes 3° to 14° E and latitudes 3° to 14° N. In the computation of the free-air gravity anomaly, the effects of atmospheric corrections, free-air reduction and latitude correction were considered. Since it is important to consider the topographic correction in an area where the topography is large, we considered the topographic corrections based on Shuttle Radar Topography Mission (SRTM 30) data set when computing the Bouguer anomaly. From our comparison, it was observed that XGM2019e_2159 derived gravity anomalies have a best-fit relationship with the terrestrial data than the other four GGMs. While further analysis is needed, the preliminary results show that our method has the potential to effectively evaluate and indicate gravity field models that can be useful for modelling the gravity field of the Earth over the study area.

Keywords: Free-air gravity anomaly, Bouguer gravity anomaly, Global gravity field models.

How to cite: Bako, M. and Kusche, J.: Evaluating the gravity anomalies over Nigeria from global gravity field models and  new terrestrial gravity anomalies, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-3952, https://doi.org/10.5194/egusphere-egu23-3952, 2023.

The Gravity Recovery and Climate Experiment (GRACE) satellite has been widely used to monitor changes in terrestrial water storage anomalies (TWSA), which vertically integrate water storage changes from the land surface to the deepest aquifers. Isolation of groundwater storage anomalies (GWA) from TWSA requires information of other water budget components from auxiliary datasets, e.g., Land Surface Model (LSM) output, or in-situ/remotely sensed based data. Using auxiliary datasets to account for water budget components have revealed large biases and uncertainties, especially over regions with complicated hydrological processes, leading to accumulating errors in GRACE-GWA estimates. Comparisons of GRACE-GWA with in-situ observations permit evaluating how accurately we can isolate groundwater storage signals from TWSA. Goodness-of-fit (GOF) indices e.g., Spearman correlation, Nash-Sutcliffe Efficiency (NSE), and the Kling-Gupta Efficiency (KGE), are commonly applied hydrologic fit metrics that express similarity of time series. Such metrics are used in our study to compare GRACE-GWA estimations and in-situ observations. Our results showed that GOF indices failed to capture the different characteristics of GRACE-GWA timeseries. Spearman correlation requires a monotonic relationship, an assumption violated given the seasonal amplitudes of GRACE-GWA. Using a Pearson correlation is ill-advised given serial correlation and non-normality. NSE is biased and influenced by skewness and periodicity, which is given since the data is seasonal in nature. KGE is based on the assumptions of data linearity and data normality. Non-normality in GRACE-GW time series violates the implicit assumptions underlying KGE. The goal of this work is to improve interpretation and use of GOF metrics to validate GRACE-GWA estimates, highlighting the importance of assessing multiple GOF criteria beyond simply correlation often applied in GRACE studies. We show that a rigorous assessment of GOF enhances our ability to interpret GRACE-GWA.
Acknowledgement:
The researcher, Mohamed Akl, is funded by a full PhD scholarship from the Ministry of Higher Education of the Arab Republic of Egypt.

How to cite: Akl, M., Thomas, B., and Clarke, P.: Evaluation of GRACE-derived Groundwater Signal Accuracy using Developed Statistical Framework, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-3357, https://doi.org/10.5194/egusphere-egu23-3357, 2023.

ESA and NASA are currently intensifying their long-term efforts on a collaborative implementation of a next generation mass change and gravity monitoring satellite mission under the umbrella of the NASA-ESA Joint Programme Planning Group sub-group 1. MAss-change and Geosciences International Constellation (MAGIC) is the joint NASA/ESA constellation concept based on NASA’s MCDO and ESA’s NGGM studies. The main objective of MAGIC is to extend the mass transport time series from previous gravity missions such as GRACE and GRACE-Follow on with significantly enhanced accuracy, spatial and temporal resolutions and to demonstrate the operational capabilities of MAGIC. The concept is based on a joint ESA/NASA Mission Requirements Document (MRD) which summarizes the goal requirements of the global scientific community (including requirements from the IGWSG report, IUGG, MCDO, etc.). The first pair of the MAGIC Constellation will be implemented via a NASA/DLR fast-paced cooperation to ensure continuity of observations of GRACE-Follow On, with some potential ESA in-kind contributions for a new generation of accelerometers. The second pair will be implemented by ESA with some potential NASA in-kind contributions for the Laser Tracking Instrument.

This paper will address the novel science and applications enabled by MAGIC for the fields of hydrology, cryosphere, oceanography and solid Earth and demonstrate the significant added value of MAGIC constellation for unravelling and understanding mass transport and mass change processes in the Earth system.

How to cite: Daras, I., Tsaoussi, L., March, G., Massotti, L., Carnicero Dominguez, B., and Carraz, O.: ESA/NASA Mass change And Geosciences International Constellation (MAGIC) mission concept – science and application prospects, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-13535, https://doi.org/10.5194/egusphere-egu23-13535, 2023.

The main objective of the joint ESA/NASA Mass-change And Geoscience International Constellation (MAGIC) is to extend the mass transport time series from previous gravity missions such as GRACE and GRACE-Follow on with significantly enhanced accuracy, spatial and temporal resolutions. The concept is based on a joint ESA/NASA Mission Requirements Document (MRD). The first pair of the MAGIC Constellation will be implemented via a Germany-USA fast-paced cooperation to ensure continuity of observations of GRACE-Follow On, with some potential ESA in-kind contributions. The second pair will be implemented via a Europe-USA cooperation with some potential NASA in-kind contributions. The target launch date will be compatible to maintain at least 4 years of combined operations.

The current baseline scenario consists of a polar pair (P1) at an altitude of 488 km and an inclination of 89° without ground track control, and an inclined pair (P2) at 397 km and 70° inclination with a 5-day repeat sub-cycle, in order to ensure ground track homogeneity and a constant quality of resulting near-real time service products.

In the frame of extensive full-fledged numerical simulations with realistic error assumptions regarding instrument performances and background model errors, the expected performance of the resulting short- to long-term gravity field products is evaluated. In this contribution, the main focus lies on the quantification of the added value of P2 and the relative contributions of P1 and P2 to the combined constellation solution. In particular, the achievable performance for short-term products (daily, 5-day) will be evaluated. In addition, we will analyze and quantify the value of P2 alone over the regions covered by the 70° inclined orbit. From the processing side, using spherical harmonics as base functions, this requires also an adequate treatment of the polar gap areas. Finally, we will match all results against the MRT/MRTD requirements and will evaluate the impact on various fields of science and service applications (continental hydrology, cryosphere, oceans, solid Earth, geodesy).

How to cite: Pail, R., Abrykosov, P., and Science Team, T. M.: MAGIC – The value of the second pair, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-4372, https://doi.org/10.5194/egusphere-egu23-4372, 2023.

GRACE-like missions (GRACE, GRACE-FO) are used to map the global time-varying Earth gravity field, which has brought a revolution in geodesy as well as the other subjects of geophysics. Their key payloads are mainly the inter-satellite ranging system: K-Band Ranging system (KBR) for GRACE, KBR and laser ranging interferometer (LRI) for GRACE-FO, of which both measure the distance variations between the twin satellites; the accelerometers to recover the non-gravitational force on the satellites; the satellite attitude measurement components such as star cameras (SCA), Inertial Measurement Unit (IMU) and LRI Fast Steering Mirror (FSM); and GPS receivers for precise orbit determination. Currently, the observation equations used to establish the gravity field recovery are based on observations from inter-satellite range (or range rate) and GPS orbit. However, we will show that the three-dimensional orientation change of the line-of-sight (LOS) connecting both satellites, i.e., the angular velocity vector of the LOS, contains gravity information perpendicular to the LOS. If future missions can measure the angular velocity with sufficient precision, this will increase the resolution of the satellite pair in the East-West direction and decrease the stripe effects in the North-South direction, thus further improving the accuracy of the gravity field solution. We developed observation equations based on the dynamic approach for the angular velocity sensing (AVS) observations and solved them jointly with the observation equations obtained from GPS and KBR/LRI. Our simulation results show that the angular velocity can indeed recover the gravity field in combination with GPS and the results are better than those obtained using only a combination of KBR/LRI and GPS. The optimal results are obtained when the gravity field is solved by combining AVS, KBR/LRI and GPS at the same time. We further analyzed the accuracy requirements of the angular velocity sensing that would allow for improving gravity field solutions in the next generation of gravity missions.

How to cite: Yan, Y., Müller, V., Wang, C., and Heinzel, G.: Potential of Angular Velocity Sensing for the gravity field recovery in GRACE-like missions, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-15011, https://doi.org/10.5194/egusphere-egu23-15011, 2023.

NASA/JPL and DLR/Airbus are conducting a joint study of a quantum gravity gradiometer (QGG) technology demonstration concept for advancing mass change measurements. The study outcomes also include near- and long-term science and technology roadmaps for this technology. Studies of gravity gradiometer concepts for mass change measurements have been reported in the literature for the past several years. These studies have considered various quantum metrological implementations, in standalone and constellation of satellite missions, as hybridization of the quantum methods with the conventional satellite-to-satellite tracking methods, and the infusion of quantum technologies in configurations other than a gradiometer to advance mass change measurements.

In this paper we report the results of work by the science sub-group of this study team. We report on the technical formulation of a science validation scheme for the tech-demo concept. The scheme includes the validation of the observable measurement model, and validation of its performance characteristics at various time-resolutions and accuracies targeted by the tech-demo. We present these results against a backdrop of the developments in the atomic, molecular and optical physics community that will lead to the desired highest precision measurements.  A discussion of such results is expected to prompt a wider engagement with the scientific community on the long-term planning and deployment of this quantum technology to benefit mass change observations.

How to cite: Bettadpur, S., Chiow, S., Wiese, D., Lutchcke, S., Loomis, B., Flechtner, F., and Schubert, C.: Quantum gravity gradiometer technology demonstration concept, and the pathway to future mass change science. , EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-10811, https://doi.org/10.5194/egusphere-egu23-10811, 2023.