G4.2

The Combination Service for Time-variable Gravity Fields (COST-G) of the International Association of Geodesy (IAG) provides combined monthly gravity fields of its associated and partner Analysis Centers (ACs). In November 2020, the combination of monthly GRACE-FO gravity fields started its operational mode, providing consolidated L2 (spherical harmonics) and L3 (gridded and post- processed) products with a latency of currently 3 months. We present an overview and quality assessment of the available products.

COST-G aims at the extension of its service to include further GRACE and GRACE-FO analysis centers. In January 2020 a collaboration with representatives of five Chinese ACs was initiated, who provided GRACE time-series according to the COST-G requirements. We present the results of a test combination with the Chinese AC models, including comparison and quality assessment of all contributing time-series and validation of the combined gravity fields.

How to cite: Meyer, U., Lasser, M., Jäggi, A., Dahle, C., Flechtner, F., Kvas, A., Behzadpour, S., Mayer-Gürr, T., Lemoine, J.-M., Koch, I., Flury, J., Bourgogne, S., Groh, A., Eicker, A., Förste, C., Luo, Z., Ran, J., Shen, Y., Zhao, Q., and Feng, W. and the COST-G Team: Combination Service for Time-variable Gravity Fields (COST-G): operational GRACE-FO combination and validation of Chinese GRACE time-series, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2416, https://doi.org/10.5194/egusphere-egu21-2416, 2021.

The commonly used filters (e.g. Gaussian smoothing, decorrelation and DDK filtering) applied to GRACE spherical harmonic gravity field solutions generally lead to reduced resolution, signal damping and leakage. This work is dedicated to improving spatial resolution and reducing signal damping by developing a regularization method with spectral constraints to spherical harmonics. Before constructing the spectral constraints, we create spatial constraints over global grids (covering lands, oceans and the boundaries between lands and oceans) from the a priori information of GRACE spherical harmonic models. Since we are solving geopotential coefficients rather than mascon grids, we further transfer the spatial constraints into the spectral domain according to the law of variance-covariance propagation, leading to spectral constraints regarding geopotential coefficients. In our work, the regularization method with spectral constraints was demonstrated to have comparable ability as mascon modelling method to enhance the spatial resolution and signal power besides reducing signal leakage. Applying the presented method with spatial constraints, we produced the first time series of high-resolution gravity field solutions expressed as geopotential coefficients complete to degree and order 180. Our analyses over the global and regional areas show that our high-resolution solutions are in good agreement with CSR and JPL mascon solutions.

How to cite: Chen, Q., Kusche, J., Shen, Y., and Zhang, X.: High-resolution GRACE Monthly Gravity Field Solutions Expressed as Geopotential Coefficients, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9594, https://doi.org/10.5194/egusphere-egu21-9594, 2021.

Besides a K-Band Ranging System (KBR), GRACE-FO carries a Laser Ranging Interferometer (LRI) as a technology demonstration to provide measurements of inter-satellite range changes. This additional measurement technology provides supplementary observations, which allow for cross-instrument diagnostics with the KBR system and, to some extent, the separation of ranging noise from other sources such as noise in the on-board accelerometer (ACC) measurements.

The aim of this study is to incorporate the two ranging systems (LRI and KBR) observations in ITSG-Grace2018 gravity field recovery. The two observation groups are combined in an iterative least-squares adjustment with variance component estimation used to determine the unknown noise covariance functions for KBR, LRI, and ACC measurements. We further compare the gravity field solutions obtained from the combined solutions to KBR-only results and discuss the differences with a focus on the global gravity field and LRI calibration parameters.

How to cite: Behzadpour, S., Kvas, A., and Mayer-Gürr, T.: GRACE Follow-On Gravity Field Recovery from Combined Laser Ranging Interferometer and Microwave Ranging System Measurements, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9415, https://doi.org/10.5194/egusphere-egu21-9415, 2021.

A key component of any model is the accurate specification of its quality. In gravity field modelling from satellite data, as it is done with the observation collected by GRACE Follow-On, usually least-squares adjustments are performed to obtain a monthly solution of the Earth’s gravity field. However,
the jointly estimated formal errors usually do not reflect the error level that could be expected but provides much lower error estimates. We take the Celestial Mechanics Approach (CMA), developed at the Astronomical Institute, University of Bern (AIUB), and extend it by an empirical modelling of the noise based on the post-fit residuals between the final GRACE Follow-On orbits, that are co-estimated together with the gravity field, and the   observations, expressed in position residuals to the kinematic positions and in K-band range-rate residuals. We compare and validate the solutions that employ empirical modelling with solutions that do not contain sophisticated noise modelling by examining the stochastic behaviour of the respective post-fit residuals, by investigating areas where a low noise is expected and by inspecting the mass trend estimates in certain areas of global interest. Finally, we investigate the influence of the empirically weighted solutions in a combination of monthly gravity fields based on other approaches as it is done in the COST-G framework.

How to cite: Lasser, M., Meyer, U., Arnold, D., and Jäggi, A.: Comparison of empirical noise models for GRACE Follow-On derived with the Celestial Mechanics Approach, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2701, https://doi.org/10.5194/egusphere-egu21-2701, 2021.

In GRACE data processing the geophysical background models, which are needed to compute the monthly gravity field solutions, usually enter as error-free. This means that model errors could influence and distort the gravity field solution.

The geophysical models which influence the solution the most are the atmosphere and ocean dealiasing product (AOD1B) and the ocean tide model. In this presentation we focus on the ocean tide model and on incorporating its stochastic information in data processing.

We use the FES2014 ocean tide model presented as a spherical harmonic expansion till degree and order 180. The information about its uncertainties and the correlations between different spherical harmonics is provided by the research unit NEROGRAV (New Refined Observations of Climate Change from Spaceborne Gravity Missions). In a first step, the stochastic properties of the tide model are considered to be static and are expressed as variance-covariance matrices (VCM) of the spherical harmonics of the 8 main tidal waves till degree and order 30. The incorporation of this stochastic information is done by setting up the respective ocean tide harmonics as parameters to be solved for. Since ocean tides cannot be freely estimated within monthly GRACE solutions, the provided VCMs for the 8 tidal waves are used for constraining the tidal parameters.

This procedure was used to compute monthly gravity field solutions for the year 2007. For a comparison, we computed also monthly gravity fields without taking into account the stochastic information on ocean tides. In this contibution we present and discuss the first results of this comparison.

How to cite: Panafidina, N., Koenig, R., Neumayer, K., Dahle, C., and Flechtner, F.: Impact of the stochastic model of the ocean tides on GRACE monthly gravity field solutions, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15292, https://doi.org/10.5194/egusphere-egu21-15292, 2021.

This work is part of the Research Group New Refined Observations of Climate Change from Spaceborne Gravity Missions (NEROGRAV), which is funded by the German Research Foundation (DFG). The goal of NEROGRAV is to develop new analysis methods and modeling approaches to improve the resolution, accuracy, and long-term consistency of mass transport series from the GRACE and GRACE-FO missions. This can only be obtained by improving the sensor data, background models, and processing strategies for satellite gravimetry. Within NEROGRAV, the joint Geodesy and Meteorology group at the University of Bonn is responsible for the investigation of the atmospheric and hydrological effects on the dealiasing of GRACE/GRACE-FO observations of the Earth’s gravity field.

In the present study we compare 3-hourly data from the ERA-Interim realanysis with a grid size of 50 km based on a hydrostatic model of the atmosphere and the houly data of the non-hydrostatic COSMO reanalysis with a grid size of 6 km (COSMO-REA6, Bollmeyer et.al (2015), QJRMS, 141(686), 1-15.). To date, atmospheric mass variability has been studied largely through data from hydrostatic models of the atmosphere. Therefore a direct evaluation of the total atmospheric mass variability including non-hydrostatic effects compared to a hydrostatic background model is necessary. Further, GRACE/GRACE-FO is expected to be sensitive to the atmospheric water mass variability. Since a high resolution atmospheric model provides an intensified water cycle, a more localised and enhanced mass variability within all water components is expected in COSMO-REA6.

The objectives of this talk are to (1) present the evaluation results of non-hydrostatic effects and water mass transports on the atmospheric mass variability and (2) assess the scale effects of a coarse vs a fine resolution representation of the atmospheric mass. Both objectives place an emphasis on the contributions of the atmospheric hydrological cycle in two views: the systematic effects are investigated by the mean values, while spatial variability effects are investigated using a principal component analysis. The study concentrates on the summer season 2007 over the CORDEX (North Atlantic, European region) domain.

How to cite: Dixit, S., Friederichs, P., and Hense, A.: Evaluation of the regional reanalysis COSMO-REA6 vs ERA-Interim for improving the dealiasing analysis of GRACE/GRACE-FO mission data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14940, https://doi.org/10.5194/egusphere-egu21-14940, 2021.

Technological advances in satellite geodesy have been demanding more and more accurate gravity field models but also precise measurements of the movement of water along the Earth system. GRACE-FO (GFO) mission is dedicated to monitor the Earth with a purpose of estimating the gravity field and the hydrological cycles. For the extraction of monthly gravity field models the non-gravitational accelerations are essential. The performance of GFO accelerometers (ACC) is not the optimal.  The ACC measurements present immense spikes, spurious signals and bias jumps on all three axes affecting the validity of the measurements. The bias jumps are similar to those presented at GRACE measurements and they have been related to the satellites’ entrance to and exit from the Earth’s shadow. The dominant spikes, mainly appearing in the equatorial region, have been connected to the thermal sensitivity of the instrument or the orientation of the magnetic field lines. We propose an alternative dataset generated from Level 1A of GFO C with corresponding Gaussian weights and an optimal correction of the bias jumps, along with the estimation of linear and quadratic trends using the Least Squares methodology in the frequency domain and in all three axes. The method does not remove spikes, nor does it interpolate missing values. The new 1B dataset with estimated variances shows no spike effects in the frequency domain contrastingly to the existing ACT Level 1B data. Also, a preliminary analysis of the daily amplitudes of the orbital period and semi-period components of the ACT Level 1B data set spanning one year, reveals a strong periodic signal of ~ 153 days. This signal vanishes when the proposed weighted data set is used. This signal could be related to calibration deficiencies or a systematic error in the ACC data that requires further study. The same weighted filtering approach is proposed for the ACC measurements of Swarm C satellite, a LEO constellation that measures the magnetic field of the Earth. The ACC measurements of Swarm display low signal to noise ratio due to an increased thermal sensitivity of the instrument. A weighted Gaussian filter applied on the Swarm ACC measurements reduces the contribution of the dominant spikes in the frequency domain and displays the non-gravitational signals more clearly leading to a more extended use of Swarm non-gravitational accelerations measurements.

How to cite: Tzamali, M. and Pagiatakis, S.: GRACE-FO accelerometer data: An alternative approach using Least Squares Spectral Analysis, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6906, https://doi.org/10.5194/egusphere-egu21-6906, 2021.

How to cite: Yan, Y., Wang, C., Müller, V., Zhong, M., Liang, L., Zhu, Z., Mu, Q., and Niu, H.: The re-analysis on the raw data processing of KBR and LRI on GRACE-FO, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-793, https://doi.org/10.5194/egusphere-egu21-793, 2021.

The GRACE Follow-On satellites were launched on 22nd May 2018 to continue the measurement of Earth’s gravity field from the GRACE satellites (2002-2017). A few weeks later, an inter-satellite laser link was established with the novel Laser Ranging Interferometer (LRI), which offers an additional measurement of the inter-satellite range next to the one provided by the conventional microwave ranging instrument. The LRI is the first optical interferometer in space between orbiters, which has demonstrated to measure distance variations with a noise below 1 nm/√Hz at Fourier frequencies around 1 Hz, well below the requirement of 80 nm/√Hz. In this talk, we provide an overview on the LRI, present the current status of the instrument and show results regarding the characterization of the instrument. We will address impulse events that are apparent in the accelerometer and LRI range acceleration data, most of which are expected to be micro-meteorites. Other short-term disturbances in the ranging data will be addressed as well. We conclude with some learned lessons and potential modifications of the interferometry for future geodetic missions.

How to cite: Müller, V., Misfeldt, M., Müller, L., Wegener, H., and Heinzel, G.: Laser Ranging Interferometer on GRACE Follow-On: Current Status, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9870, https://doi.org/10.5194/egusphere-egu21-9870, 2021.

In this talk we present the current status of our investigations regarding variations of the LRI scale factor with spotlight on the thermal environment of the LRI. Furthermore, we describe an alternative derivation of the scale factor through LRI telemetry data.

In the current SDS processing scheme for deriving the LRI scale factor, a cross-calibration to the KBR range is employed, which numerically estimates the LRI scale and a time-tag offset by minimizing the difference between KBR and LRI range. Typical numerical values are in the order of 2.2*10^-6 for the scale and a few tens of microseconds for the time-tag offset. The scale shows some recurring features on large time scales, which we were investigating in depth.

At first, we use a LRI telemetry based model for the nominal laser frequency (see https://doi.org/10.5194/egusphere-egu2020-15569), which already reduces the LRI scale to below ±5*10^-8, but does not suppress the features occurring on a 3-month time scale. To address these, we investigate thermal variations of the LRI instrument and its subsystems. We do not expect the temperatures to directly influence the laser frequency, but rather assume a proportionality of temperature and phase, which would manifest in tone errors at 1 CPR and 2 CPR. With our analysis, we were able to derive linear coupling factors for mapping temperature variations to errors in the LRI ranging data. With this tone error correction applied, the difference between LRI and KBR range can be reduced by about 60% at low frerquencies. Currently, we’re investigating the influence of our correction on the 1 CPR and 2 CPR amplitudes and their differences w.r.t. the KBR range.

Our goal is to derive a model for the LRI scale factor, which uses only LRI telemetry and temperature sensors. That would be especially beneficial in case the KBR observation become unavailable in GRACE-FO, and is furthermore helpful for the design of future laser ranging instruments.

How to cite: Misfeldt, M., Müller, V., Müller, L., Wegener, H., and Heinzel, G.: Thermal Influence on the LRI Scale Factor, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1242, https://doi.org/10.5194/egusphere-egu21-1242, 2021.

For the monitoring of mass transport and mass distribution in the Earth’s system, the gravity field and its temporal variations provide an important source of information. Dedicated satellite missions like GRACE and GRACE-FO allow to resolve the Earth’s time-variable gravity field based on ultra-precise inter-satellite ranging. In addition, any (non-dedicated) Low Earth Orbiting (LEO) satellite equipped with an on-board GNSS receiver may also serve as a gravity field sensor. For this purpose, the collected GNSS data is used to derive kinematic LEO orbit positions that can subsequently be utilized as pseudo-observations for gravity field recovery. Although this technique is less sensitive and restricted to the long wavelength part of the gravity field, it provides valuable information, particularly for those months where no inter-satellite ranging measurements are available from GRACE or GRACE-FO. Furthermore, the increasing number of operational LEO satellites makes it attractive to produce combined Multi-LEO gravity field solutions that will take advantage of the variety of complementary orbital configurations and can offer additional sensitivities to selected coefficients of solutions based on inter-satellite ranging.

At the Astronomical Institute of the University of Bern (AIUB) GPS-based kinematic orbits are routinely processed for various LEO satellites like missions dedicated to gravity (GOCE, GRACE/-FO), altimetry (Jason, Sentinel), or further constellations of Earth-observing satellites like SWARM. Beside conventional ambiguity-float orbits, also ambiguity-fixed orbits are recently being computed based on new phase bias and clock products of the Center for Orbit Determination in Europe (CODE). The kinematic orbit positions offer the opportunity to derive time series of monthly gravity field solutions for the different LEO satellites that are eventually combined on the level of normal equations.

In this contribution, we will present first results of our effort to generate a combined time series of monthly gravity field solutions based on the kinematic orbits of multiple LEO satellites. In a first step, the focus is laid on the GRACE/-FO missions that provide the longest time series in terms of collected GNSS data and that will therefore serve as a backbone for future combinations. We analyze the impact of accelerometer data on the recovery of time-variable mass variations. This will be particularly important for the handling of non-dedicated gravity missions, for which accelerometer measurements are usually not available. Furthermore, we study and compare the performance of gravity field recoveries based on ambiguity-float and ambiguity-fixed kinematic orbit solutions. We assess our results with respect to superior gravity field models based on inter-satellite ranging for selected areas with strong mass change signals like in Greenland, West-Antarctica or the Amazon river basin.

How to cite: Grombein, T., Lasser, M., Arnold, D., Meyer, U., and Jäggi, A.: Time-variable gravity field recovery from kinematic positions of Low Earth Orbiting satellites, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7708, https://doi.org/10.5194/egusphere-egu21-7708, 2021.

The Swarm satellite constellation provides GPS data with sufficient accuracy to observe the large-scale mass transport processes occurring at the Earth’s surface since 2013. We illustrate the signal content of the time series of monthly gravity field models. The models are published on quarterly basis and are the result of a combination of the individual models produced by different gravity field estimation approaches, by the Astronomical Institute of the University of Bern, the Astronomical Institute of the Czech Academy of Sciences, the Institute of Geodesy of the Graz University of Technology and the School of Earth Sciences of the Ohio State University. We combine the models at the solution level, using weights derived from a Variance Component Estimation, under the framework of the International Combination Service for Time-variable Gravity Fields (COST-G).

We estimate the monthly quality of the models by comparing with GRACE and GRACE-FO products and illustrate the improvement of the combined model as compared to the individual models. We present the high signal-to-noise ratio of this uninterrupted time series of models, smoothed to 750km radius, over large hydrological basins. Finally, we compare the behavior of degree 2 and 3 coefficients with GRACE/GRACE-FO and SLR.

How to cite: de Teixeira da Encarnacao, J., Arnold, D., Bezdek, A., Dahle, C., Guo, J., van den IJssel, J., Jaeggi, A., Klokocnik, J., Krauss, S., Mayer‐Guerr, T., Meyer, U., Sebera, J., Shum, C., Visser, P., and Zhang, Y.: Seven years of monthly low-degree gravity field models from Swarm GPS data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7422, https://doi.org/10.5194/egusphere-egu21-7422, 2021.

      Although the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE FO) satellite missions play an important role in monitoring global mass changes within the Earth system, there is a data gap of about one year spanning July 2017 to May 2018, which leads to discontinuous gravity observations for monitoring global mass changes. As an alternative mission, the SWARM satellites can provide gravity observations to close this data gap. In this paper, we are dedicated to developing alternative monthly time-variable gravity field solutions from SWARM data. Using kinematic orbits of SWARM from ITSG for the period January 2015 to September 2020, we have generated a preliminary time series of monthly gravity field models named Tongji-Swarm2019 up to degree and order 60. The comparisons between Tongji-Swarm2019 and GRACE/GRACE-FO monthly solutions show that Tongji-Swarm2019 solutions agree with GRACE/GRACE-FO models in terms of large-scale mass change signals over amazon, Greenland and other regions. We can conclude that Tongji-Swarm2019 monthly gravity field models are able to close the gap between GRACE and GRACE FO.

How to cite: Zhang, X., Chen, Q., and Shen, Y.: Preliminary monthly gravity field models from kinematic orbits of SWARM Satellites, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9839, https://doi.org/10.5194/egusphere-egu21-9839, 2021.

The GRACE mission (2002-2017) delivered temporal gravity field solutions of the Earth for 15 years. It's successor, GRACE follow-on (GRACE-FO) is continuing it's legacy since May 2018. The time series of monthly gravity fields revealed global mass redistribution in in the near surface layer of the Earth with unprecedented accuracy. This assessed a completely new observable in geoscience disciplines and has become a crucial data product for climate research.
Despite the groundbreaking success and relevance of the GRACE mission(s) for Earth observation and climate science, no further successor gravity mission is planned, yet. Summarized by the name Next Generation Gravity Mission (NGGM) concepts for future gravimetry missions have been proposed and analyzed for a while. As an outcome of these studies the so called Bender-configuration (two GRACE-like satellite pairs, one in a polar orbit and a second in an inclined orbit around 60° to 70°) is the concept currently favored by the scientific community for a candidate of the next gravity mission to be realized.

However, an other concept still remains interesting due to specific advantages that might contribute to future improvements of gravity missions. In order to emphasize this, we present results of a full closed loop-simulation for a different ll-SST approach, the so called pendulum. It offers a quite similar overall performance with just two satellites. For this configuration the satellites are following each other in orbits with slightly different longitudes of the ascending nodes, thus the inter-satellite measurement direction is varying between along-track and cross-track. This configuration makes an interferometric laser ranging (LRI) quite challenging on the technical level. Nevertheless, the LRI accuracy is not necessarily needed. The relevance of the pendulum configuration has also been shifted into the focus of the French MARVEL mission proposal.

In this contribution we analyze in detail the performance of the pendulum formation with the main parameters being the angle between along-track and cross-track component of the ranging direction at the equator, and the mean distance between the satellites. We conduct the angle variation for different mean ranges and assumed ranging accuracies. As reference, the GRACE and Bender concepts are simulated, as well. The orbit simulations are performed using a derivative of the ZARM/DLR XHPS mission simulator including high precision implementations of non-gravitational accelerations.
The different concepts and configurations include complete GRACE-FO like attitude control and realistic environment models. State-of-the-art instrument noise models based on GRACE/-FO are used to generate observation data for accelerometer (ACC), range dependent inter satellite ranging (KBR/LRI), kinematic orbit solution (KOS) and star camera (SCA). For the gravity recovery process we use the classical variational equation approach. As for real GRACE processing, ACC calibration parameter are estimated and KOS and KBR range-rate observations are weighted by VCE.

How to cite: Wöske, F. and Rievers, B.: Evaluation of Pendulum NGGM Scenarios by Full Closed-Loop Simulation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12257, https://doi.org/10.5194/egusphere-egu21-12257, 2021.

In the context of an increased public interest in climate-relevant processes, a number of studies on Next Generation Gravity Missions (NGGMs) have been commissioned to better map mass transport processes on Earth. On the basis of the successfully completed gravity field missions CHAMP, GOCE and GRACE as well as the current satellite mission GRACE-FO, different concepts were examined for their feasibility and economic efficiency. The focus is on increasing the spatiotemporal resolution while simultaneously reducing the known error effects such as the aliasing of temporal gravity fields due to under-sampling of signals and uncertainties in ocean tide models. An additional inclined pair to a GRACE-like satellite pair (Bender constellation) is the most promising solution. Since the costs for a realization of the Bender constellation are very high, this contribution focuses on alternative concepts in the form of different constellations and formations of small satellites. The latter includes both satellite pairs and chains consisting of trailing satellites. The aim is to provide a cost-effective alternative to the previous gravity field satellites while simultaneously increasing the spatiotemporal resolution and minimizing the above mentioned error effects. In numerical closed-loop simulations, various scenarios will be conducted which differ in orbit parameters like shape and number of orbits, the number of satellites per orbit and instrument performances. Additionally, the impacts from the co-parametrization of non-tidal temporal gravity field signal and ocean tides on the gravity field solutions, obtained by the different concepts, will be investigated. In particular the possibilities and limits with multiple satellites pairs for achieving the highest possible spatial and temporal resolution in (sub-)daily temporal gravity fields shall be analysed in detail.

How to cite: Pfaffenzeller, N. and Pail, R.: Simulation study on gravity field determination with small satellites in NGGM, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5341, https://doi.org/10.5194/egusphere-egu21-5341, 2021.

Satellite gravity missions, like GRACE and GRACE Follow-On, successfully map the Earth’s gravity field and its changes, but the boundaries of spatial and temporal resolution need to be pushed further. The major enhancement from GRACE to GRACE-FO is the laser interferometry instrument which enables a much more accurate inter-satellite ranging. However, the accelerometers used for observing the non-conservative forces have merely been improved and are one major limiting factor for gravity field recovery. Inertial sensors based on cold atom interferometry (CAI) show promising characteristics, especially their long-term stability at frequencies below 10^-3 Hz is very beneficial. The CAI concept has already been successfully demonstrated in ground experiments. In space, an even higher sensitivity is expected due to increased interrogation time of one interferometer measurement cycle.

In this contribution, we investigate potential next-generation gravity missions (NGGM) following the GRACE design, employing an LRI with GRACE-FO characteristics and the utilisation of CAI accelerometry. The combination of CAI technology with a classic electrostatic accelerometer is evaluated as well. The sensor performances are tested via closed-loop simulations for different scenarios and the recovered gravity field results are evaluated. In order to achieve a realistic model of the atomic interferometer, noise levels depending on the architecture of the sensor and its transfer function are included. Here, also the effect of variations of the non-gravitational accelerations during one interferometer cycle is analyzed.

Another crucial aspect for satellite missions is the drag compensation. Its requirement is reduced by two orders of magnitude when using a CAI accelerometer due to its better known scale factor. The feasibility of such requirements is assessed with respect to simulated satellite dynamics for several altitudes and drag compensation parameters.

H.W. acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy – EXC 2123 “QuantumFrontiers, Project-ID 390837967“. A.K. acknowledges initial funding for the DLR Institute by the Ministry of Science and Culture of the German State of Lower Saxony from “Niedersächsisches Vorab”. A.H. acknowledges support by DLR-Institute for Satellite Geodesy and Inertial Sensing.

How to cite: Knabe, A., Wu, H., Schilling, M., HosseiniArani, A., Müller, J., Pereira dos Santos, F., and Beaufils, Q.: Future Satellite Gravity Missions enhanced by Cold Atom Interferometry Accelerometers, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7612, https://doi.org/10.5194/egusphere-egu21-7612, 2021.

Frequent droughts and floods in the Chao Phraya river basin, which contributes about 66% to Thailand’s GDP, have cost the country’s socio-economic development in several ways. We quantified the Land Water Storage (LWS) in the basin using the three data products, i.e., two mascons and one spherical harmonic in terms of anomaly time series of equivalent water depth or volume, from the Gravity Recovery and Climate Experiment (GRACE) satellite data from April 2002 to June 2017. Since all three data products were highly correlated (r>0.9), the arithmetic mean was used to avoid bias in any particular product. LWS showed a linear trend of 9.8 mm/yr equivalent to 1.6 km³/yr in the basin. The flood and drought events were also well captured by the LWS dynamics in the basin. The severe floods of 2011, primarily resulting from the heavy rainfall of 1439 mm, which was 143 % of the long-term average in the rainy season, led to a maximum value of 430 mm (68.8 km³) in the LWS anomaly during September 2011. The drought in March 2016 was also evident with a minimum LWS anomaly of -334 mm (-53.44 km³). All the multi-year flood and drought years were recorded in the LWS time series with a lag of up to two months from rainfall. Since the minimum rain during the dry periods (i.e., November to April) was almost consistent, the extreme events were supposed to be triggered mainly by the variable maximum rainfall occurring during the monsoon season. The methodology can be used for efficient water management and policymaking in the data-scarce river basins globally. Future work includes filling the data gap between GRACE and GRACE Follow-On data, followed by the assessment of anthropogenic impacts (i.e., groundwater abstraction and reservoir management) on water storage dynamics in the basin.

How to cite: Abhishek, A. and Kinouchi, T.: Droughts and Floods Captured by Land Water Storage in Chao Phraya River Basin during 2002-2017, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-370, https://doi.org/10.5194/egusphere-egu21-370, 2021.

Knowledge of the variances and covariances of gridded terrestrial water storage anomalies (TWS) as observed with GRACE and GRACE-FO is crucial for many applications thereof. For example, data assimilation into different models, trend estimations, or combinations with other data set require reliable estimations of the variances and covariances. Today, the Level-2 Stokes coefficients are provided with formal variance-covariance matrices which can yield variance-covariance matrices of the gridded data after a labourious variance propagation through all post-processing steps, including filtering and spherical harmonic synthesis. Unfortunately, this is beyond the capabilities of many, if not most, users.

This is why, we developed a spatial covariance model for gridded TWS data. The covariance model results in non-homogeneous, non-stationary, and anisotropic covariances. This model also accommodates a wave-like behaviour in latitudinal-directed correlations caused by residual striping errors. The model is applied to both VDK3 filtered GFZ RL06 and ITSG-Grace2018 TWS data. 

With thus derived covariances it is possible to estimate the uncertainties of mean TWS time series for any arbitrary region such as river basins. On the other hand, such time series uncertainties can also be derived from the afore mentioned formal covariance matrices. Here, only the formal covariance matrices of ITSG-Grace2018 are used which are also filtered with the VDK3 filter. All together, we are able to compare globally the time series uncertainties of both the modelled and formal approach. Further, the modelled uncertainties are compared to empirical standard deviations in arid regions in the Arabian, Sahara, and Gobi desert where residual hydrological signal can be neglected. Both in the temporal and spatial domain they show a very satisfying agreement proving the usefulness of the covariance model for the users. 

How to cite: Boergens, E., Kvas, A., Dobslaw, H., Eicker, A., Dahle, C., and Flechtner, F.: Uncertainties of TWS Time Series for Arbitrary Regions - Modelled vs. Formal Covariances, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1259, https://doi.org/10.5194/egusphere-egu21-1259, 2021.

Correlated errors in the monthly spherical harmonic coefficient (SHC) solutions provided by the GRACE data centers are estimated and removed using the destriping method of Crowley and Huang (2020). Regional estimates for mass change are calculated across Canada using the simple basin average technique of Swenson and Wahr (2002) as well as a simple mascon approach developed by the Canadian Geodetic Survey. A comparison with mascon solutions from the GRACE data centers demonstrates excellent agreement and in some cases reveals larger amplitudes and added temporal structure. This approach does not require additional constraints/dependencies, smoothing, normalizations or scaling factors and can easily be applied to any regional geometry without the need to calculate a global solution. Solutions tend to agree well when data quality is good and diverge when errors are larger. This is expected and demonstrates the underlying uncertainties that remain. The similarity in solutions using such different methodologies provides confidence in the time series solutions. We conclude with a regional validation that uses water level changes in the Great Lakes of North America to demonstrate the effectiveness of the method. The Great Lakes are large enough that GRACE clearly detects changes in their water levels. At the same time, the lakes are close enough to each other that distinguishing signals between adjacent lakes remains a challenge for any method.

References:

Crowley, J.W., and J Huang, A least-squares method for estimating the correlated error of GRACE models, Geophysical Journal International, Volume 221, Issue 3, June 2020, Pages 1736–1749, https://doi.org/10.1093/gji/ggaa104.

Swenson, S., and J. Wahr, Methods for inferring regional surface-mass anomalies from Gravity Recovery and Climate Experiment (GRACE) measurements of time-variable gravity, J. Geophys. Res., 107(B9), 2193, doi:10.1029/2001JB000576, 2002.

How to cite: Crowley, J. and Huang, J.: Simple regional analyses are still possible once correlated errors are removed, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5688, https://doi.org/10.5194/egusphere-egu21-5688, 2021.

The satellite missions Gravity Recovery And Climate Experiment (GRACE) and GRACE Follow-On record the change in the gravity field, which is then related to water mass redistribution near the Earth's surface and disseminated as monthly fields of Total Water Storage Change (TWSC). GRACE products effectively carry signal information only above spatial scales of about 300 km, which limits their application in regional hydrological applications. At present, several GRACE products are available at 0.5° or 1° grid cells, but they are only an interpolated version of the coarse resolution GRACE products and do not offer additional physical information. 

In this study we implement a statistical downscaling approach that assimilates high resolution TWSC fields from the WaterGAP hydrology model (WGHM), precipitation fields from 3 models, evapotranspiration and runoff from 2 models, with GRACE data to improve its resolution. The downscaled product exploits dominant common statistical modes between all the datasets to inform the estimates of TWSC. An improvement in the spatial resolution is obtained from using WGHM that incorporates the geometry of various water compartments and simulates spatio-temporal changes in TWSC due to climate forcing, land use land cover change, and human intervention. Therefore, the downscaled product at a 0.5° grid is able to capture physical attributes of water compartments at a spatial resolution better than the available GRACE products. 

How to cite: Sneeuw, N., Vishwakarma, B. D., and Zhang, J.: Statistical downscaling of GRACE products to improve spatial resolution, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10022, https://doi.org/10.5194/egusphere-egu21-10022, 2021.

Taking into account sphericity is one of the most relevant questions of interest for gravity researchers today. It’s especially important in data analysis of regional surveys and satellite missions.

Modern satellite missions are characterized by high accuracy of measurements, as well as a high degree of detail, which makes it possible to construct detailed grid density models of Earth and Moon, however, when automating this process, the following problems arise:

- long duration of the inversion process;

- need for a large amount of RAM when using standard approaches to solving the linear inverse problem of gravity prospecting for grid models;

- high sensitivity of gravity inversion algorithms to the upper cells;

The first problem can be solved by inverting of gravity in the spectral domain using the fast Fourier transform. In this case, the time complexity of the inversion algorithms is reduced by times, which significantly accelerates the selection of the model.     

To reduce the memory used, it is necessary to memorize the gravity spectrum for only one cell for each pair of coordinates depth - latitude, since cells with at the same depth and latitude have the same gravitational effects, shifted by the step of cells in the grid model.

Finally, to increase the sensitivity of the inversion algorithms to deep cells, you can use the variable parameter of the gradient descent step (learning rate in machine learning), depending on the depth as an exponential or any other function, in combination with regularization.

The proposed approach was applied to the data of the GRAIL mission, and as a result, a density model of the Moon was constrained with the following grid steps: 0.5^o in latitude, 0.7^o (pi / 512) in longitude and 10 km in depth.

The fitted model was used to estimate the possible parameters of the sources of lunar mascons. It stands to mention the differences in the geometry of the mascon sources, which can be divided into two groups: isometric sources and sources with channels ascending to the surface, through which, probably, lunar basalts entered the surface.

The proposed approach allows constrain density models of celestial bodies fast enough using a personal computer (less than an hour for a model with the parameters mentioned above), and also takes into account the weak sensitivity of standard inversion algorithms to deep cells.

How to cite: Chepigo, L., Lygin, I., Bulychev, A., and Kirill, K.: Spherical gravity inversion of GRAIL data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-40, https://doi.org/10.5194/egusphere-egu21-40, 2021.

GOCE Satellite Gravity Gradiometry (SGG) data have been widely used in gravity field research in order to provide improved representations of the gravity field spectrum either in the form of Global Geopotential Models (GGMs) or grids at satellite altitude. One of the key points in utilizing SGG observations is their proper filtering, in order to remove noise and long-wavelength correlated error, while the signals in the GOCE measurement bandwidth (MBW) should be preserved. Due to the gradiometer’s design, the GOCE satellite can achieve high accuracy and stable measurements in the MBW of 0.005 Hz to 0.1 Hz. The gravity gradient in MBW are at an equivalent accuracy level, while   are of lower accuracy. Outside of the MBW, systematic errors, colored noise, and noise with sharp peaks are observed, especially in the frequencies lower than 0.005 Hz. With that in mind, the present work focuses on the investigation of various filtering options ranging from Finite Impulse Response (FIR) filters, Infinite Impulse Response (IIR) filters, and filtering based on Wavelets. The latter are employed given their inherent characteristic of being localized both in frequency and space, meaning that the signal can be decomposed at different levels, thus allowing multi-resolution approximation (MRA). The analysis is performed with one month of GOCE SGG data in order to conclude on the method that provides the overall best results. SGG observations are reduced to a GGM in order to account for the long- and medium-wavelengths of the gravity field spectrum. Then, various filter orders are investigated for the FIR and IIR filters, while selective reconstruction is employed for the WL-MRA. Evaluation of the results is performed in terms of the smoothness of the filtered fields and the Power Spectral Density (PSD) functions of the entire GOCE tensor.

How to cite: Pitenis, E. A., Mamagiannou, E. G., Natsiopoulos, D. A., Vergos, G. S., and Tziavos, I. N.: GOCE SGG filtering with FIR, IIR and wavelet MRA , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1679, https://doi.org/10.5194/egusphere-egu21-1679, 2021.